A Waste Heat Assessment of a Manufacturing Facility With Consideration for Demand Matching Through Thermal Energy Storage

Due to the significant amounts of waste heat rejected, waste heat recovery is widely recognized as an important engineering task for improving energy efficiency. For example, in 2021, 67% of the energy consumed in the United States (US) was rejected to the environment, primarily as waste heat [1]. The industrial sector, specifically, has been targeted for waste heat recovery due to the high amounts of waste heat produced and because it has applications to which the waste heat could be applied [2–7]. For example, in the US, it is estimated that 20–50% of the energy consumed in the industrial sector is ultimately rejected to the environment as waste heat [3] and in the European Union (EU), it is estimated that the waste heat potential is 300 TWh/year [5]. Waste heat is rejected over a range of temperatures, but much waste heat is rejected at relatively low temperatures. For example, in US industries, it is estimated that 60% of the waste heat is at temperatures less than 232 °C [3] and, in the EU, it is estimated that 33% is rejected at temperatures less than 200 °C [5].

Methods to assess waste heat potential [8] include bottom-up surveys [9], bottom-up estimations [3,7], top-down estimates [10], or a combination. Often these assessments are estimates for entire countries, e.g., Refs. [3,7,11,12], or for a specific industry, particularly for energy-intensive manufacturing industries, e.g., aluminum production [13]. Bottom-up estimates are a common approach [8]. This approach uses efficiency ratios for equipment or processes used in the industry of interest, and then aggregates the losses to determine the waste heat [8]. The data used in these calculations, e.g., process temperatures and efficiencies, come from a variety of sources such as prior literature and researcher experience. Regardless of the methodology, these kinds of assessments which report waste heat potential at large scale (e.g., entire industries or countries) are useful for identifying sources of waste heat and assessing the quality of waste heat and the overall potential impact waste heat recovery would have for various industries. For example, focusing on glass manufacturing, cement manufacturing, iron and steel manufacturing, aluminum production, metal casting, industrial boilers, and ethylene furnaces, it is estimated that approximately 60% of the waste heat in the US manufacturing is below 230 °C and 90% is below 316 °C. Much of this waste heat comes from steam boilers. However, technologies such as cement kilns reject higher-quality waste heat [3]. In the UK, it is estimated that the waste heat potential for sources less than 250 °C is 16.7–17.4 TWh/year and the mechanical engineering subsector has been identified as an important subsector for waste heat recovery [12].

However, the development of waste heat recovery systems and technology also needs more granular data that includes information such as temporal fluctuations in the waste heat temperature and flowrates [14]. This is a similar situation to designing solar or wind energy technologies. It is well established in those fields that there are significant supply-side fluctuations that impact the energy output, and which must be accounted for when designing the system, e.g., by using hour-by-hour simulations with programs such as the System Adviser Model [15]. For waste heat recovery, this kind of data is particularly necessary for the development of recovery technology that utilizes waste heat from one process in order to be used in a different one, i.e., the source process is different than the sink. In these kinds of situations, the fluctuations in the sources of the waste heat and in the demand can be different, and the recovery system must be designed to accommodate the fluctuations. Knowing fluctuation in temperature, flowrates, and frequency of availability of the waste heat is beneficial to match it to an application [14,16]. This need is acute for the recovery of low-temperature waste heat where one key challenge is matching it to an industrial application [2,17].

Despite the need, data on waste heat from individual facilities or processes which include temporal variations are limited. The data are even more limited for facilities that primarily produce low-quality waste heat even though low-temperature waste heat is known to be most prevalent. Surveys tend to focus on high-quality facilities. For example, a thermodynamic analysis of cement plant located in Turkey was conducted, and it was found that the rotary kiln was the process with the highest energy loss at 49,080 kW followed by the pyro-processing tower (22,790 kW). These two processes also had the highest rate of exergy loss at 54,847 kW and 19,825 kW, respectively [18,19]. However, temporal variations were not reported. Another survey provides data on the operation of a cupola within an engine casting plant in order to demonstrate a methodology and highlight the importance matching waste heat sources with sinks [14]. Without more surveys and additional, temporal data, the design of low-temperature waste heat recovery systems is challenging.

The current work helps to address this knowledge gap by conducting a waste heat survey of a manufacturing facility which primarily rejects low-quality waste heat. Various waste heat sources were identified, and the exhaust streams were measured and reported. An energetic and exergetic analysis of this waste heat was conducted. Then the waste heat is compared to the estimated space heating requirements for the facility to examine one potential option for utilizing the waste heat. Additionally, the impact using thermal energy storage (TES) to better match the waste heat supply to the space heating demand is investigated by modeling the recovery of waste heat from some of the waste heat sources and applying it to the space heating demand of a prototype warehouse facility. The initial cost and simple payback of the recovery systems are determined.

The facility selected for the waste heat assessment is a manufacturing facility located in North Dakota. The facility specializes in automated assembly, manufacture of plastic components via injection molding, design and build of injection molding molds, and metal fabrication. It also includes cleanroom production space. The facility is heated by a conventional firetube boiler that burns natural gas to produce steam to heat the building and provide steam for processes. The facility was built around 1980 and is approximately 24,651 m² spread across two buildings with approximately 21% of the floor space dedicated to warehouse space, 4% to office space, and the remainder for manufacturing. The walls are primarily concrete while the roof is primarily steel construction.

Initially, a plant-wide, physical inspection of the facility was conducted to identify potential sources of significant waste heat. Sources were limited to those with a fluid exhaust stream that is rejected to the atmosphere, because those sources allow for waste heat to be more easily recovered than sources that reject waste heat via other mechanisms, e.g., radiation. As such, sources such as the hot injection molding presses and the plastic parts exiting the molds were ignored. Through the physical survey, the following items in the facility were identified as potentially significant sources of waste heat:

• boiler flue;

• dryers to dry polypropylene pellets (polypropylene (PP) dryer);

• chiller loop for the Heating, Ventilation, and Air Conditioning (HVAC) system (chiller);

• plant vacuums;

• deaerator for the boiler;

• compressed air dryer;

• electroplating air handler.

To assess the waste heat from these sources, the temperature, flowrate, and frequency of the exhaust were measured directly, obtained from company records, or determined via calculations. The method utilized depended on a number of factors such as access to a location to measure the exhaust flow and availability of company records on a particular source.

The facility uses a 224 kW firetube boiler burning natural gas to generate steam that is used in the plant processes as well as for heating. The heating system uses the steam to heat water which is then pumped to air handlers. It is operated continuously. The average temperature of the flue gas was determined to be 128 °C using the temperature probe integrated into the exhaust stack and averaging company records of that stack temperature. Company records indicated this temperature fluctuated slightly over the past 9 months, with a minimum exhaust temperature of 110 °C and a maximum temperature of 142 °C during that time period.

