Multivariate statistical log log-facies classification on a shallow marine reservoir

Sedimentary facies are important in reservoir characterization because flow properties are commonly assigned using facies-specific correlations. Multivariate statistical methods provide a powerful vehicle to extract facies responses from different well logs, to predict facies in uncored wells and evaluate uncertainty.Previous study shows a difficulty in bin selection to accurately reproduce the samples' conditional probability distribution. In this paper, a new method uses empirical beta distributions to model the distribution of petrophysical properties conditional to facies. Petrophysical property distributions are assumed conditionally independent, simplifying the use of Bayes rule.Three multivariate statistical methods (beta-Bayesian, multinomial logistic regression, and discriminant analysis) are examined in this paper using log and facies data from a western African sandstone reservoir. Three derived probability logs compare the prediction performance of the statistical methods as well as illustrate influences of log combinations and sample size. Two-way analysis of variance compares prediction accuracy of the models. For a given dataset, there are no significant differences (with 90% confidence) in predictions by the three methods. Additional logs improve prediction accuracy from 30 to above 80%. Final prediction accuracy is 82 to 90% for these three algorithms. Including 20 to 25% of the complete core and facies data in model construction provides accurate predictions; models were validated against the data not used in model construction. The fitted classification models can generate three-dimensional log-derived facies distributions for geologic modeling and reservoir simulation. The three methods are straightforward, efficient, and have quantifiable prediction errors.