Dynamic Investigation of Thermochemical Heat Upgrade and Alternative Industrial Heating Technologies

Abstract

Industrial process heat production is critical to achieving sustainability in our society. Avoiding fossil fuels and reducing electricity consumption for heat production are critical aspects of creating sustainable industries. Exploiting waste heat streams by upgrading them into useful high-temperature heat is an interesting idea for reducing the CO₂ footprint industrial processes. In line with this, the present study’s main objective is to investigate a novel thermochemical heat upgrade system based on the SrBr₂/H₂O working pair for the petrochemical industry, which is practically driven only by low-temperature waste heat streams. This innovative system, which exploits a waste heat stream of 200 °C and upgrades it to 250 °C to make it suitable for industry utilization, achieves a nominal coefficient of performance of 0.605. The examined system is compared with three other alternatives, including a natural gas boiler with 86% efficiency, a hybrid solar thermal unit with an auxiliary natural gas boiler, and a high-temperature heat pump with a coefficient of performance of two. The nominal industrial heat production is 2.2 MW for the thermochemical heat upgrade system. The dynamic investigation is conducted under the climate conditions of Denmark and Greece. The high-temperature heat pump’s annual electricity consumption is 6.94 GWh. In contrast, the annual heat consumed by the natural gas boiler is 16.12 GWh, without integrating the solar thermal unit. For the hybrid system, the maximum daily contribution of the solar thermal system is 87% for the climate conditions of Denmark, and the annual useful heat generated by the concentrating solar system is 1.30 GWh for the Danish climate conditions and 2.82 GWh for the Greek climate conditions.

1. Introduction

The industrial sector accounts for 25% of the EU’s final energy consumption [1] and 48% of the final CO₂ emissions [2]. Approximately 70% of the energy consumed in industrial processes such as drying, heating, and distilling is thermal energy. A significant percentage of 33% of the thermal energy is wasted due to thermal losses to the ambient environment, as flue gases, or radiative thermal losses at various temperature levels [3]. The annual EU waste heat potential is estimated at 300–350 TWh [3], which is a significant amount of thermal energy and indicates the potential for possible exploitation.

Waste heat sources (WHSs) can be categorized into three main classes, depending on the temperature of the waste heat stream. The first class is the low-temperature WHS, where the temperature of the stream is lower than 100 °C; the most representative example is the outbound cooling water from various compressing and condensing processes [4]. The second class is the medium-temperature WHS for heat stream temperatures within 100 °C and 300 °C. This temperature range includes some critical processes such as the distillation process of the chemical and petrochemical industries [4]. Finally, the high-temperature WHS is the heat stream with temperatures higher than 300 °C, such as melting and other metal refining processes [4]. Many industries have low- and medium-temperature WHS that cannot be further utilized and are released into the ambient environment. However, if these streams can be upgraded via a heat upgrade unit, they can be exploited by the same industry for other processes requiring heat. Such an industry is the petrochemical industry, which is considered an energy-intensive industry with substantial energy consumption and greenhouse gas emissions.

The petrochemical industry is a significant subsector of the chemical industry. Petrochemicals are refinery products derived by distilling or cracking crude oil, or chemicals produced from natural gas and natural gas liquids [5]. This industry is considered among the most polluting industries, since it generates toxic waste, wastewater, and greenhouse gas emissions. Furthermore, as an energy-intensive industry, it consumes large amounts of electricity and heat to meet the demand for various processes. Notably, the petrochemical industry has various low- and medium-temperature WHSs in the temperature range of 75 °C [6] to 215 °C [7]. Moreover, this industry has heat demands for processes such as distilling in the temperature range of 100 °C to 300 °C [4]. As a result, the petrochemical industry is an ideal case study for implementing waste heat recovery solutions to take advantage of low- and medium-temperature WHSs by upgrading them and exploiting them for various other processes in the same industry rather than rejecting and then releasing them into the ambient environment as waste.

Table 1. WHSs and heat demand processes for the petrochemical industry.

Industrial Process	Temperature Range [°C]
Waste Heat Sources
Bottom oil of xylene	80–215 [7]
Xylene products	80–205 [7]
Production of sodium hydroxide	75–200 [6]
Evaporation processes	147 [7]
Catalytic processes	140 [7]
Sewage	110 [7]
Reforming	104 [7]
Benzene production	98 [7]
Heat demand processes
Steam boiler	200–300 [4]
Distilling	100–300 [8]

presents the temperature ranges of the petrochemical industry’s most representative WHSs and heat demand processes.

Various heat upgrade techniques can be effectively integrated into the industrial sector to efficiently use low- and medium-temperature WHSs. One of the most well-known conventional technologies is natural gas boilers (NGBs). NGBs use the heat generated from the combustion of natural gas [9]. The overall efficiency of such boilers is reduced compared to those used for domestic applications, since the temperature of the outbound flue gases is increased [10]. The efficiency of a condensing boiler varies depending on the flue gas temperature and the excess air ratio, and it can be found in the range of 85% to 95% for flue gas temperatures greater than 100 °C [11]. Although NGBs are a widely used and reliable solution, they present high greenhouse gas emissions due to the combustion process of natural gas. Another conventional and widely used heat upgrade system for industrial applications is the vapor compression high-temperature heat pump (HTHP). These systems includes a compressor which consumes electricity to increase the heat input temperature level. For industrial applications, HTHP’s coefficient of performance (COP) varies from 1.42 for drying processes to 4.4 for crude oil heating [12]. The sink temperature can be found to range from 80 °C for water heating, with R134a as the refrigerant, to approximately 220 °C for special applications, by utilizing NH₃ to achieve high heat sink temperatures [13,14]. Wu et al. [15] investigated a single-stage HTHP with a twin-screw compressor for the process of dyeing liquid at a sink temperature of 97.3 °C. Hassan et al. [16] performed a thermodynamic analysis of a vapor compressor HTHP for water heating for industrial use with a sink temperature equal to 133 °C.

