Relative Permeability Curves Research Articles

Pore-scale modeling of wettability alteration coupled two-phase flow in carbonate porous media

The Middle East marine carbonate reservoirs are the primary targets for global crude oil exploration and production. In contrast to the clastic rock reservoirs, the marine carbonate reservoirs have undergone more complicated deposition, diagenesis and transformation, and the rock surface tends to be oil-wet or mixed-wet. One of the most effective methods for enhancing oil recovery in marine carbonate reservoirs is the use of an ion matched (IM)-surfactant (S) system to alter the wettability of rock surfaces. In this paper, we propose a microscale mathematical model of wettability alteration-coupled fluid flow by considering oil–water two-phase flow, wettability alteration, solute advection- diffusion and surfactant adsorption. The proposed microscale mathematical model is solved using the multi-component lattice Boltzmann model, and its accuracy is further verified. Finally, the effects of displacing fluid, ion-matched water concentration and surfactant concentration on oil mobilization at pore-scale are studied. Results show that, ion-matched water has a positive effect on wettability alteration, and typically shifts the cross-point of oil–water relative permeability curve to the right. The concentration of ion-matched water primarily affects fluid morphology of the wetting-phase and has little effect on phase permeability. After adding surfactant to the ion-matched water, the Euler coefficient of oil-phase gradually increases as the displacement continues, a large amount of remaining oil is gradually dispersed into scattered oil droplets and the oil-phase relative permeability is further improved.

Characterization and Inversion Method of Relative Permeability of Emulsion Flooding.

Relative permeability curves are one of the crucial factors that control the behavior of multiphase flow in petroleum reservoirs. Accurate prediction of the relative permeability curve involving emulsification and emulsion transport in emulsion flooding is vital to enhancing heavy oil recovery. In this study, a relative permeability characterization model including the emulsification mechanism and emulsion transport is developed, in which residual oil saturation and end-point permeability for water are parametrized as functions of emulsion concentration and capillary number. Based on the built characterization model, an inversion method (ensemble Kalman filter) is used to estimate the relative permeability curves of emulsion flooding. The inversion results of four sets of emulsion flooding experiments show that the errors of end points between the Johnson-Bossler-Neumann method and inversion method are less than 10%. For the continuous emulsification process in the in situ emulsion flooding tests, the inversed relative permeability curves shift between the upper and the inferior limits of the permeability. The error of residual oil saturation between the inversion and the experiment is less than 10%. In summary, this study demonstrates the feasibility of using the characterization model and inversion method to infer the relative permeability curves of emulsion flooding, which can aid in the predictions of multiphase flow in heavy oil reservoirs.

Strong effect of often-overlooked initial spilled oil distribution on subsequent soil remediation: A pore-scale perspective

The removal of spilled oil within soil by water injection is essentially an immiscible fluid displacement process. Numerous studies have been conducted to investigate the way to achieve a higher displacement efficiency. However, these studies often assumed that the pore space was initially saturated by oil only, ignoring the effect of initial oil distribution on the remediation, which led to incorrectly computed flow field and biased analysis. This work aimed to reveal the effect of initial oil distribution on flow physics during the remediation. Based on a pore-scale model and the phase-field method, the spilled oil invasion and remediation in a heterogeneous porous media were investigated, and the dynamic evolution of the phase interface was examined in particular. Four different distribution patterns of spilled oil were obtained through various velocities during the oil invasion stage, which were considered as initial states for the subsequent remediation stage. The results showed that ignoring the oil invasion process led to a more than 10% reduction in the ultimate remediation efficiency. However, the maximum interfacial area of fluids was larger and the obtained relative permeability curve was much smoother for the scenario considering the oil invasion. Besides, a higher initial water saturation led to a lower starting pressure. This work provided new pore-scale insights into the often-overlooked roles of initial phase distribution in fluid dynamics behind the remediation of oil-contaminated soil by water injection, which was of fundamental importance to the development of effective response strategy for soil contamination.

