Two-phase Flow Of Immiscible Fluids Research Articles

Analyzing Foam Injection Dynamics in Porous Media: A Combined Computational and Experimental Approach

The study of foam injection dynamics into porous media holds numerous applications, with its primary use being the optimization of the oil extraction process. Additionally, it finds utility in various other domains, including soil decontamination techniques. This study focuses on evaluating foam injection through low-cost experiments and computational models. The model integrates a classic two-phase immiscible fluid flow in a porous media framework, augmented by a mobility reduction factor to simulate foam’s impact on gas phase mobility. Simple experiments were conducted to assess water displacement using both gas and gas-foam injection methods. Results revealed that while gas injection tends to form preferential paths rapidly, leading to gas disruption, foam injection generates a more compact front, enhancing sweep efficiency by mitigating preferential path formation. The computational model successfully reproduced the experimental findings qualitatively. This research introduces a cost-effective experiment suitable for didactic purposes, illustrating complex concepts and underscoring the complementary nature of experimental and computational methodologies in advancing engineering techniques.

Influence of nanoparticle concentration on the flow regimes of crude oil – Nanosuspension in a microchannel

This paper presents the results of an investigation into the effect of silica nanoparticles on two-phase flow regimes in a Y-shaped microchannel. The following fluids were subjected to investigation: oil, water, and a water-based suspension containing SiO2 nanoparticles at a weight concentration of 1 ≤ φ ≤ 10 %. A systematic investigation of the flow regimes revealed the following: slug, parallel, and droplet regimes. The ranges of existence of the obtained flow regimes were determined and flow regime maps were constructed as a function of fluid flow rates and dimensionless numbers. The results of the study demonstrated that the slug length and frequency of slug formation are influenced by varying silica concentrations. Furthermore, the correlation between slug length and nanoparticle concentration remains consistent as the suspension flow rate increases. The dependence of the ratio of oil layer width to channel width for suspensions with varying nanoparticle concentrations was quantified. A mathematical simulation of two-phase flow of immiscible fluids was conducted. The results of the numerical simulation demonstrated the existence of the flow regimes that had been previously identified through experimentation. The aforementioned methodology may therefore be employed for the investigation of the two-phase immiscible flow of oil and nanosuspension.

Modeling Two-Phase Flow in Tight Core Plugs with an Application for Relative Permeability Measurement

Summary The two-phase flow of immiscible fluids in porous media has been studied for a long time in different disciplines of engineering. Relative permeability (kr) is one of the constitutional relationships in the general equation governing immiscible displacement that needs to be determined. Due to the complexity and nonlinear nature of governing equations of the problem, there is no unique model for relative permeability. The modified Brooks and Corey (MBC) model is the most common model for kr prediction. Here, a practical technique is presented to measure kr for low-permeability tight rocks. We use this experimental data to tune the empirical constants of the MBC model. The proposed method is based on a simple mathematical technique that uses assumptions of frontal advance theory to model the pressure drop along the core plug during two-phase immiscible displacement at constant injection flow rate. We make simplifying assumptions about the highest point on the observed pressure profile and use those assumptions to determine relative permeability of a tight rock sample. In the end, the amount of work for an immiscible displacement is calculated as the area under the pressure-profile curve. The effect of initial water saturation (Swi) and interfacial tension (IFT) is studied on the work required for an immiscible displacement. Using this concept, it is concluded that adding chemical additives such as surfactants to fracturing fluids can help the reservoir oil to remove the water blockage out of the rock matrix more easily while maintaining the flow rate at an economic level.

Virtual Element simulation of two-phase flow of immiscible fluids in Discrete Fracture Networks

In this paper we propose a primal C0-conforming virtual element discretization for the simulation of the two-phase flow of immiscible fluids in poro-fractured media modeled by means of a Discrete Fracture Network (DFN). The fractures are assumed to be made of the same isotropic rock type and to have the same width. The flexibility of the Virtual Element Method (VEM) in handling general polygonal elements allows to obtain a global conformity of the DFN mesh while preserving a fracture-independent meshing approach. The effectiveness and the robustness of the proposed numerical method are tested on DFN configurations of increasing complexity and characterized by challenging mesh geometry.

