Steady-State and Unsteady-State Two-Phase Relative Permeability Hysteresis and Measurements of Three-Phase Relative Permeabilities Using Imaging Techniques

1995 ◽  
Author(s):  
O.O. Eleri ◽  
A. Graue ◽  
A. Skauge
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
Imaging Techniques ◽  
Unsteady State ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Three Phase

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

SPE Journal ◽  
2016 ◽  
Vol 21 (03) ◽  
pp. 0799-0808 ◽  
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.

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

1979 ◽  
Vol 19 (01) ◽  
pp. 15-28 ◽  
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^

Three-Phase Relative Permeability Measurements by Unsteady-State Method

1966 ◽  
Vol 6 (03) ◽  
pp. 199-205 ◽  
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.

Experimental Study and History-Match of Near-Miscible WAG Coreflood Experiments on Mixed-Wet Carbonate Rocks

2021 ◽  
Author(s):  
Mohamed Mehdi El Faidouzi
Keyword(s):  
Relative Permeability ◽  
Carbonate Rocks ◽  
Hysteresis Model ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Recovery Method ◽  
Phase Displacement ◽  
Three Phase ◽  
Displacement Experiments ◽  
Phase Water

Abstract Water-alternating-gas (WAG) injection, both miscible and immiscible, is a widely used enhanced oil recovery method with over 80 field cases. Despite its prevalence, the numerical modeling of the physical processes involved remains poorly understood, and existing models often lack predictability. Part of the complexity stems from the component exchange between gas and oil and the hysteretic relative permeability effects. Thus, improving the reliability of numerical models requires the calibration of the equation of state (EOS) against phase behavior data from swelling/extraction and slim-tube tests, and the calibration of the three-phase relative permeability model against WAG coreflood experiments. This paper presents the results and interpretation of a complete set of two-phase and thee-phase displacement experiments on mixed-wet carbonate rocks. The three-phase WAG experiments were conducted on the same composite core at near-miscible reservoir condition; experiments differ in the injection order and length of their injection cycles. First, the two-phase water/oil and gas/oil displacement experiments and first cycles of WAG were used to estimate the two-phase relative permeabilities. Then, a synchronized history-matching procedure over the full set of WAG experiments and cycles was carried out to tune Larsen ans Skauge WAG hysteresis model—namely the Land gas traping parameter, the gas reduction exponent, the residual oil reduction factor and three-phase water relative permeability. The second part of this paper deals with the multiphase upscaling of microscopic displacement properties from plug to coarse grid reservoir scale. The two-phase relative permeability curves and three-phase WAG parameters were upscaled using a sector model to preserve the displacement process and reservoir performance. The result of the coreflood calibration indicate that the two-phase displacement and first cycles of WAG yield a consistent set of two-phase relative permeabilities. Including the full set of WAG experiments allowed a robust calibration of the hysteresis model.

A Model for Two-Phase Flow in Consolidated Materials

1969 ◽  
Vol 9 (02) ◽  
pp. 221-231 ◽  
Author(s):  
R. Ehrlich ◽  
F.E. Crane
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Relative Permeability ◽  
Viscosity Ratio ◽  
Phase Flow ◽  
Unsteady State ◽  
Adequate Description ◽  
Two Phase ◽  
Phase Saturation ◽  
Relative Permeability Curves

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

scholarly journals Steady-State Two-Phase Flow in Porous Media: Laboratory Validation of Flow-Dependent Relative Permeability Scaling

2020 ◽  
Vol 146 ◽  
pp. 03002
Author(s):  
Marios S. Valavanides ◽  
Matthieu Mascle ◽  
Souhail Youssef ◽  
Olga Vizika
Keyword(s):  
Porous Media ◽  
Steady State ◽  
Relative Permeability ◽  
Flow Rate ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Local Flow

The phenomenology of steady-state two-phase flow in porous media is recorded in SCAL relative permeability diagrams. Conventionally, relative permeabilities are considered to be functions of saturation. Yet, this has been put into challenge by theoretical, numerical and laboratory studies that have revealed a significant dependency on the flow rates. These studies suggest that relative permeability models should include the functional dependence on flow intensities. Just recently a general form of dependence has been inferred, based on extensive simulations with the DeProF model for steady-state two-phase flows in pore networks. The simulations revealed a systematic dependence of the relative permeabilities on the local flow rate intensities that can be described analytically by a universal scaling functional form of the actual independent variables of the process, namely, the capillary number, Ca, and the flow rate ratio, r. In this work, we present the preliminary results of a systematic laboratory study using a high throughput core-flood experimentation setup, whereby SCAL measurements have been taken on a sandstone core across different flow conditions -spanning 6 orders of magnitude on Ca and r. The scope is to provide a preliminary proof-of-concept, to assess the applicability of the model and validate its specificity. The proposed scaling opens new possibilities in improving SCAL protocols and other important applications, e.g. field scale simulators.

