Evaluating Productivity of a Horizontal Well

Abstract

Abstract This paper discusses an alternative approach to a horizontal well (HW)productivity evaluation. The approach is based on the exact solution to a taskof the horizontal well productivity evaluation in a 3D reservoir with correctevaluation of all boundary conditions including the no cross-flow conditions atthe top and bottom of the reservoir. Validation of the new equation for the HW productivity is made by means ofspecial asymptotic analysis. In particular, it is shown that the obtainedsolution asymptotically approaches well-known solutions for cases of simpleflow geometry. However, comparison of the new equation with solutions available from theliterature shows some differences between them. We believe that this is mostlydue to a more accurate handling of boundary conditions in the new solution. Forexample, comparison with Joshi's solution [1, 2] shows that a newly obtainsolution gives higher production rates for short length of horizontal sections(Lin the order of tens of meters) and lower rates for long horizontalwells in thin reservoirs (L ph, L?re). In the latter casereduced production rate (as compared with [1]) was obtained with due regard fora no cross-flow conditions at the top and bottom of the pay interval. Higherproduction rates in case of short length of horizontal sections can be causedby a dominating effect of 3D flow in the vicinity of a well, especially in caseof a thick pay interval. The highest discrepancy between solutions reported inthe literature and proposed in this paper found to be up to 19% for long wellsand can exceed 30% for short sidetracks (5–20 m). More detailed analysis ofsimilarities and differences between several solutions is given in the nextsections. A generalized solution for the inflow performance of a HW accounting for thedirectional values of the reservoir permeability (an orthotropic reservoir) isalso given in the paper. In particular, it is shown that in case of anisotropicreservoir orientation of a horizontal well in plane has a strong impact on itsproductivity. Introduction It seems that first solution for a linear source of finite length(horizontal well) in two-dimensional plane was obtained by Slichter in 1897 [4]- a long time before the horizontal drilling has started. Kozeni [5] and Muskatin his fundamental work [6] came very close to a solution for the inflowperformance of a horizontal well in a 3D space. Both solved more challengingmathematical problems and it looks that the only thing that prevented them fromfinding solution to the horizontal well productivity evaluation problem waslack of practical importance of such solution. Horizontal wells have almost a 50-years old history, staring in the 50'swhen several wells were drilled in the Former Soviet Union (FSU). Due to lackof experience, possible early drilling problems, inappropriate wellcompletions, absence of reliable monitoring tools, and especially the lack ofconnection between drilling (and associated increased cost) and production (andassociated increased benefits) those well were deemed uneconomical. Unfortunategeneralizations of this outcome led to the conclusion that horizontal welldrilling, as a new tool for oil production, was ineffective and less attractivethan conventional drilling. As a result, those activities were abandoned in theFSU for decades [7]. In the early 1980's the Soviet idea was used in the West when severalcompanies showed that horizontal wells could be a challenging alternative toconventional drilling. Since that time the number of horizontal wells have beenincreasing rapidly in a variety of areas such as low permeability formations, carbonate reservoirs, thin pays, reservoirs with viscous oil, and fractured gasreservoirs. Now it is beyond doubt that this technology is an effective toolfor hydrocarbon recovery. While already applied in ordinary waterflooding, horizontal wells look very promising in combination with improved oil recoverymethods and could be a superior alternative to traditional oil recovery methods[7].