Rapid evaluation of capillary pressure and relative permeability for oil–water flow in tight sandstone based on a physics-informed neural network

Efficient and accurate evaluation of capillary pressure and relative permeability of oil–water flow in tight sandstone with limited routinely obtainable parameters is a crucial problem in tight oil reservoir modeling and petroleum engineering. Due to the multiscale pore structure, there is complex nonlinear multiphase flow in tight sandstone. Additionally, wetting behavior caused by mineral components remarkably influences oil–water displacement in multiscale pores. All this makes predicting capillary pressure and relative permeability in tight sandstone extremely difficult. This paper proposes a physics-informed neural network, integrating five important physical models, the improved parallel genetic algorithm (PGA), and the neural network to simulate the two-phase capillary pressure and relative permeability of tight sandstone. To describe the nonlinear multiphase flow and the wettability behavior, five physical models, including the non-Darcy liquid flow rate formula, apparent permeability (AP) formula, and contact angle-capillary pressure relationship, are coupled into the neural network to improve the prediction accuracy. In addition, the input parameters and the structure of the physics-informed neural network are simplified based on analyzing the change rule of the oil–water flow with the main controlling factors, which can also save training time and improve the accuracy of the neural network. To obtain the data for training the coupled neural network, the dataset of tight sandstone in Ordos Basin is constructed with experimentally measured data and various fluid flow properties as constraints. The test results demonstrate that the estimated capillary pressure and relative permeability from the physics-informed neural network are in good agreement with the test ones. Finally, we have compared the physics-informed neural network with the quasi-static pore network model (QSPNM), dynamic pore network model (DPNM), and conventional artificial neural network (ANN). The calculation time of QSPNM and DPNM are hundreds of times longer than that of the physics-informed neural network. The coupled neural network has also performed much better than the conventional ANN. As the heterogeneity of pore spaces in tight sandstone increases, the advantages of the physics-informed neural network over ANN are more prominent. The prediction models generated in this study can estimate the capillary pressure and relative permeability based on only four routine parameters in a few seconds. Therefore, the physics-informed neural network in this paper can provide the potential parameters for large-scale reservoir simulation.