Determination of Lithology From Well Logs by Statistical Analysis

Abstract

Summary. This paper presents a method of predicting lithology by statistical analysis of wireline log measurements with calibration to a core lithology standard. Although an example of the technique applied to the Shublik formation of the Prudhoe Bay area, North Slope, AK, is developed and presented, the method can be applied to any field where some core has been taken. The Shublik, a complex mixture of seven clastic and carbonate rock types, presents a common problem: how can the rock lithology presents a common problem: how can the rock lithology best be identified from wireline logs? During recent work on the reservoir description of the Shublik, it became necessary to answer this question. A lithology standard must be available to calibrate against during development of a log model of lithology. For the Shublik, the core available provided an excellent sample of the total formation. Using the statistical technique of discriminant analysis, we were able to evaluate a number of log models and to choose the most appropriate one. The final log model chosen for the Shublik formation works quite well and correctly predicts lithology 75% of the time. Introduction In sedimentary basins with primarily sandstone and shale sequences, mud-log cuttings descriptions are usually adequate for most log interpretation. Log interpretation in complex reservoirs with both clastic and chemical rocks requires better means of lithology identification. Lithology is a necessary first step in any complex log-analysis program. Conventional porosity-log crossplots scaled to mixtures of sandstone, limestone, or dolomite are usually adequate to identify single or dual mineral mixtures. As reservoir lithology becomes more complex and heterogeneous, log crossplots are inadequate in classifying lithology variations. The works of Burke et al. and Clavier and Rust broadened the use of the well log in lithology identification. With the advent of computers for computational work at the wellsite and in the office, the use of more complex methods of lithology prediction can be attained. Delfiner et al. have recently shown how statistical analysis can be applied to the prediction of lithology from well log data. Their method uses a library of identified lithologies to classify well log response into discrete lithologies. Our approach is made more specific to a given field by using only the core data available from that field in building a calibrated well log model. Database Preparation The data base used for modeling the Shublik contains matched core lithology determinations and log data from 32 wells cored completely through the formation. Available logs include sonic, neutron, bulk density, and gamma ray. The Shublik formation has been divided into three zones. Starting from the top, they are Zones A, B, and C. The boundaries have been determined in all wells by characteristic gamma ray log responses; Zone B is marked by high radioactivity. Not all of the seven lithologies occur in every zone; Table 1 shows which lithologies are found in each of the three zones. To be useful, the core data must be depth-matched to the log data in each well. This matching process consisted of using the core gamma log to shift the core into close approximation of its position to the gamma ray log. The second step includes fine-tuning the match by comparing the core laboratory porosities with the sonic transit time and the core grain density with the density log. The resultant pairing of core depth with its associated geologic lithology pairing of core depth with its associated geologic lithology description and the various wireline log responses at 1-ft [0.3-m] intervals for all 2.303 ft [702 m] of core are then maintained as a data base. Statistical Analysis Discriminant analysis is an established method for classifying each observation in a data set into one of a set of mutually exclusive, exhaustive categories (i.e.. each observation is classified into only one category) on the basis of numerical data values. In our application, the categories are the lithologies existing in the Shublik, and the numerical data are the several available well logs and functions of them. Each 1 -ft [0. 3-m] interval of each well will provide one observation. It is assumed that a calibration data set is available that consists of intervals that have been both cored and logged. It is important that the match of log and core data be as accurate as possible. Discriminant analysis is explain in a number of references however, even the most elementary references assume a working knowledge of the application of matrix algebra to the geometry of multidimensional Euclidean space. In this paper, we emphasizean intuitive understanding of how discriminant analysis achieves its goal andpractical considerations in using discriminant analysis in log modeling. Additional discussion of statistical considerations is included in the Appendix. It is useful to compare discriminant analysis with the more familiar technique of multiple regression. In the latter technique, continuous data (e.g., sonic or density logs) might be used to calibrate a single function from which porosity, say, could be calculated from the logs. In discriminant analysis, a separate function is estimated for each of the several categories. Each function is evaluated through application for every observation, and the observation is assigned to the category having the largest function value. In summary, multiple regression uses numerical data to predict values of a numerical variable; discriminant analysis uses numerical data to predict discrete categories. Simple Example Applications The method of discriminant analysis can be understood best through an example. For this purpose, a simple example will be developed with data from only one zone of the Shublik. For simplicity, only three lithologies (limestone, shale, and sideritic mudrock) are used. Available logs include bulk density, sonic, neutron, and gamma ray. For this example, the data base has 81 1 observations for which core lithology and the several log values have been determined. Using One Variable The lithoporosity function, M, is a natural candidate to be a lithology discriminator. M is a function of sonic transit time and bulk density, defined to be independent of porosity. p. 599