Thermal energy storage with phase change materials in solar power plants. Economic analysis

Journal of Energy Storage 43 (2021) 103184 Available online 11 September 2021 2352-152X/© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Thermal energy storage with phase change materials in solar power plants. Economic analysis Cristina Prieto a , b , Luisa F. Cabeza c , * a Abengoa, Department of Solar Technology, Energía Solar 1, 41014 Sevilla, Spain b University of Seville, Department of Energy Engineering, Camino de Los Descubrimientos S/n, 41092, Seville, Spain c GREiA Research Group, Universitat de Lleida, Pere de Cabrera s/n, 25001 Lleida, Spain ARTICLE INFO Keywords: Concentrating solar power (CSP) Phase change material (PCM) Thermal energy storage (TES) Levelized cost of energy (LCOE) ABSTRACT Thermal energy storage (TES) increases concentrating solar power (CSP) plant capacity factors, but more important, improves dispatchability; therefore, reducing the capital cost of TES systems is very important to reduce cost of energy and serve as an enabler for commercial solar power plants. After presenting the concept of a novel cascade PCM configuration of CSP and demonstrating it energy efficiency, it is needed to develop a thoughtful economic evaluation of the concept. The goal of this paper was to investigate this system through annual modelling, engineering procurement company price quotes, and levelized cost metric comparison with a baseline case, the commercial two-tank molten salt storage system. Simulation results show that this new PCM concept decrease levelized costs of storage. The baseline of using shell and tube heat exchangers for PCM storage offers a reduction in capital and levelized cost, but this paper also shows that there are further cost reduction possibilities, as shown in the scenarios presented here, such as thermal conductivity enhancement, encapsulation of the PCM, or modification of the material to improve its thermal properties. Therefore, although the basic shell and tube PCM system has been shown to offer a cost savings, the 1.8% reduction in LCOE may not be worth the risk of further development. The shell and tube system should be a jumping off point to more appropriate technologies. The variants studied are likely to yield cost reductions in cost performance quotient (CPQ) as high at 80% and in LCOE as high as 10%, representing an unprecedented and valuable avenue of CSP plant cost reduction. 1. Introduction Commercial concentrated solar power (CSP) is more accommodating to energy storage than other solar technologies. Energy can be stored at relatively high efficiencies in the form of thermal energy. Thermal energy storage (TES) increases plant capacity factors and improves dispatchability. Reducing the capital cost of TES technologies will also result in a reduced cost of energy and ultimately serve as an enabler for commercial solar power plants [1]. The development of reliable, flexible and cost-efficient molten salt storage system has recently been acknowledged by the CSP community as a potential major enabler of a better integration of CSP with other cheap variable renewables, by potentially facilitating smart control of co-located assets through smoothening the fast variations from PV and/or wind. The integration of TES systems into large-scale CSP plants is a cost-effective way to reduce the Levelized Cost of Electricity (LCOE) in a solar plant [2–4], being the binary mixture of sodium and potassium nitrate the most used storage medium [5]. Several studies are looking for a way to reduce the cost of TES through the use of new storage material [2,3,6] and several reviews have been published with different TES technologies under development [7]. One of the development most analysed are PCMs due to their higher energy density [8]. Presently, many PCM sizing models were generated to model both PCM TES systems [9–11]. These models focus on calculating a cost per kWh of thermal energy storage. This is accomplished in one of two ways: a performance efficiency is assumed and the size is calculated directly [5,12] or a performance efficiency is calculated based on assumptions and the size is calculated [9–11]. While the latter method is considerably more accurate, it still relies on a generalization of the TES performance over the course of a whole year. This modelling method is suspect due to the inability of simple performance models to capture the realistic response of passive TES systems to transient energy flows observed in a CSP plant. This intrinsic modelling difficulty was * Corresponding author. E-mail address: [email protected] (L.F. Cabeza). Contents lists available at ScienceDirect Journal of