Separations analysis fundamentals - Principles of Chemical Separations with Environmental Applications - page 34

9 Apply the graphical method (stepping off stages) to determine the number of equilib-
rium stages needed for a given separation requirement.
10 Calculate the number of equilibrium stages using the Kremser equation.
11 Calculate the minimum number of equilibrium stages using the Underwood equation
and explain the physical significance.
12 Discuss the effect of stage efficiency on the number of required stages.
13 List sources of mass transfer resistance.
14 Calculate the overall mass transfer coefficient from the resistances in each phase.

3.2 Basic description of mass balances

A mass balance is nothing more than an accounting of material. Material balances can
be written for a specific component or they can account for all mass in a system. A simple
analogy to a mass balance would be an analysis of a personal financial budget. The overall
balance would evaluate the total money received and spent during the period of evaluation,
monthly, for example. An analysis of a specific item would be equivalent to a component
balance. For example, a certain amount of money would be budgeted for certain items
such as food, utilities, entertainment, etc. Each of these represents one component of the
overall balance.
To perform a balance, a control volume (C.V.) must be identified first to isolate the
system and the surroundings with respect to the balance. The surface of this control
volume, as shown in Figure 3.1, is termed the control surface. The control volume is
chosen to isolate the volume for evaluation, such as a complete separation process or just
a specific portion. The control surface is chosen to identify the flow of mass into or out of
the control volume. An open ( or flow) system is one in which material is transferred across
the control surface, that is, enters the C.V., leaves the C.V., or both. A closed ( or batch)
system is one in which there is no such transfer during the time interval for evaluation.
Consider a vessel in which water is added that contains some dissolved organics and
activated carbon. If the equilibration of the liquid and solid phases is of primary interest,
then the system can be treated as a closed system if the vessel is selected as the C.V. If

Control volume

Control surface

Figure 3.1 Generic control volume.