Efficient Geomechanical Simulations of Large-Scale Naturally Fractured Reservoirs Using the Fast Multipole-Displacement Discontinuity Method (FM-DDM)

Geothermal and unconventional reservoirs play an important role in supplying fuel for a growing energy demand in the United States. The development of such reservoirs relies on creating a fracture network to provide flow and transport conduits during injection and production operations. The Displacement Discontinuity Method (DDM) is frequently used for modeling the behavior of fractures embedded in elastic and poroelastic rocks. However, DDM requires the calculation of the influence among all fractures being computationally inefficient for large systems of cracks. It demands quadratic and cubic complexity of memory and solution time by direct methods, respectively, limiting its application to only small-scale situations. Recent fast summation techniques such as the Fast Multipole Method (FMM) have been used to speed up the solution of several boundary element problems using modest computational resources. FMM relies in accelerating matrix-vector products in iterative methods by splitting the computation of the influences among elements into near and far-field interactions. While the former are calculated similarly to the conventional DDM, the latter, where most of the interactions are found, are efficiently approximated by the FMM using analytical multipole and local expansions. However, in spite of its immediately apparent application in the geomechanic context, FMM has been limited to only certain fracture problems because those analytical expansions are only available for selected fundamental solutions and the development for new ones requires complex mathematical derivations even for those kernels of simple form. This work presents a new method called Fast Multipole–Displacement Discontinuity Method (FM-DDM) for an efficient flow-geomechanical simulation of large-scale naturally fractured reservoirs undergoing fluid injection and extraction. The approach combines both DDM and FMM using for the latter a kernel-independent version where multipole and local expansions are not required opening a range of potential applications within the geothermal and oil industries. Several case studies involving fracture networks with up to one hundred thousands of boundary elements were presented to evaluate accuracy, computational efficiency and applications of the FMM approach. From the results, FM-DDM showed an excellent agreement with well-known benchmark solutions outperforming DDM with linear complexity in both memory and execution time. In addition, a variety of large-scale geomechanical applications were efficiently evaluated with FM-DDM involving interactions between transverse hydraulic fractures and a fracture network, fast visualization of high-resolution stress distribution, and the design of exploitation strategies in elastic and poroelastic fractured reservoirs

Application of displacement discontinuity method to hydraulic fracture propagation in heterogeneous rocks

The development of multi-stage hydraulic fracturing technique in horizontal wells enables us to produce oil and gas at economic rate from shale formations, leading to the shale revolution in the United States. Field observations including production history, microseismic mapping, and coring in fractured zones have revealed that the heterogeneity of shale rocks such as natural fractures is likely to have a large impact on oil and gas production from shale reservoirs. In this dissertation, a new hydraulic fracturing model based on the displacement discontinuity method (DDM) was developed. The major achievements in this research include the extension of DDM to multilayered media, the modeling of the interaction with natural fractures in three dimensions, and the development of a DDM-based hydraulic fracturing simulator. The formulation of DDM was revisited, and the equivalence of DDM and BEM was mathematically demonstrated. DDM was extended to multilayered media by using the method of images. The new DDM was applied to a three-layered medium in plain strain containing vertical and horizontal cracks. A sensitivity study suggests that bi-material solutions are sufficient for three-layered media under plain strain conditions. A DDM-based hydraulic fracturing model was developed. The discretized DDM and flow equations were solved in a segregated or fully coupled manner. A new splitting scheme was proposed to improve the convergence speed of the segregated method. The interaction between hydraulic and natural fractures was modeled for both intersecting and remotely interacting cases in our simulator. Poroelastic effects were partially incorporated into DDM by assuming an undrained condition. It was found that poroelastic effects under the undrained condition were limited to the vicinity of hydraulic fractures. Hydraulic fracturing simulations were performed in the presence of synthetic natural fracture networks. Synthetic microseismic events were generated, and inversion analyses of the synthetic microseismic data were performed. It was suggested that the density of microseismic events was affected by both the areal density and length distribution of natural fracturesPetroleum and Geosystems Engineerin

Numerical Simulations of Fracture Propagation Applied to Petroleum and Geothermal Reservoir Using Finite Element Method

