Simulation Of Flow In Porous Media Research Articles

NUMERICAL INSPECTION OF TURBULENT/LAMINAR NONREACTIVE AND LAMINAR COMBUSTIVE REACTIVE FLOWS IN POROUS MEDIA

In this study, the two-dimensional (2D) axisymmetric models of the turbulent/laminar nonreactive and the laminar combustive reactive flows in porous media are simulated numerically by the finite volume method along with the SIMPLE algorithm. The turbulence is simulated by a k − ε model adapted to the porous structure due to the additional source terms. The premixed combustion of methane-air is simulated by applying the single step chemical reaction mechanism. The obtained results for the flow simulation in porous media show that the turbulent kinetic energy is amplified within the foam and separated flow regions do not form or penetrate inside the porous material in the turbulent flow model. The simulation of the premixed laminar submerged flames indicates the super adiabatic combustion in the lean mixtures and implies the flame acceleration which results in higher thermal loads in these flames. Furthermore, the stabilization process and the position of flame within the foam are examined through using different methods for convergence of the numerical code and the acquired predictions are compared to the previous results of the similar research.

A boundary reconstruction scheme for lattice Boltzmann flow simulation in porous media

A novel boundary reconstruction scheme is developed utilising the reinitialisation scheme of the Level Set Method (LSM). The proposed scheme transfers usual digitally defined step-like boundary data to continuously smooth surface data. It is confirmed that the lattice boltzmann simulation by the Interpolated Bounce-Back (IBB) Boundary Condition (BC) with the present scheme well reproduces the drag coefficients of a cylinder and a sphere. Then this numerical scheme is applied to simulate flows in porous media which have the body-centred cubic structure. The results indicate that the present scheme improves the shape representation and thus the prediction accuracy is less sensitive to grid resolutions.

Application of Constrained Interpolation Profile (CIP) Method for Numerical Simulation of Two-phase Flow in Porous Media

Constrained Interpolation Profile（CIP）法を適用した多孔質媒体内2相流動シミュレーション手法を開発する。有限差分法および格子差分と組み合わせたストリームライン法の2手法に対し，いずれも流動方程式の変形により，飽和率に関する双曲型方程式が導出され，IMPES法に組み込むことでCIP法が適用できる。適用に際しては，離散化された各点上に飽和率の値のみでならず，その空間勾配をモデル変数として加味する。空間勾配は飽和率方程式を空間微分することで得られる。これらの方程式は連立され，時間分離解法に基づき移流項と非移流項に分けられ計算される。それぞれCIPスキーム，有限差分法を用いて順に計算が実行される。数値実験の結果から，当該計算手法は一般に用いられる従来の解法に比べ，ショックフロント付近での数値拡散を抑えた高精度な解法であることが確認された。

Wavelet-based SPAI pre-conditioner using local dropping

In this work we performed an experimental study to determine if a wavelet basis can be used to build and apply a highly parallel and low density pre-conditioner known as sparse approximation of the inverse(SPAI), to solve large and sparse linear systems. Test matrices arising from discretizing a second order 3D elliptic scalar operator and from fluid flow simulation in porous media were used as test cases. The results show that low density wavelet-based SPAI pre-conditioners can be built and applied to yield good results.

Accurate multiscale finite element methods for two-phase flow simulations

In this paper we propose a modified multiscale finite element method for two-phase flow simulations in heterogeneous porous media. The main idea of the method is to use the global fine-scale solution at initial time to determine the boundary conditions of the basis functions. This method provides a significant improvement in two-phase flow simulations in porous media where the long-range effects are important. This is typical for some recent benchmark tests, such as the SPE comparative solution project [M. Christie, M. Blunt, Tenth spe comparative solution project: a comparison of upscaling techniques, SPE Reser. Eval. Eng. 4 (2001) 308–317], where porous media have a channelized structure. The use of global information allows us to capture the long-range effects more accurately compared to the multiscale finite element methods that use only local information to construct the basis functions. We present some analysis of the proposed method to illustrate that the method can indeed capture the long-range effect in channelized media.

High order Godunov mixed methods on tetrahedral meshes for density driven flow simulations in porous media

Two-dimensional Godunov mixed methods have been shown to be effective for the numerical solution of density-dependent flow and transport problems in groundwater even when concentration gradients are high and the process is dominated by density effects. This class of discretization approaches solves the flow equation by means of the mixed finite element method, thus guaranteeing mass conserving velocity fields, and discretizes the transport equation by mixed finite element and finite volumes techniques combined together via appropriate time splitting. In this paper, we extend this approach to three dimensions employing tetrahedral meshes and introduce a spatially variable time stepping procedure that improves computational efficiency while preserving accuracy by adapting the time step size according to the local Courant–Friedrichs–Lewy (CFL) constraint. Careful attention is devoted to the choice of a truly three-dimensional limiter for the advection equation in the time-splitting technique, so that to preserve second order accuracy in space (in the sense that linear functions are exactly interpolated). The three-dimensional Elder problem and the saltpool problem, recently introduced as a new benchmark for testing three-dimensional density models, provide assessments with respect to accuracy and reliability of this numerical approach.

Stochastic Eulerian model for the flow simulation in porous media. Unconfined aquifers*

This work deals with a stochastic unconfined aquifer flow simulation in statistically isotropic saturated porous media. This approach is a generalization of the 3D model we developed in [13]. In this paper we deal with a 2D model obtained via depth-averaging of the 3D model. The average hydraulic conductivity is assumed to be a random field with a lognormal distribution. Assuming the fluctuations in the hydraulic conductivity to be small we construct a stochastic Eulerian model for the flow as a Gaussian random field with a spectral tensor of a special structure derived from Darcy's law. A randomized spectral representation is then used to simulate this random field. A series of test calculations confirmed the high accuracy and computational efficiency of the method.

