Christophe Pochari, Pochari Technologies, Bodega Bay, CA.
707 774 3024, email@example.com
A 2.8 MWe thermal reactor, the net power density of the reactor is 466 kWe/m3. The overall direct material cost of the system is less than $30/kW. The total number of cycles is almost unlimited. The basic construction of the reactor consists of an atmospheric-bearing vacuum chamber which maintains a medium vacuum to reduce convective heat transfer close to zero. This reduces the complete thermal draw-down time to one year or more. A series of nickel, zirconium and tungsten coated radiant barriers form a monolithic rigid blanket around the aluminum block core, blocking the bulk of the thermal radiation. Each alumina brick is spaced with small zirconia or tungsten spacers to allow expansion and contraction of the entire block assembly. A thin-wall zirconium tank slightly larger than the volume of bricks seals off helium from the vacuum chamber. Helium gas at 5 bar is flowed through the imbedded heat exchanger tubes and exists at the bottom and sent to a secondary heat exchanger where it heats a secondary mass of compressed helium that drives a Brayton cycle gas turbine. The operating temperature of the device is 1500°C, with a 1200°C thermal drawdown to maintain a minimum of 300°C to insure the efficiency of the Brayton cycle does fall excessively. This operating temperature is no higher than standard iron smelting technology hundreds of years old, with a combination of silicon carbide, zirconium, titanium, tungsten, all used sparingly, these temperatures are below the respective melting temperature of the structure. It should be noted that there are no highly stressed parts, since the operating pressures of the helium are very low and the main vacuum chamber is loaded in compression, which allow the use of ceramic materials.
Christophe Pochari Energietechnik has developed a new form of thermal energy storage system not previously considered. It goes without saying that intermittent renewables like solar and wind require some form of storage medium. Unfortunately, after 50 years of research into energy storage, mainly for solar thermal powerplants, no commercial technology exists which can satisfy the demanding scale and endurance requirements of the modern day power grid.
If one evaluates existing schemes of storing energy via sensible heat, one finds a number of very substandard designs and worst yet, a very poor choice of material. Ultimately, a thermal energy storage system is determined almost exclusively by the intrinsic properties of the material used. Design and engineering cannot obviate a poorly conductive material, or a material that simply will not store much heat. The best possible material after examining virtually every earth-abundant elemental composition possible is aluminum oxide. Thermal Energy Storage for Medium and High Temperatures, by WD Steinmann, a recent textbook on high-temperature energy storage, makes only one mention of aluminum oxide in the entire book. A quick search on Google books brings up results for chemical reaction energy storage, where aluminum is combusted and the aluminum oxide is reduced again, but makes no mention of using it as a solid sensible storage medium. Perhaps people have simply missed the opportunity, just as no one had realized one can use pressure to build slender high payload guyed towers. An alternative explanation, and one that we must address to quell concerns of some underlying feasibility issue, is that for some reason, aluminum oxide possesses some feature that makes it an inappropriate material. But this can quickly be ruled out since it finds widespread use as a refractory brick, where durability, thermal stability, and chemical inertness are prized features.
Conventional thermal energy storage technologies are hampered by very poor volumetric power density and sluggish heat transfer due to low-density poorly conductive salts. But the historically poor choice of material and limited operating temperatures of traditional thermal energy storage schemes does not mean a much enhanced and improved system is not possible. The feasibility of the concept here is easily verified with basic heat capacity calculations. The proposal makes no use of exotic materials, methods, or technologies, it is easily manufactured with existing technology at a very low cost. Aluminum oxide has been strangely ignored as a sensible thermal energy storage candidate. Aluminum oxide possesses an essential property for viable thermal storage: high thermal conductivity and diffusivity. This attribute is essential for rapid heating and cooling. The proposed architecture consists of an insulated box filled with individual blocks of solid oxide material. Each “brick” of alumina has 40 6mm diameter channels, an average heat flux of over 40 kW/m² occurs on the channel surfaces. The specific surface area is 40 m²/m3 of brick, enough for 1600 kWh/m3 of heat transfer, allowing for very rapid power extraction. A cubic meter of aluminum oxide can be “drained” to 350°C in only one hour. The image below is a heat transfer simulation showing the hot aluminum oxide brick fluxing heat into the helium channels. Heat flux in many regions approaches 100 kW/m². The simulation was performed in SimSolid. Heat flux of the aluminum oxide block.
