Abstract

Significant uncertainty exists in the detailed 3-D distribution of lithofacies, porosity, and permeability in every reservoir. Understanding and modeling the heterogeneous 3-D distribution of these rock properties is critical for improved oil recovery and reservoir management. Geostatistical techniques are being increasingly used to generate alternative heterogeneous 3-D reservoir models that are consistent with the available data.

Although a large number of stochastic reservoir models or realizations may be available, a small number of realizations are considered in practice. Due to computer limitations, it is only possible to visualize and perform fine-scale full-field flow simulation on a limited number of realizations. Techniques are reviewed in this paper for ranking a suite of geostatistical realizations so that low-side, expected, and high-side realizations may be reliably chosen. Detailed analysis/flow simulation may then be performed on these realizations that somehow bound the uncertainty in the reservoir. Reservoir management is improved when expected and bounding cases are considered rather than using a limited number of "random" realizations.

This paper reviews a number of methods for ranking geostatistical reservoir models. These methods may be classified into three categories. The first category includes statistical methods such as simple statistics, 3-D measures of connectivity, and connectivity to specific well locations. Methods in the second class are based on approximations to flow simulation, e.g., random walk-type results. The third category is for flow-simulation based methods for a simpler process than that being considered for improved oil recovery, e.g., tracer simulation and flow simulation with coarsened models. The applicability of a number of ranking methods is illustrated with a small example.

There is no unique ranking index when there are multiple flow response variables and no ranking measure is perfect. Nevertheless, the value of ranking realizations will be quantified by examining the expected loss knowing an economic loss function and the true distribution of uncertainty.

Introduction

The primary objective of the application of geostatistical tools for reservoir modeling is to create realistic numerical geological models or realizations of the 3-D spatial distribution of lithofacies, porosity. and permeability. An often disturbing fact of geological reservoir modeling is that there are alternative realizations that honor all of the available data equally well and yet yield different reservoir performance predictions. In fact, it is often advertised that "a different realization can be obtained by simply changing a random number seed".

A fundamental principle of geostatistics is that of data integration, i.e., all known data should be honored "by construction" and not left to chance. Of course, this is not always possible; it is difficult to constrain detailed 3-D geological realizations to seismic and historical production data. We are restricting ourselves to plausible realizations. There are times when certain realizations would be rejected on the basis of familiarity with the reservoir or data not used in the geostatistical modeling such as production-related historical observations. We are not considering the rejects; only those realizations that meet all basic requirements of reasonableness are considered.

Exact prediction / decision making would require exhaustive knowledge of the spatial distribution of porosity and permeability. At any specific instant in time, there is such a single true distribution of petrophysical properties. This true distribution was created by the complex interaction of many different chemical, physical. and biological processes over geological time and would be accessible only through exhaustive sampling. In all practical situations, the unique true distribution will remain unknown.

This paper addresses the uncertainty due to incomplete information. We do not consider uncertainty due to

  1. the volume support or scale difference between core measurements and geological modeling cells,

  2. the limited flexibility of our geostatistical modeling techniques to reproduce complex nonlinear features, or

  3. numerical approximations in the subsequent flow simulator.

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