USE OF CIRCULATING WATER HEAT AT POWER PLANTS FOR ENERGY PURPOSES

E. N. SHADRIN

In 1944, in the Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute, an article by Prof. I. N. Butakov, “The Use of Circulating Water Heat at Power Plants for the Production of Electric Power,” was published. In his article Prof. I. N. Butakov showed, using a particular example, that the use of circulating-water heat in vacuum installations can be economically advantageous.

The present article is a further development of the problem put forward by Prof. I. N. Butakov.

The quantity of circulating water that must be supplied to the condenser of a steam turbine during its normal operation is

\[ W = \alpha mdN \ \text{kg/hr}, \tag{1} \]

where \(\alpha\) is a coefficient indicating what fraction of the total steam flow to the turbine enters the condenser;

\[ m \]
is the cooling ratio;

\[ d \]
is the specific steam consumption of the turbine, \(\text{kg}/\text{kWh}\);

\[ N \]
is the turbine output, \(\text{kW}\).

In the condenser, heat is transferred to this water in the amount

\[ Q = \alpha dN(i_2 - t_k)\ \text{kcal/hr}. \tag{2} \]

Here \(i_2\) is the heat content of the exhaust steam, \(\text{kcal}/\text{kg}\);

\[ t_k \]
is the condensate temperature, \({}^{\circ}\text{C}\).

If the temperature of the cooling water at the inlet to the condenser is \(t_1\), \({}^{\circ}\text{C}\), then at the outlet from the condenser the water temperature is

\[ t_2 = t_1 + \frac{i_2 - t_k}{m}\ {}^{\circ}\text{C}. \]

Water at temperature \(t_2\) may be directed, as shown in Fig. 1, to the vacuum evaporator (3) of the utilization turbine (4). In the vacuum evaporator a pressure corresponding to temperature \(t_1\) is maintained; therefore part of the water evaporates. The unevaporated water at temperature \(t_1\) again enters the condenser of the main turbine.

The quantity of steam obtained in the evaporator is determined by the formula

\[ D_y = \frac{\alpha dN(i_2 - t_k - m\Delta t)}{rx}\ \text{kg/hr}, \tag{3} \]

where \(\Delta t\) is the drop in water temperature caused by the loss of heat from the water conduit to the environment, \({}^{\circ}\text{C}\);

\[ r \]
is the latent heat of vaporization at the pressure in the evaporator, \(\text{kcal}/\text{kg}\);

\[ x \]
is the dryness fraction of the steam obtained.

This steam enters the utilization turbine 4, where, expanding, it performs work and then condenses in condenser 5.

The power of the utilization turbine is expressed by the formula

\[ N_y=\frac{\alpha dN(i_2-t_k-m\Delta t)\cdot \eta_{\text{oe}}\,(a-bt_k^y)}{860\,rx}\ \text{kW}. \tag{4} \]

Here, in addition to the notation adopted earlier, the following have been introduced:

\(\eta_{\text{oe}}\)—the relative electrical efficiency of the utilization turbine;

\(t_k^y\)—the temperature of saturated steam corresponding to the pressure in the condenser of the utilization turbine, °C;

\(a\) and \(b\)—coefficients which, at constant pressure in the evaporator, depend only on the dryness fraction \(x\) of the steam obtained.

Diagram
of the use of the heat of circulating water at plants with once-through water supply for the production of electric power

Visible labels in the diagram:

• Steam to the utilization turbine
• Circulating water to the evaporator
• Air removal
• Water from the river
• Discharge of water into the river
• Make-up water
• Closed during operation of the utilization turbine

Fig. 1

The following table gives the values of these coefficients for a pressure in the evaporator of \(0.01\text{–}0.04\) ata as a function of \(x\).

Table

If it is assumed that the main turbines must receive water at a temperature \(t_1=15^\circ\text{C}\), in order to have the design conditions for their operation, then at the outlet from the evaporator, allowing for possible losses, the temperature \(t_1\) must be somewhat higher. We shall take \(t_1=15.5^\circ\text{C}\). Consequently, the pressure in the evaporator corresponding to the temperature \(t_1=15.5^\circ\text{C}\) must be \(p_0^y=0.018\) ata, and the latent heat of vaporization \(x=588.5\) kcal/kg.

