correlations pvt scal
TRANSCRIPT
Technical DescriptionRock compressibility
325
Chapter 7Technical Description
PVT property correlations
Rock compressibility
Newman
Consolidated limestone
psi [EQ 7.1]
Consolidated sandstone
psi [EQ 7.2]
Unconsolidated sandstone
psi, [EQ 7.3]
where
is the porosity of the rock
Hall
Consolidated limestone
psi [EQ 7.4]
Cr exp 4.026 23.07�– 44.28�2+( )
6–�10=
Cr exp 5.118 36.26�– 63.98�2+( )
6–�10=
Cr exp 34.012 � 0.2–� �( )6–�10= 0.2 � 0.5� �� �
�
Cr3.63 5–�10
2�-------------------------PRa
0.58–=
326 Technical Description Water correlations
Consolidated sandstone
psi, [EQ 7.5]
psi,
where
Knaap
Consolidated limestone
psi [EQ 7.6]
Consolidated sandstone
psi [EQ 7.7]
where
Water correlations
Compressibility
Meehan
[EQ 7.8]
Cr7.89792 4–�10
2----------------------------------PRa
0.687–= � 0.17�
Cr7.89792 4–�10
2----------------------------------PRa
0.687– �0.17----------� � 0.42818–
�= � 0.17�
is the porosity of the roc
is the rock reference pressure
is
�
Pa
PRa depth over burden gradient 14.7 Pa–+�� � 2�
Cr 0.864 4–�10PRa
0.42 PRi0.42–
� Pi Pa–� �--------------------------------- 0.96 7–�10–=
Cr 0.292 2–�10PRa
0.30 PRi0.30–
Pi Pa–--------------------------------- 1.86 7–�10–=
is the rock initial pressure
is the rock reference pressure
is the porosity of the rock
is
is
Pi
Pa
�
PRi depth over burden gradient 14.7 Pi–+�� � 2�
PRa depth over burden gradient 14.7 Pa–+�� � 2�
cw Sc a bTF cTF2
+ +� � 6–�10=
Technical DescriptionWater correlations
327
where
[EQ 7.9]
where
Row and Chou
[EQ 7.10]
[EQ 7.11]
[EQ 7.12]
[EQ 7.13]
[EQ 7.14]
[EQ 7.15]
[EQ 7.16]
[EQ 7.17]
[EQ 7.18]
a 3.8546 0.000134p–=
b 0.01052– 4.77 7–�10 p+=
c 3.9267 5–�10 8.8 10–�10 p–=
Sc 1 NaCl0.7 0.052– 0.00027TF 1.14 6–�10 TF2
– 1.121 9–�10 TF3
+ +� �+=
is the fluid temperature in ºF
is the pressure of interest, in psi
is the salinity (1% = 10,000 ppm)
TF
p
NaCl
a 5.916365 100 TF 1.0357940– 10 2– TF 9.270048�+�� �
1TF------ 1.127522 103 1
TF------ 1.006741 105��+�–� �
�+
�+�=
b 5.204914 10 3– TF 1.0482101 10 5– TF 8.328532 10 9–��+�–� �
1TF------ 1.170293–
1TF------ 1.022783 102 ���+� �
�+
�+�=
c 1.18547 10 8– TF 6.599143 11–�10�–�=
d 2.51660 TF 1.11766 2–�10 TF 1.70552 5–�10�–� ��+–=
e 2.84851 TF 1.54305 2–�10 TF 2.23982 5–�10�+–� ��+=
f 1.4814–3–�10 TF 8.2969 6–�10 TF 1.2469 8–�10�–� ��+=
g 2.7141 3–�10 TF 1.5391–5–�10 TF 2.2655 8–�10�+� ��+=
h 6.2158 7–�10 TF 4.0075–9–�10 TF 6.5972 12–�10�+� ��+=
Vw a p14.22------------- b p
14.22------------- c�+� �
NaCl 1 6–�10
d NaCl 1 6–�10� e�+� �
NaCl 1 6–�10� p14.22------------- f NaCl 1 6–�10� g 0.5 p
14.22------------- h ���+�+� �
��–
�
�+�–=
328 Technical Description Water correlations
[EQ 7.19]
Formation volume factor
Meehan
[EQ 7.20]
• For gas-free water
[EQ 7.21]
• For gas-saturated water
[EQ 7.22]
[EQ 7.23]
