# 7.15: Untitled Page 160

## Chapter 7

specified, the mole fractions for the species in that stream are determined, and from the splitter physics the mole fractions for all the other streams are known. If all the mole fractions are known, then a single molar flow rate for a given species (or the overall molar flow rate) determines the other molar flow rates for that stream.

The remaining four ways in which this splitter problem can be solved are left as exercises for the students. These exercises are essential to gain a comprehensive understanding of the behavior of splitters.

7.3.2 Recycle and purge streams

In this section we analyze systems with recycle and purge streams. We begin with a system analogous to the one shown in Figure 7‐4 in which there is a mixer.

We then move on to a more complicated system analogous to the one shown in Figure 7‐5 in which there is a splitter.

EXAMPLE 7.5. Pyrolysis of dichloroethane with recycle

To illustrate a simple recycle system, we consider the pyrolysis of dichloroethane ( C H Cl ) to produce vinyl chloride ( C H Cl ) and 2

4

2

2

3

hydrochloric acid ( HCl ) . The pyrolysis reaction is not complete, and experimental measurements indicate that the conversion for a particular reactor is given by

 RC H Cl

2

4

2

C  Conversion of C H Cl

 0 . 30

(1)

2

4

2

( M

)

C2H4Cl2 2

The unreacted dichloroethane is separated from the reaction products and recycled back to the reactor for the production of more vinyl chloride as indicated in Figure 7.5a. The composition of the feed Stream #1 is 98%

dichloroethane ( C H Cl ) and 2% ethane ( C H ) on a molar basis. We 2

4

2

2

6

assume that the separation column produces a sharp separation meaning that all the dichloroethane leaves in the bottom Stream #5, and the remaining components (vinyl chloride, hydrochloric acid and ethane) leave through the distillate Stream #4. Our objective in this example is to determine the recycle flow rate in Stream #5.   Material Balances for Complex Systems

297

Figure 7.5a. Reactor‐separator with recycle

Our analysis of this process is based on Axioms I and II as given by Eqs. 7‐4 and 7‐5, and we begin with the steady form of the macroscopic mole balance to obtain

c

dA

v n

A A

R A

Axiom I:

A

(2)

A  C H , HCl , C H Cl , C H Cl 2

6

2

3

2

4

2

The global rates of production within any control volume are constrained by Eq. 7‐4 that takes the form

A N

Axiom II

N

R

 0 ,

J  C , H , Cl

(3)

JA A

A  1

For the case under consideration, the atomic matrix is given by Molecular Species  C H

HCl C H Cl C H Cl

2

6

2

3

2

4

2

carbon

 2

0

2

2

(4)

hydrogen

6

1

3

4

chlorine

 0

1

1

2

and Eq. 3 takes the form

298