Energy Storage journal homepage: www.elsevier.com/locate/est https://doi.org/10.1016/j.est.2021.103184 Received 30 December 2020; Received in revised form 30 July 2021; Accepted 1 September 2021 Journal of Energy Storage 43 (2021) 103184 2 overcome in some cases with experimental work. These experiments reinforced the low capitol cost potential of PCM TES systems. However, they still lack a realistic look at the response of passive TES systems to transient energy flows anticipated in CSP plants. Zhao et al. [13] studied the influence of different key design parameters on the performance of a packed bed PCM system for a CSP tower plant. Those authors withdraw interesting conclusions on the effect of the design parameters of the packed bed PCM tank in the costs of the storage plant, such as the dimensions of the storage tank or the needed volume of PCM to shorter operation duration while not increasing too much the capital costs. Caceres et al. [14] calculated the levelized cost of energy when suing copper foams in PCM tanks, to reduce the storage volume and increase the thermal conductivity of the storage material. This economic analysis showed that using copper foams in PCM storage systems can reduce the required storage volume by 77%, however the cost of the copper foam significantly increases the total cost of the plant. Also considering the low thermal conductivity of PCM storage systems, Jacob et al. [15] compared environmentally and economically two storage system in CSP plants: a packed be PCM system and a liquid metal-based TES system. In that study, only the capital expenditure (CAPEX) was calculated, finding that the PCM system had a lower CAPEX than previous studies about encapsulated PCM systems that could be found in the literature. Those authors already highlighted that the CAPEX of the PCM system would benefit from further optimisation with new concepts such as the cascade PCM systems. But there is not a thoughtful economic evaluation of a PCM storage plant for CSP. Moreover, the cascade PCM concept was shown as energetically effective in the first part of this study [16]. The goal of this paper was to investigate this system through annual modelling, engineering procurement company price quotes, and levelized cost metric comparison with a baseline case, the commercial two-tank molten salt storage system. 2. System description 2.1. Baseline TES system The selected baseline system for comparison was the commercial state-of-the-art indirect two-tank molten salt TES technology. Fig. 1 shows the configuration of a SP plant with this TES system. Table 1 presents the specifications of the system. This study considered a TES capacity of 6 equivalent full load hours (EFLH) of indirect storage since this is representative of systems currently commercially considered. All calculations assume the plant is located near Phoenix, AZ (United States). The considered size of the plant is 144 MW e_gross . 2.2. PCM cascade configuration for simulation The PCM system evaluated at simulation scale is based on a cascade concept, where storage tanks containing PCM with different melting temperatures are connected in series (Fig. 3). The heat transfer fluid (HTF) runs through a heat exchanger where its energy is charged and discharged. A detailed description of the PCM cascade storage system Fig. 1. Baseline plant configuration with indirect two-tank molten salt TES [17]. Table 1 Baseline CSP plant and TES specifications. Component Baseline General Plant Location Phoenix, AZ Turbine Name Plate Capacity (gross) 144 MWe_gross Plant Name Plate Capacity (net) 125 MWe_net Solar Multiple 2.0 Power Block Power Cycle Superheated steam Rankine cycle with reheat Feed-water Heaters 5 Steam Inlet Pressure 100 bar (absolute) Condenser Pressure 0.08 bar (absolute) Steam Inlet/Reheat Temperature: 373.0/373.0 ◦C Feed-water Temperature: 234 ◦C Cooling Wet Solar Field Field Style Parabolic Trough Field Layout “H” configuration # of Loops 428 Module Aperture 5.76 m Solar Field HTF Therminol VP-1 Field Supply Temperature 393 ◦C (nominal) Field Return Temperature 293 ◦C (nominal) Thermal Energy Storage Storage Type Indirect 2-tank molten salt Storage Capacity 6 equivalent full load hours (864 MWh e_gross ) Number of Tanks 3 hot/3 cold Storage Fluid Binary salt (60% NaNO 3 , 40%KNO 3 ) Storage Fluid Quantity 66,613 metric tons Hot Tank Temperature 386 ◦C Cold Tank Temperature 295 ◦C C. Prieto and L.F. Cabeza Journal of Energy Storage 43 (2021) 103184 3 evaluated in this paper and its energetic performance is developed in a previous paper [16]. Phase change materials were selected from those available in the literature [18] based on its cost per capacity (Fig. 2) There