Moreover, another class of heat upgrade systems is based on absorption and can be further classified into absorption heat pumps (AHPs) and absorption heat transformers (AHTs). The most used working pairs are LiBr/H₂O and H₂O/NH₃. The inlet stream to the evaporator of the AHP is a low-temperature waste heat stream, while a high-temperature heat load simultaneously supplies the generator. Heat is released at a medium temperature level from both the absorber and the condenser. Muhammad et al. [17] proposed a double-stage, multifunctional, open AHP with a maximum COP value of 2.39 and a heat capacity of 280.1 kW. The AHTs utilize medium-grade heat loads at the evaporator and the generator. Moreover, Cudok et al. [18] summarized the technical information of several AHTs’ installations with LiBr/H₂O, and the COP of those systems ranged from 0.44 to 0.49. At the same time, the maximum heat sink temperature of 165 °C was defined for a heat capacity of 670 kW.

However, the technologies mentioned above are limited due to the high sink temperature. Various industrial applications are in the medium-temperature range, requiring higher-temperature streams than those provided by such systems. The technology of thermochemical heat transformers (THTs) is among the most promising heat upgrade technologies for both low- and medium-temperature industrial applications. In THTs, chemical sorption reactions occur between a gas and a solid rather than a gas and a liquid. The temperature increase can be up to 280 °C, depending on the steam pressure variation [19]. Li et al. [20] investigated the performance of THTs for various salt hydrates, including SrBr₂, K₂CO₃, MgSO₄, LiOH, SrCl₂, FeCl₂, CaCl₂, (SO₄)₂, and LaCl₃. The use of SrBr₂/H₂O resulted in the highest COP_th, which was found to be equal to 0.72, the highest COP_el, which was calculated at 70.23, and the highest exergy efficiency, which was found to be 93.8% [20]. Additionally, that working pair presented the maximum heat release among all the tested pairs, equal to 284.2 kWh for a single-stage system. Furthermore, Stengler et al. [21] examined the use of the SrBr₂/H₂O working pair to achieve high reaction rates, specific thermal power, and specific energy density. This working pair is also suitable for operating at high temperatures, and therefore it can be used in various industrial processes for heat upgrade solutions. Stengler and Linder [19] extended the capability of THTs, which could also serve as thermochemical energy storage, by using the endothermic reaction for charging and the exothermic reaction for discharging the storage unit.

The previous literature review revealed the importance of heat upgrades to provide useful heat for industrial processes. The present study suggests and investigates a novel thermochemical heat upgrade solution for industrial use based on the SrBr₂/H₂O working pair. This idea is applied to the petrochemical industry, which presents an ideal case study because it has suitable waste heat streams and process heat demand temperature levels for exploiting the selected heat upgrade solution. Moreover, alternative scenarios for providing useful heat to industry are studied, i.e., using an NGB, solar thermal collectors, and an HTHP. The comparison is a critical aspect of this work because there is a lack of literature that critically compares different process heat production methodologies, including thermochemical heat upgrade solutions. The study performs dynamic simulation using the Modelica programming language [22] and Dymola’s software environment [23]. Expert fundamental energy analysis and preliminary economic and environmental investigations are performed to determine the sustainability of the suggested thermochemical solution. The present work is performed in the framework of the research project TechUPGRADE [24], whose goal is to showcase and verify an innovative thermochemical technology that achieves significantly higher temperatures while ensuring superior safety, cost-efficiency, and energy performance compared to the alternative solutions.

The paper is organized as follows: Section 2 includes the materials and methods of this study, Section 3 is devoted to the presentation of the results, and Section 4 summarizes the conclusions of this work. Specifically, Section 2 includes the mathematical background, the tool’s modeling procedure, and this work’s input parameters. Section 3 includes the dynamic behavior of the different examined scenarios and summarizes and discusses the results. Finally, Section 4 summarizes the most significant conclusions of the present work.

2. Materials and Methods

2.1. The Examined Industrial Case Study and the Methodology Used

The present case study concerns the petrochemical industry, where waste heat can be recovered from various products, by-products, and processes. Specifically, for xylene production, the bottom oil of xylene and xylene products are medium-temperature WHSs at around 200 °C [25], and the available waste heat load is approximately 2.20 MW [25], while the mass flow rate is approximately equal to 78.5 kg/s [7]. A typical process found in the chemical and petrochemical industries is distillation, with a temperature demand of close to 250 °C [4]. To provide the required heat, an intermediate thermal oil circuit is applied, assuming a specific heat of around 1.87 kJ/(kg·K) [26] and a temperature difference of 20 K. The variations in the daily demand profile for the industry can be found in Figure 1. The reported data were calculated using data from [27,28,29,30]. This is a typical profile that presents a higher load during the day and a lower load at night. It is considered to be constant throughout the year.

In this study, the dynamic simulation of the examined scenarios was performed using analytical models developed in the Modelica programming language [22], using the Dymola [23] modeling and simulation environment that includes both a graphical user interface and a solver. Simple and modular subcomponents were developed and combined to accurately simulate complicated and detailed energy system configurations. For this purpose, the standard “Modelica” [22] library, as well as the open-source libraries “Buildings” [31] and “BuildingSystems” [32], were utilized. The selection of this tool is advantageous because the solver uses an adjustable time step, which enables quick and accurate simulation of dynamic phenomena. Moreover, this tool makes it possible to integrate variable operating profiles into the model and use advanced control problems, which are very important for the suitable simulation of the studied systems. In addition, specific models that utilize real weather data were developed based on the meteorological data database of PVGIS [33]. Also, the basic modeling of the thermochemical unit was conducted with the Engineering Equation Solver [34].

The dynamic analysis was conducted for two locations, one in southern Europe and one in northern Europe. Specifically, the locations of Athens, Greece (latitude 38.0°, longitude 23.7°), and Lyngby, Denmark (latitude 55.8°, longitude 12.5°), were used in this analysis. These two locations were also selected to be studied in the framework of the TechUPAGRADE project, as they cover a warm location and a cold location in Europe, which is important for extracting useful conclusions regarding the behavior of the studied systems.

