Steady State 1D Two-Phase Flow Differentiable Modeling, Learning from Field Data and Inverse Problem Applications in Oil Wells

Anderson Carlos Faller^1,2*Saon Crispim Vieira¹Marcelo Souza de Castro^3,4

• ¹Petrobras, Santos, Brazil
• ²Universidade Estadual de Campinas, Campinas, Brazil
• ³School of Mechanical Engineering, Universidade Estadual de Campinas, Campinas, Brazil
• ⁴Centro de Estudos de Energia e Petróleo, Universidade Estadual de Campinas, Campinas, Brazil

Accurate modeling of steady-state two-phase flow is critical for the design and operation of systems in the oil and gas industry, yet traditional models often struggle to adapt to specific field conditions. This paper introduces a novel, end-to-end differentiable framework that integrates physics-informed neural networks with a Neural Ordinary Differential Equation (Neural ODE) formulation to predict pressure and temperature profiles in complex deepwater wells and pipelines. By leveraging automatic differentiation, the entire simulation becomes a trainable model, allowing for the simultaneous optimization of data-driven components and the automated tuning of physical parameters, directly from field data. Our results demonstrate that this approach achieves superior accuracy in pressure prediction compared to tuned industry-standard correlations. A key finding of this work is that pre-training the model on a large experimental dataset provides a robust physical foundation, which, when fine-tuned on sparse field data, significantly improves performance. This highlights the effectiveness of a transfer learning strategy in bridging the domain gap between experimental and real-world conditions. Our results show this two-stage approach is more effective than training specialized models on field data alone. Furthermore, the differentiable nature of the framework enables its seamless application to inverse problems; we demonstrate its use with Randomized Maximum Likelihood (RML) for uncertainty quantification and virtual sensing. This work presents a powerful new paradigm for creating self-calibrating, data-driven simulation tools with significant potential for digital twin applications.