A prediction method of oil recovery for hot water chemical flooding in heavy oil reservoirs: Semi-analytical stream tube model

Abstract Chemical agents (polymer and surfactant) assisted hot water flooding is an effective means of enhancing oil recovery in heterogeneous and heavy oil reservoirs. The rapid prediction of oil recovery through hot water chemical flooding is very important. The stream tube model is a fast analytical method for predicting water flooding recovery, but it is not suitable for hot water chemical flooding. In this paper, a permeability distribution model for multi-stream tubes is established based on permeability variation coefficient using normal distribution function for reservoir heterogeneity, Using GOMPERTZ growth function model to characterize the changes in stream tube temperature, polymer viscosity, and surfactant concentration with injection volume, Using Brooks-Corey model to describe the influence of interfacial tension and temperature on the relative permeability curve. Finally, an analytical stream tube model for hot water chemical flooding of heavy oil reservoirs was established. The time discrete method is used to solve the model, then the graphs of the relationship between oil recovery and water cut are obtained. Compared with numerical simulation methods, the prediction error of oil recovery is less than 2%, and the calculation time is reduced by 89%. This model has been successfully applied to X oilfield. Based on historical fitting, it is predicted that hot water chemical flooding can enhance oil recovery by 6.3% compared to water flooding. This paper provides a fast calculation method for predicting and evaluating the effectiveness of hot water chemical flooding in heavy oil reservoirs.

Evaluation of CO2/Water Imbibition Relative Permeability Curves in Sandstone Core Flooding—A CFD Study

Greenhouse gases such as CO2 can be safely captured and stored in geologic formations, which in turn can reduce the carbon imprint in the Earth’s atmosphere and therefore help toward reducing global warming. The relative permeability characteristics in CO2/brine or CO2/water systems provide insight into the CO2 trapping efficacy of formations such as sandstone rocks. In this research, CO2/water imbibition relative permeability characteristics in a typical sandstone core sample are numerically evaluated. This work uses transient computational fluid dynamics (CFD) simulations to study relative permeability characteristics, and a sensitivity analysis is performed based on two different injection pressures and absolute permeability values of the sandstone rock material. Results show that when the irreducible water fraction remains unchanged, the imbibition relative permeability to the non-wetting phase decreases with an increase in injection pressure within the sandstone core sample. Also, with the irreducible water fraction being unchanged, relative permeabilities to both non-wetting and wetting phases decrease with an increase in the absolute permeability of the rock material. Finally, at irreducible water saturation, relative permeability to the gas phase decreases with an increase in injection pressure.

A New model of gas-water two-phase seepage based on Newton's law of motion

The pore throat size, structure distribution, and lithology of porous media in gas reservoirs are varied, and the gas-water two-phase seepage law is complex, making it difficult to describe the seepage model. Newton's law of motion is a basic law of motion in classical mechanics, and its application in gas-water two-phase seepage modeling is an innovative practice of classical mechanics in seepage mechanics systems. Based on Newton's three laws of motion, a gas-water two-phase seepage model was established from the force analysis of fluid, and the relationship between velocity and pressure difference, pipe radius, water film thickness, viscosity, etc. was derived under the condition that the model reached a stable state, i.e., force balance. The relationship is referred to as the steady-state model. Subsequently. the equivalent permeability representation model was derived based on the steady-state model to calculate the permeability of rock samples with different channel distribution characteristics. The results were consistent with the measured values, and there is a good correspondence between channel distribution characteristics and permeability. The relative permeability calculation method was established based on the steady-state model and capillary pressure curve. The obtained relative permeability curve aligned with the two-phase seepage law and coincides with the relative permeability curve obtained by Poiseuille's law. Finally, a new productivity equation was derived based on the steady-state model, and the Inflow Performance Relationship (IPR) curve calculated by the gas well example was consistent with the traditional equation. The research results were based on the force analysis of fluid in porous media and fundamentally explored the law of fluid flow. The derived seepage model can be used to calculate reservoir permeability, the gas-water relative permeability curve, and gas well productivity analysis and to effectively guide gas reservoir development. The study was a successful application of the basic theory of mechanics in gas-water two-phase seepage in gas reservoirs.

