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 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 Techniques of High Performance Reservoir Simulation for Unconventional Challenges written by Yuhe Wang and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The quest to improve the performance of reservoir simulators has been evolving with the newly encountered challenges of modeling more complex recovery mechanisms and related phenomena. Reservoir subsidence, fracturing and fault reactivation etc. require coupled flow and poroelastic simulation. These features, in turn, bring a heavy burden on linear solvers. The booming unconventional plays such as shale/tight oil in North America demand reservoir simulation techniques to handle more physics (or more hypotheses). This dissertation deals with three aspects in improving the performance of reservoir simulation toward these unconventional challenges. Compositional simulation is often required for many reservoir studies with complex recovery mechanisms such as gas inject. But, it is time consuming and its parallelization often suffers sever load imbalance problems. In the first section, a novel approach based on domain over-decomposition is investigated and implemented to improve the parallel performance of compositional simulation. For a realistic reservoir case, it is shown the speedup is improved from 29.27 to 62.38 on 64 processors using this technique. Another critical part that determines the performance of a reservoir simulator is the linear solver. In the second section, a new type of linear solver based the combinatorial multilevel method (CML) is introduced and investigated for several reservoir simulation applications. The results show CML has better scalability and performance empirically and is well-suited for coupled poroelastic problems. These results also suggest that CML might be a promising way of precondition for flow simulation with and without coupled poroelastic calculations. In order to handle unconventional petroleum fluid properties for tight oil, the third section incorporates a simulator with extended vapor-liquid equilibrium calculations to consider the capillarity effect caused by the dynamic nanopore properties. The enhanced simulator can correctly capture the pressure dependent impact of the nanopore on rock and fluid properties. It is shown inclusion of these enhanced physics in simulation will lead to significant improvements in field operation decision-making and greatly enhance the reliability of recovery predictions. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/151858

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 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 Sequential Fully Implicit Newton Method for Reservoir Simulation written by Jiawei Li (Researcher in energy resources engineering) and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation of compositional flow and transport is critical for numerous applications in reservoir simulation. The nonlinear coupling between thermodynamics, reservoir heterogeneity, and gravitational effects makes developing an efficient nonlinear solver for compositional modeling very challenging. The Fully Implicit (FIM) discretization scheme is extensively employed in the industry, where at each Newton step, a global Jacobian matrix is generated, then the corresponding linear system is solved. FIM can often be extremely costly for field-scale compositional simulations when a large and poorly conditioned linear system needs to be solved with tiny timesteps. The Sequential Fully Implicit (SFI) method has been proposed as a promising alternative solution strategy in which the coupled problem is separated into subproblems and solved implicitly in sequence. The SFI method is more flexible and can adopt different temporal and spatial discretizations, as well as specialized linear solvers and customizable nonlinear formulations for each subproblem. Additionally, it permits the development of multiscale simulation for flow and transport, which is viewed as a computationally more efficient alternative to the single-level fine-scale approach, potentially offering significant performance improvements. However, the SFI method has a critical limitation: slow convergence of the outer loop when the subproblems are tightly coupled. This constraint prevents SFI from achieving robust performance for general flow and transport simulations, limiting the method's applicability. This thesis describes numerical approaches based on the Sequential Fully Implicit Newton (SFIN) method for accelerating the SFI method's outer loop convergence, with the goal of enabling the SFI scheme to attain robust nonlinear performance comparable to the FIM method within tightly coupled scenarios. We first develop the Sequential Fully Implicit Newton (SFIN) method for compositional flow and transport simulation, with the proper consideration of the multi-phase and multi-component phase equilibrium and the fixed total volumetric flux constraint between flow and transport problems. The SFIN method's critical step is a global Newton update at the end of each sequential iteration. The pressure and transport variables are updated concurrently during this outer Newton step to better resolve the coupling. A Krylov solver is used for the associated linear system without constructing explicit Jacobians, relying solely on matrix-vector multiplications. We show that matrix-vector multiplications can be calculated by efficiently reusing previously computed Jacobian matrices and their preconditioners' information. Second, we extend the SFIN method to address its major constraint: the choice of the primary variables for each subproblem has to be fixed during the outer iteration, which includes performing Newton iteration loops for each subproblem. We propose a zero-out strategy to deal with the variables switch, specifically when it happens between flow and transport problems. The extended SFIN method obtains significantly improved nonlinear acceleration performance for natural black oil formulation even in situations with frequent phase changes. After that, we focus on further decreasing the additional computational cost associated with the SFIN method. We propose a reduced SFIN method, which requires solving a reduced SFIN transport linear system with an appropriate existing preconditioner rather than the original SFIN linear system, followed by a single update for the pressure variables, which avoids one of the SFIN method's major costs: inversion of the transport Jacobian matrix in the Krylov solver iterations. Finally, we demonstrate how the SFIN method can be extended to other multi-physics problems. We consider coupled reservoir and multi-segment well simulations and develop a similar SFIN method for the coupling problem. We present several challenging two- and three-dimensional cases and demonstrate that the SFIN approach can dramatically reduce the number of outer and inner loop iterations when compared to the standard (non-accelerated) SFI method.

