Simulation Of Porous Media Research Articles

MESHLESS POINT COLLOCATION METHOD FOR 1D AND 2D GROUNDWATER FLOW SIMULATION

ABSTRACT For appropriate management of available groundwater, the flow behavior in the porous media has to be analyzed. Meshfree (MFree) method is an alternative numerical approach to commonly used Finite Difference Method (FDM) and Finite Element Method (FEM) to solve more complex engineering problems by simple and accurate manner. MFree method eliminates the drawback of meshing and remeshing as in FDM and FEM. Since there is no need to create a mesh, the time one would spend on conventional mesh generation can be saved. This can translate to substantial cost and time savings in modelling and simulation. In this paper, a meshless method called as Polynomial Point Collocation method (PPCM) with radial basis function has been developed for the groundwater flow simulation in porous media in one and two dimensions. The developed model has been applied for computing head distribution in a hypothetical confined aquifer having different boundary conditions and source, and sink terms. The developed model is tested with analytical and FEM solutions available in literature and found to be satisfactory.

In-silico simulation of porous media: Conception and development of a greedy algorithm

Cubic porous networks consisting of several millions of voids of different sizes are efficiently simulated through a greedy algorithm. The porous network is built on the basis of the Dual Site-Bond Model in which a cavity (site) is always larger than any of its delimiting throats (bonds). When the initial configuration of the cubic network is established by means of a random (Monte Carlo) seeding on a lattice of sites and bonds, the proper allocation of more pore elements becomes troublesome and time-consuming, and there even exists the chance of not achieving a valid pore network. The complexity of this pioneering Monte Carlo algorithm, in the best case, increases according to the third power of the number of pore elements and, in the worst case is asymptotic to infinity. Here, we have succeeded in the development of an smart non-mistake initial seeding situation of sites and bonds that behaves in the way of a greedy algorithm. An initial ordering of sites according to their sizes allows a proper assemblage of these hollows throughout the cubic lattice. From this configuration, the pore network evolves toward the most probable one by a series of legitimate random swappings between sites and bonds. The complexity of the greedy algorithm remained proportional to the cubic power of the total number of sites. In general the execution time of the greedy algorithm results to be faster than that employed with the previous Monte Carlo algorithm.

Study of Conditions for Polyacrylamide Use in Petroleum Reservoirs: Physical Flow Simulation in Porous Media

Abstr act. This article describes the reservoir’s average shear rate calculation and the rheological study of the polymer dispersion under the target reservoir conditions. It also identifies and quantifies the rock-fluid interaction parameters with this reservoir, including the total adsorption, residual resistance factor. The results confirm that the selected polymer is suitable to the target reservoir. Keywor ds: polymer, polyacrylamide, oil recovery, physical simulation, rock-fluid interaction, total adsorption, rheology.

Advanced three-dimensional multiphase flow simulation in porous media reconstructed from X-ray Microtomography using the He–Chen–Zhang Lattice Boltzmann Model

Multiphase flow is a subject of significant interest in the processing of mineral resources and to processing industries in general. Multiphase flow is of significance in the transport of reactants during the percolation of leaching solution in heaps, in the melting of metals, in phase transformation, metal foam processes, underground water transport, in gas and oil recovery and in gas sequestration, just to mention a few examples. The lattice Boltzmann model (LBM) of multiphase fluid flow has now become a collection of models with varying degrees of faithfulness to the properties of real fluids. These models are in a state of evolution as they are becoming better understood and are extended to new applications. In this paper we address the application of a single-component multiphase flow LBM known as the He–Chen–Zhang model coupled with X-ray microtomography (XMT) for the digitalization and simulation of flow in porous media. The model is used for the simulation of fluid penetration into porous samples and the analysis of capillary phenomena. Specifically, this model has been applied for the simulation of percolation in a packed bed of sand particles which is digitalized by XMT.

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.

