Two-phase Relative Permeability Research Articles

An extended JBN method of determining unsteady-state two-phase relative permeability

Relative permeability is the reduction of permeability of porous media when subjected to multiphase flow and a key parameter in subsurface hydrology. The JBN method is a well-known method of obtaining relative permeability, which measures the overall pressure drop and the effluent phase ratio versus time during two-phase displacements. By assuming no capillary pressure or gravity, the JBN method obtains the relative permeabilities to both phases at the core outlet. Since data across a range of saturations are acquired in a relatively short time, this method is widely used. This work extends the JBN method by having (1) section-wise pressure drop measurements between the core inlet, four pressure taps on the core and the outlet, (2) local saturation measurements, and (3) local phase fluxes. With these data, the extended JBN method can determine relative permeabilities to both phases at each pressure tap of the core (not just at the core outlet). The JBN extension is shown using a data set where CO2 invades a brine-filled core. From this it is found that the advantages of the extended JBN method over the regular JBN method are: (1) four times more data are obtained, and (2) data are more accurate because the capillary end effect is experimentally avoided. Avoiding the end effect results in tripling the saturation range, and obtaining relative permeabilities that are consistent with steady-state measurements and roughly 40% higher than those from the regular JBN method.

Estimation of pseudo-relative permeability curves through an analytical approach for steam assisted gravity drainage (SAGD) and solvent aided-steam assisted gravity drainage

Fluid flow through the reservoir is defined on the basis of the relative permeability which essentially captures the preferential flow of any specific fluid. Utilization of steam assisted gravity drainage (SAGD) presents challenges to the conventional understanding of relative permeability due to the introduction of heat to the reservoir. The presence of three distinct fluid phases (steam, water, and oil) in conjunction with a temperature dependency has many implications for the modelling of complex fluid dynamics. However, effective characterization of relative permeability curves is integral to successful simulation and so a model capable of representing three-phase flow is required. By implementing a simplified fractional flow analysis, this study is able to regress three-phase flow in the laboratory to a pseudo two-phase relative permeability. Modifications of conventional fractional flow theory allow for the extension of the analysis to the SAGD and solvent aided-SAGD (S-SAGD) process. Overall displacement is defined on the basis of both a microscopic component represented by modified capillary number and a macroscopic component represented by mobility ratio. Negation of the liquid-gas interaction through the assumption of waterflooding enables the generation of pseudo two-phase relative permeability curves that result in comparable performance to lab scale experiments. Because the experimentally obtained SAGD and S-SAGD results are used to construct the pseudo-relative permeability curves, our model includes the many complex fundamental changes occur in viscosity and relative permeability during SAGD and S-SAGD in the newly constructed relative permeability curves. Thus, our results offer a simplistic way to ease the compositional simulation of SAGD and S-SAGD through waterflooding approach.

A new unsteady-state method of determining two-phase relative permeability illustrated by CO2-brine primary drainage in berea sandstone

This study presents a new unsteady-state method for measuring two-phase relative permeability by obtaining local values of the three key parameters (saturation, pressure drop, and phase flux) versus time during a displacement. These three parameters can be substituted to two-phase Darcy Buckingham equation to directly determine relative permeability. To obtain the first two, we use a medical X-ray Computed Tomography (CT) scanner to monitor saturation in time and space, and six differential pressure transducers to measure the overall pressure drop and the pressure drops of five individual sections (divided by four pressure taps on the core) continuously. At each scanning time, the local phase flux is obtained by spatially integrating the saturation profile and converting this to the flux using a fractional flow framework. One advantage of this local method over most previous methods is that the capillary end effect is experimentally avoided; this improvement is crucial for experiments using low viscosity fluids such as supercritical and gas phases. To illustrate the new method, we conduct five CO2-brine primary drainage experiments in a 60.8cm long and 116mD Berea sandstone core at 20°C and 1500psi. In return, we obtain hundreds of unsteady-state CO2 and brine relative permeability data points that are consistent with steady-state relative permeability data from the same experiments. Due to the large amount of relative permeability data obtained by the new unsteady-state method, the uncertainties of the exponents in the Corey-type fits decrease by up to 90% compared with the steady-state method.

