On the Question of Comparing Various Methods for Utilizing the Heat of Exhaust Gases from Power-Plant Boilers

V. A. Bragin

In the struggle to save fuel at electric power stations, great importance attaches to reducing the heat losses with the outgoing flue gases, whose temperature still remains high. Reduction of this loss is achieved by lowering the gas temperature and by reducing the admission of cold air in the drying-and-milling system and in the boiler unit itself.

To lower the temperature of the outgoing gases, a whole series of different methods has recently been proposed and put into operation. Among them, the most attractive are such methods as increasing the main tail heating surfaces of the boiler (the economizer and the air heater). In this case the heat utilized goes toward increasing steam production in the boiler. It has been established that this way of lowering the temperature of the outgoing gases is the only correct one when burning dry fuels.

It is more difficult to lower the temperature of the outgoing gases when burning moist and sulfurous fuels. As practice shows, development of the main tail heating surfaces here does not give the desired effect, and the temperature of the outgoing gases remains on the order of 160–200°C. Therefore utilization heating surfaces have appeared, heating water or producing steam for various purposes (low-pressure economizers¹, waste-heat boilers). These heating surfaces make it possible to reduce the temperature of the outgoing gases significantly.

According to the method of utilizing the heat of outgoing gases, the following basic utilization schemes are distinguished: 1) use of the heat of outgoing gases for district-heating or agro-district-heating purposes; 2) use of the heat of outgoing gases in the thermal scheme of the station; 3) use of the heat of outgoing gases during the heating season for district-heating or agro-district-heating purposes, and in summer—in the turbine regeneration system; 4) use of the heat of outgoing gases for the needs of domestic or industrial hot-water supply; 5) use of the heat of outgoing gases for preliminary air heating in order to prevent corrosion of the air heater; 6) use of the heat of outgoing gases to obtain electric power in a waste-heat turbogenerator. The first three schemes have received the widest practical application.

To determine the economic effect from applying the indicated schemes for utilizing the heat of outgoing gases from boiler installations, it is possible to apply the method of heat balance proposed by Professor I. N. Butakov [1], which, as will be shown below, takes into account the influence on the station efficiency not only of the quantity of heat taken from the outgoing gases, but also of all

changes in the operation of the thermal scheme of the station as a whole, caused by one or another method of using this recovered heat.

In the absence of utilization of the heat of the gases, the expanded heat balance of the station (CHP plant) has the form:

\[ \frac{860 E + Q_{\mathrm{ext}}}{\eta} = \frac{860 E_t + Q_{\mathrm{ext}}}{\eta_t} + \frac{860(E - E_t)}{\eta_k}, \tag{1} \]

where

\[ \begin{aligned} E &\text{ is the generation of electric energy by the station over the period considered,}\\ &\text{for example over a year, } \mathrm{kWh/year};\\ E_t &\text{ is the same, but only for heat consumption, } \mathrm{kWh/year};\\ Q_{\mathrm{ext}} &\text{ is the delivery of heat from turbine extractions to heat consumers,}\\ &\mathrm{kcal/year};\\ \eta_k,\ \eta_t,\ \eta &\text{ are the efficiencies, respectively, of the condensing part,}\\ &\text{of back-pressure operation with complete heat utilization, and the economic}\\ &\text{efficiency of the entire station.} \end{aligned} \]

For the values of \(\eta_k\) and \(\eta_t\) we have:

\[ \eta_k=\eta_{\mathrm{boil}}\cdot\eta_{\mathrm{pipe}}\cdot\eta_{oi}\cdot\eta_{\mathrm{mech}}\cdot\eta_{\mathrm{gen}}, \tag{2} \]

\[ \eta_t = \eta_{\mathrm{pipe}}\eta_{\mathrm{boil}}\cdot \frac{ (i_1-i_2)\eta_{oi}\cdot\eta_{\mathrm{mech}}\cdot\eta_{\mathrm{gen}} +i_1-(i_1-i_2)\eta_{oi}-t_{\mathrm{cond}} }{ i_1-t_{\mathrm{cond}} } = \eta_{\mathrm{boil}}\cdot\eta_{\mathrm{pipe}}\cdot\eta_{\mathrm{mech}}^{*}\cdot\eta_{\mathrm{gen}}^{*}. \tag{3} \]

Here \(t_{\mathrm{cond}}\) is the temperature of the condensate in the district-heating boiler, \({}^{\circ}\mathrm{C}\).