Comparison of NMR simulations of porous media derived from analytical and voxelized representations

We develop and compare two formulations of the random-walk method, grain-based and voxel-based, to simulate the nuclear-magnetic-resonance (NMR) response of fluids contained in various models of porous media. The grain-based approach uses a spherical grain pack as input, where the solid surface is analytically defined without an approximation. In the voxel-based approach, the input is a computer-tomography or computer-generated image of reconstructed porous media. Implementation of the two approaches is largely the same, except for the representation of porous media. For comparison, both approaches are applied to various analytical and digitized models of porous media: isolated spherical pore, simple cubic packing of spheres, and random packings of monodisperse and polydisperse spheres. We find that spin magnetization decays much faster in the digitized models than in their analytical counterparts. The difference in decay rate relates to the overestimation of surface area due to the discretization of the sample; it cannot be eliminated even if the voxel size decreases. However, once considering the effect of surface-area increase in the simulation of surface relaxation, good quantitative agreement is found between the two approaches. Different grain or pore shapes entail different rates of increase of surface area, whereupon we emphasize that the value of the “surface-area-corrected” coefficient may not be universal. Using an example of X-ray-CT image of Fontainebleau rock sample, we show that voxel size has a significant effect on the calculated surface area and, therefore, on the numerically simulated magnetization response.

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.

Three‐dimensional simulations of biofilm growth in porous media

AbstractBiofilm growth occurs in a variety of random porous media in a range of industrial processes; prediction of its growth and subsequent influence on hydrodynamics is hence desirable. In this study, we present the first numerical 3D pore‐scale model of biofilm growth in porous media, based on a lattice Boltzmann simulation platform complemented with an individual‐based biofilm model (IbM). We use it to explore the coupled interaction between nutrient mass transport, biofilm growth, and hydrodynamics. Biofilm is shown to be very effective at reducing the permeability of porous media, particularly under nutrient limited conditions. We conclude with a direct comparison of 3D and 2D biofilm growth simulations in porous media and show the necessity of performing the simulations in 3D. © 2008 American Institute of Chemical Engineers AIChE J, 2009

Multi‐scale thermo‐fluid transport in porous media

PurposeThe purpose of this paper is to develop an empiricism free, first principle‐based model to simulate fluid flow and heat transfer through porous media.Design/methodology/approachConventional approaches to the problem are reviewed. A multi‐scale approach that makes use of the sample simulations at the individual pore levels is employed. The effect of porous structures on the global fluid flow is accounted for via local volume averaged governing equations, while the closure terms are accounted for via averaging flow characteristics around the pores.FindingsThe performance of the model has been tested for an isothermal flow case. Good agreement with experimental data were achieved. Both the permeability and Ergun coefficient are shown to be flow properties as opposed to the empirical approach which typically results in constant values of these parameters independent of the flow conditions. Hence, the present multi‐scale approach is more versatile and can account for the possible changes in flow characteristics.Research limitations/implicationsFurther validation including non‐isothermal cases is necessary. Current scope of the model is limited to incompressible flows. The methodology can accommodate extension to compressible flows.Originality/valueThis paper proposes a method that eliminates the dependence of the numerical porous media simulations on empirical data. Although the model increases the fidelity of the simulations, it is still computationally affordable due to the use of a multi‐scale methodology.

Numerical simulation of fully saturated porous materials

AbstractFully coupled, porous solid–fluid formulation, implementation and related modeling and simulation issues are presented in this work. To this end, coupled dynamic field equations with u−p−U formulation are used to simulate pore fluid and soil skeleton (elastic–plastic porous solid) responses. Present formulation allows, among other features, for water accelerations to be taken into account. This proves to be useful in modeling dynamic interaction of media of different stiffnesses (as in soil–foundation–structure interaction). Fluid compressibility is also explicitly taken into account, thus allowing excursions into modeling of limited cases of non‐saturated porous media. In addition to these features, present formulation and implementation models in a realistic way the physical damping, which dissipates energy. In particular, the velocity proportional damping is appropriately modeled and simulated by taking into account the interaction of pore fluid and solid skeleton. Similarly, the displacement proportional damping is physically modeled through elastic–plastic processes in soil skeleton. An advanced material model for sand is used in present work and is discussed at some length. Also explored in this paper are the verification and validation issues related to fully coupled modeling and simulations of porous media.Illustrative examples describing the dynamical behavior of porous media (saturated soils) are presented. The verified and validated methods and material models are used to predict the behavior of level and sloping grounds subjected to seismic shaking. Copyright © 2008 John Wiley & Sons, Ltd.

