THE BARGEOT PRINCIPLE AND THE POSSIBILITIES OF ITS USE IN THE CLIMATIC CONDITIONS OF THE USSR

P. A. MUKHACHEV

The Bargeot principle consists in using the temperature differences between the water and the air of Arctic regions to obtain mechanical energy.

The idea of converting heat into mechanical work with small temperature differences between the hot and cold sources appeared as early as the end of the nineteenth century.

Despite the theoretical justifications for the expediency of using small temperature differences for energy purposes, this idea apparently was not considered worthy of attention and for a long time found no practical application.

In 1926, Claude and Boucherot again raised this question. In a report to the Paris Academy of Sciences they presented the results of their experiments on using the temperature difference between the deep and surface waters of the seas of tropical countries for the production of mechanical energy. The experiments of Claude and Boucherot showed that, despite the low efficiency of the experimental installation owing to the bulkiness and high cost of the equipment, the question of using a small temperature difference is not an idle one, and that a successful practical solution to it promises enormous possibilities for obtaining cheap energy without expenditure of fuel.

The bulkiness of the equipment in the experimental installation of Claude and Boucherot is explained by the fact that water vapor was used as the working medium; its physical properties at low temperatures (insignificant pressures, large specific volume) lead, at higher powers, to exaggerated dimensions of the machinery, create difficulties in operating it, and considerably reduce the useful output of energy because of the large expenditures for pumping hot and cooling water, as well as for air ejection.

The shortcomings of the physical properties of water vapor at low temperatures could be eliminated if, instead of water vapor, vapors of a liquid boiling at a low temperature—such as ammonia, liquid carbon dioxide, etc.—were used as the working medium.

Thus, the idea of using a small temperature difference suggests the use, as the working medium, of substances whose physical properties are most favorable in solving the problem of obtaining mechanical energy with a small temperature drop.

The experiments of Claude and Boucherot led Bargeot to the idea of using, for obtaining mechanical energy, the natural temperature difference between water under a layer of ice and the outside air in Arctic regions.

It is known that large masses of water, being protected from the influence of the external temperature by a layer of ice, retain large quantities of heat during the winter. The temperature of water located under a layer of ice, even in the far north, is 0–4°C. Thus, the mass of water, being—

being an enormous reservoir of heat, can be used as the hot heat source in a thermodynamic cycle converting heat into mechanical work. The outside air, reaching a temperature of \(-70^\circ\mathrm{C}\), in this case is the cold heat source.

Bargeot, at the Second World Power Conference in 1930 in Berlin, proposed constructing an Arctic power plant to make use of the above-mentioned temperature difference in the following manner (the diagram is shown in Fig. 1).

Pump 1 delivers water from beneath the ice cover to evaporator 2, where this water is used to evaporate a liquid boiling at a low temperature. The vapor obtained in the evaporator serves as the working medium of the plant. The water entering the evaporator is converted there into ice, which must be continuously removed from the evaporator and transported to a dump located outside the station site. The saturated vapor of the working medium from the evaporator enters turbine 3, where it expands, doing work, after which it is directed to condenser 4, where it is cooled and condensed. The condensate is removed from the condenser by pump 5 and fed to evaporator 2.

Bargeot proposed using butane as the working medium; for it the boiling point at a pressure of 760 mm Hg is \(-0.5^\circ\mathrm{C}\), the specific gravity of the liquid at \(0^\circ\mathrm{C}\) and a pressure of 760 mm Hg is \(\gamma = 0.601\ \mathrm{kg/liter}\). Butane has the property of being almost insoluble in water. The insolubility of butane in water and its low specific gravity compared with the specific gravity of water make it possible to use an extremely simple condenser design. The condenser is a tower, at the bottom of which a grate is placed. Beginning from the grate, the tower is filled to three-quarters of its volume with a cryohydrate (refrigerating agent). The cryohydrate used is a frozen solution of common salt. The solidification temperature of the common-salt solution (the melting point of the cryohydrate) depends on the saturation of the solution and is \(-21.6^\circ\mathrm{C}\) at full saturation. The butane vapor leaving the turbine comes into contact in the condenser with pieces of cryohydrate, is cooled and converted into condensate, while the cryohydrate melts.

