+publisher:"University of Texas – Austin" +contributor:("Wheeler, Mary F")

University of Texas – Austin

1. Mital, Prashant. The enriched Galerkin method for linear elasticity and phase field fracture propagation.

Degree: MSin Engineering, Engineering mechanics, 2015, University of Texas – Austin

► This thesis focuses on the application of the discontinuous Galerkin (DG) and enriched Galerkin (EG) methods to the problems of linear elasticity and phase field… (more)

▼ This thesis focuses on the application of the discontinuous Galerkin (DG) and enriched Galerkin (EG) methods to the problems of linear elasticity and phase field fracture propagation. The use of traditional and popular continuous Galerkin method (CG) for linear elasticity has posed some challenges. For example, nonphysical stress oscillations often occur in CG solutions for linearly elastic, nearly incompressible materials. Furthermore, CG solutions produce discontinuous stresses at the finite element boundaries which need to be post-processed. Based on the success of the DG methods in solving these challenges, we attempt resolution of the same problems with the yet untested EG method. For phase field fracture propagation, the CG method has been ubiquitously used in the literature. Since the phase field displacement solution is essentially discontinuous across the crack, we hypothesize that the discontinuous DG and EG methods could offer some advantages when applied to the fracture problem. We then perform a comparative analysis of CG, DG and EG applied to the phase field equations to determine if this is indeed the case. We begin by applying a family of DG and EG methods, including Nonsymmetric Interior Penalty Galerkin (NIPG), Symmetric Interior Penalty Galerkin (SIPG), and Incomplete Interior Penalty Galerkin (IIPG) to 2D linear elasticity problems. It is shown that the EG methods are simple and robust for dealing with linear elasticity. They are also shown to converge at the same rates as the corresponding DG methods. A detailed comparison of the performance of NIPG, IIPG, and SIPG is also made. We then propose a novel monolithic scheme with an augmented-Lagrangian method for phase field fracture propagation. We apply CG, DG and EG methods to the scheme and establish convergence in space and time through numerical studies. It is shown that the Newton method used for solving the system of nonlinear equations converges faster for DG and EG than it does for CG. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Wick, Thomas (committee member).

Subjects/Keywords: Enriched Galerkin; Phase field; Fracture; Fracture propagation; Linear elasticity; Discontinuous Galerkin

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APA (6^th Edition):

Mital, P. (2015). The enriched Galerkin method for linear elasticity and phase field fracture propagation. (Masters Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/34222

Chicago Manual of Style (16^th Edition):

Mital, Prashant. “The enriched Galerkin method for linear elasticity and phase field fracture propagation.” 2015. Masters Thesis, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/34222.

MLA Handbook (7^th Edition):

Mital, Prashant. “The enriched Galerkin method for linear elasticity and phase field fracture propagation.” 2015. Web. 28 Feb 2021.

Vancouver:

Mital P. The enriched Galerkin method for linear elasticity and phase field fracture propagation. [Internet] [Masters thesis]. University of Texas – Austin; 2015. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/34222.

Council of Science Editors:

Mital P. The enriched Galerkin method for linear elasticity and phase field fracture propagation. [Masters Thesis]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/34222

University of Texas – Austin

2. Shiozawa, Sogo. Designing enhanced geothermal and hydraulic fracturing systems based on multiple stages and proppant.

Degree: MSin Engineering, Petroleum engineering, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/34589

► This report consists of two chapters. In the first chapter, designs of Enhanced Geothermal Systems (EGS) with horizontal wells, multiple stages, and proppant are discussed.… (more)

Subjects/Keywords: Enhanced geothermal and hydrulic; Fracturing systems; EGS; Proppant transport

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APA (6^th Edition):

Shiozawa, S. (2015). Designing enhanced geothermal and hydraulic fracturing systems based on multiple stages and proppant. (Masters Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/34589

Chicago Manual of Style (16^th Edition):

Shiozawa, Sogo. “Designing enhanced geothermal and hydraulic fracturing systems based on multiple stages and proppant.” 2015. Masters Thesis, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/34589.

MLA Handbook (7^th Edition):

Shiozawa, Sogo. “Designing enhanced geothermal and hydraulic fracturing systems based on multiple stages and proppant.” 2015. Web. 28 Feb 2021.

Vancouver:

Shiozawa S. Designing enhanced geothermal and hydraulic fracturing systems based on multiple stages and proppant. [Internet] [Masters thesis]. University of Texas – Austin; 2015. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/34589.

Council of Science Editors:

Shiozawa S. Designing enhanced geothermal and hydraulic fracturing systems based on multiple stages and proppant. [Masters Thesis]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/34589

University of Texas – Austin

3. -1155-8213. Addressing challenges in modeling of coupled flow and poromechanics in deep subsurface reservoirs.

Degree: PhD, Engineering Mechanics, 2018, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/2120

► In coupled flow and poromechanics phenomena representing hydrocarbon production or CO₂ sequestration in deep subsurface non-fractured reservoirs, the spatial domain in which fluid flow occurs… (more)

▼ In coupled flow and poromechanics phenomena representing hydrocarbon production or CO₂ sequestration in deep subsurface non-fractured reservoirs, the spatial domain in which fluid flow occurs is usually much smaller than the spatial domain over which significant deformation occurs. The vertical extent of the poromechanical domain can be two orders of magnitude more than the characteristic thickness of the flow domain (reservoir). The lateral extent of the poromechanical domain should also be allowed to be substantially larger than that of the flow domain to enable the imposition of far-field boundary conditions on the poromechanical domain. The typical approach is to either impose an overburden pressure directly on the reservoir thus treating it as a coupled problem domain or to model flow on a huge domain with zero permeability cells to mimic the no flow boundary condition on the interface of the reservoir and the surrounding rock. The former approach precludes a study of land subsidence or uplift and further does not mimic the true effect of the overburden on stress sensitive reservoirs whereas the latter approach has huge computational costs. The flow domain requires an areal resolution fine enough to be able to capture the underlying nonlinearities in the multiphase flow equations. If the same grid resolution is employed for the poromechanical domain, the simulator would crash for lack of memory and computing resource. With that in mind, it is imperative to establish a framework in which fluid flow is resolved on a finer grid and poromechanical deformation is resolved on a coarse grid. In addition, the geometry of the flow domain necessitates the use of non-nested grids which allows for freedom of choice of the poromechanical grid resolution. Furthermore, to achieve the goal of rendering realistic simulations of subsurface phenomena, we cannot ignore the heterogeneity in flow and poromechanical properties, as well as the lack in accuracy of the poromechanical calculations if the grid for the poromechanics domain is too coarse. This dissertation is a rendition of how we invoke concepts in computational geometry, parallel computing, applied mathematics and convex optimization in designing and implementing algorithms that tackle all the aforementioned challenges. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Landis, Chad (committee member), Huang, Rui (committee member), Balhoff, Matthew (committee member).

Subjects/Keywords: Fixed-stress split iterative scheme; Overlapping nonmatching hexahedral grids; Upscaling and downscaling; Singular value decompositions; Surface intersections; Delaunay triangulations; Mandel’s problem; Biot system; Heterogeneous poroelastic medium; Nested two-grid approach; Contraction mapping; Anisotropic poroelastic medium; Computational homogenization; Hanging nodes; Augmented Lagrangian

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APA (6^th Edition):

-1155-8213. (2018). Addressing challenges in modeling of coupled flow and poromechanics in deep subsurface reservoirs. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/2120

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Chicago Manual of Style (16^th Edition):

-1155-8213. “Addressing challenges in modeling of coupled flow and poromechanics in deep subsurface reservoirs.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://dx.doi.org/10.26153/tsw/2120.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-1155-8213. “Addressing challenges in modeling of coupled flow and poromechanics in deep subsurface reservoirs.” 2018. Web. 28 Feb 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-1155-8213. Addressing challenges in modeling of coupled flow and poromechanics in deep subsurface reservoirs. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Feb 28]. Available from: http://dx.doi.org/10.26153/tsw/2120.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-1155-8213. Addressing challenges in modeling of coupled flow and poromechanics in deep subsurface reservoirs. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://dx.doi.org/10.26153/tsw/2120

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

University of Texas – Austin

4. Li, Zhitao. Modeling and simulation of polymer flooding including the effects of fracturing.

Degree: PhD, Petroleum engineering, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/33513

► Chemical enhanced oil recovery (EOR) technology has attracted increasing interest in recent years with declining oil production from conventional oil reserves. Water flooding of heterogeneous… (more)

▼ Chemical enhanced oil recovery (EOR) technology has attracted increasing interest in recent years with declining oil production from conventional oil reserves. Water flooding of heterogeneous reservoirs with viscous oil leaves considerable amount of remaining oil even at high producing water cuts. Polymer flooding is a mature EOR technology for augmenting recovery of moderately viscous oil. Water soluble polymers are used to reduce water mobility and improve sweep efficiency. For very viscous oil, polymer flooding is a potential non-thermal approach for minimizing viscous fingering and improving both displacement sweep efficiency and volumetric sweep efficiency. Polymer manufacturing techniques has been significantly advanced since 1980’s, which provides improved polymer quality and keeps polymer price relatively low. Compared with unconventional oil recovery techniques such as hydraulic fracturing, well planned and optimized polymer flooding can be profitable even at pessimistic oil price. It is thus crucial to have a reservoir simulator that is able to accurately model polymer properties and simulate polymer flooding in complex reservoir systems. Polymer rheological behavior is dependent on polymer molecular structure, concentration, Darcy velocity, brine salinity, hardness, permeability, porosity, etc. We improved polymer rheology modeling for heterogeneous reservoirs where permeability varies for orders of magnitude. For an injection well, a large portion of pressure drop is lost near wellbore where apparent polymer viscosity as a function of Darcy velocity varies drastically. Conventional analytical well models fail to capture the non-Newtonian effect of apparent polymer viscosity and make injectivity predictions widely deviated from true solutions especially for coarse-grid simulations. We developed a semi-analytical polymer injectivity model and implemented it into UTCHEM. This model is able to handle both shear-thinning and shear-thickening polymer rheology. It successfully avoids the grid effect and matches fine-grid simulation results and analytical solutions. Another challenge is to model polymer injectivity under fracturing conditions. To maintain an economic polymer injection rate, wellbore pressure may exceed the fracture initiation pressure. We developed a framework to couple a fracture model with UTCHEM. This coupled simulator is able to model fracture propagation during polymer injection. Finally several simulation studies were conducted to show the impacts of polymer rheological behavior, loss of polymer into aquifer, near wellbore effect and fracture propagation. Advisors/Committee Members: Delshad, Mojdeh (advisor), Wheeler, Mary F. (committee member), Pope, Gary A. (committee member), Sepehrnoori, Kamy (committee member), Huh, Chun (committee member).