where
cw
b 2.0 p14.22------------- c NaCl 1 6–�10� f NaCl 1 6–�10� g p
14.22------------- h�+�+� �
�+��+� �
Vw 14.22�------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------=
is the fluid temperature in ºF
is the pressure of interest, in psi
is the salinity (1% = 10,000 ppm)
is the specific volume of Water
is compressibility of Water
TF
p
NaCl
Vw cm3 gram� �
cw 1 psi� �
Bw a bp cp2+ +� �Sc=
a 0.9947 5.8 6–�10 TF 1.02 6–�10 TF2
+ +=
b 4.228 6–�10– 1.8376 8–�10 TF 6.77 11–�10 TF2
–+=
c 1.3 10–�10 1.3855 12–�10 TF– 4.285 15–�10 TF2
+=
a 0.9911 6.35 6–�10 TF 8.5 7–�10 TF2
+ +=
b 1.093 6–�10– 3.497 9–�10 TF– 4.57 12–�10 TF2
+=
c 5 11–�10– 6.429 13–�10 TF 1.43 15–�10 TF2
–+=
Sc 1 NaCl 5.1 8–�10 p 5.47 6–�10 1.96 10–�10 p–� � TF 60–� �
3.23 8–�10– 8.5 13–�10 p+� � TF 60–� �2
+
+
�
+=
is the fluid temperature in ºF
is the pressure of interest, in psi
is the salinity (1% = 10,000 ppm)
TF
p
NaCl
Technical DescriptionWater correlations
329
Viscosity
Meehan
[EQ 7.24]
[EQ 7.25]
Pressure correction:
[EQ 7.26]
where
Van Wingen
[EQ 7.27]
where
Density
[EQ 7.28]
where
Water Gradient:
[EQ 7.29]
�w Sc Sp 0.02414446.04 Tr 252–� ��
�10� �=
Sc 1 0.00187NaCl0.5– 0.000218NaCl2.5
TF0.5 0.0135TF–� � 0.00276NaCl 0.000344NaCl1.5
–� �
+
+
=
Sp 1 3.5 12–�10 p2 TF 40–� �+=
is the fluid temperature in ºF
is the pressure of interest, in psi
is the salinity (1% = 10,000 ppm)
TF
p
NaCl
�w e 1.003 TF 1.479 2–�10– 1.982 5–�10 TF�+� ��+� �=
is the fluid temperature in ºFTF
�w62.303 0.438603NaCl 1.60074 3–�10 NaCl2+ +
Bw-------------------------------------------------------------------------------------------------------------------=
is the salinity (1% = 10,000 ppm)
is the formation volume factor
is the Density of Water
NaCl
Bw
�w lb ft3� �
g�w
144.0------------- [psi/ft]=
330 Technical Description Gas correlations
Gas correlations
Z-factor
Dranchuk, Purvis et al.
[EQ 7.30]
[EQ 7.31]
[EQ 7.32]
[EQ 7.33]
[EQ 7.34]
[EQ 7.35]
[EQ 7.36]
where
z 1 a1a2TR�---------
a3
TR3�
---------+ +� �� �� �
Pr a4a5TR�---------+
� �� �
Pr2 a5a6Pr
5
TR�-------------------
a7Pr2
TR3�
------------ 1 a8Pr2
+� �exp a8Pr2
–� �
+ + +
+
=
TR�TRTc�--------=
Tc� Tc5E3
9---------� � –=
E3 120 YH2SYCO2
+� �0.9
YH2SYCO2
+� �1.6
–� � 15 YH2S
0.5 YH2S4
–� � +=
Pr0.27PprZTR�
-------------------=
PprPPc�---------=
Pc�PcTc�
Tc YH2S1 YH2S
–� �E3+-----------------------------------------------------------=
is the reservoir temperature, ºK
is the critical temperature, ºK
is the reduced temperature
is the adjusted pseudo critical temperature
is the mole fraction of Hydrogen Sulphide
TR
Tc
TR�
Tc�
YH2S
Technical DescriptionGas correlations
331
[EQ 7.37]
Hall Yarborough
[EQ 7.38]
where
Reduced density ( ) is the solution of the following equation:
[EQ 7.41]
This is solved using a Newon-Raphson iterative technique.
