Flow Of Immiscible Fluids Research Articles

Analytical expressions for three-phase generalized relative permeabilities in water- and oil-wet capillary tubes

We analyze three-phase flow of immiscible fluids taking place within an elementary capillary tube with circular cross-section under water- and oil-wet conditions. We account explicitly for momentum transfer between the moving phases, which leads to the phenomenon of viscous coupling, by imposing continuity of velocity and shear stress at fluid-fluid interfaces. The macroscopic flow model which describes the system at the Darcy scale includes three-phase effective relative permeabilities, K i j,r , accounting for the flux of the ith phase due to the presence of the jth phase. These effective parameters strongly depend on phase saturations, fluid viscosities, and wettability of the solid matrix. In the considered flow setting, K i j,r reduce to a set of nine scalar quantities, K i j,r . Our results show that K i j,r of the wetting phase is a function only of the fluid phase own saturation. Otherwise, K i j,r of the non-wetting phase depends on the saturation of all fluids in the system and on oil and water viscosities. Viscous coupling effects (encapsulated in K i j,r with i ≠ j) can be significantly relevant in both water- and oil-wet systems. Wettability conditions influence oil flow at a rate that increases linearly with viscosity ratio between oil and water phases.

Effect of viscous cross coupling between two immiscible fluids on elastic wave propagation and attenuation in unsaturated porous media

A central issue in the theoretical treatment of a multiphase system is the proper mathematical description of momentum transfer across fluid-solid and fluid-fluid interfaces. Although recent studies have advanced our knowledge on modeling the coupling behavior between a porous framework and the fluids permeating it, the effect of viscous resistance caused by two-fluid flow on elastic wave behavior in unsaturated porous media still remains elusive. In the present study, the theoretical model developed for describing immiscible two-phase fluid flows in a deformable porous medium related to harmonic wave perturbation is generalized to account for viscous cross coupling due to relative velocity between two adjacent fluids. The corresponding dispersion relations whose coefficients feature all elasticity, inertial-drag, and viscous-drag parameters are then precisely formulated, in a physical context characterizing three compressional waves and one shear wave.To evaluate quantitatively this as-yet unknown effect, numerical calculations are conducted to solve the dispersion relations for Columbia fine sandy loam bearing an oil–water mixture as a function of water saturation and excitation frequency. Our results show that the phase speed and attenuation coefficient of the P3 wave which has the smallest speed is strongly sensitive to the presence of viscous cross coupling, as expected since this wave is attributed primarily to the out-of-phase motion of the two pore fluids. Viscous cross coupling also exerts an impact on the attenuation coefficient of the shear wave and the P1 wave whose speed is greatest, which exhibits two opposite trends at different ranges of low and high water contents. Relative differences in these wave attributes are principally independent of excitation frequency. A sensitivity analysis is carried out to assess how changes in viscous cross coupling affect these differences, revealing that some of them become more significant as viscous cross coupling is stronger.

Theoretical analyses of immiscible MHD pipe flow

In this study, effect of normally applied magnetic field on immiscible fluid flow hydrodynamic flow characteristic has been analytically investigated. Flow case modelled for two different flow patterns. The first one is low electrically conductive fluid (gasoline) inner core and higher one (salty water) outer flow regional pattern and the second one is high electrically conductive fluid inner core and lower one is outer regional flow case in a vertical circular pipe. Flow models have been modelled in differential form theoretical equations and solved with Laplace Transform method. Solved equation systems presented the dependent statement of the local flow velocity and flow rates to the magnetic field induction, pipe radius and pressure gradient. It is estimated that high electrically conductive fluid was directly affected by the magnetic forces which is created by the magnetic field, and also low electrically conductive fluid was indirectly affected from the magnetic field because of the interfacial tension between the fluids. As a result, overall velocity of the flow domain was reduced more by the magnetic forces in the event of low conductive fluid inner core and high conductive fluid outer regional flow case.

An efficient numerical method for simulating multiphase flows using a diffuse interface model

This paper presents a new diffuse interface model for multiphase incompressible immiscible fluid flows with surface tension and buoyancy effects. In the new model, we employ a new chemical potential that can eliminate spurious phases at binary interfaces, and consider a phase-dependent variable mobility to investigate the effect of the mobility on the fluid dynamics. We also significantly improve the computational efficiency of the numerical algorithm by adapting the recently developed scheme for the multiphase-field equation. To illustrate the robustness and accuracy of the diffuse interface model for surface tension- and buoyancy-dominant multi-component fluid flows, we perform numerical experiments, such as equilibrium phase-field profiles, the deformation of drops in shear flow, a pressure field distribution, the efficiency of the proposed scheme, a buoyancy-driven bubble in ambient fluids, and the mixing of a six-component mixture in a gravitational field. The numerical result obtained by the present model and solution algorithm is in good agreement with the analytical solution and, furthermore, we not only remove the spurious phase-field profiles, but also improve the computational efficiency of the numerical solver.