are possible scenarios that attempt to mitigate some of the problems inherent in the basic PCM TES system. These variations attempt to ameliorate the thermal issues of PCM storage by altering the physical layout of the PCM system or the constituent materials of the system. Current variations under consideration are: thermal conductivity enhancement, use of the optimal melting temperature PCM, use of the ideal properties of the PCM, PCM encapsulation, enhanced ideal properties, and compact heat exchanger utilization, and will be detailed later on. 2.3. Concept specifications The considered plant was a 6 h storage system for a 125 MW net parabolic trough plant using Therminol VP1® as heat transfer fluid (HTF). This storage system represents six hours of full load output in a representative day: May 25 th using Phoenix Arizona TMY2 data. There are many configurations of PCM systems that would work for the above storage performance specification of 6 h at full load. Because the simulation of the PCM system is an inherently more complex system then the two tanks baseline, there are more parameters that can be altered to adjust the performance. These parameters are summarized in Table 2. One major benefit of the PCM TES concept is its reduction of Fig. 2. Cost per kJ of each PCM considered [16]. Fig. 3. Depiction of the entire PCM cascade and a single pre-fabricated heat exchanger [16]. C. Prieto and L.F. Cabeza Journal of Energy Storage 43 (2021) 103184 4 components when compared to the baseline TES system. This is mostly due to the passive nature of the system and removal of the pumping, piping, valves, and elevating structures that are required to operate an active system like the two tanks. The main system components are: the heat exchangers, PCM, charge/discharge valve setup and salt melting equipment. The heat exchangers are the largest cost system component. They not only facilitate the transfer of energy from the HTF to the PCM, but also contain the PCM. The heat exchangers used in this project are based on prefabricated heat exchangers that can be shipped to the site. As such, the diameter and length were constrained to a shippable size. Table 3 gives the technical description of the heat exchangers. The PCM is broken down by bucket. Initially, all PCMs between the hot and cold design temperatures of the plant were considered. Table 4 gives the technical specifications for the PCMs used in the current system. The table shows the volume expansion of the salts, that is one of the main challenges of the PCM. The PCMs currently being considered undergo a density change of almost 25%, as such, thawing stress can be a serious issue. The heat exchangers oriented in a vertical orientation were proposed as an option to minimize the structural yielding in freeze-thaw cycles. This change eliminates thawing stress because the expanding liquid is given an avenue for escape. The HTF is always fed into the top of the heat exchanger and, as such, the initial PCM melting starts at the interface of the PCM and the gas in the expansion head. As the rest of the PCM melts it can expand out the avenue of previously melted PCM. Another key piece of equipment is the salt melting setup. When the plant is being constructed, the PCM must be pumped into the tanks in molten form. Although this seems like a trivial task, the mass of PCM required leads to a either a long melting process or a large melting machine [19]. Currently, this machinery has not been fully developed. A cost estimate was obtained, but an economic optimization was not completed. One avenue to higher cost savings over the baseline that was not investigated to date is the removal of the melting system altogether. If the salt can be added to the system in solid form and then melted by the hot HTF instead of a burning fossil fuel, the costs would be probably lower than those considered in this paper. Table 2 Design parameters used in the model PCM model. Parameter Description Range or typical value Number of PCMs Number of phase change materials in the cascade 1-10 PCM type Chemical formula of PCM in each bucket (sets thermal properties) All known substances Tube length Tube length for each bucket 100 - 1000 (m) Number of tubes Number of tubes in each bucket 100 - 10,000 Extent radius Extent radius of PCM around the tube for each bucket 1.5-20 (cm) Tube outer diameter Outer diameter of heat exchanger tube set by EPC 0.0254 (m) Tube inner diameter Inner diameter of tube set by EPC 0.022 (m) Alpha Void fraction of any heat transfer enhancement 0-100% Ideal melting point Ideal melting point of salt if melting point manipulation is being used ±25 Percent power block reroute The percent of the power