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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 of operating the system for 2.5 years. 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. Most prices are from 2020 and early 2021; these will go out of date rather quickly, but I hope they’re useful for order of magnitude comparisons.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., estimates of transfer loss and flash % when transferring LHe).

Recovery system installed: Jan 2021
Last update to this page: Sep2023

Quick Summary

6 superconducting magnets = 2700 L of LHe delivered annually and 5100 L of LHe liquefied annually.

Annual He replacement = $5.8k + 10% = ~$6.4k
Average yearly maintenance = $5.6k + 10% = ~$6.2k

Annual electrical cost = $7.7k + 10% = $8.4k
(+10% is to account for small errors in my estimates, moderate price increases, etc.)

This results in
$4.70 per L delivered (ignoring electricity)
$7.80 per L delivered (including electricity)
Compare that with $25 per L delivered that we are paying in 2023.

That’s a savings of $21k per year. Note: One of the magnets is a Quantum Design PPMS that had a small liquefier attached to the dewar. The savings here are compared to purchasing LHe for the other 5 superconducting magnets and the annual maintenance costs of refurbishing the small liquefier for the PPMS. The total capital costs to purchase and install the system = $309k which means the capital costs are recouped in 14 years (or sooner, as He prices continue to rise).

Note: The bulk of the annual He replacement is ~210 L of LHe lost over the course of a year; the rest is He gas cylinders, UHP He for the adsorber regeneration, and demurrage. Comparing the 210 L/yr of He lost from the recovery system to 5100 L/yr liquefied = 95% recovery (based on detailed measurements for Jun 2022 through Jun 2023). Relative to the 2700 L of LHe delivered, the recovery is 91%.

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

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

$16.40 per L delivered (ignoring electricity)
$26.90 per L delivered (including electricity)

The annual savings would only be $2k, so the capital costs aren’t recouped in a reasonable time frame (it requires more than 100 years!) However, this is still significantly less than I would pay for LHe if I don’t have to pay for electricity and, more importantly, it protects against potential catastrophe with future He shortages.

Alternate scenario 2: Only 5 superconducting magnets on the system (i.e., no PPMS)

Half of the LHe that we liquefy is for our Quantum Design PPMS (it needs about 70 L of LHe every two weeks). Removing this instrument from the recovery system reduces the amount of He lost during magnet fills and drastically reduces the amount of electricity used. However, these savings are spread across fewer L of LHe delivered, so the per L cost is still higher than the initial analysis above. The end result is

$8.60 per L delivered (ignoring electricity)
$13.80 per L delivered (including electricity)

The annual savings is $17k which recoups the capital expenses in 18 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 2.5 years of tracking data before and after every LHe transfer, my current estimate is a transfer loss of ~1.5 L LHe per fill. This is when using a vent line to capture the He gas vented from the transfer dewar but without capturing any of the He lost during the transfer line pre-cool. Using a pre-cool sheath should dramatically lower this transfer loss (see discussion here).

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 an average flash of 23%.
  • When filling the transfer dewars, I see an average flash of ~24%. This depends strongly on how long the fill takes. Slower transfers or longer (i.e., higher volume) transfer both yield a significantly higher flash percentage.
  • You need to take both of these flash %’s into account when estimating the volume to 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 ~75 L
    • Due to ~23% flash when filling the magnets, I’ll need at least 98 L in the transfer dewar.
    • Due to ~24% flash when filling the transfer dewar, I’ll need at least 129 L in the collection dewar.
    • In other words, to put 70 L in the magnets, I need to condense almost 130 L of LHe.
    • Note: Other recovery systems (e.g., Quantum Design and Cryo Tech) condense the He gas directly into the transfer dewar. For those systems, you only need to consider the flash % when filling the magnets.

Notes:

  • Only the 4.5 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 put 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 I’m always worried that I haven’t purged all the N2 from the dewar (pumping on the dewar with a little LN2 inside simply turns the LN2 into a solid!) When we purchased our second transfer dewar, I figured I’d try cooling it down directly with LHe. As long as I collect the plume from the fill, it doesn’t really matter how much LHe boils off during this initial cooldown.
  • I used a very slow flow at the beginning; I only pushed ~10 L into the dewar over a span of 3 hours. At this point, I started seeing liquid collecting in the dewar (i.e., the weight of the dewar began increasing). At this point, I increased the flow to the normal rate I use for LHe transfers.
  • By the end of the transfer, I had collected 58 L of LHe in the transfer dewar and the equivalent of ~22 L of LHe in the recovery system (i.e., pushing out 80 L of LHe from the collection dewar). That’s only ~28% flash or only an additional ~14% to cool down the dewar! – I’m honestly shocked at how well that approach worked; I was expecting a flash closer to 50% or more when starting with a warm dewar.