is the mole fraction of Carbon Dioxide
is the pressure of interest
is the critical pressure
is the adjusted pseudo critical Pressure
is the critical temperature, ºK
YCO2
P
Pc
Pc�
Tc
a1 0.31506237=
a2 1.04670990–=
a3 0.57832729–=
a4 0.53530771=
a5 0.61232032–=
a6 0.10488813–=
a7 0.68157001=
a8 0.68446549=
Z0.06125Pprt
Y------------------------------� � exp
1.2 1 t–� �2–� �=
is the pseudo reduced pressure
is
is the reduced density
(where is the pressure of interest and is the critical pressure)
[EQ 7.39]
(where is the critical temperature and is the
temperature in ºR) [EQ 7.40]
Ppr
t 1 pseudo reduced temperature�
Y
PprPPcrit-----------= P Pcrit
tTcritTR
----------=Tcrit TR
Y
0.06125Pprte1.2 1 t–� �2–
– Y Y2 Y3 Y4–+ +
1 Y–� �3----------------------------------------
14.76t 9.76t2– 4.58t3+� �Y2–
90.7t 242.2t2– 4.58t3+� �Y 2.18 2.82t+� �
+
+ 0=
332 Technical Description Gas correlations
Viscosity
Lee, Gonzalez, and Akin
[EQ 7.42]
where
Formation volume factor
[EQ 7.43]
where
Compressibility
[EQ 7.44]
where
Density
[EQ 7.45]
[EQ 7.46]
�g 10 4– K XpY� �exp=
� 1.4935 10 3–� �pMgzT--------=
BgZTRPscTscP
-------------------=
is the Z-factor at pressure
is the reservoir temperature
is the pressure at standard conditions
is the temperature at standard conditions
is the pressure of interest
Z P
TR
Psc
Tsc
P
Cg1P---
1Z--- Z�
P�------� � –=
is the pressure of interest
is the Z-factor at pressure
P
Z P
�g35.35�scP
ZT-------------------------=
�sc 0.0763�g=
Technical DescriptionOil correlations
333
where
Condensate correction
[EQ 7.47]
where
Oil correlations
Compressibility
Saturated oil
McCain, Rollins and Villena (1988)
[EQ 7.48]
where
is the gas gravity
is the pressure of interest
is the Z-factor
is the temperature in ºR
�g
P
Z
T
�gcorr0.07636�g 350 �con cgr� �� �+
0.002636350 �con cgr� �
6084 �conAPI 5.9–� �-------------------------------------------------� �� �
+
------------------------------------------------------------------------------------=
is the gas gravity
is the condensate gravity
is the condensate gas ratio in stb/scf
is the condensate API
�g
�con
cgr
�conAPI
co 7.573– 1.450 p� �ln– 0.383 pb� �ln– 1.402 T� �ln 0.256 �API� �ln 0.449 Rsb� �ln+ + + �exp=
is isothermal compressibility, psi-1
is the solution gas-oil ratio at the bubble point pressure, scf/STB
is the weight average of separator gas and stock-tank gas specific gravities
is the temperature, oR
Co
Rsb
�g
T
334 Technical Description Oil correlations
Undersaturated oil
Vasquez and Beggs
[EQ 7.49]
where
• Example
Determine a value for where psia, scf /STB, ,
��API, �F.
• Solution
[EQ 7.50]
/psi [EQ 7.51]
Petrosky and Farshad (1993)
[EQ 7.52]
where
Formation volume factor
Saturated systems
Three correlations are available for saturated systems:
• Standing
co5Rsb 17.2T 1180�g– 12.61�API 1433–+ +� � 5–�10
p------------------------------------------------------------------------------------------------------------------------------=
is the oil compressibility 1/psi
is the solution GOR, scf/STB
is the gas gravity (air = 1.0)
is the stock tank oil gravity, �API
is the temperature in �F
is the pressure of interest, psi
co
Rsb
�g
�API
T
p
co p 3000= Rsb 500= �g 0.80=
�API 30= T 220=
co5 500� � 17.2 220� � 1180 0.8� �– 12.61 30� � 1433–+ +
3000 5�10--------------------------------------------------------------------------------------------------------------------------------=
co 1.43 5–�10=
Co 1.705 7–�10 Rs0.69357�� ��g
0.1885�API0.3272T0.6729p 0.5906–=
is the solution GOR, scf/STB
is the average gas specific gravity (air = 1)
is the oil API gravity, oAPI
is the temperature, oF
is the pressure, psia
Rs
�g
�API
T
p
Technical DescriptionOil correlations
335
• Vasquez and Beggs
• GlasO
• Petrosky
These are describe below.
Standing
[EQ 7.53]
where
• Example
Use Standing’s equation to estimate the oil FVF for the oil system described by the data �F, scf / STB, , .
