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NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY
INSTITUTE FOR PETROLEUM TECHNOLOGY
AND APPLIED GEOPHYSICS
Contact during exam:
Name: Harald Asheim
Tlf.: 94959
EKSAMEN IN COURSE TPG4245 PRODUKSJONSBRØNNER
Friday decmber 5. 2003
Time: 0900 - 1300
Date for censoring: January 8. 2004
Allowed materials:
C: Specified written or non written materials.Simple calculator with empty memory.
Dataheet:
The following reservoir data is given for the Eugene Island Field:
Vertical depth : 1283 m
Oil gravity : 28.6 API (0.88)
Viscosity, gas free oil, @ reservoir temp. : 2 cp
Gas gravity : 0.65
Viscosity, gaas @ reservoir conditions : 1.3 · 10-3 cp
Reservoir pressure : 134.3 bar
Reservoir temperature : 327 K
Layer heigth, productive zone : 12 m
Drainage area, close to quadratic : 80 000 m2
Horizontal permeability : 8.2 mD
Vertical permeability : 4.1 mD
Well K-5 is completed with a 2 3/8 in. production tubing. (o.d. 60.33 mm, nominal wall thickness 4.83 mm). The wellbore diameter is 160 mm. A production test resulted in the following:
Test nr. / 1 / 2 / 3 / 4Bottom-hole pressure (bar) / 93.1 / 100.0 / 101.4 / 103.4
Oil production (Sm3/d) / 17.7 / 15.6 / 14.3 / 13.5
Gas/oil ratio (Sm3/ Sm3) / 37.9 / 42.2 / 49.7 / 42.4
Water cut % / 0.3 / 0.2 / 0.4 / 0.4
Well head temperature (K) / 306 / 304 / 304 / 303
An analysis resulted in the following (ref Ex 2000):
Gas oil ratio : 43.1 Sm3/Sm3
Viscosity, oil saturated with gas : 0.877 cP
Saturation pressure : 96.2 bar
FVF oil at saturation pressure : 1.12 m3/Sm3
Productivity index : 0.452 Sm3/d/bar
A development study concluded that to achieve the same productivity as for a vertical well, a horizontal well had to be 14.7 m long.
Specific productivity index for long horizontal well: 3.67 × 10-12 Sm3/s/m/Pa
Maximum productive well length (length of reservoir): 283 m
Pseudocritic gas pressure: 46.2 bar
Pseudocritic gas temperature: 203 K
From development studies it is decided to drill and complete a horizontal well through the whole length of the reservoir. The liner is run in hole together with a sand-screen as illustrated in figure 1.
Inner diameter, liner: 30 mm
Friction factor, liner: 0.03
The last production tubing packer will be located by the heel, TVD 1283 m, as illustrated in Fig 1. MVD along the production tubing is 1500 m.
EXERCISE 1
a) Estimate the tubing inflow pressure when producing 200 Sm3/d, neglecting pressure loss along the liner.
b) Estimate the flowing velocity aling the liner, between the toe and the heel. (suppose constant inflow density along the completed interval)
c) Estimate tubing inflow pressure when accounting for pressure loss along the liner. (Same assumptions as in Exercise 1 b)
d) Vurder (kvantitativt og kortfattet, basert på estimatene ovenfor) hvordan innstrømning og trykk langs røyret vil variere. Hvordan kan brønnkompletteringen eventuelt endres for å oppnå jevnere fordelt innstrømning. (Hva slags endringer vil du anbefale?)
d) Evaluate (quantitatively and short, based on the above estimates) how the inflow and pressure along the pipe will vary. If possible, how can you, by a recompletion achieve a more equal distribution of the inflow. (What changes would you recommend?).
EXERCISE 2
We are able to produce 200 Sm3/d until the well head pressure drops down to 10 bar, equal to the separator pressure.
a) Estimate the superficial velocity for oil and gas at the wellhead when we are producing as mentioned above.
b) Estimate flux fraction and liquid fraction (no-slip holdup and holdup), based on the Z-F operation-flux-model with the parameters: Co = 1.2, v∞ = 0.2 m/s.
c) Estimate the pressure gradient at the wellhead when we are assuming a friction factor: f = 0.015. Also estimate the bottom hole pressure by assuming a constant pressure gradient.
d) A constant pressure gradient will be an approximation because the pressure gradient will not likely be constant along the well. How will the real bottom-hole pressure deviate from the above estimate? Underlie your statement.
Figure 1 : Completion of a horizontal well on Eugene Island
Conversion factors
1 cp = 10-3 Pas
1 bar = 105 Pa
1 Darcy = 0.9869 · 10-12 m2
1 dyn/cm = 10-3 N/m
Gravity : 9.81 m/s2
Standard temperature : To = 288 k
Standard pressure : po = 1.01 bar
Gas constant : 8314.34 J/(Kmol · K)
Molecule weigth, air : 28.97
Given formulas
Productivity index, pseudo stationary oil production, radial inflow
Relationship API-gravity, specific density
Standings correlation for oil formation volume factor (SI-units)
Gas formation volume factor
Standings correlation for gas solubility (pressure in bar)
Specific, pseudo-stationary-productivity-index for a long horizontal well in a homogenous reservoir.
Pipe flow equation
Density oil, containing solution gas
General equation of state
Zuber-Findlay’s flux relation
Average, two phase flowing velocity
Volumetric flow, liquid
Volumetric flow gas
Average twophase densities
- flowing average
- volume average
Relationship between velocity and superfiscial velocity
Figure: Standing-Katz z-faktor diagram.
TPG4245 Prod.brønner
2008-8-11
HAA/alb