Nonwetting Phase Relative Permeability Research Articles

Steady-state two-phase relative permeability measurements in proppant-packed rough-walled fractures

Understanding multiphase flow in fractures filled with minerals and proppants is vital in various subsurface applications. Limited experimental data have led to reliance on correlations lacking physical basis. We conducted experiments to characterize relative permeability in rough-walled fractures packed with unconsolidated porous media. We tested fractures packed with water-wet 40/70 sand (silica) and surface-coated ceramic proppants. Brine and mineral oil were used as the wetting and non-wetting fluid phases, respectively. Steady-state (SS) drainage (non-wetting-phase displacing wetting-phase) and imbibition (wetting-phase displacing non-wetting-phase) tests were performed under a wide range of saturation histories (full-cycle and scanning-curves) to study relative permeability hysteresis of the propped fractures. Every SS drainage or imbibition test consisted of several discrete points at which fluid saturations and the corresponding relative permeability were measured by varying the fractional flow rates of fluids whilst maintaining a constant total flow rate. We analyzed residual non-wetting phase saturations and relative permeability trends to understand two-phase flow behavior in each proppant pack. High-resolution x-ray microtomography was used to understand the pore-scale topology, wettability, and to provide insights about the pore-scale displacement mechanisms involved in this study. The results showed that commonly used models to estimate relative permeabilities of fractures significantly overestimated the SS brine and oil relative permeabilities (denoted as krw and kro) measured in this study. Further analysis unveiled that the kro values during imbibition exceeded their drainage counterparts in both proppants, the ceramic proppant exhibited a lower initial water saturation and a higher end-point kro permeability at the end of the drainage displacement, as well as higher krw across all flooding processes. Updated fitting parameters for a Brooks-Corey-type relative permeability correlation are introduced. This study presents improved insights, extensive experimentally generated relative permeability data, and an updated relative permeability correlation, which can be collectively utilized to reduce uncertainties associated with continuum-scale forecasts of multiphase flow behavior in fractured subsurface formations.

Fluid-Fluid Interfacial Area and Its Impact on Relative Permeability: A Pore Network Modeling Study

SummaryRelative permeability (kr) is commonly modeled as an empirical function of phase saturation. Although current empirical models can provide a good match of one or two measured relative permeabilities using saturation alone, they are unable to predict relative permeabilities well when there is hysteresis or when physical properties such as wettability change. Further, current models often result in relative permeability discontinuities that can cause convergence and accuracy problems in simulation. To overcome these problems, recent research has modeled relative permeability as a state function of both saturation (S) and phase connectivity (X). Pore network modeling (PNM) data, however, show small differences in relative permeability for the same S-X value when approached from a different flow direction. This paper examines the impact of one additional Minkowski parameter (Mecke and Arns 2005), the fluid-fluid interfacial area, on relative permeability to identify if that satisfactorily explains this discrepancy.We calculate the total fluid-fluid interfacial areas (IA) during two-phase (oil/water) flow in porous media using PNM. The area is calculated from PNM simulations using the areas associated with corners and throats in pore elements of different shapes. The pore network is modeled after a Bentheimer sandstone, using square, triangular prism, and circular pore shapes. Simulations were conducted for numerous primary drainage (PD) and imbibition cycles at a constant contact angle of 0° for the wetting phase. Simultaneous measurements of capillary pressure, relative permeability, saturation, and phase connectivity are made for each displacement. The fluid-fluid IA is calculated from the PNM capillary pressure, the fluid location in the pore elements, and the pore element dimensional data.The results show that differences in the relative permeability at the same (S, X) point are explained well by differences in the fluid-fluid interfacial area (IA). That is, for a larger change in IA at these intersection points, the permeability difference is greater. That difference in relative permeability approaches zero as the difference in IA approaches zero. This confirms that relative permeability can be modeled better as a unique function of S, X, and IA. The results also show that an increase in IA restricts flow decreasing the nonwetting (oil) phase permeability. This decrease is caused by an increase in the throat area fraction compared to the corner area as the total area IA increases. The wetting phase relative permeability, however, shows the inverse trend in that its relative permeability is greater when IA becomes larger owing to a greater fraction of the total area associated with the corners. The area IA, however, impacts the nonwetting phase relative permeability more than the wetting phase relative permeability. Corner flow improves the wetting phase relative permeability because the wetting phase is continuous there. Finally, a sensitivity analysis shows that relative permeability is more sensitive to change in S than it is for IA for the case studied, implying that if only two parameters are used to model relative permeability, it is better to choose S and X.

