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Results
Summary Modern reservoir simulation must handle complex compositional fluid behavior, orders-of-magnitude variations in rock properties, and large velocity contrasts. We investigate how one can use nonlinear domain-decomposition preconditioning to combine sequential and fully implicit (FI) solution strategies to devise robust and highly efficient nonlinear solvers. A full simulation model can be split into smaller subdomains that each can be solved independently, treating variables in all other subdomains as fixed. In subdomains with weaker coupling between flow and transport, we use a sequential fully implicit (SFI) solution strategy, whereas regions with stronger coupling are solved with an FI method. Convergence to the FI solution is ensured by a global update that efficiently resolves long-range interactions across subdomains. The result is a solution strategy that combines the efficiency of SFI and its ability to use specialized solvers for flow and transport with the robustness and correctness of FI. We demonstrate the efficacy of the proposed method through a range of test cases, including both contrived setups to test nonlinear solver performance and realistic field models with complex geology and fluid physics. For each case, we compare the results with those obtained using standard FI and SFI solvers. NOTE: This paper is also published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.
- North America > United States (1.00)
- Europe > United Kingdom > England (0.28)
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Geologic modeling (1.00)
- Reservoir Description and Dynamics > Fluid Characterization > Fluid modeling, equations of state (0.68)
Summary Modern reservoir simulation must handle complex compositional fluid behavior, orders-of-magnitude variations in rock properties, and large velocity contrasts. We investigate how one can use nonlinear domain-decomposition preconditioning to combine sequential and fully implicit (FI) solution strategies to devise robust and highly efficient nonlinear solvers. A full simulation model can be split into smaller subdomains that each can be solved independently, treating variables in all other subdomains as fixed. In subdomains with weaker coupling between flow and transport, we use a sequential fully implicit (SFI) solution strategy, whereas regions with stronger coupling are solved with an FI method. Convergence to the FI solution is ensured by a global update that efficiently resolves long-range interactions across subdomains. The result is a solution strategy that combines the efficiency of SFI and its ability to use specialized solvers for flow and transport with the robustness and correctness of FI. We demonstrate the efficacy of the proposed method through a range of test cases, including both contrived setups to test nonlinear solver performance and realistic field models with complex geology and fluid physics. For each case, we compare the results with those obtained using standard FI and SFI solvers. This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.
- North America > United States (1.00)
- Europe > United Kingdom > England (0.28)
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Geologic modeling (1.00)
- Reservoir Description and Dynamics > Fluid Characterization > Fluid modeling, equations of state (0.68)
Abstract Reservoir simulation is an important component of reservoir development and management. Due to the heterogeneity in the subsurface formation, the accurate representation of the reservoir requires high-resolution geostatistical modeling with extremely large numbers of grid blocks in realistic models, which can be computationally prohibitive. This motivates the development of upscaling methods from fine-scale to coarse-scale by estimating the equivalent permeability. In this work, we have developed a rapid analytical method to increase the absolute permeability of heterogeneous reservoirs. The equivalent permeability for a uniform flow in a given direction is bounded by (1) the harmonic mean of the arithmetic means of the local permeabilities, calculated over each slice of cells perpendicular to the given direction (upper bound), and (2) the arithmetic mean of the harmonic means of the local permeabilities, calculated on each line of cells parallel to the given direction (lower bound). The idea is to take a value between these two bounds, and the weighting coefficient is the key for accurate results. We presented a fast algorithm to estimate the weighting coefficient in the sense of probability expectation. We compared the pressures and velocities calculated from three approaches, the fine-scale model, the coarse-scale model by numerical upscaling, and the coarse-scale model by analytical upscaling. We considered various conditions, including uncorrelated and correlated, isotropic and anisotropic, the effects of permeability variance and grid block geometry. We found that the pressures and velocities calculated from the coarse-scale model by analytical upscaling are very close to those from the coarse-scale model by numerical upscaling, i.e., the analytical method is as accurate as the numerical method, while the former can be O(10) times faster than the latter.
