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Eduard Heindl
In the longer term, mankind has to use essentially renewable energy sources. Stored energy in the form of coal, oil and natural gas are running low and due to the CO2 emission they are troublesome. Nuclear energy sources are politically controversial. The renewable energy sources with great potential are solar and wind, both forms of energy have significant temporal variations. Energy storage is always necessary, if there is a high percentage of these renewable energy sources used.
The energy storage should come on a reasonable price and compensate power generation fluctuation over several days. Only hydro storage power plants are in large commercial applications and can store some gigawatt hour (GWh). The cost of storing a kilowatt hour (kWh) is about 50 Euro in hydro storage. This price is, compared to other storage technologies, such as batteries, still very cheap. Storage cost in batteries are in best cases in the range of 1000 €/kWh. In Germany, and many other countries, there are only a few places where pumped-storage power stations can be built. Useful in particular are only a few high elevated areas in the mountains, which can be flooded without losses.
Figure 1: The basic principle of hydraulic hydro storage.
A new option could be hydraulic hydro storage, presented in this article. The basic idea is to lift a large rock mass and the store potential energy. If necessary, the rock mass is lowered again and potential energy is transformed into electricity. Approaches that try to move large masses by mechanical means, such as ropes or tracks failed due to the cost per stored kWh. However, there is the possibility to lift a large mass by hydraulic means, and therefore this path is an interesting choice. A cylinder of rock, preferably granite, within its natural environment, is separated from the surrounding. This is done by wire saws as they are used in quarries to separate large stone blocks. In this case, the wire saw is designed to cut a cylinder wall and the cylinder bottom off.
In this arrangement, water is pumped into the bottom between the cylinder and the base, resulting in a lift of the heavy granite piston. The piston is sealed against the surrounding rock. The raised piston stores the electric pump energy in form of potential energy. To earn the energy from the system, the pressurized water is feed into a turbine, connected with a generator to generate electricity. This is similar to the basic principle of a conventional hydro storage.
The key advantage of this approach lies in the extraordinarily large amount of energy that could be stored and the relatively small investments compared to a similar hydro storage. A simple calculation shows that the stored energy grows with the fourth power of the piston radius in the case when the piston height is twice the radius. This means, if a system has two times the radius, the capacity is 16 times higher! Details are presented in the information box at the end of this article.
The interesting point of this arrangement is; the amount of energy grows by to the fourth power of the radius while the production costs, mainly through the removal of the cylinder from its environment, grow only with the second power of the radius. This means, in comparison to all other known forms of storage, almost arbitrary low costs per kilowatt hour can be archived if the radius of the system is large enough.
To illustrate the relationships and dimensions to two hydraulic hydro power stations are calculated. The first power plant will have a radius of 150 meters; the second one is 500 meters.
The stored energy is obtained at a rock with a density of 2500kg/m² a reduced density of 1500 kg / m³ (this water is considered to replace the rock) and with a radius of 150m:
E = 150m 13GWh storage capacity. This is precisely the capacity of the planned storage power plant in Atdorf Schluchseewerk AG.
If we increase the radius to 500m, the capacity is growing to:
E = 500m 1614GWh! This is the current daily electricity production of Germany.
An analysis of the renewable future shows, that the mix of wind and solar energy needs, at least, a two day storage capacity. It would therefore be sufficient, if two hydraulic hydro storage, each with 500m radius, where built in Germany. The space requirements of these plants are less than two square kilometres. This is incomparably less than the corresponding reservoirs for hydro storage, flooding about 100 square kilometres. Moreover, with hydraulic hydro storage the area is not flooded and can remain in the natural state.
The concept for the storage of energy with a large piston is new and therefore only rough estimates of the costs can be calculated. However, there are already reliable figures for the components, since the individual manufacturing steps are of conventional nature. To separate the piston of a granite stone, we need a location where the granite is near to the surface. This is in the Black Forest and in many other places the case.
The first step is the mine shaft pushed forward to the desired depth (1km). Next step are two circular tunnels, each of 3km circumference. For comparison, the tunnel for the experiment at CERN near Geneva, to search for elementary particles, has a circumference of 28 km. From the surface holes are drilled to the tunnel and in these holes sawing wires for granite are introduced, which proceed from the granite extraction. Because granite is very hard, there is a substantial wear of the wire saw and the expected cost are 10 Euro per square meter of cut surface as common in granite mining. For this system that costs sum up to approximately 32 million Euro for cutting.
The construction of the tunnel is also quite expensive and cost of 50,000 € per meter is calculated resulting in 360 million €. The other components such as pumps and generators as well as connection lines depend on the exact design of the system. They are not included in the bill here, since they are independent of the technology. The system price is, without power converter, but including drilling and some other parts is at about 700 million Euro. On the first glance, this is a lot of money. The costs have to be calculated per kilowatt hour and are at 0.50 Euro/kWh far less than 50Euro/kWh as common in hydro storage.
As with all new, unproven technologies, we can not predict exactly what problems they might cause. But some ideas are presented here.
Technical problems lie mainly in the construction similar to the uncertainty in each tunnel project. Undetected tectonic disturbances can exist that lead to water ingress. However, the advantage to other tunnel projects is, we can choose the desired region and take zones, in which a very low risk of unexpected problems is expected. The cutting of the cylinder walls is difficult because the walls have to be very precise, otherwise the piston movement is disturbed, resulting in friction losses later.
The seal between the piston and the stroke volume should be good, have low losses of water, although some cubic meters per second are for large storage systems acceptable. The seal, however, requires that the outer surface has mayor cracks, existing cracks must be sealed, but what is technically well feasible with concrete and steel.
An interesting question is whether the piston can tilt. But this is not possible as long as less then half of the piston is moved above the surface. Strictly speaking, as long as its centre of gravity lies below the seal line, it can not tilt.
Another aspect is the large amount of water that will fill the cylinder capacity. The required water should be taken from a large water bodies. A water reservoir such as Lake Constance would be adequate, this would result in a maximum fluctuation of one lake level of one meter, calculated for an extremely large plant with 500m radius.
An alternative source would be sea water if the site is located near the shore line. Locations near the sea have the advantage of being able to optimally absorb the wind energy.
Ecological problems arise on a small scale for the vegetation on the piston, as this increase in a somewhat lower temperature is through the year. This slight effect in the range of two degrees can be practically ignored, it simply corresponds to the altitude.
The figure shows a storage plant with a capacity of the total daily gross electricity production in Germany. (1.600GWh)
Calculation of storage performance
The stored energy increases with the fourth power of the system radius r. This is, because the possible lifting height H growths proportional to the piston length which is chosen as two times the system radius r.
The maximum stored energy is calculated from the density of the rock Rho1 and the effective density Rho2 to consider is the hydrostatic pressure of water, as water density Rho3 substitutes the rock mass replaced. Thus, the effective density:
Rho2 = Rho1 - Rho3 (2)
The equation for the potential energy E at a height H in the gravitational field of the earth with the constant g for a mass m is
E = g * m * H (3)
The effective mass of a cylinder is calculated by
m = Pi * r ² * h * Rho2 (4)
Equation (4) in equation (3) is used, taking into account that H = r will be:
E = g * r ² * Pi * 2 * r * r * Rho2 (5)
Equation (5) summarized:
This demonstrates that the stored energy is proportional to the fourth power of the system radius.