Multiphase Flow In Porous Media Research Articles

Stress-Dependent Pore Deformation Effects on Multiphase Flow Properties of Porous Media

Relative permeability and capillary pressure are the governing parameters that characterize multiphase fluid flow in porous media for diverse natural and industrial applications, including surface water infiltration into the ground, CO2 sequestration, and hydrocarbon enhanced recovery. Although the drastic effects of deformation of porous media on single-phase fluid flow have been well established, the stress dependency of flow in multiphase systems is not yet fully explored. Here, stress-dependent relative permeability and capillary pressure are studied in a water-wet carbonate specimen both analytically using fractal and poroelasticity theory and experimentally on the micro-scale and macro-scales by means of X-ray computed micro-tomography and isothermal isotropic triaxial core flooding cell, respectively. Our core flooding program using water/N2 phases shows a systematic decrease in the irreducible water saturation and gas relative permeability in response to an increase in effective stress. Intuitively, a leftward shift of the intersection point of water/gas relative permeability curves is interpreted as an increased affinity of the rock to the gas phase. Using a micro-scale proxy model, we identify a leftward shift in pore size distribution and closure of micro-channels to be responsible for the abovementioned observations. These findings prove the crucial impact of effective stress-induced pore deformation on multiphase flow properties of rock, which are missing from the current characterizations of multiphase flow mechanisms in porous media.

Vanishing artificial diffusion as a mechanism to accelerate convergence for multiphase porous media flow

Numerical solution of the equations governing multiphase porous media flow is challenging. A common approach to improve the performance of iterative non-linear solvers for these problems is to introduce artificial diffusion. Here, we present a mass conservative artificial diffusion that accelerates the non-linear solver but vanishes when the solution is converged. The vanishing artificial diffusion term is saturation dependent and is larger in regions of the solution domain where there are steep saturation gradients. The non-linear solver converges more slowly in these regions because of the highly non-linear nature of the solution. The new method provides accurate results while significantly reducing the number of iterations required by the non-linear solver. It is particularly valuable in reducing the computational cost of highly challenging numerical simulations, such as those where physical capillary pressure effects are dominant. Moreover, the method allows converged solutions to be obtained for Courant numbers that are at least two orders of magnitude larger than would otherwise be possible.

Comprehensive comparison of pore-scale models for multiphase flow in porous media

Multiphase flows in porous media are important in many natural and industrial processes. Pore-scale models for multiphase flows have seen rapid development in recent years and are becoming increasingly useful as predictive tools in both academic and industrial applications. However, quantitative comparisons between different pore-scale models, and between these models and experimental data, are lacking. Here, we perform an objective comparison of a variety of state-of-the-art pore-scale models, including lattice Boltzmann, stochastic rotation dynamics, volume-of-fluid, level-set, phase-field, and pore-network models. As the basis for this comparison, we use a dataset from recent microfluidic experiments with precisely controlled pore geometry and wettability conditions, which offers an unprecedented benchmarking opportunity. We compare the results of the 14 participating teams both qualitatively and quantitatively using several standard metrics, such as fractal dimension, finger width, and displacement efficiency. We find that no single method excels across all conditions and that thin films and corner flow present substantial modeling and computational challenges.

Numerical investigation of viscous flow instabilities in multiphase heterogeneous porous media

A critical aspect of multiphase flow in porous media is the displacement efficiency, which measures the amount of fluid that can be pushed by another fluid driven by pressure gradient. Migration of contaminants and reservoir waterflooding are typical applications where understanding the dynamics of immiscible fluid displacement helps mitigating water resources contamination and improving hydrocarbons production, respectively. Due to large viscosity ratios, flow instabilities at fluids’ interface may arise leading to the formation of fingers, i.e., uneven fronts with elongation at the outside edge of fluids interface with strong impact on the displacement efficiency. Initial studies of viscous instabilities indicated that the development of fingers mostly depends on mobility and capillary forces, however heterogeneity of the porous domain may also affect the onset of instabilities. Therefore, the main aim of this work is to numerically investigate formation and growth of viscous fingers in heterogeneous porous media. The model used here is based on a novel control volume finite element method (CVFEM) formulation with families of FE-pairs, PnDG-Pm and PnDG-PmDG, specially tailored for Darcean flows. Dynamic mesh adaptivity enables capturing fingers development whilst saving computational overheads. Numerical experiments were performed to investigate the impact of viscosity ratio and heterogeneity on Saffmann–Taylor instabilities. Numerical simulations demonstrated that the heterogeneity of the domain triggers the early-onset formation of fingers under prescribed viscosity ratio conditions. Also, effective numerical capture of growth (in particular tip-splitting) and coalescence of dendritic finger branching induced by large viscosity ratio largely depends on mesh resolution at the fluids interface.

