Immiscible Flow Research Articles

Lattice Boltzmann method for interface capturing.

Accurately solving phase interface plays a great role in modeling an immiscible multiphase flow system. In this paper, we propose an accurate interface-capturing lattice Boltzmann method from the perspective of the modified Allen-Cahn equation(ACE). The modified ACE is built based on the commonly used conservative formulation via the relation between the signed-distance function and the order parameter also maintaining the mass-conserved characteristic. A suitable forcing term is carefully incorporated into the lattice Boltzmann equationfor correctly recovering the target equation. We then test the proposed method by simulating some typical interface-tracking problems of Zalesaks disk rotation, single vortex, deformation field and demonstrate that the present model can be more numerically accurate than the existing lattice Boltzmann models for the conservative ACE, especially at a small interface-thickness scale.

Modeling immiscible fluid flow in fractal pore medium by multiphase lattice Boltzmann flux solver

In this paper, the multiphase lattice Boltzmann flux solver (MLBFS), where the phase field model and the apparent liquid permeability model are built-in, is developed to simulate incompressible multiphase flows in fractal pore structure at the representative elementary volume scale. MLBFS takes advantage of the traditional Navier–Stokes solver (e.g., geometric flexibility and direct handling of complex boundary conditions) and lattice Boltzmann method (e.g., intrinsically kinetic nature, simplicity, and parallelism). It is easily applied to simulate multiphase flows transport in the porous medium with large density ratios and high Reynolds numbers. This study focuses on the fluid flow in fractal pore structures and provides an in-depth discussion of the effects of non-Newtonian index, fractal parameters, and density ratios on multiphase flow. The proposed model is validated with benchmark problems to test the applicability and reliability of the MLBFS in describing fluid flow in fractal pore structures with large density ratios and viscosity ratios. Simulation results show that the fractal parameters (i.e., fractal dimension, tortuous fractal dimension, porosity, and capillary radius ratio) can accurately characterize fractal pore structure and significantly affect the apparent liquid permeability. In addition, the flow rate increases with the fractal dimension and decreases with the tortuous fractal dimension, while both flow rate and apparent liquid permeability decrease as the capillary radius ratio. It is also noteworthy that the effect of nonlinear drag forces cannot be neglected for shear-thickened flows.

Analysis of Entropy Production of Immiscible Micropolar and Newtonian Fluids Flow through a Channel: Effect of Thermal Radiation and Magnetic Field

Analysis of Entropy Production of Immiscible Micropolar and Newtonian Fluids Flow through a Channel: Effect of Thermal Radiation and Magnetic Field

Pore-scale investigation on the effect of icing on relative permeability of two-phase immiscible fluids

In this study, the flow behavior and relative permeability (kr) curve of the immiscible two-phase flow accompanied by icing in a horizontal channel were studied using the lattice Boltzmann method-phase field method (LBM-PFM) coupling model at the pore-scale. A novel LBM-PFM coupled model is proposed and tested by comparison with analytical and experimental results, and good agreement is achieved in general. Then, the model is used for simulating two-phase fluids (brine water–oil) flow during icing. In addition, the effects of initial phase distribution, capillary number, and heat flux are numerically discussed. The results show that, the distribution characteristics of the relative permeability curves of the immiscible fluids during the crystallization process are determined by the initial phase distribution. The Ca number is a positive correlation function of kr, while the kr curve is not sensitive to the change of heat flux.

A pressure approach of cumulant phase-field lattice Boltzmann method for simulating multiphase flows

The cumulant lattice Boltzmann method (LBM) has been recently used to simulate multiphase-multicomponent flows by applying an external force. Furthermore, the mass and momentum are not conserved when an external force is used. In the classical approach, the third-order derivatives in density necessitate information from a large stencil of neighbors, which affects parallelization and is computationally expensive. In this paper, we propose an equilibrium distribution function in the moment space, which includes diagonal and off diagonal elements of the pressure tensor. Consequently, the interfacial tension effect can be exerted into this equilibrium function, circumventing the need for an external force. The Cahn–Hilliard equation can be coupled to the method to track the interface at multiphase-multicomponent flows. This function is applied on the moment, central, and cumulant LBM and transferred back to the discrete space to be used in Bhatnagar–Gross–Krook LBM. These key advantages include simplicity, easy-to-implement, and high parallelization capability due to removing high-order derivatives. An immiscible two-component flow between two parallel plates is simulated and compared with the analytical solution at different viscosities for the moment LBM and the cumulant LBM. Numerical results are in good agreement with analytical solutions. Moreover, a dispersed droplet in a continuous phase under shear flow is simulated to show the capability of the proposed method in the breaking-up process modeling. It is demonstrated that spurious velocities are less affected by decreasing the viscosity and cumulant LBM with the proposed function, while the interfacial tension is calculated accurately. Finally, the method has been extended for three dimensions, and two cases of a three-dimensional breakup of a liquid thread and collision of two equal droplets are studied to show the ability of this method to simulate the coalescence and breakup process.

Thermo-diffusion impact on immiscible flow characteristics of convectively heated vertical two-layered Baffle saturated porous channels in a suspension of nanoparticles: an analytical study

Thermo-diffusion impact on immiscible flow characteristics of convectively heated vertical two-layered Baffle saturated porous channels in a suspension of nanoparticles: an analytical study

Two layered immiscible flow of viscoelastic liquid in a vertical porous channel with Hall current, thermal radiation and chemical reaction

This investigation deals with the combined effects of Hall current, thermal radiation, heat source and chemical reaction on heat and mass characteristics in a vertical porous channel filled with a two layered viscoelastic liquid under the influence of oscillatory pressure gradient. The exact solution of the governing equations for the fluid velocity, temperature, and concentration are obtained by applying the regular perturbation method with appropriate boundary and interface conditions. The numerical values of the shear stress at the plates are shown in tabular form for various values of the relevant parameters, whereas those of the fluid velocity, temperature, concentration, and rate of heat transfer are displayed graphically. Our analysis indicates that with the raise of first-order chemical reaction and ratio of mass diffusion parameters, the temperature and concentration of the liquid raises. With the raise of Hall parameter the skin friction decreases at the walls of the channel. To validate the analytical results, a comparative study of the numerical evaluation of the closed-form results is performed with the results obtained by shooting technique along with the RK-fourth order method. Graphical results demonstrate that the imposed boundary and interface conditions are satisfied by the flow variables.

Three-Dimensional Visualization Reveals Pore-Scale Mechanisms of Colloid Transport and Retention in Two-Phase Flow.

Colloids are ubiquitous in the natural environment, playing an important role in facilitating the transport of absorbed contaminants. However, due to the complexities arising from two-phase flow and difficulties in three-dimensional observations, the detailed mechanisms of colloid transport and retention under two-phase flow are still not well understood. In this work, we visualize the colloid transport and retention during immiscible two-phase flow based on confocal microscopy. We find that the colloid transport and retention behaviors depend strongly on the flow rate and pore/grain size. At low levels of saturation (high flow rate) with the wetting liquid mainly present as pendular rings, the colloids can aggregate at the liquid filaments in small-grain packings and are uniformly distributed in large-grain packings. Through theoretical analysis of the pendular ring geometry, we elucidate the mechanism responsible for the strong dependence of colloid clogging behavior on solid grain size. Our results further demonstrate that even at dilute concentrations, colloids can alter the flow paths and the wetting fluid topology, suggesting a strong two-way coupling dynamics between immiscible two-phase flow and colloid transport and calling for improved predictive models to incorporate the overlooked clogging behavior.

Steady-State Two-Phase Flow of Compressible and Incompressible Fluids in a Capillary Tube of Varying Radius

We study immiscible two-phase flow of a compressible and an incompressible fluid inside a capillary tube of varying radius under steady-state conditions. The incompressible fluid is Newtonian and the compressible fluid is an inviscid ideal gas. The surface tension associated with the interfaces between the two fluids introduces capillary forces that vary along the tube due to the variation in the tube radius. The interplay between effects due to the capillary forces and the compressibility results in a set of properties that are different from incompressible two-phase flow. As the fluids move towards the outlet, the bubbles of the compressible fluid grows in volume due to the decrease in pressure. The volumetric growth of the compressible bubbles makes the volumetric flow rate at the outlet higher than at the inlet. The growth is not only a function of the pressure drop across the tube, but also of the ambient pressure. Furthermore, the capillary forces create an effective threshold below which there is no flow. Above the threshold, the system shows a weak nonlinearity between the flow rates and the effective pressure drop, where the nonlinearity also depends on the absolute pressures across the tube.

