Proper characterization of reservoir heterogeneities is a well recognized requirement to predict reservoir performance accurately. Given the large investment requirements, long development schedules, and the often uncertain economic outlook, sound decision making requires reasonable estimates of how much, and when, oil will be produced. It is no longer sufficient to estimate the total oil in place and apply an ad-hoc recovery factor to determine reserves. Average values for properties such as porosity, fluid saturations, and thickness can be used to establish the total amount of fluids in place. However, averages are less reliable once the volumetrics have been estimated; predicting fluid movement within a reservoir is more difficult because flow is greatly influenced by extreme high and low values not well characterized by average quantities. As a result, the general trend in the oil industry has been to underpredict the variability and overpredict the continuity of reservoir properties, which usually results in optimistic predictions of reservoir performance.
Geostatistics offers capabilities for improved reservoir modelling because the algorithms and heuristics apply statistical concepts to geologically based phenomena. However, geostatistics is not a magic solution to all our reservoir characterization problems; data are still required to calibrate parameters and to establish calculation-control points. For situations with minimal control data, geostatistically derived predictions of reservoir properties may not be any better than those obtained with standard mapping techniques. When more data in the form of either increased amounts of well control or seismic attributes that correlate with petrophysical quantities of interest are available, then the geostatistically derived answers become more precise. Uncertainty can be quantified by performing and analyzing multiple, equally probable realizations.
To illustrate the limitations and possible benefits of geostatistics, this paper considers the problem of areal mapping and three-dimensional modeling of reservoir properties for a field with limited well control. The relationship between the amount of well control points and/or the ability to correlate well and seismic data is considered. In this example, increasing the number of well-control points and introducing correlatable seismic attributes had the effect of reducing the uncertainty in the predicted answer at unsampled locations. The accuracy of the answers with II wells and a good seismic-to-well correlation was comparable to those calculated with 199 wells without integrated seismic data.
In addition to improved areal mapping of reservoir properties, it is also important to characterize properly the vertical variation in properties. Vertical heterogeneities strongly affect predictions of fluid flow. In particular, stratification produces preferential flow conduits that result in bypassing portions of the reservoir and early breakthrough of injected fluids at the wells. The results of simple reservoir simulations are presented to illustrate this phenomenon.
Sheldon Gorell is a Senior Staff Engineering Geoscientist at Western Atlas Software in the Western Hemisphere Operations group. He holds a Ph.D. from Stanford University in chemical engineering and has 13 years experience in the petroleum industry, focusing mostly on geostatistics, reservoir engineering and reservoir simulation issues. He is currently involved with software testing, training and marketing, and prototype software development in these areas. Previously he spent nine years at the Shell Development exploration and production research laboratory working in the areas of reservoir simulation, enhanced oil recovery and reservoir characterization for modelling fluid flow.