SELECTION OF A WATER SUPPLY SYSTEM AT ELECTRIC POWER PLANTS

E. N. SHADRIN

The data available in the literature on the selection of a water supply system are highly contradictory. Thus, A. M. Romanov [1] says that when the elevation \(H\) of the plant above the level of the water source is no more than \(12\ m\), and when the distance \(L\) is approximately \(1000\ m\), a once-through system is more advantageous; meanwhile, he indicates there that design practice gives, for once-through water supply, \(H < 16\ m\) and \(L < 2000\ m\).

At \(12\ m < H < 25\ m\) and \(1000\ m < L < 2000\ m\), the advantage of applying a once-through system must be checked from the techno-economic point of view. At \(H > 25\ m\) and \(L > 2000\ m\), the use of recirculating water supply is unquestionably advantageous.

A. A. Lagovskii [2] takes the maximum distance of the plant from the source of water supply, when a once-through cooling system is still economically more advantageous, to be \(500\ m\). V. V. Luknitskii [3] recommends taking \(H = 12\ m\) and \(L = 2000\ m\).

A. M. Kazanskii [4] indicates that a once-through system is expedient only when the water source is located in the immediate vicinity of the plant and the difference between the floor levels of the condenser room and the water level in the source is less than \(12\text{–}15\ m\).

V. A. Makeev [5] considers it more advantageous to use a natural source at \(H < 25\ m\), provided that a siphon is necessarily installed on the return line, with a height of up to \(9\text{–}9.5\ m\). American practice establishes the limit of applicability of a once-through system as an elevation of the station site above the water level of \(12\ m\), or a distance of \(1500\ m\).

In studying this question we have assumed:

1. The choice of the water supply system is not limited by the low-water discharge of the river flow.
2. The heat-transfer coefficient in the condenser remains constant.
3. The pumps deliver water in an amount corresponding to the temperature of the source water.
4. The cost of treating the circulating water is the same for the various systems.

The amount of water that the circulating pumps must deliver to the condenser of a steam turbine under design conditions is

\[ W = amdN\ \text{kg/hour}, \quad \text{where} \tag{1} \]

\(m\) — design cooling ratio;
\(d\) — specific steam consumption by the turbine in \(\text{kg}/\text{kW}\cdot\text{h}\);
\(N\) — turbine output, \(\text{kW}\);
\(a\) — coefficient indicating what fraction of the steam enters the condenser.

If we further denote by

\(m'\)—the cooling ratio at the maximum pump capacity;

\(t'^\circ C\)—the water temperature corresponding to \(m'\), then in the period when the water temperature \(t < t'\),

where

\[ W_1^{pr}=am_1^{pr}dN, \]

\[ m_1^{pr}=\frac{t_2-t_k}{t_2-t_1^{pr}}. \]

Here \(t_1^{pr}\) is the mean water temperature in the river during the period when \(t < t'\).
In the summer period, when \(t > t'\).

\[ W_2^{pr}=am'dN \ \text{kg/hour}. \]

The pumps delivering this water overcome the resistance of the condenser, the supply conduits, the water-treatment structures, and the static head.

The resistance of the condenser is

\[ H_k=Z\left(0.031\frac{L_k}{d_k}\cdot\frac{c_w^2}{2g}\beta_1+1.4\frac{c_w^2}{2g}\right)=\psi c_w^2 m \ \text{m water column}. \tag{2} \]

Here the first term characterizes the frictional resistances inside the condenser tubes, and the second—the inlet and outlet resistances; \(\beta_1\) is a coefficient taking into account the influence of the mean temperature and velocity of the water.

