Techno-Economic and Exergetic Assessment of a Small-Scale Parabolic Trough Collector System for Industrial Process Heat: A Case Study in the Tequila Industry

1. Introduction

The world faces significant challenges related to energy consumption and environmental sustainability, primarily driven by greenhouse gas emissions from fossil fuels. According to recent data, global energy consumption reached 399 EJ in 2022, with only 12.9% derived from renewable sources [1]. The industrial sector accounts for 34% of global energy use, consuming 135.66 EJ in 2021, of which 83.2% originated from non-renewable sources. Notably, 74% of industrial energy is consumed as heat, with less than 1% supplied by solar thermal technologies [1]. This reliance on fossil fuels for thermal energy represents a critical decarbonisation challenge.

Industrial heat decarbonisation requires eliminating fossil fuel dependency in heating processes, which contribute substantially to global carbon dioxide emissions [2,3]. High-temperature processes exceeding 400 °C depend heavily on natural gas and coal, presenting technical and economic barriers to net-zero objectives. Energy-intensive industries such as steel, cement, and chemicals require energy-dense fuels, making low-carbon alternatives like green hydrogen or electrification both costly and infrastructure-intensive [3,4,5]. Although waste heat recovery offers efficiency improvements, its potential often diminishes during transitions to electrified processes, biomass integration, or waste heat revalorisation, further complicating decarbonisation strategies.

A diversified portfolio of solutions is essential to overcome these challenges. Electrification via resistive heating or heat pumps addresses lower thermal demands, while hydrogen offers potential for extreme heat applications if production scales sufficiently [6,7]. Hybrid approaches, including molten salt storage or carbon capture integrated with concentrated solar power, provide flexible, cost-effective pathways to decarbonisation [7,8]. These integrated systems demonstrate the versatility required to manage intermittent renewable inputs and could eliminate billions of tonnes of emissions with large-scale deployment.

In México, the industrial sector consumes 22.79% of the country’s total energy, equivalent to over 940 PJ, with heavy reliance on non-renewable sources significantly contributing to greenhouse gas emissions [9]. This underscores the urgent need for decarbonisation strategies aligned with Sustainable Development Goal 7: ensuring affordable and clean energy for all [10]. Solar energy presents a viable pathway to reduce emissions and enhance sustainability in this context.

Solar Heat for Industrial Processes (SHIP) utilises solar thermal collectors to supply renewable heat directly to industrial operations, displacing fossil fuels in boilers and steam systems. This technology primarily targets low- to medium-temperature requirements (80–250 °C), addressing over 50% of global industrial heat demand in sectors such as food processing, textiles, and chemicals [11,12,13]. SHIP implementations employ diverse collector types, including flat-plate, evacuated tube, parabolic trough, and Fresnel designs, integrated via steam loops or hot water circuits. Thermal storage solutions such as thermocline tanks provide dispatchable heat, achieving solar fractions exceeding 50% even in variable climates [11,13,14,15]. By the end of 2024, over 1300 SHIP systems worldwide delivered a cumulative capacity of 1071 MW_th, demonstrating significant economic and environmental benefits [11,16].

Concentrated Solar Thermal (CST) technologies, particularly Parabolic Trough Collectors (PTCs), extend SHIP applications to higher temperatures (250–500 °C), addressing intensive thermal demands in sectors such as food, chemicals, and petroleum. These systems focus solar radiation onto receiver tubes containing heat transfer fluids such as thermal oil or molten salts, achieving conversion rates up to 80% in steam applications [17,18,19,20,21]. PTCs offer high energy density and can achieve solar fractions exceeding 50%, with levelised costs of heat as low as 36.9 EUR/MWh in optimal locations [17,18,20,22,23,24]. However, solar intermittency necessitates collector field oversizing, increasing land and material costs [17,19,20,22,23,24,25]. Thermal Energy Storage (TES) systems mitigate this by storing surplus daytime energy, boosting capacity factors to 46% and enabling 30–95% decarbonisation of industrial processes [17,18,19,22,23,24].

Industries with high thermal energy demands, such as tequila production, face distinct decarbonisation challenges due to their need for consistent medium-temperature heat and reliance on fossil fuels, particularly in regions with limited natural gas availability [26]. Although some tequila producers have adopted biomass boilers, constraints related to plant size and biomass availability limit this approach [26,27,28]. The Mexican tequila industry relies heavily on fuel oil to meet its intensive thermal requirements, yet the region benefits from high solar irradiance. Despite this, solar thermal hybridisation remains largely unexplored for this industry. Current research often focuses on theoretical or large-scale installations and lacks integrated techno-exergo-economic analyses for small-scale, modular PTC systems retrofitted into existing industrial sites.

This study addresses these gaps by conducting a comprehensive technical, exergetic, and economic evaluation of a small-scale PTC system integrated into a tequila production facility. The primary objectives are:

1.

To model and simulate the annual performance of a small-scale PTC system with thermal energy storage, assessing its capacity to meet specific steam demands.

2.

To perform a parametric analysis over the solar multiple (i.e., solar field size) to identify the optimal design that balances energy delivery, cost, and operational reliability.

3.

To conduct combined energy and exergy analyses, identifying thermodynamic inefficiencies under varying climatic conditions.

4.

To evaluate economic viability using the Levelised Cost of Heat (LCOH) and sensitivity analysis, while quantifying greenhouse gas emission reductions.

5.

To propose a replicable assessment framework for integrating SHIP technologies in regions with high solar irradiance and limited natural gas access.

By providing this integrated analysis, including a systematic exploration of solar field oversizing, this research establishes a scalable framework for industrial decarbonisation, offering a robust strategy for transitioning away from liquid fossil fuels in high-irradiation, gas-constrained regions.

2. Materials and Methods

2.1. Case Study Description

This study analyses the technical feasibility of integrating a parabolic trough collector (PTC) system into a large-scale tequila production facility located in Tequila, Jalisco, México. The plant operates a dual-boiler configuration to supply continuous, high-pressure saturated steam. This analysis focuses on the 2025 load demand profile, detailed in Table 1, which corresponds to 7728 operating hours per year and represents a service factor of 0.88.

The site provides favourable geographical conditions for a Solar Heat for Industrial Processes (SHIP) installation. It receives an annual solar irradiance of 2518.7 kWh m⁻², 4122 annual sunshine hours, and an average direct normal irradiance of 611 W m⁻² [29]. These solar characteristics meet or exceed the recommended thresholds for economically viable SHIP implementation, as recent literature confirms [30,31,32].

The facility satisfies its thermal energy demand through two distinct units: a 7.8 MW_th biomass boiler and a 9.81 MW_th fuel-oil boiler. The biomass unit consumes 898.58 kg h⁻¹ of agave bagasse, a solid biofuel by-product from the milling process with a higher heating value of 16840 kJ kg⁻¹. This biomass supply remains stable, is considered carbon-neutral, and provides sufficient fuel to maintain the boiler’s rated output, thus representing an optimised component of the plant’s existing energy portfolio.

Conversely, the 9.81 MW_th boiler operates entirely on fuel oil, consuming 1065 kg h⁻¹. This dependence constitutes the primary source of both carbon emissions and economic exposure. Volatile fossil fuel prices, illustrated in Figure 1, and the absence of regional natural gas infrastructure exacerbate this vulnerability. Consequently, this study focuses on displacing fossil fuel consumption in this boiler through solar thermal integration. The proposed strategy incorporates a dedicated solar thermal system designed to increase the facility’s renewable energy share from 44.29% to at least of 60%, while achieving substantial reductions in fuel oil consumption.

2.1.1. Solar Thermal System Design

This study proposes a 2.5 MW_th SHIP system to achieve a minimum renewable energy share of 60% at the tequila facility. The system supplies medium-temperature heat, directly increasing the plant’s renewable energy contribution. The solar field uses Therminol-VP1 as the heat transfer fluid (HTF) because of its thermal stability at operating temperatures up to 400 °C [34]. We selected the Power Trough 250 (PT250) model, a small-scale parabolic trough collector optimised for industrial integration in México [35]. The system incorporates a centralised thermocline thermal energy storage (TES) unit with a 5-hour capacity, using Hitec-XL salt. This configuration buffers solar intermittency, ensures operational stability, and maximises the utilisation of available solar irradiance. The TES unit maintains a more consistent steam supply to the process headers, reducing the need for auxiliary fossil fuel firing. Two helical coil heat exchangers facilitate thermal energy transfer between the solar HTF loop and the facility’s existing steam header, enabling charging and discharging of the TES tank. Table 2 details the system’s key operating specifications, and Figure 2 presents a schematic layout of the proposed installation.

2.2. System Modelling Framework

The proposed SHIP system integrates a parabolic trough collector (PTC) solar field, a single-node thermocline thermal energy storage (TES) unit, two helical coil heat exchangers (HX), and the existing fuel-oil boiler. We evaluate system performance using a validated, non-iterative thermohydraulic model coupled with comprehensive energy (first law) and exergy (second law) analyses on an hourly basis.

