LearnChemE

#### Purge Stream in a System with Recycle: Screencast

Explains what a purge stream is and why it is needed for a reactor system with recycle.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

##### Important Equations:

Material balances on mixing point

$$\dot{n}_2 = \dot{n}_1 + \dot{n}_7$$  (Note that this equation is not independent of the balances of the individual components below.)

$$x_{i,2}\,\dot{n}_2 = x_{i,1}\,\dot{n}_1 + x_{i,7}\,\dot{n}_7$$ (one equation for each component $$i$$)

where $$\dot{n}_j$$ = total molar flow rate at location $$j$$ ($$j$$ = 1 – 7)

$$x_{i,j}$$ = mole fraction of component $$i$$ at location $$j$$

Material balances on reactor

For reactants only and assuming a stoichiometric feed

$$x_{i,3}\,\dot{n}_3 = x_{1,2}\,\dot{n}_2 \cdot (1\, – \, X)$$ (where component 1 is a reactant; one equation for each reactant)

For products only

$$x_{i,3}\,\dot{n}_3 = x_{1,2}\,\dot{n}_2 \cdot X \cdot a$$ (where component 1 is a reactant; one equation for each product)

where $$a$$ is the stoichiometric coefficient of the product

$$X$$ = fractional conversion of reactants (stoichiometric feed)

For unreactive species

$$x_{i,2}\,\dot{n}_2 = x_{i,3}\,\dot{n}_3$$

Material balances on separator

(In general, a separator may not remove all of the reaction product and/or it may also remove some of the feed species.)

$$\dot{n}_3 = \dot{n}_4 + \dot{n}_5$$  (Note that this equation is not independent of the balances of the individual components below.)

$$x_{i,3}\,\dot{n}_3 = x_{i,4}\,\dot{n}_4 + x_{i,5}\,\dot{n}_5$$ (one equation for each component $$i$$)

Material balances on splitting point

$$\dot{n}_5 = \dot{n}_6 + \dot{n}_7$$ (Note that this equation is not independent of the balances of the individual components below.)

$$\dot{n}_6 = purge \cdot \dot{n}_5$$

$$\dot{n}_7 = (1\, -\, purge) \cdot \dot{n}_5$$

$$x_{i,5} = x_{i,6} = x_{i,7}$$ (one equation for each component $$i$$)

where $$purge$$ = the fraction of stream 5 that is purged

Overall atom balances

(Note that these equations are not independent of the above equations.)

molar flow rate of atomic species in (stream 1) = molar flow rate of atomic species out (stream 4 + stream 6) for each atomic species in the feed