# Browsing by Subject "Poroelasticity"

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Item Acoustic characterization of encapsulated microbubbles at seismic frequencies(2013-12) Schoen, Scott Joseph, Jr.; Hamilton, Mark F.Show more Encapsulated microbubbles, whose diameters are on the order of microns, are widely used to provide acoustic contrast in biomedical applications. But well below the resonance frequencies of these microbubbles, any acoustic contrast is due solely to their relatively high compressibility compared to the surrounding medium. To estimate how well microbubbles may function as acoustic contrast agents in applications such as borehole logging or underground flow mapping, it must be determined how they behave both at atmospheric and down-well conditions, and how their presence affects the bulk acoustic properties of the surrounding medium, most crucially its specific acoustic impedance. Resonance tube experiments were performed on several varieties of acoustic contrast agents to determine their compressibility as a function of pressure and temperature, and the results are used to estimate the effect on sound propagation when they are introduced into rock formations.Show more Item Application of displacement discontinuity method to hydraulic fracture propagation in heterogeneous rocks(2020-03-27) Hirose, Sho; Sharma, Mukul M.; Foster, John T; Kinnas, Spyridon A; Prodanovic, Masa; Espinoza, David NShow more 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 fracturesShow more Item Development of peridynamics-based hydraulic fracturing model for fracture growth in heterogeneous reservoirs(2016-05) Ouchi, Hisanao; Sharma, Mukul M.; Olson, Jon E.; Foster, John T.; Espinoza, Nicolas; Kallivokas, Loukas F.Show more Oil and gas reservoirs are heterogeneous at different length scales. At the micro-scale mechanical property differences exist due to mineral grains of different composition and the distribution of organic material. At the centimeter or core scale, micro-cracks, sedimentary bedding planes, natural fractures, planes of weakness and faults exist. At the meter or log scale, larger scale bedding planes, fractures and faults are evident in most sedimentary rocks. All these heterogeneities contribute to the complexity in fracture geometry. However, very little research has been conducted on evaluating the effect of these heterogeneities on fracture propagation, primarily due to the absence of a numerical framework capable of incorporating such heterogeneities in fracture growth models. In this dissertation we developed a novel method for simulating hydraulic fractures in heterogeneous reservoirs based on peridynamics and then utilized it to elucidate the complicated fracture propagation mechanisms in naturally fractured, heterogeneous reservoirs. Peridynamics is a recently developed continuum mechanics theory specially developed to account for discontinuities such as fractures. Its integral formulation minimizes the impact of spatial derivatives in the stress balance equation making it particularly suitable for handling discontinuities in the domain. No fluid flow formulation existed in the peridynamics framework since this theory had not been applied to fluid driven fracturing processes. In this dissertation, a new peridynamics fluid flow formulation for flow in a porous medium and inside a fracture was derived as a first step in the development of a peridynamics-based hydraulic fracturing model. In the subsequent section, a new peridynamics-based hydraulic fracturing model was developed by modifying the existing peridynamics formulation of solid mechanics and coupling it with the newly derived peridynamic fluid flow formulation. Finally, new shear failure criteria were introduced into the model for simulating interactions between hydraulic fractures (HF) and natural fractures (NF). This model can simulate non-planar, multiple fracture growth in arbitrarily heterogeneous reservoirs by solving fracture propagation, deformation, fracturing fluid pressure, and pore pressure simultaneously. The validity of the model was shown through comparing model results with analytical solutions (1-D consolidation problem, the KGD model, the PKN model, and the Sneddon solution) and experiments. The 2-D and 3-D interactions behavior between a HF and a NF were investigated by using the newly developed peridynamics-based hydraulic fracturing model. The 2-D parametric study for the interaction between a HF and a NF revealed that, in addition to the well-known parameters (the principal stress difference, the approach angle, the fracture toughness of the rock, the fracture toughness of the natural fracture, and the shear failure criteria of the natural fracture), poroelastic effects also have a large