When the heat of the exhaust gases is used for district-heating purposes, two cases may be encountered, for which the station heat balance respectively takes the form:

a) the recovered heat displaces the district-heating steam extraction (the station heat load \(Q_{\mathrm{ext}}\) is constant):

\[ \frac{860 E + Q'_{\mathrm{ext}} + Q_{\mathrm{le}}}{\eta'} = \frac{860 E'_t + Q'_{\mathrm{ext}}}{\eta'_t} + \frac{860(E-E'_t)}{\eta'_k} + Q_{\mathrm{le}}, \tag{4} \]

b) additional heat consumers are supplied by means of the recovered heat:

\[ \frac{860 E + Q_{\mathrm{ext}} + Q_{\mathrm{le}}}{\eta''} = \frac{860 E_t + Q_{\mathrm{ext}}}{\eta''_t} + \frac{860(E-E_t)}{\eta''_k} + Q_{\mathrm{le}}, \tag{5} \]

where \(Q_{\mathrm{le}}\) is the quantity of heat from the low-pressure economizer delivered to heat consumers, \(\mathrm{kcal/year}\);

\[ Q'_{\mathrm{ext}}=Q_{\mathrm{ext}}-Q_{\mathrm{le}} \quad\text{and}\quad E'_t = E_t-\frac{Q_{\mathrm{ext}}-Q'_{\mathrm{ext}}}{q} = E_t-\frac{Q_{\mathrm{le}}}{q}. \]

Here \(q\) is the quantity of heat delivered to heat consumers per one \(\mathrm{kWh}\) of electric energy generated on heat consumption, \(\mathrm{kcal/kWh}\).

From comparison of equations (1), (4), and (5), it is seen that, with utilization of the heat of the gases, in addition to the appearance of \(Q_{\mathrm{le}}\), the partial efficiencies of the processes of electric-power generation by the condensing method and on the basis of district heating also change, while with a constant station heat load the quantities \(Q_{\mathrm{ext}}\) and \(E_t\) also change.

When part of the heat from the exhaust gases is utilized, the boiler begins to deliver a larger quantity of heat and its efficiency increases; from formulas (2) and (3) it is seen that \(\eta_k\) and \(\eta_t\) increase \((\eta'_k=\eta''_k>\eta_k\) and \(\eta'_t=\eta''_t>\eta_t)\).

With a constant heat load, the supply of heat from the low-pressure economizer to heat consumers reduces the extraction of steam and, along with this, the generation of electric power for heat consumption, replacing it with unprofitable condensing generation. In this connection \([E'_m < E_m\ \text{and}\ E - E'_m > E - E_m]\), the possible fuel saving is somewhat reduced. In the second case, at the same fuel consumption, the station begins to deliver more output. In practice, the use of recovered heat for district-heating purposes usually leads to displacement of extraction steam; that is, the first case is the most common.

The dependence of the reciprocal of the station’s economic efficiency on \(Q_{\mathrm{ext}}\), obtained from formulas (4) and (5), has the form:

\[ \frac{1}{\eta'} = A' + \frac{B' - A' \cdot C'}{C' + Q'_{\mathrm{ext}}} \tag{6} \]

and

\[ \frac{1}{\eta''} = A'' + \frac{B'' - A'' \cdot C''}{C'' + Q_{\mathrm{ext}}}, \tag{7} \]

where

\[ A' = A'' = \frac{1}{\eta'_m} - \frac{860}{q} \left( \frac{1}{\eta'_k} - \frac{1}{\eta'_m} \right) = \frac{1}{\eta''_m} - \frac{860}{q} \left( \frac{1}{\eta''_k} - \frac{1}{\eta''_m} \right), \]

\[ B' = B'' = \frac{860 E}{\eta'_k} + Q_{\mathrm{eco}} = \frac{860 E}{\eta''_k} + Q_{\mathrm{eco}} \]

and

\[ C' = C'' = 860 E + Q_{\mathrm{eco}} . \]

