Bubbling ship exhaust into the ocean

Consider a fairly typical CO₂ molecule that leaves a tailpipe, spends 500 years in the air absorbing IR photons and warming the earth, and then dissolves into the ocean more-or-less permanently^[1]. Based on almost any proposed social cost of carbon, most of the harm from that emitted CO₂ happens when it’s in the atmosphere, and much less when it’s in the ocean. So in situations where we must emit CO₂, would it not be less harmful to short-cut the atmosphere part and emit the CO₂ directly into the ocean, rather than into the air?

Say you wanted to decarbonize global shipping. That would mean redesigning big boats like Suezmax cargo ships, 200 million kg monsters with 30MW engines that can go weeks at a time on the very cheapest fuels, fossil sludge so thick it’s almost asphalt.

The obvious question is whether we can electrify the ships with batteries, or perhaps power them with alternative fuels. Smart people disagree but electrifying a Suezmax ship might take 60 million kg of Li-ion batteries^[2], multiplying its cost and cutting its cargo capacity by almost half. That’s a hard sell. And the other straightforward decarbonization options – e-methanol, ammonia, biofuels —are to varying degrees even worse. That’s why there’s been hardly any progress in decarbonizing heavy marine transport.

When the obvious questions give stupid answers, it’s time to ask stupid questions. Heavy fuel oil is cheap and modern two-stroke marine diesels are amazingly economical to run. Much of that carbon is going to end up in the ocean anyway, and for a ship the ocean is right there, ready to absorb the CO₂ emissions before they do too much harm. So what happens if you just bubble ship exhaust into the ocean?

Would the CO₂ dissolve into the ocean at all?

[TLDR for this section: yes, easily and completely]

A below-waterline exhaust system would probably be combined with bubble-hull lubrication, and those systems typically work with millimeter-scale bubbles, so for these estimates we consider bubbles of radius 1 mm. We assume that pressure, temperature, and volume are constant and that the water is pure. For the pressure, we will find that most of the CO₂ dissolves in the first meter of the bubble’s motion, which corresponds to a pressure change of no more than 10%. The bubble thermally equilibrates with the ocean on a timescale of ~0.1 s, so we can treat the temperature as constant. Then only mass transfer would change the volume, but ship exhaust is 5% CO₂ by volume. Most of the remainder is insoluble nitrogen, so CO₂ dissolution will not reduce the volume significantly. Finally, the marine mixed layer is in equilibrium with 400 ppm CO₂, so it is heavily undersaturated relative to 5% CO₂. We can thus approximate it as pure water.

Using empirical estimates of drag coefficients, we find a typical vertical terminal velocity of 0.2 m/s in still water. We ignore the flow induced by the ship’s motion, and assume that all bubbles rise at 0.2 m/s.

Because the bubble surface area remains approximately constant, the rate of dissolution is proportional to the concentration of CO₂ remaining in the bubble. The concentration thus decays exponentially; we estimate its half-life. By Fick’s law, the rate of dissolution is proportional to the normal derivative of the aqueous CO₂ concentration at the bubble’s surface. This gradient is enhanced by the bubble’s velocity, as the moving fluid sweeps dissolved CO₂ away from the bubble.

The nature of the background fluid flow has a large effect on the rate of mass transfer. Large bubbles maintain free boundaries with large fluid velocities parallel to the surface. This advection greatly enhances mass transfer. However, small bubbles quickly become contaminated by surfactants that rigidify the surface. This leads to a no-slip fluid boundary condition, which damps the advective enhancement of dissolution. Empirically, the transition from small to large occurs at the millimeter scale, so our bubbles lie in a complex intermediate mass transfer regime.

We draw on theory and experiment for rigid and free bubbles to estimate the rate of mass transfer. We find a half-life of about 1s for the CO₂ concentration. This estimate is within 40% of various experimental results. In particular, Olsen et al. (2017) study small (r < 400 µm) CO₂ bubbles in seawater, and remark that “due to the high solubility of CO₂, the bubbles are depleted of CO₂ within seconds.”