The mass flowrate through the boiler flue was estimated by reviewing the monthly fuel consumption for the prior year and then using this data to conduct a mass balance on the combustion reaction. To balance the combustion reaction equation, the effluent concentration of CO₂ and O₂ were obtained from company records of boiler servicing and annual combustion test results. The boiler service records report an average boiler efficiency of 87.6% and that the exhaust contains, on average, 8.96% CO₂ and 4.9% O₂. For the analysis, the fuel is assumed to be completely combusted which is supported by the presence of oxygen in the combustion products. Natural gas is ∼95% methane, therefore, it is approximated as methane (CH₄) [20]. Incoming air for combustion was approximated as 21% oxygen and 79% nitrogen on a dry basis [21]. The average ambient relative humidity and temperature for each month of the year [22] were used to calculate the number of moles of water present to account for moisture in the air. Table 1 provides the moles of fuel consumption based on company records and the relative humidity of the incoming air used in the calculation.

In Eq. (2), $Patm$ is the atmospheric pressure,$φair$ is the average relative humidity for the given month (Table 1), $Psat$ is the saturation pressure at the associated average monthly temperature (Table 1), and $nair$ is the moles of air (2.55) which is determined by the complete combustion requirement. Due to differences in weather conditions, the average number of moles of water in the air varies by month. The result is given in Table 1.

As will be discussed in Sec. 4, the waste heat from the boiler is split into the waste heat due to fuel consumed to meet the heating load and fuel consumed to meet the process load. The split is estimated based on the fuel consumed during the summer and winter months.

This distinction is made because, if the waste heat is used for space heating, the waste heat from the boiler flue would decrease since less fuel would be needed to provide heating. However, the fuel consumed for processes in the facility would not be affected.

The PP dryers are used to remove moisture from pellets of polypropylene that are then used for producing injection molded parts. The facility utilizes four dryers that recirculate air to dry the pellets. The PP dryers utilize a desiccant to remove humidity from the air that is used to dry the pellets. When the desiccant needs to be regenerated, the dryer runs hot air through the desiccant. This hot, moist air is exhausted to the environment. The dryers regenerate at a flowrate of 0.25 kg/s per the manufacture settings. The regeneration of the PP dryers operates intermittently. To determine the frequency of regeneration and temperature of the exhaust gases, a USB-501-TC temperature logger was placed directly in the exhaust stream of one of the dryers. It recorded the temperature every 30 s for 7 days. The data showed that the dryers regenerated fairly regularly at a frequency of approximately 19 cycles per day. Figure 1 presents a representative subset of the data showing three regeneration cycles for a single dryer. For each cycle, the peak temperature during the cycle is approximately 80 °C with a duration of approximately 26 min. Individual cycles were averaged to determine an average air temperature of 67 °C when regenerating and that the regeneration for each dryer runs for an average of 8.4 h per day.

As part of the facility HVAC system, a ground-based chiller loop is used to reject heat to the environment. Water temperature and flowrate in the loop were determined by the temperature probes and flowmeter integrated into the system. The system operates continuously. The cooling water exited the facility at an average temperature of 26.7 °C and returned at 24.4 °C at a flowrate of 113.6 kg/s. There was very little variation in this temperature, e.g., ∼1 °C.

The facility utilizes two plant vacuum systems which provide vacuums for the various manufacturing processes. These vacuums continuously run at a constant speed year-round. The air removed by the vacuums is exhausted to environment. The average exhaust temperature for each vacuum was measured with a thermocouple as 32.2 °C and 46 °C. There was very little variation observed in this temperature. An anemometer was used to find the flow velocity in each vacuum using the Tchebycheff method for rectangular ducts [23]. The flowrate was calculated at 2.47 kg/s for the 46 °C exhaust and 2.38 kg/s for the 32 °C exhaust. As such, the average exhaust temperature for the two vacuums is 39.2 °C.

A deaerator is used to remove corrosive dissolved gases from the boiler makeup water. The deaerator uses a flow of steam to heat the makeup water and raise the operating pressure of the tank. An excess of steam, beyond what is required for heating, is added to carry the corrosive gasses upward and out of the vent [24]. The temperature of the venting steam was measured by a thermocouple to be 113 °C. No significant variation in this temperature was observed. The flowrate was estimated using the deaerator rating, type, and the percent makeup water [24]. A boiler servicing company was consulted to determine that the deaerator was a tray-style deaerator. A deaerator rating of 9.45 kg/s was chosen based on a discussion with the boiler servicing company and the fact that the deaerator and boiler used by the facility are relatively small [25]. The percent makeup water was calculated using records of the boiler makeup water and comparing that to the amount of water in the system. Based on this information, a deaerator flowrate of 0.008 kg/s was calculated from the methodology provided by Knox [24].

The facility uses an air handler to scrub fumes released by the chemicals used for electroplating. The air handler runs year-round at a constant rate of 0.903 kg/s based on plant records. The temperature of the exhaust was measured to be 27 °C without significant variation in this temperature.

The compressed air dryer is used to remove moisture from the compressed air supply for the facility. Occasionally, the desiccant in the dryer must be regenerated by blowing hot air through the desiccant. The exhaust from this regeneration process is a potential source of waste heat as it is normally vented. The temperature from the exhaust of this regeneration process was monitored with a USB-501-TC temperature logger. It recorded the temperature every 30 s and monitored the dryer for 7 days. As shown by the representative cycle in Fig. 2, when operating, the exhaust temperature is relatively constant at 40 °C for the first 2 h of the cycle. After the first 2 h, the temperature rapidly increases to a peak of 130 °C for a little under 2 h. The duration of the cycle at temperatures greater than 40 °C is 5.31 h and the average dryer exhaust temperature for the cycle is 108 °C. However, the regenerative process occurred highly infrequently and the duration can vary. Based on the data logger, it was only activated approximately once every 6 days. Thus, to determine the hours of operation per month, the frequency of operation was determined to be an average of ∼0.8 h per day or activating approximately five times per month. The flowrate of the exhaust was calculated from the performance curve for the 59 U-RAI blower used in the system [26]. The motor runs at 2850 rpm. To determine the flowrate from the performance curve, a conservative pressure drop of 50.3 kPa was chosen. This pressure drop is a conservative estimate, because it is the highest allowable pressure drop for that blower and thus results in the lowest flowrate and lowest estimate of waste heat that could be captured and used. The estimated flowrate used for calculations is 0.28 kg/s.