influence on the interaction between a HF and a NF if leak-off is high. The 3-D interaction study elucidated that the height of the NF, the position of the NF, and the opening resistance of the NF have a huge impact on the three-dimensional interaction behavior between a HF and a NF. The effects of different types of vertical heterogeneity on fracture propagation were systematically investigated by using domains of different length scales. This research clearly showed the mechanisms and the controlling factors of characteristic fracture propagation behaviors (“turning”, “kinking”, and “branching”) near the layer interface. In layered systems, the mechanical property contrast between layers, the dip angle and the stress contrast all play an important role in controlling the fracture trajectory. Each of these effects was investigated in detail. The effect of micro-scale heterogeneity (due to varying mineral composition) on fracture geometry was studied next. It was shown that even at the micro-scale, fracture geometry can be quite complex and is determined by the geometry and distribution of mineral grains and their mechanical properties.Show more Item Earthquakes, groundwater and surface deformation : exploring the poroelastic response to megathrust earthquakes(2018-08-10) McCormack, Kimberly Alison; Hesse, Marc; Ghattas, Omar; Flemings, Peter; Dixon, Timothy H; Wallace, LauraShow more This thesis explores the poroelastic effects of large subduction zone earthquakes using numerical models and a variety of datasets with the overarching goal of beginning to deconvolve post-seismic geodetic deformation signals -- while exploring other interesting phenomena involving the poroelastic response to earthquakes along the way. Chapter 1 sets up an elastic inverse problem used to derive the initial slip condition. We formulate an adjoint-based inversion methodology to solve for the initial condition of the coupled poroelastic forward model within a consistent, finite element framework. Chapter 2 discusses the broad hydrological effects of large subduction zone earthquakes both in general and the predicted hydrological effects of the 2012 7.6 M [sunscript w] Nicoya Peninsula earthquake. It explores how different hydro-mechanical parameters affect both the instantaneous and time-dependent response and touches on some of the limitations of the models. Chapter 3 focuses on the potential effect of poroelastic deformation on post-seismic geodetic signals. Here we look at the relationships between the co-seismic pore pressure changes and different components of poroelastic deformation. It then compares the modeled surface deformation timeseries to the measured deformation at a number of GPS stations. The last chapter walks through the suite of models and data interpolation functions included in the open source toolbox built during this project.Show more Item Efficient algorithms for flow models coupled with geomechanics for porous media applications(2016-12) Almani, Tameem Mohammad; Wheeler, Mary F. (Mary Fanett); Arbogast, Todd; Demkowicz, Leszek F.; Delshad, Mojdeh; Dhillon, Inderjit; Kumar, KundanShow more The coupling between subsurface flow and reservoir geomechanics plays a critical role in obtaining accurate results for models involving reservoir deformation, surface subsidence, well stability, sand production, waste deposition, hydraulic fracturing, CO₂ sequestration, and hydrocarbon recovery. From a pure computational point of view, such a coupling can be quite a challenging and complicated task. This stems from the fact that the constitutive equations governing geomechanical deformations are different in nature from those governing porous media flow. The geomechanical effects account for the influence of deformations in the porous media caused due to the pore pressure and can be very important especially in the case of stress-sensitive and fractured reservoirs. Considering that fractures are very much prevalent in the porous media and they have strong influence on the flow profiles, it is important to study coupled geomechanics and flow problems in fractured reservoirs. In this work, we pursue three main objectives: first, to rigorously design and analyze iterative and explicit coupling algorithms for coupling flow and geomechanics in both poro-elasitc and fractured poro-elastic reservoirs. The analysis of iterative coupling schemes relies on studying the equations satisfied by the difference of iterates and using a Banach contraction argument to derive geometric convergence (Banach fixed-point contraction) results. The analysis of explicit coupling schemes result in analogous stability estimates. In this work, conformal Galerkin is used for mechanics, and a mixed formulation, including the Multipoint Flux Mixed Finite