On the Negentropy Application in Thermoeconomics: A Fictitious or an Component Flow?*

José Santos1**, Marco Nascimento1, Electo Lora1 and Arnaldo Martínez Reyes2

1Excellence Group in Thermal Power and Distributed Generation 2Research Center in Refrigeration, Federal University of Itajubá, Itajubá-MG 37500-903, Brazil University of Oriente * Santiago de Cuba 90900, Cuba

Abstract

The introduction of the negentropy in thermoeconomics represented a great advance in the discipline, since this magnitude allows quantifying the condenser product in a steam cycle plant, which was not possible before because the condenser is a dissipative component, whose product cannot be expressed in terms of exergy. However, most authors have been applying the negentropy as a fictitious flow, joined up with the exergy flow. This paper aims at opening a discussion about the procedure for negentropy application in thermoeconomics, by showing that: (i) the original procedure leads to some inconsistencies; and (ii), a more recent approach takes all the negentropy advantages, without leading to inconsistencies, by applying the negentropy as a physical exergy component flow.

Keywords: Thermoeconomics, negentropy, fictitious flow, exergy component.

1. Introduction which seems that the condenser efficiency is greater than Thermoeconomics can be considered a new science 100%. Contradictorily, Lozano et al. (1993) used an which, by connecting Thermodynamics and Economics, equation named the condenser efficiency, consisting of the provides tools to solve problems in complex systems ratio between negentropy and enthalpy, which implicitly that can hardly or not be solved using conventional energy shows that the condenser product is the negentropy, but its analysis techniques based on the First Law of is the enthalpy. A doubt arises: what is the condenser Thermodynamics (mass and energy balance), as for instance fuel, the enthalpy or the exergy? a rational price assessment to the products of a plant based In fact, the negentropy and the enthalpy as the product on physical criteria (Erlach et al., 1999). and the fuel of the condenser (respectively) seem more Most analysts agree that exergy, instead of enthalpy consistent, because the condenser efficiency in an actual only, is the most adequate thermodynamic property to steam power cycle will always be less than 100%, and this associate with cost (originally an economic property) since efficiency would only be 100% in case it were possible to it contains information from the Second Law of transfer heat in the condenser at the same temperature, i.e., Thermodynamics and accounts for energy quality. An if the condensation temperature and the reference exergy analysis locates and quantifies the irreversibilities temperature were the same (in a reversible steam power (Valero et al., 2006). cycle). According to Torres et al. (1996), sometimes, under a The steam cycle analyzed by Lozano et al. (1993) and by thermoeconomic analysis point of view, it is necessary to Frangopoulos (1987) was a simple power plant, i.e., without consider a mass or an energy flow rate consisting of several heaters and deaerator. However, the negentropy concept was components, for example thermal, mechanical or chemical used by Uche et al. (2001) in order to define the productive exergy, or even to include fictitious flows (negentropy). structure of an actual and complex steam cycle cogeneration The negentropy flow was applied in thermoeconomics plant with heaters, deaerator, condensing steam turbine, and by Frangopoulos (1987), joined up with exergy flow. This steam extraction to feed a desalination plant. In this case, application represented a great advance in the discipline, there were other negentropy producer components, besides since it allowed one to quantify the condenser product in a the condenser. Because these other components (negentropy steam cycle plant, which was not possible before because producers) have other purposes in the plant, which can be the condenser is a dissipative component, whose product expressed in terms of exergy, auxiliary equations are needed cannot be expressed in terms of exergy. The same steam in order to attribute cost to the negentropy flows. Santos et cycle power plant was analyzed by Lozano et al. (1993), al. (2006) showed that, depending on the criteria used to also using the negentropy concept. The concept of formulate these auxiliary equations, the unit cost of power negentropy was also used by Lozano and Valero (1993) and will be overcharged, and therefore the value of the exergetic by von Spakovsky (1994) in order to define the productive unit cost of power contradicts the well-known cogeneration structure of a gas turbine cogeneration system. advantages. In the productive structure of a regenerative gas The productive structure defined by Lozano et al. (1993) turbine cogeneration system, these auxiliary equations are is basically the same used by Frangopoulos (1987), i.e., the also needed, because the regenerator (air preheater) and the condenser produces negentropy and consumes exergy. Thus, heat recovery steam generator produce both exergy and the product of the condenser is always greater than its fuel, negentropy (Lozano and Valero, 1993; Santos et al., 2008a).

