Residual Gas Saturation Revisited

SummaryThe determination of residual gas saturation in gas reservoirs fromlong spontaneous and forced-imbibition tests is addressed in thispaper. It is customarily assumed that when a gas reservoir is over-laying an aquifer, water will imbibe into the gas-saturated zonewith the onset of gas production. The process of gas displacement by water will lead to forced imbibition in areas ofhigh drawdown and spontaneous imbibition in areas of low draw-down. It is further assumed that in the bulk of the reservoir, spon-taneous imbibition will prevail and the reservoir will be water-wet.A final assumption is that the gas behaves as an incompressiblefluid. All these assumptions are challenged in this paper. A seriesof experiments is presented in which it is demonstrated that theresidual gas saturation obtained by a short imbibition test is notnecessarily the correct residual gas saturation. Imbibition tests bydifferent methods yield very different results, while saturation his-tory and core cleaning also seem to have a strong effect on thedetermination of residual gas saturation. It was found, in somecases, that the residual gas by spontaneous imbibition was unrea-sonably high. This was attributed to weak wetting conditions of thecore (no water pull by imbibition). It is expected that this work willshed some new light on an old, but not-so-well-understood, topic.

IntroductionWhen a porous medium is partially or fully saturated with a non-wetting phase, and a wetting phase is allowed to invade the porousmedium, the process is called imbibition. For the problemaddressed in this work, the nonwetting phase is assumed to be gas,and the wetting phase is assumed to be the aquifer water. If themedium is dry and the water is imbibing, then the imbibition isprimary (Swi�0). If the water is already in the medium, the imbibi-tion is secondary (Swi�0). If there is no driving force other than theaffinity to wet, the imbibition is spontaneous. If there is any otherpositive pressure gradient, the imbibition is called forced.

Numerous papers have been written on the subject of residualoil saturation from imbibition, but fewer have been prepared on thesubject of residual gas saturation from imbibition. The commonperception is that many of the principles that cover oil and gasreservoirs are the same.

Agarwal1 addressed the relationship between initial and finalgas saturation from an empirical perspective. He worked with 320imbibition experiments and segmented the database to developcurve fits for common rock classifications.

Land2 noted that available data seemed to fit very well to anempirical functional form given as

In this model, the only free parameter is the maximum observ-able trapped nonwetting phase saturation corresponding to Sgr

(Sgi�1). This expression does not predict residual phase saturation,only how residual saturation scales with initial saturation.

Zhou et al.3 studied the effect of wettability, initial water satura-tion, and aging time on oil recovery by spontaneous imbibition and

waterflooding. A correlation between water wetness and oil recov-ery by waterflooding and spontaneous imbibition was observed.

Geffen et al.4 investigated some factors that affect the residualgas saturation, such as flooding rate, static pressure, temperature,sample size, and saturation conditions before flooding. They foundthat water imbibition on dry-plug experiments was different fromwaterflooding experiments with connate water. However, they con-cluded that the residual gas saturation from the two types of exper-iments was essentially the same.

Keelan and Pugh5 concluded that trapped gas saturation existedafter gas displacement by wetting-phase imbibition in carbonatereservoirs. Their experiments showed that the trapped gas variedwith initial gas in place and that it was a function of rock type.

Fishlock et al.6 investigated the residual gas saturation as afunction of pressure. They focused on the mobilization of residualgas by blowdown. Apparently, the trapped gas did not becomemobile immediately as it expanded. The gas saturation had toincrease appreciably to a critical value for gas remobilization.

Tang and Morrow7 introduced the effect of composition on themicroscopic displacement efficiency of oil recovery by water-flooding and spontaneous imbibition. They concluded that thecation valency was important to crude/oil/rock interactions.

Chierici et al.8 tested whether a reliable value of reserves couldbe obtained from reservoir past-production performance by ana-lyzing results from six gasfield experiments. They concluded thatdifferent gas reservoir aquifer systems could show the same pres-sure performance in response to a given production schedule.

Baldwin and Spinler9 investigated residual oil saturation startingfrom different initial water saturation using magnetic resonanceimaging (MRI). They concluded that at low initial water saturation,the presence of a significant waterfront during spontaneous waterimbibition indicated that the rate of water transport was less thanthat of oil. At high initial water saturation, the more uniform satu-ration change during spontaneous water imbibition indicated thatthe rate of water transport was greater than that of oil. The patternof spontaneous imbibition depended on sample wettability, withless effect from frontal movement in less water-wet samples.

Pow et al.10 addressed the imbibition of water in fractured gasreservoirs. Field and laboratory information suggested that a largeamount of gas was trapped through fast water imbibition throughthe fractures and premature water breakthrough. The postulationwas made that such gas reservoirs would produce this gas if andwhen the bypassed gas was allowed to flow to the production inter-vals under capillary-controlled action. The question of whether therate of imbibition could enhance the production of this trapped gaswas raised. Preliminary experiments on full-diameter core piecesshowed that the rates of imbibition were extremely slow and that ifthe different imbibition experiments were performed in full-diameterplugs, the duration of the experiments would be prohibitively long.These experiments formulated the experimental strategy presentedin the following sections.

