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SPE 136805
Pore-Type Determination From Core Data Using a New
Polar-TransformationFunction from Hydraulic Flow UnitsRodolfo Soto
B. /SPE, Digitoil, Duarry Arteaga, Cintia Martin, Freddy Rodriguez
/ SPE,PDVSA Western Division
Copyright 2010, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Latin
American and Caribbean Petroleum Engineering Conference in Lima,
Peru, 13 December 2010.
This paper was selected for presentation by an SPE program
committee following review of information contained in an abstract
submitted by the author(s). Contents of the paper have not
beenreviewed by the Society of Petroleum Engineers and are subject
to correction by the author(s). The material does not necessarily
reflect any position of the Society of Petroleum Engineers,
itsofficers, or members. Electronic reproduction, distribution, or
storage of any part of this paper without the written consent of
the Society of Petroleum Engineers is prohibited. Permission
toreproduce in print is restricted to an abstract of not more than
300 words; illustrations may not be copied. The abstract must
contain conspicuous acknowledgment of SPE copyright.
AbstractA new sigmoidal function from polar transformation
enables more accurate identification of pore types in
fractured/vuggy
reservoirs. The function is based on a polar transformation that
separates the pore systems into two regionsmatrix systemsand
fracture/vug systemson the basis of hydraulic properties, reservoir
quality index (RQI), flow-zone index (FZI), andnormalized porosity.
The polar transformation exhibits a hyperbolic distribution for
intergranular/intercrystalline pore sampletypes at the point where
they deviate from the trend so that we can identify pore types more
accurately. Our new function hasbeen validated from image log data
from wells of Lagomar and/or Lagomedio fields and core data from
different fields aroundthe world, and we are certain that it will
be of great help to the geoscientist when doing a reservoir
characterization.
IntroductionA great number of reservoir systems are made up of
different lithologies and pore types. The pore types could be
matrix,fractures and vugs or a combination of these. For example,
Nelson (2001) defined four types of reservoirs to
characterizematrix and fracture systems:
Type 1 reservoirs, where fractures provide all of the storage
capacity and permeability. This type of reservoir includesthe
unconventional fractured granite basement reservoirs of the Cuu
Long basin in offshore Southern Vietnam and theAmal reservoir in
Libya.
Type 2 naturally fractured reservoirs, where the matrix has
negligible permeability but contains most if not all
thehydrocarbons. This type of reservoir includes the shale gas
reservoirs in the United States, which contain up to 780 Tcfof gas
(Franz. and Jochen, 2005); the volcaniclastic reservoir in Cupen
Mahuida field, Neuqun, Argentina (Zubiri andSilvestro, 2007), and
Agha Jari in Iran. In these reservoirs, natural fractures provide
permeability and the matrixprovides storage of most of the
hydrocarbons.
Type 3 reservoirs, where the matrix already has good primary
permeability. The fractures add to the reservoirpermeability and
can result in considerably high flow rates. Oil is trapped in both
the matrix and fractures. Examples ofType 3 reservois are the giant
Kirkut field in Iraq, Ghawar field of Saudi Arabia, Gachsaran in
Iran, Dukhan in Qatar,and the big Cusiana field of Colombia. These
reservoirs are some of the most prolific producers.
Type 4 reservoirs, where the fractures are filled with minerals.
Fractures provide no additional porosity or permeabilitybut create
a significant reservoir.
The definition of these four types of reservoirs, based on
matrix and fracture systems, does not cover all the pore
systemspresent in the real world, and in general, one of the
potential problems when more than one pore type is present in a
reservoiris related to nonreconigtion of one of the them on plug
samples and reservoirs.Determining the kind of pore types in core
and log data is not easy. Consequently, petrophysicists and
geologists developingpetrophysical models often erroneously apply
the methodologies and equations designed for
intergranular/intercrystallinereservoir systems to complex systems
(intergranular/ intercrystalline, fracture, and/or vug pore type).
However, if we have acomplex pore type system, the cementation
exponent, m, is not constant but variable; and changes in the
cementation exponentvalue can greatly affect water saturation
calculated by the Archie equation, affecting the original oil in
place (OOIP), thereserves, and the evaluation of potential pay
zones. Often, the difference between economic and noneconomic
production
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2 SPE 136805
depends on the time the presence of fractures is detected in the
life of the field. In general, for reservoir types where storageand
permeability are presented in the matrix and fractures, virtually
all potential problems are related to nonreconigtion of thefracture
system.Several investigators have attempted to solve this problem
by developing methods from core analysis (Kamath et al.,
1990Hopkins, et al., 1991; Ning and Holditch, 1993), well logging
using a series of crossplots (Asquith 1995; Soto-B. et al.