2.2.1. System Configuration And Thermohydraulic Modelling

A validated thermohydraulic routine forms the core of the model, tracking the temperature and pressure evolution of the Therminol VP-1 heat transfer fluid (HTF) through the solar field. We characterise PTC performance by segmenting the receiver tubes into discrete heat collector elements (HCEs). This discretisation allows us to account precisely for beam solar irradiation, optical and thermal losses, and the resultant HTF temperature gain. The model demonstrates predictive robustness with a relative squared error (RSE) below 3% against experimental data for both temperature and pressure calculations [36].

The heat transfer model integrates established Nusselt relationships through functional transformations, eliminating the traditional iterative dependency on convective heat transfer coefficients (h) and friction factors (f). This approach enhances computational efficiency by creating separable variable functionals (${\dot{q}}^{\prime }=f(\Delta T)$) [36]. Equation (1) presents the governing energy balance equations for an HCE, illustrating the relevant heat fluxes shown in Figure 3:

$$\left\{\begin{array}{c}{\dot{q}}_{i,\mathrm{SolAbs}}^{\prime }=IAM{\eta }_{o}W{G}_{\mathrm{bn}}\\ {\dot{q}}_{i,\mathrm{cond}}^{\prime }={\displaystyle \frac{2\pi k_{ij}(T_i-T_j)}{ln(d_j/d_i)}}\\ {\dot{q}}_{i,\mathrm{rad}}^{\prime }={\displaystyle \frac{\sigma \pi d_i(T_i^4-T_j^4)}{{\displaystyle \frac{1}{{\epsilon }_i}}+{\displaystyle \frac{(1-{\epsilon }_j)d_i}{{\epsilon }_j{d}_j}}}}\\ {\dot{q}}_{i,\mathrm{conv}}^{\prime }=f(\Delta T)\end{array}\right.$$

(1)

where ${\eta }_o$ represents the peak optical efficiency, $IAM$ is the incidence angle modifier (Figure 4) determined via ray-tracing [37], W is the collector aperture width, $G_{\mathrm{bn}}$ is the direct normal irradiance (DNI), k is thermal conductivity, T is temperature, d is diameter, $\sigma$ is the Stefan-Boltzmann constant, and $\epsilon$ is emittance.

We express the net energy balance for a PTC module of length L as:

$${\dot{Q}}_{\mathrm{PTC}}={\dot{Q}}_{\mathrm{in}}-{\dot{Q}}_{\mathrm{loss}}=A_c{G}_{\mathrm{bn}}{\eta }_o{F}_{\mathrm{soil}}IAM-{\dot{Q}}_{\mathrm{loss}}$$

(2)

where $A_c$ is the collector aperture area, $F_{\mathrm{soil}}$ is a soiling factor (0.92 in this study), and ${\dot{Q}}_{\mathrm{loss}}$ represents conductive, convective, and radiative losses.

We characterised thermal losses for the PT250 collector through simulation across a range of operating conditions. Figure 5 illustrates the non-linear relationship between thermal losses and the temperature gradient ($\Delta T_{\mathrm{loss}}=T_{\mathrm{HTF}}-T_0$) under varying DNI levels [38,39].

2.2.2. Solar Field and System Sizing

We size the solar field according to the proposed 2.5 MW_th load that the system must supply to the facility. We define the solar multiple ($SM>1$) as the ratio of the designed solar field thermal output (${\dot{Q}}_{\mathrm{des}}$) to the nominal solar contribution for the load (${\dot{Q}}_{\mathrm{load}}$):

$$SM={\displaystyle \frac{{\dot{Q}}_{\mathrm{des}}}{{\dot{Q}}_{\mathrm{load}}}}={\displaystyle \frac{{\dot{m}}_{\mathrm{SF}}{c}_{p,\mathrm{HTF}}\Delta T_{\mathrm{HTF}}}{{\dot{Q}}_{\mathrm{load}}}}$$

(3)

where ${\dot{m}}_{\mathrm{SF}}$ is the total HTF mass flow rate, $c_{p,\mathrm{HTF}}$ is the specific heat of the HTF, and $\Delta T_{\mathrm{HTF}}$ is the design temperature rise across the field.

We set the HTF flow rate per collector loop to maintain turbulent flow, which ensures appropriate heat transfer between the receiver tube and the HTF and avoids overheating, thereby preserving the receiver tube’s integrity. From this, we determine the number of parallel loops, $N_{\mathrm{loops}}$, and the total number of collectors, $N_{\mathrm{PTC},\mathrm{tot}}$. We fix the design point at solar noon on the spring equinox to ensure year-round reliability and a minimum production baseline from the SHIP system.

We size the TES to store surplus energy from periods of high solar irradiation. Equation (4) calculates the required storage volume, $V_{\mathrm{TES}}$, based on the desired storage duration, $t_{\mathrm{storage}}$, and the thermal energy density of the HTF:

$$V_{\mathrm{TES}}={\displaystyle \frac{{\dot{Q}}_{\mathrm{des}}·t_{\mathrm{storage}}}{{\rho }_{\mathrm{HTF}}{c}_{p,\mathrm{HTF}}\Delta T_{\mathrm{HTF}}}}$$

(4)

2.2.3. Storage and Hourly Dispatch Model

We model the TES as a single, one-node tank. Equation (5) updates the state of charge in terms of energy on an hourly basis:

$$Q_{\mathrm{sto}}(t+1)=Q_{\mathrm{sto}}\left(t\right)+{\dot{Q}}_{\mathrm{ch}}\left(t\right)\Delta t-{\displaystyle \frac{{\dot{Q}}_{\mathrm{TES},\mathrm{dis}}\left(t\right)}{{\eta }_{\mathrm{TES},\mathrm{dis}}}}\Delta t$$

(5)

where ${\eta }_{\mathrm{TES},\mathrm{dis}}$ is the discharge energy efficiency. We calculate the corresponding average temperature, $T_{\mathrm{avg}}\left(t\right)$, from $Q_{\mathrm{sto}}\left(t\right)$. We then derive the exergy stored, $\dot{E}{x}_{\mathrm{sto}}\left(t\right)$, from Equation (12) using $T=T_{\mathrm{avg}}\left(t\right)$. The hourly dispatch follows this sequence: we first send direct solar power to the process, ${\dot{Q}}_{\mathrm{s},\mathrm{direct}}\left(t\right)=min({\dot{Q}}_{\mathrm{PTC}}\left(t\right),{\dot{Q}}_{\mathrm{load}})$. Next, any surplus solar power, ${\dot{Q}}_{\mathrm{TES},\mathrm{ch}}\left(t\right)=max(0,{\dot{Q}}_{\mathrm{PTC}}\left(t\right)-{\dot{Q}}_{\mathrm{s},\mathrm{direct}}\left(t\right))$, charges the TES, subject to power and capacity limits. For any thermal deficit, we discharge ${\dot{Q}}_{\mathrm{dis}}\left(t\right)=min(\mathrm{deficit},{\dot{Q}}_{\mathrm{TES},\mathrm{rated}},{\eta }_{\mathrm{dis}}{E}_{\mathrm{sto}}\left(t\right))$. Finally, the boiler supplies any remaining unmet load: ${\dot{Q}}_{\mathrm{fuel}}\left(t\right)={\dot{Q}}_{\mathrm{load}}-{\dot{Q}}_{\mathrm{s},\mathrm{direct}}\left(t\right)-{\dot{Q}}_{\mathrm{TES},\mathrm{dis}}\left(t\right)$.

2.2.4. Energy and Exergy Analysis Framework

We conduct an hourly analysis to determine the system’s instantaneous and period-integrated performance. The dispatch logic prioritises direct solar use, then TES discharge, with the fuel oil boiler covering any remaining deficit.

We define the instantaneous total energy efficiency, ${\eta }_{\mathrm{I},\mathrm{tot}}$, as the ratio of the useful thermal energy delivered to the process to the total primary energy input:

$${\eta }_{\mathrm{I},\mathrm{tot}}\left(t\right)={\displaystyle \frac{{\dot{Q}}_{\mathrm{process}}\left(t\right)}{{\dot{Q}}_{\mathrm{sun}}\left(t\right)+{\dot{Q}}_{\mathrm{fuel}}\left(t\right)}}$$

(6)

where ${\dot{Q}}_{\mathrm{sun}}=G_{\mathrm{bn}}\left(t\right)A_{\mathrm{tot}}$ is the solar energy rate captured by the PTCs, and ${\dot{Q}}_{\mathrm{fuel}}={\dot{m}}_{\mathrm{fuel}}\left(t\right)·\mathrm{LHV}$ is the power delivered by the fuel. The useful thermal energy delivered to the process, ${\dot{Q}}_{\mathrm{process}}$, comprises three distinct contributions:

$${\dot{Q}}_{\mathrm{process}}={\dot{Q}}_{\mathrm{s},\mathrm{direct}}+{\dot{Q}}_{\mathrm{TES},\mathrm{dis}}+{\dot{Q}}_{\mathrm{fuel}}$$

(7)

where:

• ${\dot{Q}}_{\mathrm{s},\mathrm{direct}}$ represents the portion of solar thermal power from the PTC field (${\dot{Q}}_{\mathrm{PTC}}$) that reaches the process directly without passing through storage;
• ${\dot{Q}}_{\mathrm{TES},\mathrm{dis}}$ is the thermal power discharged from the TES to the process (positive during discharge);
• ${\dot{Q}}_{\mathrm{fuel}}$ is the useful heat supplied by the fuel-oil boiler to meet any remaining process demand.

