Download or read book Linear Solution Techniques for Reservoir Simulation with Fully Coupled Geomechanics written by Sergey Klevtsov and published by . This book was released on 2017 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geomechanics in Reservoir Simulation written by Pascal Longuemare and published by Editions TECHNIP. This book was released on 2002 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Development and Application of a Coupled Geomechanics Model for a Parallel Compositional Reservoir Simulator written by Feng Pan and published by . This book was released on 2009 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a stress-sensitive or stress-dependent reservoir, the interactions between its seepage field and in situ stress field are complex and affect hydrocarbon recovery. A coupled geomechanics and fluid-flow model can capture these relations between the fluid and solid, thereby presenting more precise history matchings and predictions for better well planning and reservoir management decisions. A traditional reservoir simulator cannot adequately or fully represent the ongoing coupled fluid-solid interactions during the production because of using the simplified update-formulation for porosity and the static absolute permeability during simulations. Many researchers have studied multiphase fluid-flow models coupled with geomechanics models during the past fifteen years. The purpose of this research is to develop a coupled geomechanics and compositional model and apply it to problems in the oil recovery processes. An equation of state compositional simulator called the General Purpose Adaptive Simulator (GPAS) is developed at The University of Texas at Austin and uses finite difference / finite control volume methods for the solution of its governing partial differential equations (PDEs). GPAS was coupled with a geomechanics model developed in this research, which uses a finite element method for discretization of the associated PDEs. Both the iteratively coupled solution procedure and the fully coupled solution procedure were implemented to couple the geomechanics and reservoir simulation modules in this work. Parallelization, testing, and verification for the coupled model were performed on parallel clusters of high-performance workstations. MPI was used for the data exchange in the iteratively coupled procedure. Different constitutive models were coded into GPAS to describe complicated behaviors of linear or nonlinear deformation in the geomechanics model. In addition, the geomechanics module was coupled with the dual porosity model in GPAS to simulate naturally fractured reservoirs. The developed coupled reservoir and geomechanics simulator was verified using analytical solutions. Various reservoir simulation case studies were carried out using the coupled geomechanics and GPAS modules.

Download or read book Development and Application of a Coupled Geomechanics Model for a Parallel Compositional Reservoir Simulator written by Feng Pan (Ph. D.) and published by . This book was released on 2009 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a stress-sensitive or stress-dependent reservoir, the interactions between its seepage field and in situ stress field are complex and affect hydrocarbon recovery. A coupled geomechanics and fluid-flow model can capture these relations between the fluid and solid, thereby presenting more precise history matchings and predictions for better well planning and reservoir management decisions. A traditional reservoir simulator cannot adequately or fully represent the ongoing coupled fluid-solid interactions during the production because of using the simplified update-formulation for porosity and the static absolute permeability during simulations. Many researchers have studied multiphase fluid-flow models coupled with geomechanics models during the past fifteen years. The purpose of this research is to develop a coupled geomechanics and compositional model and apply it to problems in the oil recovery processes. An equation of state compositional simulator called the General Purpose Adaptive Simulator (GPAS) is developed at The University of Texas at Austin and uses finite difference / finite control volume methods for the solution of its governing partial differential equations (PDEs). GPAS was coupled with a geomechanics model developed in this research, which uses a finite element method for discretization of the associated PDEs. Both the iteratively coupled solution procedure and the fully coupled solution procedure were implemented to couple the geomechanics and reservoir simulation modules in this work. Parallelization, testing, and verification for the coupled model were performed on parallel clusters of high-performance workstations. MPI was used for the data exchange in the iteratively coupled procedure. Different constitutive models were coded into GPAS to describe complicated behaviors of linear or nonlinear deformation in the geomechanics model. In addition, the geomechanics module was coupled with the dual porosity model in GPAS to simulate naturally fractured reservoirs. The developed coupled reservoir and geomechanics simulator was verified using analytical solutions. Various reservoir simulation case studies were carried out using the coupled geomechanics and GPAS modules.