Low salinity water flooding: Evaluating the effect of salinity on oil and water relative permeability curves using coupling of DLVO and geochemical reactions

Enhancing the oil recovery of carbonate reservoirs with acidic oil depends on injected brine composition and salinity throughout the low salinity water flooding. The typical description of this phenomenon on oil and water relative permeability curves is being put forward by the process-dependent interpolation function, which barely addresses the underlying fundamentals governing the direct impact of wettability alteration and geochemical reactions on flow saturation functions. The main objective of this work is to perform an integrated investigation of the effect of salinity on oil and water relative permeability curves by dynamic coupling of the Derjaguin, Landau, Verwey, and Overbeek (DVLO) theory and geochemical reactions. We studied both the single and two-phase systems using the basis of the geochemical reactions to track the variations of the wetting and non-wetting phase relative permeability curves. In the single-phase scenario, the results show the superiority of the reactive flow modeling technique with kinetic-controlled reactions, in the range between [2–4] of the Damkohler number, to yield a better result for the experimental effluent ions' concentrations than the equilibrium approach. In addition, the single-phase results under dynamic conditions propose Civan correlation as the best predictor of residual resistance factor (RRF) by numerically adjusting the correlation of coefficients based on the physical variables - salinity, dimensionless consumed ion concentration, and Peclet number. Accordingly, the results indicate a novel linkage between the single-phase and two-phase results in the sense that RRF under single-phase mode can be used to estimate the change in the wetting phase relative permeability under the two-phase mode. The single-phase methodology provides the capability for an improvement – up to 15% - in the prediction of the pressure drop curve. For two-phase cases, our procedure involved coupling the characterized geochemical reactions and the DLVO theory to consider the effect of injected water composition on contact angle as the static two-phase parameter. The phase-field method is coupled with DLVO theory to calculate the relative permeability curves for the non-wetting phase, which corresponds to the contact angle at each simulation time step. The two-phase results indicate an improvement – up to 30% - in the prediction of the recovery factor curve, on a history-matching basis, using the DLVO theory with contact angle-dependent correlation of non-wetting phase relative permeability curve. The main novelties of this study are using the single-phase dynamic permeability impairment results in calculating the variation of the wetting-phase relative permeability curve. Moreover, dynamic coupling of DLVO and non-linear contact angle-dependent correlation is used to calculate the non-wetting phase relative permeability curve. According to these novelties, more accurate prediction of the laboratory production profiles can be obtained.

Pore-scale numerical prediction of three-phase relative permeability in porous media using the lattice Boltzmann method

Three immiscible fluids systems are often encountered in energy and environmental disciplines, especially in the oil exploration field. It is essential to enhance oil recovery (EOR) by identifying the three-phase fluid flow mechanism of oil-gas-water system in complex geological structures. In the present study, a lattice Boltzmann (LB) color gradient model for three immiscible fluid flow in three-dimensional porous media is employed and validated using five benchmarks (i.e., the multiphase spinodal decomposition; the multiphase Young-Laplace test; the liquid lens; contact angles and 3D channel layered three-phase fluid flow). The effects of wettability, viscosity ratio (M) and capillary number (Ca) on the relative permeability curves are analyzed in detail. When the wetting condition is enhanced, the results indicate that the relative permeability of non-wetting phase raises while that for the wetting phase exhibits a decline. When M is not equal 1, the relative permeability of high viscosity phase is significantly increased, while the other two phases are less affected. Meanwhile, the maximal value of relative permeability does not exceed unity because of the low porosity in the porous medium. For the influence of Ca, simulation results indicate the relative permeability shows weak sensitivity to Ca.

