Thursday, March 29, 2018

Martini-Glass Energy Banks

Martini-Glass Energy Banks

All about it...

Myself when young did eagerly frequent
Doctor and sage and heard great argument
About it and about, but evermore
Came out by the same door as in I went
Omar Khayyam
as interpreted by Edward Fitzgerald

As you will have guessed, this essay has precious little to do with Martini glasses and even less to do with Martinis. Sorry 'bout that — I suppose.

It does however have something to do with energy banking.

I was thinking about the storage of energy in ways that enable us to rely on renewable energy sources such as solar energy and wind energy without worrying about sunless days and windless nights: simply gather all the energy one can while there is a surplus, save it somehow, and draw on our savings whenever necessary. I already have discussed some alternatives in other essays, in particular:

In some of these I disparaged the use of water as an energy storage medium such as in hydroelectric or pumped storage schemes. One needs to raise too much water to make it worth while, it takes too much water and too much space, and it tends to entail troublesome ecological penalties.

As I have pointed out elsewhere, one can store energy by raising masses and recover it by lowering them again; the more you raise, and the higher you raise it, the more energy you bank. Ten times as high, or ten times as much mass, and you store ten times as much energy. Ten times as much of both, and you get one hundred times as much energy, and so forth. And there are ways to store the water indefinitely with negligible loss and re-use the energy with good efficiency.

Marvellous, not so?

But I also pointed out that this requires dismaying masses of water. I here plagiarise some text I posted earlier:

The fundamental problem is that it takes a lot of mass suspended at a considerable height to store many megajoules.
Oh. What are megajoules?
A convenient measure of energy in any useful form.
Consider: 3.6 megajoules (MJ) = 1 kilowatt-hour (kWh).
You might consume more energy than 1 kWh just in roasting a joint of meat for a family meal, and yet, just 1 MJ is how much energy it takes to raise a 10 Tonne mass 10 metres. That sounds energy-cheap of course, but unfortunately, the other side of the coin is that from a ten tonne mass raised ten metres, you can barely get enough energy to prepare a meal.
So it is hard to imagine the billions of tonnes of water that power utilities need for schemes to store power in elevated storage dams.
One tonne of water occupies about 1 cubic metre, and a ten-metre column of water exerts a pressure roughly the same as atmospheric pressure, and not surprisingly, as already mentioned, if we work with molten lead instead of water, then it takes a column about 1 metre high to exert a pressure equal to one atmosphere.

If we insist on pumping fluids, it would be nicer to use say mercury or molten lead; they are much denser than water.

But they also are a lot more expensive, and have other unfortunate properties, such as toxicity and cost, and in the case of molten lead, also temperature.

And one more time, don't forget that we also are not speaking of producing energy, only of storing and recovering it. We first have to get the energy from other sources; we still will need sun, wind, coal, oil, gas, nuclear or other generators to supply the energy in the first place.

Not encouraging?


So what are the problems?

I hope climate science becomes the big thing.
And then what I want is electrical engineers to solve the world's energy problems, energy distribution problems.
I want mechanical engineers to make better transportation systems.
I want chemical engineers to develop better solar panels, and so on.
Bill Nye

Let us think harder about water. For one thing, in a lot of places, such as inland deserts, we simply do not have enough water to spend on energy storage at all. In other places we don't have the space; you can't plunk down a Boulder Dam just anywhere. Also, we don't want to use fresh water for energy storage where energy storage would interfere with the environment or compete with other needs.

As problems these aren't always and everywhere unacceptable, but more often than not they are serious. Using seawater is good where there is plenty of seawater, but historically we haven't used seawater for much of our power generation, because seawater seldom occurs high up where we can use it to drive generators. And it is more corrosive than fresh water. Granted, there are a few tidal schemes and so on, but they are limited in scope and scattered in location because the necessary conditions are rare.

On the other hand pumping seawater into high towers is a viable, environmentally friendly option almost anywhere on the coast. Often it even is advantageous to wildlife, such as by providing warm water with increased nutrient loads, or creating de facto nature reserves where people aren't permitted to hunt and fish; the real estate around the tower need not be wasted. The seawater simply could run back into the sea when exhausted, or go back into the pumping cycle if it had been necessary to filter it or otherwise treat it for whatever reasons might apply; that would reduce the need to repeat some of the treatment every time much of the water passes through.

But storing billions of tonnes of water and its potential energy takes space; a billion tonnes of water occupies a cubic kilometre, a terrifyingly huge volume.

