The Effect of the Reservoir Geometry on Horizontal Well PERFORMANCE
Authors: Azar-Nejad F. , Tortike W.S. , Ali S.M. Farouq 
Published: December 2007

Abstract
The effect of the existence of a no-flow barrier on the performance of a horizontal well and flux distribution along the wellbore are studied. Wellbore pressure was modeled using the Discrete Flux Element (DFE) Method presented in Refs. 1 through 4, with uniform potential inner boundary condition. The results of this study show that:the 100-flow barrier causes an asymmetric flux distribution along the wellbore,the equivalent pressure point is moving in time and stabilizes at late times,the location of equivalent pressure point at late times is controlled by the no-flow barrier, andthe semi-log pressure derivative at mid times (before double slope response) reflects the angle between the directions of the wellbore and the no-flow barrier.

Introduction
No-flow barriers can be modeled by the Method of Images. Therefore, the pressure inside the reservoir is to be obtained by the superposition of the pressures of the original and the image wellbores. If the barrier were not parallel or perpendicular to the horizontal well, the direction of the image well would be different from that of the coordinate axes, and consequently, from that of the principal axis of the medium. However, the original wellbore might have an arbitrary direction independent of the principal axis of the medium. Clonts and Ramey and Daviau et al. presented a uniform flux pressure solution for straight horizontal wells in the direction of one of the principal axis of the medium. As the solutions presented in Refs. 5 and 6 are obtained by the product of three 1-D solutions (Green's functions) it can be inferred that the coordinate system of their solution is parallel to the principal axis of the medium. Thus solutions presented in Refs. 5 and 6 cannot be used for modelling a vertical no-flow barrier with arbitrary direction. Azar-Nejad, Tortike and Farouq Ali presented a potential (pressure) solution for line sources with arbitrary direction (Discrete Flux Element, DFE, Method). DFE Method provides the ability for modelling a vertical barrier with arbitrary direction. Applying DFE Method one can consider different directions for:the principal axis of the medium,the coordinate axesthe wellbore, andthe no-flow barrier.

Statement of the Problem
The aim of this work isTo examine the effect of a no-flow barrier on the performance of a horizontal well.To study the flux distribution along a horizontal well line source in a semi-infinite slab reservoir.To study the effect of the angle between the directions of the wellbore and the no-flow barrier.
The model reservoir is a semi-infinite slab as shown in Figure 1. The coordinate axis are assumed to be parallel to the principal axis of the medium. The horizontal line source is extended from × = 0 to × = Lp. A vertical barrier in two different positions has been considered:It is placed at y = B and makes an arbitrary angle (0) with the wellbore direction (Figure 2).It is perpendicular to the wellbore and is located at a distance of xB from the wellbore.

Discrete Flux Element (DFE) Method
The potential equation of a line source with arbitrary configuration in an arbitrary direction can be found by applying DFE method solution presented in Refs 1 through 4:
(1)
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