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Influence of Interfacial Tensionon Gas/Oil Relative Permeabilityin a Gas-Condensate SystemHamza Asar SPE U of Petroleum and MineralsLyman L Handy SPE U of Southern California

Summary. To understand better the effect of interfacial tensions (1FT s) on gas/oil relative permeabilities, with particularemphasis on those effective in condensate reservoirs, an experimental procedure was developed and used with the highly volatilemethane/propane system. The objective was to measure steady-state relative permeabilities as functions of 1FT. Thus the 1FT wasvaried from 0.03 to 0.82 dynes/cm [0.03 to 0.82 mN/m], corresponding to pressures near the critical at a constant temperature of70 DF [21 DC]

Individual relative permeability curves obtained as a function of gas saturation approach the 45 D [0.79-rad] diagonals for bothgas and oil as the 1FT is lowered. This supports the expectation that relative permeability curves for both gas and oil becomestraight lines as the 1FT approaches zero. At the highest 1FT for which experiments were performed (0.82 dynes/cm [0.82mN/m]), the relative permeability curves approached those obtained for a nitrogen/kerosene flood for which the 1FT isapproximately 30 dynes/cm [30 mN/m].

The most important conclusions derived from this work are that I) the curvatures of the relative permeability curves diminish asthe 1FT is reduced, (2) the irreducible gas and liquid saturations approach zero as the 1FT approaches zero, and (3) relative gas/oilpermeabilities for gas-condensate reservoirs are altered from the normal relative permeabilities only at pressures, temperatures, andcompositions close to the critical point.

Introduction1FT, through capillary forces, plays an important role in determining the flow behavior of hydrocarbon fluids in porous rocks. Petroleum engineers involved in EOR are using chemicals, mainlysurfactants, to lower the 1FT between oil and water in oil reservoirs. As a result of alterations in the 1FT, the flow characteristicswill be changed. Consequently, the relative permeabilities to bothphases will be affected. 1FT s also approach zero at the critical pointfor hydrocarbon systems. This could be important in two-phase flowin condensate reservoirs.

Many factors affect relative permeability data. 1 Most of the literature concerning relative permeabilities states that they are func

tions of only saturation, saturation history, rock wettability, andpore-size distribution. Some authors have suggested that water/oilviscosity ratio can also affect relative permeabilities. 2 Althoughit has been known for some time that low 1FT s could reduce residualoil, only recently has the effect of 1FT on the relative permeabilityof hydrocarbon fluid systems been invest igated . Therefore, theprimary objective of this work is to study the influence of 1FT onthe relative permeability of a binary hydrocarbon system; namely,methane/propane mixtures. The research is an extension of studiesinitiated by Saeidi and Handy. 3 The methane/propane system isrepresentative of an idealized gas-condensate system. 4 The liquidphase can reasonably be assumed to be the wetting phase. The results obtained in this work with methane and propane clearly indicate that gas/oil relative permeability data are strong functions ofboth saturation and 1FT. Low 1FT s were obtained by conducting

the experiments near the critical point of the hydrocarbon fluid system. The experiments were carried out using Berea sandstone ata constant temperature of 70 DF [21 DC]

On the basis of the phase behavior of the methane/propane system, a new experimental technique was developed to obtain individual relative permeabilities to gas and oil. Bardon and Longeron 5have discussed a procedure for obtaining gas/oil relative permeability ratios for two-component hydrocarbon systems near the critical point. Wagner and Leach 6 studied the effect of displacementefficiency as a function of 1FT under similar conditions. In bothpapers, relative permeability data were obtained by unsteady-state

Copyright 988 Society of Petroleum Engineers

SPE Reservoir Engineering, February 1988

methods. With our procedure, the methane/propane mixtures areinitially at a pressure and temperature such that they are in the onephase region on the pressure/composition phase diagram. As fluidsare transferred into the core, the pressure is dropped through a needle valve to a predetermined level in the two-phase region. A differential pressure is imposed to create flow and to enablemeasurement of the required data. This procedure gives a steadystate measurement of relative permeabilities. It should be pointedout that liquid saturation can be built up from zero, which is thedirection in which saturations would change when a gas-condensatereservoir is produced. f he propane concentrations are higher, however, the system will be initially 100 liquid saturated. In this case,the method gives drainage (decreasing wetting-phase saturation)rather than imbibition (increasing wetting-phase saturation) relative permeability data.

