l5 viscosity correlations
TRANSCRIPT
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Crude Oil Viscosity Models and
Data
Data Quality Control Procedures
Termodinamica de Hidrocarburos
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Needs of Crude Oil Viscosity
Calculation of two-phase flow
Gas-lift and pipeline design
Fluid flow in the reservoir
Select oil production strategy
Data Quali ty Checks
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Production and Injection imply
viscosity changes
Temperature
t 1
P r e s s u r e
t 3
t 2
Gas Injection
Production t
t 3
2 Gas
Injection
Production
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Typical Viscosity Correlations
0
1
2
3
4
5
6
O i l V i s c o s i t y , c P
1000 2000 3000 4000 5000 6000
Pressure, psia
Undersaturated Oil Viscosity
Correlation ComparisonUntitled
Reg: CPTC PS S - Chevron Oil Corporation
Vazquez and BeggsKartoatmodjoBeal / StandingBeal / PipeflowKayePetroskyOsorioKhan
0
1
2
3
4
5
6
O i l V i s c o s i t y ,
c P
1000 2000 3000 4000 5000 6000Pressure, psia
Undersaturated Oil Viscosity
Correlation ComparisonUntitled
Reg: CPTC PSS - Chevron Oil Corpor ation
Vazquez and BeggsKartoatmodjoBeal / StandingKayePetroskyOsorioKhan
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Typical Viscosity Correlations
0
1
2
3
4
5
6
O i l V i s c o s i t y , c P
1000 2000 3000 4000 5000 6000
Pressure, psia
Undersaturated Oil Viscosity
Correlation ComparisonUntitled
Reg: CPTC PS S - Chevron Oil Corporation
Vazquez and BeggsKartoatmodjoBeal / StandingBeal / PipeflowKayePetroskyOsorioKhan
2
3
4
5
6
7
O i l V i s c o s i t y , c P
1000 2000 3000 4000 5000 6000
Pressure, psia
Saturated Oil ViscosityCorrelation Comparison
Untitled
Reg: CPTC PSS - C hevro n Oil Corpo ration
Beggs and RobinsonKartoatmodjoChew and Connally / AzizChew and Connally / StandingKayePetroskyOsorioOmoregieKhan
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Methods to Evaluate Oil
Viscosity
Black Oil models
Compositional models
Data
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Methods to Evaluate Fluid
Properties
G
G O ,
n y y y y ...,, 321
n x x x x ... , , 3 2 1
Black Oil Compositional
Model Formulations
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Viscosity Correlations
Black Oil Type
Correlation in terms of field derived
variables Rs, Bo, P, T, APIGeographically dependent
Corresponding States Type
Require compositional dataComplex but more reliable
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S e p a r a t o r
g a s
gas gas
Decreasing Pressure
S e p a r a t o r g a s
S e p a r a t o r g a s
gas
Standard
Conditions
S e p a r a t o r g a s
S e p a r a t o r g a s
oil oil oil oil
oil
STB
STB STB
STB
Standard
Conditions
Bg =
Rv =
Bo=
Rs=
P
2 P1
P4
P3
Reservoir
Definition of Oil & Gas PVT Properties
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Differential Liberation Tests
Gas
Oil
Hg
Stage 1 Stage 2 Stage N P= atm Stage 0
P = P b
Gas off Gas off
Gas
Oil
Hg
Stage 1 Stage 2 Stage N P= atm Stage 0
P = P b
Gas off Gas off
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Differential Test Sample
PVT Data at T=80o
FPressure
(psig)
R s [1 ]
(SCF/STB)
B o [2 ]
(RB/STB)
Oi l Densi ty
o (gm/cc)
Gas
Deviat ion
Factor Z
Bg[3 ]
(RCF/SCF)
Gas
Gravi ty
g
1690 210 1.069 0.9022
1500 188 1.063 0.9052 0.822 0.00825 0.581
1300 165 1.056 0.9083 0.835 0.00966 0.5761100 141 1.049 0.9113 0.852 0.01162 0.573
900 117 1.042 0.9143 0.872 0.01450 0.571
700 93 1.036 0.9174 0.896 0.01906 0.572
500 68 1.029 0.9205 0.922 0.02724 0.574
300 42 1.022 0.9235 0.951 0.04593 0.581
100 15 1.014 0.9268 0.983 0.13004 0.600
0 0 1.008 0.9305 0.724
Gravity of Residual Oil = 19.2API @ 60F
[1] Cubic feet of gas at 14.7 psia and 60F per barrel of residual oil at 60F.
