Convergence analysis of fixed stress split iterative scheme for anisotropic poroelasticity with tensor Biot parameter

Dana, Saumik; Wheeler, Mary F.

doi:10.1007/s10596-018-9748-2

Cited by 38 publications

(32 citation statements)

References 34 publications

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“…We mention cell-centered finite volumes, 2 continuous Galerkin for the mechanics and mixed finite elements for the flow, [3][4][5][6] mixed finite elements for flow and mechanics, 4,7 nonconforming finite elements, 8 the MINI element, 9 continuous or discontinuous Galerkin, [10][11][12] or multiscale methods. [13][14][15] Continuous and discontinuous higher-order Galerkin space-time finite elements were proposed in the work of Bause et al 16 Adaptive computations were considered, for example, in the work of Ern and Meunier. 17 A Monte Carlo approach was proposed in the work of Rahrah and Vermolen.…”

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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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: 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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“…This indicates that sequential coupled methods could be less efficient than fully coupled methods. However, several recently published studies have shown that a fixed stress split is a robust and efficient scheme for iteratively coupling poro-elastic systems, even in the case of highly nonlinear and anisotropic problems (Mikelíc et al, 2014;White et al, 2016;Dana and Wheeler, 2018). Moreover, the type of coupling plays an important role, whether dominant by direct pore-volume couplings or indirect couplings through property changes (Rutqvist, 2017), as does the rate of change in the system.…”

Section: Code-linking Logicmentioning

confidence: 99%

TOUGH-UDEC: A simulator for coupled multiphase fluid flows, heat transfers and discontinuous deformations in fractured porous media

Lee

Kim

Min

et al. 2019

Computers & Geosciences

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A numerical simulator entitled TOUGH-UDEC is introduced for the analysis of coupled thermalhydraulic-mechanical processes in fractured porous media. Two existing well-established codes, TOUGH2 and UDEC, are coupled to model multiphase fluid flows, heat transfers, and discontinuous deformations in fractured porous media by means of discrete fracture representation. TOUGH2 is widely used for the modeling of heat transfers and multiphase multicomponent fluid flows, and UDEC is a well-known distinct element code for rock mechanics. The two codes are solved sequentially, with coupling parameters passed to each equation at specific intervals. After solving thermal-hydraulic equations within the TOUGH2 code, pressure and temperature information is imported into the UDEC model. After solving the mechanical equation within the UDEC code the calculated fracture apertures are converted to the equivalent permeability and porosity values for a TOUGH2 flow analysis. The solution is calculated by iteratively following an explicit sequence for numerical efficiency. Verifications are presented to demonstrate the capabilities of the coupled TOUGH-UDEC simulator. Three application examples of (1) shear dilation due to increased pore pressure, (2) thermal stress and (3) CO 2 injection, show that the new simulator can be an effective tool for geoengineering applications involving shear activation of fractures and faults.

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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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Convergence analysis of fixed stress split iterative scheme for anisotropic poroelasticity with tensor Biot parameter

Cited by 38 publications

References 34 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

TOUGH-UDEC: A simulator for coupled multiphase fluid flows, heat transfers and discontinuous deformations in fractured porous media

Generalized solution to the anisotropic Mandel's problem

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