We calculate each contribution using the respective component efficiencies. The direct solar contribution derives from the solar field energy efficiency (Eq. (9)), accounting for the solar input ${\dot{Q}}_{\mathrm{sun},\mathrm{in}}=G_{\mathrm{bn}}{A}_{\mathrm{tot}}$:

$${\dot{Q}}_{\mathrm{s},\mathrm{direct}}={\eta }_{\mathrm{I},\mathrm{SF}}{\dot{Q}}_{\mathrm{sun},\mathrm{in}}$$

(8)

$${\eta }_{\mathrm{I},\mathrm{SF}}={\displaystyle \frac{{\dot{Q}}_{\mathrm{gain},\mathrm{HTF}}}{{\dot{Q}}_{\mathrm{sun},\mathrm{in}}}}={\displaystyle \frac{{\dot{m}}_{\mathrm{SF}}\left(h_{\mathrm{out}}-h_{\mathrm{in}}\right)}{G_{\mathrm{bn}}{A}_{\mathrm{tot}}}}$$

(9)

The fuel-oil boiler supplies the useful heat required when solar energy and storage cannot meet the load. This contribution depends on the boiler’s energy efficiency, ${\eta }_{\mathrm{I},\mathrm{boiler}}$ (Table 2), and the fuel mass flow rate:

$${\dot{Q}}_{\mathrm{fuel}}={\eta }_{\mathrm{I},\mathrm{boiler}}·{\dot{m}}_{\mathrm{fuel}}·\mathrm{LHV}$$

(10)

Both ${\dot{Q}}_{\mathrm{s},\mathrm{direct}}$ and ${\dot{Q}}_{\mathrm{TES},\mathrm{dis}}$ account for the heat exchanger’s energy efficiency (${\eta }_{\mathrm{I},\mathrm{HX}}$ [40], Eq. (11)) in transferring thermal energy from the HTF loop to the process steam header. This formulation ensures consistent coupling between the solar field, storage, and process loads. We calculate the helical coil heat exchanger’s efficiency (${\eta }_{\mathrm{I},\mathrm{HX}}$) from its number of transfer units ($NTU$) and heat capacity rate ratio (${\dot{C}}_r={\dot{C}}_{min}/{\dot{C}}_{max}$). For a coil where the external fluid has a large heat capacity, the heat exchanger behaves analogously to a single-stream heat exchanger with ${\dot{C}}_r=0$, i.e., ${\epsilon }_{\mathrm{HX}}=1-exp(-NTU)$ [41,42].

$${\eta }_{\mathrm{I},\mathrm{HX}}={\displaystyle \frac{1}{NTU}}·{\displaystyle \frac{1}{{\displaystyle \frac{1}{{\epsilon }_{\mathrm{HX}}}}-{\displaystyle \frac{1+{\dot{C}}_r}{2}}}}$$

(11)

Exergy analysis quantifies the quality of energy flows. The specific physical exergy of the HTF is:

$${\psi }_{\mathrm{HTF}}=c_{p,\mathrm{HTF}}\left[(T-T_0)-T_{0}ln\left({\displaystyle \frac{T}{T_0}}\right)\right]+v(P-P_0)$$

(12)

where $T_0$ is the ambient temperature and v is the specific volume.

We calculate the exergy input from solar radiation using the endoreversible MPD model [43,44]:

$$\dot{E}{x}_{\mathrm{sun}}={\dot{Q}}_{\mathrm{sun},\mathrm{in}}{\eta }_{\mathrm{sun}},\mathrm{where}{\eta }_{\mathrm{sun}}=\left(1-{\left[{\displaystyle \frac{T_{\mathrm{a}}}{T_{\mathrm{sun}}}}\right]}^4\right)\left(1-{\displaystyle \frac{{\lambda }_{\mathrm{c}}{T}_0}{{\lambda }_{\mathrm{c}}{T}_{\mathrm{a}}+\sigma T_{\mathrm{sun}}^4-\sigma T_{\mathrm{a}}^4}}\right)$$

(13)

and $T_{\mathrm{sun}}=5777\mathrm{K}$, $\sigma$ is the Stefan–Boltzmann constant, $T_0$ is the ambient temperature, ${\lambda }_{\mathrm{c}}$ is the thermal conductance of the solar concentrator, and $T_{\mathrm{a}}$ is the absorber optimum temperature.

We determine the chemical exergy of the fuel oil, ${\psi }_{\mathrm{ch}}$, using the following correlation [45]:

$${\psi }_{\mathrm{ch}}=363.439·\mathrm{C}+1075.633·\mathrm{H}-86.308·\mathrm{O}+4.147·\mathrm{N}+190.798·\mathrm{S}-21.1·\mathrm{A}$$

(14)

where C, H, O, N, S, and A represent the weight percentages (dry basis) of carbon, hydrogen, oxygen, nitrogen, sulfur, and ash in the fuel, respectively. For the fuel oil in this study, the composition is 84.84% C, 7.75% H, 6.56% S, 0.64% O, 0.2% N, and 0% A. The exergy supplied by the fuel oil is $\dot{E}{x}_{\mathrm{fuel}}={\dot{m}}_{\mathrm{fuel}}·{\psi }_{\mathrm{ch}}$, where ${\psi }_{\mathrm{ch}}$ derives from Equation (14).

We define the exergy efficiency of the solar field and the heat exchanger, respectively, as:

$${\eta }_{\mathrm{II},\mathrm{SF}}={\displaystyle \frac{{\dot{m}}_{\mathrm{SF}}\Delta {\psi }_{\mathrm{HTF}}}{\dot{E}{x}_{\mathrm{sun}}}}$$

(15)

$${\eta }_{\mathrm{II},\mathrm{HX}}={\displaystyle \frac{\Delta \dot{E}{x}_{\mathrm{load}}}{\Delta \dot{E}{x}_{\mathrm{HTF}}}}={\displaystyle \frac{{\dot{m}}_{\mathrm{load}}\Delta {\psi }_{\mathrm{load}}}{{\dot{m}}_{\mathrm{SF}}\Delta {\psi }_{\mathrm{HTF}}}}$$

(16)

The instantaneous total exergy efficiency of the integrated system is:

$${\eta }_{\mathrm{II},\mathrm{tot}}\left(t\right)={\displaystyle \frac{\dot{E}{x}_{\mathrm{process}}\left(t\right)}{\dot{E}{x}_{\mathrm{sun}}\left(t\right)+\dot{E}{x}_{\mathrm{fuel}}\left(t\right)}}$$

(17)

where $\dot{E}{x}_{\mathrm{process}}$ represents the total exergy rate delivered to the process. This term comprises:

• $\dot{E}{x}_{\mathrm{s},\mathrm{direct}}$: the exergy rate from direct solar heat, which we calculate by applying Equation (12) to ${\dot{Q}}_{\mathrm{s},\mathrm{direct}}$;
• $\dot{E}{x}_{\mathrm{TES},\mathrm{dis}}$: the exergy rate from TES discharge, where the exergy of a heat stream ${\dot{Q}}_{\mathrm{TES},\mathrm{dis}}$ delivered at temperature $T_{\mathrm{HTF}}$ is $\dot{E}{x}_Q={\dot{Q}}_{\mathrm{TES},\mathrm{dis}}(1-T_0/T_{\mathrm{HTF}})$;
• $\dot{E}{x}_{\mathrm{fuel},\mathrm{out}}$: the exergy rate from the fuel-oil boiler, accounting for the boiler’s exergy efficiency.

Both $\dot{E}{x}_{\mathrm{s},\mathrm{direct}}$ and $\dot{E}{x}_{\mathrm{TES},\mathrm{dis}}$ incorporate the exergy efficiency of the heat exchanger (Equation (16)) in transferring exergy from the HTF loop to the process.

2.3. Performance, Economic, and Environmental Metrics

We employ several key parameters to assess the performance of the solar-assisted system on an annual basis. These parameters include the solar fraction and its exergy-based counterpart, the fuel saved fraction, the capacity factor, a storage cycling factor, and time-averaged energy and exergy efficiencies. These metrics offer complementary insights into the system’s energy balance, exergetic quality, economic operation, component utilisation, and thermodynamic performance.

