Effect of Perforation Density on Single Phase Liquid Flow Behavior in Horizontal Wells
Authors: Yuan H. , Sarica C. , Brill J.P. 
Published: December 2007

Abstract
Horizontal wells can have very complex flow geometries, in part due to interaction between the main flow stream and the influxes along the wellbore, and also due to completion type. In this study, the flow behavior in horizontal wells with a single perforation and with multiple perforations of perforation densities equivalent to 1, 2 and 4 shots per foot were investigated. A new test facility was designed and constructed to simulate single phase liquid flow in horizontal wells. Experiments were conducted with Reynolds numbers ranging from 5,000 to 60,000 and influx to main flow rate ratios ranging from 1/5 to 1/100 for the single injection case and from 1/100 to 1/2000 for the multiple injection case and for the no influx case. A general horizontal well friction factor expression was developed using the principles of conservation of mass and momentum. Horizontal well friction factor correlations were developed by applying experimental data to the general friction factor expressions. It was observed that the friction factor for a perforated pipe with fluid injection can be either smaller or greater than that for a smooth pipe, depending on influx to main flow rate ratios. The proposed friction factor correlation can be used in any horizontal well model which considers pressure variation along the wellbore.

Introduction
The most commonly used assumptions in studying horizontal well production behavior are: infinite conductivity, and uniform influx. Infinite conductivity assumes no pressure drop along a horizontal well, and uniform influx assumes that the influx from the reservoir is constant along a horizontal well. It has been argued in the literature that the infinite conductivity wellbore assumption is adequate for describing flow behavior in horizontal wells. Although this may be a good assumption in situations where the pressure drop along the horizontal section of the wellbore is negligible compared to that in the reservoir, it is also reasonable to expect the friction and acceleration effects to cause noticeable pressure drops in long horizontal wellbores.
In a horizontal well, depending upon the completion method, fluid may enter the wellbore at various locations along the well length. The distance between perforations may not be sufficient to achieve a stabilized velocity profile, and this may lead to different pressure behavior than for fully developed flow. The pressure distribution in a horizontal well can influence the well completion and well profile design, as well as having an impact on the production behavior of the well. Therefore, both the pressure drop vs. flow behavior along the well and the relationship between the pressure drop along the well and the influx from the reservoir need to be understood.
Flow behavior in porous wall pipes or plates has been studied by several investigators in other disciplines. Although they provide useful information to the study of horizontal well flow behavior, the results can not readily be applied in the petroleum industry.
The petroleum industry started to investigate horizontal wellbore hydraulics in the late 1980's. Investigators conducted analytical or experimental studies to investigate different aspects of horizontal well flow behavior. A friction factor correlation for horizontal wellbores was proposed by Asheim et al. which includes accelerational pressure losses due to continuous fluid influx along the wellbore. However, the literature survey reveals that experimental data are limited and theoretical studies are inconclusive for predicting frictional pressure loss in horizontal wells.
In this study, an experimental and theoretical investigation of the flow behavior in a horizontal pipe with fluid injection from a single injection point in the pipe wall and from multiple injection points in the pipe wall with perforation densities equivalent to 1, 2 and 4 shots per foot has been conducted. New correlations based on acquired experimental data were developed for the prediction of friction factors in a horizontal wellbore.

Model Development
A general model was developed to predict horizontal well friction factors.
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