On Possible Ways to Maintain High Efficiencies of Condensing Power Plants with Cheap Fuel

I. N. Butakov

Every step toward increasing the economic efficiency of a condensing power plant must be considered from the standpoint of additional capital investments; moreover, these new additional investments make it possible to realize an ever smaller relative increase in the efficiency of the installation. In the limit, this corresponds to a maximum efficiency equal to unity, the realization of which requires infinitely large funds. It is clear that in the complete absence of investment in fixed assets, i.e., when the condensing power plant in fact does not exist, the efficiency will, of course, be equal to zero. If we denote by \(K_k\) the charges in rubles for depreciation and current repairs (the capitalization factor), then schematically the dependence \(K_k = f(\eta_k)\) can be represented in the form of the curve in Fig. 1, which may be taken as a hyperbola of the form

\[ \eta_k = 1 - \frac{C_1}{C_1 + C_2 f_1(\eta_k)} . \tag{1} \]

Fig. 1.

For \(f(\eta_k)=\infty\), the efficiency \(\eta_k = 1.0\), i.e., the asymptote as in Fig. 1. For \(\eta_k = \infty\), the second asymptote is determined from the condition \(C_1 + C_2 f_1(\eta_k)=0\),

i.e., \(f_1(\eta_k)=\dots\). If \(\eta_k=0\), then \(f_1(\eta_k)=0\), as in Fig. 1. If such is the general relationship between the efficiency \(\eta_k\) and the capital-cost factor \(K_k\), then, in order to determine the specific value of the efficiency \(\eta_k\) as applied to the given local factors affecting \(\eta_k\), one must proceed from the condition of obtaining the minimum value of the cost of a kWh, which may be represented as follows:

\[ S=S_k+S_{\text{fuel}}+aS, \tag{2} \]

where \(S_k\) is the capital-cost component, \(S_{\text{fuel}}\) is the fuel component, and \(aS\) represents the remaining components (personnel wages, other expenses). Expression (2) may be written in another form:

\[ S(1-a)= \frac{f_1(\eta_k)}{8760\cdot f\cdot \Sigma N_e} + \frac{R_{\text{fuel}}\cdot 860}{\eta_k\cdot 10^6} = \]

\[ = \frac{f_1(\eta_k)}{8760\cdot f\cdot \Sigma N_e} + \frac{R_{\text{fuel}}}{1160\cdot \eta_k}. \tag{3} \]

Here \(R_{\text{fuel}}\) is the price in rubles of one Mcal in the fuel; the plant load factor is

\[ f=\frac{\Sigma N_x}{\Sigma N_e}; \]

\(\Sigma N_e\) is the installed capacity of the condensing power plant in kW, and \(\Sigma N_x\) is the operating capacity. We obtain the minimum cost of a kWh from

\[ \frac{ds}{d(\eta_k)} = \frac{f_1'(\eta_k)}{8760\cdot f\cdot \Sigma N_e} - \frac{R_{\text{fuel}}}{1160(\eta_k)^2} =0, \]

whence

\[ f_1'(\eta_k)\cdot(\eta_k)^2 = 7.55\cdot \Sigma N_e\cdot f\cdot R_{\text{fuel}}. \tag{4} \]

From (1) we determine the value

\[ f_1(\eta_k) = \frac{C_1}{C_2} \left( \frac{1}{1-\eta_k}-1 \right) = \frac{C_1}{C_2}\cdot \frac{1}{1/\eta_k-1} \tag{5} \]

and the first derivative

\[ f_1'(\eta_k) = \frac{C_1}{C_2}\cdot \frac{1}{(1-\eta_k)^2}, \]

after which expression (4) is transformed into

\[ f_1'(\eta_k)\cdot \eta_k^2 = \frac{C_1}{C_2}\cdot \frac{1}{(1-\eta_k)^2}\cdot \eta_k^2 = 7.55\cdot \Sigma N_e\cdot f\cdot R_{\text{fuel}}. \tag{6} \]

From this we obtain

\[ 1/\eta_k = 1+ \sqrt{ \frac{C_1}{C_2}\cdot \frac{1}{7.55\cdot \Sigma N_e\cdot f\cdot R_{\text{fuel}}} }. \tag{7} \]

For the selected magnitude of the total \(\Sigma N_e\) capacity of the condensing power plant and of its individual turbogenerators with their known initial and final steam parameters, the efficiency \(\eta_k\) is also determined. Also known in this case is the cost per Mcal \(R_{\text{fuel}}\) in the fuel, and the load factor \(f\) is specified. Then from (6) we find the value of the second asymptote.

