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.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.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.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.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, KundanThe 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).Item Multiscale Methods for Fluid-Structure Interaction with Applications to Deformable Porous Media(2012-10-19) Brown, DonaldIn this dissertation we study multiscale methods for slowly varying porous media, fluid and solid coupling, and application to geomechanics. The thesis consists of three closely connected results. We outline them and their relation. First, we derive a homogenization result for Stokes flow in slowly varying porous media. These results are important for homogenization in deformable porous media. Traditionally, these techniques are applied to periodic media, however, in the case of Fluid-Structure Interaction (FSI) slowly varying domains occur naturally. We then develop a computational methodology to compute effective quantities to construct homogenized equations for such media. Next, to extend traditional geomechanics models based primarily on the Biot equations, we use formal two-scale asymptotic techniques to homogenize the fully coupled FSI model. Prior models have assumed trivial pore scale deformation. Using the FSI model as a fine-scale model, we are able to incorporate non-trivial pore scale deformation into the macroscopic equations. The primary challenge here being the fluid and solid equations are represented in different coordinate frames. We reformulate the fluid equation in the fixed undeformed frame. This unified domain formulation is known as the Arbitrary Lagrange-Eulerian (ALE). Finally, we utilize the ALE formulation of the Stokes equations to develop an efficient multiscale finite element method. We use this method to compute the permeability tensor with much less computational cost. We build a dense hierarchy of macro-grids and a corresponding collection of nested approximation spaces. We solve local cell problems at dense macro-grids with low accuracy and use neighboring high accuracy solves to correct. With this method we obtain the same order of accuracy as we would if we computed all the local problems with highest accuracy.Item Non-Linear Drying Diffusion and Viscoelastic Drying Shrinkage Modeling in Hardened Cement Pastes(2010-07-14) Leung, Chin K.The present research seeks to study the decrease in diffusivity rate as relative humidity (RH) decreases and modeling drying shrinkage of hardened cement paste as a poroviscoelastic respose. Thin cement paste strips of 0.4 and 0.5 w/c at age 3 and 7 days were measured for mass loss and shrinkage at small RH steps in an environmental chamber at constant temperature. Non-linear drying diffusion rate of hardened cement was modeled with the use of Fick's second law of diffusion by assuming linearity of diffusion rate over short drops of ambient relative humidity. Techniques to determine drying isotherms prior to full equilibration of mass loss, as well as converting mass loss into concentration of water vapor were developed. Using the measured water vapor diffusivity, drying shrinkage strain was modeled by the theory of poroviscoelasticity. This approach was validated by determining viscoelastic properties from uniaxial creep tests considering the effect of aging by the solidification theory. A change in drying diffusion rate at different RH was observed in the 0.4 and 0.5 w/c pastes at different ages. Drying diffusion rate decreases as RH drops. This can be attributed to a change in diffusion mechanisms in the porous media at smaller pore radius. Shrinkage modeling with an average diffusion coefficient and with determined viscoelastic parameters from creep tests agreed well compared to the shrinkage data from experiments, indicating that drying shrinkage of cement paste may be considered as a poroviscoelastic reponse.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.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.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.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.Item Thermo-Poroelastic Modeling of Reservoir Stimulation and Microseismicity Using Finite Element Method with Damage Mechanics(2012-02-14) Lee, Sang HoonStress and permeability variations around a wellbore and in the reservoir are of much interest in petroleum and geothermal reservoir development. Water injection causes significant changes in pore pressure, temperature, and stress in hot reservoirs, changing rock permeability. In this work, two- and three-dimensional finite element methods were developed to simulate coupled reservoirs with damage mechanics and stress-dependent permeability. The model considers the influence of fluid flow, temperature, and solute transport in rock deformation and models nonlinear behavior with continuum damage mechanics and stress-dependent permeability. Numerical modeling was applied to analyze wellbore stability in swelling shale with two- and three-dimensional damage/fracture propagation around a wellbore and injection-induced microseismic events. The finite element method (FEM) was used to solve the displacement, pore pressure, temperature, and solute concentration problems. Solute mass transport between drilling fluid and shale formation was considered to study salinity effects. Results show that shear and tensile failure can occur around a wellbore in certain drilling conditions where the mud pressure lies between the reservoir pore pressure and fracture gradient. The fully coupled thermo-poro-mechanical FEM simulation was used to model damage/fracture propagation and microseismic events caused by fluid injection. These studies considered wellbore geometry in small-scale modeling and point-source injection, assuming singularity fluid flux for large-scale simulation. Damage mechanics was applied to capture the effects of crack initiation, microvoid growth, and fracture propagation. The induced microseismic events were modeled in heterogeneous geological media, assuming the Weibull distribution functions for modulus and permeability. The results of this study indicate that fluid injection causes the effective stress to relax in the damage phase and to concentrate at the interface between the damage phase and the intact rock. Furthermore, induced-stress and far-field stress influence damage propagation. Cold water injection causes the tensile stress and affects the initial fracture and fracture propagation, but fracture initiation pressure and far-field stress are critical to create a damage/fracture plane, which is normal to the minimum far-field stress direction following well stimulation. Microseismic events propagate at both well scale and reservoir-scale simulation; the cloud shape of a microseismic event is affected by permeability anisotropy and far-field stress, and deviatoric horizontal far-field stress especially contributes to the localization of the microseismic cloud.