Extrapolation of viscosity data for liquids

Author

Julius Irwin Gnapp, New Jersey Institute of Technology

Document Type

Thesis

Date of Award

6-30-1961

Degree Name

Master of Science in Chemical Engineering - (M.S.)

Department

Chemical Engineering

First Advisor

Saul I. Kreps

Second Advisor

Jerome J. Salamone

Third Advisor

Joseph Joffe

Abstract

The method of finite-difference recurrence relations* is here applied to viscosity-temperature data to determine whether it offers an improved means of extrapolating such data. The best of the existing parametric correlations, which is considered to be that of Andrade, was found to be subject to important departures from linearity and dependent upon the particular data points used in its formulation. The proposed method is non-parametric in that it does not require an assumption of the explicit function relating viscosity with temperature. Instead, it assumes that there is a linear relation between successive values of viscosity at equal intervals of temperature. This relation would take the form

u_k = A_1k-1 + A₂ u_k-2 + A₃ u_k-3

where

u_k is the viscosity at the end of the kth interval;

u_k-1, u_k-2 and u_k-3 are the known viscosities at the ends of the three previous temperature intervals;

A₁, A₂ and A₃ are the coefficients (A_j) to be determined. The A. coefficients are calculated by the least squares method for the best fit of the values of viscosity at n successive, equally spaced stations on the curve which has been faired through the available experimental data. When the coefficients have been determined, the above relation can be used for extrapolating the experimental viscosity-temperature curve.

The effectiveness of this method in the extrapolation of viscosity-temperature data was investigated by deter mining the recurrence relations for three n-paraffins and three n-1-olefins and comparing the predicted values of viscosity with actual experimental values and with Andrade predictions at corresponding temperatures. A total of 6 trials was conducted for each compound, using 7 stations, 8 stations and 9 stations of both "unsmoothed" data (actual published values) and "smoothed" data (from faired curve).

The results of the investigation indicate that under optimum conditions this method can provide extrapolations with an accuracy of ± 2 per cent over distances of 40°0 to 60°C. Although no one method of applying the recurrence relations was consistently superior to the Andrade method, it was found that for most of the compounds tested, at least one of the trials was superior. When there is a radical difference between viscosities predicted by recurrence relations based on n = 9, n = 8 and n = 7, it is considered that the inconsistency of the experimental data is demonstrated. Inconsistencies in the data may be due to experimental error, but more often are manifistations of discontinuities in the viscosity-temperature function of the liquid which result from changes in molecular assoc¬iation with temperature. In this situation the assumption that the function may be represented by a finite-difference recurrence relation with constant coefficients is invalid¬ated. Discontinuities have a somewhat milder effect on this method in comparison with parametric correlations, although not to the hoped for degree.

* Mendelson A. and S. S. Manson, The Extrapolation of Families of Curves by Recurrence Relabions, With Application to Creep-Rupture Data, J. Basic Eng., Vol. 2, Dec. 1960, pp. 839-847.

Recommended Citation

Gnapp, Julius Irwin, "Extrapolation of viscosity data for liquids" (1961). Theses. 3160.
https://digitalcommons.njit.edu/theses/3160