DEM-LBM simulation of stress-dependent absolute and relative permeabilities in porous media

In this work, stress-dependent absolute and relative permeabilites in porous media are studied using the discrete element method and lattice Boltzmann method. The change of absolute permeability and porosity during compaction is found follow a power-law relation. The stress-dependent absolute permeability in homogeneous pack is in agreement with the prediction of Carman-Kozeny equation. Porosity exponent is increased due to the existence of vugs but is decreased with fractures. Relative permeability, on the other hand, is found not only affected by pore structure of compacted media, but also properties of fluids and rock surface. Our simulations indicate that relative permeability of wetting phase increases slightly with increasing stress, due to the formation of more continuous pathways. Relative permeability of non-wetting phase, however, either increases or decreases depending on viscosity ratio and capillary number. It is found that lubrication effects play an important role in the stress sensitivity of relative permeability.

A more generalized model for relative permeability prediction in unsaturated fractal porous media

Although lots of models for relative permeability prediction have been developed in literature, the effect of pore geometric tortuosity on relative permeability has not been well discussed, as usually the tortuosity of pores with various sizes is assumed the same. However, there is a high possibility that tortuosity is unequal and increases with the decrease in pore size. A new and more generalized analytical model for relative permeability prediction has been developed based on the fractal characteristics of pore size distribution (PSD) and tortuosity in porous media. The analytical expressions of relative permeability for wetting phase and nonwetting phase have been derived, which are the function of normalized wetting phase saturation, PSD fractal dimension, tortuosity fractal dimension and the ratio of the entry capillary pressure to the maximum capillary pressure. The studies show that the increasing PSD fractal dimension and tortuosity fractal dimension can significantly reduce wetting phase relative permeability, but the increase in nonwetting phase relative permeability is insignificant. The developed model has been validated with relative permeability experimental data and compared with other classic relative permeability models. The comparison results demonstrate the reliability of the relative permeability model developed in this paper.

Investigation on Flow Behaviour in Porous Media During Water Flooding and Following CO2 Flooding Using MRI

This article addresses the use of MRI technique to follow the process of oil, water, supercritical CO2 multiphase flow in consolidated sandstone core plug at a typical reservoir temperature and pressure condition. 2D images at various times and quantitative saturation curves were obtained during all stages of the flooding process. The fronts and interfaces between displaced and displacing fluids were also dynamics monitored in situ during water and subsequent supercritical CO2 flooding process. The results showed that the process of CO2 flooding enhanced oil recovery more than 10% based on the previous water flooding. A method of predicting the relative permeability and capillary pressure curves was successfully extended and applied to CO2 flooding, the capillary pressure, the wetting and non-wetting phase relative permeability curves were simultaneously estimated from the capillary end saturation profiles, which were measured with MRI technique. These curves are important and required in various reservoir simulations for evaluating hydrocarbon recovery processes.

Comparison of different models for predicting drainage relative permeability using pore scale numerical simulation of supercritical carbon dioxide and brine flow.

In today’s technologically growing and cost optimisation era, Digital Rock Physics (DRP) is becoming a potential alternative tool to the high cost and time-consuming method of Special Core Analyses (SCAL), for the estimation of reservoir fluid properties. The key objective of this study is to compare different models for predicting drainage relative permeability using pore scale numerical simulation of supercritical carbon dioxide and brine flow, the former being the non-wetting phase and the latter being the wetting phase. The simulations are done on an established computational fluid dynamics (CFD) simulator: ANSYS-CFX. From the simulations, we obtain the saturation values. Using these values and four common models found in the literature, we collaborate the J-function prediction model and capillary pressure values to calculate the relative permeability for the wetting and non-wetting phases. In this study, it is concluded that the Brooks-Corey-Burdine model produces the best relative permeability curves. It is demonstrated that the pore size distribution index (λ) has a positive correlation with the wetting-phase relative permeability and an inverse relation with the non-wetting phase relative permeability. Noteworthy to mention that during the study, it was found that when the J-function is substituted into the relative permeability equations, the predicted relative permeabilities of wetting and non-wetting phase outcomes appears to be more representative, yet simple to compute. The robust methodology described in this paper to evaluate the simulation results with various established models is generic and could be useful in current day oil field practices to serve as a cost-effective alternative to SCAL experiments and form key inputs for typical oil field development planning.

