Page1 of 8
NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY
INSTITUTE FOR PETROLEUMTECHNOLOGY
AND APPLIED GEOPHYSICS
Contact during exam:
Name:Harald Asheim
Tlf.:94959
EXAM IN COURSE TPG4245 PRODUCTION WELLS
Fridaydecember 2. 2005
Time: 0900 - 1300
Dato for censoring: week 51
Allowed materials:
C:Specified written or non written materials. Simple calculator with empty memory.
Field scenario
The Stoltenberg reservoir contains oil. The following data is given:
Initial reservoirpressure:220 bar
Height reservoir layer:50 m
Reservoir temperature:70 C
Wellbore diameter:240 mm
Reference depth:2000 m
MVD:2450 m
Depth water oil contact:2200 m
Heigth payzone:20 m
Specific oil density:0.8
Specific gas density::0.7
Oil formation volume factor at reservoir conditions:1.05
Viscosity, dead oil
at atmospheric pressure and standard temperature:1.5 cp
Reservoir oil density:766 kg/m3
Separator pressure:10 bar
Gas oil ratio:5.5 Sm3/ Sm3 Saturation pressure, reservoir oil : 9 bar
Horizontal well productivity index:80 Sm3/d/bar.
Reservoir oil viscosity:1.4 cp
Chosen
- production tubing:120 mm id, 136 mm od
- casing:180 mm id, 194 mm od
Initially the well produced 1000 Sm3/d. After a few years of production, the reservoir pressure is expected to have dropped to 150 bar. We will in this case evaluate how this affects the production, and if artificial lift is something to consider.
EXERCISEE 1 Down hole pump (25%)
a)What is the well able to produce without artificial lift when the reservoir pressure is 150 bar?
b)What pressure increase must be delivered by a down-hole pump to mitigate the demand of 1000 Sm3/d.
EXERCISE2 Gas lift (50%)
We are able to inject gas: 1.8. 105 Sm3/d into the production tubing through a gas-injection-valve at a depth of 2000 m, i.e 2450 m MVD.
a)Estimate the liquid density and gas density at ”representative conditions for the production tubing”, given below.
b)Estimate flux fraction, at ”representative conditions”
c)Estimate liquid fraction and state the flow regime.
d)Estimate wellhead pressure at a production of 1000 Sm3/d.
”Representative conditions” for gas lift calculations.
In this exam we will perform the calculations at the following “representative conditions” for the production tubing. We are assuming thermodynamic equilibrium between the free gas and the solubilized gas in the oil.
Pressure:100 bar
Temperature:60 oC
z-factor for the gas:0.8
Gas viscosity0.012 cP
Oil viscosity0.52 cP
Interfacial tension5 dyn/cm
Gas solubility in the oil85 Sm3/ Sm3
Formation volume factor, oil1.24 m3/ Sm3
(The pressure gradient will change when pressure and temperature are altered along the well. Our “representative conditions” may be considered as a linearization of the pressure gradient. If “the representative conditions” are within reasonable limits compared to the average in the production tubing, this would give acceptable estimates. These will possible later be refined by numerical integration: likewise calculations for intervals along the pipe. Not here.)
EXERCISE3 Gas-injection (25%)
Technically considered, we are pumping the gas into the annulus at the wellhead. The gas is flowing between the casing and the production tubing, down to the injection-valve.
a)Estimate necessary nozzle size to achieve 1 bar pressure loss over the gas-injection-valve *)
b)Estimate gas-pressure at the wellhead to be able to inject the planned gas rate*)
*)For these calculations you may do the following assumptions
Average annulus gas temperature:60 C
Average gas z-factor:0.8
Formulas:
Fluidproperties(SI-units, pressure in bar):
Gas density:
Density for gas saturated oil:
FVF, saturated oil
FVF, oil above bubble point:
where:
FVF, gas:
Gas solubility in oil:
Viscosity, gas saturated oil:
µod: viscosity, gas-free oil at surface pressure and reservoirtemperature
;
Undersaturated oil:
One phase flow in reservoir and well
Inflow performance:
Exponential decline curve:
Pipe flow equation:
Friction factor correlation:
Reynolds number: for circular pip:
Pressure loss through nozzles:
Vertical wells, radial inflow
Pseudo stationary, radial PI:
Pseudo stationary inflow
Transient well pressure change:
Skin pressure loss:
Skin at partial penetration:
Horizontal wells
Long wells, stationary inflow:
Short wells, stationary inflow:
Scaling rules for anisotropic permeability:
Scaling rule for a circular wellbore:
Skin for location of HW in the reservoir layer:for b > 5 rw
Inflow density:
Inflow with pressure loss alongthe well:
Deviation from linear PI
Forcheimer’s equation:
F. equated for radial inflow:
Vogels inflow performance:
Segregated oil/water, or gas/oil
Stationary water-back:
Stationary water cone:
Flow in deviated layers:
-αw : stable deviation angle on the contact surface between the fluids:
Gas flow
Adiabatic ”EOS”:
Radial inflow:
Flow in deviated pipe:
Through nozzles:
Critic pressure loss:
Two phase flow in pipes
Rising/sinkingvelocity for small bubbles/droplets:
where: K = 1.53 for bubbles in liquid. K = 2.75-3.1 for droplets in gas
Rising velocity/sinking velocity for Dumitrescububbles:
Velocity and superfisialvelocity:
Flux relation:
Stationary liquid fraction:
Pipe flow equation:
Volume based two phase density:
Two phase friction factor:
fo(Rem) : one phase correlation, for two phase Reynoldsnr:
Slip multiplicator:
Liquid flux fraction:
Critical velocity:
Superficial velocity, as a function of total rate and fraction:
Cinematic wave velocity:
Conversion factors
1 cp=10-3 Pas
1 bar=105Pa
1 Darcy=0.9869 10-12 m2
1 dyn/cm=10-3 N/m
Constants, definitions
Standard temperature:288 Kelvin
Standard pressure:1.01 bar
General gas constant:8314 J/kmolK
Molecule weight, air:28.97 kg/kmol
Gravity:9.81 … m/s2
API-gravity:
TPG4245 Prod.brønner
16.11.2018
IPTAdmin/372/HAA/alb