From formulas (6) and (7) it is clearly seen that

\[ \frac{1}{\eta''} < \frac{1}{\eta'} < \frac{1}{\eta} \quad \text{and} \quad \eta'' > \eta' > \eta . \]

The dependences \(1/\eta'\) on \(Q'_{\mathrm{ext}}\) and \(1/\eta''\) on \(Q_{\mathrm{ext}}\), represented by formulas (6) and (7), are shown by one and the same hyperbola in Fig. 1 [hyperbola 3 corresponds to a heating-season duration of \(2500\ \text{h/year}\), and hyperbola 4 to \(5500\ \text{h/year}\)]. The curves are plotted for a station with two turbine-generators of types AT-25-1 and AK-25-1, for which:

\[ 860E = 301000\ \frac{\text{million kcal}}{\text{year}}; \]

\[ \eta_{\mathrm{boil}} = 0.865; \qquad \eta_m = 0.822; \qquad \eta_k^{AT} = 0.242; \qquad \eta_k^{AK} = 0.248; \qquad P_{\mathrm{ext}} = 1.2\ \text{ata}; \]

\[ q = 3730\ \text{kcal/kWh}; \qquad Q_{\mathrm{eco}}^{\mathrm{h}} = 3.0\ \text{million kcal/h}. \]

In the same figure, the hyperbola of the dependence \(1/\eta\) on \(Q_{\mathrm{ext}}\) is marked by the number 1 (there is no recovery).

Let us write the heat balance of a condensing station with use of the heat of exhaust gases in the regenerative feedwater-heating system:

\[ \frac{860E}{\eta^{P}} = \frac{860E}{\eta^{P}_{k}}, \tag{8} \]

or

\[ \frac{1}{\eta^{P}} = \frac{1}{\eta^{P}_{k}} . \tag{9} \]

In the absence of utilization:

\[ \frac{1}{\eta}=\frac{1}{\eta_k}. \tag{10} \]

For the value of \(\eta_k^p\) we have:

\[ \eta_k^p=\eta_{kot}^p \cdot \eta_{pot}\cdot \eta_{toi}^p \cdot \eta_{mex}\cdot \eta_{chen}\cdots . \tag{2′} \]

From a comparison of the efficiency of electric-power generation, \(\eta_k\) and \(\eta_k^p\), according to formulas (2) and (2′), it is seen that, when the heat of the exhaust gases is used in the turbine-regeneration system, there occurs a change in the efficiency of the boiler unit and in the absolute internal efficiency. In connection with utilization, the boiler efficiency increases \((\eta_{kot}^p>\eta_{kot})\), and \(\eta_k\) must increase. On the other hand, heating the turbine condensate by the exhaust gases leads to a reduction in regenerative extraction, which lowers the absolute internal efficiency \((\eta_{toi}^p<\eta_{toi})\), and hence also \(\eta_k\). But since the increase in \(\eta_{kot}\) is greater in absolute magnitude than the decrease in \(\eta_{toi}\), the efficiency \(\eta_k\) increases and, correspondingly, \(\eta^p=\eta_k^p\).

Fig. 1.

The utilization scheme under consideration also leads to the failure to obtain a certain fuel saving owing to a deterioration of the thermal efficiency of the cycle: the reduction in regenerative extraction leads to a reduction in the generation of the kilowatt-hours advantageous to us without loss in the condenser. The combined use of the heat of the exhaust gases (for district-heating purposes and in the regeneration system) and the use of the utilized heat for domestic or industrial hot-water supply needs are not considered here, since the changes in the station heat balance in that case and the determination of their effectiveness are analogous to the utilization schemes discussed above.

For preliminary heating of the air before it enters the air heater, it is more advantageous to use extraction steam from the turbines, as has in fact been established in practice. Indeed, increasing the amount of extraction steam reduces the heat loss with the circulating water of the condensing section and expands the generation of electricity on the basis of heat consumption throughout the year. Therefore we also shall not consider this utilization scheme.