And if we store the water in a cylindrical tower, the simplest and most obvious option, then the output from a full tower comes out at high pressure, yielding lots of power.

High pressure is good.

The pressure is what we apply to generate power, and the higher the pressure, within limits, the more power we can generate. However, by the same token, the last several percent of the output will yield hardly any power at all because it is under hardly any pressure. The maximal energy we can get is the mass of the water times the height through which it falls. So we want to store our power in the form of as much water as we can manage and held as high as we can store it.

This involves all sorts of engineering complications because of realities of pressures and leaks and foundations and structural design. Not being that kind of engineer, I avoid most of the practical details and leave them to the structural and power engineers. This is a refrain I repeat periodically and unapologetically throughout this essay, which deals with just enough engineering to urge the importance of certain principles.

Firstly, let us repeat, a ground-level cylindrical vessel, or in fact any broad-based vessel, is not satisfactory. As I have pointed out in another article, a large fraction of the water in such a vessel is wasted because when the vessel is nearly empty the water column is not high enough to give you workable pressure. All that the bottom few metres of your expensive water store are good for is to raise the rest of the water column high enough to give good pressure.

One can improve matters by mounting the vessel on a high place, or building it on a tall stem, with the power generation equipment at the bottom of the outlet, far below the reservoir. That amounts to narrowing the base of your energy store. Most big water towers use that trick, though not on the scale that we shall be discussing here, and not using their power for more than delivering the water.

I propose that we consider that trick too, but increase the stem height more than usual, so that the water still delivers a thoroughly usable pressure until the vessel (and even most of the stem) is empty. There should be no technical obstacle to mounting the vessel on a tower say 100-200 metres high. In a typical tall building each floor is roughly 3 metres high so such a stem height would be equivalent to some 30-60 stories; that is high, even impressive, but nothing dramatic. A strong, attractive shape for such a tower would be a hyperboloid, though most towers in that height range currently seem to be cylindrical, because the constant diameter simplifies tower builders' jobs.

But again, such details are for the engineers to specify — get used to that refrain, because I repeat it fairly often.

But those engineering details need not amount to technological barriers.

If our proposal is to be defeated on technological grounds, it will be by the sheer volume of water we would need to suspend up in the sky, not the height of the tower.

Considerations and approaches

We cannot solve our problems with the same thinking we used when we created them.
Albert Einstein

A column of 10 metres of water exerts a pressure of about one atmosphere, so a column 100-200 metres high would give about 10-20 atmospheres of pressure. That would be well within practical engineering ranges, both for storage and for generating power. If we use seawater, which is slightly denser than freshwater, the figures will be roughly 3% better, but still not different enough to affect any of our assumptions seriously, whether for good or ill.

Unless you already know the answer, you should be wondering about why we should want to build the towers so high. Height is expensive and dangerous, surely? And extra water is cheap, especially seawater.

Well yes, but to build the tower twice as high, up to a point, is less expensive than building two towers, and reduces the need for extra foundations, real estate, and equipment in an extra structure. Given the same mass of water a higher tower stores more energy and delivers it at higher pressure, which permits more efficient power conversion. In fact, the same mass of water, twice as high, stores and delivers at least twice as much energy. Of course, there are practical considerations, but decisions about the best design compromises are the responsibility of the engineers. Figures and forms I assume in this discussion are no more than examples to illustrate principles.

Furthermore, it is important to maintain perspective; the first full-scale tower (ignoring smaller prototypes and trial designs etc) will not be the only tower; even if you did build one tower large enough to serve an entire country much larger than Liechtenstein, that simply would leave you with unacceptable problems of power generation, distribution, and maintenance. We may look forward to water-tower "farms", much as we have wind-turbine farms, though it might be better to put isolated towers near to where the water or power is wanted.

If it should prove economical (which I doubt, but again, ask the engineers) to build towers so much higher that the pressure in the effective column of water becomes difficult to control, generators partway up the column could draw power and reduce the working pressure on the lower turbines.

You might wonder whether there is any point to discussing such nonsensically high structures at all, but that is not something to dismiss without serious engineering assessment. Consider: the Millau Viaduct is a bridge mounted on masts in southern France. Its tallest mast measures 343 metres high, which supports a very heavy road and heavy traffic.

At the time of writing no one is has yet begun to complain about the durability of the viaduct.