It must be noted that several attempts have been made in thepast to group data from different reservoirs or conditions andquantify the value of residual gas saturation.1,11–13 Such group-ings are fairly broad and are used as guidelines for the currentwork. Crowell et al.11 discussed the efficiency of gas recovery bywater imbibition. It was shown that gas recovery was a strongfunction of the initial gas saturation and that the maximum recov-ery was obtained at zero initial water saturation. The experimentswere done with Berea cores. Similar results were obtained forBoise sandstone cores. Free imbibition or forced imbibition at aconstant flow rate seemed to have no difference in terms of finalrecovery of gas in Boise sandstone. A slight increase in gas

. . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

max

11 1

gi

gr

gi

gr

SS

SS

=� �

+ −� ��

December 2001 SPE Reservoir Evaluation & Engineering 467

Residual Gas Saturation RevisitedApostolos Kantzas, SPE, U. of Calgary and TIPM Laboratory; Minghua Ding, TIPM Laboratory; and

Jong Lee, SPE, Petro-Canada Oil and Gas

Copyright © 2001 Society of Petroleum Engineers

This paper (SPE 75116) was revised for publication from paper SPE 59782, first presentedat the 2000 SPE/CERI Gas Technology Symposium, Calgary, 3–5 April. Original manuscriptreceived for review 11 July 2000. Revised manuscript received 6 September 2001. Paperpeer approved 24 October 2001.

recovery with a reduction of interfacial tension was observed inBerea slabs. The effect of permeability seemed to be rather con-voluted when different sandstones were used. Finally, it seemsthat, for the fluids tested, there was consistent behavior of the gasrecovery efficiencies irrespective of what kind of liquid (water,brine, or oil) was used.

Kleppe et al.14 developed a new method for construction of hysteresis capillary pressure relationships for use in reservoir simulation models. A set of plugs was used to get gas/oil capillarypressure curve cycles using a porous plate method. They discoveredthat the Land’s model is not applicable for that particular rock-fluidsystem. In the absence of experimental data, it was suggested thatthe residual gas saturation could be obtained from a linear rela-tionship, with the maximum residual saturation at the end of thecomplete imbibition curve.

Mattax and Kyte15 extended the imbibition theory to show thatthe time required to recover a given fraction of the oil from amatrix block is proportional to the square of the distance betweenfractures. For a given rock type and oil-to-water viscosity ratio, oil-recovery behavior can be scaled by a dimensionless parameter sim-ilar to that shown in Eq. 5. A series of scaling conditions were usedin their work to get the oil-recovery predictions from laboratoryexperimental results. The critical rate was introduced to explain theimbibition effect on the recovery of an oil reservoir.

Wardlaw and McKellar16 addressed the differences betweenconnate water saturation obtained from oil-base cores and thosepredicted from the equilibrium mercury capillary pressure datafor rocks of similar porosity. Two types of imbibition experi-ments, the submersion and the interface contact experiments,were performed; each was completed under two wettabilitymodes. It was concluded that oil deposited in a reservoir mightcreate surfaces that are partly hydrophobic. It was also concludedthat gas recovery from interface contact experiments reached avery low number, owing to a limited capacity to imbibe wateragainst gravity.

In the literature, theoretical approaches to primary imbibitionare usually associated with the principle of dimensionless time.Typical equations describing dimensionless time are shown below.

Aronofsky et al.17 and Aguilera18 presented equations that cal-culated the oil recovery from a porous matrix resulting from waterinvasion in fractured reservoirs. The equations are

for the case of a single model element, and

for the case of a total fractured reservoir in which the velocity ofadvance of the water table is uniform. In Eqs. 3 and 4, r�therecovery at any time t, R�the limit toward which the recovery con-verges, and ��a constant giving the rate of convergence.

In the figures of the Aronofsky et al.17 paper, one can see thatthe mean water rise as a function of time reaches a first plateau,where the oil recovery slows down after an accelerated period.This is followed by a second stage of water saturation to higher sat-uration values. This trend appears as though the imbibition processslows down before it starts up again. Gupta and Civan19 extendedthis work to include contact-angle effects.

Ma et al.20 determined generalized scaling criteria for sponta-neous imbibition in strongly water-wet systems. They extendedprevious work to include a dimensionless term tD so that

The constant Lc is based on geometrical considerations of thematrix block that undergoes imbibition. Ma et al.20 found that plotsof recoverable oil vs. dimensionless time fell well within the samecurve that was matched by Eq. 3 with a value of ��0.05.

ExperimentalThe sandstone core selected for the evaluation of the residual gassaturation exercise comes from two dry-gas reservoirs. Severalplugs with diameter of 2.54 cm or 3.81 cm and lengths of approxi-mately 5.0 cm were chosen. The plugs are identified as Group 1 andGroup 2 (see Table 1). The following types of tests were performed.

