The Experts below are selected from a list of 185667 Experts worldwide ranked by ideXlab platform
Mary F Wheeler - One of the best experts on this subject based on the ideXlab platform.
-
convergence analysis of two grid fixed stress split iterative scheme for Coupled Flow and deformation in heterogeneous poroelastic media
Computer Methods in Applied Mechanics and Engineering, 2018Co-Authors: Saumik Dana, Mary F WheelerAbstract:Abstract We perform a convergence analysis of a two-grid fixed stress split algorithm for the Biot system modeling Coupled Flow and deformation in heterogeneous poroelastic media. The two-grid fixed stress split scheme solves the Flow subproblem on a fine grid using a multipoint flux mixed finite element method by imposing the fixed mean stress constraint followed by the poromechanics subproblem on a coarse grid using a conforming Galerkin method in every coupling iteration at each time step. Restriction operators map the fine scale Flow solution to the coarse scale poromechanical grid and prolongation operators map the coarse scale poromechanical solution to the fine scale Flow grid. The coupling iterations are repeated until convergence and Backward Euler is employed for time marching. The convergence analysis is based on studying the equations satisfied by the difference of iterates to show that the two-grid scheme is a contraction map under certain conditions. Those conditions are used to construct the restriction and prolongation operators as well as arrive at effective elastic properties for the coarse scale poromechanical solve in terms of the fine scale elastic properties. We analyze the contraction map with a numerical result comparing the numerically computed to the theoretically obtained contraction constant for a poroelastic medium with substantial spatial variability in the poroelastic moduli.
-
the correspondence between voigt and reuss bounds and the decoupling constraint in a two grid staggered solution algorithm to Coupled Flow and deformation in heterogeneous poroelastic media
arXiv: Numerical Analysis, 2018Co-Authors: Saumik Dana, Mary F WheelerAbstract:We perform a convergence analysis of a two-grid staggered solution algorithm for the Biot system modeling Coupled Flow and deformation in heterogeneous poroelastic media. The algorithm first solves the Flow subproblem on a fine grid using a mixed finite element method (by freezing a certain measure of the mean stress) followed by the poromechanics subproblem on a coarse grid using a conforming Galerkin method. Restriction operators map the fine scale Flow solution to the coarse scale poromechanical grid and prolongation operators map the coarse scale poromechanical solution to the fine scale Flow grid. The coupling iterations are repeated until convergence and Backward Euler is employed for time marching. The analysis is based on studying the equations satisfied by the difference of iterates to show that the two-grid scheme is a contraction map under certain conditions. Those conditions are used to construct the restriction and prolongation operators as well as arrive at coarse scale elastic properties in terms of the fine scale data. We show that the adjustable parameter in the measure of the mean stress is linked to the Voigt and Reuss bounds frequently encountered in computational homogenization of multiphase composites.
-
a multiscale fixed stress split iterative scheme for Coupled Flow and poromechanics in deep subsurface reservoirs
Journal of Computational Physics, 2018Co-Authors: Saumik Dana, Benjamin Ganis, Mary F WheelerAbstract:Abstract In Coupled Flow and poromechanics phenomena representing hydrocarbon production or CO 2 sequestration in deep subsurface reservoirs, the spatial domain in which fluid Flow occurs is usually much smaller than the spatial domain over which significant deformation occurs. The typical approach is to either impose an overburden pressure directly on the reservoir thus treating it as a Coupled problem domain or to model Flow on a huge domain with zero permeability cells to mimic the no Flow boundary condition on the interface of the reservoir and the surrounding rock. The former approach precludes a study of land subsidence or uplift and further does not mimic the true effect of the overburden on stress sensitive reservoirs whereas the latter approach has huge computational costs. In order to address these challenges, we augment the fixed-stress split iterative scheme with upscaling and downscaling operators to enable modeling Flow and mechanics on overlapping nonmatching hexahedral grids. Flow is solved on a finer mesh using a multipoint flux mixed finite element method and mechanics is solved on a coarse mesh using a conforming Galerkin method. The multiscale operators are constructed using a procedure that involves singular value decompositions, a surface intersections algorithm and Delaunay triangulations. We numerically demonstrate the convergence of the augmented scheme using the classical Mandel's problem solution.