Reservoir numerical simulation method considering time-varying relative permeability during polymer flooding process

Abstract In response to the abnormal decline in liquid production capacity during the middle and later stages of chemical flooding in Chinese offshore oil fields, in-depth analysis was conducted using reservoir engineering, dynamic analysis, and reservoir simulation methods. Because of the viscoelasticity of polymer solution, the relative permeability curve of oil/water during polymer flooding is different from that during water flooding, including the minimum mobile water saturation and residual oil saturation. In this study, an interpolation coefficient ‘f’ related to polymer solution concentration was firstly proposed for simplicity. Then, reservoir numerical simulation with the self-developed simulator ‘SIMFAST’ were conducted to investigate the influence of the interpolation coefficient ‘f’ on the injector and producer performance and the applications in actual field production history matching. The results indicated that compared with the commercial simulators, the self-developed simulator with the interpolation factor could more reliably describe the characteristic of the injected polymer solution in controlling water cut rise, and more efficiently simplify the combination of parameters on relative permeability curves during polymer flooding in offshore oilfields. Finally, above reservoir simulation method considering the change of the relative permeability curves during chemical flooding, was successfully conducted in the production history matching in J oilfield in Bohai Bay China, in terms of oil rate & water cut parameters. The research results give an efficient method to investigate the fluid seepage behaviour variation and its influence on oil rate and water cut during polymer flooding in China offshore reservoirs, which offers very useful technical support for the accurate design of chemical flooding schemes.

A pore-scale investigation of viscous coupling effect on immiscible two-phase flow in porous media

Viscous coupling effect plays a significant role in immiscible two-phase flow within porous media, while its influence on relative permeability remains uncertain. In this paper, an improved MRT-based viscosity-modified multicomponent multiphase (MCMP) pseudopotential lattice Boltzmann model, capable of handling high viscosity ratio, is employed to simulate two-phase flow with different viscosities in a cross-array circular structure and a real rock structure, respectively. The applicability of this model for two-phase flow with various viscosity ratios has been verified by some typical tests. Systematically, the effects of viscosity ratio, structural configuration, and wetting condition on the relative permeability curves are investigated in conjunction with their component distributions and velocity fields at different two-phase saturations. These results indicate that due to the two-phase flow competition under different structural conditions, the viscous coupling effect has varying degrees of impacts on the mobility of thin phase and viscous phase. Further, the mechanism of two-phase lubricating effect is also discussed under different wetting conditions at Darcy flow regime.

Enhancing Oil Recovery in Eagle Ford Shale: A Multiscale Simulation Study of Surfactant Huff ’n’ Puff Methodology

In this paper, we present a simulation case study of a surfactant huff ’n’ puff pilot in the black oil window of the Eagle Ford (EF) Shale. The target horizontal well, which had been depleted for nearly 8 years, underwent stimulation via a surfactant huff ’n’ puff treatment. The surfactant was selected through laboratory screening using reservoir rock and fluid samples. After a 17-hour injection and a 1-month shut-in period, the well’s production increased fivefold from the baseline oil rate, sustaining incremental oil production for at least 2 years. The surfactant enhances oil recovery by altering rock wettability toward a more water-wet state and moderating oil/water interfacial tension (IFT). This process is modeled by surfactant adsorption in the simulator, indicating the degree of dynamic changes in relative permeability (krl) and capillary pressure (Pc) curves. We propose a comprehensive workflow comprising three stages: development of core-scale and field-scale models, sequential model calibrations, and multiobjective optimization to integrate laboratory measurements and field data from this pilot into multiscale numerical simulations. By matching oil recoveries from imbibition experiments on the core model and field production histories on the field model, krl and Pc profiles of two extreme states, basic reservoir properties, and additional reservoir properties altered during huff ’n’ puff operations are characterized. The matched core model reproduces a 15.1% incremental oil recovery for surfactant-assisted spontaneous imbibition (SASI) process relative to pure brine imbibition process. The matched reservoir model predicts the surfactant huff ’n’ puff treatment increases the oil production by 21.9% relative to water huff ’n’ puff treatment and by 52.9% relative to primary depletion for a 4-year period. The calibrated reservoir model also serves as a base case for optimizing well operation schedules through the implementation of a multiobjective genetic algorithm. The surfactant injection rate, injection time, and well shut-in time of the base case are varied to achieve higher oil production and reduced surfactant usage. Statistical analysis of eight trade-off cases indicates that optimal well operations, compared with existing practices, frequently involve increased injection rates [16.6–18.9 barrels per minute (bpm)], shorter injection periods (10–11.3 hours), and prolonged shut-indurations (49–65 days). This workflow offers valuable insights into surfactant huff ’n’ puff treatments for unconventional reservoirs, thereby facilitating the optimization of well operations and maximizing tertiary oil recovery.

