SUMMARYThis paper describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

In this work, we present the application of a fully coupled hydro‐mechanical method to investigate the effect of fracture heterogeneity on fluid flow through fractures at the laboratory scale. Experimental and numerical studies of fracture closure behavior in the presence of heterogeneous mechanical and hydraulic properties are presented. We compare the results of two sets of laboratory experiments on granodiorite specimens against numerical simulations in order to investigate the mechanical fracture closure and the hydro‐mechanical effects, respectively. The model captures fracture closure behavior and predicts a nonlinear increase in fluid injection pressure with loading. Results from this study indicate that the heterogeneous aperture distributions measured for experiment specimens can be used as model input for a local cubic law model in a heterogeneous fracture to capture fracture closure behavior and corresponding fluid pressure response.

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finitevolume discretization for the multiphase flow equations coupled with a finiteelement scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

Methane hydrates, widely found in permafrost and deep marine sediments, have great potential as a future energy source. Conventional production schemes perform poorly for challenging hydrate reservoirs with low permeability. We propose an efficient production scheme by combining hydraulic fracturing from horizontal wells and hot water circulation through fractures. A fully coupled thermo-hydro-chemical (THC) model is developed to simulate the key physical processes during gas production from a hydrate reservoir representative of typical geological settings in Shenhu, South China Sea. We found that the gas production process has two distinct stages divided by thermal breakthrough: a relatively short prebreakthrough stage and a postbreakthrough stage yielding stable gas production. Heat advection along and near the hydraulic fracture dominates the prebreakthrough stage, whereas conduction-driven thermal recovery in the volume around fractures dominates the postbreakthrough stage. We identified that the steady-state injection temperature has a strong effect on the performance of the proposed scheme while the fluid mass circulation rate has a moderate impact beyond a threshold. The proposed scheme proves to be efficient and robust over a range of reservoir conditions with respect to initial hydrate saturation and intrinsic permeability, including their spatial heterogeneities, thereby offering a promising solution for challenging reservoir conditions.

Conventional principles of the design and operation of geologic carbon storage (GCS) require injecting CO2 below the caprock fracturing pressure to ensure the integrity of the storage complex. In nonideal storage reservoirs with relatively low permeability, pressure buildup can lead to hydraulic fracturing of the reservoir and caprock. While the GCS community has generally viewed hydraulic fractures as a key risk to storage integrity, a carefully designed stimulation treatment under appropriate geologic conditions could provide improved injectivity while maintaining overall seal integrity. A vertically contained hydraulic fracture, either in the reservoir rock or extending a limited height into the caprock, provides an effective means to access reservoir volume far from the injection well. Employing a fully coupled numerical model of hydraulic fracturing, solid deformation, and matrix fluid flow, we study the enabling conditions, processes, and mechanisms of hydraulic fracturing during CO2 injection. A hydraulic fracture's pressure‐limiting behavior dictates that the near‐well fluid pressure is only slightly higher than the fracturing pressure of the rock and is insensitive to injection rate and mechanical properties of the formation. Although a fracture contained solely within the reservoir rock with no caprock penetration, would be an ideal scenario, poroelastic principles dictate that sustaining such a fracture could lead to continuously increasing pressure until the caprock fractures. We also investigate the propagation pattern and injection pressure responses of a hydraulic fracture propagating in a caprock subjected to heterogeneous in situ stress. The results have important implications for the use of hydraulic fracturing as a tool for managing storage performance.

A new approach for treating the mechanical interactions of overlapping finite element meshes is presented. Referred to as embedded mesh methods here, these overlapping mesh methods typically include a foreground solid mesh and a background Euler fluid grid or solid mesh. A number of different approaches have been used in previous work to characterize the interactions of the background and foreground meshes at the interface. Lagrange multipliers are well suited to enforce the continuity constraints but care must be taken such that the resulting formulation is stable. Several Lagrange multiplier techniques are examined in this work and applied to coupling solid meshes and fluid-structure interaction type problems. In addition, details regarding implementation in a two-step, multi-material, Arbitrary Lagrangian Eulerian (ALE) code are presented. Example problems demonstrate convergence and applicability to a range of problems. In particular, the fluid-structure interaction examples focus on blast applications.

A fully coupled thermomechanical model of the nanoscale deformation in amorphous SiO2 due to laser heating is presented. Direct measurement of the transient, nonuniform temperature profiles was used to first validate a nonlinear thermal transport model. Densification due to structural relaxation above the glass transition point was modeled using the Tool‐Narayanaswamy (TN) formulation for the evolution of structural relaxation times and fictive temperature. TN relaxation parameters were derived from spatially resolved confocal Raman scattering measurements of Si–O–Si stretching mode frequencies. Together, these thermal and microstructural data were used to simulate fictive temperatures which are shown to scale nearly linearly with density, consistent with previous measurements from Shelby et al. Volumetric relaxation coupled with thermal expansion occurring in the liquid‐like and solid‐like glassy states lead to residual stresses and permanent deformation which could be quantified. However, experimental surface deformation profiles between 1700 and 2000 K could only be reconciled with our simulation by assuming a roughly 2 × larger liquid thermal expansion for a‐SiO2 with a temperature of maximum density ~150 K higher than previously estimated by Bruckner et al. Calculated stress fields agreed well with recent laser‐induced critical fracture measurements, demonstrating accurate material response prediction under processing conditions of practical interest.

Fluid‐driven fracture propagation is widely observed in various geological processes and crucial to many applications of geological engineering. Developing robust and accurate numerical strategies has significance in advancing the scientific understanding and engineering applications related with fluid‐driven fracture propagation. We present a finite element‐finite volume strategy using asymptotic fracture tip enrichment to model the fluid‐driven fracture propagation in three‐dimensional Cartesian meshes under the viscosity‐dominated regime, in which the fluid viscosity‐related process is the dominant energy dissipation mechanism. We use the finite element method to discretize the balance of linear momentum equation for the deformed solid and the finite volume method to discretize the Reynolds equation that governs the fluid flow. In order to track the evolving fracture front in heterogeneous media, we extend the implicit level set approach originally proposed for the displacement discontinuity method. Through this process, a signed distance‐based fracture propagation criterion naturally emerges and is suitable for the viscosity‐dominated regime when solid toughness becomes irrelevant. Critically, we enrich the fluid volume treatment near the fracture front using the tip asymptotic solution. This enrichment strategy is crucial to overcome the mesh nonconformity caused by the arbitrary intersections between propagating fracture front and underlying Cartesian meshes. We compare the numerical results with analytical solutions of the KGD problem and the penny‐shape problem, and illustrate the mesh size and time step‐insensitivity of the numerical results due to the tip enrichment technique. Also, we demonstrate the capabilities of the proposed method to model fluid‐driven fracture propagation in various heterogeneous media.