Shapes and sizes

Experts get their expert fun
Ex cathedra telling one
Just how nothing can be done
          Piet Hein

Now, the water vessel itself could most obviously be cylindrical, open at the top and half as high as wide, because that is the most economical shape for an open-topped, floored cylinder of a given radius (after all, why not open-top? Open-top works for hydroelectric dams, doesn't it? And it is cheaper than adding a roof. And at that height above ground, not many birds or bats will be a problem, and no one in a helicopter is likely to drop in to steal our seawater).  

Well, let us examine that idea. We won't want to build a 200 metre tower just to perch a bucket of water; the idea is to store enough water high enough to power a city for long enough to be worth while. We might want to do so to tide over a period in which there is no sunshine, wind or wave power, nuclear or fossil fuel power, or whatever forms of power generation might be locally important. The stored water also might be useful in smoothing out power demand so that we could run on base load power supply. When our power demand is too low to consume the base-load power level, we can use the excess power production for adding to our stores of masses of water as high as might be practical. When our demand is too high for economical use of  power from the base-load generators, so that power production becomes very expensive, we can meet excess demand by running accumulated water through the output power turbines.

So, let's think 200 metres high. Ten tonnes falling through ten metres gives one kilowatt hour. Falling through 200 metres the same amount of water gives twenty kilowatt hours, enough to power a typical first-world household for a day or two. A million tonnes would should do for about 100000 families, say a small city. Similarly, a billion tonnes could supply a large country (ignoring problems of distribution etc). Or those billion tonnes could supply enough topping-up power to keep a modest sized country going for a month.

These figures are deliberately simplistic, intended to demonstrate principles, not to propose practical designs. At all times bear in mind that the idea is not to have one tower delivering full power for a whole country all year round. The towers are to accumulate energy when power sources are available at levels greater than consumption, and to generate power to supplement and smooth out the available supplies when the demand is greater than the available sources can realistically supply.

If we think of using a billion tonnes of fresh water, then in many countries we would have problems of supply and disposal, but they would hardly apply where we could use sea water, unless we also wished to desalinate our output, which would complicate matters, because we would need special arrangements to dispose of the salty discarded water. But that is not a complication we need consider here, though salt water at the appropriate pressures certainly should improve the economy of a modern desalination plant. It should in fact be adequate for desalination of brackish water.

For our purposes I shall assume that we are sited on the coast and that we take suitably strained and cleaned water from the sea. That is not as simple as it sounds, but it will do for purposes of our discussion.

But that big cylinder of water up there. Suppose it is 100 metres deep and 100 metres in radius. That would amount to  roughly 3 million tonnes of water at a mean height of 250 metres. However, when one speaks of millions of tonnes of water, one needs to be careful in designing the shape of the container. A flat-bottomed hollow cylinder with a wide base is not a suitable shape to suspend by the centre of its base; it would require massive reinforcing, which would add to the cost and reduce the stem's capacity to support the mass of water. Also, the water pressure inside the cylinder would be a lot greater near the bottom of the cylinder than near the top, and that would have to be taken into account as well. And the water near the top would be more profitable than near the bottom because it would be further from the ground, meaning that it would store more energy per tonne. In fact, in our example the water right at the top would be at a total altitude 100 metres higher, 300 metres. It accordingly would yield 50% more energy per tonne than water at the top of the stem (the bottom of the vessel) at an altitude of just 200 metres. 

Now, there are so many variables in calculating the best shape for the reservoir on top of the stem, that there is no simple optimum; the choice would depend on  the materials in use, the size of the structure, weather and earthquake proofing, difficulty of construction, the expected working life of the structure (nothing lasts forever) — all sorts of things. No single design would equally efficiently suit all climates and situations. So one thing I am sure of is that whatever shape I propose, some engineer who has had the patience to read so far will shoot it down in contempt. That doesn't bother me much, because if he were asked to suggest anything better, some other engineer would shoot down his alternatives as well. (Note that I speak here of male engineers, not so much because I am inclined to expect female engineers to be a bit more tolerant of my amateurish attempts to talk sense, as because of a personal distaste for clumsy PC circumlocution such as s/he.)

There are however several variables of interest.  For instance how high the bulk of the water can be held, how securely, safely and efficiently the shape and material can hold a full load, the sea, how costly the building process might be, how attractive the design might look, how efficiently and effectively the water can be extracted from the supply — you are welcome to add to the list.

