Numerical modelling of double diffusion driven reactive flow transport in deformable fluid-saturated porous media with particular consideration of temperature-dependent chemical reaction rates

Numerical methods ave used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. in particular, thp temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAG and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed The coupled problem is divided into two subproblems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, if is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.

Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate. (c) 2005 Elsevier Ltd. All rights reserved.

Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media

DEM modelling of the motion of coarse fractions of the charge inside SAG mills has now been well established for more than a decade. In these models the effect of slurry has broadly been ignored due to its complexity. Smoothed particle hydrodynamics (SPH) provides a particle based method for modelling complex free surface fluid flows and is well suited to modelling fluid flow in mills. Previous modelling has demonstrated the powerful ability of SPH to capture dynamic fluid flow effects such as lifters crashing into slurry pools, fluid draining from lifters, flow through grates and pulp lifter discharge. However, all these examples were limited by the ability to model only the slurry in the mill without the charge. In this paper, we represent the charge as a dynamic porous media through which the SPH fluid is then able to flow. The porous media properties (specifically the spatial distribution of porosity and velocity) are predicted by time averaging the mill charge predicted using a large scale DEM model. This allows prediction of transient and steady state slurry distributions in the mill and allows its variation with operating parameters, slurry viscosity and slurry volume, to be explored. (C) 2006 Published by Elsevier Ltd.

Effects of geological inhomogeneity on high Rayleigh number steady state heat and mass transfer in fluid-saturated porous media heated from below

A parametric study is carried out to investigate how geological inhomogeneity affects the pore-fluid convective flow field, the temperature distribution, and the mass concentration distribution in a fluid-saturated porous medium. The related numerical results have demonstrated that (1) the effects of both medium permeability inhomogeneity and medium thermal conductivity inhomogeneity are significant on the pore-fluid convective flow and the species concentration distribution in the porous medium; (2) the effect of medium thermal conductivity inhomogeneity is dramatic on the temperature distribution in the porous medium, but the effect of medium permeability inhomogeneity on the temperature distribution may be considerable, depending on the Rayleigh number involved in the analysis; (3) if the coupling effect between pore-fluid flow and mass transport is weak, the effect of the Lewis number is negligible on the pore-fluid convective flow and temperature distribution, hut it is significant on the species concentration distribution in the medium.

Effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in deformable fluid-saturated porous media heated from below

In this paper, a solution method is presented to deal with fully coupled problems between medium deformation, pore-fluid flow and heat transfer in fluid-saturated porous media having supercritical Rayleigh numbers. To validate the present solution method, analytical solutions to a benchmark problem are derived for some special cases. After the solution method is validated, a numerical study is carried out to investigate the effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in fluid-saturated media when they are heated from below. The related numerical results have demonstrated that: (1) medium thermoelasticity has a little influence on the overall pattern of convective pore-fluid flow, but it has a considerable effect on the localization of medium deformation, pore-fluid flow, heat transfer and mineralization in a porous medium, especially when the porous medium is comprised of soft rock masses; (2) convective pore-fluid flow plays a very important role in the localization of medium deformation, heat transfer and mineralization in a porous medium. (C) 1999 Elsevier Science S.A. All rights reserved.

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

Finite element modelling of dissipative structures for nonequilibrium chemical reactions in fluid-saturated porous media

We use the finite element method to model and predict the dissipative structures of chemical species for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. In particular, we explore the conditions under which dissipative structures of the species may exist in the Brusselator type of nonequilibrium chemical reaction. Since this is the first time the finite element method and related strategies have been used to study the chemical instability problems in a fluid-saturated porous medium, it is essential to validate the method and strategies before they are put into application. For this purpose, we have rigorously derived the analytical solutions for dissipative structures of chemical species in a benchmark problem, which geometrically is a square. Comparison of the numerical solutions with the analytical ones demonstrates that the proposed numerical method and strategy are robust enough to solve chemical instability problems in a fluid-saturated porous medium. Finally, the related numerical results from two application examples indicate that both the regime and the magnitude of pore-fluid flow have significant effects on the nature of the dissipative structures that developed for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. The motivation for this study is that self-organization under conditions of pore-fluid flow in a porous medium is a potential mechanism of the orebody formation and mineralization in the upper crust of the Earth. (C) 2000 Elsevier Science S.A. All rights reserved.

Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Surface diffusion of adsorbed molecules in porous media: Monolayer, multilayer, and capillary condensation regimes

This review provides an overview of surface diffusion and capillary condensate flow in porous media. Emphasis has been placed on the distinction between purely surface diffusion, multilayer surface diffusion, and, capillary condensate flow.

A new equation for macroscopic description of capillary rise in porous media

Capillary rise in porous media is frequently modeled using the Washburn equation. Recent accurate measurements of advancing fronts clearly illustrate its failure to describe the phenomenon in the long term. The observed underprediction of the position of the front is due to the neglect of dynamic saturation gradients implicit in the formulation of the Washburn equation. We consider an approximate solution of the governing macroscopic equation, which retains these gradients, and derive new analytical formulae for the position of the advancing front, its speed of propagation, and the cumulative uptake. The new solution properly describes the capillary rise in the long term, while the Washburn equation may be recovered as a special case. (C) 2004 Elsevier Inc. All rights reserved.

Three-dimensional simulation of the rolling of a saturated fibro-porous media

This paper describes recent advances made in computational modelling of the sugar cane liquid extraction process. The saturated fibro-porous material is rolled between circumferentially grooved rolls, which enhance frictional grip and provide a low-resistance path for liquid flow during the extraction process. Previously reported two-dimensional (2D) computational models, account for the large deformation of the porous material by solving the fully coupled governing fibre stress and fluid-flow equations using finite element techniques. While the 2D simulations provide much insight into the overarching cause-effect relationships, predictions of mechanical quantities such as roll separating force and particularly torque as a function of roll speed and degree of compression are not satisfactory for industrial use. It is considered that the unsatisfactory response in roll torque prediction may be due to the stress levels that exist between the groove tips and roots which have been largely neglected in the geometrically simplified 2D model. This paper gives results for both two- and three-dimensional finite element models and highlights their strengths and weaknesses in predicting key milling parameters. (c) 2005 Elsevier B.V. All rights reserved.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.