SPE Journal
Volume 16,
Number 2,
June 2011,
pp. 401-410
Summary
In this work, we present a simple polynomial relationship for the effective
well radius of a well completed with a vertical, infinite-conductivity,
penny-shaped hydraulic fracture as a function of fracture diameter. It is based
on an analytical solution for steady-state, single-phase flow to a circular,
constant-pressure surface in an infinite porous medium. This solution is
extended to a vertical, penny-shaped fracture in the center of a plane circular
reservoir. The effective well radius increases with increasing fracture
diameter to approximately 0.2 times the fracture diameter for a fracture
diameter equal to the reservoir thickness. As a rule of thumb, the productivity
of a well with an infinite-conductivity, penny-shaped fracture exceeds the
openhole productivity for fracture diameters larger than one-third of the
reservoir thickness. The productivity of a well with a fracture diameter equal
to the reservoir thickness is approximately twice the openhole productivity.
The adverse effect of fracture conductivity can be estimated by a simple
formula that relates fracture efficiency to the productivity index of a well
with an infinite-conductivity fracture and to the ratio of the flow capacity of
the fracture to that of the reservoir.
© 2011. Society of Petroleum Engineers
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History
- Original manuscript received:
18 February 2008
- Revised manuscript received:
20 July 2010
- Manuscript approved:
2 August 2010
- Published online:
25 January 2011
- Version of record:
17 June 2011
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