During the 1s half-life, the bubbles rise 0.2 m. We refer to this as the “half-distance.” We plot this distance over a wider range of bubble size:

Approximate half-distance for millimeter-scale bubbles.

At this scale, the half-distance is roughly 100 radii. The curve is non-monotone due to the transition from rigid to free bubbles.

According to this estimate, once the bubbles have risen 1 m, they have lost > 95% of their CO₂. This justifies our assumption of constant pressure, as the relevant part of the process occurs in a narrow pressure range. Moreover, a ship would inject bubbles at least several meters below the waterline (typical drafts are 10-15m for medium to large cargo vessels). Therefore, our calculations suggest that nearly all the exhaust CO₂ will enter solution before it reaches the ocean surface. This conclusion is robust to moderate (order one) changes to the assumptions above.

Throughout, we have assumed that the background concentration of CO₂ in seawater is zero. This would break down if the exhaust saturated the water surrounding the ship. As a test case, we consider a 350 m long 100k DWT container ship loaded to 60k tons steaming at 16 kn. At a typical engine load of 23 MW, it produces about 50 m³/s (55 kg/s) of exhaust. The dimensionless constant in Henry’s law for CO₂ at STP is close to 1, so the ship exhaust would saturate about 20 m³/s of seawater. On the other hand, the ship displaces about 1400 m³/s of seawater through its forward motion. Thus, if the exhaust perfectly mixed in the displaced volume, it would be 30x undersaturated. This would not significantly slow dissolution. Perfect mixing seems unlikely, but 5% mixing would suffice.

How long would the CO₂ stay in the ocean?

[TLDR for this section: in most cases less than 10% of the CO₂ would still be in the ocean after 100 years]

To estimate how long the dissolved CO₂ from the ship will stay in the ocean, we added CO₂ to the top layer of the UVic Earth System Climate model and compared its evolution with an unperturbed model run. This is roughly equivalent to increasing the CO₂ concentration uniformly in the first 50 m of the global ocean. After spatial averaging, the results agree well with a one-dimensional diffusion model on the half-line with zero boundary data (signifying the unperturbed atmospheric concentration).

Blue —total CO₂ that has outgassed to the atmosphere in the UVic model.
Gold — exponential fit. Green — 1D diffusion fit.

Because the UVic model is nearly linear, these results closely approximate the geographical mean of outgassing. Only about 5% of the CO₂ remains in the ocean after 100 years^[3]. This is no surprise—we are injecting CO₂ into the mixed layer of the ocean, which is nearly in equilibrium with the atmosphere. Only a small fraction of the CO₂ remains isolated from the atmosphere after decades. This fraction likely corresponds to carbon that has diffused downward across the thermocline.

The mean sequestration rate is low, but we expect some areas of the ocean to retain much more carbon due to downwelling. To test this hypothesis, we examine the spatial distribution of the pulse carbon that has moved below 200 m in the early stage of the UVic model run.

Concentration of excess CO₂ below 200 m depth in UVic model 20 years after pulse. This approach to CO₂ persistence came from Ken Caldeira, and the simulations were conducted with Long Cao.

These results reflect the strong downwelling in the subpolar North Atlantic. Given the high degree of heterogeneity, it seems reasonable to conjecture that the North Atlantic sequesters carbon several times better than average. If this is true, 10–20% of North Atlantic ship exhaust could remain sequestered for 100 years^[4].

The North Atlantic hosts about 10% of global shipping, so a worldwide implementation of the ship-bubbling strategy might sequester 5-7% of global shipping emissions. Since global shipping emits ~1 GtCO₂/yr, that makes bubbling ship exhaust into the ocean a <100 MtCO₂/yr strategy.

