# 7.26: Untitled Page 171

## Chapter 7

We now recall Eq. 30d along with Eq. 32f and combine that result with Eq. 42c to obtain

( M

)

  ( M )

(48)

N2 1

N2 4

This result could also be obtained directly by enclosing the entire system in a control volume and noting that the rate at which nitrogen enters the system should be equal to the rate at which nitrogen leaves the system.

At this point we can use Eq. 44d along with Eq. 47 and Eq. 48 to eliminate all the molar flow rates and obtain an expression in which  is the only unknown.

 

2  1  Y

5

  Y Y 

1

(3

)

1   (1  C  CY) 

(49)

2

2

CY

Y

This result provides a solution for the fraction of Stream #4 that must be purged, i.e.,

3  5 Y C

2C 1

Y 

2

      

 

(50)

1   1  C  1 CY

2

Given the following data:

C  conversion  0 . 70

Y  yield  0 . 50

  mole fraction of ethylene entering the reactor  0 . 05

  ( M ) ( M )

 0 . 2658

O2 1

N2 1

21 79

we determine the fraction of Stream #4 that must be purged to be

  0 . 2874 .

7.4 Sequential Analysis for Recycle Systems

In Examples 7.5 and 7.6 we saw how the presence of a recycle stream created a loop in the flow of information. The determination of the molar flow rate of dichloroethane entering the reactor shown in Figure 7.5a required information about the recycle stream, i.e., information generated by the column used to purify the output stream for the process. The determination of the molar flow rate of ethylene entering the reactor shown in Figure 7.6a required information     Material Balances for Complex Systems

319

about the recycle stream, i.e., information generated by the absorber used to separate the ethylene oxide from the output of the reactor. For the systems described in Examples 7.5 and 7.6, it was possible to solve the linear set of equations simultaneously as we have done in other problems. However, most chemical engineering systems are nonlinear as a result of thermodynamic conditions and chemical kinetic models for reaction rates (see Chapter 9). For such systems it becomes difficult to solve the system of equations globally, and in this section we examine an alternative approach.

In Figure 7‐7 we have illustrated a flowsheet for the manufacture of ethyl alcohol from ethylene that was presented earlier in Chapter 1. Here we see Figure 7‐7. Flowsheet for the manufacture of ethyl alcohol from ethylene several units involving recycle and purge streams, and we need to think about what happens in those individual units in an operating chemical plant. Each unit is being monitored constantly on a day‐to‐day basis, and the data is interpreted in terms of macroscopic balances around each unit. If a mass or mole balance is not satisfied, there is a problem with the unit and a solution needs to be found.   320