A distillation column is producing 84.4 moles per hour of
methanol-water when operating at a reflux ratio of 0.908. Distillate composition is 91.5 percent
methanol (molar basis). Specific heat
data of methanol is 0.65 BTU per pound per degree Fahrenheit. Molecular weight of methanol is 32.04. Enthalpy of the distillate, HD is 1388 BTUs
per pound mole. Residue is collected at
a rate of 132.4 pound-moles per hour when molar flow rate of the feed is 216.8
pound-moles per hour. Condenser duty is
given as 2.478 million BTUs per hour.
Solution:
Sensible enthalpy of methanol is equal to specific heat times the temperature difference. Feed to the distillation column enters via a preheater at 80 degrees Fahrenheit.
Sensible heat of methanol is equal to 0.65 times (100 minus 80) or 13 BTU per pound of methanol.
Molecular weight of methanol is 32.04.
Enthalpy of liquid methanol is 13 times 32.04 equal to 416.52 BTUs per pound mole.
Sensible heat of water is equal to one times (100 minus 80) or 20 BTU per pound of water
Molecular weight of water is 18.02
Enthalpy of liquid water is 20 times 18.02 equal to 364 BTUs per pound mole of water
Accounting for methanol and water mole fractions in the mixture, enthalpy of methanol-water liquid is equal to 0.00565 times 416.52 plus 0.99435 times 364 plus heat of solution (minus 120) or 240.717 BTUs per pound mole of methanol-water liquid. Please note that heat of solution methanol mixture is minus 120 BTUs per pound mole.
Note that waste residue exchanges heat with incoming feed before leaving the system.
Heat added is equal to the sum of heat going with distillate, residue, and condenser load minus enthalpy with the incoming feed. This simplifies to 2.714 million BTUs per hour.