Solution 1
a) Natural production
First investigation of shut in well:
Bottom hole pressure: pw = pR = 150 bar
Static pressure difference:
Well head pressure: pth =150-150.3 =-0.3 bar
We are observing that the well head pressure of a shut-in well is less than the separator pressure, i.e. the well will not produce from its own energy alone.
b) Production: 1000 Sm3/d, with pump
Bottomhole pressure:
Static pressure difference:
Flow:
Flow velocity:
Reynolds number:
Friction factor =0.024
Pressure loss due to friction when flowing:
Necessary inlet pressure to the production tubing
Bottom-hole pressure:
Necessary pressure increase across the pump: Dp = pt - pw = 25 bar
Solution 2
a) Fluid densities
Gas density:
Gas molecular weight: Mg = 0.7 . 28.97= 20.3
Gas density:
Gas saturated oil:
b) Superficial velocities
Injected gas being dissolved in the oil: DR=Rs – Rti = 85 – 5.5 = 79.5 Sm3/ Sm3
Free gas flow in the pipe: qgf = qgi - DRqo= 1.8. 105 - 79.5.1000 =1.0. 105 Sm3/d
Gas formation volume factor:
Superficial velocity, gas:
Superficial velocity, liquid:
Total superficial velocity: vm = vsg + vsl = 2.23 m/s
Liquid flux fraction: ll = 1.27/2.23 = 0.57
c) Liquid fraction and flow-regime
The liquid flux fraction is somewhat larger than 0.5, so there will be more liquid than gas. The liquid will not likely be completely continuous. The regime may be characterized as hopping. Since the total velocity is reasonable large and the surface tension is quite small, the gas will probably be finely distributed.
To get an estimate of the rising velocity we may as a basis apply the formula for small bubbles in a continuous liquid:
Liquid fraction, we choose a distribution factor: Co = 1.2
Two phase density:
d) X-mas tree pressure.
Bottom-hole pressure:
”Kvasi” static pressure loss:
Two phase friction factor:
Reynolds number:
Multiplicator:
Frictionfactor: fTP = 0.93 . 0.0175 = 0.0163
Pressure loss due to friction when flowing:
Well head pressure.
Solution 3
a) Nozzle size
Down hole injection pressure : pgi = pw +Dp =137.5 bar
Gas density, at injection pressure:
Formation volume factor:
Down hole volume flow: Qg = qg . Bg = (1.8 . 105 )( 6.87 .10-3)/86400= 1.43 .10-2 m3/s
Pressure loss relation:
Effective nozzle cross section:
Effective nozzle diameter: dc =2.1. 10-2 m = 21 mm
b) Well head pressure
Annular area:
Flow velocity in the annulus: vg =1.43 .10-2 /1.1 .10-2 =1.31 m/s
At this modest flowing velocity, the friction due to flow will be small. If we neglect the friction due to flow, we get the following well head pressure: