Pumped storage output multiple expansion tanks few reservoirs


 * The No Solid Moving Parts Nearly Reversible Heat Engine idea leads to many possible designs. This page discusses the Pumped storage output multiple expansion tanks few reservoirs design.


 * Please note that this article is being edited and much of it is not finished. The beginning and the last section seems to be correct.



This design aims for a machine installed at a pumped storage site with lakes at two elevations and an existing hydroelectric pump / generator. The generator is used to extract the excess energy gathered from the ambient air by the heat engine.

The first design principle is near reversibility. Whenever other requirements conflict, near reversibility must come first. When a valve is opened, the pressures should be almost the same and the flow will run for a while and then stop. Whenever water flows, a slight change of circumstances must cause the flow to reverse. Thus, for example, if water is to be released into the bottom lake, there must be a small change which would cause the water to flow out of the lake into the machine. This cannot happen if the water being released forms a tall column. Therefore, there must be a low-pressure water tank at the bottom of the machine, and sometimes water must naturally flow into it. Any design which lacks a low-pressure water tank at the bottom would have to keep all of the lowered water inside a high-pressure tank.

Specific Design goals

 * Energy is stored by raising water a large distance from one open lake to another. The reservoirs are not closed tanks, which would be either too small or too expensive.
 * Many compression / expansion tanks capable of the rapid heat exchange needed for isothermal operation provide maximal heat flow at the daily high and low temperatures.
 * Each tank is dedicated to a narrow pressure range, resulting in less wear due to fatigue.
 * The machine must release water into the open bottom lake during compression and raise water from that open lake during expansion. Otherwise the maximum daily energy output would be limited by the volume of high-pressure water tanks.

Physical layout
The machine comprises reservoirs, hydrostatic tanks, siphon tanks, connecting valves, and manifolds.

The hydrostatic and siphon tanks are parallel in many ways. They are literally arranged in two parallel slanted lines descending from the top lake to the bottom lake. The roles of air and water are parallel but reversed: air moves from one hydrostatic tank to the next through a valve, while water moves from one siphon tank to the next through a valve. Water at slightly different pressures is supplied via the "even" ("odd") manifold to even (odd) numbered hydrostatic tanks, while air of slightly different pressure is similarly supplied to alternating siphon tanks via a pair of manifolds.

Air is compressed or expanded in the hydrostatic tanks, and during the process is transferred from one to the next via a carefully arranged tubes with one valve between each pair of tanks. Water is raised or lowered via the siphon tanks, and a U tube with a valve connects each pair of siphon tanks.

Both kinds of tanks are connected to both neighboring tanks, with valves between every pair of tanks; both are divided into even and odd numbered tanks, and each tanks is connected to the appropriate even or odd manifold. The hydrostatic manifolds carry water pressure from the top lake to the bottom of the hydrostatic tanks. The low pressure manifolds carry air slightly above or below atmospheric pressure to the siphon tanks.

Lakes and reservoirs
There are two open lakes and one closed reservoir. The top lake surface and the closed reservoir are at about the same height. The surface inside the closed reservoir ...

This article is being revised. Below here, there is no reference to the low-pressure siphon tanks which couple water motion to air compression and expansion.

Two are at the top, and differ in surface elevation by about the height of an expansion tank. They are called the top and middle lakes, and they drain via reversing valves into a pair of manifolds (called the even and odd manifolds) which connect to every other tank. During the first half of every operational step, the top lake is connected to the even manifold and the middle lake to the odd manifold. During the second half of every step, these connections are reversed so the top lake connects to the odd manifold and the middle lake to the even manifold. The bottom lake is at the bottom of the valley, tens or hundreds of meters lower.

Hydrostatic Compression / Expansion tanks
There is an even number of uniformly spaced hydrostatic compression / expansion / heat exchange tanks leading down the slope of the valley. These tanks are always open to the hydrostatic head of either the upper or middle lake, so their operating pressure is nearly constant. (This is true even while the machine is idle as the temperature drops, assuming that it is better to avoid the stress of a large pressure change).

A design variation would provide separate compression and expansion tanks, since the compression tanks need cooling (with heat pipes leading upward to a heat sink) while the expansion tanks need heating (with heat pipes leading from a lower heat source to the tanks).

With a single set of tanks, both heat pipes extend into the tanks. If either heat sink or source is not at ambient temperature, then valves must be provided in the heat pipes to prevent unwanted heat flow.

High pressure storage / heat trapping tanks
A large collection of high pressure gas storage and heat trapping tanks at the bottom of the valley serve to store high pressure gas after it is compressed at the daily low temperature, and to trap heat as the ambient temperature rises, until the high-pressure gas is allowed to expand at the daily high temperature. These tanks are always open to the hydrostatic head of the top lake (assuming it is better to keep them at high pressure at all times than to leave them at atmospheric pressure while the energy is stored in the upper lake). When the temperature rises, the tank pressure rises as a small amount of gas expands downward in a narrow U tube which attaches to the hydrostatic manifold. These tanks achieve nearly perfect isobaric (constant pressure) heating.