block mass flow that is first routed through the hottest bucket 0-100% Heat exchanger material Material being used to build the heat exchanger (sets thermal properties) Stainless steel Table 3 Technical description of heat exchangers used in the system. Type Single pass shell and tube Diameter 4.3 (m) Length 19.8 (m) Count 64 Material 310 or 304 stainless steel Configurations HTF flows in tube side while PCM is stored on shell side. Heat exchangers are arranged into groups in series and parallel to achieve correct effective tube length and numbers. Table 4 Technical description of materials used in the system [18]. Variable Bucket 1 Bucket 2 Bucket 3 Bucket 4 Chemical (mass %) NaNO 3 NaCl (33%) KCl (24%) LiCl (43%) NaOH (80%) NaCl (20%) MgCl 2 (60%) KCl (20.4%) NaCl (19.6%) Melting point (◦C) 310 346 370 380 Enthalpy of fusion (kJ/kg) 172 280 370 400 Thermal conductivity liquid (W/m-K) 0.56 0.68 0.87 1.08 Thermal conductivity solid (W/m-K) 0.56 2.65 2.35 2.29 Solid density (kg/ m 3 ) 1929 1897 2104 2055 Liquid density (kg/m 3 ) 1882 1512 1743 1609 Specific heat (kJ/ kg•K) 1.82 1.34 2.01 1.04 Kinematic viscosity (m 2 / 2) 1.51E-06 7.94E-07 1.92E-06 9.63E-07 Volumetric expansion (%) 2.5% 25.5% 20.7% 27.7% Mass in system (kg) 3,122,644 7,292,907 6,527,257 3,747,172 Table 5 Financial and incentive assumptions from CSP FOA with modifications. Financial assumptions Value Comments Analysis period 30 years — Inflation rate 2.5 % — Real discount rate 8.0 % — Federal tax 34%/ year National Energy Technology Laboratory (NETL) 2007 State tax 6%/ year NETL 2007 Property tax 0 — Sales tax 7.75% — Insurance 0.50% — Loan term 20 years — Loan rate 8.00 % — Loan (Debt) fraction 50.0% NETL 2007 Federal depreciation rate — MACRS Mid-Quarter Convention for solar State depreciation rate — MACRS Mid-Quarter Convention for solar PPA escalation rate 1% — Minimum required IRR 12.0% NETL 2007 Minimum required debt service coverage ratio (DSCR) 1.40 — Incentives: Federal investment tax credit (ITC) 30% was 10% in DE-FOA-0000104 Cost assumptions Value Comments Contingency Included in EPC quote — Engineer, procure, construct Included in EPC quote SAM default of 16% was used on DE Project, Land, Misc. Included in EPC quote SAM default of 3.5% was used on DE Percentage of direct costs subject to Sales Taxes 80% SAM default C. Prieto and L.F. Cabeza Journal of Energy Storage 43 (2021) 103184 5 3. Economic analysis The physical and performance dissimilarities of the two systems mean that a simple performance-based comparison is not an effective way to determine which system is more fit. As such, an economic analysis was needed in order to generate levelized cost vs. performance metrics like LCOE. This allowed for the two technologies to be compared in a direct way. The economic analysis was carried out with detailed cost estimates of both systems by an engineering, procurement and construction (EPC) contractor. After several iterations on the cost, final prices were determined for each system. The Solar Advisor Model (SAM) version 2009.10.13 was used to calculate the levelized cost of energy (LCOE) so that the various concepts can be compared to each other and to the baseline plant. Because SAM is not equipped to analyse the performance of these new storage schemes, the “Generic Fossil, Utility IPP” plant type is used in SAM, which requires the reduction of the TRNSYS performance results to a single annual capacity factor. Financial parameters are taken, in part, from a Department of Energy (DOE) Funding Opportunity Announcement (DEFOA-0000104) on baseload concentrating solar power generation, which outlined a financial model for use with SAM. Assumptions used in the financial model are summarized in Table 5. The resulting ranges of LCOE are subject to the ±20% EPC cost uncertainty required by accepted estimating practices. 4. Scenarios considered 4.1. Thermal conductivity enhancement (TCE) When considering thermal conductivity enhancement there is a range of available homogeneity: fully homogeneous, realistic homogeneous, and non-homogeneous. A fully homogeneous system might be evenly spaced nanoparticles. A realistic homogeneous system might be a large pore metal foam, carbon foam, or loose metal fill. A nonhomogeneous system might be fins or large stacked structures. Fig. 4 shows an example of each of these systems on a macro- and micro-scale. Due to their extreme costs, fully homogeneous systems are outside of the scope of this study. This leaves realistic homogeneous and nonhomogeneous systems to be considered. The performance of nonhomogeneous systems is not anticipated to be acceptable for our application, therefore, realistic homogeneous systems are