[2] Barrels of oil at indicated pressure and temperature per barrel of residual oil at 60F.[3] Barrels of oil plus liberated gas at indicated pressure and temperature per barrel of
residual oil at 60F.
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Differential Test Sample
Viscosities at T=80o
FPressure
(psig)
Oi l Viscos i ty
(cp)
Calculated
Gas Viscosi ty
(cp)
Oil/Gas
Viscos i ty
Ratio
1690 (P b ) 35.4
1500 40.0 0.0146 2740
1300 45.2 0.0140 3230
1100 51.2 0.0134 3820
900 58.5 0.0129 4530
700 68.4 0.0124 5520
500 82.5 0.0120 6880
300 102.1 0.0116 8800
100 127.6 0.0113 11300
0 177.0 0.0106 16700
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Variation of Oil Viscosity
O
i l V i s c o s i t y
T = constant
Pb
Single Phase FlowTwo Phase Flow
Gas Out ofSolution
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Data Quality Tests
Does oil viscosity from a DL test increase aspressure decreases?
Do densities vary smoothly with pressure?
Do solution gas oil ratios vary smoothly withpressure?
Do the reported properties vary substantially, fromreported properties of other fluids from similarlocations? (Abnormal variability)
Do all components from a recombined reservoirfluid satisfy the recombination ratio? (materialbalance check)
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Data Preparation & Screening
RoutineAutomatic labeling of each DL test
Remove outliers by using numerical first
derivatives forward and backwardExtract bubble point pressures
Selection of suitable correlations and
range for pseudo critical properties
Minimum number of points in data set
should be 4
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A Consistent Data Set…
Differential Liberation Test (API = 22.53, T = 357.8 K)
0
1
2
3
4
5
6
7
0 50 100 150 200 250 300Pressure (bar)
V i s c o s i t y ( c p )
0.8
0.82
0.84
0.86
D e n s i t y ( g / c m 3
)
Viscosity (cp) Density ( g/cm3)
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Extrapolated Molecular weight
Boiling Point T, and Vcm
1
10
100
1000
10000
0.5 0.6 0.7 0.8 0.9 1
Oil Specific Gravity
V c m
/ f t 3 / l b - m o l , T b / R
0
200
400
600
800
1000
1200
M o l e c u l a r W e i g h t
Vcm Vcm (ex) Tb (R)
Tb (R) (ex) Mwm Mwm (ex)
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Data Screening
Differential Liberation Test (API = 45, T = 319 K)
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200 250
Pressure (bar)
V i s c o s i t y ( c p )
0.6
0.64
0.68
0.72
D e n s i t y ( g / c m 3
)
Viscosity (cp) Density ( g/cm3)
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Differential Liberation Test (API = 35.7, T = 380 K)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
40 60 80 100 120 140 160 180
Pressure (bar)
V i s c o s i t y ( c p )
0.66
0.68
0.7
0.72
0.74
0.76
D e n s i t y ( g / c m 3 )
Viscosity (cp) Density ( g/cm3)
Data Screening
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Data ScreeningDifferential Liberation Test (API = 32.43, T = 361.7 K)
0.4
0.8
1.2
1.6
2
20 80 140 200 260 320
Pressure (bar)
V i s c o s i t y ( c
p )
0.7
0.72
0.74
0.76
0.78
0.8
D e n s i t y ( g / c m
3 )
Viscosity (cp) Density ( g/cm3)
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Differential Liberation Test (API = 32.1 T = 333.1 K)
720
722
724
726
728
730
20 40 60 80 100 120
Pressure (bar)
T c m ( K
)
198
200
202
204
206
M w m ( g
/ g m o l )
Tcm (K) Mwm
Data Screening
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Data Sets and Property Ranges
Range of input data. SI units and values in are indicated in parenthesis.
