Three-phase Relative Permeability Research Articles

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.

Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

Immiscible water-alternating-gas (WAG) flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency. Nevertheless, considering the complicated phase behavior and various multiphase flow characteristics, gas tends to break through early in production wells in heterogeneous formations because of overriding, fingering, and channeling, which may result in unfavorable recovery performance. On the basis of phase behavior studies, minimum miscibility pressure measurements, and immiscible WAG coreflood experiments, the cubic B-spline model (CBM) was employed to describe the three-phase relative permeability curve. Using the Levenberg–Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially, optimization of production performance including pressure drop, water cut, and the cumulative gas–oil ratio was performed. A novel numerical inversion method was established for estimation of the water–oil–gas relative permeability curve during the immiscible WAG process. Based on the quantitative characterization of major recovery mechanisms, the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment. The proposed method is reliable and can meet engineering requirements. It provides a basic calculation theory for implicit estimation of oil–water–gas relative permeability curve.

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

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.

Characterization of two- and three-phase relative permeability of water-wet porous media through X-Ray saturation measurements

We present experimental investigations of multi-phase (two-phase (oil/water, oil/gas) and three-phase (oil/water/gas)) relative permeabilities performed on laboratory scale rock cores. Two- and three-phase relative permeabilities data were obtained on two core samples (a Sand-pack and a Berea sandstone) by way of a Steady-State (SS) technique. Spatial and temporal dynamics of in-situ saturations along core samples were directly measured through an X-Ray absorption technology. The latter rendered detailed distributions of (section-averaged) fluid flow phases through the medium, which can then be employed for the characterization of relative permeabilities. The technique also enabled us to clearly identify the occurrence of end-effects during the experiments and to quantify the reliability of corrective strategies. For the oil/water settings we considered low and high viscosity oil, our findings supporting the observation that relative permeability to oil and water was sensitive to oil viscosity. Three-phase experiments were performed by following an IDI (Imbibition-Drainage-Imbibition) saturation path. The complete experimental data-base is here illustrated and juxtaposed to results obtained by the implementation of simple and commonly employed three-phase relative permeability models. In the three-phase setting, water and gas relative permeabilities display an approximately linear dependence on the logarithm of their own saturation. Consistent with the observation that oil behaves as an intermediate phase in our system, three-phase oil relative permeabilities lie in between those of their two-phase counterparts. Our data-set stands as a reliable reference for further model development and testing, as only a limited quantity of three-phase data are currently available.

Estimation of Three-Phase Relative Permeabilities for a Water-Alternating-Gas Process by Use of an Improved Ensemble Randomized Maximum-Likelihood Algorithm

Summary In this paper, a modified ensemble randomized maximum-likelihood (EnRML) algorithm has been developed to estimate three-phase relative permeabilities with consideration of the hysteresis effect by reproducing the actual production data. Ensemble-based history matching uses an ensemble of realizations to construct Monte Carlo approximations of the mean and covariance of the model variables, which can acquire the gradient information from the correlation provided by the ensemble. A power-law model is first used to represent the three-phase relative permeabilities, the coefficients of which can be automatically adjusted until production history is matched. A damping factor is introduced as an adjustment to the step length because a reduced step length is commonly required if an inverse problem is sufficiently nonlinear. A recursive approach for determining the damping factor has been developed to reduce the number of iterations and the computational load of the EnRML algorithm. The restart of reservoir simulations for reducing the cost of reservoir simulations is of significant importance for the EnRML algorithm where iterations are inevitable. By comparing a direct-restart method and an indirect-restart method for numerical simulations, we optimize the restart method used for a specific problem. Subsequently, we validate the proposed methodology by use of a synthetic water-alternating-gas (WAG) displacement experiment and then extend it to match laboratory experiments. The proposed technique has proved to efficiently determine the three-phase relative permeabilities for the WAG processes with consideration of the hysteresis effect, whereas history-matching results are gradually improved as more production data are taken into account. The synthetic scenarios demonstrate that the recursive approach saves 33.7% of the computational expense compared with the trial-and-error method when the maximum iteration is 14. Also, the consistency between the production data and model variables has been well-maintained during the updating processes by use of the direct-restart method, whereas the indirect-restart method fails to minimize the uncertainties associated with the model variables representing three-phase relative permeabilities.

