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NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF PETROLEUM ENGINEERING
AND APPLIED GEOPHYSICS
Academic contact during exam:
Name: Harald Asheim
Tel.:
45065771
CONTINUATION EXAM 2013 IN TOPIC TPG4245 PRODUCTION WELLS
Permitted aids:
C:
Specified printed and handwritten material allowed. Certain, simple calculator allowed.
Specified aids: A list of formulae is enclosed after the exam questions.
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Continuation Exam 2013
The following data are given
Initial Pressure
Reservoir Temperature
Gas gravity
Diameter production pipeline
Length production pipeline
Reservoir depth
Height of reservoir layer
Well Diameter
Gas z-factor at reservoir conditions
Gas viscosity at reservoir conditions
Gas formation factor at reservoir conditions:
Interfacial tension of water-gas
Reservoir pressure:
Gas Production:
Water production:
Density of produced water:
Inflow Characteristics: (units: Pa, Sm3 / s)
140 bar
61 C
0.58
174.6 mm
2040 m
1850
51 m
300 mm
0.86
0.0168 cP
0.007 m3/Sm3
60 dyn / cm
140 bar
0.5∗ 106 Sm3 / d
74 m3 / d
1010 kg/m3
pw  pR  26500  qg  1410  qg2
Slip Relation, liquid droplets in the gas: (vo: sinking speed drops)∗ 106
vl  vg  vo
a) Water solubility in gas at reservoir conditions is 1.7 gram/Sm3. Estimate the error
we make by assuming that all water is in liquid phase.
b) Estimate the superficial velocity for gas and water in the production pipe
c) Estimate water fraction (water holdup) in the bottom of the well
d) Gas production is increased from 0.5 to 0.6 ∗ 106 Sm3 / d. Estimate the resulting
water fraction at the bottom of the well.
e) Estimate water production (measured at the tubing head), shortly after the gas
production has been increased.
f) Estimate the steady state water production rate.
g) Estimate the time from the gas production has been increased, till steady state
water production has been achieved.
h) The calculations above require simplifying assumptions. Discuss these and how
these may affect the estimates above.
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Formulae
Rising/sinking velocity for small bubbles/drops:
 g  d    

vo  K 
2


0.25
K = 1.53 for bubbles. K = 2.75-3.1 for drops
 g 

vD  0.347 g D 1 
l 

Rise velocity for Dumitrescu bubbles:
Velocities:
vg 
vsg
yg

vsg
vl 
1  yl 
vsl
yl
Drift flux relation:
vg  Co vl  vo
Usually Co= 1—1.4
Stationary liquid fraction:
Flux fraction:
1
yl  
2
2
 vsg

v
v

 Co sl  1  4Co sl
vo
vo
 vo


v
1  vsg
 
 Co sl  1
2  vo
vo

l  vsl / vm
Volume averaged density: TP   g y g  l yl
Flow averaged density:  m   g g   l l
2

1
dp  TP g x dx   g vsg dv g   l vsl dvl  cTP f o m vm dx  0
2
d
Pipe flow relation:
fo : 1-phase friction factor correlation,
for 2-phase Reynolds number:
Slip multiplier:
Critical velocity
Re m 
 m vm d
m
 g yl 1  l 2  l 1  yl l 2
cTP 
 m yl 1  yl 
:
vm* 
p
 m g

p
l l 1  l 
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Superficial velocity, at given total velocity:
Kinematic wave velocity:
vk 
vsl
yl

vm
2

vm  vo  yl  vo yl
vsl 
Co 1  yl   yl
vm  vo Co  2Co vo yl  Co  1vo yl 2
Co 1  yl   yl 2
Unit conversions
1 cp
= 10-3 Pas
1 Darcy = 0.9869  10-12 m2
1 bar =
105Pa
1 dyn/cm
=
10-3 N/m
Physical constants, definitions
Standard temperature
:288 K
Standard pressure:
1.01 bar
General gas constant
:8314
Mole weight air
28.97 kg/kmole
Acceleration of gravity
:9.81 … m/s2
Reference condtion
Standard temperature
Standard pressure
15 C
1 atm
: