Fuzzy ruling between core porosity and petrophysical logs: Subtractive clustering vs. genetic algorithm–pattern search

Porosity, the void portion of reservoir rocks, determines the volume of hydrocarbon accumulation and has a great control on assessment and development of hydrocarbon reservoirs. Accurate determination of porosity from core analysis is highly cost, time, and labor intensive. Therefore, the mission of finding an accurate, fast and cheap way of determining porosity is unavoidable. On the other hand, conventional well log data, available in almost all wells contain invaluable implicit information about the porosity. Therefore, an intelligent system can explicate this information. Fuzzy logic is a powerful tool for handling geosciences problem which is associated with uncertainty. However, determination of the best fuzzy formulation is still an issue. This study purposes an improved strategy, called hybrid genetic algorithm–pattern search (GA–PS) technique, against the widely held subtractive clustering (SC) method for setting up fuzzy rules between core porosity and petrophysical logs. Hybrid GA–PS technique is capable of extracting optimal parameters for fuzzy clusters (membership functions) which consequently results in the best fuzzy formulation. Results indicate that GA–PS technique manipulates both mean and variance of Gaussian membership functions contrary to SC that only has a control on mean of Gaussian membership functions. A comparison between hybrid GA–PS technique and SC method confirmed the superiority of GA–PS technique in setting up fuzzy rules. The proposed strategy was successfully applied to one of the Iranian carbonate reservoir rocks.