**Birol Kılkı¸s**

Turkish Society of HVAC&R Engineers, Ankara 06680, Turkey; baskan@ttmd.org.tr

† Submitted to the SDEWES Special Issue of Energies based on the conference paper "An Exergy-Based Optimum Control Algorithm for Rational Utilization of Waste Heat from the Flue Gas of Coal-Fired Power Plants" in the Proceedings of the 13th SDEWES Conference as underlined in the Acknowledgements.

Received: 8 January 2019; Accepted: 12 February 2019; Published: 25 February 2019

**Abstract:** Waste heat that is available in the flue gas of power plant stacks is a potential source of useful thermal power. In reclaiming and utilizing this waste heat without compromising plant efficiency, stacks usually need to be equipped with forced-draught fans in order to compensate for the decrease in natural draught while stack gas is cooled. In addition, pumps are used to circulate the heat transfer fluid. All of these parasitic operations require electrical power. Electrical power has unit exergy of almost 1 W/W. On the contrary, the thermal power exergy that is claimed from the low-enthalpy flue gas has much lower unit exergy. Therefore, from an exergetic point of view, the additional electrical exergy that is required to drive pumps and fans must not exceed the thermal exergy claimed. Based on the First-Law of Thermodynamics, the net energy that is saved may be positive with an apparently high coefficient of performance; however, the same generally does not hold true for the Second-Law. This is a matter of determining the optimum amount of heat to be claimed and the most rational method of utilizing this heat for maximum net exergy gain from the process, under variable outdoor conditions and the plant operations. The four main methods were compared. These are (a) electricity generation by thermoelectric generators, electricity generation with an Organic-Rankine Cycle with (b) or without (c) a heat pump, and (d) the direct use of the thermal exergy that is gained in a district energy system. The comparison of these methods shows that exergy-rationality is the best for method (b). A new analytical optimization algorithm and the exergy-based optimum control strategy were developed, which determine the optimum pump flow rate of the heat recovery system and then calculate how much forced-draft fan power is required in the stack at dynamic operating conditions. Robust design metrics were established to maximize the net exergy gain, including an exergy-based coefficient of performance. Parametric studies indicate that the exergetic approach provides a better insight by showing that the amount of heat that can be optimally recovered is much different than the values given by classical economic and energy efficiency considerations. A case study was performed for method (d), which shows that, without any exergy rationality-based control algorithm and design method, the flue gas heat recovery may not be feasible in district energy systems or any other methods of utilization of the heat recovered. The study has implications in the field, since most of the waste heat recovery units in industrial applications, which are designed based on the First-Law of Thermodynamics, result in exergy loss instead of exergy gain, and are therefore responsible for more carbon dioxide emissions. These applications must be retrofitted with new exergy-based controllers for variable speed pumps and fans with optimally selected capacities.

**Keywords:** flue gas heat recovery; exergy; coefficient of performance; thermoelectric generator; organic rankine cycle; district energy systems

#### **1. Introduction**

About two-thirds of the energy of the input fuel in conventional thermal power plants is wasted in stacks and cooling towers. Although, from environmental and health points of view, thermal power plants should be located relatively far from cities, in many developing countries, especially old coal-fired thermal power plants with quite low thermal efficiencies (even less than 30%) are located in close proximity to metropolitan cities, such as in New Delhi. Air pollution is a significant concern in these areas, including the Badarpur coal power plant [1]. For example, the air-quality index rose to 1010 on 8 November 2017 [2]. While the only reason for pollution is not the coal-fired power plants, the waste heat from these plants may be utilized in district energy systems to partly offset air pollution by substituting the need for thermal energy, like the heating of buildings, if the reclaimed heat from the power plants that can be delivered to the built environment is not small [3,4]. In typical coal-fired power plants, the condenser is run through an open-loop water circuit while using river water. Although river water is returned to the river without much loss, the water temperature is substantially increased. Flue combustion gases are rejected through a stack. Other industries that have the potential for waste heat recovery in their stacks, in addition to thermal power plants, include the textile industry [5]. In other studies, flue gas heat recovery is found to be beneficial, especially in high-moisture coals that are based on the First-Law of Thermodynamics [6]. The same type of approach is applicable to studies regarding pressurized pulverized coal combustion [7].