Subjects/Keywords: Chemical EOR; Polymer flooding; UTCHEM; Reservoir simulation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Li, Z. (2015). Modeling and simulation of polymer flooding including the effects of fracturing. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/33513

Chicago Manual of Style (16^th Edition):

Li, Zhitao. “Modeling and simulation of polymer flooding including the effects of fracturing.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/33513.

MLA Handbook (7^th Edition):

Li, Zhitao. “Modeling and simulation of polymer flooding including the effects of fracturing.” 2015. Web. 28 Feb 2021.

Vancouver:

Li Z. Modeling and simulation of polymer flooding including the effects of fracturing. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/33513.

Council of Science Editors:

Li Z. Modeling and simulation of polymer flooding including the effects of fracturing. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/33513

University of Texas – Austin

5. -8477-1384. A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation.

Degree: PhD, Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/32535

► This dissertations focuses on solving the advection problem with the motivation of simulating transport in porous media. A quadrature based Eulerian-Lagrangian scheme is developed to… (more)

▼ This dissertations focuses on solving the advection problem with the motivation of simulating transport in porous media. A quadrature based Eulerian-Lagrangian scheme is developed to solve the nonlinear advection problem in multiple spatial dimensions. The schemes combines the ideas of Lagrangian traceline methods with high order WENO reconstructions to compute the mass that flows into a given cell over a time step. These schemes are important since they have a relaxed CFL constraint, and can be run in parallel. In this thesis we provide two improvements to Eulerian-Lagrangian schemes. To do this an integration based WENO (IWENO) interpolation technique is derived by reconstructing the primitive function and differentiating. This technique gives a high order reconstruction of the mass at an arbitrary point. This WENO scheme is used to solve the linear advection problem. A scheme is derived by backwards tracing of quadrature points located on mesh elements. The mass at these tracepoints is used to compute the mass in the trace region, without resolving its boundary. This process defines a high order quadrature Eulerian-Lagrangian WENO (QEL-WENO) scheme that solves the multi-dimensional problem without the need for a spatial splitting technique. The second improvement is for solving the nonlinear advection problem using an approximate velocity field. The velocity field is used to transport mass in the manner of a standard Eulerian-Lagrangian scheme. Then a flux correction is applied to compute the flow across the tracelines. The contribution is to use a variation of the IWENO technique to reduce the stencil size of this computation. Numerical results are presented demonstrating the capabilities of the scheme. An application to two-phase flow in porous media is provided. Advisors/Committee Members: Arbogast, Todd James, 1957- (advisor), Balhoff, Matthew T (committee member), Chen, Thomas (committee member), Gonzalez, Oscar (committee member), Vasseur, Alexis F (committee member), Wheeler, Mary F (committee member).

Subjects/Keywords: Hyperbolic transport; Semi-Lagrangian; Finite volume; Characteristics; Traceline; WENO reconstruction; Compact stencil; Two-phase

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APA (6^th Edition):

-8477-1384. (2015). A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32535

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-8477-1384. “A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/32535.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-8477-1384. “A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation.” 2015. Web. 28 Feb 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-8477-1384. A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/32535.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-8477-1384. A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32535

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

University of Texas – Austin

6. Elahi Naraghi, Morteza. Modeling complex spatial patterns in reservoir models using high order spectra.

Degree: PhD, Petroleum Engineering, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/47139

► One of the most challenging issues in reservoir modeling The important goal of reservoir modeling is to generate a map of geologic attributes that can… (more)

▼ One of the most challenging issues in reservoir modeling The important goal of reservoir modeling is to generate a map of geologic attributes that can yield predictions of hydrocarbon production. Mostly, the primary source of information for creating such a map is borehole measurements, which are only available at sparse locations. Reservoir modeling constrained to the available data along the wells allows us to generate multiple realizations for the whole reservoir. In order for these realizations to yield robust estimates of the uncertainty in reservoir performance prediction, it is imperative that they exhibit connectivity characteristics that are typical for the geological system being modeled. Different algorithms have been developed to stochastically simulate reservoir properties using sparse measured data. In these methods, the spatial variability represented by the underlying joint distribution is in the form of the spatial covariance. The major drawback of traditional variogram-based modeling is that they are not able to reproduce complex spatial patterns. Multiple-point statistical algorithms, however, can reconstruct such curvilinear features. In this study, we study the link between the multiple point spatial pattern connectivity and the Fourier spectrum. This will allow us to infer statistical functions describing reservoir connectivity more efficiently. This can be further sub-divided into two approaches based on the availability of data and information. We also propose methods for selecting an optimum training image when there is ambiguity associated with it, and integrating non-stationary secondary information into the simulation framework. Then, we develop a simulation algorithm in Fourier domain. We will show that the amplitude of Fourier transform can be calculated directly from power spectrum (Fourier transform of covariance function). The phase identification can be achieved by either solving an optimization problem to match the available conditioning data or from higher order spectra such as bispectrum or trispectrum. Finally, we present a new framework for integrating dynamic data and performing history matching. We show how polyspectra affect the production behavior and therefore, we can use the production measurements at well location to identify amplitude and phase within the proposed framework. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Srinivasan, Sanjay (advisor), Sepehrnoori, Kamy (committee member), Sen, Mrinal K (committee member), Spikes, Kyle T (committee member), Foster, John T (committee member).

Subjects/Keywords: Reservoir characterization; Geostatistics; Reservoir modeling; Complex spatial patterns; High order spectra; Multiple-point statistical algorithms; Multiple-point spatial pattern; Fourier spectrum; Reservoir connectivity; Simulation algorithm; History matching; Polyspectra

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Elahi Naraghi, M. (2016). Modeling complex spatial patterns in reservoir models using high order spectra. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/47139

Chicago Manual of Style (16^th Edition):

Elahi Naraghi, Morteza. “Modeling complex spatial patterns in reservoir models using high order spectra.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/47139.

MLA Handbook (7^th Edition):

Elahi Naraghi, Morteza. “Modeling complex spatial patterns in reservoir models using high order spectra.” 2016. Web. 28 Feb 2021.

Vancouver:

Elahi Naraghi M. Modeling complex spatial patterns in reservoir models using high order spectra. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/47139.

Council of Science Editors:

Elahi Naraghi M. Modeling complex spatial patterns in reservoir models using high order spectra. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/47139

University of Texas – Austin

7. Mohammad Reza Beygi, Mohammad Reza. Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes.

Degree: PhD, Petroleum engineering, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/45556

► Enhanced oil recovery (EOR) techniques have the potential to improve hydrocarbon recovery and project economics substantially. Characterizing fluid displacement and the relevant multiphase flow properties… (more)

▼ Enhanced oil recovery (EOR) techniques have the potential to improve hydrocarbon recovery and project economics substantially. Characterizing fluid displacement and the relevant multiphase flow properties are essential to modeling EOR processes to reliably forecast the performance and economics. The spatial-temporal distribution of fluids spans a broad spectrum of composition and saturation spaces. In addition, a fundamental understanding of characteristic parameters of interphase mass-transfer in various EOR applications is crucial to capture and model fluid displacement. Relative permeability is a critical characteristic petrophysical property for modeling fluid displacement in porous media. Also, hysteresis phenomena govern physics of fluid flow in many subsurface applications such as multicyclic EOR processes, geological CO2 sequestration, and natural gas storage. Capillary trapping is the essence of hysteresis to trap fluids. In this research, we developed a high-fidelity computational tool for integrating compositional three-phase relative permeability and hysteresis to assist in accurate modeling of multicycle and compositional EOR methods. This viable tool can be implemented into general-purpose reservoir simulators to model field-scale projects. It consists of an integrated compositionally-consistent three-phase relative permeability and three-phase hysteresis models. The developed three-phase relative permeability model is valid on entire saturation and composition spaces, is simple with one free parameter for each phase, and is versatile for all phases and wettability states. The general model is saturation-path dependent and adopts a linear saturation-weighted interpolation scheme for calculation of relative permeability parameters. For the compositional relative permeability modeling, we developed a general framework applicable to hydrocarbon and non-hydrocarbon phases. The developed framework provides a pragmatic approach for adding the direct impact of composition, pressure, and temperature and is independent of the conventional phase-labeling method. The proposed framework unifies thermodynamics, petrophysics, and geochemistry to enhanced relative permeability modeling. Relative permeability parameters are calculated based on a mapping scheme of current-state bulk and interphase Gibbs free energy onto corresponding initial-state values. We applied the developed framework to modeling lowsalinity waterflood and complex fluid displacement of near-critical fluids. The three-phase hysteresis model provides a general and straightforward approach for calculation of capillary trapping in multicyclic processes. The developed hysteresis model provides a set of cycle-dependent relative permeability curves and applies to any three-phase relative permeability model by incorporating the free-saturation concept. We implemented the developed toolbox into two in-house compositional reservoir simulators (i.e., IPARS and UT-DOECO2). Several synthetic field cases are discussed to validate the implemented models… Advisors/Committee Members: Delshad, Mojdeh (advisor), Wheeler, Mary F. (Mary Fanett) (advisor), Pope, Gary A (committee member), Sepehrnoori, Kamy (committee member), Mohanty, Kishory K. (committee member), Arbogast, Todd (committee member).

