Gibbs Free Energy Analysis of Processes

1. Gibbs Free Energy Analysis of Processes Daniel Beneke LPPD group seminar 10/8/2009

2. ∆G= ∆H-T∆S • ∆G indicates the amount of work to be added or rejected to a process • -vevalue means process produces work • +ve value means work has to be added to make process feasible

3. Gibbs Free Energy of Reaction • From the Gibbs Free Energy of formation we can obtain an indication of the degree to which the reaction will proceed: • a large negative value is indicative of a high equilibrium conversion - simple process potentially viable • a large positive number is indicative of a reaction that has a very small equilibrium extent – process will potentially need to be more complex

4. Chemical Equilibrium Considerations • We know that for any reaction we can write K = exp(- ∆G R /RT) • K is the equilibrium constant, function of temperature only • ∆G R is the Gibbs Free Energy of the reaction as written. • For a reaction to be useful in a process the value of K at the operation temperature must be “reasonable” • This is equivalent to saying, for a reaction to be of use in practice the equilibrium conversion must not be too small

5. The Additional Tool: The 2nd Law of Thermodynamics • The use of the first law of T/D (quantity of energy) together with the second law of T/D (quality of energy) allows us to assess the efficiency of chemical processes • One can therefore set target efficiencies for the process based on thermodynamic insights • On existing flow sheets or processes, we can determine inefficiencies in the process and address these inefficiencies

6. Process Example • Wnett=∆Gprocess=84.8 kJ/mol • Q=∆Hprocess=36.8 kJ/mol (Endothermic) • ∆Sprocess=-161 J/mol.K • ∆Gprocessis +ve at all Temperatures, becoming more +ve at higher temperatures

7. Process CH4, H2O, CO2 CH3OH Heat and Work In Process CH4, H2O, CO2 CH3OH Heat required by process WorkIn Heat from surroundings surroundings Integrating Work and Heat Addition Quantity of work entering with the heat can be calculated from a heat pump

8. Reactor at TH Products Reactants To To QH = ∆Hrxn Heat Pump Wmin Surroundings at To A Chemical Process as a Heat Pump Matching the heat and work requirements implies: • For the one step process: • ∆Grxn = 84.8 kJ/mol • ∆Hrxn = 36.8 kJ/mol • As ∆Grxn > ∆Hrxn cannot match heat and work requirements

9. Process Example • Thermodynamics indicate that the process is infeasible as a simple process • Consider a 2 step process: STEP 1 STEP 2

10. Process Example STEP 1 STEP 2 ∆Gprocess=-29kJ/mol ∆Hprocess=-128 kJ/mol (Exothermic) ∆Sprocess=-332J/mol.K ∆Gprocessis -veat low temperatures, and +veat higher temperatures Reaction will run at low temperatures • ∆Gprocess=113 kJ/mol • ∆Hprocess=165 kJ/mol (Endothermic) • ∆Sprocess=171 J/mol.K • ∆Gprocessis +ve at low temperatures, and -veat higher temperatures • Reaction will run at high temperatures

11. Process Example

12. Process Example Black Box Endothermic reactor: An energy balance yields: A Reversible exergy balance yields:

13. Process Example • Assuming ∆G and ∆H are constant, we can calculate a Temperature TH where the process runs reversibly • For the Endothermic process (STEP 1): • TH= 950 K

14. Process Example • Exothermic reaction can be viewed in the same way: • For the Exothermic process (STEP 2): • TC= 380 K

15. Process Example • Wnett= Win +Wout • Win and Wout are given by: • Therefore Wnett is given by: • For a reversible process, Wnett, must be equal to ΔGrxn overall

16. Surroundings at To Win Heat Pump Heat Engine Wout Control Volume QH QC i TH TC e Rxn 1 Rxn 2 QH = ΔH298rxn 1 QC = ΔH298rxn 2 Work Integrated Process For the overall process: • Can do an exergy balance • Satisfying the ∆G relationship requires that we put the heat in at the correct temperature • Can also integrate work flows

17. Process Example • The values for TH and TC calculated will satisfy the equation • There is in fact a range of temperatures that will satisfy the equation • Work integration!

18. 700 Commercial processes 600 Work must be added to process in this region 500 400 [K] Minimum required work C T 300 Work can be produced in this region 200 100 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 T [K] H Process Example

19. Rxn 1 Rxn 2 CH4, H2O, CO2 CO, H2 CH3OH Heat Out Work In Work Out Heat In Hot Cold CH4, H2O, CO2 CO, H2 CH3OH Heat Out at Low Temperature Wnett Representation of Work Integrated Process Heat In at High Temperature Additional heat

20. Conclusions • We have developed a method to analyze work flows in processes • This approach gives insights into work requirements and process design • It identifies opportunities and targets • Allows process integration to be considered at high level • Do not require detailed process information

21. Conclusions • We do not need to consider detailed flow sheet to work integrate • The overall G rxn and Hrxn tell us what the nett heat and work requirements are • We have investigated the ways we can put the required work in • We can predict operating temperatures and pressures using this approach • Hence can guide choice of chemistry and experimental program using these ideas