On the Technical, Economic, and Environmental Impact of Mobilized Thermal Energy Storage: A Case Study

Abstract

Mobilized thermal energy storage (M-TES) systems present a viable alternative to traditional heating systems to meet the heat demands of dispersed consumers. This report uses a case study in Lebanon to provide a techno-economic evaluation of the M-TES system. The compatibility of M-TES with current heating systems was assessed by investigating the design specifications of the heating system. The results show that underfloor heating systems and fan coil heating systems are compatible with M-TES. Several operating schedules for M-TES were also developed, considering various transit methods. The study calculated the payback period (PBP) and net present value (NPV) for each case while estimating the costs and revenues for M-TES. Additionally, this study computed the quantity of CO₂ emissions reduction for different M-TES configurations. The optimal operating strategy involves using two containers and three transportation cycles per day, achieving the highest NPV, a PBP of 3 years, and a yearly CO₂ emissions reduction of 44,787.9 kg.

1. Introduction

Energy consumption and environmental protection are currently two of the most challenging global issues. Innovative solutions for energy savings and a reduction in GHG emissions are urgently needed. The residential energy consumption category plays an important role worldwide due to its large share in overall energy consumption. Since space heating and domestic hot water use account for most of the energy consumption in residential structures, an effective heat supply is essential to meeting energy and environmental goals [1,2].

The International Energy Agency estimates a 37% increase in the world’s energy needs by 2040 [3]. Additionally, a recent study indicates that buildings consume nearly 32% of the world’s total energy [4]. Due to the harmful effects of fossil fuels, rising energy demands, and dwindling natural resources, researchers have increasingly focused on renewable energy sources and innovative materials to tackle these issues [5,6]. Renewable energy goals have been set to supply 20% of the global energy demand [7].

Many people live in rural areas globally. However, the extension of district heating (DH) networks to those areas is not usually economical due to the high initial investment. The more common heating systems are small-scale and use fossil fuels. Thus, substitutes that can effectively provide heat in an environmentally friendly way should be considered. For dispersed consumers, M-TES technology has become a viable option [8,9,10,11]. Heat can be derived from multiple sources without the limitations of networks and then brought to users flexibly. This system allows for the exploitation of renewable energy sources like bioenergy, solar energy, and geothermal.

To minimize buildings’ energy consumption and waste heat, an M-TES system can be used to transfer heat to various consumer groups. This M-TES system harnesses waste heat from industrial sources like power plants, steel or cement mills, and sewage sludge incinerators [12,13,14]. PCMs are utilized to store heat in a container, which is subsequently delivered to consumers for water- and space-heating applications [10,15,16,17]. In contrast to materials for sensible heat storage, PCMs are chosen for their capacity to release or absorb significant thermal energy quantities, called latent heat [18,19]. Compared to conventional heating systems with fossil fuel bases, M-TES for heat provision may drastically cut the consumption of primary energy and energy wastage, and reduce carbon dioxide emissions by as much as 95% [20,21].

Over the years, numerous studies have been conducted to gain a deeper understanding of M-TES technology. Research has primarily focused on storage materials, containers, and economic evaluations. The phase change materials (PCMs) employed in M-TES systems comprise organic sugar alcohols such as erythritol [22,23,24] and mannitol [22,25], in addition to inorganic hydrated salts like sodium acetate trihydrate [26,27,28], sodium hydroxide [29], and magnesium chloride hexahydrate [30].

Multiple M-TES container designs have been created and evaluated to guarantee efficient charging and discharging operations. These designs consist of direct-contact, shell-and-tube, detachable, encapsulated, and sorptive varieties [15]. Financial evaluations of the M-TES system have shown that heating costs are directly associated with the distance required to transport waste heat to the final user, while they are inversely associated with the demand for heat [31]. Sensitivity analysis indicates that heating expenses are more responsive to the cost of PCMs compared to other variables [28].

Mobilized thermal energy systems have been embraced in various advanced countries, including China [12], Germany [28], and Japan [32].