The core facet of this technology is the embedded resistive heater and gas channels. Without this design, only very sluggish heating and cooling would occur, no matter how high the heat capacity of the material. This is what allows rapid and near complete transfer of heat from the hot solid into the gas and from the resistive heater back into the brick. The choice of resistive heating element material is narrowed to titanium and tungsten, as nickel-chrome would melt at the desired temperature. Titanium is cheaper and infinitely available and with a high melting point of 1668°C, it is sufficient for this particular application. Titanium possesses a resistivity of 7.5 times higher than tungsten, so less current is needed, or conversely, a larger filament can be used to increase its structural stability. At 900°C, corresponding to the mean temperature of the unit, aluminum oxide has a thermal conductivity of 7.95 W-mK and a high heat capacity of 1235 J/kg-K. The thermal diffusivity is 2 mm²/s. The density of aluminum oxide is 3950 kg/m3, so a cubic meter of the material raised to 1500°C and lowered all the way down to 250°C would possess a sensible thermal energy of 1653 kWh, unparalleled by any other low-cost material. It’s important to stress that the system undergoes no phase change so it is very stable, only a slight thermal expansion occurs. The coefficient of thermal expansion for aluminum oxide is 0.0000086 meters per degree Kelvin, translating into a volume change of 1 percent for the unit in question. Such a volume change is easily accounted for by a slight lateral spacing of the bricks. The bricks are free to expand longitudinally as there is a gap between the entrance of the gas channels at the top. The maximum stress developed in the channels is less than 0.10 MPa from the pressurized helium passing through, resulting in minimal crack propagation. To mitigate leakage of the helium between the sections of aluminum oxide blocks, the blocks are lined or clad with 1mm thick zirconium metal. The blocks are undersized relative to the zirconium cladding to allow for thermal expansion. The slow cracking of the brittle aluminum oxide block is not a concern since the gas is sealed off from the block by the zirconium liner. Total zirconium usage is 0.22 kg/kW, or 618,000 tons for a 2,800,000 MW grid. World reserves of zirconium exceed 32 million tons. Zirconium silicate sells for $3500/ton containing 65% zirconium dioxide, zirconium dioxide is 74% zirconium, or $7.2/kg. Including the cost of the calcium reduction agent, we can safely place the direct cost of zirconium at $8/kg, or $2/kW. The system can tolerate almost infinite thermal cycling since the rate of heating and cooling is quite gradual, with the system cooling at a rate of 20°C per minute, which can qualify as “thermal shock”. Thermal shock intensity is usually measured by pouring very hot objects into a bath of cool liquid where cooling rates are in the hundreds of degrees per minute. Even if cracks appear in the zirconium sealing tubes after tens of thousands of thermal cycles, helium leakage is still prevented by the installation of a steel housing that seals the entire unit off from the atmosphere which doubles as a vacuum chamber for the multi-layer insulation to function. Closed-cycle helium gas turbines form the essential technological component of this energy storage architecture. They are the ideal solution and are required due to the corrosiveness of carbon dioxide or nitrogen at high temperatures against the aluminum oxide bricks. Neon, argon, and krypton could also be used. Helium has a density of 1.4 kg/m3 at a pressure of 30 bar and a temperature of 800°C. Helium’s non-corrosiveness would massively extend turbine blade life to the point where blade life is entirely determined by creep, compared to existing oxy-fuel turbines which experienced intensive erosion and oxidation which cause premature blade failure. Advances in single-crystal nickel alloys allow for turbine inlet temperatures over 1100°C.
Helium closed cycle gas turbines have incredible power density, with 170 MW units being only 6 meters in length! Closed Cycle helium gas turbines have very low mass flow rates, with only around 1 kg/s-MWe. To minimize the pressure drop across the aluminum oxide block heat exchanger, the flow circuit is kept relatively short. The total pressure drop is less than 0.2 bar across a 200mm long channel section, the viscosity of helium at 750°C and 30 bar is 0.052 cP. There are a total of 20,000 flow channels in the 11.5 MWh unit.