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 An Introduction to Reservoir Simulation Using MATLAB GNU Octave written by Knut-Andreas Lie and published by Cambridge University Press. This book was released on 2019-08-08 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents numerical methods for reservoir simulation, with efficient implementation and examples using widely-used online open-source code, for researchers, professionals and advanced students. This title is also available as Open Access on Cambridge Core.

Download or read book Iteratively Coupled Reservoir Simulation for Multiphase Flow in Porous Media written by Bo Lu and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully implicit and IMPES are two primary reservoir simulation schemes that are currently used widely. However, neither of them is sufficiently accurate or efficient, 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.

Download or read book General Purpose Compositional Simulation for Multiphase Reactive Flow with a Fast Linear Solver written by Changhe Qiao and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir simulation is an important tool for petroleum engineers to predict oil production andoptimize the management of oil fields. Fluids in oil and gas reservoirs are complex. In many cases,reservoir fluids consist of three or more phases and contain a large number of species that can reactwith each other. Many existing models (black oil, compositional and reactive transport models)were developed to simulate fluids with a specific fluid characterization. In this dissertation, ageneral modeling framework is developed that allows for simulation of different fluid types andprocesses. Based on the general framework we developed a new in-house simulator that we namedPennSim.Reservoir simulators spend over 90% CPU time on the linear solver for reservoir models withover one million grid blocks. The performance of iterative linear solvers depends on the choice ofthe preconditioner, the design of which depends on the knowledge of the PDEs. We designedadvanced multistage preconditioners based on the PDE structure. New decoupling strategies wereproposed for the constraint pressure residual method. Advantageous performance is demonstratedand over three times speed-up is shown.We applied the general modeling framework to design novel models to explore the mechanismsof enhanced oil recovery (EOR). With coupled surface complexation reaction and multiphase flow,we proposed a numerical model for low salinity waterflooding for carbonates. The wettablilityalteration was modeled by detailed description of fluid and surface reactions. Our model is the firstpredictive model for low salinity EOR in carbonates. We also designed the coupled compositionaland reactive model for water-alternating CO2 injection. Injectivity changes were predicted forinjection water with different compositions.This dissertation aims to cover the generic modeling, numerical simulation and fast iterativesolvers for multiphase multicomponent flow and transport in porous media. PennSim wasdeveloped and its manual is available in supplemental materials.

Download or read book An Introduction to Reservoir Simulation Using MATLAB GNU Octave written by Knut-Andreas Lie and published by Cambridge University Press. This book was released on 2019-08-08 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to the simulation of flow and transport in porous media, written by a developer of numerical methods. The reader will learn how to implement reservoir simulation models and computational algorithms in a robust and efficient manner. The book contains a large number of numerical examples, all fully equipped with online code and data, allowing the reader to reproduce results, and use them as a starting point for their own work. All of the examples in the book are based on the MATLAB Reservoir Simulation Toolbox (MRST), an open-source toolbox popular popularity in both academic institutions and the petroleum industry. The book can also be seen as a user guide to the MRST software. It will prove invaluable for researchers, professionals and advanced students using reservoir simulation methods. This title is also available as Open Access on Cambridge Core.