2.3.1. Energy-Based and Exergy-Based Solar Fraction

The energy-based solar fraction ($S{F}_{\mathrm{I}}$) indicates the direct contribution of solar energy to the overall process load. We formally define it as the ratio of the useful thermal energy supplied by the solar collector array and the thermal energy storage system to the total energy demand over a given period, typically one year. Equation (18) expresses this relationship:

$$S{F}_{\mathrm{I}}={\displaystyle \frac{Q_{\mathrm{s},\mathrm{direct}}+Q_{\mathrm{TES},\mathrm{dis}}}{Q_{\mathrm{process}}}}$$

(18)

where $Q_{\mathrm{s},\mathrm{direct}}$ is the useful energy delivered directly by the solar collectors to the process, $Q_{\mathrm{TES},\mathrm{dis}}$ is the energy discharged from the thermal energy storage (TES) to meet the load, and $Q_{\mathrm{process}}$ is the total energy required to meet the process load over the same accounting period. These terms correspond to the cumulative hourly values of ${\dot{Q}}_{\mathrm{s},\mathrm{direct}}$ and ${\dot{Q}}_{\mathrm{TES},\mathrm{dis}}$ defined in Eqs. (8) and the dispatch logic, respectively. A higher solar fraction indicates that a greater proportion of the heat demand originates from solar-derived sources, thereby reducing reliance on auxiliary energy. However, designing for a very high solar fraction often entails diminishing returns because it requires a disproportionately larger collector installation area and increased thermal storage capacity to bridge low-irradiance periods. These factors can compromise the economic and spatial feasibility of the project.

While the conventional solar fraction accounts for energy quantity, an exergy-based solar fraction ($S{F}_{\mathrm{II}}$) provides insight into the quality of the supplied energy. We define this metric as the ratio of the exergy delivered by the solar collectors and the TES to the total exergy output required by the process:

$$S{F}_{\mathrm{II}}={\displaystyle \frac{E{x}_{\mathrm{s},\mathrm{direct}}+E{x}_{\mathrm{TES},\mathrm{dis}}}{E{x}_{\mathrm{process}}}}$$

(19)

where $E{x}_{\mathrm{s},\mathrm{direct}}$ is the exergy content of the useful heat from the solar collectors, $E{x}_{\mathrm{TES},\mathrm{dis}}$ is the exergy of the heat discharged from storage, and $E{x}_{\mathrm{process}}$ is the total exergy output required by the process. Both $E{x}_{\mathrm{s},\mathrm{direct}}$ and $E{x}_{\mathrm{TES},\mathrm{dis}}$ incorporate the exergy efficiency of the heat exchanger (Eq. (16)) in transferring exergy from the HTF loop to the process. This formulation recognises that not all thermal energy is equally useful for performing work; for instance, a lower-temperature heat source carries less exergy. Therefore, the exergy-based fraction offers a more nuanced evaluation of how effectively the system’s solar input matches the thermodynamic quality demanded by the process.

2.3.2. Fuel Saved Fraction and Capacity Factor

The fuel saved fraction ($FSF$) quantifies the reduction in auxiliary fuel consumption achieved by integrating solar energy. We define it as the fraction of boiler energy or fuel saved relative to a baseline scenario in which a boiler-only system meets the entire load:

$$FSF={\displaystyle \frac{m_{\mathrm{fuel},\mathrm{base}}-m_{\mathrm{fuel}}}{m_{\mathrm{fuel},\mathrm{base}}}}$$

(20)

where $m_{\mathrm{fuel},\mathrm{base}}$ is the fuel consumed by the boiler in the baseline case, and $m_{\mathrm{fuel}}$ is the fuel consumed by the auxiliary heater in the solar-assisted configuration. This parameter directly reflects the fossil fuel savings and the associated reduction in operational costs and emissions.

In contrast to these load-based metrics, the capacity factor ($CF$) measures how effectively the system utilises its hardware. Although the term often applies to electricity generation, we adapt its underlying principle here to evaluate the solar thermal plant. We define it as the ratio of the actual energy output from the system over a given period to the theoretical maximum energy output generated if the system operated continuously at its nominal power output throughout that entire period:

$$CF={\displaystyle \frac{Q_{\mathrm{s},\mathrm{direct}}}{Q_{\mathrm{design}}·\Delta t}}$$

(21)

where $Q_{\mathrm{s},\mathrm{direct}}$ is the actual energy output from the solar field over the time period $\Delta t$, and $Q_{\mathrm{design}}$ is the nominal design energy output of the system. A high capacity factor indicates that the installed infrastructure—including the solar collectors and the power block—operates intensively and consistently, which dramatically improves the economic viability of the plant by optimising the return on capital investment.

2.3.3. Storage Cycling Factor and Time-Averaged Efficiencies

To characterise the utilisation of the thermal energy storage, we introduce a storage cycling factor. This parameter, evaluated over a given period, indicates how many times the nominal energy capacity of the TES is effectively used:

$$Cycle{s}_{\mathrm{TES}}={\displaystyle \frac{Q_{\mathrm{TES},\mathrm{dis}}·\Delta t}{Q_{\mathrm{TES},\mathrm{capacity}}}}$$

(22)

where $Q_{\mathrm{TES},\mathrm{dis}}$ is the average discharge rate from the TES over the period $\Delta t$, and $Q_{\mathrm{TES},\mathrm{capacity}}$ is the nominal energy storage capacity. This cycling factor provides insight into the operational intensity of the storage unit. A higher number of cycles over a season, for example, suggests that the store charges and discharges frequently, which may affect its thermal performance and long-term durability.

Finally, we evaluate the overall thermodynamic performance of the system by computing time-averaged energy and exergy efficiencies. Unlike instantaneous efficiencies, which fluctuate with operating conditions, these values integrate the respective instantaneous efficiencies over the entire year. We define the time-averaged total energy efficiency (${\overline{\eta }}_{\mathrm{I},\mathrm{tot}}$) as:

$${\overline{\eta }}_{\mathrm{I},\mathrm{tot}}={\displaystyle \frac{{\displaystyle {\int }_0^t{\dot{Q}}_{\mathrm{process}}\left(t\right)\mathrm{d}t}}{{\displaystyle {\int }_0^t\left[{\dot{Q}}_{\mathrm{sun}}\left(t\right)+{\dot{Q}}_{\mathrm{fuel}}\left(t\right)\right]\mathrm{d}t}}}$$

(23)

Similarly, we define the time-averaged total exergy efficiency (${\overline{\eta }}_{\mathrm{II},\mathrm{tot}}$) as:

$${\overline{\eta }}_{\mathrm{II},\mathrm{tot}}={\displaystyle \frac{{\displaystyle {\int }_0^t\dot{E}{x}_{\mathrm{process}}\left(t\right)\mathrm{d}t}}{{\displaystyle {\int }_0^t\left[\dot{E}{x}_{\mathrm{sun}}\left(t\right)+\dot{E}{x}_{\mathrm{fuel}}\left(t\right)\right]\mathrm{d}t}}}$$

(24)

These integrated efficiencies provide a robust, single-figure assessment of the system’s ability to convert incoming energy and exergy resources into useful products over a full year of operation. They thus complement the other metrics by capturing the cumulative effect of part-load behaviour and transient conditions.

2.3.4. Economic Assessment Methodology

The analysed process involves different investment and operational costs. Therefore, we compare two scenarios for the steam supply to the factory: the fuel-oil scenario (FF) and the solar field integration scenario (SHIP). Using the economic data from both cases, we apply the present value method, conduct a cost distribution analysis, and determine the payback period to evaluate the feasibility of using a SHIP system. We define the cash flow benefit of using the more economic technology as:

$$B=C_{\mathrm{FF}}-C_{\mathrm{SHIP}}$$

(25)

where $C_{\mathrm{FF}}$ is the total generation cost using the fuel-oil boiler, and $C_{\mathrm{SHIP}}$ is the total generation cost using the SHIP system. The total energy generation cost (for both FF and SHIP) includes:

$$C=OPEX+C_{\mathrm{a}}$$

(26)

where the operating expenditure ($OPEX$) accounts for the day-to-day operational costs: $OPEX=C_{\mathrm{F}}+C_{\mathrm{E}}+C_{\mathrm{OM}}$. Here, $C_{\mathrm{F}}$ is the total fuel cost, $C_{\mathrm{E}}$ is the total electricity cost, $C_{\mathrm{OM}}$ is the operation and maintenance cost, and $C_{\mathrm{a}}$ is the amortisation cost. For the fuel cost, we consider the monthly price of fuel oil, as detailed in Table 3. Table 4 displays the OPEX and CAPEX costs for the FF scenario. These values correspond to a 9.81 MW_th fuel-oil boiler, which we scale down proportionally to the solar field’s rated design in subsequent calculations to maintain a consistent energy basis.

