In recent years, with the increased availability of powerful computers, there has been much emphasis placed on improving the characterization of heterogeneities in reservoirs for simulation purposes. Software packages are becoming available which enable geologists and engineers to combine their field knowledge with the sophisticated techniques of geostatistics to generate stochastic simulations of the geological and petrophysical reservoir data. These simulations produce a (theoretically infinite) number of possible "realizations" of the reservoir, honoring the available data points and having the same histogram and spatial variability as the data. Fluid flow simulations appropriate to the recovery project being evaluated can be performed on an array of possible realizations to give a range of possible outcomes for important quantities such as the oil recovery factor. The object of the procedure is to facilitate a quantification of the uncertainties caused by the lack of detailed knowledge of the reservoir heterogeneity. This paper addresses two difficulties associated with the above procedure - those of "image selection" and "upscaling". The stochastic simulations of the reservoir geology are usually performed on fine-scale grids to incorporate all the lithological data available from logs, cores and seismic. Before performing fluid flow simulations it is necessary to choose a few possible realizations representing the "best", "worst" and "average" cases. This is the problem of image selection. It is also necessary to use averaging procedures for the petrophysical parameters in order to scale the grid to a size accessible to reservoir simulations. This is the problem of upscaling. It is particularly difficult to devise efficient upscaling procedures for permeability because it is a transport parameter. It will be shown how random walk methods provide an efficient and accurate alternative to costly fine-scale finite difference computations for upscaling and image selection in reservoir characterization. Simulations are performed on a variety of different realizations of the permeability distribution, generated by geostatistical, fractal and boolean methods, including the difficult case of sandstone/shale reservoirs. Both 2d and 3d examples are presented. Comparisons are made with finite difference simulations and with a variety of approximate methods suggested in the literature.
Reservoir characterization is the process by which information about the geology and flow properties of a petroleum reservoir (from well-logs, cores, seismic, depositional analysis etc.) is translated into a gridded computer model, suitable for input into reservoir simulators. It is necessary for estimating important production profitability measures such as hydrocarbons-in-place and recovery factors. Conventionally, reservoir characterization has been based on surface modeling - assuming a "layer-cake" model for the reservoir and interpolating surfaces from well data and seismic. Geological information from a study of the depositional environment or from outcrop analogues has been used to shape the model according to the geologists' mental picture. This type of modeling is really the quantification of the geologists' prejudice. It oversimplifies the reservoir geology and results in failures in predicting field performance. It is a major source of error in production forecasts. Conventional modeling has been aided by the development of commercial software packages that are based on modern graphic workstations and incorporate sophisticated data manipulation and 3d visualization techniques.