Numerical Modeling and Simulation of Fully Coupled Processes of Reactive Multiphase Flow in Porous Media

Numerical Modeling and Simulation of Fully Coupled Processes of Reactive Multiphase Flow in Porous Media

Simulation of multi-component multi-phase fluid flow in two-dimensional anisotropic heterogeneous porous media using high-order control volume distributed methods

In this paper, flow of multi-component two-phase fluids in highly heterogeneous anisotropic two-dimensional porous media is studied using computational methods suitable for unstructured triangular and/or quadrilateral grids. The physical model accounts for miscibility and compressibility of fluids while gravity and capillary effects are neglected. The governing equations consist of a pressure equation together with a system of mass conservation equations. For solving pressure equation, a new method called Control Volume Distributed Finite Element Method (CVDFEM) is introduced which uses Control Volume Distributed (CVD) vertex-centered grids. It is shown that the proposed method is able to approximate the pressure field in highly anisotropic and heterogeneous porous media fairly accurately. Moreover the system of mass conservation equations is solved using various upwind and central schemes. These schemes are extended from one-dimensional to two-dimensional unstructured grids. Using a series of numerical test cases, comparison is made between different approaches for approximation of the hyperbolic flux function. Semi one-dimensional high-order data reconstruction procedures are employed to decrease stream-wise numerical diffusion. The results suggest that the Modified Dominant Wave (MDW) scheme outperforms other hyperbolic schemes studied in this paper from both accuracy and computational cost points of view.

A novel methodology for synthesizing the wetting capillary pressure curve of rocks through sorptivity data

Capillary pressure as a function of moisture content is an essential element in the modelling of multiphase flow in porous media, such as rocks. The constitutive relationship predicting the capillary pressure as a function of fluid saturation in these materials has been the focus of many studies in the literature, as the direct experimental determination of the former is usually time-consuming and not quite straightforward, owing to the topologically complicated pore structure of rocks. In this paper, we perform a systematic analysis of the interrelation between capillary pressure curves (CPC) and the corresponding imbibition curves to evaluate the parameters influencing the entire diffusive process. The aim is the reconstruction of the wetting CPC from sorptivity test data through back analysis, within the framework of the Van Genuchten model. We perform numerical simulations with finite elements, using as input synthetic models of CPC with one, two and three degrees of freedom, the latter being the widely accepted Van Genuchten model. The effectiveness and the limitations of the different models used and the sensitivity of the imbibition curves to each degree of freedom are investigated and critically evaluated. The whole investigation is assisted by theoretical estimations of the sorptivity coefficient, as a function of the model parameters and the measured quantities. The results of our analysis provide not only a clarification of the aforementioned interrelation, but also a relatively simple procedure for reconstructing synthetically the wetting CPC.

An extension of Darcy’s law incorporating dynamic length scales

We propose a physics-based, macroscale formulation of multiphase porous-media flows that both honors the validity of Darcy’s law in steady or near-steady flows and accommodates the effects of heterogeneities and nonlinearities in unsteady flows. The new formulation recognizes that parameters characterizing the system operate at different length-scales. In particular, the use of Darcy’s law, predicated on the assumption of near-steady flows, requires dynamic length scales, owing to the possibility of rapid fluctuations in rock properties and fluid saturations attributable to heterogeneity and nonlinearity. We accommodate these dynamic length-scales through dynamic spatial averaging. The length and position of the averaging window are characterized by the length of the mixing zone and the direction of propagation of information in the transport process. We validate the proposed formulation by comparing highly accurate, two-dimensional numerical solutions against core-scale displacement experiments. The proposed paradigm is consistent with the classical multiphase Darcy formulation, in the sense that the latter also represents the results of an averaging approach.