considered. Assuming that the thermal conductivity enhancement will be realistically homogeneous, Eq. (1) can be used to derive the bulk thermal conductivity of an enhanced PCM storage material according to Mesalhy bulk thermal conductivity equation [20]: kbulk =[kpcm + π ( 1− α 3 π √−1− α 3 π )(kTCE −kPCM)][kPCM +1− α 3(kTCE −kPCM)] kpcm +[4 3 1− α 3 π √(1− α ) + π  1− α 3 π √− (1− α )](kTCE −kPCM) (1) This equation was implemented into the PCM TRNSYS component to allow for systems with a new bulk thermal conductivity to be modelled [16]. Additionally, the specific heat and density are also updated based on the thermal conductivity enhancement material being used and the specified void fraction ( α ). Once the model was capable of calculating a bulk thermal conductivity, specific heat, and density based on a composite void fraction, it was used to generate a break-even function. A break-even function is a curve showing the amount of money that can be spent on TCE for a range of systems with the same LCOE. To calculate this function, a set of 15 systems were parametrically derived with the same annual capacity factor. The TCE level of each system was modified to meet a target average thermal conductivity improvement for the system. The Fig. 4. Typical representation of fully homogeneous, realistic homogeneous, and non-homogeneous thermal conductivity enhancement techniques. C. Prieto and L.F. Cabeza Journal of Energy Storage 43 (2021) 103184 6 improvement in the average thermal conductivity ranged from 1.4 to 30 times the average thermal conductivity over all the buckets. The breakeven function represents TCE costs for each system if it were to perfectly match the LCOE of the basic system (i.e. no real economic improvement). This value is plotted against TCE level in Fig. 5. The break-even function represents the maximum TCE cost to achieve a lower LCOE. It is also important to note where the cost reduction is occurring in the system. It immediately becomes apparent what level of TCE is most appropriate for a shell and tube based PCM system. Although cost savings go up as TCE level is increased, the trend is one of diminishing returns. This trend exists because there is a shift in the thermodynamic constraint to the resistance on the HTF side as more TCE is added to the PCM. With no TCE in the system, the heat transfer is constrained by the surface area of the heat exchanger and the thermal conductivity of the PCM. As TCE is added the constraint of the PCM thermal conductivity is alleviated leading to systems with drastically reduced heat exchanger costs. However, around 6-10 times the thermal conductivity of the PCM, this bottleneck is largely minimized. At this level of TCE, the constraint shifts to the internal convection of the HTF. As more TCE is added to the system, the thermal resistance of the HTF convection remains unchanged and the system still requires the same heat exchanger area. Coupling the diminishing benefit of increasing TCE with cost, it becomes clear that a low level of TCE is optimal. As the level of TCE is increased by decreasing the void fraction, the volume and cost of TCE material increases linearly. Therefore, there is an optimal amount of TCE for any given material based on the break-even cost, the material cost, and the material thermal conductivity. With the break-even function for our system, it is possible to assess the viability of different TCE materials. The break-even function shows that having the most thermally conductive material possible is not necessarily the best approach. To the contrary, it shows that a material with the appropriate thermal conductivity and a low cost is likely to have a much lower system cost then a high-tech, high thermal conductivity, expensive material. Before the materials are listed, it is important to note that an in-depth compatibility study has not been performed. Material corrosion in the presence of the materials was kept in mind in the selection but it was not thoroughly researched. First, metals were considered. Metals tend to have high thermal conductivity and known commodity prices. Furthermore, many metals like steel and aluminium have well developed recycle bound waste streams: available pre-manufactured used materials that are on their way to be reformed into another product. Since the TCE material is not a load bearing material, the strength and grain purity are not of huge concern and scrap or recycled material represents a perfect source. Table 6 shows a list of metallic materials considered as TCE candidates. Additionally, non-metallic materials were considered (Table 7). These materials may offer better thermal properties; however, their prices are considerably