Element method as a special case, is used for the flow model. For fractured poro-elastic media, our iteratively coupled schemes are adaptations, due to the presence of fractures, of the classical fixed stress-splitting scheme, in which fractures are treated as possibly non-planar interfaces. The second main objective in this work is to exploit the different time scales of the mechanics and flow problems. Due to its physical nature, the geomechanics problem can cope with a coarser time step compared to the flow problem. This makes the multirate coupling scheme, the one in which the flow problem takes several (finer) time steps within the same coarse mechanics time step, a natural candidate in this setting. Inspired by that, we rigorously formulate and analyze convergence properties of both multirate iterative and explicit coupling schemes in both poro-elastic and fractured poro-elastic reservoirs. In addition, our theoretically derived Banach contraction estimates are validated against numerical simulations. The third objective in this work is to optimize the solution strategy of the nonlinear flow model in coupled flow and mechanics schemes. The global inexact Newton method, combined with the line search backtracking algorithm along with heuristic forcing functions, can be efficiently employed to reduce the number of flow linear iterations, and hence, the overall CPU run time. We first validate these computational savings for challenging two-phase benchmark problems including the full SPE10 model. Motivated by the obtained results, we incorporate this strategy as a nonlinear solver framework to solve the nonlinear flow problem in multirate iteratively coupled schemes. This leads to a scheme that reduces both the number of flow and mechanics linear iterations efficiently. All our numerical implementations in this work are built on top of our in-house reservoir simulator (IPARS).Show more Item Hydraulic fracture modeling with finite volumes and areas(2016-08) Bryant, Eric Cushman; Sharma, Mukul M.; Foster, John TShow more In Chapter 1, a finite volume-based arbitrary fracture propagation model is used to simulate fracture growth and geomechanical stresses during hydraulic fracture treatments. Single-phase flow, poroelastic displacement, and in situ stress tensor equations are coupled within a poroelastic reservoir domain. Stress analysis is used to identify failure initiation that proceeds by failure along Finite Volume (FV) cell faces in excess of a threshold effective stress. Fracture propagation proceeds by the cohesive zone (CZ) model, to simulate propagation of non-planar fractures in heterogeneous porous media under anisotropic far-field stress. In Chapter 2, we are concerned with stress analysis of both elastic and poroelastic solids on the same domain, using a FV-based numerical discretization. As such our main purposes are twofold: introduce a hydromechanical coupling term into the linear elastic displacement field equation, using the standard model of linearized poroelasticity; and, maintain the continuity of total traction over any multi-material interfaces (meaning an interface over which residual stresses, Biot’s coefficient, Young’s modulus, or Poisson’s ratio vary). In Chapter 3, we are concerned with modeling fluid flow in cracks bounded by deforming rock, and specifically, inside those initial discontinuities, softening regions and failed zones which constitute the solid interfaces of propagating hydraulic fractures. To accomplish this task the Finite Area (FA) method is an ideal candidate, given its proven facility for the discretization and solution of 2D coupled partial differential equations along the boundaries of 3D domains. In Chapter 4, rock formations’ response to a propagating, pressurized hydraulic fracture is examined. In order to initiate CZ applied traction-separation processes, an effective stress tensor is constructed by additively combining the total stress with pore pressures multiplied into a scalar factor. In effect, this scalar factor constitutes the Biot’s coefficient as acts inside the CZ. Integral analysis at the cohesive tip is used to show that this factor must be equal to the Biot’s coefficient in the bounding solid (for a small-strain constitutive relation). Also, effects of an initial residual stress state are accounted for.Show more Item Linear and nonlinear poroviscoelasticity, and fracture properties of gelatin-based hydrogels(2022-08-08) Chen, Si (Ph. D. in engineering mechanics); Ravi-Chandar, K.; Huang, Rui; Landis, Chad M.; Lu, Nanshu; Keitz, BenjaminShow more Hydrogels are polymer networks embedded in a solvent which is usually predominantly water. Due to the solvent diffusion and rearrangement of the polymer network, hydrogels exhibit poroelastic and