In this work, the cost of the consumed electricity was equal to EUR 240/MWh [35] for Lyngby, Denmark, and equal to EUR 233.0/MWh for Athens, Greece [36]. Also, the CO₂ emissions factors for electricity production were equal to 117.0 kg_CO2/MWh_e for Denmark’s electricity grid [37] and 252.44 kg_CO2/MWh_e [38] for the Greek one. Regarding the cases with natural gas consumption, the specific CO₂ emissions factor was selected at 65.0 kg_CO2eq/MWh [39] for both locations, and the average natural gas cost in the European Union was considered equal to EUR 70.0/MWh [40] for both locations.

2.2. The Thermochemical Heat Upgrade Design

2.2.1. Description of the Thermochemical Configuration

This study modeled and simulated a novel thermochemical heat transformer for heat upgrade. This system can be integrated with low- and medium-grade heat sources and solar thermal systems (STSs). First, the low- or medium-temperature waste heat stream dehydrates the salt. The water vapor is then compressed to reach a higher pressure level. In the hydration process, the salt is hydrated at this higher water vapor pressure, releasing heat at a higher temperature that is suitable for various industrial applications. The thermochemical system with the waste heat recovery and the process of heat production is depicted in Figure 2. The cycle is practically a thermochemical heat absorber with the SrBr₂/H₂O working pair. A thermodynamic analysis of the cycle was carried out with a model developed using the Engineering Equation Solver [35]. More details about the principles of this design can be found in the previous literature [19,21,41]. The design parameters of the THT for heat upgrade within the petrochemical industry are given in

Table 2. Parameters of the thermochemical heat upgrade unit.

Source of Waste Heat for the Dehydration Part
Heat transfer fluid	Thermal Oil
Inlet temperature [°C]	200
Outlet temperature [°C]	185
Mass flow rate [kg/s]	78.5
Specific heat capacity [kJ/(kg·K)]	1.87
Heat input in the dehydrator [kW]	2200
Source of waste heat for the evaporation process (including preheating)
Heat transfer fluid	Thermal Oil
Inlet temperature [°C]	185
Outlet temperature [°C]	112
Mass flow rate [kg/s]	10.52
Specific heat capacity [kJ/(kg·K)]	1.87
Heat input in the evaporator [kW]	1437.2
The heat demand for the distillation process
Heat transfer fluid	Thermal Oil
Inlet temperature [°C]	230
Outlet temperature [°C]	250
Mass flow rate [kg/s]	58.8
Specific heat capacity [kJ/(kg·K)]	1.87
Heat production in the hydrator [kW]	2200

. The working fluid for the heat transfer was thermal oil with a specific heat capacity of 1.87 kJ/(kg·K) [26]. The mass flow rate of the thermal oil from the process heating production was 78.5 kg/s, and it was appropriately selected to have the desired heat rate. The initial thermodynamic study was used to calculate the remaining mass flow rates, as listed in Table 2. During the design of the heat exchangers, a pinch point of 10 K was considered. It should be highlighted that the COP of the system in the nominal design conditions was considered at 0.605, after conducting some basic thermodynamic calculations. The nominal hydration temperature was 260 °C, the nominal dehydration temperature was 175 °C, and the nominal industrial heat production was approximately 2.2 MW. Moreover, in this design, the temperature lift of the thermochemical heat transformer was 85 °C, and the system’s lift was 65 °C due to the pinch points in the heat exchangers. It is important to state that the heat exchangers were properly designed to ensure the optimal exploitation of the waste heat stream. Generally, it was found that the COP did not have high variation when the operational conditions varied in reasonable ranges.

Figure 3a illustrates the configuration developed for the thermochemical process in the Dymola environment. The main component of the thermochemical heat upgrade process is depicted in Figure 3b, where the calculations of the temperature lift process among the waste heat stream (down) and the heat upgrade stream (up) are described in detail. This configuration adjusts the necessary temperature and mass flow rate sensors to monitor and check the simulated process efficiently.

2.2.2. Basic Mathematical Modeling of the Thermochemical Configuration

The heat transfer fluid energy balance in the dehydration part of the THT system can be written as follows:

$${\mathrm{Q}}_{\mathrm{d}\mathrm{e}\mathrm{h}}={\dot{\mathrm{m}}}_{\mathrm{d}\mathrm{e}\mathrm{h}}\cdot {\mathrm{c}}_{\mathrm{p},\mathrm{d}\mathrm{e}\mathrm{h}}\cdot ({\mathrm{T}}_{\mathrm{i}\mathrm{n},\mathrm{d}\mathrm{e}\mathrm{h}}-{\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{d}\mathrm{e}\mathrm{h}})$$

(1)

The heat transfer fluid energy balance in the evaporator of the THT system can be written as follows:

$${\mathrm{Q}}_{\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{p}}={\dot{\mathrm{m}}}_{\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{p}}\cdot {\mathrm{c}}_{\mathrm{p},\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{p}}\cdot ({\mathrm{T}}_{\mathrm{i}\mathrm{n},\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{p}}-{\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{p}})$$

(2)

The heat transfer fluid energy balance in the hydration part of the THT system can be written as follows:

$${\mathrm{Q}}_{\mathrm{h}\mathrm{y}\mathrm{d}}={\dot{\mathrm{m}}}_{\mathrm{h}\mathrm{y}\mathrm{d}}\cdot {\mathrm{c}}_{\mathrm{p},\mathrm{h}\mathrm{y}\mathrm{d}}\cdot ({\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{h}\mathrm{y}\mathrm{d}}-{\mathrm{T}}_{\mathrm{i}\mathrm{n},\mathrm{h}\mathrm{y}\mathrm{d}})$$

(3)

