Energy Balance Reactions

Energy Balance Reactions: For Non-reaction processes: ΔH=ΣmiHi(outlet)-ΣmiHi(inlet) Q-Ws=ΔH+ΔEk+ΔEp Ws=0 (when no moving parts) Q=ΔU (for closed systems) Q=ΔH (for open systems) 8.1 FERMENTER: Stoichiometric Equation: C12H22O11+H2O→2C6H12O6→4C2H5OH+4CO2 T=298K (assuming isothermal conditions) P=1atm Energy Balance in fermenter: ΔH=4(ΔHformation Ethanol) +4(ΔHformation CO2)-2(ΔHformation glucose) Enthalpies of formation ΔHformation (Ethanol) =-276.5kJ/mol ΔHformation (CO2) =-393.5kJ/mol ΔHformation H2O (l) = -285.8 kJ/mol ΔHformation H2O (g) = -241.8 kJ/mol ΔHformation (glucose) (g) =-1250 kJ/mol ΔHformation (sucrose) (g) =-2220kJ/mol Therefore, ΔH= [4(-276.5) +4(-393.5)-2(-1250)] = -180kJ/mol

CALCULATIONS: From the stoichiometric reaction: Sucrose balance:

Min of molasses=5170 kg/hr But, sucrose content in molasses=52% Sucrose=0.52*5170 =2688.4 kg/hr Moles of sucrose=2688.4/342=7.860 kmol Nout of sucrose= 1344.16/342=0.393 kmol Water balance: Nin=20691.130 /18=1149.50 kmoles Nout=20549.64/18=1141.64 kmoles

CO2 balance: Nout =13143.288/44=29.871 kmoles C2H5OH balance: Nout= 13,740.71/46=29.871 kmoles nin (mol) 7.860 1149.50 0 0

Hin(kJ/mol) -2220 -285.8 -276.5 -393.5

species C12H22O11 H2 O C2H5OH CO2

nout(mol) 0.393 1141.64 29.871 29.871

Table 8.1 Energy Balance across the fermenter Now, extent of reaction: ζ= [(nC12H22O11) out-(n C12H22O11) in]/ ( ‫ ע‬C12H22O11) = (0.393-7.860)/-1=-7.861 mol/hr Now, energy Balance: Q-Ws=ΔH+ΔEk+ΔEp Now, ΔEk=0 (Kinetic changes) ΔEp =0 (horizontal unit) Q-Ws=ΔH Assumption:

Hout(kJ/mol) -2220 -285.8 -276.5 -393.5

Power input=1.6 watt/kg of input Total input=275213.135kg/hr Power Input=Ws=440.341 ΔHo =793.126 KW Q=ΔH+Ws=793.126+440.341= 1233.47kw/hr 8.2 DISTILLATION COLUMN: Assumptions:  Temperature of distillate=82oC  Boiling point of ethanol=78.5oC  Boiling point of water=100oC  Feed enters at 25oC  ΔHv = enthalpy of vaporization CALCULATIONS:  For ethanol in distillate: ΔH=ΔHv + ∫CpdT=38.58 +∫ (103.1*10-3)dT = 38.58+5.516 = 44.034 kJ/mol 

For water in distillate:

ΔH=ΔHv+∫CpdT + ∫CpdT =40.656+5.655-1.6211=44.69 kJ/mol  Ethanol in residue: ΔH =ΔHv+∫CpdT =38.58+103.1*10^-3(100-25) =46.3125kJ/mol  Water in residue: ΔH =ΔHv+∫CpdT =40.656+75.4*10^-3(100-25) =46.311 kJ/mol Species

Feed

Distillate

Residue

nin(mol) Hin(kJ/mol) nout(mol) Hout(kJ/mol) nout(moles) Hout(kJ/mol) Ethanol 29.871 Water

1149.113

0

20.798

44.034

3.07

46.3125

245.09

44.69

904.02

46.311

Table 8.2 Energy balance across the Distillation Column ΔH=475455.042 kJ Q=mCpΔT=ΔH

Cp=43.99kJ/kgoC ΔT=75oC , Therefore, Steam required, m=144.11 kg/hr 8.3 RECTIFICATION COLUMN: Assumptions:  Feed Temperature- 78.5oC  Distillate Temperature-78.5oC  Residue-100OC Species Ethanol Water

Feed nin(mol) 301.20

Distillate Hin(kJ/mol) nout(mol)

Residue Hout(kJ/mol) nout(moles) Hout(kJ/mol)

Table 8.3 Energy Balance across the Rectification column ΔH=14246.71kJ/mol Q=mCpΔT=ΔH therefore, m= 4.32kg of steam/hr 8.4 DEHYDRATION COLUMN Species nin(mol) ethanol water

Hin(kJ/mol)

nout(mol)

Table 8.4 Energy Balance of the dehydration column ΔH=10,000 KJ Therefore, steam requirement is, m=10.571kg of steam/hr

Hout(kJ/mol)