Numerous studies have been conducted to encourage the adoption of M-TES. Materials were selected and evaluated through experiments. Erythritol, a polyhydric alcohol with the chemical formula C₄H₁₀O₄, has a melting point of 118 °C and a latent heat of 339 kJ/kg, is recommended for its outstanding thermostability and its appropriateness for thermal energy storage at medium and low temperatures [33]. In-depth studies on M-TES systems utilizing erythritol have investigated its thermal and flow characteristics inside the container, along with its abilities for thermal energy storage and discharge [11].

Numerical and experimental studies were carried out to enhance the design of M-TES containers. Laboratory-scale testing configurations were established to assess M-TES performance against indirect/direct-contact thermal energy storage systems [31]. Different optimization techniques for the containers, including elevating the flow rate of the thermal oil, constructing channels prior to charging, and implementing wall heating, have been investigated [9,10].

Although many studies have investigated the properties and efficiency of M-TES in laboratory settings, additional research into its technological and economic feasibility and environmental effects is crucial for promoting its broader use. Prior studies have provided economic assessments and suggestions for system improvements along with the identification of key problems [31]. Nonetheless, these findings might not be directly applicable to M-TES projects worldwide because of different energy markets and national policies. Furthermore, heating system design standards vary by region. This paper seeks to evaluate the worldwide feasibility of adopting M-TES technology in Lebanon.

This study provides a novel and practical evaluation of mobilized thermal energy storage (M-TES) systems as an alternative to traditional heating systems, particularly for dispersed consumers. By leveraging a detailed case study in Lebanon, the research highlights the technical feasibility, economic viability, and environmental benefits of M-TES systems. The findings demonstrate how M-TES can integrate with existing heating systems, utilize waste heat, and significantly reduce CO₂ emissions, offering a practical solution for dispersed consumers.

The structure of this research is outlined as follows: initially, the case study and the concept of M-TES are presented. Next, the compatibility of M-TES with current heating systems is examined. Various transportation models are analyzed alongside different operating strategies (OSs), with the M-TES container design created using mathematical modeling. Subsequently, the expenses and earnings related to the M-TES system in this work are assessed, including an evaluation of the payback period (PBP) and net present value (NPV). Ultimately, the environmental impact is assessed by determining the yearly decrease in CO₂ emissions.

2. Study Case

An eight-story suburban building covering 4800 m² in Beirut, the coastal zone of Lebanon, was selected as the heating recipient. The heating demand per unit area is specified as 40 kWh/m² per year [34]. The total heating load for this study is computed as 192 MWh over the heating period of the year, considered 70 days per year. Exhaust steam produced from a regional thermal energy plant is employed as the heat medium. The parameters of the exhaust steam include a pressure of 0.361 MPa, a flow rate of 68.7 t/h, an average temperature of 140 °C, and an annual energy output of 91,000 MWh. The thermal energy plant is located about 23 km from the heating recipient.

3. Components and Operation of the M-TES System

The M-TES system comprises several components: a recipient, heat source, heat exchanger, container, vehicle, valve, pump, and other fittings. The process begins with transporting the M-TES container to the heat source area, such as a power plant, steel mill, or coking plant, where it is infused with industrial waste heat (IWH). Utilizing PCM as a latent thermal energy storage (LTES) technology, heat is charged within the container. The operation sequence is as follows: initially, at the heat source, the IWH charges the PCM inside the container. It is then delivered to the allocated recipient by a transport vehicle, where it provides the stored thermal energy for space heating or residential hot water use. Once the heat is discharged, the container is returned to the heat source location for recharging. Figure 1 illustrates the M-TES system.

Different candidates for the recovery of industrial waste heat (IWH) were evaluated based on their phase transition temperatures and latent heats. Benzamide has a phase transition temperature of 127 °C and a latent heat of 170 kJ/kg, while Stibene transitions at 124 °C with a latent heat of 167 kJ/kg. Benzoic acid transitions at 122 °C with a latent heat of 143 kJ/kg. Succinic anhydride and acetanilide both transition at 119 °C, with latent heats of 204 kJ/kg and 222 kJ/kg, respectively. MgCl⋅6H₂O transitions at 117 °C with a latent heat of 168 kJ/kg. Quinone transitions at 115 °C with a latent heat of 171 kJ/kg. Catechol transitions at 104 °C with a latent heat of 207 kJ/kg [20,36,37]. Among these, erythritol is identified as the optimal PCM for this study due to its high latent heat and suitable phase transition temperature.

