2.6.2. Natural Draught Pressure and *EXF*

Since heat is drawn from the hot flue gas in the stack, the flue gas cools down and the average flue gas temperature in the stack *Tg* reduces, which reduces the natural draught pressure (*PD*). Equation (12) shows the relationship between *Tg* and *PD* [24]. According to this equation, draught decreases with a decrease in the average flue gas temperature. At a given time *t*, the change in the draught pressure, Δ*PD*, only depends on the amount of decrease in Δ*Tg* if some heat is recovered from the flue gas, as given in Equation (14).

$$P\_D = \mathbb{C} \cdot P\_{\text{atm}} \cdot H \cdot \left(\frac{1}{T\_o} - \frac{1}{T\_\%}\right) = \mathbb{C}' \cdot \left(\frac{1}{T\_o} - \frac{1}{T\_\%}\right) \tag{kPa} \tag{12}$$

where,

$$T\_{\mathcal{S}} \sim \frac{T\_{\mathcal{S}^{in}} + T\_{\mathcal{S}^o}}{2} \tag{13}$$

$$
\Delta P\_D = \left(\frac{C'}{T\_\%^2}\right) \cdot \Delta T\_\% \tag{kPa}
$$

where,

*<sup>C</sup>* A constant for coal-fired plant stacks, 0.0342 K·m−<sup>1</sup>

*C C*·*Patm*·*H*

Atmospheric pressure at the given elevation at the


In order to resume the original natural draught, the installation of a new hot-gas type industrial forced-draught fan in the stack or oversizing, an existing one will be necessary. For new power plants with flue gas heat recovery, the stack height may be selected higher in order to avoid a fan, but in this case, the embodiment recovery of energy and exergy of the extra stack material and construction must be considered against energy and exergy savings by the associated heat recovery. The motors of these fans may operate on on-site power in a thermal power plant. Especially, if the power plant is a combined-cycle plant, the average power generation efficiency is about 0.52 in Europe [13]. For other industrial plants, like in the textile industry, electricity is mostly received from the grid. The average efficiency of grid-feeding power plants, especially in developing countries, is about 30% or even less. This efficiency, when coupled with transmission and transformation losses, makes the case even worse based on the total CO2 emissions responsibility in a broader perspective if the fuel mix mainly consists of fossil fuels [25]. This additional CO2 emissions responsibility in terms of the equivalent useful heat that is to be lost in a typical thermal power plant also needs to be considered in the calculations if the grid power is used in the heat recovery system. The draught fan simultaneously needs to maintain the original . *mg*, which is given by Equation (15) [24].

$$
\dot{m}\_{\mathcal{S}} = 0.65 \cdot \overline{A}\_{\mathcal{S}} \sqrt{2gH \cdot \left(1 - \left[\frac{T\_o}{T\_{\mathcal{S}}}\right]\right)}\tag{15}
\\
\tag{15}
$$

Equation (15) takes the molar mass of the flue gas and the outside air as equal, and the frictional resistance and heat losses in the stack walls and any heat exchanger inside the stack to be negligible. Here, *Ag* is the average cross-sectional area of the stack, in the unit of m2, along with stack height (*H*). On the other hand, if *Tg* decreases, then . *mg* also decreases:

$$
\Delta \dot{m}\_{\mathcal{S}} = \frac{0.65 \cdot \overline{A\_{\mathcal{S}}}}{2\sqrt{2gH \cdot \left(1 - \frac{T\_{\theta}}{T\_{\mathcal{S}}}\right)}} \cdot \left(\frac{T\_{o}}{T\_{\mathcal{S}}^{2}}\right) \cdot \Delta T\_{\mathcal{S}} \tag{16}
$$

Therefore, while the draught fan needs to compensate for both the decreases in the gas flow rate and the decrease in the draught pressure, the required fan power, *EF* (almost equal to fan exergy demand), at a given electric motor and fan efficiency of *ηFM* will consist of the product of Δ*PD* and Δ . *mg*, as given in Equation (17).

$$E\_F = E\_{XF} = \frac{\Delta P\_D \cdot \Delta \dot{m}\_{\mathcal{g}}}{\eta\_{FM}} \tag{15W} \tag{17}$$

#### *2.7. Rating Metrics*

Four metrics were identified for rating the performance of waste heat recovery from the flue gas. These metrics may be related to CO2 emissions responsibility, energy efficiency, and exergy efficiency.