\[ \frac{C_1}{C_2} = -\left(\frac{1}{\eta_k}-1\right)^2 \cdot 7.55 \cdot \sum N_e \cdot f \cdot R_{\text{fuel}} . \tag{8} \]

From (8) it is evident that the position of the vertical asymptote \(\frac{C_1}{C_2}\) of hyperbola (1) depends substantially on \(R_{\text{fuel}}\), so that with cheap fuel \(-\frac{C_1}{C_2}\) will move noticeably closer to the ordinate axis and, consequently, hyperbola (1) will rise more steeply toward the asymptote \(\eta_k = 1.0\); thus the value \(K_k = f_1(\eta_k)\) for a given value of \(\eta_k\) will be relatively small, and hence the permissible capital investments may prove insufficient to make it possible to build a condensing power plant with a high efficiency. It is known, for example, that when natural gas is used as fuel, the cost of a condensing power plant is reduced by 20–30% because it lacks the fuel-handling facilities customary for coal-fired thermal power stations. The specific cost of constructing a condensing power plant, according to Teploelektroproekt data, is 850 rubles/kW for higher-grade coals with 200 MW units and \(\sum N_e = 1200\) MW at steam parameters of 130 ata, \(565^\circ/565^\circ\)C; thus for natural gas \(850 \cdot 0.75 = 640\) rubles/kW¹. Then the permissible specific cost of a condensing power plant is

\[ \frac{C_{\text{st}}}{\sum N_e} = \frac{f_1(\eta_k)}{0.13 \cdot \sum N_e} = \frac{7.55 \cdot f \cdot R_{\text{fuel}}}{0.13} \left(\frac{1}{\eta_k}-1\right) = 640, \tag{9} \]

whence

\[ \frac{1}{\eta_k} = 1+\frac{640 \cdot 0.13 \cdot 7}{7.55 \cdot 0.8 \cdot 25} = 4.83 \]

and, consequently, \(\eta_k = 0.207\). Here deductions for depreciation of equipment of 10% and for current repairs of 3% have been adopted, i.e., 0.13 in all. It is thus evident that, at a cost of 25 rubles per ton of standard fuel, the efficiency of a condensing power plant on natural gas does not exceed the efficiency of a medium-pressure condensing power plant (30–35 ata). The situation will be still worse when cheap strip-mined coals are used, when, for example, at the Irsha-Borodino open pit in Krasnoyarsk Territory the cost of a ton of standard fuel will not exceed 10–15 rubles, while the fuel-handling facilities of the condensing power plant there will be larger than with higher-grade coals, so that the specific cost of capital investment may in this case be expected to be even higher than 850 rubles/kW.

Such a substantial reduction in the efficiency \(\eta_k\) means an increase in the specific consumption of standard fuel, which gives grounds for assuming the need to raise the temperature of the flue gases from boiler units, to worsen the vacuum in turbines, to abandon supercritical steam parameters, to abandon steam reheat, etc. Undoubtedly, this would be a regressive evolution in the development of thermal power installations. Ways must be found here that are in harmony with the achievements of advanced heat-engineering science and technology.

One such way may be to reduce the cost of equipment through a new design; examples of this in the past were water and air economizers, which provided cheaper specific heating surfaces than boiler surfaces. This made it possible to reduce—

…a reduction in the temperature of the flue gases. To this same category one should also assign the rejection of multi-drum boilers, the introduction of screens, the creation of once-through boilers, etc. No one can assert that inventive work aimed at reducing the cost of units has been exhausted. Undoubtedly, of great importance here is also the cheapening of the manufacturing technology of units, of their installation and of the construction of condensing power plants, as well as the work of metallurgists and metal scientists to reduce the cost of grades of metal and, first of all, the search for new ways of obtaining cheap and higher-quality steels, and also the search by chemists for entirely new materials of the polymer type. In this way we shall approach a reduction in the capitalization factor \(K_k\), the magnitude of which is determined from the hyperbola of the dependence of the efficiency \(\eta_k\) on \(K_k\), shown in Fig. 1 of the present article. The asymptote \(C_1 C_2\) of this hyperbola will prove to be closer to the origin if we wish to retain the efficiency \(\eta_k\) at the same level as with more expensive fuel. This, in turn, will determine a steeper rise of the hyperbola and a smaller value of \(K_k\), and hence smaller permissible capital investments. Thus, the first way of preserving high efficiencies \(\eta_k\) lies in creative work to develop new, cheaper units and in reducing the cost of construction of condensing power plants.