less commoditized. Furthermore, they will likely involve more processing cost then their metallic counterparts as well defined recycle bound waste streams do not exist. From this list the break-even function was used to match materials to certain levels of TCE based on the cost and thermal conductivity of the material. Stepping from one level of TCE to the next results in a decrease in system cost. At the same time, this step requires an increase in volume of TCE material and cost. The first step from 1 to 1.4 times the thermal conductivity of the PCM results in large cost savings but does not require Fig. 5. Break-even cost of the 15 TCE ordered by amount of TCE. Table 6 Metals considered as thermal conductivity enhancement materials [21]. Metal Conductivity [W/m•K] Density [kg/m 3 ] Price [$/lb] Silver 410 10295 18.3 Copper 378 8779 7.7 Aluminium 230 2635 2.0 Brass 150 8667 3.0 Tungsten 136 10215 47 Zinc 104 6922 2.2 Cadmium 90 8387 6.6 Platinum 72 21255 39.29 Nickel 66 8772 16 Iron 53 7765 0.104 Lead 31 10992 2.3 Table 7 Non-metallic materials considered. Material Conductivity [W/ m•K] Density [kg/ m 3 ] Price [$/kg] Reference Silicon carbide 300 3100 2.5 [22] Graphite fibres 1000 1880 10.0 [23] Beryllium oxide 106 2979 363.4 [24] Carbon foam 1950 2210 100.0 [25] C. Prieto and L.F. Cabeza Journal of Energy Storage 43 (2021) 103184 7 a large amount of TCE material. The next step, however, yields smaller reduction in the plant cost but results in the same increase in TCE cost. At some point, based on the price of each thermal conductivity improvement step, the cost reduction of the plant is no longer larger than the cost of the additional TCE material. For example, Fig. 6 shows the cost reduction optimum for aluminium to be somewhere about five to six times the average PCM thermal conductivity. This optimal level of thermal conductivity enhancement is different for each material based on the thermal conductivity and the price. Table 8 shows the result of this analysis for each material. The pool of materials has been greatly reduced to only the materials that show LCOE reduction. These materials are then plotted as function of TCE level on the break-even function to give some idea of the best material available and the best level of TCE. Fig. 7 shows the materials of interest with the Fig. 6. Plant cost reduction at various levels of thermal conductivity enhancement for aluminium based enhancement. Table 8 Thermal conductivity enhancement materials that showed promise towards system cost reduction with selected void fraction and cost. Material Conductivity multiplier (-) Foam cost ($) Void fraction (-) Aluminium Raw 7.4 2,368,298 0.919 Processed 7.4 4,640,591 0.919 Brass Raw 2.5 4,726,152 0.959 Processed 2.5 9,452,304 0.959 Iron Raw 6.2 5,490,521 0.8891 Processed 6.2 10,981,041 0.8891 Silicon carbide Raw 8.6 2,619,800 0.977 Processed 8.6 10,479,199 0.977 Graphite fibres Raw 1.4 16,082,511 0.994 Processed 1.4 20,103,139 0.994 Fig. 7. TCE materials of interest with error bars representing unknown processing cost. C. Prieto and L.F. Cabeza Journal of Energy Storage 43 (2021) 103184 8 break-even curve. Additionally, it shows the break-even curves for systems with 4% and 6% LCOE reduction. Based on this plot aluminium has been chosen as the best TCE material. This is based on not only the possibility of it giving us the lowest cost system but also on its low processing and cost uncertainty. To reach the ideal thermal conductivity multipliers seen in Fig. 7, high void fractions are required: 0.919 for aluminium. However, as discussed, high processing costs cannot be tolerated. This means that highly engineered products like foams are not an appropriate way to reach the required void fractions. An obvious choice to reduce processing cost is to use a natural packing approach. Here, minimal processing would be used to grind or cut the TCE before submersion into the PCM. Natural packing is used in a thermocline to achieve necessary void fractions because the sand and gravel filler is unprocessed. It is necessary to test if the proper void fraction for our system can be achieved with natural packing. Based on correlations derived by Wen and Yu, the void fraction of a system using natural packing can be calculated using a sphericity equation, Eq. (2) [26]: Φ=1 14 α 3(2) where: Φ =sphericity α =void fraction This equation is based on the sphericity of the object being packed. Natural objects have a sphericity defined by the similarity between their shape and a perfect sphere; objects like stones tend to have a high level of sphericity where objects with flake-like structures tend to have the lowest level of sphericity in nature, somewhere near 