A virtual element method for the two-phase flow of immiscible fluids in porous media

A virtual element method for the two-phase flow of immiscible fluids in porous media

Methodology for the assessment of cleanability and geometry optimization using flow simulation on the example of dimple-structured pipe surfaces

The hygienic design of machinery, e.g. in the food and pharmaceutical industries, has so far mainly been based on empirical guidelines. Recently developed, efficient models for the numerical simulation of cleaning processes promise a real optimization of the geometry with respect to cleaning. To realize this potential, an approach is provided, which takes into account the variety of cleaning tasks and allows for a generalized evaluation of the cleanability. It is demonstrated on the example of film-like soils in dimple-structured pipes. In this approach, the cleaning behaviour is investigated qualitatively as a function of the relevant cleaning mechanisms and relative to the reference case of a smooth pipe. The overall cleaning performance is calculated from a weighted average of the individual performances. The flow simulations in ANSYS fluent are based on the Reynolds averaged Navier–Stokes equations. The soil behaviour is modelled as a boundary condition to minimize calculation times. Only in the case of viscous shifting, a transient two-phase flow of immiscible fluids is simulated. Three different dimple structures are investigated, where the spherical dimple with sharp edges yields the best results. Through the subsequent optimization of its shape, the cleaning performance even exceeds the value of the smooth pipe.

Computational homogenization of fully coupled multiphase flow in deformable porous media

In this paper, a computational modeling tool is developed for fully coupled multiphase flow in deformable heterogeneous porous medium that consists of complex and non-uniform micro-structures using the dual continuum scales based on the computational homogenization approach. The first-order homogenization technique is employed to perform the multi-scale analysis. The governing equations of two-phase flow of immiscible fluids, including an equilibrium equation and two mass continuity equations, are considered based on the appropriate main variables. According to the well-known Hill–Mandel principle of macro-homogeneity, the proper energy types are defined instead of conventional stress power for linking micro- and macro-scales, which plays a significant role in determination of consistent microscopic fields. The finite element squared strategy is utilized to resolve the two scales simultaneously. The periodic and linear boundary conditions are exploited in the micro-scale analysis, and the macroscopic quantities such as stress tensor, inertial force vector, flux vectors and fluid contents are determined from the boundary information of microscopic domain. Moreover, a general approach is defined depending on the type of boundary condition in which the macroscopic tangent operators can be extracted directly from the converged microscopic Jacobian matrix. Finally, in order to illustrate the efficiency and accuracy of the proposed computational algorithm, several numerical examples are solved, and the effects of various parameters, such as boundary conditions, RVE types, RVE length scale, and volume fraction of heterogeneities are investigated.

Numerical simulation of two-phase flow of immiscible fluids by the finite element, discontinuous Galerkin and level-set methods

The subject of the paper is the numerical simulation of two-phase flow of immiscible fluids. Their motion is described by the incompressible Navier-Stokes equations with different constant density and viscosity for different fluids. The interface between the fluids is defined with the aid of the level-set method using a transport first-order hyperbolic equation. The Navier-Stokes system is equipped with initial and boundary conditions and transmission conditions on the interface between the two fluids. This system is discretized by the Taylor-Hood P2/P1 conforming finite elements in space and the second-order BDF method in time. The transport level-set problem is solved with the aid of the space-time discontinuous Galerkin method. Numerical experiments demonstrate that the developed method is accurate and robust.

Chebyshev wavelets collocation method for simulating a two-phase flow of immiscible fluids in a reservoir with different capillary effects

At least in the last 10 years, considerable effort has been given to studying the dynamics of fluid flow in porous media. The phenomena is widely applicable in many areas of science and engineering. In many cases, the effect of capillary pressure and discontinuities in the two-phase flow dynamics is not fully clear, especially in petroleum reservoirs. In this paper, we introduce a new method based on the Chebyshev wavelets collocation method and the so-called operational matrices of integration. The method was implemented specifically for an oil–water-phase flow in heterogeneous reservoir using different capillary pressure treatments. Convergence and accuracy of this method were established and used to simulate the partial differential equations governing the two-phase model. The method incorporates the various conditions of the complex governing equations as a single system. The system is subsequently reduced into a simple set of algebraic equations making the problem easier to solve. Numerical results showed that the method is able to account for the expected discontinuities occurring in the flow process. It was also found that these discontinuities or jumps in the two-phase flow are caused by the capillary pressure as expected physically.

Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel

This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solution of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically.

Modeling two-phase flow of immiscible fluids in porous media: Buckley-Leverett theory with explicit coupling terms

Continuum models that describe two-phase flow of immiscible fluids in porous media often treat momentum exchange between the two phases by simply generalizing the single-phase Darcy law and introducing saturation-dependent permeabilities. Here we study models of creeping flows that include an explicit coupling between both phases via the addition of cross terms in the generalized Darcy law. Using an extension of the Buckley-Leverett theory, we analyze the impact of these cross terms on saturation profiles and pressure drops for different couples of fluids and closure relations of the effective parameters. We show that these cross terms in the macroscale models may significantly impact the flow compared to results obtained with the generalized Darcy laws without cross terms. Analytical solutions, validated against experimental data, suggest that the effect of this coupling on the dynamics of saturation fronts and the steady-state profiles is very sensitive to gravitational effects, the ratio of viscosity between the two phases, and the permeability. Our results indicate that the effects of momentum exchange on two-phase flow may increase with the permeability of the porous medium when the influence of the fluid-fluid interfaces become similar to that of the solid-fluid interfaces.