Let us dwell in somewhat greater detail on the use of the heat of the exhaust gases for obtaining electricity in a special utilization installation.

For a station utilizing the heat of the exhaust gases according to the indicated scheme, the expanded heat balance may be represented in the following form:

a) the electricity from the utilization installation supplies additional electrical consumers:

\[ \frac{860\mathcal{E}+Q_{otb}+860\mathcal{E}_{ut}}{\eta_{I}^{e}} = \frac{860\mathcal{E}_{t}+Q_{otb}}{\eta_{tI}^{e}} + \frac{860(\mathcal{E}-\mathcal{E}_{t})}{\eta_{kI}^{e}} + 860\mathcal{E}_{ut}, \tag{11} \]

b) the electricity from the utilization installation displaces part of the condensing kWh of the main machines (the electrical load of the station is constant):

\[ \frac{860\mathcal{E}+Q_{otb}}{\eta_{II}^{e}} = \frac{860\mathcal{E}_{t}+Q_{otb}}{\eta_{tII}^{e}} + \frac{860(\mathcal{E}-\mathcal{E}_{t}-\mathcal{E}_{ut})}{\eta_{kII}^{e}} + 860\mathcal{E}_{ut}. \tag{12} \]

Here

\[ 860\mathcal{E}_{ut}=\eta_{ut}\cdot Q_{end}, \tag{13} \]

where \(\eta_{ut}\) is the efficiency characterizing the process of electricity generation by the utilization installation (its absolute electrical efficiency).

With utilization of the heat of the gases, the boiler efficiency increases and, correspondingly, so do \(\eta_k\) and \(\eta_t\) \((\eta_{tI}^{e}=\eta_{tII}^{e}>\eta_t\) and \(\eta_{kI}^{e}=\eta_{kII}^{e}>\eta_k)\), while all losses associated with the production of electricity in the utilization installation are charged to the boiler. In addition, in the first case the station begins to deliver a larger amount of electricity to consumers, while in the second case it partly replaces unfavorable condensing kWh.

The dependence of the reciprocal of the economic efficiency of the station on \(Q_{otb}\) may be obtained from equations (11) and (12):

\[ \frac{1}{\eta_{I}^{e}} = A_{I}^{e} + \frac{B_{I}^{e}-A_{I}^{e}\cdot C_{I}^{e}}{C_{I}^{e}+Q_{otb}} \tag{14} \]

and

\[ \frac{1}{\eta_{II}^{e}} = A_{II}^{e} + \frac{B_{II}^{e}-A_{II}^{e}\cdot C_{II}^{e}}{C_{II}^{e}+Q_{otb}}, \tag{15} \]

where

\[ A_{I}^{e}=A_{II}^{e} = \frac{1}{\eta_{I}^{e}} - \frac{860}{q} \left( \frac{1}{\eta_{kI}^{e}} - \frac{1}{\eta_{tI}^{e}} \right) = \frac{1}{\eta_{tII}^{e}} - \frac{860}{q} \left( \frac{1}{\eta_{kII}^{e}} - \frac{1}{\eta_{tII}^{e}} \right), \]

\[ B_{I}^{e} = \frac{860\mathcal{E}}{\eta_{kI}^{e}} + 860\mathcal{E}_{ut}, \qquad B_{II}^{e} = \frac{860\mathcal{E}}{\eta_{kII}^{e}} - 860\mathcal{E}_{ut} \left( \frac{1}{\eta_{kII}^{e}}-1 \right), \]

\[ C_{I}^{e}=860\mathcal{E}+860\mathcal{E}_{ut} \quad \text{and} \quad C_{II}^{e}=860\mathcal{E} \]

are constant quantities.

