THERMAL ENERGY STORAGE APPARATUS
20220155026 · 2022-05-19
Assignee
Inventors
Cpc classification
Y02E60/14
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
F01K3/16
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F28F21/02
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F28D2020/0013
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
Y02E10/50
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
Y02E70/30
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
F28D2020/0078
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F01K3/14
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
International classification
F28D20/00
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
Abstract
The present invention provides a thermal energy storage apparatus comprising a housing which defines a hollow interior chamber, the chamber arranged in use to house graphite solids material in an inert gas atmosphere therewithin; and at least one conduit arranged to extend through the hollow interior chamber via inlet and outlet openings in the housing, the conduit being sealingly fitted to the housing at the inlet and outlet openings, and an exterior surface of the or each conduit being arranged in a close facing relationship with the graphite solids material located within the hollow interior chamber, wherein, in use, the or each conduit is arranged for conveying a flow of a fluid therethough such that in a first configuration, said flow transfers thermal energy to the graphite solid material, and in a second configuration, the graphite solid material transfers thermal energy to said flow.
Claims
1. A thermal energy storage apparatus comprising: a housing which defines a hollow interior chamber, the chamber arranged in use to house graphite solids material in an inert gas atmosphere therewithin; and at least one conduit arranged to extend through the hollow interior chamber via inlet and outlet openings in the housing, the conduit being sealingly fitted to the housing at the inlet and outlet openings, and an exterior surface of the or each conduit being arranged in a close facing relationship with the graphite solids material located within the hollow interior chamber, wherein, in use, the or each conduit is arranged for conveying a flow of a fluid therethrough such that in a first configuration, said flow transfers thermal energy to the graphite solid material, and in a second configuration, the graphite solid material transfers thermal energy to said flow, and wherein the fluid is a thermal (heat) energy transfer fluid (HTF) which operates such that: in the first configuration, the flow of fluid conductively heats the or each conduit, and the conduit conducts and radiates heat towards the graphite solid material, and in the second configuration, the graphite solid material conducts and radiates heat towards the or each conduit, and the conduit conductively heats the flow of fluid therewithin.
2. (canceled)
3. The thermal energy storage apparatus according to claim 1, wherein the graphite solid material is repeatedly heated and cooled by the respective transfer of thermal energy, into and from, the flow of said thermal energy transfer fluid.
4. The thermal energy storage apparatus according to claim 1, wherein when the apparatus is arranged with a single conduit, then to operate with both the first and the second configurations, the conduit is adapted to convey different fluids sequentially therethrough.
5. The thermal energy storage apparatus according to claim 4, wherein said conduit comprises a material suitable for conveying a flow of HTF or a supercritical fluid when in the first configuration, and said conduit comprises a material suitable for conveying a flow of a supercritical fluid when in the second configuration.
6. The thermal energy storage apparatus according to claim 4, wherein said conduit comprises a material suitable for conveying a flow of HTF or a supercritical fluid when in the first configuration, and said conduit comprises a material suitable for conveying a flow of HTF when in the second configuration.
7. The thermal energy storage apparatus according to claim 1, wherein when the apparatus is arranged with at least two conduits, then to operate with the first configuration, the apparatus is adapted to convey fluid in a first conduit, and to operate with the second configuration, the apparatus is adapted to convey fluid in a second, separate conduit.
8. The thermal energy storage apparatus according to claim 7, wherein said first conduit comprises a material suitable for conveying a flow of HTF or a supercritical fluid, and said second conduit comprises a material suitable for conveying a flow of a supercritical fluid.
9. The thermal energy storage apparatus according to claim 7, wherein said first conduit comprises a material suitable for conveying a flow of HTF or a supercritical fluid, and said second conduit comprises a material suitable for conveying a flow of HTF.
10. The thermal energy storage apparatus according to claim 5, wherein the HTF is at least one of the group comprising: liquid sodium (Na), liquid potassium (K), liquid NaK (77.8% K), liquid tin (Sn), liquid lead (Pb), and liquid lead-bismuth (PbBi) (45%/55%).
11. The thermal energy storage apparatus according to claim 5, wherein the supercritical fluid is at least one of the group comprising: carbon dioxide (CO.sub.2), methane (CH.sub.4), ethane (C.sub.2H.sub.6), propane (C.sub.3H.sub.8), ethylene (C.sub.2H.sub.4), propylene (C.sub.3H.sub.6), methanol (CH.sub.3OH), ethanol (C.sub.2H.sub.5OH), acetone (C.sub.3H.sub.6O), and nitrous oxide (N.sub.2O).
12. The thermal energy storage apparatus according to claim 7, wherein the first and second conduit comprises a material with an operating temperature range of about 550° C. to about 1000° C.
13-18. (canceled)
19. A thermal energy storage module comprising: a plurality of the thermal energy storage apparatus according to claim 1; the housing of each of said apparatus being adapted to be mounted and suspended from a frame which is locatable inside of an intermodal shipping container; and the inlet and outlet openings of the or each conduit which are provided at the housing being externally connected to an input and an output manifold, which in use are for conveying a flow of the fluid through the conduit(s).
20. The thermal energy storage module according to claim 19, wherein each of the plurality of thermal energy storage apparatus has one or more relevant sensors to measure a condition of the graphite solids material therewithin.
21. The thermal energy storage module according to claim 20, wherein the conditions measured include one or more of the group comprising: temperature of the graphite solids material, the amount of inert gas pressure, and the amount of oxygen present.
22. The thermal energy storage module according to claim 20, wherein a programmable logic controller (PLC) is provided, such that signals from relevant sensors for monitoring the graphite solids material are connected to the PLC, and related responsive electronic control devices are controlled by the PLC, wherein the PLC is programmed to monitor the relevant sensors and to control the fluid flow to the module.
23. (canceled)
24. A method of operating a closed-loop power generation system with a thermal (heat) energy transfer fluid (HTF) as the working fluid, the power generation system comprising a thermal energy storage apparatus, and a HTF turbine generator, the method comprising: storing energy using the high temperature thermal energy storage apparatus comprising graphite solids material; and then, at a time when the energy is needed: using the stored thermal energy to heat the components of a flow of HTF by placing these components into contact with the thermal energy storage apparatus via the heat exchanger; and placing a flow of the resulting HTF into fluid communication with a downstream HTF turbine generator.
