ECONOMICS OF THE STATIONARY PART WHEN USING THE HEAT OF EXHAUST STEAM FROM STEAM LOCOMOTIVES¹

Eng. V. P. LEBEDEV

As is known, in existing steam locomotives about 50% of the heat of the fuel burned in the fireboxes is lost with the exhaust steam, which is discharged through the cone into the atmosphere, and approximately 43% of the heat consists of the remaining losses: with the outgoing gases, mechanical unburned fuel, and other losses; only about 7% is converted into useful work. The heat losses, converted into fuel, amount to approximately 59 million tons of high-grade fuel per year for the entire locomotive fleet of the country, out of the 250 million tons of fuel produced in the country.

Hence the necessity becomes apparent of achieving an increase in the economy of the steam locomotive by all means, while at the same time not overly complicating the already complex construction of the locomotive.

Work to improve the economy of the steam locomotive is being carried out by various ways and methods, in various directions. One of the possible solutions for improving the economy of the steam locomotive was proposed by the Honored Worker of Science and Technology, Professor-Doctor of the Tomsk Polytechnic Institute I. N. Butakov, in his work “On the Problem of Utilizing the Heat of Exhaust Steam from Steam Locomotives.” The solution of the problem is briefly as follows.

After the steam engines of the locomotive, the exhaust steam is directed into a gas-suction turbine and, after it, into the tender, converted into a heat accumulator. At the experimental stage, the tender of an FD locomotive with a water capacity of 44 m³ may serve as such a tender, so that subsequently a transition may be made to tenders with a capacity of 90–100 m³. The exhaust steam in the accumulator tender heats the water to 95°. Upon the arrival of the locomotive at the depot, during the servicing period, the hot water is drained into an underground reservoir. From the underground reservoir (Fig. 1), the hot water in winter is directed for district-heating purposes, and also for generating electric power in vacuum turbines; after that, at a temperature of 45°, it may be directed to special greenhouses for soil heating for growing vegetables throughout the year. Such is the scheme for utilizing the heat of the exhaust steam of steam locomotives proposed by I. N. Butakov.

We believe that such a solution does not introduce any significant complication of the steam locomotive and at the same time raises the economy of the steam locomotive to as much as 15%, which brings the steam locomotive closer to the electric locomotive.

In putting this problem into practice, we shall have, on the one hand, fuel savings, and on the other hand, inevitable expenses connected with alteration, additional equipment, acquisition of equipment, etc. The profitability of installing a plant for utilizing the heat of ex-

exhaust steam from steam locomotives, obviously, will take place in the case where the annual savings will prevail over the annual expenditures.

Fig. 1

The solution of this question will depend on many conditions and, first of all, on the intensity of traffic on the given section of railway, on the magnitude of heat consumption at the given railway junction, etc.

Fuel savings

When a utilization installation is applied at one or another railway junction, a certain quantity of fuel must be freed up, which was inevitably consumed before the use of the utilization installation.

Let us consider the individual components of fuel savings as a result of using the exhaust heat of steam from steam locomotives.

As was indicated above, part of the hot water, especially in the winter period, must go to meet the needs of heat consumers. This is, above all, the heating of buildings. Before the use of the utilization installation, these heat consumers consumed some quantity of heat—$W_1$ kcal/year, and, consequently, some quantity of standard fuel—$B_{om}$ t/year.

Knowing the heat consumption of the district or settlement $W_1$, as well as the average value of the boiler-house efficiency $\eta_{om}$, one can determine with sufficient accuracy the quantity of fuel—$B_{om}$, which will be:

\[ B_{om}=\frac{W_1}{Q_p^H \eta_{om}}=\frac{W_1}{7000 \cdot \beta_{om} \cdot 10^3}\; t/year. \tag{1} \]

With the use of the utilization installation, this quantity of fuel—$B_{om}$—will no longer need to be consumed in the given district; consequently, it will constitute a definite saving.

In addition, at the other part of the hot water, a certain quantity of electrical energy will be generated during the year. Thus, the existing electric power station can be relieved of generating the same quantity of electric energy—$E_{year}$; consequently, it will not be necessary to burn fuel at the power station in the corresponding quantity—$B_e$ t/year.

