The concept of exergy was proposed in 1956 by Zorant Rant, and was developed between 1964 and 1967 by Rabek, Szargut & Petela, Baehr, Brodyanski, Fratscher, Elsner, Nitsch, Bergmann & Schmidt. Since the formalization of the exergy concept, the development of exergy analysis can be differentiated into three periods ^[2]. During the first period (1971-1984), which corresponds to "exergy in chemical processes", the calculation of exergetic efficiency was introduced to the process technical efficiency; the second period (1989-1995) was "economic optimization and thermodynamic methods"; and in the third period (1996-2016), "exergy of society", the equilibrium thermodynamics and exergy extended to form an interdisciplinary approach to wastewater treatment, biofuels production, and second generation biodiesel, which are important approximations to the economic, environmental and ecological dimensions, along with the framework of sustainable business development.

From the technical efficiency and productivity standpoint, the exergetic analysis measures the system's capacity to bring about a productive change, because it allows the reassignment of resources, costs and performance. The interdisciplinary relationship between exergy and economics was developed at the University of Zaragoza ^[3]. In the last twenty years, exergoeconomics has gone through different methodologies: Average Cost (AVCO), Exergy Cost Calculation (EXCO), Specific Exergy Cost (SPECO), Functional Analysis (TFA), and Functional Analysis Engineering (EPT) ^[4].

In ^[5], four sustainability elements were articulated to the industrial debate: social, economic, environmental, and technological. The most important relationship of flows reported in the literature specifies the schematic representation of the exergy flowing between the society and the environment ^[6]. Furthermore, Suresh et al. ^[7] identified that hidden costs imply impacts of the industrial production on the environment and society, which in monetary terms form the core of research projects, with the methodology called "4E". In a more integrating context, Khoshgoftar et al. ^[8] applied the new discipline exergoeconomic as a specific fusion between the exergy analysis and its endogenous economic valuation, developed through indicators.

A system is a complex entity formed by a set of elements (a machine, living beings or an economic system) that are its basic components, and by the relationships between them and their environment. The aggregation level provides a breakup of the process' total irreversibility into its components, while the efficiency (η) indicates the exergetic performance of the equipment where the irreversibilities are located.

The physical structure of a system, plus the definition of the productive purpose of each equipment constitute the productive structure of a thermal system, which is vital for the exergoeconomic analysis and supports the integrated measurement of rational efficiency. In the exergoeconomic conceptual framework, the cost of the product includes the cost of both the internal and the external (residues) irreversibilities.

According to their nature, three types of unwanted products are considered: derivative by-products (D), losses (L) and residues (R). The productive structure of a process has n components (plus the component 0 that corresponds to the environment M) interconnected by flows that characterize its exergy. An exergy flow from component I to component J is represented by . When it comes to specific exergy (J/kg), it is noted with . Each component consumes resources from others or from M, to produce (P) effects on other products or on M. Consequently,

The product (P) has two different destinies according to (3): a flow (PA) that could be a resource for another product, and another flow (PR) that is not used by any other component, or is part of the final product, so it is a residue (Fig. 1).

FIG

It builds the thermodynamic function that enables the evaluation of hidden costs, in terms of the resources exergy that the system requires ^[3].

The exergetic cost of a flow is E*; the exergetic unit cost of flow E is denoted as k*; consequently, the exergetic cost of a flow (component) is

On the other hand, the exergetic costs of resources, products and residues are denoted as follows: F* = k* F; p* = k* p; R* = k* R. In case of specific exergy,

Three propositions are considered to measure rational efficiency: 1) the exergetic cost of all flows depends on the costs of input resources, thus, the cost of input flows to the system will be equal to its exergy, its unitary exergetic cost is one; 2) all costs generated in the production process must be included in the final cost of the products, and the cost of the loss flows is null, that is, F* = SP*; and 3) if several products leave the same equipment, the training process will be the same and will have the same exergetic unitary cost.

The allocation of the exergetic cost is proportional to the exergy the flows contain, and the exergetic cost of the residue is added to the equipment where it originates. The exergoeconomic cost Π ($/kg) is the product of the unit cost C ($/J), multiplied by the flow of specific exergy in (J/kg). Therefore,

The exergetic cost of residues (R*) can be produced both in the equipment in which the flow is produced and along a chain of flows and equipment of the production process. The exergoeconomic rule states that the cost of the resources is allocated to the useful product.

Combining equations (1) and (7) result in equation (8):

Denominating R* as the cost of the resources that have been used to generate the flow of the residual PR, the equation (7) becomes equation (9):

Thus, the total cost of producing the generic component (P) is given by (10).

Figure 2 shows the residue formation chain. The mitigation/compensation (R) resource flow is the resource 0 described in equations (3-8), increasing the cost structure.

FIG. 2

The cost of the exergetic operation of the equipment (CEX) is the product of the resource exergetic unit cost and the flow of the irreversibilities, explained by (11).

The cost of the equipment operation (CO) is the product of the unit cost of the resource by the flow of the irreversibilities (12).

The conceptual operation of the refrigeration thermal machine is a thermal cycle of Heating, Ventilating, and Air Conditioning-Refrigeration (HVAC-R) (Fig. 3). The real cycle develops four ideal thermodynamic stages: two isothermal and two isentropic in León-GT. These stages result from the interaction of the four devices and the refrigerant fluid that extracts heat from the box (cooling chamber). In the ideal cycle, exergy is not destroyed ^[9].

