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A staggered finite element procedure for the coupled Stokes-Biot system with fluid entry resistance

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Abstract

We develop a staggered finite element procedure for the coupling of a free viscous flow with a deformable porous medium, in which interface phenomena related to the skin effect can be incorporated. The basis of the developed simulation procedure is the coupled Stokes-Biot model, which is supplemented with interface conditions to mimic interface-related phenomena. Specifically, the fluid entry resistance parameter is used to relate the fluid flux through the interface to the pressure jump across the interface. The attainable jump in pressure over the interface provides an effective way of modeling sharp pressure gradients associated with the possibly reduced permeability of the interface on account of pore clogging. In addition to the fluid entry resistance parameter, the developed simulation strategy also includes the possibility of modeling fluid slip over the porous medium. Sensitivity studies are presented for both the fluid entry resistance parameter and the slip coefficient, and representative two- and three-dimensional test cases are presented to demonstrate the applicability of the developed simulation technique.

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Acknowledgements

All simulations in this work were performed using the open source software package Nutils [42] (www.nutils.org).

Funding

This research was sponsored by the Dutch TKI New Gas foundation, under grant number TKITOECARBFRAC2016, with financial support from EBN, Neptune Energy, and Wintershall Noordzee.

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Authors and Affiliations

  1. Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands

    E. A. Bergkamp, C. V. Verhoosel, J. J. C. Remmers & D. M. J. Smeulders

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  1. E. A. Bergkamp
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  2. C. V. Verhoosel
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  3. J. J. C. Remmers
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  4. D. M. J. Smeulders
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Correspondence to E. A. Bergkamp.

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Bergkamp, E.A., Verhoosel, C.V., Remmers, J.J.C. et al. A staggered finite element procedure for the coupled Stokes-Biot system with fluid entry resistance. Comput Geosci 24, 1497–1522 (2020). https://doi.org/10.1007/s10596-019-09931-7

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