viscoelastic behaviors. The two behaviors are usually coupled and may influence other mechanical properties, such as fracture. While there is much work on modeling and simulation of poroelasticity, viscoelasticity, and fracture, there is still a need for more experimental work that explores the response of the material and the calibration of the material response. In this dissertation, three large suites of experiments were performed under nonhomogeneous conditions to characterize the linear and nonlinear poroelasticity, viscoelasticity, and fracture in gelatin-based hydrogels. First, the poroelasticity of gelatin-based hydrogel of two different compositions is examined through drying and swelling experiments, achieved by adjusting the humidity levels in an environmentally controlled enclosure. The deformation of the specimens was quantified through Digital Image Correlation. The experimental measurements were compared with the simulations based on the Finite Element Method (FEM) implemented on the public domain code FEniCS, to provide a way to calibrate the material parameters both for linear and nonlinear poroelasticity. Second, the coupled poroelastic and viscoelastic behaviors of hydrogels were explored through simultaneous swelling/drying and creep experiments also in a controlled environment. This work showed that the decomposition of the volumetric and isochoric deformation provides a way to separate the poroelastic and viscoelastic behaviors. According to the experimental results, the volumetric deformation was dominated by water diffusion, and isochoric deformation was influenced by both viscoelasticity and poroelasticity. A nonlinear poroviscoelastic theory was developed based on a two-potential formulation under a thermodynamic framework, that successfully captured the coupled power-law creep and swelling/drying behaviors. Finally, the fracture behavior of hydrogels was explored under various conditions through poroelastic diffusion and viscoelastic creep. The viscoelastic J-like integral based on Schapery's theory was calculated from the measured displacement field and served as a characteristic parameter for crack growth in quasi-steady conditions. To further explore the poroelastic influence on the crack tip, fracture tests of immersed-crack-tip conditions were performed, which showed that water diffusion decreased the fracture energy.Show more Item On an inverse-source problem for elastic wave-based enhanced oil recovery(2011-08) Jeong, Chanseok,1981-; Kallivokas, Loukas F.; Huh, Chun; Ghattas, Omar; Lake, Larry W.; Manuel, Lance; Stokoe, Kenneth H.Show more Despite bold steps taken worldwide for the replacement or the reduction of the world’s dependence on fossil fuels, economic and societal realities suggest that a transition to alternative energy forms will be, at best, gradual. It also appears that exploration for new reserves is becoming increasingly more difficult both from a technical and an economic point of view, despite the advent of new technologies. These trends place renewed emphasis on maximizing oil recovery from known fields. In this sense, low-cost and reliable enhanced oil recovery (EOR) methods have a strong role to play. The goal of this dissertation is to explore, using computational simulations, the feasibility of the, so-called, seismic or elastic-wave EOR method, and to provide the mathematical/computational framework under which the method can be systematically assessed, and its feasibility evaluated, on a reservoir-specific basis. A central question is whether elastic waves can generate sufficient motion to increase oil mobility in previously bypassed reservoir zones, and thus lead to increased production rates, and to the recovery of otherwise unexploited oil. To address the many questions surrounding the feasibility of the elastic-wave EOR method, we formulate an inverse source problem, whereby we seek to determine the excitations (wave sources) one needs to prescribe in order to induce an a priori selected maximization mobility outcome to a previously well-characterized reservoir. In the industry’s parlance, we attempt to address questions of the form: how does one shake a reservoir?, or what is the “resonance” frequency of a reservoir?. We discuss first the case of wellbore wave sources, but conclude that surface sources have a better chance of focusing energy to a given reservoir. We, then, discuss a partial-differential-equation-constrained optimization approach for resolving the inverse source problem associated with surface sources, and present a numerical algorithm that robustly provides the necessary excitations that maximize a mobility metric in the reservoir. To this end, we form a Lagrangian encompassing the maximization goal and the underlying physics of the