If the pressure in the condenser of the utilization turbine is taken as 0.01 ata, then for the most frequently encountered conditions, when the steam pressure before the main turbine is \(p_0=30\) ata and the temperature of this steam is \(t_0=400^\circ\text{C}\), the pressure

in the condenser of the main turbine \(p_k = 0.04\) ata, the internal relative efficiency is \(\eta_{oi} = 0.787\), the cooling ratio \(m = 60\), \(\alpha = 0.8\), \(d = 5\ \text{kg/kWh}\), \(\eta_{oe} = 0.7\), \(x = 0.95\); the power \(N_y = 0.05 N\), calculated by formula (4), i.e., the power of the utilization turbine in this case amounts to 5% of the power of the main turbines.

Fig. 2 gives a nomogram for determining the quantity of steam obtained in the evaporator and the power of the utilization turbine for various values of the quantities entering into equation 9. The rule for using the nomogram is clear from Fig. 2.

A distinctive feature of such a utilization installation, as compared with ordinary power installations, is the large expenditure for its own needs.

Fig. 2

This expenditure consists chiefly of the energy required to supply cooling water for the purposes of condensing the exhaust steam in the condenser of the utilization turbine and for removing air from the condenser.

To the cooling water in the condenser of the utilization turbine there is transferred heat, in kcal/h,

\[ Q_y = \alpha dN(i_2 - t_k - m\Delta t)\left(1 - \frac{\eta_{0i}^{y} h_{ad}}{rx}\right), \tag{5} \]

where \(\eta_{oi}^{y}\) is the internal relative efficiency of the utilization turbine;

\[ h_{ad}=a-bt_{k}^{y} \]

is the adiabatic drop between the initial and final pressures in the utilization turbine.

The quantity of cooling water \(W_y\) required for condensing the exhaust steam is determined from the heat-balance equation of the condenser. In the case of mixing condensation this equation may be written as

\[ \alpha dN(i_2-t_k-m\Delta t) \left(1-\frac{\eta_{oi}^{y}h_{ad}}{rx}\right) +t_1^y \cdot W_y = t_2^y \left[ W_y-\alpha dN\frac{(i_2-t_k-m\Delta t)}{rx} \right]. \]

Here \(t_1^y\) is the temperature of the cooling water at its inlet to the condenser of the utilization installation, °C,

\(t_2^y\) is the same at the outlet from the condenser.

If, for winter conditions, \(t_1^y=1^\circ\text{C}\) is taken, and if it is assumed that, when a mixing condenser is used, \(t_2^y=t_k^y\), then the quantity of cooling water is

\[ W_y= \frac{ \alpha dN(i_2-t_k-m\Delta t) \left( 1-\frac{\eta_{oi}^{y}\cdot h_{ad}}{rx} \right) }{ t_k^y-1 } \ \text{kg/hr}. \tag{6′} \]

Then the power expended on pumping the cooling water for the condenser of the utilization turbine is

\[ N_{vod}=\frac{W_yH_y}{3.66\cdot10^5\cdot\eta_n}\ \text{kW}, \tag{6} \]

where \(H_y\) is the head of the pumps delivering this water. The head \(H_y\), with a mixing condenser, includes the elevation height \(H_n\) of the utilization installation, the frictional and local resistances \(H_{tr}\), in m water column, but is reduced by the amount \(H_p\), in m water column, of the difference between the barometric column and the column corresponding to the pressure in the condenser of the low-pressure turbine. If the elevation height \(H_n\) of the utilization installation is less than 10 m and a barometric condenser cannot be used, then the head \(H_y\) must be increased by an amount equal to the difference \(H_p-H_n\), in order to allow for pumping the cooling water out from under vacuum.

Expression 6 represents, in the axes \(N_{vod}\), \(t_k^y\), the equation of a hyperbola whose ordinates decrease as \(t_k^y\) increases. The asymptotes of this hyperbola are determined if we put \(N_{vod}=\infty\); then \(t_k-1=0\) and \(t_k^y=1\). If \(t_k^y=\infty\), then \(N_{vod}=0\). The point needed for constructing the hyperbola is found by putting \(t_k^y=0\).

Then

\[ N_{vod}= \frac{ \alpha dN(i_2-t_k-m\Delta t) \left( 1-\frac{\eta_{oi}^{y}\cdot h_{ad}}{rx} \right) }{ 3.66\cdot10^5\cdot\eta_n }. \]

In Fig. 3 such a hyperbola is constructed for the example considered earlier. Much more complicated is the question of removing the air entering the condenser: first, with the steam from the evaporator, in which gases are released from the circulating water of the main turbines; second, with the cooling water of the utilization turbine; and third, through leaks in the entire part of the path that is under vacuum.

