Two-Phase Steady-State and Unsteady-State Relative Permeability Prediction Models

Abstract A consolidated porous medium is mathematically modeled by networks of irregularly shaped interconnected pore channels. Mechanisms are described that form residual saturations during immiscible displacement both by entire pore channels being bypassed and by fluids being isolated by the movement of an interface within individual pore channels. This latter mechanism is shown to depend strongly on pore channel irregularity. Together, these mechanisms provide an explanation for the drainage-imbibition-hysteresis effect. The calculation of steady-state relative permeabilities, based on a pore-size distribution permeabilities, based on a pore-size distribution obtained from a Berea sandstone, is described. These relative permeability curves agree qualitatively with curves that are generally accepted to be typical for highly consolidated materials. In situations where interfacial effects predominate over viscous and gravitational effects, the following conclusions are reached.Relative permeability at a given saturation is everywhere independent of flow rate.Relative permeability is independent of viscosity ratio everywhere except at very low values of wetting phase relative permeability.Irreducible wetting-phase saturation following steady-state drainage decreases with increasing ratio of nonwetting- to wetting-phase viscosity.Irreducible wetting-phase saturation following unsteady-state drainage is lower than for steady-state drainage.Irreducible nonwetting-phase saturation following imbibition is independent of viscosity ratio, whether or not the imbibition is carried out under steady- or unsteady-state conditions. Experiments qualitatively verify the conclusions regarding unsteady-state residual wetting-phase saturation. Implications of these conclusions are discussed. Introduction Natural and artificial porous materials are generally composed of matrix substance brought together in a more or less random manner. This leads to the creation of a network of interconnected pore spaces of highly irregular shape. Since the pore spaces of highly irregular shape. Since the geometry of such a network is impossible to describe, we can never obtain a complete description of its flow behavior. We can, however, abstract those properties of the porous medium pertinent to the type of flow under consideration, and thus obtain an adequate description of that flow. Thus, the Kozeny-Carmen equation, by considering a porous medium as a bundle of noninterconnecting capillary tubes, provides an adequate description of single-phase provides an adequate description of single-phase flow. With the addition of a saturation-dependent tortuosity parameter in two-phase flow to account for flow path elongation, the Kozeny-Carmen equation has been used to predict relative permeabilities for the displacement of a wetting permeabilities for the displacement of a wetting liquid by a gas. It has long been recognized that relative permeability depends not only on saturation but permeability depends not only on saturation but also on saturation history as well. Naar and Henderson described a mathematical model in which differences between drainage and imbibition behavior are explained in terms of a bypassing mechanism by which oil is trapped during imbibition. Fatt proposed a model for a porous medium that consisted of regular networks of cylindrical tubes of randomly distributed radii. From this he calculated the drainage relative permeability curves. Moore and Slobod, Rose and Witherspoon, and Rose and Cleary each considered flow in a pore doublet (a parallel arrangement of a small and pore doublet (a parallel arrangement of a small and large diameter cylindrical capillary tube). They concluded that, because of the different rates of flow in each tube, trapping would occur in one of the tubes; the extent of which would depend upon viscosity ratio and capillary pressure. SPEJ p. 221

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Generalized Relative Permeability Coefficients during Steady-State Two-Phase Flow in Porous Media, and Correlation with the Flow Mechanisms

Multiphase Flow in Porous Media ◽

10.1007/978-94-017-2372-5_6 ◽

1995 ◽

pp. 135-168 ◽

Cited By ~ 2

Author(s):

D. G. Avraam ◽

A. C. Payatakes

Keyword(s):

Porous Media ◽

Steady State ◽

Relative Permeability ◽

Two Phase Flow ◽

Flow In Porous Media ◽

Phase Flow ◽

Two Phase ◽

Permeability Coefficients ◽

Flow Mechanisms

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Relative Permeability Characterization for Water-Alternating-Gas Injection in Oil Reservoirs

SPE Journal ◽

10.2118/166650-pa ◽

2016 ◽

Vol 21 (03) ◽

pp. 0799-0808 ◽

Cited By ~ 2

Author(s):

H.. Shahverdi ◽

M.. Sohrabi

Keyword(s):

