Berkeley lab-led team works on storing CO2 underground to extract electricity

Aug 09, 2011 By Dan Krotz
This looks like a maze, but it's actually a schematic of a way to combine CO2 storage and geothermal energy production. Starting with CO2 on the left, follow the arrows to learn how the proposed pilot test will work.

About a year from now, two nondescript shipping containers will be installed in a field in Cranfield, Mississippi. They’ll house turbines designed to generate electricity in a way that’s never been done before. If initial tests go well, the technology could lead to a new source of clean, domestic energy and a new way to fight climate change.

A team led by Lawrence Berkeley National Laboratory (Berkeley Lab) scientists hopes to become the first in the world to produce electricity from the Earth’s heat using CO2. They also want to permanently store some of the CO2 underground, where it can’t contribute to climate change.

The group received $5 million from the Department of Energy earlier this summer to design and test the technology.

“This is the first project intended to convert geothermally heated CO2 into useful electricity,” says Barry Freifeld, a mechanical engineer in Berkeley Lab’s Earth Sciences Division who leads the effort.

The idea is to inject CO2 three kilometers underground into a sedimentary layer that’s 125 degrees Celsius. CO2 enters a supercritical state under these conditions, meaning it has both liquid and gas properties.

The CO2 will then be pulled to the surface and fed into a turbine that converts heat into electricity. Next, it will loop back underground and through the cycle again. Over time, some of it will be permanently trapped in the sediment. More CO2 will be continuously added to the system to keep the turbines spinning.

The technology could help offset the cost of geologic carbon storage, a promising climate change mitigation strategy that involves capturing CO2 from large stationary sources and pumping it deep underground. This enables the burning of fossil fuels without releasing the greenhouse gas into the atmosphere. But it’s expensive.

“Carbon storage takes a lot of power – large pumps and compressors are needed. We may be able to bring down its costs by generating electricity on the side,” says Freifeld.

It also offers a new way to tap geothermal energy, which is a tough sell in arid regions where every drop of water is spoken for. For more than a decade, scientists at Berkeley Lab and elsewhere have theorized that supercritical CO2 can be used instead of water. Their work has shown that supercritical CO2 is better than water at mining heat from the subsurface. But no one has tried to do it until now.

In the project’s first stage, Ohio-based Echogen Power Systems will design a turbine that can handle “dirty” supercritical CO2 laden with hydrocarbons and water accrued during its subsurface journey. Scientists from the University of Texas at Austin will analyze the environmental impacts of the process over its entire life span.

Berkeley Lab scientists will use numerical models to predict how the reservoir will evolve over time as more and more CO2 courses through it. They’ll also determine how much energy can be extracted from the CO2 by coupling reservoir models with Echogen’s turbine models.

In the second stage, the team will build and test the turbine. If that goes well, they’ll operate it during a pilot test at the Southeast Regional Carbon Sequestration Partnership’s Cranfield site, where a Department of Energy-funded CO2 injection project has been underway since 2009. The site’s three-kilometer deep reservoir has proven to be an ideal site for carbon sequestration. Much of the infrastructure needed for the test is already in place, including injection and production wells. The CO2 will come from a pipeline operated by Texas-based Denbury Resources.

It’s too early to tell how much electricity the technology can generate in the U.S. That depends on the scale of carbon capture and storage operations and the availability of deep reservoirs that can both heat and store CO2.

The technology also takes advantage of a problem common to conventional geothermal energy. Between five and ten percent of the water injected in these systems is “lost” as it travels through the pore spaces. As this happens, more water must be added, perhaps from municipal sources that have little to spare.

“But we actually want some of the CO2 to become trapped,” says Freifeld. “Our approach relies on this gradual loss as a way to store a power plant’s CO2 underground rather than emitting it into the atmosphere. Our planned demonstration is the first attempt at proving that we can simultaneously mitigate greenhouse gas induced and generate clean baseload power using .”

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Techno1
2.3 / 5 (3) Aug 09, 2011
LOL.

Must be other articles about this on the WEB already.

Apparently, lots of people just Googled CO2 phase diagram, or else Google predicted I was going to search it... scary stuff...
Techno1
1 / 5 (4) Aug 09, 2011
Slightly irrelevant, but not quite, since they mention GW and CO2...

http://en.wikiped...ki/Earth

Coldest surface temp: -89.2C

Sublimation point for CO2: -78.5C @ 1 atm...

