Relative Permeability Model Research Articles

Predicting gas–water relative permeability using Nuclear Magnetic Resonance and Mercury Injection Capillary Pressure measurements

Relative permeability functions are useful in understanding gas–water two–phase flow in rocks and reservoirs. When direct laboratory data of relative permeability are not available for evaluating gas-water two-phase flow in rocks and reservoirs, indirect prediction models using gas-water relative permeability functions are widely used.In this research, four typical existing predicting models of relative permeability based on capillary pressure are investigated (the Purcell, Burdine, Brooks–Corey and Li models). These models notably simplify the gas–water spatial distribution in rocks: the Purcell, Burdine and Brooks–Corey models all assume that gas flows in large tubes, while water flows in small tubes, and irreducible water adsorbed on tube surfaces is not considered. Alternatively, the Li model considers irreducible water adsorbed on tube surface; however, the proportion of irreducible water, mobile water and gas are assumed to be constant in tubes with different radii, as this model was derived from a single tube flow structure.This research proposes a new relative permeability model in which the pore–size distribution, the tortuosity and the gas–water spatial distribution are all considered. A bundle of capillary tubes model and modified single-tube flow model are applied in the proposed model. Capillary tubes in the rock are divided into large tubes and small tubes. In large tubes, the water phase contacts the tube surface and is partially adsorbed onto the surface and partially mobile, while gas phase flows in the center of tubes and is surrounded by water. In small tubes, only irreducible water exists. Variables in the proposed model such as the thickness of irreducible water, mobile water and gas are usually unknown. Combined with a capillary pressure curve, the shift of the transversal time (T2) distribution of Nuclear Magnetic Resonance is used to determine these variables.The proposed model is validated by experimental data from six rock samples that have different lithology, diagenesis characteristics, pore structure characteristics, irreducible water saturation and different grades of T2 distribution shifts. The model results are compared with the calculated values from other four existing models and the experimental data. Our results show that the proposed model matches the experimental data better than other models, and diagenesis and pore structure characteristics are more sensitive to the proposed model than is lithology.

Acquisition and analysis of transient data through unsteady-state core flooding experiments

Dynamic displacement experiments and numerical two-phase flow estimation program are presented in this study. Unsteady-state core-flooding system was designed and utilized for oil–water dynamic displacement experiment. Two in situ sandstone core plug samples were used to investigate relative permeability via diesel and 3 wt % brine as non-wetting and wetting phase fluids. The transient data (pressure drop and produced fluid volume) were collected automatically for oil–water relative permeability computation. For relative permeability analysis, an inverse method program was constructed with four components: (a) an IMPE finite-difference numerical simulator of the flow through the core; (b) functional Cory-type power law model of relative permeability in terms of a set of adjustable parameters found by minimizing an objective function; (c) the objective function formed by the sum of the square of the differences between the observations and calculated data; (4) the Gauss–Newton with Levenberg–Marquardt modification procedure for the least-squares problem to minimize the objective function definition. All the above processes are embodied in relative-permeability calculation program, RCP, which is constructed in this study using FORTRAN language.

Evaluation of gas condensate reservoir behavior using velocity dependent relative permeability during the numerical well test analysis

Abstract Gas condensate is one of the most different fluids in reservoir simulation due to retrograde condensation in case of pressure reduction. In this kind of fluids, two phenomena named negative inertia and positive coupling, become significant in the high velocity zone around the wellbore. In this study, a modified black oil simulator is developed that take into account the velocity dependent relative permeability. Against the industrial simulator that assumes linear variation of transmissibilities by pressure, modified black oil nonlinear equations are solved directly without linearization. The developed code is validated by ECLIPSE simulator. The behavior of two real gas condensate fluids, a lean and a rich one, are compared with each other. For each fluid, simulations of PVT experiments are carried out to calculate black oil property applying Coats approach for gas condensate fluids. For both fluids, the proposed models for gas condensate velocity dependent relative permeability show different influence of velocity on relative permeability in the same conditions. Moreover, it is observed that higher flow rate of gas production leads to more condensate production during constant rate well testing.