Filling and emptying the storage tanks occurs by displacement of water. During compression, high pressure gas displaces water in the tanks, and during expansion, water flows down into the storage tank from the fixed size output tank as gas flows upward at constant pressure.

Gas flow (top) manifold
Above the tanks, the top manifold attaches to every tank, providing a valve between each tank, and a free valve for the top and bottom tanks.


 * Probably wrong: the top free valve connects to the open air, and the bottom free valve connects upward to the high pressure storage tanks which start full of water.

Hydrostatic pressure (even and odd) manifolds
Below the tanks are the even and odd manifolds. The top tank, the third tank, and every odd tank below that drain into to the odd manifold, and the even tanks including the last or bottom tank drain into the even manifold. There are no valves in the even and odd manifolds, except for a valve on the bottom tank which connects either to the even manifold or to a pipe extending below the open water of the bottom lake.

Low pressure compression / expansion tanks
The requirements for nearly perfect reversibility together with the need to move large amounts of energy dictates that not all tanks can be at the pressure produced by the distance from the tank to the upper lakes.

Operation sequence
The machine runs compression steps when the ambient temperature is low, and expansion steps when the ambient temperature is high. Each step transfers nearly a full tank of water from one lake to the other, and a fixed volume of high pressure compressed gas into or out of the storage tanks, displacing water. Counting the water displaced from or added to the storage tank, each step transfers exactly one full tank of water to or from the lower lake.

Insofar as this is achieved, it is clear why the machine pumps more water up in expansion mode than it lowers in compression mode, even though each step transfers exactly one full tank of water: The machine runs more expansion steps than compression steps. This occurs because each compression step stores more air molecules into the storage tanks than each expansion step takes out.

First compression half step
The compression step begins with all valves of the top manifold closed, and the crossing valves switched so that the top lake connects to the middle manifold and the middle lake to the lower manifold. All of the odd numbered tanks are full of water. The bottom tank, connected to the top lake, has a charge of fully compressed air.

Compression must begin with a tankfull of air and end by disposing of a tankfull of water. The top tank is usually full of water, and if so, it will drain down through the lower manifold and back up to the middle lake during this half-step. That water will eventually make its way down to the bottom lake as it compresses air, so that the level of the middle lake will remain at a constant displacement below the level of the upper lake.

The free valve of the uppermost tank, and every other valve below that, are opened so that the second and third tanks are connected, etc. Since the bottom tank is an even tank, it is unpaired during this half-step, and its free valve is opened and the fully compressed air rises into the storage tank, displacing water. The pressure of the air in the storage tank is balanced by the hydrostatic pressure of the upper lake connected via the middle manifold to the bottom tank. This leaves the bottom tank completely full of water.

Air fills the top tank, and water drains from the top lake via the even manifold into the second tank, compressing air and displacing it into the water filled third tank. A similar process occurrs in the other pairs of tanks. This flow stops by itself when the hydrostatic pressure pushing water into the even tank equals the gas pressure in the next lower odd tank. The even tanks end full of water.

Second compression half step
The second half step begins as all valves are closed in the upper manifold. Then the crossing valves are switched so that the upper lake connects to the odd manifold which always drains every odd numbered tank, including the top tank, and the middle lake connects to the even manifold which drains the even numbered tanks, including the bottom tank. The newly captured atmospheric pressure air in the top tank is compressed, as is the air in every odd numbered tank. The pressure increase is dictated by the height difference between the top and middle lakes. All of the even numbered tanks should be completely full of water so there will be no flow in the even manifold. The piping is arranged so that when valves are closed, the air ends up confined to the lower tank of a pair.

The second half step continues as the valves from the odd numbered tanks and their water-filled lower neighbors are opened. The air in the odd tanks flows up through the valve into the even tanks, and water flows out of the even tanks through the even manifold to the middle lake. However, accounting for all of the water, the net flow must be from the middle lake into the even manifold, since during the first half step, the top tank drained into the middle lake.

There must be some flow into the bottom lake, but it is not yet clear how this flow can be made reversible so that it stops by itself. Also it is not clear how getting to the bottom lake is connected with doing work, as it must be. And it is not clear exactly why the lower tanks need to be the same size as the upper tanks, since the maximum charge of air has much smaller volume in the lower tanks.