Unsteady-State Relative Permeability Curves Derived From Saturation Data and Partial Derivatives Using Magnetic Resonance Imaging

Unsteady-State Relative Permeability Curves Derived From Saturation Data and Partial Derivatives Using Magnetic Resonance Imaging

Investigation of smoothed particle hydrodynamics (SPH) method for modeling of two-phase flow through porous medium: application for drainage and imbibition processes

The drainage and imbibition processes are critical mechanisms in petroleum engineering. These processes in a porous medium are controlled by surface forces and pressure gradients. The study of these processes in the pore scale by common simulators always has limitations in multiphase flow modeling. Also, obtaining relative permeability curves through laboratory analysis requires expensive equipment. Additionally, these laboratory experiments are quite expensive and may introduce significant uncertainties. For this purpose, this study investigated the creation of relative permeability curves and their effect on oil production. Initially, single-phase fluid and two-phase droplet flow within a fracture with both soft and rough surfaces were utilized to validate the formulation of the Smoothed Particle Hydrodynamics (SPH) method. Then, by using three randomly constructed porous medium models, the imbibition and drainage processes have been studied. Finally, sensitivity study has been carried out on critical parameters related to fluid flow dynamics in the porous environment, including pressure changes, wettability, and heterogeneity in drainage and imbibition processes. The simulation results were consistent with current theories; therefore, it is reasonable to consider SPH to characterize the fluid flow dynamic during the drainage and imbibition processes. According to sensitivity studies, pressure gradient (residual saturation of displaced fluid is about 5.65% and 8.44%) and heterogeneity (the residual saturation of the displaced fluid was 4.04% and 2.98%) have the largest impact on flow modeling in both drainage and imbibition processes and wettability (the residual saturation became 36.62% and 5.12%) has significant effect on the drainage process through porous medium. In general, fluid flow dynamic studies can be performed using the SPH method to model fluid flow in simple and complex porous medium under various flow conditions. The SPH method can also be used as an applicable tool to investigate the hydrocarbon fluids flow within larger geometries in the future.

Effects of Externally Applied Stress on Multiphase Flow Characteristics in Naturally Fractured Tight Reservoirs

Externally applied stress on the rock matrix plays a crucial role in oil recovery from naturally fractured tight reservoirs, as local variations in pore pressure and in-situ tension are expected. The published literature severely lacks in evaluations of the characteristics of hydrocarbons, displaced by water, in fractured reservoirs under the action of externally applied stress. This study intends to overcome this knowledge gap by resolving complex time- and stress-dependent multiphase flow by employing a coupled Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) solver. Extensive three-dimensional numerical investigations have been carried out to estimate the effects of externally applied stress on the multiphase flow characteristics at the fracture–matrix interface by adding a viscous loss term to the momentum conservation equations. The well-validated numerical predictions show that as the stress loading increases, the porosity and permeability of the rock matrix and capillary pressure at the fracture–matrix interface decrease. Specifically, matrix porosity decreases by 0.13% and permeability reduces by 1.3% as stress increases 1.5-fold. Additionally, stress loading causes a decrease in fracture permeability by up to 29%. The fracture–matrix interface becomes more water-soaked as the stress loading on the rock matrix increases, and thus, the relative permeability curves shift to the right.