Hydraulic fracturing is a major technique in reservoir stimulation to enhance production. Better understanding of mechanisms of hydraulic fracturing is essential for designing hydraulic fracture treatments. Multiple physical processes are involved in hydraulic fracturing propagation and active in determination of the growth of a propagating flow induced fracture. The rock deformation, fracture mechanical responses, fluid flow and thermal diffusion need to be coupled studied to represent the realistic behaviors in the petroleum and geothermal reservoir. In this work, motivated by the limitations of the existing fracture simulators and urgent needs for true 3D hydraulic fracturing model, three-dimensional numerical approaches implemented in finite element method are developed to simulate rock failure and coupled hydraulic and thermal fracture propagation problems. Due to the complex geological conditions of rock formation such as nonlinearity, anisotropy, heterogeneity and existence of large discontinuity, the behaviors of realistic rock in the reservoir are extremely difficult to be characterized and modeled. Finding a suitable and affordable constitutive model for rocks is a crucial part in the rock mechanics and its applications in petroleum industry. Multi-scale virtual multidimensional internal bonds (VMIB) model and continuum damage model are presented in this work providing solutions from different aspects on solving the nonlinear responses of rock. Moreover, the phenomenon and cause of mesh size sensitivity due to using local strain softening model are introduced. Verified by the simulation results, the mesh size sensitivity is minimized through adopting nonlocal damage theory. Three dimensional element partition method (3D EPM) is adopted to represent the mechanical behaviors of fracture surface such as contact and friction of closed fracture surfaces. Taking advantage of efficiency and simplicity of 3D EPM, the fracture mechanical response and moving boundary conditions in the hydraulic fracturing process are well represented, especially for true 3D simulation. Though the fracture process is a fully coupled nonlinear problem, the present dissertation studies the hydraulic and thermal effects separately. The 3D thermal fracture propagation due to transient cooling in quasi-brittle rock is studied using VMIB model combined with 3D EPM. The nonlinearities of mechanical behaviors and thermal parameters of the solid material were captured by introducing nonlinear VMIB model into thermo-mechanical coupled governing equations. On the aspects of fluid flow, poroelastic model and lubrication theory are introduced based on different flow mechanisms. Lubrication theory integrally considered the physical behaviors of both rock formation and fluid. The unknown variables are solved by trial and iterations. Nonlocal damage model and the relative technique are adopted for the first time in hydraulic fracturing simulation. To capture the hydraulic fracture propagation in natural fractured formation, the modified poroelastic model is developed to simulate the hydraulic fracturing especially for the hydraulic fracture problem with complex geometry and boundary conditions such as hydraulic and natural fractures interaction. Though the model needs improvement on the accuracy and stability, the overall tendency of fluid pressure distribution and fracture propagation can be captured considering the computational feasibility and efficiency. The new numerical model is a promising tool for predicting and understanding the complex processes of hydraulic fracturing and its interaction with natural fractures in unconventional reservoir under finite element method framework

THREE-DIMENSIONAL MODELING OF HYDRAULIC AND NATURAL FRACTURE INTERACTIONS AND ITS APPLICATIONS IN RESERVOIR STIMULATION

The ultralow permeability of the unconventional and geothermal reservoirs can be increased for economic production by hydraulic fracturing. Natural fractures and other discontinuities are inseparable elements of unconventional reservoir rock masses. During stimulation, hydraulic fractures often interact with the natural fractures to form a fracture network which communicates with the rock matrix. This study is an effort to develop numerical models for simulation of these interactions and cast light on the mechanisms involved in the stimulation of naturally-fractured reservoir. State-of-the-art simulators are developed to investigate the different aspects of stimulation in naturally-fractured rocks. The models include a 2D elastic model that couples rock deformation and fluid flow, a 2D fully-coupled poroelastic model, and an integrated 3D HF-NF model with pressure dependent leak-off. Rock deformation and stresses are modeled using two- and three-dimensional displacement discontinuity (DD) method. Contact elements are used to represent the closed natural fractures along with the Mohr-Coulomb criterion to determine the contact status of the fractures. Fracture propagation is modeled using a mixed-mode propagation scheme. A novel fracture coalescence scheme is integrated in the 3D HF-NF model to investigate intersection problems for a wide range of NF dip angles and strikes. The simulation results indicate that propagation from critically-stressed and favorably-oriented natural fractures significantly contributes to the stimulation of enhanced geothermal systems (EGS). Wing-crack propagation which starts at injection pressures below the minimum horizontal stress and continues at pressures slightly above the minimum stress may lead to the generation of NF networks in en echelon pattern. The analyses regarding the stress conditions revealed that wing-cracks are likely to form when the confining stress is not significantly high. Conditions that lead to higher leakoff and development of back-stress such as high rock permeability, low reservoir pressure, and low injection rates were found to limit the propagation of wing-cracks. The simulation results indicate that hydraulic fractures experience pressure drop upon intersection with permeable natural fractures. The pressure drop is followed by an increase in the injection pressure as the hydraulic fracture pressurizes the natural fracture. Moreover, the results show that the HF may propagate in other directions away from the NF when it is partially arrested by the natural fractures. Simultaneous interaction with multiple NFs and/or stress barriers was found to result in complex HF geometries with non-uniform fracture aperture distributions that could, in turn, affect proppant placement. The simulation results indicate that the increase in the injection pressure that follows a period of pressure drop in the EGS field experiments is likely caused by fracture containment near natural fractures and stress barriers. The DFIT results revealed that the interaction between the hydraulic and natural fractures impact the pressure transient behavior. Our results show that the closure of natural fractures which often precedes that of the HF could result in a signature similar to that of the system stiffness/compliance. The simulation result indicate that the multiple closure humps that is observed in some filed data such as one in the FORGE EGS site can be explained by the closure of a HF-NF system

3-D Stress Redistribution During Hydraulic Fracturing Stimulation And Its Interaction With Natural Fractures In Shale Reservoirs