Measurement of Three-Phase Relative Permeability with IFT Variation

2005 ◽  
Vol 8 (01) ◽  
pp. 33-43 ◽  
Author(s):  
Yildiray Cinar ◽  
Franklin M. Orr
Keyword(s):  
Experimental Data ◽  
Relative Permeability ◽  
Oil And Gas ◽  
Gas Injection ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Rich Phase ◽  
Injection Process ◽  
Three Phase ◽  
Relative Permeability Curves

Summary In this paper, we present results of an experimental investigation of the effects of variations in interfacial tension (IFT) on three-phase relative permeability. We report results that demonstrate the effect of low IFT between two of three phases on the three-phase relative permeabilities. To create three-phase systems in which IFT can be con-trolled systematically, we used a quaternary liquid system composed of hexadecane(C16), n-butanol (NBA), water (H2O), and isopropanol (IPA). Measured equilibrium phase compositions and IFTs are reported. The reported phase behavior of the quaternary system shows that the H2O-rich phase should represent the "gas" phase, the NBA-rich phase should represent the "oil" phase, and the C16-rich phase should represent the "aqueous" phase. Therefore, we used oil-wet Teflon (PTFE) bead packs to simulate the fluid flow in a water-wet oil reservoir. We determined phase saturations and three-phase relative permeabilities from recovery and pressure-drop data using an extension of the combined Welge/Johnson-Bossler-Naumann (JBN) method to three-phase flow. Measured three-phase relative permeabilities are reported. The experimental results indicate that the wetting-phase relative permeability was not affected by IFT variation, whereas the other two-phase relative permeabilities were clearly affected. As IFT decreases, the oil and gas phases become more mobile at the same phase saturations. For gas/oil IFTs in the range of 0.03 to 2.3 mN/m, we observed an approximately 10-fold increase in the oil and gas relative permeabilities against an approximately 100-fold decrease in the IFT. Introduction Variations in gas and oil relative permeabilities as a function of IFT are of particular importance in the area of compositional processes such as high-pressure gas injection, where oil and gas compositions can vary significantly both spatially and temporally. Because gas-injection processes routinely include three-phase flow (either because the reservoir has been water-flooded previously or because water is injected alternately with gas to improve overall reservoir sweep efficiency), the effect of IFT variations on three-phase relative permeabilities must be delineated if the performance of the gas-injection process is to be predicted accurately. The development of multicontact miscibility in a gas-injection process will create zones of low IFT between gas and oil phases in the presence of water. Although there have been studies of the effect of low IFT on two-phase relative permeability,1–14 there are limited experimental data published so far analyzing the effect of low IFT on three-phase relative permeabilities.15,16 Most authors have focused on the effect of IFT on oil and solvent relative permeabilities.17 Experimental results show that residual oil saturation and relative permeability are strongly affected by IFT, especially when the IFT is lower than approximately 0.1 mN/m (corresponding to a range of capillary number of 10–2 to 10–3). Bardon and Longeron3 observed that oil relative permeability increased linearly as IFT was reduced from approximately 12.5 mN/m to 0.04 mN/m and that for IFT below 0.04, the oil relative permeability curves shifted more rapidly with further reductions in IFT. Later, Asar and Handy6 showed that oil relative permeability curves began to shift as IFT was reduced below 0.18 mN/m for a gas/condensate system near the critical point. Delshad et al.15 presented experimental data for low-IFT three-phase relative permeabilities in Berea sandstone cores. They used a brine/oil/surfactant/alcohol mixture that included a microemulsion and excess oil and brine. The measurements were done at steady-state conditions with a constant capillary number of 10–2 between the microemulsion and other phases. The IFTs of microemulsion/oil and microemulsion/brine were low, whereas the IFT between oil and brine was high. They concluded that low-IFT three-phase relative permeabilities are functions of their own saturations only. Amin and Smith18 recently have published experimental data showing that the IFTs for each binary mixture of brine, oil, and gas phases vary as pressure increases(Fig. 1). Fig. 1 shows that the IFT of a gas/oil pair decreases as the pressure increases, whereas the IFTs of the gas/brine and oil/brine pairs approach each other.

Simulation of Two-Phase Flow in Reservoir Rocks Using a Lattice Boltzmann Method

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 917-927 ◽  
Author(s):  
Thomas Ramstad ◽  
Pål-Eric Øren ◽  
Stig Bakke
Keyword(s):  
Steady State ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Lattice Boltzmann ◽  
Two Phase Flow ◽  
Constitutive Relations ◽  
Phase Flow ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Rock Microstructure

Summary We present results from simulations of two-phase flow directly on digitized rock-microstructure images of porous media using a lattice Boltzmann (LB) method. The implemented method is performed on a D3Q19 lattice with fluid/fluid and fluid/solid interaction rules to handle interfacial tension and wetting properties. We demonstrate that the model accurately reproduces capillary and wetting effects in pores with a noncircular shape. The model is applied to study viscous coupling effects for two-phase concurrent annular flow in circular tubes. Simulated relative permeabilities for this case agree with analytical predictions and show that the nonwetting-phase relative permeability might greatly exceed unity when the wetting phase is less viscous than the nonwetting phase. Two-phase LB simulations are performed on microstructure images derived from X-ray microtomography and process-based reconstructions of Bentheimer sandstone. By imposing a flow regulator to control the capillary number of the flow, the LB model can closely mimic typical experimental setups, such as centrifuge capillary pressure and unsteady- and steady-state relative permeability measurements. Computed drainage capillary pressure curves are found to be in excellent agreement with experimental data. Simulated steady-state relative permeabilities at typical capillary numbers in the vicinity of 10−5 are in fair agreement with measured data. The simulations accurately reproduce the wetting-phase relative permeability but tend to underpredict the nonwetting-phase relative permeability at high wetting-phase saturations. We explain this by pointing to percolation threshold effects of the samples. For higher capillary numbers, we correctly observe increased relative permeability for the nonwetting phase caused by mobilization and flow of trapped fluid. It is concluded that the LB model is a powerful and promising tool for deriving physically meaningful constitutive relations directly from rock-microstructure images.

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