Electrical rock typing using Gaussian mixture model to determine cementation factor

Abstract

Many studies have worked on the estimation of fluid saturation as an important petrophysical property in hydrocarbon reservoirs. Based on Archie's law, proper determination of cementation factor (m) can lead to accurate values of water saturation. Given that the m is mainly affected by electrical properties of rock, electrical quality index (EQI) can be used to estimate m through a novel rock typing technique. Despite the efficient applicability of EQI for the classification of rocks, with similar electrical behaviors, into distinct electrical rock types (ERTs), manual implementation of this method is time-consuming and gets excessively more difficult for larger datasets. In this work, a fast automated version of EQI methodology was presented. As a fuzzy clustering algorithm, Gaussian mixture model (GMM) was implemented on a large quantity of carbonate and sandstone samples to cluster them into distinct ERTs based on EQI values. To this end, 100 data points were randomly selected for testing purposes, and the remaining data points were used as training subsets for carbonate and sandstone samples. An innovative hybrid EQI-GMM approach was developed to determine the optimum number of clusters. Furthermore, results of two commonly-used criteria, namely Schwarz's Bayesian Criterion (BIC) and Akaike Information Criterion (AIC), showed that they fail to specify ERTs properly. The predicted values for m by the hybrid EQI-GMM approach were more accurate (RMSE is 0.0167 and 0.0056 for carbonate and sandstone samples, respectively) than outputs of the traditional Archie’s law (RMSE is 1.6697 and 0.1850 for carbonate and sandstone samples, respectively).