Question

San Diego Gas & Electric provides natural gas composed of 92 mol% methane, 7.0 mol% ethane, & 1.0 mol% nitrogen. 100 mol/hr of this gas is fed to a furnace with 30% excess air. The fractional conversion of both methane and ethane is only 90% and no NOx is formed. The selectivity (CO2:CO) is 20. Using only component molar flow rates draw and label the process flow diagram, show that there are 0 degrees of freedom, and write down the appropriate equations but do not solve. Use both the molar balanxe method and atom balanxe method.

Answer 1

Total flow = 100 mol/hr

Component flow rates

Methane flow = 92 mol/hr

Ethane flow = 7 mol/hr

Nitrogen flow = 1 mol/hr

1. Mole balance

Moles of methane burnt 90% = 92 * 0.9 = 82.8 mol/hr

Moles of ethane burnt 90% = 7 * 0.9 = 6.3 mol/hr

Nitrogen is inert in the process.

With the given information of Moles of CO₂ / CO = 20, we get

CH₄ + (3/2)O₂ ---> CO + 2H₂O (moles of methane following this reaction (M₁) = 82.8 /21)

CH₄ + 2O₂ ---> CO₂ + 2H₂O (moles of methane following this reaction (M₂) = 82.8 * 20/21)

C₂H₈ + 3O₂ ---> 2CO + 4H₂O (moles of ethane following this reaction (E₁) = 7 /21)

C₂H₈ + 4O₂ ---> 2CO₂ + 4H₂O (moles of ethane following this reaction (E₂) = 7 * 20/21)

Theoretical O₂ required can be computed using mole balance equation as below:

Moles of O₂ (O₁) = (3/2 * M₁ + 2 * M₂ + 3 * E₁ + 4 * E₂) * 10/9 (Considering 100% conversion)

Moles of O₂ fed to furnace (30 % excess) = O₁ * 1.3 moles/hr

Since all quantities are stated in the problem, there are 0 degrees of freedom

1. Atom Balance

Molecules of methane burnt 90% (C₁) = 92 * 0.9 N_A molecules/hr

Molecules of ethane burnt 90% (D₁) = 7 * 0.9 N_A molecules/hr

With the given information of Molecules of CO₂ / CO = 20, we get

CH₄ + 3O ---> CO + 2H₂O (molecules of methane following this reaction (M₁) = C₁ /21)

CH₄ + 4O ---> CO₂ + 2H₂O (molecules of methane following this reaction (M₂) = C₁ * 20/21)

C₂H₈ + 6O ---> 2CO + 4H₂O (molecules of ethane following this reaction (E₁) = D₁ /21)

C₂H₈ + 8O ---> 2CO₂ + 4H₂O (molecules of ethane following this reaction (E₂) = D₁ * 20/21)

Molecules of CO formed = M₁ + 2E₁ molecules/hr

Molecules of CO₂ formed = M₂ + 2E₂ molecules/hr

Theoretical atoms of O required can be computed using atom balance equation as below:

Atoms of O (O₁) = (3 (M₁ + 2E₁) + 4(M₂ + 2E₂))* 10/9 atoms/hr (Considering 100% conversion)

Atoms of O fed to furnace (30 % excess) = O₁ * 1.3 atoms/hr