Performance of Horizontal Wells with Irregular Geometry
Authors: Azar-Nejad F. , Tortike W.S. , Ali S.M. Farouq 
Published: December 2007

Abstract
Performance of wellbores with curvilinear geometry in isotropic and anisotropic rectilinear reservoirs is studied. The possibility of modeling a curvilinear wellbore by a horizontal well with straight configuration is investigated. The results show that, in anisotropic reservoirs, the pressure (potential) and pressure derivative are highly dependent on wellbore configuration. However, in isotropic reservoirs a curvilinear wellbore can be modeled by a horizontal well with the same producing length. Also, the effect of a no-flow boundary perpendicular to the wellbore axis (vertical barrier) is studied. The results show that the flux distribution around the center of the wellbore is asymmetric. In all the cases the inner boundary condition of the sources is assumed to be of uniform potential which is modeled by Discrete Flux Element, DFE, Method.

Introduction
Due to the geological and drilling restrictions, configuration of horizontal wellbores is more curvilinear rather than straight. Several potential (pressure) equations exist for horizontal wellbores with straight configuration (Clonts and Ramey, Daviau et al., Goode et al., Odeh and Babu, and Kuchuk et al.). As the potential (pressure) solutions provided by Refs. 1 through 5 are for a uniform flux inner boundary condition, to simulate an infinite conductivity solution, the use of an equivalent pressure point (Refs. 1 through 3) or an average pressure (Ref. 5) are suggested. However, Rosa and Carvalho and Azar-Nejad, Tortike and Farouq Ali showed that the equivalent pressure point is moving in time.
Azar-Nejad, Tortike and Farouq Ali presented an analytical potential solution, Discrete Flux Element, DFE, Method for sources with uniform flux or uniform potential inner boundary conditions. Discrete Flux Element, DFE, Method is a general potential solution that call be applied to wellbores and fractures with arbitrary configuration in reservoirs with arbitrary outer boundary conditions, operating under steady state or unsteady state conditions. Applying the solutions provided by Refs. 1 through 5, one has to assume a straight configuration for the wellbore. Here, through an example, it will be shown that the well configuration in anisotropic reservoirs has a significant effect on wellbore performance. Also, the effect of the reservoir geometry on the performance of the wellbore will be investigated by introducing a vertical barrier perpendicular to the wellbore.

Statement of the Problem
The main objectives of this paper are:to investigate whether a curvilinear line source can be modeled by a horizontal line source with straight configuration, andto study the effect of a vertical barrier on the performance of a horizontal wellbore.

Physical Models
To study the effect of the wellbore configuration on the performance of the wellbore a 1/4 of a circle with dimensionless radius equal to 0.2 in an isotropic and an anisotropic rectilinear reservoir is considered (Figure 1). The potential equation is modeled by Discrete Flux EIement, DFE, Method given by Refs. 7 through 12.
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