2010),pressure transient analysis, and 3D seismic data. Each of
those methods has certain advantages, limitations, applicability
andreliability.This paper discusses a new methodology to recognize
the presence of more than one pore type from permeability and
porositycore data.
Hydraulic Flow Unit Classification Using Reservoir Quality Index
(RQI) and Flow Zone Index (FZI)
The first step in this methodology is to apply the concepts of
reservoir quality index (RQI) and flow unit indicator (FZI)
toclassify core data in hydraulic flow units (HFU) according to
Amaefule et al. (1993). This concept lets us average the
rockproperties with minimal error. In this case, the RQI and FZI
parameters are calculated using the following relationships:
=core
corematrix *0314.0RQI k
.
.................................................................................(1)
)1/(( corecore =z .
...............................................................................
........................(2)
zRQIFZI =
................................................................................................................(3)
( )Zlog log(FZI) )RQIlog( +=
...............................................................................................(3a)
Therefore, a plot of RQI versus z on log-log scale will
delineate the flow units with FZI constant for each unit.
However,these equations were developed assuming a matrix system
where the porosity and permeability are
intergranular/intercrystalline, which means they may not be
sufficient for more complex formations.
Polar Arm and AngleThe second step is to validate whether the
hydraulic flow units belong to more than one pore system. We found
that a good
way to identify the pore type of the core data is to make a
transformation of FZI and z called the polar arm, r:
( )[ ]1FZI* 2 += zr .
......................................................................................................(4)and
calculate the polar angle as:
)ATAN(FZIpolar = .
............................................................................................................(5)
If we plot the polar arm vs. polar angle (Fig. 1), we can see
that polar transformation exhibits a hyperbolic distribution
forintergranular/intercrystalline pore samples. On that plot we
have used core data from reservoirs in different parts of the
world:Venezuela, the USA, Iraq and Saudi Arabia. Those core data
sets also include some fractured/vuggy data sets known from
labdata. It is easy to see that fractured/vuggy pore samples
deviate from the hyperbolic trend and let us identify pore types
moreaccurately. We have developed a sigmoidal function that
separates the plot into two regions:
( )[ ]{ }/Dr-C-+A+B/ exp1regionpolar = .
............................................................................................
(6)where A = -3.5916207; B = 5.06265818; C = -0.72243226; D =
0.371324681.
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SPE 136805 3
Above the sigmoidal function, the data fall into the fracture or
vuggy system, and below that region, they belong to
theintergranular/intercrytalline system. If RQI, z, and FZI are
calculated using a spreadsheet, it is easy to also calculate Eqs.
4, 5,and 6 and compare the values from Eqs. 5 and 6: if the value
calculated from Eq. 5 is less than or equal to the value
calculatedfrom Eq. 6, the core data are intergranular, but if not
the core data pore type could be fractured or vuggy. We also
validatedthis sigmoidal function with image log data from the data
set of the Lagomar and Lagomedio fields in the Cretaceousformation
at Lake of Maracaibo in Venezuela.
Fig. 1Sigmoidal function diferentiates pore type systems from
core data using polar transformation of FZI and z.
Flow Properties Determination for Fracture Pore SystemsAccording
to Tiab et al. (1993), for a naturally fractured or vuggy reservoir
system, permeability is given as a function of totalporosity,
specific surface area, and m as follows:
2
12
2gv )1(1
t
mt
SFSk
=
+.
.........................................................................................................(7)
Therefore, following the hydraulic flow units concept, Ohen et
al. (2001) defined RQI for fractured systems as
1-20.0314 FRQI mt
k=
, .
......................................................................................................(8)
and therefore the relationship between RQI and FZI defined in
Eq. 3 for a fractured system is as follows:
( )Zlog log(FRZI) )FRQIlog( += .
....................................................................................(9)And
using the same concept of hydraulic units, HU, for a matrix pore
system, a plot of FRQI versus z on a log-log scale willdelineate
the flow units (Soto B. et al. 1993, 2001).
