Summary
Scale up and parallel reservoir simulation represent two distinct approaches for the simulation of highly detailed geological or geostatistical reservoir models. In this paper, we discuss the complementary use of these two approaches for practical, large scale reservoir simulation problems. We first review our recently developed approaches for upscaling and parallel reservoir simulation. Then, several practical large scale modeling problems, which include simulations of multiple realizations of a waterflood pattern element, a four well sector model, and a large, 130 well segment model, are addressed. It is shown that, for the pattern waterflood model, significantly coarsened models provide reliable results for many aspects of the reservoir flow. However, the simulation of at least some of the fine scale geostatistical realizations, accomplished using our parallel reservoir simulation technology, is useful in determining the appropriate level of scale up. For models with a large number of wells, the upscaled models can lose accuracy as the grid is coarsened. In these cases, although field-wide performance can still be predicted with reasonable accuracy, parallel reservoir simulation is required to maintain sufficiently refined models capable of accurate flow results on a well by well basis. Finally, some issues concerning the use of highly detailed models in practical simulation studies are discussed.
Introduction
Reservoir description and flow modeling capabilities continue to benefit from advances in computing hardware and software technologies. However, the level of detail typically included in reservoir characterizations continues to exceed the capabilities of traditional reservoir flow simulators by a significant margin. This resolution gap, due to the much larger computational requirements of flow simulation, has driven the development of two specific technologies: scale up and parallel reservoir simulation. These two technologies represent very distinct approaches—scale up methods attempt to coarsen the simulation model to fit the hardware, while parallel reservoir simulation technology attempts to extend computing capabilities to accommodate the detailed model.
The purpose of this paper is to present and discuss ways in which to utilize these two technologies in a complementary fashion for the solution of practical large scale reservoir simulation problems. Toward this end, we first discuss our previously developed capabilities for scale up1,2 and parallel reservoir simulation.3 Next, the two technologies are applied to several reservoirs represented via highly detailed (i.e., on the order of 1 million cells) geostatistical models. Various production scenarios are considered. It will be shown how the direct simulation of the highly detailed models (using parallel reservoir simulation technology on an IBM SP) can be used to assess and guide the scale up procedure and to establish the appropriate level of coarsening allowable. We will show that, once this level is established, upscaled models can be used to evaluate multiple geostatistical realizations.
We additionally apply the detailed simulation results to develop general guidelines for the degree of scale up allowable for various types of simulation models; e.g., pattern, sector and large segment models. Our general conclusion is that our scale up technology, as currently used, is quite reliable when sufficient refinement is maintained in the coarsened model. We show that when many wells are to be simulated, the upscaled models can begin to lose accuracy, particularly when well by well production is considered. This is due in part to the fact that, in the coarse models, wells are separated by very few grid blocks, and degradation in accuracy results.
There have been many previous studies directed toward the development of parallel reservoir simulation technology and many studies aimed at the development of scale up techniques. To our knowledge, this is the first effort that considers the complementary use of both. Here we will very briefly review the recent literature on both parallel reservoir simulation and upscaling techniques. For more complete discussions of previous work, refer to Refs. 1-3.
Traditional techniques for upscaling rely on the use of pseudorelative permeabilities. Although often applied in practice, the use of pseudorelative permeabilities can lead to inaccuracies in some cases.4,5 This is largely due to the high degree of process dependency inherent in the pseudorelative permeability approach; i.e., pseudorelative permeability curves are really only appropriate for the conditions for which they are generated. The deficiencies in the traditional pseudorelative permeability methodology have motivated work in several areas. This includes the generation of more robust pseudorelative permeabilities,6,7 the use of higher moments of the fine scale variables,5 and the nonuniform coarsening approach applied in this study (discussed in Nonuniform Coarsening Method for Scale Up). Generalizations of the nonuniform coarsening approach described in Refs. 1 and 2 have also been presented.8,9
Parallel reservoir simulation is an area of active research. Recent publications emphasize the development of scalable algorithms designed to run efficiently on a variety of parallel platforms.10–13 Most recent implementations involve distributed memory platforms such as a cluster of workstations. The typical size of a simulation model run in parallel is on the order of 1 (or a few) million grid blocks, though results for a 16.5 million cell model have been reported.11 Most parallel implementations are based on message passing techniques such as the message passing interface standard (MPI). Several of the parallel simulation algorithms, including our own, are based on a multilevel domain decomposition approach. This entails communication between domains in a manner analogous to that used in standard domain decomposition approaches.
Multi-Fidelity Bayesian Approach for History Matching in Reservoir Simulation