The total useful energy and exergy per month for a waste heat source was determined by multiplying Eq. (5) or Eq. (6) by the amount of time the waste heat stream is active for a given month. For those components that have intermittent operation (PP dryers and compressed air dryer), the average amount of time the waste stream is active per month was calculated using the frequency and length of operation measured and discussed in Sec. 2. This frequency of operation was assumed to be the same for non-observed times as for observed times.

The space heating load for the facility was determined using the boiler efficiency from company records and gas consumption history. To estimate how much natural gas is consumed for processes and how much is consumed for heating, the consumption of the boiler during the months with the lowest heating requirement was assumed to be entirely for process steam. The months with the lowest heating requirements were determined by comparing the heating degree days for each month. The number of degree days in a day is the difference between the balance temperatures (the ambient temperature where thermal losses from the building are offset by the internal energy generation of the building is historically 18.3 °C for a room temperature of 24 °C) and the day's average temperature. The number of degree-days is proportional to the heating load. The monthly number of degree days is the sum of the daily degree days in that month. Table 3 shows the degree days per month for Fargo, ND, a representative city in the region that records degree days [22]. Table 3 shows that June, July, and August combine for 44 degree days. The other 9 months total 7212 degree days. Additionally, individually, any other month has at least four times the number of degree days as June, July, or August. Thus, June, July, and August are assumed to have negligible heating requirements and that natural gas consumed in those months is for processes. The variations in the consumption in those three months are assumed to be due to variations in the demand from the processes. The average consumption for those months was used to estimate the amount of fuel needed to provide steam for industrial processes in the facility. This consumption was subtracted from the remaining months to yield the gas consumption specifically for heating. This method assumes the process steam demand is similar year-round.

The monthly energy for heating was calculated by taking the gas consumption for heating times the heating value of natural gas (39.5 MJ/m³ [27]) times the efficiency of the boiler. Figure 3 shows the estimated energy used to heat the facility. The graph shows that no energy is required for heating during the months of June, July, and August per the degree-day data. It also shows that the months requiring the greatest amount of heat are January, February, March, and December. This trend is consistent with the number of heating degree days mentioned above. Based on this analysis, the total annual, amount of energy required to heat the facility is 8.46 TJ.

As discussed in Sec. 2, the waste heat varies temporally. Additionally, the thermal demand to which the waste heat is applied has its own schedule. TES could be used to help increase the overlap between these two schedules and increase utilization of the waste heat. Due to the temperature of the available waste heat from this facility, it is well-matched for space heating demand. To investigate how thermal storage could be used to better match the waste heat to space heating, an initial analysis is conducted. Models are constructed to investigate using part of the waste heat from the industrial facility to meet the space heating demand for the Department of Energy prototype warehouse building in compliance with the ANSI/ASHRAE/IES Standard 90.1 [28]. As shown in Fig. 4, a simple recovery system is modeled wherein during periods of excess waste heat, i.e., waste heat energy exceeds demand, part of the waste heat goes to the demand while part goes to the thermal storage unit. Then during periods of excess demand, i.e., demand exceeds the waste heat, energy is drawn from storage to help meet those demands. In this model, the excess waste heat is stored in a packed-bed TES unit consisting of loosely packed rocks or pebbles. Rock bed storage is used because it is often used when air is the heat transfer fluid. Estimates for the initial costs for such a recovery system and for an alternative that uses water for the TES are developed. The purpose of this analysis is not to exactly predict the demand of the manufacturing facility, but to create a representative space heating demand schedule to compare to the frequency of the waste heat and to examine the potential for using thermal energy storage to better match the supply (waste heat) to the demand (space heating).

Short-term simulations of representative weeks are conducted to show the impact of TES at the hourly level. Then long-term simulations of the full heating season (nine months from September to May) are conducted to investigate using the waste heat to meet the monthly and seasonal space heating demand for the prototype warehouse. Based on these long-term simulations and the estimated initial cost, the simple payback periods for the waste heat recovery systems are estimated.

For this analysis, only relatively clean, i.e., not expected to have harsh or toxic chemicals, particulate material, etc., waste heat sources are utilized. The clean sources are the exhaust from the polypropylene dryers and the plant vacuums (Fig. 4). The exhaust streams from these sources are hot and moist air.

In Eq. (11), G is the mass flux of the air flow through the bed (determined by the cross-sectional area and mass flowrate through the bed) and D is the particle diameter. These governing equations were solved using explicit finite difference.

Table 4 provides key inputs and parameters for the model. For a capacity of C = 0.125, Eq. (18) and the rock properties (Table 4) require a mass of 31,182 kg of rock. For a nominal temperature difference of 25 °C, this represents a TES with a thermal capacity of 190 kWh. To house this rock with an assumed void fraction of 0.41, a storage unit 2.032 m long with a cross-sectional area of 10.16 m² is assumed (total volume of 20.65 m³). The ratio of length to cross-sectional area is kept constant for other capacities. Thus, at a capacity of C = 1, the storage vessel is 5.747 m long with a cross-sectional area of 28.735 m² (total volume of 165.14 m³). For short-term simulations, simulations are conducted assuming the TES is initially discharged (T_b = 25 °C) and initially charged (T_b = 43 °C, average waste heat temperature). For long-term simulations, the bed initial temperature is 25 °C.

An estimate of the initial cost of a system and TES to recover and store the waste heat was developed. Costs were developed for three primary systems:

• Waste heat recovery system without thermal storage (aka no storage);

• Waste heat recovery system with rock bed TES;

• Waste heat recovery system with water TES.

The initial, unoptimized design of the recovery system with rock storage, is given in Fig. 5. The major components for the system are an air-to-air heat exchanger (AA-HX), fans, and the TES unit (vessel and material). Schematics for the recovery system without storage and for the system with water TES are provided in the  Appendix. For the no storage system, it is the same with the one described in Fig. 5, except the rock bed TES and associate ducting are removed (Fig. 23). For the water storage system (Fig. 24), additional major components include air-to-water heat exchangers (AW-HX and WA-HX) and pumps for adding and removing energy from the water TES. For the system with water TES, the costs were estimated using water, rather than rocks, to store surplus waste heat. The water TES was sized to have the same thermal capacity of the rock TES based on a nominal temperature difference of 25 °C (Table 4), a specific heat of 4.178 kJ/kg·K, and a density equal to 991 kg/m³. As such, to achieve the same thermal capacity as the C = 0.125 case, 6650 kg of water are needed and the vessel size is 6.62 m³. For the C = 1 case, 52,485 kg of water and a 52.96 m³ vessel are needed.

