FUEL SAVINGS WHEN USING HEAT LOSSES IN THE CONDENSER OF A TURBINE UNIT TO PREHEAT MAKE-UP WATER FOR THE HEATING NETWORK

V. A. Bragin, V. I. Bespalov, L. A. Belev,
N. N. Galashov

(Presented by the scientific seminar of the Department of Thermal Power Plants)

To improve the economy of thermal power plants, efforts are made to use the heat losses in the condensers of district-heating turbine units caused by the presence of ventilation steam flows into the condensers. For this purpose, in the condensers of a number of turbines (T-50-130, T-100-130) special built-in tube bundles are provided; in other machines the condensers themselves are used after minor reconstruction. Most often the indicated loss is eliminated by cooling the condenser or the built-in bundle with return network water, or, when there are significant water withdrawals from the network, with make-up water of the heating network. Under the conditions imposed by the maximum permissible temperature of the turbine exhaust hood, it is most expedient to carry out cooling with make-up water of the heating network. In this case it is possible to utilize the heat losses in the condensers of a number of machines. The possibilities for cooling with return network water are narrower, and they decrease as the outdoor-air temperature falls, since the temperature of the return network water rises. A number of works [1, 2] are devoted to the question of determining fuel savings when eliminating heat losses in condensers by heating network water. Below we consider the change in the economy of a district-heating turbine unit when using the heat loss in the condenser to heat make-up water for the heating network.

When heat losses in the condenser are eliminated, the machine begins to operate completely according to the heat schedule. The change in the economy of the station is determined under the condition of constant delivery of electric and heat energy to consumers. The change in the power of the turbine unit is compensated by the power of the replacing condensing power station. The diagram of the main heat flows in the turbine unit when the condenser is cooled by circulating water is shown in Fig. 1, a; when it is cooled by make-up water of the heating network—in Fig. 1, b.

In the case of cooling the condenser with circulating water, the heat consumption for the turbine unit will be equal to

\[ Q_{\mathrm{TU}} = Q_{\mathrm{T}} + 860 N_{\mathrm{e}} + Q_{\mathrm{k}} + Q_{\mathrm{p}} . \tag{1} \]

Here \(Q_{\mathrm{T}}\) is the heat supplied from the controlled extraction to consumers;
\(N_{\mathrm{e}}\) is the power at the generator terminals;
\(Q_{\mathrm{k}}\) is the heat loss in the condenser (with the rotary diaphragm fully closed);

\(Q_{\mathrm{p}}\) is the mechanical losses of the turbine and generator and the heat losses by the elements of the turbine unit.

When the circulating water is replaced by make-up water from the heating network, and at a constant load \(Q_t\), the vacuum in the condenser deteriorates, and the steam flow to the extraction and to the turbine is reduced. In this case the heat consumption of the turbine unit will be:

\[ Q_{\mathrm{tu}1}=Q_{\mathrm{t}1}+Q_{\mathrm{i}}+860N_{\mathrm{e}1}+Q_{\mathrm{p}1}=Q_t+860N_{\mathrm{e}1}+Q_{\mathrm{p}1}. \tag{2} \]

Here \(Q_k\) is the heat used to preheat the make-up water of the heating network in the condenser.

The index “1” in (2) indicates that the quantity refers to the operating mode of the turbine unit when the condenser is cooled by make-up water.

In (1) and (2) it may be assumed with sufficient accuracy that \(Q_{\mathrm{p}}\simeq Q_{\mathrm{p}1}\). Then the reduction in the heat consumption of the turbine unit will be equal to:

\[ \Delta Q_{\mathrm{tu}}=Q_{\mathrm{tu}}-Q_{\mathrm{tu}1}=Q_k+860\left(N_{\mathrm{e}}-N_{\mathrm{e}1}\right). \tag{3} \]

The decrease in turbine power occurs as a result of a reduction in the heat drop of the low-pressure section \((p_k<p_{k1})\), a reduction in the steam flow to the controlled extraction, and a reduction in the steam flow to regeneration.