Relative permeability for multiphase flow for oven-dry to full saturation conditions

Numerical simulation of supercritical CO2 (CO2) injection into deep geologic reservoirs often requires the modeling of multifluid flow and transport. The classical capillary and relative permeability models assume that the residual water is immobile and irreducible. This assumption is not in agreement with the flow process for CO2 injection into a saline aquifer. In this paper, the relative permeability (kr)–saturation (S) relationships for both the aqueous and non-aqueous phases are derived for oven-dry (i.e., zero liquid saturation) to full saturation conditions by extending the classical kr–S relationships. The extended relative permeability models reduce to the corresponding classical forms when the aqueous saturation is higher than the critical value, but deviates from the latter when the aqueous saturation is lower than the critical value. The implementation of the extended models in the STOMP multifluid flow and transport model is demonstrated by the simulation of dry CO2 injection from a vertical well into a homogeneous reservoir. The extended models overcome the limitations of the classical models and can simulate the dry-out processes associated with the residual water. The extended models are expected to simulate CO2 injection and the subsequent processes (e.g., the dry-out of brine and salt precipitation) more accurately than the classical models.

Investigation of uncertainty in CO2 reservoir models: A sensitivity analysis of relative permeability parameter values

Numerical reservoir models of CO2 injection in saline formations rely on parameterization of laboratory-measured pore-scale processes. We performed a parameter sensitivity study and Monte Carlo simulations to determine the normalized change in total CO2 injected using the finite element heat and mass-transfer code (FEHM) numerical reservoir simulator. Experimentally measured relative permeability parameter values were used to generate distribution functions for parameter sampling. The parameter sensitivity study analyzed five different levels for each of the relative permeability model parameters. All but one of the parameters changed the CO2 injectivity by <10%, less than the geostatistical uncertainty that applies to all large subsurface systems due to natural geophysical variability and inherently small sample sizes. The exception was the end-point CO2 relative permeability, kr,CO20, the maximum attainable effective CO2 permeability during CO2 invasion, which changed CO2 injectivity by as much as 80%. Similarly, Monte Carlo simulation using 1000 realizations of relative permeability parameters showed no relationship between CO2 injectivity and any of the parameters but kr,CO20, which had a very strong (R2=0.9685) power law relationship with total CO2 injected. Model sensitivity to kr,CO20 points to the importance of accurate core flood and wettability measurements.

Three-Phase Oil Relative Permeability in Water-Wet Media: A Comprehensive Study

We report experimental three-phase oil relative permeability in two water-wet media (a sandpack and a Berea sandstone core) along different saturation paths. Three oils with different viscosities, compositions, and spreading coefficients were used in the measurements. The data show that oil relative permeability can vary significantly along different saturation paths. Most importantly, we find that despite the significant (orders of magnitude) variation of oil relative permeability along different saturation paths, the oil relative permeability in each medium can be collapsed into a single relative permeability curve, once they are plotted as a function of mobile oil saturation. However, this collapsed curve varies depending on the porous media. We show that the same behavior occurs in the relative permeability data published over the past 50 years. These observations indicate that the key factor in differences between oil permeabilities in the same porous media is changes in the residual oil saturation. We examine the performance of most commonly used relative permeability models, i.e., Corey, Saturation-Weighted Interpolation (SWI), and Stone against our data. Given the importance of residual oil saturation, we fit the experimental data along different saturation paths by treating the residual oil saturation in these models as the fitting parameter while keeping the other parameters constant. We find that the Corey and SWI models fit the data very well while the Stone model performs poorly at low saturations. We find that residual oil saturation is a nonlinear function of gas/water saturation as opposed to linear relationship previously suggested by others.

New analytical formulas for prediction of gas–liquid relative permeabilities through fractures – Part I: Incompressible flow

Considering the fact that flow in fractured formations is fracture dominated, relative permeabilities through fractures must be well understood. Contrary to reservoir rocks, there is no standard experimental procedure for measurement of relative permeabilities through fractures. Furthermore, existing techniques are generally inconsistent, time consuming, expensive, complicated, and may fail due to technical difficulties encountered while performing the experiments. Thus, developing an analytical model for accurate prediction of relative permeabilities through fractures is of vital importance for treating one of significant uncertainties associated with characterization and simulation of fractured reservoirs.Historically, the straight-line relative permeability model (X-curve) has been widely used in numerical simulation of fractured reservoirs. However, experimental measurements of gas–liquid relative permeabilities through fractures have revealed high degrees of phase interference which cannot be well represented by the X-model. In this work, idealized flow configurations of stratified and segregated flow are assumed in order to make the analytical derivation tractable without the need of using numerical techniques. Then, basic fluid flow equations are combined to develop simple analytical models for gas–liquid flow in each of the patterns. Combining the models with Darcy's law leads to closed-form analytical expressions for explicit calculation of gas and liquid relative permeabilities through fractures. The relationships simply state that the relative permeabilities depend on several parameters one of which being the saturation, whereas they were considered to be only functions of the saturation in the classic X-model. Afterwards, the formulas are further simplified by adopting a realistic assumption. Eventually, the validity of the derived relative permeability expressions is checked by comparing their predictions with available experimental data. The results show that the ability of the segregated model to accurately predict experimental data is considerably poorer than that of the stratified model. Therefore, the generalized relative permeability expressions proposed for the stratified pattern must be used to describe the dynamics of gas–liquid flow in fractures. It addition to robustness, other advantages of the newly presented formulas such as simplicity, cost effectiveness, and being explicit and analytic make their implementation in numerical simulators straightforward.

