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Viscosity

Pure compound viscosities are only available for use with internal mixture viscosity routines. They cannot be used if no internal mixture routine is selected. For CAPE-OPEN version 1.1 external calculations, pure compound viscosities are evaluated for each compound as mixture viscosities with composition set to unity for that compound and zero for all other compounds.

Liquid mixture viscosity

Liquid mixture viscosity is calculate through logarithmic mixing:

\begin{displaymath}\ln \eta^L_m = \sum^{c}_{i=1} z_i \ln \eta^L_i\end{displaymath}

where zi are either the mole fractions (for molar averaging) or alternatively the weight fractions for mass averaging.

For mass averaging, composition derivatives are approximate due to normalization of the mass fractions.

Pure compound liquid viscosity

Temperature Correlation

The parameters for the temperature correlation for liquid viscosity of pure compounds are available through TEA's PCD data files.

Letsou-Stiel

The Letsou-Stiel method (1973) for liquid viscosity of pure compounds:

$\displaystyle \xi$ $\textstyle =$ $\displaystyle 2173.424 T^{1/6}_{c,i} \over \sqrt{M_i} P^{2/3}_{c,i}$
$\displaystyle \xi^{(0)}$ $\textstyle =$ $\displaystyle ( 1.5174 - 2.135 T_r + 0.75 T^2_r ) 10^{-5}$
$\displaystyle \xi^{(1)}$ $\textstyle =$ $\displaystyle ( 4.2552 - 7.674 T_r + 3.4 T^2_r ) 10^{-5}$
$\displaystyle \eta^L_i$ $\textstyle =$ $\displaystyle ( \xi^{(0)} + \omega \xi^{(1)} ) / \xi$

If the temperature is above the critical temperature of the compound, vapor viscosity is used instead.

Reid et al

The simple temperature correlation given in Reid et al. (RPS liquid viscosity, see A439) can also be used:

\begin{displaymath}\log \eta = A + B / T\end{displaymath}

The parameters A and B are available through TEA's PCD data files.

Per compound

When selecting the Per Compound routine, the above methods can be selected on a per-compound basis in the compounds tab.

Vapor mixture viscosity

All vapor mixture viscosity derivatives are determined by perturbation.

Wilke

Mixture vapour viscosities are computed using:

\begin{displaymath}\eta^L_m = \sum^{c}_{i=1} {x_i \eta^L_i \over \sum x_i \phi_{ij}}\end{displaymath}

where the interaction parameters φij are calculated by Wilke's (1950) method:

\begin{displaymath}\phi_{ij} = ({1 + \sqrt{ \eta_i / \eta_j } (M_i / M_j)^{1/4})^2\over\sqrt{ 8 (1 + M_i / M_j) } }\end{displaymath}

Brokaw

Mixture vapour viscosities are computed using:

\begin{displaymath}\eta^L_m = \sum^{c}_{i=1} {x_i \eta^L_i \over \sum x_i \phi_{ij}}\end{displaymath}

where the interaction parameters φij are calculated by Brokaw's method:

$\displaystyle \phi_{ij}$ $\textstyle =$ $\displaystyle S A \sqrt{ \eta_i / \eta_j }$
$\displaystyle sm$ $\textstyle =$ $\displaystyle \left( 4 \over (1+M_j/M_i) (1+M_i/M_j) \right)^{1/4}$
$\displaystyle A$ $\textstyle =$ $\displaystyle {sm \over \sqrt{M_i/M_j}}\left( 1 + {(M_i/M_j - (M_i/M_j)^{0.45}......(1 + M_i/M_j)} +{(1 + (M_i/M_j)^{0.45}) \over \sqrt{sm} (1 + M_i/M_j)}\right)$

If the Lennard-Jones energy parameter, ε, and the Stockmayers polar parameter, δ, are known, S is calculated from:

\begin{displaymath}S = {1 + \sqrt{ (T/\epsilon_i) (T/\epsilon_j) } + {\delta_i......+ \delta^2_i / 4}\sqrt{1 + T/\epsilon_j + \delta^2_j / 4}}\end{displaymath}

Otherwise, it is approximated by S = 1.

ε and δ can be estimated from:

$\displaystyle \epsilon$ $\textstyle =$ $\displaystyle 65.3 T_{c,i} Z^{3.6}_{c,i}$
$\displaystyle \delta$ $\textstyle =$ $\displaystyle 1.744~10^59 {\mu^2 \over V_{b,i} T_{b,i}}$

where μ is the dipole moment in C*m and Vb the volume change of boiling in m3/kmol.

Pressure correction

Vapour viscosities are a function of pressure and a correction is normally applied. Mixture properties are computed with the "normal" mixing rules:

$\displaystyle \rho_c$ $\textstyle =$ $\displaystyle 1 / V_{c,m}$
$\displaystyle \rho_r$ $\textstyle =$ $\displaystyle \rho / \rho_c$
$\displaystyle \xi$ $\textstyle =$ $\displaystyle 2173.4241 T^{1/6}_{c,m} / \sqrt{M_m} P^{2/3}_{c,m}$
$\displaystyle A$ $\textstyle =$ $\displaystyle \exp (1.4439 \rho_r) - \exp (-1.111 \rho^{1.85}_r)$
$\displaystyle B$ $\textstyle =$ $\displaystyle 1.08~10^{-7} A / \xi$
$\displaystyle \eta_{hp}$ $\textstyle =$ $\displaystyle \eta + B$

where ρ is the vapour mixture molar density.

Pure compound vapor viscosity

Temperature Correlation

The parameters for the temperature correlation for vapor viscosity of pure compounds are available through TEA's PCD data files.

Kinetic Gas Theory

The pure compound vapor viscosity can be computed with the Chapman-Enskog kinetic theory (see Hirschfelder et al. 1954 and A391-393):

$\displaystyle T^*$ $\textstyle =$ $\displaystyle T / \epsilon$
$\displaystyle \Omega_v$ $\textstyle =$ $\displaystyle a (T^*)^{-b} + c / \exp(d T^*) + e / \exp(f T^*)$
$\displaystyle \eta^V$ $\textstyle =$ $\displaystyle 26.69~10^-7 sqrt(M T) / \sigma^2 (\Omega_v + 0.2 \delta^2 / T^*)$

where the collision integral constants are

$a=1.16145$

$b=0.14874$

$c=0.52487$

$d=0.77320$

$e=2.16178$

$f=2.43787$

Yoon and Thodos

The vapor pure compound viscosity may also be computed with the Yoon and Thodos method:

$\displaystyle \xi_i$ $\textstyle =$ $\displaystyle 2173.4241 T^{1/6}_{c,i} / \sqrt{M_i} P^{2/3}_{c,i}$
$\displaystyle \eta^V_i$ $\textstyle =$ $\displaystyle {1 + a T^b_r - c \exp (d T-r) + e \exp (f T_r)\over 10^8 \xi}$

where the constants a through f are given by:

Hydrogen Helium Others
a=47.65 a=52.57 a=46.1
b=0.657 b=0.656 b=0.618
c=20.0 c=18.9 c=20.4
d=-0.858 d=-1.144 d=-0.449
e=19.0 e=17.9 e=19.4
f=-3.995 f=-5.182 f=-4.058

Per compound

When selecting the Per Compound routine, the above methods can be selected on a per-compound basis in the compounds tab.