-
adaptive enriched galerkin methods for miscible displacement problems with entropy residual stabilization
Journal of Computational Physics, 2017Co-Authors: Sanghyun Lee, Mary F WheelerAbstract:We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) Coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele-Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for Coupled Flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient Flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to Flow and transport. Enriched Galerkin approximations for Coupled Flow and transport system.Entropy residual stabilization for enriched Galerkin to stabilize higher order transport scheme.Dynamic mesh adaptivity for viscous fingering in two and three dimensions.
-
numerical convergence study of iterative coupling for Coupled Flow and geomechanics
Computational Geosciences, 2014Co-Authors: Andro Mikelic, Bin Wang, Mary F WheelerAbstract:In this paper, we consider algorithms for modeling complex processes in porous media that include fluid and structure interactions. Numerous field applications would benefit from a better understanding and integration of porous Flow and solid deformation. Important applications in environmental and petroleum engineering include carbon sequestration, surface subsidence, pore collapse, cavity generation, hydraulic fracturing, thermal fracturing, wellbore collapse, sand production, fault activation, and waste disposal, while similar issues arise in biosciences and chemical sciences as well. Here, we consider solving iteratively the coupling of Flow and mechanics. We employ mixed finite element method for Flow and a continuous Galerkin method for elasticity. For single-phase Flow, we demonstrate the convergence and convergence rates for two widely used schemes, the undrained split and the fixed stress split. We discuss the extension of the fixed stress iterative coupling scheme to an equation of state compositional Flow model Coupled with elasticity and a single-phase poroelasticity model on general hexahedral grids. Computational results are presented.
Jihoon Kim - One of the best experts on this subject based on the ideXlab platform.
-
Development of the T+M Coupled Flow-geomechanical simulator to describe fracture propagation and Coupled Flow-thermal-geomechanical processes in tight/shale gas systems
Computers and Geosciences, 2013Co-Authors: Jihoon Kim, George J MoridisAbstract:We developed a hydraulic fracturing simulator by coupling a Flow simulator to a geomechanics code, namely T+M simulator. Modeling of the vertical fracture development involves continuous updating of the boundary conditions and of the data connectivity, based on the finite element method for geomechanics. The T+M simulator can model the initial fracture development during the hydraulic fracturing operations, after which the domain description changes from single continuum to double or multiple continua in order to rigorously model both Flow and geomechanics for fracture-rock matrix systems. The T+H simulator provides two-way coupling between fluid-heat Flow and geomechanics, accounting for thermo-poro-mechanics, treats nonlinear permeability and geomechanical moduli explicitly, and dynamically tracks changes in the fracture(s) and in the pore volume. We also fully account for leak-off in all directions during hydraulic fracturing.We first test the T+M simulator, matching numerical solutions with the analytical solutions for poromechanical effects, static fractures, and fracture propagations. Then, from numerical simulation of various cases of the planar fracture propagation, shear failure can limit the vertical fracture propagation of tensile failure, because of leak-off into the reservoirs. Slow injection causes more leak-off, compared with fast injection, when the same amount of fluid is injected. Changes in initial total stress and contributions of shear effective stress to tensile failure can also affect formation of the fractured areas, and the geomechanical responses are still well-posed. © 2013 .