Dataset No Points. Variable Minimum Maximum
#1 2343 Oil Density: lbm/ft3
(g/cm 3 )
35.11
(0.562)
57.31
(0.92)
#2 150 Oil Density, lbm/ft3
(g/cm 3 )
24.31
(0.389)
57.50
(0.921)
#1 2343 Oil Viscosity, cp 0.132 78.30
#2 150 Oil Viscosity, cp 0.13 68.90
#1 2343 Temperature, R (K ) 540 (300) 766 (425.5)
#2 150 Temperature, R (K ) 537 (303.9) 762 (423.3)
#1 2343 Pressure, psia (MPa) 14.7 (0.1) 5601.7 (38.62)
#2 150 Pressure, psia (MPa) 102.7 (0.708) 5434.7 (37.47)
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Original Pedersen’s Model
o o o
o
m
o
m
co
cm
co
cm m T ,P
MW
MW
P
P
T
T T ,P
3 2 1
5173 .0
m
847 .1
ro
3
m MW 10 378 .7 000 .1
847 .1
ro o 031 .0 000 .1
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Correlations for the Reference
Fluid
TP .1 T .T 1847.7998 - exp /
C10
8 2 1 1 10 5043 1906 168
PT 10 87 .8 T 10 7057 .6 P 001272 .0
T
P 0.4775 T 8775.2881 - T .5418 321 2
T
1 50992
7 3 9
2 / 1 3 / 1
C10
Density
Viscosity
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Extended Pedersen Viscosity
Model
B AMW
MW
V
V
T
T T T ,P
3.9243 -
10 C
m
0.9841
10 cC
cm
0286 .1
2
10 cC
cm m
2902 .2 4471 .0
sb
1362 .0
sb
R ,o s API R
R
R A
R ,o
o o C10
.C10 c
C10
10 C
cm
3
ob
o T ,P 1930 .0 1388 .2 T
V P 02359 .0
B
B 2606 .0 exp B
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Lohrentz Bray and Clark
Viscosity Model4th degree polynomial in reduced
density
Requires pseudocritical properties(usually evaluated from compositions)
See class notes & papers included in
our web site
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Lohrentz Bray and Clark
Viscosity Model
1
5
1
4 1 4
10
i
r i
i
/ *
a
3 2 2 1 6 1 /
cm /
wm /
cm P M T
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Lohrentz Bray and Clark
Extended Viscosity Model
1
9 8 7
6
5
4 3 2 1
T
P
exp
T P
P API R M LBC
r
cm
sr wm R ,o
R ,o R ,o o
Extended LBC
Parameter
Value
Parameter
Value
= -0.80425 = -0.37144
= 1.498864 = -2.47265
= 2.76244 = 0.840063
= 0.206572 = -0.02235
= -3.0795 = 0.047899
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Errors are Defined as…
100
erimental exp
predicted erimental exp
100
erimental exp
predicted erimental exp
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Lohrentz Bray and Clark
Extended Viscosity Model
Calibration Set
0.1
1
10
100
0.1 1 10 100
Experimental Viscosity (cp)
P r e d i c t e d V i s c o s i t y
( c p )
Extended LBC
Data Set 1:
2324 points
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Extended Pedersen
(Validation Set)
Validation Set0.1
1
10
100
1000
0.1 1 10 100 1000
Experimental Viscosity (cp)
P
r e d i c t e d V i s c o s i t y ( c p ) Extended Pedersen
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Extended LBC
(Validation Set)
Validation Set
0.1
1
10
100
1000
0.1 1 10 100 1000
Experimental Viscosity (cp)
P r
e d i c t e d V i s c o s i t y ( c p )
Extended LBC
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Statistical SummaryExtended Pedersen (EP) and Extended
LBC (ELBC) Viscosity Models
Validation Set (Nv = 150 po ints )
Ranges MeanStandardDeviat ion Min imum Maximum
Experimental
Viscosi ty ( ) 2.58 9.19 0.13 68.90
Extended Pedersen
(EP) () 2.88 10.91 0.10 89.09
Error (EP) % -0.35 32.37 -165.08 60.75
Absolute Error (EP)% 23.24 22.45 0.08 165.08
Extended LBC () 1.90 5.62 0.17 40.96
Error (LBC) % -1.41 25.00 -111.35 44.83
Absolute Error(LBC) % 19.15 16.04 0.26 111.34
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Conclusions
Developed new oil viscosity model
which can be easily implemented in
simulatorsTuning of parameters can be done
with simple linear regression
Predictions better than existingcorrelations
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Future Work
Test model with correlations for Bo
and Rs (see paper AIChe-87h)
Investigate the dependence of initialparameters with Differential Set
parameters (API, Rsb, T, Bob)
Extend the model to heavier oils
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Adapted Pedersen’s Model
with C10 as Reference FluidData Set 1:
2343 points
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Predicted vs Experimental
Viscosity from Khan’s model
Data Set 1:
2343 points
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Predicted vs Experimental
Viscosity from Petrosky’s model
Data Set 1:
2343 points
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Predicted vs Experimental
Viscosity from Pedersen’s model
Data Set 2:
150 points
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Predicted vs Experimental
Viscosity from our model
Data Set 2:
150 points
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Predicted vs Experimental
Viscosity from Khan’s model
Data Set 2:
150 points
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Predicted vs Experimental
Viscosity from Petrosky’s model
Data Set 2:
150 points
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Comparison of Petrosky vs.
our model
Data Set 2:
150 points
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Performance when parameters
are tuned for each DL set
Data Set 1:
2343 points