• Solution
[EQ 7.55]
[EQ 7.56]
bbl / STB [EQ 7.57]
Vasquez and Beggs
[EQ 7.58]
where
Bo 0.972 0.000147F1.175+=
= Rs(�g/�o)0.5 + 1.25 T [EQ 7.54]
and
is the oil FVF, bbl/STB
is the solution GOR, scf/STB
is the gas gravity (air = 1.0)
is the oil specific gravity = 141.5/(131.5 + �API)
is the temperature in �F
F
Bo
Rs
�g
�o
T
T 200= Rs 350= �g 0.75= �API 30=
�o141.5
131.5 30+------------------------- 0.876= =
F 350 0.750.876-------------� � 0.5
1.25 200� �+ 574= =
Bo 1.228=
Bo 1 C1Rs C2 C3Rs+� � T 60–� ��API�gc
-----------� �� �
+ +=
is the solution GOR, scf/STB
is the temperature in �F
is the stock tank oil gravity, �API
is the gas gravity
Rs
T
�API
�gc
336 Technical Description Oil correlations
, , are obtained from the following table:
Table 7.1 Values of C1, C2 and C3 as used in [EQ 7.58]
API � 30 API > 30
C1 4.677 10 -4 4.670 10-4
C2 1.751 10 -5 1.100 10-5
C3 -1.811 10 -8 1.337 10 -9
C1 C2 C3
Technical DescriptionOil correlations
337
• Example
Use the Vasquez and Beggs equation to determine the oil FVF at bubblepoint pressure for the oil system described by psia, scf / STB,
, and �F.
• Solution
bb /STB [EQ 7.59]
GlasO
[EQ 7.60]
[EQ 7.61]
[EQ 7.62]
where
Petrosky and Farshad (1993)
[EQ 7.63]
where
Undersaturated systems
[EQ 7.64]
pb 2652= Rsb 500=
�gc 0.80= �API 30= T 220=
Bo 1.285=
Bo 1.0 10A+=
A 6.58511– 2.91329 Bob�log 0.27683 Bob�log� �2
–+=
Bob� Rs�g�o-----� �� � 0.526
0.968T+=
is the solution GOR, scf/STB
is the gas gravity (air = 1.0)
is the oil specific gravity,
is the temperature in �F
is a correlating number
Rs
�g
�o �o 141.5 131.5 �API+� ��=
T
Bob�
Bo 1.0113 7.2046 5–�10 Rs0.3738
�g0.2914
�o0.6265
------------------� �� �
0.24626T0.5371+3.0936
+=
is the oil FVF, bbl/STB
is the solution GOR, scf/STB
is the temperature, oF
Bo
Rs
T
Bo Bobexp co pb p–� �( )=
338 Technical Description Oil correlations
where
Viscosity
Saturated systems
There are 4 correlations available for saturated systems:
• Beggs and Robinson
• Standing
• GlasO
• Khan
• Ng and Egbogah
These are described below.
Beggs and Robinson
[EQ 7.65]
where
Taking into account any dissolved gas we get
[EQ 7.66]
where
• Example
Use the following data to calculate the viscosity of the saturated oil system. �F, , scf / STB.
• Solution
is the oil FVF at bubble point, psi.
is the oil isothermal compressibility, 1/psi
is the pressure of interest, psi
is the bubble point pressure, psi
Bob pb
co
p
pb
�od 10x 1–=
is the dead oil viscosity, cp
is the temperature of interest, �F
is the stock tank gravity
x T 1.168– exp 6.9824 0.04658�API–( )=
�od
T
�API
�o A�odB
=
A 10.715 Rs 100+� � 0.515–=
B 5.44 Rs 150+� � 0.338–=
T 137= �API 22= Rs 90=
Technical DescriptionOil correlations
339
�cp
�cp
Standing
[EQ 7.67]
[EQ 7.68]
where
[EQ 7.69]
[EQ 7.70]
[EQ 7.71]
where
Glas�
[EQ 7.72]
[EQ 7.73]
[EQ 7.74]
and
[EQ 7.75]
[EQ 7.76]
x 1.2658=
�od 17.44=
A 0.719=
B 0.853=
�o 8.24=
�od 0.32 1.8 7�10
�API4.53
-------------------+� �� �� � 360
T 260–------------------� � a=
a 100.43 8.33
�API-----------+� �
=
is the temperature of interest, �F
is the stock tank gravity
T
�API
�o 10a� � �od� �b=
a Rs 2.2 7–�10 Rs 7.4 4–�10–� �=
b 0.68
108.62 5–�10 Rs
----------------------------------- 0.25
101.1 3–�10 Rs
-------------------------------- 0.062
103.74 3–�10 Rs
-----------------------------------+ +=
is the solution GOR, scf/STBRs
�o 10a �od� �b=
a Rs 2.2 7–�10 Rs 7.4 4–�10–� �=
b 0.68
108.62 5–�10 Rs
----------------------------------- 0.25
101.1 3–�10 Rs
-------------------------------- 0.062
103.74 3–�10 Rs
-----------------------------------+ +=
�od 3.141 10�10 T 460–� � 3.444– �APIlog� �a=
10.313 T 460–� �log� � 36.44–=
340 Technical Description Oil correlations
where
Khan
[EQ 7.77]
[EQ 7.78]
where
Ng and Egbogah (1983)
[EQ 7.79]
Solving for , the equation becomes,
[EQ 7.80]
where
uses the same formula as Beggs and Robinson to calculate Viscosity
Undersaturated systems
There are 5 correlations available for undersaturated systems:
• Vasquez and Beggs
• Standing
is the temperature of interest, �F
is the stock tank gravity
T
�API
�o �obppb-----� � 0.14–
e2.5 4–�10–� � p pb–� �
=
�ob0.09�g
0.5
Rs1 3� �r
4.5 1 �o–� �3---------------------------------------------=
is the viscosity at the bubble point
is
is the temperature, �R
is the specific gravity of oil
is the specific gravity of solution gas
is the bubble point pressure
is the pressure of interest
�ob
�r T 460�
T
�o
�g
pb
p
�od 1+� �log �log 1.8653 0.025086�API– 0.5644 T� �log–=
�od
�od 10101.8653 0.025086�API– 0.5644 T� �log–� �
1–=
is the “dead oil” viscosity, cp
is the oil API gravity, oAPI
is the temperature, oF
�od
�API
T
Technical DescriptionOil correlations
341
• GlasO
• Khan
• Ng and Egbogah
These are described below.
Vasquez and Beggs
[EQ 7.81]
where
where
Example
Calculate the viscosity of the oil system described at a pressure of 4750 psia, with �F, , , scf / SRB.
Solution
psia.
�cp
�cp
Standing
[EQ 7.82]
�o �obppb-----� � m=
= viscosity at
= viscosity at
= pressure of interest, psi
= bubble point pressure, psi
�o p pb�
�ob pb
p
pb
m C1pC2exp C3 C4p+( )=
C1 2.6=
C2 1.187=
C3 11.513–=
C4 8.98 5–�10–=
T 240= �API 31= �g 0.745= Rsb 532=
pb 3093=
�ob 0.53=
�o 0.63=
�o �ob 0.001 p pb–� � 0.024�ob1.6 0.038�ob
0.56+� �+=
342 Technical Description Oil correlations
where
GlasO
[EQ 7.83]
where
Khan
[EQ 7.84]
where
Ng and Egbogah (1983)
[EQ 7.85]
Solving for , the equation becomes,
[EQ 7.86]
where
uses the same formula as Beggs and Robinson to calculate Viscosity
is the viscosity at bubble point
is the pressure of interest, psi
is the bubble point pressure, psi
�ob
p
pb
�o �ob 0.001 p pb–� � 0.024�ob1.6 0.038�ob
0.56+� �+=
is the viscosity at bubble point
is the pressure of interest, psi
is the bubble point pressure, psi
�ob
p
pb
�o �ob e9.6 5–�10 p pb–� �
�=
is the viscosity at bubble point
is the pressure of interest, psi
is the bubble point pressure, psi
�ob
p
pb
�od 1+� �log �log 1.8653 0.025086�API– 0.5644 T� �log–=
�od
�od 10101.8653 0.025086�API– 0.5644 T� �log–� �
1–=
is the “dead oil” viscosity, cp
is the oil API gravity, oAPI
is the temperature, oF
�od
�API
T
Technical DescriptionOil correlations
343
Bubble point
Standing
[EQ 7.87]
where
Example:
Estimate where scf / STB, �F, , �API.
Solution
[EQ 7.88]
psia [EQ 7.89]
Lasater
For
[EQ 7.90]
For
[EQ 7.91]
[EQ 7.92]
For
[EQ 7.93]
For
Pb 18Rsb�g
---------� �� � 0.83 yg�10=
= mole fraction gas =
= bubble point pressure, psia
= solution GOR at , scf / STB
= gas gravity (air = 1.0)
= reservoir temperature,�F
= stock-tank oil gravity, �API
yg 0.00091TR 0.0125�API–
Pb
Rsb P Pb�
�g
TR
�API
pb Rsb 350= TR 200= �g 0.75= �API 30=
�g 0.00091 200� � 0.0125 30� �– 0.193–= =
pb 18 3500.75----------� � 0.83 0.193–�10 1895= =
API 40�
Mo 630 10�API–=
API 40�
Mo73110
�API1.562
---------------=
yg1.0
1.0 1.32755�o MoRsb�� �+-----------------------------------------------------------------=
yg 0.6�
Pb0.679exp 2.786yg( ) 0.323–� �TR
�g-----------------------------------------------------------------------------=
yg 0.6�
344 Technical Description Oil correlations
[EQ 7.94]
where
Example
Given the following data, use the Lasater method to estimate .
, scf / STB, , �F, . [EQ 7.95]
Solution
[EQ 7.96]
[EQ 7.97]
psia [EQ 7.98]
Vasquez and Beggs
[EQ 7.99]
where
Example
Calculate the bubblepoint pressure using the Vasquez and Beggs correlation and the following data.
