Multiphase-Flow Physics-Informed Neural Network for Pressure Field Prediction in a Middle East Low-Permeability Carbonate Reservoir

Abstract Low-permeability carbonate reservoirs in the Middle East exhibit strong heterogeneity and complex subsurface flow behavior. However, Conventional numerical simulation becomes time-consuming, and history matching remains challenging. This paper aims to develop a physics-informed neural network for bottomhole pressure. The model predicts pressure in low-permeability reservoirs characterized by high permeability contrasts and developed interlayers. We organize the monthly single-well dynamic data into 12-month sequences. Each sequence contains injection intensity, oil, water, gas and liquid rates, voidage-replacement and net injection-production indicators, and historical pressure-context variables. The core innovation constructs a physically constrained loss function that embeds a physics-analog pressure-change term and trend-consistency penalty into TCN training, enforcing reservoir-consistent pressure evolution. The analog term links injection-production state, lagged pressure change, and short-term production response. The PI-TCN and non-physics TCN use identical inputs and network settings. Samples are chronologically divided into 80% training and 20% prediction sets to validate robustness under limited, nonstationary field data. Application of the PI-TCN to a typical low-permeability carbonate reservoir in the Middle East shows strong agreement between predicted and historical bottomhole pressure. In the held-out prediction period, R2 reaches 0.9717, while Relative L2, RMSE, and MAPE are 0.0066, 20.98 psi, and 0.481%, respectively. Compared with the physics-agnostic TCN under identical inputs, time window, network backbone, and chronological split, the proposed method increases R2 from 0.5756 and reduces RMSE, MAPE, and Relative L2 by approximately 74.2%, 69.6%, and 72.0%, respectively. During the transition from low-pressure fluctuation to pressure recovery, the PI-TCN follows the observed recovery path more accurately and avoids the aggressive extrapolation produced by the baseline model. The reconstructed pressure response remains consistent with injection-production support, pressure memory, and pressure-change direction, enabling reliable short-term pressure-trend prediction and two-month forecasting under nonstationary operating conditions. This study proposes a multiphase-flow physics-informed temporal convolutional network method. It integrates dynamic injection-production representation, an explicit pressure-change physics constraint, and chronological sequence learning, overcoming the dual limitations of poor generalization in purely data-driven models and the high data requirements of full reservoir simulation. The method provides an explainable computational tool for rapid pressure monitoring, production-policy adjustment, and field development decision support.