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Contaminant Flow and Transport Simulation in Cracked Porous Media Using Locally Conservative Schemes

Published online by Cambridge University Press:  03 June 2015

Pu Song  and
Shuyu Sun
Pu Song*
Affiliation:
Department of Mathematical Sciences Clemson University, Clemson, SC 29634, USA
Shuyu Sun*
Affiliation:
Department of Mathematical Sciences Clemson University, Clemson, SC 29634, USA Computational Transport Phenomena Laboratory (CTPL), Division of Physical Sciences and Enginerring (PSE), King Abdullah University of Science and Technology (KAUST), 4700 King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Abrabia
*
Email: pus6@pitt.edu
Corresponding author. URL:http://web.kaust.edu.sa/faculty/ShuyuSun/, Email: shuyu.sun@kaust.edu.sa
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Abstract

The purpose of this paper is to analyze some features of contaminant flow passing through cracked porous medium, such as the influence of fracture network on the advection and diffusion of contaminant species, the impact of adsorption on the overall transport of contaminant wastes. In order to precisely describe the whole process, we firstly build the mathematical model to simulate this problem numerically. Taking into consideration of the characteristics of contaminant flow, we employ two partial differential equations to formulate the whole problem. One is flow equation; the other is reactive transport equation. The first equation is used to describe the total flow of contaminant wastes, which is based on Darcy law. The second one will characterize the adsorption, diffusion and convection behavior of contaminant species, which describes most features of contaminant flow we are interested in. After the construction of numerical model, we apply locally conservative and compatible algorithms to solve this mathematical model. Specifically, we apply Mixed Finite Element (MFE) method to the flow equation and Discontinuous Galerkin (DG) method for the transport equation. MFE has a good convergence rate and numerical accuracy for Darcy velocity. DG is more flexible and can be used to deal with irregular meshes, as well as little numerical diffusion. With these two numerical means, we investigate the sensitivity analysis of different features of contaminant flow in our model, such as diffusion, permeability and fracture density. In particular, we study Kd values which represent the distribution of contaminant wastes between the solid and liquid phases. We also make omparisons of two different schemes and discuss the advantages of both methods.

Keywords

65M1265M1565N3076D0776S05Mixed finite element methodsdiscontinuous Galerkin methodsreactive transport equationflow equation
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 4 , August 2012 , pp. 389 - 421
Copyright
Copyright © Global-Science Press 2012

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