Effect of outer boundary condition, reservoir size, and CO2 effective permeability on pressure and CO2 saturation predictions under carbon sequestration conditions

AbstractA TOUGH2 simulation was conducted to investigate how the change of key model parameters affects pressure and CO2 saturation response to CO2 injection into a deep CO2 storage reservoir. Given a domain of 100 × 100 km and a formation permeability of 10−13 m2, outer boundary condition does not have a significant impact on pressure increase and CO2 saturation results. In a simulation period of 30 years of CO2 injection + 100 years of post CO2 injection, with a total CO2 injection volume of 6.3×107 m3 at T = 47°C and P = 10.5 MPa (equivalent mass of 30 million tonnes of CO2), there is no pressure difference between the no flow boundary case and the open boundary case given a domain size of 100 x 100 km (a total storage formation pore volume of 1011 m3 at T = 47°C and P = 10.5 MPa), and the maximum CO2 plume radius difference is 0.5%. However, given a domain size of 10 × 10 km, outer boundary condition significantly affects pressure simulation results. At t = 130 years, the pressure increase in the no flow boundary case is 56.5 times of the pressure increase in the open boundary case at the cell 50 m away from the injection well. For the 10 × 10 km case, the impact of outer boundary condition on CO2 saturation results is relatively small. The change in formation permeability significantly affects pressure increase results, while the change in CO2 relative permeability model only affects pressure increase results at cells close to the CO2 injector. © 2016 Society of Chemical Industry and John Wiley &amp; Sons, Ltd

Characterization of heterogeneity in the Heletz sandstone from core to pore scale and quantification of its impact on multi-phase flow

In this study we present the results of an extensive multiscale characterization of the flow properties and structural and capillary heterogeneities of the Heletz sandstone. We performed petrographic, porosity and capillary pressure measurements on several subsamples. We quantified mm-scale heterogeneity in saturation distributions in a rock core during multi-phase flow using conventional X-ray CT scanning. Core-flooding experiments were conducted under reservoirs conditions (9MPa, 50°C) to obtain primary drainage and secondary imbibition relative permeabilities and residual trapping was analyzed and quantified. We provide parameters for relative permeability, capillary pressure and trapping models for further modeling studies. A synchrotron-based microtomography study complements our cm- to mm-scale investigation by providing links between the micromorphology and mm-scale saturation heterogeneities.

On a universal structure for immiscible three-phase flow in virgin reservoirs

We discuss the solution for commonly used models of the flow resulting from the injection of any proportion of three immiscible fluids such as water, oil, and gas in a reservoir initially containing oil and residual water. The solutions supported in the universal structure generically belong to two classes, characterized by the location of the injection state in the saturation triangle. Each class of solutions occurs for injection states in one of the two regions, separated by a curve of states for most of which the interstitial speeds of water and gas are equal. This is a separatrix curve because on one side water appears at breakthrough, while gas appears for injection states on the other side. In other words, the behavior near breakthrough is flow of oil and of the dominant phase, either water or gas; the non-dominant phase is left behind. Our arguments are rigorous for the class of Corey models with convex relative permeability functions. They also hold for Stone’s interpolation I model [5]. This description of the universal structure of solutions for the injection problems is valid for any values of phase viscosities. The inevitable presence of an umbilic point (or of an elliptic region for the Stone model) seems to be the cause of this universal solution structure. This universal structure was perceived recently in the particular case of quadratic Corey relative permeability models and with the injected state consisting of a mixture of water and gas but no oil [5]. However, the results of the present paper are more general in two ways. First, they are valid for a set of permeability functions that is stable under perturbations, the set of convex permeabilities. Second, they are valid for the injection of any proportion of three rather than only two phases that were the scope of [5].