-
formulation and sequential numerical algorithms of Coupled fluid heat Flow and geomechanics for multiple porosity materials
International Journal for Numerical Methods in Engineering, 2012Co-Authors: Jihoon Kim, Eric Sonnenthal, Jonny RutqvistAbstract:Formulation and sequential numerical algorithms of Coupled fluid/heat Flow and geomechanics for multiple porosity materials J. Kim ∗ , E. Sonnenthal, and J. Rutqvist Earth Sciences Division, Lawrence Berkeley National Laboratory. 1 Cyclotron Road 90R1116, Berkeley, CA 94720, USA SUMMARY We generalized constitutive relations of Coupled Flow and geomechanics for the isothermal elastic double porosity model in the previous study to those for the non-isothermal elastic/elastoplastic multiple porosity model, finding coupling coefficients and constraints of the multiple porosity model, and determining the upscaled elastic/elastoplastic moduli as well as relations between the local strains of all materials within a gridblock and the global strain of the gridblock. Furthermore, the coupling equations and relations between local and global variables provide well-posed problems, implying that they honor the dissipative mechanism of Coupled Flow and geomechanics. For numerical implementation, we modified the fixed-stress sequential method for the multiple porosity model. From the a priori stability estimate, the sequential method provides numerical stability when an implicit time stepping algorithm is used. This sequential scheme can easily be implemented by using a modified porosity function and its porosity correction. In numerical examples, we observe clear differences among the single, double, and multiple porosity systems, and the multiple porosity model can reflect high heterogeneity that exists within a gridblock. We also identify considerably complicated physics in Coupled Flow and geomechanics of the multiple porosity systems, which cannot accurately be detected in the unCoupled Flow simulation. KEY WORDS: double porosity, multiple porosity, poromechanics, multiple interacting continua (MINC), fractured reservoirs, fixed-stress split 1. INTRODUCTION Coupled fluid, heat, and mechanical processes are important in many engineering fileds. In mechanical engineering, Coupled heat and mechanics (e.g., thermoelasticity, thermoplasticity) are considered to analyze interactions between deformation of a material body and thermal stress [1, 2]. Rapid movement of the body such as vibration can be a source in heat Flow, and heat induces additional stress in mechanics, which can expand the body. In turn, the expanded body affects accumulation in heat Flow because of the change in material volume. Coupled fluid, heat, and mechanical processes are also critically important in geo-engineering [3]. In geotechnical engineering, an increase (or decrease) of pore pressure causes dilation (or shrinkage) of porous media, which changes strain and stress fields [4, 5, 6, 7, 8]. These changes also affect pore-volume, resulting in variation of pore-pressure, again. In petroleum engineering, changes in permeability as well as porosity induced by geomechanics are critical issues in order to predict fluid Flow and production accurately, for example, in hydraulic fracturing, reservoir compaction, and gas-hydrate recovery [9, 10, 11, 12, 13, 14]. In geological carbon storage, the effect of large scale injection ∗ Correspondence to: J. Kim, Earth Sciences Division, Lawrence Berkeley National Laboratory. 1 Cyclotron Road 90R1116, Berkeley, CA 94720, USA. Email: JihoonKim@lbl.gov
-
stability and convergence of sequential methods for Coupled Flow and geomechanics drained and undrained splits
Computer Methods in Applied Mechanics and Engineering, 2011Co-Authors: Jihoon Kim, Hamdi A Tchelepi, Ruben JuanesAbstract:Abstract We perform a stability and convergence analysis of sequential methods for Coupled Flow and geomechanics, in which the mechanics sub-problem is solved first. We consider slow deformations, so that inertia is negligible and the mechanical problem is governed by an elliptic equation. We use Biot’s self-consistent theory to obtain the classical parabolic-type Flow problem. We use a generalized midpoint rule (parameter α between 0 and 1) time discretization, and consider two classical sequential methods: the drained and undrained splits. The von Neumann method provides sharp stability estimates for the linear poroelasticity problem. The drained split with backward Euler time discretization ( α = 1) is conditionally stable, and its stability depends only on the coupling strength, and it is independent of time step size. The drained split with the midpoint rule ( α = 0.5) is unconditionally unstable. The mixed time discretization, with α = 1.0 for mechanics and α = 0.5 for Flow, has the same stability properties as the backward Euler scheme. The von Neumann method indicates that the undrained split is unconditionally stable when α ⩾ 0.5. We extend the stability analysis to the nonlinear regime (poro-elastoplasticity) via the energy method. It is well known that the drained split does not inherit the contractivity property of the continuum problem, thereby precluding unconditional stability. For the undrained split we show that it is B-stable (therefore unconditionally stable at the algorithmic level) when α ⩾ 0.5. We also analyze convergence of the drained and undrained splits, and derive the a priori error estimates from matrix algebra and spectral analysis. We show that the drained split with a fixed number of iterations is not convergent even when it is stable. The undrained split with a fixed number of iterations is convergent for a compressible system (i.e., finite Biot modulus). For a nearly-incompressible system (i.e., very large Biot modulus), the undrained split loses first-order accuracy, and becomes non-convergent in time. We also study the rate of convergence of both splits when they are used in a fully-iterated sequential scheme. When the medium permeability is high or the time step size is large, which corresponds to a high diffusion of pressure, the error amplification of the drained split is lower and therefore converges faster than the undrained split. The situation is reversed in the case of low permeability and small time step size. We provide numerical experiments supporting all the stability and convergence estimates of the drained and undrained splits, in the linear and nonlinear regimes. We also show that our spatial discretization (finite volumes for Flow and finite elements for mechanics) removes the well-documented spurious instability in consolidation problems at early times.