The total amount of helium needed is only 1.5 kg for an 11.5 MW unit. Total helium reserves are estimated at 8 million tons. The size of the global power grid is 2,800,000 MW, so we need only 5000 tons of helium to power the entire world with helium closed cycle gas turbine aluminum oxide energy storage banks, or less than 0.06% of global reserves, a trivial amount. In contrast, numerous analysts have calculated that powering the entire world grid with lithium-ion nickel cobalt-manganese batteries would result in a total mineral demand that exceeds current reserves. But even if this weren’t the case, the cost savings alone would force any power plant owner to employ this technology or something very similar over the current $150-200/kW battery banks. In contrast, the Tesla “MegaPack” has a capacity of 3.8 MWh in a volume of 42 cubic meters, or a paltry 90 kWh/m3. This means our technology has 6.66x times the volumetric power density than the best battery storage systems presently available. Since lithium-ion battery chemistry has reached close to the physical limit, there is unlikely to be any significant improvement in the foreseeable future since any further enhancement comes at a severe safety penalty. A large-scale lithium-ion battery pack would be a significant fire and explosive hazard, especially considering the each at which saboteurs could fire small and medium caliber rounds (7.62x 5.56x, 308, .30-06 etc) into them. In the U.S, such calibers are readily available, which would make these battery packs a prime target. In contrast, a sensible thermal energy bank is not-pressurized and is entirely inert, there are no flammable, toxic, corrosive or otherwise dangerous substances that can be released in the air. An essential point to highlight is that this energy storage architecture allows solar farms to eliminate the need for inverters since the resistive heaters make optimal use of the low voltage high current power. So-called “round-trip efficiency”, which battery evangelists constantly propound, plays an insignificant role in the appraisal of an energy storage technology. The power density and the cost per kWh are the primary attributes that warrant attention. It should not come as a surprise that a high heat capacity material paired with a very high-efficiency turbomachine can outperform ionic electrical energy storage by a large margin. Only 6% of the solid-brick stack is occupied by the heat exchanger channels and an additional 1% from the embedded resistive heating element. Now that we have evaluated the critical energetic parameters of the technology, we can turn to the techno-economics of the entire energy storage bank. The basic component of this system is aluminum oxide brick. Aluminum comprises 6% of the earth’s crust, so its theoretical cost as an oxide form is close to zero since no electrolysis and reduction reactions are needed. Bauxite purified via the Bayer process can be directly crushed into alumina powder and melted down to form low-porosity alumina bricks. Aluminum oxide powder has a direct cost of only $500/ton, for an 11.3 MWh storage bank, the cost is $36,000, or only $3.23/kW. The insulation and resistive heating element add another negligible $0.5/kW. After the oxide brick, insulation, and resistive heaters, the only significant cost component is the turbine and compressor. Besides the compressor, there is the cost of a metallic structure to seal any helium from leaking into the atmosphere. It should be noted that the “heat exchanger” is encompassed within the energy storage bank, so no external metallic heat exchanger is needed. A 7mm thick steel containment structure houses the oxide bricks, the weight of this structure is only 3 tons and costs only $2000 at a steel price of $700/ton. We are then left with the helium closed-cycle gas turbine. With a power density of over 8 kW/kg, the total nickel-alloy usage for the gas turbine is only 170 kg. Assuming a total material fabrication cost of 8 times raw material costs which are placed at $20/kg, the gas turbine cost is only $27,000 or $20/kW. The turbine is sized for 1350 kW or 8.37 hours of power at 1.35 MW. These numbers are entirely arbitrary as they are sized for Christophe Pochari Engineering’ high-altitude wind turbine. The system can be scaled to any solar farm regardless of size and the high output RPM of the helium turbine permits a massive decrease in the size of the synchronous generator. The output electrical frequency can be precisely modulated to grid standards of ±200 mHz by slightly varying the RPM of the turbine by controlling the flow of helium into the heat exchanger. Since heat transfer plays a big role in the storage bank’s long-term storage efficiency, large units will deplete much slower due to the square-cube law. Additionally, larger turbo machinery in the multi-megawatt scale benefits from lower tip losses and higher overall mechanical efficiency. The CAPEX number for the closed-cycle turbine appears low compared to open-cycle industrial gas turbines which are manufactured for about $130/kW, but it is consistent with the reduced material used due to the higher power density of the helium cycle. Finally, a thermal “battery” can be charged and discharged almost indefinitely, while a conventional lithium-ion cell can barely hold 3000 cycles without losing a substantial portion of its initial charge. A thermal energy storage system of this kind would last in excess of 40 years with proper maintenance. This technology (and other variations of the principle of solid thermal energy storage), is the only method currently known that can store the 3000 GW to meet the demands of the global electrical grid.