Evaluation of the interFoam solver in the prediction of immiscible two-phase flow in imbibition and drainage on the pore-doublet system

Drainage and imbibition at low to moderate capillary number, are very important phenomena, in which the SCAL data are derived. In this venue, there is an increasing trend to apply computational fluid dynamic models at pore scale to extract the required parameters for multiphase flow study. Before applying these methods, their abilities to capture the real performance of fluids at the pore scale with corresponding capillary numbers should be validated. Moreover, due to the dimensional difference from pore to core scale, rigorous statistical methods are required to successfully extract the corresponding SCAL parameters. Hence for any model, before constructing any SCAL data via digital methods, validation at the pore scale along with the investigation of the possible effect of the dimensional change from pore to core scale are significant priorities. In this study, the performance of interFoam, a solver for immiscible two-phase flow from OpenFOAM, at the pore scale is evaluated. An image of the pore doublet system is digitized and meshed with different resolutions to capture the contact angle movement. The average pore diameters are different, and the pore diameter pathway varies. The experimental results are extracted from an article, which extensively performed the tests for different imbibition and drainage regime on this pore doublet system. Moreover, a sensitivity analysis on mesh geometry, refinement near boundaries, and contact angle is conducted. The drainage simulation and experimental results in the pore doublet system are in good agreement with each other. As expected, the displacement happens in the larger diameter and bypasses the wetting fluid in the narrow constriction. In imbibition, the displacement first takes place in the smaller constriction and then the wetting phase starts invading the larger diameter pore. From the sensitivity analysis, it is concluded that the instability of the front is mainly related to the slip condition at the walls. Moreover, the spreading of wetting film near the wall is prevalent at very low contact angles. The results show that the solver can predict the flow behavior in imbibition and drainage on the pore doublet system and the results are comparable with the experiments.

Study of relaxation processes in a two-phase flow model

This work concerns the analysis of the relaxation processes toward thermodynamical equilibrium arising in a compressible immiscible two-phase flow. Classically the relaxation processes are taken into account through dynamical systems which are coupled to the dynamics of the flow. The present paper compares two types of source terms which are commonly used: a BGK-like system and a mixture entropy gradient type. For both systems, main properties are investigated (agreement with second principle of thermodynamics, existence of solutions, maximum principle,...) and numerical experiments illustrate their asymptotic behaviour.

Study of Two Layered Immiscible Fluids Flow in a Channel with Obstacle by Using Lattice Boltzmann RK Color Gradient Model

Lattice Boltzmann method (LBM) is employed in the current work to simulate two-phase flows of immiscible fluids over a square obstacle in a 2D computational domain using the Rothman-Keller color gradient model. This model is based on the multiphase Rothman-Keller description, it is used to separate two fluids in flow and to assess its efficacy when treating two fluids in flow over a square obstacle with the objective of reducing turbulence by adjusting the viscosities of the two fluids. This turbulence can cause major problems such as interface tracking techniques in gas-liquid flow and upward or downward co-current flows in pipes. So, the purpose of the study is to replace a single fluid with two fluids of different viscosities by varying these viscosities in order to reduce or completely eliminate the turbulence. The results show that to have stable, parallel and non-overlapping flows behind the obstacle, it is necessary that the difference between the viscosities of the fluids be significant. Also, showing that the increase in the viscosity ratio decreases the time corresponding to the disappearance of the vortices behind the obstacle. The results presented in this work have some general conclusions: For M≥2, the increase in the viscosity difference leads to an increasing of friction between fluids, reducing of average velocity of flow and decreasing the time corresponding to the disappearance of the vortices behind the obstacle. However, for M≤1/2, the opposite occurs.