Therefore one may write:

\[ B_{\mathrm{e}}=\frac{\mathcal{E}_{\mathrm{egd}}\,860}{Q_p^{n}\eta_{st}10^3} =\frac{\mathcal{E}_{\mathrm{egd}}\,860}{7000\cdot \eta_{st}10^3}\; t/\text{yr}. \tag{2} \]

The amount of electrical energy that can be generated by the utilization plant depends on the amount of hot water delivered and on the amount of heat going to district heating. If we denote the amount of water delivered by each steam locomotive by \(P_2\) (\(t/\)locomotive) and by \(n\) the number of locomotives arriving each hour, then the annual amount of electrical energy that the utilization plant can provide is expressed as follows:

\[ \mathcal{E}_{\mathrm{egd}}=23770P_2n-0.0000766W_1\ \frac{\text{kWh}}{\text{yr}}. \tag{3} \]

Therefore the amount of fuel that will not have to be burned at the electric power station, and, consequently, the fuel saving achieved, is:

\[ B_{\mathrm{e}}=\frac{(23770P_2n-0.0000766W_1)\cdot 860}{7000\cdot \eta_{st}10^3}\ t/\text{yr}. \tag{4} \]

The third component of fuel saving will be on the steam locomotive itself. This saving will result from the fact that the steam boiler will be fed with water heated in the tender-accumulator. For our case, taking into account the indications of practice, we estimated this possible fuel saving at 6%. For each depot the annual consumption of standard fuel per locomotive is always known; therefore, if by \(B_1\) we denote the average annual consumption of standard fuel per locomotive before conversion, and by \(m\) the number of converted locomotives on the line toward the depot from two sides in the case of a through depot and from one side in the case of a terminal depot, then the possible fuel saving on locomotives from changing the boiler feed to heated water is written as:

\[ B_{n.k}=0.06B_1m\ t/\text{yr}. \tag{5} \]

The fourth component of fuel saving should be obtained at intermediate railway water-pumping stations, in view of the fact that the need for locomotives to take on water at intermediate stations is eliminated. The fuel saving at water-pumping stations will be determined as

\[ B_{\mathrm{vod}}=\frac{N_k\cdot 632.3\cdot 8760}{7000\eta_{\mathrm{vod}}10^3} =\frac{12n\cdot 632.3\cdot 8760}{7000\eta_{\mathrm{vod}}\cdot 10^3} =\frac{66500\cdot 10^3n}{7000\cdot 10^3\eta_{\mathrm{vod}}}\ t/\text{yr}. \tag{6} \]

Water after the utilization plant, at a temperature of \(45^\circ\), can also be used for agrotechnical purposes, which may be of great significance under the severe climate conditions of Siberia.

The use of agro-district-heating would make it possible to provide fresh vegetables not only to the population of the given railway junction, but also to the population of other points. If it is assumed that, in the absence of the heat of the water, such greenhouses would nevertheless have to be heated, then we would have had to expend a certain amount of fuel—\(B_{a.t}\); but, using the warm water after the utilization plant, we must count this amount of fuel—\(B_{a.t}\)—as a saving, which is not difficult to calculate. Knowing the amount of heat required to heat the greenhouses, \(W_2\), we can write:

\[ B_{a.t}=\frac{W_2}{7000\eta_{kom}}\ t/\text{yr}. \tag{7} \]

Thus, we have the total fuel saving from the use of the heat of steam-locomotive exhaust steam in the amount of:

\[ B = B_{ot} + B_{z} + B_{p.v} + B_{vod} + B_{a.t}\, m/200 \tag{8} \]

In addition to the indicated fuel saving, there will be further saving, which we do not take into account here: this is, first, because the section speed should increase, owing to the elimination of stops for taking on water; second, owing to the use of chemically purified water there will be less deposition of scale in locomotive boilers, and this gives better use of fuel and will reduce repair costs; moreover, the number of kilometers of run from washout to washout should increase, which will bring greater saving in monetary expenditures.

We do not take these additional items of saving into consideration, assuming that they will go toward covering the expenses connected with transporting an additional quantity of water in the tender in the event its capacity is increased to 90–100 \(m^3\), although it must be said that the power of the locomotive, as a rule, is not fully utilized, so that the additional weight of the transported water will only help to reduce the specific fuel consumption.