Download or read book Advanced Petroleum Reservoir Simulation written by M. R. Islam and published by John Wiley & Sons. This book was released on 2010-10-26 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Petroleum Reservoir Simulation Add precision and ease to the process of reservoir simulation. Until simulation software and other methods of reservoir characterization were developed, engineers had to drill numerous wells to find the best way to extract crude oil and natural gas. Today, even with highly sophisticated reservoir simulations software available, reservoir simulation still involves a great deal of guesswork. Advanced Petroleum Reservoir Simulation provides an advanced approach to petroleum reservoir simulation, taking the guesswork out of the process and relying more thoroughly on science and what is known about the individual reservoir. This state of the art publication in petroleum simulation: Describes solution techniques that allow multiple solutions to the complete equations, without linearization. Solves the most difficult reservoir engineering problems such as viscous fingering. Highlights the importance of non-linear solvers on decision tree with scientific argument. Discusses solution schemes in relation to other disciplines and revolutionizes risk analysis and decision making. Includes companion software with 3-D, 3-phase multipurpose simulator code available for download from www.scrivenerpublishing.com. By providing a valuable tool to support reservoir simulation predictions with real science, this book is an essential reference for engineers, scientists and geologists.

Download or read book Modern Advances in Software and Solution Algorithms for Reservoir Simulation written by Rami Mustafa Younis and published by Stanford University. This book was released on 2011 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: As conventional hydrocarbon resources dwindle, and environmentally-driven markets start to form and mature, investments are expected to shift into the development of novel emerging subsurface process technologies. While these processes are characterized by a high commercial potential, they are also typically associated with high technical risk. The time-to-market along comparable development pipelines, such as for Enhanced Oil Recovery (EOR) methods in the Oil and Gas sector, is on the order of tens of years. It is anticipated that in the near future, there will be much value in developing simulation tools that can shorten time-to-market cycles, making investment shifts more attractive. There are two forces however that may debilitate us from delivering simulation as a scientific discovery tool. The first force is the growing nonlinearity of the problem base. The second force is the flip-side of a double edged sword; a rapidly evolving computer architecture scene. The first part of this work concerns the formulation and linearization of nonlinear simultaneous equations; the archetypal inflexible component of all large scale simulators. The proposed solution is an algorithmic framework and library of data-types called the Automatically Differentiable Expression Templates Library (ADETL). The ADETL provides generic representations of variables and discretized expressions on a simulation grid, and the data-types provide algorithms employed behind the scenes to automatically compute the sparse analytical Jacobian. Using the library, large-scale simulators can be developed rapidly by simply writing the residual equations, and without any hand differentiation, hand crafted performance tuning loops, or any other low-level constructs. A key challenge that is addressed is in enabling this level of abstraction and programming ease while making it easy to develop code that runs fast. Faster than any of several existing automatic differentiation packages, faster than any purely Object Oriented implementation, and at least in the order of the execution speed of code delivered by a development team with hand-optimized residuals, analytical derivatives, and Jacobian assembly routines. A second challenge is in providing a generic multi-layered software framework that incorporates plug-in low-level constructs tuned to emerging architectures. The inception of the ADETL spurred an effort to develop the new generation AD-GPRS simulator, which we use to demonstrate the powers of the ADETL. We conclude with a thought towards a future where simulators can write themselves. The second part of this work develops nonlinear methods that can exploit the nature of the underlying physics to deal with the current and upcoming challenges in physical nonlinearity. The Fully Implicit Method offers unconditional stability of the discrete approximations. This stability comes at the expense of transferring the inherent physical stiffness onto the coupled nonlinear residual equations that are solved at each timestep. Current reservoir simulators apply safe-guarded variants of Newton's method that can neither guarantee convergence, nor provide estimates of the relation between convergence rate and timestep size. In practice, timestep chops become necessary, and they are guided heuristically. With growing complexity, convergence difficulties can lead to substantial losses in computational effort and prohibitively small timesteps. We establish an alternate class of nonlinear iteration that converges and that associates a timestep to each iteration. Moreover, the linear solution process within each iteration is performed locally. Several challenging examples are presented, and the results demonstrate the robustness and computational efficiency of the proposed class of methods. We conclude with thoughts to unify timestepping and iterative nonlinear methods.