problem, expressed through the side imposition of the governing partial differential equations. We seek to satisfy the first-order optimality conditions, whose vanishing gives rise to a systematic process that, in turn, leads to the prescription of the wave source signals. We explore different (indirect) mobility metrics (kinetic energy or acceleration field maximization), and report numerical experiments under three different settings: (a) targeted formations within one-dimensional multi-layered elastic solids system of semi-infinite extent; (b) targeted formations embedded in a two-dimensional semi-infinite heterogeneous elastic solid medium; and (c) targeted poroelastic formations embedded within elastic heterogeneous surroundings in one dimension. The numerical experiments, employing hypothetical subsurface formation models subjected to, initially unknown, ground surface wave sources, demonstrate that the numerical optimizer leads robustly to optimal loading signals and the illumination of the target formations. Thus, we demonstrate that the theoretical framework for the elastic wave EOR method developed in this dissertation can systematically address the application of the method on a reservoir-specific basis. From an application point of view and based on the numerical experiments reported herein, for shallow reservoirs there is strong promise for increased production. The case of deeper reservoirs can only be addressed with further research that builds on the findings of this work, as we report in the last chapter.Show more Item On the use of the finite element method for the modeling of acoustic scattering from one-dimensional rough fluid-poroelastic interfaces(2014-05) Bonomo, Anthony Lucas; Hamilton, Mark F.; Chotiros, Nicholas P.Show more A poroelastic finite element formulation originally derived for modeling porous absorbing material in air is adapted to the problem of acoustic scattering from a poroelastic seafloor with a one-dimensional randomly rough interface. The developed formulation is verified through calculation of the plane wave reflection coefficient for the case of a flat surface and comparison with the well known analytical solution. The scattering strengths are then obtained for two different sets of material properties and roughness parameters using a Monte Carlo approach. These numerical results are compared with those given by three analytic scattering models---perturbation theory, the Kirchhoff approximation, and the small-slope approximation---and from those calculated using two finite element formulations where the sediment is modeled as an acoustic fluid.Show more Item Peridynamic model of poroelasticity based on Hamilton's principle(2017-08-10) Xu, Xiao, active 21st century; Foster, John T., Ph. D.; Sepehrnoori, KamyShow more Porous media theories play an important role in many branches of engineering. Despite significant advances, the existing theories suffer from many limitations and drawbacks when dealing with problems with discontinuities like fractures. The difficulties inherent in these problems arise from the basic incompatibility of spatial discontinuities with the partial differential equations that are used in the classical porous media theories. Peridynamics, a relatively new nonlocal formulation of continuum mechanics based on integral equations, provides a path forward in modeling spatial discontinuities in the field of solid mechanics. In this thesis, the nonlocal formulation of peridynamics is successfully combined with finite deformation poroelasticity. First, a thorough derivation of finite deformation poroelasticity based on extended Hamilton's principle is conducted. Then we include the integral formulation of peridynamic theory when deriving the nonlocal momentum balance equations for poroelasticity once again using extended Hamilton's principle. To complete our nonlocal poroelasticity theory, we also develop a new class of peridynamic constitutive models. Finally, the correspondence of our peridynamic poroelasticity theory to the classical finite deformation poroelasticity theory is shown by demonstrating that our peridynamic equations can be reduced to the classical momentum balance equations for poroelasticity if smooth and homogeneous deformation is assumed.Show more Item Poroelastic modeling of basement fault reactivation caused by saltwater disposal near Venus, Johnson County, Texas(U.S. Rock Mechanics / Geomechanics Symposium, 2020-06-28) Haddad, Mahdi; Eichhubl, PeterShow more To assess the potential for fault reactivation in response to wastewater injection near Venus, Texas, we conducted fully coupled 3D poroelastic finite element simulations for a site-specific geomechanical analysis. We find that simulations using the best estimates of in situ stress azimuth and fault orientation, and the Byerlee’s friction coefficient of 0.6 do not predict fault reactivation, in contrast to observed seismicity patterns. Increasing the maximum horizontal stress azimuth by 10° and the basement fault dip by 5°, both within the uncertainty space of the input parameters, and lowering the friction coefficient of the fault in the basement to 0.35, leads to fault reactivation in the basement as observed. Using the same model geometry but a friction coefficient of 0.6 leads to fault reactivation within Ellenburger, which is inconsistent with observed hypocenter depths at Venus. Expanding the model domain from 5 disposal wellbores to 35 increases the excess pore pressure which favors basement fault reactivation. These simulations demonstrate the sensitivity of geomechanical models of fault reactivation in response to injection requiring high-quality field parameters and help refine the azimuths of the horizontal stresses, the basement fault dip, and the basement fault friction coefficient on the basis of earthquake hypocenter temporal distribution.Show more Item Simulation and production evaluation of multiple-stage hydraulic fracturing in horizontal wellbores(2017-08) Haddad, Mahdi; Sepehrnoori, Kamy, 1951-; Olson, Jon E.; Chin, Lee Y.; Delshad, Mojdeh; Mohanty, Kishore K.; Espinoza, David N.Show more Shale formations have globally emerged as the sustainable hydrocarbon resources in the advent of the technologies for the economic production from these formations: horizontal drilling combined with multiple-stage hydraulic fracturing. The viable production from these resources requires a maximized stimulated reservoir volume encompassing a complex induced fracture network, which is highly dependent on the stimulation design. The optimization of the ultimate recovery requires integrated fracturing models with reservoir models in virtue of the limitations on the field data acquisition and their reliability, the high-cost of re-stimulation plans, and low-fidelity current reservoir simulation workflows. We proposed 2D and 3D hydraulic-fracturing models on the basis of the cohesive zone model (CZM) and extended finite element method (XFEM) with a combination of the following capabilities: (1) inclusion of fracture intersections via pore-pressure coupling; (2) fully-coupled poroelasticity in matrix, continuum-based leakoff, and slit flow in fracture(s) with the cohesive behavior for fracture growth. These models were validated in comparison with KGD solution, and were employed for the hydraulic-fracturing design and understanding microseismic event distributions. Moreover, the output of these models in a specific 2D case was integrated with a reservoir simulation workflow for the prediction of long-term production from the induced fracture network. Our 2D and 3D fracture-intersection cases demonstrate the significant role of the following parameters in the growth pattern of fractures upon intersection: (1) the length of the initially open segment of the natural fracture at the intersection; (2) the horizontal stress contrast; (3) the distance between the injection point and the intersection. Notably, hydraulic fracturing in higher depths with higher horizontal stress contrasts and closer injection points to the intersection causes more extensive natural-fracture opening and shear slippage. Also, we demonstrated the application of the proposed 3D fracture intersection model for further understanding of the anomalies observed in the Vaca Muerta Shale. This study revealed that the microseismic events at shallower depths, later times, and deviated from the expected planar distribution are mainly associated with shear slippage along weak interfaces due to the induced stresses by hydraulic fracturing. Thereby, our explicit modeling of fluid infiltration into the natural fracture(s) at the intersection leads to better understanding of the nature of microseismic events. Our multiple-stage, multiple-wellbore, hydraulic-fracturing model for naturally fractured reservoirs includes the operational and field components during the shale stimulations such as perforation tunnel length distribution, horizontal wellbores, stochastically-retrieved fully-cemented natural-fracture network, plugs for the stage stimulation (via connector elements), and external stimulation scenarios (controlled by programming the connector elements in an external user subroutine). The application of this model on synthetic cases shows the following: (1) sequential fracturing with limited number of clusters per stage leads to more control on the cluster stimulation in the presence of the non-uniform perforation tunnel length distribution and wellbore model; (2) proportional cluster efficiency with the perforation tunnel