Modelling of Undulating Wellbore Trajectories
Authors: Sharma R. , Zimmerman D. , Mourits F. 
Published: March 2010

Abstract
A technique for the efficient modelling of horizontal and undulating well trajectories is presented. In order resolve the fluid saturation and pressure, the layer containing the undulating wel1bure is refined in the vertical direction. The undulating wellbore is then represented by a series of discrete, cylindrical well bore segments which arc parallel the principal grid directions. The pressure drop and liquid holdup within the wellbore are determined through a material balance equation and multiphase pipe flow correlation.
Several examples illustrating the application of this method are given for the modelling of undulating well trajectories. A comparison between the source/sink model and the discretized wellbore model for undulating wells is made. It is demonstrated that the discrelized wellbore model should be used when the total wellbore pressure drop is comparable to the drawdown pressure. The effect of capillary pressure is also examined for several different well trajectories. Finally, the effect of well trajectory for the production from a thin oil column with bottom water drive and a gas cap is examined.

Introduction
Interest in horizontal well has increased dramatically in recent years due to improved drilling technology and increased efficiency and economy of oil recovery operation. This improvement results from the extensive contact between the reservoir and the horizontal well giving rise to lower fluid velocities around the wellbore, while providing economical total flow rates.
There are three methods used to represent horizontal wells in reservoir simulation. The first approach is the source/sink representation. This method is applicable when the frictional pressure drop along the wellbore is small compared to the well drawdown pressure(1). Furthermore the line source/sink method can yield erroneous results when wellbore backflow occurs (2) or when the reservoir permeability is high due to the presence of fractures.
The second approach is very comprehensive and requires the simulations solution of equations of the conservation of mass, momentum and energy in the wellbore together with the reservoir bore and its vicinity is important for accurate predictions. Because of the comprehensive treatment of the wellbore, the computational cost of this approach is high and therefore may be prohibitive simulations it may not be necessary to model the detailed flow phenomenon in the wellbore. A good approximation of the pressure drop phase saturation and composition distribution in the wellbore usually surfaces.
The third approach termed "the diserenzed wellbore model", couples the wellbore and reservoir flow equations by edaciously casing the wellbore flow equation in a form similar to the reservoir flow equations. Thus, efficient numerical techniques that have been developed for reservoir simulation ncan be used to accurately model the wellbore flow.
In reality, horizontal wells are not perfectly horizontal and can have complex well trajectories. These well trajectories can result in either slanted or undulating wells. For typical cases the horizontal well trajectory can vary by as much as ±5 m. Figure 1 shows a schematic representation of such an undulating well.