Findings that lead to an indication of environmental and economic benefits are mostly based on energy savings. Researchers have also looked into exergy analyses, but almost all of the research was limited to the component basis in order to determine the major exergy destruction points and the overall exergy efficiency [8]. Kaushik et al. [9] determined that the exergy analyses were used to determine the components with the greatest exergy destruction, especially the boiler in coal-based thermal power plants. Heat recovery steam generators and flue gas exhausts to the stack were the focus of other analyses, e.g., [10]. In a typical coal-fired power plant, almost two-thirds of the energy of the coal that is consumed is wasted in the form of heat [11]. In Figure 1, the combined-cycle thermal power plant with a bottoming cycle, which is shown in inset (a) generates only power and all of the waste heat is rejected by some means to the environment, mostly by cooling towers to the atmosphere, which also wastes water. This conflicts with the environment, energy, and water nexus needs of today's world [12]. In inset (b) of Figure 1, however, a part of the heat in the flue gas is recovered in the stack. Condenser heat may also be reclaimed in this process, which reduces the need and the size of the cooling towers. However, if the flue gas is cooled too much in the heat recovery process, then the natural draught in the stack decreases to a point that a draught fan might be needed, which consumes electrical energy. The difference between the unit exergies of electric power and reclaimed thermal power is an important performance metric, which is often ignored. The reclaimed heat then may be utilized in a district heating loop, in addition to the power that is delivered to the customers.

According to EU/2004/8/EC [13], because heat is delivered to customers that are located outside in a metered and useful manner, such a plant qualifies as a cogeneration plant (CHP). According to the same Directive, this plant may qualify for a high-efficiency plant if such a plant results in at least 10% fuel savings in terms of Primary Energy Savings Ratio (*PES*). However, the district heating system needs a pumping station (PS) in the district in order to circulate the heating water in the district loop and a heat exchanger (HE) at the interface of the two closed thermal loops, namely D and P. To recover the heat from the flue gas (in loop P) a pumping system is required. Exergy is gained in the form of heat, but at the same time, exergy is required in the pumps, which is mostly driven by electric power. If the exergy gain in the heat recovery process is less than the exergy demand of the draught fan and circulating pumps, then this system will not contribute from an exergy rationality point of view. The amount of heat that may be recovered has an optimum value, which depends on the stack height (*H*). The stack height may be chosen to be higher during the design stage of the power plant instead of installing a fan to the stack. Yet, this requires embedded exergy of additional material and additional construction work for the stack. This requires a careful optimization for the

stack height. Stack height, *H,* is crucial both in the performance of the power plant and waste heat recovery. In thermal power plants, especially if coal is used, then *H* may be quite high in order to keep the pollutants elevated enough in the atmosphere. Therefore, *H* in meters is also a function of the pollutant (Sulfur) content. Today, in large thermal power plants, the stack height may reach up to 150 m. The minimum stack height is calculated by the following equation in the literature:

$$H \ge 4.33 \cdot (F \cdot S)^{0.3} \tag{1}$$

In Equation (1), 4.33 is a factor of the rule of thumb in order to assure sufficient natural draught, *PD* (Also see Equation (12) in Section 2.6.2), *F* is the coal consumption rate in kg per hour, and *S* is the Sulphur content in the percentages of the coal used. If, for example, a thermal power plant consumes 40 ton (40,000 kg) per hour of coal with 0.4% Sulphur content, then the necessary stack height will be 79 m.

