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8/8/2019 TORRES-VERDIN Salt Saturation in-Sut
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March-April 2004 PETROPHYSICS 141
Assessment of In-Situ Hydrocarbon Saturation in the Presence of Deep
Invasion and Highly Saline Connate Water1
Carlos Torres-Verdn2, Bovan K. George
2, Mojdeh Delshad
2, Richard Sigal
3,
Farid Zouioueche3, and Barbara Anderson
4
INTRODUCTION
The drilling of wells with heavy mud causes large over-
balance pressures, resulting in deep invasion of mud filtrate
into porous and permeable layers. In the past, the effect of
mud-filtrate invasion on induction logs has been studied
using simplified models of radial invasion. The simplest
invasion model is the step invasion profile, which assumes
a completely flushed zone of resistivityRxo and diameterDi,
beyond which lies the undisturbed (virgin) formation of
resistivity Rt. Such a model embodies three unknowns (Rt,
Rxo,andDi) that, in theory, can be resolved using three resis-
tivity logs exhibiting complementary depths of investiga-
tion. This is a useful but idealistic approach because a sharp
boundary seldom exists between the completely flushed
PETROPHYSICS, VOL. 45, NO. 2 (MARCH-APRIL 2004); P. 141156; 22 FIGURES, 5 TABLES
ABSTRACT
This paper describes a field study undertaken to quan-
tify the effects of mud-filtrate invasion on resistivity
induction logs. The objective is to assess in-situ gas satu-
ration in a low-porosity carbonate formation. A large dis-crepancy between the salinity of connate water and drill-
ing mud is responsible for the presence of a substantial
low-resistivity annulus in the near-wellbore region. This
annulus suppresses the sensitivity of electromagnetic
induction currents to detecting gas saturation in the virgin
zone. A quantitative explanation for the presence of the
low-resistivity annulus is presented based on the physics of
mud-filtrate invasion.
The process of mud-filtrate invasion is modeled with a
two-dimensional chemical flood simulator that includes
the effect of salt mixing between mud filtrate and connate
water. Radial resistivity profiles are obtained from the
simulated spatial distributions of water saturation and salt
concentration using Archies law. These profiles confirm
the presence of the low-resistivity annulus in the transi-
tion region between the flushed and virgin zones. Numeri-
cal simulation of induction logs validates the agreement
between the mud-filtrate invasion model and the available
wireline induction logs.
An extensive sensitivity analysis is performed to quan-tify the effect of several petrophysical parameters on the
spatial distributions of water saturation and salt concen-
tration. Results from this study show that the pre-annulus
and annulus segments of the radial resistivity profile
remain insensitive to initial water saturation, thereby
impeding the estimation of in-situ gas saturation from
resistivity induction logs alone. Modeling of the process
of mud-filtrate invasion is the only possible way to esti-
mate in-situ hydrocarbon saturation from induction logs.
It is also found that laterolog measurements are only mar-
ginally affected by the presence of a low-resistivity annu-
lus.
The sensitivity analysis described in this paper pro-
vides a rigorous quantitative method to assess the effects
of different types of muds on the invaded zone prior to
drilling.
Manuscript received by the Editor July 4, 2003; revised manuscript received February 4, 2004.1Originally presented at the SPWLA 44th Annual Logging Symposium, June 22-25, 2003, Galveston, Texas, paper K.2The University of Texas at Austin, Austin, Texas USA.
3Anadarko Petroleum Corporation4Schlumberger-Doll Research, Ridgefield, CT
2004 Society of Petrophysicists and Well Log Analysts. All rights reserved.
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zone of resistivity Rxo and the undisturbed formation of
resistivity Rt. In the past, slightly more sophisticated radial
parametric models of mud-filtrate invasion have been used
for interpretation, including three-stage ramp and annulus
resistivity profiles. Actual radial fluid saturation and resis-
tivity profiles can be quite complex and largely depend on
specific petrophysical properties of the rock as well as on
the properties of the fluids involved. A specific radial para-
metric model of electrical resistivity cannot be uniquely
interpreted from resistivity induction data alone without
prior knowledge of the fluid and rock-fluid formation prop-erties.
The study presented in this paper is focused on a
gas-bearing carbonate formation. This formation was pene-
trated by well X-2 using a heavy freshwater base mud,
thereby causing an overbalance pressure in excess of 1000
psi. Table 1 describes the properties of the mud used to drill
well X-2. Lithology in the gas-bearing zone consists of
inter-layered carbonates along with fine-grained clastics
and shales. Porosity of the gas-bearing formation is low,
usually less than 15%, hence contributing to deep invasion.A major challenge faced in theevaluation of this reservoiris
the deep invasion of mud filtrate adversely affecting the
response of resistivity measurements. Gas saturation of the
formation is about 80-85% with the remaining pore space
occupied by irreducible connate water. Salinity of the mud
filtrate is about 2,000 ppm whereas the salinity of connate
water is about 200,000 ppm. Dual Induction Logs (DIL*)
acquired in well X-2 (shown in Figure 1) exhibit a reverse
resistivity profile where deep dual-induction (ILD) read-
ings (20-22 ohm-m) are lower than the medium dual-induc-
tion readings (ILM, 25-30 ohm-m). Both ILD and ILM
readings are lower than the shallow, Rxo readings (90-100ohm-m) indicated by MSFL and SFL.
A nearby well, here identified as X-1, was drilled a few
hundred feet away from well X-2. This well was drilled
with a light mud resulting in very shallow invasion. Table 2
describes the properties of the mud used to drill well X-1.
Resistivity logs acquired in well X-1 exhibit a normally
ordered resistivity profile across the same carbonate forma-
tion (shown in Figure 2) with the following array induction
(AIT*) readings: AIT90 = 50-60 ohm-m, AIT60 = 40-50
ohm-m and AIT10 = 30-35 ohm-m. In addition to Array
Induction data, Dual Laterolog (DLL*) data were acquired
in well X-1 (shown in Figure 3). Well X-1 is considered a
key well in the present study due to both negligible invasionand the availability of extensive log and core data. Rock
core and well-log data acquired in well X-1 are used as a
benchmark in the present work. This well provides a unique
reference to quantify the effect of mud-filtrate invasion on
142 PETROPHYSICS March-April 2004
Torres-Verdn et al.