#### 2.7.1. Performance Coefficients

The metrics that are related to performance coefficients are given in Equations (18)–(20). In Equation (18), the exergy-based coefficient of performance (*COPEX*) is a product of the *COP* and the unit exergy gain from waste heat recovery, Δ*εf*. Usually, the unit exergy gain, namely (1 − *Tfi*/*Tfo*), is small. Therefore, *COPEX* will be far less than one, if a proper design recovery system is installed and the fluid flow rate is not dynamically controlled with an exergy-based control algorithm and a frequency-controlled electric motor for the circulation pump. This means that the heat recovery system is not rational. For example, if these temperatures are 300 K and 360 K, respectively, then the unit exergy of the fluid at the supply point, Δ*ε<sup>f</sup>* is only 0.167 W/W. From Equation (18), the traditional *COP* value of the recovery system must be greater than 6 in order to satisfy the condition of *COPEX* approaching one. This condition imposes strong design constraints on *EXF* and *EXCP*. This is an early indication regarding the importance and relevance of the Second-Law of Thermodynamics before attempting an economic and environmental analysis about waste heat recovery from the flue gas. A similar discussion of the author outside the context of waste heat recovery from flue gas is also valid for ground-source heat pumps [26]. In this case the heat pump only consumes electrical energy and provides thermal energy. Then:

$$\text{COPEX} = \text{COP} \cdot \Delta \varepsilon\_f = \text{COP} \times \left(1 - \frac{T\_{fi}}{T\_{fo}}\right) \tag{COPEX} \to 1\tag{18}$$

$$COPEX = \frac{E\_{XNET}}{E\_{XF} + E\_{XCP}} \tag{19}$$

$$\text{COP} = \frac{Q}{E\_{XF} + E\_{XCP}} \tag{\text{COP} > 1} \tag{20}$$

#### 2.7.2. Fuel Savings

The exergy-based Primary Energy Savings Ratio, *PESR,* in percentage is based on 1 W of power generation. The original *PES* term in EU/2004/8/EC [13] was modified by the REMM model [25,27]. In Equation (21), *CHPEη* is a known value (power generation efficiency) for the given plant at design conditions [27]. The term 0.73 corresponds to (1 − *ψRref*), which is related to the reference value of (1 − 0.27) for the on-site CHP applications. The values 0.52 and 0.80 are the reference efficiencies for separate power and heat generation, respectively [13], based on 1 W of power generation.

$$PES\_R = \left( 1 - \frac{1}{\left( \left[ \text{CHPE} \eta \cdot \left( \frac{1}{0.52} + \frac{Q\_f}{0.80} \right) \right] \cdot \frac{0.73}{\left( 1 - \psi\_R \right)} \right)} \right) \times 100 \tag{21}$$

#### 2.7.3. Carbon Dioxide Emissions Replacement

The third metric is related to the CO2 emission replacement rate. The CO2 emissions savings rate (kg CO2/s) that is attributable to net exergy recovery, *EXNET,* from the flue gas for a pulverized coal power plant with coal properties of adiabatic flame temperature of 2850 K and 30,000 kJ/kg lower heating value (LHV) with no condensation in the stack and the wet coal input, as well as the CO2 content of 3.6 kg CO2/kg coal, was derived, which is given in Equation (22) [28,29]:

$$
\dot{C}O\_2 = E\_{XNET} \times 1.7 \cdot 10^{-4} \tag{22}
$$

### 2.7.4. Thermal Efficiencies

As the fourth metric, the First-Law and Second-Law efficiencies, *η<sup>I</sup>* and *ηII,* may be monitored for the rating and evaluation of the system, as given in Equations (23) and (24).

