Abstract
Precisely predicting rock facies leads to adequate reservoir characterization by improving the porosity-permeability relationships to estimate the properties in non-cored intervals. It also helps to accurately identify the spatial facies distribution to perform an accurate reservoir model for optimal future reservoir performance. In this paper, comparative conditional posterior probabilities of continuous well facies distribution has been estimated through Linear Discriminate Analysis (LDA) and Kernel Support Vector Machine (KSVM) given the well log interpretations in a well within sandstone formation in South Rumaila Oil Field, located in Iraq.
The explanatory variables are depth, neutron porosity, water saturation, shale volume. The multinomial response factor is the vertical discrete Lithofacies sequence that only encompasses of sand, shaly sand, and shale. The Lithofacies were modeled given the well logs data through LDA and KSVM and comparisons were done between the measured and predicted Lithofacies distribution in order to determine the best classification method to be considered for Lithofacies prediction at other wells in the reservoir. The LDA was chosen to estimate the maximum likelihood and minimize the standard error for the relationships between lithofacies and well logs data. The Linear discriminate Analysis seeks a linear transformation (discriminate function) of both the independent and dependent variables in order to produce a new set of transformed values that provides a more accurate discrimination concerning dimensionality reduction. Beta distribution of facies has been considered as prior knowledge and the resulted predicted probability (posterior) distribution has been estimated from LDA based on Bayes theorem that represents the relationship between predicted probability (posterior) with the conditional probability and the prior knowledge. The linear discriminant analysis has been accomplished considering the cross-validation in addition to splitting the data into train and test process. Through assessing the LDA models, the cross-validation was adopted as an optimal solution to estimate the continuous lithofacies distribution because the total true correct summation is more valuable than the splitting data method.
Then, the KSVM has been adopted to estimate the continuous predicted probability Distribution of Lithofacies. KSVM is a supervised statistical learning algorithm that recognizes the discrete classes for the given data based on maximizing the margin around the separating hyperplane and the decision function is fully specified by a subset of the supporting vectors. The posterior distribution has been validated using the true and predicted facies counts matrix that estimated by KSVM.
In comparison between the LDA and KSVM, it was prominent that KSVM is better than LDA because it has more total true correct summation than LDA. Also, nonlinear separations of components is handled well by using KSVM. In addition and after depicting the vertical well sand, shale, and shaly sand posterior distribution from both LDA and KSVM, it was shown that KSVM prediction is more compatible between the sand posterior values with the high records of neutron porosity along with low intervals of shale volume. Consequently, the KSVM was considered for Lithofacies prediction in the other wells in the reservoir to be a solid basis for the geospatial modeling.
