Upload
anonmsacc
View
208
Download
1
Embed Size (px)
Citation preview
ORIGINAL PAPER - EXPLORATION GEOLOGY
Bimodal pore size behavior of the Shajara Formation Reservoirsof the Permo-Carboniferous Unayzah Group, Saudi Arabia
K. E. Al-Khidir • A. A. Al-Quraishi •
A. A. Al-Laboun • M. S. Benzagouta
Received: 29 September 2010 / Accepted: 21 March 2011 / Published online: 5 April 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract The sandstones of the Permo-Carboniferous
Shajara Formation form the main part of the Unayzah
Reservoir in the Greater Arabian Basin. It is divided into
three reservoirs, namely from base to top Lower, Middle,
and Upper Shajara reservoirs. Mercury intrusion technique
was carried out on representative sandstone samples col-
lected from the type section and the three reservoirs are
generally characterized as heterogeneous megaporous res-
ervoirs. The best reservoir quality is assigned to the lower
sand unit of the Lower Shajara followed by the Middle
Shajara Reservoir. One sample collected from the upper
part of the Lower Shajara was described as low quality due
to its fine grain characteristic and its proximity to the
unconformity surface. Reservoir quality is controlled to a
large extent by the depositional facies and specifically by
rock texture illustrated by petrophysical description. The
quality of the three reservoirs of the Shajara Formation,
increases with the increase of grain size and grain sorting.
Keywords Shajara Reservoirs � Shajara Formation �Unayzah Group � Pore size distribution
Introduction
The Permo-Carboniferous Unayzah Reservoirs are oil and
gas bearing in more than 30 oil and gas fields in Saudi
Arabia. These reservoirs are partially represented in out-
crops by the Shajara, Safra, and Shiqqah sandstones of the
Unayzah Group. These formations are exposed as a thin
belt below the Khuff carbonates in central Arabia.
Fossil plants of the late Carboniferous–early Permian
age were first reported at the town of Unayzah by El-
Khayal et al. (1980). Later, the term Unazyah Formation
was informally introduced by Al-Laboun (1982) as sili-
ciclastics and minor carbonate section at the base of the
Khuff Formation. This definition was adopted by Aramco
Stratigraphic Committee (1983) and formally defined by
Al-Laboun (1987)in the American Association of Petro-
leum Geologist (AAPG). The Unayzah Formation was then
correlated with its equivalent units in different parts of the
Greater Arabian basin (Al-Laboun 1988) and its type
locality was established within Unayzah town with a ref-
erence section assigned at Wadi Ash-Shajara at the
Qusayba depression, Al-Qasim region (Fig. 1).
The subsurface informal reference section (Hawtah-1) of
the Unayzah Formation was studied by Ferguson and
Chambers (1991). The section consists of two sandstone
intervals separated by a coarsening upward siltstone unit.
Similarly, McGillivray and Husseini (1992) divided the
Unayzah Formation in the Hawtah–Hazmiyah fields into
two informal sequences identified as Unayzah A and
Unayzah B members. The two members are separated by a
red-brown siltstone or fine-grained silty sandstone. Senalp
and Al-Dauji (1995) studied the stratigraphy and sedimen-
tation of the Unayzah Reservoir in central Arabia. They
redefined the Unayzah Formation at its type locality by
introducing the term ‘‘basal Khuff clastics’’ (Ash-Shiqqah
K. E. Al-Khidir (&) � M. S. Benzagouta
Department of Petroleum and Natural Gas Engineering,
King Saud University, Riyadh, Saudi Arabia
e-mail: [email protected]
A. A. Al-Quraishi
Oil and Gas Research Institute, King Abdulaziz City for Science
and Technology, Riyadh, Saudi Arabia
A. A. Al-Laboun
Department of Geology, King Saud University,
Riyadh, Saudi Arabia
123
J Petrol Explor Prod Technol (2011) 1:1–9
DOI 10.1007/s13202-011-0007-5
member) of the Khuff Formation to be the upper contact of
the Unayzah Formation.
Evans et al. (1997) studied the stratigraphic trap in the
Permian Unayzah Formation, in Usaylah-1, central Arabia,
and they reported that the trap is an up dip pinch out. An oil
column 31 ft thick is encountered in the eolian sandstone
facies of the upper part of the Unayzah Formation. Later,
Wender et al. (1998) divided the Early Permian Unayzah
Formation into three units, the Unayzah-A Reservoir,
Unayzah Siltstone Member, and Unayzah-B Reservoir.
Melvin and Spraque (2006) studied origin and stratigraphic
architecture of glaciogenic sediments in Permian–Carbon-
iferous lower Unayzah sandstones in eastern central Saudi
Arabia. They subdivided the lower Unayzah sandstones
into three members, from base to top are: Unayzah C
Member, Unayzah B Member, and an un-named middle
Unayzah member.
Reservoir characteristics of the Permo-Carboniferous
Unayzah Formation, at Wadi Shajara was thoroughly
investigated through field and petrophysical examinations.
An exposed clastic sequence consisting of three sandstone
intervals separated by two mudstone units were observed
(Fig. 2). The clastic sequence is bounded from top and
bottom, by two regional unconformities, namely sub-Khuff
and sub-Unayzah unconformity, respectively. Based on
Saudi Stratigraphic Code (1983), a group is defined as a
lithostratigraphic unit bounded by two regional unconfo-
rmities. Therefore, we propose raising the Permo-Carbon-
iferous Unayzah Formation to a group status and identify a
new formation named Shajara Formation (Al-Khidir 2007).
The term Unayzah Formation was restricted to the upper
unit of the group which is best represented in its original
type locality in Unayzah town, while the term Shajara
Formation was assigned to the Lower unit which is best
represented at Wadi Ash-Shajara (Laboun 2010). Depend-
ing on sub-Unayzah unconformity, sub-middle Shajara
local unconformity, the lower mudstone interval, and sub-
Khuff unconformity (Fig. 2), the Shajara Formation was
divided into three members, from base to top: the Lower
Shajara, the Middle Shajara, and the Upper Shajara
(Al-Khidir 2007).
The Shajara Reservoirs of the Shajara Formation is oil
and gas bearing in many fields in Saudi Arabia. In addition,
it is the principal Paleozoic clastic reservoir. To our
knowledge no petrophysical examination was conducted on
the surface samples of the Shajara Formation. The aim of
this work is to categorize the Shajara reservoirs by char-
acterizing the pore geometry and the pore aperture sizes of
the sandstones. This is done by integrating capillary pres-
sure obtained by the mercury injection porosimetry tech-
nique, petrofacies determination and lithofacies description
of outcrop samples collected.
Experimental work
The most obvious and straightforward measurements of
pore size are with geometric analysis of images of indi-
vidual pores. This can be done using various types of
microscopy on thin sections or other flat soil surfaces, or
tomography. Image-based techniques can be prohibitively
tedious because enough pores must be analyzed to give an
adequate statistical representation. Therefore, the determi-
nation of pore geometry and pore aperture size using
mercury injection technique is believed to be more helpful
in categorizing rocks by pore types (i.e. nanno, micro,
meso, macro or mega). Autopore III 9420 mercury intru-
sion unit was used to determine the capillary pressure,
porosity, pore throat accessibility, and pore level hetero-
geneity of the three reservoirs comprising the Shajara
Formation. This was conducted on nine outcrop sandstone
samples selected among 13 samples from the type section.
All samples except for one (SJ3) are friable sand and their
locations are presented in stratigraphic column illustrated
in Fig. 2.
Samples’ permeability (k) was calculated utilizing Pur-
cell’s equation (1948) stated as:
K ¼ 14; 260� k� /�Zs¼1
s¼0
dSHg
Pc
ð1Þ
where, k is a lithology factor (equal to 0.216), dSHg is
incremental mercury saturation and Pc is the capillary
pressure measured in psi.
The pore aperture size is calculated utilizing Washburn
equation expressed as:
Fig. 1 Location map of the studied area
2 J Petrol Explor Prod Technol (2011) 1:1–9
123
r ¼ 2� r� cos hPc
ð2Þ
where, r is the pore radius in micron, r is the surface tension
of mercury in Dynes/cm, h is the contact angle of mercury
in air and Pc is the capillary pressure in Dynes/cm2.
To reveal the heterogeneity of the investigated reser-
voirs, the pore aperture distribution (PSD) was plotted as a
function of pore radius. The PSD function is defined as the
rate of change of mercury intrusion volume with respect to
the difference of pore radius logarithm relative to the
maximum value of that term. To confirm the findings of the
PSD plots, the cumulative percent of mercury saturation
was plotted with respect to log pore radius.
On average, the pore throats entered by a non-wetting
fluid (mercury) at 35% saturation (R35) or less during a
capillary analysis, represent the pores that dominate fluid
flow in a reservoir samples (Kolodzie 1980). The pore
throat corresponding to a mercury saturation of 35% was
evaluated using Winland equation expressed as:
LogR35 ¼ 0:732þ 0:588� log k � 0:864� log / ð3Þ
Pittman (2001) reported that, pore throat radius
corresponding to the apex has the potential for delineating
Fig. 2 Stratigraphic column of
the type section of the Permo-
carboniferous Shajara
Formation of the Unayzah
Group, Wadi Shajara, Qusayba
area, al Qassim district, Saudi
Arabia, N 26�52 17.4, E 43�36
18
J Petrol Explor Prod Technol (2011) 1:1–9 3
123
stratigraphic traps in the same manner as the pore aperture
corresponding to 35th percentile of a cumulative mercury
saturation curve, which was developed by Winland.
Therefore, the pore aperture size corresponding to the
apex (Rapex) was determined from Pittman equation stated
as follows:
LogRapex ¼ �0:117þ 0:475� Logk � 0:099� Log/
ð4Þ
Results and discussion
In order to determine the behavior of the pore geometry of
Shajara Reservoirs, samples capillary pressures were
measured and the measurements were used to determine
the pore size distribution. Figure 3 is the pore size distri-
bution of sample SJ1 representing the Lower Shajara
Reservoir. This sample is characterized as red in color,
medium grain size and moderately well sorted. The figure
indicates a bimodal pore size distribution of two distinct
pore sizes, minor macro pores of sizes less than 10 lm and
major mega pores with size greater than 10 lm according
to Libny et al. classification (2001). Within the mega pores
there exist a variation in pore size. The sample is charac-
terized with maximum pore radius of 173.9 lm, and a
minimum radius of 0.01 lm, and an average pore size of
41.6 lm. Variation in pore size distribution demonstrates
the possibility of anisotropy. This anisotropy is well
defined in Fig. 4 where three distinct tracks have been
obtained. The pore radii of the first track ranges from 60.2
to 173.9 lm. The second represents pore radii varying from
0.1 to 60.2 lm, whereas the third track is characterized by
very low pore radii ranging in size from 0.1 to 0.01 lm.
Sample SJ2 is the second sample representing the Lower
Shajara Reservoir. It is described as medium-grained, well
sorted sandstone. Figure 5 is the pore size distribution of
the sample indicating a bimodal pore size distribution with
Fig. 3 Incremental and cumulative PSD versus pore radius of sample
SJ1 from the Lower Shajara Reservoir
Fig. 4 Cumulative % SHg versus pore radius of sample SJ1 from the
Lower Shajara Reservoir
Fig. 5 Incremental and cumulative PSD versus pore radius of sample
SJ2 from the Lower Shajara Reservoir
Fig. 6 Cumulative % SHg versus pore radius of sample SJ2 from the
Lower Shajara Reservoir
4 J Petrol Explor Prod Technol (2011) 1:1–9
123
a maximum pore radius of 173.9 lm, and an average pore
size of 25.4 lm. Again two distinct pore sizes exist with
majority of the sizes classified as megapores. Figure 6
confirms the heterogeneity of the sample as presented by
multiple tracks with distinctive pore radius ranges.
Sample SJ3 of the Lower Shajara Reservoir is charac-
terized with finer grain size when compared to samples SJ1
and SJ2. Such grain size variability as well as compaction
noticed through grains visual inspection is believed to be
due to the sample proximity to the unconformity surface.
This is reflected in a drastic drop in permeability of sample
SJ3 as stated in Table 1. The sample is also identified with
bimodal pore size distribution with skewness towards finer
pore size as indicated in Fig. 7. The sample is characterized
with narrower range of pore radii variation and smaller
pore sizes compared to that of samples SJ1 and SJ2. Again,
Fig. 8 exhibits two tracks of pore radii ranging in size from
10 to 45 lm, and from 1 to 10 lm.
Grain size assessment, pore size distributions and calcu-
lated petrophysical properties of porosity and permeability
of samples SJ1, SJ2 and SJ3 can help assessing the Lower
Shajara Reservoir. This can be confirmed by the Winland
R35 and Pittman Rapex (Table 1). Based on the grain size
description and the obtained porosity and particularly per-
meability, it can likely be stated that the average pore size
decreases as the grain size gets finer and as a consequence
flow capacity declines. This is observed as we proceed
upward in the reservoir. Based on that and the reservoir
classification utilizing the Winland R35, the lower part of the
reservoir can be classified as megaporous (pore radius
greater than 10 lm), whereas the upper portion of the res-
ervoir represented by sample SJ3 is classified as macropo-
rous (pore radius between 2 and 10 lm) with lower flow
capacity as stated by the low permeability value (Table 2).
Middle Shajara Reservoir were characterized using
samples SJ7, SJ8 and SJ9. Sample SJ7 is described as
coarse-grained, moderately well sorted sandstone. This
sample is characterized by bimodal pore size distribution as
shown in Fig. 9 with pore radii ranging from 1.2 to
180.8 lm with an average value of 46.15 lm. The sample
heterogeneity is revealed in Fig. 10, where two tracks of
pore radii exists. The first represents a pore radii ranging
from 10 to 180.8 lm, whereas the second represents pore
radii that vary from 1.2 to 10 lm.
Table 1 Petrophysical properties of samples tested
Petrophysical facies U (%) K (mD) R35 (lm) Rapex (lm) h (feet) U avg. (%) K avg. (mD) Reservoir
Sj-1 29.2 1,680 23 18.6 11.8 31.1 1,592 Lowe Shajara Reservoir
Sj-2 35.5 1,955 21.3 19.6 3.9
Sj-3 34.2 56 2.7 3.6 1.6
Sj-7 35.1 1,472 18.2 17.2 13.4 33.4 1,407 Middle Shajara Reservoir
Sj-8 31.9 1,344 18.7 16.8
Sj-9 31.5 1,395 19.3 16.9 0.9
Sj-11 36.2 1,197 15.7 15.5 13.1 29.9 1,204 Upper Shajara Reservoir
Sj-12 28.2 1,440 21.7 17.4
Sj-13 25.4 973 18.8 14.6 6.5
Fig. 7 Incremental and cumulative PSD versus pore radius of sample
SJ3 from the Lower Shajara Reservoir
Fig. 8 Cumulative % SHg versus pore radius of sample SJ3 from the
Lower Shajara Reservoir
J Petrol Explor Prod Technol (2011) 1:1–9 5
123
Sample SJ8 is also identified as medium-grained, mod-
erately well sorted sandstone. This sample is characterized
with bimodal pore size distribution as shown in Fig. 11
with an average pore radius of 28.65 lm indicating smaller
average pore size than that of sample SJ7. The heteroge-
neity of this sample is affirmed in Fig. 12 which displays
Table 2 Lithofacies description of samples tested
Facies no. Color Grain size Sorting Hardness
SJ-1 Red Medium-grained Moderately well sorted Friable
SJ-2 Yellow Medium-grained Well sorted Friable
SJ-3 White–pink Fine-grained Poorly sorted Hard
SJ-7 Red Coarse-grained Moderately well sorted Friable
SJ-8 Red Medium-grained Moderately well sorted Friable
SJ-9 Yellow Medium-grained Moderately well sorted Friable
Sj-11 Yellow Medium-grained Poorly sorted Friable
SJ-12 Yellow Very coarse-grained Moderately sorted Friable
SJ-13 Light brown Coarse-grained Moderately sorted Friable
Fig. 9 Incremental and cumulative PSD versus pore radius of sample
SJ7 from the Lower Shajara Reservoir
Fig. 10 Cumulative % SHg versus pore radius of sample SJ7 from the
Lower Shajara Reservoir
Fig. 11 Incremental and cumulative PSD versus pore radius of
sample SJ8 from the Lower Shajara Reservoir
Fig. 12 Cumulative % SHg versus pore radius of sample SJ8 from the
Lower Shajara Reservoir
6 J Petrol Explor Prod Technol (2011) 1:1–9
123
two tracks of pore radii. The first is for a pore radii that
range in size from 37 to 180.8 lm, whereas the second is
characterized by pore radii varying in size from 1 to
10 lm.
Similar to the above two samples of the Middle Shajara
Reservoir, sample SJ9 is described as medium-grained,
moderately well sorted sandstone. This sample is charac-
terized with bimodal pore size distribution as indicated in
Fig. 13 with an average pore radius of 73.9 lm indicating
the largest mean pore size for this section of the reservoir.
Further verification of heterogeneity of this sample is
indicated in Fig. 14 which indicates two tracks of pore
radii, ranging in size from 10 to 164.4 lm and 1 to 10 lm.
Based on the outcomes obtained and the Winland R35 and
Pittman Rapex (Table 1), the whole Middle Shajara Reser-
voir is classified as megaporous reservoir with good flow
capacity.
The Upper Shajara Reservoir is also represented by
three samples, namely from base to top SJ11, SJ12, and
SJ13. Sample SJ11 is identified as medium-grained, poorly
sorted sandstone. This sample is characterized with bimo-
dal pore size distribution as illustrated in Fig. 15. This
variation in pore size distribution is proved in Fig. 16
where three tracks of pore distribution are observed. The
first track is for pore radii varying in size from 30 to
173.9 lm. The second track represents distribution of pore
radii ranging in size from 0.1 to 30 lm. The third track
represents a very small pore radii range of 0.01–0.1 lm.
This sample has a mean pore radius of 42.9 lm.
Sample SJ12 is identified as very coarse-grained, mod-
erately sorted sandstone. This sample is also characterized
with bimodal pore size distribution as illustrated in Fig. 17.
This sample possesses an average pore radius of 67.7 lm.
The pore heterogeneity is verified in Fig. 18 where two
Fig. 13 Incremental and cumulative PSD versus pore radius of
sample SJ9 from the Lower Shajara Reservoir
Fig. 14 Cumulative % SHg versus pore radius of sample SJ9 from the
Lower Shajara Reservoir
Fig. 15 Incremental and cumulative PSD versus pore radius of
sample SJ11 from the Lower Shajara Reservoir
Fig. 16 Cumulative % SHg versus pore radius of sample SJ11 from
the Lower Shajara Reservoir
J Petrol Explor Prod Technol (2011) 1:1–9 7
123
tracks of pore size distribution exist. The first having pore
radii ranging in size from 36 to 173.9 lm, whereas the
second ranges from 3.6 to 36 lm.
Sample SJ13 represents the upper section of the reser-
voir. It is described as coarse-grained, moderately sorted
sandstone. Again it is characterized with bimodal pore size
distribution as illustrated in Fig. 19 with an average pore
radius of 25.2 lm. This sample is also considered hetero-
geneous as indicated in Fig. 20 where three distinct tracks
of pore radii are observed. Reservoir classification of the
Upper Shajara can be considered as megaporous.
In an overall view, and based on the relationship of R35
and Rapex presented in Fig. 21, the reservoir quality of the
Shajara Formation increases with the increase in mean pore
radius corresponding to the apex and to that corresponding
to 35% mercury saturation. Good correlation was obtained
Fig. 17 Incremental and cumulative PSD versus pore radius of
sample SJ12 from the Lower Shajara Reservoir
Fig. 18 Incremental and cumulative % SHg versus pore radius of
sample SJ12 from the Lower Shajara Reservoir
Fig. 19 Incremental and cumulative PSD versus pore radius of
sample SJ13 from the Lower Shajara Reservoir
Fig. 20 Cumulative % SHg versus pore radius of sample SJ13 from
the Lower Shajara Reservoir
Fig. 21 Winland R35 versus Pittman Rapex
8 J Petrol Explor Prod Technol (2011) 1:1–9
123
for the R35 versus Rapex and all samples mean pore sizes are
grouped at megaporous category except for sample SJ3
which falls on macroporous category confirming the pre-
viously discussed pore size identification. In conclusion,
grain and pore size variability are the controlling factor on
the Shajara reservoir quality assessment.
Conclusions
• The three reservoirs of the Shajara Formation are
characterized as heterogeneous reservoirs.
• In general, the three Shajara Reservoirs are classified as
megaporous, with average pore size of 22, 49 and
45 lm for the Lower, Middle, and Upper Shajara
Reservoirs, respectively. However, the best reservoir
quality is assigned to the lower sand unit of the Lower
Shajara followed by the Middle Shajara Reservoir.
• Pore radius corresponding to the apex and that corre-
sponding to the 35% mercury saturation confirms the
reservoir classification indicating megaporous reser-
voirs except for SJ3 of the Lower Shajara which has
low quality due to its fine grain characteristic and its
proximity to the unconformity surface.
• An excellent correlation factor of 0.93 was obtained
when Winland R35 was plotted versus Pittman Rapex.
• Reservoir quality is controlled to a large extent by the
depositional facies and specifically by rock texture
illustrated by petrophysical description. The quality of
the Shajara Formation reservoirs increases with the
increase in grain size and grain sorting.
Open Access This article is distributed under the terms of the
Creative Commons Attribution Noncommercial License which per-
mits any noncommercial use, distribution, and reproduction in any
medium, provided the original author(s) and source are credited.
References
Al-Khidir KE (2007) Reservoir characteristics of the Unayzah
formation. MSc thesis, King Saud University, Riyadh, Kingdom
of Saudi Arabia
Al-Laboun AA (1982) Subsurface stratigraphy of the Pre-Khuff
formations in central and northwestern Arabia. PhD thesis, King
Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
Al-Laboun AA (1987) Unayzah Formation: a new Permo-Carboniferous
unit in Saudi Arabia. Am Assoc Petrol Geol Bull 71(1):29–38
Al-Laboun AA (1988) The distribution of the Carboniferous–Permian
Siliciclastics in the Greater Arabian Basin. Geol Soc Am Bull
100(3):362–373
El-Khayal AA, Chaloner WG, Hill CR (1980) Paleozoic plants from
Saudi Arabia. Nature 285:33–34
Evans DS, Bahabri BH, Al-Qtaibi AM (1997) Stratigraphic trap in the
Permian Unayzah Formation, Central Saudi Arabia. GeoArabia
2:259–278
Ferguson GS, Chambers TM (1991) Subsurface stratigraphy, depo-
sitional history, and reservoir development of the early-to-late
Permian Unayzah Formation in Central Saudi Arabia. In: Paper
SPE 21394 presented at the middle east oil show held in Bahrain,
Nov. 16–19
Kolodzie SJ (1980) Analysis of pore throat size and use of the
Waxman–Smits equation to determine OOIP in spindle field. In:
Paper SPE 9382, 55th annual fall technical conference, Colorado
Libny L, Roberto R, Quaglia A, Porras JC, and Lazarde H (2001)
Bimodal behavior of mercury injection capillary pressure curve
and its relationship to pore geometry, rock quality and produc-
tion performance in a laminated and heterogeneous reservoir. In:
SPE 69457 presented at Latin America and Caribbean Petroleum
Engineering Conference, Argentina, March 25–28
McGillivray JG, Husseini MI (1992) The Paleozoic petroleum
geology of central Arabia. Am Assoc Petrol Geol Bull 76(10):
1473–1490
Melvin J, Sprague A (2006) Origin and stratigraphic architecture of
galciogenic sediments in Permian-Carboniferous Lower Unay-
zah Sandstones, Eastern Central Saudi Arabia. GeoArabia
11(4):105–152
Pittman ED (2001) Estimating pore throat size in sandstones from
routine core analysis data
Purcell WR (1948) Capillary pressures—their measurement using
mercury and the calculation of the permeability therefrom,
AIME, T.P.2544
Senalp M, Al-Dauji A (1995) Stratigraphy and sedimentation of the
Unayzah Reservoir, Central Saudi Arabia. In: Husseini MI (ed)
The middle east petroleum geosciences, Geo 94, Gulf Petrolink,
Bahrain, vol 2, pp 837–847
Wender LE, Bryant JW, Dicken MF, Neville AS, Al-Moqbel AM
(1998) Paleozoic (Pre-Khuff) hydrocarbon geology of the
Ghawar area, Eastern Saudi Arabia. GeoArabia 3(2):273–302
J Petrol Explor Prod Technol (2011) 1:1–9 9
123
ORIGINAL PAPER - EXPLORATION GEOPHYSICS
Theory of 3-D angle gathers in wave-equation seismic imaging
Sergey Fomel
Received: 26 September 2010 / Accepted: 24 January 2011 / Published online: 22 February 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract I present two methods for constructing angle
gathers in 3-D seismic imaging by downward extrapola-
tion. Angles in angle gathers refer to the scattering angle at
the reflector and provide a natural access to analyzing
migration velocity and amplitudes. In the first method,
angle gathers are extracted at each downward-continuation
step by mapping transformations in constant-depth fre-
quency slices. In the second method, one extracts angle
gathers after applying the imaging condition by trans-
forming local offset gathers in the depth domain. The
second approach generalizes previously published algo-
rithms for angle-gather construction in 2-D and common-
azimuth imaging.
Keywords Geophysics � Seismic imaging �Velocity analysis � Amplitude analysis
Introduction
Wave extrapolation provides an accurate method for seis-
mic imaging in structurally complex areas (Biondi 2006;
Etgen et al. 2009). Wave extrapolation methods have
several known advantages in comparison with direct
methods such as Kirchhoff migration thanks to their ability
to handle multi-pathing, strong velocity heterogeneities,
and finite-bandwidth wave-propagation effects (Gray et al.
2001). However, velocity and amplitude analysis in the
prestack domain are not immediately available for wave
extrapolation methods. To overcome this limitation, sev-
eral authors (de Bruin et al. 1990; Prucha et al. 1999;
Mosher and Foster 2000; Rickett and Sava 2002; Xie and
Wu 2002; Soubaras 2003; Sava and Fomel 2003, 2005,
2006) suggested methods for constructing angle gathers
from downward-continued wavefields. Angles in angle
gathers are generally understood as the reflection (scatter-
ing) angles at reflecting interfaces (Xu et al. 2001;
Brandsberg-Dahl et al. 2003). Angle gathers facilitate
velocity analysis (Liu et al. 2001; Stork et al. 2002) and
can be used in principle for extracting angle-dependent
reflectivity information directly at the target reflectors
(Sava et al. 2001). Stolk and de Hoop (2002) assert that
angle gathers generated with wavefield extrapolation are
genuinely free of artifacts documented for Kirchhoff-gen-
erated angle gathers (Stolk and Symes 2002, 2004).
There are two possible approaches to angle-gather
construction with wavefield continuation. In the first
approach, one generates gathers at each depth level con-
verting offset-space-frequency planes into angle-space
planes simultaneously with applying the imaging condi-
tion. The offset in this case refers to the local offset
between source and receiver parts of the downward con-
tinued prestack data. Such a construction was suggested,
for example, by Prucha et al. (1999). This approach is
attractive because of its localization in depth. However,
the method of Prucha et al. (1999) produces gathers in the
offset ray parameter as opposed to angle. As a result, the
angle-domain information becomes structure-dependent:
the output depends not only on the scattering angle but also
on the structural dip.
In the second approach, one converts migrated images in
offset-depth domain to angle-depth gathers after imaging
of all depth levels is completed. Sava and Fomel (2003)
suggested a simple Radon-transform procedure for
S. Fomel (&)
Bureau of Economic Geology, John A. and Katherine G. Jackson
School of Geosciences, The University of Texas at Austin,
University Station, Box X, Austin, TX 78713-8924, USA
e-mail: [email protected]
123
J Petrol Explor Prod Technol (2011) 1:11–16
DOI 10.1007/s13202-011-0004-8
extracting angle gathers from migrated images. The
transformation is independent of velocity and structure.
Rickett and Sava (2002) adopted it for constructing angle
gathers in the shot-gather migration. Biondi and Symes
(2004) demonstrate that the method of Sava and Fomel
(2003) is strictly valid in the 3-D case only in the absence
of cross-line structural dips. They present an extension
of this method for the common-azimuth approximation
(Biondi and Palacharla 1996).
In this paper, I present a more complete analysis of the
angle-gather construction in 3-D imaging by wavefield
continuation. First, I show how to remove the structural
dependence in the depth-slice approach. The improved
mapping retains the velocity dependence but removes the
effect of the structure. Additionally, I extend the second,
post-migration approach to a complete 3-D wide-azimuth
situation. Under the common-azimuth approximation, this
formulation reduces to the result of Biondi et al. (2003)
and, in the absence of cross-line structure, it is equivalent
to the Radon construction of Sava and Fomel (2003).
Traveltime derivatives and dispersion relationships
for a 3-D dipping reflector
Theoretical analysis of angle gathers in downward con-
tinuation methods can be reduced to analyzing the geom-
etry of reflection in the simple case of a dipping reflector in
a locally homogeneous medium. Considering the reflection
geometry in the case of a plane reflector is sufficient for
deriving relationships for local reflection travel time
derivatives in the vicinity of a reflection point (Goldin
2002). Let the local reflection plane be described in
{x, y, z} coordinates by the general equation
x cos aþ y cos bþ z cos c ¼ d; ð1Þ
where the normal angles a, b, and c satisfy
cos2 aþ cos2 bþ cos2 c ¼ 1; ð2Þ
The geometry of the reflection ray paths is depicted in
Fig. 1. The reflection travel time measured on a horizontal
surface above the reflector is given by the known
expression (Slotnick 1959; Levin 1971)
tðhx; hyÞ ¼2
v
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2 þ h2
x þ h2y � hx cos aþ hy cos b
� �2q
;
ð3Þwhere D is the length of the normal to the reflector from
the midpoint (distance MM0 in Fig. 2)
D ¼ d � mx cos a� my cos b; ð4Þmx and my are the midpoint coordinates, hx and hy are the
half-offset coordinates, and v is the local propagation
velocity.
According to elementary geometrical considerations
(Figs. 1, 2), the reflection angle h is related to the previ-
ously introduced quantities by the equation
cos h ¼ DffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2 þ h2
x þ h2y � hx cos aþ hy cos b
� �2q : ð5Þ
Explicitly differentiating Eq. 3 with respect to the
midpoint and offset coordinates and utilizing Eq. 5 leads to
the equations
tmx� ot
omx¼ � 2
vcos h cos a; ð6Þ
tmy� ot
omy¼ � 2
vcos h cos b; ð7Þ
reflector
surface
SR
θ
θ
O
S"
S’
Fig. 1 Reflection geometry in 3-D (a scheme). S and R and the
source and the receiver positions at the surface. O is the reflection
point. S0 is the normal projection of the source to the reflector. S00 is
the ‘‘mirror’’ source. The cumulative length of the incident and
reflected rays is equal to the distance from S00 to R
S R
OM’
S"
θ
S’reflector
θ
M
Fig. 2 Reflection geometry in the reflection plane (a scheme). M is
the midpoint. As follows from the similarity of triangles S00SR and
S0SM; the distance from M to S0 is twice smaller than the distance
from S00 to R
12 J Petrol Explor Prod Technol (2011) 1:11–16
123
thx� ot
ohx¼ 4
v2 thx sin2 a� hy cos a cos b� �
; ð8Þ
thy� ot
ohy¼ 4
v2 thy sin2 b� hx cos a cos b� �
: ð9Þ
Additionally, the traveltime derivative with respect to
the depth of the observation surface is given by
tz �ot
oz¼ � 2
vcos h cos c ð10Þ
and is related to the previously defined derivatives by
the double-square-root equation
�v tz ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2
4tmx� thx
ð Þ2� v2
4tmy� thy
� �2
r
þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2
4tmxþ thx
ð Þ2� v2
4tmyþ thy
� �2
r:
ð11Þ
In the frequency-wavenumber domain, Eq. 11 serves as
the basis for 3-D shot-geophone downward-continuation
imaging. In the Fourier domain, each tx derivative
translates into -kx/x ratio, where kx is the wavenumber
corresponding to x and x is the temporal frequency.
Equations (6), (7), and (10) immediately produce the
first important 3-D relationship for angle gathers
cos h ¼ v
2x
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik2
mxþ k2
myþ k2
z
q: ð12Þ
Expressing the depth derivative with the help of the
double-square-root Eq. 11 and applying a number of
algebraic transformations, one can turn Eq. 12 into the
dispersion relationship
ðk2mxþ k2
myÞ sin2 h
v2þ ðk2
hxþ k2
hyÞ cos2 h
v2
¼ 1
4x2kmx
khy� kmy
khx
� �2þ4x2 cos2 hv2
sin2 hv2
:
ð13Þ
For each reflection angle h and each frequency x, Eq. 13
specifies the locations on the four-dimensional
(kmx; kmy
; khx; khy
) wavenumber hyperplane that contribute
to the common-angle gather. In the 2-D case, Eq. 13
simplifies by setting khyand ky to zero. Using the notation
kmx¼ km and khx
¼ kh; the 2-D equation takes the form
k2m sin2 hþ k2
h cos2 h ¼ 4x2
v2cos2 h sin2 h ð14Þ
and can be explicitly solved for kh resulting in the
convenient 2-D dispersion relationship
kh ¼2x sin h
v
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 4k2
mv2
x2 cos2 h
r: ð15Þ
In the next section, I show that a similar simplification is
also valid under the common-azimuth approximation.
Equations (13) and (15) describe an effective migration of
the downward-continued data to the appropriate positions
on midpoint-offset planes to remove the structural
dependence from the local image gathers.
Another important relationship follows from eliminating
the local velocity v from Eqs. 11 and 12. Expressing v2
from Eq. 12 and substituting the result in Eq. 12, we arrive
(after a number of algebraical transformations) to the fre-
quency-independent equation
tan2 h ¼k2
z ðk2hxþ k2
hyÞ þ ðkhx
kmxþ khy
kmyÞ2
k2z ðk2
mxþ k2
myþ k2
z Þ: ð16Þ
Equation (16) can be expressed in terms of ratios kmx=kz
and kmy=kz; which correspond at the zero local offset to
local structural dips (zmxand zmy
partial derivatives), and
ratios khx=kz and khy
=kz; which correspond to local offset
slopes. As shown by Sava and Fomel (2005), it can be also
expressed as
tan2 h ¼k2
hxþ k2
hyþ k2
hz
k2mxþ k2
myþ k2
z
; ð17Þ
where khzrefers to the vertical offset between source and
receiver wavefields (Biondi and Shan 2002).
In the 2-D case, Eq. 16 simplifies to the form, inde-
pendent of the structural dip:
tan h ¼ kh
kz; ð18Þ
which is the equation suggested by Sava and Fomel
(2003). Equation (18) appeared previously in the theory of
migration-inversion (Stolt and Weglein 1985).
Common-azimuth approximation
Common-azimuth migration (Biondi and Palacharla 1996)
is a downward continuation imaging method tailored for
narrow-azimuth streamer surveys that can be transformed
to a single common azimuth with the help of azimuth
moveout (Biondi et al. 1998). Employing the common-
azimuth approximation, one assumes the reflection plane
stays confined in the acquisition azimuth. Although this
assumption is strictly valid only in the case of constant
velocity (Vaillant and Biondi 2000), the modest azimuth
variation in realistic situations justifies the use of the
method (Biondi 2003).
To restrict equations of the previous section to the
common-azimuth approximation, it is sufficient to set the
cross-line offset hy to zero assuming the x coordinate is
oriented along the acquisition azimuth. In particular, from
Eqs. 8, 9, we obtain
hx sin a ¼ vt
2sin h ð19Þ
J Petrol Explor Prod Technol (2011) 1:11–16 13
123
thx¼ 4hx
v2tsin2 a ¼ 2
vsin h sin a; ð20Þ
thy¼ � 4hx
v2tcos a cos b ¼ � 2
vsin h cot a cos b : ð21Þ
With the help of Eqs. 6, 7, and 10), Eq. 21 transforms to
the form
thy¼ tmy
tan htan a
¼ tmy
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2
4tmxþ thx
ð Þ2q
�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2
4tmx� thx
ð Þ2q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2
4tmxþ thx
ð Þ2q
þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2
4tmx� thx
ð Þ2q ;
ð22Þ
suggested by Biondi and Palacharla (1996). Combining
Eqs. 6, 7, 10, and 20 and transforming to the frequency–
wavenumber domain, we obtain the common-azimuth
dispersion relationship
ðk2hxþ k2
myþ k2
z Þ ðk2mxþ k2
myþ k2
z Þ ¼4x2
v2ðk2
myþ k2
z Þ; ð23Þ
which shows that, under the common-azimuth
approximation and in a laterally homogeneous medium,
3-D seismic migration amounts to a cascade of a 2-D
prestack migrations in the in-line direction and a 2-D zero-
offset migration in the cross-line direction (Canning and
Gardner 1996).
Under the common-azimuth approximation, the angle-
dependent relationship (13) takes the form
k2mx
sin2 hþ k2hx
cos2 h ¼ 4x2
v2cos2 h sin2 h; ð24Þ
which is identical to the 2-D Eq. 14. This proves that
under this approximation, one can perform the structural
correction independently for each cross-line wavenumber.
The post-imaging Eq. 16 transforms to the equation
tan2 h ¼k2
hx
k2myþ k2
z
; ð25Þ
obtained previously by Biondi et al. (2003). In the
absence of cross-line structural dips ðkmy¼ 0Þ; it is
equivalent to the 2-D Eq. 18.
Algorithm I: Angle gathers during downward
continuation
This algorithm follows from Eq. 13. It consists of the
following steps, applied at each propagation depth z:
1. Generate local offset gathers and transform them to
the wavenumber domain. In the double-square-root
migration, the local offset wavenumbers are immedi-
ately available. In the shot gather migration, local
offsets are generated by cross-correlation of the source
and receiver wavefields (Rickett and Sava 2002).
2. For each frequency x, transform the local offset wave-
numbers khx; khy
into the angle coordinates sin h=v
according to Eq. 13. The angle coordinates depend on
velocity but do not depend on the local structural dip. In
the 2-D case, each frequency slice is simply the km; kh
plane, and each angle coordinate corresponds to a circle
in that plane centered at the origin and described by
Eq. 14. Figure 3 shows an example of a 2-D frequency
slice transformed to angles.
3. Accumulate contributions from all frequencies to
apply the imaging condition in time.
This algorithm is applicable for targets localized in
depth. The local offset gathers need to be computed for all
lateral locations, but there is no need to store them in
memory, because conversion to angles happens on the fly.
The algorithm outputs not angles directly, but velocity-
dependent parameters sin h=v: Alkhalifah and Fomel
(2009, 2011) have recently extended this algorithm to
transversally isotropic media.
Algorithm II: Post-migration angle gathers
The second algorithm follows from Eq. 16. It applies after
the imaging has completed and consists of the following
steps applied at each common-image location:
1. Generate and store local offset gathers. In the double-
square-root migration, the local offsets are immedi-
ately available. In the shot gather migration, local
Fig. 3 Constant-depth constant-frequency slice mapped to reflection
angles according to the 2-D version of Algorithm I. Zero offset
wavenumber maps to zero (normal incidence) angle. The top rightcorner is the evanescent region
14 J Petrol Explor Prod Technol (2011) 1:11–16
123
offsets are generated by cross-correlation of the source
and receiver wavefields.
2. Estimate the dominant local structural dips at the
common image point by using one of the available dip
estimation methods: local slant stack, plane-wave
destruction, etc.
