Effect of Scale Up and Aggregation on the Analysis of Interference Tests

Abstract

The objectives of this paper are to demonstrate the impact of detailed and small-scale heterogeneities upon interference tests. Specific issues encountered when interference tests are analyzed in reservoirs with complex geological properties are discussed. These issues relate to questions concerning the use of low-resolution models, the degree of aggregation, methodology of scale up and the reliability of conventional methods of analysis. Introduction This work provides guidelines concerning the evaluation of interference or pulse tests in reservoirs with complex geology. In the process, the paper demonstrates the role of small-scale heterogeneities on the responses of interference tests and how those heterogeneities may affect the analysis of a test. In the past, it has been suggested that interference and pulse tests provide a better measure of reservoir heterogeneity.1 Our work also permits us to examine the consequences of working with a low vertical resolution as is normally done in most analyses. It is important to recognize the choice of this kind of model because the consequences of such a choice have a significant bearing on the spatial and petrophysical relationships we wish to determine. The importance of not ignoring the vertical resolution is demonstrated. The choice we make regarding the scale at which we analyze data influences the characteristics of the model we use to describe the reservoir, and this in turn will have a significant bearing on our evaluation of fluid movement in injection-production schemes. In doing so, we also illustrate the consequences of aggregation and scale up. The results of this study were obtained by the model given in Christie and Blunt2 as it provides information on a very fine scale and is thus particularly suited to meet the goals of this study. Literature Review The issue of heterogeneity as it relates to well performance and pressure tests may be traced to Cardwell and Parsons.3 Using deterministic methods, these authors considered steady, radial flow to a well in a reservoir in the form of a circle, and showed that the equivalent transmissivity, Te, (kh/μ) is bounded by the volume-weighted arithmetic and harmonic means. The earliest work on statistical methods that is the most often quoted is that of Warren and Price.4 On the basis of numerical experiments of pressure-buildup tests, they concluded that a porous medium that is assumed to consist of a quilt or patchwork of porous elements that are randomly distributed in 3D may be represented by a porous rock with a permeability equal to the geometric mean of the permeability of the individual elements. Although Warren and Price4 do not specifically recognize that the properties of rocks are usually correlated, at least weakly, on all scales, it has been shown that the effective permeability, keq, of a 2D system under the assumption that the porous body is a lognormal, sub isotropic and ergodic medium is equal to the geometric mean of the permeability of the individual elements. For 3D systems, however, their result is only approximately correct.5 Technically, one should expect the equivalent permeability to be tensor.6