Physics Informed Deep Learning for Well Test Analysis

Balakrishna DR, Kamalkumar Rathinasamy, Avijit Das, Keerthi Ashwin, Vani Sivasankaran, Soundararajan Rajendran

Abstract:

Well Test Analysis is a section of reservoir engineering that best describes the reservoir characteristics with principles of fluid flow in porous media using pressure transient analysis. The transient pressure distribution for fluid flowing through the wellbore, across the porous reservoir model, at a constant terminal flow rate can be determined by solving the partial differential equation-diffusivity equation, along with the set of boundary conditions that define the reservoir model. Since the diffusivity equation has a non-linear quadratic term, it is either solved analytically by ignoring the quadratic term and thus compromising the model accuracy or solved using numerical approaches that is complex and time-consuming. This study provides an alternative and simpler approach to determine the pressure distribution using the Neural Networks method. This method could be applied to any type of reservoir that has a defined diffusivity equation and boundary conditions to predict the pressure distribution with good accuracy. To validate this approach and demonstrate the accuracy of the neural network with a greater level of confidence, for the purpose of this study, we have chosen to validate against analytical solution as it could be applied to all types of reservoir models in generic form.

Typical neural network-based approaches, however, were not yielding good results for Well Test Analysis as it needed bulk data since they typically ignored physical insights from the scientific system under consideration. In this paper, this problem is resolved by Physics informed neural networks that are trained to solve supervised learning tasks while honoring any given physics law.