No, Heavy Fluid Pumped Hydro Isn’t Remotely Reasonably Or Economically Viable

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A recent online discussion on gravity storage brought the usual suspects out of the woodwork. Proponents of heavy fluid pumped hydro reared their sludgy heads this time. Follow along for why this is a silly idea, as all gravity storage options that aren’t pushing water uphill turn out to be.

As a reminder, gravity storage is very basic stuff. The math is Grade 5. The science is Grade 7. Mass times the acceleration due to gravity times height. Kilograms times 9.8 meters per second squared times height in meters. Joules are the unit of energy this produces, and a million of them is about 0.28 kWh. Yes, Joules are tiny. A ton of mass at 100 meters of height has about that much potential energy, so if you were to suspend it with a crane with an electric regenerating winch, you would get about that much electricity out of it. This is why the mere thought of suspending blocks of concrete or steel in mid air with a crane would never occur to any rational, STEM competent person, unless they were venally selling it to STEM-illiterate enthusiasts with open wallets.

What is heavy fluid pumped hydro? Well, let’s start with pumped hydro, then let’s go on to the ‘problem’ that heavy fluid pumped hydro ‘solves.’ We’ve been pumping water uphill to store electricity since 1907. All it takes is a hill, a reservoir at the top, a reservoir at the bottom, a tunnel or some really strong pipes, and some reversible hydroelectric turbines. Pump lots of dirt cheap water up to a really simple upper reservoir through a tunnel through rock with really simple electric turbines. When you need electricity, let the water flow back down through the tunnel and turbines to generate electricity.

Hills have been around since the Earth coalesced out of ball of space dust. The first reservoir was probably built around 2500 BCE in Egypt. We’ve been building tunnels since about 520 BCE, when a Greek tyrant named Polycrates built a kilometer-long tunnel to bring fresh water for the city’s 20- or 30-thousand residents. The first hydroelectric turbine was probably built in 1882 in Wisconsin, USA, of all places. This is not remotely challenging technology.

Yet some people think it really needs improving on. One of those groups are the heavy fluids folks. Their concerns are some combination of a lack of vertical distance, a lack of water, or a lack of places to put pumped hydro. Let’s start with the last one.

ANU global pumped hydro site map courtesy ANU

See all of those dots? A few years ago the Australian National University and a group of people led by researcher Matt Stocks did a geographical information system study. They had a computer look for all the places on Earth for which there was decent data where it was possible to put a couple of reservoirs within a small handful of kilometers. They ignored places with less than 400 meters of vertical distance between reservoirs (remember that height thing in the basic science). They eliminated anywhere there was running water, to avoid messing up streams or rivers. They avoided places that were protected areas, mostly parks and the like. They picked places that were fairly close to existing transmission lines, so it would be easy to bring electricity to and from the reservoirs.

They found a rather absurd number of sites that met these criteria. Many of the big blank spots on the map above are just places where an incredibly small number of people live, and there’s no transmission or even good data sets. They found 100 times the resource potential for pumped hydro as the total amount of energy storage that their study concluded was required for all decarbonization. If only 0.5% of the sites, one in 200, pan out, that’s 50% of the problem solved.

There aren’t a shortage of sites to put closed loop, off-river, pumped hydro electricity storage. That’s two of the objections knocked off the list, places to put it where there is sufficient height. Oh, wait, say the pumped hydro critics. What about the Great Plains of the USA, the Prairies of Canada, and the Northern European Plain? Those are a subset of the blank spots to the north of the map. Apparently these people have never heard that we can transmit electricity, or that there’s this thing called the grid that we can have storage assets on.

This leaves the third criteria, having enough water. Let’s imagine a pretty big pumped hydro facility, one with 30 GWh of storage, about 7,700 Tesla Megapacks, the big grid storage one. Its height difference is 500 meters. Its round-trip efficiency is about 80%. It would require around 28 million cubic meters of water. That sounds like a lot.

How much fresh water does the USA consume daily? About 1,200 million cubic meters. Do pumped hydro facilities consume the water? No, it just goes up and down, with a bit of evaporation requiring topping off. Pumped hydro facilities don’t require a new 28 million cubic meters of water every day, they just play with the water they have. 30 GWh of storage requires about one-fortieth of a single day’s water consumption, and doesn’t consume it. That’s about one sixteen-hundredth of the USA’s annual water consumption. When pumped hydro facilities are built, sometimes the developers just let them fill up with rain water, although that’s fairly slow. Many are certainly replenished with rain sufficiently to require that excess water be fed into nearby streams or rivers. Others run pipes or build temporary channels from nearby rivers or lakes.

