Proceedings

of the Tomsk Polytechnic Institute, awarded the Order of the October Revolution and the Order of the Red Banner of Labor, named after S. M. Kirov

Volume 205                                                                                                                1972

Increasing the Load of Extraction Stages of District Heating Turbines Based on Snow Melting

N. A. Popov

(Presented by the Department of Industrial Thermal Power Engineering and by the scientific seminar of the Thermal Power Engineering Faculty)

Increasing the load of the lower extraction stages of district heating turbines, when the heat load is less than their capacity, can be carried out by organizing the melting of snow at the places where it is collected, instead of transporting it to dumps.

Without touching in this article on the economic side of the question, let us consider the technical possibilities of introducing this additional heat load.

It is known that during snowfall and in the spring-autumn period of the year, when the outdoor-air temperature \(t_n\) is higher than the design temperature of the thermal power plant \(t_n^{\mathrm{TPP}}\), the extraction stages of district heating turbines are underloaded in terms of heat.

Turning to the normal heating schedule of water temperatures in the heat network (Fig. 1), we see that the loading of the extraction stages during snow melting can be performed by additionally increasing (from \(t_n^{\mathrm{TPP}}\)) the temperature difference by the amount \(\delta t\). In the limiting case, the line defining this additional difference (at a constant flow rate of network water) will be represented by a dashed line equidistant from the return-water temperature line \(\tau_{20}\).

The upper boundary of the interval of outdoor-air temperatures at which snow melting can be carried out on the basis of district heating is taken to be the temperature \(t_n = 0^\circ\mathrm{C}\).

In addition, for the purposes of snow melting, heat extraction from the extraction stages can be used owing to the troughs in the daily schedules of ventilation load in municipal, public, and, partly, industrial buildings during the hours when the ventilation systems with air heating in these buildings are not operating.

Thus, for the purposes of snow melting, a portion of the heat capacity of turbine extraction stages equal to the following can be used:

\[ \Delta Q_{\mathrm{ex}}^{\mathrm{sm}} = \left(cG' \delta t^{\mathrm{sm}} + cG_v' \Delta t_v^{\mathrm{sm}}\right)\cdot 10^{-3} \quad \text{MJ/h}, \tag{1} \]

where \(\Delta Q_{\mathrm{ex}}^{\mathrm{sm}}\) is the additional heat capacity of the extraction stages of district heating turbines at the design outdoor-air temperature for snow melting, MJ/h;

\(c\) is the heat capacity of network water, J/kg·h;

\(G^{\mathrm{sm}}\) is the total flow rate of network water in the heat network, kg/h;

\[ \delta \tau^{\mathrm{st}}=\tau'_1{}^{\mathrm{st}}-\tau_{10}^{\mathrm{st}} \]
is the amount by which the temperature in the supply main is increased at \(t_{\mathrm{n}}^{\mathrm{st}}\), °C;

\[ \tau'_1{}^{\mathrm{st}} \]
is the water temperature in the supply main under the increased schedule at \(t_{\mathrm{n}}^{\mathrm{st}}\), °C;

\[ \tau_{10}^{\mathrm{st}} \]
is the water temperature in the supply main under the normal heating schedule at \(t_{\mathrm{n}}^{\mathrm{st}}\), °C;

\[ G'_{\mathrm{v}} \]
is the design flow rate of network water to those ventilation installations which do not operate during snow-melting hours, kg/s;

\[ \Delta \tau_{\mathrm{v}}^{\mathrm{st}}=\tau_1^{\mathrm{st}}-\tau_{2\mathrm{v}}^{\mathrm{st}} \]
is the difference between the water temperatures before and after the heaters of the ventilation installations at \(t_{\mathrm{n}}^{\mathrm{st}}\), °C.

The design outdoor-air temperature for snow melting is taken as the average, over the duration of occurrence, of the outdoor-air temperature in the interval from \(t_{\mathrm{n}}=0^\circ\mathrm{C}\) to \(t_{\mathrm{n}}^{\mathrm{TPP}}\).

Fig. 1. Normal schedule of water temperatures in the heat network, adjusted to account for the heat load for snow melting

The amount of heat that can be used during the heating season for snow-melting purposes is

\[ Q_{\mathrm{st}}^{\mathrm{year}}=cG'\delta\tau^{\mathrm{st}}n_1+cG'_{\mathrm{v}}\Delta\tau_{\mathrm{v}}^{\mathrm{st}}n_2)\cdot 10^{-6}\ \text{MJ/year}, \tag{2} \]

where \(n_1\) is the number of hours during the heating season for which the calculated additional thermal capacity of the turbine extractions is used by increasing the temperature of the network water after the main heaters;

\(n_2\) is the number of hours for which the thermal capacity of the ventilation systems is used for snow melting.

