Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 374, Issue 2078, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2015.0424
Keywords
reactive transport; geochemical modelling; moving boundary problem; similarity solution
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Funding
- Institute of Geophysics, Planetary Physics and Signatures (IGPPS) at Los Alamos National Laboratory [230859]
- National Science Foundation [EAR0739803, EAR1239281]
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We propose a new composite similarity variable, based on which a similarity solution is derived for reaction front propagation in fracture-matrix systems. The similarity solution neglects diffusion/dispersion within the fracture and assumes the existence of a sharp reaction front in the rock matrix. The reaction front location in the rock matrix is shown to follow a linear decrease with distance along the fracture. The reaction front propagation along the fracture is shown to scale like diffusion (i.e. as the square root of time). The similarity solution using the composite similarity variable appears to be applicable to a broad class of reactive transport problems involving mineral reactions in fracture-matrix systems. It also reproduces the solutions for non-reactive solute and heat transport when diffusion/dispersion/conduction are neglected in the fracture. We compared our similarity solution against numerical simulations for nonlinear reactive transport of an aqueous species with a mineral in the rock matrix. The similarity solutions agree very well with the numerical solutions, especially at later times when diffusion limitations are more pronounced. This article is part of the themed issue 'Energy and the subsurface'.
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