The COP of the THT is the ratio of useful heat production to heat input in the system, as given by the following equation:

$$\mathrm{C}\mathrm{O}\mathrm{P}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{h}\mathrm{y}\mathrm{d}}}{{\mathrm{Q}}_{\mathrm{d}\mathrm{e}\mathrm{h}}+{\mathrm{Q}}_{\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{p}}}}$$

(4)

The temperature lift of the thermochemical heat transformer is calculated as follows:

$${\mathrm{T}}_{\mathrm{l}\mathrm{i}\mathrm{f}\mathrm{t},\mathrm{T}\mathrm{H}\mathrm{T}}={\mathrm{T}}_{\mathrm{h}\mathrm{y}\mathrm{d}}-{\mathrm{T}}_{\mathrm{d}\mathrm{e}\mathrm{h}}$$

(5)

The temperature lift of the system is calculated as follows:

$${\mathrm{T}}_{\mathrm{l}\mathrm{i}\mathrm{f}\mathrm{t},\mathrm{s}\mathrm{y}\mathrm{s}}={\mathrm{T}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}}-{\mathrm{T}}_{\mathrm{w}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{e}}$$

(6)

2.3. Scenario with Natural Gas Boiler

2.3.1. Description of the Natural Gas Boiler Configuration

The first alternative scenario concerns the NGB configuration. This NGB produces the necessary heat to meet the industrial heat demand; based on the mean demand profile, an input parameter is defined by the “demand_profile” component. The overall developed model is illustrated in Figure 4. Moreover, the NGB is designed based on an existing open-source “Buildings” library model named “BoilerPolynomial”. The operation of the NGB is controlled through a proportional derivative (PD) controller that dynamically adjusts the fuel heat input to maintain a steady temperature at the boiler outlet. The necessary parameters for the operation of the respective subcomponents are the nominal efficiency and efficiency curves, the type of fuel, the nominal capacity, and the overall UA value.

The exact composition of natural gas varies depending on the extraction site, but the main component is methane. The lower heating value of natural gas is approximately 35,055 MJ/Nm³ [42]. Considering a density value of 0.77 kg/m³, the corresponding lower heating value is 45,526 kJ/kg. The NGB’s efficiency heavily depends on the temperature and the excess air ratio [43]. The higher the flue gas temperature, the lower the boiler efficiency [43]. Additionally, the higher the excess air ratio, the lower the boiler efficiency [43]. The boiler efficiency for a flue gas temperature of 270 °C and an excess air ratio of 1.05 is approximately 86%, assuming a linear correlation between the boiler efficiency and the exit flue gas temperature for temperatures greater than 60 °C [42]. Except for the boiler efficiency, some other efficiencies may be useful to describe the boiler performance, such as the thermal and combustion efficiencies, with typical values of 85% and 87%, respectively [44]. The thermal efficiency of gas boilers varies between 76% and 81% if the calculations are based on the higher heating value, which is equal to 50,488 kJ/kg [10]. For the subsequent simulations, the efficiency of the NGB is considered to be constant, and its value is equal to 86% [42]. The use of constant efficiency is an assumption of this work.

2.3.2. Basic Mathematical Modeling of the Natural Gas Boiler Configuration

The efficiency of the NGB (η_NG) is defined as the quotient of the useful heat (Q_u,NG) against the fuel heat (Q_B,NG) of the boiler, as in the following equation:

$${\mathsf{\eta }}_{\mathrm{N}\mathrm{G}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{u},\mathrm{N}\mathrm{G}}}{{\mathrm{Q}}_{\mathrm{B},\mathrm{N}\mathrm{G}}}}$$

(7)

The natural gas consumption (${\dot{\mathrm{m}}}_{\mathrm{B}}$) is calculated by using the lower heating value (H_u), as follows:

$${\dot{\mathrm{m}}}_{\mathrm{B}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{B},\mathrm{N}\mathrm{G}}}{{\mathrm{H}}_{\mathrm{u}}}}$$

(8)

The COP of the thermochemical heat transformer can be written as follows:

$$\mathrm{C}\mathrm{O}\mathrm{P}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{h}\mathrm{y}\mathrm{d}}}{{\mathrm{Q}}_{\mathrm{u},\mathrm{N}\mathrm{G}}}}$$

(9)

In this case, the energy efficiency (η_en,NG) of the system is calculated as follows:

$${\mathsf{\eta }}_{\mathrm{e}\mathrm{n},\mathrm{N}\mathrm{G}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{h}\mathrm{y}\mathrm{d}}}{{\mathrm{Q}}_{\mathrm{B},\mathrm{N}\mathrm{G}}}}$$

(10)

2.4. Scenario with the Hybrid Solar and Auxiliary Natural Gas Boiler System

2.4.1. Description of the Hybrid Solar–Gas Boiler Configuration

The following alternative scenario concerns the use of a hybrid system with an STS and an auxiliary NGB. The respective configuration is depicted in Figure 5. Similar to the first alternative scenario, the calculations concerning the industrial process are included in the component named “Process”. The NGB model is identical to the one used in the first alternative scenario. In this model, a submodel of a concentrated solar thermal collector, named “collector”, is developed. For the collector’s proper operation, the necessary geometrical parameters, as well as information regarding the working fluid of the unit, are the input parameters. In addition, the weather conditions are simulated using the two developed models, namely “weatherdata” and “solRadTra”. These components are based on the location’s weather data input with an hourly time step. The necessary meteorological data for every examined location are retrieved from the Photovoltaic Geographical Information System (PVGIS) [33]. This tool provides hourly data on a typical meteorological year by selecting a specific location’s exact geographical coordinates (latitude and longitude).

The interface between the web tool and the developed models for the TechUPGRADE research project [24] is realized through a developed component script that suitably retrieves the necessary meteorological input for the heat upgrade analysis from text files generated using the PVGIS tool. The longitude and latitude location parameters are required for the presented models to adjust the data to a location’s local time. This previously tested and validated procedure can efficiently support any given location. The meteorological parameters are shown in an hourly time step and specifically include the ambient air temperature, the ambient relative humidity, the global horizontal irradiance, the diffuse horizontal irradiance, the direct normal irradiance, the wind speed and direction, and the ambient pressure.