Similarly, during expansion, there must be a point at which water is drawn up from the bottom lake.

earlier description...
The heat engine will lower water to compress air,

expanding air will do work on water, forcing it down into U tube and up into the upper reservoir

After confined gas absorbs heat, the pressure rises. Before the gas is allowed to expand, a taller column of water is positioned above it, so that the hydrostatic pressure of the column matches the pressure of the hot gas. Thus, although the volume of water displaced by the expanding gas is the same, a larger quantity of water is moved. A larger force acts through the same distance. More work is done. More water ends up in the top reservoir than was present at the start of the cycle.

At the daily low, ... cold air ... At the daily high, ...

manifold below the tanks

volume of water lowered is volume change of air volume of water raised is again the volume change the amount of air is constant

The heat engine will pump water upward whenever the ambient is hot enough to provide excess energy, and will temporarily compress cold air when the weather forcast says the current temperature is at a minimum.

[still working on this. A (hopefully small) second upper reservoir, slightly higher (or lower) than the upper lake is needed. During compression, every other tank is completely full of water. Air is moved from one tank to the next lower tank by connecting them at the top and letting water flow from the slightly higher reservoir into the higher tank, displacing the air into the lower tank and water from the lower tank up into the other upper reservoir. Not nearly as clear as the system with multiple reservoirs but multiple tanks has many advantages]

Because all compression and expansion must take place while connected to the same upper reservoir, a single working-gas tank will not suffice. The design specifies a series of tanks, each connected from its bottom port past a water pressure gauge and through a valve to the upper reservoir by a dedicated water pipe sufficiently large to avoid turbulent flow during expansion and compression of gas in the tank. The resulting system has a larger surface area devoted to heat exchange, and hence produces more power than the earlier design. Also, a tank used with a wide range of pressures repeatedly expands and contracts, and so might have a shorter useful life than many tanks each dedicated to a narrow range of pressures.

Heat sinks and sources are attached to the tanks by gravity-feed heat pipes. The heat sink, used during compression, is located above the tank. Heat pipes extend downward from the heat sink into but not through the tank. Liquid refrigerant in the bottom of a heat pipe evaporates as working gas warms due to work done on it during compression, and condenses at the relatively cool top of the heat pipe, delivering heat to the heat sink. Valves in the heat pipes are closed when the tank is not producing heat. A chimney above the heat sink carries lighter hot air upward, supplimented with a fan if necessary.

The heat source, used during expansion, is located below the tank. Heat pipes extend upward from the heat source into but not through the tank, delivering heat to relatively cool gas inside the tank as the working gas cools after doing work on the rising water. Valves in the heat pipes are closed when the tank is not consuming heat. A flue extending downward below the heat source carries heavier cool air downward. A fan is available if necessary.

A large high-pressure gas conduit runs from the top of each tank to the next, with one valve beside each tank, so that any pair of adjacent tanks can be connected by closing the flanking valves and opening the central valve. Thus, each tank is directly connected to a water pressure gauge and three valves, including the water valve at the bottom, and two gas valves at the top.

During a time of low temperature, … [still working this out. Having tanks at different levels makes it complicated…]

How expanding gas pushes additional water upward
During the compression phase, cold air is pressurized by a column of water with upper surface at the upper lake level, and lower surface inside the compression tank, near the level of the lower lake. The gas pressure is determined by the number of moles of gas present, the temperature, and the volume. Water will flow until the gas pressure matches the hydrostatic pressure determined by the density of water and the vertical distance between the two water surfaces.

When active compression is finished (valves are no longer being opened and closed), and the ambient temperature begins to rise, heat is conducted into the high pressure compressed gas tank located near the lower lake surface. The gas pressure increases, and water flows downward into the U tube which descends well below the surface of the lower lake before rising to the upper lake. The hydrostatic pressure increases because the vertical distance between the two water surfaces has increased. The amount of work done on the vertical column of water is
 * $$\int_{V_1}^{V_2} P(V) dV $$.

But ...

Description of how to build a model of this system
Originally written for posting to krazyletter.com and elsewhere.

I'm working on a new design (see also a description on my blog), but this is one which you can build a model of, and the model will work. It will be extremely cost effective when built on a large scale. It will refill the reservoir behind a hydroelectric dam from a reservoir below the dam, using only ambient heat, and increasing the amount of power available substantially. Using the excess electricity from many of these machines, hydrogen gas can be made to power cars. Carbon dioxide can be removed from the air, reversing global warming (if enough of these are built). There will be no need to use oil (which is good feedstock for making things) as fuel.

The machine consists of nothing but dams and reservoirs, tanks, pipes, valves, and some sensors and automatic control equipment. It uses water and air to store energy. The machine lowers raised water while compressing cold air. Then that air is heated as the day warms up. Then the machine uses the hot compressed air to raise water. We must show that the machine raises more water than it lowered.

It is well known that heating compressed air at constant pressure increases the volume. The machine will raise the same amount of air for a given volume of compressed air at a given pressure, regardless of the temperature of the air. So if you heat up your air, you can raise more water.