If you want more energy storage, just make the top and bottom reservoirs bigger. Bigger reservoirs are remarkably easy to build. They are the least difficult part of pumped hydro. Because of the nature of reservoirs as three-dimensional volumes, expanding them 10 meters in all directions produces non-linear results. Let’s take a simple example. Suppose you have a cube 40 meters on a side. It has a volume of 64,000 cubic meters. Let’s expand it 10% in all directions, turning it into a cube 44 meters on a side.

Does the volume and hence the mass of water it could hold increase by 10% to 70,400 cubic meters? No, it expands to 85,184 cubic meters, a full 33%. Double the sides of the cube to 80 meters and the volume isn’t doubled to 128,000 cubic meters but shoots up to 512,000 cubic meters, a full 8 times as much water and hence mass.

It’s a bit difficult, in other words, to figure out what problem the heavy fluid folks think that they are solving. Are they making it cheaper? Are they making it more convenient to find fluids? Are they increasing the number of sites with 400 meters of head height or more? Well, no.

What are they claiming? That by using heavier fluids, they can reduce height or volume of fluids, typically by 60%. Remember, it’s mass times acceleration due to gravity times height. There are no exponents in there, unlike with the volume of reservoirs cubing or wind energy swept area squaring or wind velocity power cubing. The increase of energy for pumped hydro by making the fluid heavier is linear. Double the mass of the fluid and you get double the potential energy storage.

If the heavy fluid folks were playing with something where there was an exponent, like swept area of wind turbines or velocity of the wind, they would be on to something. But they aren’t. They are playing with linear stuff, the mass of fluids.

How are they doing that? One proposed method involves using brine solutions, which are mixtures of water and high concentrations of salts like sodium chloride or calcium chloride and are 10% to 40% heavier for the same volume. Magnetorheological fluids, iron filings in water or oil, are 2.5 to 4 times denser. Fluorinated synthetic oils (40% to 90% denser) and glycerin mixtures (15% to 25%) have also been considered due to their higher densities and stable properties. But no one is trying to commercialize any of the above.

There is one firm out there which is trying to commercialize a different solution, fine-milled solids in a suspension in water. What does that mean? A suspension is a bunch of solid particles floating in a liquid. Leave them alone and they’ll sink to the bottom or float to the top eventually. How dense the resulting heavy fluid is determined by the mixture density formula, which is pretty basic. These aren’t solutions, which are like a full jar of marbles that you add water to without increase the volume of the jar. The solid particles displace water.

They are asserting that their fluid has 2.5 times more mass per cubic meter as water. As a result, they can use 40% of the water or 40% of the height and get the same energy storage. Given that neither water or height are remotely limited resources or particularly hard to exploit, this is a bit of head-scratcher, but maybe it’s cheaper?

Bigger, heavier particles sink to the bottom faster. Bigger, lighter particles rise to the surface faster. Hence, fine-milled solids, on the scale of micrometers or nanometers. There are 1,000,000 micrometers and 1,000,000,000 nanometers in a meter. They are tiny particles. You might be thinking to yourself, how do we make particles of stuff that small, and how much does it cost? Good question.

Ball milling is a widely used method, where materials are ground in a rotating cylindrical chamber with steel or ceramic balls, achieving particle sizes in the micrometer range through repeated impact and friction. Jet milling employs high-velocity jets of compressed air or gas to accelerate particles and cause them to collide, effectively producing sub-micrometer particles. Cryogenic milling cools materials to cryogenic temperatures using liquid nitrogen before milling, making them more brittle and easier to grind — ideal for heat-sensitive materials. Attrition milling involves grinding material by friction and shear forces in a mill with rotating discs or arms, producing fine and uniform particles for various industrial applications.

Is any of this cheap? Not really. Let’s start with the raw materials. The firm in question is coy about what fine-milled solid they are using in their patented fluid, but they have said in public statements that it’s a common substance used in oral medications, basically a harmless substance that increases volume enough that patients can swallow or swish the active ingredients. The most common of these is microcrystalline cellulose made from wood pulp, but its density is much lower than water.

My first thought was that the secret sauce might be silicon dioxide, also known as colloidal silicon, commonly used as a bulking agent in tablets. The colloidal part is important for this. Colloidal suspensions are different than non-colloidal ones in a few ways, but the significant one is that the particles don’t settle out, being fine enough to stay in the mixture through Brownian motion. Milk is a colloidal suspension of fat globules, casein micelles, and dissolved lactose and minerals, as a common example. If a substance isn’t colloidal, all the heavy bits fall out of the liquid and create a layer of mud on the bottom of whatever they are in.