The initial cost of the recovery systems was estimated from the cost for the major components and from additional costs associated with ducting, installation, etc. From the price and characteristics of the AA-HX provided by a seller [30], a correlation trend line between the price of the AA-HX ($) and the air flowrate (CFM), with a correlation coefficient R² > 0.8, was obtained. From this correlation, the minimum price of the AA-HX that can handle the peak waste heat air flow was estimated. The peak air flowrate (5.8 kg/s) occurs when all the waste heat sources are active. Similarly, the size of the fans was selected based on the peak air flowrate and the cost estimated from seller prices [31]. For the water storage system, cost estimates were obtained for the additional components (two air-to-water heat exchangers (AW-HX) and two pumps). Based on the price list and property description provided by a manufacturer for AW-HXs [32], a correlation trend line between price and the air flowrate (CFM), with a correlation coefficient R² > 0.8, was obtained. It was used to calculate the unit price based on the HX based on the peak of air flowrate of the waste heat sources. The cost of the pump was estimated based on the listed price for a pump capacity of 20 GPM [33]. The pump flowrate was estimated from the heat transfer rates required from the thermal storage to meet the building demand (based on the rock TES system model predictions) and assumed a temperature drop of ∼10–15 °C in the AW-HX.

The cost of the containment vessel for the TES was estimated from prices listed by a seller [34] for plastic containments that could contain rock or water and could be buried underground. A relationship between tank size (m³) and cost ($) for tank sizes between 20 m³ and 60 m³ was established from a linear regression as shown in Fig. 6. A separate but similar expression for tanks less than 20 m³ was also developed (y = 487·x—3832). The cost for the rock was estimated at ∼$0.02/kg [35]. The local utility cost for water is $7.40/1000 gallons [36]. As such, the cost of water for C = 0.5 only adds $50 and thus is neglected.

Based on the relative cost for ducting and labor in a prior published industrial waste heat utilization system [37], the cost for the ducting and labor was estimated as a percentage of the total price. For the no storage system, the cost of the ducting and other minor components was estimated at approximately 10% of the total price. For the systems with TES (both rock and water), the percentage for ducting was estimated using 12% to account for the more complex ducting and plumbing. The labor and installation costs were estimated as 28% of the total sum of the other items.

The simple payback for the systems was calculated by dividing the estimated initial total cost by the annual energy cost savings. The energy savings for a year were estimated by the long-term (nine-month heating season) simulations which calculated the fraction of the space heating demand that the waste heat recovery system could provide. For the water-based TES, it was assumed that it would be able to meet a similar fraction as an equivalently sized (by thermal capacity) rock TES. This energy savings represents a decrease in natural gas consumed by the building heating system. Thus, energy provided by the waste heat recovery system was converted into displaced natural gas by using the North Dakota Heat Content of Natural Gas Deliveries to Consumers (BTU per cubic foot). Then, using the 2022 North Dakota Natural Gas Industrial Price (Dollars per thousand cubic feet) published by the Energy Information Administration (EIA), the annual energy cost savings were calculated [38,39].

As shown in Fig. 7, a model of a non-refrigerated warehouse was developed in trnsys. The basic building information is provided in Table 5. The major TRNSYS components used include Type 56 for modeling the warehouse building, Type 921 for simulating the air conditioning units, Type 139 for representing the gas-fired furnace used for space heating, and Type 15 as the TMY3 weather data reader. The details of the building are available on the DOE website [28]. It has a total floor area of 4598 m² with a slab-on-grade foundation, metal building wall exterior wall construction, and a metal building roof (metal surface plus roof insulation) construction. In the model, the building was divided into three thermal zones: bulk storage, fine storage, and office. Table 5 provides additional building details. Simulations were conducted using weather data for Fargo, ND.

As shown in Fig. 8, a mesh refinement and time-step analysis were conducted for the TES model. This analysis was done by setting the initial bed temperature to 30 °C and then providing an inlet temperature of 50 °C. The TES was considered fully charged when the tank reached near equilibrium (outlet fluid temperature of 49.9 °C) with the incoming air. This analysis was conducted for capacities of 1 and 0.25. Figure 8(a) shows the time to charge as a function of number of nodes. For subsequent analyses, 50 nodes were used because it is in the independence region for both capacities. Figure 8(b) shows the effect of time-step for the same charging conditions and using the 50 nodes. For subsequent simulations, a time-step of 30 s or less was used because it is independent for both TES capacities.

The building model was calibrated by comparing the trnsys model predictions to the energyplus simulations for Rochester, MN (AIA climate zone 1), as shown in Fig. 9. The energyplus model was developed by the Pacific Northwest National Laboratory, and the simulation results were used by the U.S. Department of Energy to evaluate published versions of the building energy code and formulate proposed amendments to the code [28]. The weather in Rochester, MN is similar to Fargo, ND (the location for subsequent simulations), so the calibration result is meaningful. The normalized mean bias error (NMBE) between the trnsys model and energyplus data from the DOE is −2.11% while the coefficient of variation of root mean square errors (CVRMSE) is 6.47%. According to the ASHRAE Guideline 2014 [40], acceptable error margins are within ±5% for the NMBE and 15% for the CVRMSE. Therefore, these calibration results validate the trnsys model, affirming its reliability for simulation results discussed later.

Table 6 summarizes the mean temperatures, flowrates, operational frequency, and the exergy and energy content of the waste heat from each source mentioned in Sec. 2. Additionally, it provides the estimated annual useful energy from each waste heat source. A breakout of the percentage each waste heat source contributes to the total useful energy and exergy is provided in Fig. 10. For the PP dryers and vacuums, the annual useful energy is for all four dryers and the two vacuums. The flowrate shown in Table 6 is the flowrate when that component is in operation. The most significant source of waste heat is the chiller which rejects an order of magnitude greater amount of energy than any other source. However, the quality of this waste heat is very low with an average temperature of only 27 °C. The air handler also has an average temperature (27 °C) near ambient. Sources like these with exhaust temperatures so close to ambient are more difficult to recover. The second and third most significant sources are the vacuums and boiler, respectively. At a temperature of 46 °C, waste heat from the vacuums would be sufficient for space heating. The boiler flue is the highest quality waste heat measured in the facility at ∼130 °C.

Of the seven sources, five operate continuously while two operate intermittently. Continuous operation is beneficial for waste heat recovery. However, even in sources that are operated continuously, there can be variations in the amount of waste heat. The boiler flue has a varying flowrate (0.369–0.821 kg/s) for each month based on the monthly natural gas consumption. Additionally, as noted, there are variations in the temperature from 110 °C to 142 °C. As such, this continuous source has longer-term variations, e.g., month-to-month, in the amount of waste heat it produces. As shown by the data in Sec. 2, intermittent sources, like the PP and air dryers, have shorter-term fluctuations in both temperature and flowrate. The air dryer only operates approximately once per five days while PP dryers cycle on and off approximately 19 times per day. Waste heat recovery of these sources would benefit from a storage mechanism. The air dryer in particular highlights the challenges of intermittent sources. While the temperature of the waste heat from the air dryer is sufficient for applications such space and water heating (average of ∼108 °C with a peak of 130 °C), the infrequency of the source makes it more challenging to utilize because there is a short burst of waste heat followed by long periods of inactivity. The PP dryers operational frequency is much higher than the air dryer (∼8 h/day versus 0.8 h/day), but the cycles are short (<30 min) which results in a pulsating source. For intermittent sources such as these, a storage system could be used to capture the burst of activity and dissipate on-demand over a longer period of time. This would make the recovered waste heat more user-friendly.