1FT for a two-phase, two-component system approaches zero asthe system approaches the critical point. For any two-comp.onentsystem, such as methane/propane, the 1FT between the two phasesis a function of only composition and pressure, provided that thetemperature remains constant. 7 In this work, relative permeabilities to gas and oil were obtained at different 1FT levels by changing the composition or the pressure of the experiment near the criticalregion of the methane/propane system.

Possible effects on the phase behavior of gas condensates as aresult of the presence of porous media were investigated. The literature on this subject is contradictory but the results obtained seem

to lend support to results reported by Sigmund et al 8; namely,that the porous medium has little or no effect on the equilibriumphase behavior.

Hysteresis effect on the relative permeability (drainage and imbibition) were also investigated, though not extensively. Relativepermeability data for the gas-condensate systems were comparedwith conventional Welge-type experimental relative permeabilitywith kerosene and nitrogen as the flowing fluids.

Experimental ProceduresFluid Properties Relative permeability studies for multiphase flowof any hydrocarbon system require knowledge of the equilibriumchemical and physical properties of the fluid system in addition to

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1600

1400

1200

:: 1000( f )Q .

800w0::: : l( f )

6 0 0( f )

w0::Q.

400

200

00 0 6 0.7 0 8 0.9 LO

MOLE PERCENT METHANE ( )

Fig. 1-Pressure/temperature phase diagram for a methane/propane mixture at 70 F.

the properties of the reservoir rock. F or a gas-condensate system,it will be sufficient to know the fluid properties as functions of composition and pressure for only one specified reservoir temperature.In our case, data for methane/pro pane were required at room temperature, 7 DF [21 DC].

The methane/propane system has been studied extensively by Sageet al. 9. IO who determined its equilibrium phase behavior and PVTproperties. They studied the system in the temperature range of 40to 190 DF [4 to 88 D C] Rutherford 11 reported data only for a temperature of llODF [43 D C]

0.022

0.020

0.018

0.016il.

CL 0.014 u2

r0.012 ::

u; I f )000.010 uu I f )

I f )

:;: >I f ) 0.008 9

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42

40

38

I< >

W 36:

cr:-

b

z0

n 2zWf -

...J404LL0::wt -Z

PRESSU RE PSIA)

Fig. 6-IFT of the methane/propane mixture as function ofpressure at 70F.

pose. These were calculated from Sage et al s data and plottedon Fig. 4. The molecular weights of the coexisting vapor and liquid phases were also required. These were easily calculated fromthe data at 70F [21C] and are shown on Fig. 5.

Prediction of IFT 's for light hydrocarbon binary mixtures as functions of pressure and temperature has been madc possible by corre

lations developed by Hough and Stegemeier7

and Hough andWarren. 14 These correlations with Sage et al s data were used toestimate 1FT's for the methane/propane system at the conditionsused in our experiments. The results of these calculations are plotted in Fig. 6.

The procedures for calculating g for the flowing fluids and thecorresponding gas saturation require knowledge of the volumetricfractions of gas and liquid for a given pressure and overall fluid

DISCHARGE CORE

PRESS.GAUGE,

N2 RESERVOIR

Fig. 8-Schematic diagram of the experimental apparatus.

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composition in the two-phase region. Fig. 7 shows the relation bctween pressure and gas volume percent. The parameter for the individual curves is the mole fraction of methane in the totalmethane/propane system. The method for calculating thesc curvesis given in the Appendix.

Experimental Apparatus. A consolidatcd Berea sandstone corewas used throughout the course of this experimental work. The sandstone was fired at 700F [371C] to destroy any clays that couldhave adversely affected permeability, although the experiments wererun in the absence of water. Because measurement of the pressuredrop across the core was essential to obtain the individual relativepermeabilities, the lowest-permeability Berea sandstone availablewas chosen. This would maximize the pressure drop across the coreand hence give more reliable data.

The core was I t [0.3 mj in length and 2 in. [5 cm) in diameter(cross-sectional area was 3.14 in. 2 [20.27 cm 2 ]) . The porosity wasmeasured in the laboratory and found to be 20 . The supplier ofthe Berea sandstone corc reported the absolute permeability beforefiring to be around 100 md. The measured absolute permeabilitywas 193 md. Fired cores normally have absolute permeabilitieshigher than the unfired ones. The core was fitted into a rubber sleevewith a 2-in. [5-cm) stainless steel plug at each end. Holes of Ys-in.[0.3-cmj diameter were drilled through the centers of the plugs totransmit fluids in and out of the core. The absolute permeabilityof the core was obtained using nitrogen as the flowing fluid.