**Figure 1.** Adaptation of a coal plant to a cogeneration system.

There are four main methods that are available in the literature for utilizing the thermal power exergy claimed along the stack height, once it is reclaimed from the flue gas. These methods, which appear in the literature, may be grouped in the following manner, as will be compared later in the manuscript:


In all of the above methods (a)–(d), the forced-draught fan in the stack and fluid circulation pumps are necessary for claiming the thermal power exergy, in addition to the power conversion equipment. If, for all models, the thermal energy claimed is fixed (100 kW in following methods) and the flue gas inlet temperature is the same for all models, then the forced-draught fan power demand is the same, but the circulation pump power demand changes, depending upon the equipment that is used in each model.

#### *Aims of the Research Work*

The main objective of this research is to first close the gap in the literature by a new model concerning the missing investigation of exergy rationality regarding the industrial waste heat utilization with parasitic losses. In so-doing, the study compares the different specific methods of utilizing the heat that is available in the flue gas of coal-fired thermal power plant stacks by developing exergy-based new metrics and a control algorithm in order to maximize the benefits of utilizing such waste heat in the industry and the built environment. Each method was analyzed in terms of the First and Second-Law efficiency, the coefficient of performance (*COP*), and exergy-based *COP* (*COPEX*) prior to the analysis of a case study for the selected methods.

#### **2. Materials and Methods**

Waste heat recovery from hot flue gas flowing across the stacks of power plants have a wide potential, but such systems must be exergetically investigated, designed, and controlled in order to achieve a net positive exergy gain and net-negative carbon dioxide (CO2) emissions responsibility in practice. The comparison of the methods (a) to (d) is provided in the following.

#### *2.1. Method (a): Power and Heat Generation with Thermoelectric Generators*

Oswaldo et al. [14] presented the design and development of a new solid-state TEG using thermoelectric modules for the experimental analysis of the technical viability for the uses of waste heat in industrial processes, like forging, hot rolling, industrial refrigeration systems, boilers, and ceramic kilns for a maximum temperature gradient of 1073 K. Their prototype test results that were based on the First-Law of Thermodynamics showed the feasibility of TEGs in reclaiming the industrial waste heat. However, the study did not directly consider the Second-Law and the parasitic exergy demand due to the use of a cooling circuit with electrically driven pump. Memon and Khawaja [15] have also developed a direct heat harvesting method while using a hot plate with heat-stove TEG for electrical performance testing. They acknowledged the presence of electric power demand for cooling the TEG units by forced-air circulation. Yet, their analysis did not address the exergy difference between the thermal exergy that was reclaimed and the electrical power exergy.

In this context, the use of an array of TEG modules facing the flue gas in the stack that are externally cooled by a hydronic circuit with a pump is depicted in Figure 2 for further analysis in this study. The heat that is recovered by the cooling circuit and the electric power that are generated by the TEG array are to be connected to external loads. The arrangement in Figure 2 comprises method (a).

According to Figure 2, 8 kW of electrical power is generated by the TEG array that has a First-Law efficiency of 0.08. This amount is, at the same time, the amount of electrical power exergy because the unit exergy of electricity is virtually 1 kW/1 kW. Heat from the back side of TEG array is reclaimed by a hydronic circuit and heat exchangers, with an efficiency of 0.55 by using pump(s), which demand 5 kW of electric power (including stack fan power demand), while 100 kW of thermal power at 700 K drives the system. An additional draught fan compensates for the natural draft loss due to the cooling of the flue gas. The Second-Law efficiency is 0.11, while the First-Law efficiency is 0.60 and the *COP* is 12.6. Such a relatively high *COP* leads to the impression that such a system is beneficial and techno-economically attractive. Yet, if *COP* is re-defined in terms of exergy (Equation (2)), namely *COPEX*, then the exergo-environmental properties of the model changes substantially.

$$\text{COPEX} = \frac{\text{Net Energy Gain}}{\text{Total Energy Input}} = \frac{8 \text{ kW} + 3.4 \text{ kW} - 5 \text{ kW}}{58 \text{ kW} + 5 \text{ kW}} = 0.10 \tag{2}$$

