A data-driven model for predicting the effect of temperature on oil-water relative permeability

Several empirical models have been proposed by scholars to capture the temperature's impact on relative permeability for a specific rock/fluid system, often using very limited dataset of measured relative permeability values, which makes these models inapplicable to a wider range of rock-fluid characteristics. The current study presents a new data-driven model to predict the two-phase oil/water relative permeability over a wide range of temperature in unconsolidated sand and sandstone formations. We found that the carbonate rock systems have different characteristics and the reported high temperature relative permeability data for them is limited, which prevented us from including them alongside the sand systems. For developing the model, the Least Square Support Vector Machine (LSSVM) in the form of a supervised learning approach was implemented, in which the coupled simulated annealing optimization technique was employed for calculation of LSSVM hyper-parameters. To gather a comprehensive dataset for constructing the model, 626 experimental oil relative permeability and 547 experimental water relative permeability data points were obtained from the open literature. To identify the doubtful data points (the outliers) the method of Leverage Value Statistics was applied. The temperature (ranging from 21 to 200 degrees C), water saturation, oil viscosity (ranging from 0.42 to 1190 cP), water viscosity (ranging from 0.136 to 1.1 cP), and the absolute permeability (ranging from 152 to 95,000 mD) were used as the independent variables in the model. The statistical analysis of the obtained LSSVM for prediction of relative permeability demonstrated that the coefficient of determination, root mean square error, and average absolute error were 0.9987, 0.0111, and 5.36% for oil relative permeability and 0.9991, 0.0056, and 8.40% for water relative permeability. The comparison of statistical parameters of this model with other reported relative permeability models showed that this model is more reliable for estimating the oil and water relative permeability including its dependence on temperature and therefore it can be used for reservoir simulation studies, when experimentally measured data are not available.