$$\eta\_I = \frac{Q\_f}{Q\_\mathcal{J} + E\_{CP}} \tag{23}$$

$$\eta\_{II} = \frac{E\_{Xf} - E\_{XCP}}{E\_{Xg}} \tag{24}$$

#### **3. Results**

Table 1 compares methods (a) to (d) with source exergy at 58 kW prior to the selection of a method. As observed from Table 1, method (d) has the highest thermal efficiency (*ηI*) and the second highest *COP*, *ηII* and *COPEX*. Other methods have greater inconsistencies. Method (d) delivers heat at 340 K in this example, which is sufficiently high for district energy systems and it may also be used in absorption/adsorption cooling equipment. Provided that the distance between the plant and the district is not too far, method (d) is selected as a feasible option for practical applications. In the case study, a coal-based thermal power plant is going to be retrofitted with a flue gas heat recovery system. The design inputs and conditions are given in Table 2. The equations that are given in the method may be expressed in terms of the fluid (water) flow rate, . *mf* . Thus, by introducing the flow rate . *mf* , in all terms, then taking a derivative, and equating it to zero to find the optimum flow rate. Equation (5) may be maximized. This will be a time-dependent solution in terms of all time-dependent variables that either depend on atmospheric conditions and part-load conditions, like *Tg*, . *mg*, *To*, *Tfo*, *Tfi*, and variables that are related to the D Loop, as identified in previous Figure 6.

**Table 1.** Comparison of the four methods with source exergy at 58 kW.


**Table 2.** Design data for the case study.



**Table 2.** *Cont.*

#### *3.1. Results of the Analysis of the P Loop-Case Sdudy*

In this study, a step-by-step solution is introduced, where the flow rate is changed incrementally to find the optimum point, which is subjected to the condition that the flue gas outlet temperature is not lower than the condensation temperature, *Tgc*, which is often taken at 420 K for coal combustion and low Sulfur content fuel oils [30]. Reducing the temperature of the flue gas in the stack may be associated with other adverse phenomena. It is very important that the minimum flue gas temperature is maintained and not violated in order to prevent the acid dew point from being reached. Figure 8 shows the results for the given initial and operating conditions. According to Figure 8 with a flue gas temperature of 600 K, there is an optimum fluid flow rate, which maximizes the net exergy gain from the flue gas. However, for certain cases of design and operational variables, an optimum fluid flow rate may not be found. In such a case, the solution approaches either the lowest flow rate or the highest flow rate, within an economical range. The variation of the maximum *ENET* points for different outdoor-air temperatures when the fluid flow rate is fixed at each optimum point is shown in Figure 9. According to Figure 9, *ENET* decreases with an increase in the outdoor-air temperature. If the inlet temperature of the flue gas is 500 K instead of 600 K, then *COPEX* decreases below the threshold value of one and the optimum solution for the fluid flow rate approaches the lower bound, which is shown in Figure 10.

**Figure 8.** Variation of exergy-based coefficient of performance (*COPEX*) with a fluid flow rate with flue gas temperature 600 K. Note: Here Flue gas input exergy is ignored in calculating *COPEX*.

**Figure 9.** Variation of *COPEX* with outdoor air temperature, *To*. Note: Here flue gas input exergy is included.

**Figure 10.** Variation of COPEX with a fluid flow rate with flue gas temperature 500 K.

According to Figure 10, the maximum *COPEX* that is possible is just one at the lowest flow rate, which means that the exergy that is gained by the circulating fluid is equaled to the total exergy demand of the parasitic equipment, such as the stack fan and the circulating pump. In other words, the net exergy gain is zero. These results show that the performance is highly sensitive to the flue gas inlet temperature, outdoor temperature, and the flow rate of the fluid in the P loop. Therefore, the circulation pump must be dynamically and digitally controlled to maintain *COPEX* as greater than one. There may be cases when the heat recovery system needs to be stopped. The solution starts with a minimum fluid flow rate and the temperature decrease in the flue gas in the stack is calculated first (see Equation (25)). Subsequently, the other performance variables are calculated, as provided in Table 3.