In this case study, erythritol emerged as an ideal PCM for the M-TES system because of its high latent heat capacity (330 kJ/kg) and fusion temperature of 118 °C, which is suitable for most heat sources [8,9,10]. Additionally, erythritol is nontoxic and eco-friendly, as it is commonly used as a food additive. Therefore, erythritol was selected as the PCM for this study. Since erythritol dissolves in water, direct heating with steam is not possible. Instead, thermal oil, specifically Therminol55, is used for heat transfer.

Table 1. Thermo-physical properties of the selected phase change material and heat transfer fluid [38,39,40,41,42].

Item	T (°C)	Density (kg/m3)	Cp (kJ/kg·K)	Thermal Conductivity (W/m·K)	Latent Heat (kJ/kg)	Melting Point (°C)	Flash Point (°C)	Boiling Temperature (°C)	Viscosity (kg/(m·s))	Dynamic Viscosity (MPa·s)
Erythritol (PCM)	20	1480	1.35	0.732	339	118	-	-	0.02895	-
	140	1300	2.74	0.326			-	-	0.01602	-
Therminol55 (HTF)	33	865	1.94	0.1273	-	-	177	351	-	25.2
	130	797	2.3	0.1156	-	-			-	1.71

lists the thermo-physical properties of erythritol and Therminol55.

4. Adaptation to Current Heating Systems

At the operational site, the M-TES container is utilized to warm the return water of the current heating system. Nevertheless, due to the PCM solution solubility, direct heating by the M-TES system is not possible, so an oil–water heat exchanger is mounted. An oil tank is included in the circulation loop to handle oil expansion. Common endpoints for heating systems include radiators, underfloor heating, and fan coil units. According to local practices, the supply water temperatures for these endpoints should be 80 °C, 50 °C, and 40 °C, respectively [43]. However, maintaining a stable water temperature throughout the discharge process is challenging due to fluctuating heat release. For radiator systems, the M-TES system heats the return water, which is then further heated by a boiler to reach the required temperature. This method is not advisable or investigated in this work due to the additional costs and greenhouse gas emissions associated with the boiler. For systems with fan coil units or underfloor heating, the return water can be effortlessly warmed to the appropriate temperature and directly pushed into the heating system. Furthermore, a mixing valve is used to blend the return and inflow water to maintain a stable temperature.

The integration of M-TES systems with existing heating systems, such as floor heating and fan coil units, involves several key steps. For floor-heating systems, M-TES systems can be integrated using an oil–water heat exchanger to transfer heat from the PCM to the water circulating in the floor-heating pipes. The M-TES container should be installed near the existing heating system, with the heat exchanger connected to the return water line of the floor-heating system, ensuring proper insulation to minimize heat loss. The M-TES system will heat the return water, which is then circulated back into the floor-heating pipes, with a mixing valve used to maintain a stable water temperature. Similarly, fan coil units can be easily integrated with M-TES systems using an oil–water heat exchanger. The M-TES container should be placed close to the fan coil unit, with the heat exchanger connected to the return water line of the fan coil system, ensuring all connections are secure and insulated. The M-TES system will heat the return water, which is then circulated through the fan coil units, with a mixing valve used to regulate the water temperature. Installation recommendations include ensuring the installation site is prepared with adequate space for the M-TES container and heat exchanger, using high-quality, insulated pipes to connect the M-TES system to the existing heating system, and installing safety valves and pressure relief devices to handle any pressure buildup, ensuring compliance with local safety regulations and standards. Maintenance recommendations include conducting regular inspections of the M-TES system, including the container, heat exchanger, and connections; cleaning the heat exchanger periodically to ensure efficient heat transfer; monitoring the condition of the PCM and thermal oil; replacing or replenishing them as needed to maintain optimal performance; and regularly calibrating the mixing valves and temperature sensors to ensure accurate temperature control.