Relative Permeability ◽

Gas Injection ◽

Hysteresis Effect ◽

Oil Reservoirs ◽

Unsteady State ◽

Two Phase ◽

Water Alternating Gas ◽

Three Phase ◽

Phase Water ◽

Wag Injection

Summary Large quantities of oil usually remain in oil reservoirs after conventional waterfloods. A significant part of this remaining oil can still be economically recovered by water-alternating-gas (WAG) injection. WAG injection involves drainage and imbibition processes taking place sequentially; therefore, the numerical simulation of the WAG process requires reliable knowledge of three-phase relative permeability (kr) accounting for cyclic-hysteresis effects. In this study, the results of a series of unsteady-state two-phase displacements and WAG coreflood experiments were used to investigate the behavior of three-phase kr and hysteresis effects in the WAG process. The experiments were performed on two different cores with different characteristics and wettability conditions. An in-house coreflood simulator was developed to obtain three-phase relative permeability values directly from unsteady-state WAG experiments by history matching the measured recovery and differential-pressure profiles. The results show that three-phase gas relative permeability is reduced in consecutive gas-injection cycles and consequently the gas mobility and injectivity drop significantly with successive gas injections during the WAG process, under different rock conditions. The trend of hysteresis in the relative permeabilty of gas (krg) partly contradicts the existing hysteresis models available in the literature. The three-phase water relative permeability (krw) of the water-wet (WW) core does not exhibit considerable hysteresis effect during different water injections, whereas the mixed-wet (MW) core shows slight cyclic hysteresis. This may indicate a slight increase of the water injectivity in the subsequent water injections in the WAG process under MW conditions. Insignificant hysteresis is observed in the oil relative permeability (kro) during different gas-injection cycles for both WW and MW rocks. However, a considerable cyclic-hysteresis effect in kro is observed during water-injection cycles of WAG, which is attributed to the reduction of the residual oil saturation (ROS) during successive water injections. The kro of the WW core exhibits much-more cyclic-hysteresis effect than that of the MW core. No models currently exist in reservoir simulators that can capture the observed cyclic-hysteresis effect in oil relative permeability for the WAG process. Investigation of relative permeability data obtained from these displacement tests at different rock conditions revealed that there is a significant discrepancy between two-phase and three-phase relative permeability of all fluids. This highlights that not only the three-phase relative permeability of the intermediate phase (oil), but also the three-phase kr of the wetting phase (water) and nonwetting phase (gas) are functions of two independent saturations.

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An Improved Unsteady-State Procedure for Determining the Relative-Permeability Characteristics of Heterogeneous Porous Media (includes associated papers 8028 and 8777 )

Society of Petroleum Engineers Journal ◽

10.2118/6720-pa ◽

1979 ◽

Vol 19 (01) ◽

pp. 15-28 ◽

Cited By ~ 69

Author(s):

P.M. Sigmund ◽

F.G. McCaffery

Keyword(s):

Porous Media ◽

Relative Permeability ◽

Capillary Rise ◽

Test Method ◽

Oil Reservoir ◽

Sample Length ◽

Unsteady State ◽

Relative Permeabilities ◽

Two Phase ◽

Core Samples

Abstract With typical heterogeneous carbonate coresamples, large uncertainties of unknown magnitudecan occur in the relative permeabilities derived using different methods. This situation can beimproved by analyzing the recovery and pressureresponse to two-phase laboratory displacement tests by a nonlinear least-squares procedure. Thesuggested technique fits the finite-differencesolution of the Buckley-Leverett two-phase flowequations(which include capillary pressure) to theobserved recovery and pressure data. The procedureis used to determine relative-permeability curves characterized by two parameters and their standarderrors for heterogeneous cores from two Albertacarbonate reservoirs. Introduction Several recent investigations have recognizedpossible problems when obtaining reliable two-phasedisplacement data from heterogeneous carbonate core samples. Huppler stated that waterfloodresults on cores with significant heterogeneitiescan be sensitive to flooding rate, core length, andwettability, and that these effects should beconsidered before applying the laboratory results atfield flooding rates. Brandner and Slotboomsuggested that realistic displacement results maynot be obtainable when vertically flooding aheterogeneous core with a nonwetting phase becauseof the fluid's inability to maintain a properdistribution when the sample length is less than the height of capillary rise. Ehrlich noted thatstandard relative-permeability measurement methodsusing core plugs cannot be applied when the media are heterogeneous. Archer and Wong reported that application of theconventional Johnson- Bossler - Neumann (JBN)methods for determining relative permeabilities froma waterflood test could give erroneous results forheterogeneous carbonate as well as for relativelyhomogeneous porous media having a mixed wettability (see Refs. 1, 6, and 7). The observedstepwise or humped shape of water relativepermeability curves mainly were attributed to theeffect of water breakthrough ahead of the main floodfront entering into the JBN calculation. Archer andWong suggested that such abnormally shapedrelative-permeability curves do not represent theproperties of the bulk of the core sample, and proposed the use of a reservoir simulator forinterpreting laboratory waterflood data. The work referred to above provides the majorbackground for this study involving the developmentof an improved unsteady-state test method tocharacterize the relative-permeability properties ofheterogeneous carbonate core samples. The methodcan be applied to all porous media, regardless ofthe size and distribution of the heterogeneities.However, the presence of large-scaleheterogeneities, especially in the form of vugs, fractures, and stratification, could cause the derivedrelative-permeability relations to be affected by viscosityratio and displacement rate. Remember also that extrapolation of any core test data to a field scaleis associated with many uncertainties, particularlyfor heterogeneous formations. The inclusion ofcapillary pressure effects permits the interpretationof displacement tests at reservoir rates. The proposed calculation procedure extends theapproach suggested by Archer and Wong in thatthe degree of fit between observed laboratory dataand simulator results is quantified. We suggest thatrelative-permeability curves for a variety of rocktypes can be expressed in terms of two adjustable parameters and their standard error estimates.To illustrate the method, the results of displacementtests performed on cores from Swan Hills Beaverhill Lake limestone oil reservoir and Rainbow F KegRiver dolomite oil reservoir are interpreted. SPEJ P. 15^

