Advances in Engineering Advances in Engineering features breaking research judged by Advances in Engineering advisory team to be of key importance in the Engineering field. Papers are selected from over 10,000 published each week from most peer reviewed journals.
Applied Mathematical Modelling, Volume 37, Issues 18–19, 2013, Pages 8533-8542.
Zhijie Xu, Paul Meakin
Energy Resource Recovery & Management, Idaho National Laboratory, Idaho Falls, ID 83415, USA and
Carbon Resource Management Department, Idaho National Laboratory, Idaho Falls, ID 83415, USA and
Center for the Physics of Geological Processes, University of Oslo, Norway and
Institute for Energy Technology, Kjeller, Norway.
Abstract
An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter{Alpha} that represents the effects of microscopic heterogeneity. The parameter {Alpha}, confined to the range of [−0.5, 0.5] for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and ε. Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.