*Mark of Schumberger
TABLE 1 Summary of measured mud properties for Well X-2 (the well that exhibits deep invasion).
Depth Mud Weight Viscosity Loss Control Chloride W/L Solids
(ft) (ppg) (cp) Material (lb/gal) Ph (ppm) (cc/30 min.) (%)
X215 NativeX920 8.8 35 6 8.5
X500 9 33 6 8
X080 8.9 36 6 8 1200
X540 9 38 6 8.8 1000 14 5.2
X015 9 38 8 8 900 13 5
X375 9.1 38 8 8.5 900 11
X730 9.1 37 8 8.5 900 11 Bit Trip
X200 9.1 50 8 9.9 800 9.2
X300 9.1 50 8 10 950 9.6 5.7
TABLE 2 Summary of measured mud properties for WellX-1 (the well that exhibits negligible invasion).
Depth Mud Weight Viscosity Chloride
(ft) (ppg) (cp) Ph (ppm)
X444 1.2 81 8.1 1250
X497 1.1 81 8 400
X552 0.96 82 8.1 280
X559 1.1 82 8.02 260
X592 1.2 82 8.02 240
X608 1.2 82 8 230
X608 9 82 8.03 320
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March-April 2004 PETROPHYSICS 143
Assessment of In-Situ Hydrocarbon Saturation in the Presence of Deep Invasion and Highly Saline Connate Water
FIG. 1 Plot of the basic suite of measured wireline logs in Well X-2, including dual induction readings.
FIG. 2 Plot of the basic suite of measured wireline logs in Well X-1, including array induction readings.
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the resistivity logs acquired along the same carbonate for-
mation in well X-2.
Lower-than-normal deep resistivity readings cause over-
estimation of connate-water saturation, which results in
underestimated hydrocarbon reserves. The study reported
in this paper was undertaken to quantify the effect ofmud-filtrate invasion on resistivity logs. It was anticipated
that proper modeling of the mud-filtrate invasion profile
would help to correct deep resistivity readings and hence to
improve estimates of in-situ water saturation using existing
well-log data. Preliminary studies performed prior to the
work reported in this paper had suggested the presence of a
substantial low-resistivity annulus as the cause of the low
resistivity readings in well X-2.
In the past, presence of low-resistivity annuli has been
discussed by several authors, including Dumanoir et al.,
1957, Gondouin et al., 1964, Ramakrishnan and Wilkinson,
1999, and Zhang et al., 1999. However, a consistent andsystematic petrophysical explanation for the origin and
properties of such an annulus has not been presented before
in light of actual field data. This paper develops a consistent
explanation for the presence of a low resistivity annulus
based on the physics of mud-filtrate invasion and salt mix-
ing between mud filtrate and irreducible connate water. The
model of mud-filtrate invasion is benchmarked against
measured borehole induction resistivity data and conclu-
sions are drawn concerning the interpretation of in-situ
hydrocarbon saturation in the virgin zone.
Invasion of mud filtrate into the formation is modeled asa two-dimensional (2D) axisymmetric chemical flood pro-
cess. Filtrate invasion is simulated to obtain cross-sections
of water saturation as a function of depth and radial distance
away from the borehole wall. Cross-sections of salt concen-
trations are also obtained by modeling the mixing of salt
between the invading fresh mud filtrate and the highly
saline connate water. As shown below, the radial variation
of salt concentration within the invasion zone is responsible
for the presence of a low resistivity annulus around the
borehole.
NUMERICAL SIMULATION
OF MUD-FILTRATE INVASION
Mud-filtrate invasion is treated in an equivalent manner
to the process of water injection into a gas reservoir.
Accordingly, two-phase immiscible fluid flow is assumed
144 PETROPHYSICS March-April 2004
Torres-Verdn et al.
FIG. 3 Plot of the basic suite of the measured wireline logs in Well X-1, including dual laterolog readings (compare to the inductionlogs shown in Figure 2).
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in the simulations of mud-filtrate invasion (Dewan and
Chenevert, 2001, and Semmelbeck et al., 1995). Rate of
invasion of mud filtrate across the borehole wall is calcu-
lated as a flow rate function resulting from mudcake
buildup (Wu et al., 2001). The flow of mud filtrate through
mudcake can be described by Darcys law, i.e.,
QkA P
hf
mc
=m
D, (1)
where Qfis the flow rate of mud filtrate across the borehole
wall, kis the mud cake permeability, A is the cross-sectional
area through which the filtrate flows,m is the viscosity of fil-trate, hmc is the thickness of mud cake, and DP is the pressuredrop across the mud cake.
In this paper, flow of mud filtrate across the mudcake is
modeled using an axisymmetric version of the 3D
multi-phase, multi-component compositional simulator
UTCHEM, developed by The University of Texas at Austin(Saad, 1989, and Delshad et al., 1996). Both dynamic
growth of mudcake thickness and dynamic decrease of
mudcake permeability are coupled to formation properties
(Wu et al., 2001). This process results in a dynamic
monotonic decrease of flow rate across the borehole wall.
After a short initial spurtof mud-filtrate invasion, the rate of
flow is found to reach a steady-state value specific to a par-
ticular layer. In the present work, the layer-dependent rate
of mud-filtrate invasion is assumed to be the steady-state
value yielded by the simulations of invasion. The simula-
tion of mud-filtrate invasion can also take into account sev-
eral cycles of mudcake rub-off and buildup.Assumptions made by the reservoir simulation model are
those of multi-component immiscible fluid displacement
governed by Darcys law and mass balance. The general
form of the mass balance equation for the k-th component
can be written as
f r r
tC C u D Rk k k k l l kl
l
n
k
p
( ) (~
) ,+ -
=
=
1
(2)
where f is porosity, Ck is the overall concentration of com-ponent k per unit pore volume, Ckl is the concentration of
component k in phase l, rk is fluid density, ul is the Darcyflux for phase l, Rk is the total source/sink term for compo-nent, kand
~Dkl the dispersive flux, defined as
~, D S K C k l l k l k l = f (3)
where Sl is the saturation for phase l, and Kkl is a dispersion
tensor. The latter tensor includes contributions from molec-
ular diffusion and hydrodynamic dispersion (Bear, 1979). A
more detailed discussion of both model formulation and
solution algorithm used by UTCHEM may be found in Saad
(1989) and Delshad et al. (1996).