-
stability and convergence of sequential methods for Coupled Flow and geomechanics fixed stress and fixed strain splits
Computer Methods in Applied Mechanics and Engineering, 2011Co-Authors: Jihoon Kim, Hamdi A Tchelepi, Ruben JuanesAbstract:Abstract We analyze stability and convergence of sequential implicit methods for Coupled Flow and geomechanics, in which the Flow problem is solved first. We employ the von Neumann and energy methods for linear and nonlinear problems, respectively. We consider two sequential methods with the generalized midpoint rule for tn+α, where α is the parameter of time discretization: namely, the fixed-strain and fixed-stress splits. The von Neumann method indicates that the fixed-strain split is only conditionally stable, and that its stability limit is a coupling strength less than unity if α ⩾ 0.5. On the other hand, the fixed-stress split is unconditionally stable when α ⩾ 0.5, the amplification factors of the fixed-stress split are different from those of the undrained split and are identical to the fully Coupled method. Unconditional stability of the fixed-stress split is also obtained from the energy method for poroelastoplasticity. We show that the fixed-stress split is contractive and B-stable when α ⩾ 0.5. We also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward Euler method in time. From the estimates, the fixed-strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable. The fixed-stress split, however, is convergent for a fixed number of iterations, showing better accuracy than the undrained split. Even when we cannot obtain the exact local bulk modulus (or exact rock compressibility) at the Flow step a priori due to complex boundary conditions or the nonlinearity of the materials, the fixed-stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus, such as the dimension-based estimation, by which the employed local bulk modulus is less stiff than the exact local bulk modulus. We provide numerical examples supporting all the estimates of stability and convergence for the fixed-strain and fixed-stress splits.
Ruben Juanes - One of the best experts on this subject based on the ideXlab platform.
-
were the may 2012 emilia romagna earthquakes induced a Coupled Flow geomechanics modeling assessment
Geophysical Research Letters, 2016Co-Authors: Ruben Juanes, Birendra Jha, Bradford H Hager, John H Shaw, Andreas Plesch, L Astiz, James H Dieterich, Cliff FrohlichAbstract:Seismicity induced by fluid injection and withdrawal has emerged as a central element of the scientific discussion around subsurface technologies that tap into water and energy resources. Here we present the application of Coupled Flow-geomechanics simulation technology to the post mortem analysis of a sequence of damaging earthquakes (Mw = 6.0 and 5.8) in May 2012 near the Cavone oil field, in northern Italy. This sequence raised the question of whether these earthquakes might have been triggered by activities due to oil and gas production. Our analysis strongly suggests that the combined effects of fluid production and injection from the Cavone field were not a driver for the observed seismicity. More generally, our study illustrates that computational modeling of Coupled Flow and geomechanics permits the integration of geologic, seismotectonic, well log, fluid pressure and Flow rate, and geodetic data and provides a promising approach for assessing and managing hazards associated with induced seismicity.
