Summary and Introduction from the First Annual Report covering the period from June 1, 1995 - May 31, 1996.
This research consists of development and implementation of several key issues in the petroleum reservoir simulation area into an Integrated Parallel Accurate Reservoir Simulator (IPARS). This is the goal of the Advanced Computational Technology Initiative (ACTI) project for the New Generation Framework for Petroleum Reservoir Simulation. Development of the IPARS framework, which is intended to support a variety of reservoir simulation models on both parallel and single processor computers as well as generalized well management, has been partially completed. The code for this framework is written for a distributed memory, message passing computers. The code is being tested by porting an existing chemical flooding simulator, UTCHEM, under the framework. Preliminary results indicate that the design of the IPARS framework is suitable for both the new generation code being developed and for existing simulators.
In addition, IPARS is being coupled with an enhanced version of DAGH (Distributed Adaptive Grid Hierarchies), an object-oriented infrastructure providing support for parallel adaptive computations using hierarchical adaptive mesh-refinements and multigrid techniques. DAGH forms the foundational layer of a computational toolkit for the Binary Black-Hole NSF Grand Challenge project. This effort involves integrating the domain-specific features of IPARS and the convenience of its high-level interface, with efficient distributed dynamic data-management provided by DAGH. The goal is to develop a complete problem solving environment for the development and execution of computational experiments on models of subsurface reactive flow systems. Enhancements to the infrastructure being considered include a real-time graphical interface for interactive experimentation and visualization.
During the first year of the research program, we have also completed the mathematical formulation of a fully implicit equation of state (EOS) compositional model with capability of reducing it to a black-oil model. Algorithms for several important fluid-related calculations such as phase-stability analysis, flash calculation and phase-state identification have been developed and tested. Early results show that the algorithms for these tasks are robust and efficient compared to more traditional approaches.
Investigation of discretization schemes for the fully implicit EOS compositional model using higher-order flux limited schemes on adaptive grids and implementation of a parallel distributed-adaptive-grid-hierarchy (DAGH) software has made considerable progress as well. Two codes for solving a scalar conservation law have been written to test the hierarchy of the DAGH package. Preliminary results for a Buckley-Leverett problem indicate the potential of the hierarchy.
Development of logically rectangular multiblock discretizations for handling complex geometries has achieved promising results. We have developed and analyzed accurate and globally conservative methods for connecting multiblock grids through the use of special elements that are defined in the cracks between blocks. We noted that the grids on different blocks do not have to "match-up,'' thus allowing substantial freedom in defining the grid within each block. On each block, an expanded mixed finite element method is used to spatially discretize the flow equations on a logically rectangular grid that is mapped to a regular rectangular grid. The expanded mixed method reduces to a cell-centered finite difference method on each block and easily handles full permeability tensors while still preserving O(h2) accuracy. These schemes have been implemented for single-phase flow and numerical results confirm their accuracy and conservation properties.
Investigation of less implicit time-stepping approach has also been performed by studying efficient nonlinear and linear iterative strategies for the fully implicit formulation. We have studied Newton/Krylov methods, where a global Newton method with linesearch backtracking and forcing term selection is used to perform the nonlinear iteration. Within each nonlinear iteration, a Krylov iterative method such as GMRES or BiCGSTAB is used to solve the Jacobian system. Effective and parallel preconditioners for these methods have been investigated and are being implemented in a simulator for further test.
Enhancement to the linear and nonlinear solvers of the Portable Extensible Toolkit for Scientific computation (PETSc) software package has also made significant progress. We have focused on the design and implementation of efficient, practical, and scalable preconditioners, use of computer memory hierarchies, flexible and scalable nonlinear solvers based on Newton-like methods, and flexible code for time evolution of discrete partial differential equation problems. Some of the direct and iterative linear solvers have been tested on both sequential and parallel computers for their efficiency and robustness. Tests by direct insertion the linear solvers in two existing simulators, UTCHEM, and an EOS compositional simulator, UTCOMP, show that the linear solvers are robust and efficient compared to those originally implemented in the simulators.
Another accomplishment is the development of a geostatistically-based upscaling technique for multiphase flow in heterogeneous reservoirs. Using geostatistical tools, the method constructs layered models for the absolute permeability field, which are then employed to obtain the effective permeability by minimizing a flow residual between runs with fine and coarse grids. Satisfactory results were obtained for two-phase problems involving a wide range of correlation lengths. Extension of the method to three-phase flow is underway.
The interpretation of partitioning tracer tests using the method of inverse modeling with genetic algorithms has yielded promising results. The approach being developed will take account of the stochastic nature of the inverse problem.
The overall objective of this research is to develop a new-generation framework for reservoir simulator suitable for massively parallel computers and clusters of heterogeneous workstations. The next generation of reservoir simulators will need to be able to run realistic high-resolution reservoir studies; to model complex physical processes in a realistic manner; to perform conditional simulation efficiently and rapidly; and to integrate field management constraints both at the surface and subsurface. These requirements raise a variety of research problems, and the tools being developed in this project will initially serve as vehicles for studying ideas and algorithms aimed at these problems.
Several important aspects of this research program in the petroleum reservoir simulation area are
All of these tasks have been initiated and some of the tasks have been simultaneously carried out by the research teams at Argonne National Laboratory and The University of Texas at Austin during the first year of the program. The work plan and status of the project has been efficiently managed and monitored at these two research institutions with collaboration with industrial partners of the project.
In this report, we will detail our progress for the above tasks for the first year of the project. Section 1 describes the structure of the IPARS framework. Section 2 gives the governing equations for characterizing multiphase, multicomponent flow problems in a porous medium and solution procedure to these equations. Algorithms for some important fluid-related calculations are also included in this section. Section 3 details discretization schemes for the fully implicit EOS compositional model using higher-order flux limited schemes on adaptive grids, and mixed finite element method for flow in heterogeneous multiblock domains. Dynamic local mesh refinement using a parallel distributed-adaptive-grid-hierarchy (DAGH) software is given in Section 4. Section 5 summarizes our efforts on the development, enhancement, and testing of efficient and parallel linear and nonlinear solvers of the PETSc package for the simulator. The development of a geostatistically-based upscaling technique for multiphase flow in heterogeneous reservoirs is described in Section 6. Section 7 shows the progress in the development of a stochastic optimization approach to the solution of reservoir and aquifer characterization problems using partitioning interwell tracer test data using genetic algorithms.
For a copy of the full report, write to:
Gary A. Pope
Center for Petroleum & Geosystems Engineering
The University of Texas at Austin
CPE 2.502
Austin, TX 78712
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