Part IV - Well productivity estimating methods
.pdfAn Infinite Conductivity
Vertical Fracture
MZ-solution (2004):
q |
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2 kh p |
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2 |
L / 2 |
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2re |
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re |
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L / 2 |
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arctan |
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rw |
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2re |
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Asymptotic behavior:
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2khL p |
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L |
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arctan |
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qF |
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2re |
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September 15, 2012 |
Part IV - Modern well stimulation |
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31 |
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methods (Gubkin - IFP program) |
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A Long Horizontal Well
MZ-solution (2004):
qHW |
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2 kh p |
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2re |
2 |
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2re |
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L |
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h |
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h |
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B ln |
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1 |
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arctan |
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2re |
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2rwe |
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Asymptotic behavior: |
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arctan |
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2re |
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2 |
qHW |
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2khL p |
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h |
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h |
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r |
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e |
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2r |
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w |
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September 15, 2012 |
Part IV - Modern well stimulation |
32 |
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methods (Gubkin - IFP program) |
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A Long Horizontal Well vs Infinite Conductivity Long Vertical Fracture
Asymptotic behavior: |
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qF |
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h |
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q |
HW |
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2r e |
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e |
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w |
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If h = 10 m, re = 100 m, rw = 0.1 m, then 0.0927
qF 1 0.0927 1.0927
qHW
September 15, 2012 |
Part IV - Modern well stimulation |
33 |
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methods (Gubkin - IFP program) |
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Well Performance Comparisons
Production rate calculations (MZ-solution)
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500 |
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m3/d |
400 |
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rate, |
300 |
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VW |
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Production |
200 |
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SW |
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HW |
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100 |
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FW |
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0 |
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60 |
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100 |
120 |
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Well lengh, m |
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September 15, 2012 |
Part IV - Modern well stimulation |
34 |
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methods (Gubkin - IFP program) |
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Well Interference
a) |
Wells in line |
b) Wells in grid |
D
D
D
re
re
- vertical well
- horizontal well
September 15, 2012 |
Part IV - Modern well stimulation |
35 |
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methods (Gubkin - IFP program) |
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Vertical Wells in Line
Total inflow into (2n+1) vertical wells with a distance D between them:
q |
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2k h p(2n 1) |
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2 |
nD |
2 |
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2re |
nD |
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re |
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B |
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2n 1 ln |
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ln |
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1.85 |
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2 |
nD |
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arctan |
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rw |
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D |
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D |
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September 15, 2012 |
Part IV - Modern well stimulation |
36 |
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methods (Gubkin - IFP program) |
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Vertical Wells in Line
Pressure distribution for 2 horizontal wells in line:
psxy |
psyz |
psxz |
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September 15, 2012 |
Part IV - Modern well stimulation |
37 |
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methods (Gubkin - IFP program) |
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Vertical Wells in Grid
Total inflow into (2n+1) vertical wells with a distance D between them:
q |
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2kh p(2n 1)2 |
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2.9re |
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2.9rw |
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B 2n 1 |
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ln |
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ln |
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(2n 1)D |
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D |
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September 15, 2012 |
Part IV - Modern well stimulation |
38 |
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methods (Gubkin - IFP program) |
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Vertical Wells in Grid
Pressure distribution for 3x3 horizontal wells in grid:
psxy |
psyz |
psxz |
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September 15, 2012 |
Part IV - Modern well stimulation |
39 |
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methods (Gubkin - IFP program) |
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Effect of well interference on total
production |
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Total production rate vs number of wells |
Input data: |
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h = 10 m |
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Sm3/d |
10000 |
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re= 5000 m |
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Without interference |
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8000 |
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rate, |
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6000 |
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production |
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4000 |
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With interference |
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2000 |
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Total |
0 |
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0 |
10 |
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30 |
40 |
50 |
60 |
Number of w ells
Q(15 wells without interference) = Q(26 wells with interference)
September 15, 2012 |
Part IV - Modern well stimulation |
40 |
|
methods (Gubkin - IFP program) |
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