Two publications give the skin factor due to restricted entry to flow at thewellbore. Restricted entry occurs when only part of the productive sand is opento flow. This can be caused by partial penetration or by perforating a portionof the sand. penetration or by perforating a portion of the sand. It isrecognized that in some cases restricted entry may be due to pluggedperforations or to insufficient number of perforations. This situation, thoughit will result in an additional skin factor, is not what is discussed in thisarticle. One of the publications gives the skin factor for three cases. Thefirst is for a partially penetrating well; the second is for a well producingfrom only the central portion of the productive interval; and the third is fora well in which several equally spaced intervals are open to flow. The secondpublication presents charts for estimating the skin factor when presents chartsfor estimating the skin factor when the open interval starts at eight differentlocations and covers a range of thickness of 20 to 200 ft. In this article skinfactor as a function of sand thickness, location of the open interval, and thewellbore radius is given in a general equation form:

ht 0.825 kH Sr = 1.35 ----- ---1 {1n ht -------- + 7) hp kV

kH - 0.49 + 0.1 1n h ---------- kV

.1n r - 1.95}, .............................(1) wc

where

Sr = skin factor due to restricted entry, ht = total sand thickness, ft (m), hp = length of perforated interval, ft (m), kH/kV = ratio of horizontal tovertical permeability, rwc = corrected wellbore radius, ft (m), and is givenby

0.2126(Zm/ht + 2.753) r = r e wc w

for y greater than 0, and rwc = rw for y=0,

y = distance between the top of the sand and the top of the open interval, and zm = distance between the top of the sand and the middle of the openinterval.

The relation between y, hp, and Zm is

Zm = y+hp/2...........................................(2)

Because of symmetry, Zm/ht 0.5. A plot of rwc/rw vs. Zm illustrating thesymmetry is shown in Fig. 1.

Discussion of Eq. 1

The radius of drainage rd does not appear in Eq. 1. This is because sr isvery insensitive to rd. For example, an increase in rd from 330 to 6,600 ftincreases Sr from 43.38 to 43.50, when ht=300, y = 0, and rw = 0.25. The valueof sr is most sensitive to the ratio of the open interval to the sandthickness, and to the sand thickness. Comparison between sr values calculatedby Eq. 1 and read from Refs. 1 and 2 is given in Fig. 2. The comparison isgood, and Eq. 1 is adequate for engineering calculations. The use of Eq.1 isillustrated by the following example. Calculate Sr when ht=200 ft, hp=40 ft, rw= 0.25ft, and y=80ft.

P. 964

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