3. After the imaging has completed, transform local-
offset gathers into the slant-stack domain either by
slant-stacking in the fz; hx; hyg physical domain or by
radial-trace construction in the fkz; khx; khyg Fourier
domain (Sava and Fomel 2003).
4. Using estimated dips, convert slant stacks into angles
by applying Eq. 16. The mapping from offset-depth
slopes to angles is illustrated in Fig. 4.
The last two steps can be combined into one. It is
sufficient to compute the effective offset h ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2
x þ h2y þ ðhxzy � hyzxÞ2
qand apply the basic 2-D angle
extraction algorithm to the effective offset gather.
The second method is applicable to selected common-
image gathers, which can be spread on a sparse grid. The
local offset gathers need to be computed and stored at all
depths. The method works independent of the velocity. The
main disadvantage is the need to estimate local structural
dips. In the common-azimuth approximation, only the
cross-line dip is required (Biondi et al. 2003). In the 2-D
case (zero cross-line dip), the method is dip-independent
(Sava and Fomel 2003).
Discussion
Since the first presentation of the 3-D angle-gather theory
(Fomel 2004), many new research results have appeared in
the literature. By the end of 2000s, prestack 3-D reverse-
time migration has become a standard tool for depth
imaging in structurally-complex areas, and it is becoming
feasible to generate 3-D angle gathers as part of routine
processing (Luo et al. 2010; Vyas et al. 2010; Xu et al.
2010). The most important new theoretical developments
are the ability to extract angle information from time-shift
angle gathers (Sava and Fomel 2006; Vyas et al. 2010), the
ability to extract not only reflection-angle but also azimuth
information (Xu et al. 2010), and the extension of the
angle-gather theory to anisotropy (Biondi 2007; Alkhalifah
and Fomel 2009, 2011).
Conclusions
Angle gathers present a natural tool for analyzing velocities
and amplitudes in wave-equation imaging. I have discussed
two approaches for angle-gather construction. In the first
approach, angle gathers are constructed on the fly at dif-
ferent depth steps of the wave extrapolation process. In the
second approach, angle gathers are extracted from the
local-offset gathers after imaging has completed. The
second method was previously presented for the 2-D case
and for the case of a common-azimuth approximation. Both
approaches have advantages and disadvantages. The pref-
erence depends on the application and the input data
configuration.
Acknowledgments I am grateful to Nanxun Dai, John Etgen,
Sergey Goldin, and Paul Sava for enlightening discussions.
This publication is authorized by the Director, Bureau of Economic
Geology, The University of Texas at Austin.
Open Access This article is distributed under the terms of the
Creative Commons Attribution Noncommercial License which per-
mits any noncommercial use, distribution, and reproduction in any
medium, provided the original author(s) and source are credited.
Fig. 4 Mapping from the offset
slope plane to angles according
to Algorithm II. Zero slopes
map to zero (normal-incidence)
angle
J Petrol Explor Prod Technol (2011) 1:11–16 15
123
References
Alkhalifah T, Fomel S (2009) Angle gathers in wave-equation
imaging for VTI media. In: 79th Ann. Internat. Mtg, Soc. Expl.
Geophys., Expanded Abstracts. Soc. of Expl. Geophys., pp
2899–2903.
Alkhalifah T, Fomel S (2011) Angle gathers in wave equation
imaging for transversely isotropic media. Geophys Prospect, vol
59. doi:10.1111/j.1365-2478.2010.00930.x
Biondi B (2003) Narrow-azimuth migration of marine streamer data.
In: 73rd Ann. Internat. Mtg, Soc. Expl. Geophys. Expanded
Abstracts. Soc. of Expl. Geophys., pp 897-900
Biondi B (2007) Angle-domain common-image gathers from aniso-
tropic migration. Geophysics 72:581–591
Biondi B, Fomel S, Chemingui N (1998) Azimuth moveout for 3-D
prestack imaging. Geophysics 63:574–588
Biondi B, Palacharla G (1996) 3-D prestack migration of common-
azimuth data. Geophysics 61:1822–1832
Biondi B, Shan G (2002) Prestack imaging of overturned reflections
by reverse time migration. In: 72nd Ann. Internat. Mtg, Soc.
Expl. Geophys., pp 1284–1287
Biondi B, Symes W (2004) Angle-domain common-image gathers for
migration velocity analysis by wavefield-continuation methods.
Geophysics 69:1283–1298
Biondi B, Tisserant T, Symes W (2003) Wavefield-continuation
angle-domain common-image gathers for migration velocity
analysis. In: 73rd Ann. Internat. Mtg, Soc. Expl. Geophys.,
Expanded Abstracts. Soc. of Expl. Geophys., pp 2104–2107
Biondi BL (2006) 3-D seismic imaging. Society of Exploration
Geophysicists
Brandsberg-Dahl S, de Hoop MV, Ursin B (2003) Focusing in dip and
AVA compensation on scattering-angle/azimuth common image
gathers. Geophysics 68:232–254
Canning A, GHF Gardner (1996) A two-pass approximation to 3-D
prestack migration. Geophysics 61:409–421
de Bruin CGM, Wapenaar CPA, AJ Berkhout (1990) Angle-
dependent reflectivity by means of prestack migration. Geo-
physics 55:1223–1234
Etgen J, Gray SH, Zhang Y (2009) An overview of depth imaging in
exploration geophysics. Geophysics 74:WCA5–WCA17
Fomel S (2004) Theory of 3D angle gathers in wave-equation
imaging. In: 74th Ann. Internat. Mtg., Soc. of Expl. Geophys.,
pp 1053–1056
Goldin SV (2002) Theoretical aspects of 3-D DMO. In: 72nd Ann.
Internat. Mtg, Soc. Expl. Geophys., Expanded Abstracts. Soc. of
Expl. Geophys., pp 2333–2336.
Gray SH, Etgen J, Dellinger J, Whitmore D (2001) Seismic migration
problems and solutions. Geophysics 66:1622–1640
Levin FK (1971) Apparent velocity from dipping interface reflections.
Geophysics 36: 510–516 (Errata in GEO-50-11-2279)
Liu W, Popovici A, Bevc D, Biondi B (2001) 3D migration velocity
analysis for common image gathers in the reflection angle
domain. In: 71st Ann. Internat. Mtg, Soc. of Expl. Geophys.,
pp 885–888.
Luo M, Lu R, Winbow G, Bear L (2010) A comparison of methods
for obtaining local image gathers in depth migration. In: 80th
Ann. Internat. Mtg, Soc. Expl. Geophys., Expanded Abstracts.
Soc. of Expl. Geophys., pp 3247–3251.
Mosher C, Foster D (2000) Common angle imaging conditions for
prestack depth migration. In: 70th Ann. Internat. Mtg, Soc. of
Expl. Geophys., pp 830–833.
Prucha M, Biondi B, Symes W (1999) Angle-domain common image
gathers by wave-equation migration. In: 69th Ann. Internat. Mtg,
Soc. of Expl. Geophys., pp 824–827.
Rickett JE, PC Sava (2002) Offset and angle-domain common image-
point gathers for shot-profile migration. Geophysics 67:883–889
Sava P, Biondi B, Fomel S (2001) Amplitude-preserved common
image gathers by wave-equation migration. In: 71st Ann.
Internat. Mtg, Soc. of Expl. Geophys., pp 296–299.
Sava PC, Fomel S (2003) Angle-domain common-image gathers by
wavefield continuation methods. Geophysics 68:1065–1074
Sava PC, Fomel S (2005) Coordinate-independent angle-gathers for
wave equation migration. In: 75th Ann. Internat. Mtg, Soc. Expl.
Geophys., Expanded Abstracts. Soc. of Expl. Geophys., pp
2052–2055.
Sava PC, Fomel S (2006) Time-shift imaging condition in seismic
migration. Geophysics 71:S209–S217
Slotnick MM (1959) Lessons in Seismic Computing. Society of
Exploration Geophysics, Tulsa (Edited by R. A. Geyer).
Soubaras R (2003) Angle gathers for shot-record migration by local
harmonic decomposition. In: 73rd Ann. Internat. Mtg., Soc. of
Expl. Geophys., pp 889–892.
Stolk C, de Hoop MV (2002) Seismic inverse scattering in the ‘‘wave-
equation’’ approach. In: CWP-417: Colorado School of Mines.
Stolk CC, Symes WW (2002) Artifacts in Kirchhoff common image
gathers. In: 72nd Ann. Internat. Mtg, Soc. Expl. Geophys.,
Expanded Abstracts. Soc. of Expl. Geophys., pp 1129–1132.
Stolk CC, Symes WW (2004) Kinematic artifacts in prestack depth
migration. Geophysics 69:562–575
Stolt RH, Weglein AB (1985) Migration and inversion of seismic
data. Geophysics 50:2458–2472
Stork C, Kitchenside P, Yingst D, Albertin U, Kostov C, Wilson B,
Watts D, Kapoor J, Brown G (2002) Comparison between angle
and offset gathers from wave equation migration and Kirchhoff
migration. In: 72nd Ann. Internat. Mtg, Soc. Expl. Geophys.,
Expanded Abstracts. Soc. of Expl. Geophys., pp 1200–1203.
Vaillant L, Biondi B (2000) Accuracy of common-azimuth migration
approximations. In: SEP-103: Stanford Exploration Project,
pp 157–168.
Vyas M, Mobley E, Nichols D, Perdomo J (2010) Angle gathers for
RTM using extended imaging conditions. In: 80th Ann. Internat.
Mtg, Soc. Expl. Geophys., Expanded Abstracts. Soc. of Expl.
Geophys., pp 3252–3256.
Xie, XB, Wu RS (2002) Extracting angle domain information from
migrated wavefield. In: 72nd Ann. Internat. Mtg, Soc. Expl.
Geophys., Expanded Abstracts. Soc. of Expl. Geophys.,
pp 1360–1363.
Xu S, Chauris H, Lambare G, Noble M (2001) Common-angle
migration: a strategy for imaging complex media. Geophysics
66:1877–1894
Xu S, Zhang Y, Tang B (2010) 3D common image gathers from
reverse time migration. In: 80th Ann. Internat. Mtg, Soc. Efxpl.
Geophys., Expanded Abstracts. Soc. of Expl. Geophys.,
pp 3257–3262.
16 J Petrol Explor Prod Technol (2011) 1:11–16
123
ORIGINAL PAPER - EXPLORATION GEOPHYSICS
The basic components of residual migration in VTI media usinganisotropy continuation
Tariq Alkhalifah • Sergey Fomel
Received: 3 May 2010 / Accepted: 3 March 2011 / Published online: 24 March 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract We introduce anisotropy continuation as a
process which relates changes in seismic images to per-
turbations in the anisotropic medium parameters. This
process is constrained by two kinematic equations, one for
perturbations in the normal-moveout (NMO) velocity and
the other for perturbations in the dimensionless anisotropy
parameter g. We consider separately the case of post-stack
migration and show that the kinematic equations in this
case can be solved explicitly by converting them to
ordinary differential equations using the method of char-
acteristics. When comparing the results of kinematic ana-
lytical computations with synthetic numerical experiments
confirms the theoretical accuracy of the method.
Keywords Velocity continuation � Residual migration �Anisotropy
Introduction
A well-known paradox in seismic imaging is that the
detailed information about the subsurface velocity is
required before a reliable image can be obtained. In prac-
tice, this paradox leads to an iterative approach to building
the image. It looks attractive to relate small changes in
velocity parameters to inexpensive operators perturbing the
image. This approach has been long known as residual
migration. A classic result is the theory of residual post-
stack migration (Rothman et. al. 1985), extended to the
prestack case by Etgen (1990). In a relatively recent paper,
Fomel (1996) introduced the concept of velocity continu-
ation as the continuous model of the residual migration
process. All these results were based on the assumption of
the isotropic velocity model.
Recently, emphasis has been put on the importance of
considering anisotropy and its influence on data. Alkhalifah
and Tsvankin (1995) demonstrated that, for TI media with
vertical symmetry axis (VTI media) and mild lateral
inhomogeneity, just two parameters are sufficient for per-
forming all time-related processing, such as normal
moveout (NMO) correction (including non-hyperbolic
moveout correction, if necessary), dip-moveout (DMO)
correction, and prestack and poststack time migration in a
homogeneous medium. One of these two parameters, the
short-spread NMO velocity for a horizontal reflector, is
given by
vnmoð0Þ ¼ vv
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 2dp
; ð1Þ
where vv is the vertical P-wave velocity, and d is one of
Thomsen’s anisotropy parameters (Thomsen 1986). Taking
vh to be the P-wave velocity in the horizontal direction, the
other anisotropy parameter, g, is given by
g � 0:5v2
h
v2nmoð0Þ
� 1
� �¼ �� d
1þ 2d; ð2Þ
where � is another of Thomsen’s parameters. In addition,
Alkhalifah (1998) has showed that the dependency on just
two parameters becomes exact when the vertical shear wave
velocity (VS0) is set to zero. Setting VS0 = 0 leads to
T. Alkhalifah (&)
Physical Sciences and Engineering Division, King Abdullah
University for Science and Technology (KAUST),
Thuwal, Saudi Arabia
e-mail: [email protected]
S. Fomel
Bureau of Economic Geology,
The University of Texas at Austin, Austin, TX, USA
e-mail: [email protected]
123
J Petrol Explor Prod Technol (2011) 1:17–22
DOI 10.1007/s13202-011-0006-6
remarkably accurate kinematic representations. It also
results in much simpler equations that describe P-wave
propagation in VTI media. Throughout this paper, we use
these simplified, yet accurate with respect to conventional
data processing objectives, equations, based on setting
VS0 = 0, to derive the continuation equations. Because we
are only considering time sections, and for the sake of sim-
plicity, we denote vnmo by v. Thus, time processing in VTI
media, depends on two parameters (v and g), whereas in
isotropic media only v counts. To emphasize the importance
of anisotropy to the dip moveout process, Alkhalifah (2005)
introduced residual dip moveout for VTI media.
In this paper, we generalize the velocity continuation
concept to handle VTI media. We define anisotropy con-
tinuation as the process of seismic image perturbation
when either v or g change as migration parameters. This
approach is especially attractive, when the initial image is
obtained with isotropic migration (that is with g = 0). In
this case, anisotropy continuation is equivalent to intro-
ducing anisotropy in the model without the need for
repeating the migration step.
For the sake of simplicity, we start from the post-
stack case and purely kinematic description. We define,
however, the guidelines for moving to the more com-
plicated and interesting cases of prestack migration and
dynamic equations. The results open promising oppor-
tunities for seismic data processing in the presence of
anisotropy.
The general theory
In the case of zero-offset reflection in homogeneous media,
the ray travel distance, l, from the source to the reflection
point is related to the two-way zero-offset time, t, by the
simple equation
l ¼ 1
2vgt; ð3Þ
where vg is the group velocity, best expressed in terms of
its components, as follows:
vg ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2
gx þ v2vv2
gs
q:
Here vgx denotes the horizontal component of group
velocity, vv is the vertical P-wave velocity, and vgs is the
vv-normalized vertical component of the group velocity.
Under the assumption of zero shear-wave velocity in VTI
media, these components have the following analytic
expressions:
vgx ¼v2 px 1þ 2 g� 2 g ps
2ð Þ2� v2 1þ 2 gð Þ px
2 � ps2; ð4Þ
and
vgs ¼1� 2 v2 g px
2ð Þ ps
2� v2 1þ 2 gð Þ px2 � ps
2; ð5Þ
where px is the horizontal component of slowness, and ps is
the normalized (again by the vertical P-wave velocity vv)
vertical component of slowness. The two components of
the slowness vector are related by the following eikonal-
type equation (Alkhalifah 1998):
ps ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2 px
2
1� 2 v2 g px2
s: ð6Þ
Equation (6) corresponds to a normalized version of the
dispersion relation in VTI media.
If we consider v and g as imaging parameters (migration
velocity and migration anisotropy coefficient), the ray
lengthl can be fixed through the imaging process. This
implies that the partial derivatives of with respect to the
imaging parameters are zero. Therefore,
ol
ov¼ ovg
ovt þ vg
ot
ov¼ 0; ð7Þ
and
ol
og¼ ovg
ogt þ vg
ot
og¼ 0: ð8Þ
Applying the simple chain rule to Eqs. (7) and (8), we
obtain
ot
ov¼ ot
ososov;
ot
og¼ ot
ososog; ð9Þ
where otos ¼ �ps, and the two-way vertical travel time is
given by
s ¼ vgst:
Combining Eqs. (7–9) eliminates the two-way zero-offset
time t, which leads to the equations
osov¼ ovg
ov
sps vgsvg
; ð10Þ
and
osog¼ ovg
ogs
ps vgsvg: ð11Þ
After some tedious algebraic manipulation, we can
transform Eqs. (10) and (11) to the general form
osov¼ sFv px; v; gð Þ; ð12Þ
and
osog¼ sFg px; v; gð Þ: ð13Þ
18 J Petrol Explor Prod Technol (2011) 1:17–22
123
Since the residual migration is applied to migrated data,
with the time axis given by s and the reflection slope given byosox ; instead of t and px, respectively, we need to eliminate px
from Eqs. (12) and (13). This task can be achieved with the
help of the following explicit relation, derived in Appendix 1,
p2x ¼
2 sx2
1þ v2 1þ 2 gð Þ sx2 þ S
; ð14Þ
where sx = osox, and
S ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� 8 v2 g sx
2 þ 1þ v2 1þ 2 gð Þ sx2ð Þ2
q:
Inserting Eq. (14) into Eqs. (12) and (13) yields exact,
yet complicated equations, describing the continuation
process for v and g. In summary, these equations have the
form
osov¼ sfv
osox; v; g
� �ð15Þ
and
osog¼ sfg
osox; v; g
� �: ð16Þ
Equations of the form (15) and (16) contain all the
necessary information about the kinematic laws of anisotropy
continuation in the domain of zero-offset migration.
Linearization
A useful approximation of Eqs. (15) and (16) can be
obtained by simply setting g equal to zero in the right hand
side of the equations. Under this approximation, Eq. (15)
leads to the kinematic velocity-continuation equation for
elliptically anisotropic media, which has the following
relatively simple form:
osov¼ v s 2 v2 � vv
2ð Þ sx2 1þ v2 sx
2ð Þvv
2 þ v4 sx2
: ð17Þ
It is interesting to note that setting v = vv, yields
Fomel’s expression for isotropic media (Fomel 1996) given
by
osov¼ v s sx
2: ð18Þ
Alkhalifah (1998) have shown that time–domain
processing algorithms for elliptically anisotropic media
should be the same as those for isotropic media. However,
in anisotropic continuation, elliptical anisotropy and
isotropy differ by a vertical scaling factor that is related
to the difference between the vertical and NMO velocities.
In isotropic media, when velocity is continued, both the
vertical and NMO velocities (which are the same) are
continued together, whereas in anisotropic media
(including elliptically anisotropic) the NMO-velocity
continuation is separated from the vertical velocity one,
and Eq. (17) corresponds to continuation only in the NMO
velocity. This also implies that Eq. (17) is more flexible
than Eq. (18), in that we can isolate the vertical velocity
continuation (a parameter that is usually ambiguous in
surface processing) from the rest of the continuation
process. Using s ¼ zvv; where z is depth, we immediately
obtain the equation
osovv¼ � s
vv;
which represents the vertical velocity continuation.
Setting g = 0 and v = vv in Eq. (16) leads to the fol-
lowing kinematic equation for g-continuation:
osog¼ sv4 sx
4
1þ v2 sx2: ð19Þ
We include more discussion about different aspects of
linearization in Appendix 2. The next section presents the
analytic solution of Eq. (17). Later in this paper, we
compare the analytic solution with a numerical synthetic
example.
Ordinary differential equation representation:
anisotropic rays
According to the classic rules of mathematical physics, the
solution of the kinematic equations (15) and (16) can be
obtained by solving the following system of ordinary dif-
ferential equations:
dx
dm¼ �s
ofmosx
;dsdm¼ �ssx
ofm
osxþ sm;
dsm
dm¼ s
ofm
omþ smfm;
dsx
dm¼ sxfm:
ð20Þ
Here m stands for either v or g, sx = osox, fm ¼ os
om. To trace
the v and g rays, we must first identify the initial values
x0,s0,sx0, and sm0 from the boundary conditions. The vari-
ables x0 ands0 describe the initial position of a reflector in a
time-migrated section, sx0 describes its migrated slope,
andsm0 is simply obtained from Eqs. (15) or (16).
Using the exact kinematic expressions for f, the results
in rather complicated representations of the ordinary dif-
ferential equations. The linearized expressions, on the other
hand, are simple and allow for a straightforward analytical
formulation of the ray tracing system.
From kinematics to dynamics
The kinematic g-continuation equation (17) corresponds to
the following linear fourth-order dynamic equation
J Petrol Explor Prod Technol (2011) 1:17–22 19
123
o4P
ot3 ogþ v2 o4P
ox2 ot ogþ tv4 o4P
ox4¼ 0; ð21Þ
where the t coordinate refers to the vertical traveltime s,
and P (t, x, g) is the migrated image, parameterized in the
anisotropy parameter g. To find the correspondence
between Eqs. (17) and (21), it is sufficient to apply a ray-
theoretical model of the image
Pðt; x; gÞ ¼ Aðx; gÞf ðt � sðx; gÞÞ ð22Þ
as a trial solution to (21). Here the surface t = s (x, g) is
the anisotropy continuation ‘‘wavefront’’—the image of a
reflector for the corresponding value of g, and the function
A is the amplitude. Substituting the trial solution into the
partial differential equation (21) and considering only the
terms with the highest asymptotic order (those containing
the fourth-order derivative of the wavelet f), we arrive at
the kinematic equation (17). The next asymptotic order (the
third-order derivatives of f) gives us the linear partial
differential equation of the amplitude transport, as follows:
1þ v2s2x
� � oA
ogþ 2v2sx sg � 2v2ss2
x
� � oA
oxþ v2A
� 2sxsxg þ sgsxx � 6v2ss2xsxx
� �¼ 0: ð23Þ
We can see that when the reflector is flat (sx = 0 and
sxx = 0), equation (23) reduces to the equality
oA
og¼ 0;
and the amplitude remains unchanged for different g. This
is of course a reasonable behavior in the case of a flat
reflector. It does not guarantee although that the ampli-
tudes, defined by Eq. (23), behave equally well for dipping
and curved reflectors. The amplitude behavior may be
altered by adding low order terms to Eq. (21). According to
the ray theory, such terms can influence the amplitude
behavior, but do not change the kinematics of the wave
propagation.
An appropriate initial value condition for Eq. (21) is the
result of isotropic migration that corresponds to the g = 0
section in the (t, x, g) domain. In practice, the initial value
problem can be solved by a finite-difference technique.
Synthetic test
Residual post-stack migration operators can be obtained by
generating synthetic data for a model consisting of dif-
fractors for given medium parameters and then migrating
the same data with different medium parameters. For
example, we can generate diffractions for isotropic media
and migrate those diffractions using an anisotropic migra-
tion. The resultant operator describes the correction needed
to transform an isotropically migrated section to an
anisotropic one, that is the anisotropic residual migration
operator.
Figure 1 shows such synthetic operators overlaid by
kinematically calculated operators that were computed
with the help of Eq. (17) (the continuation equations for
the case of smallg). Despite the inherent accuracy of the
synthetic operators, they suffer from the lack of aperture
in modeling the diffractions, and therefore, beyond a
certain angle the operators vanish and start to deviate.
The agreement between the synthetic and calculated
operators for small angles, especially for the g = 0.1
case, promises reasonable results in future dynamic
implementations.
0
0.5
1.0
1.5
Tim
e (s
)
-0.6 -0.4 -0.2 0 0.2 0.4
Distance (km)
0.60
0.5
1.0
1.5
Tim
e (s
)
-0.6 -0.4 -0.2 0 0.2 0.4
Distance (km)
0.6
Fig. 1 Residual post-stack
migration operators calculated
by solving Eq. (17), overlaid
above synthetic operators. The
synthetic operators are obtained
by applying TI post-stack
migration with g = 0.1 (left)and g = 0.2 (right) to three
diffractions generated
considering isotropic media.
The NMO velocity for the
modeling and migration is
2.0 km/s
20 J Petrol Explor Prod Technol (2011) 1:17–22
123
Conclusions
We have extended the concept of velocity continuation in
isotropic media to continuations in both the NMO velocity
and the anisotropy parameter g for VTI media. Despite
the fact that we have considered the simple case of post-
stack migration separately, the exact kinematic equations
describing the continuation process are anything, but simple.
However, useful insights into this problem are deduced from
linearized approximations of the continuation equations.
These insights include the following observations:
• The leading order behavior of the velocity continuation
is proportional to sx2, which corresponds to small or
moderate dips.
• The leading order behavior of the g continuation is
proportional to sx4, which corresponds to moderate or
steep dips.
• Both leading terms are independent of the strength of
anisotropy (g).
In practical applications, the initial migrated section is
obtained by isotropic migration, and, therefore, the residual
process is used to correct for anisotropy. Setting g = 0 in
the continuation equations for this type of an application is
a reasonable approximation, given that g = 0 is the starting
point and we consider only weak to moderate degrees of
anisotropy (g & 0.1). Numerical experiments with syn-
thetically generated operators confirm this conclusion.
Acknowledgments Tariq Alkhalifah would like to thank KAUST
and KACST for their financial support, and Sergey Fomel likes to
thank the University of Texas, Austin for its support.
Open Access This article is distributed under the terms of the
Creative Commons Attribution Noncommercial License which per-
mits any noncommercial use, distribution, and reproduction in any
medium, provided the original author(s) and source are credited.
Appendix 1
Relating the zero-offset and migration slopes
The chain rule of differentiation leads to the equality
px ¼ot
ox¼ � ps
osox; ð24Þ
where ps ¼ � otos : It is convenient to transform equality (24)
to the form
osox¼ � px
ps: ð25Þ
Using the expression for ps from the main text, we can
write Eq. (25) as a quadratic polynomial in px2 as follows
ap4x þ bp2
x þ c ¼ 0; ð26Þ
where
a ¼ �2v2g;
b ¼ osox
� �2
v2ð1þ 2gÞ þ 1;
and
c ¼ � osox
� �2
:
Because g can be small (as small as zero for isotropic
media), we use the following form of solution to the
quadratic equation
p2x ¼
2c
�b�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 � 4acp
(Press et al. 1992). This form does not go to infinity asgapproaches 0. We choose the solution with the negative
sign in front of the square root, because this solu-
tion complies with the isotropic result wheng is equal to
zero.
Appendix 2
Linearized approximations
Although the exact expressions might be sufficiently con-
structive for actual residual migration applications, linear-
ized forms are still useful, because they give us valuable
insights into the problem. The degree of parameter
dependency for different reflector dips is one of the most
obvious insights in the anisotropy continuation problem.
Perturbation of a small parameter provides a general
mechanism to simplify functions by recasting them into
power series expansion over a parameter that has small
values. Two variables can satisfy the small perturbation
criterion in this problem: The anisotropy parame-
terg (g � 1) and the reflection dip sx (sx v� 1 or px
v � 1).
Setting g = 0 yields Eq. (17) for the velocity continu-
ation in elliptical anisotropic media and
osog¼ v4 s sx
4 �3 vv2 þ 2 v4 sx
2 þ v2 4� vv2 sx
2ð Þð Þ1þ v2 sx
2ð Þ vv2 þ v4 sx
2ð Þ : ð27Þ
which represents the case when we initially introduce
anisotropy into our model.
Because px (the zero-offset slope) is typically lower than
sx (the migrated slope), we perform initial expansions in
terms of y = px v. Applying the Taylor series expansion of
J Petrol Explor Prod Technol (2011) 1:17–22 21
123
Eqs. (12) and (13) in terms of y and dropping all terms
beyond the fourth power in y, we obtain
osov¼ v s px
2 2 v2 � vv2ð Þ
vv2
� v3 s px4 2 v2 � vv
2ð Þ v2 � 2 1þ 6 gð Þ vv2ð Þ
vv4
; ð28Þ
and
osog¼ v4 s px
4 4 v2 � 3 vv2ð Þ
vv2
: ð29Þ
Although both equations are equal to zero for px=0, the
leading term in the velocity continuation is proportional to
px2, whereas the the leading term in the g continuation is
proportional to px4. As a result the velocity continuation has
greater influence at lower angles than the g continuation. It
is also interesting to note that both leading terms are
independent of the size of anisotropy (g).
Despite the typically lower values of px, expansions in
terms of sx are more important, but less accurate. For small
sx, px & sx, and, therefore, the leading-term behavior of sx
expansions is the same as that of px. As a result, we arrive
at the equation
osov¼ v s 2 v2 � vv
2ð Þ sx2
vv2
þ v4
�� v s 2 v2 � vv
2ð Þvv
4þ s 2 v2 � vv
2ð Þv vv
2
þ 12 g s 2 v2 � vv2ð Þ
v vv2
�sx
4; ð30Þ
and
osog¼ v4 s 4 v2 � 3 vv
2ð Þ sx4
vv2
: ð31Þ
Most of the terms in Eqs. (30) and (31) are functions of
the difference between the vertical and NMO velocities.
Therefore, for simplicity and without a loss of generality,
we set vv = v and keep only the terms up to the eighth
power in sx. The resultant expressions take the form
osov¼ v s sx
2 þ 12 v3 g s sx4 � 4 v5 g 4� 25 gð Þ s sx
6
þ 4 v7 g 5� 83 gþ 144 g2� �
s sx8 ð32Þ
and
osog¼ v4 s sx
4 � v6 1� 20 gð Þ s sx6
þ v8 1� 54 gþ 156 g2� �
s sx8: ð33Þ
Curiously enough, the second term of the g continuation
heavily depends on the size of anisotropy (*20g). The first
term of Eq. (32) (* sx2) is the isotropic term; all other terms
in Eqs. (32) and (33) are induced by the anisotropy.
References
Alkhalifah T (1998) Acoustic approximations for processing in
transversely isotropic media. Geophysics 63:623–631
Alkhalifah T (2005) Residual dip moveout in VTI media. Geophys
Prosp 53:1–12
Alkhalifah T, Tsvankin I (1995) Velocity analysis for transversely
isotropic media. Geophysics 60:1550–1566
Etgen J (1990) Residual prestack migration and interval velocity
estimation. PhD thesis, Stanford University
Fomel S (1996) Migration and velocity analysis by velocity
continuation
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992)
Numerical recipes, the art of scientific computing. Cambridge
University Press, Cambridge
Rothman DH, Levin SA, Rocca F (1985) Residual migration—
applications and limitations. Geophysics 50:110–126
Thomsen L (1986) Weak elastic anisotropy. Geophysics 51:1954–
1966 (discussion in GEO-53-04-0558-0560 with reply by author)
22 J Petrol Explor Prod Technol (2011) 1:17–22
123
ORIGINAL PAPER—PRODUCTION ENGINEERING
Investigation of polymer and surfactant-polymer injectionsin South Slattery Minnelusa Reservoir, Wyoming
Panqing Gao • Brian Towler
Received: 29 April 2010 / Accepted: 20 December 2010 / Published online: 29 January 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract This paper presents an investigation of the
enhanced oil recovery (EOR) potential in the South Slat-
tery Minnelusa formation. The South Slattery Field, which
is characterized by low permeability and high saline brine,
is stepping into the economic limits of secondary water-
flood. A chemical flooding simulation model which was
based on experimental parameters was set up for the
potential investigation of EOR. Both polymer and surfac-
tant-polymer floods were investigated. The recoveries of
these EOR methods are presented, and the development
efficiencies are analyzed.
Keywords Polymer flood � Surfactant-polymer flood �Low permeability � High salinity
List of symbols
Hwj Average thickness of injection well
Hwj Thickness of injection well
a Heterogeneous factor
Hoi Thickness of response producer
i Response producer
j Injection well
Qwj Injection rate of polymer solution
Qw Total injection rate of region
V Injection volume in 1 year
HPAM Partially hydrolyzed polyacrylamide
PV Pore volume
IPV Inaccessible pore volume
IFT Interfacial tension
Introduction
The South Slattery Field is on the southwest toe of a large
anticlinal structure, which is on the eastern flank of the
Powder River basin. Its priority pay zone is the Minnelusa
A, which is a sequence of carbonates and sandstones
formed in the Permian age. These rocks were deposited in a
shallow evaporitic basin, and responses to sea-level chan-
ges were recorded. The stacking pattern, or parasequences
consist of (1) a marine flood of a dune field and carbonate
deposition, (2) shallowing marine deposition due to eu-
static lowering of the sea level, and (3) renewed progra-
dation of eolian dune fields (Sheppy 1986). Just as the
unconformity at the top of the Minnelusa has long been
recognized as an important trapping mechanism, these
parasequence boundaries can also provide significant traps
because the geomorphic relief on the dune fields was lar-
gely preserved during each transgression. The dominant
trapping mechanism is stratigraphic. According to Sheppy,
there are minor Cretaceous muddy sandstones and pro-
ductive sandstones in the upper part of the sequence. But
the Permo-Pennsylvanian Minnelusa ‘‘A’’ Formation is the
principal reservoir (Towler 1991). Figure 1 shows the
structure on the top of the Minnelusa formation. Table 1
presents the reservoir properties of the Minnelusa.
From 1964 to 1995, the field was in the depletion stage;
the primary drive mode had been shown to be a solution
gas drive, in conjunction with fluid expansion, aquifer
influx, and gravity drainage (Towler 1991). At the end of
P. Gao (&) � B. Towler
Department of Chemical and Petroleum Engineering,
University of Wyoming, Laramie, WY, USA
e-mail: [email protected]
P. Gao � B. Towler
Enhanced Oil Recovery Institute,
University of Wyoming, Laramie, WY, USA
123
J Petrol Explor Prod Technol (2011) 1:23–31
DOI 10.1007/s13202-010-0002-2
this stage, the average individual water cut in the north-
eastern zone was relatively low, while the southwest part
showed a high water cut. At the end of 1995, a holistic
water flood began, and oil recovery rate was significantly
increased. The interest in this simulation was initially
spurred by the fact that the water cut kept increasing and
the oil production rate kept decreasing in the past several
years. Figure 2 shows that the oil production rate in this
field began to decline since 2003. The water cut rose sig-
nificantly due to the water injection. To slow down the oil
production decline, an investigation of enhanced oil
recovery (EOR) becomes necessary. In this EOR simula-
tion model, two methods, polymer and surfactant-polymer
(SP) floods, were investigated.
Eclipse has been employed to conduct the simulation
investigation. E100 has been used to finish the history
matching of the depletion and water flooding. Polymer and
surfactant models were used to model the chemical injec-
tions. The parameters of chemical simulation were all from
relative laboratory investigation.
Screening criteria and feasibility investigation
Polymer flood
Use of the polymeric waterflood is a technique to enhance
oil recovery from a reservoir by improving the reservoir
sweep and reducing the amount of injection fluid needed to
produce the same amount of oil (Sorbie and Phil 1991).
Polymer floods work by adding a certain amount of water-
soluble polymers to the injection fluid to increase the vis-
cosity of the injectant (Chang et al. 2006). In this way, the
mobility ratio between the displaced phase and displacing
phase can be reduced significantly, and the sweep volume
is increased accordingly.
Two ways were investigated to optimize the mobility
control: increasing the concentration and increasing the
molecular weight. The former method is a question of
economics; the later one, however, is a question of tech-
nical feasibility (Wang and Li 2006; Carcoana 1991). The
change of molecular weights would result in the basic
changes in the polymer solution properties and the solu-
tion-rock properties, such as residual reduction factor,
adsorption, shear thinning, and inaccessible pore volume
(Pu and Yin 2008; Kaminsky and Szafranski 2007). These
parameters will impact the formation injectivity and
determine the feasibility of the process. Therefore, the first
task of the polymer flood for a given reservoir is to fix an
injection system both technically and economically; espe-
cially for reservoirs with strong heterogeneity (Gharbi
2001; David and Gary 2003), the optimization of the
polymer injection system is extremely important. In this
research, three kinds of polymer of different molecular
weights were used to estimate the effects of polymer flood
in this field.
According to industry experience, the criteria for devel-
oping a successful polymer flood include the following:
1. The oil gravity is greater than 25�API with an oil
viscosity less than 30 cp at reservoir conditions.
2. Oil saturation greater than 30% and light intermediates
desirable.
3. The oil reservoir depth must be less than 8,000 ft with
a reservoir temperature less than 175�F.
4. Formation permeability should be greater than 20 mD
with a net thickness (sandstones preferred) of greater
than 10 ft is favorable.
-5280 -2640 0 2640 5280 7920-5280
-2640
0
2640
5280
Fig. 1 The structure map of Minnelusa formation
Table 1 Property of the South Slattery Field
Property Value
Porosity (%) 15.20
Permeability (mD) 23.34
Depth (ft) 3,785
Density (�API) 32
Initial GOR (SCF/STB) 80
Initial reservoir pressure (Psi) 3,244
Bubble point pressure (Psi) 491
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
5000
10000
15000
20000
25000
30000
35000
J-64 S-77 M-91 J-05
Oil
Pro
duct
ion
bbl/d
Date
wat
er c
ut %
Fig. 2 Regional oil production and water cut history
24 J Petrol Explor Prod Technol (2011) 1:23–31
123
5. Salinity environment which depends on the selected
polymer.
Surfactant-polymer flood
The success of an SP flood depends upon the ability to
propagate the surfactant and polymer, overcome chemical
adsorption, and improve the sweep efficiency and dis-
placement efficiency (Osterrloh and Jante 1992; Gabitto
2006). The mechanism mainly combines the function of the
surfactant in decreasing interfacial tension and the function
of the polymer in mobility control. The former function is
used to improve the displacement efficiency; the later
function is used to increase the sweep efficiency.
There are several factors that influence the actual SP
process, which includes the mobility control design, sur-
factant concentration, residual permeability reduction,
surfactant retention, dispersion of the surfactant slug, and
the rheological behavior of surfactant solution in a porous
medium (Gabitto 2006). With regard to the design of the
flood process, all factors should be taken into account,
and correlations should also be considered. For a field-
scale SP flood, the screening criteria are similar to that of
a polymer flood. What must be mentioned is that net pay
is not a critical consideration for an SP flood and the
favorable viscosity can increase to 35 cp at reservoir
conditions.
Fundamental modeling
The research mainly covered the history match, analysis of
the current injection and production system, and the esti-
mation of different EOR methods. The simulation model
was based on the properties of the South Slattery Field. A
110 9 114 grid model consisting of three layers was
defined to describe the reservoir. Totally, 25 wells were
involved in the simulation. The active cell number was
13,266.
History match
The important history matching indices included water cut,
production, reservoir pressure, bottomhole pressure, and
production GOR. The accuracy of history matching is
important to the following simulation work. In the history
match, the RMS errors are less than 6.5% averagely.
Instead of explaining the history matching in detail here,
the author made analysis of history matching to have more
space to illustrate the EOR simulation.
The depletion stage was from 1964 to 1985. Seven
production wells were drilled during this stage. The main
mechanism has been shown to be solution gas drive, in
conjunction with fluid expansion and gravity drainage. By
analyzing the geological data and the development history,
the bottom water breakthrough also played an important
role, especially in slowing the pressure drop. The invading
aquifer, which intruded into the southwest nose of the
reservoir, resulted in an imbalance of the reservoir pres-
sure, thus an imbalance of the production and water cut. At
the end of this stage, the average individual water cut in the
northeastern zone was less than 5%, while the southwestern
part was roughly 65%.
The water flood began in 1995. Three injectors started
injecting in this year. The oil production rate was
increased by 60%. During the water flood, the imbalance
of pressure and a low sweep volume factor also existed.
