20130211 Problem 4-60
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ChE 210: Example Problem 4.60
02/11/2013
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 à CH3OH
ξ ≡ mol CO/h
Step 2: Draw and label the process flow diagram. •
n5 = y CO,5 = yH2,5 = yN2,5 = y CH3OH,5 =0 •
•
n1 = 100 mol / h
n2 =
y CO,1 =0.320
Recycle (5)
•
•
•
n3 =
n4 =
n6 =
y CO,2 =
y CO,3 =
y CO,4 =
y CO,6 =
yH2,1 =0.640
yH2,2 =
yH2,3 =
yH2,4 =
yH2,6 =
yN2,1 =0.040
yN2,2 =0.130
yN2,3 =
yN2,4 =
yN2,6 =
y CH3OH,1 =0 Fresh Feed (1)
y CH3OH,2 =0 Reactor Feed (2)
y CH3OH,4 =0 Gas Stream (4)
y CH3OH,6 =0 Gas Product (6)
Reactor
y CH3OH,3 = Reactor Effluent (3)
Condenser
•
nCH3OH,7 = Liquid Product (7)
Step 3: Identify any process specifications and write equations in terms of the variables on the process flow diagram.
n 5 mol recycle = 5 → 5n 1 = n 5 1mol fresh feed n 1
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ChE 210: Example Problem 4.60
02/11/2013
Step 4: Identify the variables to solve for.
n CH3OH,7 Find: fsp,CO =
n 6
y CO,6
yH2,6
yN2,6
y CO,2n 2 − y CO,3n 3 y CO,2n 2
fOverall,CO =
y CO,1n 1 − y CO,6n 6 y CO,1n 1
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 (𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! 𝑛!"!!",! ) 3 atom balances (C H N) 1 physical constraint (𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1) 0 process specifications _______________________________________ 1 D of F
Mixing:
7 unknowns (𝑛! 𝑦!",! 𝑦!!,! 𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! ) 3 molecular balances (CO H2 N2) 2 physical constraint (𝑦!",! + 𝑦!!,! = 0.87; 𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1) 1 process specifications (5𝑛! = 𝑛! ) _______________________________________ 1 D of F
Reactor:
8 unknowns (𝑛! 𝑦!",! 𝑦!!,! 𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! 𝑦!"!!",! ) 3 atom balances (C H N) 2 physical constraints (𝑦!",! + 𝑦!!,! = 0.87; 𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1) 0 process specifications _______________________________________ 3 D of F
Condenser: 10 unknowns (𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! 𝑦!"!!",! 𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! 𝑛!"!!",! ) 4 molecular balances (CO H2 N2 CH3OH) 2 physical constraint (𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1; 𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1) 0 process specifications _______________________________________ 4 D of F
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ChE 210: Example Problem 4.60
02/11/2013
Step 7 (atomic): Write all of the equations for the selected subsystem. Overall C:
𝑦!",! 𝑛! − 𝑦!",! 𝑛! − 𝑛!"!!",! = 0
H:
2𝑦!!,! 𝑛! − 2𝑦!!,! 𝑛! − 4𝑛!"!!",! = 0
O:
𝑦!",! 𝑛! − 𝑦!",! 𝑛! − 𝑛!"!!",! = 0
N:
2𝑦!!,! 𝑛! − 2𝑦!!,! 𝑛! = 0
PC:
𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1
Mixing CO:
𝑦!",! 𝑛! + 𝑦!",! 𝑛! − 𝑦!",! 𝑛! = 0
H 2:
𝑦!!,! 𝑛! + 𝑦!!,! 𝑛! − 𝑦!!,! 𝑛! = 0
N 2:
𝑦!!,! 𝑛! + 𝑦!!,! 𝑛! − 𝑦!!,! 𝑛! = 0
Total:
𝑛! + 𝑛! − 𝑛! = 0
PC:
𝑦!",! + 𝑦!!,! = 0.87 𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1
PS:
5𝑛! = 𝑛!
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:
𝑦!",! 𝑛! − 𝑦!",! 𝑛! = 0
H 2:
𝑦!!,! 𝑛! − 𝑦!!,! 𝑛! = 0
N 2:
𝑦!!,! 𝑛! − 𝑦!!,! 𝑛! = 0
CH3OH: 𝑦!"!!",! 𝑛! − 𝑛!"!!",! = 0 Total:
𝑛! − 𝑛! − 𝑛!"!!",! = 0
PC:
𝑦!",! + 𝑦!!,! = 0.87
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ChE 210: Example Problem 4.60
02/11/2013
Step 10 (atomic): Solve 𝑛! = 500 𝑚𝑜𝑙/ℎ 𝑛! = 600 𝑚𝑜𝑙/ℎ 𝑦!!,! = 0.148 𝑛! = 27.03 𝑚𝑜𝑙/ℎ 𝑛!"!!",! = 24.33 𝑚𝑜𝑙/ℎ 𝑦!!,! = 0.568 𝑦!",! = 0.284 𝑦!",! = 0.291 𝑦!",! 𝑛! = 149.68 𝑚𝑜𝑙/ℎ 𝑓!",!" = 0.143 𝑓!"#$%&&,!" = 0.760
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ChE 210: Example Problem 4.60
02/11/2013
Step 6 (extent): Define units for ξ Step 7 (extent): Complete a degree of freedom analysis. Overall:
6 unknowns (𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! 𝑛!"!!",! 𝜉) 4 molecular balances (CO H2 N2 CH3OH) 1 physical constraint (𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1) 0 process specifications _______________________________________ 1 D of F
Mixing:
7 unknowns (𝑛! 𝑦!",! 𝑦!!,! 𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! ) 3 molecular balances (CO H2 N2) 2 physical constraint (𝑦!",! + 𝑦!!,! = 0.87; 𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1) 1 process specifications (5𝑛! = 𝑛! ) _______________________________________ 1 D of F
Reactor:
9 unknowns (𝑛! 𝑦!",! 𝑦!!,! 𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! 𝑦!"!!",! 𝜉) 4 molecular balances (CO H2 N2 CH3OH) 2 physical constraints (𝑦!",! + 𝑦!!,! = 0.87; 𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1) 0 process specifications _______________________________________ 3 D of F
Condenser: 10 unknowns (𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! 𝑦!"!!",! 𝑛! 𝑦!",! 𝑦!!,! 𝑦!!,! 𝑛!"!!",! ) 4 molecular balances (CO H2 N2 CH3OH) 2 physical constraint (𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1; 𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1) 0 process specifications _______________________________________ 4 D of F
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ChE 210: Example Problem 4.60
02/11/2013
Step 8 (extent): Write all of the equations for the selected subsystem. Overall CO:
𝑦!",! 𝑛! − 𝑦!",! 𝑛! − 𝜉 = 0
H 2:
𝑦!!,! 𝑛! − 𝑦!!,! 𝑛! − 2𝜉 = 0
N 2:
𝑦!!,! 𝑛! − 𝑦!!,! 𝑛! = 0
CH3OH:−𝑛!"!!",! + 𝜉 = 0 PC:
𝑦!",! + 𝑦!!,! + 𝑦!!,! = 1
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.
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