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). Calculate the
condenser load when the bubble point of the liquid is 150 degrees Fahrenheit,
and dew point of vapor is 153.5 degrees Fahrenheit. Latent heat of vaporization of methanol and water is 468 and 1006
BTUs per pound, respectively. Specific
heat data of methanol is 0.65 BTU per pound per degree Fahrenheit. Molecular weight of methanol is 32.04.
Solution:
The vapors leave the top of the distillation column at 153.5 degrees Fahrenheit. Their enthalpy can be calculated by adding enthalpy contribution of both methanol and water. Enthalpy of methanol vapors is equal to the sum of sensible enthalpy and latent enthalpy.
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 (153.5 minus 80) or 47.775 BTU per pound of methanol
Latent enthalpy of methanol is 468 BTU per pound.
Enthalpy of methanol vapor is 47.775 plus 468 equal to 515.775 BTUs per pound of methanol
Molecular weight of methanol is 32.04
Enthalpy of methanol vapor is 515.775 times 32.04 or 16,525.431 BTUs per pound mole of methanol
Sensible heat of water is equal to one times (153.5 minus 80) or 73.5 BTU per pound of water
Latent enthalpy of methanol is 1006 BTU per pound of water
Enthalpy of water vapor is 73.5 plus 1006 equal to 1079.5 BTUs per pound of water
Molecular weight of water is 18.02
Enthalpy of methanol vapor is 1079.5 times 18.02 equal to 19,452.59 BTUs per pound mole of water
Accounting for methanol and water mole fractions in the mixture, enthalpy of methanol-water vapor is equal to 0.915 times 16,525.431 plus 0.085 times 19,452.59 or 16,774.24 BTUs per pound mole of methanol-water vapor.
This vapor mixture is condensed and produces a liquid that is split into two streams, distillate and reflux.
The liquid leaves the condenser at 150 degrees Fahrenheit.
Sensible heat of methanol is equal to 0.65 times (150 minus 80) or 45.5 BTU per pound of methanol
Enthalpy of liquid methanol is 45.5 times 32.04 or 1,457.82 BTUs per pound mole of methanol
Sensible heat of water is equal to one times (150 minus 80) or 70 BTU per pound of water
Enthalpy of liquid water is 70 times 18.02 equal to 1,261.4 BTUs per pound mole of water
Accounting for methanol and water mole fractions in the mixture, enthalpy of methanol-water liquid is equal to 0.915 times 1,457.82 plus 0.085 times 1,261.4 or 1441.12 BTUs per pound mole of methanol-water vapor.
Vapors is equal to D times (R plus 1) or 84.4 times (0.908 plus 1) or 161.035 pound moles
Heat removed is equal to 161.035 times (16774.24 minus 1441.12) or 2.469 ´106 BTUs.