PORE SCALE INVESTIGATION ON THE EFFECT OF TEMPERATURE ON THREE-PHASE REACTIVE FLOW IN POROUS MEDIA USING THE LATTICE BOLTZMANN METHOD

In this study, the process of carbonate rock acidification with three-phase immiscible fluid [water, oil, and supercritical carbon dioxide (scCO<sub>2</sub>)] reactive flow in nonisothermal condition at pore scale was simulated by the lattice Boltzmann method (LBM). The three immiscible fluids' flow, solute transport, and heat transfer were solved by the Shan-Chen multiphase multicomponent lattice Boltzmann model, mass transport lattice Boltzmann model, and multicomponent thermal lattice Boltzmann model, respectively. The solid phase was updated by the volume-of-pixel method. In addition, the effect of temperature on the multiphase multicomponent reactive flow was numerically investigated. The results show that the dissolution rate is determined by three-phase distribution. The increase of temperature can accelerate the dissolution rate and decrease the inhibition influence of the non-acid phase on dissolution. Furthermore, the influence of temperature decreases with the increase of inlet velocity and oil wettability.

NUMERICAL ANALYSIS OF TWO IMMISCIBLE FLUIDS IN POROUS MEDIA BY THE MULTISCALE AND HOMOGENIZATION METHODS

This paper proposes a numerical model for simulating an immiscible compressible two-phase flow in a periodic heterogeneous porous media with application to a coal-bed methane extraction system. Methane flow in a coal sample submerged in water is simulated using the multiscale homogenization method and the averaged macroscopic approach. A weak formulation is used to discretize the governing equations coupled with the boundary conditions using the finite element method and solved using the open-source code Freefem++. It was observed that the general behavior of both methods was in good agreement with actual gas saturation evolution. However, the multiscale approach provided more information regarding the global pressure evolution behavior of the mitigating gas.

New insights into the Haines jump in immiscible two-phase flow displacement

In this study, we develop a numerical model of two-phase flow with a series of different contact angles θ based on real feature structures from scanning electron microscopy. Meanwhile, the interface dynamics during the Haines jump are analyzed based on a typical model of the pore throat system. We found that under different wetting conditions, a series of fluid displacement patterns can be regarded as the minimum pressure drop displacement state for the completion of the constant flow displacement task. Moreover, the Haines jump event is no longer an unfavorable energy event that leads to rapid dissipation of energy but a favorable energy event derived by the system under specific constraints to avoid extra work. These new findings provide new insights into the wettability effect as well as the physical origin of the Haines jump event.

Numerical Study on the Migration of Leaked Oil in Submarine Sediment Caused by Pipeline Leakage Using Two-phase Flow Model

Oil leakage from submarine pipelines can cause severe environmental problems and economic losses. In this study, a two-phase immiscible flow model in porous media is proposed to simulate the migration of leaked oil caused by the leakage of a buried submarine pipeline in sandy sediment. The relationship between saturation, pore pressure, and relative permeability of different fluids in porous media is considered in present model, which is distinguished from previous studies. The spilled oil spreads radially from the leakage point into surrounding sediment driven by the leakage velocity. Moreover, it continues to migrate in sediment under the capillary pressure and gravity. Interestingly, the effect of wave-induced transient response on the ultimate migration of spilled oil in a sandy sediment is negligible. However, increasing sediment porosity can greatly enhance the upward migration of leaked oil based on systematically parametric analysis. Meanwhile, the migration rate of leaked oil decreases with increasing oil density or viscosity. The oil-contaminated area significantly expands with the increase of leakage rate. Fitting formulas between dimensionless time required for the leaked oil to reach the overlying seawater and non-dimensional influencing parameters are well established, which can provide useful guidelines for similar disasters.

A flow map for core/shell microdroplet formation in the co-flow Microchannel using ternary phase-field numerical model

Core/shell microdroplets formation with uniform size is investigated numerically in the co-flow microchannel. The interface and volume fraction contour between three immiscible fluids are captured using a ternary phase-field model. Previous research has shown that the effective parameters of microdroplet size are the physical properties and velocity of the three phases. By adjusting these variables, five main flow patterns are observed in numerical simulations. A core/shell dripping/slug regime is observed when the inertia of the continuous phase breaks the flow of the core and shell phases and makes a droplet. In the slug regime, the continuous phase has less inertia, and the droplets that form are surrounded by the channel walls, while in the dripping regime, the shell phase fluid is surrounded by the continuous phase. An increase in continuous-fluid or shell-fluid flow rate leads to dripping to a jetting transition. When three immiscible liquids flow continuously and parallel to one another without dispersing, this is known as laminar flow. In the tubing regime, the core phase flows continuously in the channel's central region, the shell phase flows in the annulus formed by the core phase's central region, and the continuous phase flows between the shell phase fluid and channel walls. In order to discriminate between the aforementioned flow patterns using Weber and Capillary numbers and establish regime transition criteria based on these two dimensionless variables, a flow regime map is provided. Finally, a correlation for shell thickness using shell-to-core phase velocity ratio and conducting 51 CFD simulations was proposed.

