# 20130211 Problem 4-60

September 4, 2017 | Author: sakiku | Category: Chemical Reactor, Equations, Hydrogen, Chemical Engineering, Chemical Process Engineering

#### Description

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

1

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

2

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

3

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

4

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

5

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.

6