-
stability and convergence of sequential methods for Coupled Flow and geomechanics drained and undrained splits
Computer Methods in Applied Mechanics and Engineering, 2011Co-Authors: Jihoon Kim, Hamdi A Tchelepi, Ruben JuanesAbstract:Abstract We perform a stability and convergence analysis of sequential methods for Coupled Flow and geomechanics, in which the mechanics sub-problem is solved first. We consider slow deformations, so that inertia is negligible and the mechanical problem is governed by an elliptic equation. We use Biot’s self-consistent theory to obtain the classical parabolic-type Flow problem. We use a generalized midpoint rule (parameter α between 0 and 1) time discretization, and consider two classical sequential methods: the drained and undrained splits. The von Neumann method provides sharp stability estimates for the linear poroelasticity problem. The drained split with backward Euler time discretization ( α = 1) is conditionally stable, and its stability depends only on the coupling strength, and it is independent of time step size. The drained split with the midpoint rule ( α = 0.5) is unconditionally unstable. The mixed time discretization, with α = 1.0 for mechanics and α = 0.5 for Flow, has the same stability properties as the backward Euler scheme. The von Neumann method indicates that the undrained split is unconditionally stable when α ⩾ 0.5. We extend the stability analysis to the nonlinear regime (poro-elastoplasticity) via the energy method. It is well known that the drained split does not inherit the contractivity property of the continuum problem, thereby precluding unconditional stability. For the undrained split we show that it is B-stable (therefore unconditionally stable at the algorithmic level) when α ⩾ 0.5. We also analyze convergence of the drained and undrained splits, and derive the a priori error estimates from matrix algebra and spectral analysis. We show that the drained split with a fixed number of iterations is not convergent even when it is stable. The undrained split with a fixed number of iterations is convergent for a compressible system (i.e., finite Biot modulus). For a nearly-incompressible system (i.e., very large Biot modulus), the undrained split loses first-order accuracy, and becomes non-convergent in time. We also study the rate of convergence of both splits when they are used in a fully-iterated sequential scheme. When the medium permeability is high or the time step size is large, which corresponds to a high diffusion of pressure, the error amplification of the drained split is lower and therefore converges faster than the undrained split. The situation is reversed in the case of low permeability and small time step size. We provide numerical experiments supporting all the stability and convergence estimates of the drained and undrained splits, in the linear and nonlinear regimes. We also show that our spatial discretization (finite volumes for Flow and finite elements for mechanics) removes the well-documented spurious instability in consolidation problems at early times.
-
stability and convergence of sequential methods for Coupled Flow and geomechanics fixed stress and fixed strain splits
Computer Methods in Applied Mechanics and Engineering, 2011Co-Authors: Jihoon Kim, Hamdi A Tchelepi, Ruben JuanesAbstract:Abstract We analyze stability and convergence of sequential implicit methods for Coupled Flow and geomechanics, in which the Flow problem is solved first. We employ the von Neumann and energy methods for linear and nonlinear problems, respectively. We consider two sequential methods with the generalized midpoint rule for tn+α, where α is the parameter of time discretization: namely, the fixed-strain and fixed-stress splits. The von Neumann method indicates that the fixed-strain split is only conditionally stable, and that its stability limit is a coupling strength less than unity if α ⩾ 0.5. On the other hand, the fixed-stress split is unconditionally stable when α ⩾ 0.5, the amplification factors of the fixed-stress split are different from those of the undrained split and are identical to the fully Coupled method. Unconditional stability of the fixed-stress split is also obtained from the energy method for poroelastoplasticity. We show that the fixed-stress split is contractive and B-stable when α ⩾ 0.5. We also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward Euler method in time. From the estimates, the fixed-strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable. The fixed-stress split, however, is convergent for a fixed number of iterations, showing better accuracy than the undrained split. Even when we cannot obtain the exact local bulk modulus (or exact rock compressibility) at the Flow step a priori due to complex boundary conditions or the nonlinearity of the materials, the fixed-stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus, such as the dimension-based estimation, by which the employed local bulk modulus is less stiff than the exact local bulk modulus. We provide numerical examples supporting all the estimates of stability and convergence for the fixed-strain and fixed-stress splits.
-
A locally conservative finite element framework for the simulation of Coupled Flow and reservoir geomechanics
Acta Geotechnica, 2007Co-Authors: Birendra Jha, Ruben JuanesAbstract:In this paper, we present a computational framework for the simulation of Coupled Flow and reservoir geomechanics. The physical model is restricted to Biot’s theory of single-phase Flow and linear poroelasticity, but is sufficiently general to be extended to multiphase Flow problems and inelastic behavior. The distinctive technical aspects of our approach are: (1) the space discretization of the equations. The unknown variables are the pressure, the fluid velocity, and the rock displacements. We recognize that these variables are of very different nature, and need to be discretized differently. We propose a mixed finite element space discretization, which is stable, convergent, locally mass conservative, and employs a single computational grid. To ensure stability and robustness, we perform an implicit time integration of the fluid Flow equations. (2) The strategies for the solution of the Coupled system. We compare different solution strategies, including the fully Coupled approach, the usual (conditionally stable) iteratively Coupled approach, and a less common unconditionally stable sequential scheme. We show that the latter scheme corresponds to a modified block Jacobi method, which also enjoys improved convergence properties. This computational model has been implemented in an object-oriented reservoir simulator, whose modular design allows for further extensions and enhancements. We show several representative numerical simulations that illustrate the effectiveness of the approach.
