Direct prediction of capillary pressure curves from cross-size digital rock images based on a spatial pyramid pooling convolutional network

Capillary pressure is a determining factor in the distribution and migration of fluids in porous media, directly influencing reservoir permeability, fluid saturation, and recovery efficiency. Conventional experimental and numerical methods are costly and limited in capturing complex pore structures. Existing data-driven methods, while addressing some limitations, neglect essential physical constraints and rely on pre-computed parameters rather than directly predicting from images, resulting in inadequate adaptability to cross-size data. We hereby propose a novel physics-informed deep learning framework, namely the three-dimensional spatial pyramid pooling convolutional long short-term memory-convolutional neural network with physical information embedding (3DSPP-ConvLSTM-CNN-PI). This model can directly predict capillary pressure curves from digital rock images of various sizes without the need for intermediate parameter calculations. The model uses a 3DSPP module to adaptively capture cross-size pore geometric features and explicitly embed critical physical parameters, such as computed tomography resolution, interfacial tension, and contact angle distribution. The model is trained on 1512 capillary pressure-saturation curves extracted from five digital sandstone samples and tested on 303 unseen data cases, achieving superior performance [R ²=99.3%, mean absolute error=2.89%, root mean square error=4.46%] compared to baseline and support vector regression models. Validation on three new sandstone types demonstrates robust generalization and inference speeds over 90% faster than pore network simulations. This highlights the model's precision, efficiency, and practical capability in predicting the seepage characteristics of porous media.