... that reduce the cost of phase behavior computation include the reduced variable method and the shadow region method ( Pan and Tchelepi 2011 ; Rasmussen et al. 2003 ). Abstract In this study, we utilize deep neural networks to approximate operators of a nonlinear partial differential equation (PDE...

... Abstract The Physics Inspired Machine Learning (PIML) is emerging as a viable numerical method to solve partial differential equations (PDEs). Recently, the method has been successfully tested and validated to find solutions to both linear and non-linear PDEs. To our knowledge, no prior studies...

... immiscible transport problem (Buckley-Leverett). The model is able to produce an accurate physical solution both in terms of shock and rarefaction and honors the governing partial differential equation along with initial and boundary conditions. We test various hypothesis (uniform and non-uniform initial...

... smoother solver partial differential equation elliptic partial differential equation Introduction In a typical reservoir simulator, both pressure equations and saturation equations are required to solve [ 1 ]. The pressure solution phase may control the whole solution time of linear systems...

... Abstract For the solution of nonlinear equations resulting due to the implicit discretization of reservoir simulation partial differential equations, Newton's method has been an overwhelming choice. By providing robust and a considerably faster performance, the inexact Newton's methods offer...

... equation reservoir society of petroleum engineers horizontal well partial differential equation venezuela Introduction Analysis of the horizontal well-test response is much more difficult than for a vertical well-test data because of the curved/twisted trajectory and the pressure evolution...

... ABSTRACT We present a method for handling non-linear partial differential equations having solutions that develop steep fronts. Traditional methods for solving such problems (the finite difference and finite element methods) implicitly assume a simple form for the solution over a limited domain...

... solves for the pressure and the Darcy velocity simultaneously, as a system of first order partial differential equations. By solving for u = −(k/µ)Vp as one term, we minimize the difficulties occurring in standard methods caused by differentiation or differencing of p and multiplying by rough...