Mesoscale SPH modeling of fluid flow in isotropic porous media

A novel numerical technique—Smoothed Particle Hydrodynamics (SPH) is used to model the fluid flow in isotropic porous media. The porous structure is resolved in a mesoscopic-level by randomly assigning certain portion of SPH particles to fixed locations. A repulsive force, similar in form to the 12-6 Lennard-Jones potential between atoms, is set in place to mimic the interactions between fluid and porous structure. This force is initiated from the fixed porous material particle and may act on its nearby moving fluid particles. In this way, the fluid is directed to pass through the porous structure in physically reasonable paths. For periodic porous systems formed by intersecting solid material with straight parallel fluid channels, the Kozeny formula of permeability was reproduced successfully, which, to a great extent, validates the reliability of the developed SPH model. Further, SPH simulations for the fluid flows induced by an applied streamwise body force in two-dimensional porous structures of different porosities are performed. The macroscopic Darcy's law is confirmed to be valid only in the creeping flow regime. The derived relationship of permeability versus porosity is compared with some existing numerical results/experimental data, which demonstrates that the present SPH model is able to capture the essential features of the fluid flow in porous media.     

Nonlinear acceleration waves in porous media

We review three theories explaining why waves in a diffusion problem can travel with a finite speed. We then briefly look at a class of equivalent fluid theories for sound propagation in porous media. Finally, we derive a Cattaneo model for an elastic material containing a distribution of voids. Nonlinear acceleration wave motion in such a class of materials is also considered.     

A multi-grid technique for coupling fluid flow with porous media flow

In this paper, we consider the coupling of fluid flow with porous media flow. A multi-grid finite element method for the coupled Stokes–Darcy problem with the Beavers–Joseph interface condition is proposed and discussed. The optimal error estimates are obtained. Numerical experiment is given to verify the theoretical analysis and indicate the accuracy and efficiency of the multi-grid method.     

A finite element approach for multiphase fluid flow in porous media

The main scope of this work is to carry out a mathematical framework and its corresponding finite element (FE) discretization for the partially saturated soil consolidation modelling in presence of an immiscible pollutant. A multiphase system with the interstitial voids in the grain matrix filled with water (liquid phase), water vapour and dry air (gas phase) and with pollutant substances, is assumed. The mathematical model addressed in this work was developed in the framework of mixture theory considering the pollutant saturation-suction coupling effects. The ensuing mathematical model involves equations of momentum balance, energy balance and mass balance of the whole multiphase system. Encouraging outcomes were achieved in several different examples.     

On some multiscale algorithms for sector modeling in multiphase flow in porous media

A multiscale algorithm for a multiphase filtration problem is proposed. Filtration fluxes on a fine grid are determined from the solution of the pressure equation on a coarse grid. Further, the domain is decomposed into subdomains with an acceptable number of cells and the full second boundary condition filtration problem is solved using the fluxes. The support operator method has been improved for a complex structure cell for solution of the pressure equation on a coarse grid. This method is a high resolution one: a divergence operator has the approximation of the second order, while fluxes have the approximation of the first order. At the same time, the method allows revealing the solution’s properties related to a fine grid structure.     

Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media

In this study, two microfluidic devices are proposed as simplified 1-D microfluidic analogues of a porous medium. The objectives are twofold: firstly to assess the usefulness of the microchannels to mimic the porous medium in a controlled and simplified manner, and secondly to obtain a better insight about the flow characteristics of viscoelastic fluids flowing through a packed bed. For these purposes, flow visualizations and pressure drop measurements are conducted with Newtonian and viscoelastic fluids. The 1-D microfluidic analogues of porous medium consisted of microchannels with a sequence of contractions/expansions disposed in symmetric and asymmetric arrangements. The real porous medium is in reality, a complex combination of the two arrangements of particles simulated with the microchannels, which can be considered as limiting ideal configurations. The results show that both configurations are able to mimic well the pressure drop variation with flow rate for Newtonian fluids. However, due to the intrinsic differences in the deformation rate profiles associated with each microgeometry, the symmetric configuration is more suitable for studying the flow of viscoelastic fluids at low De values, while the asymmetric configuration provides better results at high De values. In this way, both microgeometries seem to be complementary and could be interesting tools to obtain a better insight about the flow of viscoelastic fluids through a porous medium. Such model systems could be very interesting to use in polymer-flood processes for enhanced oil recovery, for instance, as a tool for selecting the most suitable viscoelastic fluid to be used in a specific formation. The selection of the fluid properties of a detergent for cleaning oil contaminated soil, sand, and in general, any porous material, is another possible application.     