Fig. S shows a schematic of the experimental equipment used

to measure the individual relative permeabilities and their ratiosfor the methane/propane system. The main components of the experimental apparatus are I) a two-accumulator assembly, (2) thecore, (3) the backpressure regulator (BPR in figure) along with itsconstant -pressure-decline-rate assembly, (4) pressure and differential pressure gauges and transducer (PT in figure), (5) chromatographic and recording equipment, and (6) a gas-flow wet test meter.These components will be discussed in detail.

Two accumulators with 200-in. 3 [32S0-cm 3) capacity each anda 3,OOO-psig [20.7-MPa) safe working pressure were used. Thepistons in these accumulators were equipped with two consecutivehigh-pressure Viton O-rings. The two accumulators were arrangedin a parallel setup so that they could be used for preparation of themethane/propane mixtures. A nitrogen tank was attached to the endof each of the accumulators so that nitrogen could be used as thepressurizing fluid. The ot her end transported the methane/propane

mixture into the core. The mixture pressure was measured witha pressure gauge. All valves used in construction of the apparatuswere stainless steel needle valves.

The core assembly consisted of a thick-walled steel jacket witha 2.25-in. [5.7-cm) ID. The steel jacket contained the sleeved core.The annular space between the core and the inside walls of the jacketwas filled with mineral oil to provide the required overburden pressure. The two ends of the steel jacket were fitted with two steelscrew caps that fit tightly against the stainless steel plugs at the endsof the core. The two steel screw caps were equipped with highpressure rings to prevent any oil leak to the outside or into the sandstone. The rubber'sleeve fits the core and the two stainless steelplugs at each end tightly. Gauge IS wire was wrapped very tightlyover the plugs to prevent oil from leaking into the core at the rubber/steel-plug contact. The steel jacket had two taps. A pressuregauge was mounted on one of the taps to read the overburden pressure, and a manual hydraulic pump was connected to the other tapto raise the overburden pressure to the required level. A differential pressure gauge with a maximum lp of 10 psi [69 kPa) wasmounted between the upstream and downstream ends of the coreassembly. Two valves were installed to shut off the differential pressure gauge in cases when the measurement of l p was not desiredor when it was essential to minimize the dead volume in the tubing.

The core was connected through tubing and a needle valve tothe backpressure regulator and to thc assembly t provide a constant rate of pressure decline. The backpressure regulator was pressurized by a nitrogen tank. The constant-pressure-decline-rate setupconsisted of a small nitrogen reservoir connected to the backpressure regulator at one end and to a pressure regulator with a 0- to60-psig [0- to 414-kPa) delivery pressure at the other. The latter

260

pressure regulator was connected to a small sandstone core to provide a constant mass flow rate from the N 2 reservoir. This setupwould guarantee that the transient part of this experimental workwould take place at a constant pressure-decline rate (i,e dp dt constant). This experimental procedure was first used by Saeidi andHandy,3 and the mathematical proof is discussed in their paper.

Between,the core and the backpressure regulator, a pressure gaugeand a potentiometric-type pressure transducer with ranges of 0 to2,000 psig [0 to 13,S MPa) were mounted to read the pressure ofthe core. The pressure gauge gave a quick reading of the pressure,while the pressure transducer, which was connected to a recorder,gave a continuous record of the pressure decline during the depletion part of the experiment. The pressure transducer was connected to a lIS-V, 60-cycle/sec [60-Hzl, 10-V DC power supply. Thepower supply was used to provide a constant 10-V DC source forthe pressure transducer and 0.1-V DC for the recorder.

The fluids from the core flowed through the backpressure regulator to a Beckman GC-2 chromatograph for analysis of methaneand propane content. The chromatograph was equipped with athermal-conductivity bridge as the detector. The column materialwas Porapak QTM. The chromatograph was operated at 212F[100C]. Helium was used as carrier gas at a flowing pressure of40 psi [276 kPaj. The filament current was always set at 300 rnA.At these conditions, the retention time for methane was 30 secondsand that for propane was 120 seconds. The output from the chromatograph was connected to a recorder to record the methane andpropane peaks.