, scf / STB, , �F, . [EQ 7.100]
Solution
Pb8.26yg
3.56 1.95+� �TR�g
----------------------------------------------------=
is the effective molecular weight of the stock-tank oil from API gravity
= oil specific gravity (relative to water)
Mo
�o
Table 7.2 Values of C1, C2 and C3 as used in [EQ 7.99]
API < 30 API > 30
C1 0.0362 0.0178
C2 1.0937 1.1870
C3 25.7240 23.9310
pb
yg 0.876= Rsb 500= �o 0.876= TR 200= �API 30=
Mo 630 10 30� �– 330= =
yg550 379.3�
500 379.3� 350 0.876 330�� �+------------------------------------------------------------------------- 0.587= =
pb3.161 660� �
0.876--------------------------- 2381.58= =
PbRsb
C1�gexpC3�APITR 460+----------------------� �� �
--------------------------------------------------
1C2------
=
yg 0.80= Rsb 500= �g 0.876= TR 200= �API 30=
Technical DescriptionOil correlations
345
psia [EQ 7.101]
GlasO
[EQ 7.102]
[EQ 7.103]
where
for volatile oils is used.
Corrections to account for non-hydrocarbon components:
[EQ 7.104]
[EQ 7.105]
[EQ 7.106]
[EQ 7.107]
pb500
0.0362 0.80� �exp 25.724 30680---------� �
------------------------------------------------------------------------------
11.0937----------------
2562= =
Pb� �log 1.7669 1.7447 Pb�� �log 0.30218 Pb�� �log� �2
–+=
Pb�Rs�g-----� �� � 0.816 Tp
0.172
�API0.989
---------------
� �� �� �
=
is the solution GOR, scf / STB
is the gas gravity
is the reservoir temperature,�F
is the stock-tank oil gravity, �API
Rs
�g
TF
�API
TF0.130
PbcPbc
CorrCO2 CorrH2S CorrN2���=
CorrN2 1 a1�API a2+– TF a3�API a4–+ �YN2
a5�APIa6 TF a6�API
a7 a8–+ YN22
+
+
=
CorrCO2 1 693.8YCO2TF1.553–
–=
CorrH2S 1 0.9035 0.0015�API+� �YH2S– 0.019 45 �API–� �YH2S+=
346 Technical Description Oil correlations
where
Marhoun
[EQ 7.109]
where
Petrosky and Farshad (1993)
[EQ 7.111]
[EQ 7.108]
is the reservoir temperature,�F
is the stock-tank oil gravity, �API
is the mole fraction of Nitrogen
is the mole fraction of Carbon Dioxide
is the mole fraction of Hydrogen Sulphide
a1 2.65 4–�10–=
a2 5.5 3–�10=
a3 0.0391=
a4 0.8295=
a5 1.954 11–�10=
a6 4.699=
a7 0.027=
a8 2.366=
TF
�API
YN2
YCO2
YH2S
pb a· Rsb �g
c �od TR
e� � � �=
is the solution GOR, scf / STB
is the gas gravity
is the reservoir temperature,�R
[EQ 7.110]
Rs
�g
TR
a 5.38088 3–�10=
b 0.715082=
c 1.87784–=
d 3.1437=
e 1.32657=
pb 112.727Rs
0.5774
�g0.8439
-------------------X�10 12.340–=
Technical DescriptionOil correlations
347
where
GOR
Standing
[EQ 7.112]
where
Example
Estimate the solution GOR of the following oil system using the correlations of Standing, Lasater, and Vasquez and Beggs and the data:
psia, �F, , . [EQ 7.113]
Solution
scf / STB [EQ 7.114]
Lasater
[EQ 7.115]
For
[EQ 7.116]
For
is the solution GOR, scf/STB
is the average gas specific gravity (air=1)
is the oil specific gravity (air=1)
is the temperature, oF
X 4.561 5–�10 T1.3911 7.916 4–�10 �API1.5410–=
Rs
�g
�o
T
Rs �gp
18yg�10
--------------------� �� � 1.204
=
is the mole fraction gas =
is the solution GOR, scf / STB
is the gas gravity (air = 1.0)
is the reservoir temperature,�F
is the stock-tank oil gravity, �API
yg 0.00091TR 0.0125�AP–
Rs
�g
TF
�API
p 765= T 137= �API 22= �g 0.65=
Rs 0.65 765
18 0.15–�10----------------------------� � 1.204
90= =
Rs132755�oygMo 1 yg–� �-----------------------------=
API 40�
Mo 630 10�API–=
API 40�
348 Technical Description Oil correlations
[EQ 7.117]
For
[EQ 7.118]
For
[EQ 7.119]
where is in �R.