This work examines the different solar collecting areas with a benchmark value of 3000 m². A small tank acting like a buffer tank is used with a volume of 10 m³. The continuous industry demand makes using a larger tank unprofitable; thus, a relatively small tank volume was selected.

2.4.2. Basic Mathematical Modeling of the Hybrid Solar–Gas Boiler Configuration

The collector’s solar thermal efficiency (η_th,col) is the ratio of the useful thermal production (Q_u,sol) to the incident solar energy (Q_sol), as shown in the following equation:

$${\mathsf{\eta }}_{\mathrm{t}\mathrm{h},\mathrm{c}\mathrm{o}\mathrm{l}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{u},\mathrm{s}\mathrm{o}\mathrm{l}}}{{\mathrm{Q}}_{\mathrm{s}\mathrm{o}\mathrm{l}}}}$$

(11)

The useful heat production of the solar thermal collector is calculated as follows:

$${\mathrm{Q}}_{\mathrm{u},\mathrm{s}\mathrm{o}\mathrm{l}}={\dot{\mathrm{m}}}_{\mathrm{c}\mathrm{o}\mathrm{l}}\cdot {\mathrm{c}}_{\mathrm{p},\mathrm{c}\mathrm{o}\mathrm{l}}\cdot ({\mathrm{T}}_{\mathrm{f},\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{T}}_{\mathrm{f},\mathrm{i}\mathrm{n}})$$

(12)

The incident solar energy is calculated as follows:

$${\mathrm{Q}}_{\mathrm{s}\mathrm{o}\mathrm{l}}={\mathrm{A}}_{\mathrm{c}\mathrm{o}\mathrm{l}}\cdot {\mathrm{G}}_{\mathrm{b}}$$

(13)

The thermal efficiency can be approximated using the following polynomial equation:

$${\mathsf{\eta }}_{\mathrm{t}\mathrm{h},\mathrm{c}\mathrm{o}\mathrm{l}}={\mathrm{a}}_0\cdot \mathrm{K}-{\mathrm{a}}_1\cdot {\displaystyle \frac{{\mathrm{T}}_{\mathrm{f},\mathrm{i}\mathrm{n}}-{\mathrm{T}}_{\mathrm{a}\mathrm{m}}}{{\mathrm{G}}_{\mathrm{b}}}}-{\mathrm{a}}_2\cdot {\displaystyle \frac{{{(\mathrm{T}}_{\mathrm{f},\mathrm{i}\mathrm{n}}-{\mathrm{T}}_{\mathrm{a}\mathrm{m}})}^2}{{\mathrm{G}}_{\mathrm{b}}}}-{\mathrm{a}}_3\cdot {\displaystyle \frac{{{(\mathrm{T}}_{\mathrm{f},\mathrm{i}\mathrm{n}}-{\mathrm{T}}_{\mathrm{a}\mathrm{m}})}^3}{{\mathrm{G}}_{\mathrm{b}}}}-{\mathrm{a}}_4\cdot {\displaystyle \frac{{{(\mathrm{T}}_{\mathrm{f},\mathrm{i}\mathrm{n}}-{\mathrm{T}}_{\mathrm{a}\mathrm{m}})}^4}{{\mathrm{G}}_{\mathrm{b}}}}$$

(14)

For the present case study, a Parabolic Trough Collector (PTC) is used with a₀ = 0.7408, a₁ = 0.0432 W/m²K, a₂ = 0.000503 W/m²K², and a₃ = a₄ = 0 [45,46]. This PTC is the Eurotrough module. The mass flow rate for the STS is equal to 4 kg/s [46].

The incident angle modifier (K) is calculated as the product of two different angle modifier factors, one for the longitudinal direction (K_L) and one for the transversal direction (K_T). The following three equations demonstrate how these three parameters are calculated:

$${\mathrm{K}=\mathrm{K}}_{\mathrm{L}}\cdot {\mathrm{K}}_{\mathrm{T}}$$

(15)

$${\mathrm{K}}_{\mathrm{L}}={\mathrm{b}}_0\cdot \cos \left({\mathsf{\theta }}_{\mathrm{L}}\right)-{\mathrm{b}}_1\cdot {\mathsf{\theta }}_{\mathrm{L}}-{\mathrm{b}}_2\cdot {\mathsf{\theta }}_{\mathrm{L}}^2-{\mathrm{b}}_3\cdot {\mathsf{\theta }}_{\mathrm{L}}^3-{\mathrm{b}}_4\cdot {\mathsf{\theta }}_{\mathrm{L}}^4$$

(16)

$${\mathrm{K}}_{\mathrm{T}}={\mathrm{c}}_0\cdot \cos \left({\mathsf{\theta }}_{\mathrm{L}}\right)-{\mathrm{c}}_1\cdot {\mathsf{\theta }}_{\mathrm{T}}-{\mathrm{c}}_2\cdot {\mathsf{\theta }}_{\mathrm{T}}^2-{\mathrm{c}}_3\cdot {\mathsf{\theta }}_{\mathrm{T}}^3-{\mathrm{c}}_4\cdot {\mathsf{\theta }}_{\mathrm{T}}^4$$

(17)

In this work, the following coefficients regarding the K_T factor are used [46]: b₀ = 1, b₁ = 5.25 · 10⁻⁴, b₂ = 2.86 · 10⁻⁵, b₃ = b₄ = 0 and c₀ = 1, c₁ = c₂ = c₃ = c₄ = 0.

