Abstract
We develop a mathematical model for the interaction of the mechanics of a three-dimensional permeable reservoir or aquifer with the flow through wells. We apply a model reduction technique that represents the wells as one-dimensional channels with arbitrary configuration in the space and we introduce proper coupling conditions to account for the interaction of the wells with the bulk region. The resulting problem consists of coupled partial differential equations defined on manifolds with heterogeneous dimensionality. To highlight the potential of this modeling approach in the description of realistic scenarios, we combine it with a suitable discretization method and we discuss the results of preliminary simulations on an idealized test case containing two wells.
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References
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Cerroni, D., Radu, F., Zunino, P. (2021). A Mixed Dimensional Model for the Interaction of a Well with a Poroelastic Material. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_123
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DOI: https://doi.org/10.1007/978-3-030-55874-1_123
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