Steady-state 1D two-phase flow differentiable modeling: learning from field data and inverse problem applications in oil wells

Accurately modeling steady-state two-phase flow is critical for the design and operation of systems in the oil and gas industry; however, traditional models often struggle to adapt to specific field conditions. This study 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. By leveraging automatic differentiation, the entire simulation functions as 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. We found that a transfer learning strategy, pretraining on a large experimental dataset to establish a robust physical foundation, followed by fine-tuning on sparse field data, significantly outperforms models trained on field data alone. Furthermore, the differentiable nature of the framework enabled seamless application to inverse problems, demonstrated via Randomized Maximum Likelihood (RML) for uncertainty quantification. These findings illustrate the effectiveness of bridging the domain gap between experimental and real-world conditions, presenting a powerful new paradigm for creating self-calibrating, data-driven simulation tools with significant potential for digital twin applications.