#### *2.2. Method (b): Power Generation with Organic Rankine Cycle Turbines*

Another method that is investigated in the literature is driving an ORC turbine after reclaiming the heat of the flue gas and transporting it to the external of the stack. A low-temperature external load through a hydronic circuit that is driven by a pump cools the ORC. The electric power that is generated by ORC turbines depends upon the source temperature while the First-Law efficiency is around 10%. Lecompte et al. [16] applied ORC technology to an electric arc furnace with a First-Law efficiency of about 13%. This efficiency is higher when compared to other lower source temperature applications. Another study investigated the technical aspects of modular ORC systems over a broad range of heat source temperatures with different working fluids [17]. A payback period that was slightly less than five years was predicted at a source temperature of around 700 K based on the First-Law and economic benefits of ORC systems. The principle of this method (b), as modeled in this study, is extended in Figure 3.

**Figure 3.** Exergy claim by Organic-Rankine cycle (ORC) and its waste heat.

#### *2.3. Method (c): Power Generation with Organic Rankine Cycle and then Converting to Heat by a Heat Pump*

By converting electric power to thermal power with a COP greater than 1, a heat pump may be tailored to the ORC, depending upon the dominant load on the demand side. This method (c) is shown in Figure 4. Re-converting claimed power exergy to thermal power exergy even with a COP, of 4.0 in this case, is not rational. For a break-even condition, the COP of the heat pump needs to be 1/(1 − 300 K/320 K) = 16, which is practically not possible in the field with today's technology. This indicates that several heat recovery systems may not be exergetically rational and practical while they are responsible for more CO2 emissions than saved. This gap is also evident in the study of He et al. [18], in which the feasibility of reclaiming additional electrical power from the waste heat of a fuel cell by an ORC system coupled with a heat pump was investigated, thus establishing a

bottoming cycle. This study claimed that, at an optimum operating temperature, the results are favorable according to the First-Law. Among the few studies that involved the exergy concept in the evaluation of medium-temperature heat recovery from industrial gases with ORC technology and CO2 transcritical cycles, Ayachi et al. [19] have presented their pinch analysis for source temperatures between 438 K and 420 K. However, the case was only taken in a pinch problem domain.

**Figure 4.** Exergy claim by ORC and it's waste heat where ORC power is then used in a Ground-source Heat Pump (GSHP).

#### *2.4. Method (d): Direct use of the Thermal Exergy in ae District Energy System*

Especially when a district energy system is close-by, waste heat from power plants gains additional importance. One method is to recover heat directly from the flue gas. Based on the First-Law, Xu et al. [20] had considered reclaiming heat from the ventilating air methane in a hot-air power generator. The authors had concluded that the overall system efficiency for a decarbonizing process with a hot air power generator reached 27.1%, which is better than the standalone reference systems. The arrangement of tube banks in the stack needs careful investigation. A horizontal tube or an inclined tube bank occupying the whole cross-sectional area of the stack may be effective but reduces the natural draft. Tube banks that are attached to the stack walls, which leave a large portion of the cross section free for the gas flow, may be preferable, but a careful case-by-case analysis needs to be conducted. In this aspect only, Erguvan and MacPhee [21] had performed energy and exergy analyses for several tube bank configurations in waste heat recovery applications. The method of direct heat recovery from the flue gas is depicted in Figure 5 with the relevant exergy formulations.

**Figure 5.** Thermal exergy recovery.

#### *2.5. The Necessity for an Exergy-Based Model*

There is a necessity for developing an exergy-based model for a thorough comparison of methods (a) to (d). In addition, the heat that is optimally recovered at the stack(s) of a large power plant, *Qf*, may be utilized in a district energy system. In this case, the distance between the power plant and the district, *L*, which is subject to the condition *L* < *Lmax,* where *Lmax* is the maximum distance, should be exergetically rational as well as the exergy that is demanded by the pumping stations, *EXPS*. Exergy rationality for both of the loops is defined in Equations (3) and (4).