The general energy balance in the storage tank can be written as follows:

$${\mathrm{Q}}_{\mathrm{s}\mathrm{t}}={\mathrm{Q}}_{\mathrm{u}}-{\mathrm{Q}}_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}-{\mathrm{Q}}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}$$

(18)

The stored energy (Q_st) in the thermal tank is as follows:

$${\mathrm{Q}}_{\mathrm{s}\mathrm{t}}=\mathsf{\rho }\cdot {\mathrm{c}}_{\mathrm{p}}\cdot \mathrm{V}\cdot {\displaystyle \frac{\mathrm{d}{\mathrm{T}}_{\mathrm{s}\mathrm{t}}}{\mathrm{d}\mathrm{t}}}$$

(19)

The thermal losses (Q_loss) of the thermal tank are written as follows:

$${\mathrm{Q}}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}={\left(\mathrm{U}\mathrm{A}\right)}_{\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{k}}\cdot ({\mathrm{T}}_{\mathrm{s}\mathrm{t}}-{\mathrm{T}}_{\mathrm{a}\mathrm{m}})$$

(20)

The hybrid system comprises an STS, an auxiliary NGB, and a thermal tank. This system uses the NGB to heat thermal oil from the solar tank if needed. In this case, the system energy efficiency is calculated as follows:

$${\mathsf{\eta }}_{\mathrm{e}\mathrm{n},\mathrm{h}\mathrm{y}\mathrm{b}\mathrm{r}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{h}\mathrm{y}\mathrm{d}}}{{\mathrm{Q}}_{\mathrm{B},\mathrm{N}\mathrm{G}}+{\mathrm{Q}}_{\mathrm{s}\mathrm{o}\mathrm{l}}}}$$

(21)

2.5. Scenario with High-Temperature Heat Pump

2.5.1. Description of the High-Temperature Heat Pump Configuration

This scenario incorporates an HTHP to upgrade the waste heat stream. The overall model layout of this scenario is illustrated in Figure 6. As previously mentioned, the industrial process stream that requires upgrading is represented by the “Process” component. The heat pump component is based on an existing model derived from the open access “Buildings” library.

HTHPs are an efficient and environmentally friendly technology used for heat upgrades. HTHPs are primarily used in industrial applications to replace fossil fuels in heat production and heat upgrading processes. They typically elevate source temperatures of around 50–100 °C to heat sink temperatures of above 100 °C, but they can also achieve much higher temperatures (above 200 °C) when incorporating the appropriate refrigerant [47].

For temperature increases of between 30 and 80 °C and sink temperatures of above 100 °C, experimental COP values ranged between 1.6 and 3.1 [48]. For a source temperature of 200 °C and a sink temperature of 250 °C, as in the present case study, the COP of an HTHP working with decane was calculated using the open-source tool CoolProp [49], coupled to the Modelica programming language. The results indicated a COP value of 2.0, which falls within the abovementioned range. The selection of decane as the working fluid was based on its high critical temperature of 321.4 °C, which suits the present scenario, and its efficient performance in high-temperature applications.

2.5.2. Basic Mathematical Modeling of the High-Temperature Heat Pump Configuration

The HTHP’s performance is modeled as COP, which is defined as the ratio of the heat transferred to the sink against the electrical energy consumed by the compressor.

$$\mathrm{C}\mathrm{O}\mathrm{P}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}}{{\mathrm{P}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}}}$$

(22)

The equations for the basic thermodynamic modeling of an HTHP can be found in a previous study [50].

3. Results and Discussion

3.1. Dynamic Analysis of the Thermochemical Heat Upgrade Scenario

The results for the main scenario, which incorporates the thermochemical heat upgrade system, are presented in this section. The weekly distributions of the heat flow rate for both the WHS and the heat demand stream are illustrated in Figure 7. The respective mass flow rates follow the same trend every week. The mass and heat flow rates follow the same trend as the industrial demand profile. The maximum value of the heat demand is 2.08 MW, whereas its minimum value is 1.05 MW. The respected mass flow rate values are 55.53 kg/s and 28.08 kg/s. The annual energy produced for the heat demand of the distillation process is 13.83 GWh.

3.2. Dynamic Analysis of the Natural Gas Boiler Scenario

The results of the scenario, which utilizes the NGB, are shown in this section. The heat flow rates of the fuel heat and the heat produced from the process on a weekly basis are depicted in Figure 8. The mass and heat flow rates follow the same trend as the industrial demand profile. The efficiency of the NGB is 86%. The maximum value for the fuel heat stream is 2.42 MW, whereas the minimum value is 1.23 MW. The maximum value for the process heat stream is 2.08 MW, whereas the minimum value is 1.06 MW. The annual energy consumed by the NGB due to fuel combustion is 16.12 GWh, whereas the annual energy demand of the process is 13.86 GWh.

Table 3. Energy produced (E_u,NG) and consumed (E_B,NG) by the NGB, operational costs, and equivalent CO₂ emissions annually.

Parameter	Value
Energy of waste heat source (Ewaste)	22.87 GWh
Energy of heat demand (Ehd)	13.83 GWh
Energy produced by natural gas boiler (Eu,NG)	13.86 GWh
Energy consumed by natural gas boiler (EB,NG)	16.12 GWh
Annual equivalent CO2 emissions	1,047,611.5 kgCO2eq/year
Annual operational cost	EUR 1,128,197.0/year

presents the annual energy produced by the NGB (E_u,NG) compared to the total yearly available energy from the waste heat source (E_waste). The energy produced by the NGB must match the annual energy of the industrial heat demand (E_hd), which is achieved in practice. Table 3 presents the yearly equivalent CO₂ emissions and the estimated operational costs. The annual operational cost is based on the average price of natural gas in the European Union, which is generally a value that fluctuates by country and other geopolitical factors.