Multiple-Mixing-Cell Method for Three-Hydrocarbon-Phase Displacements

Summary Low-temperature oil displacements by carbon dioxide involve complex phase behavior, in which three hydrocarbon phases can coexist. Reliable design of miscible gasflooding requires knowledge of the minimum miscibility pressure (MMP), which is the pressure required for 100% recovery in the absence of dispersion or as defined by slimtube experiments as the “knee” in the recovery curve with pressure in which displacement efficiency is greater than 90%. There are currently no analytical methods to estimate the MMP for multicomponent mixtures exhibiting three hydrocarbon phases. Also, the use of compositional simulators to estimate MMP is not always reliable. These challenges include robustness issues of three-phase equilibrium calculations, inaccurate three-phase relative permeability models, and phase identification and labeling problems that can cause significant discontinuities and failures in the simulation results. How miscibility is developed, or not developed, for a three-phase displacement is not well-known. We developed a new three-phase multiple-mixing-cell method that gives a relatively easy and robust way to determine the pressure for miscibility or, more importantly, the pressure for high-displacement efficiency. The procedure that moves fluid from cell to cell is robust because it is independent of phase labeling (i.e., vapor or liquid), has a robust way to provide good initial guesses for three-phase flash calculations, and is also not dependent on three-phase relative permeability (fractional flow). These three aspects give the mixing-cell approach significant advantages over the use of compositional simulation to estimate MMP or to understand miscibility development. One can integrate the approach with previously developed two-phase multiple-mixing-cell models because it uses the tie-line lengths from the boundaries of tie triangles to recognize when the MMP or pressure for high-displacement efficiency is obtained. Application of the mixing-cell algorithm shows that, unlike most two-phase displacements, the dispersion-free MMP may not exist for three-phase displacements, but rather a pressure is reached in which the dispersion-free displacement efficiency is maximized. The authors believe that this is the first paper to examine a multiple-mixing-cell model in which two- and three-hydrocarbon phases occur and to calculate the MMP and/or pressure required for high displacement efficiency for such systems.

Numerical modeling of combined low salinity water and carbon dioxide in carbonate cores

This paper investigates the combined effect of injecting low salinity water (LSWI) and carbon dioxide (CO2) on oil recovery from carbonate cores. The combined effect of LSWI and CO2 injection on oil recovery was predicted by performing several 1D simulations using measured reservoir rock and fluid data. These simulations included the effect of salinity on both miscible and immiscible continuous gas injection (CGI), simultaneous water-alternating-gas (SWAG), constant water-alternating-gas (WAG), and tapered (WAG). For SWAG and constant and tapered WAG, both seawater and its dilutions were simulated. CO2 was injected above its minimum miscibility pressure. Baker's three-phase relative permeability model was modified to account for the effect of salinity on the water/oil relative permeability. The results show that SWAG, whether using seawater or its dilutions, outperformed all other tertiary injection modes in terms of oil recovery. Moreover, the SWAG process has both the highest tertiary recovery factor (TRF) and the lowest utilization factor (UF). This study highlights the advantage of using low salinity water along with miscible CO2. The miscible CO2 displaces the residual oil saturation whereas the low salinity water boosts the production rate by increasing the oil relative permeability through wettability alteration towards more a water-wet state. The latter finding was supported by comparing our simulations with the two corefloods reported by Chandrasekhar and Mohanty (2014). These corefloods were conducted in SWAG tertiary mode using seawater and its dilutions. Fractional flow analysis shows that SWAG with low salinity water requires less injected solvent compared to SWAG with seawater and miscible CGI.

Efficient Experimental-Data Acquisition for Miscible CO2 Water-Alternating-Gas-Injection Corefloods in Carbonate