$$T\_{\mathcal{S}^0} = T\_{\mathcal{S}^i} - \left(\frac{\dot{m}\_f}{\dot{m}\_\mathcal{\mathcal{S}}}\right) \cdot \left(\frac{\mathbb{C}\_{pf}}{\mathbb{C}\_{P\mathcal{S}}}\right) \left(\frac{\rho\_f}{\rho\_\mathcal{\mathcal{S}}}\right) \cdot \left(T\_{fo} - T\_{fi}\right) \tag{25}$$

**Table 3.** Calculations for the case study. Note: Here Flue gas input exergy is ignored in calculating *COPEX*.


#### *3.2. Implications of the Analysis for the D Loop*

The heat recovered at the stack(s) of a large power plant, *Qf* may be utilized in a district energy system. Such a D Loop, as identified in the previous Figure 6, should also consider the distance between the power plant and the district *L*, which is subject to the condition *L* ≤ *Lmax* and the exergy that is demanded by the pumping stations, *EXPS*. Exergy rationality for this condition is defined in Equation (26):

$$Q\_D \cdot \left(1 - \frac{T\_{Dout}}{T\_{Din}}\right) > E\_{XPS} \tag{26}$$

where,

$$Q\_D = Q\_f \cdot \eta\_{HED} \tag{27}$$

The exergy demand of power stations in the district circuit is a function of *QD* for a given Δ*T* in the circuit, which is typically 20 K at the design conditions in district heating. The constant term *ao* in Equation (29) is an empirical value, which is 0.6 km. In Equation (30), n depends upon the exergy of district heating supply in terms of *Tdo*. The value of *Tref* is 283.15 K (the average ground temperature in winter). 333.15 K represents a traditional district heating supply fluid temperature of 60 ◦C.

$$
\Delta T = \left( T\_{\text{Din}} - T\_{\text{Do}} \right) \tag{28}
$$

$$L \le L\_{\text{max}} = a\_o + \left(\frac{Q\_D}{1000}\right)^n \times \left(\frac{\Delta T}{20}\right)^{1.3} \qquad \left(Q\_D > 1000 \text{ kW\cdot h}, \Delta T \le 30 \, ^\circ \text{C}\right) \tag{29}$$

$$m = 0.6 \times \left(\frac{\left(1 - \frac{T\_{ref}}{T\_{Dv}}\right)}{\left(1 - \frac{T\_{ref}}{333.15}\right)}\right)^{(1/3)}\tag{30}$$

$$T\_{\rm Do} = T\_{fo} - \Delta T\_{HED} \tag{31}$$

$$T\_{fo} = T\_{\wp v} - \Delta T\_{HEG} \tag{32}$$

The typical temperature drop in the heat exchangers in a district energy system is targeted for 2.5 K each. Therefore:

$$T\_{Do} \sim T\_{\\$^0} - \text{5 K} \tag{33}$$

$$dE\_{XPS} = \frac{\Delta E\_{XPS}}{\Delta L} \tag{34}$$

$$L\_{\text{max}} < \frac{Q\_D \cdot \left(1 - \frac{T\_{\text{Di}}}{T\_{\text{Dv}}}\right)}{2 \cdot dE\_{\text{XPS}}} \tag{35}$$

#### *3.3. Development of the Control Unit to Maximize the Exergy Gain*

The maximization of the net exergy gain and *COPEX* is related to the flow rate of the fluid through the circulating pump in the P loop first. All of the relevant inputs are gathered every five minutes and then processed for the optimum flow rate for this given time increment. The processed information for the optimum flow rate is fed to the driver of the variable-speed pump. The optimum pump speed is then checked for condensation of the flue gas in the stack (*Tgo* > *Tgc*) and the pump capacity. The flue gas temperature entering the stack fan is also checked against the temperature resistance of the fan. Efficiency changes in the heat exchangers are purposefully ignored. Figure 11 shows a simple flowchart of the process. If the thermal demand on the district side is lower than the optimum heat output at the same time interval, and then the surplus heat is stored in a thermal storage system (TES) before the necessary amount is sent to the district through a heat exchanger.

