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Cost Analysis

The goal of this page is to provide an overview of the upfront and ongoing costs for the He recovery system. This is based on my limited experience and an operating time of just one year. I’m sure there are aspects that I have overlooked, but I hope this provides at least some useful context for those just starting on this adventure. All prices are from 2020 and early 2021; these will go out of date rather quickly, but I hope they’re useful for order of magnitude comparisons. I have also included some practical data here that I couldn’t find when I first started this project (e.g., accurate estimates of transfer losses and flash % when transferring LHe).

Quick Summary

5 superconducting magnets = 870 L of LHe delivered annually.

Annual LHe loss = ~30 L/yr = $630 + 10% = ~$700

Average yearly maintenance = $2.4k + 10% = ~$2.7k. Annual electrical cost = $4k + 10% = $4.4k (+10% is to account for small errors, moderate price increases, etc.)

This results in $3.81 per L delivered (ignoring electricity) or $8.65 per L delivered (including electricity) Compare that with $23 per L delivered that we were paying in 2020 and early 2021.

That’s a savings of $18k per year. The total capital costs to purchase and install the system = $309k which means the capital costs are recouped in 17 years (sooner, as He prices continue to rise).

Note: ~30 L/yr of transfer loss vs. 870 L/yr delivered = 97% recovery (theoretical).


Alternate scenario 1: Only the NMR facility on the system (3 magnets)

This results in slightly lower capital costs. I would have somewhat lower transfer losses. I would liquify fewer L of He, so there would be a longer time between maintenance events and less electricity used. However, I would also spend more time keeping the collection dewar and transfer dewar cold and the costs would be spread over fewer L of LHe delivered per year. The end result is

$6.92 per L delivered (ignoring electricity) or $16.46 per L delivered (including electricity)

The annual savings would only be $5k, so the capital costs aren’t recouped until ~44 yrs! But, that’s still significantly less than I was paying for LHe and it sidesteps problems during shortages (quotas, etc.)


Alternate scenario 2: Add a Quantum Design PPMS to the system

I have everything setup and ready to add a Quantum Design PPMS (this is the second magnet on the 3rd floor). This magnet currently has a cold head that liquifies the boil-off directly back into the cryostat. However, the cold head is long past the expected lifetime and the performance is dropping. Without the cold head, the magnet needs 40 L of LHe every week! This will have the system running at almost 100% capacity and we’ll end up delivering a total of ~3000 L of LHe annually. This results in much shorter maintenance cycles which means a higher yearly maintenance cost; but, that cost is now spread out over more L of LHe with very little time spent simply keeping things cold. This results in

$2.60 per L delivered (ignoring electricity) or $5.03 per L delivered (including electricity)

The annual savings is $23k (compared to the annual cost of servicing a cold head on the PPM + traditional LHe costs for the other magnets) which recoups the capital expenses in 11 years.


Practical Data:

First, I want to address several questions that I had difficulty getting answers to when I was first planning my system.

What is the transfer loss when filling a magnet?

  • It ranges from roughly 3/4 L to 2 L per magnet fill, depending on fill technique and time.
  • I couldn’t find anything more than hand-waving estimates for this, so I weighed a dewar and then used it to cool a warm transfer line until I got a nice flame followed by venting the dewar. I repeated this with several warm transfer lines and measured the final weight. This gave an estimate of ~0.75 L of LHe for cooling a warm transfer line and venting the pressure in the dewar.
  • After 1 year of fills in the NMR facility, I observe an average transfer loss of ~0.8 L per fill.
  • The data from the other magnets give transfer losses ranging from 1-2 L per fill. This is partly due to the high back pressure for those magnets further from the recovery system (you can see the He escaping from the inlet during the fills!), but also due to filling technique – my colleague who fills the FTICR magnet has a rather more cavalier technique than I do and sprays quite a bit of LHe out of the transfer line while fiddling with the inlet port…  I’m pretty sure that 2 L transfer loss could be reduced to ~1.0-1.2 L per fill with a more careful approach.

How much LHe needs to be condensed for every L that goes in the magnet? (i.e., what is the vaporization loss or “flash” during a LHe transfer?)

  • For magnet fills, I see 10%-20% flash. This appears to depend strongly on how long the fill takes: My magnet fills take ~30 min and I observe ~20% flash. My colleague fills his FTICR magnet in ~10 min and consistently gets ~10% flash. When averaged over all 5 magnets across 1 year I get a an average flash of ~18%.
  • When filling the transfer dewars, I see an average flash of ~30%. I suspect this higher % is due to the higher pressure in the source dewar. I get much higher flash when the collection dewar is at 6-8 psig vs. 3-4 psig. However, if the pressure is too low (e.g., 1-2 psig), the transfer rate is quite slow and that also leads to a very high flash. Pushing the LHe out with a push gas, like we do for magnet fills, should reduce the flash; but, this requires expensive UHP He.
  • You need to take both of these flash %’s into account when estimating the volume you will condense over the course of a year. For example, 

13 weeks of boil off in the NMR facility = ~70 L

Transfer losses for 3 fills bump this up to ~73 L

Due to ~20% flash when filling the magnets, I’ll need at least 91 L in the transfer dewar.

Due to ~30% flash when filling the transfer dewar, I’ll need at least 136 L in the collection dewar.

In other words, to put 70 L in the magnets, I need to condense 136 L of LHe.

Notes:

  • Only the 3 L of transfer loss in this example is truly lost; the flash volume is all collected by the recovery system.
  • It’s important to keep this extra volume in mind when estimating when to start condensing LHe for an upcoming fill as well as estimating the maintenance schedule of the LHeP, how much electricity is used per year, etc. 
  • This also demonstrates that you need to have more He in your system than just the LHe that you want to end up in the magnet.