Fig. 1

The common-salt solution and butane condensate flow down under the grate, and owing to their different specific gravities and the insolubility of butane in water, these two liquids will be one beneath the other and can easily be removed separately from the condenser. The salt solution is removed from the condenser by pump 6 and enters an open channel located on the station site, where, at an air temperature below the solidification temperature, it freezes, and the cryohydrate thus obtained returns again to the condenser.

The Bargeot principle, a general description of the project for a plant in Hudson Bay with a capacity of 10,000 h.p., and the design cost of this plant are given in two articles in the journal World Power: 1. “Generation of Electri-”

energy from the energy of unfrozen water beneath the surface of the ice,” 1929, September. 2. “Energy supply in Arctic regions,” 1930, October.

In these articles the profitability of the Barjot installation is demonstrated by the following considerations:

1. The economic efficiency of an actual installation should be on average 4%, i.e., it is possible to obtain electric power fairly efficiently without the expenditure of expensive fuel, the delivery of which to some northern regions is very difficult.

2. It is possible to construct a combined installation consisting of a hydroelectric station and the proposed installation. The minimum base capacity of such a combined installation would increase severalfold, since the described process is most effective during the period of least capacity of hydroelectric stations. Therefore it is illogical to burn coal and put reserve steam stations into operation when the heat contained in unfrozen water can so easily be converted into mechanical work.

3. Capital expenditures amount to only about one quarter of the cost of a hydroelectric station of the same capacity and under the most favorable local conditions. The estimated cost of the station designed for Hudson Bay, with a capacity of 10,000 hp, is 415,800 dollars, i.e., the cost per installed hp is 41.5 dollars. The payback period of the station is 10 years.

During the discussion at the World Power Conference, Barjot referred to an experimental installation already built in Siberia, under the direction of Academician P. P. Lazarev.

Subsequent reports on the construction and operation of the station in Hudson Bay or elsewhere, as well as on the station in Siberia which Barjot mentioned at the World Power Conference, are absent from the literature. This last circumstance compels further work on the question of using the temperature difference between air and water in Arctic regions to be based chiefly on the two articles indicated, in which very scanty data are given. From these articles one can borrow only the fundamental theoretical formulation of the question, while the techno-economic considerations concerning the profitability of the proposed installations must be completely reconsidered and, in many respects, supplemented. It is necessary to work out fully the theoretical and design-calculation parts of the proposed installation.

Techno-economic calculations for any installations using heat of low potential cannot be made without taking into account the expenditure of energy for their own needs. Barjot, evidently, paid insufficient attention to this and evaluated the economy of the installation by the average economic efficiency \(\eta = 4\%\), without taking account of the expenditure of energy for its own needs, i.e., he gave the gross efficiency.

In the present case, an evaluation of the economy and profitability of the station by the economic efficiency, calculated even with allowance for its own needs, is entirely insufficient. Of far greater significance will be a coefficient showing the fraction of the energy delivered to the consumer out of the total generated, i.e.,

\[ \eta = \frac{E_{\text{net}}}{E_{\text{gross}}}, \quad \text{where} \]

\(E_{\text{net}}\) and \(E_{\text{gross}}\) are the quantity of electric energy delivered to the consumer and generated at the station.

The decisive importance, however, must belong to the synthesizing techno-economic indicator—the cost of a unit of electric power delivered by the station.

It is incorrect to state that, owing to the absence in the operating cycle of high pressures (above 1 atm), the evaporators and condensers can be made of cement rather than metal, which would substantially reduce capital investment. This statement is valid only for the winter period of station operation. In summer, in order to keep butane in liquid form at high outdoor-air temperatures, it is necessary either to have some special metal cylinders, or to have evaporators and condensers made of metal for pressures on the order of 5–6 atm.

