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Mundell & Kirkner 1988
Mundell, J.A. and Kirkner, D.J. (1988). Numerical studies of dissolution-induced moving boundary problems from aqueous diffusion in porous media. Journal of Geophysical Research 93: doi: 10.1029/88JB00332. issn: 0148-0227.

Two fixed-mesh, finite element formulations are presented for numerically solving the diffusional mass transport equations involving reversible heterogeneous reactions leading to moving boundaries in porous media. Both schemes assume the existence of local equilibrium between the solid and fluid phases and are based on particular forms of the weak variational statement of the governing differential equations. A front-tracking-type (FT) method is derived from the selection of the aqueous concentration as the primary variable, whereas a formulation similar to enthalpy- type (ET) schemes used to simulate heat conduction with phase change results from the selection of the total component concentration as the primary unknown. The results are compared to analytical solutions for one- and two-component systems involving the dissolution of quartz at 550¿C and 1000 bars and calcium carbonate at 35¿C, respectively. It was found that for problems with significant mass contributions by the reactive solid phase, the FT scheme yields more accurate results than the ET formulation for an equivalent grid and time discretization. While this numerical accuracy is a result of the ability of the FT scheme to capture the discontinuous behavior of the field variable at the moving interface, it is achieved through the use of a more complex numerical algorithm to obtain the converged solution. Realistic, multicomponent systems involving multiple moving boundaries and other chemical reactions increase the complexity of FT formulations, encouraging further development and modification of the ET method to improve its performance.

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Abstract

Keywords
Geochemistry, Chemical evolution, Volcanology, Physics and chemistry of magma bodies
Journal
Journal of Geophysical Research
http://www.agu.org/journals/jb/
Publisher
American Geophysical Union
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