determination of residual oil saturation in a carbonate reservoir

8/10/2019 Determination of Residual Oil Saturation in a Carbonate Reservoir

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Copyright 2001, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the SPE Asia Pacific Improved Oil RecoveryConference held in Kuala Lumpur, Malaysia, 8–9 October 2001.

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Abstract

Single-well tracer testing has been widely accepted as a

standard method for measuring residual oil saturation to

waterflood. Residual oil saturation is an important

parameter in the evaluation of tertiary oil recovery

potential for depleted reservoirs. At an advanced stage of

depletion, Leduc, a Canadian carbonate reservoir, has

been considered as a candidate for enhanced oil

recovery. As part of the evaluation process, single-welltracer tests were conducted at two watered-out producers

to determine residual oil saturation to waterflood. The

tracer production profiles were found to be highly

skewed with long tails and early arrival times, which are

typical for carbonate reservoirs. Two different models,

namely a double-porosity model where tracer could

distribute between the flowing and non-flowing pores

through mass transfer and a single-porosity model where

a fictitious water drift rate was assumed in the test zone,

were used to interpret the data. It was found that either

model could match the data to the same degree of

accuracy regardless of the flow mechanisms assumedand the residual oil saturation derived from these two

models were 35% and 38% respectively. This

demonstrates the robust nature of the test that the non-

uniqueness of the match does not affect residual oil

saturation determination. The residual oil saturation

determined by simple analytical models including mass

balance method, peak method and mean retention

volume method were all in the range of 34% to 38%, in

excellent agreement with the simulation results. As

well, the Sorw obtained by the SWTT method compared

favorably with those determined by interwell tracing

(35%) and sponge coring (33%).

Introduction

The amount of oil left in a reservoir after secondary

operations is needed to evaluate the potential of

enhanced oil recovery processes. Various conventiona

methods for Sorw determination, such as productionhistory, laboratory waterflood tests, core analyses

logging, log-injection-log, interwell and single-wel

tracing tests (SWTT) have been extensively reported and

compared1-3 in the literature; each technique offers

certain advantages, limitations and different depths of

investigation. Of all the methods available to date1,2

SWTT is unique in its large and variable depth of

investigation, and relatively free of the near-well bore

effect. SWTT is still the most widely accepted methodin the industry for measuring residual oil saturation

though an increasing number of interwell tracer testing

has been reported recently4,5. Since its invention in

1971, more than 200 SWTT have been run both in

sandstone and carbonate reservoirs to determine residua

oil saturation to waterflood Sorw.

Deans6,7 and Tomich8 have described the single-

well tracer testing methods for measuring Sorw. It is

based on the chromatographic separation of partitioning

and non-partitioning tracers in the test zone, a well-

known phenomenon in chemistry for hundred years

Single-well tracer test, which constitutes the mostcommon application of partitioning tracers in the oi

industry4, has been well demonstrated for homogeneous

sandstone reservoirs. It has, however, been recognized

to have some shortcomings when applied to

heterogeneous carbonate reservoirs owing to the

complicated pore structure and microscopicconformance, which could render long production tails

SPE 72111

Determination of Residual Oil Saturation in A Carbonate ReservoirJoseph Tang, Pei-Xin Zhang, China Istitute of Atomic Energy, JT Petroleum



2 J.S.TANG SPE 72111

and extreme dilution of the tracer profiles. Special

interpretation techniques and design procedures are

required to cope with the tracer response characteristics

arising from the double porosity structure of carbonates.

Though various methods for residual oil

saturation measurement in Leduc have been revealed

and compared in a previous paper 5, the effects of double

porosity on SWTT in carbonates have never been

addressed. This paper focuses on the physics,

characteristic tracer response, interpretation techniques

and the unique features of SWTT in double-porosity

vuggy carbonate reservoirs.

