Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition
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We consider a reactive transport model in a fractured porous medium. The particularity appears in the conditions imposed at the interface separating the block and the fracture, which involves a nonlinear transmission condition. Assuming that the fracture has thickness ε, we analyze the resulting problem and prove the convergence toward a reduced model in the limit ε↘0. The result is a model defined on an interface (the reduced fracture) and acting as a boundary condition for the equations defined in the block. Using both formal and rigorous arguments, we obtain the reduced models for different flow regimes, expressed through a moderate or a high Péclet number.
KeywordsFractured porous media Upscaling Reactive transport Nonlinear transmission conditions
Mathematics Subject Classification (2010)35B45 35D30 35K57 65M12 76M45 76M50
ISP and KK are members of the International Research Training Group NUPUS funded by the German Research Foundation DFG (GRK 1398), the Netherlands Organization for Scientific Research NWO (DN 81-754) and by the Research Council of Norway (215627). They also acknowledge the Akademia grant supporting this work. Also, the work of ISP is supported by the Shell-NWO/FOM CSER programme (project 14CSER016). We thank Prof. M. van Sint Annaland (Eindhoven) for the discussions about the nonlinear transmission conditions in the context of reactive flows. Also, we are grateful to the anonymous referees for their valuable suggestions and the critical reading. Last but not least we thank Prof. W. Jäger (Heidelberg) for stimulating discussions, guidance and continuous support.
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