The recovery factor was 36.13% at the end of the history
match of the primary and secondary phases. According to
the outcomes of simulations, only some of the producers
responded to the injected water. Others were still domi-
nated by the solution gas drive. Some un-swept areas were
left, especially the north part of the reservoir, which has
not been swept well by the water flood. There were two
factors which formed the rich zone of the remaining oil in
the central reservoir: (1) the unevenness of production and
injection and (2) the heterogeneous nature of the reservoir.
There is also a blind side on the boundary of the reservoir
where it is difficult to form a circulation of the reservoir
fluids in a closed region.
Development adjustment
A robust network pattern is fundamental to a successful
water flood. As analyzed above, the existing well pattern
was imperfect. To improve the sweep efficiency and to
raise the recovery, a pattern adjustment was necessary.
Based on the outcomes of the history match, three new
injectors were assigned to the rich remaining oil zone
(designated New-1, 2, and 3). Meanwhile, to minimize the
imbalance of the reservoir pressure, three producers were
converted to injectors. The new pattern has five injectors
and nine producers (some producers were shut in during
the water flood), as seen in Fig. 3b.
Result The adjustment has improved the flood efficiency
significantly by comparing the oil saturation maps with
different well patterns. Through the saturation change, we
can see that the un-swept areas were mobilized gradually
after the network adjustment. The number of responding
producers increased. As shown in Fig. 4, the incremental
recovery of the new well pattern is much higher than that
of the old one. When the water cut reaches 97% in 2038,
the adjusted pattern has an incremental recovery of
3.85%.
J Petrol Explor Prod Technol (2011) 1:23–31 25
123
EOR investigation
The significant improvement in oil recovery makes EOR
technologies more and more widely accepted in the
petroleum industry. In this research, the simulation method
was used to estimate the feasibility of some EOR methods
at the South Slattery Field. As we know, the adoption of an
EOR method mainly depends on the characteristics of the
reservoir and the efficiency of the current development.
Theoretically, the Slattery Field has the conditions for the
success of the EOR methods mentioned above. The
research evaluated the development efficiencies of the
EOR methods. Several plans were designed to optimize the
key indices for different EOR methods. According to the
economic injection volume of chemical in Daqing, China,
the simulated chemical injection in this research was fixed
at 0.7 PV. In order to compare the efficiency of different
injections, all processes take the same injection volume.
Polymer flood
To find a reliable polymer-flood injection system, several
factors have been investigated to optimize the injection
parameters, such as the molecular weight, injection rates,
and solution concentration. Here, the optimization of
molecular weight for the polymer flood is presented.
Laboratory data
All of the polymer properties are a function of the
molecular weight in polymer flooding. At the same con-
centration, the key viscosity parameter will increase with
the molecular weight. This research investigated three
molecular weights and demonstrated how the behavior
changed when the polymer solutions were injected into the
formation. The molecular weights adopted were 4, 6, and 9
millions (HPAM). The viscosity curves are shown in
Fig. 5. The adsorption curves are shown in Fig. 6.
Viscosity and injection parameters
Based on the mobility control function, the viscosity loss is
the first concern for the application. In the model, several
factors which related to viscosity loss have been consid-
ered. The loss from the pipeline flow (surface and well-
bore) and the perforations was also estimated. A shearing
model based on lab experiments has been used. The tested
loss from brine was based on NaCl; the viscosity change at
STA-1
KRA-F22
BUR-1430 BUR-18
HAM-1
KRA-C2
KRA-4
KRA-5
KRA-6
MID-361
STA-362
STA-652
KRA-4430
-1600 -800 0a
b
800 1600 2400 3200 4000
-1600 -800 0 800 1600 2400 3200 4000
-320
0-2
400
-160
0-8
000
800
1600
2400
-3200-2400
-1600-800
0800
16002400
STA-1
KRA-F22
BUR-1430 BUR-18
HAM-1
KRA-C2
KRA-4
KRA-5
KRA-6
MID-361
STA-362
STA-652
KRA-4430
New-1
New-1
-1600 -800 0 800 1600 2400 3200 4000
-1600 -800 0 800 1600 2400 3200 4000
-320
0-2
400
-160
0-8
000
800
1600
2400
-3200-2400
-1600-800
0800
16002400
Fig. 3 a Existing network, b network after adjustment
0.0
4.0
8.0
12.0
16.0
0 5 10 15 20 25 30 35
New Pattern
Old Pattern
Time (Years)
Incr
emen
tal r
ecov
ery
(%)
Fig. 4 Incremental recoveries for different networks
26 J Petrol Explor Prod Technol (2011) 1:23–31
123
different salinities was illustrated in the simulation. Taking
the viscosity loss into account, the injection concentration
is fixed at 1,200 ppm to maintain the effective viscosity
(adsorption). Injectivity reflects both the characteristics of
the formation and the properties of the injected solution.
For polymer floods, the injectivity is not only the parameter
of interest, also demonstrated is the change of reservoir
properties when the polymer solution is injected. The rel-
evant formulas for initial individual rate used in this
research are the following:
Hwj ¼1
a � nXn
i¼1
Hwj þ Hoi
2; ð1Þ
Qwj ¼HwjPmj¼1 Hwj
� V � PV : ð2Þ
Results
When the polymer solution was injected into the formation,
the sweep efficiency was significantly increased, as seen in
Fig. 7 (6-million molecular weight). The channels formed
by the water flood were improved, and the polymer caused
the flood to move into the un-swept zones.
According to the predictions for different polymers, at
0.7 PV injection volume, the 6-million MW had the best
incremental recovery factor of 24.74%; the recovery factor
of the 9-million MW was 22.01%; the factor of the 4-mil-
lion MW was 23.59%, as seen in Fig. 8. The difference
happened after 0.5 PV injection, mainly because the rela-
tively high molecular weight polymer had a lower recovery
in flank zones. With increasing injection time, the 6-million
MW polymer had an improved recovery efficiency, and the
efficiency difference between the 6 million and the 9 mil-
lion was enlarged. The cause of this phenomenon was that
the injectivity of the 9-million polymer solution decreased
due to the unsuitability between the formation and the
polymer solution. By increasing the molecular weight to 9
million, there was a sharp downtrend in injectivity due to
the effect of adsorption, and the decrease in permeability,
especially near KRA-4430 and BUR-4330, was significant
at the late injection phase. As a result, the recovery rate
significantly decreased, as seen in Fig. 9.
Application concerns
Compared with successful floods, the polymer flood in the
South Slattery field will have a longer development period,
0
10
20
30
40
50
60
70
0 200 400 600 800 1000 1200 1400
Vis
cosi
ty (
mP
a.s)
Polymer Concentration (mg/L)
6 Million
4 Million
9 Million
Fig. 5 Viscosities of different polymers at different concentration
0
20
40
60
80
100
120
0 500 1000 1500 2000 2500
4-million
6-million
9-million
Concentration of polymersolution (PPM)
Ads
orpt
ion
dens
ity (
µg/g
)
Fig. 6 Adsorptions of polymers at different concentration
Fig. 7 Oil saturation after polymer flood (6 million)
0.0
6.0
12.0
18.0
24.0
30.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
MW_1
MW_2
MW_3
Injection Volume (PV)
Incr
emen
tal R
ecov
ery
(%)
Fig. 8 Incremental recoveries from polymer at different injection
volumes
J Petrol Explor Prod Technol (2011) 1:23–31 27
123
mainly because the injectivity of the whole field is favor-
able for a short-term injection. The average model per-
meability is only 23.3 mD. Developmentally, the well
density is another unfavorable factor. The field injection
rate is much lower than the capacity of the pore volume.
Furthermore, the well spacing may fail to form effective
driving pressure during a polymer application.
One more concern is the effects of high salinity in the
reservoir fluid. The salinity of the Minnelusa formation
water is relatively high. The initial salinity was close to
seawater. The sodium salt accounts for around 92.5%; the
calcium salt accounts for 5.5%; the magnesium salt
accounts for the rest. The compositional analysis of the
produced water can be seen in Table 2. Two main effects
of the high salinity should be considered. One effect is
the viscosity loss of polymer solution. In a high-salinity
environment, the tendency of scrolling makes the motions
of molecular chains weak, which gives rise to a serious
viscosity loss. The other effect is polymer adsorption. The
high salinity will speed up and increase the adsorption.
The effect of divalent ions especially should not be
ignored.
Surfactant-polymer flood
Compared with a polymer flood, the use of surfactant
makes SP flooding more complicated. The slug design
plays an important role in a flood. To develop a successful
flood, adequate design of the injection process is required.
Based on the literature and the experience of successful
floods, two injection processes were simulated. The dif-
ference between these two processes is the use of pre-
polymer. In the first process, a pre-polymer slug was used.
The initial thinking was that a small slug of pre-polymer
solution can partially solve the channeling which was
formed by the water flood.
Laboratory data
Surfactant Parameters of an anionic surfactant were used.
Viscosity versus concentration is shown in Fig. 10. For the
measurement of adsorption, Berea sandstone was used (the
brine used to prepare the surfactant solution was 3.2%wt
NaCl). The plot of the adsorption densities at different
solution concentrations is shown in Fig. 11. Figure 12
shows the interfacial tension (IFT) change at different
surfactant concentrations (measuring environment:
1,200 ppm polymer solution system, measured with crude
oil from another Minnelusa field with similar oil proper-
ties). The 6-million MW polymer was used (the optimum
polymer in the polymer flooding section, properties seen
above).
Injection case
Process 1:
1. Pre-flush 6 months (0.3 PV) water flood, which was
the volume of brine to lower resident salinity.
2. Pre-polymer 0.15 PV, 1,000 ppm polymer solution,
which was to minimize by-passing and channeling, and
0.0
6.0
12.0
18.0
24.0
30.0
0 5 10 15 20 25 30 35
6_Miliion
9_Miliion
4_Miliion
Time (Year)
Incr
emen
tal R
ecov
ery
(%)
Fig. 9 Incremental oil recovery from polymer at different times
Table 2 Field water sample analysis
Components Produced water Injection water
Calcium (mg/L) 911 2.53
Iron (mg/L) 1.24 \0.01
Magnesium (mg/L) 156 0.11
Sodium (mg/L) 21,400 332
Potassium (mg/L) 342 0.28
Barium (mg/L) \0.01 \0.01
Bicarbonate (as CaCO3) (mg/L) 499 381
Carbonate (as CaCO3) (mg/L) 0 30
pH, std. Units 7.31 8.79
Chloride (mg/L) 29,101 35
Sulfate (mg/L) 4,507 310
40
44
48
52
56
0 500 1000 1500 2000 2500
Concentration of Surfactant (mg/L)
Vis
cosi
ty o
f S-P
sys
tem
(m
p.s)
Fig. 10 Solution viscosity at different surfactant concentrations
(1,200 mg/L polymer solution system)
28 J Petrol Explor Prod Technol (2011) 1:23–31
123
to make sure that the surfactant-polymer slug, can
reach a considerable volumetric coverage.
3. S-P slug 0.45 PV, the main slug of surfactant and
polymer, the concentration of surfactant was
1,200 ppm, concentration of polymer was 1,200 ppm.
4. Mobility buffer 0.10 PV, 600 ppm polymer solution,
which was a dilute solution. The purpose was to drive
the S-P slug and banked-up fluids toward the produc-
tion wells.
5. Chase water This fluid was injected to reduce the cost
of continuous injection of polymer.
Process 2:
Based on the above procedure, process 2 removed the
pre-polymer slug, and the slug size of S-P was increased
to 0.6 PV.
Flood efficiency and recovery
The predictions of the two processes that showed the dis-
placement efficiency in the central reservoir were signifi-
cantly improved due to the desaturation function of
surfactant; the remaining oil zone was minimized since the
sweep efficiency has been improved significantly. How-
ever, the southeastern corner still had a remaining oil rich
zone, principally due to the low injectivity of well KRA-
4430. The injection volume from KRA-4430 was not
enough to mobilize the oil bank further. Figure 13 shows
the oil saturation distribution after process 1.
The oil saturation distribution showed that process 1 had
the better sweep efficiency. The pre-polymer slug played
its role. But the displacement efficiency of process 1,
especially in the relatively high-perm zone, was a little
lower than that of process 2. Compared with the polymer
flood at 0.70 PV of injection, process 1 had another 2.49%
incremental recovery in addition to what the polymer flood
did. The recovery factor of process 1 showed 0.43% higher
than that of process 2.
The difference between the results of processes 1 and 2
can be accredited to the pre-polymer slug. In the process 1,
the 0.1 PV of low concentration polymer solution had a
profile control function which slightly improved flow
environment of the following injections. The injected sur-
factant had a wider sweep area compared with the injection
in process 2.
The incremental recovery and water cut of process 1 are
shown in Fig. 14. According to the water cut curve, from
0.26 PV injection volume, the water cut began decreasing,
not as significantly as the polymer flood did; however, it
0
1
2
3
4
5
6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Ads
orpt
ion
Den
sirt
(m
g/g)
Surfactant concentration (wt%)
Fig. 11 adsorption densities of surfactant at different concentrations
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0 0.05 0.1 0.15 0.2 0.25
Inte
rfac
ial T
ensi
on (
mN
/m)
Surfactant Concentration wt%
Fig. 12 Interfacial tension at different surfactant concentrations
Fig. 13 Remaining oil distribution after the buffer slug
0
5
10
15
20
25
30
60.0
65.0
70.0
75.0
80.0
85.0
90.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Incr
emen
tal r
ecov
ery
(%)
Injection Volume (PV)
Water Cut
Incremental Recovery
Wat
er C
ut %
Fig. 14 Water cut and incremental recovery against injection volume
in S-P (process 1)
J Petrol Explor Prod Technol (2011) 1:23–31 29
123
kept the water cut from increasing for a longer time; thus,
the peak oil period was extended.
Application concerns
Besides the above concerns about the polymer flood, the SP
injection has a few more issues to be considered: the
estimation of the critical micelle concentration at the res-
ervoir conditions which depends on the salinity and pH.
The salinity distribution after 14 years of water injection is
a critical factor to the evaluation of chemical injections.
The employed simulator is not able to simulate ion
exchange and the existence of emulsions. But the desatu-
ration function is perfect to reflect the residual oil satura-
tion change based on IFT alteration. A further research
would be needed to investigate the estimation of mecha-
nisms of the surfactant-related injection which could be
used to offer verified parameters for a detailed simulation
research.
Discussion
The recovery factory for each case can be seen in Table 3.
The incremental value displays the incremental recovery
based on the adjusted water flood. The optimum polymer
flood has a recovery contribution of 8.80%. The optimum
surfactant-polymer process has another 2.49% incremental
recovery based on polymer flood. Economics analysis is
necessary for the comparison and estimation of these EOR
methods in the further research.
Due to the high salinity of Minnelusa water at the
Slattery, the effects of salinity which relates to the viscosity
loss of polymer floods and the interfacial tension change
during a surfactant injection were considered cautiously.
Making a further estimation of salts distribution in the
formation is necessary. Specifically, the viscosity losses of
polymer floods also include the effects of shear. The vis-
cosity loss from reservoir flow was considered accurately
in the model. The losses from other factors should also be
modeled accurately for a further polymer simulation.
Combining the lab analysis, the damages due to chemical
floods, like chemical adsorptions, wettability alteration,
and permeability reduction have to be considered to esti-
mate the injection efficiency.
Conclusion
1. Based on the water-flooding history match, the
recovery was 36.13% of the water flood. To get a
better effect in EOR simulation, a network adjustment
was made to improve the injection and production
pattern. The ultimate recovery of the new well pattern
is 3.85% higher than that of the old pattern.
2. The polymer flood significantly improved the sweep
efficiency. For the three kinds of polymers of different
molecular weights, the 6-million MW polymer was
more suitable for the South Slattery Field. The
estimated incremental recovery was 8.80% compared
with that of water flood.
3. The optimum S-P process increased the recovery by
2.49% compared to the polymer flood at 0.70 PV of
injection. The use of pre-polymer slug improved
development efficiency after a sort. The analysis of
the predictions showed the remaining oil saturation
that mainly depended on the sweep efficiency of SP
slug.
Acknowledgments Support for this work by the Enhanced Oil
Recovery Institute of the University of Wyoming, under the direction
of David Mohrbacher, is gratefully acknowledged.
Open Access This article is distributed under the terms of the
Creative Commons Attribution Noncommercial License which per-
mits any noncommercial use, distribution, and reproduction in any
medium, provided the original author(s) and source are credited.
References
Carcoana A (1991) Applied enhanced oil recovery. New Jersey,
Prentice Hall
Chang HL, Zhang ZQ, Wang QM, Xu ZS, Guo ZD, Sun HQ, Cao XL,
Qi Q (2006) Advances in polymer flood and alkaline/surfactant/
polymer processes as developed and applied in the People’s
Republic of China. J Petrol Technol 58:84–89
David B, Gary A (2003) Selection and screening of polymers for
enhanced-oil recovery. Presented at the SPE/DOE improved oil
recovery symposium, Tulsa, OK, 19–23 Apr 2006, Paper SPE
113845
Gabitto JF (2006) Combined microbial surfactant-and-polymer sys-
tem for improved oil mobility and conformance control.
Presented at the 2006 SPE annual technical conference and
exhibition, San Antonio, TX, Paper SPE 102328
Table 3 Recovery Summary of different EOR Methods
Method Polymer Surfactant-polymer
Simulation case 4 million 6 million 9 million Process 1 Process 2
Ultimate recovery (%) 58.21 60.78 59.13 63.27 62.84
Incremental value of OOIP (%) 6.23 8.80 7.15 11.29 10.86
30 J Petrol Explor Prod Technol (2011) 1:23–31
123
Gharbi RBC (2001) A knowledge-based system for optimal economic
design of improved recovery processes. Presented at the SPE
Asia Pacific oil and gas conference and exhibition, Jakarta, Paper
SPE 68765
Kaminsky RD, Szafranski RC (2007) Guidelines for polymer flood
evaluation and development. Presented at the international
petroleum technology conference, Dubai, Paper IPTC 11200
Osterrloh WT, Jante MJ (1992) Surfactant-polymer flood with anionic
PO EO surfactant microemulsions containing polyethylene
glycol additives. Presented at the SPE/DOE improved oil
recovery 8th symposium, Tulsa, OK, Paper SPE 24151
Pu H, Yin D (2008) Feasibility study and pilot test of polymer flood in
third class reservoir of Daqing oilfield. Presented at the 2008
SPE North Africa technical conference and exhibition, Marrak-
ech, Paper SPE 111720
Sheppy RJ (1986) Slattery field, Powder River Basin, Wyoming:
a multidisciplinary interpretation of a complex Minnelusa
(Permian) field. In: Wyoming Geological Association sympo-
sium on Rocky Mountain oil and gas fields. Wyoming Geolog-
ical Association, Casper, pp 245–256
Sorbie KS, Phil D (1991) Polymer-improved oil recovery. CRC Press,
Florida
Towler BF (1991) Simulation of South Slattery Field, a Minnelusa
‘A’ Reservoir. Presented at the Rocky Mountain regional
meeting and low-permeability symposium, Denver, CO, Paper
SPE 21816
Wang YP, Li H (2006) Commercial success of polymer flood in
Daqing oilfield—lessons learned. Presented at 2006 SPE Asia
Pacific oil and gas conference and exhibition, Adelaide, Paper
SPE 100855
J Petrol Explor Prod Technol (2011) 1:23–31 31
123
ORIGINAL PAPER - PRODUCTION GEOLOGY
Mapping the productive sands of Lower Goru Formation by usingseismic stratigraphy and rock physical studies in Sawan area,southern Pakistan: a case study
Khyzer Munir • M. Asim Iqbal • Asam Farid •
Syed Mohammad Shabih
Received: 11 May 2010 / Accepted: 6 January 2011 / Published online: 24 February 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract This study has been conducted in the Sawan
gas field located in southern Pakistan. The aim of the study
is to map the productive sands of the Lower Goru For-
mation of the study area. Rock physics parameters (bulk
modulus, Poisson’s ratio) are analysed after a detailed
sequence stratigraphic study. Sequence stratigraphy helps
to comprehend the depositional model of sand and shale.
Conformity has been established between seismic stratig-
raphy and the pattern achieved from rock physics investi-
gations, which further helped in the identification of gas
saturation zones for the reservoir. Rheological studies have
been done to map the shear strain occurring in the area.
This involves the contouring of shear strain values
throughout the area under consideration. Contour maps
give a picture of shear strain over the Lower Goru For-
mation. The identified and the productive zones are
described by sands, high reflection strengths, rock physical
anomalous areas and low shear strain.
Keywords Stratigraphy � Rock physics � Rheology �Sawan
Introduction
Sawan field lies in southern Indus Basin that is extending
between 24� and 28�N latitude and from 66�E longitude to
the eastern boundary of Pakistan (Zaigham and Mallick
2000). To go with the prominent convergence and the late
Paleocene collision between the Indian and the Eurasian
plates in the north Pakistan, the area was also affected by
the translation between Indian plate and Afghan Craton in
the northwest (Banks and Warburton 1986) and by territory
convergence between Arabian Plate and Afghan Craton
(Zaigham and Mallick 2000). The effect of the western rift
margin of the Indian plate dominance can be observed in
the form of many normal fault and horst and associated
grabens on the seismic sections and also in the form of
Sibbi-Jacobabbad, Khairpur, Mari-Kandkot highs as its
surface expressions (Michalchuk 2006). The study area to
go with other parts of southern Indus Basin has thick
Mesozoic–Tertiary sedimentary sequences overlain by
Quaternary sediments (Kadri 1995). The area was tecton-
ically stable until the Jurassic and probably Early Creta-
ceous but rifting started to occur during Late Cretaceous
and Early Paleocene, the effects of which can be seen on
seismic sections, where the post-Eocene strata are either
not affected or very less deformed. Information about the
description and deposition of various rock units is available
in literature (e.g. Kadri 1995; Shah 1977). The present
study is confined to the discussion on Cretaceous rock with
K. Munir
King Abdulaziz City for Science and Technology (KACST),
P.O. Box 6086, Riyadh, Saudi Arabia
e-mail: [email protected]
M. A. Iqbal (&)
Physical Science and Engineering Division, King Abdullah
University of Science and Technology, P.O. Box 2104, Building
1 Room 3209, Thuwal, 23955-66900 Jeddah, Saudi Arabia
e-mail: [email protected]
A. Farid
Department Of Petroleum Geosciences, The Petroleum Institute,
P.O. Box 2533, Ruwais Building, Abu Dhabi,
United Arab Emirates
e-mail: [email protected]
S. M. Shabih
Norwegian Energy Company ASA (NORECO),
Nykirkebakken 2, 4025 Stavanger, Norway
e-mail: [email protected]
123
J Petrol Explor Prod Technol (2011) 1:33–42
DOI 10.1007/s13202-011-0003-9
special reference to the Goru Formation. Cretaceous rocks
are widely distributed in different parts of Lower Indus
Basin. There is wide range of lithological heterogeneity in
these rocks, mainly attributed to change in sediment supply
and environmental conditions. The thick (?760 m) Neo-
comian Sembar Formation consists of black shale, which is
silty and has interbeds of black siltstone and nodular
argillaceous limestone. There are some sandstone beds as
well. The siliciclastics were probably derived from the
Indian Shield and have sand in more abundance in the
eastern parts of the basin, while the western part is more
silty and shaley (Kadri 1995). The Aptian-Albian Goru
Formation is mainly composed of black to gray and locally
maroon shale/mudstone in the lower part. The upper part of
Lower Goru is composed of sandstone that is of significant
importance in terms of its reservoir character in different
parts of the southern Indus Basin, to go with Sawan area.
Sandstone is rare in the upper part of the Formation that has
shale as dominant lithology. The name Lower Goru is used
for the lower sandy part of the Formation, whereas the
upper shale unit is termed as Upper Goru (Kadri 1995). The
generalized depositional environments of the Formation
appear to be relatively deep marine, with minor shallow
phases of benthic rich fauna being indicated. The Lower Goru
may, however, represent barrier to deltaic environments.
The overlying Cretaceous rocks include light gray,
white colour thin-bedded argillaceous Parh Limestone that
is overlain by mixed siliciclastics and carbonates of
Mughal Kot Formation while Fort Munro Formation with
its sandy, argillaceous limestone and the overlying Pab
Sandstone being the other younger Cretaceous rock units in
the Southern Indus Basin
Sawan gas field Fig. 1 is one of the major gas producing
areas with early–late Cretaceous Lower Goru Formation
acting as the potential reservoir here. During the past two
decades these sands have emerged to be a significant
hydrocarbon producer from the Middle and Lower Indus
Basin in Southern Pakistan. The Sawan gas field comprises
total proven reserves of 2–2.5 TCF gas. Total of five wells
have been used in the study. The Lower Goru Formation is
Fig. 1 Location map of the studied area
34 J Petrol Explor Prod Technol (2011) 1:33–42
123
found to be productive in only three wells out of six (i.e.
Sawan-01, Sawan-02 and Sawan-03). The other three wells
(Gajwaro-01, Judge-10 and Nara-01) are unproductive
within the Lower Goru Formation C Sand horizon. Seismic
stratigraphy approach has been used to understand the
stratigraphic system of the area. The analysis of seismic
stratigraphy, seismic attributes, rock physics parameters
helps us to delineate the sands which can act as reservoirs
in the area.
Seismic sequence stratigraphy
Seismic sections provide the best means of recognizing
onlap and toplap patterns within the depositional sequences
and well control can provide data for the distinction
between coastal and marine facies within the sequences
(Vail et al. 1977). The seismic stratigraphic interpretation
method depends upon the observation of all the seismic
parameters (continuity, amplitude, apparent frequency,
configuration, reflection terminations, search for unconfo-
rmities, and their classification within uniform units to
define seismic ‘‘facies’’ and then on the 3D analysis of their
lateral and vertical variations) (Ravenne 2002).
The horizons are identified by using the synthetic seis-
mograms prepared for Sawan-01 and Gajwaro-01 wells.
The lateral changes in facies are mapped using the
sequence stratigraphic analysis after Ahmed et al. 2004.
The seismic stratigraphic interpretation is based on
regional E–W seismic lines. Figure 3 shows the interpre-
tation over line PSM96-114. The late Jurassic Chiltan
Limestone can be recognized easily as a strong reflector on
these lines at around 2.5sec TWT. Three sequence
boundaries have been identified in Fig. 2 (i.e. SB1, SB2
and SB3). SB-1 is recognized as the first sequence
boundary that exists within Sembar Formation and gets
downlap at the top of the Chiltan.
The sequence up to SB1 comprises the downlapping pro-
grades of the Sembar above Chiltan. SB2 is identified as the
second sequence boundary. The sequence between SB1 and
SB2 is a lowstand system tract (LST) dominated by the
slopping fans. SB3 is the third sequence boundary that exists
within the Lower Goru Formation. SB2 is followed by a
gradual rise in sea level until it approaches a maximum
flooding surface (MFS) between SB2 and SB3. The onlapping
pattern demonstrates a transgressive nature for the sequence.
There are prograding sands trapped in the A, B and C
horizons of the Lower Goru Formation. These can be easily
identified on the seismic sections as bright spots as shown
in Fig. 3.
Sand shale sequences of Lower Goru Formation
The Early Cretaceous silciclastics of Sembar and Goru
Formations were deposited on the top of an extensive
carbonate platform (Chiltan Limestone). Sembar–Goru
Play is an important petroleum system of the studied area.
Various stratigraphic traps are found, most of which are gas
Fig. 2 Sequence stratigraphic interpretation on an EW regional seismic line. The section is flattened on the Chiltan Limestone. Three sequence
boundaries, MFS and reflection termination patterns like onlaps, downlaps and topsets are clearly visible (after Ahmed et al. 2004)
J Petrol Explor Prod Technol (2011) 1:33–42 35
123
producing. Lower Goru is divided into three members or
intervals ‘‘A’’, ‘‘B’’ and ‘‘C’’ (Fig. 3). Above Sembar and
Goru Formations, lay the Tertiary Ranikot Formation and
Sui Main Limestone. Goru Formation consists of inter-
bedded sandstone, shale and siltstone with very thin-bedded
limestone (Kazmi and Jan 1997).
The bottom layers of the Lower Goru Formation con-
sists of sands interlayered with shales which are further
divided into as Sand A, Sand B, Sand C and Sand D in the
studied area as shown in Fig. 4. The upper portion of
Lower Goru comprises thick shales which are acting as
regional seal. Sembar Formation acts as a source rock for
this petroleum system. Sands B and C are serving as a
potential gas reservoirs in this area.
Figure 5 is developed from Fig. 2 and shows the depo-
sitional pattern of Sembar–Goru petroleum system. The
system has been deposited on the Chiltan Limestone which
acted as the platform for deposition. The Sembar deposi-
tion is marked by various drops and rise in sea level.
Between SB1 and SB2 is the SEQ A which demonstrated
the lowstand time. It constitutes the lowstand slope fan and
the prograding delta. The delta downlaps over the slope
fan. Between SB2 and MFS is the SEQ B and is the
highstand time. Between MFS and SB3 is the SEQ C and is
the lowstand time. It is characterised by lowstand fan and
prograding delta. After SB3 lithologies have been termed
as SEQ D and constitute Lower Goru deposition. Lower
Goru horizons A Sand, B Sand and C Sand are dominated
by progrades. Various sand bodies have been identified by
these reflection patterns.
Fig. 4 The stratigraphic column showing the subdivisions of Lower
Goru Formation into Sand intervals A, B, C and D after Ahmed et al.
2004
Fig. 3 Bright spots seen in the A, B and C Sand horizons of Lower Goru Formation. Bright spots are named accordingly to the horizons in which
they occur
36 J Petrol Explor Prod Technol (2011) 1:33–42
123
Rock physics
Well log data and petrophysical analysis provide the basic
input for the rock physics analysis and the generation of
different lithology classes (Bachrach et al. 2004). Rock
physics modelling has been performed by Gommesen et al.
2004 to study porosity and fluid effects on the elastic
properties. According to models the elastic properties of
the studied formation are primarily controlled by porosity
and to secondary degree by the changes in fluids.
The seismic interval velocities from different CDP
locations, corresponding to the Lower Goru interval are
employed for a series of mathematical calculations for
calculating different rock physics parameters, such as bulk
modulus, and Poisson’s ratio. Two-way seismic times and
their corresponding interval velocities (P) are noted at all
the CDP locations. They are then converted to the S-wave
velocities and densities using the Castagna’s and Gar-
dener’s equations, respectively. This data is finally used for
calculating each of the rock physics parameter.
Royle and Bezdan 2001 have demonstrated the com-
parison of shear wave velocity estimation techniques.
The equation Vp = 1.16Vs ? 1.36 (km/s) by Castagna
et al. 1985 has been used to convert P wave velocities to
S-wave velocities. The relationships between compres-
sional wave and shear wave velocities were discussed by
Castagna et al. 1985 for clastic silicate rocks. There has
been increased use of Vp, Vs and Vp/Vs in seismic explo-
ration for estimation of porosity, lithology and saturating
fluids in particular seismic intervals (Castagna et al. 1985).
Figure 6a shows the crossplots for the Sawan-01 well
and Fig. 6b shows the crossplots for Gajwaro-01 well.
Each of the mentioned rock physics parameter is dis-
cussed separately in the following.
Bulk modulus
Primary and shear wave velocities are used in the following
equation to calculate the bulk modulus which is the mea-
sure of compressibility
K ¼ q ðV2p � 4 =3 V2
s Þ
where q is the density obtained from the equation den-
sity = 0.31 9 (Vp)1/4 as demonstrated by Gardner et al.
1974. Vp is the primary wave velocity and Vs is the shear
wave velocity obtained from Vp.
Using this equation we calculated the bulk modulus for
our potential reservoir, Sand C, for all the seismic lines
Fig. 5 Depositional pattern of Lower Goru Formation (after Ahmed et al. 2004)
J Petrol Explor Prod Technol (2011) 1:33–42 37
123
Fig. 6 a Low GR, low impedance, good effective porosity, Poisson’s
ratio (0.25–0.35) and low water saturation suggest that the reservoir is
productive in Sawan-01 well. b The reservoir is marked by low
effective porosity, relatively higher impedance and lower Poisson’s
ratio (0.2–0.3) for Gajwaro-01 well
38 J Petrol Explor Prod Technol (2011) 1:33–42
123
present in the study area. These values are then contoured
in Fig. 7, to highlight the anomalous zones with low bulk
modulus values when compared with the surroundings. The
producing C Sand exhibit the high values of bulk modulus
apart from places where hydrocarbons occur. Figure 7
represents the variation of bulk modulus in the study area.
Poisson’s ratio
This is basically the ratio of compressibility and rigidity, or
the readiness of a compressed material to bulge. It has been
calculated at the same location and time interval as the bulk
modulus, using the following equation
m ¼ 0:5 V2p � 2V2
s
� �.V2
p � V2s
� �
Therefore, Poisson’s ratio for Sand C is calculated on all the
seismic lines and is then contoured Fig. 8. This map dif-
ferentiates the dry sands and gas sands on the basis of low
and high value contours. The values of the gas saturated
areas are in between 0.28 and 0.31 which are confirmed by
well Sawan-01 which is 0.28 for the same interval.
Rheological studies
Rheological studies are carried out to understand the
occurrence of stress and strains on Lower Goru sands in the
study area. These include the measurement of longitudinal
strain, shear strain and total stresses which are discussed
individually in the following.
Shear strain
In order to calculate the shear strain, the angle which all the
faults form with the vertical is required. Shear strain will in
fact be the tangent of that particular angle, and it is cal-
culated at all the points where the major faults are evident.
Shear strain values are also contoured to show the degree
of shear (angular) deformation in the area as described on
Fig. 9. It also shows that the productive wells lies in the
low shear strain area and the nonproductive wells in the
high shear strain area.
Uncertainty analysis
Figure 10 shows the correlation between the velocities
derived from sonic log (Sawan-01) and interval velocities
for the line PSM96-115. The figure shows a fair correlation
between the velocities. Also, Fig. 11 shows a correlation
between the velocities derived from sonic log (Gajwaro-01)
and interval velocities for the line PSM96-115. Figure shows
a reasonable correlation between the velocities. The corre-
lation for both the wells suggests that the calculations done
for the rock physical studies are reasonable.
Fig. 7 Contour map prepared for bulk modulus values estimated for the whole area. It is clear from the map that all the six wells fall in the
anomalous zone with comparatively low values
J Petrol Explor Prod Technol (2011) 1:33–42 39
123
Since the aim of the study was to map the productive
sands of the Lower Goru Formation, Figs. 7 and 8 shed
some light on the occurrence of productive sands. The
high values of Poisson’s ratio and low values of bulk
modulus suggest the gas saturation for the sands as
calibrated with the wells. The reservoir is bounded by
the contour values (0.28–0.31) of Poisson’s ratio. The
map also highlights favourable areas for hydrocarbon
saturation in the study area. The areas with Poisson’s
ratio values greater than 0.28 other than the wells should
be evaluated in detail for possible hydrocarbon
accumulations.
Fig. 8 Contour map prepared for the Poisson’s ratio values through out the study area. It is evident that all the six wells lie in a zone where the
Poisson ratio values are on the higher side. This shows that the sands encountered at these well locations are filled with gas
Fig. 9 The contour map prepared for the shear strain values in the studied area. It is clear from the map that the strain produced at dry well
(Gajwaro-01, Judge-01 and Nara-01) locations is relatively more than the producing gas wells
40 J Petrol Explor Prod Technol (2011) 1:33–42
123
Conclusions
The following conclusion can, therefore, be drawn:
1. The bulk modulus map (Fig. 7), confirms that the
locations where the above-mentioned wells were
drilled falls within low value contours, thus, favouring
the hydrocarbon presence over there.
2. The Lower Goru Sands are confirmed to be gas
saturated through a Poisson’s ratio contour map
(Fig. 8), that suggest high values for these well
locations as compared with Sawan-01 well data.
3. A correlation has been established between the
sequence stratigraphic studies with the bulk modulus
and the Poisson’s ratio maps, for marking the gas
saturation zones. Therefore, the relatively higher
Poisson’s ratio closures favours the occurrence of
hydrocarbons.
4. The Poisson’s ratio map can be compared to Fig. 5
which suggests a match between the bright spots and
high Poisson’s ratio closures.
5. The shear strain contour map implies that the produc-
ing gas wells (Sawan-01, Sawan-02, Sawan-03) lies in
Fig. 10 The crossplot shows
the correlation between the
velocities derived from sonic
log (Sawan-01) and interval
velocities for the line PSM96-
115. Figure shows a fair
correlation between the
velocities
Fig. 11 The crossplot shows
the correlation between the
velocities derived from sonic
log (Gajwaro-01) and interval
velocities for the line PSM96-
115. Figure shows a fair
correlation between the
velocities
J Petrol Explor Prod Technol (2011) 1:33–42 41
123
the low shear strain area whereas the dry wells
(Gajwaro-01, Nara-01) falls relatively in the relatively
high shear strain area.
6. The reservoir is productive in low strain area, as this is
necessary for the trap generation.
7. The well Gajwaro-01 lies considerable distance away
from the centre of bright spot A (Fig. 3) which is
attributed to its nonproduction, although gas shows
have been reported for the well.
8. Study suggests that a bright spot B could be saturated
with gas and may yield production if evaluated
properly.
Acknowledgments The work presented here is based on the prin-
cipal authors’ masters study (2005–2007) at Quaid-i-Azam Univer-
sity. We acknowledge subsequent suggestions from Dr. Nadeem
Ahmed for this study. The Directorate General of Petroleum Con-
cessions is acknowledged for the release of seismic and well data
used.
Open Access This article is distributed under the terms of the
Creative Commons Attribution Noncommercial License which per-
mits any noncommercial use, distribution, and reproduction in any
medium, provided the original author(s) and source are credited.
References
Ahmed N, Fink P, Sturrock S, Mahmood T, Ibrahim M (2004)
Sequence stratigraphy as predictive tool in Lower Goru Fairway,
Lower and Middle Indus Platform, Pakistan. PAPG, ATC
Bachrach R, Beller M, Liu Ching C, Shelander D, Dutta N (2004)
Combining rock physics analysis, full waveform prestack
inversion and high-resolution seismic interpretation to map
lithology units in deep water: a Gulf of Mexico case study. The
Leading Edge, pp 378–383
Banks BP, Warburton J (1986) Passive-roof, duplex geometry in the
frontal structures of the Kirthar and Suleiman belts, Pakistan.
J Struct Geol 8:229–237
Castagna PJ, Batzle LM, Eastwood LR (1985) Relationships between
compressional-wave and shear-wave velocities in clastic silicate
rocks. Geophysics 50(4):571–581
Gardner GHF, Gardner LW, Gregory AR (1974) Formation velocity
and density—the diagnostic basics for stratigraphic traps.
Geophysics 39:770–780
Gommesen L, Hansen PH, Pedersen MJ, Marsden G, Schiott RC
(2004) Rock physics templates and seismic modeling of chalk
reservoirs in the South Arne Field of the Danish North Sea. In:
EAGE 66th conference and exhibition, Paris
Kadri IB (1995) Petroleum geology of Pakistan. Graphic Publishers,
Karachi, Pakistan, pp 93–108
Kazmi AH, Jan MQ (1997) Geology and tectonics of Pakistan.