**Figure 11.** Data processing and control of the pump speed.

The data that is collected along with pollution variables, like the CO2 concentration and the sulfur content, is quite crucial in monitoring the environmental impact of all industrial installations on an instantaneous basis. Thermal power plants are not an exception as a major player in global warming. Therefore, such performance and control data that is available in thermal power plants may be incorporated into a central Internet-based control center and the data re-processed for a national or even global scale to optimize not all the thermal power plants, but also all of the industrial installations. This will then complete the exergy economy loop, which is very important for decoupling sustainable growth from CO2 emissions [31].

#### **4. Conclusions**

Waste heat recovery from the flue gas in thermal power plant stacks are important from environmental and economical points of view, especially in developing countries, where the plant efficiencies are low and mostly in relatively close vicinity of urban areas. This provides the opportunity for replacing some CO2 emissions in the urban area if the recovered heat is distributed in the form of a district heating system. However, there are certain challenges, one of the most important of which is that the design of such recovery systems need to be based on the Second-Law of Thermodynamics due to the fact that the unit exergy of the heat that is claimed is much lower than the unit exergy of electricity that is used to drive the related ancillaries and installed draught fan to the stack. In this respect, the minimum COP of the heat recovery system, on average, has to be 6.0. This poses serious challenges for the design of the gas-to-water type of heat exchangers. This study has shown that, not only in a poor design, but also at any time during the operation, the net exergy gain may be negative (*COPEX* < 1), because the exergetic performance is very sensitive to operational and climatological conditions. The case study has further exemplified this possibility, such that COPEX may become less than one any time, even with incremental variations in the dynamic conditions. In order to avoid this risk, a complete analytical model was presented, which enables the analysis of such a system in terms of the optimum water flow rate in the closed heat reclaiming circuit for the maximum exergetic coefficient of performance at given outdoor and operating conditions of the power plant.

In plant retrofits for this purpose, however, the stack should not be replaced with a new one with a new heat exchanger inside. Instead, the original stack must be retrofitted with minimal work. In fact, this is the second challenge. In order to avoid this challenge on a large-scale plant, the heat recovery unit may be a separate unit before the stack. However, this will disturb the original design performance of the stack and a larger fan might be needed in addition to other ancillaries that are related to the separate heat recovery unit. A cassette type heat exchanger or heat exchangers may be inserted at different levels of the stack with minimum invasion and minimum disturbance to the

flow [32,33]. There are other studies in the literature, which bring the heat source to condensation temperature and then remove the moisture and recover more heat [34]. However, a similar approach will increase the exergy demand of the fan system to discharge the flue gas, since there will be almost no natural draught left in the remaining voyage of the flue gas. Under all of these considerations, the model that is developed in this study addresses multiple challenges and promises optimal heat recovery controls. Case study and performance calculations regarding four methods showed that the definition of *COP* is limited to economic evaluations while the "ambient, free" resources like air, sea water, and ground are ignored. In fact, especially when waste heat in the industry is considered, the waste heat needs to be considered as an input energy and exergy, while it is not so abundant like air or sea water and they have definitely a quantifiably potential of added value in the energy sector.

**Funding:** This research received no external funding.

**Acknowledgments:** The manuscript is a revised and expanded version of an original scientific contribution that was presented at the 13th Conference on Sustainable Development of Energy, Water and Environment Systems (SDEWES) that was held during 30 September and 4 October 2018 in Palermo, Italy entitled "An Exergy-Based Optimum Control Algorithm for Rational Utilization of Waste Heat from the Flue Gas of Coal-Fired Power Plants." Four models for flue gas exergy recovery were identified and compared explicitly in terms of *COP*, *COPEX*, First and Second-Law efficiencies and the direct thermal utilization in a district energy system model was selected by using this new comparison algorithm. All text was revised and four new figures were added.

**Conflicts of Interest:** The author declares no conflict of interest.