The cooling water of the main turbines, circulating in the closed loop condenser--evaporator--condenser, is continuously deaerated in the vacuum evaporator. Therefore the quantity of air dissolved in it should be insignificant.

Air can enter only through leaks. In this case the most vulnerable parts of the path are those under vacuum. For reliability of the calculation, we shall nevertheless take the full quantity of air dissolved in the circulating water of the main turbines. But in what follows we shall not take into account the air entering through leaks.

Fig. 3

Such an assumption may be made, first, because an exact accounting of the quantity of this air is impossible owing to the absence of experimental data in installations of this kind, and, second, because the inflow of air through leaks is of great importance in installations with surface condensers, where this quantity constitutes a large part of the total quantity of air entering the condenser.

By Henry’s law, the quantity of air \(G_v\), in kg, dissolved in \(W\ \text{m}^3\) of water, at an arbitrary partial pressure, may be expressed by the equation:

\[ G_v = a_p p_v W, \tag{7'} \]

where \(a_p\) is the coefficient of weight solubility of air in water, showing what quantity of air in kg can be absorbed by \(1\ \text{m}^3\) of water at a partial air pressure of \(1\ \text{kg}/\text{cm}^2\); thus, in the cooling water of the utilization installation, the dissolved air, in kg/h, is

\[ G_{v.x} = 10^{-3} a_{p.x} \cdot p_{v.x} \cdot W_y. \tag{7''} \]

Here \(a_{p.x}\) is taken for \(t_y'\);

\(p_{vx}=1-p_{px}\), where \(p_{px}\) is the pressure of saturated steam at \(t_1^y\), found from saturated-steam tables.

Similarly, we obtain the amount of air dissolved in the circulating water of the main turbines,

\[ G_{vg}=a_{pg}p_{vg}amdN \ \text{kg/hour}. \]

Here the values \(a_{pg}\) and \(p_{vg}=1-P_{p2}\) are taken for \(t_2\). Thus, in all it will be necessary to remove air

\[ G_v=10^{-3}\left\{(a_{px}p_{vx}\cdot W_y+a_{pg}p_{vg}amdN)-a_k\left[W_y+\frac{adN(i_2-t_k-m\Delta t)}{r x}\right]p_{vk}\right\} \tag{7} \]

In formula 7 the last term takes into account the amount of air leaving with the water from the condenser of the utilization installation. The value of the solubility coefficient \(a_k\) and the partial pressure of the air \(p_{vk}\) at the outlet of the water from the condenser are taken for the temperature of this water. It should be noted that the amount of air leaving the condenser of the utilization installation with the cooling water amounts to fractions of a percent relative to the amount of air removed from the installation. Therefore it may be disregarded, i.e., in formula (7) the last term may be taken equal to zero.

In order to reduce the power expenditure for removing this air, it is advisable to use the fractional method, which consists in preliminary degassing near the tops of the barometric columns of the cold and warm water. A diagram of such a fractional method is given in the above-mentioned article by Prof. I. N. Butakov, and therefore we shall not describe it.

The pressures at which preliminary degassing takes place may be taken from experience with an installation mounted on one steamship and having approximately the same initial and final parameters. These pressures will be: first stage—0.1 ata, second—0.05 ata, and third stage—the pressure in the condenser. With such a distribution of pressures among the degassing stages, in the first stage 90% of the total amount of air will be removed, in the second—5%, and in the third—about 5%; i.e., in this case not all the air will be compressed from the pressure in the condenser to atmospheric pressure, but only part of it. Therefore the amount of work expended on air removal will also be smaller.

It should be pointed out that the choice of the number and locations of the preliminary degassing points belongs to the category of technical-economic questions. We shall not examine this question here, since it lies beyond the scope of the present article.

If it is assumed that air removal will be carried out by a mechanical extractor, then the power of the latter, depending on \(t_k^y\), is determined by the formula

\[ N_d=\frac{adN\Phi}{\eta_n} \ \text{kW}. \]

The dependence of the coefficient \(\Phi\), as a function of \(t_k^y\), is given in Fig. 4. The dependence of \(N_d\) on \(t_k^y\) is presented in Fig. 3 for the example considered earlier. In this case the efficiency of the compressor installation for a polytropic compression process is taken as \(\eta_n=0.6\).

