Davit, Y. and Wood, B. D. and Debenest, G. and Quintard, M.
(2012)
Correspondence between one and twoequation models for solute
transport in tworegion heterogeneous porous media.
Transport in Porous Media
.
(Submitted)

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Abstract
In this work, we study the transient behavior of upscaled models for solute transport in tworegion porous media. We focus on the following three models: (1) a time nonlocal, twoequation model (2eqnlt). This model does not rely on time constraints and, therefore, is particularly useful in the shorttime regime, when the time scale of interest (t) is smaller than the characteristic time (T1) for the relaxation of the effective macroscale parameters (i.e., when t ≤ T1); (2) a time local, twoequation model (2eq). This model can be adopted when (t) is significantly larger than (T1) (i.e., when t » T1); and (3) a oneequation, timeasymptotic formulation (1eq∞). This model can be adopted when (t) is significantly larger than the time scale (T2) associated with exchange processes between the two regions (i.e., when t » T2). In order to obtain some physical insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in simple cases. The main result of this paper is to show that there is weak longtime convergence of the solution of (2eq) toward the solution of (1eq∞) in terms of standardized moments but, interestingly, not in terms of centered moments. Physically, our interpretation of this result is that the spreading of the solute is dominating higher order nonzero perturbations in the asymptotic regime.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1525 
Deposited By:  Peter Hudston 
Deposited On:  04 Jul 2012 08:13 
Last Modified:  29 May 2015 19:13 
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