Subjects/Keywords: Three-phase; Relative permeability; Hysteresis; Aqueous; Near-critical fluid; Low-tension gas flood; Gibbs free energy; Foam; EOR; Electrolyte

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APA (6^th Edition):

Mohammad Reza Beygi, M. R. (2016). Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/45556

Chicago Manual of Style (16^th Edition):

Mohammad Reza Beygi, Mohammad Reza. “Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/45556.

MLA Handbook (7^th Edition):

Mohammad Reza Beygi, Mohammad Reza. “Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes.” 2016. Web. 28 Feb 2021.

Vancouver:

Mohammad Reza Beygi MR. Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/45556.

Council of Science Editors:

Mohammad Reza Beygi MR. Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/45556

8. -5603-2533. Efficient algorithms for flow models coupled with geomechanics for porous media applications.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/46503

► 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,… (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… Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Arbogast, Todd (committee member), Demkowicz, Leszek F. (committee member), Delshad, Mojdeh (committee member), Dhillon, Inderjit (committee member), Kumar, Kundan (committee member).

Subjects/Keywords: Poroelasticity; Biot system; Fixed-stress split iterative coupling; Undrained split iterative coupling; Explicit coupling; Single rate scheme; Multirate scheme; Banach fixed-point contraction; Fractured poroelastic media; A priori error estiamtes; Global inexact Newton methods

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APA (6^th Edition):

-5603-2533. (2016). Efficient algorithms for flow models coupled with geomechanics for porous media applications. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/46503

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Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-5603-2533. “Efficient algorithms for flow models coupled with geomechanics for porous media applications.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/46503.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-5603-2533. “Efficient algorithms for flow models coupled with geomechanics for porous media applications.” 2016. Web. 28 Feb 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-5603-2533. Efficient algorithms for flow models coupled with geomechanics for porous media applications. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/46503.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-5603-2533. Efficient algorithms for flow models coupled with geomechanics for porous media applications. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/46503

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

University of Texas – Austin

9. -3958-8871. A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2018, University of Texas – Austin

URL: http://hdl.handle.net/2152/68968

► Multiscale modeling of subsurface flow and transport is a major area of interest in several applications including petroleum recovery evaluations, nuclear waste disposal systems, CO₂… (more)

▼ Multiscale modeling of subsurface flow and transport is a major area of interest in several applications including petroleum recovery evaluations, nuclear waste disposal systems, CO₂ sequestration, groundwater remediation and contaminant plume migration in heterogeneous porous media. During these processes the direct numerical simulation is computationally intensive due to detailed fine scale characterization of the subsurface formations. The main objective of this work is to develop an efficient multiscale framework to reduce usage of fine scale properties associated with advection and diffusion/dispersion, while maintaining accuracy of quantities of interest including mass balance, pressure, velocity, concentration. Another purpose of this work is to investigate the adaptivity criteria in transport and flow problems numerically and/or theoretically based on error estimates. We propose a new adaptive numerical homogenization method using numerical homogenization and Enhanced Velocity Mixed Finite Element Method (EVMFEM). We focus on upscaling the permeability and porosity fields for slightly (nonlinear) compressible single phase Darcy flow and transport problems in heterogeneous porous media. The fine grids are used in the transient regions where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [85]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this dissertation, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium. We have also derived a priori error estimate for a parabolic problem using Backward Euler and Crank-Nicolson method in time and EVMFEM in space. Next, we have established a posteriori error estimate in EVMFEM setting for incompressible flow problems. We first propose the flux reconstruction for error estimates and prove the upper and lower bound theorems. Next, the explicit residual-based estimates and the recovery-based error estimates with the post-processed pressure are derived theoretically. Numerical experiments are conducted to show that the proposed estimators are effective indicators of local error for incompressible flow problems. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Arbogast, Todd (committee member), Balhoff, Matthew (committee member), Tsai, Yen-Hsi Richard (committee member), Wildey, Tim (committee member).

Subjects/Keywords: Enhanced velocity; Numerical homogenization; Adaptive mesh refinement; Multiscale methods; Error estimates; A posteriori error; A priori error; SPE10 dataset

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APA (6^th Edition):

-3958-8871. (2018). A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68968

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Chicago Manual of Style (16^th Edition):

-3958-8871. “A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/68968.

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Author name may be incomplete

MLA Handbook (7^th Edition):

-3958-8871. “A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme.” 2018. Web. 28 Feb 2021.

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Author name may be incomplete

Vancouver:

-3958-8871. A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/68968.

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Author name may be incomplete

Council of Science Editors:

-3958-8871. A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/68968

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

University of Texas – Austin

10. -5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.

Degree: PhD, Aerospace Engineering, 2019, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/5474

► The hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking,… (more)

▼ The hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking, HDG methods combines the advantages of both discontinuous Galerkin (DG) methods and hybridized methods. In particular, it enjoys the benefits of equal order spaces, upwinding and ability to handle large gradients of DG methods as well as the smaller globally coupled linear system, adaptivity, and multinumeric capabilities of hybridized methods. However, the main bottleneck in HDG methods, limiting its use to small to moderate sized problems, is the lack of scalable linear solvers. In this thesis we develop fast and scalable solvers for HDG methods consisting of domain decomposition, multigrid and multilevel solvers/preconditioners with an ultimate focus on simulating large scale problems in fluid dynamics and magnetohydrodynamics (MHD). First, we propose a domain decomposition based solver namely iterative HDG for partial differential equations (PDEs). It is a fixed point iterative scheme, with each iteration consisting only of element-by-element and face-by-face embarrassingly parallel solves. Using energy analysis we prove the convergence of the schemes for scalar and system of hyperbolic PDEs and verify the results numerically. We then propose a novel geometric multigrid approach for HDG methods based on fine scale Dirichlet-to-Neumann maps. The algorithm combines the robustness of algebraic multigrid methods due to operator dependent intergrid transfer operators and at the same time has fixed coarse grid construction costs due to its geometric nature. For diffusion dominated PDEs such as the Poisson and the Stokes equations the algorithm gives almost perfect hp – scalability. Next, we propose a multilevel algorithm by combining the concepts of nested dissection, a fill-in reducing ordering strategy, variational structure and high-order properties of HDG, and domain decomposition. Thanks to its root in direct solver strategy the performance of the solver is almost independent of the nature of the PDEs and mostly depends on the smoothness of the solution. We demonstrate this numerically with several prototypical PDEs. Finally, we propose a block preconditioning strategy for HDG applied to incompressible visco-resistive MHD. We use a least squares commutator approximation for the inverse of the Schur complement and algebraic multigrid or the multilevel preconditioner for the approximate inverse of the nodal block. With several 2D and 3D transient examples we demonstrate the robustness and parallel scalability of the block preconditioner Advisors/Committee Members: Bui-Thanh, Tan (advisor), Demkowicz, Leszek F (committee member), Ghattas, Omar (committee member), Raja, Laxminarayan L (committee member), Shadid, John N (committee member), Waelbroeck, Francois L (committee member), Wheeler, Mary F (committee member).

Subjects/Keywords: Hybridized discontinuous Galerkin; Fast solvers; Multigrid; Multilevel; MHD; Domain decomposition

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APA (6^th Edition):

-5494-1880. (2019). Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/5474

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Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-5494-1880. “Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://dx.doi.org/10.26153/tsw/5474.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-5494-1880. “Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics.” 2019. Web. 28 Feb 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Feb 28]. Available from: http://dx.doi.org/10.26153/tsw/5474.

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Author name may be incomplete

Council of Science Editors:

-5494-1880. Fast and scalable solvers for high-order hybridized discontinuous Galerkin methods with applications to fluid dynamics and magnetohydrodynamics. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/5474

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University of Texas – Austin

11. -5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/68171

► Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work,… (more)

▼ Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work, we investigate the behavior and numerical treatment of multiphase flow in porous media. To be more specific, we take the sequestration of CO₂ in geological media as an example. Mathematical modeling and numerical study of carbon sequestration helps to predict both short and long-term behavior of CO₂ storage in geological media, which can be a benefit in many ways. This work aims at developing accurate and efficient numerical treatment for problems in porous media on non-rectangular geometries. Numerical treatment of Darcy flow and transport have been developed for many years on rectangular and simplical meshes. However, extra effort is required to extend them to general non-rectangular meshes. In this dissertation work, for flow simulation, we develop new H(div)- conforming mixed finite elements (AT and AT [superscript red] ) which are accurate on cuboidal hexahedra. We also develop the new direct serendipity finite element (DS [subscript r] ), which is H¹ -conforming and accurate on quadrilaterals and a special family of hexahedra called truncated cubes. The use of the direct serendipity finite element reduces the number of degrees of freedom significantly and therefore accelerates numerical simulations. For transport, we use the newly developed direct serendipity elements in an enriched Galerkin method (EG), which is locally conservative. The entropy viscosity stabilization is applied to eliminate spurious oscillations. We test the EG-DS [subscript r] method on problems with diffusion, transport, and coupled flow and transport. Finally, we study two-phase flow in heterogeneous porous media with capillary pressure. We work on a new formulation of the problem and force the continuity of the capillary flux with a modification to conquer the degeneracy. The numerical simulation of two-phase flow is conducted on non-rectangular grids and uses the new elements. Advisors/Committee Members: Arbogast, Todd James, 1957- (advisor), Wheeler, Mary F (committee member), Ghattas, Omar (committee member), Demkowicz, Leszek F (committee member), Hesse, Marc A (committee member).