GEN IV reactors, while they are unlikely to see the light of day due to irrational fear and excessive cost driven by regulation, much of the engineering literature pertaining to the construction of these devices can be transposed to high-temperature energy storage. The design of heat temperature heat exchanger and non-Rankine power cycles is highly applicable to this thermal energy storage system. Many GEN IV reactor developers plan on using Brayton cycles over Rankine cycles at up to 900°C. Some designs propose helium cycles while others supercritical CO2. But either way, the design of high-temperature heat exchangers, materials, and design methodologies. The use of a split pressure heat exchanger. The split pressure exchanger represents an elegant engineering effort to decouple the pressure of the main working fluid, the helium driving the turbine, from the same inert gas that flows through the channels of the hot alumina bricks to deliver thermal energy to the turbine. A high specific surface area heat exchanger can effectively transfer, with very minimal losses, the heat from a separate mass of helium within the block channels to the turbine and compressor. The motivation behind the design of such a scheme is simple. A Brayton cycle desires a pressure ratio as high as possible, this is not much of an issue at “only” 950°C, because nickel alloys can retain tensile strength to operate at even a very high-pressure ratio of 50 bar. But such a pressure ratio is impossible to maintain in the 1500°C zirconia heat exchanger pipes that prevent the helium from leakage and cracking the brittle alumina blocks. The separation of the two gas sections is simple and poses negligible losses or disadvantages. Like all technologies, this system relies on two chemical elements to work. These are zirconium and helium. Zirconium is essential since it is abundant yet has a high melting point, it can be used for non-heavily stressed parts in the high-temperature zone. Vanadium is another candidate, with a high melting point of 1910°C and high abundance, it can be used to construct the heat exchanging tubes if zirconium proves unsatisfactory. Occasionally, tungsten and silicon fiber (Nicalon and Tyranno) are used for more heavily stressed parts, and the rest of the system, mainly the turbomachinery, is comprised principally of nickel, chromium, and cobalt ferrous alloys. The second essential element is helium, without it, such a scheme fails miserably. No metal can survive exposure to a reactive compound such as nitrogen, water vapor (steam), or CO2 for thousands of hours at a time at elevated temperatures. Only an inert monatomic gas such as helium can satisfy this essential requirement. Helium scarcity should not serve to dissuade the development of this technology for a simple reason: the quantities required by the heat exchanger and turbine are so negligible per kW that even scaling to the entire global electrical demand does not put a dent in the global helium supply. As long as natural gas is produced, helium will be available.
This technology requires the closed-helium Brayton cycle to work, supercritical carbon dioxide will not likely be commercialized in the near future due to corrosion of the nickel alloys, despite immense hype about this new form of power cycle technology. Carbon dioxide when exposed to hot nickel alloys forms nickel and chromium carbides on the surface of the blades, this will cause premature failure and result in poor turbine endurance. A grid-scale energy storage scheme must be able to last well in excess of 100,000 hours of use or an equivalent number of cycles. While supercritical CO2 cycles have higher efficacies at lower temperatures than helium, this is the price to pay for a long-lasting powerplant. Since the maximum temperature of the aluminum oxide temperature is 1500°C, well below the 1880°C zirconium melting point, the minimum temperature is 300°C, the mean temperature of the alumina is thus 900°C, but the mean temperature for the Brayton turbine is only 650°C, where its efficiency will be determined. We can manually calculate what percent the turbine spends at the lower temperature settings per minute. Since the maximum temporal variation in temperature is 1200°C, but the gas is not allowed to rise above 1000°C for blade creep constraints, the temperature rises and falls by 11.66°C per minute, which is a very gradual thermal fluctuation that minimizes stresses to the metal grain structure. We can create seven isolated temperature profiles corresponding to 8.6-minute time frames, one from 300 to 400°C, one from 400 to 500°C, one from 500 to 600°C, one from 600 to 700°C, one from 700 to 800°C, one from 800 to 900°C, and one from 900 to 1000°C. We can add up these 7 temperature increments and sum their total efficiencies and divide by the number to arrive at a mean turbine efficiency. The