TPG4150 Reservoir Recovery Techniques 2015
Exercise 1
1
Exercise 1 – Review of PVT behavior and simple volumetric reservoir calculations
Conversion factors
1 bar = 100.000 pascal = 14,50 psi
1 m3 = 35,31 ft3 = 6,290 bbl
Definitions:
Formation volume factor
Solution gas-oil ratio
Fluid compressibility
Pore compressibility
Total compressibility
(reservoir volume of fluid)
(surface volume of fluid)
(surface volume of solution gas)
Rso =
(surface volume of oil)
1 ∂V
c = − ( )T
V ∂P
1 ∂φ
c r = + ( )T
φ ∂P
B=
c T = cr +
∑c S
i i
i =o,w, g
Expansion due to compressibility
Gas law for hydrocarbon gas
Reservoir oil density
Reservoir gas density
Reservoir water density
ΔV = V2 − V1 ≈ −V1 c(P2 − P1 )
PV = nZRT
ρ oS + ρ gS Rso
ρoR =
Bo
ρ gS
ρgR =
Bg
ρ
ρwR = wS
Bw
Reservoir data (reservoir is initially undersaturated):
V = 109 m 3
Gross reservoir volume
Porosity
φ = 35%
Water saturation
Sw = 25%
Pressure
P = 303 bar
Pore compressibility
Water compressibility
Gas density at surface
Oil density at surface
Water density at surface
Water formation volume factor
c r = 4 ⋅10 −5 bar −1
c w = 5 ⋅10 −5 bar−1
ρgS = 0, 5 kg / sm 3
ρoS = 760 kg / sm3
ρwS = 1030 kg / sm 3
Bw = 1, 05
In the following, use values for Bo , Rso and Z from the figures on the next page as needed.
Part 1.
1.
2.
3.
4.
5.
6.
7.
8.
Derive and compute following fluid parameters:
An expression for oil compressibility expressed in Bo
An approximate value for initial Bo
An approximate value for initial compressibility of oil
An expression for gas formation volume factor expressed in Z and P
An expression for gas compressibility expressed in Z and P
An approximate value for initial compressibility of gas
At which pressure is the gas compressibility highest?
An approximate value for initial Bg
9. An approximate value for initial oil density in the reservoir
10. An approximate value for initial gas density in the reservoir
Norwegian University of Science and Technology
Department of Petroleum Engineering and Applied Geophysics
Professor Jon Kleppe
20.8.15
TPG4150 Reservoir Recovery Techniques 2015
Exercise 1
2
11. An approximate value for initial water density in the reservoir
Part 2.
1.
2.
3.
4.
5.
6.
Compute following initial volumes for the reservoir:
Pore volume (rm3)
Hydrocarbon pore volume (rm3)
Water pore volume (rm3)
Oil reserves, OOIP (sm3)
Solution gas reserves (sm3)
Water reserves (sm3)
Part 3. Volumetric calculations for an undersaturated reservoir:
The reservoir is producing oil only until the pressure reaches 230 bar. Use initial oil compressibility.
1. Neglect pore and water compressibilities and compute oil recovery in % of OOIP
2. Neglect water compressibility and compute oil recovery in % of OOIP
3. Compute oil recovery in % of OOIP with all compressibilities included
Part 4. Volumetric calculations for a gas cap reservoir:
Assume (hypothetically!) that the reservoir has a gas cap of equal volume to that of the oil zone, and that we can
• neglect that gas comes out of solution,
• assume that the relative volumes in the reservoir are constant, and
• we can use fluid parameters at initial pressure.
Again let the reservoir produce only oil until the pressure reaches 230 bar.
1. Compute oil recovery in % of OOIP with all compressibilities included
2. Compute oil recovery in % of OOIP if only gas compressibility is included
Part 5. Volumetric calculations for a reservoir under water injection:
If the reservoir is to be pressure maintained through water injection, and the oil production initially is kept at
3000 sm3 per day, what water injection rate is required?
Rso and Bo vs. P
Z-factor vs. P
600
1
1.300
Bo
400
1.200
300
200
1.100
100
0
0.95
Z-factor for gas
500
Formation-volume factor
Solution gas-oil ratio (scf/bbl)
Rso
0.9
0.85
0.8
1.000
0
1000
2000
3000
4000
5000
Pressure (psia)
0.75
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Pressure (psia)
Norwegian University of Science and Technology
Department of Petroleum Engineering and Applied Geophysics
Professor Jon Kleppe
20.8.15