A tremendous technical difficulty in the design and construction of the stations under consideration consists in organizing the removal of ice from the station grounds. The amount of ice obtained from the water evaporating the butane is 200–300 tons/MW·h.

In Bargeot’s design there is no indication of how, and where, such an enormous quantity of ice is to be removed.

In 1932, engineers P. P. Akimov and V. N. Rukavishnikov, on assignment from Glavenergo, provided considerations concerning the profitability of applying the Bargeot method under USSR conditions (Northern Siberia). The work was published in the journal Energetika, 1935, No. 4.

In this work the authors set themselves the task of determining the limiting outdoor-air temperature at which the use of the Bargeot installation is possible, and of selecting the most suitable substance for the working fluid of the installation. As a result of the calculations performed, and taking into account the consumption of energy for auxiliary needs, the authors came to the conclusion that the limiting outdoor-air temperature at which rational use of Bargeot installations is possible should be taken as −15°. Since in a considerable part of Siberia the average temperature of the winter months lies below −15°C, the use of the installations under consideration is quite possible over a fairly long period of time. Propane or butane is recommended as the working fluid.

In the calculations presented, a significant part of the energy expenditures for auxiliary needs is not taken into account. Among the unaccounted expenditures is also the expenditure for removing ice from the evaporators and from the station grounds.

The determination of expenditures for auxiliary needs was made on the basis of the incorrect assertion that the type of working fluid does not affect these expenditures. Therefore, the determination of the specific expenditures of working fluid, water, and cryohydrate was made for ammonia, the properties of which have been well studied, on the assumption that the same specific expenditures would occur with any other working fluid.

In calculations of the utilization of installed capacity as a function of air temperature, no account was taken of the circumstance that, when the air temperature rises above the design value (the design air temperature is the temperature for which the installation has been calculated), the turbine vacuum will worsen, and in connection with this there will be an underproduction of energy. Consequently, the useful output of energy depends on the expenditure of energy for auxiliary needs and on the underproduction of energy due to the deterioration of vacuum at air temperatures above the design value.

Taking account of all the indicated factors, which were not included in the calculations of engineers Akimov and Rukavishnikov, must undoubtedly also change the final conclusion of these authors.

The topic “Use of the temperature difference between water and air in Arctic regions for obtaining mechanical energy” was assigned in 1934 for development at the Energy Institute of the Academy of Sciences of the USSR. The responsible investigator for the topic was N. P. Stul’nikov. The report on the first stage of the work, relating to the end of 1935, contained only preliminary considerations on a number of questions.

It must be stated that Bargeot’s method has not yet found practical application. The probable reason for this situation is the insufficient profitability of Bargeot installations under the conditions of North America, where the construction of such installations was contemplated.

In connection with the development of industry and transport and the increased demand for electric power in Northern Siberia, Bargeot’s idea can be used successfully, since the climatic conditions of the north of Siberia are more favorable for such installations than the conditions of North America.

Since the cooling body in Bargeot’s installation is a cryohydrate of table salt, for which the lowest possible temperature is \(-21.6^\circ\mathrm{C}\), operation of the installation with the best effect will occur at air temperatures of \(-25^\circ\mathrm{C}\) and below. Consequently, operation of the installations with maximum effect is possible for five months of the year. The total duration of operation of the installations must be established by techno-economic calculations. It may be expected that effective operation is possible for 6–7 months of the year.

To determine the overall economy of Arctic installations, let us make an approximate calculation. We shall take the following data for the calculation: installation power \(N = 1000\) kW, working fluid—butane.

The principal properties of butane are: specific gravity of liquid butane—0.601 kg/l; heat capacity of liquid butane \(C_1 = 0.55\) kcal/kg°C. The latent heat of vaporization and the pressure at various temperatures are given in Table 1.

