Page 152 - Separation process principles 2

Chapter 4

Single Equilibrium Stages

and Flash Calculations

The simplest separation process is one in which two phases almost perfect separation is achieved in a single stage. If the
in contact are brought to physical equilibrium, followed separation factor is only 1.10, an almost perfect separation
by phase separation. If the separation factor between two requires hundreds of stages. In this chapter, only a single
species in the two phases is very large, a single contacting equilibrium stage is considered, but a wide spectrum
stage may be sufficient to achieve a desired separation of separation operations is described. In all cases, the
between them; if not, multiple stages are required. For calculations are made by combining material balances with
example, if a vapor phase is in equilibrium with a liquid phase equilibria relations. When a phase change such as
phase, the separation factor is the relative volatility, a, of a vaporization occurs, or when heat of mixing effects are
volatile component called the light key, LK, with respect to a large, an energy balance must be added. In the next chapter,
less-volatile component called the heavy key, HK, where arrangements of multiple stages, called cascades, are
WK,HK = KL~/K~~. separation factor is 10,000, an described.
If
the
4.0 INSTRUCTIONAL OBJECTIVES

After completing this chapter, you should be able to:
Explain what an equilibrium stage is and why it may not be sufficient to achieve a desired separation.
Use the Gibbs phase rule to determine the number of intensive variables that must be specified to fix the remaining
intensive variables for a system at equilibrium.
Extend Gibbs phase rule to include extensive variables so that the number of degrees of freedom (number of
variables minus the number of independent relations among the variables) can be determined for a continuous
separation process.
Explain and utilize ways that binary vapor-liquid equilibrium data are presented.
Define relative volatility between two components of a vapor-liquid mixture.
Use T-y-x and y-x diagrams of binary mixtures, with the concept of the q-line, to determine equilibrium phase
compositions.
Understand the difference between minimum- and maximum-boiling azeotropes and how they form.
Use component material-balance equations with K-values to calculate bubble-point, dew-point, and equilibrium-
flash conditions for multicomponent mixtures.
Use triangular phase diagrams for ternary systems with component material balances to determine equilibrium
compositions of liquid-liquid mixtures.
Use distribution coefficients, usually determined from activity coefficients, with component material-balance
equations to calculate liquid-liquid phase equilibria for multicomponent systems.
Use equilibrium diagrams with component material balances to determine equilibrium-phase amounts and
con~positions for solid-fluid systems (leaching, crystallization, sublimation, desublimation, and adsorption) and
for light gas-liquid systems (absorption).
Calculate phase amounts and compositions for multicomponent vapor-liquid-liquid systems.

4.1 THE GIBBS PHASE RULE AND
depend on system size. Intensive variables are temperature,
DEGREES OF FREEDOM
pressure, and phase compositions (mole fractions, mass
The description of a single-stage system at physical equilib- fractions, concentrations, etc.). Extensive variables include
rium involves intensive variables, which are independent mass or moles and energy for a batch system, and mass or
of the size of the system, and extensive variables, which do molar flow rates and energy transfer rates for a flow system.