25. (canceled)
26. The method according to claim 24, wherein the HTF is used to operate the turbine to generate electricity.
27. (canceled)
28. A method of operating a thermal energy storage apparatus, the method comprising: making a fluid connection to a housing, the housing comprising a hollow interior chamber substantially filled with graphite solids material in an inert gas atmosphere, the housing having at least one conduit arranged to extend through the hollow interior chamber via inlet and outlet openings in the housing, the conduit being sealingly fitted to the housing at the inlet and outlet openings, an exterior surface of the or each conduit being arranged in a close facing relationship with the graphite solids material located within the hollow interior chamber; conveying a flow of a thermal (heat) energy transfer fluid (HTF) from an upstream source via the fluid connection into the or each conduit, thereby transferring thermal energy to the graphite solid material until a desired graphite temperature is reached; then, at a future time, when the thermal energy is needed downstream, the method further comprises: making a fluid connection to the housing, using the stored thermal energy to heat the components of a flow of HTF by placing these components into contact with the thermal energy storage apparatus in the or each conduit; and placing a flow of the resulting HTF into fluid communication with a downstream supercritical fluid turbine generator.
29. The method according to claim 24, wherein the HTF is a supercritical fluid.
30. The method according to claim 29, wherein the supercritical fluid is a carbon dioxide (sCO.sub.2) working fluid in a Brayton Cycle turbine generator.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0043] A preferred embodiment of the invention will now be described, by way of example only, with reference to the accompanying drawings in which:
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DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
[0073] This disclosure relates generally to to the field of energy storage, and in particular to an apparatus and method for the storage and use of thermal (or heat) energy. The inventors have devised a process which makes maximum use of carbon in the form of graphite as a high-efficiency thermal energy storage medium, which has been found to exhibit an increase in its thermal energy storage capacity as its temperature is increased.
[0074] The conversion of thermal energy to steam to drive a steam generator is very mature power generation technology, which normally requires steam with a temperature in the range 400 to 580° C. It is known that this technology is limited to a conversion efficiency of about 36%, and in addition, the physical chemistry of a steam power plant means that there long effective “start-up” time for the plant to generating power. The low conversion efficiency means that such power plants need economies of scale to make them viable, but this also means they will be capital cost intensive.
[0075] Graphite is known to be able to be heated to very high temperatures (over 1200° C.) so it is well-suited to be the basis for high temperature storage of heat or as a buffer to heat generation in high temperature plant. In experiments conducted by the inventors, and which are attached in
[0076] Referring specifically to
[0077] Supercritical carbon dioxide (sCO.sub.2) is a fluid state of carbon dioxide where it is held at or above its critical temperature and critical pressure. Carbon dioxide usually behaves as a gas in air at standard temperature and pressure (STP), or as a solid (dry ice) when frozen. If the temperature and pressure are both increased from STP to be at or above the critical point for carbon dioxide, it can adopt properties midway between a gas and a liquid. More specifically, it behaves as a supercritical fluid above its critical temperature (304.25 K, 31.1° C.) and critical pressure (72.9 atm, 7.39 MPa, 73.9 bar), expanding to fill its container like a gas but with a density like that of a liquid. Reference should be made to
[0078] As a working fluid, sCO.sub.2 has desirable properties such as being chemically stable, low-cost, non-toxic, non-flammable and readily available. Such properties are therefore useful in closed-loop power generation applications, when looking for a non-flammable working fluid to use with graphite. sCO.sub.2 power cycles (Brayton Cycle) typically operate between 500° C. and 900° C.
[0079] In the case of sCO.sub.2, the higher the temperature the more efficient energy conversion from thermal to electricity. Some studies show that under 600° C. the conversion efficiency is same as steam cycle (Rankine Cycle) but over about 650° C. then efficiencies can reach 58% at 850° C.
[0080] An sCO.sub.2-based turbine was recently operated at 50% efficiency. In it the sCO.sub.2 was heated to 700° C. It required less compression and it reaches full power in 2 minutes, whereas steam turbines need at least 30 minutes. The prototype generated 10 MW and is only approximately 10% the size of a comparable steam turbine.
[0081] In effect, this means that, using sCO.sub.2 in combination with the thermal energy storage capacity of Graphite could significantly and synergistically multiply the electrical power produced per unit of input energy required.
[0082] In addition, due to its high fluid density, sCO.sub.2 enables extremely compact and highly efficient turbomachinery. It can use simpler, single casing body designs whereas steam turbines require multiple turbine stages and associated casings, as well as additional inlet and outlet piping. Power generation systems that use traditional air Brayton and steam Rankine cycles can be upgraded to sCO.sub.2 to increase efficiency and power output.
[0083] Furthermore, due to its superior thermal stability and non-flammability, direct heat exchange from high temperature sources is possible, permitting higher working fluid temperatures and therefore higher cycle efficiency. And unlike two-phase flow, the single-phase nature of sCO.sub.2 eliminates the necessity of a heat input for phase change that is required for the water to steam conversion, thereby also eliminating associated thermal shock stress, fatigue stress and corrosion.
[0084] Apart from cost effectiveness and efficiency the questions of safety is crucial because of the possibility of a graphite fire if the graphite at high temperature comes into contact with oxygen (or air). Prior systems which utilise graphite as a thermal energy storage medium, were (and are) susceptible to catastrophic failure because of their design. When electrical heating elements directly heat a large block of graphite with embedded conduit to convert the stored energy into steam, there is a high level of risk of fire.
[0085] In the present disclosure, the graphite is encased in a fully welded shell and embedded with multiple conduits in the form of heat exchangers, useful for both heating up the graphite block as well as for provision of heat energy to the supercritical fluid. The use of multiple suspended panels of graphite with multiple embedded conduits connected externally to input and output manifolds readily allows the charging of heat transfer fluid and the removal of heated heat transfer fluid. The heat transfer rate and heat extraction rate can therefore be regulated by flow control valves on the manifolds. Finally, the sealed graphite panels may be purged with argon and presence of oxygen monitored by oxygen sensors. Thermocouples are inserted in each panel allowing the temperature of each panel to be monitored and flow regulated as required, to maximise performance.