Single-well Tracer Test

In a single-well tracer test, a reacting partitioning

(primary) tracer, together with other non-reacting

partitioning or non-partitioning tracers (mass balance

tracers), is injected and produced through the same well

following a shut-in period of 3 to 20 days. During shut-

in, the primary tracer will undergo hydrolysis to generate

a non-partitioning secondary tracer. Hydrolysis is

necessary to destroy flow reversibility, which causes the

injected partitioning and non-partitioning tracers, once

separated in the reservoir, to produce back at the same

time. Starting from the same spot in the reservoir at

backflow, the secondary tracer will arrive at the wellbore

earlier than the primary tracer in a volume Vn less than

the injected volume Vi. Based on the chromatographic

theory, the separation of primary and secondary tracers

can be quantitatively related to Sorw. Under ideal

conditions,

orw

orwc

n

i

n

p

S1

SK 11

V

V

V

V

−+=β+== (1)

where V p, Vn, are the arrival volumes for the primary

and secondary tracers respectively, <L3>, Vi = total

injection volume, <L3>, K c = partition coefficient of the

primary tracer.

SWTT in Carbonate Reservoirs

Carbonate reservoirs are characterized by the presence of

double porosity. Two different pore structures with

vastly different permeability and connectivity can be

identified. The capacitance model proposed by Coats

and Smith9,10 has been widely used to model the complex

double-pore system in carbonates. It can be visualized

that water and tracer flow in the connected, high permeability pores and the tracer can transfer into the

dead-end pores by diffusion. The transfer stops when

the tracer concentrations in the flowing and dead-end

pores become equal. It can be conjectured that the

double-porosity media behave like single-porosity for

extremely fast or slow transfer rates.

Because of the slow transfer of tracers into and

out of the dead-end pores during SWTT, the tracer

profiles for carbonates are highly skewed and “non

ideal” as compared with those from the sandstone tests11

In this study, different models were tried to delineate the

impact of mass transfer on tracer production thereby

estimating residual oil saturation from the tracer data.

Models for SWTT in Carbonates

1. Single-porosity Model

Prior to the invention of the double-porosity model

single-porosity model with artificial drift was used to

interpret the tracer profiles for carbonate reservoirs12. A

high, artificial drift rate was assumed to simulate the

extreme dilution and long production tail. The radial

dispersion-convection-reaction equation (RDCR) with

linear drift can be written to describe tracer propagation

in reservoir during SWTT.

Continuity Equation for injection water

( ) ( ) 0urur

r =θ∂∂

+∂∂

θ (2)

Continuity Equation for Tracer j

( ) ( ) ( )

θ∂

∂

θ∂∂

+

∂

∂

∂∂

=

+θ∂∂

+∂∂

+∂

∂β+

θ

θ

j,w

2

j,w

r

j j,wr j,w

j,w

j

CD

r

1

r

CrD

r r

1

R uCr

1ruC

r r

1

t

C1

(3)

R j is a reaction term (R j<0 for secondary tracer

R j>0 for primary tracer) for tracer j. The RDCE with no

drift was first solved numerically by Deans et al7 using a

mixing cell model and then semi-analytically by

Brigham et al13. A finite difference simulator was

written by Tomich et al8 to numerically solve the RDCR

equation coupled with linear drift. For a complicated



SPE 72111 DETERMINATION OF RESIDUAL OIL SATURATION IN A CARBONATE RESERVOIR 3

case of multi-layer reservoirs with irreversible flow, a

non-linear least square program called CASTEM14 isavailable for automating the cumbersome matching

process. The single-porosity model, though satisfactory

for homogeneous sandstones, needs to assume a

fictitious drift rate to match the highly skewed tracer

profiles arising from the double porosity of carbonates.

This inadequacy called for the development of a real

double-porosity model for carbonates.

2. Double-porosity Model

The double porosity feature was incorporated into a 1-D

radial mixing cell model by Deans et al15 according to

Eqs.4 and 5. The second order dispersion term was

omitted in the formulation and the dispersion in flowing

pores was modeled by numerical dispersion hence the

cell size.

