Asymptotic Dykstra-Parsons Estimates and Confidence Intervals

Abstract

The Dykstra-Parson (DP), the most popular heterogeneity static measure among petroleum engineers, may be at a significant error, in particular when assumptions are made about the permeability distribution (parametric approaches) that may lead to unrealistic reservoir performance predictions and unsuccessful development plans. This paper presents the development of an asymptotic distribution of the Dykstra-Parsons coefficient that is independent of the probability distribution of the permeability variable. The effectiveness (bias and confidence intervals) of the proposed approach is demonstrated by comparing the results those obtained using the classical method, and well-known parametric methods, under different scenarios of reservoir maturity levels (i.e., number of wells), and degree violations of the log-Normal probability density function assumption. The results show that in the vast majority of the case studies the proposed approach outperformed previously reported methods, in particular, resulted in a significant reduction of the bias and, with confidence intervals always including the estimated DP coefficient. In addition, an excellent agreement was observed between the asymptotic cumulative distribution of the DP coefficient and the corresponding empirical distribution for sample sizes as low as 100, which allows classifying reservoirs according to their DP coefficient with high success rates.