[0086] In summary, the apparatus and method of operation disclosed has the following advantages: safety—all conditions for graphite fire designed out; transportable—can be moved using intermodal frame and shipping; scalable—modules can be added as required, and the panels are designed for high volume manufacture; and efficiency—the synergy of the optimised temperature of operation for both the non-flammable working fluid sCO.sub.2, and the increased heat storage capacity of graphite.
[0087] Referring to
[0088] The thermal energy storage panels 102 are suspended from mounting frames 105 to which they are bolted. The mounting frames 105 are in turn suspended from cross 30 members 104 supported between upper rails 103 of the housing 101 of the thermal energy storage module 100.
[0089] Each of the thermal energy storage panels 102 includes embedded conduits, which carry a heat transfer fluid and enable heat to be recovered from the thermal energy storage panels. Inlet conduits 113, 114 deliver heat transfer fluid to each thermal energy storage panel 102 from inlet manifolds 115, and after being heated, the heat transfer fluid is passed from each thermal energy storage panel 102 via outlet conduits 117, 118 connected to outlet manifolds 119.
[0090] When the demand for electrical energy exceeds the supply, a heat transfer fluid is passed through the conduits embedded in the graphite to extract the stored heat for use. The system is quick to warm up the power generating system (e.g., sCO.sub.2 turbine or some other supercritical fluid turbine) used for power generation.
[0091] A plurality of thermal energy storage modules 100 may be used in a system with different thermal energy storage modules being switched in to receive excess energy as the amount of excess energy increases. Similarly, different thermal energy storage modules 100 may be brought on-line to permit recovery of stored energy as demand increases above the available supply of energy.
[0092] The use of a plurality of thermal energy storage panels in the thermal energy storage module described herein, and the method of their operation, constrains the possibility of a graphite fire. When the graphite in each thermal energy storage panel is encased in a chamber which has a high temperature stainless steel skin and with the void space filled with an inert gas, such as argon gas. The condition of the inert gas may be continuously monitored, and the module unit shut down or its operating temperature reduced when the condition of the inert gas in a thermal energy storage panel is lost. For example, the pressure of the inert gas may be monitored and the module shut down if the pressure in one thermal energy storage panel drops below a predetermined level, or if while temperature is stable the pressure does not remain within predefined limits. The thermal energy storage panels may also include an oxygen sensor to monitor for presence of oxygen and the heating may be shut down if oxygen is detected in any significant amount.
[0093] Each thermal energy storage panel may have a plurality of temperature sensors such as thermocouples to measure graphite temperature at multiple locations within the panel. The graphite can be heated to a maximum operating temperature (e.g., about 550-1000° C., preferably about 700-900° C.), which is synchronous with sCO.sub.2, and which is also well below the temperature at which a graphite fire can be initiated or sustained (i.e., >1400° C.).
[0094] The thermal energy storage module may comprise 8 thermal energy storage panels, with each one containing 2200 kg of graphite. Each thermal energy storage panel is separated from the adjacent energy storage panels in the module, and each energy storage panel is encased by a high temperature steel skin. This separates the graphite mass into small sub-units, which are each below the critical mass required for initiation or maintenance of a graphite fire.
[0095] The thermal energy storage module is designed to extract heat efficiently through the embedded conduits in the form of heat exchanger tubes in the graphite of each thermal energy storage panels. The current embodiment of the thermal energy storage module has been rated to extract 3.6 MWh of thermal energy over 4 hours but can be designed to extract more or less over a shorter or longer period of time depending on the various parameters (e.g., heat transfer fluid, flow rate, etc.) chosen to suit the particular application, without departing from the fundamental design principles discussed herein.
[0096] At the plant storage system level thermal energy storage modules may be connected in “trains” where a train consists of thermal energy storage modules connected in series and/or in parallel depending on the output conditions required for that plant.
[0097] In
[0098] The walls of the housings in
[0099] Mounting flanges 121 are provided extending from the tops of the end walls 215, 25 216 and include respective mounting holes 223. The flanges 121 are used to suspend the panel 102 from the mounting frame 105 by bolting them to the mounting frame via the mounting holes 223. Each flange may comprise an extension of one of the end walls 215, 216 beyond the respective side wall 213 to which it is joined (i.e., the flange may be cut from the same piece of sheet material as the end walls 215, 216 from which they extend). By suspending the thermal energy storage panel from the flanges 121 rather than supporting it from below, the resulting tension in the side walls due to gravity of the graphite core acting on the housing allows them to resist buckling to maintain good thermal communication with the graphite core. The curved shape of the housing where the side walls 215, 216 join the bottom wall 214 through a bend 271 also tends to keep the metal walls pressed against the graphite core.
[0100] Vents 251 are provided in the top wall 217 of the housing to allow venting during welding together of the housing walls. These holes may be plugged (e.g., by welding after 5 the panel walls are joined), or they may be used to accommodate sealed cable ports through the wall to pass instrumentation cables such as thermocouple wires into the housing, as fill ports to provide an argon blanket to the graphite core, to accommodate a filling nozzle to fill the void space and/or an internal reservoir with graphite powder or other thermally conductive media, or to accommodate a connection to an external reservoir to maintain the 10 level of such materials when the graphite core and housing expand and contract during thermal cycling. In the illustrated embodiment, one of the vents 251 is used to accommodate sealed cable ports 161 through the wall to pass instrumentation cables such as thermocouple wires into the housing. The cable port 161 is also used as fill ports to provide the argon blanket to the graphite core. A second vent 251 is used to accommodate 15 a filling nozzle 163 to fill the void space and/or an internal reservoir with the graphite powder or other thermally conductive media.
[0101] Further holes 252, 253 are provided in the top wall 217 of the housing to allow passage of the conduit outlets 117, 118 respectively. Similarly holes 254, 255 are provided in the side wall 216 of the housing to allow passage of the conduit inlets 114, 113 respectively.
[0102] Referring to
[0103] The number of “U” shaped sections 428 provided in the serpentine portions 425, 426, 427 can vary depending on the application. For example, for low flow rates with long discharge durations, the fewer the number of “U” shaped sections 428 may be required and conversely for high flow rates with short discharge durations more “U” shaped sections 428 may be required.
