Summary
This paper describes a simple and easy-to-construct numerical model for the
calculation of the stabilized productivity of a hydraulically fractured well
pro-ducing at a constant well pressure. The model takes into account both Darcy
and non-Darcy pressure losses in the fracture. Dimensionless charts are
pre-sented that illustrate productivity improvement as a function of fracture
length, fracture conductivity, and non-Darcy flow. For dimensionless fracture
lengths in excess of 0.2, constant-pressure produc-tivities are significantly
lower than constant-rate productivities as predicted, for example, by the
McGuire-Sikora productivity improvement chart. The maximum difference is 20%
for an infinite-conductivity fracture with a length of unity. Both fracture
conductivity and non-Darcy flow adversely affect well productivity; the
reduction in productiv-ity is larger for longer fractures.
Introduction
The productivity of a well is commonly expressed by a productivity index
defined as the ratio of production rate and difference between average
reservoir pressure and well pressure. Stabilized productivity refers to
production from a well in the semisteady-state flow regime (i.e., the regime
beyond the initial transient regime), during which flow in the reservoir is
dominated by the reservoir boundaries. In the past, most studies on the
stabilized productivity of hydraulically fractured wells were about
steady-state production or semisteady-state production at a constant rate. As
we shall demonstrate in this paper, the type of well boundary condition has a
significant effect on productivity, especially for long fractures. For
production by pressure depletion, characterized by declining production rates,
constant well pressure is a more appropriate boundary condition.
In the late 1950s, McGuire and Sikora (1960) presented a productivity
improvement chart for fully penetrating fractured wells producing at a constant
rate under semisteady-state flow conditions based on electrical analog model
experiments. The chart shows production improvement vs. fracture conductivity
for various fracture lengths. The McGuire-Sikora chart is a classic in the
fracturing literature and is being used to this day.
In the early 1960s, Prats (1961) presented a theoretical study on the
productivity of a fully penetrating fractured well under steady-state flow
conditions. He showed that the effect of a fracture can be represented by an
apparent or effective wellbore radius, which depends on fracture length and
fracture conductivity. For fractures that are relatively small and have an
infinite conductivity, the effective wellbore radius is equal to half the
fracture half-length. In a follow-up study, Prats et al. (1962) demonstrated
that this result also holds for stabilized flow of a slightly compressible
liquid.
In the mid-1970s, Holditch presented a production improvement chart
(included in Lee 1989) based on experiments with a numerical reservoir
simulator, which essentially confirmed the earlier results of McGuire and
Sikora. Although based on production at constant rate, the McGuire-Sikora and
Holditch charts are also being used for production at declining production
rates (Lee 1989).
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
18 June 2004
- Revised manuscript received:
14 September 2005
- Manuscript approved:
3 October 2005
- Version of record:
20 March 2006
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