In addition to the possibility of supplying heat from a TPP for snow melting on the basis of district heating, certain conditions are also necessary under which this possibility could be realized.

These conditions include the discharge of meltwater and the transport of heat for snow melting without disrupting the normal operation of the existing sewerage system and heat networks.

Below, the possibility of fulfilling these conditions will be shown.

Fig. 2 presents a schematic diagram of an installation for melting snow at a customer connection. Here, the melted circulating water is taken by pump 1 from the receiver of housing 2 and, after passing through mud trap 3, is directed to heat exchangers I and II. In heat exchanger I it is heated by the heat of the network water (during hours when customers have no load for hot-water supply or ventilation), and in heat exchanger II by the heat of the return water from local customer systems. From the heat exchangers the heated water goes to nozzles 4, by means of which it is sprayed and, passing through the layer of snow, melts it. The meltwater is discharged into the sewerage system from the upper part of the receiver of the snow-melting unit.

Fig. 2. Schematic diagram of a surface-contact installation for melting snow

Since an additional resistance (heat exchanger II) is introduced downstream of the local systems, the head developed by the elevator will not be sufficient to overcome this additional resistance. Under these conditions it is necessary to install a low-head mixing pump 5 on the jumper of the heating system.

As indicated above, when organizing snow melting it is necessary to observe two additional conditions:

1) the possibility of passing meltwater without disrupting the normal operation of the existing city sewerage system,

2) not exceeding the design flow rate of network water during the snow-melting period.

If we consider an approximate daily schedule of hot-water consumption for domestic draw-off needs, shown in Fig. 3, we see that the average daily flow rate of hot water $G_{\mathrm{hw}}^{\mathrm{av}}$ is approximately

45% of the maximum, which determines the carrying capacity of sewer collectors from individual buildings or blocks of development.

Fig. 3. Approximate daily schedule of hot-water supply for a residential building

In order not to disrupt the operation of the sewer system, snow melting must be carried out during those hours of the day when there is no discharge of water from hot-water supply fixtures, or when it is reduced to the average daily value, i.e., over \(T_{\mathrm{st}}\) hours. When hot water is used, it is usually diluted to a temperature of \(38\text{--}40^\circ\mathrm{C}\). Therefore, the amount of diluted water discharged into the sewer system will increase by 50% and is shown in the graph by a dashed line. Then the capacity of the snow-melting units according to the first condition for the given built-up area should be:

\[ G_{\mathrm{st}}^{k} \leq 1.5\,G_{\mathrm{gv}}^{\mathrm{sr}} \quad\text{— when melting snow during the daytime hours,} \]
\[ G_{\mathrm{st}}^{k} \leq 3.3\,G_{\mathrm{gv}}^{\mathrm{sr}} \quad\text{— the same during the nighttime hours,} \tag{3} \]

where

\[ G_{\mathrm{gv}}^{\mathrm{sr}} = 0.175\,F_{\mathrm{kv}}\cdot z\cdot n\cdot h\cdot 10^{-3}, \ \frac{\mathrm{kg}}{\mathrm{h}}, \tag{3-1} \]

\(F_{\mathrm{kv}}\) — built-up area, \(\mathrm{m}^2\);

\(z\) — rate of hot-water consumption per person per day, \(\mathrm{kg}/(\text{person}\cdot\text{day})\);

\(n\) — number of stories of the buildings;

\(h\) — floor height, \(\mathrm{m}\).

The capacity of snow-melting units according to the second condition in the general case is written as:

\[ G_{\mathrm{st}}^{c} = \frac{ \left(G_{\mathrm{gv}}^{\mathrm{sr}}+G_{v}^{\prime}\right) \left(\tau_{1}^{\mathrm{st}}-\tau_{\mathrm{p1}}^{\mathrm{st}}\right)c\cdot\eta_{\mathrm{st}} }{ r-c_{c}t_{\mathrm{n}}^{\mathrm{st}} } + \]

\[ + \frac{ \left(G_{\mathrm{gv}}^{\mathrm{sr}}+G_{v}^{\prime}+G_{0}^{\prime}\right) \left(\tau_{\mathrm{sr}}^{\mathrm{st}}-\tau_{\mathrm{p2}}^{\mathrm{st}}\right)c\eta_{\mathrm{st}} }{ r+c_{c}t_{\mathrm{n}}^{\mathrm{st}} }, \ \mathrm{kg}/\mathrm{h}, \tag{4} \]

where \(G'_0\) is the calculated flow rate of district-heating water for heating over the given built-up area, \(\mathrm{kg/h}\);