C1-Continuous relative permeability and hybrid upwind discretization of three phase flow in porous media

Three-phase flow in a reservoir model has been a major challenge in simulation studies due to slowly convergent iterations in Newton solution of nonlinear transport equations. In this paper, we examine the numerical characteristics of three-phase flow and propose a consistent, “C1-continuous discretization” (to be clarified later) of transport equations that ensures a convergent solution in finite difference approximation.First, we examine three-phase relative permeabilities that are critical in solving nonlinear transport equations. Three-phase relative permeabilities are difficult to measure in the laboratory, and they are often correlated with two-phase relative permeabilities (e.g., oil-gas and water-oil systems). Numerical convergence of non-linear transport equations entails that three-phase relative permeability correlations are a monotonically increasing function of the phase saturation and the consistency conditions of phase transitions are satisfied. The Modified Stone’s Method II and the Linear Interpolation Method for three-phase relative permeability are closely examined for their mathematical properties. We show that the Linear Interpolation Method yields C1-continuous three-phase relative permeabilities for smooth solutions if the two phase relative permeabilities are monotonic and continuously differentiable.In the second part of the paper, we extend a Hybrid-Upwinding (HU) method of two-phase flow (Lee, Efendiev and Tchelepi, ADWR 82 (2015) 27-38) to three phase flow. In the HU method, the phase flux is divided into two parts based on the driving forces (in general, it can be divided into several parts): viscous and buoyancy. The viscous-driven and buoyancy-driven fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total velocity. The pure buoyancy-induced flux is shown to be only dependent on saturation distributions and counter-current. In three-phase flow, the buoyancy effect can be expressed as a sum of two buoyancy effects from two-phase flows, i.e., oil-water and oil-gas systems. We propose an upwind scheme for the buoyancy flux term from three-phase flow as a sum of two buoyancy terms from two-phase flows. The upwind direction of the buoyancy flux in two phase flow is always fixed such that the heavier fluid goes downward and the lighter fluid goes upward.It is shown that the Implicit Hybrid-Upwinding (IHU) scheme for three-phase flow is locally conservative and produces physically-consistent numerical solutions. As in two phase flow, the primary advantage of the IHU scheme is that the flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions as a function of time, or (Newton) iterations. This is in contrast to the standard phase-potential-based upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the transition between co-current and counter-current flows.

Modeling of Two-Phase Relative Permeability in Cambrian and Early Miocene Sandstone Reservoirs: A Case Study, Egypt

The relative permeability is the ratio of the effective permeability to the absolute permeability. Due to the importance of relative permeability in reservoir simulation, there is a dominant need to upscale it. So, several models were introduced to modeling the relative permeability. Some correlation models were dependent on capillary pressure measurements, while other models did not require such measurements. In this study, four relative permeability correlation models were chosen to apply them on two sandstone reservoir (labeled A and B) data sets. The two reservoirs belong to different ages and depositional environments. Both reservoirs are located in the Southern Gulf of Suez, Egypt. Reservoir A is the Nubian sandstone of Cambrian age. Reservoir B is the Nukhul clastic of Early Miocene age. The data sets include laboratory measurements of unsteady-state gas–oil relative permeability and steady-state water–oil relative permeability tests. The results indicate that the practical and modified Corey models were the most applicable model for the studied reservoirs. Additionally, prediction of relative permeability at saturation end points was carried out based on using routine core porosity and permeability by introducing new empirical equations. The relative permeability was used to identify rock wettability, water cut, water cutoffs and the areal and vertical sweep efficiencies.

Controlling effect of fractures on gas accumulation and production within the tight sandstone: A case study on the Jurassic Dibei gas reservoir in the eastern part of the Kuqa foreland basin, China

Using Dibei tight sandstone gas reservoir in the eastern part of the Kuqa foreland basin as an example, this paper discusses tight sandstone reservoir fractures characterization, its effect on storage space and gas flow capacity, and its contribution to gas accumulation, enrichment and production in tight sandstone reservoir by using laser scanning confocal microscope (LSCM) observation, mercury intrusion capillary pressure (MICP) testing, and gas-water two-phase relative permeability testing. The statistics of laser scanning confocal microscopy observation showed that the microstructural fractures width in the Dibei gas reservoir was mainly 8–25 μm, and the associated micro-fractures width was mainly 4–10 μm. Additionally, the throat radius was mainly 1–4 μm. The fractures width was significantly wider than the throat radius that served as the main channel of in gas flow. In addition, it illustrated that the samples with developed fractures became easier for gas to flow under equal porosity condition, because of lower expulsion pressure, higher mercury injection saturation, and increased gas relative permeability based on the physical simulation experiment of gas charging into core samples with saturated water, mercury injection and gas-water two-phase permeability experiments. Furthermore, it had been concluded that the fractures control tight gas in the following aspects: (1) Fractures play a significant role in reservoir property improvement. The isolated pores were linked by the fractures to form connective reservoir spaces, and dissolution is prone to occur along the fractures forming new pores. The fractures with bigger width are reservoir space as well. (2) Fractures increased fluid flow capacity because it decreased the starting pressure gradient, and it increased gas effective permeability. Thus, fractures improved the gas injection efficiency as well as gas production. (3) Fractures that developed in different time and spatial places have different effects on gas accumulation, enrichment, and production in tight sandstone reservoirs.

Interpretation of two-phase relative permeability curves through multiple formulations and Model Quality criteria

Abstract We illustrate the way formal model identification criteria can be employed to rank and evaluate a set of alternative models in the context of the interpretation of laboratory scale experiments yielding two-phase relative permeability curves. We consider a set of empirical two-phase relative permeability models (i.e., Corey, Chierici and LET) which are typically employed in industrial applications requiring water/oil relative permeability quantifications. Model uncertainty is quantified through the use of a set of model weights which are rendered by model posterior probabilities conditional on observations. These weights are then employed to (a) rank the models according to their relative skill to interpret the observations and (b) obtain model averaged results which allow accommodating within a unified theoretical framework uncertainties arising from differences amongst model structures. As a test bed for our study, we employ high quality two-phase relative permeability estimates resulting from steady-state imbibition experiments on two diverse porous media, a quartz Sand-pack and a Berea sandstone core, together with additional published datasets. The parameters of each model are estimated within a Maximum Likelihood framework. Our results highlight that in most cases the complexity of the problem appears to justify favoring a model with a high number of uncertain parameters over a simpler model structure. Posterior probabilities reveal that in several cases, most notably for the assessment of oil relative permeabilities, the weights associated with the simplest models is not negligible. This suggests that in these cases uncertainty quantification might benefit from a multi-model analysis, including both low- and high-complexity models. In most of the cases analyzed we find that model averaging leads to interpretations of the available data which are characterized by a higher degree of fidelity than that provided by the most skillful model.

A NOVEL FRACTAL MODEL FOR TWO-PHASE RELATIVE PERMEABILITY IN POROUS MEDIA

Multiphase flow in porous media is very important in various scientific and engineering fields. It has been shown that relative permeability plays an important role in determination of flow characteristics for multiphase flow. The accurate prediction of multiphase flow in porous media is hence highly important. In this work, a novel predictive model for relative permeability in porous media is developed based on the fractal theory. The predictions of two-phase relative permeability by the current mathematical models have been validated by comparing with available experimental data. The predictions by the proposed model show the same variation trend with the available experimental data and are in good agreement with the existing experiments. Every parameter in the proposed model has clear physical meaning. The proposed relative permeability is expressed as a function of the immobile liquid film thickness, pore structural parameters (pore fractal dimension Dfand tortuosity fractal dimension DT) and fluid viscosity ratio. The effects of these parameters on relative permeability of porous media are discussed in detail.

New Relationship Between Resistivity Index and Relative Permeability

Relative permeability as an important petrophysical parameter is often measured directly in the laboratory or obtained indirectly from the capillary pressure data. However, the literature on relationship between relative permeability and resistivity is lacking. To this end, a new model of inferring two-phase relative permeability from resistivity index data was derived on the basis of Poiseuille's law and Darcy's law. The wetting phase tortuosity ratio was included in the proposed model. The relative permeabilities computed from the capillary pressure data, as well as the experimental data measured in gas–water and oil–water flow condition, were compared with the proposed model. Both results demonstrated that the two-phase permeability obtained by proposed model were generally in good agreement with the data computed from capillary pressure and measured in the laboratory. The comparison also showed that our model was much better than Li model at matching the relative permeability data.