5. Operating Strategy and Container Design

In the study, a continuous 24 h space-heating requirement is considered, necessitating approximately 2.75 MWh of heat daily. Meeting this demand with a single M-TES container is impractical due to manufacturing and transportation challenges. Conversely, using too many containers for one user is not advisable, as the containers represent the primary upfront M-TES system cost. The optimal solution is to manage two containers with a specified number of round trips daily. While one container is discharging heat at the recipient, the second one is being transferred to and from the heat source location for recharging. This alternating operation ensures a continuous 24 h heating supply for the users.

The number of round trips for the container conveyance daily (n) is a crucial factor in M-TES system performance. Given the steady heat requirement of 2.75 MWh daily, the M-TES can either operate frequently with compact containers or less frequently with high-capacity containers. The benefit of using compact containers is the significantly lower initial cost. However, this approach increases transportation costs and greenhouse gas (GHG) emissions due to more frequent trips.

To compare different operating strategies, the M-TES system was analyzed with two, three, four, five, six, seven, and eight transportation runs daily. For instance, with two containers and two transportation cycles, one container discharges its heat at the recipient, while the second is transferred to the heat source site for recharging. After discharging, the first container is transported back to the heat source site, and the second container, now charged, is delivered to the recipient area. This alternating process ensures a continuous 24 h heating supply, with each container meeting half of the daily heating demand (1.375 MWh).

In this work, a cubic direct-contact M-TES container is developed, comprising 70% phase change material and 30% thermal oil. The temperature within the container is kept at 120 °C for both the molten PCM and the thermal oil. The stored heat in the M-TES container is categorized into three components: PCM latent heat, PCM sensible heat, and thermal oil heat energy, as outlined by the corresponding equation [44].

$$Q=m_{PCM}∆H+m_{PCM}{C}_{P,PCM}∆T+m_{oil}{C}_{P,oil}∆T$$

(1)

In this context, $m_{PCM}$ represents the PCM weight, $∆H$ is the PCM latent heat, $C_{P,PCM}$ denotes the PCM specific heat, and $∆T$ is the temperature difference. Based on the erythritol and thermal oil thermo-physical properties listed in Table 1, 0.18 MWh as thermal energy can be stored in a 1 m³ M-TES container, as derived from Equation (1). Furthermore, a 1 m³ M-TES container can provide 0.13 MWh of thermal energy to the recipient, considering an efficiency of 80% and 10% heat loss during transit and discharge [44]. Equation (2) is utilized to compute the number of M-TES containers required for various (n) values.

$$V={\displaystyle \frac{Q_d}{0.13n}}$$

(2)

In this equation, $Q_d$ is the end user’s daily heat need, (n) is the number of daily visits, and 0.13 is the thermal energy storage capacity of a 1 m³ M-TES container.

A shell-and-tube container design was used in this study, in which HTF flows through the shell side while PCM is contained within the tubes as shown in Figure 2 and Figure 3. This design enhances heat exchange due to the larger surface area. We selected aluminum tubes for their high thermal conductivity, light weight, and low cost [45]. A staggered layout of aluminum tubes was chosen due to its higher convection coefficient than an aligned arrangement [46]. The system’s heat transfer efficiency is improved by this design. The arrangement includes a storage tank within the container. Erythritol is placed within aluminum tubes inside the storage tank, and the area on the shell side that surrounds the tubes is filled with heat transfer fluid (HTF).

The research presents an in-depth explanation of the spacing and specifics of the staggered design. In order to maximize heat transfer, the oil’s inlet and outflow pipelines are also carefully planned. In order to ensure that the oil completely envelops all of the aluminum tubes for optimal thermal efficiency, the HTF enters the container from the bottom and leaves at the top.

As stated in Equation (2), the mass and volume of the container are computed in accordance with the needs for the heat supply.

Table 2. Capacity and weight details of M-TES containers.

