A theoretical analysis of vertical flow equilibrium
The assumption of Vertical Flow Equilibrium (VFE) and of parallel flow conditions, in general, is often applied to the modeling of flow and displacement in natural porous media. However, the methodology for the development of the various models is rather intuitive, and no rigorous method is currently available. In this paper, we develop an asymptotic theory using as parameter the variable R{sub L} = (L/H){radical}(k{sub V})/(k{sub H}). It is rigorously shown that present models represent the leading order term of an asymptotic expansion with respect to 1/R{sub L}{sup 2}. Although this was numerically suspected, it is the first time that is is theoretically proved. Based on the general formulation, a series of models are subsequently obtained. In the absence of strong gravity effects, they generalize previous works by Zapata and Lake (1981), Yokoyama and Lake (1981) and Lake and Hirasaki (1981), on immiscible and miscible displacements. In the limit of gravity-segregated flow, we prove conditions for the fluids to be segregated and derive the Dupuit and Dietz (1953) approximations. Finally, we also discuss effects of capillarity and transverse dispersion.
- Research Organization:
- University of Southern California, Los Angeles, CA (United States). Dept. of Chemical Engineering
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG22-90BC14600
- OSTI ID:
- 10115700
- Report Number(s):
- DOE/BC/14600-17; ON: DE92001018
- Resource Relation:
- Other Information: PBD: Jan 1992
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
RESERVOIR ROCK
FLOW MODELS
ENHANCED RECOVERY
EQUATIONS
LAMINAR FLOW
CAPILLARIES
DISPERSIONS
PARTIAL DIFFERENTIAL EQUATIONS
SERIES EXPANSION
SOLUBILITY
020300
990200
DRILLING AND PRODUCTION
MATHEMATICS AND COMPUTERS