Institutt for petroleumsteknologi og anvendt geofysikk
Exam i course:
TPG 4245 Produksjonsbrønner
Academic contact during examination: Harald Asheim
Phone: 73 59 49 59
Examination date: 21. desember 2013
Examination time (from-to): 0900 - 1300
Permitted examination support material: C
-
3 paper sheets A4, hand written or printed
Language: English
Number of pages: 5
Checked by:
____________________________
Date
Signature
ASSIGNMENT BASIS
Approximate reservoir geometry is illustrated below
Reservoir Data:
Reservoir Temperature:
Reservoir pressure:
Depth:
Gas gravity:
Oil gravity:
Gas / oil ratio:
Saturation pressure:
Oil formation volume factor:
Horizontal permeability:
Vertical permeability:
Viscosity:
72 C
233 bar
2200 m
0.98
0.808
148 Sm3/Sm3
173 bar
1.49 m3/Sm3
100 mD
5 mD
5 cP
Design criteria and assumptions:
- Pressure loss reservoir-wellbore should not exceed 35 bar.
- Well drilled with the bit diameter: 200 mm.
- Production target: qo = 600 Sm3 / d
- Average velocity along the completed interval at least: 1.5 m / s (to remove fines).
- Friction factor, flow in pipes: f = 0.02.
- Liner inner diameter: 50 mm along the completed interval,
- Production Pipe inner diameter: 100 mm, length 3000 m, from the end the
completed interval to the separator at surface.
- Two-phase slip flow parameters: Co = 1.2, vo = 0
- Separator pressure: 30 bar.
- Gas Formation Factor at separator pressure and temperature: Bg = 0.036
Task 1: Well Location, productivity
a) Estimate productivity index for wellbore trajectory "a" indicated in the figure above
( completed interval: 500m along the shortest reservoir axis)
b ) Estimate productivity index for wellbore trajectory "b" indicated in the figure above
( completed interval: 500m along the shortest reservoir axis)
c ) Investigate to which degree inclined wellbore trajectory may affect the productivity
index
d) Investigate the need for inflow control to achieve constant inflow density along the
completed interval. (In case you have not achieved a trustworthy estimate of the
productivity index, J = 15 Sm3/d/bar may be used. )
e ) Examine the proposed well design and consider changes.
Task 2 : Completion, production
It has been decided to locate the well along the longest reservoir axis: Lw = 1000m.
Specific productivity index to be used for design purposes: jL  5  1012 m3 / s / Pa / m .
Constant inflow density assumed, achieved by orifice based ICD.
a) Estimate tubing inlet pressure with production rate: qo = 600 Sm3 / d
b ) Estimate tubing inlet pressure gradient
c ) Where the production pipe will gas first begin to be released
d ) Estimate the flow speed at the end of the production pipe (at Xmas tree ) , when
the well produces naturally (without choking ) at rate: qo = 600 Sm3 / d
e ) Consider gas lift versus downhole pumping for sustainable design rate beyond
natural plateau period
Unit conversions
1 cp
=
1 Darcy =
10-3 Pas
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 :
Acceleration of gravity :9.81 … m/s2
28.97 kg/kmole
Formulae
Fluid properties (SI, pressure in bar):
Density, gas saturated oil:
l 
o o   g o Rs
Bo
  g
Formation factor saturated oil,: Bo  0.9759  9.52  10  
  o

4
0.5


 Rs  0.410 T  103 



1.2
104 2.81 Rt 3.10 T 171  o 118  g 1102
p 
Bo  Bob  b 
 p
o
pM  g
g 

zRT Bg
Above saturation pressure:
Gas density
:
 g o po T z
Bg 

g
p T o zo
Formation factor, gas:
Gas solubility:
Rs  5.90  10 3  g 10 2.14 /  o 10 0.00198 T 0.797 p  1.4 
1.205
Single phase flow in reservoir and well
1
qo
J
Inflow characteristics:
pw  pR 
Flow in pipe:
dp   v d v   g x dx 
Velocity:
v
Q
d2 / 4
Friction factor correlation: f  0.16  Re 0.172 with: Re 
1  2
f v dx  0
2 d
vd

Horizontal wells:
Long wells, pseudo steady : J 
6  kh


xe
h 
h
 3  ln
 S  
Lw  2rw

 Lw
2kh
Short wells, steady: J 


LD / 
h 
h
 ln
 o Bo  ln

 S  
Lw / 4
Lw  2rw


6 kh
Generally, pseudo steady: J 
 D

h 
h
o Bo 
f a  3  ln
 S  
Lw  2rw

 2 Lw
 o Bo  
Geometry factor:
L
fa  w
L
2
 
 1  Lw L  
L
L

1  0.53   1.15  0.164 

 0.45  Lw L 
D
D
 


ps 
Skin pressure loss:
qo  o Bo
S
2 k Lw
Scaling rules for anisotropic permeability: kˆ  k x k y
Inclined wells
Geometric skin: Sb  ln 2  0.69

yˆ  y k x k y  y

L̂w  Lw 1   2  1 cos 2 
Equivalent length:
Inflow control
Inflow density: qL  jL  pR  pw x 
Specific productivity index: j L  J
Bo
Lw
Pressure drop reservoir – sand face: pR  pw 
1
qL
jL
Pressure drop along production liner, constant qL: pw 
8

2
3
f 2 5 qL Lw
3  d
2
1  L  2
Orifice based inflow control: pc    c  qL
2  nc Ac 
Two phase flow in pipes
 g  d    

Rising/sinking velocity for small bubbles/drops: vo  K 
2


0.25
K = 1.53 for bubbles. K = 2.75-3.1 for droplets
 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: v g  Co vl  vo
2
 vsg

v
v

Liquid fraction:
 Co sl  1  4Co sl
vo
vo
 vo

Flux fraction:
l  vsl / vm
Volume averaged density: TP   g y g  l yl
1
yl  
2

v
1  vsg
 
 Co sl  1
2  vo
vo

Flow averaged density:  m   g g   l l
2

1
dp  TP g x dx   g vsg dvg   l vsl dvl  cTP f o m vm dx  0
2
d
 m vm d
2-phase Reynolds number: Re m 
Pipe flow relation:
m