SummaryUnderstanding the physics behind which carbon dioxide (CO2) and water displace oil in the porous medium is of the utmost importance for the success of any miscible CO2 water-alternating-gas (WAG) -injection project. This involves estimating parameters such as remaining oil saturation, trapped gas saturation, and three-phase relative permeability by carrying out and by interpreting several CO2 WAG experiments representative of flows inside the reservoir (i.e., pressure and temperature conditions, fluids, capillary number). This paper presents an experimental design, an apparatus, and a procedure to carry out such experiments at reservoir conditions with extensive and up-to-date data-acquisition techniques.Two CO2/water cyclic injections were performed at reservoir conditions, on horizontal carbonate cores with light oil from a Middle East field, far above minimum miscibility pressure (MMP). Great care was given to the data-acquisition systems set for the experiments. Produced volumes were monitored to provide material balance of each phase at both reservoir and laboratory conditions with a clear separation of flashed oil, condensate, and gas. A full compositional analysis of the fluids produced was then conducted, with gas chromatography (GC) and liquid analysis of flashed oil and condensate. Differential pressure across the core was monitored for relative-permeability estimation. Finally, a dual-energy X-ray scanner was used to measure three-phase in-situ saturations, cross check material-balance results, highlight gravity segregation, and ensure that laboratory artifacts (end effects) do not influence interpretation conclusions.Several material-balance methods were investigated to accurately calculate the average saturations and the recovery factor in the presence of strong CO2/oil interactions. With our experimental design, we were able to decouple thermodynamic effects (stripping) from three-phase flow effects (sweeping) in the raw-production data. Several hysteresis features were observed, such as reduction in gas relative permeability and variation in land-trapping parameter.

Effects of liquid layers and distribution patterns on three-phase saturation and relative permeability relationships: a micromodel study.

In the current study, we used micromodel experiments to study three-phase fluid flow in porous media. In contrast to previous studies, we simultaneously observed and measured pore-scale fluid behavior and three-phase constitutive relationships with digital image acquisition/analysis, fluid pressure control, and permeability assays. Our results showed that the fluid layers significantly influenced pore-scale, three-phase fluid displacement as well as water relative permeability. At low water saturation, water relative permeability not only depended on water saturation but also on the distributions of air and diesel. The results also indicate that the relative permeability-saturation model proposed by Parker et al. (1987) could not completely describe the experimental data from our three-phase flow experiments because these models ignore the effects of phase distribution. A simple bundle-of-tubes model shows that the water relative permeability was proportional to the number of apparently continuous water paths before the critical stage in which no apparently continuous water flow path could be found. Our findings constitute additional information about the essential constitutive relationships involved in both the understanding and the modeling of three-phase flows in porous media.

Analytical expressions for three-phase generalized relative permeabilities in water- and oil-wet capillary tubes

We analyze three-phase flow of immiscible fluids taking place within an elementary capillary tube with circular cross-section under water- and oil-wet conditions. We account explicitly for momentum transfer between the moving phases, which leads to the phenomenon of viscous coupling, by imposing continuity of velocity and shear stress at fluid-fluid interfaces. The macroscopic flow model which describes the system at the Darcy scale includes three-phase effective relative permeabilities, K i j,r , accounting for the flux of the ith phase due to the presence of the jth phase. These effective parameters strongly depend on phase saturations, fluid viscosities, and wettability of the solid matrix. In the considered flow setting, K i j,r reduce to a set of nine scalar quantities, K i j,r . Our results show that K i j,r of the wetting phase is a function only of the fluid phase own saturation. Otherwise, K i j,r of the non-wetting phase depends on the saturation of all fluids in the system and on oil and water viscosities. Viscous coupling effects (encapsulated in K i j,r with i ≠ j) can be significantly relevant in both water- and oil-wet systems. Wettability conditions influence oil flow at a rate that increases linearly with viscosity ratio between oil and water phases.

Technology Focus: EOR Performance and Modeling (January 2015)