Preparation of Core Plugs and Brine. All data presented in thispaper are based on plugs (Groups 1 and 2) that were cleaned in theDean Stark apparatus before any testing. All initial imbibition testsare denoted “as is.” All the plugs were also cleaned in the DeanStark apparatus between imbibition tests. The values of air perme-ability, porosity, and brine permeability were measured. The resultsobtained are summarized in Table 1. Synthetic formation brine, witha density of 1.0306 g/cm3 and a pH value of 4.5, was used for mostexperiments. The brine formula is shown in Table 2. As requested,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)2

1D

cw nw

kt t

L

σφ µ µ

=

. . . . . . . . . . . . . . . . . . . . . . . . . . . (4)1

[1 (1 )]tr R et

λ

λ−

∞= − −

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)(1 )tr R e λ−∞= −

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)max

max

gi

gr gr

g

SS S

S=

468 December 2001 SPE Reservoir Evaluation & Engineering

TABLE 1—ROUTINE CORE PROPERTIES

Core PlugID

Diameter(cm)

Length(cm)

Porosity(fraction)

Air Permeability(md)

Brine Permeability(md)

1-1 3.66 3.675 0.186 2 17

1-2 3.68 4.05 0.141 100 52

1-3 3.66 4.01 0.139 442 118

1-4 3.655 4.02 0.123 183 154

1-5 3.675 4.15 0.147 578 105

1-6 3.64 4.05 0.310 149 21

1-7 3.655 3.93 0.267 372 221

1-8 3.65 3.94 0.278 194 66

2-1 2.485 4.015 0.139 490 290

2-2 2.495 4.585 0.087 26 33

2-3 2.49 3.865 0.104 252 54

2-4 2.50 3.53 0.152 674 271

2-5 2.495 3.65 0.164 820 640

2-6 2.495 4.045 0.133 643 421

2-7 2.495 3.425 0.140 507 268

2-8 2.485 3.915 0.158 1,283 925

2-9 2.485 3.385 0.176 984 793

owing to the unavailability of brine at the time, troubleshootingwith the cores in some experiments was done with tap water.

Imbibition Experiments. Two types of experiments were per-formed: air/brine spontaneous-imbibition tests and forced-imbibitiontests. Both primary spontaneous-imbibition tests and secondaryspontaneous-imbibition tests were conducted for all core plugs.Imbibition was monitored by measuring the change of weight of thecore plugs as a function of imbibition time. Two methods were usedfor this purpose in the primary spontaneous-imbibition tests. In onemethod, performed manually, the weight change was measuredevery 5 minutes for the first 24 points, once per 30 minutes for thefollowing 15 points, and once per 24 hours for the final six points(for a total time period of 1 week). To take a weight measurement,the core was removed from the imbibition cup and placed on a bal-ance. The weight change was measured, and the core was placedback into the imbibition cup. Subsequently (and to eliminate possibleerrors with core removal from the imbibition cup), an automaticweight-measurement method was developed. A core plug was suspended by a line in a beaker containing the brine. The beakercontaining the core and brine was balanced against a fixed-weightmetal cylinder. This cylinder rested on an electronic balance thatwas in turn connected to a computer. As water imbibed in the core,its weight increased, thus reducing the weight of the cylinder on thebalance. The timestep for data recording and the change in weight

of the core suspended in the brine was recorded automatically. Thesecondary imbibition tests were performed with the core plugs at aninitial water saturation, which was obtained after the core was satu-rated with water and drained in the centrifuge. Two different sec-ondary spontaneous-imbibition conditions were obtained by gasdrainage in the centrifuge at 1,000 and 6,000 revolutions per minute(RPM), respectively. The corresponding endface capillary pressuresat these two speeds are 35 kPa and 1200 kPa.

The forced-imbibition tests were performed on each plug tocheck the difference in gas recovery between the spontaneousimbibition and the forced imbibition. The forced-imbibition exper-iments also included the primary forced-imbibition test and thesecondary forced-imbibition test by brine flooding at a constantflow rate of 2 cm3/hr. The secondary forced-imbibition test fol-lowed a primary spontaneous-imbibition test based on dry core. Theinjected brine volume and pressure drop across the core plug wererecorded during all the experiments. The forced-imbibition testsserve a dual purpose. First, in conjunction with the spontaneous-imbibition tests, they can be used for the determination of theAmott index to water. This can then be used as a wettability indi-cator. Second, it was always assumed that water influx occursunder low capillary-number conditions. If at the end of the sponta-neous test Sgr is reached, then the forced-imbibition test can beused to measure endpoint brine permeability. However, because itwas observed that gas saturation decreases significantly with theforced-imbibition test, the gas-saturation values obtained were alsoused in the interpretation process to assess the expected residualgas saturation at reservoir conditions.

To address issues related to reproducibility of the results,effects of water salinity, and effects of measurement procedure,several repeat tests were performed in most of the plugs. Therepeat tests were all done for the spontaneous-imbibition test with-out initial water saturation. Before each test, the cores were subjected to a Dean Stark type of cleaning. There is always theconcern that microscopic changes occur in the rock when suchcleanup cycles take place. This concern must be taken into accountwhen the results are interpreted.

