# 5.28: Untitled Page 89

- Page ID
- 18222

## Chapter 5

*V*

*V * *V * *V*

(5‐9)

*A*

*B*

*mix*

By definition, an ideal gas mixture obeys what is known as *Amagatʹs Law, * i.e.

*V*

0 *, * Amagatʹs Law

(5‐10)

*mix*

Amagat’s law can also be expressed as

*A * *N*

*V*

*V , * Amagatʹs Law

(5‐11)

*A*

*A * 1

In the gas phase the mole fraction is generally denoted by *y * while *x * is *A*

*A*

reserved for mole fractions in the liquid phase. For ideal gas mixtures it is easy *Figure 5‐1*. Constant pressure, isothermal mixing process

*Two‐Phase Systems* & *Equilibrium Stages *

159

to show, using Eqs. 5‐1f, 5‐2 and 5‐3, that the mole fraction is given by *y*

*p p *

(5‐12)

*A*

*A*

This is an extremely convenient representation of the mole fraction in terms of the partial pressure; however, one must always remember that it is strictly valid only for an ideal gas mixture.

EXAMPLE 5.1. Flow of an ideal gas in a pipeline

A large pipeline is used to transport natural gas from Oklahoma to Nebraska as illustrated in Figure 5.1. Natural gas, consisting of methane with small amounts of ethane, propane, and other low molecular mass *Figure 5.1*. Transport of natural gas from Oklahoma to Nebraska hydrocarbons, can be assumed to behave as an ideal gas at ambient temperature. At the pumping station in Glenpool, OK, the pressure in the 20‐inch pipeline is 2,900 psia and the temperature is *T * 90 F . At the o

receiving point in Lincoln, NE, the pressure is 2,100 psia and the temperature is *T * 45 F . The mass average velocity of the gas at 1

Glenpool is 50 ft/s. Assuming ideal gas behavior and treating the gas as 100% methane, we want to compute the following:

a) Mass average velocity at the end of the pipeline

b) Mass and molar flow rates at both ends of the pipeline.

This problem has been presented in terms of a variety of units, and it is sometimes convenient to express all variables in terms of SI units as follows: