Page 239 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

CHAPTER

9
Phase equilibria

9.1 Introduction
Phase equilibrium data pertaining to the transferable component(s) is essential for design of any mass
transfer process. Interphase mass transfer between immiscible phases occurs in the direction required
to attain equilibrium, and its rate depends on the departure from equilibrium, i.e., how far away is the
concentration of species i from the equilibrium concentration. Equilibrium concentration is inde-
pendent of the amount/relative proportion of the two phases, and the locus of equilibrium concen-
tration data generates the equilibrium distribution curve for each distributed component. The data can
be presented either at constant temperature (isothermal data) or at constant pressure (isobaric data).
Equilibrium distribution of the transferable component(s) represents the limiting composition(s) of the
phases in each ideal stage of contact. The designer calculates the separation attainable in a mass
transfer process consisting of one or more ideal contacting stages by estimating the equilibrium
concentration(s) from phase equilibrium thermodynamics.
Generally speaking, whenever a dynamic equilibrium is established between phases, the con-
centration of the species within individual phases (equilibrium
concentration) is uniform and is fixed by the system temperature
and pressure. In case of steady state, the species concentrations
Equilibrium and Steady State
and the thermodynamic parameters (temperature, pressure, etc.)
may not essentially be the same at all locations within a phase,
but at every location, these do not vary with time. Hence, the
equilibrium condition encompasses a steady-state condition, but the converse is not true.

9.2 Representation of concentration
The concentration of species i in a phase can have different representations. Usually, mole fraction or
a quantity proportional to it, e.g., partial pressure of component in gas-liquid or gas-solid system is
used to denote concentration in the gas phase. Traditionally the concentration of more volatile
component in the liquid phase is x, and the same in vapor or another liquid phase richer in the
component is denoted by y. In most situations, x and y denote mole fraction of the transferable
species. Mole ratios X and Y maybeusedtorepresent molesof i per mole of phase free of component
i,i.e., X ¼ x/(1 x) and Y ¼ y/(1 y).

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