A Statistical Study of Reservoir Permeability Distributions

A framework is proposed that delimits the range of possible probability density functions (p.d.f.'s) for permeability. Based on two models, the bulk permeability k1 is proposed to have a p.d.f. such that (k1)P is approKimately normally distributed for -1≤p≤+1. The log-normal p.d.f. obtains for p=0. The framework is validated in three ways: (1) The proposal is shown to be self consistent in that combinations of the two models give bulk permeabilities with p.d.f.'s for which -1≤p≤+1; (2) The exponent estimate ß varies between -0.3 and + 1.0 for six data sets; (3) The behavior of several data sets investigated by others is explained by the framework. lntersample correlation does not influence ß for the cases analyzed. A knowledge of ~ for a data set is shown to be useful when estimating average permeabilities and when developing correlations to predict permeability. The behavior of conventional heterogeneity measures with p is studied. A heterogeneity measure which is twice as efficient as the Dykstra-Parsons coefficient is proposed.