Graphic Publishers, Karachi, Pakistan
Michalchuk RB (2006) Synthetic seismograms and physical proper-
ties generated from sediments in Maxwell Bay, Antarctica—a
study of climate history. Middlebury, Vermont
Ravenne Ch (2002) Stratigraphy and oil: a review. Part 1: exploration
and seismic stratigraphy: observation and description. Oil and
Gas Science and Technology, Rev. Editions Technip, IFP,
57(3)211–250
Royle A, Bezdan S (2001) Shear-wave velocity estimation tech-
niques: a comparison: CSEG convention, Geo-X Systems Ltd, 1
Shah SMI (1977) Stratigraphy of Pakistan. Geol Surv Pakistan,
Quetta, Pakistan, vol 12, pp 43–51
Vail PR, Mitchum RM, Thompson S (1977) Seismic stratigraphy and
global changes of sea level. Part 3: relative changes of sea level
from coastal onlap, applications to hydrocarbon exploration.
AAPG Memoir
Zaigham NA, Mallick KA (2000) Prospect of hydrocarbon associated
with fossil-rift structures of the southern Indus basin, Pakistan.
Am Assoc Pet Geol Bull 84(11):1833–1848
42 J Petrol Explor Prod Technol (2011) 1:33–42
123
ORIGINAL PAPER - PRODUCTION GEOPHYSICS
Micro-earthquake monitoring with sparsely sampled data
Paul Sava
Received: 1 October 2010 / Accepted: 10 February 2011 / Published online: 3 March 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract Micro-seismicity can be used to monitor the
migration of fluids during reservoir production and hydro-
fracturing operations in brittle formations or for studies of
naturally occurring earthquakes in fault zones. Micro-
earthquake locations can be inferred using wave-equation
imaging under the exploding reflector model, assuming
densely sampled data and known velocity. Seismicity is
usually monitored with sparse networks of seismic sensors,
for example located in boreholes. The sparsity of the sensor
network itself degrades the accuracy of the estimated loca-
tions, even when the velocity model is accurately known.
This constraint limits the resolution at which fluid pathways
can be inferred. Wavefields reconstructed in known velocity
using data recorded with sparse arrays can be described as
having a random character due to the incomplete interference
of wave components. Similarly, wavefields reconstructed in
unknown velocity using data recorded with dense arrays can
be described as having a random character due to the
inconsistent interference of wave components. In both cases,
the random fluctuations obstruct focusing that occurs at
source locations. This situation can be improved using
interferometry in the imaging process. Reverse-time imag-
ing with an interferometric imaging condition attenuates
random fluctuations, thus producing crisper images which
support the process of robust automatic micro-earthquake
location. The similarity of random wavefield fluctuations
due to model fluctuations and sparse acquisition is illustrated
in this paper with a realistic synthetic example.
Keywords Microearthquakes � Imaging � Interferometry
Introduction
Seismic imaging based on the single scattering assumption,
also known as Born approximation, consists of two main
steps: wavefield reconstruction which serves the purpose of
propagating recorded data from the acquisition surface
back into the subsurface, followed by an imaging condition
which serves the purpose of highlighting locations where
scattering occurs.
This framework holds both when the source of seismic
waves is located in the subsurface and the imaging target
consists of locating this source, as well as when the source
of seismic waves is located on the acquisition surface and
the imaging target consists of locating the places in the
subsurface where scattering or reflection occurs. In this
paper, I concentrate on the case of imaging seismic sources
located in the subsurface, although the methodology dis-
cussed here applies equally well for the more conventional
imaging with artificial sources.
An example of seismic source located in the subsurface
is represented by micro-earthquakes triggered by natural
causes or by fluid injection during reservoir production or
fracturing. One application of micro-earthquake location is
monitoring of fluid injection in brittle reservoirs when
micro-earthquake evolution in time correlates with fluid
movement in reservoir formations. Micro-earthquakes can
be located using several methods including double-differ-
ence algorithms (Waldhauser and Ellsworth 2000),
Gaussian-beam migration (Rentsch et al. 2004, 2007),
diffraction stacking (Gajewski et al. 2007) or time-reverse
imaging (Gajewski and Tessmer 2005; Artman et al. 2010).
Micro-earthquake location using time-reverse imaging,
which is also the technique advocated in this paper, follows
the same general pattern mentioned in the preceding
paragraph: wavefield-reconstruction backward in time
P. Sava (&)
Center for Wave Phenomena, Colorado School of Mines,
1500 Illinois Str., Golden, CO 80401, USA
e-mail: [email protected]
123
J Petrol Explor Prod Technol (2011) 1:43–49
DOI 10.1007/s13202-011-0005-7
followed by an imaging condition extracting the image, i.e.
the location of the source. The main difficulty with this
procedure is that the onset of the micro-earthquake is
unknown, i.e. time t = 0 is unknown, so the imaging
condition cannot be simply applied as it is usually done in
zero-offset migration. Instead, an automatic search needs to
be performed in the back-propagated wavefield to identify
the locations where wavefield energy focuses. This process
is difficult and often ambiguous since false focusing loca-
tions might overlap with locations of wavefield focusing.
This is particularly true when imaging using an approxi-
mate model which does not explain all random fluctuations
observed in the recorded data. This problem is further
complicated if the acquisition array is sparse, e.g. when
receivers are located in a borehole. In this case, the sparsity
of the array itself leads to artifacts in the reconstructed
wavefield which makes the automatic picking of focused
events even harder.
The process by which sampling artifacts are generated is
explained in Fig. 1a–d. Each segment in Fig. 1a corre-
sponds to a wavefront reconstructed from a receiver. For
dense, uniform and wide-aperture receiver coverage and
for reconstruction using accurate velocity, the wavefronts
overlap at the source position (Fig. 1b). This idealized
situation resembles the coverage typical for medical
imaging, although the physical processes used are differ-
ent. However, if the velocity used for wavefield recon-
struction is inaccurate, then the wavefronts do not all
overlap at the source position (Fig. 1c), thus leading to
imaging artifacts. Likewise, if receiver sampling is sparse,
reconstruction at the source position is incomplete
(Fig. 1d), even if the velocity used for reconstruction is
accurate. The cartoons depicted in Fig. 1a–d represent an
ideal situation with receivers surrounding the seismic
source, which is not typical for seismic experiments. In
those cases, source illumination is limited to a range which
correlates with the receiver coordinates.
In general, artifacts caused by unknown velocity fluc-
tuations and receiver sampling overlap and, although the
two phenomena are not equivalent, their effect on the
reconstructed wavefields are analogous. As illustrated in
the following sections, the general character of those arti-
facts is that of random wavefield fluctuations. Ideally, the
imaging procedure should attenuate those random wave-
field fluctuations irrespective of their cause in order to
support automatic source identification.
Conventional imaging condition
Assuming data D x; tð Þ acquired at coordinates x function of
time t (e.g. in a borehole) we can reconstruct the wavefield
V x; y; tð Þ at coordinates y in the imaging volume using an
appropriate Green’s function G x; y; tð Þ corresponding to
the locations x and y (Fig. 2)
V x; y; tð Þ ¼ D x; tð Þ �t G x; y; tð Þ; ð1Þ
where the symbol *t indicates time convolution. The total
wavefield U y; tð Þ at coordinates y due to data recorded at
(a) (b) (c) (d)
Fig. 1 Schematic representation of focus constructions using time
reversal. Each line in the plots represents a wavefront reconstructed at
the source from a given receiver. The panels represent the following
cases: a dense acquisition, complete angular coverage and correct
velocity, b dense acquisition, partial angular coverage and correct
velocity, c dense acquisition, partial angular coverage and incorrect
velocity, and d sparse acquisition, partial angular coverage and
incorrect velocity. Panel d represents the worst case scenario for
micro-earthquake imaging
receivers
y
x seismic
in borehole
source
Fig. 2 Illustration of the variables x and y used for the description of
the conventional and interferometric imaging procedures
44 J Petrol Explor Prod Technol (2011) 1:43–49
123
all receivers located at coordinates x is represented by the
superposition of the reconstructed wavefields V x; y; tð Þ:
U y; tð Þ ¼Z
x
dx V x; y; tð Þ: ð2Þ
A conventional imaging condition (CIC) applied to this
reconstructed wavefield extracts the image RCIC yð Þ as the
wavefield at time t = 0
RCIC yð Þ ¼ U y; t ¼ 0ð Þ: ð3Þ
This imaging procedure succeeds if several assumptions
are fulfilled: first, the velocity model used for imaging has to
be accurate; second, the numeric solution to the wave-
equation used for wavefield reconstruction has to be
accurate; third, the data need to be sampled densely and
uniformly on the acquisition surface. In this paper, I assume
that the first and third assumptions are not fulfilled. In these
cases, the imaging is not accurate because contributions to
the reconstructed wavefield from the receiver coordinates do
not interfere constructively, thus leading to imaging
artifacts. As indicated earlier, this situation is analogous to
the case of imaging with an inaccurate velocity model, e.g.
imaging with a smooth velocity of data corresponding to
geology characterized by rapid velocity variations.
Different image processing procedures can be employed
to reduce the random wavefield fluctuations. The procedure
advocated in this paper uses interferometry for noise can-
cellation. Interferometric procedures can be formulated in
various frameworks, e.g. coherent interferometric imaging
(Borcea et al. 2006) or wave-equation migration with an
interferometric imaging condition (Sava and Poliannikov
2008).
Interferometric imaging condition
Migration with an interferometric imaging condition (IIC)
uses the same generic framework as the one used for the
conventional imaging condition, i.e. wavefield reconstruc-
tion followed by an imaging condition. However, the dif-
ference is that the imaging condition is not applied to the
reconstructed wavefield directly, but it is applied to the
wavefield which has been transformed using pseudo-Wigner
distribution functions (WDF) (Wigner 1932). By definition,
the zero frequency pseudo-WDF of the reconstructed
wavefield U y; tð Þ is
W y; tð Þ ¼Z
thj j �T
dth
Z
yhj j � Y
dyhU y� yh
2; t � th
2
� �
� U yþ yh
2; t þ th
2
� �; ð4Þ
where Y and T denote averaging windows in space and
time, respectively. In general, Y is three dimensional and T
is one dimensional. Then, the image RIIC yð Þ is obtained by
extracting the time t = 0 from the pseudo-WDF, W y; tð Þ,of the wavefield U y; tð Þ:RIIC yð Þ ¼ W y; t ¼ 0ð Þ: ð5Þ
The interferometric imaging condition represented by Eqs.
4 and 5 effectively reduces the artifacts caused by the
random fluctuations in the wavefield by filtering out its
rapidly varying components (Sava and Poliannikov 2008).
In this paper, I use this imaging condition to attenuate noise
caused by sparse data sampling or noise caused by random
velocity variations. As suggested earlier, the interferomet-
ric imaging condition attenuates both types of noise at
once, since it does not explicitly distinguish between the
various causes of random fluctuations.
The parameters Y and T defining the local window of the
pseudo-WDF are selected according to two criteria (Cohen
1995). First, the windows have to be large enough to
enclose a representative portion of the wavefield which
captures the random fluctuation of the wavefield. Second,
the window has to be small enough to limit the possibility
of cross-talk between various events present in the wave-
field. Furthermore, cross-talk can be attenuated by select-
ing windows with different shapes, for example Gaussian
or exponentially decaying. Therefore, we could in principle
define the transformation in Eq. 4 more generally as
W y; tð Þ ¼Z
thj j �T
dthWT t; thð ÞZ
yhj j � Y
dyhWY y; yhð Þ
� U y� yh
2; t � th
2
� �U yþ yh
2; t þ th
2
� �; ð6Þ
where WT and WY are weighting functions which could
represent Gaussian, boxcar or any other local functions
(Artman 2011, personal communication). For simplicity, in
all examples presented in this paper, the space and time
windows are rectangular with no tapering and the size is
selected assuming that micro-earthquakes occur sufficiently
sparse, i.e. the various sources are located at least twice as far
in space and time relative to the wavenumber and frequency
of the considered seismic event. Typical window sizes used
here are 11 grid points in space and 5 grid points in time.
Example
I exemplify the interferometric imaging condition method
with a synthetic example simulating the acquisition
geometry of the passive seismic experiment performed at
the San Andreas Fault Observatory at Depth (Chavarria
et al. 2003; Vasconcelos et al. 2008). This numeric
J Petrol Explor Prod Technol (2011) 1:43–49 45
123
experiment simulates waves propagating from three micro-
earthquake sources located in the fault zone (Fig. 3), which
are recorded in a deviated well located at a distance from
the fault. For the imaging procedure described in this
paper, the micro-earthquakes represent the seismic sources.
This experiment uses acoustic waves, corresponding to the
situation in which we use the P-wave mode recorded by the
three-component receivers located in the borehole
(Figs. 4b, 5b). The three sources are triggered 40 ms apart
and the triggering time of the second source is conven-
tionally taken to represent the origin of the time axis.
The goal of this experiment is to locate the source
positions by focusing data recorded using dense acquisition
in media with random fluctuations or by focusing data
recorded using sparse acquisition arrays in media without
random fluctuations. In the first case, the imaging artifacts
are caused by the fact that data are imaged with a velocity
model that does not incorporate all random fluctuations of
the model used for data simulation, while in the second
case, the imaging artifacts are caused by the fact that the
data are sampled sparsely in the borehole array. The third
case is a combination of acquisition with two sparse arrays,
and imaging with an inaccurate velocity model.
Figures 6a and b, 7a and b and 8a and b show the
wavefields reconstructed in reverse time around the target
location. From left to right, the panels represent the
wavefield at different times. As indicated earlier, the time
at which source 2 focuses is selected as time t = 0,
although this convention is not relevant for the experiment
and any other time could be selected as reference. The
experiment depicted in Fig. 6a and b corresponds to
modeling in a model with random fluctuations and
1 40ms
40ms
3
2
Fig. 3 Geometry of the sources used in the numeric experiment. The
horizontal and vertical separation between sources is 250 m. The
sources are triggered with 40 ms delays in the order indicated by their
numbers. Time t = 0 is conventionally set to the triggering moment
of source 2
(a)
(b)
Fig. 4 a Wavefields simulated in random media and b data acquired
with a dense receiver array. Overlain on the model and wavefield are
the positions of the sources and borehole receivers. The boxed areacorresponds to the images depicted in Fig. 6a and b
(a)
(b)
Fig. 5 a Wavefields simulated in smooth media and b data acquired
with a sparse receiver array. Overlain on the model and wavefield are
the positions of the sources and borehole receivers. The boxed areacorresponds to the images depicted in Fig. 7a and b
46 J Petrol Explor Prod Technol (2011) 1:43–49
123
migration in a smooth background model. In this experi-
ment, the data used for imaging are densely sampled in the
borehole, i.e. there are 81 receivers separated by approxi-
mately 12 m. In contrast, the experiment depicted in
Fig. 7a and b corresponds to modeling and migration in the
smooth background model. In this experiment, the data are
sparsely sampled in the borehole, i.e. there are only six
receivers obtained by selecting every 16th receiver from
the original set. In all cases, panels (a) correspond to
imaging with a conventional imaging condition, i.e. simply
(a)
(b)
Fig. 6 Images corresponding to
migration of the denselysampled data (Fig. 4b) modeled
in the random velocity by
a conventional IC and
b interferometric IC using the
background velocity. The left-most panel shows focusing at
source 1, the middle panelshows focusing at source 2, and
the right-most panel shows
focusing at source 3. The
overlain dots represent the exact
source positions
(a)
(b)
Fig. 7 Images corresponding to
migration of the sparselysampled data (Fig. 5b) modeled
in the background velocity by
a conventional IC and
b interferometric IC using the
background velocity. The left-most panel shows focusing at
source 1, the middle panelshows focusing at source 2, and
the right-most panel shows
focusing at source 3. The
overlain dots represent the exact
source positions
(a)
(b)
Fig. 8 Images corresponding to
migration of the dual sparselysampled data (Fig. 9b) modeled
in the random velocity by
a conventional IC and
b interferometric IC using the
background velocity. The left-most panel shows focusing at
source 1, the middle panelshows focusing at source 2, and
the right-most panel shows
focusing at source 3. The
overlain dots represent the exact
source positions
J Petrol Explor Prod Technol (2011) 1:43–49 47
123
select the reconstructed wavefield at various times, and
panels (b) correspond to imaging with the interferometric
imaging condition, i.e. select various times from the
wavefield transformed with a pseudo-WDF of 11 grid
points in space and 5 grid points in time. For this example,
WDF window corresponds to 44 m in space and 2 ms in
time.
Figure 6a shows significant random fluctuations caused
by wavefield reconstruction using an inaccurate velocity
model. The fluctuations caused by the random velocity and
encoded in the recorded data are not corrected during
wavefield reconstruction and they remain present in the
model. Likewise, Fig. 7a shows significant random fluc-
tuations caused by reconstruction using the sparse borehole
data. However, the pseudo-WDF applied to the recon-
structed wavefields attenuates the rapid wavefield fluctua-
tions and leads to sparser, better focused images that are
easier to use for source location. This conclusion applies
equally well for the experiments depicted in Fig. 6a and b
or 7a and b.
The final example corresponds to the case of acquisition
with two separate sparse arrays (Fig. 9a, b). As expected,
the wavefields are far less noisy after the application of the
WDF, and the focusing is increased due to the larger array
aperture. This facilitates an automatic procedure for
focusing identification, since most of the spurious noisy is
eliminated from the image.
Finally, I note that the 2D imaging results from this
example show better focusing than what would be expected
in 3D. This is simply because the 1D acquisition in the
borehole cannot constrain the 3D location of the micro-
earthquakes, i.e. the azimuthal resolution is poor, espe-
cially if scatterers are not present in the model used for
imaging. This situation can be improved using data
acquired in several boreholes or using additional informa-
tion extracted from the wavefields, e.g. polarization of
multicomponent data.
Conclusions
The interferometric imaging condition used in conjunction
with time-reverse imaging reduces the artifacts caused by
random velocity fluctuations that are unaccounted-for in
imaging and by the sparse wavefield sampling on the
acquisition array. The images produced by this procedure
are crisper and support automatic picking of micro-earth-
quake locations. Imaging with sparse arrays allows
increased aperture for identical acquisition cost with that of
a narrower but denser array. At the same time, a larger
aperture improves focusing of the events, thus facilitating
automatic event identification. The interferometric imaging
procedure has a similar structure to conventional imaging
and the moderate cost increase is proportional to the size of
the windows used by the pseudo-Wigner distribution
functions. The source positions obtained using this proce-
dure can be used to monitor fluid injection or for studies of
naturally occurring earthquakes in fault zones.
Acknowledgments This work is supported by the sponsors of the
Center for Wave Phenomena at Colorado School of Mines and by a
research grant from ExxonMobil. The reproducible numeric examples
in this paper use the Madagascar open-source software package freely
available from http://www.reproducibility.org.
Open Access This article is distributed under the terms of the
Creative Commons Attribution Noncommercial License which per-
mits any noncommercial use, distribution, and reproduction in any
medium, provided the original author(s) and source are credited.
References
Artman B, Podladtchikov I, Witten B (2010) Source location using
time-reverse imaging. Geophys Prospect 58:861–873
Borcea L, Papanicolaou G, Tsogka C (2006) Coherent interferometric
imaging in clutter. Geopysics 71:SI165–SI175
Chavarria J, Malin P, Shalev E, Catchings R (2003) A look inside the
San Andreas Fault at Parkfield through vertical seismic profiling.
Sci Agric 302:1746–1748
Cohen L (1995) Time frequency analysis: Signal processing series.
Prentice Hall, Englewood Cliffs
(a)
(b)
Fig. 9 a Wavefields simulated in random media and b data acquired
with two sparse receiver arrays. Overlain on the model and wavefield
are the positions of the sources and borehole receivers. The boxedarea corresponds to the images depicted in Fig. 8a and b. The toptraces in b correspond to the vertical array, and the other traces
correspond to the sparse deviated array
48 J Petrol Explor Prod Technol (2011) 1:43–49
123
Gajewski D, Anikiev D, Kashtan B, Tessmer E, Vanelle C (2007)
Localization of seismic events by diffraction stacking, In: 76th
annual international meeting, SEG, Expanded Abstracts,
pp 1287–1291
Gajewski D, Tessmer E (2005) Reverse modelling for seismic event
characterization. Geophys J Int 163:276–284
Rentsch S, Buske S, Luth S, Shapiro SA (2004) Location of
seismicity using Gaussian beam type migration. In: 74th annual
international Meeting. Society of Exploration Geophysicists,
pp 354–357
Rentsch S, Buske S, Luth S, Shapiro SA (2007) Fast location of
seismicity: a migration-type approach with application to
hydraulic-fracturing data. Geophysics 72:S33–S40
Sava P, Poliannikov O (2008) Interferometric imaging condition for
wave-equation migration. Geophysics 73:S47–S61
Vasconcelos I, Snieder R, Sava P, Taylor T, Malin P, Chavarria A
(2008) Drill bit noise illuminates the San Andreas fault. EOS.
Trans Am Geophys Union 89:349
Waldhauser F, Ellsworth W (2000) A double-difference earthquake
location algorithm: method and application to the northern
Hayward fault. Bull Seismol Soc Am 90:1353–1368
Wigner E (1932) On the quantum correction for thermodynamic
equilibrium. Phys Rev 40:749–759
J Petrol Explor Prod Technol (2011) 1:43–49 49
123
REVIEW PAPER - EXPLORATION GEOPHYSICS
Delineating deep basement discontinuitiesof Qarun Lake Area, Egypt
Ahmad S. Helaly • Ahmed A. El-Khafeef
Received: 12 December 2010 / Accepted: 3 October 2011 / Published online: 21 October 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract The current study is mainly concerned with the
description and analysis of the available aeromagnetic
anomalies using different methodologies. Some structural
elements could be deduced from the qualitative interpre-
tation of such magnetic anomalies. The analysis of the
worked magnetic maps, which included the total intensity
magnetic map, reduced to-pole map, upward-continued
maps, downward-continued maps, anomaly separation
based on their wavelengths, or anomaly widths and
enhanced horizontal gradient filtering aided in divulging
the structural regime of the basement rocks, as well as the
shallower features. As a result of the investigation, a
basement tectonic map of the study area was constructed.
This map shows that the area is portrayed by the presence
of several major alternating basement swells and troughs in
belts trending ENE–WSW, N–S, NE–SW and E–W. These
major trends with the other minor trends dissected the
basement surface into several tilted fault blocks forming
anticlinal and synclinal zones with various depths and
directions. These structural elements are shown in the
basement tectonic map, and named Camel Pass-Abu Roash
high, El-Sagha high, El Faras-El faiym high and Qattrani-
El Gindi low trends.
Keywords Magnetic � Matching filtering �Horizontal gradient � Continuation
Introduction
The area under study is located to the west of the Nile
River, within the northeastern portion of the Western
Desert of Egypt. It lies between latitudes 29�000 and
30�000N and Longitudes 30�000 and 31�180E (Fig. 1),
covering a total surface area of about 14,350 km2.
The surface geology of the north Western Desert, in
general, is characterized by almost featureless terrain of
simple geologic nature. The exposed rocks are generally of
Tertiary age interrupted by some spots of Cretaceous out-
crops around Abu Roash area and Bahariya Oasis.
Because the north Western Desert tract is located within
the unstable belt of Egypt, there are a number of folding
and faulting structures within its sedimentary section that
caused lateral variations in compositions and thicknesses of
the affected sequences.
In general, the geophysical magnetic method is mainly
based on the measurements and analysis of small variations
in the earth’s magnetic field within any area. An aero-
magnetic map is a reflection of the distinctions in the
magnetic properties of the underlying rocks. Therefore,
these variations encountered in the measured magnetic
field are attributed to the distribution of the subsurface
magnetically polarized rocks.
The sedimentary rocks are of weaker magnetic proper-
ties than the underlying basement rocks, especially the
mafic rocks. Therefore, the magnetic methods are used to
delineate the structural and lithological configuration of the
basement rocks. Estimating the depths to the basement
surface with basement determination methods is compa-
rable to the calculation of the thicknesses of the overlying
sedimentary rocks. That is important for hydrocarbon
exploration, since the hydrocarbons can be found mainly in
the sedimentary section, where the configuration of the
A. S. Helaly
Department of Geophysics, Faculty of Science,
Ain Shams University, Abbassia, Cairo, Egypt
A. A. El-Khafeef (&)
Exploration Department, Egyptian Petroleum
Research Institute, Nasr City, Cairo, Egypt
e-mail: [email protected]
123
J Petrol Explor Prod Technol (2011) 1:51–64
DOI 10.1007/s13202-011-0012-8
basement rocks reflects the size and shape of any sedi-
mentary basin and ridge that form the source rocks and
trapping elements.
The main type of available geophysical data for the
current study is an aeromagnetic map showing the distri-
bution of the total intensity magnetic anomalies within the
study area (Fig. 3). The current study involves the quali-
tative analysis of the available aeromagnetic data.
Geologic setting
The distribution of the different rock types exposed in the
area under study is shown in the geological map (Fig. 2),
which was compiled from the Egyptian Geological Survey
and Mining Authority (1981). This map reveals that, the
exposed outcrops of this area range in age from Eocene to
Recent.
The Eocene rocks are composed of limestone with some
flints, mainly blanketing most of the southwestern portion
of the study area, around the Faiyum Depression. Mean-
while, the Miocene deposits mainly cover the northwestern
portion of the area. The Miocene deposits are separated
from the Eocene rocks by narrow belt of Oligocene rocks
outcropping north of Birket Qarun and are composed of
cross-bedded sandstones and gravels with interbeds of
shales and limestones. To the east, the Pleistocene–Recent
sediments mainly cover the narrow strip of the Nile Valley,
around the cultivated lands, with local Pliocene outcrops
covering the older rocks. Surficial deposits in the form of
sand dunes running generally in a north northwesterly
direction also represent the Pleistocene–Recent rocks.
Fig. 1 Locaion map of the
study area
Fig. 2 Geological map of the
study area (Geological Survey
of the Egypt 1981)
52 J Petrol Explor Prod Technol (2011) 1:51–64
123
Basaltic flows and sheets, which are believed to be of Late
Oligocene–Early Miocene age, are exposed in some
localities in this area, e.g., Gabal Qatrani, south of Cairo,
and west of the Nile Valley. Gabal Qatrani is situated to the
north of the study area.
Geomorphologically, the studied area, as a part of the
north Western Desert of Egypt, is generally a rocky plat-
form of low altitude, which has been characterized through
its recent history by arid climatic condition. Therefore, its
main geomorphologic features are primarily due to the
wind action (Said 1962). The area exhibits a vast pene-
plain, which is covered in many places by wind-blown
sands, sand sheets, and gravels.
Generally, the main geomorphologic features of the
north Western Desert are: the absence of well marked
drainage lines, the presence of some parallel belts of sand
dunes of different lengths running mainly in a NNW
direction, the presence of plateaus that are capped by
resistant Eocene and Miocene limestone, and the presence
of numerous extensive and deep-in depression, e.g. Ba-
hariya Oasis, Faiyum and Wadi El-Rayian depressions.
The second and third depressions are located in the study
area.
Structurally, the north Western Desert has been exten-
sively described by many workers, e.g. Said (1962), You-
ssef (1968), Meshref and El-Sheikh (1973), El-Gezerry
et al. (1975), El-Sirafe (1985), Meshref (1980), Abu El-Ata
(1988), Hantar (1990), Meshref (1990), and others.
The north Western Desert, where the area under inves-
tigation lies, is dominated by faults, many of which are step
normal faults having a NE–SW, E–W, NW–SE and N–S
trends. Some of these faults suffered strike-slip movements
during a part of their history. There are also a large number
of hanging faults affecting the shallower parts of the sec-
tion and usually of limited throw. These faults are common
in the northern part of the region.
Most folds owe their origin to compressional movements,
which affected the area during the Late Cretaceous–Early
Tertiary tectonic event. These folds have an ENE–WSW trend
and a periclinal geometry. In addition, there are other folds,
which owe their origin to normal or horizontal displaced faults
(Hantar 1990).
Main concepts
There are some principles should be taken into consider-
ation when working with the magnetic data. The interpre-
tation of magnetic data is not unique, because it is
controlled by many factors; for example, depth to top of the
causative feature, its shape, its azimuth, its magnetic sus-
ceptibility, that is mainly related to its petrographical
2.5 0 2.5 5 7.5 10
Km.
-140.0
-120.0-100.0
-80.0
-70.0-60.0-50.0-40.0
-30.0-20.0-10.0
0.010.0
20.030.0
40.050.0
60.070.080.0
100.0110.0
120.0140.0
160.0180.0200.0220.0
nt
29 0
030
00
29 0030 00
30 00 31 00
31 0030 00
0 0 2 -
00
1-
00
1-
-100
- 10 0
-1
00
0
0
0
0
0
0
0
0
0
00 1
001
0 01
10
0
0 01
10
0
2 00
002
002
00 2
00
2
20
0
Fig. 3 Total intensity
aeromagnetic of the study area
J Petrol Explor Prod Technol (2011) 1:51–64 53
123
composition. Such factors are related to the subsurface
anomalous features that produce their magnetic signatures
at the surface. The availability and use of some of these
factors during the interpretation reduce the ambiguity in the
magnetic interpretation. Such factors can be taken from
the available well data and regional geology of the area.
The available magnetic data for this study have been cor-
rected for the diurnal variations, instrument drift, and for
the errors in positioning and height keeping.
Insights on the original magnetic data
The close study of the total intensity aeromagnetic map
(Fig. 3) indicates that most of the observed anomalies show
ENE–WSW trend patterns with some sharp gradients at
varying locations. Since the magnetic maps are related
directly to the basement rocks’ features, therefore, this
indicates the presence of a basement relief change. This is
because any sudden change in the magnetic contour spac-
ing over a relative short distance suggests a discontinuity in
the basement rocks, lithological variations within the
basement rocks, or both.
The analysis of Fig. 3 (total intensity magnetic map)
shows the existence of a major ENE–WSW low magnetic
anomaly parallel to Birket Qarun, bounded between two
magnetic highs at the northwestern and southeastern por-
tions of the study area, with some superimposed smaller
anomalies. The magnetic gradient to the northwestern
portion is rather gentler than that of the southern one. The
effects of the sub-topographic relief of the dissected
basement surface and/or the small variations in suscepti-
bility of its composing rocks caused such magnetic highs
and lows. The occurrence of some basement intrusions into
the sedimentary cover of the study area complicated the
aeromagnetic pattern. The combined effect of these
anomalies with the regional field of the geomagnetic field
produced such observed aeromagnetic data. Therefore, the
aeromagnetic map can be described in terms of the fol-
lowing parameters, the anomaly’s areal extension, shape,
amplitude in gammas and the gradient.
Analysis of the magnetic data
The processing of the aeromagnetic anomalies is based on
the analysis of the computer-digitized information using
different processing techniques at different altitudinal
levels from the compiled aeromagnetic data shown in
Fig. 3. These techniques involve; first the reduction to the
north magnetic pole. The reduced to the north magnetic
pole digitized data were used for further investigative
techniques that helped integratively to deduce the structural
set-up for the basement of the considered area.
Reduction to the north magnetic pole
Since the study area is positioned within a low-latitude
region in the northern hemisphere, the original aeromag-
netic data subjected to reduction to the north-pole. A
reduction-to-pole (RTP) transformation is standardly
applied to the aeromagnetic data to minimize the polarity
effects. These effects are manifested as a shift of the main
anomaly from the center of the magnetic source and are
due to the vector inclination of the measured magnetic
field. The RTP transformation usually involves an
assumption that, the total magnetizations of most rocks
align parallel or anti-parallel to the Earth’s main field
(declination = 3.439�, inclination = 43.279�, and IGRF
total intensity value = 42,989 nT, for the study area). This
assumption probably works well for the Tertiary units in
the surveyed area, which are the focus of interpretation.
The RTP aeromagnetic data, computed from the grid of
total-field magnetic data, are shown in Fig. 4. This figure
shows a kind of general northward shift of the magnetic
anomalies, with the appearance of some sort of sharper
magnetic gradients in the central part of the study area with
a general ENE–WSW trend; in addition to a shorter N–S
trend at the middle-eastern side of the study area.
Upward continuation
Because of the potential nature of the potential fields (like
in Gravity and Magnetic), they can be calculated at any
elevation above (and in some cases below) the level of
measurements, that is, if there is neither gravity nor mag-
netic sources between these two levels. This procedure is
called the upward continuation of potential field. It is
generally a useful and physically meaningful filtering
operation. It allows smoothing the field and eliminating
small anomalies (noises) in the form of noises from the
near surface objects. In the spectral domain, upward con-
tinuation can be written as:
Fðu; vÞ ¼ sðu; vÞ � f u; vð Þ
Fðu; vÞ ¼ sðu; vÞ1þ asðu; vÞ2
� f ðu; vÞð1Þ
where f(u,v) is the spectrum of the field to be transformed.
F(u,v) is the spectrum of transformed (upward or down-
ward continued) field. s(u,v) is the spectrum of the trans-
formation and the small regularization parameter.
The upward continuation of the reduced to the pole data
to an altitude above the measurements level will eliminate
the effects of possible near-surface noises that may result in
54 J Petrol Explor Prod Technol (2011) 1:51–64
123
misleading responses. In the same time, upward-continued
maps reflect the general configuration of the main sources
of the magnetic anomalies, which is mainly the surface of
basement rocks. This will, definitely, reduce the resolution
of the magnetic anomalies.
In the current study, the upward-continued magnetic
response was determined at three levels, 1 km (Fig. 5), 2 km
(Fig. 6) and 3 km (Fig. 7) above the level of measurements.
A closer look at those three maps showed that Fig. 5 exhibits
more resolvable anomalous features than in Figs. 6 and 7.
That is expected, since we are going further away from the
magnetic sources, the smaller sources will be reduced in
their responses. The upward-continued map at 1 km shows
relative smaller anomalies superimposed on the wider
regional magnetic responses. The two levels of 2 and 3 km
upward-continued maps are showing more general pattern
for the basement surface. This reflects that, there is a major
plutonic uplift trending ENE–WSW within the study area. In
addition, it can be noticed that, the big negative anomaly in
Fig. 5, at the northwestern part of the study area, is reduced
in its areal extension and amplitude, as shown in Fig. 7.
Downward continuation
Downward continuation highlights the high frequency
content of a gridded magnetic data set, just as if the data
had been acquired at a lower survey height. Theoretically,
the field can also be continued downwards until the con-
tinuation level does not cross any field sources. However, it
has been proved that, this operation is unstable because it
greatly magnifies the existing noise and makes the field
unusable.
To deal with this problem; some relaxation (regulari-
zation) techniques can be used. In the current study, that
can be done through the use of Tikhnonov regularization
parameter. The Tikhonov regularization parameter b(Tikhonov and Arsenin 1977) is important in the optimi-
zation process. Kristofer and Yaoguo (2007) explained
that, in order to find the optimal data misfit, a Tikhonov
parameter, b, is chosen based on the optimal model
weighting. The regularization parameter is chosen, so the
optimal solution is neither over-smoothing nor under-
smoothing the data (i.e. fitting the noise or the signal).
Several values for this parameter were tried to find the best
for the data under study. This parameter was chosen such
that the resulted data using the selected parameter’s value
show some sort of similarity (in its overall representation)
to the pattern of the original data to be downwardly
continued.
The reduced-to-pole data (Fig. 4) is subjected to the
downward continuation, with Tikhonov regularization
parameter of 10-4, to transform the studied data to be as
2.5 0 2.5 5 7.5 10
Km.
-190-160-140-130-120-110-100-90-80-70-60-50-40-30-20-10
0103040607090
110120140160180190220250310
nt
29 0
030
00
29 0030 00
30 00 31 00
31 0030 00
00
2-
0 0 1 -
001-
-1
00
- 1 0 0
-100
-100
-100
0
0
0
0
0
0
1 00
00
1
00
1
0 0 1
10
0
002
00
2
20
0
003
00
4
Fig. 4 Reduction to the Pole
(RTP) map for the study area
J Petrol Explor Prod Technol (2011) 1:51–64 55
123
taken at lower levels. Downward-continued data to a rel-
atively shallow depth will emphasize the residual compo-
nents (of shallower sources) making the map noisier (as
shown in Fig. 8). While, downwardly continued data to
deeper depths will show less noisy-manifestations. Know-
ing that the average depth to the basement surface in the
study area is in the range of about 4.5 km as known from
some deep wells, the reduced-to-pole data were continued
downwardly to three levels 1, 3, and 5 kilometers, as shown
in Figs. 8, 9, and 10, respectively. As we are going deeper,
below the original level of measurement, such downward-
continued maps reflect the combined effect of the strikes of
the subsurface structural elements, direction of magneti-
zation, as well as the susceptibility contrasts between the
sedimentary section and the underlying/surrounding base-
ment. These structural features shown on such maps are
slightly different, and will be discussed separately.
For the downward-continued map to 1 km depth
This map (Fig. 8) shows that, a -125 gamma contour line
is located at the southeastern portion of the study area,
while a ?250 gamma contour lines are located within the
middle portion of the study area with an ENE–WSW trend
and accompanied by a number of smaller or local
anomalies in a scattered fashion. This reflects the irregular
nature of the closer-to-surface causative features; except
the northwestern portion of the study area which shows
some sort of less heterogeneity. The contour gradient is
sharper in the middle portion of the study area and towards
the south, but shows gentler behavior at the northern part of
the study area. Many smaller wavelength local anomalies
can be seen in this map, revealing the existence of limited
small subsurface features, in either their composition and/
or their altitude.
For the downward-continued map to 3 km depth
This map (Fig. 9) shows more relative regular contour lines
with local features of different trends and amplitudes. As
this map shows a downward-continued picture, it is clear
that as we approaching the basement surface, so the mag-
netic effect will get bigger (in its positivity and negativity).
Therefore, the middle portion of the study area shows
relative high magnetic values (up to ?750 gammas at the
eastern part), while also the negativity increased in the
northern part of the study area down to -250 gammas).
The many localized features, in some localities, are signs
that the basement surface still not reached yet. Sharper
contour gradients can be seen especially at the southern
-155.0-136.1-122.0-112.2-104.9-99.8-95.7-92.2-88.6-84.9-80.9-75.8-70.4-64.6-58.4-52.1-45.8-39.7-33.9-27.9-20.2-11.5-0.311.423.435.549.664.177.389.5
102.1120.9140.1157.0172.0191.9222.1264.4
nt
29 0
030
00
29 0030 00
30 00 31 00
31 0030 00
- 2 0 0
00
2-
00
1-
00
1-
- 1 0 0
- 1 0 0
-100
00 1 -
0
0
0
0
0
0
100
001
001
1 0 0
10
0
00
2
0 0 2
200
003
30
0
2.5 0 2.5 5 7.5 10
Km.
Fig. 5 Upward-continues RTP
map to 1-km level
56 J Petrol Explor Prod Technol (2011) 1:51–64
123
29 0
030
00
29 0030 00
30 00 31 00
31 0030 00
00 1
-
001-
- 10 0
-1
00
0
0
0
0
0
0
100
001
00 1
10
0
002
2 00
00
3
-128.2-114.4
-104.4-95.9
-89.3-85.9
-82.9-80.2
-77.6
-74.4-70.4
-65.4-60.0
-54.3-48.4
-43.2-38.2
-33.5-28.7
-23.1-16.3
-8.5
-0.18.6
18.029.0
40.451.9
63.374.2
86.7102.8
119.2
135.9151.8
170.5195.2
231.2
nt
2.5 0 2.5 5 7.5 10
Km.
