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1. -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

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 (6th 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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Chicago Manual of Style (16th Edition):

-5603-2533. “Efficient algorithms for flow models coupled with geomechanics for porous media applications.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed May 07, 2021. http://hdl.handle.net/2152/46503.

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MLA Handbook (7th Edition):

-5603-2533. “Efficient algorithms for flow models coupled with geomechanics for porous media applications.” 2016. Web. 07 May 2021.

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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 May 07]. Available from: http://hdl.handle.net/2152/46503.

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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

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Author name may be incomplete


University of Texas – Austin

2. -1155-8213. Addressing challenges in modeling of coupled flow and poromechanics in deep subsurface reservoirs.

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

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

APA (6th 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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Author name may be incomplete

Chicago Manual of Style (16th Edition):

-1155-8213. “Addressing challenges in modeling of coupled flow and poromechanics in deep subsurface reservoirs.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed May 07, 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 (7th Edition):

-1155-8213. “Addressing challenges in modeling of coupled flow and poromechanics in deep subsurface reservoirs.” 2018. Web. 07 May 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 May 07]. 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

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