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Author: Timothy Myung Joon Yeo
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Languages : en
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Many applications of the numerical modeling of coupled flow and deformation for subsurface reservoirs are based on the assumption of small deformation. This approximation makes two assumptions: the displacement gradients in the reference configuration are infinitesimal, and the displacement itself is very small compared to the characteristic length of the problem of interest. The small deformation approximation is usually valid in subsurface reservoirs because a typical reservoir rock is stiff and, therefore, exhibits small deformation. However, this assumption may not be valid in some subsurface reservoirs that experience substantial compaction or shear. Some examples demonstrate the substantial subsidence due to a large amount of hydrocarbon production, underground water removal, and softening of the rock due to thermal injections. Accounting for large deformations can be particularly important in fractured or faulted reservoirs. There, fractures can have a significant impact on the fluid flow by acting as flow conduits or flow barriers. Considering that fractures and faults typically have a very small aperture, even small deformation or small tangential slip of the fracture could significantly impact the flow by changing flow directions or fracture permeability. Therefore, a new numerical framework for coupled fluid flow, large deformation, and large slip for fractured and faulted reservoirs is developed by employing the mixed standard Galerkin finite element and two-point flux approximation finite volume methods. The developed framework models the fracture as a large deformation frictional contact using the Node-To-Segment (NTS) contact element with the penalty formulation. The algorithms to dynamically update flow connections around the fracture and their transmissibility are presented for non-matching grids along the fracture due to the tangential slip. The coupled equations are solved in a fully coupled way using the Newton-Raphson method with the active set strategy. In order to model the realistic behavior of the fracture, fracture permeability is updated depending on the fracture states, stress, and deformation. The linear slip-weakening model and gravity are also incorporated in the model. The developed framework is verified with several benchmark problems having analytical solutions, including the single fracture slip problem, the Mandel problem, and the strip footing problem. Afterward, the relative errors of the coupled flow and small deformation model are computed for various model problems with various material properties in order to investigate the applicability of the coupled small deformation model. Finally, the developed framework was applied to model fluid injection into the faulted overburden-reservoir-underburden system in order to model the reactivation of the fault. Even though the stiffness of the system is high and deformation is indeed small, the coupled large deformation model indicates a faster increase in the fault slip area compared to the small deformation model. A separate section of the dissertation presents a framework to solve the small deformation frictional contact problem using the method of augmented Lagrangian with the polynomial pressure projection (PPP) stabilization. This method successfully suppresses spurious oscillations on the normal contact traction and demonstrates the capability to precisely apply the constraints on the contact without introducing additional global degrees of freedom.
Author: Timothy Myung Joon Yeo
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ISBN:
Category :
Languages : en
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Book Description
Many applications of the numerical modeling of coupled flow and deformation for subsurface reservoirs are based on the assumption of small deformation. This approximation makes two assumptions: the displacement gradients in the reference configuration are infinitesimal, and the displacement itself is very small compared to the characteristic length of the problem of interest. The small deformation approximation is usually valid in subsurface reservoirs because a typical reservoir rock is stiff and, therefore, exhibits small deformation. However, this assumption may not be valid in some subsurface reservoirs that experience substantial compaction or shear. Some examples demonstrate the substantial subsidence due to a large amount of hydrocarbon production, underground water removal, and softening of the rock due to thermal injections. Accounting for large deformations can be particularly important in fractured or faulted reservoirs. There, fractures can have a significant impact on the fluid flow by acting as flow conduits or flow barriers. Considering that fractures and faults typically have a very small aperture, even small deformation or small tangential slip of the fracture could significantly impact the flow by changing flow directions or fracture permeability. Therefore, a new numerical framework for coupled fluid flow, large deformation, and large slip for fractured and faulted reservoirs is developed by employing the mixed standard Galerkin finite element and two-point flux approximation finite volume methods. The developed framework models the fracture as a large deformation frictional contact using the Node-To-Segment (NTS) contact element with the penalty formulation. The algorithms to dynamically update flow connections around the fracture and their transmissibility are presented for non-matching grids along the fracture due to the tangential slip. The coupled equations are solved in a fully coupled way using the Newton-Raphson method with the active set strategy. In order to model the realistic behavior of the fracture, fracture permeability is updated depending on the fracture states, stress, and deformation. The linear slip-weakening model and gravity are also incorporated in the model. The developed framework is verified with several benchmark problems having analytical solutions, including the single fracture slip problem, the Mandel problem, and the strip footing problem. Afterward, the relative errors of the coupled flow and small deformation model are computed for various model problems with various material properties in order to investigate the applicability of the coupled small deformation model. Finally, the developed framework was applied to model fluid injection into the faulted overburden-reservoir-underburden system in order to model the reactivation of the fault. Even though the stiffness of the system is high and deformation is indeed small, the coupled large deformation model indicates a faster increase in the fault slip area compared to the small deformation model. A separate section of the dissertation presents a framework to solve the small deformation frictional contact problem using the method of augmented Lagrangian with the polynomial pressure projection (PPP) stabilization. This method successfully suppresses spurious oscillations on the normal contact traction and demonstrates the capability to precisely apply the constraints on the contact without introducing additional global degrees of freedom.
