# Splitting schemes for the thermoporoelasticity problem in fractured media

• Ammosov Dmitry A., dmitryammosov@gmail.com Multiscale Model Reduction Laboratory, Ammosov North-Eastern Federal University, 42 Kulakovsky Street, Yakutsk 677000, Russia
• Vasilyeva Maria V., vasilyevadotmdotv@gmail.com Department of Computational Technologies, Ammosov North-Eastern Federal University, 42 Kulakovsky Street, Yakutsk 677000, Russia; Institute for Scientific Computation, Texas A&M University, College Station, TX 77843-3368
• Babaei Masoud, masoud.babaei@manchester.ac.uk The University of Manchester, School of Chemical Engineering and Analytical Science, Manchester, M13 9PL, UK
• Chung Eric T., tschung@math.cuhk.edu.hk Department of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SAR
Keywords: thermoporoelasticity, double porosity, double permeability, dual continuum, discrete fracture model, finite element method, mathematical modeling, splitting schemes, fixed stress splitting, mixed-dimensional problem

### Abstract

We consider the thermoporoelasticity problem in the fractured geothermal reservoir. We use a hierarchical fracture representation, where small-scale highly connected fractures are represented by the classical dual porosity model and large-scale dense fractures are represented with the use of a discrete fracture model. The mathematical model is described by a coupled system of equations for temperature and pressure in the coupled dual continuum porous media with discrete fractures, where deformations are considered based on the effective media approach. For the numerical solution, we construct unstructured grids that resolve large-scale fractures explicitly on the grid level for the mixed-dimensional formulation of the pressure and temperature equations. The discrete system is constructed based on the finite element method with an implicit scheme for approximation by time. For effective solution of the obtained coupled system of equations for pressures, temperatures, and displacements for multicontinuum media, we present and study the splitting schemes based on fixed stress splitting. The results of the numerical simulation for the two-dimensional problem and a numerical study of the splitting schemes for the model problems are presented for two sets of parameters to show stability of the proposed schemes.

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How to Cite
Ammosov, D., Vasilyeva, M., Babaei, M. and Chung, E. (2020) “Splitting schemes for the thermoporoelasticity problem in fractured media”, Mathematical notes of NEFU, 26(4), pp. 98-118. doi: https://doi.org/10.25587/SVFU.2019.73.18.009.
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Section
Mathematical Modeling