Investigation of the relative permeabilities in two-phase flow of heavy oil/water and three-phase flow of heavy oil/water/gas systems

An experimental study was conducted to investigate two-phase and three-phase relative permeability behavior in a multi-phase flow, which involved a typical Canadian bitumen. A series of isothermal core flood experiments were conducted on an unconsolidated core composed of cleaned Athabasca sand matrix and relative permeabilities of the involved phases were determined. Drainage and imbibition processes for two-phase water/oil flow and oil saturation reversal in a three-phase oil/water/gas flow, which is encountered in a typical air injection process were examined. A history matching technique was used to determine relative permeabilities for two-phase water/oil and gas/liquid systems. A strong hysteresis was observed in both wetting phase and nonwetting phase relative permeabilities. The endpoint relative permeability of oil was higher than the end-point relative permeability of water by two orders of magnitude in two-phase water/oil experiments. Similar end-point relative permeability ratio was observed in two-phase liquid/gas experiments. Using the determined relative permeabilities for two-phase flows, Stone's first and second model and Baker's interpolation model were used to predict the fluid production in the three-phase flow. Despite showing a satisfactory prediction for liquid production, all models showed a significant deviation for produced gas at the early stages of the three-phase flow experiment.

AN ANALYTICAL MODEL FOR TWO-PHASE RELATIVE PERMEABILITY WITH JAMIN EFFECT IN POROUS MEDIA

Jamin effect, which is a capillary pressure obstructing the drop/bubble flow through the narrow throat, has an important effect on the multiphase flow in the low permeability reservoir porous media. In this work, a novel model for the relative permeability with Jamin effect is developed to study the two-phase flow through porous media based on the fractal theory. The proposed relative permeability is expressed as a function of the applied pressure difference, shape parameters of the drop/bubble, the physical parameters of the wetting and nonwetting fluids, and microstructural parameters of porous media. Good agreement between model predictions and available experimental data is obtained, and the advantage of the present fractal model can be highlighted by comparisons with the empirical model predictions. Additionally, the influences of Jamin effect on the two-phase relative permeability are discussed comprehensively and in detail. The model reveals that the length ratios ([Formula: see text] and [Formula: see text]) have significant effects on the relative permeabilities. It is also found that the nonwetting phase relative permeability strongly depends on the interfacial tension, applied pressure difference, viscosity ratio and porosity of porous media at the lower wetting phase saturation. Furthermore, the fractal model will shed light on the two-phase transport mechanism of the low permeability reservoir porous media.

The study of relative permeability and residual gas saturation at high pressures and high temperatures

This paper presents the results of laboratory investigation conducted with reservoir rock plugs recovered from the Gas reservoir in the North West Shelf of Western Australia. The experiments were conducted in reservoir conditions (High Pressure (HP = 41.37 MPa) and High Temperature (HT = 433.15 K)). The aim of this study was to determine residual gas saturation and quantify the effect of reservoir conditions (HP/HT) on gas-brine relative permeability. The experimental data have been analysed using relative permeability concept. Both wetting and nonwetting phase relative permeability were generated using explicit methods, i.e, Hasslar and Corey model (Power Model). The power model is then used to match experimental data through modifying the parameters of the Corey correlation. Several core plugs were used by this study representing different reservoir quality rocks in the reservoir. The core plugs were in different dimensions, the short core plugs measured around 5 cm in length while the long core plug measured 19.41 cm. The aim of using longer core plugs was to minimise the effect of capillarity and end-effects on the relative permeability measurements. Since permeability measurement under the test conditions depends on pressure drop across the core plugs. Cited as : Sidiq, H., Amin, B., Kennaird, T. The study of relative permeability and residual gas saturation at high pressures and high temperatures. Advances in Geo-Energy Research, 2017, 1(1): 64-68, doi: 10.26804/ager.2017.01.06

