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Analytical solutions for flow in porous media with multicomponent cation exchange reactions
Author(s) -
Venkatraman Ashwin,
Hesse Marc A.,
Lake Larry W.,
Johns Russell T.
Publication year - 2014
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 - 10.1002/2013wr015091
Subject(s) - porous medium , conservation law , conservation of mass , dispersion (optics) , riemann problem , thermodynamics , chemistry , flow (mathematics) , phase (matter) , groundwater , mathematics , mechanics , porosity , physics , geotechnical engineering , geology , mathematical analysis , riemann hypothesis , organic chemistry , optics
Multicomponent cation exchange reactions have important applications in groundwater remediation, disposal of nuclear wastes as well as enhanced oil recovery. The hyperbolic theory of conservation laws can be used to explain the nature of displacements observed during flow with cation exchange reactions between flowing aqueous phase and stationary solid phase. Analytical solutions have been developed to predict the effluent profiles for a particular case of heterovalent cations (Na + , Ca 2+ and Mg 2+ ) and an anion (Cl − ) for any combination of constant injection and constant initial composition using this theory. We assume local equilibrium, neglect dispersion and model the displacement as a Riemann problem using mass action laws, the charge conservation equation and the cation exchange capacity equation. The theoretical predictions have been compared with experimental data available at two scales—the laboratory scale and the field scale. The theory agrees well with the experimental data at both scales. Analytical theory predictions show good agreement with numerical model, developed using finite differences.