Expressing the constants of formula (15), respectively, through \(A_{I}^{e}\), \(B_{I}^{e}\), and \(C_{I}^{e}\), and carrying out simple transformations, we obtain:

\[ \frac{1}{\eta_{\mathrm{II}}^{\mathrm{e}}} = A_{1}^{\mathrm{e}} + \frac{B_{1}^{\mathrm{e}}-A_{1}^{\mathrm{e}}\cdot C_{1}^{\mathrm{e}}-860\,\mathcal{E}_{ym}\left(1/\eta_{k\mathrm{I}}^{\mathrm{e}}-A_{1}^{\mathrm{e}}\right)} {C_{1}^{\mathrm{e}}+Q_{om6}-860\,\mathcal{E}_{ym}} . \tag{15′} \]

Since the quantity \(A_{1}^{\mathrm{e}}<1.0\), it follows from formulas (14) and (15′) that, under the conditions of one and the same station, \(1/\eta_{\mathrm{II}}^{\mathrm{e}}<1/\eta_{\mathrm{I}}^{\mathrm{e}}<1/\eta\) and \(\eta_{\mathrm{II}}^{\mathrm{e}}>\eta_{\mathrm{I}}^{\mathrm{e}}>\eta\). In addition, the indicated utilization schemes make it possible to obtain condensate for boiler feed, which is especially important at high pressures.

The principal advantages of obtaining electric power over other methods of using the recovered heat are:

1. The production of electric power ensures year-round utilization and does not worsen the operating regime of the station’s main equipment.
2. This method does not conflict with the development of district heating.
3. It makes it possible to use the heat of the exhaust gases of all operating boilers of the station, since the demand for electric power usually grows more rapidly than the ability to satisfy it.
4. In addition to electric power, the station obtains condensate.
5. If there is no additional demand for electric power, then the electric power from the utilization installation displaces condensing kWh that are unfavorable for us.

The principal shortcomings of the scheme under consideration are its bulkiness and the low coefficient of utilization of the heat recovered from the exhaust gases.

The coefficient of utilization of the recovered heat can be considerably increased if the scheme proposed by V. A. Uspenskii (UOVTI) is used, according to which the heat of the circulating water is used as an insulator of the glazed surface for the needs of agro-district heating. This is in accord with the Resolution of the September Plenum of the Central Committee of the CPSU, where it is stated: “...widely use the heat wastes of industrial enterprises for heating hothouses, greenhouses, and for warming the soil.”

Then we have:

\[ \frac{860\mathcal{E}+Q_{om6}+860\mathcal{E}_{ym}+Q_{ym}^{agr}}{\eta^{*}} = \frac{860\mathcal{E}_{m}+Q_{om6}}{\eta_{m}} + \frac{860(\mathcal{E}-\mathcal{E}_{m})}{\eta_{k}^{*}} + 860\mathcal{E}_{ym}+Q_{ym}^{agr} \tag{16} \]

and

\[ \frac{1}{\eta^{*}} = A^{*} + \frac{B^{*}-A^{*}\cdot C^{*}}{C^{*}+Q_{om6}}, \tag{17} \]

where

\[ A^{*} = \frac{1}{\eta_{m}^{*}} - \frac{860}{q} \left( \frac{1}{\eta_{k}^{*}}-\frac{1}{\eta_{m}^{*}} \right), \qquad B^{*} = \frac{860\mathcal{E}}{\eta_{k}^{*}} + 860\mathcal{E}_{ym} + Q_{ym}^{agr}, \]

\[ C^{*} = 860\mathcal{E} + 860\mathcal{E}_{ym} + Q_{ym}^{agr}. \]

The use of the heat of the circulating water makes it possible considerably to increase the partial coefficients \(\eta_{m}^{*}>\eta_{m}\) and \(\eta_{k}^{*}>\eta_{k}\) and additionally to provide the agrothermal economy with heat.

For the particular example of the station indicated above, Fig. 1 presents the hyperbolic dependences represented by formulas (14)—curve 2 and (17)—curve 5.

REFERENCES

1. I. N. Butakov—Coefficient of efficiency of a thermal-power installation and of a power system. Izvestiya TPI, vol. 66, issue 2, 1948.

1. In the literature they are sometimes called utilization economizers, low-temperature economizers, and district-heating economizers. ↩