Subjects/Keywords: Multiphase flow; Porous media; Mixed finite element; H(div)-approximation; Arbogast-Tao element; Arbogast-Correa element; Direct serendipity element; Serendipity element; Enriched Galerkin method; Entropy viscosity stabilization; Capillary flux reconstruction; Heterogeneous capillary pressure; Two-phase flow

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APA (6^th Edition):

-5063-5889. (2017). Numerical analysis of multiphase flows in porous media on non-rectangular geometry. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68171

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-5063-5889. “Numerical analysis of multiphase flows in porous media on non-rectangular geometry.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/68171.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-5063-5889. “Numerical analysis of multiphase flows in porous media on non-rectangular geometry.” 2017. Web. 28 Feb 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/68171.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/68171

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

12. Thomas, Sunil George. On some problems in the simulation of flow and transport through porous media.

Degree: PhD, Computational and Applied Mathematics, 2009, University of Texas – Austin

URL: http://hdl.handle.net/2152/6575

► The dynamic solution of multiphase flow through porous media is of special interest to several fields of science and engineering, such as petroleum, geology and… (more)

▼ The dynamic solution of multiphase flow through porous media is of special interest to several fields of science and engineering, such as petroleum, geology and geophysics, bio-medical, civil and environmental, chemical engineering and many other disciplines. A natural application is the modeling of the flow of two immiscible fluids (phases) in a reservoir. Others, that are broadly based and considered in this work include the hydrodynamic dispersion (as in reactive transport) of a solute or tracer chemical through a fluid phase. Reservoir properties like permeability and porosity greatly influence the flow of these phases. Often, these vary across several orders of magnitude and can be discontinuous functions. Furthermore, they are generally not known to a desired level of accuracy or detail and special inverse problems need to be solved in order to obtain their estimates. Based on the physics dominating a given sub-region of the porous medium, numerical solutions to such flow problems may require different discretization schemes or different governing equations in adjacent regions. The need to couple solutions to such schemes gives rise to challenging domain decomposition problems. Finally, on an application level, present day environment concerns have resulted in a widespread increase in CO₂capture and storage experiments across the globe. This presents a huge modeling challenge for the future. This research work is divided into sections that aim to study various inter-connected problems that are of significance in sub-surface porous media applications. The first section studies an application of mortar (as well as nonmortar, i.e., enhanced velocity) mixed finite element methods (MMFEM and EV-MFEM) to problems in porous media flow. The mortar spaces are first used to develop a multiscale approach for parabolic problems in porous media applications. The implementation of the mortar mixed method is presented for two-phase immiscible flow and some a priori error estimates are then derived for the case of slightly compressible single-phase Darcy flow. Following this, the problem of modeling flow coupled to reactive transport is studied. Applications of such problems include modeling bio-remediation of oil spills and other subsurface hazardous wastes, angiogenesis in the transition of tumors from a dormant to a malignant state, contaminant transport in groundwater flow and acid injection around well bores to increase the permeability of the surrounding rock. Several numerical results are presented that demonstrate the efficiency of the method when compared to traditional approaches. The section following this examines (non-mortar) enhanced velocity finite element methods for solving multiphase flow coupled to species transport on non-matching multiblock grids. The results from this section indicate that this is the recommended method of choice for such problems. Next, a mortar finite element method is formulated and implemented that extends the scope of the classical mortar mixed… Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Porous media; Multiphase flow; Flow simulation; Flow models; Mortar finite element method; Darcy flow; Parallel stochastic approximation method; Reservoir simulation

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APA (6^th Edition):

Thomas, S. G. (2009). On some problems in the simulation of flow and transport through porous media. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/6575

Chicago Manual of Style (16^th Edition):

Thomas, Sunil George. “On some problems in the simulation of flow and transport through porous media.” 2009. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/6575.

MLA Handbook (7^th Edition):

Thomas, Sunil George. “On some problems in the simulation of flow and transport through porous media.” 2009. Web. 28 Feb 2021.

Vancouver:

Thomas SG. On some problems in the simulation of flow and transport through porous media. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2009. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/6575.

Council of Science Editors:

Thomas SG. On some problems in the simulation of flow and transport through porous media. [Doctoral Dissertation]. University of Texas – Austin; 2009. Available from: http://hdl.handle.net/2152/6575

13. Wang, Bin, 1984-. Parallel simulation of coupled flow and geomechanics in porous media.

Degree: PhD, Engineering Mechanics, 2014, University of Texas – Austin

URL: http://hdl.handle.net/2152/28061

► In this research we consider developing a reservoir simulator capable of simulating complex coupled poromechanical processes on massively parallel computers. A variety of problems arising… (more)

▼ In this research we consider developing a reservoir simulator capable of simulating complex coupled poromechanical processes on massively parallel computers. A variety of problems arising from petroleum and environmental engineering inherently necessitate the understanding of interactions between fluid flow and solid mechanics. Examples in petroleum engineering include reservoir compaction, wellbore collapse, sand production, and hydraulic fracturing. In environmental engineering, surface subsidence, carbon sequestration, and waste disposal are also coupled poromechanical processes. These economically and environmentally important problems motivate the active pursuit of robust, efficient, and accurate simulation tools for coupled poromechanical problems. Three coupling approaches are currently employed in the reservoir simulation community to solve the poromechanics system, namely, the fully implicit coupling (FIM), the explicit coupling, and the iterative coupling. The choice of the coupling scheme significantly affects the efficiency of the simulator and the accuracy of the solution. We adopt the fixed-stress iterative coupling scheme to solve the coupled system due to its advantages over the other two. Unlike the explicit coupling, the fixed-stress split has been theoretically proven to converge to the FIM for linear poroelasticity model. In addition, it is more efficient and easier to implement than the FIM. Our computational results indicate that this approach is also valid for multiphase flow. We discretize the quasi-static linear elasticity model for geomechanics in space using the continuous Galerkin (CG) finite element method (FEM) on general hexahedral grids. Fluid flow models are discretized by locally mass conservative schemes, specifically, the mixed finite element method (MFE) for the equation of state compositional flow on Cartesian grids and the multipoint flux mixed finite element method (MFMFE) for the single phase and two-phase flows on general hexahedral grids. While both the MFE and the MFMFE generate cell-centered stencils for pressure, the MFMFE has advantages in handling full tensor permeabilities and general geometry and boundary conditions. The MFMFE also obtains accurate fluxes at cell interfaces. These characteristics enable the simulation of more practical problems. For many reservoir simulation applications, for instance, the carbon sequestration simulation, we need to account for thermal effects on the compositional flow phase behavior and the solid structure stress evolution. We explicitly couple the poromechanics equations to a simplified energy conservation equation. A time-split scheme is used to solve heat convection and conduction successively. For the convection equation, a higher order Godunov method is employed to capture the sharp temperature front; for the conduction equation, the MFE is utilized. Simulations of coupled poromechanical or thermoporomechanical processes in field scales with high resolution usually require parallel computing capabilities. The flow models, the… Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Iterative coupling; Fixed-stress split; Linear elasticity; Thermoporoelasticity; Compositional flow; Stress-dependent permeability; Multipoint flux; General hexahedral grid; Parallel simulation

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APA (6^th Edition):

Wang, Bin, 1. (2014). Parallel simulation of coupled flow and geomechanics in porous media. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/28061

Chicago Manual of Style (16^th Edition):

Wang, Bin, 1984-. “Parallel simulation of coupled flow and geomechanics in porous media.” 2014. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/28061.

MLA Handbook (7^th Edition):

Wang, Bin, 1984-. “Parallel simulation of coupled flow and geomechanics in porous media.” 2014. Web. 28 Feb 2021.

Vancouver:

Wang, Bin 1. Parallel simulation of coupled flow and geomechanics in porous media. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2014. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/28061.