Three-dimensional microscale flow simulation and colloid transport modeling in saturated soil porous media

Transport of sub-micron colloid particles in soil porous media has been mostly studied numerically with unit-cell-based grain-scale geometries. In this study, we develop a more general approach by combining a multiple-grain pore-scale flow simulation with Lagrangian tracking of individual colloids. First, two numerical methods are applied simultaneously to solve viscous flows in a channel partially or fully packed with spherical grain particles, this allows cross-validation of the numerical methods for considered model geometries. It is demonstrated that the mesoscopic lattice Boltzmann approach can more accurately simulate three-dimensional pore-scale flows with multiple grain–grain and grain–wall contact points. Colloid transport is simulated under the combined influence of hydrodynamic forces, Brownian force, and physicochemical forces. Preliminary results demonstrate the capture of colloids by the secondary energy minimum (SEM) well. The local hydrodynamic retardation is shown to reduce the ability for colloids to move into the SEM well, but does not prevent this. Trajectories before and after the capture are also discussed.     

Using virtual reality and percolation theory to visualize fluid flow in porous media

The study of the fluid flow process through porous media can bring valuable contributions in areas like oil exploration and environmental research. In this work, we propose an interactive tool, named VRFluid, that allows visual interpretation of the three-dimensional data generated by the simulation of the fluid flow the porous media. VRFluid comprises a virtual reality engine that provides stereo visualization of the three-dimensional data, and a simulation engine based on a dynamic percolation method to model the fluid flow. VRFluid is composed of two independent main threads, the percolation simulator and the rendering server, that can operate in parallel as a pipeline. We tested our tool on a region of a mature field database, supervised by geophysicists, and obtained images of the interior of the percolation data, providing important results for the interpretation and cluster formation process.     

Combined Lattice Boltzmann and phase-field simulations for incompressible fluid flow in porous media

A Lattice-Boltzmann method for incompressible fluid flow is coupled with the dynamic equations of a phase-field model for multiple order parameters. The combined model approach is applied to computationally evaluate the permeability in porous media. At the boundaries between the solid and fluid phases of the porous microstructure, we employ a smooth formulation of a bounce-back condition related to the diffuse profile of the interfaces. We present simulations of fluid flow in both, static porous media with stationary non-moving interfaces and microstructures performing a dynamic evolution of the phase and grain boundaries. For the latter case, we demonstrate applications to dissolving grain structures with partial melt inclusions and computationally analyse the temporal evolution of the microporosity under wetting conditions at the melt-grain boundaries. In any development state of the material, the Darcy number and the hydraulic conductivity of the porous medium are evaluated for various types of fluid.     

Finite element modelling of flow,heat and mass transfer in fluid saturated porous media

Summary In this article, a short review of numerical modelling of porous medium flow, heat and mass transfer is presented. The focus of the article is mainly on the use of finite element method and velocity correction algorithm. In addition to a detailed discussion on the velocity correction scheme, some essential fundamental and application problems are solved and results are presented. Many of these results are compared against available experimental and numerical data.     

Free boundary problems in the theory of fluid flow through porous media: A numerical approach

In this paper we study from the numerical point of view elliptic free boundary problems in the theory of fluid flow through porous media by a new method. Research supported by C.N.R. in the frame of the collaboration between L. A. N. of Pavia and E. R. A. 215 of C. N. R. S. and of Paris University and carried out also with the cooperation of the Division C. E. T. I. S. of C.C.R. Euratom Ispra.     