Let the period of time when \(t > t'\) be denoted by \(\gamma_1\), in fractions of a year. Then the number of kWh spent per year on overcoming the condenser resistances will be

\[ E_1^{pr}=\frac{AadN\cdot c_w^2\psi}{3.66\cdot10^5\cdot\eta_n\cdot m^2} \left[(1-\gamma_1)m_1^{pr\,3}+\gamma_1m'^3\right]. \tag{3} \]

Usually the pumps deliver the water necessary for cooling the oil and air. The quantity of this water amounts to from 4 to 8% of the circulating-water flow for the condensers as such.

The resistance of the supply conduits is

\[ H_{vod}=\lambda\cdot\frac{L_\mathrm{e}}{d_{vod}}\cdot\frac{c_{vod}^2}{2g}\ \text{m water column}. \]

If it is assumed that, for greater reliability, two lines of conduit will be in operation, then

\[ d_{vod}=\sqrt{\frac{1.06\cdot4amdN}{2\cdot3.6\cdot10^6\pi\cdot c_{vod}}}\ \text{m}. \tag{4} \]

The number of kWh spent per year on overcoming the resistances of the conduits is

\[ E_2^{pr}= \frac{1.06adN c_{vod}^{2.5}\lambda L_\mathrm{e}^{pr}A} {1.6\eta_n\cdot2gm^{2.5}(adN)^{0.5}} \left[(1-\gamma)m_1^{pr\,3}+\gamma_1m'^3\right]. \tag{5} \]

The number of kWh spent per year on overcoming the head due to the static height is

\[ E_3^{pr}= \frac{1.06adNH_n^{pr}A}{3.66\cdot10^5\cdot\eta_n} \left[(1-\gamma_1)m_1^{pr}+\gamma_1m'\right]. \tag{6} \]

We do not take into account the expenditure of energy for overcoming the resistances of the water-treatment structures. This has been done for the reason that, first, these resistances are insignificant in comparison with those indicated above, and, second, this item of expenditure also occurs in the case of circulating water cooling.

Thus, the total expenditure of energy for supplying cooling water is

\[ E^{\mathrm{pr}}=E_{1}^{\mathrm{pr}}+E_{2}^{\mathrm{pr}}+E_{3}^{\mathrm{pr}}\ \text{kWh/year} \tag{7} \]

The full annual cost in rubles, due to the pumping of water, under the fuel-expenditure item is

\[ R_{\mathrm{tsv}}^{\mathrm{pr}}= \frac{860E^{\mathrm{pr}}}{\eta_{k}Q_{r}^{n}} \left(1+\frac{\Sigma \Delta}{100}\right) \frac{R_{T}}{1000}. \tag{8} \]

Here \(R_T\) is the cost of a ton of fuel in rubles,

\[ \left(1+\frac{\Sigma \Delta}{100}\right) \]

is the operating coefficient.

The excess consumption of steam by the turbine, in rubles, during the period when \(t>t'\), under the fuel-expenditure item is

\[ R_{\mathrm{per}}^{\mathrm{pr}}= \frac{860}{\eta_{k}Q_{r}^{n}} \left(1+\frac{\Sigma \Delta}{100}\right) \frac{R_T}{1000}\cdot \gamma_{1}A\cdot N\cdot \frac{t_{\mathrm{pr}}'''-t'}{100}. \tag{9} \]

Here \(t_{\mathrm{pr}}'''\) is the mean water temperature for the period under consideration. A more accurate calculation of the excess steam consumption is possible if the guaranteed characteristics of the turbine are known. Here, however, it is assumed that an increase in the temperature of the cooling water by \(1^\circ\text{C}\) causes an increase in steam consumption by \(1\permil\) [6].

We now proceed to the evaluation of costs depending on capital investments.

Deductions according to the capitalization factor for the condenser and the condensing installation will not enter the equation, since they are equal both in the case of a once-through system and in the case of a circulating system.