The maximum for suspended silicon dioxide is about 60%, which coincidentally gives only a 60% increase in weight. Silicon dioxide is the densest substance I was able to find that’s also used in oral medications, so there’s a sniff test problem. Its density by itself is 2.65 times that of water, but you can only mix 0.6 grams of silicon dioxide with 0.4 grams of water, and when you add the densities together it doesn’t come close to 2.5 times the mass of water.

This suggests that they aren’t using silicon dioxide, or if they are, they are getting the end mass wrong. Not getting the basics of physics right is relatively common for people who try to outdo basic pumped hydro, but let’s assume that they are competent.

What else might they be using? Probably barite, aka barium sulfate, which is 4.5 times denser than water. It is widely used in the oil and gas industry as a weighting agent in drilling fluids. It’s also widely used as a radiopaque contrast agent for X-ray imaging and other diagnostic procedures. That humans are given it to drink suggests that this is what the firm meant, and they or the people reporting don’t know that it’s not a medication, but used for diagnostic imaging.

Remember that bit about colloidal suspensions? Barite doesn’t tick that box by itself. Typically bentonite is added, a clay which increases the viscosity of water so that the bentonite particles remain colloidally suspended. This is commonly used in drilling. We’ll come back to that viscosity later.

A bit of napkin math suggests a mixture of 5% bentonite and 41% barite in water would have a density about 2.5 times that of water, and it would be a colloidal suspension. It’s entirely possible to achieve the 2.5 times mass for the same volume that the company claims, in other words.

What would this cost? What does water pumped from a lake or river cost? Permit and usage costs might be a dollar per cubic meter. Pumping it a kilometer costs 10 to 50 cents. Assuming the water source is ten kilometers away, that turns into per $2 to $6 per cubic meter. A cubic meter of water weighs a ton.

Fine milled barite typically costs $100 to $300 per ton in bulk per what I was able to find online (not being a person who operates drilling equipment). Bentonite costs about $100 per ton as well. Picking the averages, that suggests that 5% bentonite and 41% barite would cost about $87 per ton of ingredients, with 54% water added to make it 100%.

Plain water costs perhaps $4 per ton. The colloidal suspension costs about $90 per ton. That’s 22.5 times more expensive for 2.5 times as much energy storage.

What would this do to the capital costs for a reasonably-sized pumped hydro solution, that is, one that was worth building? Let’s take the 30 GWh solution above. The big claim of the firm in question is about height, so let’s take the 500 meters in the example and divide it by 2.5, giving us a nice even 200 meters. The same volume of water is required, 28 million cubic meters.

The basic pumped hydro facility would cost $3 to $9 billion to build, an average of $6 billion. Filling it would cost another $112 million, a fraction of the construction cost.

Building a 200-meter height facility with the same size tunnels and reservoirs saves a bit of construction costs, but not that much. Call it $2 to $7 billion for an average of $4.5 billion. That’s a saving of $1.5 billion perhaps. Filling it with 28 million cubic meters of $90 per cubic meter fluid, however would cost $2.5 billion. So much for that saving. Add a billion to the capital costs.

Actually a bit more. The bentonite and barite aren’t going to get to the site for free. Let’s assume that they have to travel 500 kilometers, 400 of it by rail and 100 by truck. Freight trucking in the USA costs about $0.25 per ton kilometer. Rail costs around $0.04 per ton kilometer. Add another $700 million to the cost. It’s now $1.7 billion more, about 33% more expensive, for the same energy storage.

Is this a showstopper? Not necessarily, although it’s a head-scratcher as to why anyone would pay a full third more for the same energy storage.

But let’s get back to that viscosity. How much more viscous is the 5% bentonite, 41% barite, and water mixture? 50 to 200 times more viscous, or 50 centipoise (cP) to 200 cP. The viscosity of a fluid dramatically affects its flow rate, with the flow rate inversely proportional to viscosity as described by the Hagen-Poiseuille equation. For instance, a fluid with 100 times the viscosity of water would flow at only 1% of the rate under identical pressure and diameter conditions. 50 cP would be 2% of the rate. 200 cP would be 0.5% of the flow rate.

The power output of a hydroelectric turbine is calculated by considering several factors: the height difference the water falls (head), the volumetric flow rate of water, the density of the fluid, the acceleration due to gravity, and the efficiency of the turbine. These factors are multiplied together to determine the power output.