Tracer Transfer in Flowing Pores

0y

j j

w

w

j

r j j

jy

C

L

D

S

S

f 1

f R

r r

)ruC(

t

C)1(

=

∂

∂

−=+

∂

∂+

∂

∂β+

(4)

Tracer Diffusion in Dead-end Pores

∂

∂=+

∂

∂β+

2

j

2

j j

j

jy

CDR

t

C)1( (5)

This model can fully account for the long tracer

production tail caused by slow diffusion of tracer into

and out of the dead-end pores. However, because of its

1-D limitation, it cannot handle linear drift.

3. Multiple-porosity Surface Resistance Model9,16

While Deans’ model assumed negligible surface mass

transfer resistance between the flowing and dead-end

pores and tracer diffusion in the dead-end pores being

the rate-controlling step, the Coats and Smith modelassumed slow tracer transfer between pores. The

algorithm of the Coats and Smith model is similar to that

of Deans’ except for the tracer transfer formulation.

Similarly, numerical dispersion (mixing cell) was used

to simulate physical dispersion16.

∂

∂

−−

=−φ−

−=

+∂

∂+

∂

∂β+

t

C

S

S

f 1

f )CC(

S)f 1(

k

R r r

)ruC(

t

C)1(

j

w

w

j j

w

j,m

j

r j j

j

(6)

4. Mass Balance Method

The large number of intricate parameters in the SWTT

simulators not only makes it a major task to match all

the tracer profiles, but also raises a legitimate concern of

“uniqueness” of the fit. To overcome the drawbacks in

simulation, a mass balance method was proposed by

Tang11 for fast, direct solution of S

orw from the tracer

profiles. This method draws on the theory that as Sorw

increases, more primary tracer will stay in the oil phase

where it is unavailable for hydrolysis. In the presence of

oil, the primary tracer will be hydrolyzed at a slower rate

equal to K H/(1+β):

β+

−=1

tK exp

)0(C

)t(CH

p,w

p,w (7)

where Cw,p(t) and Cw,p(0) are the primary tracer

concentrations in water at time t and 0, <W/L3>, K H =

the pseudo-first order hydrolysis rate constant for the primary tracer at reservoir conditions, <T-1>.

The two-phase hydrolysis constant, i.e.

K H/(1+β), is determined from the primary and secondary

tracer recovery curves with loss correction. Bycomparing with the K H measured in the lab, β ! and Sorw

are then calculated. Error analysis11 suggests that a 10%

error in K H renders an error of ±3% pore volume to Sorw.

There has been an argument that the hydrolysis

rate constant for the ester may not be a constant17. In

their calculation, the authors failed to account for the

extreme dilution of ester, which is typical in carbonate

SWTT. Because of dilution, the acid generated from

ester hydrolysis would be too low to trigger any self-

catalyzed reaction. The self-catalyzed reaction was

further suppressed in the presence of carbonate due to

neutralization as demonstrated in our lab study11. Mos

importantly, in contrast to the claims by the authors17

there was no appreciable change in the pH of the

produced water for the Leduc test as a result of low ester

concentration, low degree of hydrolysis (3%)

neutralization by carbonate and high buffering capacity

of the Leduc brine. Therefore, the assumption o

constant K H is justified and the error in K H is likely to be

within 10%.




5. Mean Retention Volume Method

It has been shown that the ratio of mean retention times18

for the partitioning and non-partitioning tracers is related

to Sorw in an interwell partitioning tracer test.

∫

∫ ∞

∞

=

0

j,w

0

j,w

R

dt)t(C

dt)t(tC

t (8)

orw

orwc

n,R

p,R

S1

SK 11

t

t

−+=β+= (9)

As suggested by the integral in Eq.8, production

of the complete tracer profile is needed to facilitate the

calculation of the mean retention time; early termination

of the tracer test requires extrapolation of the tracercurve to zero concentration, which will lead to large

uncertainty and hence error in Sorw calculation. The

mean retention volume method can be extended to

SWTT by assuming the same mass transfer

characteristics for the primary and secondary tracers,

small conversion and negligible hydrolysis during

injection and production.

