Production Engineering and Research - A Statistical Approach to the Interstitial Characteristics of Sand Reservoirs (T.P. 1732, Petr. Tech., May 1944) (With discussion)

Problems of oil recovery are attacked from the approaches dictated by the two strikingly dissimilar complexes that comprise an oil reservoir—the fluid complex and the interstitial complex. Knowledge of the fluid complex, due to labors in the fields of fluid mechanics and physical chemistry, has far outdistanced knowledge of the interstitial characteristics of the sand complex. This paper is concerned with the latter and applies the technique of statistics to petrographic facts—namely, porosity and permeability—dealing with what might be called petrometry. Statisticians have long worked within the problem of reconstruction of a universe oi variables by means of samples that comprise a small percentage of the universe from which the samples were drawn. Core-analysis data comply with the requisite of random sampling as stipulated by theoretical statistics. A basic concept of statistics employs t.he following substitution: 1. The results of sampling are arranged as a frequency distribution. 2. The observed frequency distribution is compared with a mathematically precise distribution. 3. If a sufficiently good agreement is found between the two, the precise distribution is substituted in all subsequent operations involving characteristics 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 is describable with but two figures. Further, these two figures, the arithmetic average and the standard deviation, are subject to mathematical manipulation. This paper demonstrates that, in some cases in the Dominguez field of Southern California, if sufficient core-analysis samples are taken over not too great a thickness of sediments, the resultant permeability and porosity assemblages give satisfactory agreement with ilormal curves. It is shown that the indications are strong that oil wells wherein a satisfactory agreement is found are predictable as to productivity. Since the predictions are made by employing the laws of chance that are operative within sedimentation, it follows that the mechanism by which the predictions were made is a basic concept of reservoir mechanics. Therefore, tentative examples are given of the application of normal curves to the solution of problems of primary and secondary recovery. Nature of Permeability Frequency Distributions Core-analysis data are made available as a tabulated depth vs. permeability profile. The nature of the distribution of permeability values within a given strati-graphic interval may be approximated from an array constructed with samples plotted in the order of their appearance with depth (accession number) against their permeability value in millidarcys. A wide variation in the nature of the distribution of K (permeability) values for