A fully-implicit hybridized discontinuous Galerkin spectral element method for two phase flow in petroleum reservoirs

A hybridized discontinuous Galerkin method with high order spectral element discretization is presented for modeling multiphase immiscible 2D fluid flow in petroleum reservoir simulations. The time dependent nonlinear governing equations for reservoir simulation are presented, and a fully coupled implicit time stepping procedure is implemented using a high order W-Rosenbrock algorithm. For incompressible fluids considered in the present study, the governing PDE's include an elliptic PDE for the pressure field and a parabolic convective diffusion equation for the saturation (water volume fraction) in a two phase oil-water system. The PDE systems are coupled through the highly nonlinear relative permeability and capillary pressure functions relating the fluid velocities of individual species to the individual species pressures and saturations. With HDG/spectral element (HDGSEM) spatial discretization of the coupled governing equations, the system constitutes an index 1 differential algebraic equation. It is shown that the W-Rosenbrock algorithm in combination with the HDGSEM method yields an efficient and effective solution procedure which demonstrates robust, high order temporal accuracy.Numerous physical tests cases are presented demonstrating that the versatility of this approach is sufficient to address the challenges in modeling heterogeneous permeability fields and geologic features of arbitrary shape with discontinuous permeability functions. It is also capable of resolving the sharp time dependent displacement fronts in oil-water systems encountered in secondary oil recovery. It is demonstrated that the high order polynomial basis functions (up to 12th order) used in the HDGSEM algorithm have the ability to resolve complex geometry and achieve accurate results utilizing a simple Cartesian mesh for non-conforming geological features. Eliminating the need to re-grid and conform the mesh to the boundaries of different geological features greatly simplifies the workflow for petroleum engineers.

Co‐Current Fluid Flow Mechanisms Within a Complex Porous Structure at the Pore Level

AbstractThis study has been addressed the mechanisms of the co‐current fluid flow in a heterogeneous porous media using the lattice Boltzmann method. Since the smallest interaction between viscous and capillary forces at the interface is of great importance, the simulations are performed with the hybrid phase‐field model at the pore level. This is because the main advantage of this model is that due to its connection with the phase‐field theory, it has a solid physical basis to record interface dynamics. Model verification is followed by recording viscous coupling effects. The relative permeability curves and the velocity profiles are compared with the analytical solution, so that the observations confirm the accuracy claim of the model. In the following, the fluid flow through the heterogeneous porous structure is simulated, so that its sweep efficiency and corresponding velocity field at the breakthrough time are discussed. The results show that increasing the injection velocity reduces the displacement efficiency and increases the velocity field fluctuations due to the viscous fingering regime. Changing the wetting conditions to strong imbibition (SI) will increase the efficiency due to the role of capillary pressure and corner flow mechanism. Also, increasing the interfacial tension in the SI and the strong drainage will increase and decrease the sweep efficiency, respectively, so the rate of changes in fully immiscible flow is much higher than the near miscible flow. The velocity fluctuations in the fully immiscible flow are more significant than in the near miscible flow, which is reasonable given the flow properties.

Stable and unstable capillary fingering in porous media with a gradient in grain size

Multiphase flows in complex porous networks occur in many natural processes and engineering applications. We present an analytical, experimental and numerical investigation of slow drainage in porous media that exhibit a gradient in grain size. We show that the effect of such structural gradient is similar to that of an external force field on the obtained drainage patterns, when it either stabilises or destabilises the invasion front. For instance, gravity can enhance or reverse the drainage pattern in graded porous media. In particular, we show that the width of stable drainage fronts scales both with the spatial gradient of the necessary pressure for pore invasion and with the local distribution of this (disordered) threshold. The scaling exponent results from percolation theory and is − 0.57 for 2D systems. Overall, introducing a dimensionless Fluctuation number, we propose a unifying theory for the up-scaling of dual immiscible fluid flows covering most classical scenarii.