Fig. 6 Upward-continues RTP
map to 2-km level
29 0
030
00
29 0030 00
30 00 31 00
31 0030 00
0 01
-
- 1 0 0
-10
0
0
0
0
0
0
001
0 01
10 0
002
2 00
-108.3
-97.7
-90.1
-83.5-77.9
-74.5
-72.1
-70.0
-67.4
-64.4
-60.5-56.0
-51.3
-46.4
-41.3
-36.1
-32.4
-28.1-23.6
-18.9
-13.2
-7.1
-0.4
7.1
15.324.2
33.5
43.0
52.8
63.0
74.8
88.3103.0
118.8
134.3
151.4
173.0
203.3
nt
2.5 0 2.5 5 7.5 10
Km.
Fig. 7 Upward-continued RTP
map to 3-km level
J Petrol Explor Prod Technol (2011) 1:51–64 57
123
Fig. 8 Downward Continued
RTP Map at Level 1-km
Fig. 9 Downward Continued
RTP Map at Level 3-km
58 J Petrol Explor Prod Technol (2011) 1:51–64
123
half of the study area. Such gradients illustrate the presence
of sharp contacts between the subsurface causative fea-
tures. These contacts are most likely of fracturing effect.
For the downward-continued map to 5 km depth
This map (Fig. 10) shows smoother contour lines with higher
amplitudes that reached ?750 gammas, while also the nega-
tive contours are showing amplitudes of -750 gammas and
less (down to -1,250 gammas). The smoothness of these
contours gives an indication that this level is within the
basement rocks and this reflects the combined effect of the
structural elements and/or the lithological variations within
the basement rocks. The gradients in those two maps are
gentler than the previous map (Fig. 8), reflecting more
homogeneity.
Extracting the magnetic sources using matching
band-pass filtering
The RTP magnetic data of the study area can be used to
illustrate this process. The shallow geologic units produce
weak, short wave length magnetic anomalies. The deeper
geologic units produce stronger magnetic anomalies with
longer wavelengths. This is reflected by varying slops in
the Fourier power spectrum of the aeromagnetic data,
which has been averaged for all azimuths as illustrated in
Fig. 11. The first step in designing a filter (using program
MFDESIGN of Phillips 1997), is to fit only the short
wavelength end of the spectrum with a straight line rep-
resenting the spectrum of a thin magnetic layer containing
a near-surface source layer (Fig. 11a). The effect of this
layer is subtracted from the spectrum, and the intermediate
wavelengths of the residual spectrum are fit with another
straight line representing the spectrum of the intermediate
source layer (Fig. 11b). This process is continued until the
long wavelength end of the spectrum is fit with the deepest
equivalent source layer (Fig. 11c). At this point, the com-
bined spectrum of all the equivalent layers should
approximately match the spectrum of the data (Fig. 11d).
Fourier bandpass filters for extracting the magnetic signals
of each of the equivalent layers are computed as the
spectrum of the individual equivalent layer divided by the
combined spectrum of all the equivalent layers (Fig. 11e).
The filters are applied to the observed data (using pro-
gram MFFILTER of Phillips 1997) to separate the mag-
netic anomalies by apparent source depth. Figure 12
contains RTP magnetic anomalies produced by shallow
geologic sources with equivalent dipole layer for this band-
pass located at 0.30 km. The intermediate wavelength map
(Fig. 13) involves RTP anomalies produced by geologic
sources at intermediate depths. The equivalent RTP
Fig. 10 Downward Continued
RTP Map at Level 5-km
J Petrol Explor Prod Technol (2011) 1:51–64 59
123
half-space for this band-pass is located at 1.18 km. Moreover,
the long wavelength map (Fig. 14) includes the anomalies
from the deepest and broadest features of the geology.
Therefore, the equivalent magnetic half space for this
band-pass is located at 3.9 km depth.
Horizontal gradient maps
The horizontal gradient (HG) method is considered as the
simplest approach to delineate the contact locations (e.g.
faults). It requires a number of assumptions about the
sources: (1) the regional magnetic field is vertical, (2) the
source magnetization is vertical, (3) the contacts are ver-
tical, (4) the contacts are isolated, and (5) the sources are
thick (Phillips 1998). In contrast, the method is the lease
susceptible to noise in the data, because it only requires the
two first-order horizontal derivatives of the magnetic field.
If T(x, y) is the magnetic field and the horizontal deriva-
tives of the field are (qT/qx and qT/qy), then the horizontal
gradient HG (x, y) is given by:
Fig. 11 In matched filtering,
the radial power spectrum, is fit
by series of linear curves
representing the power spectra
of simple equivalent magnetic
layers
60 J Petrol Explor Prod Technol (2011) 1:51–64
123
-1.55
-1.10
-0.85-0.70
-0.60
-0.50
-0.45-0.40
-0.35
-0.30
-0.25
-0.20-0.15
-0.10
-0.05
0.000.05
0.10
0.15
0.200.25
0.35
0.40
0.450.55
0.65
0.80
1.001.30
1.85
nt
29 0
030
00
29 0030 00
30 00 31 00
31 0030 00
00
0
0
0
0
0
0
0
2.5 0 2.5 5 7.5 10
Km.
Fig. 12 Short-wave length
component of RTP magnetic
data using matching filtering
29 0
030
00
29 0030 00
30 00 31 00
31 0030 00
-1
0
01-
1 0
1 0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2.5 0 2.5 5 7.5 10
Km.
-15
-11
-10-9
-8
-7
-6-5
-4
-3
-2-1
0
1
23
4
56
7
8
910
12
14
1723
nt
Fig. 13 Medium-wave length
component of RTP magnetic
data using matching filtering
J Petrol Explor Prod Technol (2011) 1:51–64 61
123
HG ðx; yÞ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffioT
ox
� �þ oT
oy
� �sð2Þ
Once the field is reduced to pole, the regional magnetic
field will be vertical and most of the source magnetizations
will be vertical, except for sources with strong remnant
magnetization such as basic volcanic rocks. This technique
has been carried out to the downward-continued data, along
the three depth levels, 1, 3, and 5 km, below the surface of
measurement. This resulted in three maps showing the
distribution of the HG features, as shown in Figs. 15, 16, and
29 0
030
00
29 0030 00
30 00 31 00
31 0030 00
- 20
0-
10
0
001-
00
1-
001-
-1
00
001-
001-
0
0
0
0
0
0
0
001
10
0
10
0
1 0 0
10
0
00
2
20
0
00
3
40
0
2.5 0 2.5 5 7.5 10
Km.
-182-157
-142-129
-120-112
-106-102
-98-94
-89-85
-79
-73-66
-59-53
-46-39
-31-22
-110
1429
4459
7590
104
119139
158174
186212
243301
nt
Fig. 14 Long-wave length
component of RTP magnetic
data using matching filtering
Fig. 15 Horizontal gradient map for 1-km downward-continued mapFig. 16 Horizontal gradient map for 3-km downward-continued map
62 J Petrol Explor Prod Technol (2011) 1:51–64
123
17. These horizontal-gradient maps are vivid, simple, and
intuitive derivative products, which reveal the anomaly
texture and highlight anomaly-pattern discontinuities. These
maps contour the steepness of the anomaly relief’s slope.
Horizontal-gradient maxima occur over the steepest parts of
potential-field anomalies, and minima over the flattest parts.
Short-wavelength anomalies are also enhanced.
Tectonic inferences of the basement discontinuities
The results and information obtained from the fore-men-
tioned critical analysis and interpretation were integrated
with the general available geologic features to construct the
predominant tectonic elements affecting the basement
discontinuities of the study area (Fig. 18).
These tectonic features are either high trends (express-
ing anticlinal zones or swell-like belts) or low trends
(referring synclinal zones or trough-like belts) and fault
trends (throwing from the high trends to the low trends).
Accordingly, the basement surface is configured by
three major swell systems and two trough belts. The
northern high belt (swell) system trends mostly ENE–
WSW with N–S splitting at the west end, which represents
the Camel Pass–Abu Roash high (Abu El-Ata 1990).
While, the second swell orients mostly NE–SW (El
Faras–El Faiyum High trend), with mostly E–W bifurca-
tion at its western part (El-Sagha high trend) and other two
small E–W, NNE–SSW bifurcations at its central part. The
main trend of this belt represents the El Faras–El Faiym
high trend.
The southwestern small third high belt (Camel-Pass
belt), that starts in NW–SE direction and ends in the mostly
N–S with E–W bifurcation at its southern end.
Moreover, the major central trough zone (Qatrani-El
Gindi low trend) that run mostly ENE–WSW with N–S
split at its western part and NW–SE split at its central part
throughout Qarun lack. While, the southeastern trough belt
orients NE–SW with two N–S and NNW–SSE splits at its
southern end. In addition, a series of separated ENE–WSW
and N–S small troughs are observed at the northern and
southwestern parts of the map, beside a series of moderate
N–S and NE–SW swells observed at the northwestern and
southwestern corners.
These high and low trends are bounded and dissected by
major and minor faults, in the form of horst blocks, graben
blocks, or step-like blocks.
Horizontal gradient maps aided in defining the location
of linear features, which in turn are related to the trend of
the structural manifestations in the area. Faults can be
traced easily along these linear features.
Results and conclusions
Through the downward-continued maps, it can be deduced
that, some of the magnetic anomalies shown in Fig. 4, have
sources within the sedimentary section, overlying the deep-
seated basement rocks. The types, magnitudes, areal
extensions, and distributions of such sources are expected
to be in close relation with the basement rocks (i.e., supra-
basement features).
It seems that, the whole area is portrayed as a part of a
major sedimentary basin interrupted by several disconti-
nuities in the form of smaller highs and lows. This reveals
the complexity of the stress effects and directions exerted
Fig. 17 Horizontal gradient map for 5-km downward-continued map
Fig. 18 Map showing integrated basement structure discontinuities
J Petrol Explor Prod Technol (2011) 1:51–64 63
123
on the area, in form of compressional and tensional stres-
ses. The predominant tectonic trends as delineated through
N60�E with intermittent N–S directions. Such basement
surface can be illustrated as being of several swells and
troughs with zones of displacement of different reliefs,
areal extensions and mainly oriented northeasterly. Block
faulting could be the most prominent structural style.
Through integrating the whole set of maps together with the
horizontal gradient maps, the faults were traced along these
maps. The resulting set of lineaments was compared with the
available well data that reached the basement surface, to
determine the relative highs and lows in the basement rocks.
Based on the integrated magnetic anomaly pattern from the
different processed techniques used in this work, a number of
magnetic highs (swells) and lows (troughs) features were
delineated. Such swells and troughs are in the form of uplifted
and down-faulted blocks within the basement. The illustra-
tions showed, the major trends of the basement features are
ENE–WSW, NE–SW, E–W and NNE–SSW trends. These
major trends are interrupted by number of minor N–S trending
faults with shorter areal extensions.
The fore-mentioned tectonic elements are shown in the
basement tectonic map, and named related to Abu El-Ata
(1990), Camel Pass–Abu Roash high, El-Sagha high,
El-Faras-El-Faiym High as well as Qatrani-El Gindi low trends.
Open Access This article is distributed under the terms of the
Creative Commons Attribution License which permits any use, dis-
tribution and reproduction in any medium, provided the original
author(s) and source are credited.
References
Abu El-Ata ASA (1988) The relation between the local tectonics of
Egypt and the plate tectonics of the surrounding regions using
geophysical and geological data
Abu El-Ata ASA (1990) The role of seismo-tectonics in establishing
the structural foundations and starvation conditions of El-Gindi
Basin, Western Desert, Egypt. In: 8th E.G.S. Proceedings of the
6th annual meeting, Cairo, pp 150–169
El-Gezerry MN, Farid M, Taher M (1975) Subsurface geological
maps of northern Egypt. Unpublished maps. General Petroleum
Company, Cairo
El-Sirafe AM (1985) Application of aeromagnetic, aero-radiometric
and gravimetric survey data in the interpretation of the geology
of Cairo-Bahariya area, north Western Desert, Ph.D Thesis, Ain
Shams University, Egypt
Hantar G (1990) North Western Desert, Chap 15. In: Said R (ed) The
geology of Egypt. A.A. Balkema, Brookfield, pp 293–319
Jeffery DP (1998) Processing and interpretation of aeromagnetic data
for the Santa Cruz Basin-Patagonia mountain area, South central
Arizona, Open-File Report 02-98, USGS
Kristofer D, Yaoguo L (2007) A fast approach to magnetic equivalent
source processing using an adaptive quadtree mesh discretiza-
tion. ASEG, Perth, pp 1–4
Meshref WM, El-Sheikh MA (1973) Magnetic tectonic trend analysis
in northern Egypt. Egypt J Geol 17(2):179–184
Meshref WM (1980) Structural geophysical interpretation of base-
ment rocks of the northwestern Desert of Egypt. Annu Geol Surv
Egypt X:923–937
Meshref WM (1990) Tectonic framework, Chap 8. In: Said R (ed)
The geology of Egypt. A.A. Balkema, Rotterdam, pp 113–157
Phillips JD (1997) Potential-field geophysical software for the PC,
version 2.2, US Geological Survey Open-File Report 97-725.
ftp://greenwood.cr.usgs.gov/pub/open-file-reports/ofr-97-0725/
pfofr.htm
Said R (1962) The geology of Egypt. Elsevier, Amsterdam
Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems.
V.H Winston and Sons, Washington, p 258
Youssef MI (1968) Structural pattern of Egypt and its interpretation.
AAPG Bull 52(4):601–614
64 J Petrol Explor Prod Technol (2011) 1:51–64
123
REVIEW PAPER - PRODUCTION ENGINEERING
Scientific research and field applications of polymerflooding in heavy oil recovery
Chang Hong Gao
Received: 6 August 2011 / Accepted: 17 October 2011 / Published online: 1 November 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract The heavy oil resources worldwide are esti-
mated at 3,396 billion barrels. With depletion of light oil,
we have to face the technical and economical challenges of
developing heavy oil fields. Due to severe viscous finger-
ing, the recoveries of heavy oil reservoirs are often below
20% or even 10%. Thermal methods have been success-
fully applied in many heavy oil fields. However, reservoirs
at great depth or thin pay zones are not good candidates for
thermal methods.
According to past experiences, polymer flood was not
recommended for oil viscosity higher than 100 centipoises.
In recent years, polymer flood becomes a promising tech-
nology for heavy oil recovery thanks to the widespread use
of horizontal wells. This paper highlights the research
advances of polymer in heavy oil recovery since 1977. In
laboratory tests, polymer achieved tertiary recovery of
more than 20% for heavy oil. A few field cases in China,
Canada, Turkey, Suriname and Oman are also reviewed
and analysed. Some field pilots have shown positive
results. Field experiences indicate the major challenge
facing polymer flooding effectiveness is to maintain good
viscosity of polymer solution.
KeyWords Polymer � Oil recovery � Heavy oil � Review
Introduction
Heavy oil refers to the crude with high density (from 10� to
20� API) and high viscosity (more than 100 cP). Heavy oil
widely exists in many basins around the world, especially
in South America, North America and Middle East. The
heavy oil resources by region are given in Fig. 1 (Meyer
et al. 2007).
Due to high demand for energy and depletion of light
oil, we have to investigate technically and economically
feasible methods to produce heavy oil. Heavy oil presents
great challenges to oil producers. The drastic viscosity
difference between heavy oil and water causes injected
water to finger through the reservoir, leaving large quan-
tities of oil behind. As a result, recovery of heavy oil was
often less than 20% or even less than 10% (Meyer 2003).
Polymer flood is the most widely used chemical EOR
method. By adding polymers to water, the water–oil mobility
is lowered. Such a change can lead to better sweep efficiency.
It is generally believed that polymer flooding cannot reduce
the residual oil saturation, but it can help to reach residual oil
saturation in shorter time (Du and Guan 2004).
Polymer flood was proved technically and economically
successful in many EOR projects worldwide (Wang et al.
2009; Sheng 2011). In field applications, polymer floods
increased recovery by 12–15% (Wang et al. 2002). The
field experiences in China showed that polymer flood was
cheaper than water flood, due to increased oil output and
reduced costs in water injection and treatment (Wang et al.
2003).
Based on past experiences, polymer flood is recom-
mended for oil viscosity less than 100 cP under reservoir
temperature, and sandstone reservoir with oil saturation
higher than 30%, reservoir permeability greater than
20 mD, net thickness more than 3 m (10 ft), and reservoir
temperature less than 90�C or 200�F (Lake et al. 1992;
Alkafeef and Zaid 2007; Gao and Towler 2011).
Most commonly used polymers include polyacrylamids
(PAM), partially hydrolyzed polyacrylamide (HPAM) and
C. H. Gao (&)
School of Engineering, University of Aberdeen,
Aberdeen AB24 3UE, UK
e-mail: [email protected]
123
J Petrol Explor Prod Technol (2011) 1:65–70
DOI 10.1007/s13202-011-0014-6
Xanthan. HPAM can be synthesized to high molecular
weights and costs less than Xanthan, therefore more pop-
ular in field applications. However, HPAM is less tolerant
to salt (Morel et al. 2008).
According to a survey, thermal methods such as steam
flood and hot water flood are the successful strategy for
producing heavy oil (Koottungal 2010). However, thermal
methods are not suitable for thin layers and deep reservoirs.
Researchers have been studying polymer flood as a possi-
ble alternative for such scenarios.
Advances in scientific research
In 1977, two scientists at Marathon Oil Company pio-
neered the research on heavy oil recovery with polymer
(Knight and Rhudy 1977). Polymer solutions with various
PAM concentrations were injected into Ottawa sand packs.
The permeability of the sand packs ranged from 3,700 to
5,900 mD. The porosity of the sand packs was around
35%. Two heavy oils were tested. One was a crude oil from
Wyoming with viscosity of 220 cP and 19.8�API. The
other sample was very viscous synthetic oil (1,140 cP). The
mobility ratio with water flood was as high as 30. Polymer
flood reduced mobility ratio to 0.34 for the 220 cP oil, and
3.2 for the more viscous crude. Polymer achieved tertiary
recovery between 19 and 31%. The results clearly dem-
onstrated the potential of polymer flood in heavy oil EOR.
In recent years, polymer flooding attracted increasing
attention in heavy oil recovery, thanks to high oil prices.
This topic has been very active in Canada.
In western Canada, Water flood only recovered 10% of
the heavy oil reserves. Aiming to improve the heavy oil
recovery, researchers tested polymer solution on displacing
three oil samples with viscosity of 280, 1,600 and 780 cP
(Wassmuth et al. 2007b). The procedure was to inject
0.5 PV (pore volume) of water into high permeability core
until water cut reached 90%. Afterwards, 6 PV of polymer
solution was injected into the core, followed by 5 PV of
water. The tested polymer concentration was 1,500 ppm,
which produced an in situ viscosity of 18 cP. The incre-
mental recovery was 16, 22 and 23% for the three oil
samples, respectively. The test result in Fig. 2 clearly
shows the acceleration of recovery process with polymer
flood.
At University of Regina, HPAM solution was tested on
homogeneous and heterogeneous sand packs (Wang and
Dong 2007). The viscosity of test oil was 1,450 cP at room
temperature of 22.5�C. The homogeneous sand had
porosity of 0.35 and permeability of 7 Darcy. The sand
pack was first flooded with water till oil recovery of 42%,
and polymer solution was subsequently injected. The ter-
tiary recoveries ranged from 4% with polymer solution of
medium viscosity, to 19% with high-viscosity polymer
solution.
In a lab study in Alberta, 0.5 PV of polymer injection
lead to 20% of tertiary heavy oil recovery. The tested crude
had a viscosity of 600–2,000 cP and a gravity of 14�API.
The injected polymer solution produced a viscosity of
25 cP (Wassmuth et al. 2007a).
In another research project, PAM solutions of various
concentrations of 500, 1,000, 5,000 and 10,000 ppm were
tested against a heavy oil sample with viscosity of 1,450 cP
(Asghari and Nakutnyy, 2008). The test media were two
sand packs with permeability of 2 and 13 Darcy. It was
discovered that polymer concentration must exceed
5,000 ppm to mobilize the test oil.
At University of Calgary, heavy oil samples with vis-
cosities ranging from 430 to 5,500 cP were flooded with
polymer solutions with effective viscosities of
3.6–359.3 cP. It was discovered that the polymer solution
must exceed certain effective viscosity to achieve a tertiary
recovery of more than 10%. This can be seen in Fig. 3
(Wang and Dong 2009).
Fig. 2 Comparison of water flood and polymer flood on 1600 cP oil
Fig. 1 Heavy oil resources by region
66 J Petrol Explor Prod Technol (2011) 1:65–70
123
The influence of oil saturation was also tested. The sand
pack was flooded till oil recovery of 35%, and polymer flood
was then initiated. It was discovered that polymer solution
with relatively low viscosity achieved good tertiary recovery
between 8 and 21%. This indicated that polymer flood could
be more effective when applied early. The tests on heteroge-
neous sand pack lead to much lower tertiary recovery, com-
pared with the results for homogeneous sands.
The heavy oil reservoirs in Saskatchewan are not suitable
for thermal methods or miscible CO2 flood. At Saskatchewan
Research Council, polymer flood was tested on heavy oil
recovery (Zhang et al. 2010). The heavy oil had a gravity of
18.3�API and a viscosity of 707 cP at 15�C. The molecular
weight of the test polymer was 8–20 million. The polymer
solution was prepared by adding 0.4 wt% of polymer to brine,
which produced a viscosity of 29 cP. Firstly, 4.7 PV of water
was injected into the sand pack with a permeability of
2.35 Darcy. Subsequently, 0.8 PV of polymer solution fol-
lowed, and finally chased by 2.85 PV of water flood. The
polymer flood recovered 13% of extra oil after initial water
flood. The test data are reproduced in Fig. 4.
For the laboratory research surveyed here, polymer flood
could lead to tertiary oil recovery of more than 10%.
However, high polymer concentration and viscosity were
required to mobilize heavy oil.
Field applications
Even though laboratory research demonstrated the poten-
tial of polymer flood in recovering heavy oil, most oil
companies are still reluctant to apply this technology in the
field. Five field cases are identified and reviewed here.
Bohai Bay, offshore China
It was estimated that more than 70% of the reserves in
Bohai Bay is heavy oil (Zhou et al. 2008). The recovery by
10 years of water flooding was only 13.5%. China National
Offshore Oil Company (CNOOC) started polymer flood in
Bohai offshore field since 2002 (Liu et al. 2010). The pilot
test on a single well lasted 500 days. The water cut drop-
ped from 95 to 54%. The incremental oil was 2,5000 m3
(157,250 bbl).
After the success of the single well treatment, polymer
was injected to four injection wells with six corresponding
production wells. The reservoir depth was 1,300–1,600 m,
and the average thickness of pay zone was 61.5 m. The
sands were poorly consolidated with porosity of 28–35%,
and average permeability of 2,600 mD (Han et al. 2006).
The reservoir temperature was about 65�C. The average
well spacing was 370 m. The water cut after polymer flood
reduced by 10%, and 17,700 m3 (111,330 bbl) of incre-
ment oil per well was produced. Till 2010, totally 53
operations of polymer flood have been conducted and the
incremental oil was about 636,000 m3 (4 MMSTB).
East bodo reservoir, Alberta Canada
The East Bodo sandstone reservoir is located in Alberta
and Saskatchewan in Canada. The reservoir had good
permeability (1,000 mD) and oil viscosity was high
(600–2,000 cP). The polymer injection with horizontal
wells was initiated in May 2006. The major challenge was
the quality of source water for mixing polymer solutions.
At the early stage, the maximum polymer viscosity pro-
duced was only 10 cP at 1500 ppm of polymer concen-
tration. No pressure resistance was observed. Later, the
water supply was changed to a fresher water source, and
the polymer solution achieved a much higher viscosity of
60 cP. The wellhead pressure increased to 6,000 kPa
(870 psi) at injection rate of 200 m3/day (1,258 bbl/day).
The production data after polymer flooding was not
reported (Wassmuth et al. 2009).
Fig. 3 Higher polymer viscosity lead to higher oil recoveryFig. 4 Oil Recovery with water flooding followed by polymer
flooding
J Petrol Explor Prod Technol (2011) 1:65–70 67
123
Tambaredjo field, Suriname
The pilot was a sandstone reservoir at 387 m (1,270 ft)
with pressure of 1,724 kPa (250 psi). The net pay zone was
6.7 m (22 ft) thick with porosity of 33% and permeability
of 3–6 Darcy. The live oil viscosity was 400 cP at reservoir
temperature 36�C (97�F). Polymer flood started in Sep-
tember 2008. The polymer concentration in the injected
fluid was 1000 ppm, which produced a viscosity of
44–60 cP. The polymer injection rate was about 32 m3/day
(200 bbl/day), which was 7–10 times less than previous
water injection rate.
Till 2010, totally 0.22 PV of the well pattern has been
injected. Polymer breakthrough occurred at two of the five-
spot wells after approximately 1 year of injection. Analysis
of polymer fluid revealed 7% viscosity reduction from
mixing tank to wellhead. It was thus estimated that 40% of
polymer viscosity was already lost before entering forma-
tion rock. The production response to polymer flood was
not reported (Manichand et al. 2010).
Turkey case study
Bati Raman was a heavy oil field located in southeast
Turkey with oil gravity of 10–15�API. Primary recovery
was only 1.5%, and CO2 flooding improved recovery up to
5%. Polymer solution was injected to improve the sweep
efficiency of CO2. Three injection wells took 10,000 bar-
rels of polymer solution each, and pressure increases were
observed. After injection was complete, the wells were shut
in for a week, and CO2 injection resumed. Increased pro-
duction was observed in 16 production wells after
3 months of injection. The total cost of the polymer
treatment was USD 445,000. The payout time was 1 year
(Topguder 2010).
Oman case study
The Marmul Field in southern Oman was discovered in
1956 and brought on stream in 1980. The OOIP was esti-
mated at 390 million m3 (2,453 MMSTB). Like many
fields in the southern Oman, Marmul was characterised by
heavy, viscous crude oil that was difficult to extract.
The Kalata formation of Marmul field was located at
610 m (2,001 ft) deep with reservoir temperature of 46�C
(115�F). The oil is medium heavy with reservoir viscosity
of 80–110 cP. It was considered a good candidate for
polymer flood.
The first small-scale polymer flood pilot took place
between 1986 and 1988, with one injector well and four
producing Wells. The OOIP of the block was estimated at
190,000 m3 (1,195 MSTB). PAM solution of 1,000 ppm
was injected at a flow rate of 500 m3/day (3,145 barrel/
day). The polymer solution gave a viscosity of 15 cP at
surface under 46�C (115�F).
From May 1986 to September 1986, a water pre-flush of
0.23 PV was injected. A polymer slug of 0.63 PV followed
till August 1987. A water post flush of 0.34 PV was
completed in January 1988. The recovery was 12% at the
end of water pre-flush, 46% at the end of polymer
flood, and 59% at the end of the post flush (Koning et al.
1988).
Because of discoveries in Oman that promised cheaper
extraction costs than the tough Marmul field, the Marmul
polymer project was shelved. Today’s economic conditions
make the various EOR techniques more feasible. Recently
petroleum development Oman (PDO) announced the start
of a large-scale polymer flood project in southern Oman.
PDO estimated that by using polymer flooding it could
raise the total percentage of oil recovered from the reser-
voir to the high 20 s or even low 30 s.
Challenges facing polymer flooding operations
Polymer flood will be more effective if applied early, when
oil saturation is well above residual oil saturation. The
major challenge in polymer flood operations is to maintain
a good polymer viscosity. Water salinity, shear degrada-
tion, thermal degradation and adsorption can severely
damage viscosity of polymer fluid. Other issues facing field
applications included low injectivity, low productivity, and
polymer plugging formations (Thomas 2008).
At Daqing field in China, a field test was performed in
1998 to investigate the effect of water salinity. Waste water
with salinity of 3,800 ppm was used to prepare polymer
solution. The test was conducted in a 395-acre block with
45 wells and OOIP of 4.45 million m3 (28 MMSTB). The
tertiary recovery was much lower compared to adjacent
areas flooded with less saline water (Wang et al. 2002).
For offshore fields, sea water is usually available for
preparing polymer solution. Test data from Dalia field
offshore Angola showed that PAM viscosity decreased
rapidly with increase in water salinity. Moreover, shearing
at the wellhead chokes caused 25–50% of loss in polymer
viscosity (Morel et al. 2008).
Existence of oxygen in polymer solution can severely
degrade polymer viscosity. Therefore, oxygen must be
removed from the polymer solution. Polymers become
unstable at high temperature. Most field applications of
polymer flooding were under reservoir temperatures of less
than 75�C (Du and Guan 2004).
At Daqing field in China, injection wells suffered from
high injection pressure and low injection rate. Fracturing
could only improve injectivity for less than 3 months.
Improved fracturing technology with resin-coated proppant
68 J Petrol Explor Prod Technol (2011) 1:65–70
123
enhanced well injectivity for up to 26 months (Wang et al.
2008).
The low permeability zones at the production wells were
also fractured to increase flow rate and recovery (Wang
et al. 2002). For example, 66 production wells were frac-
tured. After the treatments, the average fluid production
rate per well increased by 41%, and the average oil pro-
duction rate per well increased by 46%.
High polymer viscosity can improve conformance and
recovery. But polymer with too high molecular weight can
plug pore faces (Wang et al. 2002). In a field test, polymer with
molecular weight of 17 million plugged formations with
permeability ranging from 100–200 mD. But the same poly-
mer did not plug another reservoir with higher permeability.
Polymer flood in offshore fields faces more challenges
than that onshore (Raney et al. 2011). These challenges
include costs to transport chemicals, space for mixing
facilities on platform, large well spacing, and reduced
polymer viscosity when mixed with sea water.
In recent years, some operating companies started to
seriously consider EOR methods for offshore fields (Bon-
dor et al. 2005). For example, the Dalia field, 130 km
offshore Angola at water depth of 1,300 m (4,265 ft),
started to undergo polymer flood since February 2010
(Morel et al. 2010).
Conclusions
Past laboratory research showed that polymer could
increase heavy oil recovery by more than 20%. Field cases
in China, Turkey and Oman demonstrated the success of
polymer flooding in heavy oil fields.
In field applications, the major challenge is to maintain
polymer viscosity in surface injection facilities and under
reservoir conditions. Low salinity water should be used to
mix polymer solutions. Surface injection facilities should
be carefully designed to minimize shearing degradation.
It can be concluded that polymer flood is a promising
technology for recovering heavy oil. However, higher
polymer concentration will be required to mobilize heavy
oil. As a result, the cost of polymer will be significantly
higher when polymer flood is applied in heavy oil fields.
Open Access This article is distributed under the terms of the
Creative Commons Attribution License which permits any use, dis-
tribution and reproduction in any medium, provided the original
author(s) and source are credited.
References
Alkafeef AF, Zaid AM (2007) Review of and outlook for enhanced
oil recovery techniques in Kuwait oil reservoirs. IPTC 11234
presented at international petroleum technology conference,
Dubai, UAE, 4–6 December 2007
Asghari K, Nakutnyy P (2008) Experimental results of polymer
flooding of heavy oil reservoirs. Paper 2008-189 presented at the
Canadian international petroleum conference, Calgary, Canada,
17–19 June 2008
Bondor P, Hite J, Avasthi S (2005) Planning EOR projects in offshore
oil field. SPE 94637 presented at Latin American and Caribbean
petroleum engineering conference, Rio de Janeiro, Brazil, 20–23
June 2005
Du Y, Guan L (2004) Field-scale polymer flooding: lessons learnt and
experiences gained during past 40 years. SPE 91787 presented at
SPE international petroleum conference, Puebla, Mexico, 8–9
November 2004
Gao P, Towler B (2011) Investigation of polymer and surfactant-
polymer injections in South Slattery Minnelusa reservoir Wyo-
ming. J Pet Explor Prod Technol 1(1):23–31
Han M, Xiang W, Zhang J, Jiang W, Sun F (2006) Application of
EOR technology by means of polymer flooding in Bohai oil
fields. SPE 104432 presented at SPE international oil and gas
conference and exhibition, Beijing, China, 5–7 December 2006
Koning E, Mentzer E, Heemskerk J (1988) Evaluation of a pilot
polymer flood in the Marmul field Oman. SPE 18092 presented
at annual technical conference and exhibition, Houston, Texas,
2–5 October 1988
Koottungal L (2010) Worldwide EOR survey. Oil Gas J 108(14):41–53
Lake L, Schmidt R, Venuto P (1992) A niche for enhanced oil
recovery in the 1990s. Oilfield Review 4 (1)
Liu M, Wang Y, Liao X, Zhao C, Yang Q, Yan R (2010) Study and
application of profile modification in offshore fields. SPE
133812 presented at SPE Asia Pacific oil and gas conference
and exhibition, Brisbane, Australia, 18–20 October 2010
Manichand R, Mogollon J, Bergwijn S, Graanoogst F, Ramdajal R
(2010) Preliminary assessment of Tambaredjo heavy oilfield
polymer flooding pilot test. SPE 138728 presented at SPE Latin
American and Caribbean petroleum engineering conference,
Lima, Peru, 1–3 December 2010
Meyer R. (2003) Heavy oil and natural bitumen—strategic petroleum
resources. U.S. Geological Survey USGS Fact sheet FS-070-03
Meyer R, Attanasi E, Freeman P (2007) Heavy oil and natural
bitumen resources in geological basins of the world. U.S.
Geological Survey: open-file report 2007-1084
Morel D, Vert M, Jouenne S, Nahas E (2008) Polymer injection in
deep offshore field: the Delia Angola case. SPE 116672
presented at SPE annual technical conference and exhibition,
Denver, Colorado, 21–24 September 2008
Morel D, Vert M, Jouenne S, Gauchet R, Bouger Y (2010) First
polymer injection in deep offshore field Angola: recent advances
on Dalia/Camelia field case. SPE 135735 presented at SPE
annual technology conference and exhibition, Florence, Italy,
19–22 September 2011
Raney K, Ayirala S, Chin R, Verbeek P (2011) Surface and
subsurface requirements for successful implementation of
offshore chemical enhanced oil recovery. OTC 21188 presented
at offshore technology conference, Houston, Texas, 2–5 May
2011
Sheng J (2011) Modern chemical enhanced oil recovery. Gulf
Profession Publishing 2010:101–206
Thomas S (2008) Enhanced oil recovery–an overview. Oil Gas Sci
Technol 63(1):9–19
Topguder N. (2010) A review on utilization of crosslinked polymer
gels for improving heavy oil recovery in Turkey. SPE 131267
presented at SPE/EUROPEC/EAGE annual conference, Barce-
lona, Spain, 14–17 June 2010
Wang J, Dong M (2007) A laboratory study of polymer flooding for
improving heavy oil recovery. Paper 2007-178 presented at the
J Petrol Explor Prod Technol (2011) 1:65–70 69
123
Canadian international petroleum conference, Calgary, Canada,
12–14 June 2007
Wang J, Dong M (2009) Optimum effective viscosity of polymer
solution for improving heavy oil recovery. J Petrol Sci Eng 67(3-
4):155–158
Wang D, Cheng J, Wu J, Wang Y (2002) Producing by polymer
flooding more than 300 million barrels of oil what experiences have
been learnt. SPE 77872 presented at Asia Pacific oil and gas
conference and exhibition, Melbourne, Australia, 8–10 October 2002
Wang D, Zhao L, Cheng J, Wu J (2003) Actual field data show that
production costs of polymer flooding can be lower than water
flooding. SPE 84849 presented at improved oil recovery
conference in Asia Pacific, Kuala Lumpur, Malaysia, 20–21
October 2003
Wang Y, Wang D, Wan J, Luo J, Yu R, Dong Z (2008) New
development in production technology for polymer flooding.
SPE 114336 presented at SPE/DOE improved oil recovery
conference, Tulsa, Oklahoma, 19–23 April 2008
Wang D, Dong H, Lv C, Fu X, Nie J (2009) Review of practical
experience of polymer flooding at Daqing. SPE Reserv Eval Eng
12(3):470–476
Wassmuth F, Arnold W, Green K, Cameron N (2007a) Polymer flood
application to improve heavy oil recovery at east Bodo. Paper
2007-184 presented at Canadian international petroleum confer-
ence, Calgary, Canada, 12–14 June 2007
Wassmuth F, Green K, Hodgins L, Turta A (2007b) Polymer flood
technology for heavy oil recovery. Paper 2007-182 presented at
the Canadian international petroleum conference, Calgary,
Canada, 12–14 June 2007
Wassmuth F, Arnold W, Green K, Cameron N (2009) Polymer flood
application to improve heavy oil recovery at East Bodo. J Can
Pet Technol 48(2):55–61
Zhang Y, Huang S, Luo P (2010) Coupling immiscible CO2
technology and polymer injection to maximize EOR perfor-
mance for heavy oil. J Can Pet Technol 49(5):27–33
Zhou W, Zhang J, Feng G, Jiang W, Sun F, Zhou S, Liu Y (2008) Key
technologies of polymer flooding in offshore oilfield of Bohai
Bay. SPE 115240 presented at SPE Asia pacific oil and gas
conference and exhibition, Perth, Australia, 20–22 October 2008
70 J Petrol Explor Prod Technol (2011) 1:65–70
123
ORIGINAL PAPER - PRODUCTION ENGINEERING
Mathematical modeling of geomechanical behavior of tarmatduring the depletion of giant oil reservoir-aquifer systems
Ayse Pamir Cirdi • Turgay Ertekin •
Luis F. Ayala H. • Ali H. Dogru
Received: 12 April 2011 / Accepted: 2 June 2011 / Published online: 28 June 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract In this work, deformation and failure behavior
of tarmat layers during depletion of a giant reservoir–
aquifer system has been studied. Deformation response of
the tarmat to increasing pressure differential caused by
continuous depletion of reservoir is examined and a
mathematical model is developed for the study of this type
of composite systems. The geomechanical failure that takes
place when the pressure differential reaches a critical value
is also evaluated, along with the characterization of the
resulting fracture. Plate theory, maximum shear stress
failure criterion, conventional well test model, Perkins–
Kern–Nordgren (PKN) and Khristianovic–Geertsma–de
Klerk (KGD) models and flow through fractures models are
used. The developed sensitivity analysis proposes the
proper protocol to be followed in order to undertake pro-
duction design in such composite systems. The methodol-
ogy presented in this paper, ultimately, predicts fracture
width and fracture permeability that would be developed in
a system with a tarmat layer having a certain thickness and
a reservoir being produced at a certain production rate and
total depletion time.
Keywords Geomechanics � Tarmat � Numerical
modeling � Giant oil reservoir � Aquifer
List of symbols
A Cross-sectional area, L2
a, b Dimensions of the drainage area considered, L
B Formation volume factor, dimensionless
c Compressibility, Lt2/M
D Flexural rigidity coefficient, dimensionless
dx, dy, dz Incremental lengths, L
E Modulus of elasticity in tension and compression,
m/Lt2
G Shear modulus, m/Lt2
h Thickness, L
k Absolute permeability, L2
M Bending moment, mL
p Pressure, m/Lt2
q Applied load, m
q Volumetric flow rate, L3/t
rw Wellbore radius, L
t Time, t
V Shear forces, mL/t2
w Displacement (deformation), fracture width, L
x, y, z Coordinate directions
/ Porosity, dimensionless
l Viscosity, m/Lt
k Unit conversion constant (2.637 9 10-4 in
practical field units)
c Unit conversion constant (141.2 in practical
field units)
s Shear stress, m/Lt2
r Stress, m/Lt2
m Poisson’s ratio, dimensionless
Introduction
Oil resources are located in various types of reservoir
formations, varying with properties, dimensions and
A. P. Cirdi � T. Ertekin (&) � L. F. Ayala H.
Penn State University, University Park, PA, USA
e-mail: [email protected]
Present Address:A. P. Cirdi
Halliburton, Houston, TX, USA
A. H. Dogru
Saudi Aramco, Dhahran, Saudi Arabia
123
J Petrol Explor Prod Technol (2011) 1:71–80
DOI 10.1007/s13202-011-0008-4
architectures. Creating feasible production strategies with a
reasonable exploration and development plan is of great
importance in the production of these oil sources. The
process requires a good understanding of oil, reservoir
properties and existing geological architecture of the res-
ervoir of interest. Giant oil fields, being oil sources with
high production potentials, contain more than 500 million
barrels of recoverable oil as they constitute almost 75% of
the recoverable oil resources in the world.
