TK
T. Kadeethum
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This paper presents a mixed finite element framework for coupled hydro-mechanical–chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin method for reactive flow, and (2) a three-field mixed finite element method for coupled fluid flow and solid deformation. This combination ensures local mass conservation, which is critical to flow and transport in heterogeneous porous media, with a relatively affordable computational cost. A particular class of the framework is constructed for calcite precipitation/dissolution reactions, incorporating their nonlinear effects on the fluid viscosity and solid deformation. Linearization schemes and algorithms for solving the nonlinear algebraic system are also presented. Through numerical examples of various complexity, we demonstrate that the proposed framework is a robust and efficient computational method for simulation of reactive flow and transport in deformable porous media, even when the material properties are strongly heterogeneous and anisotropic.
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This paper presents a mixed finite element framework for coupled hydro-mechanical–chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin method for reactive flow, and (2) a three-field mixed finite element method for coupled fluid flow and solid deformation. This combination ensures local mass conservation, which is critical to flow and transport in heterogeneous porous media, with a relatively affordable computational cost. A particular class of the framework is constructed for calcite precipitation/dissolution reactions, incorporating their nonlinear effects on the fluid viscosity and solid deformation. Linearization schemes and algorithms for solving the nonlinear algebraic system are also presented. Through numerical examples of various complexity, we demonstrate that the proposed framework is a robust and efficient computational method for simulation of reactive flow and transport in deformable porous media, even when the material properties are strongly heterogeneous and anisotropic.
This paper presents the enriched Galerkin discretization for modeling fluid flow in fractured porous media using the mixed-dimensional approach. The proposed method has been tested against published benchmarks. Since fracture and porous media discontinuities can significantly influence single- and multi-phase fluid flow, the heterogeneous and anisotropic matrix permeability setting is utilized to assess the enriched Galerkin performance in handling the discontinuity within the matrix domain and between the matrix and fracture domains. Our results illustrate that the enriched Galerkin method has the same advantages as the discontinuous Galerkin method; for example, it conserves local and global fluid mass, captures the pressure discontinuity, and provides the optimal error convergence rate. However, the enriched Galerkin method requires much fewer degrees of freedom than the discontinuous Galerkin method in its classical form. The pressure solutions produced by both methods are similar regardless of the conductive or non-conductive fractures or heterogeneity in matrix permeability. This analysis shows that the enriched Galerkin scheme reduces the computational costs while offering the same accuracy as the discontinuous Galerkin so that it can be applied for large-scale flow problems. Furthermore, the results of a time-dependent problem for a three-dimensional geometry reveal the value of correctly capturing the discontinuities as barriers or highly-conductive fractures.
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This paper presents the enriched Galerkin discretization for modeling fluid flow in fractured porous media using the mixed-dimensional approach. The proposed method has been tested against published benchmarks. Since fracture and porous media discontinuities can significantly influence single- and multi-phase fluid flow, the heterogeneous and anisotropic matrix permeability setting is utilized to assess the enriched Galerkin performance in handling the discontinuity within the matrix domain and between the matrix and fracture domains. Our results illustrate that the enriched Galerkin method has the same advantages as the discontinuous Galerkin method; for example, it conserves local and global fluid mass, captures the pressure discontinuity, and provides the optimal error convergence rate. However, the enriched Galerkin method requires much fewer degrees of freedom than the discontinuous Galerkin method in its classical form. The pressure solutions produced by both methods are similar regardless of the conductive or non-conductive fractures or heterogeneity in matrix permeability. This analysis shows that the enriched Galerkin scheme reduces the computational costs while offering the same accuracy as the discontinuous Galerkin so that it can be applied for large-scale flow problems. Furthermore, the results of a time-dependent problem for a three-dimensional geometry reveal the value of correctly capturing the discontinuities as barriers or highly-conductive fractures.
Evaluations and interpretations of reservoir productivity are frequent in geothermal, groundwater and hydrocarbon research and applications. In this study, we consider the closure of fractures around production wells due to compaction that can affect the productivity value, i.e. the ability of subsurface formations for transporting the desired fluid to a borehole. We introduce analytical tools to evaluate and predict changes in the productivity of a deformable fractured porous media. We propose analytical models for three geometries: a rectangular fracture with zero/non-zero orientation and a circular fracture with zero orientation to maximum horizontal stress. An advanced numerical model is utilised to evaluate the impact of spatial variation of fracture aperture induced by the fracture deformation on well productivity. The developed analytical solutions using a uniform fracture aperture always either over- or underestimate the production rate. Hence, an equivalent aperture model is developed for the fracture with aperture distribution under variable contact stresses to circumvent this problem. The proposed equivalent aperture model reduces the average and maximum errors of production-rate prediction from 28% to 0.6% and from 116% to 25%, respectively. We further employ the proposed model for sensitivity analyses to illustrate the impacts of in-situ and human-controlled parameters on productivity reduction. These analyses present that the interactions among initial reservoir pressure, fracture orientation, fracture stiffness, and well pressure control productivity reduction behaviours and the maximum productivity reduction values.
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Evaluations and interpretations of reservoir productivity are frequent in geothermal, groundwater and hydrocarbon research and applications. In this study, we consider the closure of fractures around production wells due to compaction that can affect the productivity value, i.e. the ability of subsurface formations for transporting the desired fluid to a borehole. We introduce analytical tools to evaluate and predict changes in the productivity of a deformable fractured porous media. We propose analytical models for three geometries: a rectangular fracture with zero/non-zero orientation and a circular fracture with zero orientation to maximum horizontal stress. An advanced numerical model is utilised to evaluate the impact of spatial variation of fracture aperture induced by the fracture deformation on well productivity. The developed analytical solutions using a uniform fracture aperture always either over- or underestimate the production rate. Hence, an equivalent aperture model is developed for the fracture with aperture distribution under variable contact stresses to circumvent this problem. The proposed equivalent aperture model reduces the average and maximum errors of production-rate prediction from 28% to 0.6% and from 116% to 25%, respectively. We further employ the proposed model for sensitivity analyses to illustrate the impacts of in-situ and human-controlled parameters on productivity reduction. These analyses present that the interactions among initial reservoir pressure, fracture orientation, fracture stiffness, and well pressure control productivity reduction behaviours and the maximum productivity reduction values.