| (Fracture acidizing) One technique used to increase the productivity
of oil wells is to inject acid under high pressure until it fractures the porous
formation. At the point of fracture, acid flows out from the well bore along the
fracture slit dissolving the face of the slit as it flows. When the pressure on the
well is released, the faces of the slit try to come together but a small channel
usually remains where the faces have been dissolved. In addition to reacting with
the slit, some of the acid "leaks off" through the side of the slit
and is consumed in the porous rock. See Figure
CDP11-E (Fracture acidizing).
Fracture acidizing |
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| (a) Assuming steady-state flow, derive a differential equation describing the flow and reaction of the acid in the channel assuming that the reaction is mass transport-limited to the surface for flow in a slit between two surfaces separated by a distance D, | ||
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As a first approximation, assume that Sh is independent of the leak-off rate. (b) For the case of a linear leak-off rate |
solve for
the concentration profile, CA.