Leduc Field Description5

The Leduc Woodbend D-2A Pool was discovered in1947. It is situated on the eastern shelf of the Western

Canada Basin southwest of Edmonton (Fig.1). The

Nisku D2 formation is a dolomatized carbonate platform

overlying the Leduc-Woodbend D-3 reef. The reservoir

has an areal extent of 9200 hectares, a gross thickness of

45 meters and average porosity of 4%. The pool is

characterized by numerous impermeable zones resulting

from the deposition of thin peri-tidal laminate beds of

mudstone. These beds limit vertical permeability to an

average of less than 0.1 md. Horizontal permeability

varies from 1 to 1000 md, averaging 20 md throughout

the pool.The D2-A Pool has 32.7 million m3 original oil

in place. It was produced by waterflood and the

remaining oil was 57% ooip. Because of the large

amount of oil left in the reservoir, a pilot program was

undertaken to assess the potential of miscible flood. Anaccurate knowledge of residual oil saturation is required

to evaluate the pilot performance and the commercial

potential of the project. Because of low porosity,

logging and log-injection-log cannot give an accurate

reading of oil saturation. Therefore, other techniquesincluding single-well tracer testing, sponge coring and

interwell tracing technology were used to determine

residual oil saturation.

Two wells were selected for the test. Well A

was located in the pilot area while Well B was outside

the pilot. This serves the purpose of determining

residual oil saturation distribution in different areas of

the reservoir. Owing to the similarity between these two

tests, only the test in the miscible pilot, which has a

more direct influence on the miscible pilot evaluation

was described in the paper. Reservoir properties and

completion data are listed In Table 1.

Well Preparation

Well A was completed open-hole in the D2 interval

without a packer and was produced by a rod pump. The

effective thickness of the test zone was 6.2m. The depth

from the top of the production zone to the casing base

was 1564 meters. A plug was set at the bottom of D2

zone to isolate the test zone from the bottom zone

Because there was no packer set in the well, water leve

could rise during injection and fall during production

The annulus fluid, which had a volume of up to 8 m3

could mask early tracer production. Because of injection

through annulus, it was not necessary to unseat the rod

pump during the test. The oil trapped at the annulus was

circulated out of the annulus by injecting water from the

casing valve at high rate (150 m3/d) and producing backto the surface by the rod pump at 22 m3/d. This reverse

circulation was stopped after all the annulus oil was

produced or completely displaced into the formation

Water was then produced into the 64m3 storage tanks

which was later used as injection water to ensure

constant salinity environment in the test zone. The set

up for injection, production and tracer analyses were

similar to those described in the literature12,19.

Test Design

Methyl acetate was selected as the primary tracer based

on the hydrolysis rate and partition coefficient

consideration. Methyl acetate was hydrolyzed to

produce methanol as the secondary tracer. Methy

formate was unsuitable as it was hydrolyzed too fast at

the reservoir conditions. Two mass balance tracers

namely n-propanol, (a non-partitioning tracer), and




i-butanol, (a partitioning tracer with K c very close to that

for the primary tracer), were co-injected with the

primary tracer. These two tracers were used to calibrate

the primary tracer loss for direct calculation of Sorw from

the amount of methanol produced using the mass

balance method. i-Propanol was used as the cover tracer

to tag the injection water. .

K c was measured at reservoir conditions in the

lab using live oil and produced brine by a static

method11,20. The hydrolysis rate constant was obtained

by measuring the ester concentration as a function of

time at reservoir temperature. Our study indicated11 that

it was not necessary to measure K H at reservoir pressure.