Salt mixing between mud filtrate and connate water is
modeled as part of the fluid-flow simulations performed
with UTCHEM. The three most important mechanisms
causing the transport of salt in permeable media are viscousforces, gravity forces, and dispersion (diffusion) forces
where the driving mechanisms are pressure, density, and
salt concentration gradients, respectively. The transport of
salt is described by the convection-diffusion equation.
As the invading mud filtrate moves radially into the for-
mation, it mixes the uneven concentrations of salt in mud
filtrate and connate water. There are two mechanisms for
dispersive transport that take place in the mixing of fresh
and salt water, i.e., convective and molecular dispersion.
Convective dispersion is the mixing due to variations in
local velocity both in magnitude and direction. Molecular
diffusion is mixing resulting from variations in salt concen-
tration, and takes place in the absence of flow. The disper-
sion tensorKkl contained in equation (3) includes the effect
of molecular diffusion, and can be written as (for the i and j
directions)
KD
Su
S
u u
uklij
kl
ij
Tl
l
l ij
L l Tl
l
li lj
l
= + +-
td
a
fd
a a
f
( ), (4)
where Dkl is the molecular diffusion coefficient, t is atortuosity factor, aL and aT are the longitudinal and trans-verse dispersivities, respectively, dij is the Kronecker deltafunction, and uli and ulj are the components of Darcys
velocity of the phase lin the i andj directions, respectively.The first term in the right-hand side of equation (4) is due
to diffusive transport and the second term in the same equa-
tion represents dispersion due to convective transport. For
very small flow rates of mud filtration, the convective term
becomes negligible and the total mixing is caused mainly
by diffusion. For higher flow rates where the interstitial
velocity is greater than about 3 cm/day (Lake, 1989), con-
vective mixing dominates diffusive mixing. This is because
for large fluid velocities in the pores, time available for dif-
fusion will not be sufficient for complete mixing. In the
present work, the flow rate of mud filtration taking place
across a layer of thickness 2 ft is about 8 ft
3
/day. This corre-sponds to an interstitial velocity of about 320 cm/day near
the borehole wall assuming a porosity of 0.14. At such large
interstitial fluid velocities, mixing is predominantly gov-
erned by convective transport.
Two-dimensional cylindrical flow is assumed for the
numerical simulation of mud-filtrate invasion near the
borehole (i.e. 3D flow with no spatial variations in the azi-
muthal direction). A finite-difference scheme is used to
discretize and numerically solve equations (2) and (3).
March-April 2004 PETROPHYSICS 145
Assessment of In-Situ Hydrocarbon Saturation in the Presence of Deep Invasion and Highly Saline Connate Water
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Two-dimensional cross-sections of water saturation and
salt concentration are obtained directly from the simulation
results. In turn, salt concentration is transformed into an
equivalent value of connate water resistivity, Rw, using the
conversion formula (Dresser Atlas Inc., 1982)
RC T
w
w
= +
+
0012336475 82
18 390 955.
.
.,
.(5)
where Tis temperature measured in degrees Centigrade, and
Cw is salt concentration measured in ppm.
WATER SATURATION AND ELECTRICAL
RESISTIVITY IN THE INVADED ZONE
As described in the preceding section, cross-sections of
water saturation and salt concentration are obtained as the
output of the numerical simulation of mud-filtrate invasion.
In turn, values of water salinity and salt concentration are
transformed into an equivalent value of water resistivity
using equation (5). The final step is to compute the corre-sponding spatial distribution of electrical resistivity. This is
accomplished using Archies equation, namely,
SR
R
awn w
tm
=f
, (6)
where Sw is water saturation, a is the tortuosity/cementation
factor, n is the saturation exponent, f is porosity, and m isthe cementation exponent. The use of Archies law in the
present study is justified given the clastic nature of the car-
bonate sequence under consideration. In addition, the high
salinity of connate water makes it unnecessary to apply cor-
rections for the presence of clay to Archies equation. Tables
3a and 3b describe the specific values used in this study for
the various parameters included in equation (6).
Simulation of mud-filtrate invasion was performed on a
5-layer synthetic model reconstructed from the depth inter-
val X493-X551 ft of Well X-2 shown in Figure 1. As illus-
trated in Figure 4, two of these five layers were placed on
the upper and lower boundaries of the model and consisted
of impermeable shale barriers. The remaining three layers
146 PETROPHYSICS March-April 2004
Torres-Verdn et al.
TABLE 3a Summary of rock properties for well X-2.
Horiz. Perm. Vertical Perm. Tortuosity-Cementation Cementation Exponent Saturation Exponent
Porosity (md) (md) Factor, a m n
0.14 6.83 0.93 1 2 2
Table 3b Summary of mud, formation, and fluid properties for well X-2.
Invasion Initial Formation Formation Salinity of Salinity of
Time Water Temperature Pressure Mud Filtrate Connate Water
(Days) Saturation (Swi) (deg F) (psi) (ppm) (ppm)
4 0.14 98 96 2,000 200, 000
FIG . 4 Graphical description of the geometrical andpetrophysical properties of the reservoir model considered inthis paper. There are three reservoir layers (flow units) and twoimpermeable shale barriers. Porosity, vertical permeability, andthickness for the three reservoir layers are indicated on the fig-ure. The three reservoir layers exhibit a vertical permeability of0.93 md.