For the SHIP system, we compute the fuel cost from the remaining annual fuel-oil consumption required to supply the unmet process demand (${\dot{Q}}_{\mathrm{fuel}}$). We assume that operation and maintenance costs equal 10% of the CAPEX. For electricity cost, we consider the electricity usage (0.1104 USD/kWh), the demand charges for capacity (24.2193 USD/kW), distribution (4.2709 USD/kW), and VAT (16%) [46]. We compute the amortisation cost as:

$$C_{\mathrm{a}}=CRF·CAPEX$$

(27)

where $CRF$ is the capital recovery factor:

$$CRF=\left\{\begin{array}{cc}{\displaystyle \frac{1}{n}}& \mathrm{for}\mathrm{the}\mathrm{FF}\mathrm{case}\\ {\displaystyle \frac{r_{\mathrm{L}}{(1+r_{\mathrm{L}})}^n}{{(1+r_{\mathrm{L}})}^n-1}}& \mathrm{for}\mathrm{the}\mathrm{SHIP}\mathrm{case}\end{array}\right.$$

(28)

where n is the useful economic life of the asset, and $r_{\mathrm{L}}$ is the loan interest rate. The difference between $CR{F}_{\mathrm{FF}}$ and $CR{F}_{\mathrm{SHIP}}$ arises because the fuel-oil boiler is an existing asset that has already been fully paid off and therefore carries no active loan. In contrast, we assume that the SHIP system receives financing through a loan at an interest rate of 7% [47].

For the SHIP system, the CAPEX comprises:

$$CAPE{X}_{\mathrm{SHIP}}=C_{\mathrm{PTC}}+C_{\mathrm{P}}+C_{\mathrm{ST}}+C_{\mathrm{HX},\mathrm{ch}}+C_{\mathrm{HX},\mathrm{dis}}+C_{\mathrm{VP}1}+C_{\mathrm{HITECXL}}+C_{\mathrm{CW}}+C_{\mathrm{EDF}}+C_{\mathrm{CN}}$$

(29)

where each C represents the individual cost of the parabolic trough collectors (PTC), the circulation pump (P), the storage tank (ST), the charging heat exchanger (HX,ch), the discharging heat exchanger (HX,dis), the Therminol-VP1 (VP1), the Hitec XL salt (HITECXL), civil works (CW), engineering design fees (EDF), and contingency (CN). We assume that EDF and CN costs each amount to 5% of the total CAPEX. Suppliers in México provide the following costs: 1041.691 USD for 10 m² of PTC concentrating area, 15370.01 USD/m³ for Therminol VP1, and 1.7 USD/kg for Hitec XL. For the costs of the storage tank, the heat exchangers, and the circulating pump, we estimate these using the equipment purchased cost at a reference year ($C^0$) [48]:

$${log}_{10}{C}^0=K_1+K_2{log}_{10}X+K_3{\left({log}_{10}X\right)}^2$$

(30)

where X is the equipment’s capacity or size parameter, and $K_1,K_2,K_3$ are equipment-specific constants, as Table 5 shows. If the size parameter falls outside the range in Table 5, we escalate the cost with a power law. Additionally, we update the costs for the analysis year by applying a cost index (I) [48]. Equation (31) estimates the updated cost, where the reference cost index ($I^0$) is 397 for CEPCI 2001 data, the 2025 index (I) is 806.7 [48,49], and $X^0$ is the reference capacity or size parameter.

$$C=C^0\left({\displaystyle \frac{I}{I^0}}\right){\left({\displaystyle \frac{X}{X^0}}\right)}^{0.6}$$

(31)

Because fuel oil prices fluctuate (see Figure 1), the benefit B varies over the years. The total fuel costs ($C_{\mathrm{F}}$) in both scenarios escalate annually, and historical data indicate a long-term average annual escalation rate $e_{\mathrm{F}}=7.13\%$. Equation (32) updates the fuel costs accordingly. Under the Mexican Income Tax Law (LISR) [50], initial investments in machinery and equipment for renewable energy generation receive a 100% accelerated depreciation rate, allowing full deduction within a single fiscal year. The tax shield $TS$ accrues as a one-time cash benefit in year 1. Equation (33) calculates this shield, where d is the deduction fraction (0 to 1) and $\tau$ is the corporate tax rate (0.30 for México [47]):

$$C_{\mathrm{F},t}=C_{\mathrm{F},0}·{\left(1+e_{\mathrm{F}}\right)}^t$$

(32)

$$TS=CAPE{X}_{\mathrm{SHIP}}·d·\tau$$

(33)

With escalating benefit B due to rising fuel oil prices and including the tax shield, we compute the payback period using the cumulative cash flow approach:

$$CC{F}_t=-CAPE{X}_{\mathrm{SHIP}}+TS+{\displaystyle \sum _{t=1}^n}{B}_i$$

(34)

The payback period is the year $t^{*}$ where $CC{F}_t$ changes from negative to positive. For precision, we interpolate:

$$PP=t^{*}-1+{\displaystyle \frac{\left|CC{F}_{t^{*}-1}\right|}{C{F}_{t^{*}}}}$$

(35)

where the cash flow ($C{F}_t$) is:

$$C{F}_t=\left\{\begin{array}{cc}-CAPE{X}_{\mathrm{SHIP}}& t=0\\ B_t+TS& t=1\\ B_t& 2\le t\le n\end{array}\right.$$

(36)

We compute the net present value ($NPV$), including the tax shield, using Eq. (37). The project is viable and should be accepted if $NPV>0$. We also calculate the internal rate of return $i^{*}$ from Eq. (38), where the decision rule is that the project is viable when $i^{*}>i$ (the discount rate):

$$NPV=-CAPE{X}_{\mathrm{SHIP}}+{\displaystyle \frac{TS}{1+i}}+{\displaystyle \sum _{t=1}^n}{\displaystyle \frac{B_t}{{\left(1+i\right)}^t}}$$

(37)

$$0=-CAPE{X}_{\mathrm{SHIP}}+{\displaystyle \frac{TS}{1+i^{*}}}+{\displaystyle \sum _{t=1}^n}{\displaystyle \frac{B_t}{{\left(1+i^{*}\right)}^t}}$$

(38)

Finally, we compute the levelised cost of heat ($LCoH$). This metric expresses the total cost of generating heat per unit of energy delivered [51], allowing a direct comparison between the FF and SHIP scenarios on an equal footing. Among the various definitions for calculating $LCoH$, we adopt the IEA SHC Task 54 formula [52]:

$$LCoH={\displaystyle \frac{CAPEX-TS+{\sum }_{t=1}^n{\displaystyle \frac{OPEX}{{\left(1+i\right)}^t}}}{{\sum }_{t=1}^n{\displaystyle \frac{Q_{\mathrm{process}}}{{\left(1+i\right)}^t}}}}$$

(39)

2.3.5. Greenhouse Gas Emission Reductions

We calculate the reduction in greenhouse gas (GHG) emissions achieved by displacing fuel oil using its emission factor ($E{F}_{\mathrm{fuel}}$) according to Eq. (40), together with the energy supplied by the fuel oil. The IPCC Guidelines for National Greenhouse Gas Inventories provide the emission factors, which standardise GHG emissions accounting for fossil fuels [53]. For fuel oil, the emission factors are: $E{F}_{{\mathrm{CO}}_2}=77400$ kg_CO2/TJ, $E{F}_{{\mathrm{CH}}_4}=3$ kg_CH4/TJ, and $E{F}_{{\mathrm{N}}_2\mathrm{O}}=0.6$ kg_N2O/TJ.

$${\mathrm{GHG}}_{\mathrm{fuel}}=Q_{\mathrm{fuel}}·E{F}_{\mathrm{GHG},\mathrm{fuel}}$$

(40)

2.4. Design Point

The design point conditions establish the fundamental baseline for sizing solar thermal installations because they define the operational parameters at which the system optimises its peak performance. These parameters—primarily direct normal irradiance ($G_{\mathrm{bn}}$), ambient temperature ($T_{\mathrm{amb}}$), and wind speed ($v_{\mathrm{w}}$)—collectively determine the necessary aperture area for the solar field to satisfy the specific process heat demand. For this study, we set the design point to the spring equinox (March 21) at solar noon. This selection identifies the period of minimum solar zenith angle and maximum optical efficiency, thereby providing a standardised framework for evaluating the system under peak potential solar gain [54,55]. This approach ensures that the solar field reaches its full thermal capacity without exceeding the safety thresholds of the heat transfer fluid (HTF).

The operational temperature range adheres to the technical specifications of the PT250 collector, which was manufactured by Inventive Power [35]. These thermal limits facilitate high-efficiency heat transfer while preserving the thermophysical stability of the HTF under concentrated solar flux. Table 6 summarises the boundary conditions and environmental parameters that we adopt for the design point. By anchoring the methodology to these rigorous conditions, the model establishes a robust framework for performance prediction and confirms the technical viability of the SHIP system during peak thermal production intervals.