Comprehensive study of the interactions between the critical dimensionless numbers associated with multiphase flow in 3D porous media

Multiphase flow in porous media is of great interest in many engineering applications, such as geologic carbon sequestration, enhanced oil recovery, and groundwater contamination and remediation. In order to advance the fundamental understanding of multiphase flow in complex three-dimensional (3D) porous media, the interactions between the critical dimensionless numbers, including the contact angle, viscosity ratio, and capillary (Ca) number, were investigated using X-ray micro-computed tomography (micro-CT) scanning and lattice Boltzmann (LB) modeling. In this study, the 3D pore structure information was extracted from micro-CT images and then used as interior boundary conditions of flow modeling in a pore-scale LB simulator to simulate multiphase flow within the pore space. A Berea sandstone sample was scanned and then two-phase flow LB simulations were performed based on the micro-CT images. The LB-simulated water/CO2 distributions agreed well with the micro-CT scanned images. Simulation results showed that a decreasing contact angle causes a decrease in wetting-fluid relative permeability and an increase in non-wetting fluid relative permeability. A rising Ca number increases both wetting and non-wetting fluid relative permeabilities. An increasing viscosity ratio (the ratio of non-wetting fluid viscosity to wetting fluid viscosity) facilitates the increase of non-wetting fluid relative permeability and mitigates the reduction of wetting fluid relative permeability, when the contact angle decreases continuously. The primary novel finding of this study is that the viscosity ratio affects the rate of change of the relative permeability curves for both phases when the contact angle changes continuously. To the best of our knowledge, it is the first time that comprehensive interactions between these dimensionless numbers are demonstrated in a sandstone sample based on real 3D structures. We also investigated the role of the changes of flow direction and sample location on relative permeability curves. Simulation results showed that the change in non-wetting fluid relative permeability was larger when the flow direction was switched from vertical to horizontal, which indicated that there was stronger anisotropy in larger pore networks that were primarily occupied by the non-wetting fluid.

Multiphase Flow Under Heterogeneous Wettability Conditions Studied by Special Core Analysis and Pore-Scale Imaging

Summary Wettability is a major factor that influences multiphase flow in porous media. Numerous experimental studies have reported wettability effects on relative permeability. Laboratory determination for the impact of wettability on relative permeability continues to be a challenge because of difficulties with quantifying wettability alteration, correcting for capillary-end effect, and observing pore-scale flow regimes during core-scale experiments. Herein, we studied the impact of wettability alteration on relative permeability by integrating laboratory steady-state experiments with in-situ high-resolution imaging. We characterized wettability alteration at the core scale by conventional laboratory methods and used history matching for relative permeability determination to account for capillary-end effect. We found that because of wettability alteration from water-wet to mixed-wet conditions, oil relative permeability decreased while water relative permeability slightly increased. For the mixed-wet condition, the pore-scale data demonstrated that the interaction of viscous and capillary forces resulted in viscous-dominated flow, whereby nonwetting phase was able to flow through the smaller regions of the pore space. Overall, this study demonstrates how special-core-analysis (SCAL) techniques can be coupled with pore-scale imaging to provide further insights on pore-scale flow regimes during dynamic coreflooding experiments.

Disorder characterization of porous media and its effect on fluid displacement

Depending on topology of pore space, different patterns of multiphase flow in porous media are observed. By analyzing pore-scale mechanisms, a phase diagram is constructed showing that wettability and structural disorder collectively affect displacement efficiency and fluid-fluid interfacial area.

Coupled Processes in Charged Porous Media: From Theory to Applications

Charged porous media are pervasive, and modeling such systems is mathematically and computationally challenging due to the highly coupled hydrodynamic and electrochemical interactions caused by the presence of charged solid surfaces, ions in the fluid, and chemical reactions between the ions in the fluid and the solid surface. In addition to the microscopic physics, applied external potentials, such as hydrodynamic, electrical, and chemical potential gradients, control the macroscopic dynamics of the system. This paper aims to give fresh overview of modeling pore-scale and Darcy-scale coupled processes for different applications. At the microscale, fundamental microscopic concepts and corresponding mass and momentum balance equations for charged porous media are presented. Given the highly coupled nonlinear physiochemical processes in charged porous media as well as the huge discrepancy in length scales of these physiochemical phenomena versus the application, numerical simulation of these processes at the Darcy scale is even more challenging than the direct pore-scale simulation of multiphase flow in porous media. Thus, upscaling the microscopic processes up to the Darcy scale is essential and highly required for large-scale applications. Hence, we provide and discuss Darcy-scale porous medium theories obtained using the hybrid mixture theory and homogenization along with their corresponding assumptions. Then, application of these theoretical developments in clays, batteries, enhanced oil recovery, and biological systems is discussed.

