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A class of analytical solutions for multidimensional multispecies diffusive transport coupled with precipitation‐dissolution reactions and porosity changes
Author(s) -
Hayek Mohamed,
Kosakowski Georg,
Jakob Andreas,
Churakov Sergey V.
Publication year - 2012
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2011wr011663
Subject(s) - dissolution , precipitation , porous medium , porosity , partial differential equation , numerical analysis , mathematics , statistical physics , computer science , mathematical optimization , mathematical analysis , chemistry , geology , physics , geotechnical engineering , meteorology
One of the challenging problems in mathematical geosciences is the determination of analytical solutions of nonlinear partial differential equations describing transport processes in porous media. We are interested in diffusive transport coupled with precipitation‐dissolution reactions. Several numerical computer codes that simulate such systems have been developed. Analytical solutions, if they exist, represent an important tool for verification of numerical solutions. We present a methodology for deriving such analytical solutions that are exact and explicit in space and time variables. They describe transport of several aqueous species coupled to precipitation and dissolution of a single mineral in one, two, and three dimensions. As an application, we consider explicit analytical solutions for systems containing one or two solute species that describe the evolution of solutes and solid concentrations as well as porosity. We use one of the proposed analytical solutions to test numerical solutions obtained from two conceptually different reactive transport codes. Both numerical implementations could be verified with the help of the analytical solutions and show good agreement in terms of spatial and temporal evolution of concentrations and porosities.