Example
Estimate the solution GOR of the following oil system using the correlations of Standing, Lasater, and Vasquez and Beggs and the data:
psia, �F, , . [EQ 7.120]
Solution
[EQ 7.121]
[EQ 7.122]
scf / STB [EQ 7.123]
Vasquez and Beggs
[EQ 7.124]
where C1, C2, C3 are obtained from Table 7.3.
Example
Estimate the solution GOR of the following oil system using the correlations of Standing, Lasater, and Vasquez and Beggs and the data:
psia, �F, , . [EQ 7.125]
Table 7.3 Values of C1, C2 and C3 as used in [EQ 7.124]
API < 30 API > 30
C1 0.0362 0.0178
C2 1.0937 1.1870
C3 25.7240 23.9310
Mo73110
�API1.562
---------------=
p�g T� 3.29�
yg 0.359ln1.473p�g
T---------------------- 0.476+� � =
p�g T� 3.29�
yg0.121p�g
T---------------------- 0.236–� �
0.281=
T
p 765= T 137= �API 22= �g 0.65=
yg 0.359ln 1.473 0.833� � 0.476+ � 0.191= =
Mo 630 10 22� �– 410= =
Rs132755 0.922� � 0.191� �
410 1 0.191–� �------------------------------------------------------- 70= =
Rs C1�gpC2exp
C3�APITR 460+----------------------� �� �
=
p 765= T 137= �API 22= �g 0.65=
Technical DescriptionOil correlations
349
Solution
scf / STB [EQ 7.126]
GlasO
[EQ 7.127]
[EQ 7.128]
[EQ 7.129]
where
Marhoun
[EQ 7.130]
where
Rs 0.0362 0.65� � 765� �1.0937exp 25.724 22� �
137 460+--------------------------- 87= =
Rs �g�API0.989
TF0.172
---------------
� �� �� �
Pb�1.2255
=
Pb� 102.8869 14.1811 3.3093 Pbc� �log–� �0.5
– �=
PbcPb
CorrN2 CorrCO2 CorrH2S+ +---------------------------------------------------------------------------=
is the specific gravity of solution gas
is the reservoir temperature,�F
is the stock-tank oil gravity, �API
is the mole fraction of Nitrogen
is the mole fraction of Carbon Dioxide
is the mole fraction of Hydrogen Sulphide
�g
TF
�API
YN2
YCO2
YH2S
Rs a �gb
�oc Td pb� � � �� �
e=
is the temperature, �R
is the specific gravity of oil
is the specific gravity of solution gas
is the bubble point pressure
[EQ 7.131]
T
�o
�g
pb
a 185.843208=
b 1.877840=
c 3.1437–=
d 1.32657–=
e 1.398441=
350 Technical Description Oil correlations
Petrosky and Farshad (1993)
[EQ 7.132]
where
Separator gas gravity correction
[EQ 7.134]
where
Rspb
112.727------------------- 12.340+� � �g
0.8439 X�101.73184
=
[EQ 7.133]
is the bubble-point pressure, psia
is the temperature, oF
X 7.916 4–�10 �g1.5410 4.561 5–�10 T1.3911–=
pb
T
�gcorr �g 1 5.912 5–�10 �API TFsepPsep114.7-------------� � log� � �+� �
=
is the gas gravity
is the oil API
is the separator temperature in �F
is the separator pressure in psia
�g
�API
TFsep
Psep
Technical DescriptionOil correlations
351
Tuning factors
Bubble point (Standing):
[EQ 7.135]
GOR (Standing):
[EQ 7.136]
Formation volume factor:
[EQ 7.137]
[EQ 7.138]
Compressibility:
[EQ 7.139]
Saturated viscosity (Beggs and Robinson):
[EQ 7.140]
[EQ 7.141]
[EQ 7.142]
Undersaturated viscosity (Standing):
[EQ 7.143]
Pb 18 FO1Rsb�g
---------� �� � 0.83 �g�10�=
Rs �gP
18 FO1�g�10�
-----------------------------------� �� � 1.204
=
Bo 0.972 FO2� 0.000147 FO3 F1.175� �+=
F Rs�g�o-----� �� � 0.5
1.25TF+=
coFO4 5Rsb 17.2TF 1180�g– 12.61�API 1433–+ +� � 5–�10
P---------------------------------------------------------------------------------------------------------------------------------------------=
�o A�odB
=
A 10.715 FO5 Rs 100+� � 0.515–�=
B 5.44 FO6 Rs 150+� � 0.338–�=
�o �ob P Pb–� � FO7 0.024�ob1.6 0.038�ob
0.56+� � �+=
352 Technical Description Oil / water
SCAL correlations
Oil / waterFigure 7.1 Oil/water SCAL correlations
where
Corey functions
Water
(For values between and )
[EQ 7.144]
Kro
Krw
0 1
Swmin
Kro(Swmin)
Swmin Swcr 1-Sorw
Sorw’Krw(Sorw)
,Swmax,
Krw(Swmax)
is the minimum water saturation
is the critical water saturation (�� )
is the residual oil saturation to water ( )
is the water relative permeability at residual oil saturation
is the water relative permeability at maximum water saturation (that is 100%)
is the oil relative permeability at minimum water saturation
swmin
swcr swmin
sorw 1 sorw– swcr�
krw sorw( )
krw swmax( )
kro swmin( )
Swcr 1 Sorw–
krw krw sorw( )sw swcr–
swmax swcr– sorw–---------------------------------------------------
Cw=
Technical DescriptionGas / water
353
where is the Corey water exponent.
