Estimation of Permeability from Wireline Logs in a Middle Eastern Carbonate Reservoir Using Fuzzy Logic

Abstract

Abstract Permeability is one of the most difficult properties to predict, especially in carbonate reservoirs. The most reliable data of permeability, obtained from laboratory measurements on cores, do not provide a continuous profile along the depth of the formation. This paper presents the use of fuzzy logic modeling to estimate permeability from wireline log data in a Middle Eastern carbonate reservoir. In this study, correlation coefficients are used as criteria for checking whether a given wireline log is suitable as an input for fuzzy logic modeling. The coefficients are enhanced if they are evaluated with respect to the logarithm of core-based permeability values of the given well. After training the fuzzy model on a layer in a given well, permeability predictions were made for other layers in the same well. These predictions were in excellent agreement with permeability values obtained from cores. It was also observed that Subtractive Clustering technique gives better predictions of permeability when compared with Grid Partitioning technique. A parametric study was also conducted to see the effect of type and number of membership functions, combination of log input parameters, and data size on predictions of permeability. The possibility of training the fuzzy program on one well and testing it for other wells in the same formation is also explored. Introduction Reality does not work in black and white but in shades of grey. Fuzzy logic uses the benefits of approximate reasoning. It simulates the human expert's reasoning process much more realistically than do conventional expert systems. It is an efficient tool for modeling the kind of uncertainty associated with vagueness, imprecision, and/or a lack of information regarding a particular problem. Fuzzy logic is simply an application of recognized statistical techniques. Recently, fuzzy logic has achieved considerable attention in several areas of geosciences. The oil industry has shown considerable interest in the fuzzy logic technique to predict permeability in un-cored wells. Fuzzy logic is simply an application of recognized statistical techniques and is an extension of conventional Boolean logic (zeros and ones) developed to handle the concept of partial truth, i.e., values between complete truth (ones) and totally false (zeros). This paper presents fuzzy logic modeling to predict permeability using conventional open-hole logs. Literature Review Permeability prediction is a challenge to reservoir engineers due to the lack of tools that measure them directly. It is a function of pore throats rather than pore size, and therefore can not be related directly to the electrical logs. There is a weak correlation between porosity and permeability as is shown by the spread of points on typical crossplots of porosity and permeability. Fuzzy logic can be used as a simple tool for confirming known correlations or as a powerful predictor in wells where core samples are not available. Cuddy [1] implemented fuzzy logic for litho-facies and permeability prediction. In the first phase of his study, fuzzy logic was applied for lithofacies prediction form well logs in Viking field, Southern North Sea. Three major lithofacies associations were recognized from core studies. A well with substantial core coverage was used to calibrate litho-facies and permeability predictor for the older wells. Using the fuzzy relationships between the described lithofacies and electrical logs, litho-facies were predicted in a second well. The prediction success in this second well between the predicted facies and "hidden" described facies is 73%, with the majority of the "failed" predictions falling into the next-closest litho-facies type rather than one with completely different reservoir characteristics.