Constraining Description of Randomly Heterogeneous Reservoirs to Pressure Test Data: A Monte Carlo Study

Abstract

ABSTRACT Stochastic simulation techniques are increasingly used to model reservoir heterogeneity. However, the value of such techniques depends largely on their ability to provide models of reservoir properties that are conditioned to all available information. In particular, pressure test data impose constraints on the permeability distribution around the corresponding wells. More precisely, the permeability derived from the analysis of a pressure curve is viewed as a permeability average in the vicinity of the well. A Monte-Carlo methodology is proposed in this study to characterize such averaging. Several permeability fields corresponding to various distribution models are generated using geostatistical simulation techniques. A pumping test is numerically simulated in each of these laterally non-uniform reservoirs, then analyzed automatically with a type-curve fitting algorithm to estimate the apparent permeability around the well. For each permeability distribution model considered, this analysis allows defining the volume of averaging as well as the type of permeability averaging to be applied within such volume. The volume of averaging is found approximately independent of the underlying permeability distribution model and smaller than that given by traditional definitions of radius-of-drainage. Within such volume and for practical test durations, the averaging relating small scale permeabilities to well test permeabilities largely depends on the statistical characteristics of the permeability field and may significantly differ from the traditional geometric mean. This averaging is particularly sensitive to the intensity and spatial connectivity of permeability variations. The averaging formula quantified by such study can be used for conditioning stochastic permeability fields to pressure test information. Selective sampling schemes based upon simulated annealing can be applied within the geostatistical simulation algorithm to force the generated permeability fields to locally match any particular average imposed by well test data.