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in the interval X506-X536 ft, correspond to separate flow
units within the actual reservoir formation. The finite-dif-
ference grid used in the numerical simulation of mud-fil-
trate invasion consisted of 60 grid steps in the radial direc-
tion and 4 grid steps per layer in the vertical direction.
Radial grid steps were increased in geometrical progressionfrom the borehole wall into the formation in order to prop-
erly reproduce the rapid spatial variations of fluid satura-
tion and salt concentration in the near-borehole region. This
grid was also the result of a refinement study undertaken to
assess the internal consistency and numerical accuracy of
the simulated cross-sections of water saturation and salt
concentration.
Capillary pressure data (shown in Figure 5) from labora-
tory measurements for the drainage cycle is available for
the permeable reservoir layers described in Figure 4.
Because of the lack of laboratory capillary pressure for the
imbibition cycle, the available drainage-cycle data were
used in the numerical simulations for the imbibition cycle
of capillary pressure. The water-gas relative permeability
data used for the numerical simulation of mud-filtrate inva-
sion is shown in Figure 6 (henceforth referred to as Type-A
water-gas relative permeability curves). Capillary pressure
and relative permeability curves were assumed the same for
the three reservoir layers shown in Figure 4.
Figure 7 shows a radial profile of the numerically simu-
lated cross-sections of water saturation and water resistivity
taken through the center of the upper (and thicker) reservoir
layer graphically described in Figure 4. Petrophysical prop-
erties of this layer are given in Tables 3a and 3b as well as in
Figure 4. Simulation of mud-filtrate invasion was per-
formed assuming an invasion time of four days. The inva-
sion profile shows a radial length of invasion of about 7
feet, whereas the salinity profile, represented as Rw, shows
that salt concentration near the borehole is very low, equal
March-April 2004 PETROPHYSICS 147
Assessment of In-Situ Hydrocarbon Saturation in the Presence of Deep Invasion and Highly Saline Connate Water
FIG. 6 Plot of the original (TYPE A) water-gas relative perme-ability curves. The dark and light lines represent relative perme-ability curves as a function of water saturation for water and gasfluid fractions, respectively.
FIG. 7 Plots of water resistivity (Rw) and water saturation (Sw)as a function of radial distance away from the borehole wall. Thetwo curves were obtained from the 2D numerical simulation ofthe process of mud-filtrate invasion assuming an invasion timeof four days. The radial profile is taken through the upper reser-voir layer shown in Figure 4.
FIG. 5 Plot of capillary pressure as a function of water satura-tion measured on rock core samples. Only the drainage cycle ofthe capillary pressure curve was available for the studydescribed in this paper. The imbibition cycle of capillary pres-sure was assumed equal to the drainage cycle.
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to that of mud filtrate. Salt concentration begins to increase
at a radial distance of about 4 feet from the borehole wall
and it attains a maximum value (equal to that of the salinity
of connate water) at a radial distance of about 6 feet from
the borehole wall.
It becomes evident from Figure 7 that, as the invasion ofmud-filtrate progresses, the salt concentration front trails
the saturation front. This behavior results in a high-salinity,
high water saturation region at the front face of the advanc-
ing mud-filtrate column. Intuitively, it is the dephasing
and distortion of the water concentration front with
respect to the salt saturation front that causes the pres-
ence of the low-resistivity annulus. The electrical resistiv-
ity profile (Rt) calculated with the use of equation (6) shows
a low-resistivity annulus at a distance of about 5 feet from
the borehole wall (Figure 8). The deep resistivity log, with a
depth of investigation of about 5-6 feet, is for the most part
sensing an average of the electrical conductivity of the
invaded zone and the annulus region. On the other hand, the
shallow resistivity log senses the higher resistivity of about
110 ohm-m closer to the borehole wall. This model agrees
with the observed deep (ILD = 20-22 ohm-m), medium
(ILM = 25-30 ohm-m) and shallow (MSFL = 90-100
ohm-m) resistivity readings reported by the field log shown
in Figure 1. The true resistivity of the formation is about 90
ohm-m, which is much higher than the measured deep
induction resistivity (20-22 ohm-m). Water saturation cal-
culated using the true formation resistivity is about 15%
whereas that calculated using the deep induction measure-
ments is about 28-30%. Therefore, a nave reservoir evalua-
tion performed with the deep induction measurements will
result in underestimation of in-place hydrocarbon reserves
if the low resistivity annulus is not taken into account.
SENSITIVITY OF THE SPATIAL DISTRIBUTION OF
MUD-FILTRATE INVASION TO VARIOUS
PETROPHYSICAL PARAMETERS
A detailed sensitivity analysis was performed to assess
the effects of various invasion, rock, and fluid parameters
on the simulated two-dimensional cross-sections of electri-
cal resistivity. Reference formation and fluid properties
used in the simulations are summarized in Tables 3a and 3b
as well as in Figure 4. Moreover, the capillary pressure and
relative permeability curves used as reference are the ones
described in Figures 5 and 6, respectively.
The sensitivity analysis described below consisted of
making slight changes to the benchmark parameters and of
assessing the influence of such changes on the calculatedcross-sections of electrical resistivity. Results from this
sensitivity analysis are summarized in Table 4. For conve-
nience, we choose to describe the two-dimensional
cross-sections in the form of radial profiles of electrical
resistivity. Only one such radial profile is analyzed and is
taken through the center of the upper (and thicker) reservoir
layer shown in Figure 4. The radial profile is described in
terms of the following parameters: (a) Rxo, (b) Rt, (c) resis-
tivity of the annulus, Rann, (d) radial location of the resistiv-
ity annulus measured away from the borehole wall, and (c)
radial width of the resistivity annulus.
148 PETROPHYSICS March-April 2004
Torres-Verdn et al.
FIG. 8 Plot of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated from the waterand salt concentration profiles shown in Figure 7. The radial pro-file is taken through the upper reservoir layer shown in Figure 4.
FIG. 9 Plot of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated for five times ofinvasion (measured in hours or days). The radial profile is takenthrough the upper reservoir layer shown in Figure 4.