New insights on the complex dynamics of two-phase flow in porous media under intermediate-wet conditions

Multiphase flow in porous media is important in a number of environmental and industrial applications such as soil remediation, CO2 sequestration, and enhanced oil recovery. Wetting properties control flow of immiscible fluids in porous media and fluids distribution in the pore space. In contrast to the strong and weak wet conditions, pore-scale physics of immiscible displacement under intermediate-wet conditions is less understood. This study reports the results of a series of two-dimensional high-resolution direct numerical simulations with the aim of understanding the pore-scale dynamics of two-phase immiscible fluid flow under intermediate-wet conditions. Our results show that for intermediate-wet porous media, pore geometry has a strong influence on interface dynamics, leading to co-existence of concave and convex interfaces. Intermediate wettability leads to various interfacial movements which are not identified under imbibition or drainage conditions. These pore-scale events significantly influence macro-scale flow behaviour causing the counter-intuitive decline in recovery of the defending fluid from weak imbibition to intermediate-wet conditions.

Finite element solution for a coal-bed methane reservoir model

We present a mathematical model for fluid flow in porous media in the case of coal bed methane reservoirs. The model consists of a two-phase immiscible fluid flow with gas and water and takes into account desorption. We discretize the problem by a finite element method with adding a streamline diffusion term for the case of small capillary pressure. Time integration uses the fully implicit Euler scheme. Numerical experiments in radial and fully 2-D cases show the effectiveness of the model and numerical method.

Study of Multi-phase Flow in Porous Media: Comparison of SPH Simulations with Micro-model Experiments

Abstract We present simulations and experiments of drainage processes in a micro-model. A direct numerical simulation is introduced which is capable of describing wetting phenomena on the pore scale. A numerical smoothed particle hydrodynamics model was developed and used to simulate the two-phase flow of immiscible fluids. The experiments were performed in a micro-model which allows the visualization of interface propagation in detail. We compare the experiments and simulations of a quasistatic drainage process and pure dynamic drainage processes. For both, simulation and experiment, the interfacial area and the pressure at the inflow and outflow are tracked. The capillary pressure during the dynamic drainage process was determined by image analysis.

On the Construction of an Experimentally Based Set of Equations to Describe Cocurrent and Countercurrent, Two-Phase Flow of Immiscible Fluids Through Porous Media

Generalized flow equations developed for two-phase flow through porous media contain a second term that enables proper account to be taken of capillary coupling between the two flowing phases. In this study, a partition concept, together with a novel capillary pressure equation for countercurrent flow, have been introduced into Kalaydjian’s generalized flow equations to construct modified flow equations which enable a better understanding of the role of capillary coupling in horizontal, two-phase flow. With the help of these equations it is demonstrated that the reduced flux observed in countercurrent flow, as compared to cocurrent flow, can be explained by the reduction in the driving force per unit volume which comes about because of capillary coupling. Also, it is shown experimentally that, because fluids flow through a void space reduced in magnitude due to the presence of immobile irreducible and residual saturations, the capillary coupling parameter should be defined in terms of a reduced porosity, rather than in terms of porosity. Moreover, it is shown statistically that the countercurrent relative permeability curve is proportional to the cocurrent relative permeability curve, the constant of proportionality being the capillary coupling parameter. Finally it is suggested that one can eliminate the need to determine experimentally countercurrent relative permeability curves by making use of an equation constructed for predicting the magnitude of the capillary coupling parameter.

Case study of using boundary integration technique in reservoir modeling of single- and two-phase immiscible fluid flow

Abstract Petroleum reservoir simulation is a process of modeling the complex physical phenomena inside a reservoir. The goal is to determine how hydrocarbons and water behave and how local reservoir characteristics affect the oil and gas recovery in the reservoir. This study presents an application of two rigorous analytical based numerical schemes in petroleum engineering, so called the Boundary Element Method (BEM) and its hybrid form, the Dual Reciprocity Boundary Element Method (DRBEM). They are proven to be able to provide a computationally efficient means of handling single- and multi-phase flow in a homogeneous medium through the comparison with results obtained by COMSOL. The accuracy can be further enhanced by incorporating singularity programming and Laplace transformation techniques; hence an alleviation of numerical errors caused by singularities and a time derivative is achieved. It is observed that these two methods can be an alternative tool to analyze pressure transient performance in both single- and multi-phase flow, and estimate the saturation change during an immiscible displacement process. In addition, it has been shown that there are numerous potential areas of oil recovery where COMSOL can be a useful and successful means of research and design advancement.