Author:
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Languages : en
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Author: Mohamad Jammoul
Publisher:
ISBN:
Category :
Languages : en
Pages : 358
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Book Description
Subsurface problems are inherently challenging because they involve multiple physical processes interacting with each other. Numerical models tend to break down the system into smaller problems that are easier to solve and that could be coupled within one framework. Fractured reservoirs are especially difficult to model due to the variety of physical processes that act at different scales. These processes include (1) fracture propagation, (2) flow through fractures and through the matrix, (3) hydrocarbon phase behavior, and (4) poroelastic deformations. Modeling the interaction between these processes plays an integral role in designing many energy and environmental applications. The primary objective of this work is to construct a holistic framework that can model flow and geomechanics in fractured reservoirs using computationally efficient algorithms. The framework can handle complex multiphysics problems including: multiphase flow, mechanical deformations, the capability to stimulate new fractures or activate existing ones, and the ability to seamlessly switch between propagation and production scenarios within the same simulation study. The approach includes coupling the in-house reservoir simulator (IPARS) with a phase-field fracture propagation model. In addition to hydraulic fracturing problems, the framework can model flow and geomechanics on fixed fracture networks with dynamic aperture variations. It can also simulate multiphase flow through natural fractures using general semi-structured grids. Two numerical schemes are introduced to improve the efficiency of computations. A multirate approach is proposed to enhance the performance of the L-scheme for decoupling the phase-field and displacement equations. A domain decomposition scheme is also presented to perform space-time refinement for flow through fractured reservoirs. Local time stepping and spatial mesh refinement can be used in the vicinity of the fractures while taking large grids cells with coarse time steps everywhere else in the reservoir. This motivates space and time adaptive mesh refinement in reservoir simulations
Author: G.H. Spence
Publisher: Geological Society of London
ISBN: 1862393559
Category : Science
Languages : en
Pages : 421
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Book Description
Naturally fractured reservoirs constitute a substantial percentage of remaining hydrocarbon resources; they create exploration targets in otherwise impermeable rocks, including under-explored crystalline basement; and they can be used as geological stores for anthropogenic carbon dioxide. Their complex behaviour during production has traditionally proved difficult to predict, causing a large degree of uncertainty in reservoir development. The applied study of naturally fractured reservoirs seeks to constrain this uncertainty by developing new understanding, and is necessarily a broad, integrated, interdisciplinary topic. This book addresses some of the challenges and advances in knowledge, approaches, concepts, and methods used to characterize the interplay of rock matrix and fracture networks, relevant to fluid flow and hydrocarbon recovery. Topics include: describing, characterizing and identifying controls on fracture networks from outcrops, cores, geophysical data, digital and numerical models; geomechanical influences on reservoir behaviour; numerical modelling and simulation of fluid flow; and case studies of the exploration and development of carbonate, siliciclastic and metamorphic naturally fractured reservoirs.
