1. Design of cold compressor systems. Operational and economical aspects. Decker L. Tucson, June 29, 2015

2. 2 Contents. 1.Introduction 2.2K Refrigeration cycles 3.CAPEX 4.OPEX 5.Discussion & Conclusion

3. 3 Contents. 1.Introduction 2.2K refrigeration cycles 3.CAPEX 4.OPEX 5.Discussion & Conclusion

4. 4 Introduction. [1] Claudet S., Lebrun P., Tavian L, Towards cost to performance of large superfluid helium refrigeration systems, Proceedings of ICEC18, Mumbai, India 2000 TaskRefrigeration at 2K with sub-atmospheric Helium < 31 mbar PurposeCooling of advanced superconducting devices “Problem”  3 State-of-the-art solutions for vacuum compression cycles!  Which is the best – a)economically b)for flexibility? Solution – for a) [b) not part of this analysis] Analysis available by S. Claudet et al. [1] –only applicable for large capacities ~ 10kW at 1.8K ObjectiveElaboration of economic criteria for the optimisation of cold compressor systems in the range of Q* = 100 W to 10 kW

5. 5 Contents. 1.Introduction 2.2K Refrigeration cycles 3.CAPEX 4.OPEX 5.Discussion & Conclusion

6. 6 Assumptions: —Heating @ ambient w/o electric power —  lub acc. to [1] (efficiency of lubricated screw) —  dry =  lub / 1.5 (efficiency of dry pump) 2K Refrigeration cycles. Warm compression. HP LP 1.9K Heat load Q* 23 mbar 4.5K Refrigerator Warm vacuum pump << atm T r (return temp.) Ambient heater [1] Claudet S., Lebrun P., Tavian L, Towards cost to performance of large superfluid helium refrigeration systems, Proceedings of ICEC18, Mumbai, India 2000

7. 7 2K Refrigeration cycles. Cold compression. HP LP 1.9K Heat load Q* 4.5K Refrigerator 23 mbar T r (return temperature) LP 4 Cold compressors Assumptions: —N° of CC stages 4 —Suction pressure 1 st CC23 mbar a —Suction temp. 1 st CC3.4 K —Pressure CC1  CC298 mbar a —Pressure CC2  CC3320 mbar a —Pressure CC3  CC4620 mbar a —Discharge pressure CC41.1 bar a —Adiabatic efficiency 75 % —CC heat inleak: state-of-the-art

8. 8 2K Refrigeration cycles. Mixed compression. HP LP 1.9K Heat load Q* 23 mbar 4.5K Refrigerator << atm T r (return temperature) 2 – 3 Cold compressors Warm vacuum pump Assumptions: —N° of CC stages2 - 3 —Same as for warm compression —Same as for cold compression —  p last CC to WVP10 % (of CC discharge pressure)

9. 9 Contents. 1.Introduction 2.2K Refrigeration cycles 3.CAPEX 4.OPEX 5.Discussion & Conclusion

10. 10 CAPEX = C1 + C2 + C3. CAPEX C1. C14.5K Refrigerator C1 =A r Q* 1.9K n + B[M EUR] Q* 1.9K 1.9K load[kW] A, B, n(proprietary) rspecific equiv. 4.5K load induced by 1.8K load [1] [1] Claudet S., Lebrun P., Tavian L, Towards cost to performance of large superfluid helium refrigeration systems, Proceedings of ICEC18, Mumbai, India 2000 2 3 4

11. 11 CAPEX = C1 + C2 + C3. CAPEX C2 & C3. C2Warm vacuum pump (WVP) C2 = D (Q* 1.9K /p s ) m + E[M EUR] Q* 1.9K 1.9K load[kW] p s WVP suction press.[bar] D, E, m(proprietary) C3Cold compressors (CC) C3 =F (m* 1.9 T i 0.5 /p i ) k [M EUR] m* 1.9 1.9K massflow[kg/s] T i CC i inlet temp.[K] p i CC i inlet pressure[mbar] F, k(proprietary) all CCs and related PFHXs, piping etc. mounted in 4.5K refrigerator