[0104] The conduits may be made, for example, from 253MA austenitic stainless steel (or any suitable high temperature thermally conductive material such as 800H austenitic steel, 800HT or alloys such as Inconel and Incoloy), and may have a nominal outside diameter in the range of for example 26.67 mm to 42.16 mm. In the present embodiment the nominal outside diameter is 33.4 mm but the outside diameter may vary to be greater or smaller than this depending on the particular circumstances of the application. The conduit 426, 439, 440, and associated conduit inlet 113, 114 and first and second conduit outlet 117, 118 are preferably formed with at least some sections of the tube assembly taking a coiled or serpentine form suitable for compression (like a spring) during assembly (e.g., the serpentine portions 425, 426, 427 and the outlet sections 438, 439), such that when the housing 102 expands due to thermal expansion, the resulting stresses from the movement of the conduit configuration does not exceed the mechanical properties of the conduit material.
[0105] Referring to
[0106] The conduits may be made, for example, from 253MA austenitic stainless steel (or any suitable high temperature thermally conductive material such as 800H austenitic steel, 800HT or alloys such as Inconel and Incoloy), and may have a nominal outside diameter of for example 33.4 mm in this embodiment but the outside diameter may vary to be greater or smaller than this depending on the particular circumstances of the application. In some embodiments, a smaller diameter conduit can be used such as a DN15 mm pipe with an outer diameter (OD) of 21.3 mm or a DN10 mm pipe with an outer diameter (OD) of 17.1 mm to cater for higher pressures.
[0107] Referring to
[0108] The housing is sealed around the conduit inlets 113, 114 and outlets 117, 118 where they exit the housing through the holes 252, 253, 255, 254 such that air cannot enter the housing after it is sealed. The plurality of openings 251 in the top wall 217 of the housing (as seen in
[0109] After the conduit is fabricated, pre-shaped planks of graphite 509, 512, are positioned to encompass most of the conduits. Referring to
[0110] The lower capping plank 509 is grooved 511 on one (upper) surface with the grooves having a semicircular (or preferably obround) cross-section conforming to the shape and radius of the lowest sections 440 of the conduit. The lower edges 506 of the lower capping plank 509, between the face opposite the grooved surface (i.e., the downward facing surface in
[0111] Referring to
[0112] Referring to
[0113] Preferably the abutting surfaces of the graphite planks of
[0114] The graphite planks 509, 512, are assembled to encompass the conduit 420, in the open housing, and the locating tube is inserted into the hole 522 extending through all of the planks to maintain alignment. The locating tube may engage a locating pin projecting from the base of the housing (not shown) to locate the graphite core 509, 512, within the housing. The housing is then welded closed, including sealing the openings 255, 254, 252, 253 through which the inlet conduits 113 114 and outlet conduits 117, 118 pass through the housing, to form the finished panel 102 (see,
[0115] Because the graphite planks extend to the ends of the housing and almost fully occupy the space within the housing, the load of the graphite is spread evenly across the bottom wall 214 of the housing, allowing thinner material to be used. Also, by maximising the area of graphite in contact with the walls and consequentially minimising void space, the heat transfer into the graphite by conduction may be maximised. Minimising void space also minimises the amount of trapped air that is available to react with the graphite when the panel is heated to its operating temperature.
[0116] In the present embodiment the volume of void spaces within the housing not occupied by graphite or tubing is generally in the range of 4-10% and typically 5-7% of the internal volume of the housing (at the working temperature). Correspondingly the side panel of the housing, which is the irradiated surface of the panel when in use, is generally backed by the graphite core over all but 1-5% of its area and typically 2-3% (at the working temperature) in the preferred embodiment.
[0117] In the top wall of the panels, openings 251 allow expansion of the internal air during manufacture and may be welded closed or used as ports. One of the openings 251 is shown with a filling nozzle 163 attached to permit filling of void spaces with graphite powder (refer to description of
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[0119] In the foregoing description of certain embodiments, specific terminology has been resorted to for the sake of clarity. However, the disclosure is not intended to be limited to the specific terms so selected, and it is to be understood that each specific term includes other technical equivalents which operate in a similar manner to accomplish a similar technical purpose. Terms such as “upper” and “lower”, “above” and “below” and the like are used as words of convenience to provide reference points and are not to be construed as limiting terms.
[0120] The preceding description is provided in relation to several embodiments which may share common characteristics and features. It is to be understood that one or more features of any one embodiment may be combinable with one or more features of the other embodiments. In addition, any single feature or combination of features in any of the embodiments may constitute additional embodiments.
[0121] In addition, the foregoing describes only some embodiments of the inventions, and alterations, modifications, additions and/or changes can be made thereto without departing from the scope and spirit of the disclosed embodiments, the embodiments being illustrative and not restrictive.
[0122] Furthermore, the inventions have described in connection with what are presently considered to be the most practical and preferred embodiments, it is to be understood that the invention is not to be limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the inventions. Also, the various embodiments described above may be implemented in conjunction with other embodiments, e.g., aspects of one embodiment may be combined with aspects of another embodiment to realise yet other embodiments. Further, each independent feature or component of any given assembly may constitute an additional embodiment.
EXPERIMENTAL SECTION
Example 1—Calculation of Energy Storage Capacities
[0123] The energy storage capacity of the thermal energy storage apparatus can be dependent on the operating temperature. The operating temperature can be adjusted based on the thermal (heat) energy transfer fluid used.
[0124] The use of a supercritical fluid as a heat transfer fluid effect increases operating temperature range which increases energy storage capacity. Increases in operating temperature can also increase energy storage capacity as the heat capacity of graphite increases with temperature as shown in
Energy Storage Capacity
[0125] The calculation of energy storage capacity can be calculated from
[0126] For example, if steam was used which typically provides an operating temperature of 400° C. to 600° C., the energy stored by graphite at that temperature range is 110 kWht/tonne of graphite. This is calculated from
[0127] If a supercritical fluid such as sCO.sub.2 was used which typically provides higher operating temperatures compared to steam, the energy stored by graphite at an operating temperature of 700° C. to 900° C. is 130 kWht/tonne of graphite. This is calculated from
Energy Conversion Efficiencies
[0128] The energy produced during discharging can then be determined by the type of energy generator used, such as steam power generation or supercritical fluid generation (as in Brayton cycle generators using sCO.sub.2).