Table 1

| | | \multicolumn{6}{c}{Temperature °C} |
|---|---:|---:|---:|---:|---:|---:|---:|
| | | 0 | −5 | −10 | −15 | −20 | −25 |
| Pressure | mm Hg | 775 | 760 | 525 | 425 | 340 | 270 |
| Pressure | ata | 1.052 | 1.031 | 0.715 | 0.578 | 0.463 | 0.367 |
| Latent heat of vaporization | kcal/kg | 92.98 | 94.09 | 95.16 | 96.20 | 97.21 | 98.20 |

As stated, the calculations given below are approximate and have been made under a number of simplifying assumptions. Their purpose is only to establish the order of magnitude of the techno-economic indicators characterizing an installation operating on the Bargeot cycle under certain conditions. More exact calculations cannot yet be made, since a number of aspects connected with the operation of installations of this kind still require technical refinement.

Thermal Calculation

Evaporator. In the evaporator, evaporation of the working fluid takes place when the heating medium—water—freezes. Thus, the initial temperature of butane vapor may be taken as \(t_1 = 0^\circ\mathrm{C}\).

The vapor pressure in this case is \(p_1 = 775\) mm Hg \(= 1.05\) ata.

We shall take the dryness fraction approximately as \(x_1 = 1\).

The heat content of the vapor is \(i_1 = i'_1 + x_1 r_1\),

where \(i'_1\) is the heat content of the liquid,

\(r_1\) is the latent heat of vaporization.

Since \(t_1 = 0^\circ\mathrm{C}\), \(i'_1 = 0\), and

\[ i_1 = r_1 . \tag{1} \]

Turbine. The heat content of the vapor at the turbine outlet is

\[ i_2 = i'_2 + x_2 r_2 . \tag{2} \]

The heat content of the liquid at the temperature in the condenser \(t_2\) is

\[ i'_2 = C_p t_2 \tag{3} \]

The latent heat of vaporization at temperature \(t_2\) is found from Table 1.

To determine \(x_2\), we write an equation based on the property of the adiabatic process, according to which the entropy \(S = \mathrm{const}\), i.e.

\[ S = S'_1 + \frac{x_1 r_1}{T_1} = S'_2 + \frac{x_2 r_2}{T_2}. \]

The entropy of the liquid is

\[ S' = C_p \ln \frac{T}{273}. \]

Since \(t_1 = 0\), \(S'_1 = 0\).

From the equation \(S = \mathrm{const}\) we have:

\[ x_2 r_2 = \left(\frac{x_1 r_1}{T_1} - S'_2\right)T_2 . \tag{4} \]

The adiabatic heat drop is

\[ H_0 = i_1 - i_{2t}\ \mathrm{kcal/kg}. \tag{5} \]

The specific steam consumption at normal load is

\[ d = \frac{860}{H_0 \eta_{0e}} . \tag{6} \]

In the subsequent calculations we take \(\eta_{0e} = 0.6\).

The heat content of the vapor at the turbine outlet is

\[ i_2 = i_1 - \eta_{0i} H_0 . \tag{7} \]

We take \(\eta_{0i} = 0.7\).

The specific consumption of water for the formation of vapor in the evaporator is

\[ d_w = \frac{d(i_1 - i'_2)}{t_w + r_w}\ \mathrm{kg/kWh}, \tag{8} \]

where

\(t_w\) is the temperature of the water entering the evaporator,

\(r_w\) is the latent heat of fusion of ice.

Let us take \(t_w+r_w=80\ \mathrm{kcal/kg}\).

The specific consumption of cryohydrate is

\[ d_{\mathrm{cr}}=\frac{d(i_2-i'_2)}{C_p(t''-t'_{\mathrm{cr}})+r_{\mathrm{cr}}}\ \mathrm{kg/kWh}, \tag{9} \]

where

\(t''_{\mathrm{cr}}, t'_{\mathrm{cr}}\) are the temperature of the cryohydrate during melting and upon entering the condenser,

\(C_p\) is the heat capacity of the cryohydrate.

We take \(C_p=1\ \mathrm{kcal/kg\,^{\circ}C}\), \(t''_{\mathrm{cr}}=t_2\), and \(r_{\mathrm{cr}}=80\ \mathrm{kcal/kg}\).