George J Moridis - One of the best experts on this subject based on the ideXlab platform.
-
sequentially Coupled Flow and geomechanical simulation with a discrete fracture model for analyzing fracturing fluid recovery and distribution in fractured ultra low permeability gas reservoirs
Journal of Petroleum Science and Engineering, 2020Co-Authors: Yongzan Liu, George J Moridis, Lijun Liu, Juliana Y LeungAbstract:Abstract More accurate characterization and prediction of the in-situ distribution of fracturing fluid in fractured reservoirs are needed for enhancing well productivity. In this study, an implicit-sequentially Coupled Flow/geomechanics simulator incorporating an efficient discrete fracture model is developed to model fluid distribution and recovery performance of ultra-low permeability gas reservoirs. The finite-volume and finite-element methods are used for space discretization of the Flow and geomechanics equations, respectively, while the backward Euler method is employed for time discretization. The Flow and geomechanics equations are solved sequentially based on fixed-stress splitting. An efficient discrete-fracture model is used to explicitly model the fractured system. Flexible unstructured gridding is employed to model arbitrarily-oriented fractures. The interrelations among pore volume, permeability and geomechanical conditions are considered dynamically using two-way Coupled Flow and geomechanics computations. The geometry of fracture (networks) due to hydraulic fracturing has significant impacts on the fracturing fluid recovery efficiency and ensuing fluid distribution. Under the same injection volume, the fracturing fluid recovery is higher when the fracture geometry is planar. Fluid recovery is relatively lower whenever natural fractures are activated during fracturing treatments; Flowback time is also shortened when complex fracture network with enlarged fracture interface is present. Fracturing fluid in hydraulic fractures may leak off into the natural fractures and subsequently imbibes into the surrounding matrix due to capillarity effects. The fracturing fluid recovery and in-situ fluid distribution are sensitive to the shut-in duration and fracture closure behavior. This study analyzes the Coupled Flow-geomechanical responses of fractured gas reservoirs during the post-fracturing periods. Understanding the fate of the fracturing fluid can provide insights on, to some extent, the stimulated fracture volume, size of the water invasion zone, and efficiency of the fracturing design. The simulation predictions can also provide more accurate initial reservoir conditions (e.g. distributions of different phases and pressure) for long-term well performance estimation.
-
Development of the T+M Coupled Flow-geomechanical simulator to describe fracture propagation and Coupled Flow-thermal-geomechanical processes in tight/shale gas systems
Computers and Geosciences, 2013Co-Authors: Jihoon Kim, George J MoridisAbstract:We developed a hydraulic fracturing simulator by coupling a Flow simulator to a geomechanics code, namely T+M simulator. Modeling of the vertical fracture development involves continuous updating of the boundary conditions and of the data connectivity, based on the finite element method for geomechanics. The T+M simulator can model the initial fracture development during the hydraulic fracturing operations, after which the domain description changes from single continuum to double or multiple continua in order to rigorously model both Flow and geomechanics for fracture-rock matrix systems. The T+H simulator provides two-way coupling between fluid-heat Flow and geomechanics, accounting for thermo-poro-mechanics, treats nonlinear permeability and geomechanical moduli explicitly, and dynamically tracks changes in the fracture(s) and in the pore volume. We also fully account for leak-off in all directions during hydraulic fracturing.We first test the T+M simulator, matching numerical solutions with the analytical solutions for poromechanical effects, static fractures, and fracture propagations. Then, from numerical simulation of various cases of the planar fracture propagation, shear failure can limit the vertical fracture propagation of tensile failure, because of leak-off into the reservoirs. Slow injection causes more leak-off, compared with fast injection, when the same amount of fluid is injected. Changes in initial total stress and contributions of shear effective stress to tensile failure can also affect formation of the fractured areas, and the geomechanical responses are still well-posed. © 2013 .