12. 12 CAPEX evaluation. Refrigeration @ 4.5K  reference base. reference: CAPEX {x kW @ 4.5K}

13. 13 CAPEX evaluation. Impact on 4.5K refrigerator by warm compression (WVP). reference WVP

14. 14 CAPEX evaluation. Impact on 4.5K refrigerator by mixed compression. 3 CCs; return ~ 19K reference 2 CCs; return ~ 13K WVP 4 CCs; return ~ 25K

15. 15 CAPEX evaluation. Adding CAPEX for cold compressors (C3). 3 CCs reference 2 CCs 4 CCs

16. 16 CAPEX evaluation. Adding CAPEX for warm compressors (C2). reference WVP WVP for 3 CCs WVP for 2 CCs

17. 17 Contents. 1.Introduction 2.2K Refrigeration cycles 3.CAPEX 4.OPEX 5.Discussion & Conclusion

18. 18 O14.5K Refrigerator O1 =(Q* 1.9K r  ) t y t p c el [EUR] Q* 1.9K 1.9K Load[kW] rSpecific equiv. 4.5K load induced by 1.8K load [1]  Specific power input per refrigeration @ 4.5K (empiric / proprietary) t y Yearly operation time6’000 h/y t p Payback time10 y c e Specific cost of electricity0.15 EUR/kWh OPEX = O1 + O2 + O3. OPEX 1.

19. 19 OPEX = O1 + O2 + O3. OPEX 2 & 3. O2Warm vacuum pump (WVP) O2 =P WVP t y t p c el [EUR] P WVP Power input WVP[kW] = P T /  T P T Isothermal power[kW]  T Isothermal efficiency acc. to [1] O3Cold compressors (CC) O3negligible! [1] Claudet S., Lebrun P., Tavian L, Towards cost to performance of large superfluid helium refrigeration systems, Proceedings of ICEC18, Mumbai, India 2000

20. 20 OPEX evaluation. Refrigeration @ 4.5K  reference base. reference 3 CCs 2 CCs 4 CCs WVP

21. 21 OPEX evaluation. Adding OPEX for cold compressors (C3).  OPEX of CCs negligible! reference 3 CCs 2 CCs 4 CCs

22. 22 OPEX evaluation. Adding OPEX for warm compressors (C2). WVP for 2 CCs WVP for 3 CCs WVP!!! reference

23. 23 Contents. 1.Introduction 2.2K Refrigeration cycles 3.CAPEX 4.OPEX 5.Discussion & Conclusion

24. 24 Discussion & Conclusion. CAPEX for low 1.9 K loads reference < 200W @ 1.9K: only WVP < 500W @ 1.9K: only 2CCs w/WVP e.g. dry claw pumps (small, cheap, less eff.) screw compressors (big, expensive, efficient) 3 CCs 2 CCs 4 CCs WVP

25. 25 Discussion & Conclusion. Results —Results in good accordance with [1] for 4.5K refrigerator —[1]: extra CC system  for large capacities ~ 10 kW —This paper: CCs in 4.5K refrigerator  for small to medium capacities Remarks —Many assumptions and simplifications as basis of work —No exact science!Good tool for cost estimate! (based on costs for 4.5K refrigerator) [1] Claudet S., Lebrun P., Tavian L, Towards cost to performance of large superfluid helium refrigeration systems, Proceedings of ICEC18, Mumbai, India 2000

26. 26 Discussion & Conclusion. Future analysis on —Impact of load > 500W on PFHX, 4.5K refrigerator and WVP dimensions  indicator for 2, 3 or 4 CCs —Sensitivity of results on p in and T in @ 1st CC —Impact of part load scenarios, e.g. —extra CC stage for part load —SFC —etc. [1] Claudet S., Lebrun P., Tavian L, Towards cost to performance of large superfluid helium refrigeration systems, Proceedings of ICEC18, Mumbai, India 2000

27. Thank you for your attention.