Fig. 1

The hourly heat saving for the turbine unit, taking into account the replacement power, is:

\[ \Delta Q_{\mathrm{et}}=\Delta Q_{\mathrm{tu}}-q_z\left(N_{\mathrm{e}}-N_{\mathrm{e}1}\right) =Q_k-\left(q_z-860\right)\left(N_{\mathrm{e}}-N_{\mathrm{e}1}\right). \tag{4} \]

Assuming the mechanical losses of the turbine and generator losses, for a small \(\Delta N_{\mathrm{e}}=N_{\mathrm{e}}-N_{\mathrm{e}1}\), to be approximately constant, equation (4) may be written as:

\[ \Delta Q_{\mathrm{et}}=Q_k-\left(q_z-860\right)\left(\Delta N_1+\Delta N_2+\Delta N_3\right). \tag{5} \]

Here \(q_z\) is the specific heat consumption for electric-power generation at the replacement condensing power plant;

\(\Delta N_1\), \(\Delta N_2\), and \(\Delta N_3\) are the changes in turbine power, respectively, due to the reduction in the heat drop of the low-pressure section, due to the reduction in steam flow to the controlled extraction, and due to the reduction in steam flow to regeneration.

The heat used to preheat the make-up water in the condenser may be represented as:

\[ Q_{\mathrm{i}}=Q_k+860\left(\Delta N_1\pm\Delta N_4\right)-\Delta Q_k, \tag{6} \]

where \(\Delta N_4\) is the change in the power of the steam flow passing into the condenser in the high-pressure part of the turbine. The sign of \(\Delta N_4\) is determined by the direction of change in the internal relative efficiency of the high-pressure part. If the efficiency increases as the steam flow through the turbine decreases, then \(\Delta N_4\) must be subtracted; if it decreases, then \(\Delta N_4\) must be added. With a small change in the steam flow through the high-pressure part, the efficiency for this part of the turbine may be considered unchanged with sufficient accuracy, and then \(\Delta N_4=0\). In the following discussion it is assumed that \(\Delta N_4 \approx 0\).

\[ \Delta Q_k = D_k(\bar{t}_{k1}-\bar{t}_k). \]

Here \(D_k\) is the ventilation leakage of steam into the condenser; \(\bar{t}_k\) and \(\bar{t}_{k1}\) are the enthalpies of the condensate at the outlet from the condenser when it is cooled by circulating water and by the make-up water of the heating network.

The change in turbine power \(\Delta N_3\) occurs because of changes in the steam parameters in the chambers of the unregulated extractions and in the steam flow to these extractions, and also as a result of the change in pressure in the condenser. At a constant leakage of steam into the condenser, the main influence here is exerted by the change in steam flow to the extraction; therefore \(\Delta N_3\) may be expressed through \(\Delta N_2\) as

\[ \Delta N_3 = \alpha_p \cdot \Delta N_2. \]

Denoting by \(e\) the specific generation of electric power based on the heat supplied to heat consumers from the regulated extraction, one may write

\[ \Delta N_2+\Delta N_3=\Delta N_2(1+\alpha_p)=e(1+\alpha_p)Q_h. \tag{7} \]

Then, taking (6) and (7) into account, equation (5), after transformations, takes the form

\[ \Delta Q_{et}=Q_k[1-e(1+\alpha_p)(q_3-860)]-\Delta N_1\cdot[1+860e(1+\alpha_p)](q_3-860)+ \]
\[ +\Delta Q_k e(1+\alpha_p)(q_3-860). \tag{8} \]

The value of \(\Delta N_1\) for the unit can be determined most accurately from the experimental curve \(\Delta N_1=f(p_k)\) or in accordance with the recommendations set forth in [2, 3].

When operating with a peak unit and an increased pressure in the chamber of the regulated extraction, the steam flow to the condenser with the rotary diaphragm closed increases; therefore \(Q_k\) increases. The hourly saving in heat consumption for the turbine unit can also be determined in this case from (8). It is only necessary to take into account the changes in \(Q_k\), \(e\), \(\alpha_p\), \(\Delta N_1\), and \(\Delta Q_k\), as well as the source of steam supply for the peak heating unit. The hourly saving in this mode will be denoted by \(\Delta Q'_{et}\).

The fuel saving over the period of operation without the peak heater (the first period) will be equal to [1]

\[ \Delta B_{tu}=\frac{\displaystyle\int_0^{\tau_1}\Delta Q_{et}\cdot d\tau}{7000\cdot\eta_{ku}}, \tag{9} \]

where \(\tau_1\) is the total duration of the first period;
\(\eta_{ku}\) is the average efficiency of the boiler unit over this period.