Author: Kamy Sepehrnoori
Publisher: Elsevier
ISBN: 0128196882
Category : Technology & Engineering
Languages : en
Pages : 306
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Book Description
The development of naturally fractured reservoirs, especially shale gas and tight oil reservoirs, exploded in recent years due to advanced drilling and fracturing techniques. However, complex fracture geometries such as irregular fracture networks and non-planar fractures are often generated, especially in the presence of natural fractures. Accurate modelling of production from reservoirs with such geometries is challenging. Therefore, Embedded Discrete Fracture Modeling and Application in Reservoir Simulation demonstrates how production from reservoirs with complex fracture geometries can be modelled efficiently and effectively. This volume presents a conventional numerical model to handle simple and complex fractures using local grid refinement (LGR) and unstructured gridding. Moreover, it introduces an Embedded Discrete Fracture Model (EDFM) to efficiently deal with complex fractures by dividing the fractures into segments using matrix cell boundaries and creating non-neighboring connections (NNCs). A basic EDFM approach using Cartesian grids and advanced EDFM approach using Corner point and unstructured grids will be covered. Embedded Discrete Fracture Modeling and Application in Reservoir Simulation is an essential reference for anyone interested in performing reservoir simulation of conventional and unconventional fractured reservoirs. - Highlights the current state-of-the-art in reservoir simulation of unconventional reservoirs - Offers understanding of the impacts of key reservoir properties and complex fractures on well performance - Provides case studies to show how to use the EDFM method for different needs
Author: Jian Huang
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Within fractured reservoirs, such as tight gas reservoir, coupled processes between matrix deformation and fluid flow are very important for predicting reservoir behavior, pore pressure evolution and fracture closure. To study the coupling between gas desorption and rock matrix/fracture deformation, a poroelastic constitutive relation is developed and used for deformation of gas shale. Local continuity equation of dry gas model is developed by considering the mass conservation of gas, including both free and absorbed phases. The absorbed gas content and the sorption-induced volumetric strain are described through a Langmiur-type equation. A general porosity model that differs from other empirical correlations in the literature is developed and utilized in a finite element model to coupled gas diffusion and rock mass deformation. The dual permeability method (DPM) is implemented into the Finite Element Model (FEM) to investigate fracture deformation and closure and its impact on gas flow in naturally fractured reservoir. Within the framework of DPM, the fractured reservoir is treated as dual continuum. Two independent but overlapping meshes (or elements) are used to represent these kinds of reservoirs: one is the matrix elements used for deformation and fluid flow within matrix domain; while the other is the fracture element simulating the fluid flow only through the fractures. Both matrix and fractures are assumed to be permeable and can accomodate fluid transported. A quasi steady-state function is used to quantify the flow that is transferred between rock mass and fractures. By implementing the idea of equivalent fracture permeability and shape-factor within the transfer function into DPM, the fracture geometry and orientation are numerically considered and the complexity of the problem is well reduced. Both the normal deformation and shear dilation of fractures are considered and the stress-dependent fracture aperture can be updated in time. Further, a non-linear numerical model is constructed by implementing a poroviscoelastic model into the dual permeability (DPM)-finite element model (FEM) to investigate the coupled time-dependent viscoelastic deformation, fracture network evolution and compressible fluid flow in gas shale reservoir. The viscoelastic effect is addressed in both deviatoric and symmetric effective stresses to emphasize the effect of shear strain localization on fracture shear dilation. The new mechanical model is first verified with an analytical solution in a simple wellbore creep problem and then compared with the poroelastic solution in both wellbore and field cases. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/149448
Author: Saumik P. Dana
Publisher:
ISBN:
Category :
Languages : en
Pages : 372
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Book Description
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
Author: Daegil Yang
Publisher:
ISBN:
Category :
Languages : en
Pages : 173
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Book Description