Council of Science Editors:

Wang, Bin 1. Parallel simulation of coupled flow and geomechanics in porous media. [Doctoral Dissertation]. University of Texas – Austin; 2014. Available from: http://hdl.handle.net/2152/28061

14. Phillips, Phillip Joseph. Finite element methods in linear poroelasticity: theoretical and computational results.

Degree: PhD, Computational and Applied Mathematics, 2005, University of Texas – Austin

URL: http://hdl.handle.net/2152/2365

► Linear Poroelasticity refers to fluid flow within a deformable porous medium under the assumption of relatively small deformations. Some of the areas that are being… (more)

▼ Linear Poroelasticity refers to fluid flow within a deformable porous medium under the assumption of relatively small deformations. Some of the areas that are being modeled with the equations of linear poroelasticity include reservoir engineering, soil mechanics and, more recently, biomedical engineering. The purpose of this dissertation is to present original results for the development, analysis and application of numerical finite element algorithms in the field of linear poroelasticity. A fully coupled finite element method involving continuous elements for displacements and a mixed space for flow is developed (CG/Mixed). Existence, uniqueness and optimality results are provided. The norm measuring the pressure error, however, depends on the value of the constrained specific storage coefficient. For degenerate values, this leads to a slightly weaker optimality result. For the not untypical case of a null constrained specific storage coef- ficient, the solution produced by the CG/Mixed scheme sometimes produces non-physical pressure oscillations, a phenomenon referred to as locking. One potential remedy is to eliminate the continuity requirement for the elements approximating displacements. Therefore, a family of schemes which couples discontinuous elements for displacements and a mixed space for flow is introduced (DG/Mixed). Existence and uniqueness are established, optimal a priori error estimates are provided, and some success in the removal of locking is shown. Direct verification of several benchmark analytical solutions shows that solutions in linear poroelasticity can lack regularity. This sometimes manifests in pressure boundary layers which might degrade the rate of convergence of numerical solutions. The situation can often be ameliorated with the development of adaptive grid refinement strategies. This motivates a posteriori estimates in terms of computable residual quantities. Interestingly, it is also shown that the CG/Mixed method can be combined with adaptive grid refinement as an alternative means to eliminate locking. The produced algorithms are then applied to some interesting application areas. In one instance, they are used to analyze the deformation and pressure dynamics in a cantilever bracket. Additionally, a variety of miscellaneous problems ranging from subsidence and well placement to scuba suit design highlight intriguing applications. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Elasticity; Fluid dynamics

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APA (6^th Edition):

Phillips, P. J. (2005). Finite element methods in linear poroelasticity: theoretical and computational results. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/2365

Chicago Manual of Style (16^th Edition):

Phillips, Phillip Joseph. “Finite element methods in linear poroelasticity: theoretical and computational results.” 2005. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/2365.

MLA Handbook (7^th Edition):

Phillips, Phillip Joseph. “Finite element methods in linear poroelasticity: theoretical and computational results.” 2005. Web. 28 Feb 2021.

Vancouver:

Phillips PJ. Finite element methods in linear poroelasticity: theoretical and computational results. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2005. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/2365.

Council of Science Editors:

Phillips PJ. Finite element methods in linear poroelasticity: theoretical and computational results. [Doctoral Dissertation]. University of Texas – Austin; 2005. Available from: http://hdl.handle.net/2152/2365

15. Singh, Gurpreet, 1984-. Coupled flow and geomechanics modeling for fractured poroelastic reservoirs.

Degree: PhD, Petroleum Engineering, 2014, University of Texas – Austin

URL: http://hdl.handle.net/2152/28473

► Tight gas and shale oil play an important role in energy security and in meeting an increasing energy demand. Hydraulic fracturing is a widely used… (more)

▼ Tight gas and shale oil play an important role in energy security and in meeting an increasing energy demand. Hydraulic fracturing is a widely used technology for recovering these resources. The design and evaluation of hydraulic fracture operation is critical for efficient production from tight gas and shale plays. The efficiency of fracturing jobs depends on the interaction between hydraulic (induced) and naturally occurring discrete fractures. In this work, a coupled reservoir-fracture flow model is described which accounts for varying reservoir geometries and complexities including non-planar fractures. Different flow models such as Darcy flow and Reynold's lubrication equation for fractures and reservoir, respectively are utilized to capture flow physics accurately. Furthermore, the geomechanics effects have been included by considering a multiphase Biot's model. An accurate modeling of solid deformations necessitates a better estimation of fluid pressure inside the fracture. The fractures and reservoir are modeled explicitly allowing accurate representation of contrasting physical descriptions associated with each of the two. The approach presented here is in contrast with existing averaging approaches such as dual and discrete-dual porosity models where the effects of fractures are averaged out. A fracture connected to an injection well shows significant width variations as compared to natural fractures where these changes are negligible. The capillary pressure contrast between the fracture and the reservoir is accounted for by utilizing different capillary pressure curves for the two features. Additionally, a quantitative assessment of hydraulic fracturing jobs relies upon accurate predictions of fracture growth during slick water injection for single and multistage fracturing scenarios. It is also important to consistently model the underlying physical processes from hydraulic fracturing to long-term production. A recently introduced thermodynamically consistent phase-field approach for pressurized fractures in porous medium is utilized which captures several characteristic features of crack propagation such as joining, branching and non-planar propagation in heterogeneous porous media. The phase-field approach captures both the fracture-width evolution and the fracture-length propagation. In this work, the phase-field fracture propagation model is briefly discussed followed by a technique for coupling this to a fractured poroelastic reservoir simulator. We also present a general compositional formulation using multipoint flux mixed finite element (MFMFE) method on general hexahedral grids with a future prospect of treating energized fractures. The mixed finite element framework allows for local mass conservation, accurate flux approximation and a more general treatment of boundary conditions. The multipoint flux inherent in MFMFE scheme allows the usage of a full permeability tensor. An accurate treatment of diffusive/dispersive fluxes owing to additional velocity degrees of freedom is also presented. The… Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Multi-point flux; Mixed finite element; Compositional flow; Gas-flooding; Full tensor permeability; Locally mass conservative; Accurate fluxes; Poroelastic; Geomechanics; Non-planar fractures; Hydraulic fracturing; Iterative coupling

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APA (6^th Edition):

Singh, Gurpreet, 1. (2014). Coupled flow and geomechanics modeling for fractured poroelastic reservoirs. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/28473

Chicago Manual of Style (16^th Edition):

Singh, Gurpreet, 1984-. “Coupled flow and geomechanics modeling for fractured poroelastic reservoirs.” 2014. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/28473.

MLA Handbook (7^th Edition):

Singh, Gurpreet, 1984-. “Coupled flow and geomechanics modeling for fractured poroelastic reservoirs.” 2014. Web. 28 Feb 2021.

Vancouver:

Singh, Gurpreet 1. Coupled flow and geomechanics modeling for fractured poroelastic reservoirs. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2014. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/28473.

Council of Science Editors:

Singh, Gurpreet 1. Coupled flow and geomechanics modeling for fractured poroelastic reservoirs. [Doctoral Dissertation]. University of Texas – Austin; 2014. Available from: http://hdl.handle.net/2152/28473

16. Al-Hinai, Omar A. Mimetic finite differences for porous media applications.

Degree: PhD, Computational and Applied Mathematics, 2014, University of Texas – Austin

URL: http://hdl.handle.net/2152/25032

► We connect the Mimetic Finite Difference method (MFD) with the finite-volume two-point flux scheme (TPFA) for Voronoi meshes. The main effect is reducing the saddle-point… (more)

Subjects/Keywords: Mimetic Finite Difference; Mixed finite elements; Finite volume method; Two-point flux approximations; Monotonicity; Elliptic PDE; Reservoir simulation; Two-phase flow; Voronoi diagrams; PEBI grids; Fractures; Hydraulic fractures

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APA (6^th Edition):

Al-Hinai, O. A. (2014). Mimetic finite differences for porous media applications. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/25032

Chicago Manual of Style (16^th Edition):

Al-Hinai, Omar A. “Mimetic finite differences for porous media applications.” 2014. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/25032.

MLA Handbook (7^th Edition):

Al-Hinai, Omar A. “Mimetic finite differences for porous media applications.” 2014. Web. 28 Feb 2021.

Vancouver:

Al-Hinai OA. Mimetic finite differences for porous media applications. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2014. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/25032.

Council of Science Editors:

Al-Hinai OA. Mimetic finite differences for porous media applications. [Doctoral Dissertation]. University of Texas – Austin; 2014. Available from: http://hdl.handle.net/2152/25032

17. Kong, Xianhui. Petrophysical modeling and simulation study of geological CO₂ sequestration.

Degree: PhD, Petroleum Engineering, 2014, University of Texas – Austin

URL: http://hdl.handle.net/2152/24803

► Global warming and greenhouse gas (GHG) emissions have recently become the significant focus of engineering research. The geological sequestration of greenhouse gases such as carbon… (more)

▼ Global warming and greenhouse gas (GHG) emissions have recently become the significant focus of engineering research. The geological sequestration of greenhouse gases such as carbon dioxide (CO₂) is one approach that has been proposed to reduce the greenhouse gas emissions and slow down global warming. Geological sequestration involves the injection of produced CO₂ into subsurface formations and trapping the gas through many geological mechanisms, such as structural trapping, capillary trapping, dissolution, and mineralization. While some progress in our understanding of fluid flow in porous media has been made, many petrophysical phenomena, such as multi-phase flow, capillarity, geochemical reactions, geomechanical effect, etc., that occur during geological CO₂ sequestration remain inadequately studied and pose a challenge for continued study. It is critical to continue to research on these important issues. Numerical simulators are essential tools to develop a better understanding of the geologic characteristics of brine reservoirs and to build support for future CO₂ storage projects. Modeling CO₂ injection requires the implementation of multiphase flow model and an Equation of State (EOS) module to compute the dissolution of CO₂ in brine and vice versa. In this study, we used the Integrated Parallel Accurate Reservoir Simulator (IPARS) developed at the Center for Subsurface Modeling at The University of Texas at Austin to model the injection process and storage of CO₂ in saline aquifers. We developed and implemented new petrophysical models in IPARS, and applied these models to study the process of CO₂ sequestration. The research presented in this dissertation is divided into three parts. The first part of the dissertation discusses petrophysical and computational models for the mechanical, geological, petrophysical phenomena occurring during CO₂ injection and sequestration. The effectiveness of CO₂ storage in saline aquifers is governed by the interplay of capillary, viscous, and buoyancy forces. Recent experimental data reveals the impact of pressure, temperature, and salinity on interfacial tension (IFT) between CO₂ and brine. The dependence of CO₂-brine relative permeability and capillary pressure on IFT is also clearly evident in published experimental results. Improved understanding of the mechanisms that control the migration and trapping of CO₂ in the subsurface is crucial to design future storage projects for long-term, safe containment. We have developed numerical models for CO₂ trapping and migration in aquifers, including a compositional flow model, a relative permeability model, a capillary model, an interfacial tension model, and others. The heterogeneities in porosity and permeability are also coupled to the petrophysical models. We have developed and implemented a general relative permeability model that combines the effects of pressure gradient, buoyancy, and capillary pressure in a compositional and parallel simulator. The significance of IFT variations on CO₂ migration and trapping is… Advisors/Committee Members: Delshad, Mojdeh (advisor), Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Reservoir simulation; Petrophysical modeling; CO₂ sequestration; Coreflood; Global warming; CCS; CO₂ flood; High performance computing

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APA (6^th Edition):

Kong, X. (2014). Petrophysical modeling and simulation study of geological CO₂ sequestration. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/24803

Chicago Manual of Style (16^th Edition):

Kong, Xianhui. “Petrophysical modeling and simulation study of geological CO₂ sequestration.” 2014. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/24803.

