Available mixing rules for liquid viscosity

You can use one of the following mixing rules to calculate the bulk liquid viscosity of a Fluid Type.

SimSci Mixing Rule

where

hm is the liquid viscosity of the mixture

hi is the liquid viscosity of pure component i

xi is the molar composition fraction of component i in the liquid phase

This is the default mixing rule.

Molar Average

Logarithmic Molar Average

Logarithmic Mass Average

Power Molar Average

where

r is an exponent that you specify in the Fluid Editor

ASTM Mixing Rule

where

wi is the weight composition fraction of component i in the liquid phase

f is a specified parameter

TRAPP (transport property prediction)[2,3]

We evaluate the liquid viscosity based on the deviations in a reference fluid, which we assume to be the pure liquid of a reference component, R. We use the following equations to calculate the liquid viscosity of the mixture (hm):

where

hm0 is the liquid viscosity of the mixture at low pressure, which we calculate by using the liquid viscosities from the Lee-Kesler equation of state (EOS) and the SimSci mixing rule

DhENSKOG is a calculated[4] correction factor based on the hard sphere assumption to account for size differences between component molecules

Ei are a set of constant coefficients taken from literature[5]

rc,R is the density of reference component R at its critical temperature and pressure

rc,i is the density of component i at its critical temperature and pressure

MR is the molar mass of reference component R

Pisat is the vapor pressure of component i at the system temperature (T)

PRsat(T0) is the vapor pressure of reference component R at temperature T0

risat is the saturated liquid density of component i at the system temperature (T)

rRsat(T0) is the saturated liquid density of reference component R at T0

wi is the acentric factor of component i

wR is the acentric factor of reference component R

Zc,i is the critical compressibility factor of component i

Zc,R is the critical compressibility factor of reference component R

Because we evaluate the vapor pressure and saturated liquid density of the reference fluid at T0, we must iteratively solve for fi.

Typically, you use this mixing rule for systems of non-polar components when Tr > 0.7.

Quadratic Mixing Rule (VISCQMR)

where

kij is the binary interaction parameter between components i and j

aij, bij, cij, and dij are constant coefficients taken from the VISCQMR data bank that the Fluid Type uses

You use the controls in the Liquid Viscosity Quadratic Mixing Rule Bank area in the Transport Mixing Rules section of the Fluid Editor to add VISCQMR data banks to your Fluid Type. See Add a VISCQMR data bank to your Fluid Type for more information.

If kij = 0 for all component pairs, the quadratic mixing rule reduces to the logarithmic molar average:

References

1. Wauquier, J. Petroleum Refining V. 1: Crude Oil, Petroleum Products, Process Flowsheets; Institut Francais du Petrole Publications; Editions Technips: Paris, 1995; p. 130.

2. Leland, T. W.; Robinson, J. S.; Suther, G.A. Statistical Thermodynamics of Mixtures of Molecules of Different Sizes. Trans. Farad. Soc. 1968, 64, 1447-1460.

3. Ely, J. F.; Hanley, H. J. M. Prediction of Viscosity and Thermal Conductivity in Hydrocarbon Mixtures- Computer Program TRAPP. Proceedings of the 60th Annual Convention of the Gas Processors Association, San Antonio, TX, USA, Mar 23, 1981.

4. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 1977; pp. 498-502.

5. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 1977; pp. 493-497.