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Information Technology > Scientific Computing (0.57)
- Information Technology > Mathematics of Computing (0.36)
- Information Technology > Modeling & Simulation (0.35)
Summary Simulation problems encountered in reservoir management are often computationally expensive because of the complex fluid physics for multiphase flow and the large number of grid cells required to honor geological heterogeneity. Multiscale methods have been proposed as a computationally inexpensive alternative to traditional fine-scale solvers for computing conservative approximations of the pressure and velocity fields on high-resolution geocellular models. Although a wide variety of such multiscale methods have been discussed in the literature, these methods have not yet seen widespread use in industry. One reason may be that no method has been presented so far that handles the combination of realistic flow physics and industry-standard grid formats in their full complexity. Herein, we present a multiscale method that handles both the most widespread type of flow physics (black-oil-type models) and standard grid formats such as corner-point, stair-stepped, and perpendicular bisector (PEBI), as well as general unstructured, polyhedral grids. Our approach is derived from a finite-volume formulation in which the basis functions are constructed by use of restricted smoothing to effectively capture the local features of the permeability. The method can also be formulated easily for other types of flow models, provided that one has a reliable (iterative) solution strategy that computes flow and transport in separate steps. The proposed method is implemented as open-source software and validated on a number of two- and three-phase test cases with significant compressibility and gas dissolution. The test cases include both synthetic models and models of real fields with complex wells, faults, and inactive and degenerate cells. Through a prescribed tolerance, the solver can be set to either converge to a sequential solution or the fully implicit solution, in both cases with a significant speedup compared with a fine-scale multigrid solver. Altogether, this ensures that one can easily and systematically trade accuracy for efficiency, or vice versa.
- Europe > Norway > Norwegian Sea (0.46)
- Europe > United Kingdom > North Sea (0.28)
- North America > United States > California (0.28)
- Europe > Norway > North Sea (0.28)
- Europe > United Kingdom > North Sea > Southern North Sea > Southern Gas Basin > Silver Pit Basin > Caister Murdoch System (CMS) > Block 44/22a > Watt Field (0.99)
- Europe > United Kingdom > North Sea > Central North Sea > Ness Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Tofte Formation (0.99)
- (9 more...)
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Information Technology > Modeling & Simulation (0.94)
- Information Technology > Software (0.86)
Abstract This paper presents our work on developing a platform for high performance reservoir simulations, which is developed to support the implementation of various reservoir simulators on distributed-memory parallel systems. This platform employs MPI (Message Passing Interface) for communications and OpenMP for shared-memory computation. It provides structured grids due to its simplicity and cell-centered data for each grid cell. The platform has a distributed matrix and vector module and a map module. The map connects the grid and linear system modules. Commonly-used Krylov subspace linear solvers are implemented, including the restarted GMRES method and the BiCGSTAB method. It also has an interface to a parallel algebraic multigrid solver, BoomerAMG from HYPRE. Parallel general-purpose preconditioners and special preconditioners for reservoir simulations are also developed. The numerical experiments show that our platform has excellent scalability and it can simulate giant models with hundreds of millions of grid cells using thousands of CPU cores.
- Europe (0.93)
- Asia > Middle East (0.68)
- North America > United States > Texas (0.46)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (0.68)
- Reservoir Description and Dynamics > Fluid Characterization > Phase behavior and PVT measurements (0.67)
- Reservoir Description and Dynamics > Fluid Characterization > Fluid modeling, equations of state (0.46)
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (0.46)
Summary Flow diagnostics, as referred to herein, are computational tools derived from controlled numerical flow experiments that yield quantitative information regarding the flow behavior of a reservoir model in settings much simpler than would be encountered in the actual field. In contrast to output from traditional reservoir simulators, flow-diagnostic measures can be obtained within seconds. The methodology can be used to evaluate, rank, and/or compare realizations or strategies, and the computational speed makes it ideal for interactive visualization output. We also consider application of flow diagnostics as proxies in optimization of reservoir-management work flows. In particular, by use of finite-volume discretizations for pressure, time of flight (TOF), and stationary tracers, we efficiently compute general Lorenz coefficients (and variants) that are shown to correlate well with simulated recovery. For efficient optimization, we develop an adjoint code for gradient computations of the considered flow-diagnostic measures. We present several numerical examples, including optimization of rates, well placements, and drilling sequences for two- and three-phase synthetic and real field models. Overall, optimizing the diagnostic measures implies substantial improvement in simulation-based objectives.
- Europe > Norway (1.00)
- North America > United States > Texas (0.68)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Tofte Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Not Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Ile Formation (0.99)
- (10 more...)
- Well Drilling > Drilling Operations (1.00)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- (10 more...)
- Information Technology > Modeling & Simulation (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (1.00)
- Information Technology > Software (0.68)
Summary Finding a pressure solution for large and highly detailed reservoir models with fine-scale heterogeneities modeled on a meter scale is computationally demanding. One way of making such simulations less compute-intensive is to use multiscale methods that solve coarsened flow problems by use of a set of reusable basis functions to capture flow effects induced by local geological variations. One such method, the multiscale finite-volume (MsFV) method, is well-studied for 2D Cartesian grids but has not been implemented for stratigraphic and unstructured grids with faults in three dimensions. We present an open-source implementation of the MsFV method in three dimensions along with a coarse partitioning algorithm that can handle stratigraphic grids with faults and wells. The resulting solver is an alternative to traditional upscaling methods, but can also be used for accelerating fine-scale simulations. To achieve better precision, the implementation can use the MsFV method as a preconditioner for Arnoldi iterations using the generalized minimal residual (GMRES) method or as a preconditioner in combination with a standard inexpensive smoother. We conduct a series of numerical experiments in which approximate solutions computed by the new MsFV solver are compared with fine-scale solutions computed by a standard two-point scheme for grids with realistic permeabilities and geometries. On the one hand, the results show that the MsFV method can produce accurate approximations for geological models with pinchouts, faults, and nonneighboring connections, but on the other hand, they also show that the method can fail quite spectacularly for highly heterogeneous and anisotropic systems in a way that cannot efficiently be mitigated by iterative approaches. Thus, the MsFV method is, in our opinion, not yet sufficiently robust to be applied as a black-box solver for models with industry-standard complexity. However, extending the method to realistic grids is an important step on the way toward a fast and accurate multiscale solution of large-scale reservoir models. In particular, our open-source implementation provides an efficient framework suitable for further experimentation with partitioning algorithms and MsFV variants.
- Europe > Norway (0.93)
- North America > United States > Texas (0.46)
- Europe > United Kingdom > North Sea > Central North Sea > Ness Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Tofte Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Not Formation (0.99)
- (7 more...)
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Information Technology > Software (0.86)
- Information Technology > Artificial Intelligence > Representation & Reasoning (0.46)
Multilevel Preconditioners for a New Generation Reservoir Simulator
Wu, Shuhong (State Key Laboratory of EOR, RIPED, PetroChina) | Xu, Jinchao (Penn State Univ.) | Zhang, Chen-Song (Academy of Mathematics and System Sciences) | Li, Qiaoyun (RIPED, PetroChina) | Wang, Baohua (RIPED, PetroChina) | Li, Xiaobo (RIPED, PetroChina) | Li, Hua (RIPED, PetroChina)
Abstract As a result of the interplay between advances in computer hardware, software, and algorithms, we are now in a new era of large-scale simulation. Fine-scale reservoir simulations focus on fine reservoir characterization, accurate flow description, efficient nonlinear and linear solvers, and parallel implementation. In this paper, we discuss a multilevel preconditioner in the new-generation simulator HiSim developed by RIPED, PetroChina. This preconditioner relies on the method of subspace corrections (MSC) to solve large-scale linear systems arising from fully implicit methods in reservoir simulations. Unlike traditional purely algebraic methods, the proposed preconditioner takes into account some of the properties of pressure, saturation, and implicit well variables. We investigate the efficiency and robustness of the proposed method by applying it to a million-cell benchmark problems, and a real-world matured reservoir with high heterogeneity, high water-cut, geological faults, and complex well scheduling. The numerical results indicate that the proposed method is robust with respect to the heterogeneity, anisotropy, and number of wells.