[0129] The theoretical power conversion efficiency of a steam power generator is about 36% and the theoretical power conversion efficiency of a supercritical fluid generator is 45%.
[0130] As such, for steam power generation operating between 400° C. to 600° C., energy conversion is 40 kWhe/tonne (110 kWht/tonne of graphite×36% efficiency).
[0131] For supercritical fluid generation operating between 700° C. to 900° C., energy conversion is 59 kWhe/tonne (130 kWht/tonne of graphite×45% efficiency).
[0132] It can therefore be seen that supercritical power generation is greater than steam power generation due to higher operating temperatures and improved efficiencies of Brayton cycle generators compared to steam powered generators. For the example calculation above, the sCO.sub.2 power generating potential per tonne of graphite is 47% higher than for steam power generation (59 kWhe/tonne/40 kWhe/tonne×100%).
Example 2—Optimising Transfer of Thermal Energy from High Temperature Fluid to the Graphite Solid Material
[0133] An apparatus using a pumped circuit or loop of electrically heated heat transfer fluid (HTF) was developed to optimise the charging of the thermal energy storage apparatus with HTF to minimise charge time while avoiding overheating. An exemplary embodiment was built as well as CAD variants as shown in
[0134] The thermal energy storage apparatus is suitable for renewable energy generators to store and use energy as required. The thermal energy storage apparatus of the present invention is designed to match the requirements of the emerging Bryton Cycle generators using supercritical CO.sub.2 (sCO.sub.2). The thermal energy storage apparatus can be charged (heated up) using electrically heated HTF up to 800° C.
[0135] The control software to operate the thermal energy storage apparatus was developed using Matlab as shown in
[0136] Strategy 1. Cascaded PID: 2 separate PIDs were used, one for the Pump and one for the Heater. The Heater PID was always active while the pump PID was activated only when the heater power reached its maximum heating capacity.
[0137] For strategy 1, the PIDs were used for controlling the heating rate of the heater and the flow of the pump to control the rise time, settling time and the overshoot of the B4 Temperature. The heater PID is always active, and the pump PID is activated when the heater power reaches its maximum. This is to stabilize B4 Temperature even when the parts reach its maximum capacity. The actuator behaviour and temperature response for strategy 1 is shown in
[0138] For strategy 1, the control range of the pump speed can be limited i.e., From 0.5 L/min to 1.4 L/min which leads to limited control of heat transfer during the Pump PID. This limitation led to a 10% overshoot.
[0139] Strategy 2. PID based on the operation phase: 2 PIDs were implemented for the heater, where the PID switches were based on the operating phase. Throughout the operation, the pump speed is set to maximum.
[0140] Strategy 2 was developed to address issues with strategy 1. In strategy 2, the heater has two different PIDs based on the phase that it is operating. The first controller is activated during the heating phase, and the second controller during the stabilizing and storing phase as shown in
[0141] The pump rate is set to maximum (for example, 1.4 L/min) at all the phases as the heat circulation in the HTF is higher when the pump rate is at maximum. The actuator behaviour and temperature response for Strategy 1 is shown in
[0142] A proportional-integral-derivative controller (PID controller or three-term controller) is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control. A PID controller continuously calculates an error value as the difference between a desired setpoint (SP) and a measured process variable (PV) and applies a correction based on proportional, integral, and derivative terms (denoted P, I, and D respectively).
[0143] Strategy 2 typically provided desired results with lower overshoot and lower settling time. The present Applicant surprisingly found that: when the pump flowrate was increased, the overshoot and the undershoot was reduced due to the increase in heat transfer within the HTF which provided better control over its temperature; when the HTF is pumped through the radiator at a low flowrate, the cooling rate was increased due to increase in contact time, and having the least volume of HTF in the system took the least time to heat up and cool down. This relates to the specific heat formula Q=mcΔT (equation 1), wherein when mass increases, the energy needed to heat the HTF also increases. Q is the energy transfer, m is mass of a substance, c is the specific heat, ΔT is the change in temperature.
[0144] A comparison of strategies 1 and 2 is shown in Table 1, below.
TABLE-US-00001 TABLE 1 Strategy outcome comparison Properties Strategy 1 Strategy 2 Change Rise Time 64.6 s 73.5 s increased by 13.7% Overshoot 8.1° C. (10%) 3.8° C. (4.8%) decreased by 53% Undershoot 2.5° C. (3%) 0.5° C. (0.6%) decreased by 80% Settling Time 154.9 s 108.6 s decreased by 30%
[0145] Although the rise time in strategy 2 increased, the other properties improved. An important factor is the settling time; all the heated energy in the HTF before reaching the setpoint is not stored in the thermal energy storage apparatus and is directed to the tank. Use of strategy 2 was typically more preferred.
[0146] The main limitation of this system in
[0147] In some instances, there can be a delay between the code execution and the response from the actuator components in the system. These are due to the multiple classes and libraries used in Matlab. However, use of an industrial system can likely reduce these issues.
[0148] In the proof-of-concept system of Example 2, the system may not have enough power to start all the components in the system all at once. When they are started at once, the system can momentarily lose energy and stop operation. For uninterrupted operation, the components are started sequentially.
[0149] When the pump flowrate was increased, the overshoot and the undershoot was reduced as the heat circulation in the HTF increased with the flowrate, and the temperature difference between the heater and the radiator inlet was minimised. Hence the PID settling time was reduced with high flowrate.
[0150] The cooling rate of the radiator increased when flowrate decreased as the energy extraction from the HTF increased with the increased contact time.
[0151] Having a lower volume of HTF in the system reduces the time to heat up and cool down. When the volume increases, the energy needed to raise that mass to the desired temperature also increases. Since the capacity of the heater to supply energy is limited, the time taken to achieve the target temperatures increases. Using less HTF in the thermal energy storage apparatus is typically more efficient as the energy used in the heating phase and stabilizing phase is reduced.
The heating time, cooling time and the shutting downtime can be adjusted depending on the following factors: use of a pump with higher flowrate range; selecting an inlet conduit and fitting bore size of the pump to be larger (at least 50%) than the pump outlet conduit size; use of minimal HTF volume in the thermal energy storage apparatus; and implement the software in an industrial system with dedicated computer and wired connections.