That's 10.7C colder than the Sublimation point of CO2..

I've never noticed this before.

Has anyone else?

CO2 freezes out at the South Pole AT THE SURFACE during the coldest winters?

If this is the case, there could be MOTHERLOADS of CO2 trapped under lays in the water-ice in the South Pole, or in gas bubbbles in the ice, since the upper troposphere is also below the sublimation point on some occasions...

So if this is happening, why hasn't this been detected or talked about as much publicly?

10.7C below the sublimation point is a very big deal, and implies getting below the sublimation point could even be a common occurence.

How much CO2 is trapped in water-ice in antarctica?
Techno1
1 / 5 (3) Aug 09, 2011
This Explains why historical and pre-historical concentrations of CO2 in the atmosphere and ocean are deflected to a lower slope on the Keeling curve after a VEI 6 eruption, and go negative after a VEI 7 eruption (Toba, Taupo, Tambora, etc.)

I found a graph a few days ago that I didn't quite understand, because the corelation between volcanism and CO2 seemed at the time to be opposite of what you would expect intuitively.

You would expect that if plants die off after a volcano, then CO2 would go UP, since there wouldn't be anything removing CO2 from the atmosphere.

However, according to the chart anyway, CO2 went down enormously after Toba, and then hit almost rock bottom after Taupo.

If all the plants were dead/dying, then the only place this CO2 could have gone is sequestration in Greenland and Antarctic Ice Caps during the peak of the Ice Age.

This suggests Antarctica may contain several dozen to several hundred Parts Per Million equivalent of CO2 trapped in the Ice.
Techno1
1 / 5 (4) Aug 09, 2011
If this is the case, then there should actually be entire layers of CO2 ice, at least in some locations, at the Toba and Taupo layers in antarctic ice.

Some of it may have already outgased or tunneled through the water-ice, or be trapped in bubbles...

But you should theoretically be able to find actual layers of CO2 ice, if you take cores in the right locations.

What they would need to do is find the Toba and Taupo layers at the most heavily protected, deepest, and shaded locations in the ice caps and take core samples in those locations, and QUICKLY get them inside containers before the CO2-ice warms.

CO2 should be in concentrations as high as 0.4 grams to FOUR grams per square centimeter of surface area (with respect to the actual ground level surface of the ice,) near these coldest, most protected locations, and sequestered "somewhere" between the Toba layer and a few years after the Taupo layer...assuming little or no out-gasing since then...

continued...
Techno1
1 / 5 (3) Aug 09, 2011
The amount of 0.4grams to four grams mentioned above depends on how bad the freeze-out really was.

If it was a near-total freezeout of CO2 over several years, as data suggests, then we could be talking about as much as 300 to 400 parts per million equivalent stored in the ice, at least initially.

This would be close to 4 grams per centimeter of ground level surface area in the densest, most protected samples, where the least melting and out-gasing would have occured.

Even if half of the gas has already escaped since then, there would still be as much as a few dozen to 200 parts per million equivalent in the ice.

Any significant melting of antarctica would release this CO2 into the atmosphere, adding 50, 100, even 200 PPM CO2, and would make the existing Keeling Curve look like a square dance.
Techno1
1 / 5 (3) Aug 09, 2011
Yeah, check this:

http://www.esrl.n.../trends/

The minimums in the Keeling Curve corespond to late SEPTEMBER, which is the boundary of the Northern hemisphere summer and autumn, and the Southern Hemisphere Winter and Spring.

This is in EXACT agreement with the above hypothesis that Antarctica may experience partial freeze-outs of CO2 during the coldest days of winter (and in some cases, the CO2 may be permanently trapped under water-ice).

Forgive my ignorance, but I do not know if anyone else has ever noticed this, so I don't know...

This suggests around 60% of excess CO2 gets frozen out during the winter (as opposed to the notion that seasonal variation in plant life somehow accounts for this).

That is, humans and other sources are actually releasing around 5 or 6 parts per million excess per year, but Antarctica permanently traps 3 or 4 parts per million equivalent during it's winter.
Techno1
1 / 5 (3) Aug 09, 2011
So if 50 to 200PPM remained trapped from Toba and Taupo...

