A multiscale fixed stress split iterative scheme for coupled flow and poromechanics in deep subsurface reservoirs

Dana, Saumik; Ganis, Benjamin; Wheeler, Mary F.

doi:10.1016/j.jcp.2017.09.049

Cited by 90 publications

(65 citation statements)

References 24 publications

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“…An equidistant partition of the time interval is applied with time-step size = 10 from t 0 = 0 to T = 100. Initial conditions are inherited from the analytic solutions (27)- (29). As boundary conditions, we apply exact Dirichlet boundary conditions for the normal displacement on the top, left, and bottom boundaries.…”

Section: Mandel's Problemmentioning

confidence: 99%

“…39,40 For nonlinear problems, one combines a linearization technique, eg, the L-scheme, 41,42 with the splitting algorithm; the convergence of the resulting scheme can be proved rigorously. 32,33 Finally, we would like to mention some valuable variants of the fixed-stress splitting scheme: the multirate fixed-stress method, 43 the multiscale fixed-stress method, 29 and the parallel-in-time fixed-stress method. 44 This paper is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

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On the optimization of the fixed‐stress splitting for Biot's equations

Storvik

Both

Kumar

et al. 2019

Numerical Meth Engineering

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Summary In this work, we are interested in efficiently solving the quasi‐static, linear Biot model for poroelasticity. We consider the fixed‐stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well known that the convergence properties of the method strongly depend on the applied stabilization/tuning parameter. We show theoretically that, in addition to depending on the mechanical properties of the porous medium and the coupling coefficient, they also depend on the fluid flow and spatial discretization properties. The type of analysis presented in this paper is not restricted to a particular spatial discretization, although it is required to be inf‐sup stable with respect to the displacement‐pressure formulation. Furthermore, we propose a way to optimize this parameter that relies on the mesh independence of the scheme's optimal stabilization parameter. Illustrative numerical examples show that using the optimized stabilization parameter can significantly reduce the number of iterations.

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Section: Mandel's Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the optimization of the fixed‐stress splitting for Biot's equations

Storvik

Both

Kumar

et al. 2019

Numerical Meth Engineering

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“…In Klar et al (2013), the coupled flow and geomechanics hydrate reservoir simulation is implemented entirely in FLAC 2 D. A fully coupled simulator using a mixed finite element for both the fluid fields and mechanical fields has been developed by Yang et al (2014). A dual-mesh framework using a different methodology than that of Millstone was developed by Dana et al (2018), in which finite elements are used for both the mechanics and flow, but the formulation was limited to single-phase poroelastic flow.…”

Section: Background and Motivationmentioning

confidence: 99%

Simulation of Gas Production from Multilayered Hydrate-Bearing Media with Fully Coupled Flow, Thermal, Chemical and Geomechanical Processes Using TOUGH+Millstone. Part 2: Geomechanical Formulation and Numerical Coupling

2019

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The TOUGH+Millstone simulator has been developed for the analysis of coupled flow, thermal and geomechanical processes associated with the formation and/or dissociation of CH 4 hydrates in geological media. It is composed of two constituent codes: (a) a significantly enhanced version of the TOUGH+HYDRATE simulator, v2.0, that accounts for all known flow, physical, thermodynamic and chemical processes associated with the behavior of hydrate-bearing systems undergoing changes and includes the most recent advances in the description of the system properties, coupled seamlessly with (b) Millstone v1.0, a new code that addresses the conceptual, computational and mathematical shortcomings of earlier codes used to describe the geomechanical response of these systems. The capabilities of the TOUGH+Millstone code are demonstrated in the simulation and analysis of the system flow, thermal and geomechanical behavior during gas production from a realistic complex offshore hydrate deposit. In the second part of this series, we describe the Millstone geomechanical simulator. The hydrate-dependent, rate-based poromechanical formulation is presented and solved using a finite element discretization. A novel multimesh coupling scheme is introduced, wherein interpolators are automatically built to transfer data between the finite difference discretization of TOUGH+ and the finite element discretization of Millstone. We provide verification examples against analytic solutions for poroelasticity and a simplified demonstration problem for mechanically induced phase change in a hydrate sediment.

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“…Abousleiman et al 27 presented the analytical solution to Mandel's problem accounting for material transverse isotropy. In addition to elucidating the mechanical responses to material anisotropy, the solution has served as a benchmark for the validation of various numerical codes including the finite element method, 28,29 mixed finite element method, 30–33 and multirate fixed‐stress split iterative algorithm 34–36 . It has been also utilized to test commercial simulators 37 for coupled flow and geomechanics.…”

Section: Introductionmentioning

confidence: 99%

Generalized solution to the anisotropic Mandel's problem

Liu

Abousleiman

2020

Num Anal Meth Geomechanics

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Summary Existing solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel‐Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction.

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A multiscale fixed stress split iterative scheme for coupled flow and poromechanics in deep subsurface reservoirs

Cited by 90 publications

References 24 publications

On the optimization of the fixed‐stress splitting for Biot's equations

On the optimization of the fixed‐stress splitting for Biot's equations

Simulation of Gas Production from Multilayered Hydrate-Bearing Media with Fully Coupled Flow, Thermal, Chemical and Geomechanical Processes Using TOUGH+Millstone. Part 2: Geomechanical Formulation and Numerical Coupling

Generalized solution to the anisotropic Mandel's problem

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