The real question is how much more water is raised than lowered? Is it just a few drops? That depends on how much you heat the air. If you double the absolute temperature, you double the volume. But if you raise the temperature from freezing to hot (0degC to 30degC = 273K to 303K), that is only about a 10% increase in the absolute temperature, so the volume will increase only by about 10%. So the machine will raise at most 10% more water than it lowered if the air goes from 273K to 303K. A real machine would be lowering the whole lake, and raising 10% extra which would be used to generate electricity. Instead of needing rain to refill the reservoir, the daily temperature variation will do it. Building a reservoir on the top of a mountain will work, because you don't need a river to fill it. You just need a reservoir at the bottom as well.

A model will be not so hard to build. Now I know why I was saving all of those soda bottles I have... You need two big plastic tubs of water, one at the top of an outdoor staircase (or better, a long hill) one at the bottom, hundreds (or at least 16) two or three liter soda bottles, a lot of cheap garden hose, and a way of making reliable valves cheap (you need one for every tank). You really need to be able to open and close a bunch of these at once. You need a T joint for every bottle, which screws into the top of the bottle (hopefully it is made from the original bottle cap) and which attaches to cut ends of garden hose.

The maximum pressure developed is equal to the "head" of water, i.e., 15 psi for every 30 feet of elevation. So if the equipment withstands ordinary water pressure, you are in excellent shape unless you are building a very big model.

You cut the bottoms off the soda bottles and effectively seal the top sections together so you get two threaded fittings at top and bottom of each tank.

The machine has two separate parts which can be demonstrated separately. The real machine uses one upper reservoir (open surface) and a large tank half full of water with a closed top that can hold pressure or a partial vacuum. But for one part of the demonstration, we don't need the large sealed tank. A set of connected tanks compresses air using a pair of upper reservoirs at different heights, or raises the level of the water in one upper reservoir while allowing compressed air to expand. For this, you connect one hose with a valve between the top T of every tank. Then you connect a hose with no valve between the bottom T of every even numbered tank (so the bottoms of all even numbered tanks are connected) and between every odd numbered tank as well. The last two tanks have only one bottom connection. The first and second tanks connect to the bottom of both upper reservoirs. That is, both reservoirs have T's on the bottom, and a hose with a valve connects one reservoir to both upper tanks, and the other reservoir to the other side of the T's of the upper tanks.

To compress air using this setup, first close all of the valves and let water flow from an upper reservoir down into both the even and odd tanks. The water will rise higher into the lowest tanks, compressing air there more. This sort of compression is called irreversible because a small change will not change it into expansion, and it isn't what the machine does after it is running. We are just setting it up initially.

Now that all of the tanks contain some air and some water, we want to move all of the water into say the even tanks by letting the compressed air in the odd tanks rise into the even tanks. So open valves between the lower odd tanks and the next higher even tank. Water will immediately flow upward from the bottom hoses into the odd tanks, and push most of the air into the even tanks. The exact geometry of the tanks is important here and will need some tweaking. Then close the valves. This is the normal working setup: half of the tanks are full of water, and the other half contain compressed air. The air in the highest tanks is compressed less than the air in the lower tanks. To compress the air more, make sure the higher reservoir is connected to the tanks with the air in them. Water will flow down from the highest reservoir into the tanks, compressing the air. Then, move the air downward by opening the valves leading to the water filled tanks. Since the reservoir which is slightly lower than the other is connected to these tanks, more water will flow into the upper tanks and the air will move into the lower tanks. It may be necessary to adjust the height of the reservoirs to achieve this.

Next, compress the air which has been forced downward. Close the valves and swap the reservoirs. More water will flow into the tanks with the air because a higher reservoir has been attached. When this stops, open the other set of valves and the air will flow down another step. Keep going, and the air will end up in the bottom tank compressed.

The other set of connected tanks pumps water from the lower reservoir to the upper reservoir, using low-pressure air to move the water upward a small distance each step, or using descending water to create low-pressure air. The setup is almost exactly the same, except it is turned over. The valves and hoses connecting each tank to the next neighbor goe on the bottom, while the jumper hoses connecting even numbered tanks and odd numbered tanks goes on the top. Water flows from one tank to the next, while the low pressure air connects either to the even or the odd tanks, while the others are open to atmospheric pressure. The valves from even to next higher odd tank are closed, and the extra air pressure is applied to the even tanks. The pressure pushes water from the even numbered tank down through the hose with the open valve and up into the next higher odd numbered tank. This happens to all pairs of tanks at once. Then all of the valves are closed, the valves which were closed before are opened, and the extra pressure is connected to the odd tanks. The water rises another step.

To get a small pressure difference from water flowing downward, just reverse the operation. Air will flow out of the hose connected to the lower tank of each pair.