Summary
An analytic solution in terms of the Laplace transformation is presented to
calculate the pressure distribution in multizone, composite reservoirs
intercepted by a finite horizontal well that is oriented normal to the plane
interfaces in an infinite field. A three-zone reservoir is analyzed for
illustrative purposes, with the horizontal well traversing a thin
high-permeability central zone confined between two parallel planes
representing the natural fracture, and with the well completed in the adjacent
zones. The method provides the transient pressure field for each of the three
zones, allowing analyses of the flow fields both within the fracture and within
the reservoir as a function of pertinent parameters. The computational scheme
considered is both viable and robust. To our knowledge, this topic is yet to be
analyzed in this fashion analytically.
The numerical results presented are limited to a parametric study of (1)
transient well pressures and their time derivative and (2) steady-state flux
and flow-rate distributions at the fracture faces as a function of distance
from the well. A steady-state correlation of the productivity index is also
provided.
We discovered that of the two generally accepted procedures for estimating
the average well pressure, the one based on well rates proportional to the
local permeability and well length gives results consistent with our model,
whereas the one requiring equal average pressure at each well segment
introduces significant disturbances to the flow field near the fracture-well
intercepts, at least when small and large well lengths are present, as is the
case in the problem under consideration. This subject needs additional
investigation.
© 2012. Society of Petroleum Engineers
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History
- Original manuscript received:
23 November 2010
- Revised manuscript received:
10 May 2011
- Manuscript approved:
12 September 2011
- Published online:
16 April 2012
- Version of record:
11 June 2012
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