Characterization of two-phase flow in porous media using global mobility

Abstract Proper characterization of multi-phase flow in porous media is of significant importance in selecting and optimizing the performance of a given oil reservoir. The main factors influencing the characterization of multi-phase flow in porous media include: microscopic pore structure, movable fluid saturation, nonlinear seepage characteristics and clay minerals composition, and etc. However, it is very difficult to quantitatively study the multi-phase flow process in porous media, because there is no clear relationship between the oil production rate and the physical parameters of oil reservoir, particularly in low permeability reservoirs. Furthermore, on-going research activities has led to the discovery that it has been a challenge to tell why two oil reservoirs with the same degree of permeability (i.e. low permeability) have far different production performances. In an attempt to comprehend this challenge, a concept of global mobility by Li and Horne (2005, 2006) derived from the Li-Horne model was proved to be a new approach for evaluating the seepage capacity in imbibition system, because it can unify oil and water phase mobility into one model and take many static and dynamic physical parameters into accounts. In this paper, the global mobility concept is applied and verified to characterize the mobility of a multi-phase flow and evaluate the production performance from core to field scale. Comparisons between the global mobility concept and other characterization methods were conducted based on various flooding experiments and field data tests from rock/oil/water systems and rock/oil/polymer systems with different porosities and permeabilities. The results showed that there is a linear relationship between the global mobility and the production performance which is better than the other methods, and the application range of the global mobility was extended. In addition, a convenient and empirical approach was proposed to obtain the global mobility with relative permeability data. Its feasibility has been preliminarily proved through five case studies, and the demonstration is that the global mobility could be an effective parameter to characterize a two-phase flow in porous media and evaluate the production performance for field application.

Effect of desiccation on shut-in benefits in removing water blockage in tight water-wet cores

Water blockage is a type of formation damage that occurs because of capillary discontinuity at the interface between high-capillarity matrix and low-capillarity fracture. This water blockage causes a reduction in oil relative permeability and the need for higher drawdown to allow flowback after hydraulic fracturing. To remove this blockage, shut-in is believed to be effective because it dissipates the water blockage from the matrix-fracture interface deeper into the matrix through capillary imbibition.However, field data demonstrates mixed results – Some field data report shut-in as beneficial, whereas others detrimental. This paper investigates desiccation as one of the main reasons for the mixed shut-in implications. From the perspective of multiphase flow in porous media, our history-matched core-scale model reveals that shut-in can offer some benefits in desiccated water-wet cores but cause further damage in non-desiccated ones. Regardless of the desiccation, our simulation results show that immediate flowback can help ensure high oil relative permeability and remove the trapped water at the matrix-fracture interface more quickly. In a desiccated core, both immediate flowback and shut-in result in the same maximum regained oil relative permeability; however, in a non-desiccated core, immediate flowback results in a higher maximum regained oil relative permeability than shut-in.

Laboratory study of oscillatory multiphase flow in porous medium with chemically active skeleton

A laboratory study is conducted of high-viscosity mineral oil displacement by an acid solution in a synthetic porous medium with a chemically active skeleton. The skeleton is made of a mixture of glass balls and particles of sodium bicarbonate. The displacement is driven by the pressure difference between the inlet and outlet sides of the working cell and is accompanied by a gas-producing chemical reaction. The study is focused on the self-oscillating mode of the reaction wave propagation. This mode manifests itself in the appearance of periodically generated secondary waves and is accompanied by pressure oscillations. The experiments show that the amplitude of the pressure oscillations at the reaction front is directly proportional to the driving pressure difference, and that the frequency of the oscillations does not depend on it.