Download or read book New Techniques for Reduced order Modeling in Reservoir Simulation written by Zhaoyang Jin and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir simulation is widely applied for the management of oil and gas production and CO2 storage operations. It can be computationally expensive, however, particularly when the flow physics is complicated and many simulation runs must be performed. This has motivated the development of reduced-order modeling (ROM) procedures, where the goal is to achieve high degrees of computational speedup along with reasonable solution accuracy. In this work we develop and apply two types of ROM methods -- one based on proper orthogonal decomposition (POD) and piecewise linearization, and one based on deep learning. We first develop a POD-based ROM, referred to as POD-TPWL, to simulate coupled flow-geomechanics problems. In POD-TPWL, proper orthogonal decomposition, which enables the representation of solution unknowns in a low-dimensional subspace, is combined with trajectory piecewise linearization (TPWL), where solutions with new sets of well controls are represented via linearization around previously simulated (training) solutions. The over-determined system of equations is projected into the low-dimensional subspace using a least-squares Petrov-Galerkin procedure. The states and derivative matrices required by POD-TPWL, generated by an extended version of Stanford's Automatic-Differentiation-based General Purpose Research Simulator, are provided in an offline (pre-processing or training) step. Offline computational requirements correspond to the equivalent of 5-8 full-order simulations, depending on the number of training runs used. Runtime (online) speedups of O(100) or more are achieved for new POD-TPWL test-case simulations. The POD-TPWL model is tested extensively for a 2D coupled problem involving oil-water flow and geomechanics. It is shown that POD-TPWL provides predictions of reasonable accuracy, relative to full-order simulations, for well-rate quantities, global pressure and saturation fields, global maximum and minimum principal stress fields, and the Mohr-Coulomb rock failure criterion, for the cases considered. A systematic study of POD-TPWL error is conducted using various training procedures for different levels of perturbation between test and training cases. The use of randomness in the well bottom-hole pressure profiles used in training is shown to be beneficial in terms of POD-TPWL solution accuracy. The procedure is also successfully applied to a prototype 3D example case. We next apply the POD-TPWL reduced-order modeling framework to simulate and optimize the injection stage of CO2 storage operations. The use of multiple derivatives, meaning that the linearizations are performed around different training solutions at different time steps, is described and assessed. Two example cases are presented, and the ability of the POD-TPWL model to accurately capture bottom-hole pressure, when time-varying CO2 injection rates are prescribed, is demonstrated. It is also shown that, for these examples, the reduced-order models can provide accurate estimates of CO2 molar fraction at particular locations in the domain. The POD-TPWL model is then incorporated into a mesh adaptive direct search optimization framework where the objective is to minimize the amount of CO2 reaching a target layer at the end of the injection period. The POD-TPWL model is shown to be well suited for this purpose and to provide optimization results that are comparable to those obtained using full-order simulations. POD-TPWL preprocessing computations entail a (serial) time equivalent of about 6.7 full-order simulations, though the resulting runtime speedups, relative to full-order simulation, are about 100--150 for the cases considered. Finally, we develop a new deep-learning-based ROM for reservoir simulation. The reduced-order model is based on an existing embed-to-control (E2C) framework and includes an auto-encoder, which projects the system to a low-dimensional subspace, and a linear transition model, which approximates the evolution of the system states in low dimension. In addition to the loss function for data mismatch considered in the original E2C framework, we introduce a physics-based loss function that penalizes predictions that are inconsistent with the governing flow equations. The loss function is also modified to emphasize accuracy in key well quantities of interest (e.g., fluid production rates). The E2C ROM is shown to have interesting parallels with POD-TPWL. The new ROM is applied to oil-water flow in a 2D heterogeneous reservoir. A total of 300 high-fidelity training simulations are performed in the offline stage, and the network training requires 10-12~minutes on a Tesla V100 GPU node. Online (runtime) computations achieve speedups of O(1000) relative to full-order simulations. Extensive test case results, with well controls varied over large ranges, are presented. Accurate ROM predictions are achieved for global saturation and pressure fields at particular times, and for injection and production well responses as a function of time. Error is shown to increase when 100 or 200 (rather than 300) training runs are used to construct the E2C ROM.

Download or read book Reservoir Simulations written by Shuyu Sun and published by Gulf Professional Publishing. This book was released on 2020-06-18 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir Simulation: Machine Learning and Modeling helps the engineer step into the current and most popular advances in reservoir simulation, learning from current experiments and speeding up potential collaboration opportunities in research and technology. This reference explains common terminology, concepts, and equations through multiple figures and rigorous derivations, better preparing the engineer for the next step forward in a modeling project and avoid repeating existing progress. Well-designed exercises, case studies and numerical examples give the engineer a faster start on advancing their own cases. Both computational methods and engineering cases are explained, bridging the opportunities between computational science and petroleum engineering. This book delivers a critical reference for today's petroleum and reservoir engineer to optimize more complex developments. - Understand commonly used and recent progress on definitions, models, and solution methods used in reservoir simulation - World leading modeling and algorithms to study flow and transport behaviors in reservoirs, as well as the application of machine learning - Gain practical knowledge with hand-on trainings on modeling and simulation through well designed case studies and numerical examples.

