San Diego Gas & Electric provides natural gas composed of 92 mol% methane, 7.0 m

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.

Explanation / Answer

Total flow = 100 mol/hr

Component flow rates

Methane flow = 92 mol/hr

Ethane flow = 7 mol/hr

Nitrogen flow = 1 mol/hr

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

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

Molecules of ethane burnt 90% (D1) = 7 * 0.9 NA 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

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