Recent Advances in Modelling the Viscosity of Dense Fluids

N. Riesco & V. Vesovic

Imperial College London

Why do we need accurate and reliable viscosity values?

for more reliable process characterisation andprocess simulation;

for optimal design of process equipment;

for precision in the fluid flow monitoring;

The viscosity values are required over the wholephase space and relevant data cannot usually beobtained by experimental means alone;

What prediction methods are available?

1. Empirical: simple correlations; group methods;

2. Methods based on theoretical framework: macroscopic - where the viscosity is linked either to

thermodynamic quantities or advantage is taken of universal scaling behaviour;

molecular - based essentially on kinetic theory; molecular simulation;

Viscosity

Athabasca Bitumen, Canada (8.6oAPI)

1

10

100

1000

10000

100000

1000000

10000000

0 50 100 150 200 250 300

Temperature (oC)

Oil

Vis

cosi

ty (c

p)

Viscosity

CH4 @ 273 K

0.0

0.1

0.2

0.3

0.4

0.5

0 100 200 300 400 500 600

Density / kg/m3

m

Pa.s

C6-C16 mixture; 298K, 1 bar

Question?

Providing we know the intermolecular potential for a particular molecular interaction, can we calculate the transport properties of a fluid consisting of those molecules?

- dilute gas; - dense fluid;

Viscosity of CH4

R. Hellmann, E. Bich, E. Vogel, A.S. Dickinson, V.Vesovic, J. Chem. Phys. 129, 064302 (2008).

Viscosity of H2O

R. Hellmann, E. Bich, E. Vogel, A.S. Dickinson, V.Vesovic, J. Chem. Phys. 131, 014303 (2009).

Viscosity of Dense Fluids

No usable kinetic theory available

Enskog’s approach:- rigid spheres- uncorrelated velocities before thecollision

Enskog’s approach

rigid body interaction uncorrelated velocities before the collision

– molar density;(0) – viscosity at zero density; – radial distribution function at contact ; – measure of excluded volume;

.52

exAVN 8299.0

220 11

C1 @ 350 K

VW approach

21

22

2

)0(22

)0(

)0(22

)0(

12

2,

iii

iii

ii

iiii T

i

T

i

21*)0(

iii

i

220 11

VW approach

The link between and , through the hardsphere diameter, is now broken;

3

158 AN

31

5.01y

y

3

6

ANy

We now have two effective diameters: a - associated with excluded volume; c - associated with collisional dynamics;

VW prediction method

Calculate i and i for each pure species; Use mixing rules to evaluate ij and ij ;

no binary interaction parameters; Use Enskog’s equivalent for mixtures to

calculate the mixture viscosity;

Requires no dense viscosity data on mixtures; No adjustable parameters;

V. Vesovic, W.A. Wakeham, Chem. Eng. Sci., 44(10), 2181, (1989);D. Royal, V. Vesovic, J.P.M. Trusler, W.A. Wakeham, Molec. Phys. 101(3), 339, (2003).

Natural Gas (11 comp: 84% CH4, 10% N2, 3% C2H6 )

CH4

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 50 100 150 200 250

Pressure, bars

% (C

alc.

-Exp

.)/Ex

p.

260K280K300K320K

V. Vesovic - Flow Assurance: Reliable and Accurate Prediction of the Viscosity of Natural Gas, SPE-107154-PP, (2007).Experimental data: Schley, P., Jaeschke, M., Kuchenmeister, C. and Vogel, E., Int. J. Thermophys. (2004) 25 1623.

- vibrating-wire viscometer

- accuracy ±0.5%.

R32-R134a; liquid saturation viscosity

D. Royal, V. Vesovic, J.P.M. Trusler, W.A. Wakeham, Int. J. Refrig. 28(3), 311, (2005).Experimental data: D. Ripple, O. Matar, J. Chem. Eng. Data, 38, 560, (1993); R. Heide, DKV-Tagunsbericht, 23, 225, (1996); A. Laesecke, R.F. Hafer, D.J. Morris, J. Chem. Eng. Data, 46, 433, (2001).

-15

-10

-5

0

5

10

220 240 260 280 300 320 340T / K

/

%

VW-chain model

m

A.S. de Wijn, V. Vesovic, G. Jackson, J.P.M. Trusler,– J. Chem. Phys. 2008, 128, 204901;A.S. de Wijn, N. Riesco, V. Vesovic, G. Jackson, J.P.M. Trusler,– J. Chem. Phys.2012, 136, 074514

1.0

3.0

5.0

7.0

1 3 5 7 9 11 13 15 17

Number of C atoms

Num

ber o

f seg

men

ts, m

Viscosity vs. SAFT

m = 1+(C-1)/3

A.S. de Wijn, V. Vesovic, G. Jackson, J.P.M. Trusler,– J. Chem. Phys. 2008, 128, 204901

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4.0

250 300 350 400 450 500 550 600

SAFT-HSSAFT-VR

Binary alkane mixtures; 298K

A. Aucejo, M.C. Burguet, R. Munoz, J.L. Marques, J. Chem. Eng. Data, 40, 141, (1995).

Alkane mixtures; 293K<T<313K

J. Wu, Z. Shan, A.A. Asfour, Fluid Phase Equil., 143, 263-274, 1998;J. Wu, A.H. Nhaesi, A.A. Asfour, Fluid Phase Equil., 164, 285-293,1999.

C10-C20-C24 mixture

A.J. Queimada, S.E. Quinones-Cisneros, I.M. Marrucho, J.A.P. Coutinho, E.H. Stenby,Int. J. Thermophys., 24, 1221-1239, 2003.

C7-C24 mixture

A.J. Queimada, S.E. Quinones-Cisneros, I.M. Marrucho, J.A.P. Coutinho, E.H. Stenby,Int. J. Thermophys., 24, 1221-1239, 2003.

C7-C24 mixture

A.J. Queimada, S.E. Quinones-Cisneros, I.M. Marrucho, J.A.P. Coutinho, E.H. Stenby,Int. J. Thermophys., 24, 1221-1239, 2003.

Issues with VW

How do we incorporate into the VW,advances of SAFT-HS?

How do we include site specificinteractions in VW?

Highly asymmetric mixtures, rich in lightcomponent;

Conclusions

We are now in the position to accurately calculate the viscosity of dilute gas directly from the intermolecular potential by means of classical trajectory method.

supplement experimental data at low and high temperature where the experiments are difficult or less accurate;

provide data for fluids that are difficult to measure

For dense fluids progress is hindered by the lack of theory;

VW method is one attempt to link viscosity to the molecular properties;

It provides an accurate, self-consistent method, free of adjustable parameters, to predict the viscosity of dense fluid mixtures;