Statistically Analyzing Core Data

Abstract

Abstract A knowledge of rock properties is required to predict the size and performance of a hydrocarbon reservoir. The usual methods of establishing rock properties are through analysis of core samples and electric log data. Each method provides a large number of data points from minute segments of the reservoir. Assuming the sampling procedure has provided an unbiased representative set of data, a statistical approach can be applied to the analysis to obtain a characteristic set of representative parameters. Several techniques are available for resolving the collected data into a set of porosity and permeability values. Some methods often require considerable time or more than a layman's knowledge of statistics. A procedure is proposed which emphasis Pearson's system for defining a distribution type and other auxiliary statistical parameters to ascertain the most representative measure for a set of data. This procedure is readily adaptable to computer programming which provides rigorous statistical results in a form that can be analyzed with limited supplemental knowledge. The method minimizes the analysis time required to resolve the data into a meaningful form and is more thorough than a purely empirical approach dependent upon graphic illustrations. Results are presented so that vertical and areal variations in porosities and permeabilities are readily discernible. The method provides for determining effective permeability, or permeability cutoff, resulting in a minimum distortion in the used data and guidelines for considering the adequacy of the sample sizes. Introduction The use Of core analysis to determine representative values for permeability, porosity and fluid saturation is common. There are several methods for determining a numerical representation for these parameters, all of which employ statistical tools to a greater or lesser degree of sophistication. The purpose of this article is to show how the use of more sophisticated statistical methods can accelerate and facilitate the selection of these reservoir measures. The procedure provides the engineer a better opportunity to concentrate on constructing a more accurate representation of the reservoir configuration. Use of an electronic computer is necessary for the full utilization of this procedure. The computer program should generate the frequency tables, statistical measures and Pearson's constants for defining the distribution, thus allowing the selection of the most representative measure. Empirical Statistics The tedium of manually analyzing core data can be eliminated by using a data processing program to resolve the data into a frequency table allowing analysis to proceed immediately. A common method of analysis relies on graphic illustrations for determining the type of distribution and the selection of a representative measure; however, such a method has a tendency to oversimplify and distort because it is intended to be applied to symmetrical distributions. A major consideration in using a computer to generate the frequency tables is determination of the interval size. It is common in the preparation of these tables to employ preset data intervals. If a variable interval is to he used, it is necessary that the data be arrayed for selection of the appropriate interval. Results provided from a preset interval do not always afford the best frequency table and may influence a graphic analysis. Fig. l is a presentation of data having a limited range. Histogram A is this data using 2-percent intervals and covering only four intervals. Histogram B is the same data presented in 1-percent intervals. It is apparent that the 1-percent intervals give a better presentation of the data. Additionally, linearly shifting the intervals can even more appropriately illustrate the distribution characteristics. Fig. 2 is the same data shifted about the mean while retaining the size of the interval. Permeability should generally be transformed to a logarithmic scale for better analysis. Selection of a proper log base is important because the base affects the log data as the interval size affects an arithmetic scale. The graphic method requires that the data can be approximated by a straight line when plotted on probability paper. Certain core data will result in distributions which do not adapt themselves to this procedure. Fig. 3 illustrates both a symmetrical and an asymmetrical distribution. It is difficult to approximate an asymmetrical distribution (Curve A) by a straight line. JPT P. 497ˆ