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Towards Relative Permeability Measurements in Tight Gas Formations

E3S Web of Conferences ◽

10.1051/e3sconf/202014605001 ◽

2020 ◽

Vol 146 ◽

pp. 05001

Author(s):

Denis Dzhafarov ◽

Benjamin Nicot

Keyword(s):

Steady State ◽

Relative Permeability ◽

Water Saturation ◽

Gas Permeability ◽

Tight Gas ◽

Two Phase ◽

Pressure Step ◽

Injection Ratio ◽

Insight Into ◽

Good Agreement

Relative permeability is a concept used to convey the reduction in flow capability due to the presence of multiple fluids. Relative permeability governs the multiphase flow, therefore it has a significant importance in understanding the reservoir behavior. These parameters are routinely measured on conventional rocks, however their measurement becomes quite challenging for low permeability rocks such as tight gas formations. This study demonstrates a methodology for relative permeability measurements on tight gas samples. The gas permeability has been measured by the Step Decay method and two different techniques have been used to vary the saturations: steady state flooding and vapor desorption. Series of steady-state gas/water simultaneous injection have been performed on a tight gas sample. After stabilization at each injection ratio, NMR T2, NMR Saturation profile and low pressure Step Decay gas permeability have been measured. In parallel, progressive desaturation by vapor desorption technique has been performed on twin plugs. After stabilization at each relative humidity level the NMR T2 and Step Decay gas permeability have been measured in order to compare and validate the two approaches. The techniques were used to gain insight into the tight gas two phase relative permeability of extremely low petrophysical properties (K<100 nD, phi < 5 pu) of tight gas samples of Pyrophyllite outcrop. The two methods show quite good agreement. Both methods demonstrate significant permeability degradation at water saturation higher than irreducible. NMR T2 measurements for both methods indicates bimodal T2-distributions, and desaturation first occurs on low T2 signal (small pores). Comparison of humidity drying and steady-state desaturation technique has shown a 12-18 su difference between critical water saturation (Swc) measured in gas/water steady-state injection and irreducible saturation (Swirr) measured by vapor desorption.

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Three-Phase Relative Permeability Measurements by Unsteady-State Method

Society of Petroleum Engineers Journal ◽

10.2118/1225-pa ◽

1966 ◽

Vol 6 (03) ◽

pp. 199-205 ◽

Cited By ~ 23

Author(s):

A.M. Sarem

Keyword(s):

