# 4.19: Untitled Page 74

- Page ID
- 18207

## Chapter 4

*Figure 4‐11*. Primary cuts for the two‐column distillation unit distillation unit. In order to construct a control volume that joins the primary cuts of streams #3 and #4, we have two choices. One choice is to *enclose the second* *column* by joining the primary cuts of streams #3, #4 and #5, while the second choice is illustrated in Figure 4‐12 where we have shown Control Volumes I and II. If Control Volume II were constructed so that it joined streams #3, #4 and #5, it would not be connected to the *single source* of the necessary information, i.e., the mass flow rate of stream #1. In that case, the information about stream #5

would cancel in the balance equations and we would not be able to determine the mass flow rate in stream #5.

Since the data are given in terms of mass fractions and the mass flow rate of stream #1, the appropriate macroscopic balance is given by Eq. 4‐7. For steady-state conditions in the absence of chemical reactions, the three species mass balances are given by

(4‐98)

Since convective effects will dominate at the entrances and exits of the two

*Multicomponent systems*

130

*Figure 4‐12*. Control volumes for two‐column distillation unit control volumes, we can neglect diffusive effects and express the three mass balances in the form

Species Balances:

(4‐99)

Here we have represented the fluxes in terms of the mass fractions since the stream compositions are given in terms of mass fractions that are constrained by Constraints:

(4‐100)

Before attempting to determine the flow rates in streams 2, 3, 4 and 5, we need to perform a degree of freedom analysis to be certain that the problem is well-posed.

We begin the analysis with Control Volume II, and as our *first step* in the degree of freedom analysis we list the process variables as

131