Steady-State Relative Permeability Measurements of Tight and Shale Rocks Considering Capillary End Effect

Relative permeability (kr) data are the key factors for describing the behaviour of the multi-phase flow in porous media. During the kr measurements of low-permeability rocks, high capillary pressure can cause a significant liquid hold-up at the core outlet. This liquid hold-up, which is known as capillary end effect (CEE), is the main difficulty for laboratory measurements of relative permeability (kr) for tight and shale rocks. In this paper, a novel method is proposed to correct the CEE during the steady-state relative permeability (SS-kr) measurements. The integrity of the proposed method is evaluated by a set of artificially generated data and the experimental SS-kr data of an Eagle Ford shale sample. It is shown that accurate kr data can be obtained using the proposed technique. This technique can be used to estimate reliable kr data without any saturation profile measurement equipment, such as CT scan or MRI.

A POD Coupled Adaptive DEIM (POD-ADEIM) Reduced-Order Model for Incompressible Multiphase Flow in Porous Media

The multiphase fluid flow in porous media is one of the most fundamental phenomena in various physical processes, such as oil/gas flow in reservoir, subsurface contamination dispersion, chemical separation, etc. Due to its importance, the efficient and accurate solution and prediction of multiphase flow in porous media is highly required in engineering applications and mechanism studies, which has been a research hot spot with increasing interest in recent years. However, the strong nonlinearity implicated in the multiphase flow model has brought great challenges for the computation and analysis. In addition, the permeability in Darcy-type pressure equation is always represented as a high contrast coefficient, which further complicates the simulation difficulty especially for high fidelity prediction and decision-making process. In this study, we attempt to apply one popular global model reduction method, namely Proper Orthogonal Decomposition (POD), to accelerate the simulation of incompressible multiphase flow in porous media. The cornerstone of POD is processing information from a sequence of snapshots (or instantaneous solutions) to identify a set of basis functions to construct a low-dimensional space, the most energetic part of these basis functions is then selected to represent the solution of the original system. In our work, one key point is how to establish the accurate POD reduced order model (ROM) for incompressible mul-tiphase porous flow problems. According to Li et al. [1], the traditional Galerkin projection method (directly project the original governing equation into the low-dimensional space spanned by basis functions) is incapable of introducing the fluid saturation and permeability located on the cell face in POD-ROM for incompressible multiphase flow whether in homogeneous or heterogeneous porous media, thus we adopt the matrix operation method (project the discrete governing equation instead of the original governing equation into the low-dimensional space spanned by basis functions) to build the POD-ROM in this study. Based on the proposed POD-ROM framework, we use the implicit method to solve the (non-) wetting-phase pressure and saturation equations. However, in the implicit solution of the pressure and saturation equations, the standard POD-ROM alone sometimes cannot yield an expected acceleration owing to two main reasons: (1) the nonlinearity between pressure and saturation is sensitive, thus the saturation would change largely even with slight pressure change. And the small error of pressure results would lead to a large deviation of saturation, which in turn exerts negative impacts on the computation of pressure; (2) the complexity for computing a projected nonlinear term in POD-ROM still depends on the dimension of the original full-order system, it is unavoidable in conventional POD-ROM. Therefore, more POD modes are needed to be used in order to achieve the prescribed numerical accuracy, which could worsen the speed up efficiency of proposed POD-ROM. To further reduce the computational complexity of POD-ROM to speed up the implicit solution of pressure and saturation equations, another model reduction method called Discrete Empirical Interpolation Method (DEIM) [2] is applied to treat the projected nonlinear term in the proposed incompressible multiphase porous flow POD-ROM. Different from previous studies, we develop an adaptive DEIM (ADEIM) in this work to achieve a more flexible selection of the interpolation points. Combined the POD-ROM with ADEIM, a POD-ADEIM-ROM for incompressible multiphase flow in porous media is established. The computational efficiency and numerical accuracy of the proposed model is validated through several representative numerical examples. Numerical results indicate that an outstanding acceleration (2~3 orders of magnitude faster) without sacrificing numerical accuracy significantly is obtained from the proposed model when comparing to the traditional solution method that without any acceleration technique. In addition, the effects of POD mode number, the distribution of permeability field, and the mesh density on the overall performances of the proposed model are investigated in detail.

