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Mathematical and Computational Considerations of a Model of Microbiologically Induced Calcite Precipitation Public Deposited

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  • In this paper, we discuss two possible modifications to a numerical solution method for a model of microbiologically induced calcite precipitation (MICP). MICP provides a means to seal cracks in the surfaces of geological structures. From a mathematical and computational point of view MICP has very interesting features which make it challenging for numerical solution methods to solve the system. First, there are multiple sensitivities to every element of the system, and computational approximations to the solutions to any part of the system can effect the solution of this part very strongly. Second, a subset of the chemical reactions occur much faster than the remainder of the system. A solution method must use a fine discretization parameter to capture these dynamics, while the system must be solved on a large time scale in order for the calcite precipitation to occur. The third challenge with MICP is that some reaction terms are discontinuous; thus, traditional numerical error bounds may not apply.
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