This study focuses on a three-layered composite sys-
tem, typical of giant oil fields in the Middle East. Upper
layer contains mobile reservoir fluids, middle layer is
referred as the tarmat, and the bottom layer is a high
pressure water aquifer. Tarmat is an extremely viscous
hydrocarbon layer, mainly composed of tar or bitumen,
which exists between oil and water contact. In many
cases, the tarmat acts as a permeability barrier between
the reservoir and its aquifer. This composite system is
depicted in Fig. 1.
The main objectives of this study are: (1) the charac-
terization of the geomechanical behavior and eventual
failure of the tarmat layer as a response to hydrocarbon
production and the associated significant increase in pres-
sure differential between the depleting reservoir and its
aquifer; and (2) the evaluation of the system behavior after
geomechanical failure of the tarmat takes place. The latter
part of the analysis involves the characterization of the
fracture and its permeability and the resulting communi-
cation between the aquifer/reservoir system.
Tarmat deformation analysis
By recognizing the tarmat layer as a flat plate with a
thickness significantly smaller than its areal dimensions,
plate theory can be used for the analysis of tarmat defor-
mation. Plate theory extends the findings of the theory of
beams for these types of structural elements (Boresi and
Schmidt 2003; Bickford 1998; Timoshenko and Woi-
nowski-Krieger 1959). The tarmat plate is assumed to be
simply supported having rectangular shapes and lateral
dimensions that are perpendicular to x and y axes.
Deformations can take place in both x and y directions.
Tarmat response under uniform and non-uniform loading
has been studied, and the resulting forces are a conse-
quence of the developed normal and shear stresses. Fig-
ure 2 shows a deformed plate with the resulting forces, the
way they act and their relations with each other. These
forces include bending and twisting moments (M’s), and
shear forces (V), which occur throughout the plane due to
the load (q).
For this system, a balance of forces in x and y directions
yield the following equilibrium equation relating the
resulting moments generated by the applied load (Boresi
and Schmidt 2003):
o2Mx
ox2þ o2My
oy2þ o2Mxy
oyoxþ o2Myx
oxoy¼ q ð1Þ
where q = load applied to the system. A plate subjected to
transverse loading with certain distribution is displaced
perpendicular to its middle plane. Strain–displacement
relations can be derived following the definitions of normal
and shear stresses in terms of plane displacement or
deformation (w), as follows:
Fig. 1 Schematic representation of the system under consideration
Fig. 2 Bending moments, shear forces on deformed plate, force resultants acting on the plate element
72 J Petrol Explor Prod Technol (2011) 1:71–80
123
rx¼�Ez
1�m2
o2w
ox2þm
o2w
oy2
� �; ry¼�
Ez
1�m2
o2w
oy2þm
o2w
ox2
� �
sxy¼�Ez
1�m21�mð Þ o2w
oxoy
� �
ð2Þ
These expressions, when substituted into definitions of
bending and twisting moments, yield:
Mx ¼�Zh=2
�h=2
zrxdz¼Do2w
ox2þ m
o2w
oy2
� �
My ¼�Zh=2
�h=2
zrydz¼Do2w
oy2þ m
o2w
ox2
� �; D¼ Eh3
12 1� m2ð Þ
Mxy ¼�Myx�Zh=2
�h=2
zsxydz¼D 1� mð Þ o2w
oxoy
ð3Þ
where D is referred as flexural rigidity. Expressions in
Eq. 3 can be substituted in Eq. 1 to allow the derivation of
the biharmonic equation, shown below as Eq. 4:
Do4w
ox4þ 2
o4w
ox2oy2þ o4w
oy4
� �¼ q; Dr2 r2w
� �¼ q ð4Þ
In this study, all of the edges of the plate are considered
to have simply supported boundary conditions. There are
two main conditions to be satisfied by simply supported
edges. First, the displacement (w) must be equal to zero at
the edges and any moment that coincides in direction with
the direction of the edge must be equal to zero. Therefore,
the following boundary conditions are to be satisfied by the
y = constant and x = constant edges:
y - constant: w ¼ 0; My ¼ Do2w
oy2þ m
o2w
ox2
� �¼ 0
x - constant: w ¼ 0; Mx ¼ Do2w
ox2þ m
o2w
oy2
� �¼ 0
ð5Þ
The biharmonic equation, the fourth degree differential
equation in Eq. 4, can thus be solved with these four boundary
conditions and a relevant loading expression, to obtain the
expression for transverse deformation w(x,y). For the case of a
uniform loading, for example, the following solution can be
found for plate transverse deformation:
wðx; yÞ ¼ 16q0
p6D
Xm;odd
Xn;odd
sin mpxa sin npy
b
mn ma
� �2þ nb
� �2� �2
ð6Þ
Once the transverse deformation is found, stresses and
bending and twisting moments and twisting moments
across the plate can be calculated using Eqs. 2 and 3.
Tarmat failure analysis
In order to evaluate the tarmat behavior at the moment of
geomechanical failure, tarmat deformation analysis should
be coupled with a failure criterion. There are a number of
theories that predict failure as a function of prevailing
stresses. For example, the maximum shear stress failure
theory, as originally developed by Charles Coulomb and
Henry Tresca, indicates that the failure point is reached
when the maximum shear stress in the material becomes
equal to the value of the shear stress at yielding. This point,
which indicates the occurance of failure is referred as yield
strength. Yield strenght is a property of the material which
needs to be experimentally determined by uniaxial com-
pression or uniaxial tension test. The Mohr–Coulomb
failure (internal friction) criterion is another common way
of evaluating failure by relating shearing resistance to
contact forces, friction and cohesion that is present among
the rock grains and it is deemed to be appropriate for the
prediction of failure in brittle materials. Other failure cri-
teria include the maximum normal stress failure criterion,
Hoek–Brown failure criterion, Von Mises failure criterion,
and the octahedral shear stress theory, among others.
If the maximum shear stress failure criterion is utilized,
principle stresses must be calculated for the material. They
can be estimated by implementing Eq. 7 below:
r1;2 ¼ �rx þ ry
2�
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirx � ry
2þ s2
xy
rð7Þ
In this equation, maximum values for the stresses must
be used. In a simply supported plate, these occur at the
center of the structure. At the center of the plate, maximum
stresses are given by the expressions:
rxð Þmax¼ �6Mx
h2; ry
� �max¼ � 6My
h2;
sxy
� �max¼ � 6Mxy
h2
ð8Þ
It can be shown that for the case of interest,
r2 r1h 0h ; r3 ¼ 0 ð9Þ
Therefore, if r2j j exceeds rYS of the material, failure
occurs (Gere 2001; Bickford 1998).
Fracture width and fracture permeability analysis
For the purpose of fracture width analysis, two different
hydraulic fracturing models have been used: the Perkins–
Kern–Nordgren (PKN) and the Khristianovich–Zheltov–
Geertsma–deKlerk (KGD) models. They relate fracture
width to properties of fluid and rock in the fractured sys-
tem. The working fluid in our model is the aquifer water
and the rock is represented by the tarmat. In both models,
J Petrol Explor Prod Technol (2011) 1:71–80 73
123
the most influential fluid properties are viscosity and spe-
cific gravity and influential rock properties are Poisson’s
ratio, Young’s modulus of elasticty. Additional variables of
importance are fluid injection rate and fracture length.
Fracture thickness is a property that is not influential in
PKN model but is influential in KGD model. Inputs into the
analysis protocol used in this study are viscosity and spe-
cific gravity of water, Poisson’s ratio and Young’s Modulus
of Elasticiy of tarmat, reservoir production rate and
thickness of tarmat. Reservoir production rate is assumed
close to fluid injection/breakthrough rate since both are
expected to create a similar pressure differential in mag-
nitude and direction.
The problem is thus approached as an inverse problem,
in which fracture width is estimated as a function of res-
ervoir production rate. In this problem, thickness of tarmat
represents the fracture penetration length. In the hydraulic
fracturing analog, fracture length is the parameter that
helps to express the penetration of the crack created while
in the case of our interest, the target crack penetration is the
tarmat thickness. Fracture thickness in the KGD model is
assumed to correspond to this fracture length. Both the
PKN and KGD models are shown to be in agreement when
the fracture thickness is assumed to be as long as the line
that is drawn at the points on the plate where shear stress is
99% of the maximum shear stress.
The expressions for fracture width calculation for the
PKN and KGD models are presented below in Eq. 10,
respectively:
w ¼ 0:3ql 1� vð Þ h0=2ð Þ
G
1=4 p4
c� �
; G ¼ E
2 1þ vð Þ
w ¼ 0:29ql 1� vð Þ h0=2ð Þ2
Ghf
" #1=4p4
� �ð10Þ
In these expressions, G is the shear modulus. Figure 3
explains fracture thickness and fracture length orientation
for a hydraulic fracturing case and the problem studied
here.
Once fracture width is estimated, the associated fracture
permeability can be calculated. For example, fracture
permeability can be related to fracture width by equaling
the Poiseuille’s Law in parallel plates to Darcy’s law in
porous media (Craft and Hawkins 1959) which yields the
expression:
q ¼ P1 � P2ð ÞA0w2
12lh0
; k ¼ 54� 106w2 ð11Þ
A similar expression can be independently derived by
considering the case of the flow of hydraulic fracturing
fluids through induced fractures (Yew 1997). Yew (1997)
assumed that fractures have a narrow opening of constant
width all through the fracture thickness. If the flowing fluid
is assumed to be an incompressible Newtonian fluid, Yew
(1997) shows that fracture width and permeability can be
related by Eq. 12:
w2
12¼ k; k ¼ 5:45� 107w2 ð12Þ
Reservoir depletion and pressure transient model
At this stage of the analysis, reservoir depletion must be
considered in order to recreate the magnitude of the load
placed on the tarmat place. In order to relate pressure
depletion with time evolution, the standard computational
procedure of classical well test model is followed (Ear-
lougher 1977; Lee 1982). Reservoir is single phase and
square-shaped. Well is assumed to be located at the center
of the drainage area. In this procedure, dimensionless time
is converted to actual time and dimensionless pressure is
converted into actual pressure. Dimensionless production
rate is used as an intermediate step in these calculations.
The solutions for dimensionless pressure drop (pd) versus
Fig. 3 Fracture length, fracture width and fracture thickness in a hydraulic crack
74 J Petrol Explor Prod Technol (2011) 1:71–80
123
dimensionless time (td) tabulated by Earlougher (1977) for
the case pressure variation at the center of the rectangular-
shape reservoirs are utilized. Equations 13, 14 and 15 give
the expressions for dimensionless production rate, dimen-
sionless pressure and dimensionless time, respectively:
qD ¼cBqplkhPi
ð13Þ
DPD ¼Pi � P
PiqD
ð14Þ
tD ¼kkt
/lcr2w
; tDA ¼ tD
r2w
A; tDA ¼
kkt
/lcAð15Þ
Results and discussions
Tarmat failure analysis
Figure 4 shows the expected deformation response as a
function of an uniformly applied loading along with the
associated failure envelope for two reservoir scenarios with
different properties. In these figures, deformation versus
loading behavior is investigated until the point where
maximum shear stress failure criterion predicts geome-
chanical failure. The rectangular plate deformation model
is used to model the behavior of the tarmat. In these figures,
it is readily seen that thicker the tarmat, the larger the
pressure drop required to trigger geomechanical failure. At
the same time, the thinner the tarmat, the larger the
deformation experienced by the tarmat prior to the onset of
failure. Inspection of Fig. 4 reveals that as the Young’s
modulus of elasticity and yield strength becomes larger, the
pressure differential required for the tarmat to fail increases
while its deformation is expected to slightly decrease.
Figure 5 displays the magnitude and nature of the
effects caused by the principal parameters of this analysis
on failure pressure including lateral dimensions, yield
strength and Poisson’s ratio of the tarmat. Each of the
figures is drawn considering critical pressures and
deformations that occur until critical pressure is reached. It
is observed that in smaller drainage areas, more pressure
differential is required to fail tarmat, tarmat having higher
yield strength, requires more pressure differential until
failure and tarmat with smaller Poisson’s ratios, requires
more pressure differential until the failure point. All of
these parameters indicate a direct proportionality with
tarmat thickness and magnitude of pressure required to fail
the tarmat.
Figure 6 displays a comparison between deformation
versus loading and associated failure envelope of uniform
loading (a) and non-uniform loading (b). For a tarmat with
a certain thickness, lateral dimensions, Young’s modulus of
elasticity, Poisson’s ratio and yield strength, more pressure
differential is required to observe failure in the case of non-
uniform loading. A comparison of Fig. 6a and b reveals a
slightly more deformation in the case of a uniform loading.
Figure 7 displays a comparison between loading versus
thickness for different lateral dimensions of tarmat in the
cases of uniform loading (a) and non-uniform loading (b);
respectively. A similar comparison can be made for yield
strength and Poisson’s Ratio effects. For a tarmat of certain
influential properties more pressure differential is required
to observe geomechanical failure in the case of non-uni-
form loading.
Reservoir depletion model
This study has been conducted for two different drainage
area assumptions. In each case, production rate has been
varied between 1,000 and 10,000 STB/day. Reservoir
properties assigned in this analysis are given in Table 1
below.
Figure 8 provides a comparison of different drainage
area assumptions while production rate influences on
pressure and time relationship can also be observed. Fig-
ure 8a and b represent the analysis with drainage area
assumption of 51.65 and 200 acres. As production rate
increases, a certain pressure differential is reached in a
shorter period of time. For reservoirs with smaller drainage
0
5
10
15
20
25
30
Δ P, psi
(a)
Δh
, ft
0
5
10
15
20
25
30
0 1,000 2,000 3,000 0 1,000 2,000 3,000
ΔP, psi
(b)
Δh
, ft
Fig. 4 Deformation versus
loading with associated failure
envelope. a E = 3,000,000 psi,
rYS = 30,000 psi,
a = b = 750 ft, v = 0.30,
b E = 5,500,000 psi,
rYS = 50,000 psi,
a = b = 750 ft, v = 0.30
J Petrol Explor Prod Technol (2011) 1:71–80 75
123
areas, it takes less time to reach a certain pressure differ-
ential than it does for those with larger drainage areas.
Fracture permeability characterization
In PKN and KGD models, which are used to predict
fracture width, production rate from the reservoir above
that would make a similar effect as injection rate from the
aquifer below has been used as an input flow rate. The
production rates that have been used in the analysis with
conventional well test model is used in this part of the
study. The production rates are changed between 1,000 to
10,000 STB/day. The same analysis that is relating pro-
duction rate and width has been repeated for a possible
0
1,000
2,000
3,000
4,000
5,000
6,000
ho, ft
(a)
ΔP
, psi
a=b=500 ft
a=b=600 ft
a=b=750 ft
a=b=1,100 ft
a=b=1,500 ft
a=b=4,000 ft
E=4,000,000 psiσYS=40,000 psiv =0.30
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
ho, ft
(b)
Δ P, p
si
σYS=30,000 psi
σYS=15,000 psi
σYS=50,000 psi
σYS=75,000 psi
σYS =100,000 psi
E=4,000,000 psiv =0.3a=b=750 ft
0
500
1,000
1,500
2,000
2,500
3,000
20 40 60 80 100 120
20 40 60 80 100 120 20 40 60 80 100 120
ho, ft
(c)
ΔP
, psi
v =0.10
v =0.50v =0.40
v =0.30
v =0.20E=4,000,000 psiσYS=40,000 psia=b=750 ft
Corresponding Drainage Areas
(500 ft)2=5.75 acres (600 ft)2=8.28 acres (750 ft)2=12.94 acres (1,100 ft)2=27.83 acres (1,500 ft)2=51.65 acres (4,000 ft)2=368.00 acres
Fig. 5 a Loading versus thickness for various lateral dimensions
(E = 4,000,000 psi, rYS = 40,000 psi, v = 0.30). b Loading versus
thickness for various yield strengths (E = 4,000,000 psi, v = 0.30,
a = b = 750 ft). c Loading versus thickness for various Poisson’s
ratios (E = 4,000,000 psi, rYS = 40,000 psi, a = b = 750 ft)
0
10
20
30
Δ h, f
t
ΔP, psi
0
10
20
30
0 1,000 2,000 3,000 4,000 5,000 0 2,000 4,000 6,000 8,000
Δh
, ft
ΔP, psi
(a) (b)
Fig. 6 Comparison of deformation versus loading with associated failure envelope with a uniform, and b non-uniform loading assumption
(E = 8,000,000 psi, rYS = 75,000 psi, a = b = 750 ft, v = 0.30)
76 J Petrol Explor Prod Technol (2011) 1:71–80
123
range of tarmat thicknesses varying between 30 and 100 ft.
Figure 9 includes the relationship between fracture width
and production rate for PKN and KGD models, for various
properties and relationship between fracture permeabil-
ity and fracture width. It should be noted that Eq. 1
refers to the first method and Eq. 2 refers to the second
method.
In both models, Young’s modulus of elasticity is
observed to be inversely proportional with fracture width.
A system with known properties encounters a wider
fracture width if the reservoir at the top of the system is
being produced with a higher production rate. Wider
fracture widths would be created in systems with thicker
tarmat layers. PKN model predicts larger widths than
KGD does. Difference in this prediction is largest in
systems with high reservoir production rates and thick
tarmat layers.
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
ho, ft
ΔP
, psi a=b=500 ft
a=b=600 ft
a=b=750 ft
a=b=1,100 fta=b=1,500 fta=b=4,000 ft 0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
20 40 60 80 100 120 140 20 40 60 80 100 120 140
ho, ft
ΔP
, psi
a=b=500 ft
a=b=600 ft
a=b=750 ft
a=b=1,100 ft
a=b=1,500 ft
a=b=4,000 ft
(a) (b)
Fig. 7 Comparison of loading versus thickness graphs for various lateral dimensions with uniform and non-uniform loading assumption
Table 1 Hydrocarbon reservoir properties
Property Value Unit
l 0.72 cp
Ø 0.25 fraction
B 1.3 rb/stb
k 400 md
h 200 ft
c 0.0000015 psi-1
rw 0.5 ft
Pi 9,000 psi
Fig. 8 Pressure differential versus time differential graphs for various flow rates. a Cross-sectional area = 51.65 acres, b cross-sectional
area = 200 acres
J Petrol Explor Prod Technol (2011) 1:71–80 77
123
Coupled analysis protocol
This part of the section outlines the methodology followed
in this study coupling each individual step. Suggested
protocol is explained through the use of a composite sys-
tem. Properties of each layer of the composite system are
given in Table 2.
First step involves construction of deformation versus
loading with associated failure envelope. This relation is
dependent on Young’s modulus of elasticity, yield
strength, Poisson’s ratio and lateral dimensions of the
tarmat. Figure 10a represents the outcome of the study on
this relationship. By entering the chart at the 80 ft tarmat
thickness line, magnitudes of deformation and pressure
are found to be 15 ft and 432 psi, respectively, at the time
of failure. Second step involves the use of conventional
well test model to obtain the relationship between pres-
sure differential and time, for various flow rates within
the range chosen. Figure 10b represents the results of this
analysis (data used in this analysis are from the hydro-
carbon reservoir part of Table 2). Two different times
chosen are 3 and 7 days. In the analysis, the failure
pressure of 432 psi from the first stage is used with the
production rates for 3 and 7 days as 5,000 and
2,000 STB/day, respectively. This is followed with the
fracture width determination and permeability analysis
using the PKN and KGD models. A selected range of
production rates and tarmat thicknesses are considered.
Relation between fracture width and production rate is the
output of Figure 11 is the output (data is presented in
tarmat and fluid sections of Table 2). The 80 ft thickness
from family of thickness curves in PKN and KGD models
0.006
0.014
0.022
0.030
q, STB/d
w, i
n
0.006
0.014
0.022
0.030
q, STB/d
w, i
n
0.006
0.014
0.022
0.030
0 0q, STB/d
w, i
n
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
0 2,000 4,000 6,000 8,000 10,00
0 2,000 4,000 6,000 8,000 10,000 12,00 0 2,000 4,000 6,000 8,000 10,000 12,000
12,00 0.0000 0.0100 0.0200 0.0300 0.0400
w, in
k, d
arcy
equation 1 equation 2
(a)
(c) (d)
(b)
Fig. 9 Width versus production rate graphs for various tarmat
thicknesses for PKN and KGD models. a E = 3,000,000 psi,
v = 0.30, hf = 47.82 ft, b E = 5,500,000 psi, v = 0.30,
hf = 47.82 ft, c E = 3,000,000 psi, v = 0.30, hf = 47.82 ft, d frac-
ture permeability versus fracture width
78 J Petrol Explor Prod Technol (2011) 1:71–80
123
is selected. Fracture widths for 2,000 STB/day are pre-
dicted to be 0.0140 and 0.0130 in. Fracture widths for
5,000 STB/day are predicted to be 0.0180 and 0.0165 in;
respectively. Final step of the analysis is determination of
the permeability as related to the fracture widths. Average
values of fracture widths of 0.0135 and 0.0173 in yield
fracture permeabilities of 10,500 and 16,000 darcy,
respectively (Fig. 12).
Summary and conclusions
In this study, we have examined the tarmat deformation
and failure behavior of a giant oil reservoir-aquifer system
undergoing a depletion process. The fracture that develops
after failure is characterized and its permeability is deter-
mined. In the analysis, plate theory, maximum shear stress
failure criterion, classical well test analysis theory, PKN
model, KGD model, and fracture flow models are used. A
sensitivity analysis is conducted by varying the reservoir,
rock and fluid properties. The proposed methodology,
predicts fracture width and fracture permeability that
would be created in a system with a tarmat layer of certain
thickness as a function of rate of depletion and total
depletion time. In the proposed analysis protocol, each
analysis step focuses on the behavior of a layer individu-
ally. As an alternative approach the composite system in its
entirety can be analyzed by coupling of each layer. This
will allow computation of the fracture penetration rate
through the tarmat layer as a function of time. Also, as a
continuation of the work presented in this paper, we would
like to take the proposed solution one step further by
integrating the formulated geomechanical model with the
fluid flow (and/or heat flow) models so that all of the
unknowns are solved simultaneously.
Within the bounds of the analysis protocol presented in
this paper, following conclusions are drawn:
1. As thickness of tarmat increases, total deformation that
occurs until the failure point decreases, and pressure
differential that is required to fail the tarmat increases.
2. As Young’s modulus of elasticity and yield strength of
tarmat increase, pressure differential that is required to
fail tarmat increases, and magnitude of deformation
that occurs until failure of tarmat decreases.
Table 2 Properties of composite system
Property Value Unit
Hydrocarbon reservoir
A 51.65 acres
2,250,000 ft2
l 0.72 c
Ø 0.25 fraction
B 1.3 rb/stb
k 400 md
h 200 ft
c 1.5E-06 psi-1
rw 0.5 ft
Pi 9,000 psi
Tarmat
v 0.3 –
E 8,000,000 psi
a 1,500 ft
b 1,500 ft
h 80 ft
rYS 30,000 psi
Fluid
c 1 –
l 1 cp
0
15
30
45
0 200 400 600 800
ΔP, psi
Δh,
ft
E=8,000,000 psiσYS=30,000 psiv =0.30
a=b=1 500 ft
h=30 ft
h=40 ft
h=50 ft
h=60 fth=70 ft
h=80 fth=90 ft
h=100 ft
0
100
200
300
400
500
600
011
Δ t, days
ΔP
, psi
q=1,000 STB/d
q=2,000 STB/d
q=3,000 STB/d
q=4,000 STB/d
q=5,000 STB/d
q=6,000 STB/d
q=7,000 STB/d
q=8,000 STB/d
q=9,000 STB/d
q=10,000 STB/d
1 2
(a) (b)
Fig. 10 a Deformation versus loading with associated failure envelope (E = 8,000,000 psi, rYS = 30,000 psi, a = b = 1,500 ft, v = 0.30).
b Pressure differential versus time differential graphs for various flow rates (cross-sectional area = 51.65 acres)
J Petrol Explor Prod Technol (2011) 1:71–80 79
123
3. As lateral dimensions of tarmat increase, pressure
differential that is required to fail the tarmat decreases.
4. As yield strength of tarmat increases, pressure differ-
ential that is required to fail the tarmat increases.
5. As Poisson’s ratio of tarmat increases, pressure
differential that is required to fail the tarmat decreases.
6. A case of non-uniform loading requires more pressure
and the system experiences less deformation until
failure as compared to a similar case with uniform
loading configuration.
7. The PKN model predicts larger fracture widths than
the KGD model does. The difference in predictions
becomes more obvious in the presence of thick tarmat
layers and high production rates.
8. The PKN and the KGD models predict wider fracture
widths for higher reservoir production rates and thicker
tarmat layers.
Open Access This article is distributed under the terms of the
Creative Commons Attribution License which permits any use,
distribution and reproduction in any medium, provided the original
author(s) and source are credited.
References
Bickford WB (1998) Advanced mechanics of materials. Addison-
Wesley, Menlo Park
Boresi AP, Schmidt RJ (2003) Advanced mechanics of materials.
Wiley, Hoboken
Craft BC, Hawkins MF (1959) Applied petroleum reservoir engi-
neering. Prentice Hall, Upper Saddle River
Earlougher RC Jr (1977) Advances in well test analysis, society of
petroleum engineers of AIME. Dallas, TX
Gere JM (2001) Mechanics of materials, 5th edn. Brooks-Cole,
Pacific Grove
Lee J (1982) Well testing, society of petroleum engineers of AIME.
Dallas, TX
Timoshenko S, Woinowski-Krieger S (1959) Theory of plates and
shells. McGraw Hill, Hightstown
Yew CH (1997) Mechanics of hydraulic fracturing. Gulf Publishing
Company, Houston
0.006
0.010
0.014
0.018
0.022
0.026
0.030
q, STB/d
w, i
n
PKN modelE=8,000,000 psiv =0.30hf =47.82 ft
2
1
0.006
0.010
0.014
0.018
0.022
0.026
0.030
0 4,000 8,000 12,000 0 4,000 8,000 12,000
q, STB/d
w, i
n
KGD modelE=8,000,000 psiv =0.30hf=47.82 ft
2
1
(a) (b)Fig. 11 Width versus
production rate graphs for
various tarmat thicknesses
(PKN and KGD model)
(E = 8,000,000 psi, v = 0.30,
hf = 47.82 ft)
0
10,000
20,000
30,000
40,000
50,000
60,000
0.0000 0.0100 0.0200 0.0300 0.0400
w, in
k, d
arcy
equation 1 equation 2
1 2
Fig. 12 Fracture permeability
versus fracture width
80 J Petrol Explor Prod Technol (2011) 1:71–80
123
ORIGINAL PAPER - PRODUCTION ENGINEERING
Prediction of reservoir performance in multi-well systems usingmodified hyperbolic model
Y. B. Adeboye • C. E. Ubani • O. Oribayo
Received: 29 March 2011 / Accepted: 13 August 2011 / Published online: 15 September 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract Decline curve analyses are usually based on
empirical Arps’ equations: exponential, hyperbolic and
harmonic decline. The applicable decline for the purpose of
reservoir estimates is usually based on the historical trend
that is seen on the well or reservoir performance. This
remains an important tool for the reservoir engineer, so that
the practice of decline curve analysis has been developed
over the years through both theoretical and empirical
considerations. Despite the fact that the fundamental
principles are well known and understood, there are aspects
which can still lead to a range of forecast and reserve
estimates that until now have not been investigated. In this
work, a model was developed considering the effect of well
aggregation and interference in multi-well systems. This
approach accounts for the entire production history of the
well and the reservoir, and thus reduces the influence of
well interference effects on decline curve analysis. It pro-
vides much better estimates of reserves in multi-well sys-
tems. The models were validated with field data from
different wells. Production decline data from different
wells in a reservoir were analyzed and used to demonstrate
the application of the developed model.
Keywords Decline curve � Well aggregation �Interference � Forecast � Reserve estimates
List of symbols
NP Production (liter)
qi Initial oil production rate (liter/year)
b Constant
Di Constant
q Oil production rate (liter/year)
t Production time
NPx Cumulative oil production (liter)
qx Cumulative oil production rate (liter/year)
tx Cumulative production time (year)
DCA Decline curve analysis
Introduction
Production of hydrocarbons declines due to a decline in
reservoir energy and/or increases in producing water cut.
Graphical plots of performance data provide a time-tested,
frequently used technique known as ‘‘decline curve’’ for
estimating ultimate recovery and/or reserves to be expected
from a well, reservoir or field.
Decline curve analysis is used for analyzing declining
production rates and forecasting future performance of oil
and gas wells. Forecasting future production is essential in
economic analysis of exploration and production expendi-
tures. Hence, the analysis of production decline curves
represents a useful tool for forecasting future production
from wells and reservoirs. The basis of this procedure is
that factors which have affected production in the past will
continue to do so in future.
Y. B. Adeboye (&)
Department of Petroleum and Gas Engineering,
University of Lagos, Akoka, Yaba, Lagos, Nigeria
e-mail: [email protected]
C. E. Ubani
Department of Petroleum and Gas Engineering,
University of Port-Harcourt, Port-Harcourt, Nigeria
O. Oribayo
Department of Chemical Engineering,
University of Lagos, Akoka, Yaba, Lagos, Nigeria
123
J Petrol Explor Prod Technol (2011) 1:81–87
DOI 10.1007/s13202-011-0009-3
Most conventional decline curve analyses are based on
the classic works of Arps (1970) and Fetkovich (1980),
which illustrate the analysis of well performance data using
empirically derived exponential, harmonic and hyperbolic
functions. Although the study of Arps (1970) is completely
empirical, its simplicity and the fact that it requires no
knowledge of reservoir or well parameters make its use
widespread in the upstream petroleum industry, particu-
larly for production prediction and estimating reserves
from production decline behavior. However, our observa-
tion is that the Arps’ method completely ignores the
flowing pressure data, does not account for changing pro-
duction conditions and changing gas properties with time
(reservoir pressure); thus, it yields inconsistent results
(unreliable matches and poor extrapolation).
Regarding the research works of Fetkovich (1980) and
Fetkovich et al. (1998), we noticed that their works discuss
the use of Arps’ hyperbolic relations and that they do
provide a semi-analytical result for gas flow behavior
which, unfortunately, is never valid in practice. To address
the impact of pressure-dependent gas properties on the
evaluation of gas production data, Fraim and Watten
Barger (1987) presented a decline type curve for gas res-
ervoir systems. Although the Fraim and Watten Barger
(1987) approach is more rigorous than simply using the
hyperbolic model, the Fraim solution is not universal. The
decline type curves not only permit forecast of well per-
formance, but also estimate reservoir properties (i.e., flow
capacity in kh) as well as oil in place.
The Fetkovich method was improved upon by the
introduction of two additional type curves, which were
plotted concurrently with the normalized rate type curves:
the rate integral function and derivative function, which
help in smoothing the often noisy character of production
data and in obtaining a more unique match (Blasingame
et al. 1991). The Blasingame et al. (1991) method is similar
to that of Fetkovich in that they use type curves for pro-
duction data analysis. However, the primary difference is
that the modern method incorporates the flowing pressure
data along with production rates and use analytical solu-
tions to calculate hydrocarbons in place.
McCray (1990) developed a time function that would
transform production data for systems exhibiting variable
rate or pressure drop performance into an equivalent sys-
tem produced at a constant bottom-hole pressure, which
was extended by Blasingame et al. (1991) to an equivalent
‘‘constant rate’’ analysis approach. The issue of variable,
non-constant bottom-hole pressures in gas wells was
addressed by Palacio and Blasingame (1993). They intro-
duced new methods, which use a modified time function
for analyzing the performance of single phase liquid or gas
wells. One of the shortcomings of this method is that it
completely ignores the flowing pressure data; thus, when
applied, there is always underestimation or overestimation
of reserves. Besides, it does not account for changing
production conditions and thus cannot always provide a
reliable estimate of recoverable hydrocarbons in place, and
changing gas properties with time (reservoir pressure) are
not accounted for; thus, gas reserves are usually
underestimated.
Fetkovich et al. (1998) was the first to apply the concept
of using type-curves to transient production. The research
methodology of Fetkovich (1980) and Fetkovich et al.
(1998) was the same as that of Arps (1970) depletion for
the analysis of boundary-dominated flow and constant
pressure type curves originally developed by Van Everd-
ingen and Hurst for transient production. Type-curve
matching is essentially a graphical technique for visual
matching of production data using pre-plotted curves on a
log–log paper. The most valuable feature of type curves
lies not in the analysis, but in the diagnostics. Fetkovich
et al. (1998) presented the theoretical basis for Arps’ pro-
duction decline models using the pseudo-steady state flow
equation. The decline type curves not only permit forecast
of well performance, but also estimate reservoir properties
(i.e., flow capacity in kh) as well as oil in place.
The Fetkovich method was improved upon by the
introduction of two additional type curves, which were
plotted concurrently with the normalized rate type curves
that help in smoothing the often noisy character of pro-
duction data and in obtaining a more unique match
(Blasingame et al. 1989). McCray TL (1990) developed a
time function that would transform production data for sys-
tems exhibiting variable rate or pressure drop performance
into an equivalent system produced at a constant bottom-hole
pressure, which was extended by Blasingame et al. (1991) to
an equivalent ‘‘constant rate’’ analysis approach.
The issue of variable, non-constant bottom-hole pressures
in gas wells was addressed by Palacio and Blasingame
(1993). They introduced a new method which uses a modi-
fied time function for analyzing the performance of single
phase liquid or gas wells. The method of Blasingame et al.
(1991) is similar to that of Fetkovich in that they use type
curves for production data analysis. However, the primary
difference is that the modern method incorporates the
flowing pressure data along with production rates and use
analytical solutions to calculate hydrocarbons in place.
Rodriguez and Cinco-Ley (1993) developed a model for
production decline in a bounded multi-well system. The
primary assumptions in their model are that the pseudo-
steady state flow condition exists at all points in the res-
ervoir and that all wells produce at a constant bottom-hole
pressure. They concluded that the production performance
of the reservoir was shown to be exponential in all cases, as
long as the bottom-hole pressures in individual wells were
maintained constant. Camacho et al. (1996) improved the
82 J Petrol Explor Prod Technol (2011) 1:81–87
123
Rodriguez–Cinco-Ley model by allowing individual wells
to produce at different times.
Valko et al. (2000) presented a ‘‘multi-well productivity
index’’ concept for an arbitrary number of wells in a
bounded reservoir system. Li and Home (2005) and Guo
et al. (2007) proposed semi-analytical, direct solutions for
determining average reservoir pressure, rate and cumula-
tive production for gas wells produced at a constant bot-
tom-hole flowing pressure. These authors also assumed the
existence of pseudo-steady state flow, but proved that the
concept was valid for constant rate, constant pressure or
variable-rate/variable pressure production.
Despite the wide use of decline curve analysis and type-
curve matching of oil well, they sometimes over-predict or
underestimate reserves. The subjectivity of other methods
along with the need for pressure data necessitates the
development of our model, which does not require pressure
data and also eliminates the subjectivity of the analysis.
The specific objectives of this paper are to:
• develop a model to estimate reserve and predict
reservoir performance for multi-well reservoir system
using production data analysis;
• demonstrate the applicability of the newly developed
model by validating it with existing models and field
data.
Model development
The new model is a modification of that used by Arps.
The basic assumptions are:
1. Whatever causes controlled the trend of a curve in the
past will continue to govern its trend in the future in a
uniform manner.
2. According to Fetkovich, if production from each well
in a reservoir or field followed the exponential decline
solution, the total decline curve analysis production
from the reservoir or field would be better estimated
using hyperbolic decline model.
A hyperbolic decline occurs when the decline rate is no
longer constant. Compared to exponential decline, the
following two hyperbolic decline curve equations estimate
a longer production life of the well.
For hyperbolic decline
NP ¼qb
i
ðb� 1ÞDifðq1�b � q1�b
i Þg ð2:1Þ
and
q ¼ qi
ð1þ bDitÞ1b
ð2:2Þ
Combining Eq. 2.1 with 2.2 yields the expression given
as
NP ¼qb
i
ðb� 1ÞDi
qi
ð1þ bDitÞ1b
!1�b
�q1�bi
8<:
9=; ð2:3Þ
Further simplification of Eq. 2.3 yields the equations:
NP ¼qb
i
ðb� 1ÞDiðqiÞ1�b ð1þ bDitÞ
b�1b � 1
� �n oð2:4Þ
NP ¼qi
ðb� 1ÞDið1þ bDitÞð1þ bDitÞ
�1b
h i� 1Þ
n oð2:5Þ
NP ¼qi
ðb� 1ÞDifð1þ bDitÞð
q
qi� 1Þg ð2:6Þ
NP ¼1
b� 1ð ÞDi1þ bDitð Þðq� qiÞf g ð2:7Þ
NP ¼1
ðb� 1ÞDifðqþ qbDit � qiÞg ð2:8Þ
NPðb� 1ÞDi ¼ fðqþ qbDit � qiÞg ð2:9ÞNPðb� 1ÞDi þ qi ¼ qf1þ bDitg ð2:10Þ
q� NPðb� 1ÞDi þ qi
f1þ bDitgð2:11Þ
Equation 2.11 is derived from the hyperbolic solution,
but can be used for both the exponential and harmonic
solution; thus, the developed equation is a general
equation.
When cumulative production (Np) is expressed in terms
of the previous cumulative production (Npx) and production
rate q over a period of time, the equation obtained is given
as
Np ¼ NPx þ qðt � txÞ ð2:12Þ
Substituting for Np in Eq. 2.11 gives
q� ðNPx þ qðt � txÞÞðb� 1ÞDi þ qi
f1þ bDitgð2:13Þ
qf1þ bDitg ¼ ðNPx þ qðt � txÞÞðb� 1ÞDi þ qi ð2:14Þqf1þ bDitg ¼ NPxðb� 1ÞDi þ qðt � txÞðb� 1ÞDi þ qi
ð2:15Þqf1þ bDitg � qðt � txÞðb� 1ÞDi ¼ NPxðb� 1ÞDi þ qi
ð2:16Þqfð1þ bDitÞ � ½ðt � txÞðb� 1ÞDi�g ¼ NPxðb� 1ÞDi þ qi
ð2:17Þ
J Petrol Explor Prod Technol (2011) 1:81–87 83
123
Rearranging Eq. 2.17 yields
q ¼ NPxðb� 1ÞDi þ qi
fð1þ bDitÞ � ½ðt � txÞðb� 1ÞDi�gð2:18Þ
By simplifying the denominator and if t - tx & t, then
q ¼ qi þ NPxðb� 1ÞDi
1þ tDið2:19Þ
In the case of forecast or prediction of reservoir
performance for a multi-well system, Eq. 2.19 can be
used, but Di is replaced by Dt
Then Eq. 2.19 is the modified hyperbolic model that can
be used to calculate the future production rate based on the
initial production rate qt, previous cumulative production
Npx, and constants Dt and b for a multi-well reservoir
system. The procedure for determining model parameters,
i.e., Di- and b-values is the same as that in the hyperbolic
model and is shown in Appendix A
Model validation
In this study, the basic principle/fundamental concept used
is that of Arps’ model; hence, result from the developed
model is validated with Arps’ exponential and hyperbolic
model using the production data from reservoirs (A and B)
given below as case study.