The cost of one linear meter of water conduit in rubles, installed, is

\[ S_{\mathrm{vod}}=a+bd_{\mathrm{vod}} \tag{10} \]

Here the coefficients \(a\) and \(b\) may be taken as constant within known limits of variation of \(d_{\mathrm{vod}}\). They take into account the laying of a double water conduit:

\[ S_{\mathrm{vod}}=a+b\cdot \frac{(amdN)^{0.5}}{2300\cdot c_{\mathrm{vod}}^{0.5}}. \tag{11} \]

The sum of the annual capitalization deductions for the water conduit is

\[ R_{\mathrm{vod}}^{\mathrm{pr}}= \frac{S_{\mathrm{vod}}\cdot L_{0}^{\mathrm{pr}}u}{100} = \frac{u}{100}\cdot L_{0}^{\mathrm{pr}} \left[ a+b\frac{(amdN)^{0.5}}{2300\cdot c_{\mathrm{vod}}^{0.5}} \right]. \tag{12} \]

Here \(L_{0}^{\mathrm{pr}}\) is the actual length of the water conduit, and \(u\) is the deductions in percent.

The cost of the pumping station \(S_{\mathrm{nas}}=f(N_{\mathrm{nas}})\) is taken to be proportional to its capacity \(N_{\mathrm{nas}}\), where \(N_{\mathrm{nas}}\) is in hp, and \(f\) is a numerical coefficient representing the cost of machinery per 1 hp with complete installation, foundations, and also the cost of premises.

\[ R_{\mathrm{nas}}^{\mathrm{pr}}= \frac{S_{\mathrm{nas}}\cdot u}{100} = 1.36\,\frac{u\cdot f}{100}\cdot \frac{E^{\mathrm{pr}}}{A} \tag{13} \]

where \(E^{\mathrm{pr}}\) is taken from equation 7.

Thus, the sum of the annual costs associated with supplying water to the station, for the once-through system, is

\[ R_{\Sigma}^{pr}=R_{u.v}^{pr}+R_{per}^{pr}+R_{vod}^{pr}+R_{nas}^{pr}. \tag{14} \]

We now proceed to an estimate of the costs for a recirculating cooling system. For this purpose we additionally introduce the following notation:

\(t''\)—the average water temperature in the basin during the period when \(t<t'\);

\(t_{ob}'''\)—the same for the period when \(t>t'\);

\(m''\)—the cooling ratio corresponding to \(t''\)

\[ m''=\frac{i_2-t_k}{t_2-t''}. \]

Here, as before, \(t_s-t_2=\mathrm{const}\).

The number of kWh expended per year to overcome the resistance of the condenser is

\[ E_1^{ob}=\frac{adNC_w^{2}A\psi}{3.66\cdot 10^5\cdot \eta_n\cdot m^2} \left[(1-\gamma_2)m''^3+\gamma_2 m'^3\right], \tag{15} \]

where \(\gamma_2\) is a coefficient characterizing what part of the year is occupied by the period when \(t>t'\).

The number of kWh expended per year to overcome the resistance of the water conduits is

\[ E_2^{ob}= \frac{1.06\,adNC_{vod}^{2.5}A\lambda L_z^{ob}} {1.6\cdot 2g\cdot m^{2.5}(\alpha dN)^{0.5}} \left[(1-\gamma_2)m''^3+\gamma_2m'^3\right]. \tag{16} \]

If we denote the head determined by the leveling height and the free head before the nozzles by \(H_n^{ob}\), then the number of kWh expended to overcome this head is

\[ E_3^{ob}= \frac{1.06adNA\cdot H_n^{ob}} {3.66\cdot 10^5\eta_n} \left[(1-\gamma_2)m''^3+\gamma_2m'^3\right]. \tag{17} \]

The correct choice of head before the nozzles is of considerable importance. In design, \(H_n^{ob}\) may be taken as being on the order of 6–8 m [7]. In this case its value may be taken the same both for spray basins and for cooling towers. The P-16 nozzle requires a head of 12 m [8].

For Kerting-type nozzles, the most advantageous head under normal conditions is 4.7 m.

