5. Inflow deviation for horizontal wells
5.1 Formation damage and skin factor for horizontal wells
It takes longer to drill a horizontal well, so the productive intervals are
vulnerable to infiltration over a longer period of time. In addition,
horizontal bore holes tend to be mechanically unstable, because the
horizontal and vertical tensions are different. Therefore, the formation
damage is normally higher for horizontal than for vertical wells.
Formation damage will usually occur near the well. The influx there is
radial, and thus quite similar to that of vertical wells. It is therefore
reasonable to represent skin pressure loss similarly as for vertical wells.
However, the skin factor for horizontal wells relates to the completed
length, Lw;
S H  p S
2 k
Lw
qo  o Bo
(5-1)
The definition (5-1) differs from the skin factor for vertical wells (3-2),
which relates to the height of the reservoir, h. This difference may lead to
paradoxes at the comparison between the skin factors for the vertical and
horizontal wells.
In the previous chapter, we assumed that the horizontal well was drilled in
the middle of the reservoir layer, and derived formulas out of this. Most
"horizontal wells" differ from this geometrically. This changes flow patterns
and pressure. Change in pressure will be represented through the geometric
skin factor, defined in accordance with (5-1) above.
5.2 Well outside the middle of the reservoir
During drilling, the well has to be steered after some recordable layer or
horizon. It will usually be appropriate to add the well in good distance from
the gas or water zone. The well will therefore usually not be in the middle
of the reservoir. Figure 5.1 illustrates the influx of a well 2 meters below
the hanging wall, in a 10 meters thick reservoir.
Figure 5.1 Well beyond the middle of the reservoir
Butler / 1994 / presents the mathematical solution for the fluids to flow to
a well beyond the middle of the reservoir. From the mathematical solution,
the geometric skin factor may be derived
2
2
1  rw   b  
Sb   ln 
   sin
 
2  2h  
h  
(5-2)
When the well is located in a reasonable distance from the upper/lower walls
(b >> rw),(5-2) becomes
1
 b 
Sb  ln  sin  ....... for : b  5rw
h 

(5-3)
Figure 5.2 shows how skin factor for the well location varies with well
position.
Figure 5.2 Skin factor due to the well being placed outside the centre.
We see that (5-3) will be sufficient for all purposes, with the exception of
wells which lie at the very boudaries. When the path is not far away from the
centre, the skin factor, according to Figure 5.2 is very modest.
5.3 Inclined wells
5.3.1 Geometric skin factor
Figure 5.3 shows the pressure distribution (and current vectors) around an
inclined well
Figure 5.3 Beveled set well in starting point
 b x 
S ( x )  ln  sin

h 

1
Where the well is close to the lying or hanging wall, this will reduce the
inflow. Using (5-3), the average skin factor because of such shielding is
estimated to
Ŝ 1 
1 h 2
 Sb db  ln 2  0.693...
h h 2
(5-5)
5.3.2 The effect of anisotropy on inclined wells
Anisotropy can be included by scaling the height (4-15) and permeability (416). For inclined wells, the height scaling causes inclination change.
Figure 5.4 illustrates an inclined well in an anisotropic layer. The well
trajectory in the real, anisotropic, reservoir is shown by the line Lw.
Anisotropy factor for the reservoir: . provides the height scaling factor.
The well trajectory equivalent, isotropy system, L̂w is obtained after scaling
the height. Inclination angle after scaling is denoted by ̂ .
Figure 5.4 Angle change by scaling
From the figure 5.4 follows the relationship between the completed length in
the real and equivalent systems:
w 
 

Lw
 1   2  1 cos2 
L̂w

0.5
(5-7)
The relationship between the inclinations can then be expressed as
cosˆ  w cos
(5-8)
Thus, the productivity index of an inclined well an anisotropy reservoir is
expressed below. This result is obtained using (4-19), and applied arithmetic
of (5-5), (5-6) and the geometrid skin factor suggested above S=0.57.
J 
2 k H h
 4 r  cos 3


h
 o Bo  ln e w
   w cos  ln
 0.57  
h
4
 rw   1


(5-9)
From (5-9) follows that with reduced vertical permeabilities, an inclined
well be more favorable than a horizontal, (with same complement length).
Figure 5.5 below compares estimates with formulas for the horizontal well (414), scaled to anisotropy, and tilted set well (5-9), for the parameters [h=
10m, Lw=50m, re=200m, rw=0.1m, =1cP, kH=1m2].
Figure 5.5 Productivity index, depending on the anisotropy
Figure 5.5 shows that a horizontal well will be marginally more favorable at
small anisotropies. At large anisotropies, a tilted set well have far better
productivity. In the case in which the vertical permeability approaches zero,
as with continuous shale layers, the productivity of a horizontal well
becomes very small. An inclined well will cut through the layers and is
therefore not much affected.
References
Cinco-Ley, H., Miller, FG, Ramey, HJJr.: "Well Test Analysis for Slanted
Wells"
SPE 5131, Annual meeting, Houston, Texas, Oct.6-9, 1974,
Cinco-Ley, H., Ramey, HJJr., Miller, FG: "Pseudo-skin Factor for PartiallyPenetrating Directionally-Drilled Wells"
SPE 5589, Annual meeting, Dallas, Texas, Sept.. 28 - Oct.1, 1975,
JPT, Nov. 1975, p. 1392
Besson, J.: "Performance of Slanted and Horizontal Wells on an Anisotropic
Medium"
SPE 20965, Europec, The Hague, 22-24 October 1990
1991 Renard, G. & Dupuy, JM: "Formation Damage Effects on Horizontal WellFlow Efficiency"
JPT July 1991, 786
Butler, R.: Horizontal Wells for the Recovery of Oil, Gas and Bitumen.
Calgary, 1994
1997 Asheim, H. & Oudeman, P.: "Determination of Perforation Schemes to
Control Production and injection Profiles along Horrizontal Wells"
SPE Drilling & Completion, March 1997, 13