Oil
(For values between and )
[EQ 7.145]
where
Gas / waterFigure 7.2 Gas/water SCAL correlations
Cw
swmin 1 sorw–
kro kro swmin( )swmax sw– sorw–
swmax swi– sorw–-----------------------------------------------
Co=
is the initial water saturation and
is the Corey oil exponent.
swi
Co
KrgKrw
0 1Swmin Swcr Sgrw
Swmin,Krg(Swmin)
Sgrw,Krw(Sgrw)
Swmax,Krw(Smax)
354 Technical Description Gas / water
where
Corey functions
Water
(For values between and )
[EQ 7.146]
where is the Corey water exponent.
Gas
(For values between and )
[EQ 7.147]
where
is the minimum water saturation
is the critical water saturation (�� )
is the residual gas saturation to water ( )
is the water relative permeability at residual gas saturation
is the water relative permeability at maximum water saturation (that is 100%)
is the gas relative permeability at minimum water saturation
swmin
swcr swmin
sgrw 1 sgrw– swcr�
krw sgrw( )
krw swmax( )
krg swmin( )
swcr 1 sgrw–
krw krw sgrw( )sw swcr–
swmax swcr– sgrw–---------------------------------------------------
Cw=
Cw
swmin 1 sgrw–
krg krg swmin( )swmax sw– sgrw–
swmax swi– sgrw–-----------------------------------------------
Cg=
is the initial water saturation and
is the Corey gas exponent.
swi
Cg
Technical DescriptionOil / gas
355
Oil / gasFigure 7.3 Oil/gas SCAL correlations
where
Corey functions
Oil
(For values between and )
[EQ 7.148]
0
Sliquid
1-Sgcr 1-SgminSwmin Sorg+Swmin
Swmin,Krg(Swmin)
Sorg+Swmin,Krg(Sorg)
Swmax,Krw(Smax)
is the minimum water saturation
is the critical gas saturation (�� )
is the residual oil saturation to gas ( )
is the water relative permeability at residual oil saturation
is the water relative permeability at maximum water saturation (that is 100%)
is the oil relative permeability at minimum water saturation
swmin
sgcr sgmin
sorg 1 sorg– swcr�
krg sorg( )
krg swmin( )
kro swmin( )
swmin 1 sorg–
kro kro sgmin( )sw swi– sorg–
1 swi– sorg–------------------------------------
Co=
356 Technical Description Oil / gas
where:
Gas
(For values between and )
[EQ 7.149]
where
Note In drawing the curves is assumed to be the connate water saturation.
is the initial water saturation and
is the Corey oil exponent.
swi
Co
swmin 1 sorg–
krg krg sorg( )1 sw– sgcr–
1 swi– sorg– sgcr–--------------------------------------------------
Cg=
is the initial water saturation and
is the Corey gas exponent.
swi
Cg
swi
Technical DescriptionPseudo Variables
357
Pseudo variables
Pseudo pressure transformationsThe pseudo pressure is defined as:
[EQ 7.150]
It can be normalized by choosing the variables at the initial reservoir condition.
Normalized pseudo pressure transformations
[EQ 7.151]
The advantage of this normalization is that the pseudo pressures and real pressures coincide at and have real pressure units.
Pseudo time transformationsThe pseudotime transform is
[EQ 7.152]
Normalized pseudo time transformationsNormalizing the equation gives
[EQ 7.153]
Again the advantage of this normalization is that the pseudo times and real times coincide at and have real time units.
m p� � 2 p� p� �z p� �---------------------- pd
pi
p
�=
mn p� � pi�izipi
--------- p� p� �z p( )--------------------- pd
pi
p
�+=
pi
m t� � 1� p� �ct p� �------------------------ td
0
t
�=
mn t� � �ici1
� p� �ct p� �------------------------ td
0
t
�=
pi