The test design, together with the K H and K c for various

tracers, is summarized in Table 2

Injection Phase

The concentration of the cover tracer i-propanol, which

was used to tag the injection water, was 0.49%. It was

pre-mixed with the injection water in the water storage

tanks. There was a small background of methanol in the

methyl acetate, as some of the acetate might have been

hydrolyzed already in the storage drum. This

background was to be subtracted from the methanol

production profile. The methyl acetate, i-butanol and n-

propanol concentrations were 2.36% 0.63% and 0.67%

respectively and precision pumps were used to meter the

tracers accurately into the injection water stream. The

bank volume, i.e., the volume of the primary tracer bank,

was 14.9 m3 and the total injection volume was 52.3 m3.

The injection was through annulus at 92 m3/d, so theinjection was completed in less than a day. The

injection water was heated to 65-68oC by a steam truck

at the wellhead to avoid temperature change in the test

zone.

Shut-in and Production

Because of the slow hydrolysis of methyl acetate, the

well was shut in for 9.3 day to allow sufficient methanol

to be generated. After shut-in, water was produced back

through the tubing by the rod pump. A total of 219 m3

of water was produced from the well at a rate of 22 m3/d,corresponding to 10 days of production. The production

period was prolonged purposely so as to produce as

much tracers as possible to facilitate mass balance and

retention time calculations. Water samples werecollected from the well-head and immediately

refrigerated. Tracer concentrations were analyzed on

site using a gas chromatograph. Salinity and pH were

also monitored regularly.

Results and Discussion

The radii of investigation for this test were 7 m for the

primary tracer methyl acetate and 10 m for the non

partitioning tracer i-propanol. Methyl acetate was

located closer to the wellbore due to partitioning hence

slower propagation. Well A had a produced oil cut o

1% prior to the SWTT. The low oil cut is a positive

indication of presence of low mobility oil, probably

close to residual saturation, in the test zone.

Characteristics of the Tracer Profiles

All the tracer profiles display the characteristics of

moderate dispersion, extreme dilution, early arrival and

long production tails. Significant amounts of tracer

were still produced after the production of 4 injection

volumes. Due to the long production tails, the mean

retention volumes of the tracers except methanol and i-

butanol were all over 1000m3, almost twenty times

higher than the total injection volume (Table 3).

All tracers experienced extreme dilution. For

instances, n-propanol was produced back at a maximum

concentration of 0.08%, an 8 time dilution of the

injection concentration 0.63%. As well, the maximum

concentration of the cover tracer i-propanol was 0.37%

25% lower than the injection concentration of 0.49%

Extreme dilution and anomalously high dispersion can

be attributed to tracer diffusion into and diluted with the

water in the dead-end pores.All the tracer peaks arrived earlier than

anticipated. The peak volumes for methyl acetate, i

butanol and n-propanol were approximately 24 m3

which was lowered than the injection volume of 44 m3

(total injection volume – 0.5*bank volume). Early tracerarrival is due to tracer diffusing back from the dead-end

pores into the flowing pores during production.

The tracer recovery levels for the Leduc test

were considered to be high by the carbonate reservoir

standard because of the prolonged production and ideadownhole conditions. The recoveries were 70% for al

tracers (Table 3). The conversion of methyl acetate to

methanol was only 3%, which was lower than the

targeted conversion of 10-30% commonly adopted for

SWTT. Five models were used to interpret the tracer

data.




Double-porosity model

The double-porosity model assumed no drift and the

skewed profiles were simulated by adjusting the

effective pore diffusion coefficient L. Dispersion was

controlled by the grid size. The match was found to be

insensitive to the oil saturation in the dead-end pores

!orw, the simulated tracer profiles were hardly affected by varying !orw from 30 to 40%. Since it is immaterial

as to what value !orw was used in the simulation, same

oil saturation was assigned to both flowing and dead-end

pores. The best match was at Sorw= !orw=35%. Since it

is believed that the oil saturation in the dead-end pores

should be higher than that in the flowing pores, the Sorw

of 35% thus underestimates the total pore-average

residual oil saturation. Only a single layer was required

for matching the tracer data.