How much He is lost when cooling down a warm transfer dewar?

  • This depends a lot on the technique. I’ve tried pre-cooling with LN2, purging it, pumping out the N2 gas, etc. I find that process time consuming and am always paranoid that I haven’t purged all the N2 from the dewar. I figured I’d try cooling our second transfer dewar directly with LHe – as long as I’m collecting the plume from the fill, it doesn’t matter how much boils off.
  • I used a very slow flow at the beginning; I only pushed ~10 L into the dewar over 3 hours. Once I started seeing liquid collecting in the dewar (i.e., once the weight began increasing), I increased the flow to a normal rate.
  • By the end, I had collected 58 L of LHe in the transfer dewar and the equivalent of ~22 L of LHe in the recovery system (starting with 80 L of LHe in a commercial dewar). That’s only ~28% lost to flash (only ~12% to cool down the dewar!) – I’m honestly shocked at how well that worked; I was expecting to lose 50% or more.


Cost Estimates

With good values for transfer loss, flash %, average boil-off rates, and the annual fill schedule we can estimate the total V of LHe that we’ll condense in one year. We also need to top off the transfer dewar occasionally to keep it cold between magnet fills and we need to run the LHe plant periodically to keep the collection dewar cold. This adds more hours to the system, affecting the estimated maintenance schedule and electrical costs. The CryoMech LHe plant has an on/off mode that runs at a 40% duty cycle when not actively condensing LHe to keep the collection dewar cold while using less energy. The purifier, however, needs to be turned on and off as needed (keeping in mind the ~8 hr cool down time).

Total boil-off (5 magnets) = 12.5 L/week = ~700 L/yr
Transfer losses = 23 magnet fills x 1.2 L/fill = ~30 L/yr = ~730 L/yr
20% flash when filling magnets = ~870 L/yr delivered30 % flash when filling transfer dewar = ~1250 L/yr condensed
Plus ~675 L to keep the transfer dewar cold between fills = ~2000 L/yr

At 22 L/day & 40% duty cycle when not condensing, the LHeP runs ~4800 hrs/yr

The purifier runs ~2700 hrs/yr

Estimated average annual maintenance cost:
Automatic purifier:
Replace oil adsorber ($2k) every 25,000 hrs = every 11 yrs Replace cold head ($6k) every 40,000 hrs = every 17 yrs
LHeP22:
Replace oil adsorber ($2.5k) every 25,000 hrs = every 5 yrs Replace cold head ($6.8k) every 40,000 hrs = every 8 yrs
Misc costs (ground pin, purity sensor, etc) every few years.
Average yearly cost = ~$1.8k/yr

Note: if the oil adsorbers are replaced on schedule, the cold heads can last much longer than 40,000 hrs. As long as the oil adsorbers are replaced on schedule, you can run the cold head until the performance begins to decline.

We don't have pay for our electricity; some people have to, so I include an electrical estimate here for reference. My university has a contracted rate of $0.07/kWhr. The automated purifier is 3.1 kW and the LHeP is 10 kW. Using the estimated run times from above = ~$4k/yr in electricity for my facility. To compare this cost with commercial LHe, I calculate the cost per L “delivered” (i.e., what I actually push out of the transfer dewar). For example, a commercial 100 L liquid cylinder from our current supplier has never arrived to us with more than 85 L in it; so the cost of the dewar + shipping + demurrage has us paying $23 per L delivered. Taking the total annual cost above divided over the 870 L of LHe that I push out of the transfer dewars in one year gives me

$3.81 per L delivered (ignoring electricity)

$8.65 per L delivered (including electricity)

vs. $23 per L delivered from our commercial supplier.

This is an annual savings of $18k compared to what we were paying for commercial LHe. We can compare this with the total cost of purchase and installation: CryoMech system = $220k

Renovation costs = $57k
Misc = $32k (parts for manifolds, LHe transfer dewars, etc.)

Giving a total capital cost = $309k

With a savings of $18k/yr we recoup these capital costs in ~17 years.


Recovery Performance

~30 L/yr of transfer loss vs. 870 L/yr delivered = 97% recovery

97% is the theoretical recovery based on the average numbers above. To measure the actual recovery %, I measure the total amount of He in the recovery system before and after each magnet fill (storage tanks + collection dewar + transfer dewars + empty collection bag). Comparing the volume of He collected between fills against the total expected boil-off (based on the average boil-off values for each magnet) and averaging this difference over one year gives an estimate of any leaks in the system. Similarly, comparing the volume of He in the recovery system before and after a specific fill against the expected boil-off for that specific magnet (averaged over a year of fills) gives an estimate of the transfer loss for that magnet. I get 95% recovery for the first year of operation. I have improved things over time, so looking at just the last 5-6 months of operation, I get 98% recovery.

Misc Info
For reference, my average boil-off rates and fill schedules are
NMR facility

  • 1 AlOx + 1 Magnex + 1 Bruker = 5.4 L/week
  • 4 fills/yr = every 13 weeks

SSNMR

  • Magnex = 3.0 L/week
  • 3 fills/yr = every 17 weeks

FTICR

  • Varian horiz. bore = 4.0 L/week
  • 8 fills/yr = every 6.5 weeks

Transfer dewar = 1.3 L/day = 9.1 L/week

  • Topped off after each fill (15 times a year)

PPMS (not yet connected to recovery system)

  • Quantum Design = 4.0 L/day = 28 L/week
  • expect to fill each week or every two weeks

Transfer dewar with heater = 2.1 L/day = 15 L/week

  • This will be used to fill the PPMS, so it will be topped off every 1-2 weeks