Reservoir A: case study
This reservoir is an integrated oil and gas reservoir with
major oil reserves with two wells drilled through it and still
producing up to date. The off-take built up rapidly from
2001 and reached a peak of 4852.64 stb/d by August 2001.
Subsequently, off-take has shown natural decline from the
wells. The predominant drive mechanism is both the aquifer
and gravity; hence the values of b ranging from 0.5–0.8 will
be acceptable for DCA. There is currently pressure main-
tenance and artificial lift scheme in this reservoir due to the
high viscosity of the oil. In this multi-well reservoir, the
producing drainage points do not display any visible decline
trend that can be useful for DCA; thus it is recommended to
carry out the DCA first on reservoir basis, and then on the
drainage points with established trends. Due to the inter-
connectivity test carried out, it was discovered that there
was possibility of interference between these wells; hence
reservoir is suitable for use as case study.
Reservoir B: case study
This is an oil reservoir with little gas reserves. It has three
wells drilled through it and two are still producing to the
present. The off-take built up rapidly from 1974 and
reached a peak of 6763.88 stb/d by April 1994. Subse-
quently, the off-take has shown a natural decline, with
beaning down of the wells. The predominant drive mech-
anism is aquifer. The well that has quit production is due to
depletion of reservoir energy. There is currently neither
pressure maintenance nor artificial lift in this reservoir.
Presently, there is poor production allocation in terms of
well performance, hence reservoir B is a suitable multi-
well reservoir system for case study.
Data analysis
The production data from reservoir A and B were analyzed
using conventional Arps’ exponential and hyperbolic
decline models, juxtaposing the results obtained to validate
the developed model. The production curves shown in
Figs. 1, 2, and 3 were plotted using each of the model for
reservoirs A and B, respectively. From each plot, the model
parameters shown in Tables 1 and 2 for exponential,
hyperbolic and developed models were determined using
the procedure shown in Appendix A. Having substituted
the obtained parameters shown in Tables 1 and 2 in
Fig. 1 Exponential decline production plot for reservoir A
Fig. 2 Hyperbolic decline production plot for reservoir A
84 J Petrol Explor Prod Technol (2011) 1:81–87
123
exponential, hyperbolic and developed models, the pro-
duction rate decline curves shown in Figs. 4, 5 6 and 7
were obtained.
Results and discussions
The basic principle/fundamental concept used is that of
Arps’ model; hence, results from the developed model are
compared with those of Arps’ exponential and hyperbolic
model. The comparison demonstrated in Fig. 4, 5, 6 and 7
reveals that the exponential model tends to underestimate
reserves and production rates, while the hyperbolic model
over-predicts the reservoir performance. The accurate
prediction, using the developed model, is achieved due to
the fact that: the use of cumulative production rate in the
Fig. 3 Hyperbolic decline production plot for reservoir B
Table 1 Model parameters
Parameters obtained
from graph
For multi-well
reservoir system A
For multi-well
reservoir system B
Slope -0.668 -0.302
Nominal decline factor
Di (/year)
-0.2438 -0.1102
Effective decline factor (d) 0.21637 0.10437
Table 2 Model parameters
Parameters obtained
from graph
For multi-well
reservoir system
A
For multi-well
reservoir system
B
Hyperbolic exponent (b) 0.765 0.945
Nominal decline factor
Di (/year)
0.07024 0.0484
Decline rate factor, Dt (/year) 0.06667 0.0463
Decline rate factor, Dt (/year) 0.000183 0.000127
Fig. 4 Production rate decline comparison of the three models
Fig. 5 Production comparison of the three models
Fig. 6 Production rate decline comparison of the three models
Fig. 7 Production comparison of the three models
J Petrol Explor Prod Technol (2011) 1:81–87 85
123
new model takes into cognizance the effect of well inter-
ference (volumetric mass influx) by new wells, which steal
from other wells. The pressure data are not used in this
case. Also, the adverse effects of downtime experienced
using a model that only relates the rate and time are
reduced, because ‘gaps’ in the production data during
periods of no production disappear when cumulative pro-
duction is integrated in the developed modified hyperbolic
model.
The consequence of underestimating or over-predicting
reserves is that it will affect the investment decisions. This
is because production forecasts, together with product
prices, operating costs and investments, are used to deter-
mine the project economics. Revenue is then predicted
when pricing forecasts are combined with the volumes
forecast. Production forecast data are also used to develop
expense forecasts. These forecasts are made on the basis of
production volumes and the forecasts of active completions
and related operational considerations. In turn, profit can be
predicted based on expected revenue and expenses. Profit
predictions will be used for work planning and project
justification.
However, the forecasts have direct dollar impacts far
beyond an organization. Based upon these forecasts, a
company can supply and coordinate marine and pipeline
transportation resources required to get the oil and gas to
market. On the other hand, forecasting too low may lead to
purchase of expensive spot capacity to handle the extra
production. In the longer term, forecasts affect more stra-
tegic decisions such as whether a producing property
should be kept or sold, the long-term availability of capital
for new projects, and whether a company should adjust its
pipeline or marine transportation capacity.
Conclusion
Based on the present study, the following conclusions may
be drawn in the cases studied:
1. The limitations of the Arps’ hyperbolic decline model
have been corrected by taking into cognizance the
effect of well aggregation and interference in multi-
well systems using high level reservoir data.
2. The comparison of model predictions using the
reservoir production data demonstrated that the devel-
oped modified hyperbolic model had the best predic-
tion compared to the exponential and the harmonic
models in the cases studied.
3. The study also revealed that decline analysis and
reserve estimation based on decline analysis must be
carried out with good understanding of the factors that
control the decline.
Open Access This article is distributed under the terms of the
Creative Commons Attribution License which permits any use, dis-
tribution and reproduction in any medium, provided the original
author(s) and source are credited.
Appendix A: Determination of the hyperbolic exponent,
initial nominal and effective decline constant
for hyperbolic decline as stated in the economic analysis
and investment decision by Ikoku (1985), University
of Port Harcout, Nigeria
This is a curve-fitting procedure based on reading three
points from a smooth curve representing a set of data points
in the most direct method of analyzing hyperbolic decline
curves. The procedure is as follows
For multi-well system A
From Fig. 2,
a. Select points (t1, q1) and (t2, q2)
t1 = 1 year, q1 = 4475 bbl/day
t2 = 7 years, q2 = 2750 bbl/day
b. Read t3 at q3 ¼ffiffiffiffiffiffiffiffiffiq1q2p
q3 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4475� 2750p
¼ 3508 t3 = 3.8 years
c. Calculate Did
� �¼ t1þt2�2t3
t23�t1t2
= 0.0537
d. Find q0 at t = 0, q0 = 4800 bbl/day
e. Pick up any point (t*, q*) say t* = 2 years,
q* = 4200 bbl/day
f. q� ¼ qo
1þ Didð Þt�ð Þ ) d ¼ log
qoq�ð Þ
log 1þ Didð Þt�ð Þ ¼ 1:308
g. Finally, Di ¼ Di
d
� �d
h. (0.0537 9 1.308) = 0.07024/year
where d ¼ 1=b, b = 0.765.
The hyperbolic decline constant at some future time, t, is
defined by the following equation Dt:
86 J Petrol Explor Prod Technol (2011) 1:81–87
123
Dt ¼Di
1þ bDit
Therefore,
Dt ¼0:07024
1þ ð0:765� 0:07024� 1ÞDt ¼ 0:06667=year
Dt ¼0:06667
year� 1 year
365 days¼ 0:000183=day
Appendix B: Illustrating the applicability
of the modified hyperbolic model using a case study
It is required to forecast the production rate of a reservoir in
2 years’ time using DCA by Arps’ model and the modified
Arps’ model. The analysis is to be carried out at the end of
2008 after the well had produced 9 MMstb. The analysis of
the production data gave a nominal exponential decline rate
of 0.11023 pa and an estimate for the initial rate for the
forecast of 1374.17 stb/day and the hyperbolic exponent of
0.945 with an initial nominal decline rate of 0.0463/year.
This can easily be done because the equations are not of
a complex form. Using Arps’ model:
For the exponential DCA,
q ¼ q1e�Dt
Therefore,
q ¼ 1374:17e�0:11023�2 ðandÞq ¼ 1102:29 bbl/day
For the Arps’ hyperbolic DCA,
q ¼ qt
ð1þ bDttÞ1b
Therefore,
q ¼ 1374:17ð1þ ð0:945� 0:0463� 2ÞÞ�1
0:945
q ¼ 1257:44 bbl/day:
Using the modified hyperbolic model given by
q ¼ qi þ NPxðb� 1ÞDi
1þ tDi
q¼1374:17þ 9� 106�ð0:945� 1Þ� 0:0463� 1
365
� �� � 1þð2� 0:0463Þ
q ¼ 1200:24 bbl/day:
This illustrated that when the multi-well system
production forecast is done using the three models, the
exponential model underestimates the reservoir
performance while the hyperbolic overestimates the
reservoir performance, but the modified hyperbolic model
gives a better result that is higher than the value of the
exponential but lower than that of the hyperbolic model.
This is because the modified model makes use of the entire
cumulative oil production data of wells in the multi-well
system, and hence gives a better result.
References
Arps, JJ (1970) Oil and gas property evaluation and reserve estimates,
vol. 3, Reprint Series, SPE, Richardson, TX, pp 93–102
Blasingame TA, Etherington JR, Hunt EJ, Adewusi A (1989) Decline
Curve Analysis Using Type-Curves. SPE 110927
Blasingame TA, McCray, TC, Lee, WJ (1991) Decline curve analysis
for variable pressure drop/variable flowrate system. SPE 21513
Camacho VR, Rodriguez, F, Galindo-NA, Prats M (1996) Optimum
position for wells producing at constant wellbore pressure. SPE,
vol 1, pp 155–168
Fetkovich, MJ (1980) Decline curve analysis using type curves. JPT,
1065–1077
Fetkovich MJ et al (1998) Decline curve analysis using type-curves.
SPE 13169
Fraim ML, Watten Barger RA (1987) Gas reservoir decline analysis
using type curves with real gas pseudo-pressure and normalized
time. SPEFE (Dec. 1987)620
Guo B, Lyons WC, Ghalambor A (2007) Petroleum production
engineering—a computer-assisted approach. Elsevier Science &
Technology Books Publishers, Amsterdam, pp 98–105
Ikoku CU (1985) The economic analysis and investment decision, 3rd
edn. University of Port Harcourt, Nigeria
Li K, Home RN (2005) Verification of decline curve analysis models
for production prediction. SPE 93878
McCray, TL (1990) Reservoir analysis using production decline data
and adjusted time. MS Thesis, Texas A & M University College
Station, TX
Palacio JC, Blasingame TA (1993) Decline curve analysis using type
curves. SPE 25909
Rodriguez F, Cinco-Ley H (1993) A new model for production
decline. SPE 25480
Valko PP, Doublet, LE, Blasingame TA (2000) Development and
application of the multiwell productivity index (MPI). SPEJ
J Petrol Explor Prod Technol (2011) 1:81–87 87
123
ORIGINAL PAPER - PRODUCTION ENGINEERING
How to improve poor system efficiencies of ESP installationscontrolled by surface chokes
Gabor Takacs
Received: 16 April 2011 / Accepted: 28 September 2011 / Published online: 21 October 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract Electrical submersible pumping is the most
inflexible of any artificial lift system because a specific
ESP pump can only be used in a definite, quite restricted
range of pumping rates. If it is used outside the specified
range, pump and system efficiencies rapidly deteriorate and
eventually mechanical problems leading to a complete
system failure develop. When serious deviation from the
design production rate is experienced, the possible solu-
tions are (a) running a different pump with the proper
recommended operating range, or (b) using a variable
speed drive (VSD) unit. However, in case the ESP system
produces a higher than desired liquid rate, a simple and
frequently used solution is the installation of a wellhead
choke. The wellhead choke restricts the pumping rate and
forces the ESP pump to operate within its recommended
liquid rate range. This solution, of course, is very detri-
mental to the economy of the production system because of
the high hydraulic losses across the choke that cause a
considerable waste of energy. The paper utilizes NODAL
analysis to investigate the negative effects of surface pro-
duction chokes on the energy efficiency of ESP systems as
compared to the application of VSD drives. The power
flow in the ESP system is described and the calculation of
energy losses in system components is detailed. Based on
these, a calculation model is proposed to evaluate the
harmful effects of wellhead choking and to find the proper
parameters of the necessary VSD unit. By presenting a
detailed calculation on an example well using the proposed
model the detrimental effects of wellhead choking are
illustrated and the beneficial effects of using a VSD drive
are presented. Using data of a group of wells placed on ESP
production a detailed investigation is presented on the
field-wide effects of choking. The energy flows and the
total energy requirements are calculated for current and
optimized cases where VSD units providing the required
electrical frequencies are used. Final results clearly indi-
cate that substantial electric power savings are possible if
production control is executed by VSDs instead of the
present practice of using surface chokes.
Keywords Electrical submersible pumping � ESP �Oil well � Production � Optimization � Wellhead choke �Energy � Efficiency � System analysis � NODAL analysis
Introduction
The objective of any artificial lift design is to set up a lift
system with a liquid producing capacity that matches the
inflow rate from the well it is installed in. Since the
mechanical design of the lifting equipment is only possible
in the knowledge of the probable liquid rate, the designer
needs a precise estimate on the production rate attainable
from the given well. Design inaccuracies or improperly
assumed well rates can very easily result in a mismatch of
the designed and actually produced liquid volumes (Brown
1980; Takacs 2009). The main cause of discrepancies
between these rates, assuming proper design procedures are
followed, is the improper estimation of possible well rates,
i.e. inaccurate data on well inflow performance. The con-
sequences of under-, or over-design of artificial lift systems
can lead to the following:
• If the artificial lift equipment’s capacity is greater than
well inflow then the operational efficiency of the
G. Takacs (&)
University of Miskolc, Miskolc, Hungary
e-mail: [email protected]
123
J Petrol Explor Prod Technol (2011) 1:89–97
DOI 10.1007/s13202-011-0011-9
system cannot reach the designed levels; mechanical
damage may also occur.
• In case the well’s productivity is greater than the
capacity of the lifting system, one loses the profit of the
oil not produced.
Over-, and under-design of artificial lift installations
happens in the industry very often and professionals know
how to deal with them. Some lifting methods such as gas
lifting or sucker rod pumping are relatively easy to handle
since their lifting capacity can be adjusted in quite broad
ranges after installation. ESP installations, however, do not
tolerate design inaccuracies because any given ESP pump
can only be used in a specific, quite restricted range of
pumping rates. If used outside its recommended liquid rate
range, the hydraulic efficiency of the pump rapidly dete-
riorates; efficiencies can go down to almost zero. In addi-
tion to the loss of energy and the consequent decrease in
profitability the ESP system, when operated under such
conditions, soon develops mechanical problems that can
lead to a complete system failure. The usual outcome is a
workover job and the necessity of running a newly
designed ESP system with the proper lifting capacity.
One common solution for over-designed ESP systems is
the use of production chokes at the wellhead. Installation of
the choke, due to the high pressure drop that develops
through it, limits the well’s liquid rate so the ESP pump is
forced to operate in its recommended pumping rate range.
This solution eliminates the need for running a new ESP
system of the proper capacity into the well and saves the
costs of pulling and running operations. At the same time,
however, the system’s power efficiency decreases consid-
erably due to the high hydraulic losses occurring across the
surface choke.
The paper investigates the detrimental effects of surface
chokes on the power efficiency of ESP systems and dis-
cusses an alternative solution. The analysis is provided for
wells producing negligible amounts of free gas and is based
on the application of NODAL analysis principles to
describe the operation of the ESP system.
The effects of using wellhead chokes
Why use chokes
Most ESP installations are designed to operate using
electricity at a fixed frequency, usually 60 or 50 Hz. This
implies that the ESP pump runs at a constant speed and
develops different heads for different pumping rates as
predicted by its published performance curve. When
designing for a constant production rate, a pump type with
the desired rate inside of its recommended capacity range is
selected. The number of the required pump stages is
found from detailed calculations of the required total
dynamic head (TDH), i.e. the head required to lift well
fluids to the surface at the desired pumping rate. Thus, the
head versus capacity performance curve of the selected
pump can easily be plotted based on the performance of a
single stage.
For an ideal design when all the necessary parameters of
the well and the reservoir are perfectly known the pump
will produce exactly the design liquid rate since it will
work against the design TDH (1997; 2001; 2002). In this
case the head required to overcome the pressure losses
necessary to move well fluids to the separator is covered by
the head available from the pump at the given pumping
rate. This perfect situation, however, is seldom achieved;
very often inaccuracies or lack of information on well
inflow performance cause design errors and the well pro-
duces a rate different from the initial target.
The problem with the conventional design detailed
above is that the ESP installation is investigated for a single
design rate only and no information is available for cases
when well parameters are in doubt. All these problems are
easily solved if system (NODAL) analysis principles are
used to describe the operation of the production system
consisting of the well, the tubing, the ESP unit, and the
surface equipment. NODAL analysis permits the calcula-
tion of the necessary pump heads for different possible
pumping rates and the determination of the liquid rate
occurring in the total system, This will be the rate where
the required head to produce well fluids to the separator is
equal to the head developed by the ESP pump run in the
well.
Figure 1 shows a schematic comparison of the conven-
tional design with that provided by NODAL analysis.
Conventional design calculates the TDH at the design rate
only and selects the type of the ESP pump and the neces-
sary number of stages accordingly. After selecting the rest
of the equipment the ESP unit is run in the well and it is
only hoped that actual conditions were properly simulated
resulting in the well output being equal to the design liquid
rate. If well inflow performance data were uncertain or
partly/completely missing during the design phase then the
ESP system’s stabilized liquid rate is different from the
design target. NODAL calculations, however, can predict
the required head values for different liquid rates, shown in
Fig. 1 by the curve in dashed line. The well’s actual pro-
duction rate will be found where the required and the
available (provided by the pump) heads are equal, at
Point 1 in the figure.
In typical cases the actual liquid production rate is
greater than the target value. This clearly indicates inac-
curacies in the well performance data assumed during the
design process. Since the well’s required production is
90 J Petrol Explor Prod Technol (2011) 1:89–97
123
usually dictated by reservoir engineering considerations
production of a greater rate is not allowed. The problem is
caused, as shown in Fig. 1, by the fact that the actual head
requirement (actual TDH) is much less than the calculated
design TDH.
The solution of the problem, if pulling the ESP equip-
ment and replacing it with a properly designed one is not
desired, is to place a production choke of the proper
diameter at the wellhead to restrict the liquid rate to the
design target. At this rate, however, the installed pump
develops the designed operating head as shown by Point 2.
Since the actual head required for lifting the well fluids to
the surface, as found from NODAL calculations, is less
than this value, a sufficient head loss across the choke is
needed. This head loss, found between Points 2 and 3 must
be sufficient to supplement the system’s actual TDH to
reach the TDH that was used for the original design. As a
result, the head requirement of the production system is
artificially increased and the ESP pump is forced to pro-
duce the desired liquid rate.
Estimating the energy loss across wellhead chokes
The detrimental effect of choking an ESP unit is clearly
indicated by the amount of power wasted through the
surface choke. This (in HP units) can be calculated from
the pumping rate and the amount of head loss across the
choke:
Pwasted ¼ 7:368� 10�6 ql DHchoke cl; ð1Þ
where ql is the pumping rate (bpd), DHchoke the head loss
across surface choke (ft), and cl is the specific gravity of the
produced liquid.
The above power, of course, must be supplied by the
electric motor to drive the submersible pump that is being
subjected to a higher than necessary load. Since this power
is wasted, the ESP system’s power efficiency as well as the
profitability of fluid production will decrease.
Calculation of the ESP pump’s required head
by NODAL methodology
Since choking of the ESP well at the wellhead is clearly
detrimental to the lifting performance, proper design and
installation of the ESP equipment is highly important. In
case sufficiently accurate inflow performance data are
available, the use of NODAL analysis techniques allows
for an accurate installation design and eliminates the need
for using wellhead chokes (Takacs 2009).
In order to apply systems (NODAL) analysis to the ESP
installation, the variation of flowing pressures in the well
should be analyzed first. Figure 2 depicts the pressures
along the well depth (a) in the tubing string, and (b) in the
casing-tubing annulus. The well is assumed to produce
incompressible liquids at a stabilized flow rate, found from
the well’s inflow performance relationship (IPR) curve.
From the depth of the perforations up to the setting depth of
the ESP pump, pressure in the casing changes according to
the flowing pressure gradient of the well fluid which is
approximated by the static liquid gradient. This assumption
is acceptable when medium flow rates are produced
through large casing sizes; otherwise, a pressure traverse
including all pressure losses should be calculated. The
calculated casing pressure at the pump setting depth is the
pump intake pressure (pintake).
Pump Capacity
Dev
elo
ped
Hea
d
60 Hz
65 Hz
55 Hz
50 Hz
45 Hz
40 Hz
1
2
3
Head Dropthru Choke
ActualTDH
DesignTDH
Required Head
Available Head
Fig. 1 Explanation of the need for a wellhead choke
Fig. 2 Pressure distributions in an ESP installation
J Petrol Explor Prod Technol (2011) 1:89–97 91
123
At the depth of the pump discharge (which is practically
at the same depth as the intake), the pump develops a
pressure increase denoted as Dppump in the figure. The
pressure available at the ESP pump’s discharge, therefore,
can be calculated as follows:
pd ¼ pwf � Lperf � Lset
� �gradl þ Dppump; ð2Þ
where pwf is the flowing bottomhole pressure (psi), gradl
the liquid gradient (psi/ft), Dppump the pressure increase
developed by the pump (psi), Lset = pump setting depth
(ft), Lperf is the depth of perforations (ft).
Calculation of the pressure at the pump’s setting depth
required to produce the given rate is started from the sur-
face separator. The wellhead pressure pwh is found by
adding the flowing pressure losses in the flowline to the
separator pressure psep. For the single-phase liquid pro-
duction case studied in this paper, the pressure distribution
in the tubing string starts at the wellhead pressure and
changes linearly with tubing length. Tubing pressure has
two components: (1) the hydrostatic pressure, and (2) the
frictional pressure loss. By proper consideration of the
terms described we can define the required discharge
pressure of the ESP pump as follows:
p�d ¼ psep þ Dpfl þ Lsetgradl þ Dpfr; ð3Þ
where psep is the surface separator pressure (psi), Dpfl the
frictional pressure drop in the flowline (psi), Dpfr is the
frictional pressure drop in the tubing string (psi).
Since the available and the required pressures must be
equal at the ESP pump’s discharge, the simultaneous
solution of the two formulas results in the following
expression that describes the pressure increase to be
developed by the ESP pump:
Dppump ¼ psep þ Dpfl þ Lperfgradl þ Dpfr � pwf : ð4Þ
Since the ESP industry uses head instead of pressure, the
previous equation is divided by the liquid gradient to arrive
at the necessary head of the pump:
DHpump ¼ Lperf þ DHfl þ DHfr �2:3 1
cl
pwf � psep
� �; ð5Þ
where DHfl is the frictional head drop in the flowline (ft),
DHfr is the frictional head drop in the tubing string (ft).
The previous formula, if evaluated over an appropriate
range of liquid flow rates, represents the variation of the
necessary head that the pump must develop to produce the
possible liquid rates from the given well, see the curve in
dashed line in Fig. 1. For an accurate installation design the
ESP pump’s operating point must fall on this curve at its
intersection with the desired liquid rate. Based on this, the
required pump can be properly selected and no wellhead
choke will be needed to control the flow rate. This scenario,
of course, can only be followed if sufficiently accurate
inflow performance data on the given well are available.
Use of variable speed drive (VSD) units to eliminate
wellhead chokes
If, for any reason, the installation design is inaccurate and
the ESP system, after installation, produces a higher rate
than desired the use of wellhead chokes is a common
solution to control the well’s production. If a VSD is
available, however, the elimination of the choke and its
associated disadvantages can be accomplished (Divine
1979). As shown in Fig. 1, by reducing the electrical fre-
quency driving the ESP system to a level where the head
developed by the pump is equal to the head required to
produce the desired rate (Point 3) the choke is no more
needed to adjust the pumping rate.
When a VSD unit is used to control the ESP system’s
liquid rate the different components of the system behave
differently as the driving frequency is adjusted. The cen-
trifugal pump will develop different head values and will
need different brake horsepowers from the electric motor.
All these changes are described by the pump performance
curves valid at variable frequencies usually available from
manufacturers. In case such curves are missing, the Affinity
Laws (Takacs 2009; 1997) and the performance curves at a
constant frequency may be used to calculate the required
parameters at the reduced frequency: heads, efficiencies,
and brake horsepowers.
The performance parameters of the ESP motor at vari-
able frequency operation are described by two basic for-
mulae that express the change of (a) the nameplate voltage,
and (b) the power developed, both with the changes in the
electrical frequency. Actually, nameplate voltage of the
motor is adjusted by the surface VSD unit so that the
voltage-to-frequency ratio is kept constant. This is to
ensure that the motor becomes a constant-torque, variable
speed device. The applicable formula is the following:
U2 ¼ U1
f2f1
� �; ð6Þ
where f1, f2 are the AC frequencies (Hz), U1, U2 are the
output voltages at f1 and f2 (Hz, V).
The power developed by the ESP motor is linearly
proportional with the electrical frequency as shown by the
next formula:
HP2 ¼ HP1
f2f1
� �; ð7Þ
where f2, f1 are the AC frequencies (Hz), HP1, HP2 are the
motor powers available at f1 and f2 (Hz, HP).
92 J Petrol Explor Prod Technol (2011) 1:89–97
123
As described previously, the use of a VSD unit sub-
stantially modifies the power conditions of the ESP pump
and the motor. In order to fully understand the changes and
to demonstrate the beneficial effects of removing wellhead
chokes the next section details the power conditions in the
ESP system.
Power conditions in ESP installations
Power flow in the ESP system
The ESP installation’s useful output work is done by the
centrifugal pump when it lifts a given amount of liquid
from the pump setting depth to the surface. This work is
described by the useful hydraulic power, Phydr, and can be
calculated from the power consumed for increasing the
potential energy of the liquid pumped. The following for-
mula, recommended by Lea et al. (1999), can be applied to
any artificial lift installation and gives a standardized way
to compare the effectiveness of different installations:
Phydr ¼ 1:7� 10�5ql 0:433clLpump � pintake
� �; ð8Þ
where Phydr is the hydraulic power used for fluid lifting
(HP), ql the liquid production rate (bpd), Lpump the pump
setting depth (ft) and pintake is the pump suction pressure,
called pump intake pressure (psi).
The total power consumed by the system comprises, in
addition to the energy required to lift well fluids to the
surface (i.e. the hydraulic power Phydr), all the energy
losses occurring in downhole and surface components.
Thus, the required electrical energy input at the surface is
always greater than the useful power; the relation of these
powers defines the ESP system’s power efficiency.
Classification of the energy losses in ESP systems can be
made according to the place where they occur; one can thus
distinguish between downhole and surface losses (Takacs
2010). Another way to group these losses is based on their
nature and categorizes them as hydraulic and electrical.
Energy losses in the ESP system
Hydraulic losses
The sources of energy losses of hydraulic nature are the
tubing string, the backpressure acting on the well, the ESP
pump, and the optional rotary gas separator.
Tubing losses Flow of the produced fluids to the surface
involves frictional pressure losses in the tubing string; the
power wasted on this reduces the effectiveness of the ESP
installation. In case a single-phase liquid is produced, the
frictional loss in the tubing string is determined from the
total head loss, DHfr, usually taken from charts or appro-
priate calculation models. The power lost, DPfr in HP units,
is found from the following formula:
DPfr ¼ 7:368� 10�6qlDHfrcl; ð9Þ
where DHfr is the frictional head loss in the tubing (ft).
Backpressure losses The ESP unit has to work against the
well’s surface wellhead pressure and the power consumed
by overcoming this backpressure is not included in the
useful power. The necessary power to overcome the well-
head pressure (in HP units) is found from:
DPbp ¼ 1:7� 10�5qlpwh; ð10Þ
where ql is the liquid production rate (bpd) and pwh is the
wellhead pressure (psi).
Pump losses Energy losses in the ESP pump are mostly
of hydraulic nature, and are represented by published pump
efficiency curves. In most cases the pump efficiencies, as
given by the manufacturer, include the effect of the addi-
tional power required to drive the ESP unit’s protector.
Based on the actual pump efficiency, the power lost in the
pump (in HP units) is easily found:
DPpump ¼ BHP 1�gpump
100
� �; ð11Þ
where BHP is the pump’s required brake horsepower (HP)
and gpump is the published pump efficiency (%).
Electrical losses
Electrical power losses in the ESP installation occur,
starting from the motor and proceeding upward, in the ESP
motor, in the power cable, and in the surface equipment.
Motor losses The ESP motor converts the electrical energy
input at its terminals into mechanical work output at its shaft;
the energy conversion is characterized by the motor effi-
ciency. Based on published efficiency values, the power lost
in the ESP motor (in HP units) is calculated as follows:
DPmotor ¼ HPnpLoad 1� gmotor
100
� �; ð12Þ
where HPnp is the motor’s nameplate power (HP), Load is
the motor loading, fraction, and gmotor is the motor effi-
ciency at the given loading (%).
Cable losses Since the ESP motor is connected to the
power supply through a long power cable, a considerable
voltage drop occurs across this cable. The voltage drop
creates a power loss proportional to the square of the
current flowing through the system, as given here in kW
units:
J Petrol Explor Prod Technol (2011) 1:89–97 93
123
DPcable ¼3I2RT
1; 000; ð13Þ
where I is the required motor current (Amps) and RT is the
resistance of the power cable at well temperature (Ohms).
Surface electrical losses The ESP installation’s surface
components are very efficient to transmit the required
electric power to the downhole unit, their usual efficiencies
are around gsurf = 0.97. The energy wasted in surface
equipment can thus be found from:
DPsurf ¼ P1� gsurfð Þ
gsurf
; ð14Þ
where P is the sum of the hydraulic power and the power
losses, and gsurf is the power efficiency of the surface
equipment.
Example problem
In the following, a detailed calculation model is proposed
and illustrated through an example well. Energy flow in the
ESP system is determined for current conditions when a
surface choke is used to control the well’s liquid flow rate.
Then the use of a VSD unit is investigated and the required
operational frequency is determined; the energy conditions
of the modified installation are compared to the original
case.
Well data
Production data of an example well are given in Table 1.
Common calculations
First calculate those parameters that are identical for the
original, choked conditions and for the case without the
choke.
The flowing bottomhole pressure from the Productivity
Index formula is found as:
pwf ¼ pws � q=PI ¼ 1; 527� 2; 600=15:4 ¼ 1; 358 psi:
Now the pump intake pressure is calculated:
pintake ¼ pwf � 0:433cl Lperf � Lpump
� �¼ 1; 358� 0:433 0:876 4; 070� 2; 965ð Þ ¼ 939 psi:
Knowledge of these parameters permits the calculation
of the system’s useful hydraulic power from Eq. 8
Phydr ¼ 1:7 E� 5 Q ð0:433clLpump � pintakeÞ¼ 1:7E� 5 2; 600 0:433 0:876 2; 965� 939ð Þ¼ 8:2 HP ¼ 6:1 kW:
At pump suction conditions there is no free gas present,
as can be found from the Standing correlation; the oil’s
volume factor at the same pressure is found as
Bo = 1.115 bbl/STB. The total liquid volume to be
handled by the ESP pump is thus:
ql ¼ 2; 600 1:115 ¼ 2; 900 bpd; or 461m3=day:
In order to find the frictional head loss due to the flow of
the current liquid rate through the well tubing the Hazen-
Williams formula or the use of the proper graph gives a
head loss of 42 ft/1,000 ft of pipe. The total head loss in
the tubing is thus:
DHfr ¼ 42 2; 965=1; 000 ¼ 124 ft:
The energy loss corresponding to tubing frictional losses
can be calculated from Eq. 9:
DPfr ¼ 7:368E� 6 QDHfrcl
¼ 7:368E� 6 2; 600 124 0:876 ¼ 2:1 HP ¼ 1:5 kW:
Energy conditions of the current installation
This section contains calculations for the original, choked
condition and evaluates the energy conditions of the cur-
rent ESP installation.
Table 1 Production and ESP
dataWell data ESP installation data
Depth of perforations 4,070 ft Pump setting depth 2,965 ft
Tubing size 3 � in. ESP pump type GN4000
Static bottomhole pressure 1,527 psi Number of stages 99
Productivity index 15.4 bpd/psi Electrical frequency 50 Hz
Production GOR 82 scf/STB Motor NP power 104.2 HP
Production data Motor NP voltage 1,095 V
Liquid rate 2,600 STB/day Motor NP current 60 Amps
Water cut 0% ESP cable size AWG 2
Producing wellhead pressure 745 psi
Pressure downstream of choke 130 psi
94 J Petrol Explor Prod Technol (2011) 1:89–97
123
The hydraulic losses due to the backpressure at the
wellhead pressure of 745 psi are calculated from Eq. 10 as
follows:
DPbp ¼ 1:7E� 5 Q pwh ¼ 1:7E� 5 2; 600 745 ¼ 33 HP
¼ 25 kW:
From the performance curve of the GN4000 pump
operated at 50 Hz, the following parameters of the pump
are found at the current liquid rate of 461 m3/day:
HBP=Stage ¼ 0:84 HP:
Pump efficiency ¼ 66%:
Since there are 99 stages in the pump, the pump’s power
requirement is:
99 0:84 cl ¼ 99 0:84 0:876 ¼ 73 BHP:
Based on these parameters the power lost in the pump
can be calculated from Eq. 11:
DPpump ¼ 73 1� 66=100ð Þ ¼ 24:8 HP ¼ 18:5 kW:
The existing ESP motor’s rated power (see input data)
being 104.2 HP, the motor is only 70% loaded by the pump
power of 73 BHP. From motor performance data, motor
efficiency at that loading is 89%. Now the power loss in the
electric motor can be found from Eq. 12:
DPmotor ¼ 104:2 0:70 1� 89=100ð Þ ¼ 8 HP ¼ 6 kW:
In order to find the electrical losses in the downhole
cable, first the resistance of the well cable has to be found.
The installation uses an AWG 2 size electrical cable with
an electrical resistance of 0.17 Ohm/1,000 ft. The total
resistance of the downhole cable, considering well
temperature, is found as 0.658 Ohms.
The actual current flowing through the cable is equal to
the motor current found from the motor load and the
nameplate current as:
I ¼ 0:70 Inp ¼ 0:70 60 ¼ 42 Amps:
Now the electrical power lost in the cable is calculated
from the basic 3-Phase power formula (Eq. 13):
DPcable ¼ 3 I2R=1; 000 ¼ 3 4220:658=1; 000 ¼ 3:5 kW:
Finally, the power lost in the ESP system’s surface
components is to be found from Eq 14 with a surface
efficiency of 97%.
DPsurf ¼ ðPhydr þ DPfr þ DPbp þ DPpump þ DPmotor
þ DPcableÞ 1� 0:97ð Þ=0:97
¼ 1:9 kW:
Energy conditions of the modified installation
This section presents the calculations required to describe
the conditions when a VSD unit is used to control the
pumping rate instead of choking the well.
In this case the operating wellhead pressure is reduced to
the flowline intake pressure; this was measured downstream
of the wellhead choke as 130 psi. The hydraulic losses due to
the backpressure are calculated from Eq. 10 as follows:
DPbp ¼ 1:7E� 5 Q pwh ¼ 1:7E� 5 2; 600 130 ¼ 6 HP
¼ 4:4 kW:
Next the required electrical frequency is calculated
using the head performance curve of the pump for multiple
frequencies. Since the current case uses 50 Hz, metric
performance curves have to be used.
• The head developed by the pump at 50 Hz operation is
found at the current liquid rate of 461 m3/day and is
designated as Point 1.
• The head drop across the wellhead choke, corrected for
one stage, is calculated in metric units:
Drop ¼ 0:3048 2:3 pwh � Pdownstreamð Þ=cl=no: of stages
¼ 0:3048 2:3 745� 130ð Þ=0:876=99 ¼ 5 m:
• From Point 1, a vertical is dropped by the calculated
distance of 5 m; this defines Point 2.
• The frequency valid at Point 2 is read; this should be
used on the VSD unit to drive the ESP motor.
The process described here resulted in a required fre-
quency of 37 Hz for the example case.
Next the operational parameters of the GN4000 pump at
37 Hz service have to be determined. Since detailed per-
formance curves for this frequency are not available, the
use of published 50 Hz curves and the Affinity Laws is
required.
The required rate of 461 m3/day at 37 Hz operation
corresponds to the following rate at 50 Hz, as found from
the Affinity Laws:
Rate ¼ 461 50=37 ¼ 623 m3=day:
The power requirement and the efficiency of the pump
at this rate at 50 Hz operation are read from the 50 Hz
performance curves as:
BHP=stage ¼ 0:83 HP=stage; and
Pump efficiency ¼ 65%:
From these data and using the Affinity Laws again, the
power requirement of the pump at 37 Hz operation is
calculated:
BHP=stage ¼ 0:83 37=50ð Þ3¼ 0:34 HP=stage:
The efficiency of the pump remains at 65%.
Now the power needed to drive the 99 pump stages at an
electrical frequency of 37 Hz has decreased to:
99 0:34cl ¼ 99 0:34 0:876 ¼ 29 HP:
J Petrol Explor Prod Technol (2011) 1:89–97 95
123
Based on these parameters the power lost in the pump
can be calculated as (Eq. 11):
DPpump ¼ 29 1� 65=100ð Þ ¼ 10:2 HP ¼ 7:6 kW:
The operating conditions of the ESP motor change at the
modified frequency. Its nameplate power decreases from
that at 50 Hz according to Eq. 7:
Pnp ¼ 104:2 37=50ð Þ ¼ 77 HP:
Motor voltage is adjusted by the VSD unit from the
nameplate value valid at 50 Hz to the following voltage,
according to Eq. 6:
Umotor ¼ 1; 095 27=50ð Þ ¼ 810 V:
The ESP motor’s loading is found from the pump power
requirement and the modified motor power:
Loading ¼ 29=77 ¼ 38%:
The efficiency of the motor at this loading is 87%, as
found from motor performance curves. The power loss in
the electric motor can now be found from Eq. 12:
DPmotor ¼ 77 0:38 1� 87=100ð Þ ¼ 3:9 HP ¼ 2:9 kW:
When finding the electrical losses in the downhole cable,
the resistance of the cable is identical to the previous case at
0.658 Ohms. Since the nameplate current of the ESP motor at
the new frequency does not change the actual motor current is
found from the motor load and nameplate current as:
I ¼ 0:38 Inp ¼ 0:38 60 ¼ 23 Amps:
The power loss in the cable is calculated from Eq. 13:
DPcable ¼ 3 I2R=1; 000 ¼ 3 2320:658=1; 000 ¼ 1 kW:
Finally, the power lost in the ESP system’s surface
components is to be found from Eq. 14 with a surface
efficiency of 97%:
DPsurf ¼ ðPhydr þ DPfr þ DPbp þ DPpump þ DPmotor
þ DPcableÞ 1� 0:97ð Þ=0:97
¼ 0:7 kW:
Final results
Table 2 summarizes the energy conditions of the two cases.
As seen, the use of a VSD unit has increased the system
efficiency to more than twofold and system power
decreased to less than 40% of the original requirement.