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Figure 9 illustrates the sensitivity of electrical resistivity
to time of invasion. The low resistivity annulus is located at
a radial distance of 2.5 feet after 1 day of invasion. As the
invasion progresses, the annulus moves radially away from
the borehole wall. Width of the annulus also increases with
time of invasion. Hence, the resistivity measured by induc-
tion logging tools will vary depending on the time of log-
ging. The acquired resistivity readings will be erroneously
low when the spatial region of investigation of a particular
measurement comprises the annulus. An unbiased resistiv-
ity measurement can only be obtained if the logs are
acquired a short time after the onset of invasion.
Sensitivity of electrical resistivity to formation porosity
is described in Figure 10. Porosities of 0.07, 0.14 and 0.28
were considered for the analysis. When the porosity is
reduced to half (0.07) of its reference value, the annulus
moves farther away from the borehole and its width
increases. For higher porosities, the annulus remains closer
to the borehole wall and its width becomes smaller. As sug-
gested by equation (6), the electrical resistivity increases as
porosity decreases from 0.28 to 0.07.
Figure 11 shows radial profiles of electrical resistivity
simulated for different values of connate water salinity.
Connate water salinity affects the resistivity of the annulus
as well as the resistivity of the virgin formation. By con-
trast, the flushed zone resistivity remains unaffected by the
March-April 2004 PETROPHYSICS 149
Assessment of In-Situ Hydrocarbon Saturation in the Presence of Deep Invasion and Highly Saline Connate Water
TABLE 4 Summary of the calculated sensitivity of radial variations of electrical resistivity to specific perturbations of invasion,petrophysical, and fluid parameters.
Sensitivity Value of Rxo, Rann, Rt, Distance of Width of
Parameter Parameter ohm-m ohm-m ohm-m Annulus, ft Annulus, ft
Days of 6 Hrs 105 5 90 1 1
Invasion 1 Day 105 5 90 2 2
2 Days 105 5 90 3 2.5
4 Days 105 5 90 4.5 3.25
6 Days 105 5 90 5.5 3.5
Porosity Porosity/2 435 20 370 6 3
Porosity 105 5 90 4 2.5
2*Porosity 25 3 22 3 1.5
Initial Water Swi/2 105 5 360 4.5 2.5
Saturation, Swi Swi 105 5 90 4.5 2.5
2*Swi
105 5 23 4.5 3.5
Salinity of Mud Salinity 105 5 90 4.5 2.5
Filtrate 2*Salinity 54 5 90 4.5 2.5
5*Salinity 23 5 90 4.5 2.5
10*Salinity 12 5 90 4.5 2.5
Salinity of Salinity 105 5 90 4.5 2.5
Connate Water Salinity/4 105 22 270 5 2.5
Salinity/8 105 32 490 5.5 2.5
Saturation 1.5 105 5 35 4.5 2.5
Exponent, n 2 105 5 90 4.5 2.5
2.5 105 5 240 4.5 2.5
Cementation 1.5 40 2 37 4.5 2.5
Exponent, m 2 105 5 90 4.5 2.5
2.5 280 12 240 4.5 2.5
Mixing 100% 105 5 90 4.5 2.5
Efficiency 50% 55 5 90 3.5 3.5
25% 28 7 90 2.5 4.5
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presence of an annulus as it is almost entirely saturated with
mud filtrate. Figures 12 and 13 describe the sensitivity of
the radial resistivity profile to the saturation exponent, n,
and to the cementation exponent, m, respectively. A varia-
tion ofn affects mainly the undisturbed formation resistiv-
ity, whereas changes in m affect the resistivities of theflushed zone, of the annulus, and of the virgin formation.
Figure 14 describes the effect of changing the mud-fil-
trate salinity on electrical resistivity. The radial profile of
electrical resistivity across the flushed zone varies for dif-
ferent values of mud-filtrate resistivity. However, both the
resistivity of the annulus and the resistivity of the undis-
turbed formation remain unchanged.Resistivity profiles calculated for different values of ini-
150 PETROPHYSICS March-April 2004
Torres-Verdn et al.
FIG. 11 Plots of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated for three differentvalues of connate water salinity (measured in ppm). The radialprofile is taken through the upper reservoir layer shown in Figure4 and the assumed invasion time is four days.
FIG. 12 Plots of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated for three differentvalues of Archies saturation exponent, n. The radial profile istaken through the central reservoir layer shown in Figure 4 andthe assumed invasion time is four days.
FIG. 10 Plots of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated for three values offormation porosity. The radial profile is taken through the upperreservoir layer shown in Figure 4 and the assumed invasion timeis four days.
FIG. 13 Plots of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated for three differentvalues of Archies cementation exponent, m. The radial profileis taken through the upper reservoir layer shown in Figure 4 andthe assumed invasion time is four days.
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tial water saturation (Swi) are shown in Figure 15. Capillary
pressure and relative permeability curves were adjusted to
conform to the various values of initial water saturation
considered by this sensitivity analysis. The initial water sat-
uration affects both the undisturbed formation resistivity
and the width of the annulus, but has no effect on either theannulus resistivity or the flushed-zone resistivity. This is a
significant result for the present work. It means that the
pre-annulus and annulus segments of the resistivity profile
remain highly insensitive to initial water saturation. If bore-
hole resistivity measurements are only sensitive to the
pre-annulus and annulus segments of the resistivity profile,
then the same result indicates that estimation of in-situ gas
saturation is not possible from resistivity measurements
alone.
The convective and dispersive term for the salt species
contained in equation (2) can be further multiplied by a
coefficient to control the efficiency of salt mixing. A value
of one corresponds to complete mixing while a value of
zero for the same coefficient corresponds to no mixing.
Efficiency of salt mixing was of interest as there was some
preliminary indication that salt mixing could be condi-
tioned by the dual pore-size distribution exhibited by reser-
voir rocks (micro and macro porosity). The effect of salt
mixing efficiency between mud filtrate and connate water is
graphically illustrated in Figure 16. Mixing efficiency
affects the width of the annulus as well as the resistivity of
the flushed zone. However, it has no significant effect on
the resistivity of the annulus.