The thermal energy storage apparatus can also be optimised including: adjusting the pump inlet conduit radius to be at least twice the radius of the pump outlet conduit to balance the mass flow between the pump inlet and outlet conduits at higher flowrates without damaging the pump; using a pump with a larger flowrate range than required; using minimal HTF volume in the thermal energy storage apparatus as possible; avoiding starting the system components simultaneously as the system may not be able to supply the necessary current and using time gaps between the component start-ups to manage the power consumption of the system; and implementing the software in an industrial system with a dedicated computer to avoid communication delay and cut-offs. Preferably, the computer would be using wired connections to improve the stability of communication.
[0152] Example 2 was a proof-of-concept and as such for analysis, the HTF was heated to 80° C. to minimise risk and ensure safety during testing.
Thermal Energy Storage Apparatus Operation
[0153]
TABLE-US-00002 TABLE 2 Identifiers, part type and purpose Identifier Part Type Purpose B1 Flow To measure the flowrate of the HTF in the Transmitter conduits. B2 Temperature Used to measure the temperature of the HTF Transmitter before heating. B3 Pressure To monitor the pressure in the conduits. Transmitter B4 Temperature Used to measure the temperature of the heated Transmitter HTF. B5 Pressure To monitor the pressure in the conduits. Transmitter B6 Temperature To measure the temperature of the HTF leaving Transmitter E2. B7 Pressure To monitor the pressure in the conduits. Transmitter B8 Temperature To monitor the temperature inside the heater. Transmitter C1 Open Tank For storing the HTF. A sight glass is used to monitor the HTF in the tank. E1 Heater Used to heat the HTF to the desired temperature. E2 Radiator/Heat Acts as a Thermal Energy Storage Unit. It Exchanger absorbs the heat from the HTF. (conduit) G1 Pump Used to pump the HTF throughout the system. G2 Fan This cools the Heated Fluid in the E2. Q1 Valve To drain the HTF from the system. Q2 Valve To drain the balance HTF from the tank. Q3 3-way Valve To bypass the HTF based on its temperature.
[0154] When the thermal energy storage apparatus is started, it immediately enters the heating phase. The default values of the actuators are: the pump is switched on, at speed=0 L/min; the heater is at duty-period of 5 seconds with 0% duty-cycle; the 3-way valve is opened, and the HTF is bypassing the radiator to the tank; and the radiator is then switched off.
[0155] When the thermal energy storage apparatus enters the shutting down phase, the system runs the radiator and the pump at their maximum speed to cool down the HTF in the thermal energy storage apparatus to 40° C. The heater is at the duty-cycle of 0%, and the 3-way valve is directing the HTF towards the radiator.
[0156] The PID tuning was completed after multiple test runs with different P, I and D constants. The system was cooled down to a constant temperature to get consistent initial conditions.
[0157]
[0158] In respect of conduit and instrumentation diagrams, abbreviations and their parts are described in Table 2, above.
[0159] One embodiment of a conduit and instrumentation diagram for a thermal energy storage apparatus and the system process is shown in
[0160] When the HTF temperature reaches the setpoint (at the B4 temperature sensor), the valve directs the HTF through the radiator (E2 and G2). The radiator in this system simulates the behaviour of a thermal energy storage apparatus by absorbing the heat from the HTF. After exiting the radiator, the HTF goes through another set of temperature (B6) and pressure (B7) sensors and returns to the tank. When the radiator outlet temperature reaches its maximum, the system considers the thermal energy storage apparatus as charged, and the system shuts down. During the shutdown period, the pump and the radiator speed is at maximum while the heater is switched off as the system cools down to a safe temperature.
[0161] The following lists the design considerations of variation I: the 3-way valve is used to bypass the HTF with the temperature below the set point temperature. When HTF with a temperature lower than the storage temperature is passed through the thermal storage tank, it discharges the thermal energy storage apparatus can result in an inefficient storage system; the system was made to be an open system. This eliminates the need to manage the internal pressure of the system due to the changes in the volume of the HTF when it goes through temperature changes; the draining valve (Q1) is at the lowest point of the system and drains the HTF through gravity as required; the arrangement of the B1 (flow) sensor, the (pump-outlet pressure) B3 sensor and (temperature) B2 sensor allows the user to observe whether the inline filter is blocked or not (that is, if the B1 flow reading drops drastically below the set pump rate and the B3 pressure reading is increasing more than the rest of the system, it can be concluded that there is a blockage in-between the B3 sensor and the B1 sensor. As such, the blockage can be detected); the tank-outlet conduit for this system is around 100 mm higher than the lowest point.
[0162] The setup allows the system to utilize oil free of dust and dirt particles as the dust settles at the bottom of the tank; addition of a separate draining valve for the tank (Q2) allows the user to drain the tank separately such that the dust particles in the system is drained without mixing it with the rest of the oil.
[0163]
[0164] Alternate embodiments of a conduit and instrumentation diagram for a thermal energy storage apparatus and the system process is shown in
[0165] For the embodiment of the conduit and instrumentation diagram (
[0166] For the embodiment of the conduit and instrumentation diagram (
TABLE-US-00003 TABLE 3 Potential failure modes of the thermal energy storage apparatus Failure Modes Symptoms Causes Power failure The system stops completely Blown Fuse E1 not The HTF is cooled down, also Blown Fuse; heating/working inducing heat loss in the storage Faulty sensor (B1, B2 or B4); Communication failure G1 faulty Overheating the HTF which might Blown fuse; result in phase change and build Communication pressure in the system. This might failure result in an explosion and fire Faulty The heating rate in the E1 is affected Faulty temperature and ends up in either the cooling connections; sensors (B2, B4, mode of E2 or overheating the HTF Requires B6) in the E1 leading to accidents. calibration Faulty flowrate G1 is adjusted by B1 to get the Faulty wire sensor (B1) desired flowrate. The heating rate in connections; E1 is affected and ends up in either Requires the cooling mode of the storage calibration system or overheating the HTF in the heater leading to accidents. Faulty pressure The readings indicate danger mode Faulty wire sensors (B3, B5, when it is still normal pressure, connections; B7) which results in an unnecessary Requires shutdown of the system. It may also calibration indicate normal when there is high pressure in the system which may result in explosions/leaks Faulty Valves HTF could leak into the environment, Wear and tear (Q1, Q2) which could be a reactive fluid at a higher temperature. Faulty cooler System shutting down process will be Blown Fuse; (G3) delayed as the cooling process will be Communication due to natural convection than the failure forced convection from the cooler Faulty HTF cools down or heats up Blown Fuse; controllers (T1, undesirably and cause accidents. Communication T2) failure
[0167] Lowering the drain valve to the lowest position of the thermal energy storage apparatus enables the whole system to drain by gravity. The pressure release valve (PRV) is not necessary as the system specification has been changed by reducing the maximum system pressure from 10 bar to 3 bar in this embodiment.