Flow based oversampling technique for multiscale finite element methods

Oversampling techniques are often used in porous media simulations to achieve high accuracy in multiscale simulations. These methods reduce the effect of artificial boundary conditions that are imposed in computing local quantities, such as upscaled permeabilities or basis functions. In the problems without scale separation and strong non-local effects, the oversampling region is taken to be the entire domain. The basis functions are computed using single-phase flow solutions which are further used in dynamic two-phase simulations. The standard oversampling approaches employ generic global boundary conditions which are not associated with actual flow boundary conditions. In this paper, we propose a flow based oversampling method where the actual two-phase flow boundary conditions are used in constructing oversampling auxiliary functions. Our numerical results show that the flow based oversampling approach is several times more accurate than the standard oversampling method. We provide partial theoretical explanation for these numerical observations.

Direct simulation of fluid‐solid mechanics in porous media using the discrete element and lattice‐Boltzmann methods

A detailed understanding of the coupling between fluid and solid mechanics is important for understanding many processes in Earth sciences. Numerical models are a popular means for exploring these processes, but most models do not adequately handle all aspects of this coupling. This paper presents the application of a micromechanically based fluid‐solid coupling scheme, lattice‐Boltzmann discrete element method (LBDEM), for porous media simulation. The LBDEM approach couples the lattice‐Boltzmann method for fluid mechanics and a discrete element method for solid mechanics. At the heart of this coupling is a previously developed boundary condition that has never been applied to coupled fluid‐solid mechanics in porous media. Quantitative comparisons of model results to a one‐dimensional analytical solution for fluid flow in a slightly deformable medium indicate a good match to the predicted continuum‐scale fluid diffusion‐like profile. Coupling of the numerical formulation is demonstrated through simulation of porous medium consolidation with the model capturing poroelastic behavior, such as the coupling between applied stress and fluid pressure rise. Finally, the LBDEM model is used to simulate the genesis and propagation of natural hydraulic fractures. The model provides insight into the relationship between fluid flow and propagation of fractures in strongly coupled systems. The LBDEM model captures the dominant dynamics of fluid‐solid micromechanics of hydraulic fracturing and classes of problems that involve strongly coupled fluid‐solid behavior.

A DYNAMIC, ADAPTIVE, LOCALLY CONSERVATIVE, AND NONCONFORMING SOLUTION STRATEGY FOR TRANSPORT PHENOMENA IN CHEMICAL ENGINEERING

A family of discontinuous Galerkin (DG) methods are formulated and applied to chemical engineering problems. They are the four primal discontinuous Galerkin schemes for space discretization: symmetric interior penalty Galerkin, Oden-Babuška-Baumann DG formulation, nonsymmetric interior penalty Galerkin, and incomplete interior penalty Galerkin. Numerical examples of DG to solve typical chemical engineering problems, including a diffusion-convection-reaction system in a catalytic particle, a problem of heat transfer in a fixed bed, and flow and contaminant transport simulations in porous media, are presented. This article highlights the substantial advantages of DG on adaptive mesh modification over traditional methods. In particular, we propose and investigate the dynamic mesh modification strategy for DG guided by mathematically sound a posteriori error estimators.

