A Statistical Approach to the Interstitial Heterogeneity of Sand Reservoirs

Abstract

Problems of oil recovery are attacked from the approaches dictated by thetwo strikingly dissimilar complexes that comprise an oil reservoir-the fluidcomplex and the interstitial complex. Knowledge of the fluid complex, due tolabors in the fields of fluid mechanics and physical chemistry, has faroutdistanced knowledge of the interstitial characteristics of the sand complex.This paper is concerned with the latter and applies the technique of statisticsto petrographic facts-namely, porosity and permeability-dealing with what mightbe called petrometry. Statisticians have long worked within the problem of reconstruction of auniverse of variables by means of samples that comprise a small percentage ofthe universe from which the samples were drawn. Core analysis data comply withthe requisite of random sampling as stipulated by theoretical statistics. Abasic concept of statistics employs the following substitution:The results of sampling are arranged as a frequency distribution.The observed frequency distribution is compared with a mathematicallyprecise distribution.If a sufficiently good agreement is found between the two, the precisedistribution is substituted in all subsequent operations involvingcharacteristics of the sampled material. This mathematically precise distribution is also known as the normal curve, curve of error, the probability, the Gaussian, and the bell-shaped curve and isdescribable with but two figures. Further, these two figures, the arithmeticaverage and the standard deviation, are subject to mathematicalmanipulation. This paper demonstrates that, in some cases in the Dominguez field of SouthernCalifornia, if sufficient core-analysis samples are taken over not too great athickness of sediments, the resultant permeability and porosity assemblagesgive satisfactory agreement with normal curves. It is shown that the indications are strong that oil wells wherein asatisfactory agreement is found are predictable as to productivity. Since thepredictions are made by employing the laws of chance that are operative withinsedimentation, it follows that the mechanism by which the predictions were madeis a basic concept of reservoir mechanics. Therefore, tentative examples aregiven of the application of normal curves to the solution of problems ofprimary and secondary recovery. Nature of Permeability Frequency Distributions Core-analysis data are made available as a tabulated depth vs. permeabilityprofile. The nature of the distribution of permeability values within a givenstratigraphic interval may be approximated from an array constructed withsamples plotted in the order of their appearance with depth (accession number)against their permeability value in millidarcys. T.P. 1732