Expanding the above-written equation (8), we shall have:

\[ B = \frac{W_1}{7000 \cdot 10^3 \cdot \eta_{ot}} + \frac{(23770 P_2 n - 0{,}0000766 W_1)860}{7000 \cdot 10^3 \eta_{st}} + \]
\[ + \frac{W_2}{7000 \cdot 10^3 \cdot \eta_{kot}} + B_1 m \cdot 0{,}06 + \frac{66500 \cdot 10^3 \cdot n}{7000 \cdot 10^3 \cdot \eta_{vod}} . \tag{9} \]

If, in order to simplify the problem, we take the values of the coefficients, on the basis of practical considerations, as equal to:

\[ \eta_{ot}=0{,}4;\quad \eta_{st}=0{,}1;\quad \eta_{kot}=0{,}5;\quad \eta_{vod}=0{,}07 \]

and substitute \(W_1\) and \(W_2\) in megacalories per year, then expression (9) will take the form:

\[ B = 0{,}253 W_1 + 0{,}286 W_2 + n(29{,}3 \cdot P_2 + 136) + B_1 m\, 0{,}06\ \text{t/year}. \tag{10} \]

At the given price of standard fuel, the saving obtained in monetary terms can be determined as

\[ E_t = B \cdot Ts_t\ \text{rub/year}. \tag{11} \]

Thus, we have determined the fuel saving that is obtained during the year as a result of the use of a utilization installation.

Annual expenses

On the other hand, we shall have a whole series of annual expenses that must be repaid out of the saving obtained on fuel. Such annual expenses may be considered:

1) depreciation charges, current repairs, and taxes;
2) the cost of labor for servicing the utilization installation;
3) the cost of pumping water in the heating network;
4) the cost of cooling water for the condensers of the utilization installation.

As is known, to determine depreciation charges it is necessary to know the amount of fixed assets, which in the present case will consist of the following items:

1) the cost of the underground reservoir;
2) the cost of the equipment of the utilization installation;
3) the cost of the installation building;
4) the cost of converting the steam locomotive and tender;
5) the cost of the district-heating network.

Let us examine each of the components separately.

Cost of the Underground Reservoir

It is assumed that during the servicing period of the steam locomotive, the heated water should be discharged into a special reservoir located underground. This offers certain conveniences in terms of space, insulation, ease of discharging the heated water, etc. The cost of the reservoir will depend on the dimensions, which depend on the amount of water delivered, and on the material used for its construction. It is thought that such a reservoir is best made of reinforced concrete, with subsequent lining of the walls with iron to avoid water leaks, and that its volume should be taken equal to the hourly water reserve. Then its cost will be determined as

\[ S_p = VTs_p = \gamma_v P_2 n Ts_p = 0.96 P_2 n Ts_p \ \text{rub.} \tag{12} \]

If the construction cost of \(1 \ \text{m}^3\) of reservoir volume is taken as \(Ts_p = 100\) rub., then we shall have:

\[ S_p = 96 P_2 n \ \text{rub.} \tag{13} \]

Cost of the Equipment and Building of the Utilization Installation

It is rather difficult to establish, with sufficient accuracy, the cost of the equipment of the utilization installation. The difficulty of solving this problem lies in the fact that at present such equipment is not manufactured, and therefore there are no prices for such equipment. Moreover, there is no technical design, since the problem is exploratory in character. But it seems to us that it will be possible to attempt to establish, conditionally, the cost of the equipment and building of the utilization installation through the cost per installed kilowatt.

The installed capacity of the vacuum turbines will correspond to the maximum hourly generation of electric energy, which will fall in the summer period and will depend on the amount of hot water delivered.

Let us determine the maximum hourly generation of electric energy or, what is the same, the capacity of the vacuum turbines,

\[ N_{u,\mathrm{st}} = \left[ \frac{\eta_{oe} h'_T}{r_2 860}(t_1 - t_2) + \frac{\eta_{oe} h''_T}{r_1 860}(t_2 - t_3) \left(1 - \frac{t_1 - t_2}{r_2}\right) \right] 10^3 P_2 n = \]

\[ = 10^3 P_2 n \left[ \frac{0.6 \cdot 53}{563 \cdot 860} 35 + \frac{0.6 \cdot 28}{571 \cdot 860} 15 \left(1 - \frac{35}{563}\right) \right] = 2.68 P_2 n \ \text{kW}. \tag{14} \]

Here

\[ \eta_{oe} \]
— the electrical relative efficiency of the vacuum turbines;

\[ r_1 \ \text{and} \ r_2 \]
— latent heat of vaporization;

\[ h'_T \ \text{and} \ h''_T \]
— adiabatic heat drop in the turbines;

\[ t_1 \]
— temperature of the water entering from the reservoir, \(95^\circ\mathrm{C}\);

\[ t_2 \]
— temperature of the water after the first-stage evaporator, \(60^\circ\mathrm{C}\);

\[ t_3 \]
— temperature of the water after the second-stage evaporator, \(45^\circ\mathrm{C}\).