Fixed-point algorithms for stationary flow in porous media

We study from the theoretical and experimental points of view some fixed-point algorithms for solving steady-state filtration problems through porous media. The method used applies to a wide class of problems (no restrictions are made on the geometry of the domain or on the boundary conditions; capillarity effects can be treated, the medium can be inhomogeneous and anisotropic). It does not require any previous knowledge on the free boundary, it works on a fixed domain, and the computational cost is slightly more than the cost of solving a linear problem with the overrelaxation method. Moreover, it can be easily implemented in a finite element code. Many numerical tests are presented.     

Numerical parameter identification in multiphase flow through porous media

Multiphase flow is of high interest for the investigation of the behavior of waste in groundwater. The high nonlinearity of the model equations pose special problems. Here, a new parameter identification technique in this context is proposed which takes advantage of recently developed highly efficient numerical simulation techniques. It is based on a reduced Gauss-Newton technique in combination with an efficient gradient computation. Numerical experiments are performed for the McWhorter model problem.     

Finite volume schemes for two-phase flow in porous media

The system of equations obtained from the conservation of multiphasic fluids in porous media is usually approximated by finite volume schemes in the oil reservoir simulation setting. The convergence properties of these schemes are only known in a few simplified cases. The aim of this paper is to present some new results of convergence in more complex cases. These results are based on an adaptation of the H-convergence notion to the limit of discrete approximates.     

一种孔隙介质中地下水流并行计算方法

针对孔隙介质中地下水流动问题提出了一种并行数值计算方法,并基于此设计了一套专用于求解大规模三维地下水流动方程的并行计算模块。计算模块基于区域分解的方法实现对模型区域的并行求解,采用了分布式内存和压缩矩阵技术解决大规模稀疏矩阵的存储及其计算,整合多种并行Krylov子空间方法和预条件子技术迭代求解大规模线性方程组。在Linux集群系统上进行了数值模拟实验,性能测试结果表明,程序具有良好的加速比和可扩展性。     

Multi-level adaptive simulation of transient two-phase flow in heterogeneous porous media

An implicit pressure and explicit saturation (IMPES) finite element method (FEM) incorporating a multi-level shock-type adaptive refinement technique is presented and applied to investigate transient two-phase flow in porous media. Local adaptive mesh refinement is implemented seamlessly with state-of-the-art artificial diffusion stabilization allowing simulations that achieve both high resolution and high accuracy. Two benchmark problems, modelling a single crack and a random porous medium, are used to demonstrate the robustness of the method and illustrate the capabilities of the adaptive refinement technique in resolving the saturation field and the complex interaction (transport phenomena) between two fluids in heterogeneous media.     

Numerical modelling and passive flow control using porous media

The whole flow over a solid body covered by a porous layer is presented. The three main models used in the literature to compute efficiently the fluid flow are given: the reduction of the porous layer to a boundary condition, the coupling of Darcy equation with Navier-Stokes equations and the Brinkman-Navier-Stokes equations or the penalisation method. Numerical simulations on Cartesian grids using the latest model give easily accurate solutions of the flow around solid bodies with or without porous layers. Adding appropriate porous devices to the solid bodies, an efficient passive control of the two-dimensional incompressible flow is achieved. A strong regularisation of the flow is observed and a significant reduction of the vortex induced vibrations or the drag coefficient is obtained.     

Numerical study on two-phase flow through fractured porous media

Based on the flux equivalent principle of a single fracture,the discrete fracture concept was developed,in which the macroscopic fractures are explicitly described as(n-1)dimensional geometry element.On the fundamental of this simplification,the discrete-fractured model was developed which is suitable for all types of fractured porous media.The principle of discrete-fractured model was introduced in detail,and the general mathematical model was expressed subsequently.The fully coupling discrete-fractured ma...