[0168] For the embodiment of the conduit and instrumentation diagram (
[0169] For the embodiment of the conduit and instrumentation diagram (
[0170] The reason for this is when the HTF with a temperature lower than the storage temperature is passed through the thermal storage, the HTF can discharge the battery and results in an inefficient thermal energy storage apparatus. With the 3-way valve, the thermal energy storage apparatus can bypass lower temperature HTF without entering the thermal storage.
[0171] For the different embodiments, the HTF had an equal or higher skin temperature than is recommended for the heater which is 0.031 W/mm.sup.2 (20 W/in.sup.2), and the boiling point should be higher than 80° C. HTF (therminol 66) with a maximum heating rate of 0.031 W/mm.sup.2 (20 W/in.sup.2) and boiling point of 359° C. was used in Example 2.
i) Pump Speed Variation
[0172] The pump speed can be varied which can affect the temperature differences of the thermal energy storage apparatus as shown in Table 4, below.
[0173] The variation of pump speed can affect the temperature difference of the HTF (with a maximum heating power). For temperature differences of 60° C. to 10° C., a pump with a flowrate of 1.4 L/min to 8.7 L/min is preferable. Since the heater power can be controlled, a readily available pump with 0.5 L/min to 3.5 L/min was selected for the system to be operated with various heater powers.
TABLE-US-00004 TABLE 4 Pump speed variation on temperature difference Temperature HTF T fin T bulk Q rho @ T Cp @ T bulk (C.) (C.) (kW) bulk (kg/L) (J/kg/K) 80 50 2.4 0.988 1660 80 55 2.4 0.988 1660 80 60 2.4 0.988 1660 80 65 2.4 0.988 1660 80 70 2.4 0.988 1660 80 75 2.4 0.988 1660 Continued Pump specification v @ T bulk Pr @ k @ T bulk V/t (m.sup.2/s) T bulk (W/m/K) (L/min) m/t (kg/s) 17.6E−6 252 0.1163 1.4633 0.0241 17.6E−6 252 0.1163 1.7560 0.0289 17.6E−6 252 0.1163 2.1950 0.0361 17.6E−6 252 0.1163 2.9267 0.0482 17.6E−6 252 0.1163 4.3900 0.0723 17.6E−6 252 0.1163 8.7801 0.1446
ii) Conduit Size Variation
[0174] The conduit size can be varied which can affect the flow type of the thermal energy storage apparatus as shown in Table 5.
TABLE-US-00005 TABLE 5 Variation of the flow type for different conduit sizes Temperature Conduits T in T fin T bulk L k OD Wall (C.) (C.) (C.) (m) (W/m/K) (in) (in) OD (m) ID (m) 20 80 50 0.6 16.3 ⅛ 0.028 0.003175 0.0018 20 80 50 0.6 16.3 ¼ 0.035 0.00635 0.0046 20 80 50 0.6 16.3 ¼ 0.049 0.00635 0.0039 20 80 50 0.6 16.3 ¼ 0.065 0.00635 0.0030 20 80 50 0.6 16.3 ⅜ 0.035 0.009525 0.0077 20 80 50 0.6 16.3 ⅜ 0.049 0.009525 0.0070 20 80 50 0.6 16.3 ⅜ 0.065 0.009525 0.0062 20 80 50 0.6 16.3 ½ 0.035 0.0127 0.0109 20 80 50 0.6 16.3 ½ 0.049 0.0127 0.0102 20 80 50 0.6 16.3 ½ 0.065 0.0127 0.0094 Continued Pump spec HTF As V/t m/t rho cp v Ac (m2) (m2) (L/min) (kg/s) (kg/L) (J/kg/K) (m2/s) Pr 2.41E−06 0.0033 2.1950 0.0361 0.988 1660 17.6E−6 252 1.64E−05 0.0086 1.4633 0.0241 0.988 1660 17.6E−6 252 1.17E−05 0.0073 1.4633 0.0241 0.988 1660 17.6E−6 252 7.30E−06 0.0057 1.4633 0.0241 0.988 1660 17.6E−6 252 4.71E−05 0.0146 1.4633 0.0241 0.988 1660 17.6E−6 252 3.89E−05 0.0133 1.4633 0.0241 0.988 1660 17.6E−6 252 3.04E−05 0.0117 1.4633 0.0241 0.988 1660 17.6E−6 252 9.37E−05 0.0206 1.4633 0.0241 0.988 1660 17.6E−6 252 8.19E−05 0.0192 1.4633 0.0241 0.988 1660 17.6E−6 252 6.94E−05 0.0177 1.4633 0.0241 0.988 1660 17.6E−6 252 Continued k Flow (W/m/K) Q (kW) qs (kW/m2) Re. Flow type 0.1163 2.4 726.49 1,507.09 Laminar 0.1163 2.4 278.49 385.14 Laminar 0.1163 2.4 329.79 456.09 Laminar 0.1163 2.4 417.73 577.72 Laminar 0.1163 2.4 164.35 227.30 Laminar 0.1163 2.4 180.97 250.27 Laminar 0.1163 2.4 204.60 282.96 Laminar 0.1163 2.4 116.58 161.22 Laminar 0.1163 2.4 124.70 172.45 Laminar 0.1163 2.4 135.48 187.37 Laminar
[0175] When the HTF was heated using a trace heating configuration, turbulent flow was preferred to increase the flow. When the HTF was heated using a shell and tube configuration, laminar flow was preferred to avoid heat loss from the thermal energy storage apparatus.