The fuel saving for the second period is calculated analogously,

when the peak heater is switched on and the pressure in the controlled-extraction chamber is raised:

\[ \Delta B'_{\mathrm{tu}}= \frac{\displaystyle\int_{0}^{\tau_2}\Delta Q'_{\mathrm{et}}\cdot d\tau} {7000\cdot \eta'_{\mathrm{ku}}}, \tag{10} \]

where \(\tau_2\) is the total duration of the second period;
\(\eta'_{\mathrm{ku}}\) is the average efficiency of the boiler plant during this period.

In the second period, with slight fluctuations in the flow rate of make-up water for the heating network and in its initial temperature, the possibilities for using condenser heat from several units of the station decrease.

The fuel saving according to (9) and (10) does not take into account changes in the consumption of electric power for auxiliary needs. The change in fuel consumption caused by a change in the expenditure of energy for auxiliary needs can, for each operating period, be calculated according to [1] by the formulas

\[ \Delta B_{\mathrm{sn}}= \frac{\displaystyle\int_{0}^{\tau_1}\Delta N_{\mathrm{sn}}\cdot q_3\cdot d\tau} {7000\cdot \eta_{\mathrm{ku}}}, \tag{11} \]

\[ \Delta B'_{\mathrm{sn}}= \frac{\displaystyle\int_{0}^{\tau_2}\Delta N'_{\mathrm{sn}}\cdot q_3\cdot d\tau} {7000\cdot \eta'_{\mathrm{ku}}}. \tag{12} \]

Here \(\Delta N_{\mathrm{sn}}\) and \(\Delta N'_{\mathrm{sn}}\) are the changes in auxiliary power, respectively in the first and second periods. These changes are determined by the specific conditions of the station.

If the make-up water of the heating network is heated successively in the condensers of several CHPP units, then for each of them the corresponding fuel savings are calculated according to (9) and (10). It is more convenient to calculate the changes in fuel consumption according to (11) and (12) at once for the entire CHPP.

The total fuel saving for the CHPP will be equal to

\[ \Delta B_{\mathrm{tets}}= \sum_{1}^{n_1}\Delta B_{\mathrm{tu}i} + \sum_{1}^{n_2}\Delta B'_{\mathrm{tu}i} \pm \Delta B_{\mathrm{sn}} \pm \Delta B'_{\mathrm{sn}}. \tag{13} \]

Here \(n_1\) and \(n_2\) are the number of turbine units in whose condensers the make-up water of the heating network is heated successively in the first and second periods. In the general case, it may be that \(n_1=n_2\) or \(n_1>n_2\).

The consumption of electric power for auxiliary needs, depending on a number of factors and on the specific CHPP scheme, may increase or decrease when heat losses in the condensers are utilized.

From (8), the relative heat saving per turbine unit will be equal to

\[ \Delta q_{\mathrm{et}}= 1-\varepsilon(1+\alpha_{\mathrm{p}})(q_3-860) - \frac{\Delta N_1}{Q_{\mathrm{k}}} \left[1+860\varepsilon(1+\alpha_{\mathrm{p}})\right](q_3-860) + \]

\[ + \frac{\Delta Q_{\mathrm{k}}}{Q_{\mathrm{k}}} \varepsilon(1+\alpha_{\mathrm{p}})(q_3-860). \tag{14} \]

It follows from (14) that, all other conditions being equal, the relative saving will be the greater the smaller \(\Delta N_1\)—the change in the output of the low-pressure part when the pressure in the condenser is increased; the greater \(\Delta Q_k\)—the return of heat with the condensate to the turbine-unit circuit; the smaller \(e\)—the specific generation of electric power on the basis of the controlled extraction, or the higher the pressure in the chamber of the controlled extraction; the smaller the change in steam flow to the controlled extraction, and the less the increase in pressure in the condenser affects power generation through regenerative extractions (the smaller \(\alpha_p\)); and the smaller \(q_z\)—the specific heat consumption for electric-power generation at the replacement district power station.

REFERENCES

1. E. I. Benenson and G. D. Barinberg. Fuel savings when eliminating heat losses in the condenser of district-heating turbine units. Teploenergetika, 1970, No. 4.

2. G. A. Shapiro, M. A. Trubilov, Yu. V. Zakharov, V. F. Gutorov, and D. V. Mikhailov. Determination of the economy of operation of T-50-130 turbines with three-stage heating of network water. Teploenergetika, 1971, No. 11.

3. G. A. Shapiro, M. A. Trubilov, Yu. V. Zakharov, V. F. Gutorov, and I. I. Boiko. Experimental investigation of power losses due to friction and ventilation in a UTMZ turbine of type T-50-130. Teploenergetika, 1972, No. 1.