The quality of the match was excellent except

for methanol and i-butanol. In general, there was a good

match of the peak height and peak position for all tracers but the match for the long tail was only marginal.

Methyl acetate (Figure 2) peaks at about 24 m3,

significantly less than the injection volume. The

methanol profile has the same level of dispersion as the

methyl acetate profile. In comparison with the methyl

acetate fit, the match for the methanol profile, especially

in the tail, was only satisfactory (Figure 3). The fit for

the methanol profile, together with the sensitivity runs at

three Sorw levels, i.e., 40%, 35% (best) and 30%, is

shown in Figure 3. It is clear from the sensitivity study

that the residual oil saturation was 35±3%. The methyl

acetate and methanol profiles are plotted in Figure 4 forcomparison. The methanol peak is ahead of the methyl

acetate peak as predicted by the theory.

The response of the cover tracer i-propanol is

normal (Figure 5). The concentration is high at early

production and continuously declining with production

volume. The match of the mass balance tracers n-

propanol and i-butanol are displayed in Figures 6 and 7.

While the match for n-propanol was excellent, the match

for i-butanol was inferior due to sample analysis

problems.

Single-porosity with Drift

Though it is recognized that the skewed tracer response

is due to the double porosity structure in carbonates, the

profiles can be matched to the same degree of accuracy

by a single-porosity model with a fictitious high driftrate. In the single-porosity simulation, the drift rate was

set to be 0."5 m/day and the dispersion length was at

2."m. To better match the tails, a thin layer was

incorporated into the model. This layer, constituting

only 5% of the total porosity-thickness, conducted "0%

of the flow. With these parameters input into the model

the methyl acetate profile was successfully matched as

shown in Figure 8. The match of the methanol profile

together with the sensitivity study cases, is given in

Figure 9, from which the residual oil saturation was

estimated to be 38±3%. Similar to the double-porosity

model, the match for i-butanol was poor relative to other

tracers. The close agreement between the single and

double porosity models demonstrates the robust nature

of SWTT that though the fit was not unique, the flow

mechanisms assumed did not affect the determination of

Sorw to any significant extent. This is because Sorw

depends mainly on the relative separation of the primary

and secondary tracers but not the absolute flow paths of

individual tracers.

Mass Balance Method

The mass balance tracer n-propanol and cover tracer i-

propanol were used to calibrate the primary tracer lossaccording to the procedures detailed in reference ""The n-propanol curve is deemed to be more credible for

loss calibration purposes because it was injected together

with the primary tracer. Nonetheless, there is only a

subtle 2% difference between the Sorw calculated by

these two tracers. To estimate the uncertainty in Sorw

caused by the hydrolysis rate measurement error, the

calculated Sorw is plotted against hydrolysis rate in

Figure "0. It is evident that for a "0% error in K H, the

corresponding error in Sorw is only 3%. Sorw was

estimated to be 34±3% based on the n-propanol loss-

calibration curve.

Other Analytical Methods

The mean retention volume method relates Sorw with the

mean retention volume ratio for the primary and

secondary tracers through Eq.9. The mean retention

volumes for various tracers were calculated and

summarized in Table 3, from which Sorw was determined

to be 36%. In comparison, Sorw was calculated to be

38% from the primary/secondary peak volume ratio aftercorrecting for the wellbore holdup volume.

The Sorw determined by various interpretation

methods fall into the range of 34-38%. The consistency

of the results validates the interpretation techniques as

well as the credibility of the SWTT method.




Interwell Test and Sponge Coring5

To improve our confidence in Sorw measurement, an

interwell test was run at an interwell distance of 64m

using tritiated water (THO, 0.5 Curies), tritiated

methanol (TMA, 0.3 Curies) as the non-partitioning

tracers and tritiated n-butanol (TNB 0.3 Curies) as the partitioning tracer. The injection and production rates

were held constant at 20 m3/d. Depicted in Fig. 11 are

the TMA and TNB production curves. The Sorw values

were calculated to be 38%, 34% and 35%, respectively,

at three readily identifiable landmarks, i.e.,

breakthrough, half peak height and peak, the first being

least certain because of pressure surge near

breakthrough. The most probable Sorw was 35%.