Details	Data
n	2	3	4	5	6	7	8
Capacity (MWh)	1.37	0.91	0.69	0.55	0.46	0.39	0.34
Container volume (m3)	10.55	7.03	5.27	4.22	3.52	3.01	2.64
Container mass (t)	16.16	10.77	8.15	6.46	5.41	4.62	4.10
PCM (t)	11.05	7.37	5.59	4.42	3.68	3.16	2.90
Thermal oil (t)	2.49	1.65	1.24	1.00	0.84	0.71	0.66
PRF (t)	0.051	0.034	0.026	0.02	0.017	0.014	0.013
Rockwool(m2)	24.72	16.48	12.5	9.89	8.24	7.06	6.48
Pipes (t)	2.30	1.54	1.16	0.92	0.77	0.66	0.60

provides specific information on the unit’s and the container’s mass and volume.

6. Economic Study

To perform a thorough economic evaluation of the project, we will start by calculating the project cost and the expected savings. The detailed project costs for all scenarios are provided in Table 3. Currently, the existing system utilizes an oil boiler for both space heating and water heating.

Payback period (PBP) and net present value (NPV), two common capital budgeting criteria, were used to evaluate the M-TES systems’ economic feasibility under various operating strategies. These calculations were performed with a heating cost of USD 0.12/kWh and a system coefficient of performance (COP) of 0.8 [47,48]. The research was predicated on projected revenues and capital expenses that were previously predicted. Projects with a positive net present value (NPV) are financially worthwhile, whereas those with a negative NPV should be rejected [49,50]. NPV is a measure of the current value of predicted future cash flows. The calculation of NPV follows a specific formula, shown below [51]:

$$NPV=-C_0+{\displaystyle \frac{{\sum }_0^i(I_i-C_i)}{{(1+r)}^i}}$$

(3)

Here, I_i stands for income obtained in year (i); C_i stands for costs spent in year (i); r is the discount rate, which is set at 10%; and C₀ stands for the original investment cost. The time required to recoup the initial investment through produced earnings is known as the payback period (PBP). The net present value (NPV), which is determined using the formula shown below, becomes zero during this time.

$$C_0={\displaystyle \frac{{\sum }_0^i(I_i-C_i)}{{(1+r)}^i}}$$

(4)

The annual cost is directly linked to the number of cycles, which refers to each round trip of the container from the power plant to the user and back. According to feedback from local transport companies, each cycle costs USD 50.

Table 3. Project cost for different M-TES container scenarios.

Description	Unit Price [49]	n = 2	n = 3	n = 4	n = 5	n = 6	n = 7	n = 8
Container	USD 2500	USD 2500	USD 2500	USD 2500	USD 2500	USD 2500	USD 2500	USD 2500
Erythritol	USD 3.50/kg	USD 38,666.70	USD 25,777.80	USD 19,555.60	USD 15,466.70	USD 12,888.90	USD 11,047.60	USD 10,133.30
Aluminum tubes	USD 2/kg	USD 4606.60	USD 3071.10	USD 2329.80	USD 1842.60	USD 1535.50	USD 1316.20	USD 1207.20
Therminol55	USD 3/kg	USD 7466.70	USD 4952.40	USD 3733.30	USD 2986.70	USD 2514.30	USD 2133.30	USD 1981.00
PRF	USD 1510/ton	USD 76.50	USD 51.00	USD 38.70	USD 30.60	USD 25.50	USD 21.80	USD 20.00
Rockwool	USD 1/m2	USD 24.70	USD 16.50	USD 12.50	USD 9.90	USD 8.20	USD 7.10	USD 6.50
HX and pumps	USD 1.33/kWh	USD 1824.0	USD 1216.00	USD 912.00	USD 729.60	USD 608.00	USD 521.10	USD 456.00
Sum		USD 55,165.10	USD 37,584.70	USD 29,081.80	USD 23,566.00	USD 20,080.40	USD 17,547.20	USD 16,304.00
Shipping (15%)		USD 8274.76	USD 5637.70	USD 4362.27	USD 3534.91	USD 3012.06	USD 2632.08	USD 2445.61
VAT (11%)		USD 910.22	USD 620.15	USD 479.85	USD 388.84	USD 331.33	USD 289.53	USD 269.02
Total cost		USD 64,350.10	USD 43,842.50	USD 33,923.90	USD 27,489.80	USD 23,423.80	USD 20,468.80	USD 19,018.70

Table 3. Project cost for different M-TES container scenarios.