- North America > United States > Texas (0.46)
- Asia > Middle East > Saudi Arabia (0.28)
- North America > United States > California (0.28)
- Europe > Norway > North Sea > Tarbert Formation (0.99)
- Europe > Germany > North Sea > Tarbert Formation (0.99)
- North America > United States > Louisiana > China Field (0.97)
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Fluid Characterization > Phase behavior and PVT measurements (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Conformance improvement (0.87)
- Information Technology > Modeling & Simulation (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning (0.46)
Abstract Finding a pressure solution for large-scale reservoirs that takes into account fine-scale heterogeneities can be very computationally intensive. One way of reducing the workload is to employ multiscale methods that capture local geological variations using a set of reusable basis functions. One of these methods, the multiscale finite-volume (MsFV) method is well studied for 2D Cartesian grids, but has not been implemented for stratigraphic and unstructured grids with faults in 3D. With reservoirs and other geological structures spanning several kilometers, running simulations on the meter scale can be prohibitively expensive in terms of time and hardware requirements. Multiscale methods are a possible solution to this problem, and extending the MsFV method to realistic grids is a step on the way towards fast and accurate solutions for large-scale reservoirs. We present a MsFV solver along with a coarse partitioning algorithm that can handle stratigraphic grids with faults and wells. The solver is an alternative to traditional upscaling methods, but can also be used for accelerating fine-scale simulations. Approximate solutions computed by the new MsFV solver are compared with fine-scale solutions computed by a standard two-point scheme for grids with realistic permeability and geometries. The results show that the MsFV method is suitable for solving realistic permeabilities, but can fail for highly anisotropic systems. The implementation is a suitable framework for further experimentation with partitioning algorithms and MsFV variants. To achieve better precision, the implementation can use the MsFV method as a preconditioner for Arnoldi iterations using GMRES, or for smoothing cycles using Dirichlet Multiplicative Schwarz (DMS).
- Europe (0.29)
- North America > United States > Texas (0.28)
- Geology > Geological Subdiscipline > Stratigraphy (0.68)
- Geology > Structural Geology > Fault (0.46)
- Europe > United Kingdom > North Sea > Central North Sea > Ness Formation (0.99)
- Europe > Norway > North Sea > Tarbert Formation (0.99)
- Europe > Norway > North Sea > Central North Sea > Ness Formation (0.99)
- Europe > Germany > North Sea > Tarbert Formation (0.99)
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
Summary An efficient Two-Stage Algebraic Multiscale Solver (TAMS) that converges to the fine-scale solution is described. The first (global) stage is a multiscale solution obtained algebraically for the given fine-scale problem. In the second stage, a local preconditioner, such as the Block ILU (BILU), or the Additive Schwarz (AS) method is used. Spectral analysis shows that the multiscale solution step captures the low-frequency parts of the error spectrum quite well, while the local preconditioner represents the high-frequency components accurately. Combining the two stages in an iterative scheme results in efficient treatment of all the error components associated with the fine-scale problem. TAMS is shown to converge to the reference fine-scale solution. Moreover, the eigenvalues of the TAMS iteration matrix show significant clustering, which is favorable for Krylov-based methods. Accurate solution of the nonlinear saturation equations (i.e., transport problem) requires having locally conservative velocity fields. TAMS guarantees local mass conservation by concluding the iterations with a multiscale finite-volume step. We demonstrate the performance of TAMS using several test cases with strong permeability heterogeneity and large-grid aspect ratios. Different choices in the TAMS algorithm are investigated, including the Galerkin and finite-volume restriction operators, as well as the BILU and AS preconditioners for the second stage. TAMS for the elliptic flow problem is comparable to state-of-the-art algebraic multigrid methods, which are in wide use. Moreover, the computational time of TAMS grows nearly linearly with problem size.
- North America > United States (1.00)
- Europe (0.93)
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)