Hybrid Physics-Data-Driven Approach for Pressure Estimation in CO 2 -Rich Gas Injection Operations

Reliable monitoring of bottom-hole pressure (BHP) in gas injection wells is essential for reservoir management, operational safety, and the success of Enhanced Oil Recovery (EOR) and Carbon Capture, Utilization, and Storage (CCUS) projects. Particularly in offshore oilfields where the carbon dioxide content in the production is relevant, its reinjection mixed with hydrocarbon gases presents unique difficulties arising from the complex physical behavior, since flow often occurs in supercritical state. Additionally, measurements from permanent downhole gauges (PDGs) may be absent. Traditional mechanistic models and purely data-driven machine learning (ML) approaches each have limitations in handling the nonlinearities and uncertainties inherent in these systems. In this work, we address these limitations by developing a Physics-Guided Neural Network (PGNN) that combines first-principles modeling with supervised learning through a hybrid loss formulation. The methodology is validated using a comprehensive dataset from an offshore oilfield in the Brazilian Pre-salt, encompassing multiple injection cycles and varying gas compositions. Results demonstrate that the hybrid approach achieves robust BHP estimation, with error metrics around 1%, outperforming both conventional physical models and standard neural networks, especially when dealing with limited or noisy datasets. The proposed virtual sensor solution enables reliable BHP monitoring in injector wells, minimizing operational expenditures and supporting safe, efficient, and sustainable reservoir management and CO2storage.