Download or read book Use of Streamline Simulation in Large Scale Reservoir geomechanical Modeling of Reservoirs written by Behrooz Koohmareh Hosseini and published by . This book was released on 2015 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing demand for hydrocarbons and decreasing reserves have created the necessity to produce oil and gas more efficiently and economically. Increasingly, oil and gas companies are focusing on unconventional hydrocarbons; oil sands, shales and CBM. For this class of reservoir materials, the geomechanical response of the reservoir can play an important role in the recovery process. For naturally fractured, stress sensitive reservoirs or thermal recovery processes, geomechanical processes play an even greater role in efficient, economic recovery. For simulations of these processes, most research efforts have been focused on reservoir geomechanical simulations using conventional reservoir simulators coupled to geomechanical codes. While coupled reservoir-geomechanics modeling has been recently widely studied in the literature, there is no applicable methodology implemented or proposed to mitigate the challenging computational cost involved with the inclusion of geomechanics in large multimillion-cell reservoirs. Past studies so far have focused on different coupling schemes, but not on the efficient and robust simulation workflows. This research was conducted with the aim of development and application of various different strategies to include geomechanics into reservoir simulation workflows in large scale reservoirs and in a timely fashion process. The research was performed to allow the future simulators to perform high resolution reservoir-geomechanical simulations in a large scale (near field and far field) with long simulation time windows and lowest computational cost. Initially, analytical proxies were developed and recommending for implementation in lieu of complex reservoir simulations. The analytical model was for prediction of heavy oil geomechanical responses everywhere in the reservoir. The model adopted the use of the mathematical domain decomposition technique and a novel temperature front tracking developed in the very early stage of the research. As opposed to classical analytical models, the proxy predicted reservoir flow and mechanical behavior (on a synthetic case geometry with real hydraulic data) everywhere in the reservoir and in dynamic and transient flow regimes. Subsequent research was aimed at reservoir-geomechanics coupled model order reduction by use of a numerical proxy. The proxy took advantage of streamline linear space behavior and power in decomposition of the reservoir domain into sub-systems (delineation/drainage areas). The combination of localization and linearization allowed predicting both mechanical and fluid flow responses of the reservoir with only solving the pressure equation in Cartesian underlying 3D grids and the solution of saturation transport equation along only one streamline. Following this, a streamline-based reservoir-geomechanics coupling was proposed and was implemented within a Fortran-C++ based platform. The new developed technique was compared in terms of computational cost and results accuracy with the conventional hydromechanical coupling strategy that was developed on a C++ based platform by use of collocated FV-FEM discretization scheme. One of the final stages of the research explored different streamline-based reservoir-geomechanics coupling strategies for full-field reservoir simulations. Various coupling strategies including sequential coupling schemes and a semi-fully coupling scheme to embed geomechanics into streamline simulation workflow was developed and performed. Numerical software with advanced GUI was coded on QT programming language (C++ based) developed to couple mechanical simulator to streamline simulation engine. While streamline simulations were the center of the research, the last stage of research was conducted on numerical and physical stability, convergence and material balance errors of SL-based reservoir-geomechanics class of couplings. The results provided a solid foundation for proper selection of time-steps in SL-based coupling to ensure a numerically stable and physically robust hydromechanical simulation. As a result we showed that use of streamline simulation in both proxy forms and simulator forms have significant added value in full-field reservoir-geomechanics simulations.

Download or read book The Mathematics of Reservoir Simulation written by Richard E. Ewing and published by SIAM. This book was released on 2014-12-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the state of the art of the mathematical theory and numerical analysis of imaging. Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging.