Figure 11 shows the useful energy rejected for each month from each source. On average, there is ∼3042 GJ of useful waste heat rejected by the various processes each month. There is a slight fluctuation in this average value due to the variations in the boiler waste heat and the numbers of days in each month. As such, longer winter months such as January and December have slightly higher useful energy from waste heat while shorter, summer months such as June have less useful energy. The total amount of useful energy rejected over the span of one year is 36.5 TJ, however, only three components significantly contribute to the total: the chiller, the vacuums, and the boiler flue. The high flowrate of the chiller results in a substantial amount of useful energy despite an exhaust temperature near the reference temperature. The chiller accounts for 30 TJ annually which is 82% of the total useful energy (Fig. 10). To see the contributions of components other than the chiller more easily, Fig. 11(b) shows the useful energy from all the components except the chiller. After the chiller, the next largest component of waste heat is the two vacuums with a monthly average of 275.1 GJ which results in an annual total 3.3 TJ or 9% of the total, annual useful energy. These vacuums run continuously and have the second-highest flowrate. In Fig. 11, the energy from the boiler flue has been separated into the exhaust from the natural gas consumed for the heating load and the exhaust for processes. The exhaust from the natural gas burned for heating accounts for 1.3% of the total useful energy (annual total: 0.47 TJ) and the exhaust from the gas used for processes is ∼4% of the annual total (1.54 TJ). Each of the other four components (PP dryers, air handler, air dryer, and deaerator) contributed less than 2% of the total, annual useful energy (Fig. 10). These four components reject a combined 1.21 TJ of useful energy per year. Of these remaining components, the deaerator has the highest useful energy content (average per month = 54.5 GJ; annual = 0.655 TJ). Most of the useful energy from the deaerator is from the latent energy of the steam and thus would be available at approximately 100 °C. The four polypropylene dryers reject a similar amount of waste heat with an average of 40.5 GJ per month and an annual total of 0.49 TJ. The electroplate air handler and compressor air dryer reject an order of magnitude lower amount of waste heat, 0.049 TJ and 0.03 TJ, respectively. These sources have low values of useful energy for different reasons. For the air handler, the exhaust temperature (27 °C) is very near the reference temperature (25 °C) and thus this is a small temperature difference which can be utilized. For the air dryer, the exhaust temperature is relatively high (108 °C) but is operated very infrequently.

Figure 12 shows the exergy rejected by each component on a monthly basis. While Fig. 13 provides a more detailed view of the minor exergy contributions, i.e., exergy from sources excluding the contributions of the chiller and boiler which provide the majority of the rejected exergy. The total amount of exergy rejected in the facility is 842 GJ. The average exergy rejected per month is ∼70 GJ. As such, the exergy associated with the waste heat streams is approximately two orders of magnitude lower than the useful energy. This smaller value for exergy is to be expected due to the relatively low temperature of the waste heat rejected by the facility. The maximum temperature of the waste heat from any source is only ∼130 °C which is much lower than waste heat rejected for high temperature processes and equipment such as rotary kilns in cement factories. The chiller and air handler, in particular, have a drastic reduction when considered on an exergy basis compared to an energy basis. The chiller is still the largest contributor, but it goes from contributing 82% of the energy to 35% of the exergy (Fig. 10). While the air handler, which rejected the second lowest useful energy, rejects an order of magnitude lower amount of exergy than any other waste heat source. As with the useful energy, there are slight month-to-month fluctuations primarily due to the difference between winter and summer boiler usage and the length of the months, as shown in Figs. 12 and 13. However, due to the boiler flue gases making up a larger percentage of the rejected exergy compared to the rejected useful energy, these fluctuations are more significant than the fluctuations in the useful energy from the waste heat. Besides the chiller at 35% of the annually rejected exergy (24.3 GJ per month; 292 GJ annually), the largest contributor of exergy rejection is the boiler flue which rejects on average 23.3 GJ per month and accounts for 33% (280 GJ) of the estimated annual exergy rejection (Fig. 10). The exergy of the chiller makes up a much smaller percentage of the total exergy rejected because it is only 2 °C hotter than the reference temperature of 25 °C. Thus, the quality of the energy rejected by the chiller water is very low. However, the boiler flue gases are the hottest waste heat source, and it runs continuously. Thus, it makes up a much significant portion of the exergy than the energy content of the waste heat.

Each month, the deaerator and vacuums reject on average 10.4 GJ and 9.3 GJ of exergy, respectively. Annually, these two components contribute 15% (deaerator) and 13% (vacuums) to the total exergy rejected. For the low-quality facility, the deaerator provides relatively good quality waste heat at ∼113 °C which is the second highest temperature waste heat source. Thus, it contributes a more significant fraction of exergy than energy. The four polypropylene dryers reject, on average, 2.6 GJ of exergy per month and account for 4% of the annual total. The two other components, the electroplate air handler and the compressed air dryer combine for less than 0.5% of the total exergy. The air handler only rejects 0.01 GJ of exergy per month because the temperature of the exhaust stream is only 1.7 °C above the reference temperature. The air dryer rejects 0.24 GJ of exergy each month.

A key aspect of utilizing recovered waste heat is matching it to an application, i.e., a sink. Due to the low quality of the waste heat produced, space heating is a good possible match. The estimated space heating load for the facility is 8.46 TJ for an entire year. Based on the cost of natural gas, the annual cost for the fuel consumed in the facility is ∼$186,000. The natural gas consumed for heating accounts for 25% of total natural gas consumption, thus it is estimated the heating costs are ∼$46,000 per year. Since the total useful energy rejected over the course of a year is 36.5 TJ, theoretically, this waste heat could provide all the energy necessary for space heating. However, not all sources can be used for space heating due to a waste heat quality that is too low. The energy needs to be supplied at a temperature sufficiently higher, e.g., 10 °C higher, than the indoor space to provide a sufficient driving potential for heat transfer. As such, energy from the chiller and air handler is of such low quality that it not feasible to provide radiant heating. For a room at 24 °C, these two streams of waste heat are only 2.7 °C above ambient. At this temperature difference, a high surface area would be necessary for effective heat transfer. However, these sources could be used for lower temperature applications. For example, the chiller loop could be used to preheat incoming, fresh air during winter. There is a sufficient temperature difference between the incoming air in winter (approximately −13 to −2 °C in winter) and the exhaust streams (27 °C) for the heat transfer to occur in a reasonable space.