The experiments performed on nine plugs in Group 2 were notthe same for each plug. Plugs 2-1 through 2-3 were tested underone set of experimental procedures; plugs 2-4, 2-8, and 2-9 weretested under the second set of procedures, and plugs 2-5 through 2-7were tested under the third set of procedures. The detailed experi-mental procedures are shown in Table 3. The numbers 1 through 5were used to identify the sequence of spontaneous-imbibition procedures. The only reason for using tap water initially was thatthe formation brine was not available at the time.

Experimental ResultsThe customary method for plotting the recovered results in imbibi-tion experiments is to plot the volume or weight change as a func-


TABLE 2—COMPOSITIONS OF RESERVOIR BRINE

AND WATER

Synthetic Formation Brine g/L

CaCl2 12.553

MgCl2.6H2O 16.543

NaCl 29.704

KaCl 1.9401

NaHCO3 0.0144

FeSO47H2O 0.173

Tap water ppm

Al 0.033 to 0.179

Ca 32 to 66.5

Cl2 0.53 to 1.2

F2 0.63 to 0.74

Mg 10.7 to 18.1

Ni,Zn <0.004

Ka 0.38 to 1.5

Na 1.6 to 6.5

TDS 130 to 287

Hardness (CaCO3) 117 to 248

TABLE 3—EXPERIMENTAL PROCEDURES

Plugs 2-1 through 2-3 Plugs 2-4, 2-8, 2-9 Plugs 2-5 through 2-7

Primary and spontaneous imbibitionwith tap water (1)

Primary and spontaneous imbibition

with tap water (1)


with tap water (1)

Gas drainage in centrifuge to get Swirat 6,000 RPM



Secondary and spontaneousimbibition with brine at Swir (2)



Primary and spontaneous imbibitionwith brine (3)



Brine flooding at 2 cm3/hour Secondary and spontaneous

imbibition with brine at Swir (3)Secondary and spontaneousimbibition with brine at Swir (3)

Repeat primary and spontaneousimbibition with tap water (4)

Brine flooding at 2 cm3/hour Repeat primary and spontaneous

imbibition with brine (4)

Primary and spontaneous imbibitionwith brine performed automatically (5)

Repeat primary and spontaneousimbibition with brine (4)

Brine flooding at 2 cm3/hour


with brine performed automatically (5)


with brine performed automatically (5)

tion of time, or to plot a normalized recovery factor as a functionof a dimensionless time.21,22 For the analysis presented in thiswork, the data are initially plotted in the form of gas saturation inthe core as a function of experiment time.

Figs. 1 through 3 show the results of several primary and sec-ondary spontaneous-imbibition experiments for plugs 2-1, 2-4, and2-7. The results for the remaining plugs are not presented herebecause similar results were obtained for the same procedure

experiments. The figures demonstrate the variety of pathways fol-lowed in each imbibition process.

Fig. 1 describes a series of spontaneous-imbibition tests per-formed on plug 2-1 (see Table 3). Four primary-imbibition testsand one secondary-imbibition test are included. Two of the primary-imbibition tests were run with tap water, and two of thetests were run with formation brine. Four tests were run with themanual method of core-weight measurement, and one set was run

Fig. 2—Experimental data for core plug 2-4.


0

0.2

0.4

0.6

0.8

1

1 10 100 1,000 10,000 100,000

Production Time, minutes

Gas S

atu

rati

on

, fr

acti

on

Swi =0, tap water, manual, “as is”

Swi =0.469, brine, manual Swi =0.158, brine, manual Swi =0, brine, manual Swi =0, brine, automated


0

0.2

0.4

0.6

0.8

1

1 10 100 1,000 10,000 100,000


Gas S

atu

rati

on

, fr

acti

on

Swi =0, tap water, manual, “as is”

Swi =0.469, brine, manual Swi =0.158, brine, manual Swi =0, brine, manual Swi =0, brine, automated

0

0.2

0.4

0.6

0.8

1

1 10 100 1,000 10,000 100,000


Ga

s S

atu

rati

on

, fr

ac

tio

n

Swi=0, tap water, manual, “as is” Swi =0.07, brine, manual Swi =0, brine, manual Swi =0, tap water, manual Swi =0, brine, automated


with the automated-weight measurement. The “as is” test exhibit-ed the slowest rate of imbibition and the highest residual gas satu-ration. The secondary imbibition exhibited the fastest rate. Theremaining residual gas saturation values were fairly close. Tap andbrine imbibition give very similar results, except for the last stageof imbibition. In the automated-imbibition test, high initial rates ofimbibition were measured, but the residual gas values fall close tothose of the manual tests. The results for plugs 2-2 and 2-3 are sim-ilar to this 2-1 plug. It must be noted that no data are shown for thefirst minute of imbibition.