During the experiment, the fluid mixture flowed continuouslythrough the chromatograph. Samples were analyzed only when thesampling valve was rotated. The outflow end of the chromatographwas connected to a regular wet test meter for measuring cumulativc volume. In conjunction with a timer, the wet test meter wasalso used to measure the flow rate.

The equipment was housed in a constant-temperature containerfor which temperature was controlled at 70F [21C) within about1F [0.6C].

Proced ures. Composition of the saturating hydrocarbon fluid forthe core in each run was selected to give the appropriate gas/liquidflowing ratios. These compositions were obtained by combiningthe calculated amounts of methane and propane and mixing themby pumping them back and forth between the two accumulators.All systems were mixed at pressures such that the final fluid was

in the singlc-phase region. The temperature for all experiments was70F [21C]. Isocomposition lines for compositions containing lessmethane than that at the critical point (67.S mol ) intersect thetwo-phase region on the bubblepoint curve as the pressure is reduced in the core during a run.

To saturate the core with hydrocarbon, it was first saturated withnitrogen at a pressure greater than the critical pressure for themethane/propane system. The core did not contain interstitial water.Hydrocarbon of the selected composition was injected into the core,displacing nitrogen. Injection continued until the composition ofthe produced fluids as determined by chromatography was equalto that of the injected fluid. If we were concerned about a residualnitrogen saturation, the pressure was reduced into the two-phaseregion to flush out the nitrogen and then raised again to a pressure.in the single-phase region and flow continued to constantcomposition effluent.

To measure steady-state relative gas and oil permeabilities, a specific flowing GOR was chosen. From the data on Fig. 7, the specific core pressure for a particular fluid composition was selectedto give the desired flowing GOR. For those initial fluid compositions containing less methane than that at the critical point, the corewas 100% liquid saturated at initial conditions, For those initialcompositions for which the methanc content was greater than thatat the critical point. the core was considered to be 100 gas saturated. Steady-state flow was established at the selected core pressure by maintaining the core pressure with a backpressure regulator.Fluids were bled from the accumulators to the core through a precision needle valve. Rates were controlled such that phase equilibrium could be assumed when the fluids entered the core, Duringthe period in which equilibrium was being established in the core,

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-0 I . O . . . - - T ' - - - - T - - - r - - - - r - - ~.Jt

>-t - 0.8:Jiii~ 0.6::E0::LLJ

0.4LLJ

>

LLJ

0::.....J O . O K - - - - L - - - - - - - - - - - J L . . . . - - ~ - ~

o 0.0 0.2 0.4 0.6 0.8 1 0

GAS SATURATION S9)

-1.Jt- t -::JCD

LLJex:

J)

( )

Fig. 9-Postulated gas/oil relative permeabilities as functionsof saturation for / ~.Jt p= 1300 PSIG .Jt\ / - \ fig/fio = .55 / ~- /:J 0.8 \ = 0.18 dynes/em

/ 0.8 :Jiii \ m \ L3w

0.6 0.60::0:: WW CL

CL

0.4 0.4 ww >> i=~ .....J.....J 0.2 0.2 LLJw 0::0::

J n

5 0.00.0 ( )

0.0 0.2 0.4 0.6 0.8 1.0AVERAGE GAS SATURATION 5 g )

Fig. 11-Gas/oil relative permeabilities as functions of saturation for

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--.. 1.0 1.00

ep = 1100 PSIG --- ,

> I- -g fJ o = .2936>

..... I.....

:J o.S, a =0.82 dynes/em O.SCD I

CDc:x:

c:x:

0.6 l wW 0.6I:r

I:r, WW 0-0- ,

0 4 , 04 ww >> , /, .....J.....J 0.2 0.2 ww I:rI:r

Cf).....J c:x:5 0.00.0 0.0 02 0 4 0.6 OS 1.0

AVERAGE GAS SATURATION (5g )

Fig. 13-Gas/oil relative permeabilities as functions of saturation for \ >.....o.S o.S.....J \

CD \ iIic:x:c:x: \ ww 0.6 \ 0.6a::: \ a:::w ----t t - - - w0- a..