With a recirculating water-cooling system, a shore pumping station is also constructed, the purpose of which is to make up the water losses in the circulating system. These losses consist of losses due to evaporation, drift, and blowdown.

Since the cooling of the water occurs primarily as a result of evaporation, this loss can be calculated from the following considerations.

In the condenser, to the water from each kilogram of steam there is transferred

\[ i_2-t_k\simeq 520-530\ \text{kcal}. \]

The heat of vaporization at \(t=25^\circ\mathrm{C}\), which may be taken as the average for spray basins and cooling towers, is

\[ r=583.2\ \text{kcal/kg}. \]

Then, for a cooling ratio \(m=60\),

\[ P_1=\frac{530\cdot 100}{583.2\cdot 60}=1.5\%. \]

The above is confirmed by the curves in Fig. 1 [7], constructed from exact formulas.

The magnitude of drift loss \(P_2\), on the basis of experimental data, may be taken as \(0.5\)--\(0.75\%\) for tower coolers, and from \(1.5\) to \(3\%\) for spray ponds [10].

The magnitude of system blowdown, as a percentage of the total quantity of circulating water, is

where

\[ P_3=\frac{a_o P_1}{a_m-a_o}-P_2, \tag{18} \]

where

\(a_o\) is the hardness of the water, expressed in German degrees,
\(a_m\) is the maximum permissible carbonate hardness, expressed in German degrees.

Fig. 1

Depending on the composition of the make-up water and the operating regime of the installation, \(a_m\) may vary from \(7\)--\(8^\circ\) to \(12\)--\(14^\circ\) German [9].

The number of kWh expended to overcome the resistance of the supply water conduits is

\[ \mathcal{E}_{1}^{ob}= \frac{\alpha d N A L_{ep}^{pr}\cdot c_{vod}^{2.5}\rho^{0.5}\lambda} {1550\cdot 2g\eta_n m^{2.5}(\alpha dN)^{0.5}} \left[(1-\gamma_2)m''^{3}+\gamma_2 m'^{3}\right]. \tag{19} \]

The same, for overcoming the head determined by the leveling height, is

\[ \mathcal{E}_{5}^{ob}= \frac{\alpha d N A H_{pr}^{pr}\cdot P} {3.66\cdot 10^{7}\cdot \eta_n} \left[(1-\gamma_2)m''+\gamma_2 m'\right]. \tag{20} \]

Here \(P=P_1+P_2+P_3\) is the total percentage of make-up.

The total expenditure of energy for the supply of cooling water and make-up water in a recirculating system is

\[ \mathcal{E}^{ob}=\mathcal{E}_1^{ob}+\mathcal{E}_2^{ob}+\mathcal{E}_3^{ob}+\mathcal{E}_4^{ob}+\mathcal{E}_5^{ob}. \]

The total annual cost, in rubles, caused by pumping the circulating water and the make-up water is

\[ R_{u.v}^{ob}=\frac{860\mathcal{E}^{ob}}{\eta_k Q_p^n} \left(1+\frac{\Sigma A}{100}\right)\frac{R_T}{1000}. \tag{21} \]

The excess consumption of turbine steam during its operation under deteriorated vacuum, under the fuel-consumption item, is

\[ R_{per}^{ob}=\frac{860}{\eta_k Q_p^n} \left(1+\frac{\Sigma A}{100}\right)\gamma_2 \Delta N \frac{t_{ob}^{\prime\prime\prime}-t'}{100}. \tag{22} \]

The sum of the annual capital charges for the water conduit is

\[ R_{vod}^{ob}=\frac{u}{100} \left\{ L_o^{ob}\left[ a+b\frac{(amdN)^{0.5}}{2300\,c_{vod}^{0.5}} \right] + L_o^{pr}\left[ a+b\frac{P^{0.5}(amdN)^{0.5}}{23700\,c_{vod}^{0.5}} \right] \right\}. \tag{23} \]

