Unsupervised Deep Learning Algorithm to Solve Sub-Surface Dynamics for Petroleum Engineering Applications

Ordinary and partial differential equations play a significant role across various energy domain as they aid in approximating solution for complex mathematical problems. Drilling optimization and reservoir simulation are some common application that takes the form of differential equations and are dominated by their respective governing equations. Approximating the solution of such mathematical problems requires a fast and reliable methodology. However, the computational complexity increases with the dimension for the classical numerical techniques and the quality of the result is dependent upon the discretization and sampling methods of the subspace. Recent advances in deep learning techniques, based on universal approximation theorem of neural network seems promising to tackle the high dimensional problem. The solution provided by deep learning for a differential equation is in a closed analytical form which is differentiable and could be used in any subsequent computation. In the present study, the solution for the initial condition and boundary value problems in ordinary and partial differential equation by deep learning method have been analyzed. The propsed algorithm could be valuable aid for analyzing the fluid flow and reservoir simulation in an effective manner.