Saumik Dana - One of the best experts on this subject based on the ideXlab platform.
-
convergence analysis of two grid fixed stress split iterative scheme for Coupled Flow and deformation in heterogeneous poroelastic media
Computer Methods in Applied Mechanics and Engineering, 2018Co-Authors: Saumik Dana, Mary F WheelerAbstract:Abstract We perform a convergence analysis of a two-grid fixed stress split algorithm for the Biot system modeling Coupled Flow and deformation in heterogeneous poroelastic media. The two-grid fixed stress split scheme solves the Flow subproblem on a fine grid using a multipoint flux mixed finite element method by imposing the fixed mean stress constraint followed by the poromechanics subproblem on a coarse grid using a conforming Galerkin method in every coupling iteration at each time step. Restriction operators map the fine scale Flow solution to the coarse scale poromechanical grid and prolongation operators map the coarse scale poromechanical solution to the fine scale Flow grid. The coupling iterations are repeated until convergence and Backward Euler is employed for time marching. The convergence analysis is based on studying the equations satisfied by the difference of iterates to show that the two-grid scheme is a contraction map under certain conditions. Those conditions are used to construct the restriction and prolongation operators as well as arrive at effective elastic properties for the coarse scale poromechanical solve in terms of the fine scale elastic properties. We analyze the contraction map with a numerical result comparing the numerically computed to the theoretically obtained contraction constant for a poroelastic medium with substantial spatial variability in the poroelastic moduli.
-
the correspondence between voigt and reuss bounds and the decoupling constraint in a two grid staggered solution algorithm to Coupled Flow and deformation in heterogeneous poroelastic media
arXiv: Numerical Analysis, 2018Co-Authors: Saumik Dana, Mary F WheelerAbstract:We perform a convergence analysis of a two-grid staggered solution algorithm for the Biot system modeling Coupled Flow and deformation in heterogeneous poroelastic media. The algorithm first solves the Flow subproblem on a fine grid using a mixed finite element method (by freezing a certain measure of the mean stress) followed by the poromechanics subproblem on a coarse grid using a conforming Galerkin method. Restriction operators map the fine scale Flow solution to the coarse scale poromechanical grid and prolongation operators map the coarse scale poromechanical solution to the fine scale Flow grid. The coupling iterations are repeated until convergence and Backward Euler is employed for time marching. The analysis is based on studying the equations satisfied by the difference of iterates to show that the two-grid scheme is a contraction map under certain conditions. Those conditions are used to construct the restriction and prolongation operators as well as arrive at coarse scale elastic properties in terms of the fine scale data. We show that the adjustable parameter in the measure of the mean stress is linked to the Voigt and Reuss bounds frequently encountered in computational homogenization of multiphase composites.
-
a multiscale fixed stress split iterative scheme for Coupled Flow and poromechanics in deep subsurface reservoirs
Journal of Computational Physics, 2018Co-Authors: Saumik Dana, Benjamin Ganis, Mary F WheelerAbstract:Abstract In Coupled Flow and poromechanics phenomena representing hydrocarbon production or CO 2 sequestration in deep subsurface reservoirs, the spatial domain in which fluid Flow occurs is usually much smaller than the spatial domain over which significant deformation occurs. The typical approach is to either impose an overburden pressure directly on the reservoir thus treating it as a Coupled problem domain or to model Flow on a huge domain with zero permeability cells to mimic the no Flow boundary condition on the interface of the reservoir and the surrounding rock. The former approach precludes a study of land subsidence or uplift and further does not mimic the true effect of the overburden on stress sensitive reservoirs whereas the latter approach has huge computational costs. In order to address these challenges, we augment the fixed-stress split iterative scheme with upscaling and downscaling operators to enable modeling Flow and mechanics on overlapping nonmatching hexahedral grids. Flow is solved on a finer mesh using a multipoint flux mixed finite element method and mechanics is solved on a coarse mesh using a conforming Galerkin method. The multiscale operators are constructed using a procedure that involves singular value decompositions, a surface intersections algorithm and Delaunay triangulations. We numerically demonstrate the convergence of the augmented scheme using the classical Mandel's problem solution.
