Stochastic Models of Reservoir Heterogeneity: Impact on Connectivity and Average Permeabilities

Abstract

Abstract Probabilistic techniques are being increasingly used for modelling reservoir heterogeneity. A wide variety of models are now available, which all differ in their underlying assumptions, range of application, complexity of usage and computer efficiency. Each technique has its own unconditional supporters. However, for the nonspecialist, choosing one method is not trivial. Which method is best suited to a particular modelling context? After all, does it really matters from a practical, engineering point of view? These are the basic questions we are addressing here. After a review of current heterogeneity modelling techniques, a few "classical" models are compared on data from a deep-sea-fan reservoir. Fine scale, three dimensional distributions of permeability are generated using Indicator Simulations, Gaussian/Fractal Simulations and Truncated Gaussian Simulations. Common well log data and geological a priori are used for all methods. The models are then compared in terms of connectivity and distribution of average permeabilities at the scale of full-field flow simulation grid. Connected pore volume geometry on fine grids is found to be quite sensitive to the modelling technique. After upscaling, large scale permeability distributions remain sensibly different. The choice of the stochastic modelling technique has therefore a potentially important, practical impact on reservoir description. Introduction The need to model reservoir heterogeneity on a wide range of scales is now well recognized by most reservoir engineers. Traditional mapping methods, such as kriging, splines or hand contouring, are known to provide artificially and unrealistically smooth representations of reservoir parameters. The degree of smoothness induced by such techniques depends on the number of controlling data and on the distance to the data. Moreover, they can hardly be constrained to a priori geological knowledge on the reservoir internal architecture. These limitations are known to induce potentially important biases in reservoir forecasts. Numerous mapping techniques have been proposed, to overcome these shortcomings and provide more realistic reservoir descriptions. Most of them rely on probability theory, and are thus called Stochastic Modelling techniques. Unfortunately, no ideal technique has been found so far, that would yield the "best" results in all situations. "Which model to choose?" is therefore a critical question for the non-specialist wishing to use stochastic modelling techniques. In the first part, we thus extensively review the existing techniques. The discussion addresses the following issues: domain of application; impact of underlying assumptions on reservoir description data requirements; practical implementation; simplicity of usage computer efficiency. In many practical situations, however, choosing one method may be difficult, simply because several candidates appear equally adequate. But after all, does it really matter? What are the practical implications of the method being used? These questions are addressed through an example presented in part 2. This case study is by no mean general; first because problems in reservoir characterization are highly dependent on the uniqueness of the geological formations and of the available data; second, because just a few techniques, among all available, are being compared. The goal of the study is rather to propose bases for comparing heterogeneity modelling techniques, ideas for evaluating their impact on flow behaviour, and, hopefully, some general guidelines for the non-specialist. Section 2.1 presents the data on which the example is based. Stochastic modelling is discussed in section 2.2. Three methods, Gaussian/Fractal, Truncated Gaussian and Indicator simulations are compared. Comparison criteria are presented and discussed in section 2.3. P. 355^