Fully coupled simulation of fluid injection into geomaterials with focus on nonlinear near‐well behavior

Preisig, Matthias; Prévost, Jean‐Hérve

doi:10.1002/nag.1039

Cited by 15 publications

(10 citation statements)

References 23 publications

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“…The unknown variables are solid displacement u ( x ) and pressure p f ( x ). Simultaneous integration of the stress and pressure equations is achieved by computing the coupled Jacobian matrix via finite‐differencing of the residuals . The fully implicit time integration scheme is employed.…”

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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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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“…Simultaneous integration of the stress and pressure equations requires that a residual formulation be used. The elemental contribution to the Jacobian matrix can then be computed through numerical finite differencing of the residuals (e.g., ) as further explained and detailed herafter. We use a first order finite difference time‐stepping integrator (typically, backward Euler) for both geomechanical and reservoir equations.…”

Section: Two‐way Fully Coupled Solution Schemesmentioning

confidence: 99%

“…Simultaneous integration of the stress and pressure equations is achieved by computing the coupled Jacobian matrix, which is simply computed by numerical finite differencing of the residuals (e.g., ) as further explained and detailed herafter. For that purpose, it is convenient to view the global solution vectors and residuals as consisting of contributions from both the geomechanical and reservoir simulator as follows:

\underset{x^{(i)}}{msub} MathClass-rel= ({}, \begin{matrix} falsenonefalsearray \\ arrayaxis \underset{˜}{u^{(i)}} \\ arrayaxis p^{MathClass-open(i MathClass-close)} \end{matrix}) \underset{ẋ^{i}}{msub} MathClass-rel= ({}, \begin{matrix} falsenonefalsearray \\ arrayaxis \underset{˜}{{\dot{u}}^{i}} \\ arrayaxis ṗ^{MathClass-open(i MathClass-close)} \end{matrix}) \underset{r^{(i)}}{msub} MathClass-rel= ({}, \begin{matrix} falsenonefalsearray \\ arrayaxis \underset{˜}{r_{u}^{(i)}} \\ arrayaxis r_{p}^{MathClass-open(i MathClass-close)} \end{matrix})

where

\underset{x^{(i)}}{msub}

is the solution vector at iteration i and lists both nodal displacements and pressures.…”

Section: Two‐way Fully Coupled Simultaneous Solution Proceduresmentioning

confidence: 99%

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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

Prévost

2014

Numerical Meth Engineering

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SUMMARYProcedures to couple reservoir and geomechanical models are reviewed. The focus is on immiscible compressible non‐compositional reservoir–geomechanical models. Such models require the solution to: coupled stress, pressure, saturation and temperature equations. Although the couplings between saturation and temperature with stress and fluid pressure are ‘weak’ and can be adequately captured thru staggered (fixed point) iterations, the couplings between stress and pressure are ‘strong’ and require special procedures for accurate integration. As shown and discussed in detail in our previous works, two‐way coupling (i.e., simultaneous integration) of pressure and stress equations is required if poromechanical effects are to be captured accurately. In our previous work, a Galerkin implementation of both pressure and stress equations was used with equal order interpolants.However, most (if not all) reservoir simulators use a finite volume implementation of the pressure equation. Therefore, there remain important unanswered questions related to the interface between a Galerkin vertex‐centered geomechanical model with a reservoir finite volume model as such an implementation has never been attempted before. We address those issues in the following by studying the interface with both a cell‐centered and a vertex‐centered finite volume implementation of the pressure equation. Central to the success of the implementation is the computation of the Jacobian matrix. The elemental contribution to the coupling Jacobian matrix is computed through numerical finite differencing of the residuals. The procedure is detailed herein. In the following, in order to attempt to clear confusion, the simplest case of an isothermal fully saturated, slightly compressible system is presented in detail, and the various solution strategies, simplifications and shortcomings are identified. Copyright © 2014 John Wiley & Sons, Ltd.

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“…Explicit-, iterative-, and full-coupling approaches have been proposed for the two-way coupled solution of flow and geomechanics equations (Lewis and Sukirman 1993;Settari and Mourits 1994;Settari and Mourits 1998;Gutierrez et al 2001;Settari and Walters 2001;Minkoff et al 2003;Thomas et al 2003;Tran et al 2004;Jeannin et al 2007;Dean and Schmidt 2009;Preisig and Prévost 2012;Prévost 2014). The full-coupling approach is also referred to as the "fully-coupled" solution or the "fully-implicit-coupling" approach.…”

Section: Introductionmentioning

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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Fully coupled simulation of fluid injection into geomaterials with focus on nonlinear near‐well behavior

Cited by 15 publications

References 23 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

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

Robust Fully-Implicit Coupled Multiphase-Flow and Geomechanics Simulation

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