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RESEARCH PAPERS

# Predicting Productivity Index of Horizontal Wells

[+] Author and Article Information
Shaojun Wang

eProduction Solutions, a Weatherford company, 15995 N. Barkers Landing, Suite 275, Houston, Texas 77079shaojun.wang@ep-solutions.com

Joe Eaton

eProduction Solutions, a Weatherford company, 15995 N. Barkers Landing, Suite 275, Houston, Texas 77079

J. Energy Resour. Technol 129(2), 89-95 (Nov 02, 2006) (7 pages) doi:10.1115/1.2718577 History: Received May 12, 2005; Revised November 02, 2006

## Abstract

The popular Joshi model slightly overestimated the flow resistance of a horizontal well. As a result of this, the Joshi model underpredicts the productivity index (PI) of a horizontal well by a few percent. In the extreme case in which vertical permeability goes to zero, the Joshi model predicts a 0.0 stb∕day-psi PI, which is wrong. In this paper, the flow for a horizontal well is divided into three flows: the flow in the reservoir above the horizontal wellbore, the flow in the reservoir with a thickness of 2$rw$ containing the horizontal wellbore, and a flow in the reservoir below the horizontal well bore. The second flow is assumed to be pure horizontal flow. The first and third flows can be further divided into a horizontal flow and a vertical flow. In this paper, the equation for each flow is provided, and then combining these flows we give the equation to calculate the effective PI of horizontal wells. In addition, when the horizontal wellbore is not located at the h∕2 midpoint of a reservoir, the Joshi model predicts an increasing PI, which is intuitively and mathematically an incorrect trend. This paper derives a new equation to compute the PI of horizontal wells when the wellbore is eccentric relative to the reservoir midpoint. The new equation generates the correct trend.

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## Figures

Figure 1

An ellipsoidal flow drawn by a horizontal well

Figure 2

(a) The reservoir part that is above the horizontal wellbore. (b) the reservoir part that contains the horizontal wellbore. (c) the reservoir part that is below the horizontal wellbore.

Figure 3

The horizontal plane flow

Figure 4

The vertical plane flow for the first part of the reservoir.

Figure 5

The vertical plane flow for the third part of the reservoir

Figure 6

Comparison of productivity indexes predicted by existing and present models (L=2000ft)

Figure 7

Comparison of differences in productivity indexes predicted by Joshi and present models

Figure 8

Comparison of productivity indexes predicted by existing and present models (L=550ft)

Figure 9

Comparison of differences in productivity indexes predicted by the Joshi and present models (L=550ft)

Figure 10

Comparison of productivity indexes at different wellbore radii predicted by existing and present models (L=1000ft, kV∕kH=0.1)

Figure 11

Comparison of difference in productivity indexes predicted by Joshi and present models (L=1000ft, kV∕kH=0.1)

Figure 12

The effect of reservoir thickness on horizontal wells’ productivity indexes predicted by different models

Figure 13

Comparison of difference in productivity indexes predicted by the Joshi and present model

Figure 14

Effect of eccentricity on horizontal well productivity index

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