Different thermoeconomic methodologies can provide together with enthalpy (H&S Model). The goal is to different cost values when they define different productive determine the exergetic and the monetary unit cost of the structures. Cost validation is a key issue in internal flows and the final products (electric net power and thermoeconomics which has not been properly solved yet. desalted water). In the final analysis, this paper shows the However, we consider that cost validation can be designed inconsistencies of the E&S Model, the limitations of the E using the physical behavior of the plant together with Model, and the advantages of the H&S Model. thermodynamics, because irreversibility is the physical magnitude generating the cost (Valero et al., 2006). Thus, in 2. Plant Description order to be consistent with the thermodynamics, in the The plant consists of an extraction-condensing steam productive structure of an irreversible cogeneration plant, turbine cogeneration system coupled with a MED-TVC defined by any thermoeconomic approach, the fuel of each (multiple-effect thermal vapor compression) desalination component must be greater than the product (the efficiency unit. At design point, the plant produces 4,075 kW of is less than 100%) and the exergetic unit cost of power and electric net power and 2,400 m3/d of desalted water. The heat must be less than their exergetic unit costs when they external fuel exergy consumption is 24,873 kW. are produced in a power-only plant and in a conventional boiler. 2.1 Physical Model According to Valero et al. (1995), the and the Figure 1 shows the physical structure of the analyzed products (productive structure) of a system must be defined dual-purpose power and desalination plant. For the energy based on the trajectories the flows describe in the (h,s) plane and mass balance, the cogeneration system was modeled when they for the specific purpose of the plant. Valero and simulated using the Thermoflex Software. et al. (2006) stated that, although the magnitudes applied by The plant can also operate in pure condensing mode (the most thermoeconomic approaches are exergy, negentropy desalination plant is off) producing 5,300 kW of net power and money, other magnitudes, like enthalpy and , and consuming the same amount of fuel (24,873 kW). can also be used. According to Alves and Nebra (2003), At 25 bar and 330oC, the boiler generates 8.597 kg/s of physical exergy has two components, the enthalpy (h – h0) steam, out of which 4.552 kg/s are completely expanded and the negentropy -T0.(s – s0). The aim of Lazzaretto and through the turbine down to the condenser pressure (0.056 Tsatsaronis (2006) was to propose a systematic and general bar) and 4.045 kg/s are extracted from the intermediate methodology for calculating efficiency and cost in thermal stage of the turbine (at 2 bar and 136oC). The extracted systems. By joining these ideas, Santos et al. (2006) steam is used to feed the desalination plant (3.194 kg/s), the proposed a new approach (H&S Model) that takes all the deaerator (0.657 kg/s) and the heater (0.193 kg/s). The known advantages of negentropy application and avoids the condenser is cooled by using sea water, which enters at a inconsistencies cited above. In the H&S Model, negentropy temperature of 25oC and leaves at 32oC. The quality of the is applied together with the enthalpy (instead of exergy), steam at the outlet of the low pressure steam turbine is i.e., negentropy is considered a physical exergy component. 92.9%. The temperature of the boiler feed water is 106oC. Aiming at opening a discussion about the procedures for The desalination unit has 8 effects and returns the negentropy application, this work compares three different condensate at 60.2oC (1.013 bar). The process steam passes thermoeconomic approaches by applying them to cost through the thermal compressor (TC), where it is mixed allocation in a dual-purpose power and desalination plant. with the steam generated in the last effect and this mixture The first approach defines the productive structure by using condenses in the first effect (E1), transferring heat to exergy flow only (E Model). The second uses negentropy as continue the distillation process in the remaining seven a fictitious flow, joined up with exergy (E&S Model). The effects and in the auxiliary condenser (E2:8-C). This third is the new approach proposed by Santos et al. (2006), desalination unit consumes 200 kW of electric power. which uses the negentropy as an exergy component flow,

Figure 1. Physical Structure of the Dual-Purpose Power and Desalination Plant.

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