Machine Learning Assisted Prediction of Permeability of Tight Sandstones From Mercury Injection Capillary Pressure Tests

Abstract

Capillary pressure is an important parameter in both petrophysical and geological studies. It is a function of different porous media properties, in special, the pore structure of the rock. Mercury Injection Capillary Pressure (MICP) analysis is a consistent methodology for determining different petrophysical properties including porosity, and pore throat distribution. The matrix permeability is dependent on the pore size distribution but is not directly measured from MICP tests. In this work, we consider distinct parameters derived from MICP tests for the prediction of permeability by following a machine learning based approach. Firstly, a vast range of MICP test results (246 samples) related to tight sandstones is gathered with a permeability range of 0.001 to 70 millidarcy. After quality checking of dataset, different theoretical permeability models are tested on the dataset and the results are analyzed. Also, different features related to the pore throat characteristics of rock is analyzed and the best characteristics are selected for the input variables to the machine learning model. The Support Vector Regression (SVR) approach is proposed with the Radial Basis Function (RBF) kernel for the prediction of rock permeability from MICP tests. A Particle Swarm Optimization (PSO) is applied for optimization of the model meta parameters in the validation process to avoid over or underfitting. The training of the model is carried out with random selection of 80% of samples while other points are applied for testing of the model. The data analysis on the correlation between rock permeability and parameters of capillary pressure is studied and showed that using pore throat radius corresponding to saturation range of 0.4-0.8 and the median capillary pressure values obtained from the capillary pressure curves is suitable to be used as input features of the SVM model. Also, the porosity and Winland equation was considered as input features due to their acceptable correlation with the rock permeability. The results showed that the implemented SVM-PSO model can acceptably predict the experimentally measured permeability values with R2 rate of over 0.88 for training and testing datasets. This work represents an analysis of the relationship of capillary pressure curve specifications with permeability on a large MICP dataset, especially focused on tight sandstone rocks. The analysis provided new statistical and physics-based features with the highest correlations with the rock permeability that helped in significant improvement of the SVM-PSO prediction results.