MLA Handbook (7^th Edition):

Kong, Xianhui. “Petrophysical modeling and simulation study of geological CO₂ sequestration.” 2014. Web. 28 Feb 2021.

Vancouver:

Kong X. Petrophysical modeling and simulation study of geological CO₂ sequestration. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2014. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/24803.

Council of Science Editors:

Kong X. Petrophysical modeling and simulation study of geological CO₂ sequestration. [Doctoral Dissertation]. University of Texas – Austin; 2014. Available from: http://hdl.handle.net/2152/24803

18. Borden, Michael Johns. Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture.

Degree: PhD, Computational and Applied Mathematics, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2012-08-6113

► To date, efforts to model fracture and crack propagation have focused on two broad approaches: discrete and continuum damage descriptions. The discrete approach incorporates a… (more)

▼ To date, efforts to model fracture and crack propagation have focused on two broad approaches: discrete and continuum damage descriptions. The discrete approach incorporates a discontinuity into the displacement field that must be tracked and updated. Examples of this approach include XFEM, element deletion, and cohesive zone models. The continuum damage, or smeared crack, approach incorporates a damage parameter into the model that controls the strength of the material. An advantage of this approach is that it does not require interface tracking since the damage parameter varies continuously over the domain. An alternative approach is to use a phase-field to describe crack propagation. In the phase-field approach to modeling fracture the problem is reformulated in terms of a coupled system of partial differential equations. A continuous scalar-valued phase-field is introduced into the model to indicate whether the material is in the unfractured or fractured ''phase''. The evolution of the phase-field is governed by a partial differential equation that includes a driving force that is a function of the strain energy of the body in question. This leads to a coupling between the momentum equation and the phase-field equation. The phase-field model also includes a length scale parameter that controls the width of the smooth approximation to the discrete crack. This allows discrete cracks to be modeled down to any desired length scale. Thus, this approach incorporates the strengths of both the discrete and continuum damage models, i.e., accurate modeling of individual cracks with no interface tracking. The research presented in this dissertation focuses on developing phase-field models for dynamic fracture. A general formulation in terms of the usual balance laws supplemented by a microforce balance law governing the evolution of the phase-field is derived. From this formulation, small-strain brittle and large-deformation ductile models are then derived. Additionally, a fourth-order theory for the phase-field approximation of the crack path is postulated. Convergence and approximation results are obtained for the proposed theories. In this work, isogeometric analysis, and particularly T-splines, plays an important role by providing a smooth basis that allows local refinement. Several numerical simulations have been performed to evaluate the proposed theories. These results show that phase-field models are a powerful tool for predicting fracture. Advisors/Committee Members: Hughes, Thomas J. R. (advisor), Ghattas, Omar (committee member), Landis, Chad M. (committee member), Ravi-Chandar, Krshnaswamy (committee member), Wheeler, Mary F. (committee member).

Subjects/Keywords: Fracture; Phase-field; Brittle fracture; Ductile fracture; Isogeometric analysis; Bezier extraction

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APA (6^th Edition):

Borden, M. J. (2012). Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-08-6113

Chicago Manual of Style (16^th Edition):

Borden, Michael Johns. “Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/ETD-UT-2012-08-6113.

MLA Handbook (7^th Edition):

Borden, Michael Johns. “Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture.” 2012. Web. 28 Feb 2021.

Vancouver:

Borden MJ. Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-6113.

Council of Science Editors:

Borden MJ. Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-6113

19. Yuan, Changli. Commercial scale simulations of surfactant/polymer flooding.

Degree: PhD, Petroleum Engineering, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2012-08-401

► The depletion of oil reserves and higher oil prices has made chemical enhanced oil recovery (EOR) methods more attractive in recent years. Because of geological… (more)

▼ The depletion of oil reserves and higher oil prices has made chemical enhanced oil recovery (EOR) methods more attractive in recent years. Because of geological heterogeneity, unfavorable mobility ratio, and capillary forces, conventional oil recovery (including water flooding) leaves behind much oil in reservoir, often as much as 70% OOIP (original oil in place). Surfactant/polymer flooding targets these bypassed oil left after waterflood by reducing water mobility and oil/water interfacial tension. The complexity and uncertainty of reservoir characterization make the design and implementation of a robust and effective surfactant/polymer flooding to be quite challenging. Accurate numerical simulation prior to the field surfactant/polymer flooding is essential for a successful design and implementation of surfactant/polymer flooding. A recently developed unified polymer viscosity model was implemented into our existing polymer module within our in-house reservoir simulator, the Implicit Parallel Accurate Reservoir Simulator (IPARS). The new viscosity model is capable of simulating not only the Newtonian and shear-thinning rheology of polymer solution but also the shear-thickening behavior, which may occur near the wellbore with high injection rates when high molecular weight Partially Hydrolyzed Acrylamide (HPAM) polymers are injected. We have added a full capability of surfactant/polymer flooding to TRCHEM module of IPARS using a simplified but mechanistic and user-friendly approach for modeling surfactant/water/oil phase behavior. The features of surfactant module include: 1) surfactant component transport in porous media; 2) surfactant adsorption on the rock; 3) surfactant/oil/water phase behavior transitioned with salinity of Type II(-), Type III, and Type II(+) phase behaviors; 4) compositional microemulsion phase viscosity correlation and 5) relative permeabilities based on the trapping number. With the parallel capability of IPARS, commercial scale simulation of surfactant/polymer flooding becomes practical and affordable. Several numerical examples are presented in this dissertation. The results of surfactant/polymer flood are verified by comparing with the results obtained from UTCHEM, a three-dimensional chemical flood simulator developed at the University of Texas at Austin. The parallel capability and scalability are also demonstrated. Advisors/Committee Members: Delshad, Mojdeh (advisor), Wheeler, Mary F. (Mary Fanett) (advisor), Balhoff, Matthew T. (committee member), Arbogast, Todd J. (committee member), Dean, Rick H. (committee member).

Subjects/Keywords: Surfactant/polymer flooding; Non-Newtonian fluid; Phase behavior; Parallel computation

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APA (6^th Edition):

Yuan, C. (2012). Commercial scale simulations of surfactant/polymer flooding. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-08-401

Chicago Manual of Style (16^th Edition):

Yuan, Changli. “Commercial scale simulations of surfactant/polymer flooding.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/ETD-UT-2012-08-401.

MLA Handbook (7^th Edition):

Yuan, Changli. “Commercial scale simulations of surfactant/polymer flooding.” 2012. Web. 28 Feb 2021.

Vancouver:

Yuan C. Commercial scale simulations of surfactant/polymer flooding. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-401.

Council of Science Editors:

Yuan C. Commercial scale simulations of surfactant/polymer flooding. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-401

University of Texas – Austin

20. Lu, Bo, 1979-. Iteratively coupled reservoir simulation for multiphase flow in porous media.

Degree: PhD, Petroleum Engineering, 2008, University of Texas – Austin

URL: http://hdl.handle.net/2152/3880

► Fully implicit and IMPES are two primary reservoir simulation schemes that are currently used widely. However, neither of them is sufficiently accurate or ef- ficient,… (more)

▼ Fully implicit and IMPES are two primary reservoir simulation schemes that are currently used widely. However, neither of them is sufficiently accurate or ef- ficient, given the increasing size and degree of complexity of highly heterogeneous reservoirs. In this dissertation, an iterative coupling approach is proposed and developed to solve multiphase flow problems targeting the efficient, robust and accurate simulation of the hydrocarbon recovery process. In the iterative coupling approach, the pressure equation is solved implicitly, followed by the saturation equation, which is solved semi-implicitly. These two stages are iteratively coupled at the end of each time step by evaluating material balance, both locally and globally, to check the convergence of each iteration. Additional iterations are conducted, if necessary; otherwise the simulation proceeds to the next time step. Several numerical techniques are incorporated to speed up the program convergence and cut down the number of iterations per time step, thus greatly improving iterative model performance. The iterative air-water model, the oil-water model, and the black oil model are all developed in this work. Several numerical examples have been tested using the iterative approach, the fully implicit method, and the IMPES method. Results show that with the iterative method, about 20%-40% of simulation time is saved when compared to the fully implicit method with similar accuracy. As compared to the IMPES method, the iterative method shows better stability, allowing larger time steps in simulation. The iterative method also produces better mass balance than IMPES over the same time. The iterative method is developed for parallel implementation, and several test cases have been run on parallel clusters with large numbers of processors. Good parallel scalability enables the iterative method to solve large problems with millions of elements and highly heterogeneous reservoir properties. Linear solvers take the greatest portion of CPU time in reservoir simulations. This dissertation investigates advanced linear solvers for high performance computers (HPC) for reservoir simulation. Their performance is compared and discussed. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Hydrocarbon reservoirs – Simulation methods; Multiphase flow; Porous materials; Fluid dynamics; Secondary recovery of oil

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lu, Bo, 1. (2008). Iteratively coupled reservoir simulation for multiphase flow in porous media. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/3880

Chicago Manual of Style (16^th Edition):

Lu, Bo, 1979-. “Iteratively coupled reservoir simulation for multiphase flow in porous media.” 2008. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/3880.