\(\tau^{\mathrm{st}}_{\mathrm{n}1}, \tau^{\mathrm{st}}_{\mathrm{n}2}\) are the water temperatures after heat exchangers I and II at \(\tau^{\mathrm{st}}_{\mathrm{n}}\), \({}^{\circ}\mathrm{C}\);

\(\eta_{\mathrm{st}}\) is the efficiency factor of snow melting; it takes into account heat losses to the environment and with the melted water discharged into the sewer system; its value may be taken approximately within the range \(0.09\text{--}0.93\);

\(r\) is the latent heat of fusion of snow, \(\dfrac{\mathrm{kJ}}{\mathrm{kg}}\);

\(\tau^{\mathrm{st}}_{\mathrm{sr}}\) is the temperature at which the mixed return water enters heat exchanger II at \(\tau^{\mathrm{st}}_{\mathrm{n}}\), \({}^{\circ}\mathrm{C}\);

\[ \tau^{\mathrm{st}}_{\mathrm{sr}} = \frac{(G'_{\mathrm{v}} + G^{\mathrm{sr}}_{\mathrm{gv}})\tau^{\mathrm{st}}_{\mathrm{n}1} + G'_0 \tau^{\mathrm{st}}_{20}} {G'_0 + G'_{\mathrm{v}} + G^{\mathrm{sr}}_{\mathrm{gv}}}, \quad {}^{\circ}\mathrm{C}, \tag{4-1} \]

\(\tau^{\mathrm{st}}_{20}, \tau^{\mathrm{st}}_{2\mathrm{v}}, \tau^{\mathrm{st}}_{2\mathrm{gv}}\) are the return-water temperatures after the heating, ventilation, and hot-water-supply systems at \(t^{\mathrm{st}}_{\mathrm{n}}\), \({}^{\circ}\mathrm{C}\).

In open heat networks, instead of the quantity \(G^{\mathrm{sr}}_{\mathrm{gv}}\) in expressions (4) and (4-1), one should take the water flow rate for hot water supply from the supply line of the heat network.

The first term of expression (4) is the output of the snow-melting units obtained by using the heat of the district-heating water in heat exchanger I during hours when there are no hot-water-supply and ventilation loads; the second term is obtained by using, in heat exchanger II, the heat of the return water from local systems and heat exchanger I.

The optimal output of snow-melting units at an individual service connection, \(G^{\mathrm{opt}}_{\mathrm{st}}\), is determined from the minimum of the sum of the dependent annual reduced costs for snow melting, \(Z_{\mathrm{st}}\).

\[ Z_{\mathrm{st}} = K_{\mathrm{st}}(f_{\mathrm{st}} + p_{\mathrm{n}}) + \frac{G_{\mathrm{s}} \cdot P \cdot T_i}{175 \cdot G_{\mathrm{st}}} = \min, \tag{4} \]

where

\(K_{\mathrm{st}} = a_1 + b_1 G_{\mathrm{st}}\) are the initial investments in the snow-melting unit, rubles;

\(a_1, b_1\) are certain coefficients whose values, on the basis of preliminary calculations, are taken as

\[ a_1 = 400\ \text{rubles}; \qquad b_1 = 160\ \text{rubles}\cdot \mathrm{h}/10^3\ \mathrm{kg}; \]

\(G_{\mathrm{s}}\) is the amount of snow to be melted in the given snow-melting unit, \(\mathrm{kg/year}\);

\[ G_{\mathrm{s}} = \mu \cdot \varphi \cdot F_{\mathrm{kv}} \cdot h_{\mathrm{s}} \cdot \rho \cdot 10^{-3}, \quad \frac{\mathrm{t}}{\mathrm{year}}; \]

\(\mu\) is a coefficient accounting for the area of street driveways; its value may be taken within the range \(1.3\text{--}1.5\);

\(\varphi\) is the fraction of fallen snow subject to removal;

\(F_{\mathrm{kv}}\) is the built-up area, \(\mathrm{m}^2\);

\(h_{\mathrm{s}}\) is the depth of snow cover, \(\mathrm{m}\);

\(\rho_{\mathrm{s}}\) is the density of snow, \(\mathrm{kg/m^3}\);

\(f_{\mathrm{t}}\) is the fraction of annual deductions for depreciation and repair; it is taken on average for the installation as

\[ f_{\mathrm{st}} = 0.06; \]

\(p_{\mathrm{n}}\) is the standard efficiency coefficient,

\[ p_{\mathrm{n}} = 0.125; \]

\(P\) — worker’s wages, rubles/month;

175 — number of working hours per month, h/month;

\(T_i\) — expenditure of the worker’s time for servicing the snow melter during one hour of its operation, man-h.