The dense fluid pumped hydro folks are depending on the density of the fluid multiplying energy by 2.5. But what’s that one in the middle? The volumetric flow rate? The one that is 50 to 200 times slower than water? Oops. That means 25 to 80 times less energy with the ratio.

So this 33% more expensive pumped dense fluid solution would generate 25 to 80 times less energy if used with exactly the same tunnels or pipes and turbines as pumped hydro with water? Can that be solved?

Sure, massively scale up the tunnels or pipes, turbines, and pumps. The same equation that told us the fluid flow can be used to figure out how much bigger they would have to be, and at 100 cP, they would need to be 3.16 times bigger. A 10-meter diameter tunnel for pumped hydro would need to be a 32-meter diameter tunnel, and 10 times as much rock would have to be removed. The amount of rock that needs to be supported increases with the square of the diameter. This results in greater potential for deformation and collapse. A 32-meter diameter tunnel would require a lot more shoring up than a 10-meter diameter tunnel, so it’s not 3.16 times as expensive, but probably 10 times as expensive.

Tunnels are 30% to 40% of the cost of pumped hydro projects. The hypothetical $4.5 billion dense fluid pumped hydro solution would see not $1.1 to $1.3 billion for these tunnels, but $11 to $13 billion. The $2.2 billion more has suddenly become $12 billion to $14 billion more. The $6.1 billion basic water pumped hydro solution is now a third the cost of the dense fluid solution.

Is there anything else? Oh yes. Turbines are also subject to frictional losses. For well-optimized water turbines, the losses are around 1% to 3%, part of the overall losses of hydroelectric dams and pumped hydro. But they go up with viscosity, a lot. A 50 cP fluid has 50 times the friction due to the Reynolds number in the Darcy-Weisbach equation for head loss, so 50% to potentially 150%, something that couldn’t even get through the turbine due to friction, just ooze gently through the unmoving blades. A 200 cP fluid would have 400 times more friction, so wouldn’t spin the turbine at all, just ooze like the sludge it is.

As a comparison you can latch on to, shampoo has an average cP of 18. When you squeeze or pour it out of its plastic container, you can see how slowly it moves, and that squeezing it out takes a bit more energy than if it were water. It flows 18 times more slowly with the same pressure and diameter of pipe or tunnel. That would decrease turbine generation by a factor of 18. But that’s not all. Turbines don’t like friction, and that 18 cP viscosity comes with a lot of friction. In a perfect world, shampoo, after cutting recoverably potential energy by a factor of 18, would then reduce it by another 18% or so coming and going. If shampoo were as dense as barite-infused water, its two-way efficiency would be under 1%.

Barite suspended in water has a viscosity much higher than 18%. In the best possible case, 50% losses with bentonite and barite, it seems. And that’s in both directions. That means zero round-trip efficiency with all of the electricity put into the system lost to inefficiencies.

What about a tiny system, maybe 10 MW / 100 MWh, using pipes instead of tunnels? Well, the total capital cost would be high, but might be in the range of batteries. But the round-trip efficiency would kill it. A bentonite-barite suspension, which can get to the density requirements, fails in two separate ways to achieve its ends.

None of the above is remotely difficult to follow for people with basic STEM skills. Certainly the nerds I’ve talked with about dense fluid pumped hydro have just shaken their heads. I mean, it’s not Grade 7 science. Well, the cross-section and volume of cylinders is. Viscosity calculations have to wait until Grade 11 or 12, although the reality that more viscous fluids flow more slowly is introduced years earlier. Civil engineers get the Darcy-Weisbach equation in first year of college or university, but it’s entirely possible that some high schools introduce it in advanced placement course in Grade 12. It’s not hard, just not immediately useful.

The only one that’s remotely advanced is tunnel diameter concerns related to compression and collapse, which is introduced typically in the third year of civil engineering courses, but is intuitively obvious to anyone who pays attention to STEM things. It’s not like I’m a civil engineer, but it is an obvious concern and I went and found references for it.

Well, let’s go back to the silicon dioxide 60% solution. Would it be less viscous? A specific example is Ludox TM-50, a colloidal silica product with 50% SiO₂ by weight. The viscosity of Ludox TM-50 is approximately 30 cP at 25°C. For a 60% suspension, the viscosity would be expected to be significantly higher due to the increased particle concentration. 30 cP, of course, means it would deliver 30 times less energy for the same mass and see 30% efficiency losses in both directions. 60% more potential energy would turn into vastly less real energy.