Download or read book Sequential implicit Newton s Method for Geothermal Reservoir Simulation written by Zhi Yang Wong and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation of thermal multiphase fluid flow poses significant difficulties for nonlinear solvers. One approach to this problem is to solve the entire nonlinear system of equations simultaneously with a fully coupled method. However, due to the strong coupling and multiphysics interactions between equations, it is difficult to analyze and challenging to design solvers using this fully coupled method. Instead, a sequential-implicit method splits the multiphysics problem into different subproblems so that they can be each solved separately. The research described in this thesis developed and investigated sequential-implicit methods for geothermal simulation. The sequential-implicit method isolates each of the subproblems and enables the use of specialized solvers for each separate subproblem. Once each subproblem is solved in an efficient manner, the entire multiphysics problem is coupled through a sequential-implicit method. However, these sequential-implicit methods can face difficulties converging to the coupled solution. This thesis describes various sequential-implicit methods that reduce the computational cost of subsurface geothermal simulations by improving their nonlinear convergence. This split of the different physics allows for more specialized solvers such as multiscale finite volume or linear solver preconditioning methods to be built upon it. We demonstrated that for sequential-implicit geothermal simulations, a hybrid constraint strategy is necessary. This hybrid approach involves imposing a fixed pressure constraint for single-phase cells (control volumes) and a fixed density for two-phase cells. However, numerical comparisons showed that the outer loop convergence for the hybrid method on complex scenarios performed poorly in comparison to the fully coupled method. To improve on the outer loop convergence, a modified-sequential fully implicit method was investigated. Although the modified sequential-implicit method improves the outer loop convergence, the additional computational cost of the modified-sequential fully implicit method could diminish the gains from the improved convergence. One of the main contributions of this work is the development of a sequential-implicit Newton's method. Sequential-implicit methods often suffer from slow convergence when there is a strong coupling between the individual subproblems. This is due to the slow linear convergence rate of the fixed-point iteration that is used in current sequential-implicit methods. This new sequential-implicit Newton's method follows the same sequential scheme as the current sequential-implicit fixed-point method, but with a faster quadratic convergence rate compared to the current linear convergence rate. This method is not only applicable to geothermal simulation but also to all sequential-implicit multiphysics simulations. We demonstrated the effectiveness of this approach on two different multiphysics porous media problems: flow-thermal in geothermal simulation and flow-mechanics in geomechanics reservoir simulation. The numerical experiments show an improvement in outer loop convergence across all multiphysics problems and test cases considered. For some specific cases where there was a strong coupling, up to two orders of magnitude improvement was seen in the outer loop convergence for the sequential-implicit Newton's method. Following these investigations of the sequential-implicit method, we developed a sequential-implicit nonlinear solver to better solve a condensation problem in fully coupled geothermal simulation. This condensation problem is associated with the flow of cold water into a cell that is at saturated conditions that is also known as a ``negative compressibility'' problem. In order to deal with this problem, the nonlinear solver must be modified. We developed a sequential-implicit nonlinear solution strategy that overcomes this nonlinear convergence problem associated with the condensation front. For one-dimensional problems, this nonlinear solution strategy converged for all timesteps sizes, while the fully coupled strategy only converged for a limited sized timestep. Furthermore, for a two-dimensional heterogeneous problem, the largest Courant-Friedrichs-Lewy (CFL) number for this method is at least an order of magnitude larger than the CFL number that can be used with the fully coupled approach.

Download or read book Linear Solvers and Coupling Methods for Compositional Reservoir Simulators written by Wenjun Li (doctor of engineering.) and published by . This book was released on 2010 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three compositional reservoir simulators have been developed in the Department of Petroleum and Geosystems Engineering at The University of Texas at Austin (UT-Austin): UTCOMP (miscible gas flooding simulator), UTCHEM (chemical flooding simulator), and GPAS (General Purpose Adaptive Simulator). UTCOMP and UTCHEM simulators have been used by various oil companies for solving a variety of field problems. The efficiency and accuracy of each simulator becomes critically important when they are used to solve field problems. In this study, two well-developed solver packages, SAMG and HYPRE, along with existing solvers were compared. Our numerical results showed that SAMG can be an excellent solver for the usage in the three simulators for solving problems with a high accuracy requirement and long simulation times, and BoomerAMG in HYPRE package can also be a good solver for application in the UTCHEM simulator. In order to investigate the flexibility and the efficiency of a partitioned coupling method, the second part of this thesis presents a new implementation using a partition method for a thermal module in an equation-of-state (EOS) compositional simulator, the General Purpose Adaptive Simulator (GPAS) developed at The University of Texas at Austin. The finite difference method (FDM) was used for the solution of governing partial differential equations. Specifically, the new coupled implementation was based on the Schur complement method. For the partition method, two suitable acceleration techniques were constructed. One technique was the optimized choice of preconditioner for the Schur complement; the other was the optimized selection of tolerances for the two solution steps. To validate the implementation, we present simulation examples of hot water injection in an oil reservoir. The numerical comparison between the new implementation and the traditional, fully implicit method showed that the partition method is not only more flexible, but also faster than the classical, fully implicit method for the same test problems without sacrificing accuracy. In conclusion, the new implementation of the partition method is a more flexible and more efficient method for coupling a new module into an existing simulator than the classical, fully implicit method. The third part of this thesis presents another type of coupling method, iterative coupling methods, which has been implemented into GPAS with thermal module, FICM (Fully, Iterative Coupling Method) and GICM (General, Iterative Coupling Method), LICM (Loose, Iterative Coupling Method). The results show that LICM is divergent, and GICM and FICM can work normally. GICM is the fastest among the compared methods, and FICM has a similar efficiency as CFIM (Classic Fully Implicit Method). Although GICM is the fastest method, GICM is less accurate than FICM for in the test cases carried out in this study.