length (promoting the consistent perforation technology); (3) over-estimation of the cluster stimulation in the absence of the wellbore model and/or the natural-fracture network; and (4) more-viscous fracturing fluids conclude less complex induced fracture network (in agreement with the common field observations). The initial natural-fracture network in this model was retrieved from the proposed object-based method. Also, the transfer of the induced fracture network into an embedded discrete fracture model is featured by the higher fidelity in the estimation of long-term gas production from naturally fractured reservoirs. For the investigation of the effect of in-situ stresses on the reservoir engineering problems, we implemented the coupling of a geomechanics module with the UTCOMP reservoir simulator. We first validated this implementation via comparing the results with GPAS and CMG results at various cases. Our improvements in the geomechanics module (lowering the frequency of calling the geomechanics module and the order of the finite-element shape functions) significantly reduced the computational expenses while maintaining the solution accuracy. Overall, water flooding shows more sensitivity to the number of the reservoir-simulation time steps per geomechanics call than gas flooding cases (e.g., CO2 injection). Our reservoir simulation model for re-fracturing included various injection and production steps to show the effect of the re-fracturing fluid injection in a depleted formation on the ultimate recovery. This study showed the significant effect of the re-fracturing water injection in production via changing a single-phase to two-phase gas flow regime and deeper water invasion into the matrix due to the pressure depletion (after primary production)Show more Item XFEM-Based CZM for the Simulation of 3D Multiple-Cluster Hydraulic Fracturing in Quasi-Brittle Shale Formations(Springer, 2016-08-02) Haddad, Mahdi; Sepehrnoori, KamyShow more The cohesive zone model (CZM) honors the softening effects and plastic zone at the fracture tip in a quasibrittle rock, e.g., shale,which results in amore precise fracture geometry and pumping pressure compared to those from linear elastic fracture mechanics. Nevertheless, this model, namely the planar CZM, assumes a predefined surface on which the fractures propagate and therefore restricts the fracture propagation direction. Notably, this direction depends on the stress interactions between closely spaced fractures and can be acquired by integrating CZM as the segmental contact interaction model with a fully coupled pore pressure–displacement model based on extended finite element method (XFEM). This integrated model, called XFEM-based CZM, simulates the fracture initiation and propagation along an arbitrary, solution-dependent path. In this work, we modeled a single stage of 3D hydraulic fracturing initiating from three perforation clusters in a single-layer, quasi-brittle shale formation using planar CZM and XFEM-based CZM including slit flow and poroelasticity for fracture and matrix spaces, respectively, in Abaqus. We restricted the XFEM enrichment zones to the stimulation regions as enriching the whole domain leads to extremely high computational expenses and unrealistic fracture growths around sharp edges. Moreover, we validated our numerical technique by comparing the solution for a single fracture with KGD solution and demonstrated several precautionary measures in using XFEM in Abaqus for faster solution convergence, for instance the initial fracture length and mesh refinement. We demonstrated the significance of the injection rate and stress contrast in fracture aperture, injection pressure, and the propagation direction. Moreover, we showed the effect of the stress distribution on fracture propagation direction comparing the triple-cluster fracturing results from planar CZM with those from XFEM-based CZM. We found that the stress shadowing effect of hydraulic fractures on each other can cause these fractures to coalesce, grow parallel, or diverge depending on cluster spacing. We investigated the effect of this arbitrary propagation direction on not only the fractures’ length, aperture, and the required injection pressure, but also the fractures’ connection to the wellbore. This connection can be disrupted due to the near-wellbore fracture closure which may embed proppant grains on the fracture wall or screen out the fracture at early times. Our results verified that the near-wellbore fracture closure strongly depends on the following: (1) the implemented model, planar or XFEM-based CZM; and (2) fracture cluster spacing. Ultimately, we proposed the best fracturing scenario and cluster spacing to maintain the fractures connected to the wellbore.Show more