0.2. Table 9 lists the void fractions that can be achieved using naturally shaped objects. Fig. 8 also shows the maximum achievable void fraction with naturally packing object in addition to the void fraction required for our system. Clearly, natural packing will not meet the required void fraction criteria. This reintroduces the need for material processing. As discussed previously, materials that need significant processing, machining, casting, forging, or foaming, will not be cost competitive for the application. Therefore, packing materials that have an inherent engineered structure should be found. Aluminium is a heavily recycled material. As such, it may be possible to acquire pre-processed recycled aluminium that still has a highly Table 9 Maximum void fractions achievable by naturally shaped objects [25]. Material Sphericity Natural void fraction Ottawa sand 0.95 0.42 Rounded sand 0.83 0.44 Coal dust 0.73 0.46 Flint sand 0.65 0.48 Crushed Glass 0.65 0.48 Mica flakes 0.28 0.63 Fig. 8. Void fraction achievable by naturally packing shapes with given sphericity. Fig. 9. Breakeven function for different amounts of melting temperature modification. C. Prieto and L.F. Cabeza Journal of Energy Storage 43 (2021) 103184 9 engineered structure from its previous life. An example of this concept would be recycled aluminium tubes. Aluminium tubes are prolific in recycling bound waste streams in the form of used structure beams, containers, and building materials. Furthermore, these tube structures can readily achieve the void fractions required by the system. For example, if aluminium tubes with the dimensions of common soda cans were to be dumped into our PCM storage tanks, they would naturally reach a void fraction of 0.98. 4.2. Influence of the melting temperature of the PCM The effect of well-spaced PCMs was investigated as a solution to unstable operation caused by the dissimilar pinch points during charge and discharge. Instead of finding completely new PCMs slight modifications in melting point can be accomplished through doping with other salts. Currently, two national labs and several private entities are working of either the development of novel PCMs or the alteration of current PCMs. To find the most appropriate set of melting temperatures a tolerance on melting points was successively relaxed from 0 ◦C to 20 ◦C. When the tolerance was relaxed, the melting points were allowed, but not forced, to move as far as the new tolerance. Fig. 9 shows the breakeven function generated by the movement of this melting temperature modification tolerance from 0 ◦C to 20 ◦C. Similar to the TCE breakeven plot, there is a point of diminishing returns where, even though the tolerance is relaxed further, meaningful cost savings are not realized. Using this plot, a melting temperature movement tolerance of 10 ◦C was chosen and a parametric study was used to generate an acceptable set of system dimensions. These dimensions are summarized in Table 10. 4.3. Ideal properties PCM In addition to more appropriate melting points, the effect of more appropriate thermal properties was also investigated. If the enthalpies of fusion, thermal conductivities, specific heats, or densities of the PCMs currently being used are improved, the performance of the system can be improved. In order to keep the investigation grounded in reality, the PCM with the best thermal properties, MgCl 2 -KCl-NaCl, was used to set the thermal properties for all the PCMs. Once the thermal properties were assigned, a new system was parametrically derived with acceptable performance. Table 11 shows Table 10 System dimensions for the TCE storage system. Dimension Value Unit Tube diameter 0.02 m Tube length 250 m PCM radial extent bucket 1 3.75 cm PCM radial extent bucket 2 4.00 cm PCM radial extent bucket 3 3.25 cm PCM radial extent bucket 4 3.25 cm Number of tubes in bucket 1 2100 - Number of tubes in bucket 2 3600 - Number of tubes in bucket 3 3600 - Number of tubes in bucket 4 2652 - T melt bucket 1 320 ◦C T melt bucket 2 340 ◦C T melt bucket 3 360 ◦C T melt bucket 4 380 ◦C Table 11 System dimensions for the ideal thermal properties PCM storage case. Dimension Value Unit Tube Diameter 0.02 m Tube Length 250 m PCM radial extent bucket 1 3.75 cm PCM radial extent bucket 2 4.00 cm PCM radial extent bucket 3 3.25 cm PCM radial extent bucket 4 3.25 cm Number of tubes in bucket 1 2500 - Number of tubes in bucket 2 4000 - Number of tubes in bucket 3 4000 - Number of tubes in bucket 4 2500 - T melt bucket 1 320 ◦C T melt bucket 2 340 ◦C T melt bucket 3 360 ◦C T melt bucket 4 380 ◦C Thermal properties based on MgCl2-KCl-NaCl - Fig. 10. Biot number for various size capsules. C. Prieto and L.F. Cabeza