Then the cost of the equipment and building of the utilization installation is

\[ S_{u.u} = N_{u,\mathrm{st}} Ts_{u,\mathrm{st}} = 2.68 P_2 n \cdot Ts_{u,\mathrm{st}} \ \text{rub.} \tag{15} \]

According to Ryzhkin’s data, in the article “Low-Power Stations” in the journal Diesel Locomotive Economy, No. 5 for 1941, the cost of an installed kilowatt for low-power stations may be taken as equal to 5030 rubles/kW.

Since in our case there is no boiler house, the cost of an installed kilowatt will be lower. If it is assumed that the specific weight of the boiler house is 0.46, then the cost of an installed kilowatt is determined as:

\(C_{\mathrm{inst}} = 5030 \cdot 0.54 = 2420\) rubles; therefore we take \(C_{\mathrm{inst}} = 2750\) rubles.

Thus, the cost of the equipment and building of the utilization installation will be expressed, according to equation (15), as:

\[ S_{uu} = 7370 \cdot P_2\, n \ \text{rubles}, \tag{16} \]

where \(P_2\) is in tons.

Cost of Re-equipping the Locomotive and Tender

In order to make it possible to use the heat of the exhaust steam of the locomotives, the latter must undergo some re-equipment. As indicated above, the path of the steam after the steam engines must be changed. After the steam engines, the steam must be directed not into the cone, but into the low-pressure-steam turbine of the smoke exhauster and then into the tender-accumulator for accumulating and heating water. Likewise, the steam injector must be replaced by a pump, since water at a temperature of 95 degrees will have to be fed into the boiler. It follows from the foregoing that the re-equipment of the locomotive consists of the following: installation of a smoke exhauster with a low-pressure-steam turbine, a pump, steam pipelines, and conversion of the tender into an accumulator with installation of charging apparatus.

The cost of the smoke-exhauster installation is determined as 6000 rubles, the cost of the pump as 2000 rubles, and the cost of the steam pipelines as 2000 rubles. Thus, the new equipment of the locomotive will amount to 10,000 rubles. The full cost of re-equipping the locomotive itself, including installation, will come to approximately

\[ \frac{10000 \cdot 100}{40} = 25000 \ \text{rubles}. \]

If it is assumed that the cost of constructing \(1 \, m^3\) of the volume of a steam accumulator is approximately 500 rubles (Granovskii, Steam Boilers), then the re-equipment of a tender with a capacity of \(44 \, m^3\) will amount to:

\[ 500 \cdot 44 = 22000 \ \text{rubles}. \]

The total cost of re-equipping the locomotive and tender will amount to 47,000 rubles, or, rounded, may be taken as 50,000 rubles. If \(n_{\mathrm{par}}\) locomotives are subjected to re-equipment, the total expenditures will be:

\[ S_{\mathrm{per}} = 50000\, n_{\mathrm{par}} \ \text{rubles}. \tag{17} \]

Cost of the District-Heating Network

The cost of the district-heating network could also have been excluded from the item of expenses connected with the utilization installation, since the cost price of kWh and Mcal is determined free at the thermal power plant. In addition, the district-heating network has to be constructed under any method of heat supply: it is not a specific feature inherent only in the utilization installation. For completeness, however, the network component of the cost price of Mcal at the consumer is also introduced.

The cost of the network will depend on the diameter of the pipelines and their length. According to data (Kop'ev, District Heating), the cost of the network is expressed by the following relation:

\[ S_c = s l d k \ \text{rubles}, \tag{18} \]

where \(l\) is the length of the pipeline in km,
\(d\) is the diameter of the pipeline in mm,
\(k\) is the number of pipes of the given diameter; in our case we shall have \(k = 2\).
\(S\) is a coefficient, which may be taken as equal to 800.