0.4 , / 0.4 ww> / >..... /c:x: / .....J.....J 0.2 / 0.2 ww I:ra::: /

Cf).....J ;30 0.0 0.0

0.0 0.2 04 0.6 0.8 1.0

AVERAGE GAS SATURATION Sg)

Fig. 14-Gas/oi l relative permeabilities as functions of saturation for nitrogen/kerosene.

ing 1FT, the relative permeability curves tended to approach thehypothetical curves postulated for zero 1FT. Moreover, these cUrvestended at the higher tensions to approach the curves obtained inthe kerosene flood for which the 1FT was approximately 30dynes/cm [30 mN/m), as shown in Fig. 14. These curves show asharper decline in the oil relative permeability than in the gas relative permeability with increasing 1FT. At the lowest 1FT s for whichdata were obtained, the two relative permeability curves shown inFig. 10 approached the diagonals discussed earlier for zero 1FT.At the highest 1FT, the curves shown in Fig. 13 approached thoseobtained for the kerosene floods.

The relative permeability ratios as functions of saturation areshown on Fig. IS. Although the curves at all 1FT s appear to converge at low gas saturatiohs, they deviate from each other significantly at the higher values of kg}ko and the higher gas saturations.The curves approach the zero-1FT curve as the 1FT is reduced. Themost conspicuous difference between the high-1FT results and thoseat low 1FT s is the significant reduction in the wetting-phase saturation at high kg/ko ratios. This reduction is observed for 1FT sof 0.43 dynes/cm [0.43 mN/m) or lower. These effects on relative.

262

o

a:::

>-.....

::JD.....

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port the postulate that the gas and oil relative permeability curvesform two diagonals on the plot of relative permeability vs. saturation as we decrease the 1FT to zero. At the higher 1FT levels, theresults approach the familiar gas/oil relative permeability curves.This is evident if we compare the results obtained at the highest1FT with the kerosene flood, which has an 1FT of 30 dynes/cm[30 mN/mj.

Our data show that for imbibition processes, the irreducible gasand oil saturations tend to decrease as 1FT decreases. These saturations approach zero as 1FT reduces to zero. This is to be expected if we recognize that fluids are held in the pores of porous rocksby capillary forces, which are determined by 1FT and the pore radii.

For drainage processes, however, the irreducible or critical gas saturation still appears to be less than 10 even at high 1FT's.

The other features that characterize typical gas/oil relative permeabilities are also exhibited by these experimental results. Athigher 1FT's, the oil relative permeability curve declines sharplyfor small increases in gas saturation. However, the gas relative permeability declines less rapidly as the gas saturation decreases.

Some of the factors that influence the accuracy of the measurements are (I) lack of homogeneity and uniformity in the mixturesof methane and propane, (2) irregular movement of the piston inthe accumulator, (3) error in the vaporlliquid equilibrium data, (4)inaccurate reading of the values for S g and g from pertinent curvesin Fig. 7, (5) inaccurate measurement of t p across the core forthe small pressure drops associated with these very-low-viscosityfluids, and (6) limitations on the applicability of the Buckley-Leverettassumptions.

After the methane/propane mixture with the required composition was prepared, thc prcssure in the accumulator was raised toa level above the critical pressure in the single-phase region. Mixing the fluid was accomplished by transferring the whole contentfrom one accumulator to the other and then back to the originalaccumulator. Because of the time and amount of nitrogen requiredto perform the mixing, the mixing procedure was not carried further. This might cause some nonuniformity in the fluid composition of injected fluids during an experimental run. A nonuniformcomposition causes fluctuation in equilibrium fluid distribution inthe core and hence fluctuation in saturations.

The pressure differential across the piston in the accumulator wasnot always negligible during any experimental run. These varyingpressure drops caused an irregular movement of the piston insidethe accumulator and slugging of the fluid mixture into the core assembly. Slugging of fluids into the core caused the pressure dropacross the core to fluctuate. Inaccurate reading of the pressure dropcould introduce errors in the calculations of individual relative permeabilities. For different runs, the pressure drops varied from about0.2 to 1.5 psi [1.4 to 10 kPaj with a fluctuation of about 10%. Theproblem was more acute at high liquid saturations, but the total pressure drop was also higher at that time. Care should be exercisedin reading pressure differences to obtain consistent data.