MLA Handbook (7^th Edition):

Lu, Bo, 1979-. “Iteratively coupled reservoir simulation for multiphase flow in porous media.” 2008. Web. 28 Feb 2021.

Vancouver:

Lu, Bo 1. Iteratively coupled reservoir simulation for multiphase flow in porous media. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2008. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/3880.

Council of Science Editors:

Lu, Bo 1. Iteratively coupled reservoir simulation for multiphase flow in porous media. [Doctoral Dissertation]. University of Texas – Austin; 2008. Available from: http://hdl.handle.net/2152/3880

University of Texas – Austin

21. Eslinger, Owen John. Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems.

Degree: PhD, Computational and Applied Mathematics, 2005, University of Texas – Austin

URL: http://hdl.handle.net/2152/1906

► A set of discontinuous Galerkin (DG) finite element methods are proposed to solve the air-water, two-phase equations arising in shallow subsurface flow problems. The different… (more)

▼ A set of discontinuous Galerkin (DG) finite element methods are proposed to solve the air-water, two-phase equations arising in shallow subsurface flow problems. The different time-splitting approaches detailed incorporate primal formulations, such as Oden-Baumann-Babuska DG (OBB-DG), Symmetric Interior Penalty Galerkin (SIPG), Non-Symmetric Interior Penalty Galerkin (NIPG), and Incomplete Interior Penalty Galerkin (IIPG); as well as a local discontinuous Galerkin (LDG) method applied to the saturation equation. The two-phase flow equations presented are split into sequential and implicit pressure/explicit saturation (IMPES) formulations. The IMPES formulation introduced in this work uses one of the primal DG formulations to solve the pressure equation implicitly at every time step, and then uses an explicit LDG scheme for saturation equation. This LDG scheme advances in time via explicit Runge-Kutta time stepping, while employing a Kirchoff transformation for the local solution of the degenerate diffusion term. As fluid saturations may be discontinuous at the interface between two material types, DG methods are a natural fit for this problem. An algorithm is introduced to efficiently solve the system of equations arising from the primal DG discretization of the model Poisson’s Equation on conforming grids. The eigenstructure of the resulting stiffness matrix is examined and the reliance of this system on the penalty parameter is detailed. This analysis leads to an algorithm that is computationally optimal and guaranteed to converge for the order of approximation p = 1. The algorithm converges independently of h and of the penalty parameter σ. Computational experiments show that this algorithm also provides an excellent preconditioning step for higher orders of approximation and extensions are given to 2D and 3D problems. Computational results are also shown for a more general second order elliptic equation, for example, cases with heterogeneous and non-isotropic K. The numerical schemes presented are verified on a collection of standard benchmark problems and the two-phase flow formulations are validated using empirical results from the groundwater literature. These results include bounded column infiltration problems in which the soil air becomes compressed and entrapped, as well as other shallow subsurface infiltration problems. It is shown that the IMPES approach introduced holds promise for the future, especially for problems with very small, or even zero, capillary pressure. Such problems are commonly found in the SPE literature. Finally, initial computational results are shown which relate to a simplified model of the CO2 sequestration problem. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Galerkin methods; Two-phase flow

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APA (6^th Edition):

Eslinger, O. J. (2005). Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/1906

Chicago Manual of Style (16^th Edition):

Eslinger, Owen John. “Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems.” 2005. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/1906.

MLA Handbook (7^th Edition):

Eslinger, Owen John. “Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems.” 2005. Web. 28 Feb 2021.

Vancouver:

Eslinger OJ. Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2005. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/1906.

Council of Science Editors:

Eslinger OJ. Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems. [Doctoral Dissertation]. University of Texas – Austin; 2005. Available from: http://hdl.handle.net/2152/1906

University of Texas – Austin

22. Gai, Xiuli, 1970-. A coupled geomechanics and reservoir flow model on parallel computers.

Degree: PhD, Petroleum Engineering, 2004, University of Texas – Austin

URL: http://hdl.handle.net/2152/1187

► Land subsidence due to the exploitation of groundwater and hydro- carbon fluids has triggered extensive studies in coupled fluid flow and ge- omechanics simulations. However,… (more)

▼ Land subsidence due to the exploitation of groundwater and hydro- carbon fluids has triggered extensive studies in coupled fluid flow and ge- omechanics simulations. However, numerical modeling of coupled processes imposes great computational challenges. Coupled analysis for large scale full- field applications with millions of unknowns has been, historically, considered extremely complex and unfeasible. The purpose of this dissertation is to in- vestigate accurate and efficient numerical techniques for coupled multiphase flow and geomechanics simulations on parallel computers. We emphasize the iterative coupling approach in extending conven- tional fluid-flow modeling to coupled fluid-flow and geomechanics modeling. To overcome the slow convergence—a major drawback of this method—we propose new preconditioning schemes to achieve a faster convergence rate. Efficient and parallel scalable linear solvers are developed to reduce the com- putational overhead induced by the solution of discrete elasticity equations. Special communications techniques are implemented to optimize parallel effi- ciency. In this dissertation we first derive the mathematical model for multi- phase flowin a deformable porous medium. We then present a new formulation of the iterative coupling scheme and prove the optimality of two physics-based preconditioners that are traditionally used in the petroleum industry. Practi- cal strategies and new preconditioners are proposed to improve the numerical performance of the iteratively coupled approach. In addition, we develop two types of preconditioners for solving the linear elasticity system, namely, multi- level domain decomposition preconditioners using a super-coarsening multigrid algorithm and displacement decomposition preconditioners. Parallel imple- mentation issues are also addressed. Numerical examples are presented to demonstrate the robustness, efficiency and parallel scalability of the proposed linear solution techniques. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Multiphase flow – Mathematical models; Coupled problems (Complex systems) – Numerical solutions; Engineering geology – Mathematics; Rock mechanics – Mathematics

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APA (6^th Edition):

Gai, Xiuli, 1. (2004). A coupled geomechanics and reservoir flow model on parallel computers. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/1187

Chicago Manual of Style (16^th Edition):

Gai, Xiuli, 1970-. “A coupled geomechanics and reservoir flow model on parallel computers.” 2004. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/1187.

MLA Handbook (7^th Edition):

Gai, Xiuli, 1970-. “A coupled geomechanics and reservoir flow model on parallel computers.” 2004. Web. 28 Feb 2021.

Vancouver:

Gai, Xiuli 1. A coupled geomechanics and reservoir flow model on parallel computers. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2004. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/1187.

Council of Science Editors:

Gai, Xiuli 1. A coupled geomechanics and reservoir flow model on parallel computers. [Doctoral Dissertation]. University of Texas – Austin; 2004. Available from: http://hdl.handle.net/2152/1187

23. Florez Guzman, Horacio Antonio. Domain decomposition methods in geomechanics.

Degree: PhD, Engineering Mechanics, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2012-08-6120

► Hydrocarbon production or injection of fluids in the reservoir can produce changes in the rock stresses and in-situ geomechanics, potentially leading to compaction and subsidence… (more)

▼ Hydrocarbon production or injection of fluids in the reservoir can produce changes in the rock stresses and in-situ geomechanics, potentially leading to compaction and subsidence with harmful effects in wells, cap-rock, faults, and the surrounding environment as well. In order to tackle these changes and their impact, accurate simulations are essential. The Mortar Finite Element Method (MFEM) has been demonstrated to be a powerful technique in order to formulate a weak continuity condition at the interface of sub-domains in which different meshes, i.e. non-conforming or hybrid, and / or variational approximations are used. This is particularly suitable when coupling different physics on different domains, such as elasticity and poroelasticity, in the context of coupled flow and geomechanics. In this dissertation, popular Domain Decomposition Methods (DDM) are implemented in order to carry large simulations by taking full advantage of current parallel computer architectures. Different solution schemes can be defined depending upon the way information is exchanged between sub-domain interfaces. Three different schemes, i.e. Dirichlet-Neumann (DN), Neumann-Neumann (NN) and MFEM, are tested and the advantages and disadvantages of each of them are identified. As a first contribution, the MFEM is extended to deal with curve interfaces represented by Non-Uniform Rational B-Splines (NURBS) curves and surfaces. The goal is to have a more robust geometrical representation for mortar spaces, which allows gluing non-conforming interfaces on realistic geometries. The resulting mortar saddle-point problem will be decoupled by means of the DN- and NN-DDM. Additionally, a reservoir geometry reconstruction procedure based on NURBS surfaces is presented as well. The technique builds a robust piecewise continuous geometrical representation that can be exploited by MFEM in order to tackle realistic problems, which is a second contribution. Tensor product meshes are usually propagated from the reservoir in a conforming way into its surroundings, which makes non-matching interfaces highly attractive in this case. In the context of reservoir compaction and subsidence estimation, it is common to deal with serial legacy codes for flow. Indeed, major reservoir simulators such as compositional codes lack parallelism. Another issue is the fact that, generally speaking, flow and mechanics domains are different. To overcome this limitation, a serial-parallel approach is proposed in order to couple serial flow codes with our parallel mechanics code by means of iterative coupling. Concrete results in loosely coupling are presented as a third contribution. As a final contribution, the DN-DDM is applied to couple elasticity and plasticity, which seems very promising in order to speed up computations involving poroplasticity. Several examples of coupling of elasticity, poroelasticity, and plasticity ranging from near-wellbore applications to field level subsidence computations help to show that the proposed methodology can… Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Delshad, Mojdeh (committee member), Mear, Mark (committee member), Landis, Chad (committee member), Rodriguez, Adolfo (committee member).

