Abstract
A numerical method is described for the simulation of miscible and immiscible fluid flow in hydrocarbon reservoirs. A flexible gridding technique introduces both static and dynamic local grid refinement for multiple space dimensions. Operator splitting and defect correction are used to deal separately with elliptic and hyperbolic problems. The elliptic equations are discretised by mixed finite elements and solved by multigrid. Mixed finite elements provide an accurate representation of the flows and allow for a good connection with the hyperbolic equations. The method of characteristics is used for the hyperbolic problems, eliminating numerical diffusion almost completely. Nonlinear phenomena are treated by suitable Riemann solvers.
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Abbreviations
- Nd :
-
dimension = 1, 2, 3
- x, t:
-
space and time co-ordinates
- i ,j:
-
number of block, resp. face
- n:
-
= 1,..., N (chemical) component
- m:
-
= 1, . . . , M, fluid-phase (e.g., water, oil, gas)
- an, un , qn:
-
concentration, flux, and source-term of component n
- pm , vm , λm, ϱm:
-
pressure, flux, relative mobility and density of phase m
- g:
-
acceleration due to gravity
- ϰ:
-
(absolute) permeability tensor of porous medium
- u:
-
total fluid velocity
- ξ:
-
parameter along streamline
- s:
-
(water) saturation
- f(s):
-
fractional flow function
- sI :
-
inflection point
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Gmelig Meyling, R.H.J., Mulder, W.A., Schmidt, G.H. (1990). Porous media flow on locally refined grids. In: Numerical Methods for the Simulation of Multi-Phase and Complex Flow. Lecture Notes in Physics, vol 398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022310
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DOI: https://doi.org/10.1007/BFb0022310
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