Upscaling of Dynamic Capillary Pressure of Two‐Phase Flow in Sandstone

AbstractDynamic capillary pressure (DCP) is the capillary pressure defined under transient flow condition during displacement, and it is vital for predicting two‐phase behavior in porous media. This article studies the effect of pore scale force and interfacial area by using captivating Lattice Boltzmann method based on a pseudo‐potential model developed for simulating incompressible multiphase flow in porous media. We analyze the relationship between pore scale forces and DCP based on the energy conservation law and define DCP as a function of energy rate of pressure and viscosity of each phase. We present two‐phase displacement simulations on a computed tomography (CT) image‐based porous model and analyze the effects of injection rate and wettability on DCP based on the proposed upscaling method, where the wettability is defined as the contact angle of the nonwetting phase. The primary results show that (1) the DCP curves are higher than that of the quasi‐static capillary pressure, and a higher injection rate leads to a larger DCP and a faster saturation change. (2) Significant effects of wettability on DCP and the DCP coefficients are observed, where the DCP coefficient is defined as the ratio of the difference between DCP and static capillary pressure over the rate of change of saturation. A larger contact angle results in a higher DCP and a lower change rate of saturation, and consequently induces a larger DCP coefficient. The average DCP coefficient is found to vary from 4.56 × 106 to 3.55 × 105Pa · ms when the nonwetting phase contact angle changes from 140° to 105° in the saturation range of 0.3 to 0.8. This study indicates that the proposed upscaling method is valid to investigate the DCP of two‐phase flow in sandstone.

Fabrication and verification of a glass-silicon-glass micro-/nanofluidic model for investigating multi-phase flow in shale-like unconventional dual-porosity tight porous media.

Unconventional shale or tight oil/gas reservoirs that have micro-/nano-sized dual-scale matrix pore throats with micro-fractures may result in different fluid flow mechanisms compared with conventional oil/gas reservoirs. Microfluidic models, as a potential powerful tool, have been used for decades for investigating fluid flow at the pore-scale in the energy field. However, almost all microfluidic models were fabricated by using etching methods and very few had dual-scale micro-/nanofluidic channels. Herein, we developed a lab-based, quick-processing and cost-effective fabrication method using a lift-off process combined with the anodic bonding method, which avoids the use of any etching methods. A dual-porosity matrix/micro-fracture pattern, which can mimic the topology of shale with random irregular grain shapes, was designed with the Voronoi algorithm. The pore channel width range is 3 μm to 10 μm for matrices and 100-200 μm for micro-fractures. Silicon is used as the material evaporated and deposited onto a glass wafer and then bonded with another glass wafer. The channel depth is the same (250 nm) as the deposited silicon thickness. By using an advanced confocal laser scanning microscopy (CLSM) system, we directly visualized the pore level flow within micro/nano dual-scale channels with fluorescent-dyed water and oil phases. We found a serious fingering phenomenon when water displaced oil in the conduits even if water has higher viscosity and the residual oil was distributed as different forms in the matrices, micro-fractures and conduits. We demonstrated that different matrix/micro-fracture/macro-fracture geometries would cause different flow patterns that affect the oil recovery consequently. Taking advantage of such a micro/nano dual-scale 'shale-like' microfluidic model fabricated by a much simpler and lower-cost method, studies on complex fluid flow behavior within shale or other tight heterogeneous porous media would be significantly beneficial.

Non-Isothermal Compositional Model for Simulation of Multiphase Porous Media Flows

The research carried out in this work is aimed at the development of an explicit computational algorithm to simulate non-isothermal flow of multiphase multicomponent slightly compressible fluid through porous media. Such a modeling is necessary, for example, at solving practically important problems of hydrocarbon recovery via thermal methods and contaminated soil remediation via the hot steam injection. The original model and algorithm developed by the authors earlier draw the analogy with the quasi-gas-dynamic set of equations. Phase continuity equations were modified to get regularizing terms, while the type of equations was changed from parabolic to hyperbolic for the approximation by an explicit scheme with a mild enough stability condition. Since an adequate description of temperature-dependent porous media processes requires an explicit consideration of the transfer of mass and energy between the phases, the present work focuses on the generalization of the proposed approach to the case of multicomponent composition of fluids. Conservation laws are currently formulated for the components in terms of the mass concentrations of components in the phases. Constants of the phase equilibrium were used to close the set of equations. The developed model and algorithm have been verified numerically via test predictions of twoand three-phase flows, and, the phase transition of water into the gas phase at heating has been reproduced correctly.