Prediction of Fluid Flow in Porous Media using Physics Informed NeuralNetworks

摘要

In the realm of reservoir engineering,we are categorized to be in the small data regime because of thecomplex physical systems we are dealing with as well as the inherent uncertainty in our problems.Theobjective of this paper is to present a physics informed neural network(PINN)technique that is able to useinformation from the fluid flow physics as well as observed data to model the Buckley-Leverett problem.We use the classical problem of drainage of gas into a water-filled porous medium to test ourimplementation.The analytical solutions obtained using the method of characteristics are comparedwith solutions obtained using the DeepXDE library that is built on top of TensorFlow.The automatic-differentiation capability of TensorFlow allows us to interweave the underlying physics of the problemwith any observed data to come up with a data-efficient universal function approximator.The flexibilityof TensorFlow also allows us to set multiphase parameters to be trainable or not,which would ultimatelyassist in any inverse modeling efforts using the problem.Several cases are presented that highlight the importance of the coupling between observed data andphysics-informed neural networks for different parameter space.The cases demonstrate the capability ofPINNs to augment data-driven solutions.Our results indicate that PINNs are capable of capturing the overalltrend of the solution even without observed data but the resolution and accuracy of the solution are improvedtremendously once the augmentation of data and physics is implemented.Even with a large mobility ratio,the predicted solution of the PINNs seems promising.The results in our paper indicate that such methods canbe utilized to train models that could be used estimate a well-informed initial guess in a reservoir simulatorbecause they capture the overall behavior but miss the intricate details that could be circumvented withconventional reservoir simulation.The work presented in the paper demonstrates the importance and the capability of applying machinelearning approaches in reservoir engineering problems.Additionally,it gives a forward-looking approachfor the future of reservoir simulation techniques that could augment data with the physics.