Description	Unit Price [49]	n = 2	n = 3	n = 4	n = 5	n = 6	n = 7	n = 8
Container	USD 2500	USD 2500	USD 2500	USD 2500	USD 2500	USD 2500	USD 2500	USD 2500
Erythritol	USD 3.50/kg	USD 38,666.70	USD 25,777.80	USD 19,555.60	USD 15,466.70	USD 12,888.90	USD 11,047.60	USD 10,133.30
Aluminum tubes	USD 2/kg	USD 4606.60	USD 3071.10	USD 2329.80	USD 1842.60	USD 1535.50	USD 1316.20	USD 1207.20
Therminol55	USD 3/kg	USD 7466.70	USD 4952.40	USD 3733.30	USD 2986.70	USD 2514.30	USD 2133.30	USD 1981.00
PRF	USD 1510/ton	USD 76.50	USD 51.00	USD 38.70	USD 30.60	USD 25.50	USD 21.80	USD 20.00
Rockwool	USD 1/m2	USD 24.70	USD 16.50	USD 12.50	USD 9.90	USD 8.20	USD 7.10	USD 6.50
HX and pumps	USD 1.33/kWh	USD 1824.0	USD 1216.00	USD 912.00	USD 729.60	USD 608.00	USD 521.10	USD 456.00
Sum		USD 55,165.10	USD 37,584.70	USD 29,081.80	USD 23,566.00	USD 20,080.40	USD 17,547.20	USD 16,304.00
Shipping (15%)		USD 8274.76	USD 5637.70	USD 4362.27	USD 3534.91	USD 3012.06	USD 2632.08	USD 2445.61
VAT (11%)		USD 910.22	USD 620.15	USD 479.85	USD 388.84	USD 331.33	USD 289.53	USD 269.02
Total cost		USD 64,350.10	USD 43,842.50	USD 33,923.90	USD 27,489.80	USD 23,423.80	USD 20,468.80	USD 19,018.70

Figure 4 shows the total cost of the M-TES system plotted against different values of n, where n represents the number of transportation cycles per day. The values of n considered in the analysis range from 2 to 8. It shows that the initial investment cost decreases as the number of transportation cycles per day increases. This is because fewer containers are required for higher values of n, reducing the overall material and manufacturing costs.

Figure 5 shows the net present values (NPVs) of the M-TES units across various usage plans over a 20-year project. Initially, the case of n = 2 shows a significantly lower NPV compared to other cases due to its high initial cost. However, its NPV increases rapidly over time, eventually surpassing those of n = 6, n = 7, and n = 8 in the later stages. The payback periods (PBPs) for n going from 2 to 8 are 4 years, 3 years, 2 years, 3 years, 3 years, 5 years, and more than 20 years, respectively. Based on the PBP, n = 3, n = 4, and n = 5 are the best strategies to implement with M-TES. Given its lowest NPV and longest PBP, operating strategies for n = 6 and above are deemed unsuitable for this study. Furthermore, comparing the NPVs for these three strategies, n = 3 has the highest NPV, at USD 317,362, followed by n = 4, with USD 243,439, and n = 5, with USD 185,581. Therefore, given its lowest NPV and longest PBP, the operating strategy for n = 6 and above is unsuitable for this study. Based on the analysis, the two best strategies to implement are n = 3 and n = 4. The n = 3 scenario offers the highest NPV and the second lowest PBP, making it a strong candidate. Similarly, the n = 4 scenario provides the lowest PBP and the second highest NPV, making it another excellent option. These strategies balance high returns with shorter payback periods, making them the most viable options.

7. Environmental Assessment

The system’s primary flaw is the amount of diesel used in truck transportation. However, overall fuel consumption is decreased when M-TES is used in place of oil boilers. The amount of diesel saved by replacing oil boilers with M-TES is calculated by subtracting the quantity of diesel used during transportation. The energy usage (kWh) of the boiler is divided by 10 to determine the annual diesel savings. This amounts to a yearly savings of 19,200 L of diesel for a use of 192,000 kWh.