Technology Focus We can easily state that incorporating enhanced-recovery focus into field- management practices as early as possible is finally becoming the norm. No longer is enhanced oil recovery (EOR) something operators procrastinate about and not act on until the end of the life of a field. Growing recovery challenges of maturing fields definitely are one of the reasons for this historical change in focus. We should also acknowledge the effect of growing unconventional oil operations and, more importantly, their severe recovery challenges. Increasing recovery factors in tight, light reservoirs is one of the more prominent research topics in the oil industry in recent years. Last but not least, EOR is being implemented in offshore operations. This new paradigm—caring for production and recovery, optimizing production rates and recovery factors simultaneously—is being realized with significant help from new technologies. Significant enhancements in reservoir characterization, EOR chemicals, modeling capabilities (EOR software and computational power), conformance capabilities, and monitoring and control systems, along with improved understanding of flow physics, are making EOR easier for our industry. Ongoing EOR research is bringing complex EOR schemes to the industry; some of the examples are low-salinity CO2 water-alternating-gas (WAG) injection, CO2/steam injection, steam/ solvent injection, and microbial EOR. Integration for successful EOR projects is also maturing. Historically, with steam-assisted gravity drainage, we all recognized the effect of well trajectory on recovery. More recently, we have identified the relationship between massive fracture architecture and EOR in tight, light reservoirs. It is worth mentioning that unconventionals have been pushing reservoir characterization, drilling, and completions to yet another level. All that effort not only improves the performance of those special reservoirs but also makes EOR easier for conventionals. As a result of the focus on enhancing recovery for all types of reservoirs, many great technical papers were available for this feature this year. The following pages will provide some insights into how EOR is being tested for tight, light reservoirs; into low-salinity CO2 WAG experimentation; and into giant-field EOR applications. More papers can be found in the OnePetro online library, including those listed for recommended additional reading. JPT Recommended additional reading at OnePetro: www.onepetro.org. SPE 169076 Modeling of Viscous Displacement in Dual-Porosity Naturally Fractured Reservoirs: Application to Surfactant Enhanced Oil Recovery by Mojtaba Kiani, Tiorco, et al. SPE 169170 Assessment of Three-Phase Relative Permeability and Hysteresis Models for Simulation of Water- Alternating-Gas Injection in Water- Wet and Mixed-Wet Systems by Omid Shahrokhi, Heriot-Watt University, et al. SPE 169102 Low-Salinity Waterflooding at West Salym: Laboratory Experiments and Field Forecasts by B.M.J.M. Suijkerbuijk, Shell, et al. OTC 24483 Relative Permeability Effects on the Miscible CO2 WAG Injection Schemes Through Compositional Simulations of Brazilian Small-Scale Water-Wet Synthetic Presalt Reservoir by S.F. Mello, Universidade Estadual de Campinas, et al.

Prediction of three-phase oil relative permeability through a sigmoid-based model

Abstract We present a novel methodology for the prediction of three-phase oil relative permeability, k ro , through a sigmoid-based model. This modeling choice allows us to incorporate key effects of the pore-scale phase distributions into the proposed effective empirical model for k ro . Our sigmoid-based model is able to reproduce: (i) oil remobilization induced by gas injection in water-wet media; (ii) a smooth transition towards the layer-drainage regime for low oil saturations; and (iii) the consequent reduction of residual oil saturation in a three-phase system. The ability of our model to embed the effects of these processes into the estimation of oil relative permeabilities is discussed through comparison with previous experimental measurements. Two different procedures, respectively aimed at describing primary gas injection and secondary waterflooding, are proposed for data analysis and interpretation. A remarkably good agreement between model predictions and direct three-phase relative permeability measurements from the literature is observed when model parameters are estimated solely on the basis of two-phase information. The robustness of the proposed methodology is also assessed by comparing estimates of model parameters based on two-phase data against their counterparts estimated within a Maximum Likelihood framework on the basis of three-phase measurements.

Novel Three-Phase Compositional Relative Permeability and Three-Phase Hysteresis Models

SummaryMobility-control methods have the potential to improve coupled enhanced oil recovery (EOR) and carbon dioxide (CO2) storage technique (CO2-EOR). There is a need for improved three-phase relative permeability models with hysteresis, especially including the effects of cycle dependency so that more-accurate predictions of these methods can be made. We propose new three-phase relative permeability and three-phase hysteresis models applicable to different fluid configurations in a porous medium under different wettability conditions. The relative permeability model includes both the saturation history and compositional effects. Three-phase parameters are estimated on the basis of saturation-weighted interpolation of two-phase parameters. The hysteresis model is an extension of the Land trapping model (Land 1968) but with a dynamic Land coefficient introduced. The trapping model estimates a constantly increasing trapped saturation for intermediate-wetting and nonwetting phases. The hysteresis model overcomes some of the limitations of existing three-phase hysteresis models for nonwater-wet rocks and mitigates the complexity associated with commonly applied models in numerical simulators. The relative permeability model is validated by use of multicyclic three-phase water-alternating-gas experimental data for nonwater-wet rocks. Numerical simulations of a carbonate reservoir with and without hysteresis were used to assess the effect of the saturation direction and saturation path on gas entrapment and oil recovery.

