Abstract
Waterconing, as a result of oil recovery through a single well, is considered. It is assumed that a sharp transition, an interface, exists between the oil and the water and that the oil region between the cap rock and the bottom water in the lower half space is of infinite radial extent.
In this paper, we study the dynamical behavior of the oil-water interface starting from a horizontal position. We give a description in terms of the stream function and extend the vortex theory developed for fresh-salt groundwater flow problems. As a result, we find two singular integral equations: one for the shear flow along the interface and one for the flow component normal to the interface. We also give the algorithm to solve these equations and to determine the time evolution of the cone.
The problem is determined by two independent dimensionless quantities: the gravity number (G) [gravity forces/viscous forces] and the mobility ratio (M) [viscous forces in oil/viscous forces in water]. As is to be expected, these computations show that, for the schematization considered here, a stationary cone, and hence, a critical production rate (below which waterfree production is possible) does not exist. Breakthrough times are numerically determined for various values ofG andM.
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Dedicated to Prof. Ir. D. N. Dietz.
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Bruining, J., Van Duijn, C.J. & Schotting, R.J. Simulation of coning in bottom water-driven reservoirs. Transp Porous Med 6, 35–69 (1991). https://doi.org/10.1007/BF00136821
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DOI: https://doi.org/10.1007/BF00136821