Targeted methane removal

Methane has a high enough warming potential (~30-40x CO₂) that it could
be worth spending additional energy to either remove it or turn it into
CO₂. But it’s tough to efficiently purge dilute methane from air: most
techniques have to spend energy on all of the air molecules, which is a
losing proposition. If we couple intense laser light into dilute methane
mixtures, we might be able to pump several eV of energy into the
vibrational modes of the methane molecules alone, possibly triggering
efficient decomposition or combustion. My crude analysis suggests that
if the science works perfectly, there’s perhaps a marginal business case
here, assuming that carbon credits reach $100/ton CO₂ and we can build a
suitable mid-IR laser for $20/W. Not substantially crazier than
iron-chloride or other hydroxyl-radical proposals for destroying
atmospheric methane, but not a slam dunk.

The same technical approach seems much more likely to give
cost-effective (order $1/tCO₂e) methane abatement in higher
concentration (>1% CH₄) contexts such as cattle barns or some combustion
exhaust. While it looks tractable, the smaller addressable market and
permanent dependence on carbon subsidy mean it’s not for us.

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Oxidation of methane to CO₂ eliminates 97% of methane’s warming impact
when assessed over 20 years. Is it worth expending energy to burn
methane that would otherwise enter the atmosphere? We can estimate the
break-even energy for electrified combustion: over a 20 year window,
converting 1 kg of CH₄ to CO₂ is equivalent to removing 83 kg of CO₂
from the atmosphere, while electricity from natural gas emits 0.5 kg
CO_2eq/kWh. We break-even at 83 kg / (0.5 kg/kWh) = 167 kWh per kg CH₄
removed, or 100 eV per CH4 molecule removed. (If we use solar energy,
the CO_2e rate is supposedly 10x lower, so 1000 eV/molecule; wind is
allegedly 5000 eV/molecule [1].) To do obvious good, and to make any
money from carbon credits or similar, I suggest that our target energy
budget should be < 10% of break-even—i.e., electricity from natural gas
yields a 10 eV/molecule budget.

A thermally activated oxidation scheme would only fit these budgets for
relatively high concentrations of methane. Consider a large methane leak
where the air is 1 ppt (0.1% v/v) methane. Using natural gas baseload
electricity to perform bulk heating, we would have 10 eV * 1 ppt = 0.01
eV to distribute per air molecule. This would suffice to heat the air by
~40 K. Although considerably higher temperatures could be reached with
efficient counterflow heat exchange, this is not much of an energy
margin; 1 ppt methane looks like it’s right on the edge of what’s
possible to combust even with a nice catalyst. Concentrations below 1
ppt look basically out of the question because the available energy is
further spread thin. We might drop another ~10x in concentration (to 0.1
ppt) using renewable electricity, but that’s it.

One way around this problematic concentration scaling might be to
deliver energy directly to CH₄ molecules using laser light. Methane has
strong vibrational absorption bands in the mid-infrared and considerably
weaker bands in the near infrared^[1]. By resonantly coupling into one of
these bands, methane molecules can be brought to a very high vibrational
temperature, far out of equilibrium with translational/rotational
temperatures. The hope would be that we could pump enough energy into
vibrational modes such that methane molecules become extremely reactive,
and either pyrolyze or react with oxygen molecules to form CO₂.

The ceiling for success of this strategy depends on timescales. The
first relevant timescale is the vibrational-vibrational (VV) relaxation
time, i.e. the time over which optically excited molecules redistribute
their vibrational energy amongst the various vibrational modes to form a
thermal distribution; I suspect this timescale is ~1 ns^[2]. The second
(and perhaps most) relevant time scale is the vibrational-translational
(VT) relaxation time, which is the time it takes for the energy pumped
into the vibrational modes of CH₄ to bleed out into the translational
energy of the gas—i.e., how long before you’ve effectively just heated
the bulk gas. The VT timescale appears to be ~10 microseconds for dilute
CH₄ in diatomic gas at STP (e.g., [2]). To get something interesting to
happen, we should pump few-eV-scale energies into the molecule before
the VT time; perhaps bonus points if you can get few-eV-scale energies
in before the VV time. (Of course, there’s no guarantee that highly
vibrationally excited methane becomes adequately reactive for our
purposes—this part is still a leap of faith. But VT non-equilibrium
seems to be quite enabling in the domain of plasma chemistry.)