One may also speak of a second way capable of leading to the same goal. This way is the utilization of thermal wastes of power plants. With the use of cheap fuel, as indicated above, the temperature of the flue gases of boiler units must be increased. It is natural to consider here the installation, for example, of low-pressure waste-heat economizers for the purposes of district heating and especially agricultural heating, making it possible to use the heat of such economizers even in summer for heating open ground in order to grow heat-loving plants (melons, watermelons, tomatoes, etc.)*. Likewise, at less deep vacuums (\(0.05\)--\(0.07\) ata), it may prove expedient under the conditions of our severe climate—when for 7–8 months of the year the water in reservoirs remains at a temperature of \(0\)--\(2^\circ\mathrm{C}\)—to utilize the heat of the circulating water discharged in the main turbines in vacuum turbines operating on the Claude and Boucherot principle.

It is clear that particular waste-heat installations must be justified economically by the conditions of their own operation, proceeding from the fact that all their heat losses remain to the account of the main units. The waste-heat installations, for their part, are charged only with that portion of the heat which they actually use.

Waste-heat installations on the flue gases of boiler units have found some practical application in our country and have been discussed in a number of published works, for example, V. A. Komissarov’s articles on low-pressure economizers in the journal Elektricheskie stantsii, and the works of D. A. Ermakov and N. S. Vasil’ev on waste-heat boilers at the Kashira GRES (Operating Experience of the Kashira GRES, 1956, pp. 37–42). Although these waste-heat installations were treated apart from the new phenomenon—the cheapness of fuel in a number of cases—when their economic justification will look somewhat different, nevertheless these works provide good material for solving the subsequent problem. As for waste-heat installations for the utilization of heat

* At large condensing power plants, large vegetable combines (20–100 ha) should be under the jurisdiction of special state farms intended to supply neighboring cities and populated localities with fresh vegetables year-round. Their operating costs should be charged to such state farms, not to the expenses for operating low-pressure economizers.

little attention has been paid in our country to circulating water, unless one counts the article by Prof. I. N. Butakov in Izvestiya Tomskogo politekhnicheskogo instituta, vol. 63, 1941.

With a vacuum in the main turbines of \(P_2 = 0.05\) ata, steam of raw natural origin \((1^\circ\!-\!2^\circ)\) in reservoirs for large condensing power plants of the order of 1.2 million kW makes it possible to have the capacity of a recovery installation determined from the following considerations. Let us take the specific steam consumption of powerful turbogenerators of 200 MW at a vacuum of 0.035 ata and a cooling-water temperature of \(10^\circ\)C to be of the order of \(2.8\ \text{kg/kWh}\). The use of cheap grades of fuel makes it necessary to worsen the vacuum to \(0.05\!-\!0.06\) ata, which will cause either an increase in the specific steam consumption or, if part of the high-pressure section of the turbines is kept unchanged, will lead to a reduction in the capacity of the main turbines with the same total steam consumption. In the latter case, with a cooling ratio of 60 and a cooling-water temperature of \(15^\circ\)C, assuming that only 70% of the total steam flow will enter the condensers, we obtain the second-by-second flow rate of water passing through the condensers of the main turbines, with six turbogenerators:

\[ \frac{6 \cdot 200 \cdot 10^3 \cdot 2.8 \cdot 60 \cdot 0.7}{3600} = 39000\ \text{liters/sec}. \]

Using Shambadal’s formula [1], we obtain, with a three-stage evaporation at \(T_0 - T_2 = 25^\circ - 7^\circ = 18^\circ\)C, the maximum work in kcal per one liter of water heated in the condensers of the main turbines:

\[ W_{\max} = 0.00252 - \frac{0.00221}{0.877 + 3} \cdot 18^{1.8675} = 0.425\ \frac{\text{kcal}}{1\ \text{l. water}}, \]

so that the gross capacity of the recovery installation is

\[ N_{\text{gross}} = \frac{39000 \cdot 0.425 \cdot 427 \cdot 0.6}{75 \cdot 1.36} = 41500\ \text{kW}. \]

Assuming that about 30% of the gross capacity will be spent on the auxiliary needs of this installation (feeding cooling water into the mixing condenser, extracting air from the latter), one may expect to obtain a net capacity of the order of 29,000 kW, which should be directed toward satisfying the auxiliary needs of the main units of the condensing power plant, with the expectation of covering about \(1/3\) of their demand for electric power. Thanks to this, the delivery of electric power to the grid from the main turbogenerators of the condensing power plant will increase by this amount.

