Solution classroom 11 Gas: Lift
a) Maximum production rate with gas lift, at reservoir pressure 220
Relationship: qˆo 
J  p R  ps 
1  2 J  oo   go Rs  L
8 fm gx
 2d 5
Productivity index: J  17.5 / 86400  105  2.03  109
Average temperatures along the pipe 60 C
Assumed rate: 400 Sm3 / d.
Well bottom pressure: pw  220 
1
400  197 bar
17.5
Average Pressure along the pipe : (197 +10 ) / 2 = 103.5 bar .
Gas solubility at average pressure and temperature:
Rs  0.00590  0.7 102.14/0.810
0.00198  273 60 
 0.797
103.5  1.4 
1.205
 89
Assumed friction factor: fm = 0.02 .
Inserted into the formula : qˆo 

J  pR  ps 
1  2 J   oo   go Rs  L
8 fm gx
 2d 5
2.03  109  220  10 105  86400
1  2  2.03  109 800  1.22  0.7  89  2000
8  0.02  9.81
 2 0.0415
 395 Sm3 / d
b ) Maximum production rate with gas lift , at reservoir pressure 160 bar
Assumed rate: 200 Sm3 / d.
Well bottom pressure: pw  160 
1
200  149 bar
17.5
Average Pressure along the pipe : (163 +10 ) / 2 = 86.5 bar .
Gas solubility at average pressure and temperature:
Rs  0.00590  0.7  102.14/0.810
Inserted into the formula:
0.00198  273 60
 0.797
 86.5  1.4 
1.205
 72
qˆo 
2.03 109 160  10 105  86400
1  2  2.03 109 800  1.22  0.7  72  2000
8  0.02  9.81
 2 0.0415
 286 Sm3 / d
c) Gas Injection Rate
Formula: qg 
p T o 1 g x 2d 5
 qo  Rs  Rsr 
po T z
8 fm
Z - factor:
Gas density: 0.7.
Pseudo Criticals : ppc = 49 bar, Tpc = 215K ( read from the figure in Appendix 2 )
Pseudo Reduced : ppr = 86.5/49 = 1.77 , Tpr = (273 +60 ) / 215 = 1.54
Z - factor from the Standing - Katz chart : z = 0.85
Inserted in formula:
 86.5 273  15 1
9.81 2 0.0415
qˆ gi  
 1.01 273  60 0.85
8  0.44


 86400  286  72  5.5  0.32 105 Sm3 / d


d ) Assessment of the estimates
At reservoir pressure 220 bar, the rate without gas lift had previously been estimated 310 Sm3 / d.
Maximum production with gas lift 395 Sm3 / d then appears somewhat disappointing. The reason
seem to be friction along the tubing and may be ameliorated by larger tubing diameter
At reservoir pressure 160 bar : no natural production. Maximum flow rate with gas lift was estimated
286 Sm3 / d, somewhat lower than initial natural production, appears encouraging.
Comparison with numerical calculations
Figure 1 below is calculated numerically for reservoir pressure 220 bar. It shows that gas injection
provide modest oil production increase; not too far from the analytic estimate
Figure 1: Numerical computation for reservoir pressure 220 bar
Figure 2 below is calculated for reservoir pressure 160 bar. Maximum oil production is about 220
Sm3 / d, somewhat below the analytical estimate, with gas injection around 0.25.105 Sm3 / d, also s
below. The numerical calculation included slip by the relation: vg=1.1vl+0.2, while the analytic
assumed no-slip. Interface friction due to slip may be accounted for by choosing a somewhat higher
no-slip friction factor
Figure 2: Numerical computation for reservoir pressure 160 bar
The numerical calculations were based on the slip assumption: vg=1.1vl+0.2. Changes in slip
parameters will to some degree change the figures above.