Productivity of Horizontal Sinks in the Presence of Distributed Fractures
- Kozo Sato (Teikoku Oil Co., Ltd.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 1997
- Document Type
- Journal Paper
- 194 - 203
- 1997. Society of Petroleum Engineers
- 5.6.5 Tracers, 1.6 Drilling Operations, 5.8.6 Naturally Fractured Reservoir, 1.2.3 Rock properties, 4.1.5 Processing Equipment, 1.6.2 Technical Limit Drilling, 5.1.5 Geologic Modeling, 3 Production and Well Operations, 5.1.1 Exploration, Development, Structural Geology
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The steady-state productivity (Jh) of horizontal sinks (hydraulically fractured wells or horizontal wells) in the presence of regularly arranged and stochastically distributed fractures is studied. Numerical experiments are conducted in two dimensions to investigate several factors affecting Jh, which include the number of fractures, the mean of fracture lengths, fracture inclination, and horizontal-sink length and location.
For 500 simulation outcomes, parametric correlations between Jh and possible regressor variables are obtained. It was found that the overall-fracture parameters (the number of fractures and the mean of fracture lengths) alone could not yield good correlations. Including near-sink fracture configurations in a set of regressor variables improves the quality. With the developed correlations, individual contributions of the horizontal sink, near-sink fractures, and overall fractures to Jh are examined. The findings obtained in this study are of help when designing horizontal sinks to be completed in fractured reservoirs.
Because of a large reservoir contact area, horizontal sinks (hydraulically fractured wells or horizontal wells) yield production rates higher than unstimulated vertical-well rates. The productivity of horizontal sinks can reach values of two to five times higher than that of vertical wells in a homogeneous medium, which could be further improved in naturally fractured reservoirs as experienced with the horizontal wells drilled in the Austin Chalk.
There exist a number of analytical solutions for the steady-state productivity of horizontal sinks. For hydraulically fractured wells, the literature goes back to Muskat, and among many predecessors, Prats was notable in introducing the concept of an effective wellbore radius. Through the analytical solutions, effects of fracture length, fracture width, and formation and fracture permeabilities are readily accounted for. For horizontal wells, one of the earlier results was that of Merkulov (as cited in Ref. 4), and an extensive review of the subject is given by Joshi. The solutions include several factors affecting the productivity: horizontal-well length, well eccentricity, reservoir thickness and extent, formation permeability (horizontal and vertical), and permeability anisotropy.
Although these theoretical studies provide remarkable insights into the subject of horizontal-sink productivity, they are somewhat limited in applicability. For instance, when the reservoir is naturally fractured, no analytical solution is available, unless the fractured reservoir is idealized by some means, such as dual-porosity models. While it is believed that horizontal sinks may intersect several fractures and outperform their vertical counterparts, the impact of individual fractures on the horizontal-sink productivity has not been well investigated. Attempts related to this subject are those of Giger, Karcher et al., Mukherjee and Economides, Soliman et al., and Raghavan and Joshi, where a hydraulically-fractured horizontal well in a homogeneous reservoir is considered and productivity increase ratios are presented.
The current study aims at investigating the productivity of horizontal sinks in a reservoir containing distributed fractures. Individual fractures are honored without the dual-porosity idealization. For this purpose, a semi-analytical technique, the complex variable boundary element method (CVBEM), is employed, since there exists no analytical solution and the numerical schemes that require domain discretization (such as finite difference and finite element methods) are not appropriate to handle a number of fractures. The use of complex variables makes computational processes efficient and enables us to utilize a conformal mapping technique to model fractures; on the other hand, it limits the applicability to two-dimensional (2D) problems. The CVBEM is formulated based on the Cauchy's integral formula and has been successfully applied to physical processes governed by the 2D Laplace equation.
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