cycle efficiency of a Helium Brayton cycle has been shown to be 20% at 350°C, 29% at 450°C, 36% at 550°C, 41% at 650°C, 45.8% at 750°C, 49.4% at 850°C, and 52% at 950°C. The mean is then 45.89%. This number is important because it determines the net electrical storage capacity of the system, since the thermal number alone does not represent available mechanical power. A steel-silicon carbide vacuum chamber with nickel and tungsten-coated radiant barriers With the intention to increase heat retainment time to one year, a more sophisticated and potent form of thermal barrier is designed. The Stefan-Boltzmann law states that the intensity of thermal radiation is equal to the fourth power of the body’s temperature, this implies that above a certain temperature threshold, radiative heat transfer begins to overwhelm convective heat transfer in porous bodies. Most conventional insulation materials are effectively air-trapping devices, maintaining high porosity to rely on the low conductivity of air. Unfortunately, at above 600°C, they become quite ineffectual due to the overwhelming dominance of radiation, which they are ill-equipped to arrest. Electromagnetic oscillations become the dominant mode of heat transfer at these refractory temperatures, so any convective slowing insulation will be very ineffective. High temperature thermal energy storage has been historically constrained by this fact, but numerous solutions exist. Conventional refractory bricks, even with high porosity, have difficulty achieving thermal conductivity of less than 0.4 W-mK at the operating temperature of the system which reaches a maximum of 1500°C on the interior. With conventional refractory brick, with 350 millimeters of insulation, which occupies much additional volume and reduces the power density, complete thermal drawdown is as fast as 40 days for a small unit. For large-scale grid storage, we may need to provide backup for months at a time during periods when wind speeds are low or solar irradiance is zero due to permanent cloud cover. It is not acceptable to lose the complete energy contents of the system in only a month, otherwise, we are no better than batteries in this respect. A very simple solution can be adopted to solve this issue. According to basic radiative heat transfer physics, we can use a material with very low emissivity, such as highly polished metal, to very efficiently arrest the propagation of these “heat rays”. Unfortunately, aluminum, which has the lowest emissivity excluding gold and silver, cannot be used due to its low melting point, so instead, we can use nickel, zirconium, tungsten, or cobalt-coated ceramic sheets as our radiant barrier. These respective materials all have emissivity’s of below 0.25 at temperatures of up to 1500°C. Tungsten has an emissivity of 0.15 at 1500°C, nickel 0.16 at 1093°C, Zircaloy 0.24 at 1605°C, cobalt 0.23 at a 1000°C. All numbers on emissivity can be independently verified in the book ASM Ready Reference: Thermal properties of metals, by Fran Cverna, 2002. Tungsten, therefore, emerges as the most reflective, but with enough layers, these relatively small emissivity value differences contribute to a negligible difference in overall thermal flux. The sheets can also be constructed out of solid metal, since they do not have to be very thick, the cost of zirconium or nickel is minimal. If we have a total of 15 panels stacked in front of each other with a small gap of only a few millimeters, there is a natural gradient or temperature drop from the hot to the cold side. The cold side of the radiant barrier touches the steel/ceramic vessel being constantly convectively cooled by the outside air. The radiative flux of the inner-most radiant barrier is equal to the maximum temperature of the device, with each subsequent barrier experiencing a temperature drop depending on the number of panels. The total initial flux at 1550°C is 125,000 W/m² with an emissivity of 0.2. The 2nd panel, 102°C cooler, radiates 99,900 W/m², the 3rd panel 78,700 W/m², the 4th 61,000 W/m², the 5th 46,300 W/m2, the 6th, 34,700 W/m2, 7th panel, 23,400 W/m2, the 8th, 18,000 W/m2, the 9th, 12,400 W/m², the 10th, 8,300 W/m², the 11th, 5200 W/m², the 12th, 3100 W/m², the 13th, 1700 W/m², the 14th, 850 W/m², and the 15th, 363 W/m², or an average temperature adjusted radiative flux of 35,000 W/m². If we then assume exponential radiative decay at an emissivity of 0.2, the net radiative flux on the outer-most panel is only 0.0000011 W/m², or effectively zero. In reality, there will be some leakage of heat through the parameters of these radiant barrier stacks, and emissivity values will slightly differ due to specific wavelengths, but the number is low enough to be treated as zero. This does not mean multi-layer insulation has zero thermal conductivity, substantial losses occur due to the conduction through the spacers.