3.3. Dynamic Analysis of the STS with Auxiliary Natural Gas Boiler Scenario

3.3.1. Basic Analysis

The next scenario examined involves an STS integrated with an auxiliary NGB. The STS, which in this case consists of PTCs, contributes to the demand for industrial energy and reduces natural gas consumption. Figure 9 presents the useful solar heat contributed (Q_hd,sol) for industrial heat production. The useful heat produced by the STS (Q_u,sol) follows the exact same trend. Figure 10 presents the fuel heat input to the auxiliary system (Q_B,NG). Since the efficiency of the natural gas boiler remains invariable, the heat generated by the auxiliary NGB (Q_u,NG) follows the exact same trend. For the daily analysis, a typical summer day, 21 June, and a typical spring day, 21 March, are considered. It is worth mentioning that during the hours of the day when the STS produces heat and contributes to the demand, the energy generated by the auxiliary NGB is reduced. Furthermore, the profile of the solar heat is smoother than that of the useful heat. This is mainly because of the existence of the buffer tank, which is a very important component in such systems. Moreover, the useful heat produced on 21 June presents a higher maximum value than the respective maximum value on 21 March. However, during the spring day, the total hours of the day when the STS contributes are increased. The climate conditions considered for the results depicted in these figures are from Lyngby, Denmark.

Figure 11a presents the useful heat produced by the STS on a weekly basis, while Figure 11b presents the heat generated by the auxiliary NGB for the same periods. The results encompass the first weeks of June and March. During the first week of June, the fuel heat consumption of the auxiliary NGB is less than the corresponding week of March, which is a reasonable result, since the available solar irradiation intensifies during the summer months.

Additionally, Figure 12 depicts the STS’s contribution to the hybrid system on a weekly basis, whereas Figure 13 depicts the contribution on an annual basis. These results refer to a PTC aperture area of 3000 m² and a thermal tank storage volume equal to 10 m³. This tank storage is utilized as a buffer tank because the solar system makes only a small energy contribution annually. The weather data used for the dynamic simulations are from Lyngby, Denmark. It is observed that the higher the amount of useful heat produced by the STS, the higher the contribution of solar energy to the heat demand, and the lower the fuel consumption for the auxiliary NGB. The maximum contribution of the PTCs for the first week of June is 61.9%, whereas for the first week of March, it is 32.6%.

Figure 14a presents the cumulative useful energy generated by the STS (E_u,sol) annually, and Figure 14b presents the cumulative energy produced by the auxiliary NGB (E_u,NG). It is important to mention that the results for five different collective areas of the STS are presented. It is observed that if the collective area is greater, the STS’s contribution and useful heat generation are enhanced. In contrast, the auxiliary NGB system’s contribution and heat production are reduced. Specifically, for the smallest collection area of 1000 m², the curve of the auxiliary heat input is approximately linear, while for the highest collection area of 5000 m², there is a variation in the curve that causes it to deviate from its linear character.

For the selected aperture area of 3000 m², the annual useful heat generated by the STS is 1302.27 MWh for Lyngby and 2819.16 MWh for Athens. This is a rational result considering the increased solar potential of Greece compared to Denmark on an annual basis. By increasing the aperture area of the STS, its contribution increases, and the natural gas consumption decreases. For the aforementioned aperture area and the location of Lyngby, the annual useful heat generated by the auxiliary NGB is 13,277.80 MWh, and the fuel heat is 15,439.30 MWh.

3.3.2. Parametric Analysis

Table 4. Annual useful energy generated by the STS (E_u,sol) and the auxiliary NGB (E_u,NG) for various collection areas of the STS for Lyngby, Denmark.

Ac [m2]	1000	2000	3000	4000	5000
Eu,sol [MWh]	434.51	868.22	1302.27	1736.60	2169.56
Eu,NG [MWh]	13,665.70	13,471.90	13,277.80	13,083.70	12,892.30
EB,NG [MWh]	15,890.30	15,665.00	15,439.30	15,213.60	14,991.00

presents the annual energy results for various collective areas of the STS based on the location of Lyngby, whereas

Table 5. Annual useful energy generated by the STS (E_u,sol) and the auxiliary NGB (E_u,NG) for various collection areas of the STS for Athens, Greece.

Ac [m2]	1000	2000	3000	4000	5000
Eu,sol [MWh]	939.87	1877.69	2819.16	3757.44	4691.91
Eu,NG [MWh]	13,440.90	13,022.40	12,601.60	12,182.30	11,774.10
EB,NG [MWh]	15,628.90	15,142.30	14,653.00	14,165.50	13,690.80

includes the results for the location of Athens, Greece. A thermal storage tank volume equal to 10 m³ is considered. The annual useful energy produced by the STS is greater for Athens, where the available solar irradiation is also greater throughout the year. Moreover, as the collective area increases, the energy produced by the STS (E_u,sol) increases, and the energy consumed by the auxiliary NGB (E_B,NG) decreases.

Table 6. Equivalent CO₂ emissions and operational costs of the hybrid system for Lyngby, Denmark.

Ac [m2]	1000	2000	3000	4000	5000
Eu,sol [MWh]	434.51	868.22	1302.27	1736.60	2169.56
EB,NG [MWh]	15,890.30	15,665.00	15,439.30	15,213.60	14,991.00
Emissions [tCO2eq/year]	1032.87	1018.23	1003.56	988.89	974.42
Costs [EUR/year]	1,112,321	1,096,550	1,080,751	1,064,952	1,049,370

presents the annual equivalent CO₂ emissions and operational costs of the hybrid system for Lyngby, Denmark.

Table 7. Equivalent CO₂ emissions and operational costs of the hybrid system for Athens, Greece.

Ac [m2]	1000	2000	3000	4000	5000
Eu,sol [MWh]	939.87	1877.69	2819.16	3757.44	4691.91
EB,NG [MWh]	15,628.90	15,142.30	14,653.00	14,165.50	13,690.80
Emissions [tCO2eq/year]	1015.88	984.25	952.45	920.73	889.90
Costs [EUR/year]	1,094,023	1,059,961	1,025,710	991,585	958,356

presents the annual equivalent CO₂ emissions and operational costs of the hybrid system for Athens, Greece. It can be observed that the greater the aperture collective area of the STS, the lower the fuel heat needed from the auxiliary NGB. Moreover, as the useful heat produced by the STS increases, the total system’s annual CO₂ emissions and operational costs decrease. These results are valid for both the examined locations.