Another issue to consider is contaminants in the waste heat streams. The deaerator and electroplate air handler are exhaust streams, because both remove containments from their respective processes. For the deaerator, if enough energy is removed from this waste heat, the steam could condense, and this condensate may contain heavy earth metals and other pollutants. The exhaust from the electroplate air handler could also contain contaminants. Waste heat recovery from harsh environments is more challenging [41]. For example, these contaminants may require the use of non-corrosive materials in the recovery system which would increase cost. Thus, while the deaerator rejects a significant amount of exergy (124 GJ annually), without knowing the composition and concentration of the dissolved gases in the steam, it is not recommended to capture this waste heat. The boiler flue could have similar issues depending on the composition of the natural gas combusted in it. However, natural gas boilers generally have much cleaner exhaust and are a better candidate for waste heat recovery than coal-burning boilers [14]. And if energy is removed from the flue, care must be taken to not negatively affect the stack draw. Yet, there are technologies available to recover waste heat from boiler flues [42] which can result in significant savings [43]. Thus, recovery from the flue, while presenting challenges, is feasible.

With these considerations, waste heat from the chiller, the air handler, and the deaerator are ignored for a space heating application. Additionally, for space heating applications, the waste heat from boiler flue gases due to heating is also ignored. This is because, if waste heat is used to provide the space heating, this source of waste heat would decrease. The waste heat from the air dryer is also neglected due to its infrequency. Figure 14 compares the energy content of the waste heat from the remaining sources (plant vacuums, PP dryers, and boiler flue waste heat from process) to the energy for space heating on a monthly basis. During the months when heating is needed, these sources could meet theoretically up to 39% of the load which corresponds to an annual savings $17,900. Due to the pulsating nature of the PP dryer regeneration cycle, this waste heat source could be more effectively utilized with thermal storage. Even for the continuous processes (e.g., vacuums and boilers) storage could be beneficial. Space heating has daily and weekly fluctuations in demand. Thus, even waste heat from continuous processes needs to consider matching with the sink demand frequency. Consideration of these short-term fluctuations is discussed in the next section. Figure 14 also highlights the potential of seasonal of thermal storage. On a monthly basis, the waste heat is fairly consistent throughout the year, thus it significantly exceeds the heating requirement during the late spring to early fall. An effective storage mechanism could recover this excess waste heat and store it to be utilized during the months with a higher heating load. In that case, the waste heat from these sources could provide up to 63% of the heating load which corresponds to an annual savings of $28,980. Thus low cost, effective storage is necessary to maximize the waste heat utilization for this application.

The assessment also reveals at least one, relatively, simple modification to recovery the waste heat and apply it to a sink: the waste heat from the vacuums can provide space heating. At ∼40 °C, heat from the vacuum exhaust is well-suited to provide space heating, and the vacuums run continuously. Modifications to the exhausts of vacuums could allow for the exhaust from the vacuums to reject heat to the facility and provide space heating when needed and vented when not needed. Even without storage, this simple modification could theoretically provide up to 27% of the heating load and potentially save $12,400 in heating costs every year. However, this number neglects short-term mismatches between the waste heat and heating demand. With seasonal storage, the fraction could increase to 39% and $17,900 in potential savings just from the vacuums. Including the exhaust from the PP dryers in these relatively simple modifications would increase the percentage of the space heat load met by waste heat to 30% without storage and 45% with storage.

The results of the waste heat survey indicate there is a significant opportunity for waste heat to meet space heating demand. As such, models are used to investigate using waste heat (represented by the waste heat from the industrial facility) to meet the space heating demand of a prototype warehouse (for which the hour-by-hour demand is known). For this analysis, only two waste heat sources are used: the plant vacuums and the PP dryers. These two sources are used because these sources are relatively easy to access, and the exhaust is relatively clean air.

Three short-term cases are considered (Fig. 15). Each case is for one week. Case (i): high demand—the average space heating demand exceeds the waste heat supply. For Fargo and the building model, this represents a week from late winter/early spring (or late fall/early winter) or a mild mid-winter week; case (ii): medium demand—the average space heating demand is near the average waste heat supply. For Fargo, this represents a week in mid-to-late spring or early-to-mid fall; case (iii): low demand—the average space heating demand is below the average waste heat supply. For Fargo, this represents a week in late spring. These simulated weeks can be taken more generally to be cases when the demand generally exceeds the waste heat (case (i)), when the demand and waste heat are similar in magnitude (case (ii)), and when the demand is generally less than the waste heat. Using a minimum useful energy of 30 °C, the average waste heat rate is 64.4 kW. Case (i) has an average rate of 97.8 kW, while cases (ii) and (ii) have average rates of 65.6 kW and 41.3 kW, respectively. The waste heat and demand for the three cases are given in Fig. 15. The waste heat is only given for 24 h to better show the fluctuations.

Figure 16 compares the fraction of the space heating met by the waste heat for TES capacities from 0.125 to 1, and for the situation of no thermal energy storage. Having the TES initially at 25 °C (discharged) and initially at 43 °C (charged) are considered. In all cases, a system with TES increases the fraction of the demand that can be met by the waste heat. The increase in this fraction depends primarily on the case considered and whether the TES is assumed to be initially charged or discharged. In the high-demand simulation (case (i)), when the TES is initially at a state of discharge, there is a small increase in the fraction from 62.8% without storage to 65% with C = 0.125 (Fig. 16(a)). Increasing the storage capacity to C = 1 only increases the fraction to 67%. There is more of an increase in the fraction if the TES starts fully charged (Fig. 16(b)). In that case, the TES systems can meet between 66% and 74% depending on the size of the TES. The case where the presence of the TES makes the most difference is the medium demand (case (ii)) because the demand at night tends to exceed the waste heat supply, but, during the day, the heating demand is low enough to allow the TES to at least partially recharge. In this situation, without a TES, the waste heat meets ∼78% of the load, but with TES, it can jump to between 83% and 92% for an initially discharged TES and between 84% and 97% for an initially charged TES. Thus, with thermal storage, in this situation, the demand covered by waste heat increases by 8–24%. For case (iii), low demand, the TES also provides a benefit compared to no TES, however the size of the TES is not impactful. In this situation, the fraction increases from ∼90% without a TES to ∼98–100% with a TES. Due to the low initial demand at the start of the simulation, the TES can start charging immediately, and thus the difference between assuming initially charged or discharged is minor for this case. Overall, Fig. 16 shows that even a small TES (capacity of 0.125–0.25) can have a significant benefit in increasing the fraction of the demand met by the waste heat.

