Multilayered Porous Media Research Articles

An Analytical Solution to the One-Dimensional Solute Advection-Dispersion Equation in Multi-Layer Porous Media

An analytical solution to the one-dimensional solute advection-dispersion equation in multi-layer porous media is derived using a generalized integral transform method. The solution was derived under conditions of steady-state flow and arbitrary initial and inlet boundary conditions. The results obtained by this solution agree well with the results obtained by numerically inverting Laplace transform-generated solutions previously published in the literature. The analytical solution presented in this paper provides more flexibility with regard to the inlet conditions. The numerical evaluation of eigenvalues and matrix exponentials required in this solution technique can be accurately and efficiently computed using the sign-count method and eigenvalue evaluation methods commonly available. The illustrative calculations presented herein have shown how an analytical solution can provide insight into contaminant distribution and breakthrough in transport through well defined layered column systems. We also note that the method described here is readily adaptable to two and three-dimensional transport problems.

BEM Solution for Design of Trenches in Multilayered Landfills

A two-dimensional (2D) numerical model for a convection-diffusion flow of a mixture of gases through a multilayered porous medium has been developed with the aim to obtain criteria for the optimal design of venting trenches for gas collection from a landfill. The proposed numerical scheme is based on the boundary element formulation of the governing equations, in which the dual reciprocity method (DRM) is used to transform the resulting domain integrals to the boundary. The scheme is improved by the use of a domain decomposition algorithm, which allows a better representation of the physical problem. From present numerical analysis it can be concluded that it is sufficient to construct venting trenches that only cross the top covering layer of the landfill, as long as there are provided enough pathways to guarantee a gentle gas flow across the separation layers between waste layers inside the landfill. Venting structures that cross the entire depth of the repository, as it is usually done in landfill design, are not necessary.

Permeability effects of the ceramic candle filter on back-pulse cleaning system

The flow characteristics inside the ceramic candle filter system used in hot gas cleanup was investigated. The filter system admits high pressure back-pulse air to blow out the dust cake. The pressure drop across the filter barrier plays a critical role in dust removal. The filter medium and dust cakes were considered as multi-layered porous media and were then modeled using Darcy’s effective permeability model. Theκ-e model was adopted to study the turbulent flow in the filter system using FLUENT. A parametric study of the permeability of the filter media was performed to investigate the effects of dust cakes on the flow phenomena, in conjunction with the non-Darcian effect of the porous media flow and non-homogeneous boundary conditions in the inlet and the outlet.

BEM SOLUTION FOR THE PROBLEM OF FLUX OF A MULTICOMPONENT MIXTURE OF GASES OUT OF A MULTILAYER LANDFILL

SUMMARY A two-dimensional numerical model for convection-diffision flow of a multigas mixture through a multilayer porous medium was developed with the aim to be used for evaluation of emissions of gases from landfills. The proposed model is based on the boundary element-dual reciprocity method. Time-independent one-dimensional analytical solutions for a multilayer domain were found for the cases of a single gas and a two-gas mixture and used to verify the accuracy of the model. Although the proposed technique is a simple one, consisting only of boundary integrals, it was found that the technique can be applied with satisfactory accuracy to the problem at which it was initially aimed.

Multi-region boundary element analysis of unconfined seepage problems in excavations

A multi-region boundary element method (BEM) is presented for the seepage analysis in deep excavations. In the formulation, soil foundation is regarded as a multilayered porous medium possessing the zoned inhomogeneous hydraulic conductivity. Based on Darcy's law, a two-dimensional steady state differential equation with transient free surface conditions is adopted. With a fundamental solution of the potential problem, a generalized multiregion boundary element method is developed. The transient boundary conditions are treated by means of the Galerkin scheme of the θ family approximation and are imposed into the boundary integral formulation. The essential features of the BEM are that it concerns the zoned inhomogeneous hydraulic conductivity of soil media, and that the assembly of each individual region can process in the same way as in finite element method (FEM) with much less computer memory storage. Several unconfined seepage problems are solved to demonstrate the performance of the multi-region BEM.

One‐dimensional analytical solutions for the migration of a three‐member radionuclide decay chain in a multilayered geologic medium

Analytical solutions are presented for the one‐dimensional convective‐dispersive and nondispersive equilibrium transport equations of a three‐member radionuclide decay chain in a multilayered porous media. The solution for the nondispersive case is exact. The solution for the general case, although analytic in the first layer, takes a semianalytical form in the subsequent layers by virtue of its numerical integration requirements. The solutions are based on the Laplace transformation technique. Two types of boundary conditions are considered at the source, i.e., a continuous and a band release mode. The accuracy of the solutions was satisfactorily tested on a selected number of problems for which experimental and analytical solutions were available. The practical use of the solutions in a two‐dimensional domain is illustrated by a scenario of radionuclide migration from a high‐level waste repository located in a saturated multilayered aquifer.

Onset of convection in a layered porous medium heated from below

The formalism required to determine the criterion for the onset of convection in a multi-layered porous medium heated from below is developed using a straightforward linear stability analysis. Detailed results for two- and three-layer configurations are presented. These results show that large permeability differences between the layers are required to force the system into an onset mode different from a homogeneous system.