Table 2 gives calculations by the formulas presented above for various outdoor-air temperatures. The melting temperature of the cryohydrate is taken to be \(5^{\circ}\) above the air temperature.

Table 2

Determination of the energy consumption for auxiliary needs

1. Supplying water to the evaporator. The presence of a shore pumping station is provided for. The electric-power consumption for supplying water, as a percentage of that generated at the station, will be:

\[ E_1= \frac{d_w(H_1+H_2+H_3)}{102\cdot 3600\cdot \eta_n\eta_{\mathrm{mot}}}\cdot 100 = \frac{d_w(H_1+H_2+H_3)}{3670\cdot \eta_n\eta_{\mathrm{mot}}}, \]

where

\(H_1\) is the geometric delivery head, in m,

\(H_2\) is the head for overcoming the internal pressure in the evaporator, in m,

\(H_3\) is the head loss due to the resistance of the water conduits, in m,

\(\eta_n\) and \(\eta_{\mathrm{mot}}\) are the efficiencies of the pump and motor.

Let us take \(H_2+H_3=6\ \mathrm{m}\), \(\eta_n\eta_{\mathrm{mot}}=0.6\); then

\[ E_1=\frac{d_w(6+H_1)}{2200}\%. \]

The energy consumption for supplying water to the evaporator as a function of the delivery head \(H_1\) and the outdoor-air temperature is given in Table 3.

Table 3

2. Energy consumption for supplying butane from the condenser to the evaporator

\[ E_2=\frac{d\,[10(P_i-P_k)+H_3]}{3670\cdot \eta_n\eta_{\mathrm{mot}}}\ \%, \]

where

\(P_i\) and \(P_k\) are the absolute pressures in the evaporator and condenser.

We take \(H_3=5\ \mathrm{m}\) and \(\eta_n\eta_{\mathrm{mot}}=0.6\).

3. Energy consumption for removing ice from the evaporator and from the station site

We assume that removal of ice will be carried out hydraulically, with discharge under the ice of a water source.

For this method of ice removal one may write

\[ E_3=\frac{a\,d_w\,H_3}{3670\cdot \eta_n\eta_{\mathrm{mot}}}\ \%, \]

where

\(a\) is the coefficient of water consumption for removing \(1\ \mathrm{kg}\) of ice,

\(H_3\) is the head required to overcome the resistance of the water conduits and to remove the ice.

We take \(a=2\ \mathrm{kg/kg}\); \(\eta_n\eta_{\mathrm{mot}}=0.6\); \(H_3=30\ \mathrm{m}\).

4. Electric-power consumption for supplying cryohydrate to the condenser by elevator

\[ E_4=\frac{d_{\mathrm{cr}}\,H}{3670\cdot \eta_{\mathrm{el}}\eta_{\mathrm{mot}}}\ \%, \]

where

\(H\) is the delivery height of the cryohydrate,

\(\eta_{\mathrm{el}}\) is the efficiency of the elevator.

We take \(H=5\ \mathrm{m}\), \(\eta_{\mathrm{el}}\eta_{\mathrm{mot}}=0.2\).

5. Electric-power consumption for removing the salt solution from the condenser by a centrifugal pump

\[ E_5=\frac{d_{\mathrm{cr}}\,[10(1-P_k)+H_3]}{3670\cdot \eta_n\cdot \eta_{\mathrm{mot}}}\ \%. \]

We take \(H_3=5\ \mathrm{m}\), \(\eta_n\eta_{\mathrm{mot}}=0.6\).

6. Electric-power consumption for supplying cryohydrate to the elevator, for removing air from the condenser, for lighting, and other unaccounted expenditures

We estimate these at \(1\%\).

The results of calculations of the electric-power consumption \(E_2\), \(E_3\), \(E_4\), and \(E_5\), as a function of the outdoor-air temperature, are given in Table 4.

Table 4

The total consumption of electric power for auxiliaries is presented in Table 5.