Fig. 2 shows the results of the tests conducted on core plug 2-4.For this plug, there were two different secondary-imbibition tests.One test was automated, and the rest were manual. The repro-ducibility between the automated and manual tests is excellent.The “as is” core had the lowest rate of imbibition and the highestresidual gas saturation. The secondary-imbibition tests have thelowest residual gas saturation. The rate of imbibition is seen todecrease clearly with decreasing initial water saturation. Theresults of plugs 2-8 and 2-9 are similar to plug 2-4.

Fig. 3 shows the results of the tests conducted on core plug 2-7.Plug 2-7 was exposed to a series of oil/brine capillary pressure andrelative permeability tests before cleanup and additional imbibitiontesting with air/brine. The trends were similar to what wasobserved previously, except for the notable difference between thetap-water tests and the brine-imbibition tests. The results of plugs2-5 and 2-6 are similar to this plug.

DiscussionThe experiments presented in this work reveal that the mechanism ofwater influx in a gas reservoir is quite complicated. Production his-tory and saturation affect the results of gas recovery. It is apparentthat the rate of imbibition (i.e., the speed by which water invadesthe pore space) also varies with initial conditions and productionhistory. Bearing in mind that the water-influx measurements wereconducted in a small pore volume (of the order of 1 to 3 cm3), it isclear that the manual method of data collection did not have a significant effect on the trends of the results produced. However,for consistency and for more data collection at the first stage ofimbibition, the automated method should be used.

Close observation of Figs. 1 and 2 shows that in some cases,the residual gas saturations using brine (excluding tap water) arequite similar (Figs. 1 and 3) while they are quite different in othercores (Fig. 2); however, no significant difference exists in theprocedures. A second observation deals with the actual residualgas saturation. Although it appears to reach a plateau at 100 to1,000 minutes, after 2,000 minutes, many plugs show reducingresidual gas. It is as if the gas is mobilized. Two apparent expla-nations are given; the first is that gas dissolves in water (althoughwell-aerated water was used in the tests), and the second is thatthe gas bubbles become mobile through shrinkage or interfaceunpinching. This mechanism could be of importance for gasmobility at high water saturations in the reservoirs, and itdeserves further investigation.

It was also evident from the production data that the initial wet-tability and the brine salinity of the system strongly affected thegas recovery. Newly received core (“as is” state) that did not gothrough the repeated cleanup cycles had significantly higher residualgas saturation. Fig. 4 depicts the residual gas saturation measuredas a function of the estimated initial rate of imbibition, as obtainedfrom the experimental data. The imbibition rate was calculatedfrom the slope of the gas-production volume curve with time forthe first 10 minutes. The results are also presented in Table 4. Theexperimental procedure identifier is the same as in Table 3. A rea-sonable correlation exists between the two variables. High initialrates of imbibition imply that the water will rush inside the porespace and should be associated with strong water-wet conditions.When the residual gas saturation is compared to an equivalentAmott index to water, the results of Fig. 5 are obtained. Wettabilityplays a very important role in the recovery of gas through the spon-taneous-imbibition mechanism. It is believed that this mechanismis the strongest driving mechanism in the reservoir away from theperforations, and this is why it is important to understand how it isrelated to residual gas saturation. The results of oil/water systemsfrom the literature are included in the same figure.3 It can be seenthat the results obtained are opposite to the trends in the literature,an event that is quite surprising. The results of Zhou et al.3 arebased on coreflooding experiments, while the presented results inFig. 5 show only the spontaneous-imbibition results. This observa-tion alone can explain the difference. If forced-imbibition resultswere taken into account, it is expected that the gas recovery wouldincrease more for the weak wettability cores as opposed to thestrong wettability cores. However, the question posed is whetherthe coreflooding experiments are more representative than thespontaneous-imbibition tests. A capillary-number analysis indicates that the coreflooding displacement rate in our tests corresponds to a capillary number of 10�9. In the spontaneous-

Fig. 4—Residual gas saturation as a function of initial rate of imbibition.

y = 6.0853x 2

- 3.2382x + 0.6481

R 2 = 0.5654

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.05 0.1 0.15 0.2 0.25 0.3

Imbibition Rate, cm 3 /min

Resid

ual G

as S

atu

rati

on

, fr

acti

on

TABLE 4—SPONTANEOUS-IMBIBITION RATE AT THE FIRST 10 MINUTES

Plug IDImbibition Rate (cm

3/min)

Test Procedure 1 2 3 4 5

2-1 0.0527 0.1506 0.1063 0.1275 0.1524

2-2 0.0685 0.21 0.0593 0.1068 0.0855

2-3 0.1478 0.0524 0.1203 0.1254 0.0911

2-4 0.0317 0.0666 0.26 0.1281 0.1465

2-5 0.0331 0.0668 0.1122 0.1001 0.0762

2-6 0.0281 0.054 0.1102 0.1148 0.0964

2-7 0.0444 0.0571 0.1153 0.1293 0.0849

2-8 0.0814 0.0623 0.0968 0.1438 0.0468

2-9 0.082 0.0781 0.1617 0.226 0.1262


imbibition tests, the capillary pressure number is larger for the firstfew minutes of imbibition, and then it drops. As a result, both displacements are in the capillary forces-controlled regime.