Figures 17 and 18 provide the rates for the warehouse space heating demand as well as the energy provided by the waste heat with and without storage for a case (i)—high demand and case (ii)—medium demand, respectively. A system without TES is given by the “Energy—No Store” curve while the “Energy—with Store” curve is the energy provided by a system with TES. The “Energy—from TES” curve is the energy provided from the TES (Eq. (16)) and is a subset of the total value given by “Energy—with Store.” As such, it is zero when the TES is depleted or not needed. Figure 17 shows why there is only a small increase in the fraction provided by the system with an increase of TES size for the high demand, initially discharged situation. At the start of this simulation, the demand is much higher than the available waste heat and the TES does not have an opportunity to start charging until approximately half a day into the simulation (hour 12). However, the window for charging is small and so, regardless of TES size, it is not able to charge to a high degree. When the TES is not charged, the system with storage behaves like a system without storage. At approximately hour 40, there is another opportunity to charge the TES. However, there are then approximately 2.5 days during which the demand exceeds the waste heat. Neither the C = 0.25 or C = 1 have sufficient stored energy to provide much energy beyond the first of these two and a half days. Thus, a system with TES is able to meet only a slightly higher fraction than a system without TES. Figure 17 also why the fraction provided by the system is a stronger function of TES size when the TES is assumed to be initially charged. When the TES starts charged (Figs. 17(c) and 17(d)), the TES is able to help meet the high initial demand. The C = 0.25 is discharged relatively quickly, while the C = 1 TES has sufficient capacity to reach the first charging window at hour 12. This allows it to be more impactful. However, by hour 70, there is no difference between initially charged and initially discharged simulations.

The effect of TES size is more noticeable when the difference between the demand and the available waste is not as extreme, and when TES has more opportunity to recharge. This situation occurs in case (ii)—medium demand (Fig. 18). For the initially charged conditions (Figs. 18(c) and 18(d)), a system with either TES size is able to meet the load early in the simulations (e.g., hours less than 80 h). The TES works well because, during these days, the demand allows for the TES to recharge. The effect of TES size is most obvious between hours 80 and 130 when there are multiple days with high demand. During these days, the C = 1 TES is able to supply more energy and better match the load than the C = 0.25 TES. Conversely, the system without the TES oscillates rapidly between meeting the load and not meeting the load. The results show that TES can be highly beneficial to matching the variable supply with the daily variable demand, however it needs opportunities to recharge.

Additionally, the results show that a TES is able to smooth the rapid oscillations in the waste heat. The rapid oscillations make the “Energy—No Store” curve appear as if it is filling in the area under the “Demand” curve. However, it is rapidly oscillating between meeting the demand and providing a fraction of the demand. In contrast, when the TES is operating well, it can offset these oscillations and allow the waste heat recovery system to track the demand. The offsetting ability of the TES is shown by the “Energy—from TES curve.” The energy output from the TES complements the oscillations in the waste heat, e.g., increasing energy output when the waste heat is decreasing. Thus, the net effect is the system with storage is able to track the demand. As such, the “Energy—with Store” curve overlays the “Demand” curve. When considering integrating the TES with a building HVAC system, it may be beneficial to primarily use the TES compensate for oscillations in the waste heat. This way, the building heating system itself does not attempt to compensate for rapid decreases and increases in waste heat, but instead has a more consistent output with which to partner. As such, a control mechanism for the TES that smooths the rapid transitions in waste heat (rather than prioritizing meeting the load exactly) may be considered.

Figure 19 provides the fraction of the space heating demand for the warehouse that the recovery systems can meet for the nine-month period and for each month. Over the course of the heating season, the waste heat recovery system could meet from 54.5% (no storage) up to 58.8% (with TES of C = 1), approximately an 8% increase. Thus, over the course of the season, TES is beneficial and can help better utilize the waste heat. Comparing across the TES sizes, the largest increase in the fraction-of-the-demand-met occurs from no storage to a capacity of C = 0.125 (the smallest TES). The simulation of C = 0.125 had an annual fraction of 56.9%. Thus, going from no capacity to a capacity of 0.125 increased the annual fraction by approximately the same amount as going from 0.125 to 1. The reason for this can be seen by investigating the times when the TES is most impactful. It is during the shoulder seasons (e.g., November, March, April, and to a lesser degree February). For example, in March the fraction increases from 78.6% without storage to 93.1% with C = 1. Again, the largest increase is from no storage to C = 0.125 (fraction = 85.7%). The fraction increases nearly linearly with TES from C = 0.125 to C = 1. As shown in Fig. 20, it is during these shoulder months, that the demand is of similar magnitude to the waste heat. However, there is also high variability in the demand wherein it often exceeds the peak waste heat and, yet, at other times, drops below the waste heat supply to allow for the TES to recharge. As discussed with the short-term simulations, it is during these situations that effect of TES capacity on the fraction provided is most significant. However, the absolute demand during these shoulder months is much smaller than the demand during the depths of winter, e.g., December and January, (Fig. 20). During the winter months, often the waste heat is applied directly to the load and the TES does not have many opportunities to recharge. This effect can be seen from Fig. 21(a) (C = 0.125) and Fig. 21(b) (C = 1) which shows the rate of energy supplied by the TES throughout the year. The TES supplies a significant amount of energy during November and early December. Then the energy supplied by the TES is sparser until the mid-February through early April at which point, the TES again supplies a significant amount of energy. As such, for the sizes considered (C = 0.125 to C = 1), a larger size (C = 1) allows for more energy to be provided by the system during shoulder seasons as shown by the higher peaks in Fig. 21. However, during the peak heating months, due to the lack opportunities for recharge, there is less of a difference in TES sizes. As such, in geographical locations which do not have such a severe space heating demand in the depths of winter or for buildings with a lower demand, the TES will be even more beneficial. In September and May, the TES does not supply energy because the demand is low and the waste heat is able to meet the demand directly. Much larger capacity TES would be necessary to shift energy from early in the heating season, e.g., September, to the high demand periods between early December and mid-February.