Influence of relative permeability on injection pressure and plume configuration during CO2 injections in a mafic reservoir

Carbon capture and sequestration projects have traditionally targeted deep sedimentary basins; however, mafic reservoirs may also be attractive targets for CO2 disposal on the basis of permanent mineral trapping over relatively short time scales (101 to 102yr). Nevertheless, CCS development in mafic reservoirs is hampered by substantial uncertainty in fracture-controlled reservoir characteristics, particularly with respect to the effects of multi-phase fluid flow, e.g., relative permeability and capillary pressure. The present study quantifies uncertainty surrounding relative permeability effects in a basalt reservoir by developing a numerical modeling experiment on the basis of site characterization data from the Slack Canyon #2 flow top, which is one of three flow tops comprising the injection zone at the Wallula Basalt Sequestration Pilot Project in southeast Washington State. This numerical modeling experiment controls for the effects of curvature in the relative permeability models by performing an ensemble of 399 CO2 injection simulations with constant geometry and reservoir properties, while systematically varying the phase interference parameter (λ) and residual CO2 saturation (Sgr), which govern wetting and non-wetting phase relative permeability, respectively. The relative permeability parameter space is defined by selecting combinations of λ and Sgr that cover a wide range of experimental laboratory measurements. For each simulation, CO2 is injected into the reservoir for 10 years at a constant rate of 2.78kgs−1 (87,856metrictons(MT)yr−1), which is 10% of the annual injection rate proposed for one injection scenario at the Wallula Site. Results from the ensemble of simulations show that relative permeability alone can account for >50MPa of variability in the injection pressure and a two-fold difference in lateral CO2 plume migration. Additionally, this work shows that curvature in the wetting phase relative permeability model is the stronger influence on reservoir pressure accumulation, while curvature in the non-wetting phase relative permeability model strongly governs CO2 plume geometry.

Evaluation of Relative Permeability Models in CO&lt;sub&gt;2&lt;/sub&gt;/Brine System Using Mixed and Hybrid Finite Element Method

The requirement to reduce 40% carbon emission in 2020 has lead Malaysia to adopt the carbon capture and storage (CCS) technology in 2009. In this research, the pressure and transport differential equation for CO2 – brine phases flow is discretized using mixed and hybrid finite element method (MHFEM) which ensures the local continuity of the finite elements. Result shows that CO2 flow radially outward from the injection well. Three relative permeability models are investigated and it was find out that the simplified relative permeability model (SRM) has reduced the computational time by 8.3 times (when compare to Brooks and Corey model) but it is accurate for 1 year preliminary prediction. For longer period of prediction, classical Brooks and Corey and van Genuchten models shall be used.

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.

The effect of saturation path on three‐phase relative permeability

AbstractSimulation and fluid flow prediction of many petroleum‐enhanced oil recovery methods as well as environmental processes such as carbon dioxide (CO2) geological storage or underground water resources remediation requires accurate modeling and determination of relative permeability under different saturation histories. Based on this critical need, several three‐phase relative permeability models were developed to predict relative permeability; however, for practical purposes most of them require a variety of parameters introducing undesired complexity to the models. In this work, we attempt to find out if there is a simpler way to express this functionality. To do so, we experimentally measure three‐phase, water/oil/gas, relative permeability in a 1 m long water‐wet sand pack, under several saturation flow paths to cover the entire three‐phase saturation space. We obtain the in situ saturations along the sand pack using a CT scanner and then determine the relative permeabilities of liquid phases directly from the measured in situ saturations using an unsteady state method. The measured data show that at a specific saturation, the oil relative permeability varies significantly (up to two orders of magnitude), depending on the path through saturation space. The three‐phase relative permeability data are modeled using standard relative permeability models, Corey‐type, and Saturation Weighted Interpolation (SWI). Our measured data suggest that three‐phase oil relative permeability in water‐wet media is only a function of its own saturation if the residual oil saturation is treated as a function of two saturations. We determine that residual saturation is the key parameter in modeling three‐phase relative permeability (effect of saturation history).