[0176] Based on the heat transfer properties, having laminar flow in the conduits has less heat transfer compared to transient or turbulent flow as the transient or turbulent flow induces heat transfer. Since the heat loss from the conduits should be minimised, laminar flow is preferable. Another factor considered in Example 2 was the volume of the HTF in the thermal energy storage apparatus as having less HTF in the system reduces heating and cooling time. The selected pump's inlet outer diameter (OD) is ⅛ inch (˜0.3 cm), hence the conduit needs to have larger OD to facilitate a smooth flow. A ¼ inch (˜0.6 cm) OD conduit was preferred for Example 2.
[0177] From the ¼ inch (˜0.6 cm) conduit range, the conduit sizing with minimum wall thickness was chosen for ease of manufacturing as the conduits were bent with a hand pipe bender.
Example 3—Modelling of the Thermal Energy Storage Apparatus
[0178] The thermal energy storage apparatus of the present invention (such as in
[0179] The following assumptions were made: only the graphite and conduit have been modelled; the graphite has been assumed to be a single mass (i.e., no separate blocks), as such interfaces between horizontal layers of graphite have not been included. Given previous modelling experience of similar assemblies this is shown to be negligible; no heat loss from the casing has been considered, heat loss will have minimal impact on determining suitable test conditions; internal sections of the graphite that have been removed for instrumentation have not been modelled due to increased complexity of the mesh and heat transfer boundary conditions; no heat tracing has been included; it is assumed the heat tracing will be temporarily turned off while the test runs are undertaken; pressure drop was measured, however was determined to be negligible in the model; the model used 253MA conduit material properties, but can include Inconel 625, and the contact heat transfer coefficient at the conduit-to-graphite interface is set at 400 W/m.sup.2/° C. which is based on a G2 Thermo-Hydraulic Model by Dr David Reynolds PhD, MBA, BE Mech. (Hons) Rev 1.0 17 Nov. 2014. A sensitivity assessment was undertaken to validate this value of 400 W/m.sup.2/° C. The contact heat transfer coefficient is an important variable to assess during verification of the model.
[0180] The sensitivity assessment was used to confirm that a 0.01-0.05 kg/s flow rate and 300-800° C. temperature range is suitable. The sensitivity of the model was assessed against the contact heat transfer coefficient between the conduit and graphite (as this was an important variable to validate).
[0181] The results of the sensitivity assessment as shown in
[0182] The following input data were considered in the model: Graphite material properties based on CSIRO “Thermal Properties of Commercial Graphite” Test Reports by Steven Wright (2010/2011); 253MA Conduit Material Properties based on the Sandvik Datasheet (2019); Liquid Sodium Material Properties; Thermal Desktop materials library.
[0183] The following boundary conditions were considered in the model: HTF was limited to liquid sodium; Pressure set at 2 bar for a time of 300 min; HTF Flow Rate: Various fixed flow rates from 0.01 kg/s to 0.1 kg/s; HTF Inlet temperature (Charging): 800° C. or 500° C.; HTF Inlet Temperature (Discharging): 500° C. or 300° C.; Initial average Graphite Temperature (Charging): 500° C. or 300° C., and; Initial Average Graphite Temperature (Discharging): 800° C. or 500° C.
[0184] The outputs of the model were the average graphite temperature and the HTF outlet temperature of the thermal energy storage apparatus.
[0185] For the scenario during the charging phase, using an average graphite temperature of 500° C., a sodium inlet temperature of 800° C., varying sodium inlet flow from 0.01 to 0.1 kg/s and a run time of 300 minutes, the average charging graphite temperature and sodium outlet temperature is shown in
[0186] For the scenario during the discharging phase, using an average graphite temperature of 800° C., a sodium inlet temperature of 500° C., varying sodium inlet flow from 0.01 to 0.1 kg/s and a run time of 300 minutes, the average charging graphite temperature and sodium outlet temperature is shown in
[0187] For the scenario during the charging phase, using an average graphite temperature of 500° C., a sodium inlet temperature of 500° C., varying sodium inlet flow from 0.01 to 0.025 kg/s and a run time of 300 minutes, the average charging graphite temperature and sodium outlet temperature is shown in
[0188] For the scenario during the discharging phase, using an average graphite temperature of 500° C., a sodium inlet temperature of 300° C., varying sodium inlet flow from 0.01 to 0.025 kg/s and a run time of 300 minutes, the average charging graphite temperature and sodium outlet temperature is shown in
[0189] Based on the modelling, the energy transfer was also estimated. Energy transfer was calculated using the specific heat formula Q=mcAT (equation 1) for sodium HTF per simulated time interval and converted to kWh and summed per time interval to provide accumulated energy transfer Q. The accumulated energy transfer for different charging and discharging temperatures is shown in
TABLE-US-00006 TABLE 6 Charging and discharging scenarios on energy input and output Scenario: Charging: 500-800° C. Discharging: 800-500° C. Approx. Approx. Flow Charge Energy Energy Sodium mass Rate Time Sodium In Discharge Sodium Out displaced (kg/s) (min.) ΔT (° C.) (kWh) Time (min.) ΔT (° C.) (kWh) (300 min, kg) 0.01 >300 270 6.6 >300 270 6.6 180 0.02 215 260 7.1 207 260 7.1 360 0.05 132 170 7.2 123 170 7.2 900 0.1 108 100 7.2 99 100 7.2 1,800 Scenario: Charging: 300-500° C. Discharging: 500-300° C. Approx. Approx. Flow Charge Energy Sodium Energy Sodium mass Rate Time Sodium In Discharge ΔT Out displaced (kg/s) (min.) ΔT (° C.) (kWh) Time (min.) (° C.) (kWh) (300 min, kg) 0.01 300 185 4.0 276 185 4.0 180 0.015 213 185 4.2 192 185 4.2 270 0.02 165 175 4.2 150 175 4.2 360 0.025 141 160 4.2 129 160 4.2 450
[0190] Similarly, the energy transfer rate was calculated using equation 1 and is shown in
[0191] A summary of different scenarios showing the energy inputs and outputs is shown in Table 6, above.
[0192] Although the invention has been described with reference to specific examples, it will be appreciated by those skilled in the art that the invention may be embodied in many other forms.