Application to a group of wells
In order to evaluate the model proposed in the paper for
increasing the efficiency of ESP wells on surface choke
control, calculations were performed using the data of
several wells from the same field. The wells produced
API 40 gravity oil with low water cuts from relatively
shallow depths. Original installation designs were far from
ideal and most wells had downhole equipment capable of
Table 2 Energy conditions of the two cases
Component 50 Hz case 37 Hz case
Useful hydraulic power (kW) 6.1 6.1
Wellhead loss (kW) 25.0 4.4
Tubing friction (kW) 1.5 1.5
ESP pump losses (kW) 18.5 7.6
ESP motor losses (kW) 6.0 2.9
ESP cable losses (kW) 3.5 1.0
Surface losses (kW) 1.9 0.7
Total (kW) 61.5 24.2
System efficiency (%) 10 25.2
Table 3 Comparison of original and modified cases for an example field
Well no. Liquid rate pwh (psi) Line Pr. (psi) Original Modified
STB/day bpd Power (kW) Eff. (%) Freq. (Hz) Power (kW) Eff. (%)
1 1,444 1,629 805 165 53.8 3 33 13.1 12.1
2 2,000 2,132 960 120 62.7 3 31 13.5 13.7
3 1,700 1,824 700 100 57.1 6.9 38 21.6 18.3
4 3,000 3,340 920 100 73.7 9 33 26.2 25.4
5 3,000 3,340 1,180 120 73.7 9 33 26.2 25.4
6 2,600 2,900 745 130 61.5 9.9 37 24.2 25.2
7 2,400 2,642 700 150 57.3 4.6 39 23.2 11.3
8 2,700 3,007 670 175 59.9 8.1 35 25.1 19.4
9 1,600 1,749 860 120 55.4 2.5 33 13 10.7
10 1,600 1,761 540 100 50.7 7.4 41 24.9 15.0
Total power (kW) 605.8 211.0
96 J Petrol Explor Prod Technol (2011) 1:89–97
123
much higher production rates than those permitted by
reservoir engineering management and had to be choked
back. This is the reason why wellhead pressures are much
higher than the required line pressure in the gathering
system.
The most important input and calculated data are given
in Table 3. Most of the wells indicate quite high pressure
drops across the wellhead chokes that obviously involve
lots of energy wasted in the ESP system. The surface power
requirements for the original cases, of course, include these
wasted power components and the overall system effi-
ciencies are accordingly very low.
After re-designing the installations according to the
procedure proposed in this paper, application of VSD
units was assumed and the required operational fre-
quencies were determined. The modified cases, as seen
in Table 3, have much lower total energy requirements
mainly due to the removal of the wellhead choke’
harmful effect; overall system efficiencies have substan-
tially increased.
Total electrical power requirement of the well group
investigated has decreased to almost one-third of the ori-
ginal, from 606 to 211 kW. This clearly proves that using
VSDs to control the production rate of ESP wells is a much
superior solution to wellhead choking adopted in field
practice.
Conclusions
The paper investigates the power conditions of ESP
installations where the pumping rate of oversized ESP units
is reduced by placing chokes on the wellhead. Power flow
in the system with the description of possible energy losses
is presented and system efficiency is evaluated. In order to
reduce the harmful effects of wellhead chokes on system
efficiency NODAL analysis principles are used to describe
the operation of the ESP system. A detailed calculation
method is developed and example cases are presented to
find the proper frequency setting of a VSD unit to be used.
Main conclusions derived are as follows.
• The practice of controlling the pumping rate of ESP
installations by wellhead chokes can very substantially
reduce the energy efficiency of the system.
• NODAL analysis can be used to properly design an
ESP installation and/or rectify the situation without a
need to change downhole equipment.
• The proposed calculation model provides a much more
energy-efficient solution to production rate control
using VSD units.
• Several field examples are shown to prove that very
substantial energy savings can be realized by following
the proposed model.
Acknowledgments This work was carried out as part of the
TAMOP-4.2.1.B-10/2/KONV-2010-0001 project in the framework of
the New Hungarian Development Plan. The realization of this project
is supported by the European Union, co-financed by the European
Social Fund.
Open Access This article is distributed under the terms of the
Creative Commons Attribution License which permits any use, dis-
tribution and reproduction in any medium, provided the original
author(s) and source are credited.
References
Submersible pump handbook (1997) 6th edn. Centrilift-Hughes Inc.,
Claremore
The 9 step (2001) Baker-Hughes Centrilift, Claremore
Recommended practice for sizing and selection of electric submer-
sible pump installations (2002) API RP 11S4, 3rd edn. American
Petroleum Institute
Brown KE (1980) The technology of artificial lift methods, vol 2b.
PennWell Books, Tulsa
Divine DL (1979) A variable speed submersible pumping system. In:
Paper SPE 8241 presented at the 54th annual technical confer-
ence and exhibition held in Las Vegas, September 23–26
Lea JF, Rowlan L, McCoy J (1999) Artificial lift power efficiency. In:
Proceedings of 46th Annual Southwestern Petroleum Short
Course, Lubbock, pp 52–63
Takacs G (2009) Electrical submersible pumps manual. Gulf Profes-
sional Publishing, USA
Takacs G (2010) Ways to obtain optimum power efficiency of
artificial lift installations. In: Paper SPE 126544 presented at the
SPE oil and gas India conference and exhibition held in Mumbai,
20–22 January
J Petrol Explor Prod Technol (2011) 1:89–97 97
123
ORIGINAL PAPER - PRODUCTION ENGINEERING
Prediction of asphaltene precipitation using artificial neuralnetwork optimized by imperialist competitive algorithm
Mohammad Ali Ahmadi
Received: 23 August 2011 / Accepted: 17 October 2011 / Published online: 1 November 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract One of the most important phenomena in petro-
leum industry is the precipitation of heavy organic materials
such as asphaltene in oil reservoirs, which can cause diffu-
sivity reduction and wettability alteration in reservoir rock
and finally affect oil production and economical efficiency.
In this work, the model based on a feed-forward artificial
neural network (ANN) optimized by imperialist competitive
algorithm (ICA) to predict of asphaltene precipitation is
proposed. ICA is used to decide the initial weights of the
neural network. The ICA–ANN model is applied to the
experimental data reported in the literature. The performance
of the ICA–ANN model is compared with Scaling model and
conventional ANN model. The results demonstrate the
effectiveness of the ICA–ANN model.
Keywords Asphaltene � Precipitation � Artificial neural
network � Imperialist competitive algorithm � Prediction
List of symbols
R Solvent to oil ratio (g/mol)
M Molecular weight (g/mol)
W Amount of precipitated asphaltene (weight percent)
Y Function defined by Eq. 1
X Function defined by Eq. 2
x Function defined by Eq. 4
y Function defined by Eq. 5
ANN Artificial neural network
PSO Particle swarm optimization
ICA Imperialist competitive algorithm
Introduction
The precipitation and deposition of crude oil polar fractions
such as asphaltenes in petroleum reservoirs reduce consid-
erably the rock permeability and the oil recovery. So, many
researchers studied this important subject. They introduced
experimental procedures or even analytical models, but a
fully satisfactory interpretation is still lacking. The avail-
able models for description of asphaltene precipitation are
divided into two general groups. The first group consists of
thermodynamic models, which need asphaltene properties
such as density, molecular weight and solubility parameter
for prediction of asphaltene phase behavior. All those
models consider asphaltene as a pure pseudo-component,
but this assumption causes much deviation in the prediction
of asphaltene phase behavior (Pedersen et al. 1989); the
second group of models is based on the scaling approach
which explained separately. In this paper, the ability of the
artificial intelligence in establishing and predicting amount
of asphaltene precipitation is to be investigated. Artificial
intelligence have been widely used and are gaining atten-
tion in petroleum engineering because of their ability to
solve problems that previously were difficult or even
impossible to solve. One example of ability neural network
in well-log analysis. This technique has been increasingly
applied to predict reservoir properties using well-log data
(Doveton and Prensky 1992; Balan et al. 1995).
A soft sensor is a conceptual device whose output or
inferred variable can be modeled in terms of other
parameters that are relevant to the same process (Rallo
et al. 2002). According to Rallo et al. (2002), artificial
M. A. Ahmadi (&)
Department of Petroleum Engineering,
Ahwaz Faculty of Petroleum Engineering,
Petroleum University of Technology,
Kut Abdollah, Ahwaz, Iran
e-mail: [email protected];
123
J Petrol Explor Prod Technol (2011) 1:99–106
DOI 10.1007/s13202-011-0013-7
neural network (ANN) could be used as soft sensor
building approach.
The determination of network structure and parameters
is very important; some evolutionary algorithms such as
genetic algorithm (GA) (Qu1 et al. 2008), back propagation
(BP) (Tang and Xi 2008), pruning algorithm (Reed 1993),
simulated annealing (de Souto et al. 2002) can be used for
this determination. Recently, a new evolutionary algorithm
has been proposed by Atashpaz-Gargari and Lucas (2007)
which has inspired from a socio-political evolution, called
imperialist competitive algorithm (ICA).
In the present work, we propose ICA for optimizing the
weights of feed-forward neural network. Then simulation
results demonstrate the effectiveness and potential of the
new proposed network for asphaltene precipitation pre-
diction compared with scaling model (Hu and Guo 2001)
using the same data.
Scaling model
The three variables involved in the scaling equation are the
weight percent of precipitated Asphaltenes, W (based on the
weight of feed oil), the dilution ratio, R (defined as the ratio
of injected solvent volume to weight of crude oil), and the
molecular weight of solvent, M. Rassamdana et al. (1996)
combined the three variables into two (X, Y) as follows:
X ¼ R
MZð1Þ
Y ¼ W
RZ0 ð2Þ
Z and Z0 are two adjustable parameters and must be
carefully tuned to obtain the best scaling fit of the
experimental data. They suggested Z0 is a universal constant
of -2 and Z = 0.25 regardless of oil and precipitant used. The
proposed scaling equation is expressed in terms of X and Y
through a third-order polynomial function
Y ¼ A1 þ A2X þ A3X2 þ A4X3 X [ Xcð Þ ð3Þ
where Xc is the value of X at the onset of asphaltene
precipitation.
Hu et al. (2000) performed a detailed study on the
application of scaling equation proposed by Rassamdana
et al. (1996) for asphaltene precipitation. They examined
the universality of exponents Z and Z0 and found that Z0 is a
universal constant (Z0 = -2) while exponent Z depends on
the oil composition and independent of specific precipitant
(n-alkane) used. For the experimental data used, they found
also that the optimum value of Z is generally within the
range of 0.1 \ Z \ 0.5.
Despite the simplicity and accuracy of the scaling equa-
tion mentioned above, it is restricted to use at a constant
temperature and since temperature is not involved in the
scaling equation as a variable, it is not adequate for corre-
lating and predicting the asphaltene precipitation data
measured at different temperatures. Due to this issue, Ras-
samdana et al. modified their scaling equation by implanting
temperature parameter in the scaling equation. Based on the
previous equation, they defined two new variables x and y:
x ¼ X=TC1 ð4Þ
y ¼ Y=XC2 ð5Þ
in which X and Y are variables defined as in Eqs. (1) and (2)
and constant C1 and C2 are adjustable parameters. They
reported that the good fit of their experimental data can be
achieved by setting C1 = 0.25 and C2 = 1.6.
Again the new scaling equation is a third-order poly-
nomial in general form of:
y ¼ b1 þ b2xþ b3x2 þ b4x3 x [ xcð Þ ð6Þ
Hu et al. (2001) studied the effects of temperature,
molecular weight of n-alkane precipitants and dilution ratio
on asphaltene precipitation in a Chinese crude oil
experimentally. The amounts of asphaltene precipitation at
four temperatures in the range of 293–338 K were measured
using seven n-alkanes as precipitants. They found that their
experimental data could not be well correlated by setting
C1 = 0.25 and C2 = 1.6 as recommended by Rassamdana
et al. (1996). They reported that their experimental data
could be correlated successfully by choosing C1 = 0.5 and
C2 = 1.6. Regression plot of predicted asphaltene
precipitation using scaling model (Hu and Guo 2001)
against experimental data is shown in Fig. 1.
Artificial neural networks
Artificial neural networks are parallel information pro-
cessing methods which can express complex and nonlinear
relationship use number of input–output training patterns
from the experimental data. ANNs provides a non-linear
mapping between inputs and outputs by its intrinsic ability
(Hornik et al. 1990).
Fig. 1 Movement of colonies toward their relevant imperialist
100 J Petrol Explor Prod Technol (2011) 1:99–106
123
The most common neural network architecture is the
feed-forward neural network. Feed-forward network is the
network structure in which the information or signals will
propagate only in one direction, from input to output. A
three layered feed-forward neural network with back
propagation algorithm can approximate any nonlinear
continuous function to an arbitrary accuracy (Brown and
Harris 1994; Hornick et al. 1989).
The network is trained by performing optimization of
weights for each node interconnection and bias terms until
the output values at the output layer neurons are as close as
possible to the actual outputs. The mean squared error of
the network (MSE) is defined as:
MSE ¼ 1
2
XG
k¼1
Xm
j¼1
YjðkÞ � TjðkÞ� �2 ð7Þ
where m is the number of output nodes, G is the number of
training samples, YjðkÞ is the expected output, and TjðkÞ is
the actual output. The data are split into two sets: a training
data set and a validating data set. The model is produced
using only the training data. The validating data are used to
estimate the accuracy of the model performance.
Imperialist competitive algorithm
The ICA is a new evolutionary algorithm in the evolu-
tionary computation field based on the human’s socio-
political evolution (Atashpaz-Gargari and Lucas 2007).
Like other evolutionary algorithms, the ICA starts with
initial populations called countries. There are two types of
countries: colony and imperialist (in optimization termi-
nology, countries with the least cost) which together form
empires. In the imperialistic competition process, imperi-
alists try to attempt to achieve more colonies. So during the
competition, the powerful imperialists will be increased in
the power and the weak ones will be decreased in the
power. When an empire loses all of its colonies, it is
assumed to be collapsed. At the end, the most powerful
imperialist will remain in the world and all the countries
are colonies of this unique of this empire. In this stage,
imperialist and colonies have the same position and power.
The implementation procedures of our proposed
matching strategy based on ICA are described as follows.
Generating initial empire
A country formed as an array of variable values to be
optimized. In a Nvar dimensional optimization problem, this
array defined by:
Country ¼ P1;P2;P3; . . .;PNvar½ � ð8Þ
The cost of a country is found by evaluating the cost
function f :
Cost ¼ f countryð Þ ¼ f ð½P1;P2;P3; . . .;PNvar�Þ ð9Þ
The algorithm starts with the number of initial countries
(Ncountry), number of imperialist (Nimp) and number of the
remaining country are colonies that each belongs to an
empire (Ncol) the initial number of colonies of an empire in
convenience with their powers. To divide the colonies
among imperialists proportionally, the normalized cost of
an imperialist is defined by:
Cn ¼ cn �maxifcig ð10Þ
where cn is the cost of nth imperialist and Cn is its
normalized cost. Having the normalized cost of all
imperialist, the power of each imperialist is calculated by:
Pn ¼CnPNimp
i¼1 Ci
���������� ð11Þ
In the other hand, the normalized power of an
imperialist is determined by its colonies. Then, the initial
number of an imperialist will be:
NCn ¼ roundfPn � Ncolg ð12Þ
where NCn is the initial number of colonies of nth empire
and Ncol is the number of all colonies. To divide the col-
onies among imperialists, NCn of the colonies is selected
randomly and assigned them to each imperialist. The col-
onies together with the imperialist form the nth empire.
Moving colonies of an empire toward the imperialist
The imperialist countries try to improve their colonies and
make them a part of themselves. This fact is modeled by
moving all colonies toward their relevant imperialist. Fig-
ure 1 (Atashpaz-Gargari and Lucas 2007) shows this move-
ment. In this figure, the colony moves toward the imperialist
by x (is a random variable with uniform distribution) units.
x�Uð0; b� dÞ ð13Þ
where b is a number greater than 1 and d is the distance
between a colony and an imperialist. In the moving pro-
cess, a colony may reach a position with lower cost than
that of its imperialist. In this case, the imperialist and the
colony change their positions. Then, the algorithm will
continue by the imperialist in the new position and then
colonies start moving toward this position.
The total power of an empire
The total power of an empire depends on both the power of
the imperialist country and the power of its colonies. This
fact is modelled by defining the total cost by:
J Petrol Explor Prod Technol (2011) 1:99–106 101
123
TCn ¼ Cost imperialistnð Þþ nmeanfcostðcolonies of impirenÞg ð14Þ
where TCn is the total cost of then th empire, and n is a
positive number which is considered to be less than 1. A
small value for n implies that the total power of an empire
to be determined by just the imperialist and increasing it
will increase the role of the colonies in determining the
total power of an empire. The value of 0.1 for n is a proper
value in most of the implementations.
Imperialistic competition
All empires try to take the possession of colonies of other
empires and control them. The imperialistic competition
gradually brings about a decrease in the power of weaker
empires and an increase in the power of more powerful
ones. This competition is modelled by just picking some
Table 1 Compositions (mol%) and properties of the degassed Cao-
qiao crude oil and separator gas
Component Degassed oil Separator gas
CO2 0.0 2.96
N2 0.0 1.18
C1 0.0 89.37
C2 0.0 3.34
C3 0.0 2.10
i-C4 0.0 0.32
n-C4 0.0 0.26
i-C5 0.16 0.22
n-C5 0.58 0.15
n-C6 1.2 0.12
C7? 98.06
C11? 87.16
C7? molecular weight (g/mol) 503.6
C7? density (at 293 K) 0.9526
Reservoir temperature 343
Bubble point pressure at 343 K (MPa) 9.8
Gas oil ratio (GOR, m3/m3) 30.2
Saturates (wt%) 38.0
Aromatics (wt%) 47.6
n-C5 asphaltenes (wt%) 7.26
Resins (wt%) 18.6
Table 2 Comparison between the performances of ICA–ANN and
scaling model
ICA–ANN ANN Scaling
MSE 0.0032749 0.83759 0.69396
R2 0.99367 0.95586 0.96413
Fig. 2 Regression plot of prediction by scaling equation (Hu and
Guo 2001)
(a)
(b)
20 40 60 80 100 120-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1Training Data
time (samples)
5 10 15 20 25 30 35 40 45 50 55 60-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1Testing Data
time (samples)
Fig. 3 Comparison between measured and predicted asphaltene
precipitation (ICA-ANN): a training, b test
102 J Petrol Explor Prod Technol (2011) 1:99–106
123
(usually one) of the weakest colonies of the weakest
empires and making a competition among all empires to
possess this colonies.
To start the competition, first, the possession probability
of each empire is found based on its total power. The
normalized total cost is obtained by:
NTCn ¼ TCn �maxifTCig ð15Þ
where, TCn and NTCn are the total cost and the normalized
total cost of nth empire, respectively. Having the
normalized total cost, the possession probability of each
empire is given by:
10-5
100
105
grad
ient
Gradient = 0.005049, at epoch 19
10-4
10-3
10-2
mu
Mu = 0.001, at epoch 19
0 2 4 6 8 10 12 14 16 180
5
10
val f
ail
19 Epochs
Validation Checks = 6, at epoch 19
Fig. 4 Training state plot of
ICA-ANN
10-5
100
105
grad
ient
Gradient = 0.85593, at epoch 50
10-4
10-2
100
mu
Mu = 0.001, at epoch 50
0 5 10 15 20 25 30 35 40 45 500
5
10
val f
ail
50 Epochs
Validation Checks = 6, at epoch 50
Fig. 5 Training state plot of
ANN
J Petrol Explor Prod Technol (2011) 1:99–106 103
123
PPn¼ NTCnPNimp
i¼1 NTCi
���������� ð16Þ
To divide the mentioned colonies among empires,
vector P is formed as
P ¼ PP1;PP2
;PP3; . . .;PPNimp
h ið17Þ
Then the vector R with the same size as P whose
elements are uniformly distributed random numbers is
created,
R ¼ r1; r2; r3; . . .rNimp
� �ð18Þ
Then vector D is formed by subtracting R from P
D ¼ P� R ¼ D1;D2;D3; . . .;DNimp
� �ð19Þ
Referring to vector D, the mentioned colony (colonies)
is handed to an empire whose relevant index in D is
maximized.
Powerless empire will collapse in the imperialistic
competition and their colonies will be divided among other
empires. At the end, all the empires except the most
powerful one will collapse and all the colonies will be
under the control of this unique empire. In this stage,
imperialist and colonies have the same position and power.
Results and discussion
In this study, an ANN was used to build a model to predict
asphaltene precipitation using the data reported in literature
Fig. 6 Regression plot of ICA-
ANN
104 J Petrol Explor Prod Technol (2011) 1:99–106
123
(Hu and Guo 2001). The best ANN architecture was: 3-4-
10-1 (3 input units, 4 hidden neurons in first layer, 10
hidden neurons in second layer, 1 output neuron). ANN
model trained with back propagation network was trained
by Levenberg–Marquardt using three parameters: (1)
molecular weight, (2) dilution ratio, and (3) temperature as
inputs. The transfer functions in hidden and output layer
are sigmoid and linear, respectively. Physical and ther-
modynamic properties of oil used for generating experi-
mental data by Hu and Guo (2001) are shown in Table 1.
ICA is used as neural network optimization algorithm
and the MSE used as a cost function in this algorithm. The
goal in proposed algorithm is minimizing this cost func-
tion. Every weight in the network is initially set in the
range of [-1, 1]. In these simulations, the number of
imperialists and the colonies is considered 4 and 40,
respectively; parameter b is set to 2. The number of
training and testing data is 130 and 60, respectively.
0 2 4 60
1
2
3
4
5
6
Experimental
AN
N O
utpu
t
Training: R2=0.90418
Data
FitY = T
0 2 4 60
1
2
3
4
5
6
7
Experimental
AN
N O
utpu
t
Validation: R2=0.93718
Data
FitY = T
0 2 4 60
1
2
3
4
5
6
Experimental
AN
N O
utpu
t
Test: R2=0.95586
Data
FitY = T
0 2 4 60
1
2
3
4
5
6
7
Experimental
AN
N O
utpu
t
All: R2=0.92419
Data
FitY = T
Fig. 7 Regression plot of ANN
0 2 4 6 8 10 12 14 16 1810
-4
10-3
10-2
10-1
100
101
Best Validation Performance is 0.0032749 at epoch 13
Mea
n S
quar
ed E
rror
(m
se)
19 Epochs
TrainValidationTestBest
Fig. 8 Performance plot of ICA-ANN
J Petrol Explor Prod Technol (2011) 1:99–106 105
123
The simulation performance of the ICA–ANN model
and ANN model were evaluated on the basis of MSE and
efficiency coefficient R2. Table 2 gives the MSE and R2
values for the three different models of the validation
phases. Prediction of asphaltene precipitation by scaling
model is shown in Fig. 2 and prediction of asphaltene
precipitation in the training and test phase is shown in
Fig. 3. The simulation performance of the ICA–ANN
model and ANN model were evaluated on the basis of
MSE and efficiency coefficient R2. Table 2 gives the MSE
and R2 values for three different models of the validation
phases. Training state and regression plot and performance
of ICA–ANN and ANN models are shown in Figs. 4, 5, 6,
7, 8 and 9, respectively. It can be observed that the per-
formance of ICA–ANN model is better than scaling model
and ANN model.
Conclusions
The idea of ICA algorithm is that each initial point of the
neural network is selected by ICA and the fitness of the
ICA is determined by a neural network. The experiment
with experimental data reported in literature (Hu and Guo
2001) has showed that the ICA–ANN model is successfully
demonstrated on prediction of asphaltene precipitation also
predictive performance of the proposed model is better
than that of scaling model (Hu and Guo 2001) and con-
ventional ANN model. One problem when considering the
combination of neural network and ICA for prediction of
asphaltene precipitation is the determination of the optimal
neural network structure. Proposed neural network struc-
ture described in this work is determined manually.
A substitute method is to apply the ICA or another evo-
lutionary algorithm for neural network structure optimiza-
tion, which will be a part of our future work. The proposed
asphaltene precipitation prediction model may be com-
bined with existing asphaltene precipitation modeling
softwares to speed up their performance, reduce the
uncertainty and increase their prediction and modeling
capabilities.
Open Access This article is distributed under the terms of the
Creative Commons Attribution License which permits any use, dis-
tribution and reproduction in any medium, provided the original
author(s) and source are credited.
References
Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algo-
rithm: an algorithm for optimization inspired by imperialistic
competition. In: IEEE Congress on Evolutionary Computation,
pp 4661–4667
Balan B, Mohaghegh S, Ameri S (1995) SPE Eastern Regional
Conference and Exhibition, West Virginia, pp. 17–21
Brown M, Harris C (1994) Neural fuzzy adaptive modeling and
control. Prentice-Hall, Englewood Cliffs
de Souto MCP, Yamazaki A, Ludernir TB (2002) Optimization of
neural network weights and architecture for odor recognition
using simulated annealing. In: Proceedings of the international
joint conference on neural networks, vol 1, pp 547–552
Doveton JH, Prensky SE (1992) Geological applications of wireline
logs: a synopsis of developments and trends. Log Analyst
33(3):286–303
Hornick K, Stinchcombe M, White H (1989) Multilayer feed forward
networks are universal approximators. Neural Netw 2:359–366
Hornik K, Stinchcombe M, White H (1990) Universal approximation
of an unknown mapping and its derivatives using multilayer feed
forward networks. Neural Netw 3(5):551–560
Hu Y-F, Guo T-M (2001) Effect of temperature and molecular weight
of n-alkane precipitation on asphaltene precipitation. Fluid Phase
Equilib J 192:13–25
Hu Y-F, Chen GJ, Yang JT, Guo TM (2000) Fluid phase Equilib J
171:181–195
Pedersen KS, Fredenslund A, Thomassen P (1989) Properties of oils
and natural gases. Gulf Publishing, Houston
Qu1 X, Feng J, Sun W (2008) Parallel genetic algorithm model based
on AHP and neural networks for enterprise comprehensive
business. In: IEEE International conference on intelligent
information hiding and multimedia signal processing,
pp 897–900
Rallo R, Ferre-Gin J, Arenas A, Giralt F (2002) Neural virtual sensor
for the inferential prediction of product quality from process
variables. Comput Chem Eng 26:1735–1754
Rassamdana H, Dabir B, Nematy M, Farhani M, Sahimi M (1996)
Asphalt flocculation and deposition: I. the onset of precipitation.
AIChE J 42:10–22
Reed R (1993) Pruning algorithms—a survey. IEEE Trans Neural
Networks 4:740–747
Tang P, Xi Z (2008) The research on BP neural network model based
on guaranteed convergence particle swarm optimization. In:
Second international symposium on intelligent information
technology application, IITA ‘08, vol 2, pp 13–16
0 5 10 15 20 25 30 35 40 45 5010
-1
100
101
102Best Validation Performance is 0.83759 at epoch 44
Mea
n S
quar
ed E
rror
(m
se)
50 Epochs
TrainValidationTestBest
Fig. 9 Performance plot of ANN
106 J Petrol Explor Prod Technol (2011) 1:99–106
123
SHORT COMMUNICATION - PRODUCTION ENGINEERING
Experimental setup for performance characterization of a jetpump with varying angles of placement and depth
Rit Nanda • Shashank Gupta • Ajit Kumar N Shukla
Received: 5 August 2011 / Accepted: 18 September 2011 / Published online: 5 October 2011
� The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract In an oil field, when the crude cannot come to
the surface on its own due to either low pressure differ-
ential or the fluid properties like high viscosity, artificial
lift technology has to be used. The jet pump is one of the
artificial lift techniques considered to be better than other
lift systems because of no moving parts and simple
working principle. This makes it easy to monitor and
regulate. It works on the fluid power hence it can be placed
at greater depths and at varying angles with respect to the
horizontal. In a field, some wells are deeper than the others,
while some are deviated. The performance of a jet pump is
different for different cases as the parameters affecting it
are the depth and the angle of placement. These aspects
with respect to the working of the jet pump need to be
investigated and demonstrated. Hence, an effort has been
made in this paper to design an experimental setup by
which the pump efficiency with respect to depths and
angles of placement can be easily determined. The exper-
imental setup uses a jet pump driven by an electric motor
of 2.5 kW along with a measurement setup. The jet pump
was mounted on a hinged fixture and injection fluid from a
centrifugal pump was used. The gate valve was used to
throttle the flow for injection and create resistance across
the delivery line of the jet pump as a measure of increasing
depth. These flow rates were used to characterize the per-
formance of the jet pump.
Keywords Artificial lift � Jet pump � Discharge flow rate �Injection flow rate
List of symbols
Qi Injection flow rate, m3/s
Qs Suction flow rate, m3/s
Q0 Discharge flow rate, m3/s
Pd Discharge pressure, bar
g Efficiency, %
Introduction
Artificial lift is a system that lifts the fluid from bottom of
the well to the surface artificially. In a self flowing well, the
pressure at the bottom is sufficient to naturally lift the fluid
to the surface. But once the crude is produced the pressure at
the bottom of the wellbore decline makes it unable to come
to the surface of its own. High viscosity of the crude is
another reason due to which the wells do not self flow
(Takacs 2005).
One of the artificial lift techniques is to use jet pump.
Here, the fluid is circulated through a chamber, housing a
foot valve and a venturi which causes the pressure drop when
the fluid is injected before the venturi. It sets the flow in the
pipeline housing the foot valve. Armstrong (2010) in his
study has documented the working of jet pump in terms of
principle and applications. Kwon et al. (2002) has evaluated
the chamber shape effect on the efficiency of jet pump.
Irrespective of the chamber shape, it is important to
check the performance of a jet pump for wellbore deviation
and depth parameters, as the well bore is seldom vertical. To
characterize the performance of the jet pump, various tests
have been suggested by Lal (2000). The performance
characterization of jet pump for various nozzle angles has
been studied before (New 2009), but the effect of angle of
R. Nanda � S. Gupta � A. K. N. Shukla (&)
School of Petroleum Technology, Pandit Deendayal Petroleum
University, Gandhinagar, Gujarat, India
e-mail: [email protected]
123
J Petrol Explor Prod Technol (2011) 1:107–110
DOI 10.1007/s13202-011-0010-x
placement for a vertical nozzle has not been reported. This
can be checked by the experimental setup and recommen-
dation can be made to study the effect on pump performance
by angle and depth.
In the following sections, an experimental setup has
been explained to measure the efficiency of a jet pump with
varying angles of placement and depth. The effect of
diameter and nozzle–throat area ratio and its effects have
been studied before by Lima Neto 2011 and the same has
not been reported here.
Assembly of a jet pump test rig (JPTR)
The following procedure was followed while assembling a
jet pump test rig. The materials and equipments used have
been detailed in relevant steps as follows:
• A 2.5 kW powered jet pump was installed on a tank of
200 l capacity. The tank was filled to the level of
400 mm for testing purpose as shown in Fig. 1.
• A collecting tank of approximately 43 l capacity was
installed for measurement of flow rate from the jet
pump. Transparent graded tubing was used to see the
level of water in the collecting tank and simultaneous
measurement for time duration was done to calculate
the discharge flow rate.
• A hinged fixture was developed with slots for 90�, 60�,
45�, 30� and 0� hold angles. The jet pump was mounted
on the hinged arm and the fixed arm was kept as base.
Initially, the hinged arm was kept perpendicular to the
fixed arm, so that the jet pump was positioned vertical
to perform the test.
• The pump was primed and electric motor powering the
injection line was switched on.
• The gate valve fitted on the injection line was used to
control flow rates. The flow rate was measured by the
pressure drop across the orifice plate fitted in the
injection line as shown in Fig 1. Mercury manometer
was used to measure the pressure drop across the orifice.
• The discharge valve in the discharge line was used to
control the discharge flow rate and pressure gauge was
used to measure the discharge pressure. Similarly,
suction pressure gauge was used to measure the
pressure in the delivery line of the jet pump.
• The performance characteristic of jet pump was
obtained in vertical position at constant injection rates
by varying discharge flow rates. Similarly, the perfor-
mance test was done at two other angles of placement,
45� and at horizontal position.
Experimentation and computation
To evaluate the performance characteristics, values of flow
rates are calculated for various angles of placement and
depths. The computation process was carried out as under:
• The efficiency was calculated at five different points of
opening of gate valve at set injection rate. The point of
best efficiency was obtained through this which signi-
fies the operating point at given injection rate. Simi-
larly, the test was repeated for other positions.
• Now the angle of placement was changed and the
efficiency was calculated for the above injection flow
rate and the corresponding point of best efficiency was
determined. It was found that the efficiency dropped
when the angle of placement was changed from vertical
to horizontal position.
• When the gate valve fitted on delivery line was closed,
a reduction in discharge pressure signified the effect of
increased depth and the values of efficiencies were
measured at each angle of placement. It was found that
by increasing the head over the pump the efficiency
increased.
• The above steps were checked for repeatability and the
operating point was found at the nearly same point in
each case.
• Furthermore, the range of efficiency in each measure-
ment showed repeatability with previous measurements
for the same operating conditions.
Results and discussion
The performance characteristics of jet pump are reported at
two conditions:
a. Various angles of placement
b. Various depths of placement at different anglesFig. 1 Schematic of the experimental setup
108 J Petrol Explor Prod Technol (2011) 1:107–110
123
Table 1 shows that at constant injection flow rate and
discharge head the efficiency of jet pump is higher when it
is placed vertically than when it is placed horizontally.
The flow rate at vertical position is around 9% greater than
when it is placed in horizontal position. The reason to this
is attributed to greater buoyancy force due to submergence
but having dead weight of the valve same. This follows
the linear relationship as at 450, midway the corresponding
increase is around 5% only. It further shows that suction
flow rate is greater when it is positioned vertically and the
magnitude is around 22% higher while at 450, again it
follows the linear relationship reducing to 11% rise from
the minimum flow rate. Corresponding to this, there is a
5% difference in efficiency when the jet pump is placed in
vertical position and horizontal position. The analyses here
consider single phase fluid with no dissolved gas in it. As
the main flow take the fluid upward beyond the venturi,
the pressure remains positive and is sufficient for main-
taining only the flow. It does not carry any hydrodynamic
action as at fully closed position of delivery valve the
injection line act as the circulating line without harming
the pump.
Table 2 shows that at vertical position of the jet pump
the efficiency of the pump decreases if the depth of the
pump is decreased. It also shows that the discharge flow
rate increases when depth is increased. A 10% increase in
flow caters to 15% increase in head over the pump. This is
explained as with larger head it provides larger length of
the pipe which carries kinetic energy of the fluid for
longer time. Hence, jet pump works better at higher depth
and deliver large amount of fluid. At this condition, the
corresponding increase in suction flow rate is of order of
30–38%. This means that at greater depth in this case 15%
increase the force due to buoyancy make the valve
opening easy accommodating larger flux of fluid to get in.
This leads to 6 to 7 basis point increase in efficiency from
its base point. Likewise, the efficiency and discharge flow
rate curiously have nearly the same magnitude at hori-
zontal position and vertical position. It is because once the
flow commences through the foot valve, of the two
components: vertical and horizontal flows, one component
of flow becomes zero while the other is active. But when
the jet pump is at 450 both the component remains and
there is less fluid loss. This ensures that efficiency is
marginally better for 450 at greater depth. In this case it is
around 4% better. All throughout the experiment, the
injection rate is kept constant so its influence is not
accounted here with. Nevertheless, it is expected that at
larger injection power the above outcome will be
magnified.
Conclusion
The experimental setup so assembled was successful in
creating a system by which the performance of the jet
pump was characterized at different angles of placement
and depth. To enable this, unique fixture is designed. The
stress of the work is on experimental setup for performance
evaluation of a jet pump where in practical field it is dif-
ficult to make such an analysis. The success of work lies in
creating a system of arrangement through which influence
of varying angle of placement and depth is evaluated. The
range of variation of flow at vertical position to horizontal
position changed the discharge flow rate from 0.308 to
0.252 l/s which is order of 22% increase. The efficiency
was a maximum of 46% when jet pump was placed ver-
tically. It dropped to 42% at 45� when placed at greater
depth. When there was 15% decrease in discharge pressure,
there was around 10% decrease in the flow rate. The above
variations are calculated at constant operating injection
flow rates. The facility so generated can be used for future
research work on various aspects of jet pump by experi-
mentation. This study presents two interesting outcomes as
a result of testing the influence of angle of placement and
depth over jet pump: at constant depth jet pump works
better at vertical position but when it is under the influence
of both depth and angle of placement, incline position is
better once flow is commenced. It is also being an exper-
imental experience that jet pump performance is a function
of valve seating design and active pressure control is
expected to work better than the gravity and buoyancy
settled valve. At shallow depth, jet pump is expected to
perform better and the maximum limit for immersion will
be checked against vapour pressure for the working fluid.
Table 1 Influence of angle of placement on pump performance
Angle of
placement
Total
head
(bar)
Qo
(m3/s 9 103)
Qi
(m3/s 9 103)
Qs
(m3/s 9 103)
g(%)
Vertical 0.51 0.669 0.361 0.308 46
45� 0.51 0.641 0.361 0.280 44
Horizontal 0.51 0.612 0.361 0.252 41
Table 2 Influence of depth and positions on pump performance
Angle of
placement
Total
head
(bar)
Qo
(m3/s 9 103)
Qi
(m3/s 9 103)
Qs
(m3/s x 103)
g(%)
Vertical 1 0.583 0.361 0.222 38
0.85 0.521 0.361 0.160 31
450 1 0.625 0.361 0.264 42
0.85 0.563 0.361 0.202 36
Horizontal 1 0.585 0.361 0.224 38
0.85 0.531 0.361 0.171 32
J Petrol Explor Prod Technol (2011) 1:107–110 109
123
The experimental aspect of the setup developed is expected
to be extensible used for future work and create snow ball
effect in terms of the arrangement for varying angle of the
placement and depth. The authors propose that further
research can be carried out by varying the angle of place-
ment and depth for the following parameters: different
nozzle angles, different chambers shapes, varying diame-
ters, area ratio and positive and negative suction heads
(Hammoud 2006).
Acknowledgments The authors wish to acknowledge the use of
facility and technical help provided by the personnel at the fabrication
technology laboratory, Pandit Deendayal Petroleum University,
Gandhinagar, India, without whom this experiment could not have
been performed.
Open Access This article is distributed under the terms of the
Creative Commons Attribution License which permits any use, dis-
tribution and reproduction in any medium, provided the original
author(s) and source are credited.
References
Armstrong OP (2010) Summary of oil jet pump principles and
applications. SPE, Dallas
Hammoud AH 2006 Effect of design and operational parameters on
jet pump performance. In: 4th WSEAS International Conference
on fluid mechanics and aerodynamics, p 245–252.
http://www.wseas.us/e-library/conferences/2006elounda2/papers/
538-122.pdf. Accessed 29 Sept 2011
Kwon OB, Kim MK, Kwon HC, Bae DS(2002) Two-dimensional
numerical simulations on the performance of an annular jet
pump. J Vis 5(1):21–28. doi:10.1007/BF03182599
Lal J (2000) Hydraulic machines (including fluidics), testing charac-
teristics of hydraulic machines. Metropolitan Book Company Pvt
Ltd, New Delhi, pp 444–445
Lima Neto IE (2011) Maximum suction lift of water jet pumps.
J Mech Sci Tech 25(2):391–394
New TH (2009) An experimental study on jets issuing from elliptic
inclined nozzles. Exp Fluids 46(6):1139–1157. doi:
10.1007/s00348-009-0622-9
Takacs G (2005) Gas lift manual, inflow performance of oil wells.
PennWell Corp, Tulsa, p 21
110 J Petrol Explor Prod Technol (2011) 1:107–110
123