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 relative permeability model for deformable soils and its impact on coupled unsaturated flow and elasto-plastic deformation processes

Relative permeability is an indispensable property for characterizing the unsaturated flow and induced deformation in soils. The widely used Mualem model is inadequate for deformable soils because of its assumption of a rigid pore structure and the resultant unique dependence of the tortuosity factor on the volumetric water content. In this study, a unified relationship between the relative permeability and the effective degree of saturation was proposed for deformable soils by incorporating our newly developed water retention curve model into the original Mualem model, in which a new tortuosity factor was defined using the fractal dimension of flow paths and the mean radius of water-filled pores for representing the effect of pore structure variation. The modified deformation-dependent relative permeability model was verified using test data on five types of soils; the verification revealed a much better performance of the proposed model than the original model, which commonly overestimates the relative permeability of deformable soils. Finally, the proposed model was implemented in a coupled numerical model for examining the unsaturated flow and elastoplastic deformation processes in a soil slope induced by rain infiltration. The numerical results showed that the deformation-dependent nature of relative permeability has a remarkable effect on the elastoplastic deformation in the slope and that neglect of the deformation-dependent behavior of relative permeability causes overestimation of the depth of failure.

Stochastic Galerkin Formulations for $$\hbox {CO}_2$$ Transport in Aquifers: Numerical Solutions with Uncertain Material Properties

Abstract A stochastic Galerkin formulation for the transport of $$\hbox {CO}_2$$ CO 2 in a tilted aquifer with uncertain heterogeneous properties is presented. We consider a simplified physics model assuming capillary pressure to be negligible compared to hydrostatic and viscous pressure. The flow is dominated by buoyancy and capillary trapping. We assume a stochastic permeability field and a stochastic model for the uncertain relative permeabilities. We prove that the proposed stochastic Galerkin formulation results in a hyperbolic system of equations, and we devise a numerical method that captures the expected solution discontinuities. The shock-capturing solver for the flux function is combined with an adaptive quadrature method for discontinuous isosurfaces that is used to compute the discontinuous stochastic accumulation coefficient. The stochastic solver is validated against Monte Carlo sampling of an analytical solution for the deterministic problem. The sharp features of the statistics of the solution are accurately captured by the numerical solver. The polynomial chaos framework admits low-cost post-processing of the output to obtain statistics of interest. By construction of an accurate polynomial chaos surrogate model of the output, fast sampling admits calculation of risk for leakage and failure probabilities.

English

A number of relative permeability models were present in the literature, which were used to generate relative permeability data for the fluids, present in the porous medium. Some models were more significant to reservoir geology and displacement system (imbibitions and drainage system), while developing the correlations. Similarly, the same is kept in mind while performing reservoir studies. Therefore, in this study different models based on displacement system and formation geology have been compared, while including the effect of fluid saturation distribution/end point saturation in a reservoir. The generated relative permeability data by using these models have been further used to predict the reservoir performance for gas and water-displacement systems. The results based on this study showed that at lower saturations of displacing fluid (gas and/or water), the generated reservoir performance curves based on relative permeability data generated by using Corey and Wylie and Gardner models, gives higher degree of deviation on comparative basis. The behavior of these error or deviation curves for displacing phase is opposite in case of gas and water-oil displacement systems. While in case of displaced phase (oil), generally analogous behavior can be observed for both systems in terms of deviation/ error profiles trends. These reservoir performance curve(s) are of utmost significance in developing reservoir in an appropriate manner and a slight variation in relative permeability data can have a significant impact at macroscopic level.

Subphase Approach to Model Hysteretic Two-Phase Flow in Porous Media

Several existing models for immiscible two-phase flow identify trapping as the major cause of nonwetting relative permeability hysteresis. These models usually assume that relative permeability is a nonhysteretic function of the connected saturation. However, existing experimental results indicate that this assumption is not necessarily true. It is observed that while relative permeability models based on trapping, e.g., Land’s model, may capture the correct hysteresis behavior in consolidated porous media, they may be qualitatively inaccurate for the case of unconsolidated porous media, which a have lower pore-body to pore-throat aspect ratio. In order to bridge this gap, we present a novel framework for immiscible two-phase flow in which one can model relative permeability hysteresis patterns for both consolidated and unconsolidated porous media. An important aspect of this framework is the subdivision of the nonwetting phase into backbone, dendritic and trapped subphases. The closure problem now consists in modeling the volume transfer between the subphases and the relationship between the relative permeability and these subphases. For the purpose of developing, calibrating and validating our models in this framework, pore-network simulations of drainage and imbibition cycles are conducted for artificial networks as well as for a network representing Berea sandstone. Confirming results from previous works, we find a nearly nonhysteretic relationship between the nonwetting phase relative permeability and its backbone subphase. Additionally, we also observe a nonhysteretic relationship between the nonwetting backbone and trapped saturations. These observations are used to motivate constitutive relations for the proposed framework.