An efficient box-scheme for convection–diffusion equations with sharp contrast in the diffusion coefficients

In this paper, we introduce a box-scheme for time-dependent convection–diffusion equations, following principles previously introduced by Courbet in [Rech. Aérospatiale 4 (1990) 21] for hyperbolic problems. This scheme belongs to the category of mixed finite-volume schemes. This means that it works on irregular meshes (finite-volume scheme) and computes simultaneously the principal unknown and its gradient in all Peclet regimes, ranging from pure diffusion ( Pe=0) to pure convection ( Pe=+∞). The present paper focuses mainly on the design of the scheme, which is non-standard, in the case of the 1D convection–diffusion equation. The version of the scheme presented here is of first or second order depending on the local Peclet number. We extend the 1D scheme afterwards in 2D by an ADI like technique. Several numerical results on 1D and 2D test-cases of interest for flow simulation in porous media are presented, some of them exhibiting sharp contrasts in diffusion coefficients.

Stochastic Eulerian model for the flow simulation in porous media

This work deals with the stochastic flow simulation in statistically isotropic and anisotropic saturated porous media in 3D case. The hydraulic conductivity is assumed to be a random field with lognormal distribution. Under the assumption of smallness of fluctuations in the hydraulic conductivity we construct a stochastic Eulerian model for the incompressible flow as a divergenceless Gaussian random field with a spectral tensor of a special structure derived from Darcy's law. A randomized spectral representation is then used to simulate this random field. Numerical results are compared with the analytical results obtained by the small pertrubation expansion. A series of test calculations confirmed the high accuracy and computational efficiency of the method. Comparisons with asymptotically exact results show a good agreement.

Stochastic Eulerian model for the flow simulation in porous media

This work deals with the stochastic flow simulation in statistically isotropic and anisotropic saturated porous media in 3D case. The hydraulic conductivity is assumed to be a random field with lognormal distribution. Under the assumption of smallness of fluctuations in the hydraulic conductivity we construct a stochastic Eulerian model for the incompressible flow as a divergenceless Gaussian random field with a spectral tensor of a special structure derived from Darcy's law. A randomized spectral representation is then used to simulate this random field. Numerical results are compared with the analytical results obtained by the small pertrubation expansion. A series of test calculations confirmed the high accuracy and computational efficiency of the method. Comparisons with asymptotically exact results show a good agreement.

Thermodynamic Automaton Simulations of Fluid Flow and Diffusion in Porous Media

A thermodynamic automaton model of fluid flow in porous media is presented. The model is a nonrelativistic version of a Lorentz invariant lattice gas model constructed by Udey et al. (1998). In the previous model it was shown that the energy momentum tensor and the relativistic Boltzman equation can be rigorously derived from the collision and propagation rules. In the present paper we demonstrate that this nonrelativistic model can be used to accurately simulate well known results involving single phase flow and diffusion in porous media. The simulation results show that (1) one-phase flow simulations in porous media are consistent with Darcy's law; (2) the apparent diffusion coefficient decreases with a decrease in permeability; (3) small scale heterogeneity does not affect diffusion significantly in the cases considered.

Vadose Zone Composite Hydraulic Conductivity

Grid networks, consisting of nodes and line elements, are often used in porous media flow simulation. An important step in the simulation process is the quantification of the line element conductivity when the pressure or capillary potential at both end nodes is given. Under saturated condition, when the porous medium is layered, the variation of conductivity along the line element is treated by calculating a composite conductivity as the line element conductivity. The composite conductivity under saturated condition can be derived analytically and is the harmonic mean of the saturated conductivity of the layers. For the unsaturated flow in the vadose zone, analytically derived composite conductivity is not available. Heuristic rules, including weighted, geometric, and harmonic means, have been used to estimate line element conductivity in practice. The lack of agreement in estimating composite conductivity indicates that the simulation technique for the vadose zone has not reached its maturity, and that ...

Domain decomposition and multigrid solvers for flow simulation in porous media on distributed memory parallel processors

Realistic simulations of fluid flow in oil reservoirs have been proven to be computationally intensive. In this work, techniques for solving large sparse systems of linear equations that arise in simulating these processes are developed for parallel computers such as INTEL hypercubes iPSC/2 and iPSC/860. This solver is based on a combined multigrid and domain decomposition approach. The Algorithm uses line corrections solved using a multigrid method, line Jacobi and block incomplete domain decomposition as an overall preconditioner for a conjugate gradient-like acceleration method, ORTHOMIN (k). This is shown to be a factor of ten times faster on a 32-processor hypercube compared to widely used sequential solvers. Three test problems are used to validate the results which include implicit wells and faults: The first is based on highly heterogeneous two-phase flow, the second on the SPE Third Comparative Solution and the third on real production compositional data.

Glowing crystals

In this paper we propose a locally conservative Galerkin (LCG) finite element method for two-phase flow simulations in heterogeneous porous media. The main idea of the method is to use the property of local conservation at steady state conditions in order to define a numerical flux at element boundaries. It provides a way to apply standard Galerkin finite element method in two-phase flow simulations in porous media. The LCG method has all the advantages of the standard finite element method while explicitly conserving fluxes over each element. All the examples presented show that the formulation employed is accurate and robust, while using less CPU time than finite volume method.