3. Results

3.1. Design Point System Performance

The system is evaluated at the design point, defined as solar noon on the spring equinox (21 March), at which the solar zenith angle reaches its minimum, thereby maximising optical efficiency and providing a standardised baseline for performance comparison. To explore the trade-off between solar field size, thermal storage capacity, and conversion efficiency, the solar multiple ($SM$) is varied across a range of feasible configurations. Table 7 presents the key parameters obtained from the solar field simulation for each effective $SM$ value arising from the integer-module constraint.

Parametric simulations were initially conducted using a nominal $SM$ increment of 0.1, spanning from 1.1 to 1.9. Because the physical solar field must accommodate an integer number of collector modules, however, the actual $SM$ values deviate slightly from these nominal targets. In certain cases—such as the transitions between $SM=1.4$ and $1.5$, or between $SM=1.7$ and $1.8$—the required module count remains constant, yielding identical field configurations for consecutive nominal targets.

The solar field maintains constant inlet and outlet temperatures throughout all scenarios. Consequently, the temperature rise per loop and the specific heat load per collector remain uniform. The number of PTCs per loop is fixed at 62, preserving identical thermohydraulic conditions across all configurations. As a result, the Reynolds number remains constant at $4.0477\times {10}^5$ and the pressure drop at 11.088 bar for every case. The values reported in Table 7 therefore represent the effective solar multiples and their associated performance metrics at the actual installed capacity for each design-point configuration.

Table 7 reveals several important trends. As the solar multiple increases from 1.119 to 1.957, the total HTF mass flow rate, the number of parallel loops, the total aperture area, the TES volume, and the charging heat exchanger area all increase proportionally—a direct consequence of scaling the solar field. The Reynolds number and pressure drop remain invariant across all $SM$ values, confirming that the loop architecture and thermohydraulic conditions are consistent for every configuration.

Both the total energy efficiency (${\eta }_{\mathrm{I},\mathrm{tot}}$) and the total exergy efficiency (${\eta }_{\mathrm{II},\mathrm{tot}}$) decline monotonically with increasing solar multiple: ${\eta }_{\mathrm{I},\mathrm{tot}}$ falls from 0.4616 at $SM=1.119$ to 0.2638 at $SM=1.957$, whilst ${\eta }_{\mathrm{II},\mathrm{tot}}$ decreases from 0.1995 to 0.1140 over the same range. This monotonic decline reflects the diminishing marginal utilisation of the collector area as the solar field grows beyond the process heat demand. Moreover, ${\eta }_{\mathrm{II},\mathrm{tot}}$ is consistently lower than ${\eta }_{\mathrm{I},\mathrm{tot}}$ across all configurations—at $SM=1.119$, for instance, ${\eta }_{\mathrm{II},\mathrm{tot}}=0.1995$ compared with ${\eta }_{\mathrm{I},\mathrm{tot}}=0.4616$—a gap attributable to the

thermodynamic irreversibilities inherent in the solar receiver and heat exchangers.

Figure 6a–c present the hourly profiles of thermal power output, energy efficiency, and exergy efficiency, respectively, over the design day for each $SM$ configuration. Performance is lower during morning and evening hours owing to increased incidence angles and elevated thermal losses, whilst near-noon operation approaches the peak values reported in Table 7. As $SM$ increases, the peak thermal power rises substantially, generating a growing surplus available for storage in the TES.

Figure 6b shows that ${\eta }_{\mathrm{I}}$ remains close to the boiler-dominated level during periods of negligible solar contribution, but decreases markedly during hours of significant solar input. This reduction becomes more pronounced at higher $SM$ values, demonstrating that enlarging the collector field beyond the process demand progressively degrades first-law performance owing to a greater fraction of incident radiation being dissipated through optical and thermal loss mechanisms.

The exergy efficiency, ${\eta }_{\mathrm{II}}$, exhibits a complementary but opposing behaviour (Figure 6c): values during the solar operating window are higher than those recorded during boiler-dominated periods, reflecting improved thermodynamic matching between solar heat delivery and process demand. Although larger $SM$ values introduce additional irreversibilities—associated with optical interception, thermal losses, and heat transfer across finite temperature differences—the exergy efficiency of the SHIP system remains substantially higher than the fuel-only baseline across all configurations. The physical mechanisms underpinning these opposing trends in ${\eta }_{\mathrm{I}}$ and ${\eta }_{\mathrm{II}}$ are examined in Section 4.

3.2. Annual System Performance

The direct contribution of solar energy to the overall process load is quantified using the energy-based solar fraction (Equation (18)) and the exergy-based solar fraction (Equation (19)). Figure 7 shows that as $SM$ increases, the energy solar fraction rises by approximately 36% across the full parametric range, whilst the exergy solar fraction increases by approximately 33.8%. Both metrics increase most rapidly at the lowest $SM$ values—a relative change of approximately 10% between $SM=1.12$ and $SM=1.26$—before the rate of increase falls to below 1% per unit $SM$ for values above 1.4. Beyond this threshold, each incremental addition of collector area yields a marginal improvement in solar fraction of less than one percentage point, indicating a regime of clearly diminishing returns.

To supply the 2.5 MW_th process demand exclusively from the fuel-oil boiler, the facility would consume 1,841.13 tonnes of fuel oil per year. Figure 8 presents the fuel saving fraction ($FSF$) across the parametric range. As $SM$ increases, the $FSF$ rises from approximately 20.8% to 27.9%, with a mean of 25.7%. The $FSF$ increases most rapidly at low $SM$ values—a relative change of 17.8% between the first two data points—before the rate of increase falls steadily to below 1.5% beyond $SM=1.4$. The SHIP system thus reduces fuel-oil consumption across all configurations, though the incremental savings per unit of added collector area diminish substantially beyond the intermediate $SM$ range.

The utilisation of the SHIP installation is assessed using the capacity factor ($CF$) defined in Equation (21). Figure 9 presents the results. Over the full parametric range, the $CF$ varies between 22.7% and 28.8%, with a mean of 25.4%. This variation of less than 10% across all $SM$ values indicates that the solar field and TES system contribute consistently to the process load, with limited sensitivity to solar field size.

The thermal energy storage utilisation is assessed using the cycling factor defined in Equation (22). Figure 10 shows that the peak number of effective TES cycles occurs at $SM=1.258$. At lower $SM$ values, the limited solar field output reduces the charging opportunity whilst the deployed TES volume is smaller; at higher $SM$ values, the TES volume grows substantially, reducing the cycle count despite greater solar input. The variability among cycling factors spans $+32.2\%$ above and $-10.7\%$ below the mean value, indicating that an intermediate $SM$ most effectively matches the usable solar surplus to the storage volume.

Figure 11 presents the annual average total energy efficiency (${\overline{\eta }}_{\mathrm{I},\mathrm{tot}}$) and the annual average total exergy efficiency (${\overline{\eta }}_{\mathrm{II},\mathrm{tot}}$), as defined in Equations (6) and (17). The energy efficiency consistently exceeds the exergy efficiency across all $SM$ values: ${\overline{\eta }}_{\mathrm{I},\mathrm{tot}}$ ranges from 73.9% to 58.2% (mean: 66.1%), whilst ${\overline{\eta }}_{\mathrm{II},\mathrm{tot}}$ ranges from 28.6% to 23.4% (mean: 26.1%). Both efficiencies decrease monotonically with increasing $SM$ as the larger solar field incurs greater thermal losses and generates additional irreversibilities. For comparison, the stand-alone fuel-oil boiler achieves an energy efficiency of 87.8% but an exergy efficiency of only 6.31%. Although the SHIP system exhibits a lower energy efficiency than the boiler alone, the exergy efficiency of even the largest configuration (23.4%) is nearly four times higher than that of the boiler (6.31%), reflecting the superior thermodynamic quality of solar heat relative to combustion heat for this medium-temperature application. These annual efficiency values are consistent with those reported for analogous medium-temperature SHIP applications in the food and beverage industry.

The annual performance results collectively indicate that an optimal $SM$ range exists between approximately 1.2 and 1.5. Within this range, the solar fraction and fuel saving fraction achieve more than 90% of their maximum potential increase, whilst the capacity factor and TES cycle count remain near their peak values. Beyond $SM=1.5$, marginal benefits diminish and both efficiency metrics continue to decline without commensurate gains in renewable energy contribution.

3.3. Economic and Environmental Assessment Results

The economic analysis is conducted for five tax shield scenarios corresponding to deduction fractions (d) of 0%, 25%, 50%, 75%, and 100% of the applicable corporate tax rate (30%), consistent with current Mexican fiscal policy incentivising renewable energy adoption in the industrial sector.

The payback period (Equation (35)) is computed for each deduction scenario across the full range of solar multiples. Figure 12 presents these results. The shortest payback period occurs at $SM=1.258$ for all deduction scenarios, ranging from 13.39 years with full (100%) deduction to 15.56 years without deduction. Both under-sized and over-sized configurations yield longer payback periods: at $SM=1.119$ with 100% deduction the period rises to 14.08 years, whilst at $SM=1.957$ with 100% deduction it reaches 19.71 years. The maximum payback period of 21.61 years, recorded at $SM=1.957$ with 0% deduction, remains within the estimated useful asset life of 25 years; however, the economic benefit in such an extreme case would be negligible.