Treatment of Transport at the Interface Between Multilayers via the Lattice Boltzmann Method

The lattice Boltzmann method (LBM) has reached maturity in many aspects for modeling incompressible, laminar flow and heat and mass transfer. However, many issues still need to be clarified. One of those is how to deal with Neumann boundary conditions (heat, momentum, and mass fluxes) at the interface between layers of different thermophysical properties, which is the topic of this work. In this work, we try to illustrate modeling of transient and steady-state heat transfer through multilayers, ensuring continuity of the flux, temperature, momentum, velocity, or species concentration at the interface, which is not a trivial issue in any of the numerical methods. Satisfying continuity conditions at the interface using the LBM needs special treatment, because the relaxation time depends on the thermophysical properties. In this work, methods to solve this issue are introduced for solving 1-D and 2-D, unsteady heat diffusion problems However, the methods can be equally applied for multilayer immiscible fluid flow and mass transfer problems. The predictions of the LBM are compared with those of the finite-volume method (FVM).

A generic framework for design of interface capturing schemes for multi-fluid flows

A generic methodology for the design of interface capturing schemes for immiscible multi-fluid flows using the VOF (Volume-Of-Fluid) approach is outlined. Interface capturing schemes are devised as a blend of high-resolution and compressive schemes and their efficiency and accuracy are dependent on the choice of the constituent schemes and the blending function. On the basis of a set of design principles proposed in this work, we show that interface capturing schemes proposed in literature may be encompassed into a single class of GPL (Generalised Piecewise Linear)-κ schemes allowing for a unified approach for development of such schemes. This methodology is used to de-construct four existing schemes and to propose two new schemes for interface capture in an unstructured finite volume framework. The schemes are tested on challenging advection problems using both structured and unstructured grids to evaluate their performance. The new schemes perform as well as existing schemes and even outperform them on unstructured grids, while also exhibiting near Courant number independence for all test problems and grid topologies. The CUIBS (Cubic Upwind Interpolation based Blending Scheme) proposed in the study shows the best performance among all interface capturing schemes discussed herein and is applied to the study of immiscible binary fluid flows. Numerical simulations of viscous sloshing in a tank and Rayleigh–Taylor instability demonstrate the ability of the CUIBS scheme to resolve fluid–fluid interfaces with minimal diffusion.

Free Convective Flow of Electrically Conducting and Viscous Immiscible Fluid Flow in a Vertical Channel in the Presence of First‐Order Chemical Reaction

In this paper, the effects of chemical reaction on free convective flow of electrically conducting and viscous incompressible immiscible fluids are analyzed. The coupled nonlinear equations governing the heat and mass transfer are solved analytically and numerically with appropriate boundary conditions for each fluid and the solutions have been matched at the interface. The analytical solutions are solved by using regular perturbation method valid for small values of perturbation parameter and numerically by using finite difference method. The numerical results for various values of thermal Grashof number, mass Grashof number, Hartman number, viscosity ratio, width ratio, conductivity ratio, and chemical reaction parameter have been presented graphically in the presence and in the absence of electric field load parameter. In addition, the closed form expression for volumetric flow rate, Nusselt number, species concentration, and total heat rate added to the flow is also analyzed. The solutions obtained by finite difference method and perturbation method agree very well to the order of 10−4 for small values of perturbation parameter.

Secondary flow structure and thermal behaviour of immiscible two-phase fluid flow in curved channels

This paper investigates the behaviour of two non-mixing fluids flowing in a heated curved channel. In simulating this immiscible fluid flow, a multi-phase model based on VOF approach is developed for steady, turbulent, incompressible fluid flow through curved channel. The analysis examines the influence of centrifugal forces arising from channel curvature on the phase distribution and flow patterns, and their impact on the thermal characteristics. Unique flow features are identified through the interactions between the fluid phases and vortex structures of the immiscible flow in curved channels. The convective heat transfer in curved channel is appraised in relation to the behaviour of fluid components and curved channel flow parameters. Finally, the study presents a Second-Law irreversibility analysis whereby a thermal optimisation technique is developed for immiscible fluid flow through heated curved channels.