The stem itself could be any of several shapes, of which the most obvious ideas would be cylindrical, conical or pyramidal, or hyperboloidal, possibly cable-stayed, and perhaps in some combination. Cylinders are simple and therefore cheap to build (up to a point), but for very tall structures they offer less strength than the same amount of material in the shape of a hyperboloid, and incidentally they also are less aesthetically attractive. This last point might seem frivolous, but seeing how many people complain about some very beautiful wind turbines, it could become important. And one thing that should apply to all classes of design, and very likely to the vessel on top, would be the addition of helical strakes to shed wind.

Think of the vessel on top of the stem: it must bear its own weight as a box that won't collapse when empty. It must bear the internal pressure of the water that tends to burst it open from within. And it must withstand the piercing stress of the stem supporting it from beneath like a spike.  Also, it must have capacity for a lot of water, and it must not in itself be heavier than we can help, or the stem would have to be too big, dangerous, and expensive. In meeting these requirements the shape of the vessel is very important, because it is one of the major factors determining its strength, the amount of material needed to build it, and how high it holds the water, which in turn is largely determined by the centre of mass of the full water load. 

It is tempting to think in terms of a spherical vessel, which would hold the most water for a given area of wall material, but both the localised stresses from the stem below, and the internal pressures from water within would complicate that. Besides, if we do not need a roof, we could do better with a hemisphere than a sphere; in fact, a hemisphere would work nearly twice as well, even allowing for giving it a stronger wall. In terms of the volume the hemisphere could hold, its capacity would be two thirds of the capacity of a cylinder of the same depth and radius, and it would be stronger. We also could improve the stresses in a hemispherical vessel at the point where it rests on the stem by narrowing the shell around the bottom to meet the stem top in an inverted teardrop shape. That would provide a stronger base, both for holding up the structure, and resisting the internal water pressure.

There is another variable that could however increase the attractiveness of a spherical reservoir. If it were suitably designed to withstand internal pressure, it could contain a suitable amount of say, nitrogen or propane under pressure. The gas could float above the water, storing energy in about the same manner as a compressed spring, increasing the pressure by perhaps a factor of two or higher, which on the scale that we are discussing, would amount to storing a good deal of extra water in the tower. However, storing energy by compressing gas is tricky if you wish to avoid inefficiency, and the distribution of pressure as the vessel filled and emptied would be complicated, so here again evaluation of the options would be a job for the engineers.

However, in either a cylindrical or hemispherical container, the wall strength necessary to contain a fluid under pressure is roughly proportional to the diameter unless the whole wall is very thick, so in a deep container, if the wall is to be of consistent thickness, the internal diameter should decrease linearly from top to bottom, because the pressure increases linearly from top to bottom. Twice the depth gives twice the pressure. This most conveniently gives a right-angled funnel shape, which is a rough approach to the inverted teardrop.

Such a cone has half the capacity of a hemisphere of the same radius, but it also keeps the water's centre of mass higher and is easier to construct than a hemisphere. In an inverted ninety-degree cone roughly 85% of the water will be in the top half of the vessel's height, compared to 50% in the cylinder, and the conical shape is fairly strong. One could slightly increase the average height of the water mass still further by using an inverted hyperboloidal vessel shape, and possibly the strength of the vessel as well by constructing it in the form of a hyperboloid of one sheet.  (In case you are interested in that option, you might want to read some material at: )

I doubt that the advantage at this point of the exercise would be clear enough to pursue the matter here; the advantages of simply lengthening the stem slightly according to requirements would be more obvious at any rate. Let's leave the fine tuning to the engineers when they get involved; it is not a point to be settled without planning and detailed calculation.

Martini glass?

Be thankful for problems.
If they were less difficult, someone with less ability might have your job.
Jim Lovell
Subject to more work on the point, I would suggest a design in the shape of an open inverted ninety-degree cone on a hyperboloidal stalk, or some closely similar structure.

Notionally it would look rather like the diagram below (without showing any strakes for controlling wind resistance, nor stays for keeping the structure erect in earthquakes, nor details of wall thickness and other considerations):

Hence the Martini-glass appearance, minus swizzle sticks, cherries or pickles, but with lots of Martini.

Now let's think about the scale of Martini glass we might care to use. Let us suppose the stem to be the same height from ground to its tip, as the depth of the bowl from its narrow tip at the bottom, to the centre of its wide top. That is not necessarily the best in all cases, but it is a convenient assumption, though I suspect that a longer stem would be better. Let us consider some examples.