Figure 13 presents the net present value (Equation (37)) for the same deduction scenarios. The highest $NPV$ is achieved at $SM=1.258$ across all deduction levels: 0.87 million USD with 100% deduction and 0.20 million USD without deduction. For $SM\ge 1.398$, the $NPV$ becomes negative under the zero-deduction scenario. With 100% deduction, a positive $NPV$ is maintained up to $SM=1.538$ (0.26 million USD), but the $NPV$ turns negative at $SM=1.678$ and above. These results indicate that the SHIP system meets minimum profitability thresholds only within a restricted range of solar multiples and only when fiscal incentives are applied.

The internal rate of return ($i^{*}$) is evaluated using Equation (38). Figure 14 summarises the results for each deduction scenario. The discount rate ($i=6.75\%$) serves as the viability benchmark. At the optimal $SM=1.258$, the $i^{*}$ exceeds the discount rate for all deduction levels, reaching 9.51% with 100% deduction. For $SM$ values above or below this optimum, the $i^{*}$ decreases. With 100% deduction, the $i^{*}$ remains above the discount rate until $SM=1.678$ (6.40%), but falls below at $SM=1.818$ (5.36%). Without any deduction, the $i^{*}$ exceeds the discount rate only for $SM=1.258$ (7.28%) and $SM=1.119$ (6.64%); all larger configurations yield $i^{*}$ values below 6.75%.

The levelised cost of heat (Equation (39)) is computed for each configuration and compared against the fuel-oil baseline in Figure 15. The baseline $LCoH$ is 89.78 USD/MWh_th. All SHIP configurations produce a lower $LCoH$ than the baseline, regardless of solar multiple or deduction scenario. The minimum $LCoH$ occurs at $SM=1.258$ with 100% deduction, at 75.19 USD/MWh_th—a reduction of 16.3% relative to the baseline. Without deduction, the $LCoH$ at the same $SM$ is 78.25 USD/MWh_th, still 12.9% below the baseline. The $LCoH$ increases modestly at larger $SM$ values but does not exceed the baseline within the analysed range, demonstrating that SHIP integration is cost-competitive across all assessed configurations.

Across all economic metrics, $SM=1.258$ consistently emerges as the optimal configuration, yielding the shortest payback period, the highest $NPV$, the lowest $LCoH$, and the highest $i^{*}$ for every deduction scenario considered.

Figure 16 presents the annual greenhouse gas emissions for the fuel-oil baseline and for each SHIP configuration. The baseline boiler emits 5,491,994 kg of CO₂, 213 kg of CH₄, and 42.6 kg of N₂O per year. SHIP integration achieves substantial reductions in all three species. For CO₂, the smallest reduction occurs at $SM=1.119$ (31.85%) and the largest at $SM=1.957$ (37.96%); the recommended configuration ($SM=1.258$) achieves a CO₂ reduction of 33.5%, consistent with the figure reported in the Abstract. The mean CO₂ reduction across all configurations is approximately 36.0%. Reductions in CH₄ and N₂O follow proportional trends. These results confirm a meaningful environmental benefit from solar thermal integration, irrespective of the fiscal regime applied.

The annual performance, economic, and environmental results collectively demonstrate that $SM=1.258$ represents the optimal configuration across all assessed criteria. These findings provide the basis for the holistic discussion of trade-offs between solar field size, thermodynamic performance, and financial viability presented in Section 4.

4. Discussion

The parametric analysis reveals a consistent pattern of diminishing returns across thermodynamic, operational, and economic metrics as the solar multiple increases beyond approximately 1.4. The following discussion interprets these findings within the context of fundamental thermodynamic principles, assesses the economic and environmental implications of the optimal design, and situates the results within the broader literature on solar heat for industrial processes.

The opposing behaviour of ${\eta }_{\mathrm{I}}$ and ${\eta }_{\mathrm{II}}$ observed in Figure 6b,c warrants specific thermodynamic interpretation. When the fuel-oil boiler operates alone at full load, it maintains a stable flame with low excess air and modest standby losses, yielding a high first-law efficiency. The introduction of solar heat forces the boiler to modulate to a lower firing rate, and part-load operation incurs several thermodynamic penalties: the burner requires a higher excess air fraction, fixed radiation and jacket losses represent a larger proportion of the reduced fuel input, and intermittent solar availability causes on–off cycling with associated purge and re-ignition losses. These effects collectively reduce the boiler’s fuel-to-heat conversion efficiency, causing the ratio in Equation (6) to fall even though absolute fuel consumption decreases. As Figure 6b illustrates, the instantaneous energy efficiency throughout the day is lower at higher solar multiples because the boiler operates for extended periods at very low firing rates, where its first-law performance is poorest.

The exergy efficiency responds differently. Equation (17) compares the exergy of the delivered process heat—which remains essentially unchanged—against the exergy of the fuel consumed. Solar radiation enters the system as a thermodynamic input that does not feature in the denominator of Equation (17); as the solar field supplies a growing share of the load, the fuel exergy input falls substantially whilst the numerator remains approximately constant. Consequently, ${\eta }_{\mathrm{II}}$ rises with increasing $SM$, as confirmed by Figure 6c. This improvement reflects more efficient utilisation of the purchased, high-quality exergy resource, even though the total entropy generation of the plant as a whole may increase.

The physical basis for these opposing trends lies in the redistribution of entropy generation between subsystems. Combustion of a high-exergy fuel to produce low-temperature process heat is inherently irreversible and causes substantial exergy destruction; when solar heat displaces part of the fuel, the irreversibilities associated with the fuel-oil boiler diminish significantly. The solar collector itself introduces its own source of irreversibility—absorbing high-exergy solar radiation and delivering a fluid at moderate temperature—yet this solar-driven irreversibility carries no direct operating cost. Consequently, the fuel-based exergy efficiency improves even if total plant entropy generation does not decrease. Conversely, ${\eta }_{\mathrm{I}}$ falls because the boiler’s part-load degradation outweighs the benefit of the solar contribution in a metric that relates only fuel input to useful heat output. These two metrics are therefore complementary: ${\eta }_{\mathrm{I}}$ penalises the operational inefficiency of the boiler at part load, whilst ${\eta }_{\mathrm{II}}$ rewards the displacement of high-exergy fuel by solar radiation. This analysis illustrates why the performance of a SHIP plant cannot be assessed adequately from a first-law perspective alone.

The diminishing returns observed in the solar fraction and fuel saving fraction are a direct consequence of the fixed process demand and limited storage duration. When the solar field is oversized beyond the point at which the process can absorb all generated heat during peak solar hours, the excess must be dissipated. According to Equations (18) and (19), the useful energy and exergy delivered to the process cannot exceed the total demand. As the field grows larger, an increasing fraction of the installed collector area operates under conditions where the generated heat finds no sink: early morning and late afternoon hours are already thermally marginal, and midday surpluses become disproportionately large. Consequently, the ratio of usable to collected energy falls, causing the solar fractions to plateau relative to investment. The $FSF$ follows the same logic: curtailed solar energy displaces no fuel, and once $SM$ reaches the level at which all usable insolation hours are captured, the auxiliary boiler’s annual consumption reaches a lower bound that cannot be further reduced by increasing the field size alone. The fixed storage duration (5 hours) limits how much surplus can be shifted temporally; beyond this buffer capacity, further field expansion yields no additional fuel displacement.

The thermal energy storage cycles peak at $SM=1.258$, confirming this configuration as the point of optimal matching between usable solar surplus and storage volume. At lower $SM$ values, the limited field output reduces the frequency and depth of charging; at higher $SM$ values, the TES volume grows more rapidly than the available surplus, reducing cycling intensity despite greater solar input. In contrast, the capacity factor shows little sensitivity to $SM$, ranging only from 22.7% to 28.8% across the entire parametric sweep. This near-invariance indicates that the solar field and TES contribute consistently to the process load irrespective of field size—a useful insight for preliminary design, as it suggests that modest over-sizing does not significantly impair utilisation intensity.

From an economic standpoint, $SM=1.258$ emerges as the clear optimum across all metrics. The non-linear economic response to field size arises from two opposing effects. Under-sizing fails to capture sufficient solar energy, leaving the facility reliant on expensive fuel oil and foregoing potential savings. Over-sizing increases $CAPE{X}_{\mathrm{SHIP}}$ without proportional fuel savings, because excess energy is curtailed and the boiler already operates at its minimum fuel consumption floor during periods of solar availability. Consequently, the marginal economic benefit of each additional collector unit diminishes rapidly beyond the optimum. Both under-sized ($SM=1.119$) and over-sized ($SM\ge 1.398$) configurations yield inferior economic indicators across all metrics.

