Assessment of In-Situ Hydrocarbon Saturation in the ...Assessment of In-Situ Hydrocarbon Saturation in the Presence of Deep Invasion and Highly Saline Connate Water FIG.1 Plot of the

March-April 2004 PETROPHYSICS 141

Assessment of In-Situ Hydrocarbon Saturation in the Presence of Deep

Invasion and Highly Saline Connate Water1

Carlos Torres-Verdín2, 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 resistivity Rxo and diameter Di,

beyond which lies the undisturbed (virgin) formation of

resistivity Rt. Such a model embodies three unknowns (Rt,

Rxo, and Di) 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. 141–156; 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 Archie’s 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.

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.

Amajor challenge faced in the evaluation of this reservoir is

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 (90-100

ohm-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 invasion

and 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-Verdín 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 Native

X920 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


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.

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 of

mud-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 and

systematic 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 as

a 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



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).

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 Darcy’s law, i.e.,

QkA P

hf

mc

��

�, (1)

where Qf is the flow rate of mud filtrate across the borehole

wall, k is the mud cake permeability, A is the cross-sectional

area through which the filtrate flows, � is the viscosity of fil-

trate, hmc is the thickness of mud cake, and �P is the pressure

drop 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 spurt of 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 Darcy’s law and mass balance. The general

form of the mass balance equation for the k-th component

can be written as

�

��

tC C u D Rk k k kl l k l

l

n

k

p

( ) (~

) ,� � �

�

�

��

�

�1

(2)

where � 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, �k is fluid density, ul is the Darcy

flux for phase l, Rk is the total source/sink term for compo-

nent, k and~Dkl the dispersive flux, defined as

~,D S K Ckl l k l k l� �� (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 viscous

forces, 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 tensor Kkl 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

� � �

��

�

��

� �

�

( ), (4)

where Dkl is the molecular diffusion coefficient, � is a

tortuosity factor, �L and �T are the longitudinal and trans-

verse dispersivities, respectively, �ij is the Kronecker delta

function, and uli and ulj are the components of Darcy’s

velocity of the phase l in the i and j 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 ft3/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).



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 T is 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 Archie’s equation, namely,

SR

R

awn w

tm

��

, (6)

where Sw is water saturation, a is the tortuosity/cementation

factor, n is the saturation exponent, � is porosity, and m is

the cementation exponent. The use of Archie’s 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 Archie’s 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



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.

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 progression

from 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



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.

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 of

mud-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 naïve 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 calculated

cross-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.



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.

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



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

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 of n affects mainly the undisturbed formation resistiv-

ity, whereas changes in m affect the resistivities of the

flushed 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-



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 Archie’s 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 Archie’s cementation exponent, “m”. The radial profileis taken through the upper reservoir layer shown in Figure 4 andthe assumed invasion time is four days.

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 the

annulus 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 emphasized

that the Type-B relative permeability curves exhibit a much

lower value of critical water saturation than the Type-A



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.

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 zone

region, 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 Rxo

resistivity 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 addition

to 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 Archie’s 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).



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).

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 of Rxo as it is not

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 to

Rt 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.

Figure 21 shows the simulated dual-induction

(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.



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.

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



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



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 �d

392.7 222.7 155.1 Porosity is Half (0.07)

explained from the distribution of water saturation alone.

Estimation of in-situ water saturation from resistivity mea-

surements via, for instance, Archie’s 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 consistent

with 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 large

variability 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 a

low-resistivity annulus and deep invasion.

Finally, the simulation results described in this paper

indicate that numerical simulation of mud-filtrate invasion

can be used to assess the influence of a given type of 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 Austin’s 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-Verdín received a PhD degree in Engineering

Geoscience from the University of California, Berkeley, in 1991.

During 1991–1997, he held the position of Research Scientist with

Schlumberger-Doll Research. From 1997–1999, 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-

ard’s 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 SDR in

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.



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