Sensitivity analysis was also performed to assess the role
played by relative permeability on the spatial distributions
of water saturation and salt concentration. To this end, the
Type-A water-gas relative permeability curves shown in
Figure 6 were modified to construct the Type-B relative
permeability curves shown in Figure 17. It is emphasizedthat the Type-B relative permeability curves exhibit a much
lower value of critical water saturation than the Type-A
March-April 2004 PETROPHYSICS 151
Assessment of In-Situ Hydrocarbon Saturation in the Presence of Deep Invasion and Highly Saline Connate Water
FIG. 15 Plots of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated for three values ofinitial water saturation,Swi. The radial profile is taken through theupper reservoir layer shown in Figure 4 and the assumed inva-sion time is four days.
FIG. 14 Plots of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated for four values ofmud-filtrate salinity (measured in ppm). The radial profile istaken through the upper reservoir layer shown in Figure 4 andthe assumed invasion time is four days.
FIG. 16 Plots of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated for three values ofsalt mixing efficiency. The radial profile is taken through theupper reservoir layer shown in Figure 4 and the assumed inva-sion time is four days.
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curves. Simulation results for Sw and Rw, as well as for the
computed resistivity profile, Rt, using the Type-B relative
permeability curves are shown in Figures 18 and 19, respec-
tively. The water saturation front is less sharp compared to
that of the reference model (shown in Figure 7). Radial
resistivities monotonically increase in the flushed zoneregion, rising to a maximum of 155 ohm-m, then steeply
falling into the annulus region to finally reach the true for-
mation resistivity. Resistivity logs acquired in such an envi-
ronment will yield medium resistivity values (ILM) and Rxoresistivity values higher than the deep resistivity reading
(ILD). A visual comparison of Figures 8 and 19 conveys the
important message that the shape of the electrical resistivity
profile can be drastically changed with a perturbation in the
relative permeability curves. This is so because, in additionto capillary pressure, relative permeability curves control
the shape, location, and radial extent of the water saturation
front. The salt concentration front, on the other hand, is
mainly controlled by fluid transport.
Results from the above sensitivity analysis are summa-
rized in Table 4. It can be concluded that the radial location
of the low-resistivity annulus is primarily influenced by
porosity and time of invasion. The lower the porosity and
the longer the time of invasion, the longer the radial dis -
tance between the wellbore and the low-resistivity annulus.
On the other hand, the size and width of the low-resistivity
annulus are primarily controlled by (a) the difference in
salinity between connate water and mud filtrate, (b) the ini-
tial water saturation, and (c) porosity and the cementation
and saturation exponents contained in Archies formulas. It
is also found that a variation in the end points and curvature
of the relative permeability curves can drastically distort
the shape of the radial profile of electrical resistivity. Quan-
tification of the sensitivity of radial profiles of electrical
resistivity to additional mud and petrophysical parameters
can be found in George (2003).
152 PETROPHYSICS March-April 2004
Torres-Verdn et al.
FIG. 19 Plot of electrical resistivity as a function of radial dis-tance away from the borehole wall calculated from the watersaturation and salt concentration profiles shown in Figure 18 (inturn calculated assuming the TYPE-B relative permeabilitycurves shown in Figure 17).
FIG. 18 Plots of water resistivity (Rw) and water saturation (Sw)as a function of radial distance away from the borehole wall andthrough the upper reservoir layer shown in Figure 4. The twocurves were obtained from the 2D numerical simulation of theprocess of mud-filtrate invasion using the TYPE-B relative per-meability curves shown in Figure 17 and assuming an invasiontime of four days.
FIG. 17 Plots of the TYPE B relative permeability curves. Thedark and light lines represent relative permeability curves as afunction of water saturation for gas and water fluid fractions,respectively (compare to Figure 6).
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NUMERICAL SIMULATION OF BOREHOLE
RESISTIVITY MEASUREMENTS
Readings of various borehole resistivity tools were sim-
ulated numerically using as input the computed cross-sec-
tions of electrical resistivity. Figure 20 shows apparent
resistivity values simulated for dual induction, array induc-tion, and dual laterolog tools as a function of the time of
invasion, from 2 to 6 days. The shallow array induction
reading, AIT10, provides a good indication ofRxo asit isnot
affected by the presence of the annulus. This is because
after 2 days of invasion the annulus has moved away into
the formation, beyond the depth of investigation of the
AIT10 reading. Measurements performed with shallow
laterolog (LLS) and other shallow resistivity (SFL) tools
yield apparent resistivity values slightly lower than Rxo,
although gradually approach to the latter value as the annu-
lus recedes away from the borehole wall. The deep
laterolog reading, LLD, provides resistivity values closer toRt since it is only slightly affected by the presence of the
annulus. This behavior is due to basic operating principles
of resistivity logging tools, which indicate that laterolog
tools respond to resistive anomalies whereas induction
tools respond to conductive anomalies. Induction tool read-
ings AIT20, AIT30-ILM are close to 34 ohm-m and 26
ohm-m, respectively, after 2 days of invasion; the same val-
ues monotonically increase as the invasion progresses.
Induction resistivity readings, AIT60-ILD increase very
slowly, from about 24 ohm-m, whereas the deep array induc-
tion reading, AIT90, first decreases below the AIT60-ILD
value and then gradually increases from 4 days onward.
Fi gure 21 shows t he si m ul a t ed dua l -i nduct i on(DIL-SFL) tool readings assuming a cross-section of elec-
trical resistivity corresponding to an invasion time of 4 days
(Figure 8). Values of Rt and Rxo used in the simulation are
varied slightly as a function of depth based on the field logs.
The simulated log readings for ILD are about 18-25 ohm-m,
for ILM are about 28-35 ohm-m, and those for SFL are
about 70-80 ohm-m. As shown in Figure 21, the simulation
results are in close agreement with those of the measured
log data. Resistivity values fall steeply at the lower part of
the formation mainly due to increased shale content. Simu-
lated log responses for various perturbations of invasion,
petrophysical, and fluid properties are summarized in Table
5. For the reservoir model considered in this paper, it was
found that dual-induction measurements were not sensitive
to a perturbation of the value of in-situ water saturation.
