Inversion of Multiple Reservoir Parameters Based on Deep Neural Networks Guided by Lagrange Multipliers

Summary The inversion of reservoir parameters is critically important during oilfield exploration and development, as it provides precise and comprehensive information that helps reduce exploration risks by mitigating uncertainties. In this paper, we propose an intelligent inversion method using a Lagrange multipliers-guided physical residual neural network (Lg-PRNN), incorporating nonlinear variations, adaptive parameters, and Lagrange multipliers. The use of Lagrange multipliers eliminates the need to manually adjust weights in the loss function, significantly improving efficiency. By introducing nonlinear variations for time and space coordinates in the input, the Lg-PRNN can capture changes in fluid flow rates, thereby enhancing its ability to solve seepage equations under varying flow conditions. The adaptive parameters introduced in the inputs increase the flexibility of Lg-PRNN and enhance its adaptability and generalization capabilities. In two synthetic experiments and one field experiment, permeability, skin factor, and wellbore storage coefficient were accurately inverted by fitting the bottomhole pressure (BHP), demonstrating the effectiveness of the Lg-PRNN model. Compared with the latest methods utilizing neural networks, Lg-PRNN not only improves efficiency but also enhances inversion accuracy by approximately 72%.