Here \(L_o^{ob}\) is the actual length of the water conduit in the recirculating system. The sum of the annual charges for the pumping station is

\[ R_{nas}^{ob}=\frac{1.36\,u\,f\,\mathcal{E}^{ob}}{100A}. \]

The cost of the circulating-water cooler, in rubles, is

\[ S_{oxl}=10^{-3}amdN\varphi,\qquad \text{where} \]

\(\varphi\) is the cost of the cooler, in rubles, per \(1\ \mathrm{m}^3\) of cooled water. Then the sum of the annual capital charges for the cooler is

\[ R_{ox.l}=10^{-5}amdN\varphi u_{ox.l}. \tag{24} \]

The sum of the annual costs associated with the supply and cooling of water in a recirculating system is

\[ R_{\Sigma}^{ob}=R_{u.v}^{ob}+R_{por}^{ob}+R_{vod}^{ob}+R_{nas}^{ob}+R_{ox.l}. \tag{25} \]

To select the water-supply system, i.e., to determine \(H_n^{pr}\) and \(L_o^{pr}\) for which both the once-through and the recirculating systems are equivalent from the techno-economic point of view, it is necessary to solve equations 14 and 25 jointly.

\[ R_{\Sigma}^{pr}=R_{\Sigma}^{ob}. \tag{26} \]

In the coordinates \(L_o^{pr}\), \(H_n^{pr}\), this expression is the equation of a straight line, which is easy to construct by alternately setting \(L_o^{pr}\) and \(H_n^{pr}\) equal to zero.

If we put \(\eta_k=0.68\) and, as a rough approximation, take \(\lambda=0.03\), then, for \(L_o^{pr}=0\) and under the condition

\[ R_{nas}^{pr}=R_{nas}^{ob}, \]

we obtain, for the elevation of the station above the water level in the source,

\[ H_n^{pr}= \frac{ \dfrac{C_w^{2}\psi j^{ob}}{m^2} +1.06H_n^{ob}\rho^{ob} +\dfrac{2500}{ad} \left[ \gamma_2\left(t_{ob}^{\prime\prime\prime}-t'\right) -\gamma_1\left(t_{np}^{\prime\prime\prime}-t'\right) \right] }{ 1.06\rho^{pr}\cdot 0.01p_r^{ob} } + \]

\[ \frac{ \frac{2.9 \cdot 10^5 \eta_k Q_p^n}{\alpha R_T \left(1+\frac{\Sigma \Delta}{100}\right) A d N} \left\{ \frac{u L_o^{ob}}{100} \left[ a+b \frac{(a m d N)^{0.5}}{2300 c_{vod}^{0.5}} \right] +10^{-5} a m d N \varphi u_{o.kh} \right\} }{ 1.06 \rho^{pr}\cdot 0.01 p \rho^{ob} } = \frac{M}{1.06 \rho^{pr}-0.01 p \rho^{ob}} \tag{27} \]

Here

\[ j^{ob}=[(1-\gamma_2)m''^3+\gamma_2 m'^3], \]

\[ \rho^{ob}=[(1-\gamma_2)m''+\gamma_2 m'], \]

\[ \rho^{pr}=[(1-\gamma_1)m_1^{pr}+\gamma_1 m']. \]

If we set \(H_n^{pr}=0\), then

\[ L_o^{pr}= \frac{M}{ \frac{c_{vod}^{2.5}\beta \cdot j^{pr}}{963(a m d N)^{0.5}} + \frac{0.122 \eta_k Q_p^n u b \cdot m^{0.5}} {j^{pr}\alpha^{0.5}R_T \left(1+\frac{\Sigma \Delta}{100}\right) A(dNc_{vod})^{0.5}} (10.3-p^{0.5}) } \tag{28} \]

where

\[ \beta=\frac{L_e^{pr}}{L_o^{pr}}, \]

\[ j^{pr}=[(1-\gamma_1)m_1^{pr\,3}+\gamma_1 m'^3]. \]

In equations 27 and 28, the terms characterizing the energy expenditures for overcoming condenser resistance in the case of a once-through system and the resistance of the supply conduits in the case of a recirculating system have been omitted. This has been done on the grounds that, first, the costs characterized by these terms are insignificant in comparison with the other costs and, second, they enter the numerators of the fractions with opposite signs.