Another factor that could affect the relative permeability data isthe determination of the values for S g and 1: from Fig. 7. As canbe seen from that figure, at low gas volume fractions, a slight errorin determining the mixture composition of the steady-state pressure can result in a large error in reading the fluid saturation orthe fractional flow. Any error in reading ? would introduce errorsin krg and kro These results are plotted dIrectly agamst the meas-ured values of Sg

Assumptions in the calculations from the experImental dataIn -

clude the usual ones: gravity effects are negligible for horizontalflow, pressure gradients in the liquid and gas phases are equal atany cross section (negligible capillary effects), flow in the core islaminar, as required for Darcy flow, and the fluids are incompressible. All these assumptions are reasonable for these floods.

In spite of the aforementioned factors that might have influencedour relative permeability curves, the effects of 1FT obtained in thiswork conform well to expectations. Our data are compared withthose of Bardon and Longeron 5 in Fig. 16. The results agree quitewell at the lowest 1FT's. The most significant difference betweenthe two sets of data is the 1FT's at which the relative gas-to-oil permeability ratios approach those obtained at high 1FT's. For our data,this was about 1.0 dyne/cm [1.0 mN/m], whereas for Bardon and

SPE Reservoir Engineering, February1988

100.0 ------r--- ---- -- . . . . - ---

0"-

oS

t i l"-

oS 10.00

0::>I:::J

iii 1 0w:E0::Wa..

>

0.1J Ref 5 Est.)0:: 0 02 dynes/em

J _ .. 0 . 0 01 dynes/em0

I This WorkI) 0 03 dynes/em( )

0 18 ynes/em0.010.0 0.2 0 4 0.6 0.8 1.0

GAS SATURATION. Sg>

Fig. 16-Comparison of data at low 1FT s from this work withthose from Ref. 5.

Longeron it was about 0.1 dynes/cm [0.1 mN/mj. T his would appear reasonable, considering the differences in fluids, porous media, and steady-state vs. unsteady-state procedure used in the twosets of experiments.

Conclusions1. The curves of the individual relative permeabilities (k rg and

kro) vs. gas saturation tend to straighten and approach the 45[0. 79-rad j line as 1FT approaches zero.

2. Relative permeability to oil decreases more rapidly comparedwith the relative permeability to gas as 1FT is increased.

3. Residual gas and oil saturations are higher with higher 1FT.4. The gas saturation at which the gas and oil relative permea

bility curves intersect is higher as the 1FT decreases, indicating adecrease in the oil-wet character of the system.

5. The level of k ro and krg at which these two curves cross ishigher for lower values of 1FT.

6. Saturation history effects at intermediate 1FT's were investigated and appeared not to be significant in this type of experiment.

7. Relative permeability results obtained at the higher 1FT level(0=0.83 dynes/cm [0.83 mN/m]) approach those obtained for thekerosene flood, even though the nitrogen/kerosene 1FT is muchhigher.

8. The relative gas and oil permeabilities for gas-condensate reservoirs would appear to correspond td those for normal gas/oil systems except at conditions close to the critical.

9. At low 1FT' s near the critical point, liquid could flow at lowliquid saturations in condensate reservoirs.

Nomenclatureg = gas flow fraction

kg = effective permeability to gas, mdko = effective permeability to oil, md

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krg = relative permeability to gaskro = relative permeability to oil

K = equilibrium K valueng = number of moles in the gasnL = number of moles in the liquid

p = total pressure, psi [kPa]Lip = pressure drop, psi [kPa]

g = gas saturationg = average gas saturation

t = time, secondsVIg = gas volume fractionVg = volume of gas, cm 3

VL = volume of liquid, cm 3

W = weight, gWg = weight of gas, gWL = weight of liquid, gIlg = gas viscosity, cp [Pa' s]Ilo = oil viscosity, cp [Pa' s]

P = density, g/ cm 3P g = gas density, g/cm 3PL = liquid density, g/cm 3

J = 1FT, dynes/cm [mN/m] = porosity,

References

I. Geffen, T.M. et ai.: Experimental Investigation of Factors AffectingLaboratory Relative Permeability Measurements, Trans., AIME (1951)192, 99-103.

2. Odeh, A.S.: Effect of Viscosity Ratio on Relative Permeability,Trans., AIME (1959) 216,346-52.

3. ,Saeidi. A. and Handy, L.L.: Flow and Phase Behavior of GasCondensate and Volatile Oil in Porous Media, paper SPE 4891presented at the 1974 SPE California Regional Meeting, San Francisco,April 3-6.