Thus, the power delivered to the consumer will be determined as the difference between the power of the utilization turbine and the power expended on the installation’s own needs, i.e.,

\[ N_n=N_y-N_{vod}-N_d \ \text{kW}. \tag{8} \]

In Fig. 3, the solution of equation (8) with respect to \(t_k^y\) is given graphically for the data of the example considered earlier, with \(H_y = 10\) m. From Fig. 3 it is seen that the useful power of the utilization installation, at \(P_k^y = 0.01\) ata, is \(N_p = 800\) kW.

In addition, the power of the circulating pumps of the main turbine will be reduced by the amount

\[ \Delta N_{\text{c.p.}} = H_k \cdot \frac{a t d N}{3.66 \cdot 10^5 \eta_n}\ \text{kW}, \]

since the water will be supplied to the condenser of the main turbine not from the water-supply source, but from the evaporator of the utilization installation, the inclusion of which reduces the head of the circulating pumps by the amount \(H_k\).

Fig. 4

Thus, if \(H_k = 10\) m, then with a circulating-pump efficiency \(\eta_n = 0.65\), \(\Delta N_{\text{c.p.}} = 250\) kW. This power can likewise be delivered to the consumer. Consequently, in all, an additional 1050 kW will be delivered to the consumer, i.e., the increase in efficiency of the condensing station due to the inclusion of the utilization installation may amount to more than 4%.

The design temperature of the water at the inlet to the condenser of the utilization installation, \(t_1^y = 1^\circ\text{C}\), is maintained for six to seven months per year, i.e., for 4500–5000 hours per year; switching on the installation will make it possible to deliver an additional 1050 kW to the consumer. When \(t_1^y\) is increased, the power of the utilization turbine decreases. But even if the utilization factor of the installed capacity is taken as 5000 h/year, the additional useful generation will be

\[ 5000 \times 1050 = 5.25 \cdot 10^6\ \text{kWh per year}. \]

At a conventionally assumed cost of 10 kopecks/kWh, this will make it possible to save

\[ 5.25 \cdot 10^6 \cdot 0.1 = 525000\ \text{rubles per year}. \]

With a 10-percent allocation to fixed assets, this will make it possible to capitalize 5,250,000 rubles in order, without monetary damage to the national economy, to generate \(5.25 \cdot 10^6\) kWh per year. Hence the maximum permissible value of the cost of the installed kW will be

\[ \frac{5.25 \cdot 10^6}{1250} = 4200 \text{ rubles.} \]

Thus, the maximum permissible value of the cost of the installed kW should prove sufficient to implement such installations for generating electric power on the basis of using the heat of circulating water at power plants.

In addition to generating electric power directly by means of a utilization turbine, it is also necessary to note the possibility of reducing the steam consumption of the main turbine and, consequently, ensuring fuel savings by obtaining a deeper vacuum in the condenser of the main turbine. The point is that the utilization installation in a number of cases can be located in close proximity to the station. This will make it possible to use single-pass condensers with a higher cooling ratio for the main turbines, which provide a smaller difference between the temperature of the water at the inlet to and outlet from the condenser. And since the temperature \(t_1\) is assumed constant, then with a decrease in the water-heating range in the condenser, \(t_2\) will decrease, which will make it possible to obtain a deeper vacuum in the main turbine. A 1% deepening of the vacuum gives a fuel saving of approximately 1.5%.

In addition to the indicated advantages of the utilization installation, one more positive aspect of its use should be pointed out.

It is known that, with a certain elevation of the station above the water level in the source and with some distance of the station from the latter, a once-through water-supply system becomes economically disadvantageous. In such cases one switches to a recirculating water-supply system, which has a number of substantial drawbacks, namely:

1) the steam consumption of the turbine increases because of the higher temperature of the cooling water;

2) construction of circulating-water coolers requires additional area and considerable capital investment;

3) in winter there is the formation of fogs and icing of structures located in the immediate vicinity of the circulating-water cooler, etc.

If a utilization installation is included in the system of circulating water conduits, then, as studies show, the limiting delivery head of the water and the distance of the station from the water-supply source increase by approximately one and a half times, i.e., the field of application of once-through water supply is significantly expanded.

In addition, the presence of chemically purified water in the circulating circuit of the main turbine will relieve the station of difficulties caused by scale deposition in condensers, will thereby increase the utilization factor of the installed capacity, and will also make it possible to obtain additional generation of kWh that can be used to satisfy the needs of consumers.