Physics-Informed Convolutional Neural Networks for Reservoir Property Modelling Constrained by Petrophysical Knowledge

Convolutional neural networks (CNNs) have been widely used in petrophysical modeling for predicting key reservoir properties such as permeability \(\:k\), porosity \(\:\varphi\:\), and shale volume \(\:\left({V}_{sh}\right)\), existing CNN-based approaches typically lack physics-based constraints in their loss functions, limiting their ability to honor established petrophysical relationships and accurately represent the nonlinear and spatially variable characteristics inherent to geologically complex and heterogeneous formations.To address these challenges, we develop a hybrid deep learning approach that couples a convolutional neural network (CNN) with physics-based constraints. By incorporating petrophysical domain knowledge directly into the model's loss function, this architecture ensures that predicted properties remain consistent with established petrophysical relationships, while harnessing the pattern recognition strengths of CNNs. The model was trained and validated on comprehensive well log datasets from the Kadanwari Gas Field (KGF), located in the Middle Indus Basin (MIB), utilizing seven critical petrophysical inputs: flow zone indicator (FZI), pore throat factor (PTF), neutron porosity (NPHI), spontaneous potential (SP), bulk density (RHOB), bulk volume water (BVW), and gamma ray (GR). The proposed physics-informed convolutional neural network (PICNN) demonstrates superior predictive capability, achieving coefficient of determination (R²) values of 0.947 for permeability, 0.965 for porosity, and 0.908 for shale volume on the testing dataset. Furthermore, the PICNN's outputs were subjected to sequential Gaussian simulation (SGS) to generate three-dimensional (3D) property models that honor both the statistical characteristics of the input data and the spatial continuity within the reservoir. This integrated framework represents a significant advancement in computational petrophysics and offers a powerful tool for modeling complex subsurface systems.