Sponge cores were taken from an observation well

drilled near the test well (Figure 1), the average Sorw was

33%.

In spite of the vast difference in the depths of

investigation, the SWTT Sorw (34-38%) compared well

with those measured by sponge coring (33%) and by

interwell method (34-38%). The excellent agreement of

the Sorw determined by various methods enhances our

confidence in the accuracy of the Sorw recommended for

the evaluation of the tertiary pilot.

Conclusions

1. Due to the double porosity structure and tracer transfer

between the flowing and dead-end pores, the tracer

profiles for SWTT in carbonates exhibit the

characteristics of moderate dispersion, extreme

dilution, early arrival and long production tails.

2. Single-porosity drift model and double-porosity model

worked equally well in interpreting the results of

SWTT in carbonates. The Sorw were determined to be

38±3% and 35±3% for the single and double models

respectively. Non-uniqueness or the flow

mechanisms assumed did not adversely impact Sorw

determination.

3. The double-porosity model seems to be marginally

better in terms of quality of the fit and the actual

physics. However, the double-porosity simulation

was not sensitive to the oil saturation in the dead-end

pores, the 35% Sorw derived on the basis of equal

residual oil saturation in the flowing and dead-end

pores probably underestimated the pore average Sorw.

4. In addition to the simulation method, three analytical

methods, namely mass balance method (34±3%),

mean retention volume method (36%) and the peak

ratio method (38%) were used for direct calculation

of Sorw from the tracer data. The Sorw calculated wereall in the range of 34-38%.

5. Sorw from SWTT (34-38%) agrees with the

measurements by interwell testing (34-38%) and

sponge coring (33%) in spite of vastly different

depths of investigation.

Nomenclature

C = tracer concentration, <WL-3>

# = tracer concentration in dead-end pores, <WL-3>

D = dispersion coefficient, <L2T-1>

D = dispersion coefficient in dead-end pores, <L2T-1>

f = flowing fraction

K c = partition coefficient, dimensionless

K H = pseudo-first order hydrolysis rate constant, <T-1>

k m = effective mass transfer coefficient, <WT

-1

>L = dead-end pore length, <L>

R = reaction term, amount of tracer reacted per uni

volume of water per unit time, <WL-3T-1>

r = radial distance from wellbore, <L>

Sorw = residual oil saturation to water-flood

dimensionless

Sw = water saturation, dimensionless

"w = water saturation in dead-end pores, dimensionless

t = production time, <T>

tR,j = mean retention time for tracer j, <T>

ur = radial interstitial velocity, <L/T>,

uθ = angular interstitial velocity, <L/T>,Vi = total injection volume, <L3>

Vn = non-partitioning tracer retention volume, <L3>

V p = partitioning tracer peak retention volume, <L3>

y = distance into dead-end pore, <L>

Greeks

β = retardation factor, defined in Eq. 1

θ = angle in cylindrical coordinate

φ = total porosity

Subscripts

j = tracer jn = non-partitioning tracer

p = partitioning tracer

w = water phase




Acknowledgements

The authors wish to thank the China Institute of Atomic

Energy for supporting the work.

References

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of Residual Oil Saturation Techniques,” SPEFE

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(Mar 1995), 33-39

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“Interwell Residual Oil Saturation at Leduc

Miscible Pilot,” paper SPE 20543 presented at

the SPE meeting in New Orleans, (Sept. 23-26,

1990).

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(1971).

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Chemical Tracer Method for Measuring

Residual Oil Saturation,” Final Report,

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miscible flooding dispersion coefficients”,

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Saturation Measurements at Brown and East

Voss Tannehill Fields”, JPT (Jan.1978), 17-25.