Well, what about if they don’t use bentonite, a clay, but a surfactant like polysorbate. It can create colloidal suspensions of fine-milled barite too. No luck. While polysorbate requires only 1% to enable colloidal suspension, it appears, most of the viscosity comes from the fine-milled barite, not the additive that enables colloidal suspension.

Is there any way around this? Sure, heat them up. At 40° Celsius, colloidal silicon’s cP drops to 15-25, so only a 30% round trip turbine efficiency loss in the best case. A bentonite-barite solution at 40° Celsius would see a better improvement with a drop to 20 cP, but that’s still a 40% efficiency loss round-trip just for the turbines. Both are still moving 20 to 25 times more slowly than water, so are generating only 4% or 5% of what water would. Oh, and their density drops, so the potential energy per cubic meter drops as well.

And to be clear, this means that they have to get heat from somewhere. Their patent makes it clear that they’ve figured this out, at least in part, because pages are devoted to getting heat from geothermal or gas turbines as well as having heat exchangers and heat pumps all over the place.

No free lunch. This is thermodynamics. I’ll remind you of British author and scientist C.P. Snow’s version of the three laws:

  • You can’t win (that is, you cannot get something for nothing, because matter and energy are conserved).
  • You can’t break even (you cannot return to the same energy state, because there is always an increase in disorder; entropy always increases).
  • You can’t get out of the game (because absolute zero is unattainable).

Reducing viscosity with heat trades one energy problem for another. That’s thermodynamics for you, a real buzz-killer at energy industry cocktail parties.

Is it possible that the firm in question has created a non-viscous colloidal solution with some other fine-milled solid and some additives? Deeply unlikely. Viscosity of a fluid with fine-milled particles is a function mostly of the particles, which have physical mass. In fact, the finer the particles, the greater the viscosity, and the particles need to be really fine in order to be in a colloidal suspension. The properties of liquids are a very well mined field. There are high-density, low-viscosity fluids, but they are things like chloroform, mercury, and bromine. None of those are remotely sensible to use due to their varying degrees of toxicity to humans and most other lifeforms. If they have magically invented a low-viscosity, high-density fluid that isn’t in common use and was cheap, they would be selling it to the drilling industry and possibly picking up a Nobel Prize.

While I had fun running the numbers and figuring out what materials in what combinations they were likely to be using, this isn’t like the gravity energy storage system that fracks the same volume of shale over and over, crushing it into gravel, grit, and sand, degrading its turbines with grit and filling its upper reservoir with ugly gray sand. That one took me an hour of poking at it before the problem became obvious, mostly because I had never looked at fracking in any detail before. The first time I heard of this dense fluid pumped hydro proposal, the lack of a reason for it and the problems were glaringly obvious. Quantifying them and figuring out the edge cases took time, but not realizing that the solution wasn’t viable. And just as with the fracking solution, I’m not a hydroelectric engineer, a civil engineer, or a person who works with dense colloidal suspensions, so it’s not likely I have privileged knowledge.

Remember, the basics of viscous fluids moving slowly are grade school stuff, while the calculations are Grade 11 or 12. Everybody who has ever poured maple syrup, walnut oil, or molasses is intimately familiar with it. Everyone who has stirred liquid honey knows it’s a lot harder than stirring water. Tunnels three and a bit times wider being ten times the volume is Grade 7 stuff, although them being much more likely to collapse and pancake anything inside them is a bit more advanced, but still undergraduate stuff.

So the questions are the same. Why didn’t anyone ask these obvious questions of the people who ‘invented’ this? Why didn’t the governmental agencies that have given them something like $15 million ask them how they were going to get around the basics of fluid dynamics? Why didn’t any of the investors that have apparently given them a few million ask any of this? Why didn’t any of the funding organizations ask people who would be able to see the bleedingly obvious, like a Grade 11 student who just passed a test that included viscosity calculations, what they thought? Why didn’t any of them look at their slowly pouring shampoo and have a weak little lightbulb go on about what it implied about dense fluids and energy storage?

Like using cranes to lift concrete blocks as an energy storage solution, when I first heard of dense fluid pumped hydro, I assumed I’d never hear of it again because it would sink without a trace. Sadly, no. Someone always comments on its wonders when I talk about pumped hydro’s global growth rate or the failures of other types of gravity energy storage. At least now I’ll have an analysis to reply with, rather than a few scathing words about oozing sludge not being remotely a solution. Perhaps it will prevent repeat commenters.

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