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 i
i =o,w, g
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

wS
Reservoir water density
wR =
Bw

Reservoir data (reservoir is initially undersaturated):

Gross reservoir volume V = 109 m 3
Porosity
= 35%
Water saturation Sw = 25%
Pressure P = 303 bar
Pore compressibility c r = 4 10
5 bar
1

5
1
Water compressibility c w = 5 10 bar
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
 2

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 (ie. At reservoir
conditions), and that we can make the following simplifying assumptions:
• 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 reservoir pressure (303 bar).
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: 8.9.06