Sub-core permeability estimation from coreflooding experiments: Numerical analysis for evaluating accuracy and improving methods

Coreflooding experiments are one of the primary methods for reservoir rock characterization and have been developing in recent years, providing increasing detail. An advanced analysis of coreflooding experiments consists of constructing three dimensional permeability (k) maps of the core sample with sub-core resolution. Such detailed characterizations provide important information on the core heterogeneity and enable the construction of accurate numerical flow models that can reproduce experimental results. This work presents a method for estimating k, combining data from multiple coreflooding experiments, and studies the estimation accuracy considering a large number of test cases consisting of synthetic data obtained by numerical experiments. Cases include varying parameters, such as: fluid injection flow rates and types, relative permeability curves, capillary pressure functions and core heterogeneity. The new method is shown to significantly improve the estimation accuracy in comparison to methods that incorporate data only from a single experiment. Furthermore, a method for improving k estimations in regions where water is trapped is presented and its implementation is shown to increase the overall accuracy of k estimation. An additional method is considered, that requires only single-phase flow solutions, thus increasing the computational efficiency. However, it is shown to be applicable only for a small subset of cases.

The Time-Varying Characteristics of Relative Permeability in Oil Reservoirs with Gas Injection

Relative permeability is a critical parameter in reservoir numerical simulation and production prediction, intimately associated with reservoir architecture and fluid property. During gas injection development, substantial alterations in reservoir properties and fluid phase behavior induce dynamic changes in relative permeability. Clearly characterizing the time-varying features of relative permeability is very useful for an understanding of how gas injection influences fluid mobility within the reservoir and enhances recovery rates. In this paper, core displacement experiments are firstly conducted to obtain the characteristics of the relative permeability of oil and gas under various development stages and displacement conditions, further delineating the comprehensive shifts in reservoir properties at different gas injection stages. Subsequently, a novel reservoir numerical simulation method is proposed that considers the spatial and temporal segmentation of relative permeability curves in the reservoir simulation. Finally, a practical application is presented to clarify the effects of injection and production parameters on the development performance of gas flooding oil reservoirs. The results show the following: (i) Significant time-varying characteristics of relative permeability occur throughout gas injection development, in the early stages of gas injection, where most of the reservoir is at the gas injection front, and a rightward shift in relative oil and gas permeability indicates that gas injection promotes oil mobility. Conversely, in the later stages of gas injection, as the reservoir reaches the trailing edge of gas injection, the change trend in relative oil and gas permeability reverses, shifting leftward, thereby exacerbating the gas breakout phenomena. (ii) Increasing the rate of gas injection causes relative oil and gas permeability to move leftward, effectively enhancing the gas volume sweep coefficient and microscopic oil displacement efficiency at lower injection speeds while reducing development performance at higher injection speeds. (iii) An increase in gas injection pressure causes relative oil and gas permeability to shift rightward, and although it reduces residual oil saturation and enhances microscopic oil displacement efficiency, it also intensifies gas breakout phenomena and lowers the gas volume sweep coefficient. This paper provides theoretical guidance and technical support for the design of gas injection strategies, optimization of injection and production parameters, and production forecasting.

Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials

Abstract The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology.

Quantifying the Effect of Pore‐Size Dependent Wettability on Relative Permeability Using Capillary Bundle Model

AbstractRelative permeability is a key parameter for characterizing the multiphase flow dynamics in porous media at macroscopic scale while it can be significantly impacted by wettability. Recently, it has been reported in microfluidic experiments that wettability is dependent on the pore size (Van Rooijen et al., 2022). To investigate the effect of pore‐size‐dependent wettability on relative permeability, we propose a theoretical framework informed by digital core samples to quantify the deviation of relative permeability curves due to wettability change. We find that the significance of impact is highly dependent on two factors: (i) the function between contact angle and pore size (ii) overall pore size distribution. Under linear function, this impact can be significant for tight porous media with a maximum deviation of 1,000%.