The hydraulic fracturing (also called fracturing, or fracking) technique has been widely applied in many fields, such as the enhanced geothermal systems (EGS), the improvement of injection rates for geologic sequestration of CO2, and for the stimulations of oil and gas reservoirs, especially for unconventional reservoirs with extremely low permeability. The key point for the success of hydraulic fracturing operations in unconventional resources is to connect and reactivate natural fractures and create the effective fracture network for fluid flow from pores into the production wells. To understand hydraulic fracturing technology, we must to understand some other affecting factors, e.g. in-situ stress conditions, reservoir mechanical properties, natural fracture distribution, and redistribution of the stress regime around the hydraulic fracture. Therefore, an accurate estimation of the redistribution of pore pressure and stresses around the hydraulic fracture is necessary, and it is very important to find out the reactivations of pre-existing natural fractures during the hydraulic fracturing process. Generally, fracture extension as well as its surround pore pressure and stress regime are affected by: poro- and thermoelastic phenomena as well as by fracture opening under the combined action of applied pressure and in-situ stresses. In this thesis, the previous studies on the hydraulic fracturing modeling and simulations were reviewed; a comprehensive semi-analytical model was constructed to estimate the pore pressure and stress distribution around an injection induced fracture from a single well in an infinite reservoir. With Mohr-Coulomb failure criterion, the natural fracture reactivation potential around the hydraulic fracture were studied. Then, a few case studies were presented, especially with the application in unconventional natural fractured shale reservoirs. This work is of interest in interpretation of micro-seismicity in hydraulic fracturing and in assessing permeability variation around a stimulation zone, as well as in estimation of the fracture spacing during hydraulic fracturing operations. In addition, the results from this study can be very helpful for selection of stimulated wells and further design of the re-fracturing operations

Geomechanical Development of Fractured Reservoirs During Gas Production

Within fractured reservoirs, such as tight gas reservoir, coupled processes between matrix deformation and fluid flow are very important for predicting reservoir behavior, pore pressure evolution and fracture closure. To study the coupling between gas desorption and rock matrix/fracture deformation, a poroelastic constitutive relation is developed and used for deformation of gas shale. Local continuity equation of dry gas model is developed by considering the mass conservation of gas, including both free and absorbed phases. The absorbed gas content and the sorption-induced volumetric strain are described through a Langmiur-type equation. A general porosity model that differs from other empirical correlations in the literature is developed and utilized in a finite element model to coupled gas diffusion and rock mass deformation. The dual permeability method (DPM) is implemented into the Finite Element Model (FEM) to investigate fracture deformation and closure and its impact on gas flow in naturally fractured reservoir. Within the framework of DPM, the fractured reservoir is treated as dual continuum. Two independent but overlapping meshes (or elements) are used to represent these kinds of reservoirs: one is the matrix elements used for deformation and fluid flow within matrix domain; while the other is the fracture element simulating the fluid flow only through the fractures. Both matrix and fractures are assumed to be permeable and can accomodate fluid transported. A quasi steady-state function is used to quantify the flow that is transferred between rock mass and fractures. By implementing the idea of equivalent fracture permeability and shape-factor within the transfer function into DPM, the fracture geometry and orientation are numerically considered and the complexity of the problem is well reduced. Both the normal deformation and shear dilation of fractures are considered and the stress-dependent fracture aperture can be updated in time. Further, a non-linear numerical model is constructed by implementing a poroviscoelastic model into the dual permeability (DPM)-finite element model (FEM) to investigate the coupled time-dependent viscoelastic deformation, fracture network evolution and compressible fluid flow in gas shale reservoir. The viscoelastic effect is addressed in both deviatoric and symmetric effective stresses to emphasize the effect of shear strain localization on fracture shear dilation. The new mechanical model is first verified with an analytical solution in a simple wellbore creep problem and then compared with the poroelastic solution in both wellbore and field cases

Thermo-hydro-mechanical Analysis of Fractures and Wellbores in Petroleum/Geothermal Reservoirs

The thesis considers three-dimensional analyses of fractures and wellbores in low-permeability petroleum/geothermal reservoirs, with a special emphasis on the role of coupled thermo-hydro-mechanical processes. Thermoporoelastic displacement discontinuity and stress discontinuity methods are elaborated for infinite media. Furthermore, injection/production-induced mass and heat transport inside fractures are studied by coupling the displacement discontinuity method with the finite element method. The resulting method is then used to simulate problems of interest in wellbores and fractures for related to drilling and stimulation. In the examination of fracture deformation, the nonlinear behavior of discontinuities and the change in status from joint (hydraulically open, mechanically closed) to hydraulic fracture (hydraulically open, mechanically open) are taken into account. Examples are presented to highlight the versatility of the method and the role of thermal and hydraulic effects, three-dimensionality, hydraulic/natural fracture deformation, and induced micro earthquakes. Specifically, injection/extraction operations in enhanced geothermal reservoirs and hydraulic/thermal stimulation of fractured reservoirs are studied and analyzed with reference to induced seismicity. In addition, the fictitious stress method is used to study three-dimensional wellbore stresses in the presence of a weakness plane. It is shown that the coupling of hydro-thermo-mechanical processes plays a very important role in low-permeability reservoirs and should be considered when predicting the behavior of fractures and wellbores