ChE 210: Example Problem 4.60 02/11/2013

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Problem Statement: Methanol is synthesized from carbon monoxide and hydrogen in a catalytic reactor. The fresh feed to the process contains 32.0 mol% CO, 64.0 mol% H2, and 4.0 mol% N2. This stream is mixed with a recycle stream in a ratio 5 mol recycle/1 mol fresh feed to produce the feed to the reactor, which contains 13.0 mol% N2. A low single-pass conversion is attained in the reactor. The reactor effluent goes to a condenser from which two streams emerge: a liquid product stream containing essentially all the methanol formed in the reactor, and a gas stream containing all the CO, H2, and N2 leaving the reactor. The gas stream is split in two fractions: one is removed from the process as a purge stream, and the other is the recycle stream that combines with the fresh feed to the reactor. Step 1: Write down any reactions taking place.

CO + 2H2 ! CH3OH mol CO/h Step 2: Draw and label the process flow diagram.

Step 3: Identify any process specifications and write equations in terms of the variables on the process flow diagram.

5mol recycle1mol fresh feed

=n5n1 5n1 = n5

Reactor

n

1 =100mol / hyCO,1 =0.320

yH2,1 =0.640

yN2,1 =0.040

yCH3OH,1 =0Fresh Feed (1)

Condenser Reactor Feed (2)

Reactor Effluent (3)

Gas Stream (4)

Gas Product (6)

Recycle (5)

Liquid Product (7)

n

2 =

yCO,2 =

yH2,2 =

yN2,2 =0.130

yCH3OH,2 =0

n

3 =

yCO,3 =

yH2,3 =

yN2,3 =

yCH3OH,3 =

n

4 =

yCO,4 =

yH2,4 =

yN2,4 =

yCH3OH,4 =0

n

6 =

yCO,6 =

yH2,6 =

yN2,6 =

yCH3OH,6 =0

n

CH3OH,7 =

n

5 =yCO,5 =

yH2,5 =

yN2,5 =

yCH3OH,5 =0

ChE 210: Example Problem 4.60 02/11/2013

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Step 4: Identify the variables to solve for.

Find:

nCH3OH,7 n6 yCO,6 yH2,6 yN2,6

fsp,CO =yCO,2n2 ! yCO,3n3

yCO,2n2

fOverall,CO =yCO,1n1 ! yCO,6n6

yCO,1n1

Step 5: Choose to work with atomic balances or extent of reaction balances. Step 6 (atomic): Complete a degree of freedom analysis. Overall: 5 unknowns (!!! !!",! !!,! !!!!!! !"!!"!!) 3 atom balances (C H N) 1 physical constraint (!",! !+ !!!!!! + !!!!! ! !) 0 process specifications _______________________________________ 1 D of F Mixing: 7 unknowns (!!!!!"!!!!!!!!! !!!!!!"!!!!!!!! !!!!!!) 3 molecular balances (CO H2 N2) 2 physical constraint (!"!! !! !!!!,! ! !!!"! !!!",! !! !!!!!! !! !!!!!! ! !) 1 process specifications (!!! ! !!) _______________________________________ 1 D of F Reactor: 8 unknowns (!!!!!!"!!!!!!!!!!!!!!!!!"!!!!!!!!!!!!!!!!!!!!"!!",!) 3 atom balances (C H N) 2 physical constraints (!!"!! !! !!!!!! ! !!!"! ! !!"!! !! !!,! !+ !!,! = 1) 0 process specifications _______________________________________ 3 D of F Condenser: 10 unknowns (! !!",! !!,! !!,! !"!!"!! !! !"!!!!!!!,! !!!!! !"!!",!) 4 molecular balances (CO H2 N2 CH3OH) 2 physical constraint (!"!! ! !!!!! ! !!!!!! ! !! ! !",! ! !!!!!! !! !!!!!! ! !) 0 process specifications _______________________________________ 4 D of F

ChE 210: Example Problem 4.60 02/11/2013

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Step 7 (atomic): Write all of the equations for the selected subsystem. Overall C: !!"!!!! ! !!!"!!!! !"!!"!! ! !! H: !!!!!!!! ! !!!!!!!! 4!"!!",! = 0 O: !!"!!!! ! !!"!!!! ! !!!"!!"!! ! ! N: !!!!!!!! ! !!!!!!!! ! ! PC: !!"!! !! !!!!!! !! !!!,! ! ! Mixing CO: !!"!!!! ! !",!! !",!! = 0 H2: !!!!!! ! !!!!!!! ! !!!!!!!! ! ! N2: !!!!!!! ! !!!!!!! ! !!!!!!!! ! ! Total: !! ! !!! ! !!! ! ! PC: !!"!! !! !!!!!! ! !!!" !!",! + !!,! + !!!,! ! ! PS: !!! ! !! Step 8 (atomic): Identify a solution strategy, and update the degree of freedom analysis to account for all variables that can be solved for. Step 9 (atomic): Select a new subsystem and write equations to solve. Condenser CO: !!"!!!! ! !!!"!!!! ! !! H2: !!!!!!! ! !!!!!!! ! ! N2: !!,!! !!!!!! ! ! CH3OH: !"!!"!!!! ! !!"!!"!! ! ! Total: !! ! !!! ! !!"!!"!! ! ! PC: !!"!! !! !!!!!! ! !!!"

ChE 210: Example Problem 4.60 02/11/2013

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Step 10 (atomic): Solve !! ! !""!!"#!! !! ! !""!!"#!! !!!!! ! !!!"# !! ! !"!!"!!"#!! !"!!"!! ! !"!!!!!"#!! !!!!! ! !!!"# !!"!! ! !!!"# !!"!! ! !!!"# !!"!!!! = 149!!"!!"#!! !!"!!" ! !!!"# !!"#$%&&!!" ! !!!"#

ChE 210: Example Problem 4.60 02/11/2013

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Step 6 (extent): Define units for Step 7 (extent): Complete a degree of freedom analysis. Overall: 6 unknowns (!!!!!!"!!!!!!!!!!!!!!!!!!!!"!!"!!!!!) 4 molecular balances (CO H2 N2 CH3OH) 1 physical constraint (!"!! !! !!!!!! !! !!!!!! ! !) 0 process specifications _______________________________________ 1 D of F Mixing: 7 unknowns (!!!!!!"!!!!!!!!!!!!!!!!!"!!!!!!!!!!!!!!!!) 3 molecular balances (CO H2 N2) 2 physical constraint (!!"!! !! !!!!!! ! !!!"! !!!!"!! !! !!!!!! !! !!!!!! ! !) 1 process specifications (!!! ! !!) _______________________________________ 1 D of F Reactor: 9 unknowns (!!!!!!"!!!!!!!!!!!!!!!!!"!!!!!!!!!!!!!!!!!!!!"!!"!!!!!) 4 molecular balances (CO H2 N2 CH3OH) 2 physical constraints (!!"!! !! !!!!!! ! !!!"! !!!!"!! !! !!!!!! !! !!!!!! ! !) 0 process specifications _______________________________________ 3 D of F Condenser: 10 unknowns (!!!!!!"!!!!!!!!!!!!!!!!!!!!"!!"!!!!!!!!!!"!!!!!!!!!!!!!!!!!!!!"!!"!!) 4 molecular balances (CO H2 N2 CH3OH) 2 physical constraint (!!"!! ! !!!!! ! !!!!!! ! !! !!!!"!! !! !!!!!! !! !!!!!! ! !) 0 process specifications _______________________________________ 4 D of F

ChE 210: Example Problem 4.60 02/11/2013

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Step 8 (extent): Write all of the equations for the selected subsystem. Overall CO: !!"!!!! ! !!!"!!!! !! ! !! H2: !!!!!!! ! !!!!!!! ! !!! ! ! N2: !!!!!!! ! !!!!!!! ! ! CH3OH:!!!"!!"!! !! !!! ! ! PC: !!"!! !! !!!!!! !! !!!!!! ! ! Mixing *Identical to equations on page 3. Step 9 (extent): Identify a solution strategy, and update the degree of freedom analysis to account for all variables that can be solved for. Step 10 (extent): Select a new subsystem and write equations to solve. *Identical to equations on page 3.

*Solutions are the same as for the atomic balances on page 4.