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Keywords: differential equation
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Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, March 28–30, 2023
Paper Number: SPE-212202-MS
... neural network united states government reservoir geomechanics upstream oil & gas artificial intelligence machine learning journal differential equation deep learning approximation reservoir characterization physics-informed neural network simulation application wang accuracy porous...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, March 28–30, 2023
Paper Number: SPE-212217-MS
... Abstract In this study, we utilize deep neural networks to approximate operators of a nonlinear partial differential equation (PDE), within the Operator-Based Linearization (OBL) simulation framework, and discover the physical space for a physics-based proxy model with reduced degrees...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203941-MS
... In comparison, we have for physical systems sets of equations describing partial differential equations (PDE), ordinary differential equations (ODE), and differential algebraic equations (DAE) (a combination of ordinary differential equations and algebraic equations). A DAE may be described...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Conference, October 26, 2021
Paper Number: SPE-203917-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 18–20, 2013
Paper Number: SPE-163618-MS
... Many existing flow and transport models in porous media can be described by a set of partial differential equations representing conservation of mass, momentum and energy as a function of pressure and temperature, and reconciled by the equations of state. As discussed in [ 6 , 27 ], to simplify...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 2–4, 2009
Paper Number: SPE-118964-MS
... to determine the coefficients of the polynomials expansions by solving for the fluid saturations and pressures at different collocation points via the original partial differential equations. This approach is non-intrusive in that it results in independent deterministic differential equations, which similar...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 14–17, 1999
Paper Number: SPE-51908-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 14–17, 1999
Paper Number: SPE-51918-MS
... Abstract In this paper, we summarize a methodology based on multidimensional finite differencing (MDFD) for the numerical solution of partial differential equations. Although the general methodology is not new, we present some original modifications that use Cartesian-based gridding. In theory...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 14–17, 1999
Paper Number: SPE-51924-MS
... 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...
Proceedings Papers

Paper presented at the SPE Symposium on Reservoir Simulation, February 17–20, 1991
Paper Number: SPE-21225-MS
... variable this condition requires that Δx/Δt be greater than the maximum characteristic (front) velocity, in order that the domain of dependence of the difference equations contain the domain of dependence of the differential equations. This condition is necessary for stability of any explicit scheme...
Proceedings Papers

Paper presented at the SPE Symposium on Reservoir Simulation, February 6–8, 1989
Paper Number: SPE-18414-MS
... equation modeling & simulation diagonal transmissibility method discretization spe 18414 spe 18414 INTRODUCTION Conservation of mass, momentum and energy govern the behavior of fluids in porous media. These physical laws are represented mathematically by a set of partial differential...
Proceedings Papers

Paper presented at the SPE Symposium on Reservoir Simulation, February 1–4, 1987
Paper Number: SPE-16021-MS
... and microtasking on both the CRAY X/MP 48 and IBM 3090/400 four-way parallel supercomputers. differential equation implementation matrix boundary condition flow in porous media correction iteration line correction preconditioner processor efficiency subdomain upstream oil & gas decomposition...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 10–13, 1985
Paper Number: SPE-13506-MS
... 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...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 10–13, 1985
Paper Number: SPE-13516-MS
... small oscillations of the saturation at the leading and trailing part of the front. These osscilations may be due to the pure hyperbolic nature of the differential equations, since the derivative of the capillary pressure is zero. However, the solutions behave quite stable. Figure 2 shows the oil...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, January 31–February 2, 1979
Paper Number: SPE-7690-MS
... power law vector power law fluid porous media truncation error equation Engineer matrix differential equation SPE 7690 APPROXIMATE SOLUTIONS FOR FLOW ON NON-NEWTONIAN POWER LAW FLUIDS THROUGH POROUS MEDIA by Alvis E. McDonald, Member SPE-AIME, Mobil Research & Development Corp. Copyright 1979...

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