PHYSICAL CHEMISTRY

I. F. GOLUBEV, N. A. AGAEV

GENERALIZATION OF DATA ON THE VISCOSITY OF SATURATED HYDROCARBONS AT VARIOUS TEMPERATURES AND PRESSURES

(Presented by Academician V. A. Kirillin, 20 III 1963)

A generalization of data on the viscosity of saturated hydrocarbons, as well as of many other gases, was given in (¹). It was established that the most satisfactory generalized dependence is the common curve in the coordinates

\[ \left( \frac{\eta_{p,T}-\eta_T}{\eta_{(p,T)_{\mathrm{cr}}}-\eta_{T_{\mathrm{cr}}}} \right) - \frac{\rho}{\rho_{\mathrm{cr}}}. \]

Here: \(\eta_{p,T}\) is the viscosity at a given pressure \((p,\ \text{atm})\) and temperature \((T,\ ^\circ\mathrm{K})\), \(\eta_T\) is the viscosity at atmospheric pressure and the same temperature \((T,\ ^\circ\mathrm{K})\), \(\eta_{T_{\mathrm{cr}}}\) is the viscosity at atmospheric pressure and the critical temperature \((T,\ ^\circ\mathrm{K})\), \(\eta_{(p,T)_{\mathrm{cr}}}\) is the viscosity at the critical point (at \(p_{\mathrm{cr}}\) and \(T_{\mathrm{cr}}\)).

Fig. 1. Dependence of \((\eta_{p,T}-\eta_T)\) on density according to literature data:
\(I\)—for methane, \(II\)—for ethane, \(III\)—for propane.
1–12—the numbers correspond to the cited literature; 13—data of Comings (¹), 14—Kuss (¹), 15—Sage and Lacey (¹), 16—Beecher and Katz (¹), 17—Terf and Galkov (¹), 18—Smith and Brown (¹).

In this article we present a generalization in these coordinates of the experimental data on the viscosity of n-pentane, n-hexane, n-heptane, and n-octane, published in \(^{(2-4)}\). In these same papers a treatment of the experimental data in the coordinates \((\eta_{p,T} - \eta_T) - \rho\) was presented, which showed that the experimental data for all four of the listed substances, at all temperatures investigated for a given substance, lie well on one common dependence curve.

In Fig. 1, in addition to what was set forth in \(^{(1)}\), a treatment is given of the existing experimental data in these same coordinates for methane, ethane

![Figure 2 and Figure 3 graphs]

Fig. 2. Dependence of \(\eta_{(pT)\mathrm{cr}}\) (a) and \(\eta_{T\mathrm{cr}}\) (b) on molecular weight for saturated hydrocarbons \(C_1 - C_8\)

Fig. 3. Dependence of \(\eta_{(pT)\mathrm{cr}}/\eta_{T\mathrm{cr}}\) on molecular weight for saturated hydrocarbons \(C_1 - C_8\).

and propane using data published recently \(^{(3-13)}\); the density values in this case were taken from the following works: for methane \(^{(14,15)}\), ethane \(^{(16,17)}\), propane \(^{(17,18)}\).

As can be seen, for the generalization, in addition to the values \(\eta_{p,T}\) and \(\eta_T\), it is necessary to know the values of the constants \(\eta_{T\mathrm{cr}}\), \(\eta_{(p,T)\mathrm{cr}}\), \(\rho_{\mathrm{cr}}\), and the \(P - V - T\) data for the substances investigated.

On the basis of our experimental data, using the data given in \(^{(1,19,20)}\), Table 1 has been compiled.

Table 1

In Figs. 2 and 3 the dependence of \(\eta_{T_{\mathrm{cr}}}\) and \(\eta_{(pT)_{\mathrm{cr}}}\), as well as \(\eta_{(pT)_{\mathrm{cr}}}/\eta_{T_{\mathrm{cr}}}\), on molecular weight is presented.

It is seen from Fig. 2 that the dependence of the indicated quantities on molecular weight is represented in the form of smooth curves which, however, do not have a simple graphical regularity.

Therefore, it appears difficult to carry out extrapolative predictions from these curves of the values of \(\eta_{T_{\mathrm{cr}}}\) and \(\eta_{(pT)_{\mathrm{cr}}}\) for paraffin hydrocarbons with molecular weight greater than that of \(n\)-octane.

Using the data of Table 1, we constructed a generalized plot (Fig. 4), in the coordinates

\[ \left(\frac{\eta_{pT}-\eta_T}{\eta_{(pT)_{\mathrm{cr}}}-\eta_{T_{\mathrm{cr}}}}\right)-\frac{\rho}{\rho_{\mathrm{cr}}} \]

for the class of paraffin hydrocarbons from methane to \(n\)-octane inclusive. As can be seen, the experimental data for all paraffin hydrocarbons are arranged very well on one common curve.

Table 2

The values

\[ \frac{\eta_{pT}-\eta_T}{\eta_{(pT)_{\mathrm{cr}}}-\eta_{T_{\mathrm{cr}}}}, \]

corresponding to the generalized reduced curve for even values of \(\rho/\rho_{\mathrm{cr}}\), are summarized in Table 2, which may be

Fig. 4. Dependence of the viscosity of paraffin hydrocarbons in the coordinates

\[ \left(\frac{\eta_{pT}-\eta_T}{\eta_{(pT)_{\mathrm{cr}}}-\eta_{T_{\mathrm{cr}}}}\right)-\frac{\rho}{\rho_{\mathrm{cr}}}; \]

1—methane, 2—ethane, 3—propane, 4—\(n\)-pentane, 5—\(n\)-hexane, 6—\(n\)-heptane, 7—\(n\)-octane.

used for interpolation and extrapolation calculations.

A generalization is given of experimental data on the viscosity of saturated hydrocarbons from methane to octane inclusive, over wide ranges of temperatures and pressures (densities). The generalization was carried out on the basis of the theory of corresponding states in the coordinates

\[ \frac{\eta_{p,T}-\eta_T}{\eta_{(p,T)_{\mathrm{cr}}}-\eta_{T_{\mathrm{cr}}}} \;-\; \frac{\rho}{\rho_{\mathrm{cr}}} \]

and a plot of this dependence was constructed.

On the basis of the generalized reduced curve, Table 2 was compiled for the values

\[ \left( \frac{\eta_{p,T}-\eta_T}{\eta_{(p,T)_{\mathrm{cr}}}-\eta_{T_{\mathrm{cr}}}} \right) \]

for values \(0 < \frac{\rho}{\rho_{\mathrm{cr}}} \leqslant 3\), which may be used for interpolation and extrapolation calculations.

State Scientific-Research
and Design Institute of the Nitrogen Industry
and Products of Organic Synthesis

Energy Institute
Academy of Sciences of the Azerbaijan SSR

Received
19 III 1963

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