Solitary and transitional waves in pressure-driven two-layer microchannel flow

Similar to the case of the gravity-driven flow (Sisoev and Bennett 2013 Fluid Dyn. Res. 45 015503) we use the integral method to derive evolution equations modeling a pressure-driven two-layer flow of immiscible viscous fluids in a plane microchannel. It is shown that the system possesses a vast set of steady-traveling solitary and transitional waves. Analysis of the phase trajectories of the relevant dynamical system indicates the existence of families of steady-traveling periodic waves.

Characterisation of water-oil drainage process through a reservoir rock sample by digital core analysis

Oil-water relative permeability and capillary pressure of a water-wet digital core are computed using the finite-volume/volume of fluid method and mimicking traditional laboratory steady-state experiments carried out on a water saturated sample. Commercial software is used for immiscible multiphase fluid flow simulations, carried out on a low-cost multicore workstation, and the porescale data are upscaled to derive relative permeability and capillary pressure curves as function of water saturation. The digital sample is obtained by high resolution X-ray computed tomography scanning.

Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes

In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method, together with suggestions for performance optimization.

AN LBM-BASED INVESTIGATION METHOD FOR THERMAL IMMISCIBLE MIXTURE FLUID FLOW IN RECTANGULAR MULTI-JET CAVITY

An investigation method for thermal immiscible mixture fluid flow in rectangular multi-jet cavity using lattice Boltzmann method (LBM) is presented to study influence of controllable factors on quality of mixture generated from the cavity. For immiscible mixture flow, contact area of fluids has great effect on generated mixture. The basic idea is to investigate the relationship between controllable factors and contact area of key components. The contact area is obtained through numerical simulation by an improved LBM, in which temperature equation is extended to multicomponent system. A case study of thermal mixture flow in three-jet cavity using the present method is shown.

Second law analysis for Poiseuille flow of immiscible micropolar fluids in a channel

In this paper, the problem of steady Poiseuille flow of two immiscible incompressible micropolar fluids between two horizontal parallel plates of a channel with constant wall temperatures is studied in terms of entropy generation. The flow is assumed to be governed by Eringen’s micropolar fluid flow equations. The flow region is divided into two zones, the flow of the heavier fluid taking place in the lower zone-I. No slip condition is taken on the plates and at the interface continuity of velocity, micro-rotation, temperature, heat flux and shear stresses is imposed. The velocity, micro-rotation and temperature fields are derived analytically. The dimensionless quantities-entropy generation number (Ns), Bejan number (Be) and irreversibility ratio (ϕ) are analytically derived. The effects of material parameters like micropolarity (ci), couplestress (si) on the velocity, micro-rotation and temperature are investigated. The derived equation for the dimensionless entropy generation number is used to interpret the relative importance of frictions to conduction by varying viscous dissipation parameter. The entropy generation near the plates increases more rapidly in fluid I than in fluid II as viscous dissipation effects become more important in zone I. The velocity and temperature profiles are found to be in good agreement with the distributions of the dimensionless entropy generation number (Ns).

Numerical simulation of single droplet dynamics in three-phase flows using ISPH

In this study, a new surface tension formulation for modeling incompressible, immiscible three-phase fluid flows in the context of incompressible smoothed particle hydrodynamics (ISPH) in two dimensions has been proposed. A continuum surface force model is employed to transform local surface tension force to a volumetric force while physical surface tension coefficients are expressed as the sum of phase specific surface tension coefficients, facilitating the implementation of the proposed method at triple junctions where all three phases are present. Smoothed color functions at fluid interfaces along with artificial particle displacement throughout the computational domain are combined to increase accuracy and robustness of the model. In order to illustrate the effectiveness of the proposed method, several numerical simulations have been carried out and results are compared to analytical data available in literature. Results obtained by simulations are compatible with analytical data, demonstrating that the ISPH scheme proposed here is capable of handling three-phase flows accurately.

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.

Fracture-scale model of immiscible fluid flow

We present a method for modeling immiscible fluid flow in narrow fractures. The method combines a parallel-plate flow model with a recoloration approach adapted from multiple-component lattice-Boltzmann methods. The resulting numerical method is straightforward to implement and accurately reproduces the relevant fluid behavior. To demonstrate the method, single-droplet simulations are compared to analytical solutions that isolate the contributions from the in-plane and normal curvature. Simulations reproducing capillary forces inside a widening aperture are also presented. Excellent agreement is found in all cases considered. Finally, the method's ability to model fracture flow is demonstrated by deriving relative permeability curves for flow through a heterogeneous aperture created between two fractal surfaces.

