Two‐way coupling in reservoir–geomechanical models: vertex‐centered Galerkin geomechanical model cell‐centered and vertex‐centered finite volume reservoir models

Prévost, Jean‐Hérve

doi:10.1002/nme.4657

Cited by 22 publications

(20 citation statements)

References 27 publications

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“…A stabilized scheme for pressure is also adopted to counter the violation of LBB requirements. Further details can be found in Preisig and Prévost …”

Section: Branched and Intersecting Faults In Reservoir‐geomechanical mentioning

confidence: 99%

Modeling branched and intersecting faults in reservoir‐geomechanics models with the extended finite element method

Liu

Prévost

Sukumar

2019

Num Anal Meth Geomechanics

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Summary Faults are geological entities with thickness several orders of magnitude smaller than the grid blocks typically used to discretize geological formations. On using the extended finite element method (X‐FEM), a structured mesh suffices and the faults can arbitrarily cut the elements in the mesh. Modeling branched and intersecting faults is a challenge, in particular when the faults work as internal fluid flow conduits that allow fluid flow in the faults as well as to enter/leave the faults. By appropriately selecting the enrichment function and the nodes to be enriched, we are able to capture the special characteristics of the solution in the vicinity of the fault. We compare different enrichment schemes for strong discontinuities and develop new continuous enrichment functions with discontinuous derivatives to model branched and intersecting weak discontinuities. Symmetric fluid flows within the regions embedded by branched, coplanar intersecting, and noncoplanar intersecting faults are considered to verify the effectiveness of the proposed enrichment scheme. For a complex fault consisting of branched and intersecting faults, the accuracy and efficiency of the X‐FEM is compared with the FEM. We also demonstrate different slipping scenarios for branched and intersecting faults with the same friction coefficient. In addition, fault slipping triggered by an injection pressure and three‐dimensional fluid flows are modeled to show the versatility of the proposed enrichment scheme for branched and intersecting weak discontinuities.

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“…A stabilized scheme for pressure is also adopted to counter the violation of LBB requirements. Further details can be found in Preisig and Prévost …”

Section: Branched and Intersecting Faults In Reservoir‐geomechanical mentioning

confidence: 99%

Modeling branched and intersecting faults in reservoir‐geomechanics models with the extended finite element method

Liu

Prévost

Sukumar

2019

Num Anal Meth Geomechanics

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“…The preconditioner operator

scriptP

is applied to the residual

{bold-italicR}_{k} = (bold-italicB - scriptA {bold-italicX}_{k})

—that is, to the correct discrete residual form of the equilibrium and continuity equations. This fact is overlooked in . The algorithm for applying

{scriptP}^{- 1}

to the residual vector R k is

bold-italicY = {scriptP}^{- 1} {bold-italicR}_{k} \Rightarrow ([], \begin{matrix} Y_{u} \\ Y_{p} \end{matrix}) = ([], \begin{matrix} A^{- 1} & - A^{- 1} B_{1} {\tilde{S}}^{- 1} \\ 0 & {\tilde{S}}^{- 1} \end{matrix}) ([], \begin{matrix} R_{u, k} \\ R_{p, k} \end{matrix})

which takes advantage of the block‐triangular nature of

scriptP

by first updating the pressure components ( Y p ) followed by the displacement components ( Y u ) as follows:

{bold-italicY}_{p} = {\overset{S}{true}}^{- 1} {bold-italicR}_{p, k},

{bold-italicY}_{u} = A^{- 1} ((), {bold-italicR}_{u, k} - B_{1} {bold-italicY}_{p}) .