Download or read book Development of a Compositional Model Fully Coupled with Geomechanics and Its Application to Tight Oil Reservoir Simulation written by Yi Xiong and published by . This book was released on 2015 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Principles of Applied Reservoir Simulation written by John R. Fanchi and published by Elsevier. This book was released on 2005-12-08 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulate reservoirs effectively to extract the maximum oil, gas and profit, with this book and free simlation software on companion web site.

Download or read book Parallel Simulation of Coupled Flow and Geomechanics in Porous Media written by Bin Wang and published by . This book was released on 2015 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 geomechanics model, and the thermodynamics model are modularized in the Integrated Parallel Accurate Reservoir Simulator (IPARS) which has been developed at the Center for Subsurface Modeling at the University of Texas at Austin. The IPARS framework handles structured (logically rectangular) grids and was originally designed for element-based data communication, such as the pressure data in the flow models. To parallelize the node-based geomechanics model, we enhance the capabilities of the IPARS framework for node-based data communication. Because the geomechanics linear system is more costly to solve than those of flow and thermodynamics models, the performance of linear solvers for the geomechanics model largely dictates the speed and scalability of the coupled simulator. We use the generalized minimal residual (GMRES) solver with the BoomerAMG preconditioner from the hypre library and the geometric multigrid (GMG) solver from the UG4 software toolbox to solve the geomechanics linear system. Additionally, the multilevel k-way mesh partitioning algorithm from METIS is used to generate high quality mesh partitioning to improve solver performance. Numerical examples of coupled poromechanics and thermoporomechanics simulations are presented to show the capabilities of the coupled simulator in solving practical problems accurately and efficiently. These examples include a real carbon sequestration field case with stress-dependent permeability, a synthetic thermoporoelastic reservoir simulation, poroelasticity simulations on highly distorted hexahedral grids, and parallel scalability tests on a massively parallel computer.

Download or read book Mathematical Models and Finite Elements for Reservoir Simulation written by G. Chavent and published by Elsevier. This book was released on 1986-01-01 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulators for oil reservoirs have been developed over the last twenty years and are now widely used by oil companies. The research, however, has taken place largely within the industry itself, and has remained somewhat inaccessible to the scientific community. This book hopes to remedy the situation by means of its synthesized presentation of the models used in reservoir simulation, in a form understandable to both mathematicians and engineers.The book aims to initiate a rigorous mathematical study of the immiscible flow models, partly by using the novel `global pressure' approach in treating incompressible two-phase problems. A finite element approximation technique based on the global pressure variational model is presented, and new approaches to the modelling of various kinds of multiphase flow through porous media are introduced.Much of the material is highly original, and has not been presented elsewhere. The mathematical and numerical models should be of great interest to applied mathematicians, and to engineers seeking an alternative approach to reservoir modelling.

Download or read book Reservoir Simulation written by Zhangxin Chen and published by SIAM. This book was released on 2007-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with an overview of classical reservoir engineering and basic reservoir simulation methods, this book then progresses through a discussion of types of flows - single-phase, two-phase, black oil (three-phase), single phase with multi-components, compositional, and thermal. The author provides a thorough glossary of petroleum engineering terms and their units, along with basic flow and transport equations and their unusual features, and corresponding rock and fluid properties. The book also summarises the practical aspects of reservoir simulation, such as data gathering and analysis, and reservoir performance prediction. Suitable as a text for advanced undergraduate and first-year graduate students in geology, petroleum engineering, and applied mathematics; as a reference book; or as a handbook for practitioners in the oil industry. Prerequisites are calculus, basic physics, and some knowledge of partial differential equations and matrix algebra.