Steady-state two-phase relative permeability functions of porous media: A revisit

Steady-state two-phase flow experiments are performed on a sand column equipped with two differential pressure transducers and six ring electrodes to measure the pressure drop across each phase, and electrical resistance across five successive column segments, respectively. The electrical resistivity index measured across various segments of the soil column is converted to water saturation by using the Archie equation. The results are analyzed by considering the water saturation and oil/water relative permeability as power functions of water and oil capillary numbers which are employed as independent variables. Results from earlier visualization studies on a glass-etched pore network are also analyzed by a similar manner to quantify the dependence of oil and water relative permeability on capillary numbers, and correlate the estimated parameters of power functions with the viscosity ratio. The new explicit relationships of relative permeabilities and water saturation with oil and water capillary numbers set the bases for a new conceptualization of the two-phase flow at reservoir-scale where the mobility of the fluids is decoupled from saturation and become non-linear functions of the local flow rates. The variation of the relative permeability exponents with the pore system dimensionality agrees qualitatively with the scaling behavior predicted by the gradient percolation approach.

A new technique for accurately measuring two-phase relative permeability under non-Darcy flow conditions

A new steady-state technique for determining gas–water relative permeability curves for proppant packs under high confining stress conditions is presented. In this technique, a time domain reflectometry (TDR) device that can measure the saturation inside the proppant pack instantly and efficiently is introduced. De-aired water and nitrogen gas are simultaneously injected into the proppant pack under a desired confining stress, and the pressure drop and saturation are measured when steady-state conditions are reached. Two different proppant mesh sizes, 12/18 and 20/40, have been tested under four confining stresses ranging from 1000 to 4000 psi with repeatable and accurate results. In the majority of published techniques, two-phase relative permeability curves are determined by using Darcy׳s law. This might be accurate enough for low permeability formations under low flow rate conditions, but in high permeability fracture proppant packs, the non-Darcy flow effects, or inertial effects, cannot be neglected. Thus relative permeability curves neglecting inertial effects may lead to inaccurate predictions. In this paper, three flow models: the classic generalized Darcy׳s Law, the generalized Forchheimer flow model, and the two-phase Barree and Conway model (Barree and Conway, 2007) are employed to calculate and compare the relative permeability results. The experimental results show that the non-Darcy flow effects on gas relative permeability are higher than those calculated using Darcy׳s Law. In addition, the various confining stress effects on water and gas relative permeability curves are also presented. A significant decrease in gas relative permeability and minor effects on water relative permeability occur as the confining stress increases. These results help to further understand the effects of multiphase flow in porous media.

The Effect of Interfacial Tension on Two-phase Relative Permeability: A Review

In many oil recovery processes, the aim is to recover the residual oil from the reservoir by increasing the capillary number via either decreasing the interfacial tension and/or increasing the displacing fluid viscosity. Hence, it is of particular importance to identify the form of the relative permeability curves at high-capillary-number flow. Despite the tremendous amount of studies published on the form of two-phase relative permeability curves at low- and ultra-low IFT (i.e., at high-capillary-number flow), a detailed review of these works is missing from the literature. Thus, this extensive review has been conducted with the hope to bridge the gap in information. The topics covered in this survey include the description of the relative permeability, factors affecting the relative permeability, relative permeability at high-capillary-number flow, and the IFT effect on the relative permeability of oil–water, gas–water, gas–oil, and gas-condensate systems.

Laboratory-scale Investigation of Two-phase Relative Permeability

We present experimental investigations of two-phase (oil and water) relative permeability of laboratory scale rock cores through a joint use of direct X-ray measurement and flow-through investigations. Experimental data embed key information relating relative permeability to observables. In this context, direct measurement of in-situ fluid saturation through X-Ray techniques has the unprecedented ability to characterize key processes occurring during the displacement of immiscible fluids through natural permeable materials. We illustrate the benefit of employing direct X-Ray measurements of fluid saturation through a set of laboratory experiments targeted to the estimate of two-phase relative permeabilities of homogeneous samples (sand pack and Berea sandston core). Data are obtained for a range of diverse fractional flow rates and provide information at saturations ranging from irreducible water content to residual oil saturation. Our X-Ray saturation data are consistent with an interpretation of measured relative permeabilities as associated with water-wet rock conditions. The comparison of different preamble samples result high displacement efficiency and recovery factor corresponds to the high permeable and well-connected pores.

Two-Phase Immiscible Flows in Porous Media: The Mesocopic Maxwell–Stefan Approach

We develop an approach to coupling between viscous flows of the two phases in porous media, based on the Maxwell–Stefan formalism. Two versions of the formalism are presented: the general form, and the form based on the interaction of the flowing phases with the interface between them. The last approach is supported by the description of the flow on the mesoscopic level, as coupled boundary problems for the Brinkmann or Stokes equations. It becomes possible, in some simplifying geometric assumptions, to derive exact expressions for the phenomenological coefficients in the Maxwell–Stefan transport equations. Sample computations show, among other, that apparent relative permeabilities are dependent on the viscosity ratio; that the overall mobility of the phases decreases compared to the standard Buckley–Leverett formalism; and that the effect is determined by the parameter determining the “degree of mixing” between the flowing phases. Comparison to the available experimental data on the steady-state two-phase relative permeabilities is presented.