Modeling wetting-phase relative permeability hysteresis based on subphase evolution

A recently introduced subphase framework for modeling the nonwetting phase relative permeability is extended to the wetting phase. Within this framework, the wetting phase is divided into four subphases, which are distinguished by their connectivity; backbone, dendritic, isolated and corner-film subphases. The subphase saturations evolve according to inter-subphase volume transfer terms, which require modeling. An advantage of distinguishing the subphases is that wetting phase relative permeability relations as functions of these constituent subphases can be developed. In order to develop models for the inter-subphase volume transfer and the wetting phase relative permeability in a strongly wetted system, quasi-static flow simulations in pore networks were conducted to analyze the evolution of the wetting subphases during drainage and imbibition. The simulation results suggest that hysteresis trends apparent in experimentally obtained wetting phase relative permeability curves for Berea sandstone may be explained by accounting for corner-film flow.

Relative permeability of two immiscible fluids flowing through porous media determined by lattice Boltzmann method

This article applied the multiple relaxation time multicomponent/multiphase pseudopotential lattice Boltzmann model to simulate two immiscible fluids flow in 2D porous media, and analyzed the effects of capillary number (Ca), viscosity ratio (M) and wettability on the relative permeability curves. Simulation results indicate that the nonwetting phase (NWP) relative permeability increases with increasing Ca; while the effect of Ca on the wetting phase (WP) relative permeability depends on the wettability. When M>1, the NWP relative permeability increase with increasing M in a strong wetting condition because of the lubricating effect. The amplitude of the NWP relative permeability may even exceed the single phase permeability. However, the exact value of the amplitude and where it occurs depends on M and the structure of the porous media. The WP relative permeability is insensitive to M. When the porous media converts from strong wetting condition to neutral wetting condition, the NWP relative permeability decreases while the WP relative permeability increases.

Pore-Scale Characterization of Two-Phase Flow Using Integral Geometry

The pore-scale morphological description of two-phase flow is fundamental to the understanding of relative permeability. In this effort, we visualize multiphase flow during core flooding experiments using X-ray microcomputed tomography. Resulting phase morphologies are quantified using Minkowski Functionals and relative permeability is measured using an image-based method where lattice Boltzmann simulations are conducted on connected phases from pore-scale images. A capillary drainage transform is also employed on the imaged rock structure, which provides reasonable results for image-based relative permeability measurements even though it provides pore-scale morphologies for the wetting phase that are not comparable to the experimental data. For the experimental data, there is a strong correlation between non-wetting phase Euler characteristic and relative permeability, whereas there is a weak correlation for the wetting phase topology. The relative permeability of some rock types is found to be more sensitive to topological changes than others, demonstrating the influence that phase connectivity has on two-phase flow. We demonstrate the influence that phase morphology has on relative permeability and provide insight into phase topological changes that occur during multiphase flow.

Pore-scale multiphase flow modeling and imaging of CO2 exsolution in Sandstone

This study utilizes synchrotron X-ray micro-tomography and pore scale modeling to investigate the process of gas exsolution and how it affects non-wetting phase relative permeability. Exsolved gas distributions are measured on Domengine and Boise sandstone samples using synchrotron X-ray micro-tomography. Observed gas phase distributions are compared to a new model that simulates the growth and distribution of exsolved gas phase at the pore-scale. Water relative permeability curves are calculated using a Stokes flow simulator with modeled and observed gas distributions, under various conditions, such as rock geometry, and pressure depletion rates. By comparing the actual bubble distributions with modeled distributions, we conclude that exsolved gas is more likely to form and accumulate at locations with higher water velocities. This suggests that convective delivery of CO2 to the gas bubble is a primary mechanism for bubble growth, as compared to diffusive transport through the aqueous phase. For carbonated brine flowing up a fault at half a meter per day, with 5% exsolved gas, the water relative permeability is estimated to be 0.6∼0.8 for various sandstones. The reduction of water mobility reduces upward brine migration when even a small amount of exsolution occurs.