Three-phase flow in porous media: A review of experimental studies on relative permeability

We present a detailed, synthesized review of experimental studies on three-phase relative permeability published since 1980. We provide comprehensive, yet highly focused, analysis of critical aspects of the field and their evolution over the last three decades. In particular, we review the effects of saturation history, wettability, spreading, and layer drainage on the measured flow properties. We also list all the processes, rock types, fluid systems, and measurement techniques in order to provide a clear map for future studies. Behavior of the measured three-phase relative permeabilities with respect to fluid saturations, saturation histories, wettability of rock samples, spreading characteristics, interfacial tensions, and other pertinent properties are carefully discussed. Studies that use a diverse set of experimental techniques and data analysis to deduce relative permeability are included. The experimental techniques that should be utilized to reduce uncertainty are also explored. We interpret the measured properties and outcomes of different studies and compare them to substantiate distinct trends at various saturation ranges and provide ideas for new studies. This is intended to distill a clear image of where the field stands and to allow composition of possible paths for future investigations. The areas of critical relevance that have not been investigated or require further studies are highlighted.

Impact of pore-scale three-phase flow for arbitrary wettability on reservoir-scale oil recovery

Abstract Three-phase flow in porous media is of great importance in enhanced oil recovery processes such as Water-Alternating-Gas (WAG) injection. In this work we use a new three-phase flow pore-network model, which fully captures the three-phase microscopic displacement processes, including accurate descriptions of oil films and layers, and which takes realistic 3D pore geometries extracted from pore-space images as an input. The pore-scale model is used to calculate physically robust relative permeability and capillary pressure functions for a range of realistic wettability scenarios. These three-phase flow functions have been used in a heterogeneous reservoir model with a range of equiprobable geological realisations of permeability and porosity distributions to demonstrate their impact on oil recovery after water, gas or WAG injection. Simulations at the pore-scale show that the residual oil saturations for a water-wet system are higher after water flooding compared to the corresponding residual oil saturations after gas injection. Residual oil saturations for oil-wet systems are significantly lower after both water and gas injection. This is due to the presence of stable oil wetting films, which provide hydraulic connectivity at low oil saturations. Simulations at the reservoir scale show that the lowest oil recovery for a water-wet case is obtained when a single fluid (gas or water) is injected; WAG injection yields significantly higher recovery factors. If the reservoir is oil-wet, however, pure gas injection results in the highest oil recovery. Overall, field-scale recovery predictions are very sensitive to the combination of both, different geological models and different three-phase relative permeability functions. Comparing recovery factors for network-derived and empirical relative permeability models demonstrates that the uncertainty in predicting oil recovery resulting from the choice of three-phase relative permeability models can be as large as the geological uncertainty present in a model that has been history matched using production data from a prolonged waterflood. This implies that the choice of three-phase flow functions directly affects the viability of WAG projects.

Modeling of Cyclic Hysteresis of Three-Phase Relative Permeability During Water-Alternating-Gas Injection

Summary Multiphase flow takes place in many petroleum reservoirs—in particular, mature fields and reservoirs under fluid [e.g., gas, water-alternating-gas (WAG)] injection. The numerical simulation of such reservoirs requires knowledge of flow functions (i.e., relative permeability and capillary pressure). Because experimental measurement of fluid permeabilities (in particular) under three-phase-flow conditions is very time-consuming and difficult, many correlations and models were developed and these are widely used instead of measured data. In this study, we have used the results of a comprehensive set of WAG-injection coreflood experiments performed under different wettability conditions and core-permeability values to obtain relative permeabilites of oil, water, and gas under reservoir pressure and temperature. Three-phase relative permeability of each phase was obtained by history matching the measured production and differential pressure obtained in the laboratory. The results of the experiments revealed significant cyclic hysteresis effects in gas and oil relative permeability. We proposed new formulations and methodology for the modeling of cyclic hysteresis of three-phase relative permeability during WAG injection. This technique is a direct method that uses measured three-phase kr data obtained from the first cycle of WAG injection to predict the relative permeability of the subsequent cycles. The integrity of this technique was validated against the three-phase kr data obtained from our WAG experiments. We also assess the validity of the WAG-injection hysteresis model available in reservoir simulators against our three-phase relative permeability data to evaluate its performance.

