Comments Transient Energy Balances
Updated: September 20, 2017John Jechura ([email protected])
General form of the “stuff” balance equation
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Rate of Rate Rate Rate of Rate of
Accumulation In Out Generation Consumption
F1
F3F4
F5
F6Q1
Q2
Q3F2
Updated: September 20, 2017John Jechura ([email protected])
Word form of the energy balance equation
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Rate of Convection Convection Heat Across Work Across
Accumulation Energy In Energy Out Bounary Boundary
F1
F3F4
F5
F6Q1
Q2
Q3F2
Updated: September 20, 2017John Jechura ([email protected])
Transient energy balance equation
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F1
F3F4
F5
F6Q1
Q2
Q3F2
,
: :
,: :
,: :
ˆ ˆ
ˆ ˆˆ ˆ
i j k s mi inlet j outlet k m
i i i j j j k s mi inlet j outlet k m
i i i j k s mi inlet j outlet k m
dEE E Q W
dt
d UFH FH Q W
dt
d HV d UVFH FH Q W
dt dt
K P
Updated: September 20, 2017John Jechura ([email protected])
Where does heat of reaction come from?Use of heat capacity for enthalpy
The enthalpy form of the energy balance is the same whether or not there is a chemical reaction, heat of mixing, heat of absorption, etc.
These effects are artifacts of describing the enthalpy of a mixture using the heat capacity.
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ˆ ˆˆ ˆ
ref
ref
T
p ref p p refTP
T
ref p p refT
HC H H C dT C T T
T
H H C dT C T T
Updated: September 20, 2017John Jechura ([email protected])
Where does heat of reaction come from?Use of heat capacity for enthalpy
No reaction:
With chemical reaction, the reference enthalpies are different:
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10 1
10 1
10 1
ˆˆ ˆ
ˆ ˆ ˆ
ˆ ˆ
p p ref ref p ref ref
p p
dHV FH FH Q
dtdT
VC F C T T H F C T T H QdtdT
VC FC T T Qdt
10 ,0 1 ,1
10 1 ,0 ,1
ˆ ˆ ˆˆ ˆ
ˆ ˆ ˆ ˆ
p p ref ref p ref ref
p p ref ref
dTVC F C T T H F C T T H Q
dtdT
VC FC T T F H H Qdt
Updated: September 20, 2017John Jechura ([email protected])
Where does heat of reaction come from?Use of heat capacity for enthalpy
What if the reactants have different heat capacities then the products?
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1 10 0 ,0 1 1 ,1
1 10 0 1 1 ,0 ,1
ˆˆ ˆˆ ˆ
ˆˆ ˆ ˆ ˆ
pp ref ref p ref ref
pp ref p ref ref ref
d C TV F C T T H F C T T H Q
dt
d C TV F C T T C T T F H H Q
dt
Updated: September 20, 2017John Jechura ([email protected])
Where does heat of reaction come from?Enthalpy of formation as reference enthalpy
Total enthalpy is component average of individual enthalpies (if no mixing effect)
For constant heat capacities for each chemical species
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1 1 1 1
ˆˆN N N N
i i i i p i pi i pii i i i
H m H n H C m C n C
10 1
1,0 ,0 ,1 ,1
1 1
1,0 , 0 ,1 , 1 ,0 ,1
1 1 1
N N
i i i ii i
N N N
i p i ref i p i ref i i F ii i i
dHH H Q
dtdH
n H n H QdtdH
n C T T n C T T n n H Qdt
Updated: September 20, 2017John Jechura ([email protected])
Where does heat of reaction come from?Heat of formation or combustion as reference
Reference state enthalpies can be the enthalpy of formation or the heat of combustion Take care whether the heat of combustion is reported as a negative or
positive value (positive value consistent with report as heating value)
Can separate the terms for the reacting & non-reacting speciesWritten with heat of combustion as negative value
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Reacting Reacting Reacting
Nonreacting
1,0 , 0 ,1 , 1 ,0 ,1
1 1 1
,0 , 0 11
N N N
i p i ref i p i ref i i c ii i i
N
i p ii
dHn C T T n C T T n n H
dt
n C T T Q
Updated: September 20, 2017John Jechura ([email protected])
Latent heat effects
There are other latent heat effects that look like “generation” terms – changes in enthalpy not due to temperature changes
Heats associated with phase change, e.g., vaporization (solidification, dissolution, absorption, etc. are similar)
Heat of mixing
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1 1
0 0
, ,
, 0 , 1
vap
vap
TT T
p L p VvapT T T
p L vap p L vapvap
dH C dT H C dT
C T T H C T T
,
1 1
N N
i i i i Rmix mix Ri i
H x H H x H x H
Updated: September 20, 2017John Jechura ([email protected])
How to calculate the effect of heat of reaction
Heat of reaction effects are determined by the indirect path: Determine enthalpy change to take reactants to reference temperature Determine the change in enthalpy @ reference temperature Determine enthalpy change to take products from the reference temperature
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Figure 5.2
Bioprocess Engineering Principles, 2nd edPauline Doran, Elsevier Science & Technology Copyright © 2012, Elsevier Inc. All rights Reserved.