The preceding results demonstrate the benefits of TES to better match the waste heat supply to the demand. However, when considering the size of the TES, the additional cost is a factor. Table 7 provides the initial cost estimate and simple payback for a system without storage, Table 8 provides the initial cost and simple payback for a system with rock TES storage (C = 0.125 and C = 0.25), and Table 9 provides the same information for a system with water TES storage (C = 0.125 to C = 0.5). Even without storage, a waste heat recovery system would cost approximately $47 k. Nearly half of the cost is simply from an air-to-air heat exchanger to exchange energy from the waste heat stream to the building air supply. The heat exchanger is expensive, because it must be large to handle the flowrates from the combined waste heat sources. Buying multiple, smaller air-to-air exchanges did not reduce the estimated cost. The payback period is estimated to ∼10 years. While the waste heat recovery system is able to meet over half of the space heating load for the warehouse, the annual savings is only ∼$4.5 k, because natural gas is relatively low cost. This highlights the fact that any waste heat recovery system used for space heating must be low cost to be economical feasible.

Adding thermal storage does increase the cost of the overall system as shown in Tables 8 and 9. Again, for these systems, the most expensive item is the air-to-air heat exchanger. For rock storage, the TES itself only adds ∼$7 k for C = 0.125. This increases the payback period to 12.4 years, because the increase in annual savings is only ∼$200 more than the no storage system. There is a significant increase in estimated initial cost for C = 0.25 due to a much large storage vessel being required. At the lowest capacity (C = 0.125), the rock TES is the lower cost option compared to the water TES (Table 9). It is lower cost, because, while the cost of the water TES itself (vessel and material) is less than the rock TES, the cost of the additional heat exchangers and pumps for the water system significantly increases the overall cost. However, as the capacity of the TES increases, the water TES becomes the low-cost option, because the cost of the rock TES is more sensitive to size. Whether rock or water TES, the cost and payback period increase as the thermal capacity of the TES increases. While the TES does increase the payback period, it can have additional benefits. For example, as discussed in the short-term simulations, it helps to smooth out the volatility of the waste heat so that the building heating system does not have to react as quickly to rapid changes in the waste heat supply.

Because the air-to-air heat exchanger is a significant cost of the overall system, a new waste heat recovery design was developed to eliminate it. As shown in Fig. 22, this system design uses a water TES as both a heat storage device and as an intermediate between the waste heat source and the building HVAC system. In this design, the waste heat air always passes through an air-to-water heat exchanger and thus directs energy into the water TES. The TES can be simultaneously discharged by a second pump and another air-to-water heat exchanger. While large air-to-water heat exchangers are needed, these heat exchangers are lower cost than an air-to-air heat exchanger. In addition to removing the air-to-air heat exchanger, this system would also have the benefit of thermal storage which increases the annual savings. As shown in Table 10, this system is expected to have a much lower initial cost, which is estimated to be less than half the cost of a system without storage (Table 7).

In the present work, a waste heat assessment of a manufacturing facility was conducted. Using a reference temperature of 25 °C, an energy and exergy analysis revealed that 36.5 TJ of energy and 842 GJ of exergy are rejected each year. The most significant source of waste heat was the chiller (82%) but at a temperature of 27 °C, the quality is low and thus it constitutes a smaller fraction (35%) of the exergy rejected. The next most significant sources were the boiler flue (5.5% of energy, 33% of exergy, temperature of 128 °C), which was the hottest waste heat source, and the plant vacuums (9% of energy, 13% of exergy, temperature of 46 °C). The survey shows that even in a facility not typically associated with waste heat, there are significant amounts.

A key finding of the survey is quantifying the temporal fluctuations in waste heat. Some waste heat sources were continuous with a constant flowrate while others had variations in flowrate, temperature, or period of operation. These fluctuations varied from short time scales, e.g., hours, to large time scales, e.g., monthly. These results highlight the need for additional waste heat assessments to better quantify waste heat fluctuations to help advance designs for waste heat recovery.

Due to the low quality, but large quantities of the waste heat in the facility, it is well-suited to space heating. Without storage, the acceptable waste heat sources, i.e., those with an exhaust temperature greater than ∼40 °C, could theoretically meet up to 39% of the space heating load for the facility. This fraction represents a potential savings of up to ∼$17,900 per year in heating fuel costs. The analysis highlights how simple modifications to utilize low-grade waste heat can be leveraged to improve energy efficiency. For example, modifications to the exhausts of the plant vacuums could theoretically save up ∼$12,400 per year. However, the survey also indicates that to fully utilize the waste heat for space heating, TES is needed due to mismatch in fluctuations in the waste heat sources versus the space heating demand.

To investigate the effect TES on waste heat recovery, a simple waste heat recovery system with and without thermal storage was modeled and compared to the space heating demand for a prototype warehouse building. Short-term and season-long simulations were presented. The TES is highly advantageous for smoothing the fluctuations in the waste heat and for better matching the demand schedule. Both short-term and long-term simulations show that TES can increase the fraction of the demand met by waste heat. The TES is most beneficial in situations where the TES can at least partially recharge during the day. In this situation, even a small amount of storage, e.g., thermal capacity that is 12.5% or 25% of the available daily waste heat, can significantly increase the fraction of the demand met compared to a no storage situation. The initial cost estimates highlight the need to keep the recovery system low cost for reasonable payback periods. Larger TES capacities offer diminishing returns at much higher initial costs and longer payback periods. Thus, a small TES is recommended for this situation. The air-to-air heat exchanger in the recovery system is a significant cost due to the high flowrates of air from the waste heat sources. As such, to reduce initial cost, a new recovery system design, which replaces the air-to-air heat exchanger with a water-based TES, is proposed. This new design halves the initial cost of the original, no storage recovery system.

The authors would like to thank Prantik Chowdhury for helping format the paper.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$f$ =

fraction of demand met by waste heat recovery system

h =

enthalpy (kJ/kg)

m =

mass (kg)

n =

moles (mol)

s =

entropy (J/kg·K)

t =

time (s)

x =

distance along the flow axis in TES bed (m)

A =

cross-sectional area (m²)

C =

TES capacity as a fraction of waste heat available in a day

D =

rock particle diameter (m)

E =

energy (kJ)

G =

mass flux of air (kg/m²·s)

P =

pressure (kPa)

R =

gas constant (J/mol·K)

T =

temperature (K)

V =

volume (m³)

c_p =

specific heat (kJ/kg·K)

Ex =

exergy from waste heat (kJ)

$αv$ =

volumetric heat transfer coefficient (W/m³·K)

$ε$ =

bed void fraction

$ρ$ =

density (kg/m³)

$φ$ =

relative humidity

b =

bed of the TES (rocks)

c =

charging

d =

discharging

e =

exit of the bed

f =

fluid (air)

i =

species

o =

reference state

p =

product

s =

storage (TES)

D =

demand

1 =

state 1

air =

air

atm =

atmospheric

day =

in a day

fuel/mo =

fuel per month

H₂O =

water

in =

inlet

max =

maximum

min =

minimum

mo =

month

sat =

saturation

WH =

waste heat

WHR =

provided by waste heat recovery

A dot over a value indicates a flowrate per second