Appendix A Potassium Formate Property Calculations

Transcription

1 Appendix A Potassium Formate Property Calculations A.1 Potassium Formate Vapour Pressure This section describes the routine used to calculate the vapour pressure of the potassium formate solution (p sol ), with respect to solution mass concentration (X sol ) and temperature (T sol ). The routine is taken from the work of James (1998), and is based upon theoretical and empirical data. The water present in the desiccant solution is calculated using Eq. A.1. X H2 O = 100 X (A.1) X is the desiccant solution mass concentration as a percentage. The molecular weight of the desiccant solution, X m, is calculated using Eq. A.2. X m = 1 + (A.2) M H2 O and M CHKO2 are the molecular weight of water vapour ( g mol 1 ) and the potassium formate solution respectively (84.11 g mol 1 ). A, B and Z are constants, calculated using Eqs. A.3, A.4 and A.5 respectively. ( ) 1039 B = 3.42 (A.3) T sol,k 1 ( MH2 O X M CHKO2 X H2 O ) ( ) 1336 A = 2.08 T sol,k (A.4) Z = A X m A X m + B (1 X m ) (A.5) Springer International Publishing AG 2017 T. Elmer, A Novel SOFC Tri-generation System for Building Applications, Springer Theses, DOI /

2 236 Appendix A: Potassium Formate Property Calculations T sol,k is the solution temperature in K. γ is the activity coefficient of water and is calculated using Eq. A.6. γ = A (1 Z) 2 [ Z (Z 2/3)] P H20 is the vapour pressure (Pa) of the water in the desiccant solution at a given temperature, and is calculated using Eq. A.7. ( ) p H2 O = ln ( ) ( ) 2 T sol,k Tsol,K T sol,k (A.7) p sol is the vapour pressure (Pa) of the potassium formate desiccant solution, and is calculated using Eq. A.8. p sol = X m exp (γ ) ) ph2 O exp( A.2 Potassium Formate Thermophysical Calculations (A.6) (A.8) This section presents the linear regression curve functions fitted to the experimental data presented by Melinder (2007). The functions are used to calculate the thermophysical properties of the potassium formate desiccant solution, with respect to solution temperature (T sol ) and solution mass concentration (X sol ). A.2.1 Potassium Formate Density The density (kg m 3 ) of the potassium formate solution is calculated using Eq. A.9. ρ sol = T sol 0.002T 2 2 sol X sol X sol T sol X sol (A.9) A.2.2 Potassium Formate Specific Heat Capacity The specific heat capacity (J kg 1 K) of the potassium formate solution is calculated using Eq. A.10. c p,sol = T sol T 2 sol T 3 sol 44.49Xsol X 2 sol Xsol Tsol X sol T sol X 2 sol T sol T sol 2 (A.10)

3 Appendix A: Potassium Formate Property Calculations 237 A.2.3 Potassium Formate Thermal Conductivity The thermal conductivity (W m 1 K) of the potassium formate solution is calculated using Eq. A.11. k sol = T sol T sol T sol T sol Xsol X sol Xsol X sol Tsol X sol T sol X 2 sol T sol X sol T sol T sol T sol T sol 3 Xsol T sol 3 Xsol 2 (A.11) A.2.4 Potassium Formate Dynamic Viscosity The dynamic viscosity (mpa s) of the potassium formate solution is calculated using Eq. A.12. µ sol = T sol T sol T sol T sol Xsol X sol Xsol X sol Xsol Tsol X sol T sol X sol Tsol X sol T sol X sol T sol T sol T sol T sol 3 Xsol T sol 3 Xsol T sol 4 Xsol (A.12) A.3 Potassium Formate Henry s Law Constant The Henry s Law constant (wt%) is a measure of the solubility of a gas in a liquid and is taken from experimental data presented in the literature (Stephen and Stephen 1963). The Henry s Law constant of the CHKO 2 solution is shown in Eq. A.13. H CHKO2 = T sol (A.13)

4 238 Appendix A: Potassium Formate Property Calculations References James, S A new working Fluid Potassium Formate for use in absorption heat pumps. Masters of Philosophy: The University of Nottingham. Melinder, A Thermophysical properties of aqueous solutions used as secondary working fluids. PhD Thesis, KTH Energy and Environmental Technology. Stephen, H., and T. Stephen Solubilities of inorganic and organic compounds, volume 1. Binary Systems Part 1(1): 179.

5 Appendix B Thermodynamic Properties of Moist Air In this section the equations used to calculate the thermodynamic properties of moist air are presented. The air relative humidity, RH a (%), is calculated using Eq. B.1. RH a = p v p v,s 100 % (B.1) p v and p v,s are the vapour pressure and saturation vapour pressure of the air respectively in Pa. The air absolute humidity, ω a (kg vapour /kg dryair ), is calculated using Eq. B.2. p a is the pressure of the moist air in Pa (101,325 Pa) The air specific enthalpy, h a (kj kg 1 ), is calculated using Eq. B.3. T a is the air temperature in C p v ω a = p a p v h a = 1.005T a + [ω a ( T a )] (B.2) (B.3) Springer International Publishing AG 2017 T. Elmer, A Novel SOFC Tri-generation System for Building Applications, Springer Theses, DOI /

6 Appendix C IDCS Inlet Test Conditions The inlet air conditions for each of the IDCS tests are presented in Table C.1. Table C.1 IDCS inlet air conditions Test number Dehumidifier Regenerator T a ( C) RH a (%) T a ( C) RH a (%) Springer International Publishing AG 2017 T. Elmer, A Novel SOFC Tri-generation System for Building Applications, Springer Theses, DOI /

7 Appendix D Micro-tubular SOFC Stability Testing Results In this section the long term stability testing data of the micro-tubular SOFC is provided. The long term stability tests were carried out at the University of Birmingham (UoB). Figure D.1 provides a photograph of the test set up. During the stability testing the SOFC WHR was not tested. Figure D.2a shows a photograph of the micro-tubular SOFC with labelled cathode gas inlet and gas outlet. WHR provision, presented in Chap. 7, passes this gas outlet through the recupertaor heat exchanger. Figure D.2b shows a photograph of the micro-tubular SOFC control and display panel. The switch button turns the SOFC on or off. The display panel shows the operational voltage of the SOFC, heat-up/cool down time, and the total number of unit operational hours. Figure D.3 presents the long term stability testing data for the micro-tubular SOFC. Up until operational hour 75, the unit produces around 250 W of DC electrical power, at an electrical efficiency of 19.4 %. At hour 75 severe sulphur poisoning of the SOFC stack occurred resulting in no power output from the SOFC (no voltage). Once the sulphur traps were replaced, and the unit was operated for around 15 h, the SOFC recovers to a maximum power output of around 140 W DC. The micro-tubular SOFC data presented in Sect shows that the SOFC has now recovered a little more to a W electrical output. The long term stability testing results demonstrate the thermal resistance of the micro-tubular SOFC, and also its resilience to sulphur poisoning. Compared with planar-type SOFCs, these advantages show the potential of the future application of micro-tubular SOFCs. Springer International Publishing AG 2017 T. Elmer, A Novel SOFC Tri-generation System for Building Applications, Springer Theses, DOI /

8 244 Appendix D: Micro-tubular SOFC Stability Testing Result Fig. D.1 UoB micro-tubular SOFC test set-up Fig. D.2 Micro-tubular SOFC, a gas inlet and outlet, and b control and display panel

9 Appendix D: Micro-tubular SOFC Stability Testing Result 245 Fig. D.3 Micro-tubular SOFC long term stability test data