Summary
This paper presents a hybrid numerical/analytical model for the
pressure-transient response of a finite-conductivity fracture intercepted by a
horizontal well. The model dynamically couples a numerical fracture model with
an analytical reservoir model. This approach allows us to include finer details
of the fracture characteristics while keeping the computational work
manageable. For example, the fracture may have irregular shape, nonuniform
width, and variable conductivity, and the well may not intersect the fracture
at its geometric center.
In this paper, we use the hybrid model to investigate the effects of
fracture properties on the pressure-transient characteristics of a single,
finite-conductivity horizontal-well fracture. The single
horizontal-well-fracture model can be extended easily to multiply fractured
horizontal wells by superposition. The model also can be used to compute the
pseudoskin caused by the effects of nonideal fracture geometry, variable
conductivity, and flow choking around the wellbore and to investigate the
influence of fracture properties on the performance of horizontal wells.
Introduction
Fracturing horizontal wells is a common practice in tight formations (Moller
1988; Yost and Overbey 1989). Choking of flow around the horizontal well and
fracture, however, strongly influences the flow characteristics and reduces the
productivity of the fracture (Soliman et al. 1990). Fig. 1 shows the
pressure surface on the fracture plane for a square hydraulic fracture
intercepted by a horizontal well. The apex of the surface indicates the well
intersection, and the increased pressure gradients around the well highlight
the choking effect. This aspect of transverse hydraulic fractures emanating
from horizontal wells is different from vertical wells. In addition, different
fracture geometries may cause horizontal-well-fracture flow regimes that are
different from those for vertical-well fractures (Fig. 2). If the
fracture is a long rectangle, for example, linear flow dominates the flow
convergence in the fracture after a short period of radial flow. Nonrectangular
or noncircular fracture geometries may lead to unconventional flow regimes.
The effects of flow-choking, fracture geometry, and variable conductivity in
a horizontal-well fracture influence the rate of pressure change until
pseudoradial flow is established. As confirmed by our results in this paper,
the pseudoskin approach provides a good approximation only for the
pressure-transient responses of long, rectangular, horizontal-well fractures
beyond the fracture radial-flow period. For the other fracture geometries, the
pseudoskin approach is appropriate only after the onset of pseudoradial flow.
Therefore, the pseudoskin approach suggested in the literature (Soliman et al.
1990; Raghavan et al. 1997; Chen and Raghavan 1997) to incorporate the
flow-choking effect into vertical-well-fracture models (Cinco-Ley et al. 1978;
Cinco-Ley and Samaniego 1981; Cinco-Ley and Meng 1988; Ozkan and Raghavan
1991a) should not be extended beyond its suggested application.
The objective of this paper is to present a model that can be used to
understand the pressure-transient performance of a single, finite-conductivity
horizontal-well fracture without the simplifying assumptions used in the
literature (Soliman et al. 1990; Raghavan et al. 1997; Chen and Raghavan 1997;
Larsen and Hegre 1991; Larsen and Hegre 1994; Guo and Evans 1993; Horne and
Temeng 1995). In this model, the fracture flow is numerically simulated and
dynamically coupled with an analytical reservoir-flow solution. Compared with a
fully numerical approach, using an analytical solution for reservoir flow
reduces the computational work and allows us to concentrate on the details of
the fracture flow. For example, the fracture can have an irregular shape
because of geological complexities, and conductivity can be variable within the
fracture because of nonuniform gel and proppant placement or a nonplanar
fracture profile. Although not included in this paper, non-Darcy flow in the
fracture aggravated by flow convergence around the wellbore can be considered
easily by a simple modification of the transmissibilities in the numerical
model. The model presented in this paper is not limited to transverse
horizontal-well fractures, either. Because the wellbore is represented as a
source term in the fracture grid, several grids may include the wellbore source
terms to simulate the appropriate intersection of the wellbore and the fracture
plane (Fig. 3). Inherent in the numerical modeling of fracture flow,
however, are the gridding, timestepping, and wellbore representation
issues.
This paper concentrates on the solution for a single, finite-conductivity,
horizontal-well fracture. The procedure for extending the single-fracture
solutions to multiply fractured horizontal wells has already been explained in
the literature (Raghavan et al. 1997; Chen and Raghavan 1997) and is briefly
discussed in Appendix A for completeness.
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
15 September 2004
- Revised manuscript received:
24 March 2006
- Manuscript approved:
17 May 2006
- Version of record:
20 August 2006
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