The radiative flux across a series of stacked radiant barriers is not logarithmic or merely the sum of the emissivity values, it must be exponential since each barrier can only be heated to the extent it is radiated. Emissivity is merely a measure of the fraction of a body’s internal thermal energy shed as radiation, a low emissivity body radiates less than its internal thermal energy because it cannot convert the entirety of its internal kinetic vibratory energy into electromagnetic waves. It is always measured as a ratio of a perfect black or white body. The emissivity of a material must always be the inverse of the absorptivity, and vice versa, this forms the basis of Kirchhoff’s law of thermal radiation. The ability of a material to possess high or low emissivity seems to be strongly determined by its dielectric constant. Now we can calculate the convective heat transfer within the vacuum chamber. If we assume a moderately high vacuum can be attained if leakage rates are kept low, which can easily be achieved by proper seal design and a permanent vacuum pump, then the convective heat transfer is close to zero, but should be calculated anyway. A “medium vacuum” is defined as anything from 10-3 mbar to 1 mbar, with an average of 0.5 mbar, or 0.0000098 atm. Such a vacuum is readily achieved with ordinary vacuum pumps such as rotary plunger pumps, piston pumps, scroll pumps, screw pumps, rotary vane pumps, rotary piston pumps, roots pumps, and absorption pumps. Since air has a density of 1.25 kg/m3, we can assign a density of 0.00061 kg/m3. The convective heat transfer coefficient of a body of air at 1 atm at 1500°C, with a density, viscosity, and thermal conductivity corresponding to these conditions (density of 0.20 kg/m3, thermal conductivity of 0.097 W-mK, and viscosity of 0.000057 N*s/m²), with a temperature difference of 100°C at 1500°C, is 2 W/mK, if we then assume a linear decrease in molar concentration, then the coefficient drops to 0.00098 W/mK, or a thermal flux of only 0.12 W/m². Concept Group LLC has developed a high-temperature vacuum multilayer insulation system designed to operate at up to 1000°C, although little data is provided. If the thickness of the radiant barrier is 50mm and the total then the thermal conductivity is 0.0001 W/mK. Multilayer insulation in a strong vacuum can achieve values of 10^-5 W/mK, or 0.00001 W/mK, or ten times more. So our numbers are reasonably conservative since a higher temperature MLI system will experience more intensive radiative transfer, lower emissivity’s values, and more convective heat transfer since the velocity of air molecules will be proportionally higher. Note that published data on high temperature multilayer insulation by NASA shows thermal conductivity much higher, no less than 0.04 W/mK, this is due to the use of a relatively dense ceramic fibrous material between the reflective layers, which varies from 50-60 kg/mk3 (Heat Transfer in High-Temperature Multilayer Insulation, by Kamran Daryabeigi). This ceramic material has very high emissivity and thus allows radiation to heat it and permits substantial conduction through the fibrous material. The difference between the numbers experienced by NASA and our numbers is not due to some mistake in mathematics. After all, we know exactly what the temperature of each metal barrier is and what the radiative flux is. The convective heat transfer can simply be calculated by taking it as a fraction of atmospheric pressure data at the same temperature. Using the kinetic theory of gases, we can easily calculate the change in the mean free path with molar concentrations and temperature. The mean free path of air molecules at 0.01 mbar and 1000°C is 0.0439 meters, or 43 millimeters, so radiant barrier gap size makes little difference in the convective heat transfer coefficient as long as the mean free path is much greater than the gap avoiding molecule to molecule collisions with virtually all collisions occurring between the two surfaces. The mean free path of gas molecules grows to very large dimensions at low molar concentrations, but decreases at a much slower rate with higher temperatures since molecules have more inertia and velocity, and hence collide more frequently. At ATP conditions, the mean free path is only 0.0001 mm, or 430,000 times less, so the convective heat transfer coefficient should fall roughly proportionally to the molar concentration and the mean free path to radiant barrier gap ratio. With a regime of free molecular flow, defined as having a Knudsen number greater than ten, convection does not occur if the space between the obstruction is smaller than the mean free path, in such