A Hybrid Approach for the Prediction of Relative Permeability Using Machine Learning of Experimental and Numerical Proxy SCAL Data

Accurate estimation of relative permeability is one of the key parameters for decision making in upstream applications from project appraisal to field development and evaluation of various field development options. In this study, we identify Euler number (Arns et al. 2001) (a quantitative measure of fluid connectivity/distribution) and saturation as being the first-order predictors of relative permeability and develop a reliable correlation between them using machine learning of experimental special core analysis (SCAL) data and pore network simulation results. In order to achieve our objective, first, we developed a machine-learning model based on the random forest algorithm (Breiman 2001) to analyze specific SCAL data that indicates a key missing feature in the traditional saturation-based relative permeability prediction. We identified this missing feature and proposed the Euler characteristic as a potential first-order predictor of relative permeability in combination with in-situ fluid saturations. We generated “artificial” relative permeability data using pore network simulation (Valvatne and Blunt 2004) by systematically varying a set of key parameters such as pore geometry, wettability, and saturation history. Subsequently, we used machine learning to rank the importance of each parameter and identify possible correlative responses to those selected variables. At a fixed saturation (zero-dimensional volumetric abundance) and Euler number coordinates, the relative permeability is very consistent and varies insignificantly across different cases, suggesting these two parameters as first-order predictors. Euler number characterizes the fluid connectivity/distribution, while saturation represents the net volumetric fluid quantity. We believe that Euler number could be the missing first-order predictor in traditional saturation-based predictive relative permeability models, especially for connected pathway dominated flow regime. Finally, we identified the quantitative relationship between relative permeability and Euler characteristic, and present a reliable correlation to determine the relative permeability on the basis of Euler number and saturation. Copyright © 2020 Society of Petroleum Engineers