Summary
In this work, we have evaluated the productivity index (PI) of a well with a
vertical, infinite-conductivity fracture in a closed rectangular reservoir for
a wide range of fracture lengths, reservoir aspect ratios, and fracture
eccentricities. The reported PIs are based on a rigorous analytical solution
for the semi-steady-state pressure distribution created by a uniform-flux
fracture in combination with Muskat’s method to convert the uniform-flux to a
uniform-pressure solution. The PIs based on Earlougher’s shape factors are too
optimistic. The equivalent-pressure (EP) method works very well at small
fracture lengths but overestimates the PI at medium and large fracture lengths.
The average-pressure (AP) method is too pessimistic at all fracture
lengths.
Introduction
The productivity of a well with a vertical, fully penetrating, and
infinite-conductivity fracture is an important benchmark, for it represents the
maximum possible productivity of a hydraulically fractured well. The
theoretical case of a fractured well in an infinite reservoir is undisputed. In
this configuration, the fractured well can be conceived as a conventional well
with an apparent radius of exactly one quarter of the fracture length. This is
true for both incompressible (Prats 1961) and compressible flow (Kuchuk and
Brigham 1976).
The more practical case of a well with an infinite-conductivity fracture in
a bounded reservoir is less clear-cut. Here, no rigorous analytical solutions
exist from which unequivocal well productivities can be derived. The
information on hand is based on early numerical flow models of questionable
accuracy and on approximate analytical solutions that have never been tested
properly. This undesirable condition prompted the present study.
Russell and Truitt (1964) were one of the first to investigate the flow to a
fractured well in a bounded reservoir. They analyzed the transient pressure
behavior of a well with an infinite-conductivity fracture in the middle of a
square drainage area with the help of a dedicated numerical flow model. Their
late-time results found their way to the list of shape factors compiled by
Earlougher (1974). These shape factors can be directly related to well
productivity.
© 2009. Society of Petroleum Engineers
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History
- Original manuscript received:
23 August 2007
- Revised manuscript received:
15 September 2008
- Manuscript approved:
20 September 2008
- Published online:
29 April 2009
- Version of record:
22 December 2009
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