It is well known that a necessary and sufficient condition for the convergence of stationary iterative methods is that the spectral radius, ρ , of the iteration matrix,

scriptM

, is smaller than unity in magnitude .…”

Section: Numerical Modelmentioning

confidence: 99%

“…The preconditioner operator P is applied to the residual R k D .B AX k /-that is, to the correct discrete residual form of the equilibrium and continuity equations. This fact is overlooked in [35,45]. The algorithm for applying P 1 to the residual vector R k is…”

Section: Solution Strategymentioning

confidence: 99%

Accuracy and convergence properties of the fixed‐stress iterative solution of two‐way coupled poromechanics

Castelletto

White

Tchelepi

2015

Num Anal Meth Geomechanics

130

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SUMMARYThe paper deals with the numerical solution of Biot's equations of coupled consolidation obtained by a mixed formulation combining continuous Galerkin finite-element and multipoint flux approximation finite-volume methods. The solution algorithm relies on the recently developed fixed-stress solution scheme, in which first the flow problem and then the mechanical one are addressed iteratively. We show that the algorithm can be interpreted as a particular block triangular preconditioning strategy applied within a Richardson iteration. The key component to the success of the preconditioner is the sparse approximation to the Schur complement based on a pressure space mass matrix scaled by a weighting factor that depends element-wise on the inverse of a suitable bulk modulus. The accuracy of the method is assessed, making use of well-known analytical solutions from the literature. Numerical results demonstrate robustness and low computational cost of the fixed-stress scheme in accurately capturing the two-way coupling between deformation and pressure.

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“…A number of proven iterative linear solvers are used by the coupled simulator, including GMRES (default for flow), PCG, BiCGSTAB (default for geomechanics) (Saad 2003), and AMG (Briggs et al 2000). A number of preconditioning approaches are also available, including block Jacobi, ILU(n), SCMG (Alpak and Wheeler 2012), and CPR-AMG (only for flow) (Gries et al 2014).…”

Section: Mathematical Modelmentioning

confidence: 99%

Robust Fully-Implicit Coupled Multiphase-Flow and Geomechanics Simulation

Alpak

2015

SPE Journal

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Material nonlinearity, boundary and arching constraints, nonuniform reservoir flows, sliding along material interfaces, or faults are among the causes of shear deformation or changes in the total stresses and the resulting stress redistribution in hydrocarbon reservoirs. Previous studies have demonstrated that shear or nonuniform deformation and stress redistribution in subsurface formations may have significant effects on reservoir fluid flows. Thus, a two-way coupled analysis is the required approach under circumstances where the shear deformation or changes in total stresses in the reservoir cannot be neglected.A coupled multiphysics simulator is developed for the dynamic modeling of multiphase thermal/compositional flow, and poroelastoplastic geomechanical deformation. The equations that govern multiphase flow in permeable media, heat transport, and poroelastoplastic geomechanics together lead to a highly nonlinear system. Finite-volume and Galerkin finite-element methods are used for the numerical solution of thermal/compositional multiphase fluid-flow and geomechanics equations on general hexahedral grids, respectively. Because of its improved stability and rapid convergence characteristics, the resulting multiphysics system of equations is solved with a fully-implicit formulation by use of an effective implementation of the Newton-Raphson method in the default mode.The coupled simulator is by design maximally modular with self-contained flow and geomechanics modules that can be operated in a two-way coupled mode with explicit-, iterative-, and fully-implicit-coupling options. The coupled-modeling system lends itself naturally not only to near-wellbore coupled flow and geomechanical deformation problems where poroplasticity may play a more prominent role, but also to reservoir-scale simulations where both poroelasticity and poroplasticity are relevant. The coupled simulator is validated against analytical solutions for simple cases, by use of published data in the open literature. Validation results demonstrate the robust, fast, and accurate predictive capabilities of the multiphysics modeling protocol.

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Two‐way coupling in reservoir–geomechanical models: vertex‐centered Galerkin geomechanical model cell‐centered and vertex‐centered finite volume reservoir models

Cited by 22 publications

References 27 publications

Modeling branched and intersecting faults in reservoir‐geomechanics models with the extended finite element method

Modeling branched and intersecting faults in reservoir‐geomechanics models with the extended finite element method

Accuracy and convergence properties of the fixed‐stress iterative solution of two‐way coupled poromechanics

Robust Fully-Implicit Coupled Multiphase-Flow and Geomechanics Simulation

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