High Order Upwind Schemes for Two-Phase, Multicomponent Flow
- Bradley T. Mallison (Chevron Corp.) | Margot G. Gerritsen (Stanford U.) | Kristian Jessen (Stanford U.) | Franklin M. Orr (Stanford U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2005
- Document Type
- Journal Paper
- 297 - 311
- 2005. Society of Petroleum Engineers
- 5.4.3 Gas Cycling, 5.2 Reservoir Fluid Dynamics, 5.2.2 Fluid Modeling, Equations of State, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 5.2.1 Phase Behavior and PVT Measurements, 5.4.9 Miscible Methods, 5.5.7 Streamline Simulation, 5.8.8 Gas-condensate reservoirs, 4.1.2 Separation and Treating, 5.3.1 Flow in Porous Media, 5.4.2 Gas Injection Methods, 5.5 Reservoir Simulation
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In this paper, we investigate high-order finite-difference schemes forcompositional simulation. Results presented for one-dimensional (1D)gas-injection problems suggest that a third-order, essentially nonoscillatoryscheme achieves accurate results more efficiently than first-order methods;leads to an improved treatment of phase behavior; and is more robust thantraditional total variation diminishing schemes. We use phase diagrams as wellas solution profiles to analyze discretization errors. Discretization errorscan strongly affect the prediction of local displacement efficiency because ofthe nonlinear coupling introduced by the phase behavior in the system ofgoverning equations. The study explains the ability of the numerical schemes topredict local displacement efficiency. In all of our tests, we comparenumerical results to analytical and semianalytical solutions found through themethod of characteristics. Our 1D results can be extended to 3D throughconventional finite difference approaches, but we plan to apply them in astreamline-based compositional simulator.
We consider high-order upwind schemes for accurately and efficientlysimulating two-phase, multicomponent flow, with a particular interest in themodeling of multicontact miscible and near-miscible displacements. The localdisplacement efficiency of such gas-injection processes is determined by thetransfer of components between gas and oil phases. To determine thepartitioning of components into phases, compositional simulators perform costlyflash calculations. The computational costs of flash calculations can beprohibitively high in 3D simulations. Moreover, the strong nonlinear couplingintroduced by the phase behavior in these processes renders numerical solutionsvery sensitive to discretization errors. Therefore we seek high-order schemesthat accurately predict displacement efficiency while reducing thecomputational costs.
We use a comprehensive suite of 1D test problems to assess whichfinite-difference schemes are capable of effective prediction of localdisplacement efficiency. We focus on gas-injection processes in 1D to allowcomparison of numerical solutions to analytical solutions available for theRiemann problem. Our 1D results easily can be applied to 3D by conventionalapproaches or through the use of streamline-based simulation methods.
|File Size||2 MB||Number of Pages||15|
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