Two-Phase Flow: Structure, Upscaling, and Consequences for Macroscopic Transport Properties

In disordered porous media, two-phase flow of immiscible fluids (biphasic flow) is organized in patterns that sometimes exhibit fractal geometries across a range of length scales, depending on the capillary, gravitational, and viscous forces at play. These forces, as well as the boundary conditions, also determine whether the flow leads to the appearance of fingering pathways, i.e., unstable flow, or not. We present a short review of these aspects, focusing on drainage and summarizing when these flows are expected to be stable or not, what fractal dimensions can be expected, and in which range of scales. We based our review on experimental studies performed in two-dimensional Hele–Shaw cells or addressing three-dimensional porous media by use of several imaging techniques. We first present configurations in which solely capillary forces and gravity play a role. Next, we review configurations in which capillarity and viscosity are the main forces at play. Eventually, we examine how the microscopic geometry of the fluid clusters affects the macroscopic transport properties. An example of such an upscaling is illustrated in detail: for air invasion in a monolayer glass-bead cell, the fractal dimension of the flow structures and the associated scale ranges depend on the displacement velocity. This controls the relationship between saturation and the pressure difference between the two phases at the macroscopic scale. We provide in this case expressions for dynamic capillary pressure and residual fluid-phase saturations.

Time of complete displacement of an immiscible compressible fluid by water in porous media: Application to gas migration in a deep nuclear waste repository

A system of evolutionary partial differential equations (PDEs) describing the two-phase flow of immiscible fluids, such as water–gas, through porous media is studied. In this formulation, the wetting and nonwetting phases are treated to be incompressible and compressible, respectively. This treatment is indeed necessary when a compressible nonwetting phase is subjected to compression during confinement. The system of PDEs consists of an evolution equation for the wetting-phase saturation and an evolution equation for the pressure in the nonwetting phase. This system is applied to the problem of unsaturated flows to assess gas migration and two-phase flow through engineered and geological barriers for a deep repository for radioactive waste. This paper is primarily concerned with the large time behavior of solutions of this system. Under some realistic assumptions on the data, we derive estimates of the speed of propagation of the gas by water in porous media. Namely, we establish estimates of time stabilization for the water saturation to a constant limit profile. The analysis is based on the energy methods whose main idea involves deriving and studying suitable ordinary differential inequalities. We show that the time of complete displacement of a gas by water may be at most infinite or finite depending essentially on the power parameters defining the capillary pressure and the relative permeabilities. This result is then illustrated with two examples in the context of gas migration in a deep nuclear waste repository. We consider Van Genuchten’s and Brooks–Corey’s models for a two-phase water–gas system.

Estimation of Permeability and Permeability Anisotropy From Straddle-Packer Formation-Tester Measurements Based on the Physics of Two-Phase Immiscible Flow and Invasion

Summary We describe the successful application of a new method to estimate permeability and permeability anisotropy from transient measurements of pressure acquired with a wireline straddle-packer formation tester. Unlike standard algorithms used for the interpretation of formation-tester measurements, the method developed in this paper incorporates the physics of two-phase immiscible flow as well as the processes of mudcake buildup and invasion. An efficient 2D (cylindrical coordinates) implicit-pressure explicit-saturation finite-difference algorithm is used to simulate both the process of invasion and the pressure measurements acquired with the straddle-packer formation tester. Initial conditions for the simulation of formation-tester measurements are determined by the spatial distributions of pressure and fluid saturation resulting from mud-filtrate invasion. Inversion is performed with a Levenberg-Marquardt nonlinear minimization algorithm. Sensitivity analyses are conducted to assess nonuniqueness and the impact of explicit assumptions made about fluid viscosity, capillary pressure, relative permeability, mudcake growth, and time of invasion on the estimated values of permeability and permeability anisotropy. Applications of the inversion method to noisy synthetic measurements include homogeneous, anisotropic, single and multilayer formations for cases of low- and high-permeability rocks. We also study the effect of unaccounted impermeable bed boundaries on inverted formation properties. For cases where a priori information can be sufficiently constrained, our inversion methodology provides reliable and accurate estimates of permeability and permeability anisotropy. In addition, we show that estimation errors of permeability inversion procedures that neglect the physics of two-phase immiscible fluid flow and mud-filtrate invasion can be as high as 100%.

Stochastic analysis of a displacement front in a randomly heterogeneous medium

The behavior of the interface in a two-phase immiscible fluid flow in a randomly heterogeneous porous medium is investigated. The medium is described by the permeability distribution which represents a random field with given statistical characteristics. When the approach proposed is used, it turns out to be possible to relate the statistical characteristics of the interface with the statistical characteristics of the permeability field and the properties of the phases. On the basis of this relation an important characteristic of the two-phase flow, namely, the average saturation distribution in the neighborhood of the interface, can be calculated.