Simulating the deformation of fractured media requires the coupling of different models for the deformation of fractures and the formation surrounding them. We consider a cell centered finite-volume approach, termed the multipoint stress approximation (MPSA) method, which is developed in order to discretize coupled flow and mechanical deformation in the subsurface. Within the MPSA framework, we consider fractures as co-dimension one inclusions in the domain, with the fracture surfaces represented as line pairs in 2D (faces in 3D) that displace relative to each other. Fracture deformation is coupled to that of the surrounding domain through internal boundary conditions. This approach is natural within the finite-volume framework, where tractions are defined on surfaces of the grid. The MPSA method is capable of modeling deformation considering open and closed fractures with complex and nonlinear relationships governing the displacements and tractions at the fracture surfaces. We validate our proposed approach using both problems for which analytical solutions are available and more complex benchmark problems, including comparison with a finite-element discretization.
Understanding the controlling mechanisms underlying injection‐induced seismicity is important for optimizing reservoir productivity and addressing seismicity‐related concerns related to hydraulic stimulation in Enhanced Geothermal Systems. Hydraulic stimulation enhances permeability through elevated pressures, which cause normal deformations and the shear slip of preexisting fractures. Previous experiments indicate that fracture deformation in the normal direction reverses as the pressure decreases, e.g., at the end of stimulation. We hypothesize that this normal closure of fractures enhances pressure propagation away from the injection region and significantly increases the potential for postinjection seismicity. To test this hypothesis, hydraulic stimulation is modeled by numerically coupling flow in the fractures and matrix, fracture deformation, and matrix deformation for a synthetic reservoir in which the flow and mechanics are strongly affected by a complex three‐dimensional fracture network. The role of the normal closure of fractures is verified by comparing simulations conducted with and without the normal closure effect.
Shear-dilation-based hydraulic stimulations can enable commercial exploitation of geothermal energy from reservoirs with inadequate initial permeability. While contributing to enhancing the reservoir's permeability, hydraulic stimulation processes may also lead to undesired seismic activity. Here we present a three-dimensional numerical model aiming to aid increased understanding of shear-dilation based hydraulic stimulation and its consequences. The fractured reservoir is modeled as a network of explicitly represented large-scale fractures immersed in a permeable rock matrix. The numerical formulation is constructed by coupling three physical processes: fluid flow, fracture deformation, and rock matrix deformation. For flow simulations, the discrete fracture-matrix model is used, which allows fluid transport from high-permeable conductive fractures to rock matrix and vice versa. The mechanical behavior of the fractures is modeled with reversible and irreversible deformations corresponding to elastic deformation and slip. Linear elasticity is assumed for mechanical deformation and stress alteration of the rock matrix. Fractures are modeled as lower-dimensional surfaces embodied in the domain, subjected to specific governing equations for their deformation along the tangential and normal directions. Both the fluid flow and momentum balance equations are approximated by finite volume discretizations. The new numerical model is demonstrated considering a three-dimensional fractured formation with a network of 20 explicitly represented fractures. The effects of fluid exchange between fractures and rock matrix on the permeability evolution and the generated seismicity are examined for test cases resembling realistic reservoir conditions. Numerical modeling of the shear stimulation can be a powerful tool for estimating the potential performance of the stimulated reservoir, for understanding governing mechanisms, and/or for forecasting possible undesired by-products of the stimulation process. However, due to the complex structure of the fractured rock and the number of coupled physical processes involved in the stimulation process, many modeling aspects remain unresolved. Challenges include the description of the mechanical and hydraulic behavior of the UCAR ET AL. 3891
A theoretical study is performed on heat and fluid flow in partially porous medium filled parallel plate channel. A uniform symmetrical heat flux is imposed onto the boundaries of the channel partially filled with porous medium. The dimensional forms of the governing equations are solved numerically for different permeability and effective thermal conductivity ratios. Then, the governing equations are made dimensionless and solved analytically. The results of two approaches are compared and an excellent agreement is observed, indicating correctness of the both solutions. An overall Nusselt number is defined based on overall thermal conductivity and difference between the average temperature of walls and mean temperature to compare heat transfer in different channels with different porous layer thickness, Darcy number, and thermal conductivity ratio. Moreover, individual Nusselt numbers for upper and lower walls are also defined and obtained. The obtained results show that the maximum overall Nusselt number is achieved for thermal conductivity ratio of 1. At specific values of Darcy number and thermal conductivity ratio, individual Nusselt numbers approach to infinity since the value of wall temperatures approaches to mean temperature.
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