In silico study of the wettabilitty effects on gas cluster growth by solute diffusion in correlated porous media

Simulations of bubble growth in porous media are carried out with a 2D numerical automaton built on a set of hypotheses derived from experimental observations at pore scale. Various types of 2D numerical networks are used as models of porous media with the aim to study the outcome of the combined effects of the wettabilitty (homogeneous and mixed) and the spatial correlation among the porous network entities on the evolution of a gas cluster growing by solute diffusion into it. The porous networks are constructed by using a variation of the dual site bond model (DSBM) framework. For the same pore-size distribution, the DSBM can provide simulated porous media of different topological structures. Under these scenarios, numerical simulations concerning the growth pattern and the growth rate of a single gas cluster are performed.

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.

Toe-To-Heel Waterflooding. Part ll: 3D Laboratory-Test Results

Summary A new waterflooding process, toe-to-heel waterflooding (TTHW), was developed, based partly on a recently developed thermal TTH displacement process, TTH air injection (THAI). TTHW is a novel oil-recovery process that uses a horizontal producer (HP) and a vertical injector (VI). The HP has its horizontal leg located at the top of formation, while its toe is close to the VI, which is perforated at the lower part of the formation. TTHW realizes a gravity-stable displacement, in which the water/oil mobility ratio becomes less important and its detrimental effect on sweep efficiency is diminished; the injected water always breaks through at the toe, after which water cut gradually increases. A systematic investigation of the TTHW process in a Hele-Shaw laboratory model mimicking a simulated porous medium showed that the process substantially improved the vertical sweep efficiency as compared to conventional waterflooding. Following these semiquantitative tests, a more comprehensive 3D-model testing was undertaken to investigate the overall sweep efficiency of the process. The 3D model consists of a metal box filled with glass beads and saturated with oil at connate-water saturation. Oil was displaced with high-salinity brine, either in a TTH configuration or in a conventional array, using only vertical wells. A staggered line drive was used by injecting water in two vertical wells located at one side of the box and producing oil by using either an HP with its toe close to the injection line or a vertical producer located at the HP's heel position. Several TTHW tests were carried out at different injection rates. For a given injection rate, the TTHW results were compared to those of conventional-waterflooding tests. For the same amount of water injected, the ultimate oil recovery increased by a factor of up to 2, as compared to that for conventional waterflooding. All in all, the results of these investigations show that the novel TTHW process is sound and can be optimized further.

LB simulation on soot combustion in porous media

Although diesel engines have an advantage of low fuel consumption in comparison with gasoline engines, several problems must be solved. One of the major concerns is that diesel exhaust gas has more particle matters (PM) including soot, which are suspected to be linked to human carcinogen. As one of the key technologies, a diesel particulate filter (DPF) has been developed to reduce PM in the after-treatment of exhaust gas. In this study, we conduct lattice Boltzmann (LB) simulation on combustion in porous media. Results show that the combustion reaction is well simulated to observe the decrease of soot attached to the porous wall. This information is indispensable for the better design of DPF, and LB method can be a good tool for combustion simulation in porous 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.

Combustion simulation with Lattice Boltzmann method in a three-dimensional porous structure

To simulate the flow in a three-dimensional porous structure, we have used the Lattice Boltzmann method (LBM). The distribution functions for flow, temperature, and concentration fields are solved to simulate the regeneration process of diesel particulate filter (DPF). For a benchmark study, we have conducted the calculation in simple geometry. To change the flow characteristics such as porosity and tortuosity, obstacles of different number and size are selected, which are randomly placed in the duct. The flow pattern is changed with obstacle size even at the same porosity. To confirm the validity of our calculation, the results are compared with the empirical relationships of the Blake–Kozeny and Ergun equations, in the non-dimensional form using the Ergun coordinates of Reynolds number and friction factor. Numerical results show good agreements with the empirical predictions. Soot combustion is well simulated to show the effects of oxygen on the reaction rate. Finally, the real porous geometry has been tested. The porous structure of Ni–Cr metal has been obtained by the three-dimensional computer tomography technique. Results show that the inhomogeneous flow is observed, and there are regions where the temperature is locally higher. This information is indispensable for the better design of DPF. LBM can be a good tool for combustion simulation in porous media.