a scenario the gas is treated as a conductor only. In fact, the thermal conductivity of a true multilayer insulation system is so low that effectively all the heat flux occurs through the solid spacers, the edges where the panels or sheets are mounted, and through manufacturing defects. Heat loss through the helium inlet and exit hoses also accounts for a non-negligible thermal flux. If we calculate a breakdown of the major contributors to thermal leakage, it is almost exclusively the spacers, so using thick radiant barriers that remain structurally stable without risking creasing, we can dramatically decrease heat flux down to the bare physical limits. When we add spacer conduction, assuming a spacer construction material consisting of highly porous yet structural ceramic, we add around 1 watt to the heat flux. One of the central advantages of the low thermal conductivity radiant barrier vacuum insulation is that it allows us to design quite small systems, since we are less sensitive to an increase in the surface-to-volume ratio. With ultra-low conductivity insulation, we can design units as small as 1 meter in diameter which lowers manufacturing costs in great measure due to higher production volumes and simpler fabrication. The system is still limited by the tip-losses, boundary layer effect, and overall mechanical efficiency of the turbomachinery, but with this insulation system, downscaling to a small 4-5 MWe system is more than possible.
Sealing the vacuum chamber is essential for continued insulation performance. A number of options arise to effectively seal the system. One such option involves the use of solid-mechanical connections such as welds, tightly bolted flanges, low asperity gaskets or high-pressure drop surfaces that slow leakage rates down to the level that can be routinely evacuated by an online vacuum pump. A 5.6 MWe storage unit in a cylindrical geometry has a surface area of 24 m², with a dimension of 1.6 meters wide and 4.5 meters tall. As we have illustrated with these above calculations, the total heat flux is thus almost entirely due to conduction in the spacer. If a porous ceramic is used, the same material as the refractory brick as the space, and the thermal conductivity is around 0.35 W/mK, spacer conduction losses can be kept to a minimum with low spacing intervals. At an interval of 100x100mm with each individual spacer 5mm in diameter, the spacer surface area is 2500 mm²/m², or about 6.5 W/m². This translates to a complete thermal drawdown of 8.9 years. This figure is close to a standard consumer lithium-ion cell which experiences a 2-3% monthly self-discharge rate, but this number is largely prevalent for grid storage since maximum storage times will not exceed a few weeks. In fact, we can tolerate an insulation system that has a thermal conductivity that equals a 10% loss over a period of one month, or about 80 W/m².
The extreme simplicity, proven physics of sensible heat, mature turbomachinery technology, extremely low CAPEX, and simple engineering, make it almost certain that high-temperature aluminum oxide energy storage can scale to facilitate a true 100% wind and solar energy grid. The technology is inherently proven since Cowper furnaces, which are used to heat air in iron smelting plants, make use of the same brick-integral heat exchanging concept and boast very long lives. Competing technologies such as lithium-ion batteries and hydrogen are rendered extremely uncompetitive in light of this technology and one can go as far as argue they are obsolete, strictly in a grid-scale storage context. But this technology has even deeper disruptive implications. It is not merely that so-called “non-baseload” energy technologies such as wind and solar are now cemented in the energy future, but that this technology makes redundant complex and expensive “baseload” clean sources such as nuclear and geothermal, whose sole “raison d’etre” is precisely this very feature. Mono-crystalline solar panels are manufactured for only $240/kW and high-altitude wind turbines (pneumatic towers), could for the same price, with a capacity factor of 21% and 65% respectively, nuclear and geothermal must be brought down to substantially below $1000/kW in order to compete. Such a prospect is very unlikely to occur due to fundamental technological, material, and physics limitations, strongly suggesting investments in any technologies outside of wind or solar is inadvisable. The deserts of the world contain orders of magnitude more land than is needed to power human civilization many times over, if only a way to store gigawatts of energy existed, solar farms in Egypt would power all of Europe.
