A catalyzed chemical reaction in which CO (25 mol%) and the balance is H_2 is co

Question

A catalyzed chemical reaction in which CO (25 mol%) and the balance is H_2 is converted into hydrocarbons (CH_4, C_2H_6, C_3H_8, C_4H_10 and C_5H_12) and H_2O. The products from the reactor is then fed into a separator where all the gas (CO and H_2) goes to the top of the column, and the rest were withdrawn from the bottom of the column. In this process the overall CO conversion is 80%, but the per-pass conversion is only 25%. The carbon yield of each of the C_1-C_5 HC products follows the ratio 15:25:30:20:10. Determine The composition of the bottom product stream The recycle ratio (flow rate recycled/top product)

Explanation / Answer

The reactions are CO+3H2---->CH4+H2O,   2CO+5H2----> C2H6+2H2O, 3CO+7H2---->C3H8+3H2O, 4CO+ 9H2---> C4H10 +4H2O, 5CO+ 11H2---->C5H12+ 5H2O

moles of Hydrogen =25 moles

Moles of CO used = 25 moles. Overall conversion is 80%. Moless of CO converted = 25*0.8=20 moles

CO converted to CH4 is 15%. Moles of CO converted to CH4 =20*15/100= 3 moles. Moles of CH4 formed = 3 moles,moles of Water formed = 3 moles

CO converted to C2H6 is 25%. Moles of CO converted to C2H6 =20*25/100 =5 moles. Moles of C2H6 formed = , 5/2=2.5 moles, moles of water formed = 2*2.5= 5 moles

CO converted to C3H8 is 30%. Moles of CO converted to C3H8= 20*30/100= 6 moles. Mole of C3H8 formed = 6/3=2 moles, moles of water formed =2*3= 6 moles

CO converted to C4H10 is 20%.Moles of CO converted to C4H10 =20*20/100= 4 moles. Moles of C4H10 formed= 4/4= 1 moles, moles of water formed = 4 moles

CO Converted to C5H12 is 10%. Moles of CO converted to C5H12= 20*10/100= 2 moles. Moles of C5H12 formed = 2/5=0.4 moles, moles of water formed = 0.4*5=2 moles

Products contains : CH4= 3, C2H6= 2.5, C3H8= 2, C4H10 =1 and C5H12= 0.4 . H2O= 3+5+6+4+2=20 moles

total moles : 3+2.5+2+1+0.4+20 =28.9

Compositions : CH4= (3/28.9)= 0.1038, C2H6= 2.5/28.9 =0.086, C3H8= 2/28.9= 0.069, C5H12= 0.4/28.9= 0.0138 and Water = 20/28.9= 0.692

From overall plant balance, 20% of CO is unconverted , moles of CO remaiined = 25*0.2= 5 moles and hydrogen= 75*0.8*0.2= 12 moles

This gets accmulated in the purge stream.

Composition of purge : CO= 5/17= 0.294 and H2= 1-0.294= 0.706

This is also the composition of recycle,

Writing balance across the reactor and noting R is recycle. Single pass conversion is 25%.

(25 ( CO in fresh feed)+R*0.294)*0.25

unconverted = (25+R*0.294)*0.75= R*0.294 (CO in recycle)+ 5

25*0.75+R*0.294*0.75= R*0.294+5

13.75 = R*0.294*0.25

R= 187 Recycle ratio = 187/(187+17)= 0.92

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