Table 5

The flow areas of the turbine are calculated for a definite vacuum, i.e., in the present case for a definite calculated air temperature, which determines the value of the vacuum. When the air temperature deviates upward, the pressure behind the turbine will increase. This will entail, with unchanged steam consumption, a reduction in turbine output. It may be assumed approximately that the reduction in output occurs in proportion to the reduction in the thermal adiabatic drop:

\[ \frac{N_2}{N_1}=\frac{H_{02}}{H_{01}}. \]

Taking into account the stated assumption, Table 6 gives the turbine outputs, as a percentage of nominal, at various calculated and actual air temperatures.

Table 6

If one also takes into account the expenditure of energy for the plant’s own needs, then the utilization of installed capacity, in percent, will be characterized by the data given in Table 7.

Table 7

The most advantageous design air temperature will be that at which the annual generation of electric power proves to be the greatest or, equivalently, at which the greatest number of hours of utilization of installed capacity will be obtained.

It may be assumed that an air temperature of −25°C and below is observed for 3600 hours per year, an average temperature of −20°C for 700 hours, a temperature of −15°C for 400 hours, and a temperature of −10°C for 160 hours. The number of hours of utilization of installed capacity calculated under these conditions is given in Table 8.

Table 8

From Table 8 it is evident that the greatest number of hours of utilization of installed capacity is obtained at a design temperature of −20°C. The number of hours of utilization at a temperature of −25°C differs little from this. If one takes into account that the equipment for a design temperature of −20°C is bulkier and more expensive than for a temperature of −25°, then −25°C should be adopted as the design temperature. The considerations given above show that Arctic power stations operating on the Bargeot cycle can be successfully used under the climatic conditions of Northern Siberia.

To determine the economy of the station, let us make an approximate calculation of the cost of a kilowatt-hour of energy delivered by the station.

The annual expenses for the station will be

\[ S = S_1 + S_2 + S_3 + S_4,\ \text{where} \]

\(S_1\)—expenditure on wages,

\(S_2\)—depreciation expenses,

\(S_3\)—repair costs;
\(S_4\)—costs for Glauber salt.

Let us take the cost of the installed kW as 1000 rubles/kW. The average wage of one staff position is 1500 rubles/month. The staff consists of 40 persons paid for 9 months, and 10 persons paid throughout the year. Repairs are assigned to the operating personnel. Percentage deductions for depreciation are 7%. Expenditure on repair materials is 1% of the cost of the equipment. The cost of salt is 10 rubles/t. Salt consumption is 1000 t/year. The generation of electric power is

\[ E = 3650 \cdot 10 = 36500 \text{ MWh}. \]

Wage costs:

\[ S_1 = 1500 \cdot 40 \cdot 9 + 1500 \cdot 10 \cdot 12 = 720000 \text{ rubles/year}. \]

Depreciation costs:

\[ S_2 = 0.07 \cdot 1000 \cdot 10000 = 700000 \text{ rubles/year}. \]

Repair costs:

\[ S_3 = 0.01 \cdot 1000 \cdot 10000 = 100000 \text{ rubles/year}. \]

Cost of Glauber salt:

\[ S_4 = 10 \cdot 1000 = 10000 \text{ rubles/year}. \]

Total annual costs:

\[ S = 720000 + 700000 + 100000 + 10000 = 1530000 \text{ rubles/year}. \]

Cost price of the delivered kWh:

\[ C = \frac{S}{E} = \frac{1530000 \cdot 100}{36500 \cdot 1000} = 4.2 \text{ kopecks/kWh}. \]

The figure for the cost price of the delivered kWh is approximate, but it indicates the undoubtedly high economy of the proposed installations in comparison with thermal ones.

Conclusion

1. Arctic installations operating according to the Bargeot cycle can be successfully used under the conditions of Northern Siberia.

2. The cost price per unit of delivered electric power is no higher than at thermal stations in northern regions.

3. The proposed installations must necessarily operate in a system with thermal stations, or preferably with hydroelectric stations.