$$Q\_D \cdot \left(1 - \frac{T\_{Do}}{T\_{Di}}\right) > E\_{XPS} \tag{Conditional 1} \tag{3}$$

$$Q\_f \cdot \left(1 - \frac{T\_{fo}}{T\_{fi}}\right) > \left(E\_{XCP} + E\_{XF}\right) \tag{Condition 2}$$

#### *2.6. Characterization of the District Energy Model*

Figure 6 shows the new model, which enables the user to analyze several design parameters and environmental conditions, along with plant performance variables that are related to the stack. Performance constants, namely (*c*) and (*a*) regarding the exergy demand, *EXCP* of the circulation pump mainly depend upon the circuit length, pump type, and piping material and size. In the case study to be shown later in this paper, these terms are assumed to be 15 and 0.3, respectively. Figure 7 then shows the exergy flow bar for a typical heat recovery process, where the average temperature of the flue gas is 700 K. The heat recovery loop (P loop) operates between 313 K and 363 K, the average outdoor temperature in the summer *To* (also, the reference temperature, *Tref*), which renders a critical draft condition as compared to the winter at 293 K. Subsequently, one of the metrics of the Rational Exergy Management Model (REMM) as the REMM Efficiency, *ψ<sup>R</sup>* [22], as provided in Equation (5), is 0.24 [23]. This is a similar value with a solar water heater system, since the major unit exergy destruction is prior to the heat recovery, and only a low-enthalpy heat is recovered without power generation upstream, like ORC.

$$\psi\_R = \frac{\varepsilon\_{dem}}{\varepsilon\_{sup}} = \frac{\left(1 - \frac{313}{363}\right)}{\left(1 - \frac{293}{700}\right)} = 0.24\tag{5}$$

**Figure 6.** Flue gas heat recovery and district energy system model.

Although the waste heat recovery might seem to be economically beneficial and environmentally useful, if the exergy of the electrical energy that is used for the draught fan, along with pumping and driving other ancillary devices, is higher than the recovered lower exergy-heat, then the system will not contribute to the economy and the environment at large.

**Figure 7.** Exergy flow bar for the heat recovery of the flue gas in the stack.

2.6.1. Circuit P Loop: Exergy-based Optimum Heat Recovery Drive Unit for Industrial Stacks

This condition may be expressed by the objective function in Equation (6), which represents the net exergy gain in this circuit. The net exergy gain, *EXNET* must be maximized by minimizing *EXF* and *EXCP* while exergy of *Exf* is claimed from the flue gas. If the district energy system is integrated, then *ExD* replaces *Exf* and *EXPS* is introduced (Equation (7)). In certain cases, the reduction of the size of the cooling tower due to the conversion of waste heat rejection to useful heat in the stack may be substantial. Subsequently, an exergy saving term that is associated with the reduction of ancillary power demand of the cooling towers may be added to the right-hand side of the other original formulations for this research work, as given below (Equations (7)–(11)). In Equation (10), the specific heat needs to be calculated at the average fluid temperature. In Equation (11), the coefficient *c* and the exponent *a* are approximated coefficients for the pump characteristics.

$$E\_{XNET} = E\_{xf} - E\_{XF} - E\_{XCP} \tag{\text{Maximize}} \tag{6}$$

$$E\_{XNET} = E\_{xD} - E\_{XF} - E\_{XCP} - E\_{XPS} \tag{7}$$

$$E\_{Xf} = Q\_f \cdot \varepsilon\_f \tag{8}$$

$$\varepsilon\_f = \left(1 - \frac{T\_{fi}}{T\_{fo}}\right) \tag{9}$$

$$Q\_f = \dot{m}\_f \cdot \nabla\_{pf} \cdot \rho\_f \cdot \left(T\_{fo} - T\_{fi}\right) \tag{10}$$

$$E\_{XCP} = c \cdot \dot{m}\_f{}^a \times (1) / \eta\_{cp} = E\_{CP} \tag{11}$$
