Energy balance of Diethyl ether production plant. Calculation of Heat duty requirement for reactor & reboiler duty requirement for distillation column

1. 18
CHAPTER 4
ENERGY BALANCE
In this chapter, energy balance of equipments involved in the process and heat duty required
for heat exchangers is calculated.
Enthalpy balance can be done as
Enthalpy In + Heat added = Enthalpy Out + Heat Removed
Enthalpy for any stream can be found out by
∆H = m*Cp*∆T
Where, ∆H = Enthalpy change
m = Stream molar/mass flow rate (kmol/hr)
Cp = Heat capacity (J/(kmol*K))
∆T = Tstream – Treference (K)
We cannot calculate enthalpy but instead calculate enthalpy change. Assuming reference
temperature as ambient temperature (Treference = 298.15 K). For any Stream,
∆H = m*Cp*(Tstream -298.15)
In the entire stream no pure component, so heat capacity of each stream can be found out by
knowing heat capacity of pure component
CPavg = ∑ xi * CPi
Where, CPavg= heat capacity of stream
CPi = Heat capacity of component i
xi = mole fraction of component i in stream
Enthalpy of stream-1
∆H1 = F1* CP1*∆T
Average heat capacity of stream-1
CP1 = ∑ xi * CPi
2C2H5OH (C2H5)2O H2O (4.1)
Ethanol DEE

2. 19
C2H5OH C2H4 H2O (4.2)
Ethanol Ethylene
Table 4.1: Heat of reaction [5]
Component ∆HfR KJ/mol ∆Hfp KJ/mol
C2H5OH -234.95 0.0
H2O 0.0 -241.81
(C2H5)2O 0.0 -252.1
∆HR1 Product – Reactant -24.01
Component ∆HfR KJ/mol ∆Hfp KJ/mol
C2H5OH -234.95 0.0
H2O 0.0 -241.81
C2H4 0.0 52.50
∆HR2 Product – Reactant 45.64
Table 4.2: Cp data:[5]
Component A B C D E
Ethanol 102640.000 -139.630 -0.039 0.002 0.000000
Water 276370.000 -2090.100 8.125 -0.014 0.000009
Diethyl Ether 44.400 1301.000 -5.500 0.009 0.000000
Table 4.2: Cp data of ethylene:
K 298 300 400 500 600 700
J/kmol
K 43514 43723 53974 63429 71546 78492

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In table 4.3 flowrate composition average heat capacity and enthalpy is given for all streams
Table 4.3: Enthalpy of all the stream
Stream flowrate Ethanol Water DEE ethylene temp. Cp ∆H
kmol/sec
mol
fra.
mol
fra.
mol
fra. mol fra. o
C J/kmol/K J/sec
1 0.0700 0.950 0.050 0.000 0.000 37 114187.91 95917.84
13 0.1382 0.904 0.096 0.000 0.000 72 127751.76 829678.68
15 0.1382 0.904 0.096 0.000 0.000 250 288459.88 8968361.92
2 0.1379 0.431 0.326 0.229 0.017 250 259829.82 8064208.27
10 0.1379 0.431 0.326 0.229 0.017 165 171308.88 3308248.58
3 0.1379 0.431 0.326 0.229 0.017 37 106114.18 175648.69
12 0.0061 0.077 0.044 0.293 0.021 37 52982.50 3884.68
4 0.1359 0.429 0.337 0.225 0.007 37 105695.02 172392.81
14 0.1359 0.429 0.337 0.225 0.007 80 120260.97 899022.89
6 0.0315 0.002 0.000 0.964 0.034 68 147971.19 200617.86
11 0.0315 0.002 0.000 0.964 0.034 37 132661.89 50193.95
5 0.1043 0.557 0.439 0.003 0.000 109 120482.30 1055569.48
7 0.0870 0.000 0.000 0.873 0.120 37 123978.09 129433.12
9 0.0234 0.000 0.000 0.997 0.003 37 135571.69 38101.07
16 0.0670 0.860 0.140 0.000 0.000 107 144283.21 792691.93
8 0.0373 0.015 0.985 0.000 0.000 128 75440.94 289836.57
8A 0.0373 0.015 0.985 0.000 0.000 37 74580.27 33382.13

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For reaction -1 heat of reaction
∆HRT = ∆HR +[ ∑( n*CPi ) - ∑( n*CRi ) ] * ∆T
= -24010000+ [ ( 76097.79+312242.00) - ( 2 x 243525.72 ) ] x (523 – 298)
= -43312528.59 J/sec
For reaction -2 heat of reaction
∆HRT = ∆HR +[ ∑( n*CPi ) - ∑( n*CPi ) ] * ∆T
= 45640000 + [ (60876.36 + 76097.79 ) - ( 243525.72 ) ] x (523 – 298)
= 24576151.47 J/sec
ENERGY BALANCE OVER REACTOR (1)
Q (Heat) = Total heat out + Heat of Reaction – Total heat in
=8064208.27 + (-1557968.501) + 16941.24029 - 8968361.92
= -2445180.91J/sec
ENERGY BALANCE AROUND DISTILLATION COLUMN (3)
Q (Heat) = Total heat OUT – Total heat IN
= ∆H5 + ∆H6 - ∆H14
= 216592.5 + 1055569 - 922131.6
= 350029.9 J/sec
Condenser duty = m x latent heat
= 0.03153 x 27898000
= 879623.94 J/sec
Reboiler duty = 350029.9 J/sec + 879623.94 J/sec
= 1229653.84 J/sec

5. 22
ENERGY BALANCE AROUND DISTILLATION COLUMN: (4)
Q (Heat) = Total heat OUT – Total heat IN
=∆H16 + ∆H8 - ∆H5
= 792691.9 + 289836.6 - 1055569
= 26959.5 J/sec
Condenser duty = m x latent heat
= 0.067 x 39155400
= 2623411.8 J/sec
Reboiler duty = 26959.5 J/sec + 2623411.8 J/sec
= 2650371.3 J/sec
In table 4.4 enthalpy of inlet and outlet is given also heat duty required
Table 4.4: Energy balance for heat exchanger
heat inlet outlet heat
exchanger enthalpy enthalpy Duty
J/sec J/sec J/sec
10 829678.68 8968361.92 8138683.24
6 8064208.27 3308248.58 -4755959.69
2 3308248.58 175648.69 -3132599.89
12 172392.81 899022.89 726630.08
9 200617.86 50193.95 -150423.91
Waste
water
289836.57 33382.13 -256454.44
Negative(-) sign for cooling required
Positive(+) sign for heating required