An attempt was made to compare our results to those obtainedby correlations. As such, the Agarwal,1 Land,2 and Kleppe14 modelswere used for testing. Fig. 6 shows the predictions of the Landmodel as they are compared to the experimental data from the literature11 and the data for Core Group 2. The literature data fit themodel well. The Group 2 data do not fit the model but are corre-

lated to it. Thus, a modified Land model provided good agreementwith the performed experiments. The modified Land’s model is

In Fig. 7, the data for a series of long imbibition tests usingplugs of Group 1 fit the Land model fairly well. Any attempt to

. . . . . . . . . (6),experiment

max

0.5578* 0.01681

1 1

gi

gr

gi

gr

SS

SS

= +� �

+ −� ��


Fig. 5—Effect of wettability on gas recovery (Group 2).

y = 0.6619x + 0.0693

R 2 = 0.9131

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Amott Index to Water, Iw

Reco

very

Facto

r, f

racti

on

OG

IP

This work, gas

Zhou et al., oil

Fig. 6—Comparison of experimental data to Land’s model.

y = 0.5578x + 0.0168

R 2 = 0.9911

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.4 0.5

Residual Gas Saturation, Experiment

Resid

ual G

as S

atu

rati

on

, L

an

d's

Mo

del

Crowell et al. (Ref. 11)

Plug Group 2 after cleaning

Fig. 7—Comparison of long imbibition data to Land’s model (Group 1).

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1


Resid

ual G

as S

atu

rati

on

,L

an

d's

Mo

del

1 day

2 days

3 days

4 days

5 days

9 days

19 days

match our results to those of Agarwal failed. It is thus recom-mended that a few simple experiments be conducted in the labora-tory to generate the proper Land-type correlation to estimate gasrecovery as a function of water saturation given water distributionin the reservoir from logs.

Figs. 7 and 8 show the results of a series of tests in which theprimary-imbibition test was allowed to continue for 19 days. Thegas saturation seemed to decrease steadily with time for most

cores, but the actual change in gas saturation was small (less than10% pore volume between Day 2 and Day 19).

Figs. 9 and 10 show the correlation of residual gas saturationbetween the experiments and Kleppe’s model for Groups 2 and 1. Itwas observed that the predictions from Kleppe’s model are similar tothe predictions from Land’s model. A linear fit of results is alsoshown in Fig. 9 for Group 2. The conclusion from this figure is thatwhen the data fit Land’s model, they also fit Kleppe’s model well. If


Fig. 8—Residual gas saturation for long imbibition tests (Group 1).

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Imbibition Time, days

Sg

r, f

racti

on

Plug 1-2

Plug 1-5

Plug 1-4

Plug 1-3

Plug 1-6

Plug 1-8

Plug 1-1

Fig. 9—Comparison of experimental data to Kleppe’s model (Group 2).

y = 0.373x–0.0077

R2 = 0.9496

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45


Resid

ual G

as S

atu

rati

on

, K

lep

pe’s

Mo

del

Fig. 10—Comparison of long imbibition data to Kleppe’s model (Group 1).

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1


Re

sid

ua

l G

as

Sa

tura

tio

n,

Kle

pp

e's

M

od

el

19 days

the data fit a linear transformation of Land’s model, they also will fita linear transformation of Kleppe’s model. From our work to date, itdoes not appear that there is a preference for one model over the other.

A further attempt was made to correlate Sgr to Swi in a manner sim-ilar to that of Crowell et al.11; however, the attempt was unsuccessful.

Fig. 11 shows the imbibition rates for the automated experi-ments of Group 2. The scattering observed at the initial stages ofimbibition can be attributed to the different invasion mecha-nisms at the early stages of the imbibition process. Fig. 12 showsthe dimensionless time vs. recoverable gas plot that is obtained


Fig. 11—Rate of imbibition, automated tests for Group 2.

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

0.01 0.1 1 10 100 1,000 10,000

Time, minutes

Imb

ibit

ion

Rate

, cm

3/m

in

Pump rate

Plug#2-1

Plug#2-2

Plug#2-3

Plug#2-4

Plug#2-5

Plug#2-6

Plug#2-7

Plug#2-8

Plug#2-9

Fig. 12—Production as a function of dimensionless time for the data of Fig. 11 (Group 2).

0

0.2

0.4

0.6

0.8

1

0.000001 0.0001 0.01 1 100 10,000 1,000,000

Dimensionless Time

No

rmali

zed

Reco

vera

ble

Gas

Plug #2-1

Plug #2-2

Plug #2-3

Plug #2-4

Plug #2-5

Plug #2-6

Plug #2-7

Plug #2-8

Plug #2-9

Fig. 13—Effect of wettability on the initial rate of imbibition.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.2 0.4 0.6 0.8 1 1.2Amott Index to Water, Iw

Imb

ibit

ion

Rate

, cm

3/m

in

for the data of Fig. 11 with oil-reservoir analysis.3,20,22 Thedimensionless time is defined in Eq. 3. The results are qualita-tively similar to the oil-equivalent behavior. The imbibition ratesobtained from the experiment of Wardlaw and McKellar16 weresmaller when compared to the results in this work because theplugs used in their experiment were partly hydrophobic. Ofcourse, pore size and topology differences also contribute to dif-ferences in imbibition.

