Carl L. Yaws, Sachin D. Sheth, Mei HanLamar University

Beaumont, Tex.

Thermodynamic diagrams have been developed for methane and ethane. The diagrams determine volume and enthalpy as a function of pressure and temperature.

The diagrams cover a wide range of conditions and are designed for ease of use.

The enthalpy diagrams also contain constant-entropy lines, which allow engineers to solve second-law problems such as adia- batic expansion and fluid compression.

### USAGE

Thermodynamic property data such as volume and enthalpy are especially helpful to engineers and scientists in the chemical processing and petroleum refining industries.

For example, the design of process vessels for fluid storage requires knowledge of the volume of the fluids to be stored at the storage conditions (temperature and pressure). Determining the size of a reactor requires knowledge of the volume of the species at reaction conditions.

Designing heat exchangers for gases and liquids requires knowledge of the enthalpy at inlet and outlet conditions. Knowledge of enthalpy also is important in the design of reboilers, condensers, pumps, compressors, expanders, and many other types of process equipment.

### THERMODYNAMIC DIAGRAMS

The thermodynamic diagrams for methane and ethane are shown in Figs. 1 (137053 bytes)and 2. (137698 bytes) The diagrams are based on the Peng-Robinson equation of state, as improved by Stryjek and Vera.1-3 Critical constants and ideal-gas heat capacities were taken from the data compilation from AIChE's Dippr project and from previous publications by Yaws.4-7

The range of coverage for pressure is from 10 to 10,000 psia. Very limited experimental data are available at pressures greater than 1,000 or 2,000 psia. Thus, values at higher pressures should be considered rough approximations. Values at lower pressures are more accurate.

The thermodynamic diagrams cover a wide range of volumes and enthalpies. Each diagram includes:

- A two-phase region for saturated liquid and vapor
- A superheated gas region for gases at temperatures above the saturation temperature
- A subcooled liquid region for liquids at temperatures below the saturation temperature
- A supercritical region for temperatures and pressures above the critical point.

### EXAMPLE CALCULATIONS

The thermodynamic diagrams can be used in a variety of process engineering applications. Representative engineering uses are illustrated in the following three examples.

### PROCESS VESSEL SIZE

A process vessel is to contain 300 lb of methane at 400 psia and 0 F. To estimate the process vessel size, use the thermodynamic diagram to determine the volume of 300 lb of methane at the process conditions. Substitute this value (0.7 cu ft/lb) into the following equation:

Vessel size = (300 lb)(0.7 cu ft/lb) = 210 cu ft

### HEAT EXCHANGER DUTY

Methane at 200 psia and 0 F. is heated to 400 F. and fed to a plug-flow reactor at a rate of 300,000 lb/hr. To estimate the heat-exchanger duty necessary to accomplish this heating, substitute the mass flow and enthalpies from the diagram into the following equation:

Heat-exchanger duty = Mass flow (H2 - H1) = (30,000 lb/hr)(190-(-50)) BTU/lb = 7.2 million BTU/hr

where: Hi is initial enthalpy and H2 is final enthalpy.

### COMPRESSION

Methane at 40 psia and 210 F. is compressed to 1,000 psia at a rate of 20,000 lb/hr. To estimate the change in enthalpy for the compression assuming adiabatic and reversible conditions (constant entropy), substitute the mass flow and constant entropy enthalpies from the diagram into the following equation:

Enthalpy change = Mass flow (H2 - H1) = (20,000 lb/hr)(440- 70) BTU/lb = 7.4 million BTU/hr

This change in enthalpy represents energy that is required to accomplish the compression under adiabatic and reversible conditions. Under operating conditions, the actual energy required for the compression would be somewhat more, depending on the efficiency.

### REFERENCES

1. Peng, D.Y., and Robinson, D.B., Ind. Eng. Chem. Fundam.,Vol. 15, No. 1, 1976, p. 59. 2. Stryjek, R., and Vera, J.H., Can. J. Chem. Eng., Vol. 64,

1986, p. 323. 3. Stryjek, R., and Vera, J.H., Can. J. Chem. Eng., Vol. 64,

1986, p. 334. 4. Daubert, T.E., and Danner, R.P., Data Compilation of

Properties of Pure Compounds, Parts 1-4, Supplements 1 & 2,

Dippr Project, AIChE, New York City, 1985-92. 5. Yaws, C.L., Thermodynamic and Physical Property Data, Gulf

Publishing Co., Houston, 1992. 6. Yaws, C.L., and Gallant, R.W., Physical Properties of

Hydrocarbons: Vol. 1, 2nd ed., 1992; Vol. 2, 3rd ed., 1993;

Vol. 3, 1993; and Vol. 4, 1995, Gulf Publishing Co.,

Houston. 7. Yaws, C.L., Handbook of Vapor Pressure, Vols. 1-4, Gulf

Publishing Co., Houston, 1994-95.

*Copyright 1995 Oil & Gas Journal. All Rights Reserved.*