Based on the Pore Network Model of CO<sub>2</sub>-Water-Quartz System Two-Phase Flow Characteristics Study

Saline aquifer storage is considered to be one of the main ways to realize CO2 geological sequestration. The purpose of the paper is to research CO2 and water seepage characteristics under the condition of different pressure and diameter of glass sand. First, establish four kinds of sand packed beds pore network model. Secondly, measuring the gas-liquid interfacial tension, contact angle under the condition of 50°C and different pressure (5-20MPa). Finally, using the two-phase flow model, obtain the gas-liquid two-phase relative permeability curves under different conditions. The simulation results of this paper can help to predict the actual saline aquifer storage of CO2 sequestration.

Three-Phase Relative Permeability Modeling in the Simulation of WAG Injection

Summary We propose a new workflow to evaluate the effect of three-phase relative permeability models on the simulation of water-alternating-gas (WAG) injection: define a root-mean-square error to quantify differences between the models; introduce a high-uncertainty region on a ternary saturation diagram; and map simulation saturation/time paths in this ternary diagram. The display of the saturation paths, along with the high-uncertainty region, allows us to systematically analyze and understand the effect of three-phase models on recovery predictions. We apply the workflow to immiscible and miscible WAG injection, simulated by use of black-oil and compositional models. Both 2D homogeneous cases (with various reservoir conditions and injection scheduling) and realistic 3D field sector models are considered. We show that the three-phase relative permeability models can have a strong effect on recovery predictions for immiscible WAG injection, and the effect depends on initial conditions and displacement history. For compositional simulation of multicontact miscible WAG injection, the effect of three-phase models depends on the size of the three-phase-flow region before the miscibility fully develops. Simulation of carbon dioxide (CO2) flooding on a 3D field sector model reveals that the uncertainty in recovery predictions because of the various three-phase models is secondary compared with other sources of uncertainty (such as the input two-phase relative permeability data), and this may be the case in other field studies.

Relative permeability of homogenous-wet and mixed-wet porous media as determined by pore-scale lattice Boltzmann modeling

We present a pore-scale study of two-phase relative permeability in homogenous-wet porous media, and porous media altered to a mixed-wet state. A Shan-Chen type multicomponent lattice Boltzmann (LB) model is employed to determine pore-scale fluid distributions and relative permeability. Mixed-wet states are created by altering the wettability of solid surfaces in contact with the nonwetting phase at the end of steady state simulation of initially homogenous-wet porous media. To ensure accurate representation of fluid-solid interfacial areas, we compare LB simulation results to experimental measurements of interfacial fluid-fluid and fluid-solid areas determined by X-ray computed microtomography imaging of water and oil distributions in bead packs. The LB simulations are found to match experimental trends observed for fluid-fluid and fluid-solid interfacial area-saturation relationships. The relative permeability of both fluids in the homogenous-wet porous media was found to decrease with a decreasing contact angle. The relative permeability of both fluids in the altered, mixed-wet porous media was found to decrease for all mixed-wet states in comparison to the initial homogenous-wet states. The nonwetting phase relative permeability decreased significantly, while the wetting phase experienced only a minor decrease. The significance of the decrease was found to be dependent on the distribution of the unaltered solid surfaces, with less dependence on the severity of alteration.

Determination of dynamic relative permeability in ultra-low permeability sandstones via X-ray CT technique

