A framework of parallel physics-informed neural network with Laplace transform for well testing interpretation

The application of machine learning methodologies offers a novel perspective for more convenient and efficient well test interpretation. In this study, we propose a novel approach, La-PPINN (parallel physics-informed neural network based on Laplace transform), which incorporates the physical model of fluid flow in Laplace space, as well as well testing observed data for parameters inversion of reservoir and wellbore. In order to validate the proposed methodology, a classical vertical well problem in a single porous medium with an analytical solution has been employed. This has enabled us to present a comparison between the robustness and accuracy of our proposed model and those of models that do not consider the Laplace transform or parallel neural networks. Moreover, the stability of the model was tested by introducing different levels of Gaussian noise. The results demonstrate that incorporating the Laplace space representations of physical equations into the model reduces the computational complexity. Furthermore, the parallel neural network enhances the computational efficiency and accuracy. Additionally, the La-PPINN network is also shown to accurately fit the bottom-hole pressure curve and precisely invert parameters, even when a Gaussian noise is introduced, for three different reservoir types, including dual-porosity, triple-porosity, and composite reservoirs.