Relative permeability estimation using mercury injection capillary pressure measurements based on deep learning approaches

Relative permeability (RP) curves which provide fundamental insights into porous media flow behavior serve as critical parameters in reservoir engineering and numerical simulation studies. However, obtaining accurate RP curves remains a challenge due to expensive experimental costs, core contamination, measurement errors, and other factors. To address this issue, an innovative approach using deep learning strategy is proposed for the prediction of rock sample RP curves directly from mercury injection capillary pressure (MICP) measurements which include the mercury injection curve, mercury withdrawal curve, and pore size distribution. To capture the distinct characteristics of different rock samples' MICP curves effectively, the Gramian Angular Field (GAF) based graph transformation method is introduced for mapping the curves into richly informative image forms. Subsequently, these 2D images are combined into three-channel red, green, blue (RGB) images and fed into a Convolutional Long Short-Term Memory (ConvLSTM) model within our established self-supervised learning framework. Simultaneously the dependencies and evolutionary sequences among image samples are captured through the limited MICP-RP samples and self-supervised learning framework. After that, a highly generalized RP curve calculation proxy framework based on deep learning called RPCDL is constructed by the autonomously generated nearly infinite training samples. The remarkable performance of the proposed method is verified with the experimental data from rock samples in the X oilfield. When applied to 37 small-sample data spaces for the prediction of 10 test samples, the average relative error is 3.6%, which demonstrates the effectiveness of our approach in mapping MICP experimental results to corresponding RP curves. Moreover, the comparison study against traditional CNN and LSTM illustrated the great performance of the RPCDL method in the prediction of both S_o and S_w lines in oil–water RP curves. To this end, this method offers an intelligent and robust means for efficiently estimating RP curves in various reservoir engineering scenarios without costly experiments.