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.

The effect of saturation history on three-phase relative permeability: An experimental study

We investigate the effect of different saturation histories relevant to various oil displacement processes (including secondary and tertiary gas injections) on three-phase gas/oil/brine relative permeabilities of water-wet sandstone. It is found that three-phase water (wetting phase) relative permeability is primarily a function of water saturation and shows no dependency upon saturation history. Three-phase gas (nonwetting phase) relative permeability is also a function of gas saturation as well as the direction of gas saturation change. Three-phase relative permeability to oil (intermediate-wetting phase) appears to depend on all phase saturations, and saturation history have no significant impact on it. Three-phase oil relative permeability shows weak sensitivity to initial oil saturation prior to gas injection. The functional forms of oil relative permeability with saturation, particularly at low oil saturations, are also examined. It is observed that, at high oil saturations where networks of oil-filled elements govern oil flow, oil relative permeability exhibits a quartic form with oil saturation whereas, at low oil saturations where flow is believed to be controlled by layer drainage, it shows a quadratic form . The quadratic form of three-phase oil relative permeability is consistent with the theoretical interpretation of layer drainage at the pore scale.

Multiscale Simulation of WAG Flooding in Naturally Fractured Reservoirs

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 164837, ’Multiscale Simulation of WAG Flooding in Naturally Fractured Reservoirs,’ by Mohamed Ahmed Elfeel, Adnan Al-Dhahli, Sebastian Geiger, SPE, and Marinus I.J. van Dijke, Heriot-Watt University, prepared for the 2013 EAGE Annual Conference and Exhibition/SPE Europec, London, 10-13 June. The paper has not been peer reviewed. Naturally fractured reservoirs (NFRs) contain a significant amount of remaining petroleum reserves and are now being considered for water-alternating-gas (WAG) flooding as secondary or tertiary recovery. The authors face the challenge of reservoir simulation of WAG by building models at various scales, starting with pore scale and expanding to an intermediate scale and then to reservoir scale. They show how pore-network modeling and fine-grid modeling where the fractures and matrix are represented explicitly can be used to increase the accuracy of numerical simulations at field scale. Introduction A significant portion of the world’s remaining petroleum resources is located in NFRs, including supergiant fields in the Middle East. A detailed understanding of the recovery processes involved in extracting hydrocarbons from NFRs by use of enhanced-oil-recovery techniques is key to increasing ultimate recovery for such reservoirs. Waterflooding has been used with various degrees of success in NFRs. For unfavorable (i.e., mixed- to oil-wet) matrix wettability, however, waterflooding can be ineffective. Gas/oil gravity drainage (GOGD) provides an important drive mechanism that can be effective irrespective of the rock wettability. In NFRs, fractures increase the exposure of the injected gas to oil in reservoir rock, which renders GOGD more effective than it is in unfractured reservoirs. Consequently, gas injection has been applied in many NFRs. However, because the gas mobility is very high compared with that of water and oil, so is the risk of bypassed oil and gravity override, which can lead to very early gas breakthrough. This is particularly true for NFRs. WAG flooding combines the merits of the two injection fluids on macroscopic and microscopic scales while stabilizing the injection front, delaying breakthroughs, and, therefore, leading to increased oil recovery compared with continuous water or gas injection. Reservoir simulation of WAG injection is very challenging because a representative three-phase saturation model is required to predict relative permeability and capillary pressure as water and gas saturations increase and decrease alternately. Three-phase relative permeability and capillary pressure data are extremely difficult to measure experimentally. Even if experimental evaluation becomes feasible, an infinite number of saturation paths can occur in the reservoir. This necessitates the use of empirical, or interpolation, models to predict three-phase relative permeability and capillary pressure from two-phase experiments. In NFRs, capillary pressure and relative permeability functions have a major effect on fluid exchange between matrix blocks and fractures. Predicting the effects of the interplay of viscous, capillary, and gravity forces is challenging because fluid flow is viscous-dominated in the fractures while transfer between fractures and matrix blocks is dominated by capillary and gravity forces. Because most of the oil is contained inside the matrix, capillary and gravity forces can be more important in NFRs than in conventional reservoirs.

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.