Sigmoidal Function to Differenciate Pore TypeSystems
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.5 1 1.5 2 2.5 3 3.5 4
Polar Arm, r,z*(FZI2 +1)1/2
polar angle, ATAN(FZI)
USA RESERVOIR
ARAB RESERVOIR
IRAK RESERVOIR
CRETACEOUS LAKE- ALL PORETYPE
MODEL_SIGMOIDAL
SVS-225_DATE FRACTURE DESCRIPCIN
SVS-225_DATE INTERGRANULARDESCRIPCIONVLA-1562_DATE LOG IMAGEN
VUGGY
VLA-1562_DATE LOG IMAGEN FRACTURE
VLA-1562_DATE LOG IMAGENINTERGRANULAR
Fracture/Vuggs
Intercrystalline
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4 SPE 136805
Determination of Hydraulic Flow Units in a Complex Pore
System:Cretaceous Formation at Maracaibo Lake
The cretaceous formation at Maracaibo Lake contains carbonate
reservoirs with a variety of pore types (see Soto-B. et al.2010)
such as intergranular/intercrystalline, vugs and fractures. To
determine the hydraulic flow units, we used corepermeability and
porosity from Wells VLA-711, VLA-978, VLA-1562, and UD-791 from
Lagomar field and Well SVS-225from Lagomedio field. Some of that
data was reported from the core laboratory as fractured and vuggy
and was validated withimage logs (see Fig. 2).To verify the
reported data and recognize the presence of various pore types from
the other lab, we applied Eqs. 1 through 6and put the results into
Fig. 1. Then, to determine the hydraulic flow units, we applied the
procedure explained by Soto B. etal. )(using the Eqs.1 through 3
for intercrystalline pore systems and Eqs. 8 and 9 for fracture
systems. We found 11 hydraulicflow units that represent all of the
pore system types: five hydraulic units for intercrystalline
systems, five for fractures, andone for vugs (Fig. 3).
1582215822
1584615846
1582215822
1584615846
Ejemplo FM APON Cotejo PHIfracture y PHIvuggy con Registro de
Imagen FMI VLA-1562 Example APON FM, PHIvuggy and PHIfracture
matching log image of well VLA1562
Fig. 2Fracture and vuggy pore types from cores compared with the
formation microimaging (FMI) log in the VLA-1562 well.
Fig.3The hydraulic flow units appear clearly in the pore complex
system for Cretaceous Formation at Lake of Maracaibo.
Table 1 shows the ranges or limits of FZI and RQI for fractures
and intergranular pore and rock types. From this rock
typingdiscrimination, we were able to determine a complex
permeability model using fuzzy logic to predict the permeability
for all
Hydraulic Flow Units: all Pore Type SystemsCretaceus, Maracaibo
Lake
0.001
0.010
0.100
1.000
10.000
100.000
0.001 0.010 0.100 1.000z
RQI
HU1_F HU2_F HU3_F HU4_F HU5_F HU6_Interc HU7_Interc HU8_Interc
HU9_Interc HU10_interc HU11_VUG
1
2
3
4
5
67
89
10
11
Intercrystalline Flow Units
Vug Flow Units
Fracture Flow Units
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SPE 136805 5
of the pore-type systems in these reservoirs.Table 1Ranges of
FZI and RQI for Fracture and Intergranular Pore and Rock Type
ConclusionWe have found that a plot of the the polar arm, r,
against the polar angle, polar, exhibits a hyperbolic distribution
for
intergranular/intercrystalline pore samples, so that
fractured/vuggy pore samples deviate from the trend and let us
identify poretypes more accurately. The polar angle, polar, comes
from the polar-transformation of the flow zone index, FZI, and z.A
new sigmoidal function from that polar-transformation separates the
pore systems into two regions: matrix systems andfracture/vug
systems. This new methodology enabled us to discriminate the
presence of more than one pore type frompermeability and porosity
core data. When this occurs, the hydraulic flow units are
calculated more accurately and reduce theuncertainty in developing
confident permeability and water saturation models or any other
implication in the development ofpetrophysical models.
NomenclatureATAN = arctangentm = cementation exponente =
effective porositycore = core porosityt = total porosityK =
permeabilityKcore = core permeabilitySgv = grain specific surface
areaFs = pore throat shape factorFRQI = reservoir quality index for
fractured rock system.FRZI = flow zone index for fractured rock
system.FZI = flow zone index for intercrystalline rock system.r =
polar armRQImatrix = reservoir quality index for intercrystalline
rock system.polar = polar angle
PORE TYPE ROCK TYPE Range of Values of FZI and RQI
Intergranular system
FZI>259 RQI>10
124
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6 SPE 136805
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