3.4. Dynamic Analysis of the High-Temperature Heat Pump Scenario

This section presents the results of the scenario that utilizes the HTHP. The heat flow rates of the heat upgrade demand and the compressor power on a weekly basis are depicted in Figure 15. Both the mass and heat flow rates follow the same trend as the industrial demand profile. The COP of the HTHP is equal to 2.0 in this investigation.

Table 8. Operational costs and equivalent CO₂ emissions on an annual basis for Lyngby (Denmark) and Athens (Greece).

Parameter	Lyngby (Denmark)	Athens (Greece)
Electrical energy consumed [MWh/year]	6943.24	6943.24
CO2 emission on a yearly basis [kgCO2eq/year]	812,359	1,752,761
Annual cost [EUR/year]	1,666,378	1,617,775

presents the annual costs, the respective values for the compressor’s electricity consumption, and the related carbon emissions for Lyngby, Denmark, and Athens, Greece. It can be observed that the annual operational costs are slightly different between the two locations studied due to the different electricity prices, which constantly change throughout the year. For Lyngby, the CO₂ emissions are 53.7% less than for Athens, as Denmark’s electricity grid is primarily based on renewable energy. The electrical energy consumed is the same for both locations, as the weather data do not affect this.

3.5. Summary and Discussion

Table 9. Annual energy consumption, cost, and equivalent CO₂ emissions of the examined alternative scenarios for Athens (Greece) and Lyngby (Denmark).

Indexes	Lyngby (Denmark)	Athens (Greece)
Natural gas boiler
Fuel energy consumption [MWh]	16,117.10	16,117.10
Equivalent CO2 emissions [tCO2eq]	1047.61	1047.61
Annual operational cost [EUR]	1,128,197	1,128,197
Hybrid solar thermal and auxiliary natural gas boiler system
Useful energy of the solar thermal system [MWh]	1302.27	2819.16
Energy consumed by the natural gas boiler [MWh]	15,439.30	14,653.00
Equivalent CO2 emissions [tCO2eq]	1003.56	952.45
Annual operational cost of the natural gas boiler [EUR]	1,080,751	1,025,710
High-temperature heat pump
Energy consumed by the compressor [MWh]	6943.24	6943.24
Equivalent CO2 emissions [tCO2eq]	812.36	1752.76
Annual operational cost [EUR]	1,666,378	1,617,775

summarizes the alternative scenarios’ annual energy consumption and equivalent carbon dioxide emissions for Lyngby (Denmark) and Athens (Greece). These results clearly show the benefits of the thermochemical system. In other words, this table indicates the energy savings, CO₂ emission reductions, and annual cost savings of using the thermochemical design compared to the other scenarios.

The natural gas savings using a thermochemical system are 16,117.10 MWh for both locations in the context of using an NGB system. This amount is reduced to 15,439.30 MWh for Denmark (4.2% reduction) and 14,653.00 MWh for Greece (9.1% reduction) in the case of the hybrid system with the NGB and PTC collectors. The higher solar irradiation potential in this location justifies the higher natural gas savings of the hybrid system in Greece. In the case of HTHP, the electricity consumption is found to be 6943.24 MWh for both locations. These results indicate that using THT systems can yield significant energy savings in natural gas or electricity, depending on the unit studied.

The CO₂ emission reduction enabled by the thermochemical system compared to the NGB system is 1047.61 t_CO2eq annually. The CO₂ emission reduction is restricted for the hybrid system to 1003.56 t_CO2eq for Denmark and to 952.45 t_CO2eq for Greece. For the case of the HTHP, the annual CO₂ emissions are 812,36 t_CO2eq for Denmark and 1752.76 t_CO2eq for Greece. The difference in the electricity mixture between the countries explains this variation. The annual operation cost is found at EUR 1,128,197 for the NGB design for both locations, while in the hybrid scenario, it is at EUR 1,080,751 for Denmark and EUR 1,025,710 for Greece. The HTHP annual operation cost is calculated as EUR 1,666,378 for Denmark and EUR 1,617,775 for Greece. The aforementioned results indicate that the thermochemical design presents significant energy, environmental, and economic benefits compared to the other alternative solutions for industrial heat production.

4. Conclusions

This report presents the models developed for the dynamic investigation of a thermochemical heat transformer and the alternative scenarios, and the results from the dynamic simulations are illustrated accordingly. All the necessary models are developed in the Dymola environment, based on the Modelica programming language. The three alternative scenarios examined are the natural gas boiler (NGB), the high-temperature heat pump (HTHP), and a hybrid system consisting of a concentrated solar thermal system (STS) and an auxiliary NGB. The results indicate significant energy savings and equivalent CO₂ emission reductions from using the innovative thermochemical heat transformer instead of the examined conventional systems for industrial heat production.

The main conclusions of this report are summarized as follows:

• Utilizing an NGB system is a more cost-effective solution than employing a high-temperature heat pump. Notably, the hybrid solution incorporating solar thermal collectors and an NGB achieves the lowest operational cost in Denmark and Greece, resulting in an annual operating cost of EUR 1,080,751 and EUR 1,025,710, respectively.
• The HTHP is the most environmentally friendly option in Denmark, contributing the least to global warming at 812.36 t_CO2eq. In Greece, where the integration of renewable sources into the electricity grid is lower, the most environmentally friendly option is the hybrid solution, which results in 952.45 t_CO2eq.
• The hybrid system presents lower annual operational costs than the stand-alone NGB system, since the STS contributes to the petrochemical industry’s industrial heat demand in Greece and Denmark.
• The contribution of solar energy in Greece is higher than in Denmark, enhancing its performance in economic and environmental terms, as the available solar irradiation levels are higher in Greece. The annual useful heat produced by the concentrating solar system is determined at 1.30 GWh and 2.82 GWh for the weather data of Denmark and Greece, respectively.
• The energy utilized from the STS does not equal the useful energy generated by the solar thermal subsystem of the hybrid model. The main reasons for this discrepancy are the analyzed industrial heat demand profile and the lack of contribution from the STS during nighttime hours. Additionally, the thermal tank increases the contribution of the STS.