Suppose we have a tower 100 metres high, carrying a vessel 100 metres deep. It could hold over 1000000 tonnes of water at a mean height of roughly 175 metres above ground, yielding theoretically about 1.75 million kilowatt hours. By the time it has passed through the generators, it should have yielded say 600000 kilowatt hours of electricity at short notice (probably requiring less than a minute to get the turbines up to speed). A cylindrical vessel could store roughly thrice as much energy, but with the disadvantages I already have discussed. By increasing the stem height and vessel diameter and depth by about 32 metres, we could more than make up the difference in volume.

If we still maintain the proportions, doubling the height and diameter etc, we multiply the energy capacity by 16 (eight times the mass of water at twice the height at the head of the stem) yielding storage for somewhere near ten million kilowatt hours, enough to keep a sizable city going throughout a night in a temperate region, if all its other energy sources were to fail at once. If base load generators were kept running, such a Martini glass might be good for weeks.

And that is from just one Martini glass.

As for billion-tonne Martini glasses...

It might be worth splitting the interior of the vessel into say three to eight sectors, partly for reinforcement, and partly to permit balancing the load over the centre of the foundation under conditions of high wind or foundation settling. This would not be suitable for rapid response, such as for earthquakes, but could greatly increase the safety and lifespan of the structure in the long term. In quake-prone regions a metal or polymer vessel containing a few hundred tonnes of water could be suspended above the centre of the vessel for rapid sway correction in earthquake-prone regions.

As for scaling up the size of the martini glass, there obviously would be limits, but they would be surprisingly mild when one calculates them. A 100 metre high martini bowl would present only 10 atmospheres of pressure at the top of the stem, and if the stem also were 100 metres high, it would have to contain 20 atmospheres at the bottom when the bowl is full. That is a very modest figure; in fact barely interesting in power engineering terms. If we double the height of the stem, we roughly double the amount of energy for the same amount of stored water; we could quadruple it for four times the energy, and gain higher pressure  and higher efficiency at the same time. 

Quadrupling the stem height would nothing like quadruple the building costs, because most of the material would be in the bowl, which as yet we have not considered changing.

Well, what if we double the height and radius of the bowl? 

Now things get a little more complicated. Other things being equal, that would double the pressure at the collar of the stem, and the thickness of the bowl would have to double, more or less, again yielding higher pressure and higher efficiency. However, and more importantly, the area of the bowl wall would quadruple and its mass would increase by a factor of eight. 

Not so good.  

However, the volume of the bowl would increase by a factor of eight as well, and with it the mass of the water and the energy stored, and the centre of mass would be higher.

Increase the size of the bowl by a factor of four, and the pressure still would rise only by a factor of four, very manageable and with a very beneficial effect on efficiency, but the mass and volume of the bowl would increase by a factor of sixty-four, which is sobering, but we could console ourselves with the thought that we also would increase the energy stored by a factor of sixty-four.

Not so bad.

And if we quadrupled the height of the stem as well, we could store 256 times as much at eight times the pressure and with still increased efficiency.

All this is very simplistic, but it certainly makes it clear that one would have great incentive to think very hard about the appropriate scale of our martini glass.

And the quality of our foundations and our building. 


Real estate and applications

Technology sometimes gets a bad rap because of certain 
consequences that it's had on the environment and 
unforeseen problems, but we shouldn't use it as an excuse 
to reject our tools; rather, we should decide that we need 
to make better tools to solve the problems caused by the 
initial tools in a progressive wave of innovation.
Jason Silva

The land that such structures would occupy need not be wasted. It could be used for agriculture, for recreation, for solar energy, as a nature reserve, for industry or as residential areas.

If the visual effect of the Martini glass shape were locally unpopular, it could be built invisibly into other structures such as office or residential buildings. Planting vines probably would not be adequate. At night the underside of the bowl should make a profitable surface for advertising, using laser projection.

Climatically, if the tower used brackish- or seawater, and began to produce enough ice in winter, the ice could be harvested as free desalination.

In hot climates, the inside of the cone could be black, heating the water to provide power via heat pumps, or water vapour to condense for consumption.

Electricity generation need not be the only possible application. Suitable freshwater designs could be used as a source of water for emergencies such as fires, for mechanical power in factories, and for storage of irrigation water and irrigation power.   

So, what are we waiting for?

Snow and adolescence are the only problems that disappear if you ignore them long enough.
Earl Wilson

A few million dollars for prototypes and a few stages of progressively larger installations, such as sized to suit light industry, should be worth the investment.

No comments:

Post a Comment