Fundamentals of Chemical

Engineering - II

CHPE204

Dr. Yasir Ali

PREREQUISITE: CHPE202

Chapter 1

Single-Phase Systems

LIQUID AND SOLID DENSITIES

When you heat a liquid or a solid it normally expands (i.e., its density

decreases). In most process applications, however, it can be assumed with

little error that solid and liquid densities are independent of temperature.

Similarly, changes in pressure do not cause significant changes in liquid or

solid densities; these substances are therefore termed incompressible.

LIQUID AND SOLID DENSITIES

EXAMPLE: Determination of a Solution Density

IDEAL GASES

The Ideal Gas Equation of State

The ideal gas equation of state can be derived from the kinetic theory of gases by assuming

that gas molecules have a negligible volume, exert no forces on one another, and collide

elastically with the walls of their container. The equation usually appears in the form:

EXAMPLE: The Ideal Gas Equation of State

One hundred grams of nitrogen is stored in a container at 23.0 ºC and 3.00 psig.

1) Assuming ideal gas behavior, calculate the container volume in liters.

2) Verify that the ideal gas equation of state is a good approximation for the given conditions.

SOLUTION

The ideal gas equation of state relates absolute temperature, absolute pressure, and the

quantity of a gas in moles. We therefore first calculate:

IDEAL GASES

IDEAL GASES

Standard Temperature and Pressure

Doing PVT calculations by substituting given values of variables into the ideal gas

equation of state is straightforward, but to use this method you must have on hand either a

table of values of R with different units or a good memory. A way to avoid these

requirements is to use conversion from standard conditions.

For an ideal gas at an arbitrary temperature and pressure ,

IDEAL GASES

IDEAL GASES

EXAMPLE: Conversion from Standard Conditions

Butane (C4H10) at 360 ºC and 3.00 atm absolute flows into a reactor at a rate of 1100 kg/h.

Calculate the volumetric flow rate of this stream using conversion from standard

conditions.

SOLUTION

As always, molar quantities and absolute temperature and pressure must be used.

EXAMPLE: Effect of T and P on Volumetric Flow Rates

EXAMPLE: Standard and True Volumetric Flow Rates

The flow rate of a methane stream at 285 ºF and 1.30 atm is measured with an orifice

meter. The calibration chart for the meter indicates that the flow rate is 3.95×105 SCFH

(standard cubic feet per hour [ft3 (STP)/h]). Calculate the molar flow rate and the true

volumetric flow rate of the stream.

SOLUTION

EXAMPLE: The Truncated Virial Equation

Two gram-moles of nitrogen is placed in a three-liter tank at –150 ºC. Estimate the tank

pressure using the ideal gas equation of state and then using the virial equation of state

truncated after the second term. Taking the second estimate to be correct, calculate the

percentage error that results from the use of the ideal gas equation at the system conditions.

SOLUTION

THE COMPRESSIBILITY FACTOR EQUATION OF STATE

The compressibility factor of a gaseous species is defined as the ratio

EXAMPLE: Tabulated Compressibility Factors

Fifty cubic meters per hour of methane flows through a pipeline at 40.0 bar absolute

and 300.0 K.

From the given reference, z = 0.934 at 40.0 bar and 300.0 K. Rearranging Equation 5.4-2c yields

SOLUTION

The Law of Corresponding States and Compressibility Charts

It would be convenient if the compressibility factor at a single temperature and pressure were the

same for all gases, so that a single chart or table of z( T, P) could be used for all PVT calculations.

An alternative approach is presented in this section. We will show that z can be estimated

for a species at a given temperature T and pressure P with this procedure:

1. Look up (e.g., in Table B.1) the critical temperature Tc, and critical pressure Pc, of the species.

2. Calculate the reduced temperature Tr= T/Tc, and reduced pressure Pr= P/Pc .

3. Look up the value of z on a generalized compressibility chart which plots z versus Pr for

specified values of Tr.

The basis for estimating in this manner is the empirical law of corresponding states, which

holds that the values of certain physical properties of a as—such as the compressibility factor

depend to great extent on the proximity of the as to its critical state. The reduced temperature

and pressure provide a measure of this proximity; the closer Tr and Pr are to 1, the closer the

gas is to its critical state. This observation suggests that a plot of z versus Tr and Pr should be

approximately the same for all substances.

The below Figure shows a generalized compressibility chart for those fluids having a critical

compressibility factor of 0.27

A generalized compressibility chart for those fluids

The procedure for using the generalized compressibility chart for PVT calculations is

as follows:

Fig. 5.4-2 Generalized compressibility chart, low pressures

EXAMPLE: The Generalized Compressibility Chart

One hundred gram-moles of nitrogen is contained in a 5-liter vessel at 20 6 C.

Estimate the pressure in the cylinder..

SOLUTION

From Table B.1, the critical temperature and pressure of nitrogen are

Nonideal Gas Mixtures

Whether an analytical or graphical correlation is used to describe nonideal gas behavior,

difficulties arise when the gas contains more than one species. Consider, for example, the SRK

equation of state (Equation 5.3-7)

We will illustrate PVT calculations for mixtures with a simple rule developed by Kay that utilizes

the generalized compressibility charts.

EXAMPLE: Kay’s Rule

A mixture of 75% H2 and 25% N2 (molar basis) is contained in a tank at 800 atm and – 70 C.

Estimate the specific volume of the mixture in L/mol using Kay’s rule.

SOLUTION