Then in modern times, CO2 has risen 80PPM, but antarctica was secretly hiding 60% to 66% of excess, then that would mean another 120 to 160PPM has been sequestered in the past hundred years or so.

This means Antarctica COULD hold between 170PPM and 360PPM equivalent of CO2 trapped in the coldest ice near the South Pole...

I find that humans ACTUALLY make 2PPM equivalent per year from oil alone, not even counting Coal and Natural gas at all.

So what the Keeling curve actually shows is human beings and other processes are producing an excess of 5 or 6 PPM equivalent per year, and Antarctica, NOT PLANT LIFE, is sequestering 60% to 66% of the excess during it's winter, leaving a total net excess of 2PPM equivalent per year, which we get from Oil alone.

Therefore, once warming reaches the point where freezeout no longer occurs, the keeling curve will grow at least 3 times faster than it does now, if not ten times...
Techno1
1 / 5 (3) Aug 09, 2011
To test this, is very simple.

We need to take several cores which would be used for no purpose other than to be destroyed, plus a few backups.

You would take the core from the most protected locations possible from Toba and Taupo to present day, then put it in a vaccuum-sealed container and watch it melt, and then measure the amount of CO2 released.

If you take this entire core from Toba to present and melt it down, the CO2 released should be at least 0.4 gram PER CENTIMETER CROSS-SECTIONAL AREA, and as much as 4 grams, from Toba and Taupo alone, and plus about another gram or two from MODERN times...

This might not have been detected as drastically in the past, because ordinarily, core samples are preserved as near-perfectly as possible.

Nobody would "normally" take a core and then destroy the whole thing in air-tight containment to get a complete count of CO2 in the entire record...

But that's exactly what needs to be done to test this hypothesis...
Techno1
1 / 5 (3) Aug 09, 2011
Yeah, I got about another 2 parts per million from Coal alone, so not counting livestock and other stuff, like concrete production.

So just Coal Oil = 4 PPM equivalent per year made by man.

Thus we automatically know from this that the downswing of the Keeling Curve proves Antarctica is sequestering at least 2 PPM equivalent per year during it's coldest cold snaps.

Whenever temperatures get warm enough that this can no longer happen, the Keeling Curve's slope will become less jagged, but will rise to an average slope of between 4 and 6...

After a few more decades, Antarctica will warm enough to begin out-gasing all of the CO2 it has sequestered since Toba.

The Keeling Curve's slope may easily exceed 10 or more when this starts to happen, probably within a few centuries, and possibly even within some of our lifetimes...
Techno1
1 / 5 (3) Aug 09, 2011
They completely ruined these samples...

http://en.wikiped...e37.jpeg

They could not have known...

If they pulled these samples, and they are standing around outside during a warm season, which is obvious since it's daylight, then any CO2 that may have been included out-gased while they stood around like fools, smiling for the camera...

The samples must be taken in the coldest days in Winter, and they cannot be exposed like that, even though it's "below freezing". It needs to stay as cold as possible, preferably below the sublimation point...

They could not have known...what a waste...

The record monthly low temperatures at Vostok are below the sublimation point for 6 months out of the year.

The average lows are near the sublimation point for 6 months out of the year.

Since the sublimation point is several degrees warmer than most of these records, this makes my hypothesis plausible, even highly probably, and provable...
thermodynamics
5 / 5 (3) Aug 09, 2011
Techno1: Have you ever heard the term: "partial pressure?" The problem with your dissertation you just wrote is that it would only be correct if there were a high partial pressure of CO2. With the partial pressure as low as it is in the atmosphere it cannot freeze out until you reach temperatures where oxygen starts to condense. Go back and take a look at a calculation with a partial pressure of 360 ppm of an atmosphere. You will find that the CO2 is cold enough to condense but can't because the partial pressure is too low and the molecules are bouncing off faster than bouncing on.

Here is a web site that talks about phase diagrams and shows the CO2 phase diagram. You have to continue down the two-phase line when you drop partial pressure. I hope that helps.

http://stevengodd...-part-2/

Techno1
1 / 5 (2) Aug 09, 2011
To find what I'm talking about, if it's happening at all, the sample needs to be pulled on preferably the coldest day of the year, which is going to be during the perpetual night time of the antarctic winter.

They will need a NOAA quality computer weather simulation to find the location where the combination of temperature and pressure are most likely to drop below the sublimation point at near-record-low temperatures.