A growing demand for more detailed modeling of subsurface physics as ever more challenging reservoirs - often unconventional, with significant geomechanical particularities - become production targets has moti-vated research in coupled flow and geomechanics. Reservoir rock deforms to given stress conditions, so the simplified approach of using a scalar value of the rock compressibility factor in the fluid mass balance equation to describe the geomechanical system response cannot correctly estimate multi-dimensional rock deformation. A coupled flow and geomechanics model considers flow physics and rock physics simultaneously by cou-pling different types of partial differential equations through primary variables. A number of coupled flow and geomechanics simulators have been developed and applied to describe fluid flow in deformable po-rous media but the majority of these coupled flow and geomechanics simulators have limited capabilities in modeling multiphase flow and geomechanical deformation in a heterogeneous and fractured reservoir. In addition, most simulators do not have the capability to simulate both coarse and fine scale multiphysics. In this study I developed a new, fully implicit multiphysics simulator (TAM-CFGM: Texas A&M Coupled Flow and Geomechanics simulator) that can be applied to simulate a 2D or 3D multiphase flow and rock deformation in a heterogeneous and/or fractured reservoir system. I derived a mixed finite element formu-lation that satisfies local mass conservation and provides a more accurate estimation of the velocity solu-tion in the fluid flow equations. I used a continuous Galerkin formulation to solve the geomechanics equa-tion. These formulations allowed me to use unstructured meshes, a full-tensor permeability, and elastic stiffness. I proposed a numerical upscaling of the permeability and of the elastic stiffness tensors to gener-ate a coarse-scale description of the fine-scale grid in the model, and I implemented the methodology in the simulator. I applied the code I developed to the simulation of the problem of multiphase flow in a fractured tight gas system. As a result, I observed unique phenomena (not reported before) that could not have been deter-mined without coupling. I demonstrated the importance and advantages of using unstructured meshes to effectively and realistically model a reservoir. In particular, high resolution discrete fracture models al-lowed me to obtain more detailed physics that could not be resolved with a structured grid. I performed numerical upscaling of a very heterogeneous geologic model and observed that the coarse-scale numerical solution matched the fine scale reference solution well. As a result, I believed I developed a method that can capture important physics of the fine-scale model with a reasonable computation cost. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/151194
Author: Yanli Pei
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Fluid injection and production in highly fractured unconventional reservoirs could induce complex stress reorientation and redistribution. The strong stress sensitivity of fractured formations may also lead to non-negligible fracture opening or closure under the reservoir loading or unloading process. Hence, a coupled flow and geomechanics model is in high demand to assist with stress prediction and production forecast in unconventional reservoirs. In this dissertation, an enhanced geomechanics model is developed for fractured reservoirs and integrated with the in-house compositional reservoir simulator – UTCOMP for coupled flow and geomechanics modeling. The multiphase flow model is solved using the finite volume method (FVM) with an embedded discrete fracture model (EDFM) to represent flow through complex fractures. Based on static fracture assumption, the finite element method (FEM) is applied to solve the geomechanics model by incorporating fracture effects on rock deformation through pore pressure changes. An iterative coupling procedure is implemented between fluid flow and geomechanics, and the 3D coupled model is applied to predict spatiotemporal stress evolution in single-layer and multilayer unconventional reservoirs. To consider dynamic fracture properties, the geomechanics model is further enhanced by the extended finite element method (XFEM) with a modified linear elastic proppant model. The fracture surface is under the coeffects of pore pressure and proppant particles, and various enrichment functions are introduced to reproduce the discontinuous fields over fracture paths. The enhanced geomechanics model is validated against classical Sneddon and Elliot’s problem and presents a first-order spatial convergence rate. Numerical studies indicate that modeling fracture closure is necessary for poorly propped, highly stressed, or fast depleted reservoirs, and fracture opening can be significant under high permeability and low stiffness conditions. The coupled flow and geomechanics model is finally combined with a displacement discontinuity method (DDM) hydraulic fracture model to establish an integrated reservoir-geomechanics-fracture model for the end-to-end optimization of secondary stimulations. It is applied to Permian Basin and Sichuan Basin tight formations to optimize parent-child well spacing at different infill times. The integrated model provides hands-on guidelines for refracturing and infill drilling in multilayer unconventional reservoirs and can be easily adapted to other basins under their unique data
Author: Pania Newell
Publisher: Elsevier
ISBN: 0128127538
Category : Science
Languages : en
Pages : 447
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Book Description
Science of Carbon Storage in Deep Saline Formations: Process Coupling across Time and Spatial Scales summarizes state-of-the-art research, emphasizing how the coupling of physical and chemical processes as subsurface systems re-equilibrate during and after the injection of CO2. In addition, it addresses, in an easy-to-follow way, the lack of knowledge in understanding the coupled processes related to fluid flow, geomechanics and geochemistry over time and spatial scales. The book uniquely highlights process coupling and process interplay across time and spatial scales that are relevant to geological carbon storage. - Includes the underlying scientific research, as well as the risks associated with geological carbon storage - Covers the topic of geological carbon storage from various disciplines, addressing the multi-scale and multi-physics aspects of geological carbon storage - Organized by discipline for ease of navigation