In Fig. 2, in the axes \(L_o^{pr}\), \(H_n^{pr}\), a straight line is given, constructed from equations 27 and 28 for the particular example when

\[ m=60;\quad d=4.5\ \text{kg/kW·h};\quad N=25000\ \text{kW}; \]

\[ t=15^\circ\text{C};\quad c_w=2\ \text{m/sec};\quad c_{vod}=1.8\ \text{m/sec};\quad L_o^{ob}=70\ \text{m}; \]

\[ \alpha=0.8;\quad \beta=1.2;\quad H_n^{ob}=7\ \text{m};\quad \eta_k Q_p^n=1000,\quad \eta_n=0.68; \]

\[ R_T=60\ \text{rub/t};\quad \Sigma\Delta=10\%;\quad a=25;\quad b=450; \]

\[ A=5000\ \text{h/year};\quad \varphi=25\ \text{rub/m}^3\ \text{of cooling water}; \]

\[ u_{o.kh}=3\%;\quad u=10\%;\quad P=7\%;\quad \gamma_1=0.25;\quad \gamma_2=0.5. \]

From Fig. 2 it is seen that, under the adopted conditions, the limiting values for \(H_n^{pr}\) and \(L_o^{pr}\) may be taken as 20 m and 2000 m. In addition, the graph shows that an increase in geodetic height by each 10 m is equivalent to increasing the distance of the station from the water-supply source by 600–700 m.

Fig. 3 shows the changes in \(H_n^{pr}\) and \(L_o^{pr}\) as a function of the pressure before the nozzles in the cooling devices.

Figs. 4 and 5 establish that increasing the plant capacity, as well as using low-grade fuels, increases the limiting values of \(H_n^{pr}\) and \(L_o^{pr}\).

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Conclusions

1. The limiting values of the elevation of the station above the water level in the source, and the distance of the station from the latter, at which it is still expedient to use a once-through water-supply system, are variable quantities dependent on the capacity of the station, the grade and cost of the fuel used, the regenerative feedwater-heating scheme, the cost of circulating-water coolers, etc.

2. With an increase in station capacity and with the use of low-grade fuels, the limits of applicability of once-through systems are extended.

3. When selecting a water-supply system, it is necessary to take into account the rapid commissioning of capacities at our stations and in systems, as well as the conversion of stations to low-grade fuel.

References

1. Romanov A. M.—Water Supply of Power Installations, publ. 1936.

2. Lagovsky A. A.—Thermal Electric Power Stations, Gosenergoizdat, 1948.

3. Luknitsky V. B.—Electric Power Stations of Small and Medium Capacity, 1948.

4. Kazansky A. M.—Auxiliary Equipment of Turbine Installations, 1941.

5. Makeev V. A.—Condensing Devices of Steam-Power Installations, publ. 1935.

6. Berman L. D.—“Ways of Improving the Operation of Spray Ponds and Cooling Towers,” journal Rabochii energetik, No. 1, 1940.

7. Radtsig V. A.—“Spray Ponds,” journal Bulletin of Gidromez, Nos. 1–2, 1930.

8. Farforovsky B. S.—“Selection of the Magnitude of Head in Spray Ponds,” Teplo i Sila, No. 8, 1937.

9. Butakov I. N.—“A New Type of Tower Cooler,” Teplo i Sila, No. 11, 1930.

10. Berman L. D.—“Calculations of Water Regimes in Recirculating Water-Supply Systems,” Elektricheskie stantsii, No. 3, 1946.

Noted Misprints