They will then need to take a team of scientists or a robot out in this and drill the core sample and immediately put it in an air-tight container, preferably within a few seconds of pulling it out of the ice.

Again, the samples needs to be taken on the coldest day of the year, from the most highly protected and pristine area they can find, and at a location that a highly sophisticated NOAA quality model shows most likely to have a surface temperature at or below -78.5C on that day...
xznofile
not rated yet Aug 09, 2011
wait: How did it get concentrated in Antarctica? It was likely dispersed more or less equally over the rest of the world.
Techno1
1 / 5 (2) Aug 09, 2011
Thermo:

Maybe...

but...

Seems fallacious, because it assumes a static system, instead of the dynamic system with wind driven snow.

Consider above, I suggest the CO2 would get covered over by water-ice quickly, thus being impossible to get back into the atmosphere in equal amounts, at least in the short term...

But nobody's ever actually tested what I'm talking about.

I've certainly never heard anyone talk about it or mention it.

How do you know a CO2-ice crystal isn't freezing to an water-ice crystal, either directly on the surface, or in the air and falling out of the air, getting covered over?

There's no good reason that can't be happening, until you test it and prove it, because temps and pressures should allow it...

Even if it isn't happening in modern times, during the ice age when ice covered 1/3rd of the earth, the average albedo would be almost 10 points higher, and what would the temps be in antarctica? It'd easily freeze CO2 out after Toba, easy
Techno1
1 / 5 (2) Aug 09, 2011
wait: How did it get concentrated in Antarctica? It was likely dispersed more or less equally over the rest of the world.


Simple:

If the CO2 is freezing out in antarctica more than it sublimates back away, then over time it just becomes a bit of a "depositional environment" for CO2, the same way sediment would be at the mouth of a river...

The CO2 from everywhere else in the atmosphere would gradually be transported there by gas laws over several years, decades, or centuries after the super eruption(s)...

It would then freeze out during the winter, especially during the Ice Ages, and then get covered by water-ice so that it doesn't escape during the summer...

Ok, just look at water-ice caps at the poles, like the sea ice...

the CO2 in the atmosphere would behave in a similar way as water at the poles:

freezing out in winter, but thawing in summer (unless it gets covered by water-ice, in which case it would be permanently trapped).
Techno1
1 / 5 (3) Aug 09, 2011
When water-ice freezes out of the atmosphere, we call it a "blizzard"...

It can dump FEET of water-ice in a matter of hours or days, and this barely effects global partial pressures of water vapor.

CO2 would be the same. It would take several weeks or months before it would be noticed globally, because the ice caps are only about 1/10th of the earth's surface.

You're not going to freeze out the entire CO2 portion of the atmosphere in a few years. It would take centuries to do that, even after Toba and Taupo, because you need the winds and gas laws to dradually transport the CO2 through the atmosphere before it freezes out.

Freezing out drives down partial pressure locally, which would then be replaced by diffusion from other locations in the atmosphere over a period of months or years, only to be frozen out again...

If the record low is 10C below the sublimation point, how could anyone say this isn't possible until they actually take the samples and test it?
Techno1
1 / 5 (2) Aug 09, 2011
Plus, they've only got a handfull of thermometers on the entire continent of Antarctica.

Aside from infrared satellites, how do they know there aren't other locations near the South Pole which regularly have overnight lows near the Sublimation point, and have "Would-be-record lows" below -80C? (That is, had an instrument been there to record it...)

The real world doesn't obey ideal gas laws, particularly when you throw in phase changes and precipitation.

Turbulence and crap like that allows freaky things in nature, like hail stones.

I'm not saying this is definitely happening in large quantities, though it probably is.

But given the temperatures, and given Murphy's law, "Whatever can go wrong will go wrong," it almost certainly IS happening in isolated situations.

The hail storm is a good comparison.

How do you know the CO2 ice isn't getting buried under "drifts" of water-ice, unless you actually test it, in the heart of winter, so the CO2 doesn't vaporize?
Techno1
1 / 5 (2) Aug 09, 2011
I'm not picking on the scientists, but they clearly could not detect this if they pulled these samples in the warm season.

If pulled during the warm season, most of the excess CO2 would out-gas and not be detected (especially while they were standing around taking a photo...), particularly since they would never have thought of trying what I suggested under "normal" ice core science.

0.4 to 6 grams per centimeter squared cross-sectional area, SINCE TOBA, is not a lot, and would not be noticed by ANYONE unless the sample was taken in Winter and specifically looking for it.

This amount of CO2 could out gased from those cores between the drilling, the summer time "heat", and standing around, and nobody would have even known any difference. they probably didn't think about looking for it anyway.
Techno1
1 / 5 (2) Aug 09, 2011
To the argument of whether it could actually happen:

The conditions are there:

CO2 present, yes.
Temps below sublimation point, definitely.

The signature from Toba, Taupo, Tambora, and maybe Thera and Pinatubo should be there, assuming the sample is kept below the sublimation point...

Even if the "normal" Keeling Curve signature cannot be found in the ice, the volcanic signatures should be there in the heart of the ice ages...

How cold do you think Vostok was immediately after Tambora in the "year without a summer"? How about Thera? Taupo? Toba?

10C colder? 20C? 30c (Toba/Taupo)?

if the earth had thrice as much ice caps, just how cold was it at the South Pole, during "winter" during the Ice Age after Toba and Taupo?
Techno1
1 / 5 (2) Aug 09, 2011
I found that if the ice during the ice age was thrice as much as the ice caps now, in terms of area, then the average albedo of the Earth was 10 points higher.

this would mean that the average temperature of the earth would be on the order of 27C to 29C colder, not counting the fact that the CO2 MUST have frozen out immediately after Toba and Taupo if the ice covered 30% of the entire planet...

Some of this may have frozen out in the northern hemisphere, in Greenland and the Artic sea ice, and has since been released back in the atmosphere, but most of it must still be locked up in Antarctica.

Think about it. Triple the ice covered...10 points higher average albedo.

The CO2 would definitely totally freeze out in the South Pole under those conditions over several decades or centuries.

If you increased the earth's average albedo by 10 points, corresponding to tripling of ice cover, then Vostok's DAILY MEAN would be below the sublimation point 7 or 8 months out of the year
TheGhostofOtto1923
3.7 / 5 (6) Aug 09, 2011
@techno
You probably could have saved yourself some time by searching GOOGLE to see if this had occured to anyone else (it had):
http://hernadi-ke...-in.html

-Maybe you have something novel to add to that discussion?
thermodynamics
5 / 5 (2) Aug 09, 2011
TheGhostofOtto1923: Thanks for the great link. It was interesting that they seem to have used the same phase diagram I pointed to. I have to assume that techno just can't read a phase diagram, and, to answer my own question earlier, he had never heard of "partial pressure." Very simple thermodynamics with an extremely long dissertation by techno that is completely wrong.
Techno1
1 / 5 (2) Aug 10, 2011
Ok, I'm not going to argue with the experiment, but what I am going to do is present some more "circumstancial" evidence I have thought of.

http://www.esrl.n.../trends/

This shows the Keeling Curve.

Now, I can explain 3 good reasons why the Keeling Curve's slope should have gone UP after Pinatubo. Yet the data shows it went DOWN.

Pinatubo caused a slight volcanic winter, which actually lowered the average temperature by a couple tenths. Yet the Keeling Curve does not measure temperature. The Keeling Curve measures CO2 concentrations.

Reasons CO2 "should have" gone up:

A) The volcano itself should have released lots of CO2. This should have been a net increase. The cooling and SO2 are irrelevant.

B) Because of the cooling, plant life should have been less vigorous, therefore removing less CO2 from the atmosphere.

C) Because of the cooling, humans should have burned slightly more fossil fuels in winter to stay warm.

Continued...
Techno1
1 / 5 (2) Aug 10, 2011
So all of those things; A, B, and C should have served to INCREASE the slope of the Keeling Curve a few months to a year or two after the eruption.

Yet the curve shows a clear negative deflection, lowering the slope of the curve in the months and years immediately after Pinatubo. It literally went neutral for a year !

Now how do you explain that in a model where the plant life and oceans is supposedly sequestering the CO2?

If the global temp dropped a tenth or so, then the ocean should not have been able to hold more CO2.

The sun was blocked out and SO2 blocking light in the upper atmosphere, so plants and microbes should not have been as good at removing CO2.

Yes, explain why the curve is deflected negatively, when I've identified at least 3 major forcings which should have served to increase the CO2 levels faster, not slower nor lower.

antialias_physorg
not rated yet Aug 10, 2011
Sooo..."some of the CO2 will get stored in the sediment". Seems like this would reach a saturation limit quite quickly (and thereafter we have no more sequestration happening). Given that the volume of storage (and hence the CO2/sediment interface) will be very small and the amount of CO2 we'd need to sequester to make any impact is rather large this part of the experiment seems pretty nonsensical.
Techno1
1 / 5 (2) Aug 10, 2011
Ok, Ghost and Thermo:

there's lots of things that happen in nature that scientists still can't replicate in a lab.

I can't quote it due to formatting, but he says the same thing you said, it would sublimate back out as fast as it's deposited.

My argument is the same as before, that's BS, because it assumes a static system.

He does not consider the possibility of the CO2-ice being covered over quickly by water-ice before it has time to sublimate.

He also certainly doesn't consider the ice age possibility.

He also doesn't consider the world record low temperature...

And there is a setup problem with this experiment: Contact with the box, the zip lock, the rack and other physical contacts with materials which conduct heat faster than air or ice would "in the real world".

It's also absurd that the mass of material inside a zip-bag went down during the experiment. He obviously didn't have the thing closed, so he sort of ruined the control anyway...
Techno1
1 / 5 (2) Aug 10, 2011
Yes, it would reach a saturation limit quickly, which is probably one reason it hasn't been detected.

Obviously, taking samples in "summer" and standing around with them exposed like that on the ice would rule out detecting this.

I'm talking about a few grams per cm cross-section area across the entire depth of the core: tens or hundreds of meters or more. For every 1cm by 1cm cross section and however deep, there'd only need to be a few tenths to a few grams...

"The following figure shows that YTT was indeed followed by an ice age of considerable intensity and long duration. Moreover, Greenland ice cores have produced evidence of a rapid and enormous cooling event in the northern hemisphere at the time of the YTT event : the air temperature in Greenland dropped by 16oC within 160 years"

http://www.andama...xtr4.htm

How cold can it get in Vostok in an ice age, if it got 16C colder in Greenland (at least according to this study)?
Techno1
1 / 5 (2) Aug 10, 2011
History claims that New York Harbor froze over after Tambora, so that people were able to walk across it on the ice.

That's New York harbor, Salt Water, at 40 North Latitude, after a volcano that was "barely" a VEI 7, though estimated to be exactly 10 times stronger than Pinatubo, 40cu km vs 4cu km ejecta...

How cold was it in the South Pole during the following years, when you had that much reduction in solar inputs on the northern hemisphere to have frozen over New York Harbor.

Cool the northern hemisphere, and the southern has got to follow, even if it isn't as pronounced.

Cold the temperate zones THAT MUCH and the poles have to follow, whether or not it is as pronounced.

New York harbor isn't an isolated system.

I'm talking about this as an example of how freaky stuff happens in nature.

this eruption verifiably caused a famine, since crops (plant life) failed.

This should have driven CO2 UP for the same 3 reasons listed above, but it did not. Explain that...
TheGhostofOtto1923
1 / 5 (1) Aug 10, 2011
Like I said techno youre talking to the wrong people here. I am sure many more of your questions have already been addressed in that other group so why broach them here?

If you WANT answers, even answers you dont want to hear, obviously that other group is where to find them.
Husky
5 / 5 (1) Aug 14, 2011
layers of co2 might have been deposited in the arctic areas, but don't forget that not only heat, but also pressure will force back the c02 to a gaseous state. when 1 km of snow covers a frozen co2 layer it might puff despite being cold/isolated
Shootist
not rated yet Aug 14, 2011
Can this be used in fracking?

That way they can store energy underground while pumping denser, usable, energy out of the ground.
Eikka
5 / 5 (1) Aug 14, 2011
Can this be used in fracking?

That way they can store energy underground while pumping denser, usable, energy out of the ground.


That way you wouldn't get burning water out of your wells, but free selzer for everyone!
gwrede
not rated yet Aug 14, 2011
I don't know about all the specialists and professionals here, but personally I think this sounds like a good idea. I found nothing to complain about the explanation, and, this explanation was thorough and transparent (as opposed to some Italian cold fusion doctors or levitation machine inventors).

Certainly worth a rigorous test.