Exercise 1 – Review of PVT behavior and simple volumetric reservoir calculations Conversion factors 1 bar = 100.000 pascal 100.000 pascal = = 14,50 psi 14,50 psi 3 3 1 m = 35,31 ft 35,31 ft = 6,290 bbl Definitions: (reservoir volume of fluid)
Formation volume factor
B
Solution gas-oil ratio
Rso
Fluid compressibility
c
Pore compressibility
cr = +
Total compressibility
c T = cr
=
(surface volume of fluid) (surface volume of solution gas)
=
=
(surface volume of oil)
!
V 1 " V ( )T
V " P
1 "! ( )T
! " P
! c S
+
i i
i =o w g ,
Expansion due to compressibility compressibility Gas law for hydrocarbon gas
! V PV
Reservoir oil density
! oR
Reservoir gas density
! gR
Reservoir water density
! wR
=
=
,
V 2 " V 1 # "V 1 c( P2 " P1 )
nZRT
=
! oS
gS Rso
+ !
Bo ! gS
=
Bg ! wS
=
Bw
Reservoir data d ata (reservoir (reservo ir is initially unders aturated): 9
3
Gross reservoir volume Porosity Water saturation
S w
Pressure
P
Pore compressibility
cr
Water compressibility compressibility
cw
Gas density at surface
! gS
=
0, 5 kg / sm
Oil density at surface
! oS
=
760 kg / sm
Water density at surface
! wS
Water formation volume factor
Bw
In the following, use values for
V
!
Bo
,
and Z Rso and Z
= =
10 m
35% =
=
25%
303 bar "5 "1 4 ! 10 bar "5 "1 5 ! 10 bar
=
=
=
=
3 3
1030 kg / sm
3
1, 05
from the figures on the next page as needed.
Part 1. Derive and compute c ompute following follow ing fluid parameters: param eters: 1. An expression for oil compressibility expressed in
Bo
2.
An approximate value for initial
3. 4. 5. 6. 7. 8.
An approximate value for initial compressibility compressibility of oil An expression for gas formation volume factor expressed in Z and An expression for gas compressibility expressed in Z and P An approximate value for initial compressibility compressibility of gas At which pressure is the gas compressibility compressibility highest? An approximate value for initial Bg
Bo P
9. An approximate value for initial oil density in the reservoir 10. An approximate value for initial gas density in the reservoir
Norwegian University o f Science and Technology Technolog y Department of Petroleum Engineering and Applied Geophysics
11. An approximate value for initial water density in the reservoir Part 2. Compute following initial volumes for the reservoir: 1. Pore volume (rm3)
3.
Hydrocarbon pore volume (rm 3) Water pore volume (rm3)
4.
Oil reserves, OOIP ( sm 3)
5.
Solution gas reserves ( sm3) Water reserves ( sm3)
2.
6.
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
) l 500 b b / f c s ( 400 o i t a r l i 300 o s a g200 n o i t u l o100 S
Bo
1.200
r o t c a f
e m u l o v n o i 1.100 t a m r o F
0
0.95
s a g 0.9 r o f r o t c 0.85 a f Z 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
