Boundary element methods such as the displacement discontinuity method (DDM) are promising for describing the geo-mechanics of growing fractures as they reduce the dimensionality of the problem by one. Still, this advantage is overshadowed by the computational power required to model stage scale simulations of hydraulic fractures primarily due to the nonlinearity arising from fluid flow inside the fracture. Typical assumptions to improve the computational efficiency lead to the inability of simulators to describe proppant transport which is critical to treatment design. In this paper, we present a novel algorithm to increase the speed of convergence of coupled geomechanics (DDM) and fluid flow problem. The algorithm employs an analytical, local linear approximation of the Reynolds lubrication equation to solve the coupled non-linear system of equations. An initial solution is estimated through the linear system, and it is then used in the iterative solution approach for the non-linear system as an initial guess. This improvement has allowed us to use the algorithm to develop a fully three-dimensional hydraulic fracturing simulator which can run in an acceptable runtime using commonly available computational power.
Local Linearization Method for Efficient Solution of Coupled Fluid Flow and Geomechanics Problem
Shrivastava, Kaustubh, Blyton, Christopher A. J., and Mukul M. Sharma. "Local Linearization Method for Efficient Solution of Coupled Fluid Flow and Geomechanics Problem." Paper presented at the 51st U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, California, USA, June 2017.
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