Assuming further that the cost of a kilowatt-hour at a large condensing power plant with cheap fuel (25 rubles per ton of equivalent fuel), at a vacuum of 0.05 ata, will be of the order of 2.1 kopecks, we find that, at such a cost per kilowatt-hour, the recovery installation is capable of yielding per year

\[ \frac{2.1 \cdot 29000 \cdot 5000}{100} = 3.05 \cdot 10^6\ \text{rubles}. \]

As indicated above, only the heat in the fuel which it usefully consumes should be charged to the recovery installation. The total cost of the latter, therefore, is

\[ \frac{29000 \cdot 860 \cdot 5000 \cdot 25}{7000 \cdot 1000} = 0.445 \cdot 10^6\ \text{rubles/year}, \]

i.e., by \(1\ \text{kWh}\), 0.31 kopecks. Other expenses for a GRES of 130 ata, \(565^\circ/565^\circ\) C on gas with 6 units of 200 MW each amount to 0.15 kopecks/kWh [2]. Since the utilization installation has no boiler house with its fuel-handling facilities and, moreover, will share the technical administration with the turbine hall, the other expenses for it may be estimated at 0.1 kopecks/kWh, so that the annual expenditure under the item “Other expenses” will be

\[ 0.1 \cdot 29000 \cdot 5000 = 0.145 \cdot 10^6 \]

rubles. Thus, for depreciation there remains

\[ 0.305 \cdot 10^6 - (0.445 + 0.145 \cdot 10^6) = 2.46 \cdot 10^6 \]

rubles, which makes it possible, on the basis of a ten-year payback period, to capitalize the sum of \(24.6 \cdot 10^6\) rubles; consequently, per one delivered kW of the utilization installation this gives

\[ 24.6 \cdot 10^6 / 29 \cdot 10^3 = 850\ \text{rubles}. \]

This corresponds, as we saw above in the present article, to the permissible cost of an installed kW at large GRES, which must be considered sufficient, bearing in mind the absence here of a boiler house with all its fuel-handling facilities. Economic calculations carried out in 1939 in France for the installation described below at Abidjan showed that, with a useful capacity of the installation of 7000 kW, the cost of the installation itself, including the building, was determined at \(28.5 \cdot 10^6\) francs, i.e.,

\[ 28.5 \cdot 10^6 : 7000 = 4220 \]

francs/kW. The cost of an installed kW at GRES in France at that time [3] was up to 4000 francs/kW; i.e., these data lead to the same result as above.

The difficulties of designing the last stages of very powerful turbines at deep vacuums are well known. To overcome these difficulties three paths are envisaged, namely: 1) increasing the number of steam exhausts while limiting the length of the last blades; 2) increasing the length of these blades to the maximum possible extent; 3) making turbine units double-shaft, with the low-pressure part operating at a reduced speed. All these paths increase the cost of constructing turbine units. With a utilization installation, all these difficulties disappear. The usual vacuum of 0.05 ata is retained in the turbines, and the heat of the spent circulating water at a temperature of \(25^\circ\) C, if at the inlet to the condensers it had \(15^\circ\) C, is used in the utilization vacuum turbine. A temperature of \(15\text{–}18^\circ\) C is characteristic for most rivers of our country only during the summer months, and also as the annual average in the southern belt of the USSR. In the latter case there is no need for a utilization installation, since in the summer months, when water from reservoirs must be supplied directly to the condensers of the main turbines. Additional benefits from the use of vacuum turbines, moreover, should be expected because of the weakening of the possibility of supercooling the condensate in the condensers of the main turbines, and also because of the reduction in steam consumption for their ejectors as a result of deaeration of the circulating water in the utilization installation. The latter should reduce the entry of air through leaks in the condensers of the main turbines. If chemical treatment of make-up water is adopted to replace the evaporated part of the circulating water in the utilization installation, it will be possible to reduce the number of washings and cleanings of the condensers of the main turbines. All this together should ensure a certain saving of fuel.

Finally, since the utilization installation takes upon itself some part of the fuel consumption, the specific fuel consumption at the GRES itself is reduced by this amount, which will lower the cost of the kWh. The cost will also be reduced because part of the expenditure of electric power for the GRES’s own needs is transferred to the utilization installation.

The possibility of delivering an additional 28,000 kW·h to the grid will also affect the reduction in the cost of a kilowatt-hour. In addition, one should expect a decrease in the expenditure of electric power for pumping the circulating water of the main turbines, since the pressure head will often be reduced owing to a reduction in the height and distance of its delivery, as well as the cooling ratio, owing to the less deep vacuum in the condensers of the main turbines.