Subjects/Keywords: Domain decomposition; Parallel computing; Dirichlet-Neumann; Neumann-Neumann; Elasticity; Plasticity; Geomechanics; Finite elements; Mortar finite elements; NURBS

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APA (6^th Edition):

Florez Guzman, H. A. (2012). Domain decomposition methods in geomechanics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-08-6120

Chicago Manual of Style (16^th Edition):

Florez Guzman, Horacio Antonio. “Domain decomposition methods in geomechanics.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/ETD-UT-2012-08-6120.

MLA Handbook (7^th Edition):

Florez Guzman, Horacio Antonio. “Domain decomposition methods in geomechanics.” 2012. Web. 28 Feb 2021.

Vancouver:

Florez Guzman HA. Domain decomposition methods in geomechanics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-6120.

Council of Science Editors:

Florez Guzman HA. Domain decomposition methods in geomechanics. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-6120

University of Texas – Austin

24. Liu, Ruijie. Discontinuous Galerkin finite element solution for poromechanics.

Degree: PhD, Aerospace Engineering, 2004, University of Texas – Austin

URL: http://hdl.handle.net/2152/1357

Subjects/Keywords: Galerkin methods; Porous materials – Mechanical properties

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Liu, R. (2004). Discontinuous Galerkin finite element solution for poromechanics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/1357

Chicago Manual of Style (16^th Edition):

Liu, Ruijie. “Discontinuous Galerkin finite element solution for poromechanics.” 2004. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/1357.

MLA Handbook (7^th Edition):

Liu, Ruijie. “Discontinuous Galerkin finite element solution for poromechanics.” 2004. Web. 28 Feb 2021.

Vancouver:

Liu R. Discontinuous Galerkin finite element solution for poromechanics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2004. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/1357.

Council of Science Editors:

Liu R. Discontinuous Galerkin finite element solution for poromechanics. [Doctoral Dissertation]. University of Texas – Austin; 2004. Available from: http://hdl.handle.net/2152/1357

University of Texas – Austin

25. Yuan, Changli. Simulations of subsurface multiphase flow including polymer flooding in oil reservoirs and infiltration in vadose zone.

Degree: MSin Engineering, Petroleum Engineering, 2009, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2009-12-402

► With the depletion of oil reserves and increase in oil price, the enhanced oil recovery methods such as polymer flooding to increase oil production from… (more)

▼ With the depletion of oil reserves and increase in oil price, the enhanced oil recovery methods such as polymer flooding to increase oil production from water flooded fields are becoming more attractive. Effective design of these processes is challenging because the polymer chemistry has a strong effect on reaction and fluid rheology, which in turn has a strong effect on fluid transport. We have implemented a well-established polymer model within the Implicit Parallel Accurate Reservoir Simulator (IPARS), which enables parallel simulation of non-Newtonian fluid flow through porous media. The following properties of polymer solution are modeled in this work: 1) polymer adsorption; 2) polymer viscosity as a function of salinity, hardness, polymer concentration, and shear rate; 3) permeability reduction; 4) inaccessible pore volume. IPARS enables field-scale polymer flooding simulation with its parallel computation capability. In this thesis, several numerical examples are presented. The result of polymer module is verified by UTCHEM, a three-dimensional chemical flood simulator developed at the University of Texas at Austin. The parallel capability is also tested. The influence of different shear rate calculations is investigated in homogeneous and heterogeneous reservoirs. We observed that the wellbore velocity calculation instead of Darcy velocity reduces the grid effect for coarse mesh. We noted that the injection bottom hole pressure is very sensitive to the shear rate calculation. However, cumulative oil recovery and overall oil saturation appear to not be sensitive to grid and shear rate calculation for same reservoir. There are two models to model the ground water infiltration in vadose zone. One is Richard’s Equation (RE) model. And the other is two-phase flow model. In this work, we compare the two-phase model with an RE model to ascertain, under common scenarios such as infiltration or injection of water into initially dry soils, the similarities and differences in solutions behaviors, the ability of each model to simulate such infiltration processes under realistic scenarios, and to investigate the numerical efficiencies and difficulties which arise in these models. Six different data sets were assembled as benchmark infiltration problems in the unsaturated zone. The comparison shows that two-phase model holds for general porous media and is not limited by several assumptions that must be made for the RE formulation, while RE is applicable only for shallow regions (vadose) that are only several meters in depth and a fully saturated bottom boundary condition must be assumed. Advisors/Committee Members: Delshad, Mojdeh (advisor), Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Polymer flooding; Non-Newtonian fluid; Coupling flow and chemistry; Parallel computation.

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APA (6^th Edition):

Yuan, C. (2009). Simulations of subsurface multiphase flow including polymer flooding in oil reservoirs and infiltration in vadose zone. (Masters Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2009-12-402

Chicago Manual of Style (16^th Edition):

Yuan, Changli. “Simulations of subsurface multiphase flow including polymer flooding in oil reservoirs and infiltration in vadose zone.” 2009. Masters Thesis, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/ETD-UT-2009-12-402.

MLA Handbook (7^th Edition):

Yuan, Changli. “Simulations of subsurface multiphase flow including polymer flooding in oil reservoirs and infiltration in vadose zone.” 2009. Web. 28 Feb 2021.

Vancouver:

Yuan C. Simulations of subsurface multiphase flow including polymer flooding in oil reservoirs and infiltration in vadose zone. [Internet] [Masters thesis]. University of Texas – Austin; 2009. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/ETD-UT-2009-12-402.

Council of Science Editors:

Yuan C. Simulations of subsurface multiphase flow including polymer flooding in oil reservoirs and infiltration in vadose zone. [Masters Thesis]. University of Texas – Austin; 2009. Available from: http://hdl.handle.net/2152/ETD-UT-2009-12-402

University of Texas – Austin

26. De Basabe Delgado, Jonás de Dios, 1975-. High-order finite element methods for seismic wave propagation.

Degree: PhD, Computational and Applied Mathematics, 2009, University of Texas – Austin

URL: http://hdl.handle.net/2152/6864

► Purely numerical methods based on the Finite Element Method (FEM) are becoming increasingly popular in seismic modeling for the propagation of acoustic and elastic waves… (more)

▼ Purely numerical methods based on the Finite Element Method (FEM) are becoming increasingly popular in seismic modeling for the propagation of acoustic and elastic waves in geophysical models. These methods o er a better control on the accuracy and more geometrical exibility than the Finite Di erence methods that have been traditionally used for the generation of synthetic seismograms. However, the success of these methods has outpaced their analytic validation. The accuracy of the FEMs used for seismic wave propagation is unknown in most cases and therefore the simulation parameters in numerical experiments are determined by empirical rules. I focus on two methods that are particularly suited for seismic modeling: the Spectral Element Method (SEM) and the Interior-Penalty Discontinuous Galerkin Method (IP-DGM). The goals of this research are to investigate the grid dispersion and stability of SEM and IP-DGM, to implement these methods and to apply them to subsurface models to obtain synthetic seismograms. In order to analyze the grid dispersion and stability, I use the von Neumann method (plane wave analysis) to obtain a generalized eigenvalue problem. I show that the eigenvalues are related to the grid dispersion and that, with certain assumptions, the size of the eigenvalue problem can be reduced from the total number of degrees of freedom to one proportional to the number of degrees of freedom inside one element. The grid dispersion results indicate that SEM of degree greater than 4 is isotropic and has a very low dispersion. Similar dispersion properties are observed for the symmetric formulation of IP-DGM of degree greater than 4 using nodal basis functions. The low dispersion of these methods allows for a sampling ratio of 4 nodes per wavelength to be used. On the other hand, the stability analysis shows that, in the elastic case, the size of the time step required in IP-DGM is approximately 6 times smaller than that of SEM. The results from the analysis are con rmed by numerical experiments performed using an implementation of these methods. The methods are tested using two benchmarks: Lamb's problems and the SEG/EAGE salt dome model. Advisors/Committee Members: Sen, Mrinal K. (advisor), Wheeler, Mary F. (Mary Fanett) (advisor).

Subjects/Keywords: Spectral Element Method; Interior-Penalty Discontinuous Galerkin Method; Seismic modeling; Grid dispersion; Stability; Synthetic seismograms

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

De Basabe Delgado, Jonás de Dios, 1. (2009). High-order finite element methods for seismic wave propagation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/6864

Chicago Manual of Style (16^th Edition):

De Basabe Delgado, Jonás de Dios, 1975-. “High-order finite element methods for seismic wave propagation.” 2009. Doctoral Dissertation, University of Texas – Austin. Accessed February 28, 2021. http://hdl.handle.net/2152/6864.

MLA Handbook (7^th Edition):

De Basabe Delgado, Jonás de Dios, 1975-. “High-order finite element methods for seismic wave propagation.” 2009. Web. 28 Feb 2021.

Vancouver:

De Basabe Delgado, Jonás de Dios 1. High-order finite element methods for seismic wave propagation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2009. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/2152/6864.

Council of Science Editors:

De Basabe Delgado, Jonás de Dios 1. High-order finite element methods for seismic wave propagation. [Doctoral Dissertation]. University of Texas – Austin; 2009. Available from: http://hdl.handle.net/2152/6864

Open Access Theses and Dissertations