Forced oil–water displacement is the crucial mechanisms of secondary oil recovery. The knowledge of relative permeability is required in the simulation of multiphase flow in porous media. Obvious dynamic effect of capillary pressure occurs in that the formation of ultra-low permeability reservoir (the permeability is <1 × 10−3 μm2) is tight and the pores and throats are very small. In addition, the significant capillary end effect causes serious errors when calculating relative permeabilities. For these reasons, the JBN method (neglecting capillary pressure) does not apply. Therefore, the dynamic capillary pressure and capillary end effects should be taken into account. This work focuses on calculating two-phase relative permeability of ultra-low permeability reservoir through considering the dynamic capillary pressure and eliminating the influence of capillary end effects. Firstly, laboratory core scale measurements of in situ water phase saturation history based on X-ray CT scanning technique were used to estimate relative permeability. Secondly, a mathematical model of two-phase relative permeability considering the dynamic capillary pressure was established. The basic problem formulations, as well as the more specific equations, were given, and the results of comparison using experimental data are presented and discussed. Results indicate that the dynamic capillary pressure measured at laboratory core scale in ultra-low permeability rocks has a significant influence on the estimation of unsteady-state relative permeability. The mathematical calculating method was compared with the history matching method and the results were close, suggesting reliability for ultra-low permeability reservoirs. Importantly, the proposed methods allow measurement of relative permeability from a single experiment. Potentially this represents a great time savings.

Estimation of relative permeability and capillary pressure for tight formations by assimilating field production data

A novel EnKF technique together with its detailed workflow has been developed and successfully applied to simultaneously evaluate relative permeability and capillary pressure for tight formations by history matching the field production data. The power-law model is firstly used to represent the relative permeability and capillary pressure curves, while its parameters are tuned automatically and finally determined once the production data have been assimilated completely. This technique has been validated by using a synthetic 2D reservoir model with two scenarios, where two-phase and three-phase relative permeabilities together with capillary pressure curves are evaluated, respectively. The estimated relative permeability and capillary pressure have been found to improve progressively and their corresponding uncertainties are mitigated gradually as more production data are assimilated. Finally, there exists an excellent agreement between both the updated relative permeability and capillary pressure curves and their corresponding reference curves, leading to excellent history matching results. As such, the uncertainties associated with both the updated relative permeability and capillary pressure curves and the updated production profiles are reduced significantly. The capillary pressure cannot be determined as accurately as the relative permeability due to its less sensitivity to the production data.

Relative Permeability Hysteresis: Water-Alternating-Gas Injection and Gas Storage

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 161827, ’Experimental and Theoretical Investigation of Water/Gas Relative Permeability Hysteresis: Applicable to Water-Alternating-Gas (WAG) Injection and Gas-Storage Processes,’ by S. Mobeen Fatemi, SPE, and Mehran Sohrabi, SPE, Heriot-Watt University, prepared for the 2012 Abu Dhabi International Petroleum Exhibition &amp; Conference, Abu Dhabi, 11-14 November. The paper has not been peer reviewed. Accurate determination of relative permeability hysteresis is needed to predict water-alternating-gas (WAG) injection reliably. Two series of gas/water relative permeability hysteresis curves were obtained from corefloods under mixed-wet conditions. The results revealed that none of the widely used hysteresis models (e.g., Carlson and Killough models) is able to predict the observed cyclic relative permeability hysteresis for alternating injection of gas and water. The results suggest that, for mixed-wet systems, it is necessary to consider irreversible hysteresis loops for modeling both the wetting and the nonwetting phase. Introduction Because of nonwetting-phase trapping, wetting-phase relative permeability for imbibition increased compared with the drainage case and nonwetting-phase imbibition relative permeability was less than that of the drainage case. Therefore, relative permeability to a fluid at a given saturation depends on whether that saturation was obtained by approaching it from a higher or lower value. This behavior in relative permeability is the hysteresis effect. Much of the hysteresis data in the literature was obtained with saturations starting at endpoint values (i.e., irreducible-water saturation or residual-oil saturations for a water/oil system). These data usually deal with the differences between bounding relative permeabilities. Such data are more applicable to modeling reservoir processes in which phase saturations increase or decrease to an intermediate value, then change in the opposite direction. Examples include enhanced-oil-recovery methods such as WAG injection or cyclic-steam stimulation. Most of the existing relative permeability hysteresis functions were developed for strongly water-wet porous media. However, it generally is accepted that many oil reservoirs are mixed-wet. In a mixed-wet system, the oil-wet pores correspond to the largest pores in the rock, while the small pores are water-wet. There are only a few relative permeability models developed for mixed-wet porous media, of which none are included in commercial simulators. The purpose of this study was to further investigate the effect of cyclic hysteresis for water/gas systems under mixed-wet conditions. These two-phase relative permeability data are of interest for reliable simulation of processes involving cyclic changes between imbibition and drainage displacement, including WAG injection. The results of this study can be applied to underground hydrocarbon-gas storage, which usually involves cyclic pressurization (drainage) and depressurization (imbibition) on an annual basis. This is especially true if the underground formation has an active aquifer.