Then we have

\[ S_c = 800 \cdot 2 \cdot dl = 1600ld \ \text{rubles}. \tag{19} \]

The total expenditures on fixed assets connected with the utilization installation will be expressed by the following equation:

\[ S = S_{yy} + S_p + S_{\text{per}} = 746P_2 n + 1600dl + 50000 n_{\text{par}} \ \text{rubles}. \tag{20} \]

If depreciation charges are taken at 10% per annum, this will amount to:

\[ C_{a.o} = 746P_2 n + 160dl + 5000n_{\text{par}} \ \text{rubles/year}. \tag{21} \]

Here it must be borne in mind that if only the steam locomotives of one depot have been subjected to re-equipment, then half of the expenses for re-equipping the steam locomotives should be charged to the return depot, taking into account that there, too, there must be a utilization installation. Then \(n_{\text{par}}\) must be taken as two times smaller.

As for the remaining parts of the annual expenses, such as, for example, the costs of pumping water, wages, etc., they may in total be taken within the range of 100000 to 500000 rubles; in any case, in each specific case they will have to be determined separately. Here one should make a reservation concerning wage costs. The point is that these costs could also not be charged to the utilization installation when determining the profitability of applying this installation in one or another district, since these costs already exist at present. There are stokers and firemen at numerous heating appliances in various buildings of the district. The number of personnel for the utilization installation will be smaller. It seems to us that this question will have to be decided separately in each specific case.

Thus, the general expression for the item of annual expenses connected with the use of the utilization installation will be:

\[ S_{\text{year}} = 746P_2 n + 160dl + 5000n_{\text{par}} + (100000 \div 500000) \ \text{rubles/year}. \tag{22} \]

As a result, we have obtained that, with the use of the utilization installation, on the one hand, we shall obtain a quite definite saving in fuel, according to equation (11), and, on the other hand, there will also be annual expenses according to equation (22). Then

\[ E_k = E_t - S_{\text{year}} \ \text{rubles/year} \tag{23} \]

will constitute the absolute saving over the course of a year when using the utilization installation. If \(E_k > 0\), then one may speak of the expediency of this installation. If, however, \(E_k < 0\), this indicates that the use of the utilization installation in the given district is inexpedient.

It should be noted that we have said nothing about the expenses connected with the construction of agricultural district-heating facilities, but this was done because the costs of agricultural district heating must be recouped by its own production, i.e., vegetables.

To determine the absolute economy \(\mathcal{E}_k\), the nomogram in Fig. 2 has been constructed; it also gives a clear representation of the economy obtained as a function of the influencing variable factors. For a particular example, let it be given that \(n = 5\) steam locomotives arrive per hour, and each brings \(P_2 = 40\ t\) of heated water (with a tender capacity of \(90\ m^3\)); the heat of this water is used for district heating \(W_1 = 40000\ \text{Mcal/year}\), for agro-district heating \(W_2 = 40000\ \text{Mcal/year}\), and the remaining quantity of heat goes to the generation of electric—

Fig. 2

—energy. Further, let it be given that, on average, \(B_t = 2000\ t/\text{year}\) of reference fuel is consumed per steam locomotive during the year, at a price \(C_t = 60\ \text{rub}/t\). The number of converted steam locomotives is \(n_{\text{par}} = 20\). In addition, we have a heat network with a pipe length \(l = 4\ km\) and diameter \(d = 250\ mm\); we take the other expenses as equal to \(300000\ \text{rub}/\text{year}\).

Solving this example on the left-hand side of the nomogram, on the vertical ordinate dividing the nomogram into two parts, we find the resulting economy:

\[ \mathcal{E}_t = 1850000\ \text{rub}/\text{year}. \]

On the right-hand side of the nomogram we find the total annual expenses, which we lay off on the same vertical ordinate; for our example this is expressed by the sum

\[ S_{\text{year}} = 710000\ \text{rub}/\text{year}. \]

Thus, the absolute annual economy will be

\[ \mathcal{E}_k = 1850000 - 710000 = 1140000\ \text{rub}/\text{year}. \]

