This paper presents a discussion of the pressure-transient responses of horizontal wells in anticlinal structures and curved and undulating wells in slab reservoirs. It confirms that, in the absence of a gas cap, conventional horizontal-well models may be used to approximate the flow characteristics of the systems in which the trajectory of the well does not conform to the curvature of the producing structure. If a gas cap is present, however, the unconformity of the well trajectory and producing layer manifests itself, especially on derivative characteristics when the gas saturation increases around the well. In general, the most significant deviations from the conventional horizontal-well behavior are observed during the buildup periods following long drawdowns. In these cases, the pressure-transient analysis is complicated and requires detailed numerical modeling of the well trajectory and reservoir geometry in the vertical plane.
Conventional horizontal-well pressure-transient models assume that the top and bottom boundaries of the reservoir are horizontal planes; that is, the producing stratum is a slab, and the well is straight and parallel to the slab boundaries. Wells, however, may be drilled horizontally in anticlines and domes, or they may be curved or undulating in a horizontal slab reservoir.
In the literature, several reservoir shapes have been considered in the context of horizontal wells: infinite slab (Clonts and Ramey 1986; Ozkan et al. 1989; Goode and Thambynayagam 1987; Rosa and Carvalho 1989; Kuchuk et al. 1990, 1991; Ozkan and Raghavan 1990a), cylinder (Ozkan and Raghavan 1991a, 1991b), rectangular parallelepiped (Ozkan and Raghavan 1991a, 1991b; Daviau et al. 1988; Odeh and Babu 1990), and vertical no-flow boundary at an arbitrary orientation (Azar-Nejad et al. 1996a). The common feature of these reservoir models is the assumption that the top and bottom boundaries are horizontal planes. Despite the fact that the conditions at the top and bottom boundaries strongly influence the pressure-transient characteristics of horizontal wells (Clonts and Ramey 1986; Ozkan et al. 1989; Goode and Thambynayagam 1987; Ozkan 2001), the effect of the curvature of these boundaries, as in the case of anticlines and domes, has not been discussed in the literature.
Similar to the curvature of the top and bottom boundaries, the curvature or undulations of horizontally oriented wells (referred to as horizontal wells in this paper) have not attracted much attention in the pressure-transient-analysis literature. Two studies have addressed this issue specifically. Azar-Nejad et al. (1996b) considered a curved well that was a quarter of a circle (from vertical to horizontal) in a slab reservoir. They showed that especially in anisotropic reservoirs, the pressure-transient response of the curved well could not be approximated by that of a straight horizontal well of equal drilled length. This study did not address the issue of effective well length and the effect of the aspect ratio (the ratio of the distance from the well to the closest boundary and thickness of the formation).
Goktas and Ertekin (2003) discussed another common problem for horizontal wells—undulations. Their study indicated that when the vertical window of undulations becomes comparable to the formation thickness, undulations might influence the characteristics of pressure-transient responses. For practical windows of undulations that commonly result from standard drilling practices, however, the pressure-transient responses could be closely approximated by that of a straight horizontal well. This conclusion was different from that of Azar-Nejad et al. (1996b). It also must be noted that Goktas and Ertekin (2003) used the straight distance between the tips of the undulating well in the comparisons with straight horizontal wells, as opposed to the total drilled length used by Azar-Nejad et al. (1996b).