Fig. 13 indicates the effect of wettability on the initial rate ofimbibition. It was observed that the initial rate of imbibitionincreases as the water wettability increases. High rates of imbibi-tion should be associated with strong water wettability. The resultsare in agreement with the results presented in Fig. 4 and Table 4.

The problem with the predicted gas saturations has to do withthe economics of recoverable reserves. For example, in Plug 1 ofGroup 2, the residual gas of the first test was 0.615, while theresidual gas of the automated test was 0.381, and values as low as0.249 were reached. A residual gas of 0.615 can make theexploitation program uneconomic, while a residual gas value of0.249 can make the exploitation program very profitable. The dif-ferent numbers are based on the fact that slightly different meth-ods of measurement were used. In fact, when coreflooding data iscollected, the recovery factors are very high and residual gas isvery low. Thus, the identification of the expected field residual gassaturation is not straightforward.

The work and experimental results presented here address sev-eral issues related to the recovery of gas from reservoirs that aresubject to water influx. However, the results to date indicate thatthe determination of residual gas saturation is a parameter that isnot trivial to estimate. Two issues must be clarified in the evalua-tion process. One is the reservoir wettability and whether the corewettability has changed because of the coring and handlingprocess. The second is the predictive capacity of existing modelsthat is not generally applicable. Thus, testing of plugs for eachreservoir can provide the data required to calibrate a Land’s-typemodel for determining the expected residual gas saturation.

ConclusionsThe following conclusions can be drawn from this work:1. Imbibition tests by different methods yield very different

results. The string-gauge methods produce more consistentresults, thus resulting in minimum errors.

2. Saturation history and core cleaning seem to have a strongeffect on residual gas saturation.

3. Weak wetting conditions cause the residual gas by spontaneousimbibition to be unreasonably high.

4. A modified Land correlation seems to match well the experi-mental data for one reservoir, while the Land model fits datawell from the second reservoir.

5. Approximately 100 minutes, as a minimum time frame, arerequired to reach the first plateau that is commonly associatedwith equilibrium residual gas saturation.

Nomenclaturek � permeability, md

Lc � critical lengthr � recovery at time tR � specified capillary-tube radius

R� � limit toward which recovery convergesS � saturationt � production time� � constant giving the rate of convergence� � viscosity, cp� � interfacial tension, mN/m� � porosity, fraction

SubscriptsD � dimensionlessg � gas

gi � initial gasgr � residual gas

nw � nonwettingw � wetting

wi � initial waterSuperscript

max � maximum allowable

Acknowledgments

The authors acknowledge the contributions of Dan Marentette,Kevin Allsopp, Natalia Mirotchnik, and Mike Benedek of TIPMLaboratory. Permission to publish this paper by Petro-Canada Oiland Gas is gratefully acknowledged.

References1. Agarwal, R.G.: “Unsteady-State Performance of Water-Drive Gas

Reservoirs,” PhD thesis, Texas A&M U., College Station, Texas (1967).2. Land, C.S.: “Calculation of Imbibition Relative Permeability for Two-

and Three-Phase Flow From Rock Properties,” SPEJ (June 1968) 149;Trans., AIME, 243.

3. Zhou, X., Morrow, N.R., and Ma, S.: “Interrelationship of Wettability,Initial Water Saturation, Aging Time, and Oil Recovery by SpontaneousImbibition and Waterflooding,” SPEJ (June 2000) 199.

4. Geffen, T.M. et al.: “Efficiency of Gas Displacement From PorousMedia by Liquid Flooding,” Trans., AIME (1952) 195, 29.

5. Keelan, D.K. and Pugh, V.J.: “Trapped-Gas Saturations in CarbonateFormations,” SPEJ (April 1975) 149; Trans., AIME, 259.

6. Fishlock, T.P. et al.: “Experimental Studies on the Water FloodResidual Gas Saturation and Its Production by Blowdown,” SPERE(May 1988) 387.

7. Tang, G. and Morrow, N.R.: “Oil Recovery by Waterflooding andImbibition-Invading Brine Cation Valency and Salinity,” paper SCA9911 presented at the 1999 Intl. Symposium of the Soc. of CoreAnalysts, Golden, Colorado, 1–4 August.

8. Chierici, G.L., Pizzi, G., and Ciucci, G.M.: “Water Drive GasReservoirs: Uncertainty in Reserves Evaluation From Past History,”JPT (February 1967) 237; Trans., AIME, 240.

9. Baldwin, B.A. and Spinler, E.A.: “In-Situ Saturation DevelopmentDuring Spontaneous Imbibition,” paper SCA 9922 presented at the1999 Intl. Symposium of the Soc. of Core Analysts, Golden, Colorado,1–4 August.