In addition, on the ordinate dividing the right-hand part of the nomogram into two halves, we can also simultaneously determine the amount of investment in fixed assets and the cost of the heat network. Thus, for our example, the fixed assets amount to \(2500000\ \text{rub}\), and the cost of the heat network to \(1620000\ \text{rub}\). It must be said that here we proceed from the assumption that we do not pay for the water heated on the steam locomotive, since this heat would in any case have been lost—

it is scarcely so; but if one considers that, from the time we began to use waste heat, it acquired use value, then the utilization installation must bear the costs of paying for fuel, which in our case will amount per year to:

\[ \frac{40.5(95-25)}{7000 \cdot 0.6}\cdot 60 = 200000 \ \text{rub/year}. \]

Then the absolute saving will be reduced to 940000 rub/year. From these figures the effect obtained from using the exhaust heat of steam locomotives is clearly visible.

It is interesting to cite a few more figures.

Conversion of an existing railway to electric traction costs approximately 250000 rubles per 1 km and, consequently, with a line length of 120 km, construction of the railway will cost 30 million rubles, whereas in our example it would be necessary to spend only slightly more than 4 million rubles, with considerable accumulation. At the same time, the efficiency of the steam locomotive, with partial utilization of waste heat, will approach the efficiency of the electric locomotive.

Determination of the Cost of a Kilowatt-Hour and of a Megacalorie

An equally important indicator in the economics of a heat-power installation is the cost of 1 kWh and 1 Mcal.

The heat of the delivered hot water goes partly to district heating, and partly to the generation of electric power.

First of all, let us determine the total costs in which both electric and heat consumption participate. For our utilization installation such costs will be the cost of the underground reservoir \(S_p\), the cost of re-equipping the locomotive fleet \(S_{per}\), the cost of the pumps transferring water from the reservoir to the installation, the electric motors for them, installation, etc., \(S_{nas}\), which may be written as:

\[ S_Q = S_p + S_{per} + S_{nas} \ \text{rub}. \tag{24} \]

From this sum we shall determine that part of the expenses which falls on heat consumption:

\[ S_Q^m = S_Q \frac{W}{Q} \ \text{rub.}, \tag{25} \]

where \(W = W_1 + W_2\), i.e., heat for district heating and agricultural district heating, and \(Q\) is the total quantity of heat.

Now we can determine the total annual costs connected with district heating and agricultural district heating, which must be covered by the heat consumers:

\[ S^m = S_{per}^m + S_{pers}^m + 0.1(S_d^1 + S_Q^m)\frac{\text{rub}}{\text{year}}. \tag{26} \]

Here \(S_{per}^m\) are the costs connected with pumping water into the heat network; this includes the electric power expended on pumping the heat-transfer medium. \(S_{pers}^m\) are the costs of personnel for servicing the district-heating system.

Since the magnitude \(W\) of the heat consumption is known, we can now determine the cost of the megacalorie delivered, which will be

\[ r_m = \frac{S^m 10^6}{W} \ \frac{\text{rub}}{\text{Mcal}}, \tag{27} \]

where \(W\) is substituted in calories per year. Having previously determined, by equation (22), the total annual expenditures \(S_{\mathrm{yr}}\), it will be possible to determine that part of the expenditures \(S_{\mathrm{e}}\) which will be associated with the generation of electric power and must be repaid by the consumers of electric power. These expenditures are expressed as:

\[ S_{\mathrm{e}} = S_{\mathrm{yr}} - S^{m}\ \text{rubles/year} \tag{28} \]

Fig. 3

Fig. 4

Now it is easy to determine the cost of 1 kWh:

\[ r_{\mathrm{e}} = \frac{S_{\mathrm{e}}}{E_{\mathrm{yr}}}\,100\ \frac{\text{kopecks}}{\text{kWh}}. \tag{29} \]

To determine the cost of a kilowatt-hour and of a megacalorie, one may use the nomogram shown in Fig. 3.

To determine the annual output of electric power of the utilization installation, one may use the graph in Fig. 4.

If we continue the solution of our particular example and determine the cost of a kilowatt-hour and of a megacalorie, we obtain that the cost of 1 kWh will be \(23\ \frac{\text{kopecks}}{\text{kWh}}\), and the cost of 1 Mcal will be 7.5 rubles.

Noted Misprints

1. The work is being carried out under the supervision of the Honored Worker of Science and Technology, Professor-Doctor of Technical Sciences I. N. Butakov. ↩