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 Advanced Modeling with the MATLAB Reservoir Simulation Toolbox written by Knut-Andreas Lie and published by Cambridge University Press. This book was released on 2021-11-25 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many leading experts contribute to this follow-up to An Introduction to Reservoir Simulation using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST). It introduces more advanced functionality that has been recently added to the open-source MRST software. It is however a self-contained introduction to a variety of modern numerical methods for simulating multiphase flow in porous media, with applications to geothermal energy, chemical enhanced oil recovery (EOR), flow in fractured and unconventional reservoirs, and in the unsaturated zone. The reader will learn how to implement new models and algorithms in a robust, efficient manner. A large number of numerical examples are included, all fully equipped with code and data so that the reader can reproduce the results and use them as a starting point for their own work. Like the original textbook, this book will prove invaluable for researchers, professionals and advanced students using reservoir simulation methods. This title is available as Open Access on Cambridge Core.

Download or read book Advanced Nonlinear Techniques for Compositional Reservoir Simulation written by Ouassim Khebzegga and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir simulation using high-fidelity fluid models is typically employed to study subsurface displacement processes that involve complex physics. Such processes are highly nonlinear and they occur at the interplay of phase thermodynamics (phase stability and split), and rock/fluid interaction (relative-permeability). Accurate modeling of these processes requires considerable storage and computational resources. In this work, we focus on improving the nonlinear behavior of compositional simulation using two approaches: (1) understanding the nonlinearities related to flow and transport of compositional models, and proposing a robust and efficient solver, and (2) improving the portrayal of the physics of compositional models by designing a consistent and robust relative permeability model. To better characterize the convergence failures of compositional nonlinear solvers, we study the analytical and discrete forms of the component flux functions for the transport problem. We focus on isothermal, two-hydrocarbon phase models in the presence of viscous forces. As described in the literature, our analysis shows that the component flux function exhibits both kinks and inflection points. We study the kinks due to the crossing of phase boundaries, and we show their impact on residual terms. We, then, investigate the location, direction, and evolution of the inflection loci inside the two phase region. Our findings suggest that these inflection loci may exhibit complex features, as a result of which an a priori determination of such loci is computationally prohibitive. We propose a nonlinear solver that detects phase boundaries and guides the Newton update to avoid crossing these boundaries. Our numerical results show that this phase change detection solver has superior performance in comparison with both standard Newton solver and Newton solver with Appleyard chop for a wide range of cases. Due to its nonlinearity, relative-permeability is an important constitutive of the conservation equations and has a significant impact on the performance of a simulation model. Dependence of the phase relative-permeability on fluid compositions, pressure, and temperature is well-documented. In compositional reservoir simulation, however, relative-permeability is typically modeled as a function of phase saturation. Such an approach may lead to serious discontinuities in relative-permeability. To alleviate this issue, several authors have proposed models based on phase state indicators (density, parachor, Gibbs Free Energy). However, such techniques cannot represent the complete degrees of freedom that are exhibited by compositional displacements. In this work, we present a relative-permeability model based on a parameterization of the compositional space. The model is independent of the hydrocarbon phase labeling as gas or oil. We show that our proposed model (1) applies regardless of the degrees-of-freedom of the compositional displacement problem, and (2) is guaranteed to yield a continuous relative-permeability function across the entire compositional space. We have implemented this model in our research simulator, and we present test cases using traditional relative-permeability models, as well as, numerical results that compare the nonlinear performance.

Download or read book Modern Advances in Software and Solution Algorithms for Reservoir Simulation written by Rami Mustafa Younis and published by . This book was released on 2011 with total page 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 Computational Science ICCS 2004 written by Marian Bubak and published by Springer. This book was released on 2004-05-12 with total page 1376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Computational Science (ICCS 2004) held in Krak ́ ow, Poland, June 6–9, 2004, was a follow-up to the highly successful ICCS 2003 held at two locations, in Melbourne, Australia and St. Petersburg, Russia; ICCS 2002 in Amsterdam, The Netherlands; and ICCS 2001 in San Francisco, USA. As computational science is still evolving in its quest for subjects of inves- gation and e?cient methods, ICCS 2004 was devised as a forum for scientists from mathematics and computer science, as the basic computing disciplines and application areas, interested in advanced computational methods for physics, chemistry, life sciences, engineering, arts and humanities, as well as computer system vendors and software developers. The main objective of this conference was to discuss problems and solutions in all areas, to identify new issues, to shape future directions of research, and to help users apply various advanced computational techniques. The event harvested recent developments in com- tationalgridsandnextgenerationcomputingsystems,tools,advancednumerical methods, data-driven systems, and novel application ?elds, such as complex - stems, ?nance, econo-physics and population evolution.

Download or read book SIAM Journal on Scientific Computing written by and published by . This book was released on 2004 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: