MAB - Pete 310 page 1
Fall, 2002
PETE 310
Application of the Crude Oil PVT Properties in Reservoir Engineering Problems
Radial Flow of Crude Oils
Using Darcy's law in differential form to a crude oil flowing in a radial system gives:
(1)
To express the oil flow rate in STB/day we need to include the oil formation volume factor.
(2)
Separate variables and integrate by imposing the inner (wellbore) and outer (drainage area) boundaries.
(3)
Notice that we have assumed constant (or average) properties to integrate equation (3)!
(4)
Where:
Qo=oil flow rate , STB/day
h=pay zone thickness, ft
k=permeability , md (milidarcies)
∆P=difference between reservoir pressure and
bottom-hole flowing pressure
=(P - Pwf), psia
Bo=formation volume factor of oil at reservoir
pressure, bbl/STB
µo=oil viscosity, cp
rw=wellbore radius, ft
re=drainage radius, ft
The following sketch helps to identify the process
The application of this equation is limited to steady-state and laminar flow.
The fluid and the reservoir are homogeneous.
Oil production example:
Estimate the daily oil production of WELL77J in STB/day.
The following rock and fluid propertieshave been given to you.
k =1000 md
h =40 ft
re=700 ft
rw=0.5 ft
∆P=300 psia.
Pe= 3300 psia
Pwf= 3000 psia
Rs= 800 SCF/STB ( has remained constant over time)
gg=0.9 (specific gravity of separator gas)
˚API=40
T = 200 ˚F (reservoir temperature)
The PVT lab could not finish a complete Differential Depletion Test at Reservoir Temperature T=200˚F, but they gave to you the following data.
Pressure (psia) / Oil Density (gm / cc)5000 / 0.681
4500 / 0.676
4100 / 0.673
3500 / 0.666
3000 / 0.660
2500 / 0.652
2350 / 0.665
2100 / 0.673
1850 / 0.689
1600 / 0.697
You have reasons to believe that the reservoir pressure is above the bubble point pressure of the reservoir oil because the producing gas-oil ratio has remained constant. In addition you can (and must ) estimate the bubble point pressure of this reservoir fluid by using the data of the PVT report.
A plot of pressure vs density ( or pressure vs volume) at fixed temperature should give you the bubble point pressure of this oil.
We will take the bubble point pressure as Pb = 2,500 psia.
Or alternatively we can obtain this pressure from the type of plot we are more familiar with
Now we are sure that our reservoir is above the bubble point pressure.
To evaluate the formation volume factor to be used in equation (4) we first require its value at the bubble point pressure and then we correct it for a higher pressure using the oil compressibility.
Bob can be calculated from the following formula:
(5)
Where:
STO is obtained from the API gravity of the stock tank oil:
(6)
The density at reservoir conditions is obtained from the PVT report. (We interpolate between the two pressures closest to the reservoir pressure).
We can use a linear interpolation
Pressure (psia)3500 / Oil Density (gm/cc)
0.666
3300 / 0.664
3000 / 0.660
thus,
(7)
OR = (0.664)(62.37) = 41.414 lbm / cu ft(8)
The formation volume factor at the bubble point is then:
(9)
....but we need the formation volume factor above the bubble-point pressure
Therefore we need to correct for the compressibility of the oil above the Pb.
The following equation is to be used:
(10)
We need to find out a value for the isothermal compressibility.
We must use the data provided in the PVT report :
(11)
Therefore the formation volume factor at 3300 psia is:
(12)
To estimate the viscosity of the oil at reservoir conditions we will make use of the equations listed in Appendix B of your text book. The charts from Chapter 11 in your text book could also be used.
To evaluate the viscosity we follow a three step procedure:
(1) Evaluate Dead oil viscosity ( µoD ):
log (log (µoD+ 1)) = 1.8653 - 0.025086API - 0.5644 log T (13)
= 1.8653 - 0.025086 (40 ) - 0.5644 log 200
= -0.437
log (µoD+ 1)= 10 - 0.437 = 0.366
µoD= 10 - 0.366 - 1 = 1.321 cp
(2) Evaluate Saturated Oil Viscosity ( µob ) :
µob= A µoDB (14)
A =10.715 (Rs + 100)- 0515
B = 5.44(Rs+ 150)- 0338
µob = 0.374 cp
(3) Evaluate Oil viscosity above Pb
µo = µob ( Pb / P ) B (15)
B= C1P C2 exp (C3 + C4P )
= 2.6 P 1.187 exp ( -11.513 - 8.98x10-5 P )
= 0.29
µo = 0.374 ( 3300 / 2500 ) 0.29 = 0.405 cp
Finally the daily oil flow rate is:
Pretty good well !