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“Mathematical Analysis of Single-Well Tracer

Test,” U.S. Dep. Energy Rep. No

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Eighth Symposium on EOR held in Tulso

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Tables

Table 1: Reservoir Properties and Completion

Net Pay, m 6.2

Temperature C 65

Salinity ppm 177,000

Porosity 4.9%

Rock Type Vuggy carbonateTubing volume m3 2.7

Annulus volume m3 8.1

Drop in annulus vol.

during during production

m3

1.3




Table 2 Leduc 8-17 SWTT Design

Primary Tracer Methyl Acetate 2.36%

K c 2.61

K H, 10-4 hr -1 8.86

Secondary Tracer Methanol 0.006%

Mass Balance 1 n-Propanol 0.63%

Mass Balance 2 i-Butanol 0.67%K c 1.70

Cover Tracer i-Propanol 0.49%

Bank volume m3 14.9

Total inj volume m3 52.3

Injection rate m3/d 92

Shutin time d 9.27

Total production m3 219

Production rate

m3/d

22

Depth of

Investigation m

Methy Acetate 7

i-Propanol 10

Table 3 Mean Residence Volumes

and Recoveries

MRV

m3Recovery

Methanol 457 --

Methyl Acetate 1127 0.689

i-Propanol 1281 0.667

n-Propanol 1164 0.757

i-Butanol 807 0.703

Table 4 Leduc 8-17 Sorw

Leduc 8-17 SWTT

Double porosity 35±3%

2D5TRAMS 38±3%

Mass Balance 34±3%

Moment 36%Peak 38%

Sponge Coring 33%

Interwell tracing 35±2%




Figure 2 Matching of the Methyl Acetate Profile by Double Porosity Model

0

0.05

0.1

0.15

0.2

0.25

0.3

0 50 100 150 200

Production Volume m3

C o n c e n t r a t i o n %

Figure 1 Location of the Leduc Miscible Pilot and Residual Oil Saturation Tests26

Figure 3 Matching of the Methanol Profile by Double Porosity Model

0

0.005

0.01

0.015

0.02

0.025

0.03

0 50 100 150 200


C o n c e n

t r a t i o n %

Sor 30%

Sor 35%

Sor 40%




Figure 4 Comparison of Methyl Acetate and Methanol Profiles

0

0.05

0.1

0.15

0.2

0.25

0.3

0 50 100 150 200


M e t h y l A c e t a t e C o n c e n t r a t i o n

0

0.005

0.01

0.015

0.02

0.025

0.03

M e t h a n o l C o n c e n t r a t i o n

%

Secondary Tracer

Methanol

Primary Tracer

Methyl Acetate

Figure 5 Matching of the I-Propanol Profile by Double Porosity Model

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 50 100 150 200



Figure 6 Matching of the n-Propanol Profile by Double Porosity Model

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 50 100 150 200


C o n c e n

t r a t i o n %




Figure 7 Matching of the i-Butanol Profile by Double Porosity Model

0

0.02

0.04

0.06

0.08

0.1

0.12

0 50 100 150 200



Figure 9 Matching of the Methanol Profile by Single-Porosity Model

0

0.005

0.01

0.015

0.02

0.025

0.03

0 50 100 150 200



Sor 34%

Sor 38%

Sor 42%

Drift=0.15 m/day

0

0.05

0.1

0.15

0.2

0.25

0.3

0 50 100 150 200



Drift = 0.15m/d

Figure 8: Matching of the Methyl Acetate Profile by Single Porosity Model




Figure 10: Residual Oil Saturation by Mass Balance Method

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018

Hydrolysis Rate Constant KH,1/hr

S o r

Cover Tracer IPA

Mass Balance Tracer NPA

Uncertainty in KH10%

Measured KH

0.000886 1/hr

Error in Sor

3%

Figure 11: Leduc Interwell Test

Cumulative Production m3

T

r a c e r A c t i v i t y d p m / m l

determination of residual oil saturation in a carbonate reservoir

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