Machine Learning for Capillary Pressure Estimation

Capillary pressure plays an essential role in controlling multiphase flow in porous media and is often difficult to be estimated at subsurface conditions. The Leverett capillary pressure function J provides a convenient tool to address this shortcoming; however, its performance remains poor where there is a large scatter in the scaled data. Our aim, therefore, was to reduce the gaps between J curves and to develop a method that allows accurate scaling of capillary pressure. We developed two mathematical expressions based on permeability and porosity values of 214 rock samples taken from North America and the Middle East. Using the values as grouping features, we used pattern-recognition algorithms in machine learning to cluster the original data into different groups. In each wetting phase saturation, we were able to quantify the gaps between the J curves by determining the ratio of the maximum J to the minimum J. Graphical maps were developed to identify the corresponding group for a new rock sample after which the capillary pressure is estimated using the average J curve of the identified group and the permeability and porosity values of the rock sample. This method also provides better performance than the flow zone indicator (FZI) approach. The proposed technique was validated on six rock types and has successfully generated average capillary pressure curves that capture the trends and values of the experimentally measured data by mercury injection. Moreover, the proposed methodology in this study provides an advanced and a machine-learning-oriented approach for rock typing. In this paper, we provide a reliable and easy-to-use method for capillary pressure estimation in the absence of experimentally measured data by mercury injection.

Automated summary

This study proposes an advanced machine learning-based method to classify rock samples and estimate capillary pressure by using permeability and porosity values. The method outperforms traditional approaches and captures the trends and values of experimentally measured data.