l5 viscosity correlations

8/12/2019 L5 Viscosity Correlations

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Crude Oil Viscosity Models and

Data

Data Quality Control Procedures

Termodinamica de Hidrocarburos



2

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



3



4

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



5

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



Reg: CPTC PSS - Chevron Oil Corpor ation

Vazquez and BeggsKartoatmodjoBeal / StandingKayePetroskyOsorioKhan



6

Typical Viscosity Correlations

0

1

2

3

4

5

6


1000 2000 3000 4000 5000 6000

Pressure, psia



Reg: CPTC PS S - Chevron Oil Corporation

Vazquez and BeggsKartoatmodjoBeal / StandingBeal / PipeflowKayePetroskyOsorioKhan

2

3

4

5

6

7


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



7

Methods to Evaluate Oil

Viscosity

Black Oil models

Compositional models

Data



8

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



9

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



10

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


gas

Standard

Conditions



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



11

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



12

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.



13

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



14

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



15

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)



16

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



17

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)



18

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)



19

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)


0.6

0.64

0.68

0.72

D e n s i t y ( g / c m 3

)




20

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)


0.66

0.68

0.7

0.72

0.74

0.76

D e n s i t y ( g / c m 3 )


Data Screening



21

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 )




22

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



23

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)



24

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



26

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



27

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



28

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



29


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



30


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



31

Errors are Defined as…

100

erimental exp

predicted erimental exp

100

erimental exp

predicted erimental exp



33


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



34

Extended Pedersen

(Validation Set)

Validation Set0.1

1

10

100

1000

0.1 1 10 100 1000


P

r e d i c t e d V i s c o s i t y ( c p ) Extended Pedersen



35

Extended LBC

(Validation Set)

Validation Set

0.1

1

10

100

1000

0.1 1 10 100 1000


P r

e d i c t e d V i s c o s i t y ( c p )

Extended LBC



37

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



39

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



40

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



41

Adapted Pedersen’s Model

with C10 as Reference FluidData Set 1:

2343 points



44

Predicted vs Experimental

Viscosity from Khan’s model

Data Set 1:

2343 points



45


Viscosity from Petrosky’s model

Data Set 1:

2343 points



47


Viscosity from Pedersen’s model

Data Set 2:

150 points



48


Viscosity from our model

Data Set 2:

150 points



49


Viscosity from Khan’s model

Data Set 2:

150 points



50


Viscosity from Petrosky’s model

Data Set 2:

150 points



51

Comparison of Petrosky vs.

our model

Data Set 2:

150 points



52

Performance when parameters

are tuned for each DL set

Data Set 1:

2343 points

l5 viscosity correlations

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