The dehydrogenation of propane (C_3H_6) to propylene (C_3H_8) occurs according t

Question

The dehydrogenation of propane (C_3H_6) to propylene (C_3H_8) occurs according to the following reaction C_3H_8 right arrow C_3H_6 + H_2 Fresh feed containing 100% C_3H_8 is mixed with a recycle stream that contains 80 mole% C_3H_6 and 20 mole% C_3H_8 and fed to a reactor. The reactor output is fed to a separator where all of the H_2 is removed, 50 kg/hr of C_3H_8 is removed as product, and the remainder is recycled and mixed with the fresh feed. The molecular weight of C_3H_8 is 42g/mol. The single pass conversion is 40%. Determine: The flow rate of the recycle stream (kmol/hr). The composition of the stream (mole fractions) leaving the reactor. The amount of C_3H_8 required as fresh feed (kmol/hr).

Explanation / Answer

kgmoles/hr

H2 formed =1.19 kg mole/hr

From the reaction C3H8 --à C3H6+ H2

1 mole of C3H6 requires 1 mole of C3H8. Hence mole of C3H8 requires for producing 1.194 kgmoles/hr of C3H6 = 1.19*44 ( Molecular weight of C3H8)= 52.54 kg/hr

Moles of C3H8 entering = 1.19 kgmole/hr

Let R = moles of Recyle. It contains R*0.8 moles/hr of C3H8 and R*0.2 moles/hr of C3H6

Total moles of C3H8 entering= (R*0.8+ 1.19) kgmoles/hr

Conversion per pass is 40%. Hence converted={ (R*0.8+1.19)}*0.4= R*0.32+0.476

So C3H6 formed =1.19 moles/ hr and there is some C3H6 in the recycle as well which amonuts to R*0.2 .The C3H6 formed is taken as products and recycled.

So R*0.32+0.476= 1.19+R*0.2

0.476-0.2= R*(1.19-0.32), R=0.31 moles/hr

Reactor outlet contains C3H6, C3H8 and H2.

C3H6 formed= 1.19+0.31*0.2= 1.254 moles/hr, H2 formed= 1.19 mole/hr, C3H8 not consumed=

(R*0.8+1.19)*0.6= (0.31*0.8+1.19)*0.6= 0.248+0.714=0.962 moles/hr

Flow rates of stream leaving the reactor : C3H6= 1.254 moles/hr, H2= 1.19 moles/hr and C3H8= 0.962 moles/hr, tota moles = 1.254+1.19+0.962=3.406 moles/hr

Composition : C3H6= 100* (1.254/3.406)=36.8%, C3H8= 100*(0.962/3.406)= 28.2% and H2=35%

Molecular weight of R need to be calculated for converting the flow into mass flow rate. Molecualr weight of 1 mole of R= 0.2*42+0.8*44=43.6 kgmole/hr

Flow rate of recycle = 0.31*43.6=13.52 kg/hr

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