The Productivity of a Well with a Vertical Infinite-Conductivity Fracture in a Rectangular Closed Reservoir
- Jacques Hagoort (Hagoort & Associates BV)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2009
- Document Type
- Journal Paper
- 715 - 720
- 2009. Society of Petroleum Engineers
- 2.5.1 Fracture design and containment, 5.6.4 Drillstem/Well Testing, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc)
- infinite-conductivity fracture, well productivity
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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.
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.
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