Experimental Investigation of Stress-Dependency of Relative Permeability in Rock Fractures

This study investigates the stress-dependency of relative permeability in rock fractures. Previous studies provide contradictory evidence of the influence of increasing stress on the relative permeability of fractures. Some studies suggest that irreducible water saturation increases, while others show the reverse. In an attempt to resolve these differences, laboratory core flooding experiments are applied to measure the relative permeability of nitrogen–water mixtures in a fracture under various states of effective stress. Simultaneous X-ray CT measurements are made of aperture and water saturation distributions in the fracture. Two effective stress levels, 2.07 and 5.52 MPa, are applied to investigate the stress-dependency. For both states of stress, the measurements show that the relative permeability to gas is very low until a critical saturation is reached. As gas saturation increases beyond the critical value, relative permeability to gas increases quickly while water becomes essentially immobile. Results also demonstrate that increasing stress lowers the irreducible water saturation and the end-point non-wetting phase relative permeability when the experiments are conducted at the same flow rate. Using invasion percolation theory with the fracture aperture maps made at the two different effective stresses, capillary pressure curves are calculated and used to explain changes in phase interference at different stress levels. Finally, the preferential flow paths are analyzed at both stress levels. We use this analysis to reconcile flow regimes observed in earlier studies, and conclude that the differences between them can be explained by the relative importance of viscous and capillary forces. Specifically, if the experiments are designed to keep the capillary number constant, the irreducible water saturation increases with increasing confining stress. If the experiments are conducted at the same flow rate, higher confining stress decreases the irreducible water saturation, as was observed in these experiments. The analysis and data presented here also suggest that small increases in the water saturation of a fracture may dramatically reduce gas flow rates. This may present an additional and unexplored explanation for rapid production decline of gas wells in fractured reservoirs.

Application of continuum percolation theory for modeling single- and two-phase characteristics of anisotropic carbon paper gas diffusion layers

Percolation theory is used to model intrinsic and relative permeabilities as well as tortuosity in anisotropic carbon paper gas diffusion layers (GDL) and compared with existing results from lattice-Boltzmann (LB) simulations and experimental measurements. Although single- and two-phase characteristics of the carbon paper GDL are mainly affected by medium geometrical and topological properties, e.g., pore-size distribution, connectivity, and pore geometry, analyzing capillary pressure curves implies that the pore-size distribution of the carbon paper GDL is very narrow. This suggests that its effect on tortuosity and wetting- and nonwetting-phase relative permeabilities is trivial. However, integrated effects of pore geometry, surface area, connectivity, and tortuosity on intrinsic permeability might be substantial. Universal power laws from percolation theory predict the tortuosity-porosity and relative permeability–saturation curves accurately, indicating both characteristics not affected by the pore-size distribution. The permeability–porosity relationship, however, conforms to nonuniversality.

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.

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.

Effective parameterizations of three nonwetting phase relative permeability models

AbstractDescribing convective nonwetting phase flow in unsaturated porous media requires knowledge of the nonwetting phase relative permeability. This study was conducted to formulate and derive a generalized expression for the nonwetting phase relative permeability via combining with the Kosugi water retention function. This generalized formulation is then used to flexibly investigate the Burdine, Mualem, and Alexander and Skaggs models' prediction accuracy for relative nonwetting phase permeability. The model and data comparison results show that these three permeability models, if used in their original form, but applied to the nonwetting phase, could not predict the experimental data well. The optimum pore tortuosity and connectivity value is thus obtained for the improved prediction of relative nonwetting phase permeability. As a result, the effective parameterization of ( ) parameters in the modified Burdine, modified Mualem, and modified Alexander and Skaggs permeability models were found to be (2.5, 2, 1), (2, 1, 2), and (2.5, 1, 1), respectively. These three suggested models display the highest accuracy among the nine relative permeability models investigated in this study. However, the corresponding discontinuous nonwetting phase and the liquid film flow should be accounted for in future for the improved prediction of nonwetting phase relative permeability at very high and very low water saturation range, respectively.