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. This, combined with the liquefaction rate of the LHeP gives us an estimate for how many hours we need to run the purifier and LHeP. The total time that the purifier and LHeP are used per year gives us an estimate of the expected maintenance schedule and the expected electrical costs. We need to keep in mind that the transfer dewars also boil off LHe and we need to keep those cold between fills. We also need to keep the collection dewar cold when not actively liquefying He. The CryoMech LHe plant has an on/off mode that runs at a 40% duty cycle when not actively condensing LHe. The purifier, however, needs to be turned on and off as needed (keeping in mind the ~8 hr cool down time). In my case, I’m liquefying for almost 6200 hrs/yr so it’s easier to simply keep the purifier on the entire time; only turning it off for maintenance.

  • Total boil-off (6 magnets + 2 transfer dewars) = 63 L/week = ~3300 L/yr
  • Transfer losses = ~210 L/yr (observed, June 2022 through June 2023)
  • 23% flash when filling magnets = ~4300 L/yr delivered (2700 L/yr to the magnets)
  • 24 % flash when filling transfer dewar = ~5700 L/yr condensed
  • At 22 L/day & 40% duty cycle when not condensing, the LHeP should run ~7200 hrs/yr.
  • The purifier needs to run at least ~6200 hrs plus warm-up/cool-down cycles, so it’s easier to simply leave it running ~8700 hrs/yr.

Estimated average annual maintenance cost:

Automatic purifier

  • Replace oil adsorber ($2k) every 20,000 hrs = every 2.3 yrs
  • Replace cold head ($7k) every 40,000 hrs = every 4.6 yrs

LHeP22

  • Replace oil adsorber ($2.5k) every 25,000 hrs = every 3.5 yrs
  • Replace cold head ($6.8k) every 40,000 hrs = every 5.5 yrs

Misc costs (ground pin twice a year, purity sensor every couple years, etc).

Average yearly cost = ~$5.7k/yr
Note: if the oil adsorbers are replaced on schedule, the cold heads can last much longer than 40,000 hrs. With the oil adsorbers replaced on schedule, you can simply run the cold head until the performance begins to decline.

I don't have pay for our electricity in my facility, but some people have to, so I include an electrical estimate here for reference. My university has a contracted rate of $0.07/kWhr (2022). The automated purifier is 3.1 kW and the LHeP is 10 kW. Using the estimated run times from above = ~$9k/yr in electrical costs 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 $25 per L delivered. Taking the total annual cost estimated above and dividing it over the 2700 L of LHe that I push out of the transfer dewars in one year gives me

$4.70 per L delivered (ignoring electricity)
$7.80 per L delivered (including electricity)
vs. $25 per L delivered from our commercial supplier.

This is an annual savings of $21k compared to what we were paying for commercial LHe for the 5 traditional magnets and what the annual maintenance cost would be for the little liquefier on the PPMS. 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 $21k/yr we recoup these capital costs in ~14 years (11 years, if we factor in the savings of not purchasing a new cold head for the PPMS).

Recovery Performance

I have detailed records of the total amount of He in the recovery system (transfer dewars, collection dewar, storage tanks, with an empty collection bag) before and after every LHe transfer (both for transfer dewar fills and magnet cryostat fills) for the past 2.5 years. The PPMS was added to the recovery system in June of 2022, so the data between June 2022 and June 2023 is the first complete year of data with all 6 magnets on the recovery system. During this time, I pushed 5100 L of LHe out of the collection dewar, collecting 3900 L of LHe in 80 transfer dewar fills. During 55 magnet fills, I pushed 2700 L of LHe out of the transfer dewars, collecting 2100 L of LHe in the magnet cryostats. Over the course of that year, I only lost 210 L of LHe from the recovery system (comparing time points at the same position in the fill schedule). This yields a collection efficiency of 95% relative to the amount liquefied and pushed out of the collection dewar or 91% relative to the amount delivered for magnet fills.

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 = 2.6 L/week
3 fills/yr = every 17 weeks

FTICR
Varian horiz. bore = 4.6 L/week
8 fills/yr = every 6.5 weeks
Transfer dewar = 1.3 L/day = 9.1 L/week
Topped off before and after each fill = 30 times a year

PPMS
Quantum Design = 3.7 L/day = 26 L/week
26 fills/yr = every 2 weeks
Transfer dewar with heater = 2.2 L/day = 15 L/week
Topped off before and after each fill = 52 times a year