#### Date of Award

Spring 1968

#### Document Type

Dissertation

#### Degree Name

Doctor of Engineering Science in Chemical Engineering

#### Department

Chemical Engineering and Chemistry

#### First Advisor

Joseph Joffe

#### Second Advisor

Saul I. Kreps

#### Third Advisor

Hung T. Chen

#### Fourth Advisor

Jui Sheng Hsieh

#### Fifth Advisor

Dimitrios P. Tassios

#### Abstract

A generalized three parameter virial equation of state has been developed and tested for seven pure gases having different molecular characteristics. The equation has also been tested for more than thirteen binary gas mixtures using three different mixture rules. The final equation is as follows:

Z = 1 + B(T)/V + C(T)/V^{2} + D(T)/V^{3} + E(T)/V^{4} + VF(T)/e^{aV} + VG(T)/e^{bV}

The expressions for E(T), F(T), and G(T) along the critical isotherm were derived in terms of critical properties and two constants, a and b which appear in the sixth and seventh terms in the above equation from the conditions that the first and second derivatives of pressure with respect to volume are zero at the critical point. The two unresolved parameters, i.e. a and b, were established from the experimental P-V-T data along the critical isotherms of pure gases, i.e. nitrogen, carbon dioxide, propane, carbon monoxide etc. A direct minimum seeking method which operates on an error function constructed below,

E_{r} = Σ^{n}_{i=1} (Z_{i, obs} - Z_{i, cal.})^{2}/n^{2}

was used. By minimizing the function, the best value of the parameters i.e. a and b, was obtained. The second, third, and fourth virial coefficients were calculated from the Gyorog and Obert Tables (37), using the Lennard-Jones force constants obtained from the critical properties by means of generalized relationships.

The calculated compressibility factors for all of the systems were compared with the Gyorog-Obert, Redlich-Kwong, and Generalized BWR equations. The absolute average and maximum deviations from the experimental values were computed for all the systems considered in this work.

Expressions for the fugacity of components in gaseous mixtures were derived for the Joffe-Zudkevitch mixture rule. The fugacities of components in:gas mixtures and the enthalpy departures from ideal gas values were calculated for three binary gas mixtures using the Joffe-Zudkevitch and the Pitzer-Hultgren mixture rules.

The equation presented in this work gave excellent results when compared to the standard Redlich-Kwong, the generalized BWR, and the Gyorog-Obert equations of state, The equation developed in this work gave less than 1.5 percent average deviation for compressibility factors of pure gases and below 3 percent for compressibility factors of binary mixtures up to 1.8 times the critical density. The results for other thermodynamic properties are also superior to those obtained with the Redlich-Kwong and Gyorog-Obert equations.It is noteworthy that the range of applicability in the gaseous region of the three-parameter generalized virial equation developed in this study is the same as that of the eight constant Benedict-Webb-Rubin equation, i.e. up to 1.8 times the critical density.

#### Recommended Citation

Patel, Ghanshyam R., "The generalized virial equation of state" (1968). *Dissertations*. 1336.

https://digitalcommons.njit.edu/dissertations/1336