A modeling approach to droplet contact-line motion dynamics in high-density-ratio two-phase flow

The present study is to investigate the contact line dynamics in high-density-ratio two-phase flow. A two-dimensional lattice Boltzmann model for immiscible fluids flow with gravity is developed, which combines the stabilized numerical discretization for the continuous Boltzmann equation and the diffuse-interface theory. The model is developed on the basis of previous work. However, some significant modifications are made to suit the purpose of the present study, including direct calculation of macroscopic variables without post-collision process and consideration of gravity. The model and numerical method are firstly validated by various flow problems with analytical solutions. It is then used to investigate the contact line motion of a droplet attached on a substrate in shear flow. The influences of a series of flow parameters are systematically investigated and some conclusions are obtained. Above the critical Capillary number, the droplet motion exhibits break-up characteristics. In steady-slip mode, the receding contact angle, θR, decreases and advancing contact angle, θA, increases linearly with the Capillary number, Ca, while the normalized droplet velocity nearly holds constant with different values of Ca. The contact line motion is not sensitive to Reynolds number, Re. When Bond number Bo>1, both the dynamic contact angles and the droplet velocity decrease significantly with increasing Bo. The obtained results are partially compared with those reported by other investigators, and a good agreement has been reached in several aspects, such as break-up characteristics and Bond number effect.

A comparison study of multi-component Lattice Boltzmann models for flow in porous media applications

A comparison study of three different multi-component Lattice Boltzmann models is carried out to explore their capability of describing binary immiscible fluid systems. The Shan–Chen pseudo potential model, the Oxford free energy model and the colour gradient model are investigated using the multi-relaxation time scheme (MRT) algorithm to study the flow of binary immiscible fluids. We investigate Poiseuille flow of layered immiscible binary fluids and capillary fingering phenomena and evaluate the results against analytical solutions. In addition, we examine the capability of the various models to simulate fluids with significant viscosity and density contrast and suitable interface thickness. This is of great importance for large scale flow in porous media applications, where it is important to minimise the interfacial thickness from a computational point of view. We find that the Shan–Chen model can simulate high density ratios up to 800 for binary fluids with the same viscosity. Imposing a viscosity contrast will lead to highly diffusive interfaces in the Shan–Chen model and therefore this will affect significantly the numerical stability. The Free Energy model and the colour gradient model have similar capabilities on this point: they can simulate binary fluids having the same density but with significant viscosity contrast. This is of great importance to study the flow of water, supercritical CO2 and oil in porous media, for CO2 storage and Enhanced Oil Recovery (EOR) operations.

Local Nusselt number enhancement during gas–liquid Taylor bubble flow in a square mini-channel: An experimental study

Taylor bubble flow takes place when two immiscible fluids (liquid–liquid or gas–liquid) flow inside a tube of capillary dimensions within specific range of volume flow ratios. In the slug flows where gas and liquid are two different phases, liquid slugs are separated by elongated Taylor bubbles. This singular flow pattern is observed in many engineering mini-/micro-scale devices like pulsating heat pipes, gas–liquid–solid monolithic reactors, micro-two-phase heat exchangers, digital micro-fluidics, micro-scale mass transfer process, fuel cells, etc. The unique and complex flow characteristics require understanding on local, as well as global, spatio-temporal scales. In the present work, the axial streamwise profile of the fluid and wall temperature for air–water (i) isolated single Taylor bubble and, (ii) a train of Taylor bubbles, in a horizontal square channel of size 3.3 mm × 3.3 mm × 350 mm, heated from the bottom (heated length = 175 mm), with the other three sides kept insulated, are reported at different gas volume flow ratios. The primary aim is to study the enhancement of heat transfer due to the Taylor bubble train flow, in comparison with thermally developing single-phase flows. Intrusion of a bubble in the liquid flow drastically changes the local temperature profiles. The axial distribution of time-averaged local Nusselt number (Nu¯z) shows that Taylor bubble train regime increases the transport of heat up to 1.2–1.6 times more as compared with laminar single-phase liquid flow. In addition, for a given liquid flow Reynolds number, the heat transfer enhancement is a function of the geometrical parameters of the unit cell, i.e., the length of adjacent gas bubble and water plug.