FIG. 3

The exergy balance must be described in a set of equations and balances exergetics to calculate performance; this will allow to quantify the exergy destroyed in each device and the discharge line of the HVAC-R refrigeration cycle. The HVAC-R refrigeration cycle is added as a fictitious equipment to the exergy balance, because the greater anergy and irreversibility contribution are located in the compressor, due to the discharge level (AP/L) and the heat dissipation ^[10]. The balance sheets are as follows:

- Balance in compressor: between points 3 and 4 (Fig. 3).

Where T_{w, comp} is the temperature at the compression wall limit, and corresponds to the average obtained through the thermometer-infrared sensor (without contact).

- Balance in the condenser: between points 4' and 5

Where Q_H = Q₇ is the heat expelled to the environment, and T_H is the temperature T₄'. The heat balance in the condenser is Q₄' = Q₅ + Q₇.

- Balance in the discharge line of compressor: between points 4 and 4' (Fig. 3).

Where T_w,ld corresponds to the pipe wall. This equipment (unreal) is added to the system to better estimate the exergy destroyed in the cycle.

- Balance in the valve system: between points 5 and 6 (Fig.3).

- Balance in the evaporator: between points 6 and 3 (Fig. 3).

The destruction of exergy is

Where Q_L = Q₈ is the heat flux extracted from the chamber and transferred to the refrigerant, and T_L corresponds to the temperature T₈. The heat balance in the evaporator is Q₃ = Q₆ + Q₈

The sum of the destructions in equations (13-17) result in the total destruction.

The exergetic efficiency of the refrigeration cycle is

The destruction rate is the exergy consumption, due to the irreversibilities within the device or the difference between inputs and outputs in steady state.

The index of the process exergetic improvement (potential of improvement) is

The agro-industrial process in the slaughter plant of "Rastro de León" consists of self-propelled, hoisting, bleeding, flagellation, washing in a chiller, carcass processing (eviscerated, boned and quarting), classification, packing, and thermal conservation. The animal in rigor mortis was initially cooled off in a liquid cooler with chiller worm screw liquid that operates from 6-8 °C. The capacity of the trail for conservation consists of four transitional chambers of 130 m³ for internal irrigation; the load entered at 25 °C and then was thermally collided with sprinkler water (6-9 °C) to reach an average of 15 °C. The final product was frozen in a superflex camera, with a capacity of 900 m³; each camera can store up to 400-500 pigs of 150 kg or 150-200 cattle of 400 kg. The residence time in the chamber was 24 hours for pigs and 36 hours for cattle.

The refrigerant fluid used for the compression cycle was R404A. There were three ultra-freezing chambers, of 360 m³, 150 m³, 100 m³ and 50 m³. The thermal power given by the manufacturer was 15 kW, 11 kW, and 7.5 kW. The freezing temperature was -25 °C.

The productive structure was built by generating energy balances around the five equipment and the eight currents of the HVCA-R process in the cold chain (Fig. 4).

FIG. 4

We measured the changes in temperature in the freezing chambers for 12 continuous hours, and obtained average operating temperatures (TL) for the superflex camera (-4 °C), chamber freezing (-16 °C), and ultra-freezing (-25 °C) (Fig. 5).

FIG. 5

Based on Table 4 and equations (11-12), we calculated the amount of resources, products, residues, irreversibilities, exergetic efficiencies, operating exergetic costs, and operating exergoeconomic costs for each equipment and current (flow) of the refrigeration system determined in the production structure. In addition, we obtained the exergetic efficiency of each equipment and current by applying the balance equations (13-19) and the 2^nd law.

TABLE 1

The results of exergetic efficiency indicate that the highest rate of exergy destruction was located in the condenser equipment (Table 1). Consequentially, the partial inefficiencies of the five components were 11 %, 3.5 %, 18 %, 9 % and 11 %, respectively. The Grassman Engineering Diagram (Fig. 6) integrates the inefficiency analysis of each component and system, describing that the output variable, the exergy recovered or used, whose general efficiency is 69.7 % or a high total inefficiency of 30.3 %. Comparing thermal irreversibilities, the condenser presented the greatest irreversibility i or rate of exergy destruction (Fig. 7).

FIG. 6

FIG. 7

Table 2 shows a complementary tool to calculate exergetic by evaluating the exergetic operating costs and the exergoeconomic operating costs for equipment and currents (flows) of the refrigeration system. For the external electric motor, it is fulfilled that for the compressor, that for the condenser, that for the expansion valve, that and for the evaporator, that The exergoeconomics costs (Table 2) correspond to the tariffs of electric power in México (April 2017) that was $1.7724 mx/kW-h, and the cost allocation of the exergetics costs.

TABLE 2

Tables 3 shows the costs obtained for currents, and Table 4 shows the operating costs, where exergetic and exergoeconomics costs are

TABLE 3

TABLE 4

The measurement of exergoeconomic costs from the productive structure validates the calculations of rational efficiency. The highest operating costs are located in the condensation and expansion equipment, in points 4, 5 and 6 of the thermal process.