Taking the first derivative \(\dfrac{\partial Z_{\text{st}}}{\partial G_{\text{st}}}\), setting it equal to zero, and solving with respect to \(G_{\text{st}}\), we find

\[ G_{\text{st}}^{\text{opt}}= \sqrt{\frac{G_c P T_i}{175 b_1 (f_{\text{st}}+p_{\text{n}})}} , \qquad \frac{kg}{h}. \]

The design capacity of the snow melter at a separate inlet \(G'_{\text{st}}\) must be such as to satisfy the conditions for discharging thaw water into the sewer system and for not exceeding the design flow rate of district-heating water at the inlet, i.e.,

\[ G'_{\text{st}}\leqslant G_{\text{st}}^{k}; \quad G'_{\text{st}}\leqslant G_{\text{st}}^{c}, \quad G'_{\text{st}}\leqslant G_{\text{st}}^{\text{opt}} . \]

We shall present a quantitative assessment of the possibilities for snow melting on the basis of district heating using the particular example of the city of Tomsk.

According to data from the heat-network administration, the design flow rate of district-heating water is \(3\cdot10^6\ kg/h\). In view of the absence of precise data on the capacity and operating time of ventilation systems, when determining the additional capacity of the extractions of district-heating turbines for the purposes of snow melting, the second term in equation (1) is not taken into account.

In the calculations it is assumed that:

\[ \Delta t'=\tau_1'-\tau_{20}'=150-70^\circ C; \qquad P_{\text{otb}}=1.2\ \text{bar}; \]

\[ t_{\text{n}}^{\text{eq}}=-14^\circ C; \qquad t_{\text{n}}^{\text{sr}}=-7^\circ C; \qquad \delta t_{\text{st}}=10^\circ C; \]

\[ G'=3\cdot10^6\ kg/h; \qquad \eta_{\text{st}}=0.9; \qquad \mu=0.5; \qquad \varphi=0.5; \]

\[ h_c=0.5\ m; \qquad \rho_c=250\ kg/m^3; \qquad r=335000\ J/kg; \]

\[ c=4186.8\ J/kg^\circ C; \qquad n_1=1760\ h/year. \]

From the calculations given, we obtain:

1) The additional thermal capacity of the low-pressure extractions of district-heating turbines

\[ \Delta Q'_{\text{otb}}=125\cdot10^3\ MJ/h, \]

which amounts to 12.5% of the design heat supply for hot water.

2) The amount of heat that can be used for snow melting during the heating season

\[ Q_{\text{st}}^{\text{year}}=220\cdot10^6\ MJ/year. \]

3) The amount of snow that can be melted during the season

\[ G_c^{\text{year}}=565\cdot10^6\ kg/year. \]

4) We clear the built-up area of snow

\[ F_{\text{sq}}\approx 6.0\ \text{sq. km}. \]

5) Savings of standard fuel at the TPP due to the combined generation of electric and thermal energy on the basis of snow melting

\[ \Delta B_{\text{st}}=6.06\cdot10^6\ kg\ \text{s.f.}/year. \]

6) The monetary savings, at a standard-fuel price of 11.5 rubles/\(10^3\ kg\) s.f., will amount to

\[ \Delta Z_{\text{st}}=69500\ rubles/year. \]

Conclusion

1) The organization of snow melting on the basis of district heating, requiring no additional expenditures at the combined heat-and-power plant or in the heat networks, will make it possible to increase electricity generation on heat consumption and thereby improve the operating economy of heat-supply systems.

2) The most favorable conditions for snow melting are those of Siberia and the northern regions of the country, where a considerable amount of snow falls and where the design temperature of the combined heat-and-power plant has relatively low values.

3) In the example given, because of the absence of data, the dips in the daily schedules of heat consumption for ventilation have not been taken into account. Therefore the actual value of \(\Delta Q_{\text{off}}\), calculated for the conditions of the city of Tomsk, will be significantly higher.

References

1. A. V. Nikitin. Snow Melters. Publishing House of the Ministry of Municipal Economy of the RSFSR, Moscow, 1952.
2. E. Ya. Sokolov. District Heating and Heat Networks. Gosenergoizdat, Moscow–Leningrad, 1963.