The annual diesel savings from replacing oil boilers with M-TES is 19.2 m³. The truck’s yearly diesel consumption is calculated based on the number of cycles, truck consumption per kilometer, and distance traveled.

To determine the truck’s consumption per kilometer, the tractive force acting on the truck is calculated using the equation from Hucho and Sovran [52]:

$$F_{TR}=R+D+M{\displaystyle \frac{dV}{dt}}+Mgsin\theta$$

(5)

where $F_{TR}$ represents the tractive force, $R$ the tire rolling resistance, $D$ the aerodynamic drag, $M$ the mass of the vehicle, $g$ the gravitational acceleration, and θ the road inclination. The road inclination between the power plant and the university is almost null, and the truck is assumed to run at a constant velocity of 40 km/h on this road. The tire rolling resistance is given by the following equation:

$$R=W{f}_r(1+{\displaystyle \frac{V}{V_0}})$$

(6)

where $V$ is the truck speed in m/s, $V_0=3$0 m/s, and $f_r$ is the coefficient of rolling resistance and is approximately 0.008 for a truck on asphalt [53]. The weight of the truck and the trailer needed to calculate the rolling resistance is detailed in

Table 4. Truck and trailer mass.

n	2	3	4	5	6	7	8
Empty truck (Actros 4846 K) (kg)	11,268	11,268	11,268	11,268	11,268	11,268	11,268
Container mass (kg)	32,046	21,358	16,173	12,818	10,718	9156	8272
Total mass (kg)	43,314	32,626	27,441	24,086	21,986	20,424	19,540

.

The aerodynamic drag force is calculated by using the following equation:

$$D={\displaystyle \frac{1}{2}}\rho C_{D}S{V}^2$$

(7)

where ρ is the air density, which is equal to 1.4 kg/m3; $C_D$ is the drag coefficient of the truck, which is equal to 0.704 [54]; V is the truck velocity; and S the truck frontal area given by the following equation:

$$S=0.83\times b\times h$$

(8)

In this case, h stands for the truck’s height (3.6 m) and b for its base width (3 m). The following equation is utilized to compute the tractive effort needed for the vehicle to drive 1 km from point A to point B.

$$W\left(F_{TR}\right)=F_{TR}\times AB\times cos0°$$

(9)

The efficiency of heavy-duty diesel truck engines is around 46% and the diesel density is 851 kg/m³, with a lower heating value (LHV) of 42.8 MJ/kg [55]. Thus, the fuel consumption (FC) required for this truck to travel 1 km is given by the following equation:

$$FC={\displaystyle \frac{W\left(F_{TR}\right)}{\rho \times LHV\times \eta }}$$

(10)

Equation (10) enables the calculation of the truck’s fuel usage for a one-kilometer trip in each of the scenarios under consideration.

For the calculation of reduced CO₂ emissions, we consider that each kWh produced by diesel systems emits 0.264 kg of CO₂ [56].

The

Table 5. Yearly CO₂ emissions reduction for each scenario.

n	2	3	4	5	6	7	8
Fuel consumption per km	0.292	0.228	0.197	0.177	0.164	0.155	0.150
Truck yearly consumption	1879.16	2200.79	2534.66	2845.08	3171.23	3489.03	3851.21
Total volume of diesel saved	17,320.84	16,999.21	16,665.34	16,354.92	16,028.77	15,710.97	15,348.79
Yearly CO2 reduction (kg)	45,727.0	44,877.9	43,996.5	43,177.0	42,316.0	41,477.0	40,520.8

and Figure 6 below illustrate the total quantity of CO₂ emissions reduced in each scenario. These scenarios consider different numbers of transportation cycles per day (n) for the M-TES system.

When the number of cycles per day (n) increases from two to eight, the fuel consumption per kilometer decreases from 0.292 to 0.150 L of fuel per km, indicating improved fuel efficiency, and this is mainly due to the weight difference in the container in each case. However, despite this improvement, the truck’s yearly consumption rises from 1879.16 L to 3851.21 L, suggesting increased usage or distance covered. Correspondingly, the total volume of diesel saved decreases from 17,320.84 L to 15,348.79 L, and the yearly CO₂ reduction drops from 45,727.0 kg to 40,520.8 kg. This analysis shows that while higher (n) values lead to better fuel efficiency per kilometer, they also result in higher overall yearly consumption, less diesel saved, and a smaller reduction in CO₂ emissions. Given the slight difference in CO₂ emissions reduction, the operational strategy based on three transportation cycles per day remains the better option for M-TES system implementation, having the highest NPV and a better yearly CO₂ emissions reduction.