What sort of laser setup could we use to pump ~3 eV into vibrational
modes of methane within 10 us? Let’s first consider exciting the
near-infrared overtones, because this is where cheap and efficient solid
state lasers (and somewhat less cheap and efficient fiber lasers) are
available. Here the optical cross-sections are ~1e-23 cm². We would
require an intensity of at least 3 eV/(10 us*1e-23 cm²) = 5 GW/cm².
This is a huge intensity, but it’s at least imaginable to achieve by
focusing a large array of diode bars^[3]. The main trouble is that we
also require most of the light to be absorbed by the gas, or else we’ll
blow through our energy budget; even for 0.1% methane in air, this takes
10-100 km of propagation^[4]. We could try to build a high-Q resonator
that helps with this, but even if we could, it would be a bad idea for
an environmental application, as the optical surfaces would quickly get
dirty and ruin the resonator^[5].

The mid-infrared modes (3.3 um, 7.6 um) are more interesting targets
because the optical cross-sections are a hundred thousand times larger:
~1e-18 cm². The needed intensity is ~50 kW/cm², and if tuned exactly
on resonance^[6], light will be absorbed within a meter for 0.1% methane,
10 meters for 0.01% methane, etc. These are much more reasonable
figures. The challenge with this wavelength range is the lack of a
suitable light source. Quantum cascade lasers can operate around 7.6 um,
but their efficiencies are typically 5-10%, they cost something like
$1000/W, and they are not particularly bright. Another option might be
to build an optical parametric oscillator pumped by a (possibly pulsed)
fiber laser [4]; the fiber laser would probably set the cost at around
$20/W in volume, and I suspect the efficiency would again not exceed
10%. In any of these cases we’d have to be clever with the optics to
ensure that the beam didn’t diverge too quickly, etc. I’ll ignore these
very important practical issues for now.

Let’s say we have a 10% efficient light source in the mid-IR, and that
the science works super well such that 3 eV supplied per molecule leads
to 100% destruction of CH₄. We’re already at an electricity consumption
of 30 eV/molecule = 50 kWh/kg CH₄ removed. This slightly exceeds our
budget for electricity from natural gas, but is below our budget for
solar electricity. Would we be able to make money doing this? Let’s
assume that we use solar electricity that costs $0.04/kWh and carbon
credits are $100/ton CO₂. Accounting for our electricity emissions at
0.05 kg CO2_e/kWh, removing 1 kg CH₄ is equivalent to removing 80 kg CO₂.
The electricity cost is 50 kWh/kg CH₄ * $0.04/kWh = $2/kg CH4 = $25/ton
CO₂, so this leaves us some wiggle room for our cap-ex. If our capital
equipment lasts 20 years and is operated at a 25% duty cycle (because
we’re using solar), it consumes 440 kWh per rated optical watt (remember
it’s 10% wall-plug efficient) over its lifetime. If we want electricity
cost to roughly equal cap-ex (that leaves us about $50/ton CO₂ for other
op-ex and profit), the cost per optical watt should be $0.04/kWh * 440
kWh / optical W = $18 / optical W.

Looking back to our laser estimates, if we can really build a suitable
mid-IR OPO from a fiber laser for $20/W, and if carbon credits really
become $100/ton CO₂, and if all science works out perfectly, and if all
of the other little issues I swept under the rug are resolved, this very
crude analysis suggests that we’d be in business.

Of course things would look a lot better if you started by working with
a higher concentration of methane. If you went to places like cattle
barns, exhaust streams, or LNG handling areas with >1% CH4, this laser
gambit looks like it’d be well in the money even in a <$10/tCO_2e subsidy
environment. However, you’d still be talking about a small and
subsidy-dependent business, with a challenging MRV (Measurement,
Reporting & Verification) situation. A cool opportunity perhaps, but clearly not
the startup idea we’ve been looking for.

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References

[1] P. B. R. Nisbet-Jones et al., “Is the destruction or removal of
atmospheric methane a worthwhile option?,” Phil. Trans. R. Soc. A., vol.
380, no. 2215, p. 20210108, Jan. 2022, doi: 10.1098/rsta.2021.0108.

[2] J. T. Yardley and C. B. Moore, “Vibration→Vibration and
Vibration→Translation Energy Transfer in Methane‐Oxygen Mixtures,” The
Journal of Chemical Physics, vol. 48, no. 1, pp. 14–17, Jan. 1968, doi:
10.1063/1.1664460.

[3] H. H. Lim and T. Taira, “Sub-nanosecond laser induced air-breakdown
with giant-pulse duration tuned Nd:YAG ceramic micro-laser by
cavity-length control,” Opt. Express, vol. 25, no. 6, p. 6302, Mar.
2017, doi: 10.1364/OE.25.006302.

[4] T. Ren, C. Wu, Y. Yu, T. Dai, F. Chen, and Q. Pan, “Development
Progress of 3–5 μm Mid-Infrared Lasers: OPO, Solid-State and Fiber
Laser,” Applied Sciences, vol. 11, no. 23, p. 11451, Dec. 2021, doi:
10.3390/app112311451.

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