A brief note on the urge to “compare to batteries”
Alternative energy advocates often like to state that hydrogen, thermal energy storage, pumped hydro, or other energy storage schemes are a form of “battery”. Unfortunately, this is another category error. Batteries cannot and will not fulfill the role of high-intensity ultra-high cycle gigawatt energy storage, but thermal energy storage will not fulfill any roles presently occupied by batteries either, namely applications where less than 500 kW are needed. Apart from our comparison of the volumetric power density, we have been careful to not excessively pitch the technology as an alternative to “batteries”. This technology by no means makes batteries “obsolete”, batteries will be used to power small power output devices for centuries to come. This technology is a highly specialized form of energy storage system ideally suited for wind turbines and photovoltaic arrays, but it will find little use in small-scale applications. While the term “charge” and “recharge” is used to refer to the heating and cooling of the device, we found that this was necessary as the term “heating” did not evoke the “energetic” build-up and depletion characteristic of this technology. This novel thermal energy storage device is suitable for high power density applications that require extremely high endurance (tens of thousands or even hundreds of thousands of cycles), low downtime, and extremely low capital costs. Batteries are small, light, portable low-voltage power sources that are principally used for personal electronic devices. This technology requires turbomachinery to operate and thus cannot scale down to the kilowatt level without severely sacrificing mechanical efficiency. Virtually 100% of all battery packs ever built are below 1 kW, and while individual battery cells can in theory be infinitely stacked, they appear to have limited applicability to high intensity, high endurance, and large-scale high-power density energy storage. The commonly assumed reason that consumer batteries cannot scale to global grid storage is due to constraints imposed by their raw material inputs. But this is incorrect and is yet another example of man’s supercilious attitude towards nature, that he can “destroy” nature by depleting her gifts. There are orders of magnitude more nickel, cobalt, and lithium to produce enough consumer-type batteries to power the entire world’s electricity grid. A standard lithium, ion cobalt manganese cell, the Panasonic 18650 is widely used in electric sedans uses 0.083 kg/kW of lithium, 0.65 kg-kW of nickel, and 0.083 kg/kW of cobalt. The global electrical grid is 3000 GW, and we assume the capacity is equal to name-plate production capacity, but many estimates are unrealistically conservative and multiply this number for additional “reserve”. This is simply not necessary because photovoltaic and wind farms can merely be oversized. If the entire world’s electrical grid used 18650 cells, barely one year’s worth of nickel would be used, a drop in the bucket. A similar situation is found for cobalt and lithium, the so-called “mineral” constraint is an ignorant myth due to incorrect calculations. Just as helium is not a constraint for the proposed architecture, metals are by no means a constraint on building grid-scale batteries. Nickel is plentiful, the current boondoggle of building electromobility will not event place a dent in the global nickel supply. Manganese is a very abundant metal so it is not considered for this quick calculation. The principle and perhaps single reason batteries will not be used for high-intensity grid storage is due to their extremely short cycle life. Any owner of a mobile phone, digital camera, or laptop can attest to this. “Industrial” batteries do not possess different “chemistries” that can markedly change this, it is a fundamental attribute of the technology itself, just as brittleness is an attribute of concrete or heat is an attribute of friction. All “commercial” type batteries are merely versions of existing consumer-grade batteries adapted to commercial use and packaged in a more durable container with additional fireproofing. The typical consumer-grade lithium-ion cell will have trouble preserving half its original charge at barely 1500 cycles, equivalent to complete drainage and charge for four complete years. This is typically not a concern because the phone or device in question will be replaced by this time. A typical electrical grid component, such as a mains transformer, dynamo, or steam generator is rated for several hundred thousand hours of continuous use. A typical steam turbine can last 400,000 hours before overhaul is required, such a lifespan is simply physically impossible with an electrochemical device since chemical reactions will inevitably occur between the dissimilar metals halting the electrochemical activity.
Figure 2: Heat flux of the aluminum oxide block.
Figure 4: Power density of helium gas turbines relative to S-CO2 and Rankine.
Figure 5: Heat capacity tables for aluminum oxide.
All numbers stated here can be confirmed using Omni calculator https://www.omnicalculator.com/physics/specific-heat
 https://www.researchgate.net/publication/326372991_Dilatrometric_sintering_s tudy_and_characterization_of_Alumina-nickel_composites/figures?lo=1