Comments Transient Energy Balances

Transcription

1 Comments Transient Energy Balances

2 General form of the stuff balance equation Rate of Rate Rate Rate of Rate of Accumulation In Out Generation Consumption F1 Q1 F6 F2 Q3 F3 Q2 F4 F5 2

3 Word form of the energy balance equation Rate of Convection Convection Heat Across Work Across Accumulation Energy In Energy Out Bounary Boundary F1 Q1 F6 F2 Q3 F3 Q2 F4 F5 3

4 Transient energy balance equation d UK de P ˆ ˆ E E Q W i j k s, m i: inlet j: outlet k m FHˆ FHˆ Q W i i i j j j k s, m i: inlet j: outlet k m d HV d UV FHˆ FHˆ Q W i i i j k s, m i: inlet j: outlet k m F1 Q1 F6 F2 Q3 F5 F3 Q2 F4 4

5 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. T H C H H C dt C T T T P p ref p p ref T ref T Hˆ Hˆ Cˆ dt Cˆ T T ref p p ref T ref 5

6 Where does heat of reaction come from? Use of heat capacity for enthalpy No reaction: dhˆ 1 V FHˆ 0 FHˆ 1Q ˆ dt1 VC ˆ ˆ p F Cp T0 Tref Href F Cp T1 Tref Href Q 1 ˆ dt VC ˆ p FCpT0 T1Q With chemical reaction, the reference enthalpies are different: ˆ dt1 VC ˆ ˆ ˆ ˆ p F Cp T0 Tref Href,0 F Cp T1 Tref Href,1 Q 1 ˆ dt VC ˆ 0 1 ˆ,0 ˆ p FCp T T F Href Href,1 Q 6

7 Where does heat of reaction come from? Use of heat capacity for enthalpy What if the reactants have different heat capacities then the products? d Cˆ p11 T V F Cˆ ˆ ˆ ˆ p0 T0 Tref Href,0 F Cp 1 T1 Tref Href,1 Q dcˆ p11 T V F Cˆ ˆ ˆ,0 ˆ p T Tref Cp T Tref F Href Href,1 Q 7

8 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) N N N N H mhˆ nh C mcˆ nc i i i i p i pi i pi i1 i1 i1 i1 For constant heat capacities for each chemical species dh 1 dh dh 1 1 H H Q N 0 1 n H n H Q i,0 i,0 i,1 i,1 i1 i1 N N N N,0, 0,1, 1,0,1 n C T T n C T T n n H Q i p i ref i p i ref i i F i i1 i1 i1 8

9 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 species Written with heat of combustion as negative value dh 1 N N N Reacting Reacting Reacting n,0 C, T0 T n,1 C, T1 T n,0 n,1 H N i p i ref i p i ref i i c i i1 i1 i1 Nonreacting n C T T Q i1 i,0 p, i 0 1 9

10 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) T 1 vap 1 Heat of mixing T dh C pl, dt H vap CpV, dt T T T 0 0 C T T H C T T N pl, vap 0 vap pl, 1 vap T vap mix H xh H xh x H i i i i R i1 i1 N mix, R 10

11 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 reference temperature Determine enthalpy change to take products from the reference temperature Figure 5.2 Bioprocess Engineering Principles, 2 nd ed Pauline Doran, Elsevier Science & Technology Copyright 2012, Elsevier Inc. All rights Reserved. 11

12 Calculating heat of reaction from heats of combustion (values in Table C.8) Use the heat of combustion as the reference Example: Glucose Ethanol C 6 H 12 O 6 (s) 2 C 2 H 5 OH (l) + 2 CO 2 (g) Compound (state) C 6 H 12 O 6 (s) C 2 H 5 OH (l) CO 2 (g) H 0 c kj/mol kj/mol 0 kj/mol H nh nh rxn i c i c reactants products kj 71.4 mol glucose 12

13 Heat of reaction with cell growth Estimated from available electrons c H q x q kj 111 to 115 g.mol C Heat of reaction with oxygen as electron acceptor (aerobic, combustion)) H rxn kj 460 g.mol O 2 Bioprocess Engineering Principles, 2 nd ed Pauline Doran, Elsevier Science & Technology Copyright 2012, Elsevier Inc. All rights Reserved. 13

14 Heat of combustion for bacteria & yeast Can be estimated as: For general biomass (CH 1.8 O 0.5 N 0.2 ): H c bacteria H c yeast kj 23.2 g kj 21.2 g H c biomass 21.3 kj g Bioprocess Engineering Principles, 2 nd ed Pauline Doran, Elsevier Science & Technology Copyright 2012, Elsevier Inc. All rights Reserved. 14

15 Calculating heat of reaction from heats of combustion (values in Table C.8) Use the heat of combustion as the reference Example: Glucose Ethanol C 6 H 12 O 6 (s) 2 C 2 H 5 OH (l) + 2 CO 2 (g) Compound (state) C 6 H 12 O 6 (s) C 2 H 5 OH (l) CO 2 (g) H 0 c kj/mol kj/mol 0 kj/mol H nh nh rxn i c i c reactants products kj 71.4 mol glucose 15

16 Example energy balance Continuous Ethanol Fermentation Saccharomyces cerevisiae is grown anaerobically in continuous culture at 30 o C. Glucose is used as the carbon source; ammonia is the nitrogen source. A mixture of glycerol and ethanol is produced. Compound In [kg/h] Out [kg/h] Glucose 36.0 NH Cells 2.81 Glycerol 7.94 Ethanol 11.9 CO Produced H 2 O 0.15 Figure 5.9 Bioprocess Engineering Principles, 2 nd ed Pauline Doran, Elsevier Science & Technology Copyright 2012, Elsevier Inc. All rights Reserved. What is the cooling requirement to 30 o C? 16

17 Example energy balance Continuous Ethanol Fermentation We ll calculate the heat of reaction at the standard temperature (25 o C) & assume this is close enough For more accuracy we would need to cool reactants to 25 o C, calculate heat of 25 o C, & then heat up products to 30 o C Heat of reaction: H rxn = ( ) = -13,977 kj/h Since negative this heat to be removed 17

18 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 18

19 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 H rxn ) 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 19