Effect of Heterogeneity on Advection-Reaction Problem in Porous Media Using a Stochastic Eulerian Flow Model
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abstract
Flow and transport in a porous medium coupled with a reaction is influenced by the medium heterogeneity. The effective macroscopic equations for flow and reaction must incorporate such information. In this paper, we consider upscaling of the advection-reaction problem using spectral theory. The approach follows original work by Gelhar and Axness [2]. The reaction occurs between an injected chemical and a stationary mineral residing in the pore space. A one-step nonlinear bimolecular dissolution reaction takes place between the two chemical species. The heterogeneity is in flow permeability field, which is random and correlated in space. Initial distribution of the mineral surface area is considered to be linearly correlated with the permeability field. A stochastic analysis of flow, transport and reaction is performed using first-order perturbations. The reaction front propagation in the heterogeneous medium is then analyzed and field-scale expressions are obtained for the coefficients in reaction rate, effective flow velocity and longitudinal macrodispersivity. The heterogeneity is shown to influence flow, macrodispersion and reaction in porous medium. Furthermore, its presence develops inter-dependency between the three existing mechanisms.
