Three-way coupling of multiphase flow and poromechanics in porous media

Lü, Xueying; Wheeler, Mary F.

doi:10.1016/j.jcp.2019.109053

Cited by 14 publications

(6 citation statements)

References 25 publications

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“…The physical parameters used for the tests are listed in Table 1. We notice that the parameter α multiplying the pressure in the first line of (8.1) is much larger than 1 M in the second line, hence The physical domain (left) and computational domain (right) of Mandel's problem [32].…”

Section: The Mandel Problemmentioning

confidence: 99%

“…For large-scale engineering applications, the relative change in mean stress is also a widely used stopping criterion for the fixed-stress iterations: [16,20,34,4,14,32]:…”

Section: Dynamic Mesh Adaptivity Guided By the A Posteriori Error Indicatorsmentioning

confidence: 99%

“…Storvik et al [43] studied the optimal choice of the stabilization parameter used in the fixed-stress split. Lu and Wheeler [32] have recently extended the fixed-stress split to a three-way coupling, an adaptive asynchronous coupling scheme that allows over 97.5% reduction in poromechanics computational time due to not requiring the displacement to be computed for every time step.…”

Section: Introductionmentioning

confidence: 99%

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A posteriori error estimates for Biot system using Enriched Galerkin for flow

Girault

Lü

Wheeler

2020

Computer Methods in Applied Mechanics and Engineering

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We analyze the Biot system solved with a fixed-stress split, Enriched Galerkin (EG) discretization for the flow equation, and Galerkin for the mechanics equation. Residual-based a posteriori error estimates are established with both lower and upper bounds. These theoretical results are confirmed by numerical experiments performed with Mandel's problem. The efficiency of these a posteriori error estimators to guide dynamic mesh refinement is demonstrated with a prototype unconventional reservoir model containing a fracture network. We further propose a novel stopping criterion for the fixed-stress iterations using the error indicators to balance the fixed-stress split error with the discretization errors. The new stopping criterion does not require hyperparameter tuning and demonstrates efficiency and accuracy in numerical experiments.

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Section: The Mandel Problemmentioning

confidence: 99%

“…For large-scale engineering applications, the relative change in mean stress is also a widely used stopping criterion for the fixed-stress iterations: [16,20,34,4,14,32]:…”

Section: Dynamic Mesh Adaptivity Guided By the A Posteriori Error Indicatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A posteriori error estimates for Biot system using Enriched Galerkin for flow

Girault

Lü

Wheeler

2020

Computer Methods in Applied Mechanics and Engineering

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“…The specific equations of single phase poromechanics are provided in Appendix A The two-grid approach is built on top of a staggered solution algorithm (Fig. 4) in which the flow and geomechanics subproblems are solved sequentially and iteratively using a fixed stress split iterative scheme [36,37,46,45,17,59,16,24,25,23,7,8,14,58,13,53,51,6,42].…”

Section: Governing Equationsmentioning

confidence: 99%

Two-grid method on unstructured tetrahedra: Applying computational geometry to staggered solution of coupled flow and mechanics problems

Dana,

Zhao,

Jha

2021

Preprint

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We develop a computational framework that leverages the features of sophisticated software tools and numerics to tackle some of the pressing issues in the realm of earth sciences. The algorithms to handle the physics of multiphase flow, concomitant geomechanics all the way to the earth's surface and the complex geometries of field cases with surfaces of discontinuity are stacked on top of each other in a modular fashion which allows for easy use to the end user. The current focus of the framework is to provide the user with tools for assessing seismic risks associated with energy technologies as well as for use in generating forward simulations in inversion analysis from data obtained using GPS and InSAR. In this work, we focus on one critical aspect in the development of the framework: the use of computational geometry in a two-grid method for unstructured tetrahedral meshes

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“…As shown in Fig. 2b, the two-grid approach is built on top of a staggered solution algorithm in which the flow and geomechanics subproblems are solved sequentially and iteratively using a fixed stress split iterative scheme [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,21,46,47,48,49,50,51,52]. The accuracy of the two-grid method has been demonstrated for the classical Mandel's problem [53,54] in our earlier work [21].…”

Section: Motivationmentioning

confidence: 99%