Mexican fiscal policy plays a determinative role in extending the economically feasible design space. The 100% accelerated depreciation provision of the Mexican Income Tax Law (LISR) [50] substantially improves project viability at the optimal $SM$. With no deduction applied, the SHIP system delivers a positive $NPV$ only for $SM\le 1.258$, and the $i^{*}$ exceeds the discount rate for the same restricted range. With 100% deduction, a positive $NPV$ is maintained up to $SM=1.538$, and the $IRR$ remains above the discount rate until $SM=1.678$. At the optimum ($SM=1.258$), the 100% deduction reduces the payback period by approximately two years (from 15.56 to 13.39 years) and increases the $NPV$ by a factor of more than four (from 0.20 to 0.87 million USD) relative to the no-deduction case. Without this incentive, the project would remain marginally attractive only at the smallest $SM$ values, and would become financially unviable for $SM\ge 1.398$. These results confirm that accelerated depreciation substantially broadens the feasible design space and is a critical enabling condition for SHIP investment in the Mexican industrial context.

The greenhouse gas reductions achieved by the SHIP system range from 31.85% to 37.96% for CO₂ emissions, with proportional reductions in CH₄ and N₂O. In absolute terms, even the smallest configuration ($SM=1.119$) avoids approximately 1749 tonnes of CO₂ per year, whilst the largest ($SM=1.957$) avoids approximately 2085 tonnes per year. For a single industrial facility, these reductions are substantial. México’s Nationally Determined Contributions under the Paris Agreement [57] commit the country to a 22% reduction in greenhouse gas emissions by 2030 relative to a business-as-usual baseline, whilst the General Law on Climate Change mandates a 30% reduction in short-lived climate pollutants by 2030 [58]. Solar thermal integration in energy-intensive industries such as tequila production offers a direct and scalable pathway to contribute to these targets. Moreover, the facility already employs agave bagasse in a biomass boiler; the addition of solar thermal complements this existing renewable source, reduces dependence on imported fuel oil, and enhances the plant’s resilience to fossil fuel price volatility.

Our annual energy solar fraction (31.8–38.0%) lies within the range reported for continuous agro-industrial processes such as distillation and pasteurisation (typically 30–50%), though it is lower than the values of 50–60% achievable where longer thermal storage permits solar heat to be shifted across extended periods [59,60]. The average annual energy efficiency of the SHIP system (58–74%) compares favourably with published values for parabolic trough systems in industrial applications (typically 40–70%) [30,59,60]. The exergy efficiency (23–28%) is consistent with the range reported for medium-temperature solar thermal systems (20–35%) [38], though the relatively high process return temperature (48°C) in the present case reduces heat exchanger exergy efficiency compared with systems operating with lower return temperatures. The $LCoH$ of 75–80 USD/MWh_th is competitive with the 70–110 USD/MWh_th range cited in recent reviews for medium-temperature SHIP installations [30,60,61]. The lower bound of this published range typically applies to large-scale installations in high-irradiation regions, whilst the upper bound corresponds to smaller systems or less favourable solar resources. The present results, positioned at the lower end of this range, indicate that small-scale PTC systems can be cost-competitive in high-irradiation regions such as western México, particularly when supported by fiscal incentives.

Several limitations constrain the interpretation and generalisability of these results. First, the thermohydraulic model employs a constant soiling factor ($F_{\mathrm{soil}}=0.92$) and hourly-averaged meteorological data, which do not capture the effects of partial cloud cover, rapid transients, or seasonal soiling variability—factors that may be significant in the dust-prone environment of Jalisco. Second, the TES is modelled as a one-node tank, which represents a deliberate simplification relative to the thermocline design described in Section 2.2.3; this approximation neglects thermal stratification and may moderately overestimate storage performance. Third, the economic assessment excludes parasitic pumping losses and does not account for component degradation over the system’s operational lifetime. Fourth, perfect controllability of boiler modulation is assumed; in practice, part-load efficiency curves may introduce additional penalties that would further affect the energy efficiency results. These simplifications may collectively lead to a moderate overestimation of long-term economic performance, and should be addressed in future work.

Despite these limitations, the modular nature of the PT250 collector permits straightforward scaling to other heat loads and process configurations. The methodology developed here can be replicated for a different facility by adjusting the design-point DNI, process temperature requirements, and local fuel price. The optimal solar multiple is likely to shift with these parameters: a lower solar resource would favour a larger $SM$ to achieve an equivalent solar fraction, whilst a higher fuel price would improve the economic case for a larger $SM$ by increasing the marginal benefit of fuel displacement.

The central trade-off revealed by this study may be stated as follows: increasing the solar multiple raises the renewable energy share and the absolute greenhouse gas savings, but it degrades both energy and exergy efficiencies whilst diminishing economic returns. Beyond an optimal $SM$ of approximately 1.26, the marginal benefits of additional collector area become negligible under current operating and fiscal conditions. For industrial practitioners in high-irradiation, gas-constrained regions, the principal practical implication of these findings is that oversizing a solar field beyond a moderate multiple of approximately 1.3–1.5 is unlikely to be technically or economically justified. Optimal system design requires a joint assessment of thermodynamic performance, capital cost, and applicable fiscal policy. The replicable assessment framework developed here is intended to facilitate such analysis for other agro-industrial facilities seeking to accelerate the adoption of solar heat for industrial processes.

5. Conclusions

This study conducted a comprehensive techno-exergo-economic evaluation of a small-scale parabolic trough collector system integrated into a tequila production facility in Jalisco, México. A validated, non-iterative thermohydraulic model was developed and coupled with first-law and second-law analyses; a parametric sweep across seven solar multiple configurations was subsequently performed to identify the optimal system design and to characterise the trade-offs between thermodynamic performance, fuel displacement, and financial viability.

The analysis identifies $SM=1.258$ as the economic optimum across all assessed criteria. This configuration achieves an annual energy solar fraction of 32.0%, reduces CO₂ emissions by 33.5% relative to the fuel-oil baseline, and delivers a levelised cost of heat of 75.19 USD/MWh_th—16.3% below the baseline—together with a net present value of 0.87 million USD, an internal rate of return of 9.51%, and a payback period of 13.39 years under full accelerated depreciation. The annual exergy efficiency of the integrated system (23–28%) is nearly four times that of the stand-alone fuel-oil boiler (6.31%), confirming the superior thermodynamic quality of solar heat for medium-temperature process applications. A consistent pattern of diminishing returns is observed beyond $SM\approx 1.4$: beyond this threshold, additional collector area yields negligible improvements in solar fraction and fuel displacement whilst progressively degrading both energy and exergy efficiencies.

A notable thermodynamic finding of this study is the opposing response of the first-law and second-law efficiencies to increasing solar multiple: ${\overline{\eta }}_{\mathrm{I}}$ decreases owing to boiler part-load degradation, whilst ${\overline{\eta }}_{\mathrm{II}}$ improves as the displacement of high-exergy fuel reduces combustion irreversibilities. This divergence demonstrates that the performance of a hybrid solar–fossil system cannot be assessed adequately from a first-law perspective alone, and underscores the necessity of combined energy and exergy analyses in the evaluation of SHIP installations. The study further establishes that México’s 100% accelerated depreciation provision under the Income Tax Law (LISR) is a critical enabling condition: at the optimal configuration, this incentive reduces the payback period by approximately two years and increases the net present value by a factor of more than four relative to the no-deduction scenario, substantially broadening the economically feasible range of solar field sizes.

These findings contribute a replicable techno-exergo-economic framework for SHIP implementation in gas-constrained, high-irradiation industrial regions, complementing existing literature that has primarily addressed large-scale or purely theoretical installations. Unlike prior studies, this work integrates a systematic solar field oversizing analysis, quantifies the diminishing-returns threshold at $SM\approx 1.4$, and demonstrates the determinative role of fiscal policy in small-scale industrial SHIP applications. Several limitations constrain the scope of these results: the thermohydraulic model employs a constant soiling factor and hourly-averaged meteorological data; the thermal energy storage is represented as a single node—a deliberate simplification relative to the thermocline design that may moderately overestimate storage performance; and the economic assessment excludes parasitic pumping losses and component degradation over the operational lifetime. Collectively, these simplifications may lead to a moderate overestimation of long-term economic performance.

Future research should incorporate dynamic soiling models and stochastic weather simulations to better represent performance variability under real operating conditions. Investigating hybrid configurations that combine solar thermal with heat pump or biomass supplementation presents a promising avenue for improving both exergetic performance and economic outcomes. Extending the present framework to other agro-industrial sectors across Latin America could accelerate broader adoption of solar process heat and contribute meaningfully to regional decarbonisation targets. This study establishes that small-scale parabolic trough systems are technically and economically viable for medium-temperature industrial process heat in high-irradiation, fossil-fuel-dependent contexts, offering a scalable decarbonisation pathway consistent with México’s Nationally Determined Contributions under the Paris Agreement.