Updated: September 20, 2017John Jechura ([email protected])
Calculating heat of reaction from heats of combustion (values in Table C.8)
Use the heat of combustion as the reference
Example: Glucose EthanolC6H12O6 (s) 2 C2H5OH (l) + 2 CO2 (g)
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Compound (state) H0c
C6H12O6 (s) -2805.0 kJ/mol
C2H5OH (l) -1366.8 kJ/mol
CO2 (g) 0 kJ/mol
0 0 0
reactants products
1 2805.0 2 1366.8 2 0
kJ71.4
mol glucose
rxn i c i cH n H n H
Updated: September 20, 2017John Jechura ([email protected])
Heat of reaction with cell growth
Estimated from available electrons
Heat of reaction with oxygen as electron acceptor (aerobic, combustion))
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c CH q x
kJ
111 to 115 g.mol
q
2
kJ460
g.mol OrxnH
Bioprocess Engineering Principles, 2nd edPauline Doran, Elsevier Science & Technology Copyright © 2012, Elsevier Inc. All rights Reserved.
Updated: September 20, 2017John Jechura ([email protected])
Heat of combustion for bacteria & yeast
Can be estimated as:
For general biomass(CH1.8O0.5N0.2):
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kJ23.2c bacteria
Hg
kJ21.2c yeast
Hg
Bioprocess Engineering Principles, 2nd edPauline Doran, Elsevier Science & Technology Copyright © 2012, Elsevier Inc. All rights Reserved.
kJ21.3c biomass
Hg
Updated: September 20, 2017John Jechura ([email protected])
Calculating heat of reaction from heats of combustion (values in Table C.8)
Use the heat of combustion as the reference
Example: Glucose EthanolC6H12O6 (s) 2 C2H5OH (l) + 2 CO2 (g)
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Compound (state) H0c
C6H12O6 (s) -2805.0 kJ/mol
C2H5OH (l) -1366.8 kJ/mol
CO2 (g) 0 kJ/mol
0 0 0
reactants products
1 2805.0 2 1366.8 2 0
kJ71.4
mol glucose
rxn i c i cH n H n H
Updated: September 20, 2017John Jechura ([email protected])
Example energy balance – Continuous Ethanol Fermentation
Saccharomyces cerevisiae is grown anaerobically in continuous culture at 30oC. Glucose is used as the carbon source; ammonia is the nitrogen source. A mixture of glycerol and ethanol is produced.
What is the cooling requirement to keep @ 30oC?
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Compound In [kg/h] Out [kg/h]
Glucose 36.0
NH3 0.40
Cells 2.81
Glycerol 7.94
Ethanol 11.9
CO2 13.6
Produced H2O 0.15Figure 5.9
Bioprocess Engineering Principles, 2nd edPauline Doran, Elsevier Science & Technology Copyright © 2012, Elsevier Inc. All rights Reserved.
Updated: September 20, 2017John Jechura ([email protected])
Example energy balance – Continuous Ethanol Fermentation
We’ll calculate the heat of reaction at the standard temperature (25oC) & assume this is close enough For more accuracy we would need to cool reactants to 25oC, calculate heat
of reaction @ 25oC, & then heat up products to 30oC
Heat of reaction:
Hrxn = -570000 – (-556025)= -13,977 kJ/h
Since negative this heat to beremoved
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Updated: September 20, 2017John Jechura ([email protected])
Other topics from supplemental text
Use of steam tables How much steam might be needed to heat a reactor or stream How much heat is carried away by evaporated water
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Updated: September 20, 2017John Jechura ([email protected])
Closing comments
Remember that the heat of reaction is energy released not energy generated Unless we are working with nuclear reactions we do not create nor destroy
energy
Using heat of combustion (i.e., change in enthalpy upon combustion)is a valid reference state, just like enthalpy of formation Take care whether the values are reported as negative (consistent with Hrxn) or positive (reported as heating value) For biological reactions make sure you choose the higher heating value (i.e.,
where any product water is in the liquid state)
Many times you can ignore the actual reactor temperature & just use the heat of reaction at standard conditions
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