This exercise provided further confirmation that the length
of penetration of borehole induction measurements was
seriously compromised by the presence of the low-resistiv-
ity annulus.
March-April 2004 PETROPHYSICS 153
Assessment of In-Situ Hydrocarbon Saturation in the Presence of Deep Invasion and Highly Saline Connate Water
FIG. 21 Numerically simulated wireline logs of shallow anddeep dual induction (ILD and ILM, respectively), and shallowresistivity (SFL) as a function of depth across the formation ofinterest in Well X-2. The numerically simulated logs are shownas black lines. For comparison, the corresponding measuredfield logs are shown with red lines on the same plot. Theassumed invasion time is four days.
FIG. 20 Numerically simulated apparent resistivity readings ofdual induction (ILM and ILD), shallow resistivity (SFL), duallaterolog (LLS and LLD), and array induction (AIT10, AIT20,AIT30, AIT60, and AIT90) measurements. The figure showssimulated apparent resistivity readings as a function of time ofmud-filtrate invasion. For comparison, the figure also shows thecorresponding values of flushed-zone resistivity (Rxo), annu-lus-zone resistivity (Rann), and virgin-zone resistivity (Rt). Themeasurement point is taken in the middle of the upper reservoirlayer shown in Figure 4.
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It is important to remark that the relatively good agree-
ment between measured and simulated induction measure-
ments shown in Figure 21 was only possible when the inva-
sion time was set to four days. This time of invasion is con-
sistent with the drilling record of Well X-2. Such an exer-
cise indicates that, in principle, when interpreting borehole
resistivity measurements with a quantitative model of
mud-filtrate invasion, time of invasion could be inferred
from the global match of numerically simulated and mea-
sured borehole resistivity logs, assuming that porosity is
inferred from ancillary information (e.g. density logs).
However, additional petrophysical information will be
needed to properly match all the vertical fluctuations exhib-
ited by the shallow and deep reading borehole resistivity
logs, including initial water saturation, permeability, capil-lary pressure, and relative permeability, among others.
For completeness, Figure 22 shows the dual laterolog
response simulated in the presence of the electrical resistiv-
ity annulus shown in Figure 8. Simulated LLD and LLS
readings yield resistivity values of 70-80 ohm-m and 55-65
ohm-m, respectively. Such values are much closer to the
actual virgin-zone resistivity values (80-90 ohm-m) than
those yielded by the deep induction measurements. This
exercise clearly suggests that laterolog measurements are
much less affected by the presence of a low resistivity annu-
lus than induction measurements, and hence do remain sen-
sitive to a perturbation of in-situ water saturation in the vir-gin zone.
DISCUSSION AND CONCLUSIONS
Differences in salt concentration between mud filtrate
and connate water can result in salt mixing within porous
formations. Because of this, the electrical resistivity of con-
nate water will experience substantial spatial variations
radially away from the borehole wall that cannot be
154 PETROPHYSICS March-April 2004
Torres-Verdn et al.
FIG. 22 Numerically simulated shallow and deep dual laterologreadings (LLS and LLD, respectively) as a function of depthacross the formation of interest in Well X-2. The assumed inva-sion time is four days.
TABLE 5 Numerically simulated Dual Induction-SFL (DIL-SFL) log readings for various perturbations of invasion,petrophysical, and fluid parameters.
SFL ILM ILD
(ohm-m) (ohm-m) (ohm-m) Petrophysical/Fluid Parameter
83.0 27.0 23.6 2 days of invasion
90.5 36.1 25.0 4 days of invasion
94.0 45.0 27.5 6 days of invasion
21.7 20.2 20.1 Mud-filtrate salinity = 10,000 ppm
94.1 51.4 37.1 Connate water salinity = 50,000 ppm
124.6 31.4 19.8 Type B relative permeability
85.9 19.4 13.5 Initial water saturation = 0.28
92.1 34.8 23.9 Capillary Pressure is Half
34.4 19.5 14.7 Cementation Exponent m = 1.5
91.6 28.7 18.8 Saturation Exponent n = 1.5
49.6 27.9 23.0 Mixing Efficiency is Half
96.7 55.9 40.1 Mud Cake Permeability is 0.15 md
392.7 222.7 155.1 Porosity is Half (0.07)
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explained from the distribution of water saturation alone.
Estimation of in-situ water saturation from resistivity mea-
surements via, for instance, Archies law, requires that the
resistivity of formation water be known as a function of
radial distance away from the borehole wall.
Large differences in salt concentration between mud fil-trate and connate water can cause the presence of a promi-
nent low resistivity annulus some distance away from the
borehole wall. This phenomenon has been considered in a
number of previous publications dealing with the interpre-
tation of wireline resistivity logs. However, a consistent and
systematic petrophysical explanation for the origin and
properties of such an annulus has not been presented before
in light of actual field data. The origin and geometrical
characteristics of such an annulus are governed by the par-
ticular combination of petrophysical and fluid parameters,
including mud properties, time of invasion, porosity, abso-
lute permeability, relative permeability curves, capillary
pressure, initial water saturation, connate water salinity,
mud salinity, and cementation factor, among others. In turn,
the presence of a low-resistivity annulus seriously compro-
mises the radial length of penetration of borehole induction
tools thereby impairing an accurate assessment of in-situ
hydrocarbon saturation.
The above phenomena were successfully recognized and
described from well-log data acquired in an active gas-pro-
ducing field. In this particular case, a low resistivity annu-
lus was formed because of both usage of fresh water mud
and presence of extremely salty connate water. Two-dimen-
sional simulations of mud-filtrate invasion and salt mixing
yielded radial profiles of electrical resistivity consistentwith actual borehole induction data. Further sensitivity
analysis provided valuable insight into the role played by
formation and fluid properties in the creation and character-
istics of the low-resistivity annulus.
