Exercise 1 - Review of PVT Behavior and Simple Volumetric Reservoir Calculations

TPG4150 Reservoir Recovery Techniques 2007 1
Exercise 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:
(reservoir volume of fluid)
Formation volume factor B=
(surface volume of fluid)
(surface volume of solution gas)
Solution gas-oil ratio Rso =
(surface volume of oil)
1 "V
Fluid compressibility c = ! ( )T
V "P
1 "!
Pore compressibility c r = + ( )T
! "P
Total compressibility c T = cr + !c S
i =o,w, g
i i
Expansion due to compressibility !V = V2 " V1 # "V1 c(P2 " P1 )

Gas law for hydrocarbon gas PV = nZRT
! oS + ! gS Rso
Reservoir oil density !oR =
Bo
! gS
Reservoir gas density !gR =
Bg
!
Reservoir water density !wR = wS
Bw
Reservoir data (reservoir is initially undersaturated):

9 3
Gross reservoir volume V = 10 m
Porosity ! = 35%
Water saturation Sw = 25%
Pressure P = 303 bar
Pore compressibility c r = 4 !10 "5 bar "1
Water compressibility c w = 5 !10 "5 bar"1
Gas density at surface !gS = 0, 5 kg / sm 3
Oil density at surface !oS = 760 kg / sm3
Water density at surface !wS = 1030 kg / sm 3
Water formation volume factor Bw = 1, 05
In the following, use values for Bo , Rso and Z from the figures on the next page as needed.
Part 1.Derive and compute following fluid parameters:

1. An expression for oil compressibility expressed in Bo
2. An approximate value for initial Bo
3. An approximate value for initial compressibility of oil
4. An expression for gas formation volume factor expressed in Z and P
5. An expression for gas compressibility expressed in Z and P
6. An approximate value for initial compressibility of gas
7. At which pressure is the gas compressibility highest?
8. 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 Professor Jon Kleppe

Department of Petroleum Engineering and Applied Geophysics 27.8.07
TPG4150 Reservoir Recovery Techniques 2007 2
Exercise 1
11. An approximate value for initial water density in the reservoir
Part 2. Compute following initial volumes for the reservoir:

1. Pore volume (rm3)
2. Hydrocarbon pore volume (rm3)
3. Water pore volume (rm3)
4. Oil reserves, OOIP (sm3)
5. Solution gas reserves (sm3)
6. 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
1
600 1.300
Rso
Solution gas-oil ratio (scf/bbl)
500 Bo 0.95
Formation-volume factor
400 1.200
Z-factor for gas
0.9
300
0.85
200 1.100
100 0.8
0 1.000
0 1000 2000 3000 4000 5000 0.75
Pressure (psia) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Pressure (psia)
Deadline for handing in exercise: 10.9.07
Norwegian University of Science and Technology Professor Jon Kleppe

Department of Petroleum Engineering and Applied Geophysics 27.8.07

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TPG4150 Reservoir Recovery Techniques 2007 1

Exercise 1 – Review of PVT behavior and simple volumetric reservoir calculations

Expansion due to compressibility !V = V2 " V1 # "V1 c(P2 " P1 )

Reservoir data (reservoir is initially undersaturated):

Part 1.Derive and compute following fluid parameters:

Norwegian University of Science and Technology Professor Jon Kleppe

11. An approximate value for initial water density in the reservoir

Part 2. Compute following initial volumes for the reservoir:

Part 3. Volumetric calculations for an undersaturated reservoir:

Part 4. Volumetric calculations for a gas cap reservoir:

Part 5. Volumetric calculations for a reservoir under water injection:

Rso and Bo vs. P Z-factor vs. P

Deadline for handing in exercise: 10.9.07

Norwegian University of Science and Technology Professor Jon Kleppe

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