Lessons for machine learning from the analysis of porosity-permeability transforms for carbonate reservoirs

Prediction of permeability is one of the most difficult aspects of reservoir characterization because permeability cannot be directly measured by current well logging technology. This is particularly challenging for carbonate rocks. Machine learning (ML) and robust multivariate methods have been developed that have been used in many fields of study to make accurate estimators for variables of interest from both large and small datasets. ML has been criticized for utilizing approaches that are typically not interpretable. That is, it is not clear how the answers are arrived at and what aspects of input data may be resulting in inaccurate results. The current study uses a number of the mathematical algorithms that operate inside ML modules. It applies them to developing porosity-permeability transforms, with or without rock types, to two well-characterized data sets for carbonate reservoirs. One data set is from Jerry Lucia's 1995 study of carbonate rock types, and the other is from a study of the Seminole, West Texas, San Andres Unit. This study of statistical analysis of porosity-permeability transforms includes: transforming the data to normal distributions; performing cross-validation blind testing; and detecting heteroscedasticity by creating plots of residuals. Heteroscedastic data (populations with variable variance) may have an adverse impact on ML algorithms such as Random Forests (RF). We find that including lithofacies information does not greatly improve porosity-permeability transforms. We also propose a number of strategies to make ML analyses of reservoir (and other geosciences) data sets more robust and accurate.