In the French design for a 7,000 kW installation, calculations were made of the specific consumption of the principal required materials, in grams per one annual kW·h, in comparison with hydroelectric stations; it was found [4]:

It is evident from this that the specific consumption of principal materials for the 7,000 kW installation proved to be no higher than for hydroelectric stations.

The comparison in terms of the specific consumption of principal materials was made with hydroelectric stations because the arrangement of the vacuum installation for Abidjan resembles, as it were, a hydroelectric station. Figure 2 gives, in section, the installation at Abidjan. In Fig. 2 the inscriptions indicate the separate parts of the installation and the direction of movement of the warm and cold water, of the steam from the evaporator to the mixing condenser, and also the points of fractional removal of air. As can be seen from Fig. 2, triple evaporation of the warm water is provided for. The discharge of unevaporated water is directed to the condenser of the main turbines as circulating water at a temperature of 15° C. The advantages of the arrangement, as in Fig. 2, are as follows:

Fig. 2.

1) simplification of the path of the steam, as a result of which pressure losses are reduced to a minimum; 2) grouping in one vessel of all devices located under vacuum, which makes it possible to reduce the difficulties of creating the necessary sealing; 3) convenient positioning, in height, of the evaporator and condenser. The external casing of the installation is reinforced concrete,

with an external coating for tightness using a special mixture based on tar, rubber, and synthetic resin. An iron casing was rejected as less economical and as presenting serious inconvenience with a vertical arrangement of the turbine axis because of the existing vibrations.

The spent cooling water, having heated up to \(7^\circ\text{C}\) after condensation of the exhaust steam of the vacuum turbine, is collected at the bottom of the mixing condenser, whence it is discharged to an external body of water by gravity if the end of the discharge pipe is placed below the water level of the body of water, thereby providing siphon action. But this water, being deaerated, can usefully be sent to neighboring enterprises. The use of deaerated water eliminates corrosion of pipes in water conduits, which reduces their carrying capacity, increases the energy expenditure for pumping, and also leads to premature repair of the water network, associated with difficult earthworks. To avoid this, in American practice the deaeration of cold water before its supply to the water-supply network has found application and has given positive results, despite the additional costs associated with the construction of special deaeration installations for this purpose [6]. If this circumstance is taken into account in implementing heat-recovery installations, then part of the monetary costs for pumps and for constructing the pressure cooling-water conduit for mixing condensation of steam after the heat-recovery installation, as well as the cost of constructing the discharge conduit, may be charged to the enterprises using the condenser discharge water. The cost of the pumps that take the deaerated water after the condensers should, of course, be charged entirely to the enterprises using it.

From all that has been said about vacuum heat-recovery installations it follows:

1) a heat-recovery installation of the Abidjan type can indeed use part of the heat of the spent circulating water of the main turbines of a condensing power plant;

2) such heat recovery will make it possible:

a) to compensate, to some extent, for the heat losses due to deterioration of the vacuum when cheap grades of fuel are used; b) to reduce the consumption of electric power for the auxiliary needs of the main units of the condensing power plant, thereby releasing an additional share of electric power for external consumers; c) to somewhat reduce the specific fuel consumption and the monetary expenses for the fuel component of the cost of a kWh at the condensing power plant; d) to improve the operation of the condensers of the main turbines; e) to eliminate losses in the exhaust section of high-power turbines designed for introducing deep vacuums, irrespective of fuel cost and climatic conditions, using several exhausts of spent steam and two-shaft turbines with different numbers of revolutions; f) to ensure the water supply of neighboring enterprises with deaerated water from the mixing condensers of vacuum heat-recovery installations, while eliminating intense corrosion of the pipes of water conduits; g) to have a heat-recovery installation at a specific cost per kW not higher than the cost of the installed kW at the condensing power plant.

The heat-recovery installations indicated above, in the form of an LPD and in the form of vacuum turbines for using the more highly heated spent circulating water of the main turbines at shallower vacuums, may, when fuel is cheap, also not be built, if the unjustified economic expenditures on the exhaust surfaces of boilers and on obtaining a deep vacuum are compensated by an increase in the power of the power plants. This is evident from formula (7), from which it is clear that, at low values of \(R_{\text{fuel}}\), the corresponding increase in \(\sum N_{\text{e}}\) may keep \(\eta_k\) the same as with expensive fuel and a smaller capacity \(\sum N_{\text{e}}\).

1. The specific costs of constructing a condensing power plant and the prices of 1 ton of standard fuel are given in monetary units prior to 1961. ↩