Assessing the impact of geochemical mechanism and interpolation factor selection on the precision of low-salinity waterflooding modelling: a comparative study

ABSTRACT The efficacy of low salinity waterflooding (LSWF) as an enhanced oil recovery (EOR) method in carbonate formations has been well established; however, its geochemical modelling in such reservoirs remains insufficiently explored. This study aims to bridge this gap by conducting a comparative analysis of three well-recognised geochemical mechanisms including fines migration, rock dissolution/precipitation, and multi-ion exchange (MIE). Our research encompasses two parts: experimental and modelling. First, we conducted four coreflooding experiments to study the effect of LSWF on oil recovery in core scale as well as on rock wettability by measuring the contact angle of the crude oil-brine-rock system. In the next step, we created a one-dimensional compositional model in CMG-GEMTM for LSWF, validated it using the obtained experimental results, and compared the accuracy of the three geochemical mechanisms one-by-one. The results of the experimental section, confirm the positive effect of LSWF on oil recovery: 34.3% with seawater (40,000 ppm), 42.5% with LoSal-01 (10,000 ppm), 49.7% with LoSal-02 (5,000 ppm), and 60.9% with LoSal-03 (2,000 ppm). The experiments also show the wettability alteration through the reduction in the contact angle. Furthermore, the modelling results reveal that choosing MIE as the governing mechanism and sulphate concentration ([ S O 4 2 − ]) as the relevant interpolation factor (IF) leads to the most accurate LSWF model. After identifying the most accurate mechanism, we detected the wettability alteration in the model by showing the movement of oil and water relative permeability curves intersection point on the Kr-Sw diagram toward the right side.

Modeling alterations in relative permeability curves due to salinity using artificial neural networks

Modeling alterations in relative permeability curves due to salinity using artificial neural networks

Production optimization in a fractured carbonate reservoir with high producing GOR

The Gas-Oil Ratio (GOR) is a crucial production parameter in oil reservoirs. An increase in GOR results in higher gas production and lower oil production, potentially leading to well shut-ins due to economic infeasibility. This study focuses on a real fractured oil field that requires urgent production operations to reduce the producing GOR. In this study, the static model for the field was developed using commercial software, involving steps such as data collection, fault modeling, meshing, and statistical analysis to prepare for dynamic simulation. The dynamic model incorporates geometry, gridding, and rock properties from the static model, utilizing a dual-porosity approach for the naturally fractured reservoir and the Peng-Robinson equation for fluid phase behavior. Initial reservoir conditions, production history, and rock-fluid interactions were defined, with relative permeability curves indicating a water-wet reservoir and low critical gas saturation affecting the GOR. To better understand the relationship between reservoir and production parameters, a detailed sensitivity analysis was performed using the Response Surface Methodology (RSM). Following the sensitivity analysis, a history matching process was conducted using the Designed Exploration and Controlled Evolution (DECE) optimizer to validate the model for future forecasts. Six operational scenarios were defined to decrease the production GOR and enhance final recovery from the field. The results indicate that the water injection scenario is effective in preventing the GOR increase by maintaining reservoir pressure, thereby sustaining production over a longer period. This scenario also improves oil recovery by approximately 6% compared to the base case. Finally, optimization was carried out using the DECE optimizer for each scenario to fine-tune the operational parameters. The goal was to maximize oil revenue for each scenario during the optimization process. This study stands out as one of the few that provides a comprehensive analysis of production behavior and development planning for a real fractured reservoir with high producing GOR.

Experimental and numerical evaluation of relative permeability modifiers during water control in a tight gas reservoir

Relative permeability modifier (RPMs) is a water control technique that is implemented for enhancing gas recovery rates and prolonging well productive life during fracturing the tight gas reservoir. RPMs filtrate into formation for a certain depth along with the fracturing fluid to control water output by a “drag” effect on water phase only. To optimize RPM treatment, both experimental investigation and numerical simulation are used in this paper. In laboratory, transient core-flooding tests were conducted to investigate the water control performance of newly formulated polymer (RPM). The relative permeability of gas was corrected due to gas volume changes during displacement. The results showed that the selective water control effect of RPM by reducing water relative permeability dramatically with little impact on gas relative permeability. The RPM concentration was optimized as 0.01 %XSJ-14(A)+0.05 %XSJ-14(B) while injection volume as 5PV by comparison of relative permeability curves. A 2D fracture model of a tight gas model was built to compare the production before and after RPM treatment. The results of numerical simulation confirmed the different flow control effect of RPM on water and gas. A sensitivity analysis was conducted for the effect of fracture length, fracture conductivity, RPM filtration and RR value. The results indicate that there are limits of all the factor on RPM’s water control performance.