4. Kniazeff, V.J. and Naville, S.A.: Two-Phase Flow of VolatileHydrocarbons, SPEJ (March 1965) 37-45; Trans., AIME, 234.

5. Bardon, C. and Longeron, D.: Influence of Very Low InterfacialTensions on Relative Permeability, SPEJ (Oct. 1980) 391-40 I.

6. Wagner, O.R. and Leach, R.O.: Effe ct of Interfacial Tension on

Displacement Efficiency, SPEJ (Dec. 1966) 335-44; Trans., AIME,237.7. Hough, E.W. and Stegemeier, G.L.: Correlat ion of Surface and

Interfacial Tension of Light Hydrocarbons in the Critical Region, SPEJ(Dec. 1961) 259-69; Trans., AIME, 222.

8. Sigmund, P.M. et al.: Retrograde Condensation in Porous Media,SPEJ (April 1973) 93-101; Trans., AIME, 255.

9. Reamer, H.H., Sage, B.H., and Lacey, W.N.: Phase Equilibria inHydrocarbon Systems, Ind. Eng. Chern (1950) 42, No.3, 534.

10. Sage, B.H., Lacey, W.N., and Schaafsma, J.G.: Phase Equilibriain Hydrocarbon Systems, Ind. Eng. Chern (1934) 26,214.

II. Rutherford, W .M.: Miscibility Relationships in the Displacement ofOil by Light Hydrocarbons, SPEJ (Dec. 1982) 340-47; Trans., AIME,225.

12. Carr, N.L., Kobayashi, R., and Burrows, D.B.: Viscosity ofHydrocarbon Gases Under Pressure, Trans., AIME (1954) 201,264-72.

13. Smith. A.S. and Brown, G.G.: Correla ting Fluid Viscosity, Ind.Eng. Chern (1943) 35, 705.14. Hough, E.W. and Warren, H.G.: Correla tion of Interfacial Tension

of Hydrocarbons, SPEJ (Dec. 1966) 345-52; Trans., AIME, 237.

Appendix Determination of Saturation andFractional Flow

Avcrage gas saturations, S g and fractional flow, fg, determinations are essential in the measurement of relative permeability. Fig.1 gives the two-phase vapor/liquid equilibrium for the methane/pro-

264

pane system, but it does not indicate how much gas or how muchliquid can coexist at any given pressure within the two-phase region.Gas and liquid densities and molecular weights were used in conjunction with Fig. 1 to construct a family of curves to be used inthe determination of g and f g . The procedure for constructingthese curves is as follows.

I. A mixture with a given composition and pressure in the twophase region is chosen by use of Fig. 1.

2. The ratio of moles of gas to moles of liquid ng/nL) is determined by the lever principle.

3. The moles of gas and liquids are converted to volumes asfollows:

ng=Wg/M g , A-I)

nL = WL/ M v A-2)

Wg =P g Vg, A-3)

W= p V L A-4)

and

(A-5)

Solving for VgIV L gives

(A-6)

The gas volume fraction VIg is given by

VgV j g . A-7)

Vg+VL

Dividing the numerator and denominator of Eq. 12 by Vg gives

VIg = l + VLIVg

) A-S)

4. The same procedure is repeated for the same composition butdifferent pressures until one curve is constructed for the given composition. The other curves for different compositions are constructedin a similar manner. From the given pressure and original composition, fg can be calculated. Fig. 7 shows the family of curves tothe left of the critical point (or bubblepoint mixture) and also thecurves to the right of the critical point (or dewpoint mixture). Thisfigure was used to obtain the average gas saturation after determining the average gas composition in the core from the depletionpart of the experiment. The value of fg was determined from aknowledge of the mixture composition at the steady state.

SI Metric onversion Factorscp x 1.0* E-03

dynes/cm x 1.0* E+OOOF OF - 32)/I.Spsi x 6.S94757 E+OO

*Conversion factor is exact.

Pa'smN/mCkPa

SPERE

Original SPE manuscript received for review March 12, 1983. Paper accepted for publication Aug. 3, 1987. Revised manuscript received July 9,1987. Paper (SPE 11740) firstpresented at the 1983 SPE California Regional Meeting held in Ventura March 23-25.

SPE Reservoir Engineering, February 1988