8. Conclusions

This study brings to light several significant facts and conclusions. For medium- and small-scale heat consumers in particular, the M-TES system provides a workable alternative to conventional heating techniques by using phase change materials (PCMs) like erythritol. Waste heat from industrial operations is efficiently stored and supplied to end users thanks to the system’s structure, which includes storage units, transportation vehicles, thermal exchangers, and circulation devices.

The case study in Lebanon demonstrates that M-TES systems offer significant technical, economic, and environmental benefits. Technically, M-TES systems integrate well with existing heating systems and utilize PCMs like erythritol for efficient thermal energy storage. Economically, the optimal operating strategy shows a favorable payback period and net present value, making the system financially viable. Environmentally, the system significantly reduces CO₂ emissions, aligning with several UN Sustainable Development Goals.

The analysis revealed that the M-TES system can seamlessly integrate with current heating systems, such as those that use air-handling units and radiant floor systems.

The most efficient operational approach includes utilizing two containers with three transportation cycles daily, leading to a PBP of about two years. This strategy balances the initial investment costs with operational efficiency, making it economically viable.

From an environmental perspective, the M-TES system significantly decreases carbon dioxide output as compared to conventional heating systems fueled by fossil fuels. The study calculated that the yearly CO₂ reduction ranges from 40,520.8 kg to 45,727.0 kg, depending on the number of transportation cycles and truck fuel consumption. Despite the diesel consumption during transportation, the overall diesel savings and CO₂ reduction highlight the environmental benefits of the M-TES system.

This finding is consistent with the numerous Sustainable Development Goals (SDGs) of the United Nations. It promotes SDG 7: Affordable and Clean Energy by encouraging the utilization of renewable energy sources and increasing energy efficiency. It also helps with SDG 13: Fighting Climate Change by lowering the release of greenhouse gases and minimizing climate change consequences. The M-TES system also contributes to SDG 9: Innovation, Infrastructure, and Industry by driving innovation in energy storage and delivery technologies.

Future research could benefit from additional analysis on the long-term operational challenges of M-TES systems, including maintenance, system degradation, and logistical issues. Exploring broader geographical contexts would highlight the adaptability and scalability of M-TES in different regions with varying energy demands and infrastructure. Furthermore, a comparative analysis with alternative energy storage technologies, such as lithium-ion batteries, pumped hydro storage, and compressed air energy storage, would provide insights into the relative advantages and limitations of M-TES, reinforcing its viability as an alternative heating solution. In addition, we aim to conduct a comprehensive life cycle assessment (LCA) of M-TES systems. This assessment will encompass the environmental impacts of material production, system manufacturing, use, and disposal stages. By undertaking this analysis, we hope to gain a holistic understanding of the environmental footprint of M-TES systems and identify opportunities for further reducing their environmental impact. Also, we plan to assess the impact of changes in heating costs and system performance factors on the net present value (NPV) and payback period (PBP) of M-TES systems. This analysis will help to understand how market fluctuations and technological advancements could influence the economic feasibility of M-TES systems, providing a more comprehensive evaluation of their long-term viability. Additionally, a detailed study will be conducted on the impact of various parameters, including energy price fluctuations, policy changes, and maintenance costs, on the economic feasibility of M-TES systems. This analysis will help understand how these factors influence the net present value (NPV) and payback period (PBP), providing a more robust and comprehensive evaluation of the economic viability of M-TES systems.

In conclusion, the M-TES system presents a viable solution for distributed heating needs, offering both economic and environmental advantages. The system’s ability to utilize industrial waste heat and its compatibility with existing heating infrastructure make it a practical and sustainable option for lowering energy use and the release of greenhouse gases. Further investigation and advancement could enhance the system’s efficiency and broaden its application in different regions and contexts.