Analytical solutions for multiple species reactive transport in multiple dimensions |
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Authors: | Y Sun J N Petersen T P Clement |
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Institution: | a Bioprocessing Group, Battelle Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA;b Center for Multiphase Environmental Research, Washington State University, Pullman, WA 99164-2710, USA |
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Abstract: | Many numerical computer codes used to simulate multi-species reactive transport and biodegradation have been developed in recent years. Such numerical codes must be validated by comparison of the numerical solutions with an analytical solution. In this paper, a method for deriving analytical solutions of the partial differential equations describing multiple species multi-dimensional transport with first-order sequential reactions is presented. Although others have developed specific solutions of multi-species transport equations, here a more general analytical approach, capable of describing any number of reactive species in multiple dimensions is derived. A substitution method is used to transform the multi-species reactive transport problem to one that can be solved using previously published single-species solutions for various initial and boundary conditions. One- and three-dimensional examples are presented to illustrate the steps involved in extending single-species solutions to a four-species system with sequential first-order reactions. |
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Keywords: | Analytical solution Biodegradation Transport Multi-species First-order reaction |
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