New Relative Permeability Correlations for Carbonate Reservoirs through Data-Driven Modeling

Relative permeability is a crucial input to reservoir simulators for modeling reservoir performance. Conventional methods of measuring relative permeability rely on either laboratory core-flooding experiments or fine-scale computer simulations. The former method is expensive and time-consuming, and the latter often does not represent the complex characteristics of existing systems. Data mining algorithms can be implemented to estimate relative permeability with reasonable accuracy for real applications without running laboratory or computer simulation experiments. This paper aims at presenting predictive correlations for relative permeability for carbonate rocks using data-driven approaches. To achieve this aim, a scatter plot matrix was applied to analyze 225 experimental datasets, including almost 3800 relative permeability data points (observations), for predicting relative permeability. Since relative permeability measures are often unavailable exactly at residual oil saturation and connate water saturation (known as endpoints); consequently, cubic equations were fitted and solved to precisely determine these points. Next, a symbolic regression algorithm was developed to predict relative permeability in different situations: when endpoints are available or unavailable and when the rock wettability is clear or not. For this purpose, all 225 datasets were divided into training and testing groups. The correlations were tested to predict testing data, which the symbolic regression algorithm has never seen before. Finally, the most accurate correlations were presented, and a detailed analysis was carried out. The results showed a good agreement between the real and the predicted data. The developed correlations proved to be very efficient in predicting the relative permeability accurately