Simulation results presented in this paper indicate that
there is not a simple procedure to correct previously acquired
borehole induction measurements for the presence of a
low-resistivity annulus. Such a correction would require a
reliable extrapolation of the profile of electrical resistivity
beyond the annulus region. Given (a) the lack of sensitivity
of the pre-annulus and annulus regions of the resistivity pro-
file to the value of initial water saturation, and (b) the largevariability of the resistivity annulus properties, namely,
width, height, and distance from the borehole wall, an
extrapolation of resistivity beyond the annulus region is
highly non-unique. Because of the same reasons, inversion
of borehole induction logs in terms of parametric radial pro-
files of electrical resistivity (e.g. ramp and annulus profiles)
in general will not yield the radial asymptote required for the
unbiased estimation of water saturation in the virgin zone.
Despite the above complications, it is here remarked that
one of the by-products of the simulation of mud-filtrate
invasion is a cross-section of the spatial distribution of
water saturation and salt concentration in the near-borehole
region. This cross-section is consistent with the measured
borehole induction logs and is largely controlled by the
mud and petrophysical parameters assumed in the simula-tion of the phenomenon of mud-filtrate invasion. The long
radial-distance asymptote of such a cross-section becomes
a good estimate of water saturation in the virgin zone. It is
therefore concluded that, in the presence of a prominent
low-resistivity annulus and/or deep invasion, simulation of
mud-filtrate invasion to match existing borehole induction
logs is perhaps the only possible way to calculate reliable
estimates of in-situ hydrocarbon saturation.
Another significant result stemming from this paper is
that laterolog measurements could provide a practical tech-
nical alternative to overcoming the limited depth of investi-
gation experienced by induction tools in the presence of alow-resistivity annulus and deep invasion.
Finally, the simulation results described in this paper
indicate that numerical simulation of mud-filtrate invasion
can be usedto assess the influence of a given typeof mud on
the response of induction and laterolog resistivity measure-
ments. It is also possible to make use of such a simulator to
design chemical properties of muds in order to minimize
formation damage. Chemical properties of muds could also
be designed to optimize the sensitivity of borehole logging
tools and therefore to improve the accuracy of log interpre-
tation techniques used to estimate in-situ rock formation
properties.
ACKNOWLEDGEMENTS
We are obliged to Anadarko Petroleum Corporation for
permission to publish these results. UT Austins Research
Consortium on Formation Evaluation, jointly sponsored by
Baker Atlas, Halliburton, Schlumberger, and Anadarko
Petroleum Corporation, provided partial funding for the
work reported in this paper. The authors would like to thank
Ian Zhang, Hal Meyer, and two anonymous reviewers for
their constructive technical comments and editorial sugges-
tions.
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ABOUT THE AUTHORS
Carlos Torres-Verdn received a PhD degree in Engineering
Geoscience from the University of California, Berkeley, in 1991.
During 19911997, he held the position of Research Scientist with
Schlumberger-Doll Research. From 19971999, he was Reservoir
Specialist and Technology Champion with YPF (Buenos Aires,
Argentina). And since 1999, he is an Assistant Professor with the
Department of Petroleum and Geosystems Engineering of The
University of Texas at Austin, where he conducts research in for-
mation evaluation and integrated reservoir characterization. He
has served as Guest Editor for Radio Science, and is currently a
member of the Editorial Board of the Journal of Electromagnetic
Waves and Applications, and an associate editor for Petrophysics
(SPWLA) and the SPE Journal.
Bovan K. George was a graduate research assistant while pur-suing a MSc degree in Petroleum Engineering at The University of
Texas at Austin between 2001 and 2003. He currently works as a
log analyst with Oil and Natural Gas Corporation (ONGC), in
India. Bovan received a Master of Science degree in Physics from
the University of Kerala and a Master of Technology in Industrial
Physics from IIT Kharagpur, India.
Mojdeh Delshad is a research engineer with the Center for
Petroleum and Geosystems Engineering at The University of
Texas at Austin. She holds MSc and PhD degrees in Petroleum
Engineering from The University of Texas at Austin. Her research
interests are in petrophysical property modeling, enhanced oil
recovery, reservoir engineering, simulation, and groundwater
modeling and remediation. She is a member of the SPE Editorial
Review Committee.
Richard Sigal is currently a Reserach Professor at the Univer-
sity of Oklahoma with a joint appointment in the Petroleum Engi-neering and Geoscience Departments. He is also the Director of
the Mobile Core Analysis Laboratory at Oklahoma University.
Previously, Richard worked for Anadarko as part of the
engineering technology group. Before joining Anadarko he spent
21 years with Amoco mostly in their Tulsa Technology Center.
After retiring from Amoco, he worked for two years for
Halliburton in Houston. During the last 15 years, much of Rich-
ards time has been spent on understanding permeability and the
technologies used to characterize and estimate it. He worked in
Petrophysics and core measurements at Amoco and supervised the
development of Petrophysical applications at Halliburton. Among
his areas of special expertise are NMR and mercury capillary pres-
sure measurements. Richard was trained in mathematics and phys-
ics. His PhD thesis fromYeshiva University was in general relativ-
ity.
Farid R. Zouioueche is a reservoir engineer formerly with
Anadarko Petroleum Corporation. He graduated with a MSc
degree in Petroleum Engineering from The University of Texas in
Austin in 2000. His research interests cover near wellbore
remediation processes, capillary flow theory, and phase behavior.
Barbara Anderson is a principal research scientist at
Schlumberger-Doll Research in Ridgefield, CT. She joined SDRin
1966, and since that time she has worked on developing computer
codes for modeling resistivity tool response. Her ongoing goal is to
minimize uncertainty in log interpretation by integrating forward
modeling directly into the interpretation process. She is presently
working in the areas of anisotropy interpretation and inversion.Barbara is a past-president of SPWLA, and in 1996 she received
the SPWLA Distinguished Technical Achievement Award. She
received a PhD degree from Delft University in 2001.
156 PETROPHYSICS March-April 2004
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