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 2rw 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.

1.
Borisov
,
Yu. P.
, 1964,
Oil Production Using Horizontal and Multiple Deviation Wells
, Nedra, Moscow.
2.
Giger
,
F. M.
,
Reiss
,
L. H.
, and
Jourdan
,
A. P.
, “
The Reservoir Engineering Aspect of Horizontal Drilling
,”
presented at the SPE 59th Annual Technical Conference and Exhibition, Houston, Texas, Sept. 16–19, 1984
, Paper No. SPE 13024.
3.
Joshi
,
S. D.
, 1988, “
Augmentation of Well Productivity With Slant and Horizontal Wells
,”
JPT
0149-2136,
40
, pp.
729
739
.
4.
Renard
,
G.
, and
Dupuy
,
J. M.
, 1991, “
Formation Damage Effects on Horizontal-Well Flow Efficiency
,”
JPT
0149-2136,
43
, pp.
786
868
.
5.
Kuchuk
,
F. J.
, and
Goode
,
P. A.
, “
Pressure Transient Analysis and Inflow Performance for Horizontal Wells
,”
presented at the 63rd Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Houston, TX, October 2–5, 1988
, Paper No. SPE 18300.
6.
Babu
,
D. K.
, and
Odeh
,
A. S.
, 1989, “
Productivity of a Horizontal Well
,”
SPE Reservoir Eng.
0885-9248,
4
, pp.
417
421
.
7.
Goode
,
P. A.
, and
Kuchuk
,
F. J.
, 1993, “
Inflow Performance of Horizontal Wells
,”
SPE Reservoir Eng.
0885-9248,
6
, pp.
319
323
.
8.
Kuppe
,
F.
, and
Settari
,
A.
, “
A Practical Method for Determining the Productivity of Multi-fractured Horizontal Wells
,”
presented at the 47th Annual Technical Meeting of the Petroleum Society
,
Calgary, Alberta, Canada
, June 10–12, 1996, Paper No. 96–22.
9.
Helmy
,
M. W.
, and
Wattenbarger
,
R. A.
, “
Simplified Productivity Equations for Horizontal Wells Producing at Constant Rate and Constant Pressure
,”
presented at the 1998 SPE Annual Technical Conference & Exhibition
,
New Orleans, Louisiana
, September 27–30, 1998, Paper No. 49090.
10.
Fokker
,
P. A.
,
Verga
,
F.
, and
Egberts
,
P. J. P.
, “
Semi-Analytic Calculations of Horizontal Well Productivity in Fractured Reservoirs
,”
presented at the 2003 SPE Annual Technical Conference & Exhibition
,
Denver, Colorado
, October 5–8, 2003, Paper No. 84597.
11.
Butler
,
R. M.
, 1992, “
Discussion of Augmentation of Well Productivity with Slant and Horizontal Wells
,”
JPT
0149-2136,
44
, p.
942
.
You do not currently have access to this content.