But it might be cheap

The idea of a retrofit to discharge engine exhaust underwater sounds like it’d be pure hassle to a shipbuilder, with no economic rationale. But there are two reasons it might be a net moneymaker:

Sulfur scrubbing

In 2020, the International Maritime Organization tightened restrictions on sulfur content in ship exhaust. Setting aside for now the question of whether desulfurization is indeed beneficial for the environment^[5], it set off a scramble among ship owners: to either begin purchasing low-sulfur (0.5% rather than ~3%) fuel, which increases fuel costs by as much as 40%, or else to install sulfur-scrubbing systems, which cost about $2-4M.

Some scrubbers are “open loop”—spraying seawater into the exhaust stream to capture sulfur dioxide in solution, and continuously dumping the water overboard. “Closed loop” variants sometimes include a consumable base to increase the concentration of the discharge solution. However, in both cases, all of the sulfur is eventually discharged to the ocean as an acidic solution.

Based on the 2 order of mag higher solubility of SO₂ than CO₂ in seawater (~100g/L vs ~2.5g/L at 10ºC), we expect that a below-waterline exhaust system would meet both the air-release and water discharge standards set forth by the IMO without employing any separate sulfur scrubbing system.

Air lubrication

Bubbles released underneath a ship hull can substantially decrease hydrodynamic drag, by effectively decreasing liquid density and viscosity. So-called “air lubrication systems” are a fairly mature technology that generally increase fuel efficiency from 5-20%. Air lubrication systems are standard on new Royal Caribbean vessels, and have been installed as retrofits and as built-in components of Panamax and Suezmax vessels.

One cool technical aspect of ship air lubrication systems is that no specialty nozzles or other gizmos are required to create the carpet of 1-3mm bubbles. Rather, air is pumped into passive cavities in the ship hull, from which a Kelvin-Helmholtz instability at the liquid-air boundary creates the bubble-water mixture.

The obvious thing to do is plumb the ship's engine exhaust into air lubrication systems that are already used improve hydrodynamics on cargo ships. Silverstream air lubrication retrofit (left). Mitsubishi air lubrication system (right). Source: Fotopolous et al.

The amount of air typically used for lubrication is at the low end of usual exhaust flow rates for a ship of a given size. In one study of the Foreship air lubrication system on a cruise ship, 10kg/s of air were provided at 0.9 bar pressure, for a 7% fuel savings at an engine power of 20MW. At 20MW power and a typical specific fuel consumption of 0.16 kg/kWhr, the exhaust flow rate was ~50kg/s—on the same order but higher than the typical demand for lubricating air. For other ship hull-engine combinations (notably cruise ships, which burn a lot of fuel in order to generate electricity) more exhaust is generated than would be required for air lubrication systems. We haven’t seen investigations of air lubrication in higher air-flow regimes; if it turned out to be unhelpful or uneconomical to increase the amount of lubricating air to match the exhaust flow rate, then you’d be faced with only mixing a portion of the exhaust into the ocean; if this fraction fell below about 80%, you’d lose the ability to use full-sulfur fuel without an additional scrubbing system.

You might spitball that using ship exhaust in an air lubrication system might cost a little less than installing separate air lubrication and sulfur scrubbing systems[6]. That means that as near as we can tell, bubbling exhaust into the ocean might pay for itself on air lubrication and sulfur scrubbing benefits, meaning the CO₂ reduction comes for free.

Still, nobody is going to do this

So bubbling ship exhaust into the ocean might be a way to eliminate 5-7% of cargo ship emissions at near zero cost. Combine the new exhaust system for bubble-carpet lubrication of the ship’s hull and the thing could even be a moneymaker. But we don’t think anybody is going to do it.

First, if the shipping industry had the gumption for this type of complex re-engineering of their ships for the sake of emissions reduction, there is a lot of lower-hanging fruit they’d already be tackling. The biggest one is sailing slower. Bulk carriers (as opposed to container ships) are the vast majority of total ocean freight and they don’t need to move fast; if electrification and automation can reduce crew needs, then massive energy savings could offset the increased crew and capital costs of going slower (half the speed takes a quarter the energy but costs double for ship and crew). Even without going slower, there are a lot of efficiency improvements that have been developed (amazing list page 102)^[7] that could easily add up to a 25% decrease in fuel consumption without major cost or speed changes—effective but unsexy stuff like optimizing itineraries, improving propellers or hull design, measuring fuel flow better etc.

But the shipping industry isn’t doing these things. Like with so many old global industries, shipping companies operate like money printers. People employed on the money printer are disincentivized from throwing any wrenches in it. Shippers probably accept poorly optimized ships to reduce schedule risk; shipyards are probably willing to give you a fixed price bid on ship design they’ve built hundreds of times, but one with efficiency features probably comes with all sorts of contract caveats. This means a clean-sheet electric or hybrid-electric design probably isn’t quite as unlikely as the basic math might make it seem, since it will be able to incorporate lots of efficiency-boosting design features that conventional ships have been slow to adopt. But it leaves a complicated but incremental improvement like a combined air lubrication / sulfur scrubbing / exhaust bubbler system a hard sell.

We also doubt that the world would view the “ship bubbles” strategy too favorably even if someone is willing to build it. People can be weird about trading one harm for another^[8]. Ocean acidification is a harm that you’d be guilty of explicitly^[9], while CO₂ emissions are priced in as a pre-existing global problem that you can’t meaningfully be singled out for, since everyone’s already complicit to some degree. People might see you as the bad guy for mainlining kilotons of toxic exhaust into the ocean, even if you could wave pages of math at them proving that it was going to wind up there anyway, and that you were reducing net harm versus releasing it to the atmosphere.

Overall, we’re looking for startup opportunities and this clearly isn’t one. Since 5-7% is a low overall sequestration fraction and suffers a built-in PR problem, we doubt that there would be any takers for this strategy. An additional problem is that the gambit offers many marginal value centers (sulfur scrubbing, air lubrication, CO₂ mitigation), but no single clearly winning aspect that could serve as lynchpin of a go-to-market strategy. Not worth pursuing :(.

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References

[1] Vaclav Smil, Prime Movers of Globalization, MIT Press, 2010.

[2] J. E. Olsen, D. Dunnebier, E. Davies, P. Skjetne, and J. Morud, “Mass transfer between bubbles and seawater,” Chem. Eng. Sci., vol. 161, pp. 308–315, Apr. 2017, doi: 10.1016/j.ces.2016.12.047.

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[7] Higbie, R, “The rate of absorption of a pure gas into a still liquid during short periods of exposure,” Trans AIChE, vol. 31, pp. 365–389, 1935.

[8] F. Takemura and A. Yabe, “Rising speed and dissolution rate of a carbon dioxide bubble in slightly contaminated water,” J. Fluid Mech., vol. 378, pp. 319–334, Jan. 1999, doi: 10.1017/S0022112098003358.

[9] F. Deindoerfer and A. Humphrey, “Mass Transfer from Individual Gas Bubbles,” Ind. Eng. Chem., vol. 53, no. 9, pp. 755–759, Sep. 1961, doi: 10.1021/ie50621a035.

[10] International Maritime Organization, 2010 Guidelines for Exhaust Gas Cleaning Systems, MEPC.259(68), Section 10.1, 2015.

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[15] P. K. Patankar and S. T. Siingh, “Effect of aerosols on cloud formation over marine environments,” J. Atmos. Sci., vol. 57, no. 16, pp. 2684–2699, 2000. [Online]. Available: https://journals.ametsoc.org/view/journals/atsc/57/16/1520-0469_2000_057_2684_eoaoca_2.0.co_2.xml

[16] C. Paris, “Maritime emissions rule triggers split in shipping costs,” The Wall Street Journal, Dec. 23, 2019. [Online]. Available: https://www.wsj.com/articles/maritime-emissions-rule-triggers-split-in-shipping-costs-11576839601.

[17] Bryan Comer and Dan Rutherford, “Air and water pollution from ships with scrubbers,” The International Council on Clean Transportation (ICCT), Jan. 2020. [Online]. Available: https://theicct.org/publications/air-water-pollution-scrubbers-2020.

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