Relative Permeability ◽

Two Phase Flow ◽

Phase Flow ◽

Unsteady State ◽

Two Phase ◽

Three Phase ◽

Three Phase Flow ◽

State Method ◽

Permeability Data ◽

Saturation History

Abstract For the performance prediction of multiphase oil recovery processes such as steam stimulation, there is an acute need for three-phase relative permeability data. No fast and simple experimental technique, such as the unsteady-state method proposed by Welge for two-phase flow, is available for the three-phase flow. In this paper, an unsteady-state method is presented for obtaining three-phase relative permeability data; this method is as fast and easy as Welge's method for two-phase flow. Analytical expressions are derived by extension of the Buckley-Leverett theory to three-phase flow to express the saturation at the outflow face for all three phases in terms of the known parameters. It is assumed that the fractional flow and relative permeability of each phase are a function of the saturation of that phase. Other simplifying assumptions made include the neglect of capillary and gravity effects. The effect of saturation history upon relative permeability is acknowledged and attainment of similar saturation history in laboratory and field is recommended. The required experimental work and computations are simple to perform. The test core is presaturated with oil and water, then subjected to gas drive. During the test, required data are the rates of oil, water, and gas production, together with pressure drop and temperature. The ordinary gas-oil unsteady-state relative permeability apparatus can be readily modified to measure the required data. The proposed technique was applied to samples of a Berea and a reservoir core. The effect of saturation history upon relative permeability was studied on one Berea core. It was found that increase in initial water saturation has a similar effect upon three-phase relative permeability as it does in two-phase flow. Introduction In the light of increasing demand for three-phase, relative permeability data for predicting the performance of thermal and other multiphase-flow recovery processes, a simple and accurate method of experimental determination of such data is extremely desirable. Leverett and Lewis1 described the simultaneous flow method of obtaining three-phase relative permeability data. However, Caudle et al.2 reported that this method is very time consuming and cumbersome. Corey3 proposed calculating the three-phase relative permeability from measured krg data. Corey's theory is based on simplified capillary pressure curves,4 assuming a straight line relationship between 1/Pc2 and saturation. Also, Corey's method assumes a preferentially water-wet system. The simplest and quickest method of obtaining three-phase relative permeability data is the unsteady-state method where, for instance, oil and water are displaced by gas. However, in such a test the correlation of average saturation with relative permeability does not give a valid relationship because the rates of oil, water and gas flow in the sample change continuously from the upstream to downstream end. This difficulty in calculating valid relationships was solved by Welge for two-phase flow by deriving an expression from Buckley and Leverett frontal advance equations.5,6 In this paper, relations are established to determine the outflow face saturation and relative permeability to all phases in a three-phase flow displacement experiment. Proposed Method The fundamentals established by Buckley and Leverett5 for two-phase flow were extended to three-phase flow and used as a basis for the derivation of saturation equations. This approach is comparable to Welge's6 use of Buckley and Leverett theory in arriving at expressions to determine the outflow face saturation of the displacing fluid in a two-phase flow system.

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An Experimental Investigation of High and Low Salinity Waterflood Displacement Under the Steady-State Condition

10.2118/207339-ms ◽

2021 ◽

Author(s):

Abdulla Aljaberi ◽

Seyed Amir Farzaneh ◽

Shokoufeh Aghabozorgi ◽

Mohammad Saeid Ataei ◽

Mehran Sohrabi

Keyword(s):

Steady State ◽

Numerical Simulations ◽

Relative Permeability ◽

High Salinity ◽

Unsteady State ◽

Dispersion Effect ◽

Low Salinity ◽

Steady State Method ◽

State Method ◽

Relative Permeability Curves

Abstract Oil recovery by low salinity waterflood is significantly affected by fluid-fluid interaction through the micro-dispersion effect. This interaction influences rock wettability and relative permeability functions. Therefore, to gain a better insight into multiphase flow in porous media and perform numerical simulations, reliable relative permeability data is crucial. Unsteady-state or steady-state displacement methods are commonly used in the laboratory to measure water-oil relative permeability curves of a core sample. Experimentally, the unsteady-state core flood technique is more straightforward and less time-consuming compared to the steady-state method. However, the obtained data is limited to a small saturation range, and the associated uncertainty is not negligible. On the other hand, the steady-state method provides a more accurate dataset of two-phase relative permeability needed in the reservoir simulator for a reliable prediction of the high salinity and low salinity waterflood displacement performance. Considering the limitations of the unsteady state method, steady-state high salinity and low salinity brine experiments waterflood experiments were performed to compare the obtained relative permeability curves. The experiments were performed on a carbonate reservoir sample using a live reservoir crude oil under reservoir conditions. The test was designed so that the production and pressure drop curve covers a wider saturation range and provides enough data for analysis. Consequently, reliable relative permeability functions were obtained, initially, for a better comparison and prediction of the high salinity and the low salinity waterflood injections and then, to quantify the effect of low salinity waterflood under steady-state conditions. The results confirm the difference in relative permeability curves between high salinity and low salinity injections due to the micro-dispersion effect, which caused a decrease in water relative permeability and an increase in the oil relative permeability. These results also proved that low salinity brine can change the rock wettability from oil-wet or mixed-wet to more water-wet conditions. Furthermore, the obtained relative permeability curves extend across a substantial saturation range, making it valuable information required for numerical simulations. To the best of our knowledge, the reported data in this work is a pioneer in quantifying the impact of low salinity waterflood at steady-state conditions using a reservoir crude oil and reservoir rock, which is of utmost importance for the oil and gas industry.

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