10. Pow, M. et al.: “Production of Gas from Tight Naturally-FracturedReservoirs with Active Water,” J. Cdn. Pet. Tech. (1999) 38, No. 7, 38.

11. Crowell, D., Dean, G., and Loomis, A.: “Efficiency of GasDisplacement from a Water-Drive Reservoir,” USBM 6735, U.S. Dept.of the Interior, Bureau of Mines, Washington, DC (1966).

12. “Managing Water-Drive Gas Reservoirs,” GRI-93/0483, GRIPublications, Gas Research Inst., Chicago (1993).

13. Batycky, J., Irwin, D., and Fish, R.: “Trapped Gas Saturations in Leduc-age Reservoirs,” J. Cdn. Pet. Tech. (February 1998) 37, No. 2, 32.

14. Kleppe, J. et al.: “Representation of Capillary Pressure Hysteresis inReservoir Simulation,” paper SPE 38899 presented at the 1997 SPE AnnualTechnical Conference and Exhibition, San Antonio, Texas, 5–8 October.

15. Mattax, C.C. and Kyte, J.R.: “Imbibition Oil Recovery From Fractured,Water-Drive Reservoir,” SPEJ (June 1962) 177; Trans., AIME, 225.

16. Wardlaw, N.C. and McKellar, M.: “Wettability and Connate WaterSaturation in Hydrocarbon reservoirs with Bitumen Deposits,” J. Pet.Sci. Eng. (1998) 20, 141.

17. Aronofsky, J.S., Masse, L., and Natanson, S.G.: “A Model for theMechanism of Oil Recovery From the Porous Matrix Due to WaterInvasion in Fractured Rocks,” Trans., AIME (1958) 213, 17.

18. Aguilera, R.: “Graphical Solution of Imbibition Equations Used toPredict Oil Recovery by Water Influx in Naturally FracturedReservoirs,” J. Cdn. Pet. Tech. (December 1975) 27, 1528.

19. Gupta, A. and Civan, F.: “An Improved Model for LaboratoryMeasurement of Matrix to Fracture Transfer Function Parameters in Immiscible Displacement,” paper SPE 28929 presented at the 1994 SPE Annual Technical Conference and Exhibition, New Orleans, 25–28 September.

20. Ma, S., Morrow, N.R., and Zhang, X.: “Generalized Scaling ofSpontaneous Imbibition Data for Strongly Water-wet Systems,” paperCIM 95-138 presented at the 1995 Petroleum Conference of the SouthSaskatchewan Section, Regina, Saskatchewan, Canada, 16–18 October.


21. Kantzas, A. et al.: “Co-Current and Counter-Current ImbibitionAnalysis for Tight Fractured Carbonate Gas Reservoirs,” paper CIM97-181 presented at the 1997 Petroleum Conference of the SouthSaskatchewan Section, Regina, Saskatchewan, Canada, 19–22 October.

22. Morrow, N.R. et al.: “Characterization of Wettability from SpontaneousImbibition Measurement,” paper CIM 94-47 presented at the 1994 AnnualTechnical Meeting of the Petroleum Society of CIM, Calgary, 12–15 June.

SI Metric Conversion Factorsbar 1.0* E 05 � Pacp 1.0* E � 03 � Pa�s

dyne 1.0* E � 02 � mNft 3.048* E � 01 � m

in. 2.54* E 00 � cm

*Conversion factor is exact.

Apostolos Kantzas is currently a professor at the U. of Calgary,holder of a Canada Research Chair in Energy and Imaging,and the Director of the Tomographic Imaging and PorousMedia (TIPM) Laboratory. e-mail: [email protected], he held a senior research engineer position in the

Pipeline and Oil Technologies Dept. at NOVA Research andTechnology Corp. He is involved with research related to prob-lems of flow through porous media, enhanced oil recovery, soilremediation, reactor design, and tomographic imaging; hehas authored or co-authored more than 120 technical papersand 120 technical reports. Kantzas holds a Dipl. Eng. in chem-ical engineering from Aristotle U., Greece, and MA Sc. andPhD degrees in chemical engineering from the U. of Waterloo,Canada. Minghua Ding has been a research engineer in theTIPM Laboratory since 1999. e-mail: [email protected]. From1987 to 1997, she worked at China Natl. Offshore Oil Corp.(CNOOC) as a reservoir engineer. She holds a BS degree inmedical engineering from East China U. of Technology and anMS degree in petroleum engineering from the Norwegian U. ofScience and Technology. Jong Lee is a senior reservoir-engineering specialist with Petro-Canada Oil and Gas inCalgary, where he has been involved in various WesternCanada, East Coast, and international exploration and devel-opment projects, including several miscible flood and gascondensate projects, for the past 24 years. e-mail:[email protected]. He is currently working for MackenzieDelta gas exploration and development. Lee holds MSdegrees in chemical and petroleum engineering, both fromthe U. of Alberta.

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