Electrolysis and cryogenic production complex
under orbital conditions

   The following is an orbital refueling complex equipped with equipment designed to produce the main fuel components - liquid hydrogen and liquid oxygen-from water. The ORC is designed to provide an annual cargo flow at the GSO of 22.5 tons when working as a part of systems of spacecraft launch vehicles on GSO, although nothing prevents its multi-purpose use. The inclination of the ORC base orbit is 51.6.
   The process of electrolysis of water has long been mastered on Earth, and has also been used for more than one decade on orbital stations to produce oxygen for the SRW. The cost of electricity for the decomposition of water is estimated as follows. The decomposition voltage of water is 1.7 V. The amount of matter released on the electrode is determined by Faraday's laws and will be
P=eIt, where e - electrochemical equivalent, I - current strength, t - time of electrolysis. For the hydrogen ion e=1.04.10-8 kg, therefore, with the correct organization of the process, the energy consumption for the decomposition of water will be about 18.2 MJ/kg. This means 23.4 MJ per 1 kg fuel components at their ratio of 1:6. The capacity of the electrolysis plant will be 23400×0.0036=84.2 kW.
   For gas liquefaction, cryogenic installations operating according to the Claude method, using expanders or based on the Joule-Thompson effect are used, while in terrestrial conditions, the determining factor of operation is protection from the thermal radiation of the environment. The successful solution of the problem of thermal insulation is facilitated by vacuuming the cold part of the working area and storage tanks. capacity, which requires significant costs. The production of liqid oxygen (temperature 90-100 K) in terrestrial conditions does not require excessive energy consumption - its cost in prices In 1998, it was $50-90/t. It is much more difficult and energy-consuming to liquefy hydrogen. For liqid hidrogen the standard enthalpy of formation is
J=-4440 kJ/kg (according to other data -3828 kJ/kg), the enthalpy of evaporation ∆H=453 kJ/kg, temperature 20-22 .
   The conditions of the orbital flight significantly facilitate the task of thermal insulation and heat release. Nothing prevents the build-up of a multi-layer light screen-vacuum thermal insulation to any practically necessary thickness. It is quite possible to organize the shading of various elements of the cryogenic installation not only from the Sun, but also from the Earth, as well as from each other - it is known that on the shadow surface of the spacecraft, the temperature drops below 100 K.
   The efficiency of the refrigeration unit is characterized by the refrigeration coefficient
k=A/Q, where A - the work spent on weaning heat from the cooled body Q. k= /(-)-1, accordingly, the temperature of the heater and refrigerator.
   Using the orbital conditions and the pneumatic resource of the cooled gases, the following cryogenic production scheme can be implemented. Gaseous oxygen and hydrogen at a pressure of 200 atm from the electrolysis plant are fed to the primary heat exchanger-radiator (radiator) with an area of 9 m
2 , where they are cooled to 180 K. Such an area of the radiator will be obtained if the degree of blackness of its surface is close to 100%, and if it is shaded from the Sun and the Earth so that it will be periodically operational on average 65% of the flight time. If the reflectors are positioned correctly, the area found will relate to the radiated surface, and the radiator itself can be flat and double-sided.
Next, the hydrogen enters the refrigerator, where it is cooled to 80 K. Cooling is carried out by an external working fluid, while the temperature the temperature of the heater is 240 K, the cooling coefficient
k=0.5, radiator area 9.5 m2, the ideal power consumption is 1.5 kW. From the cooling machine , the hydrogen enters the expander, where adiabatic expansion takes place in several stages . The condensation of hydrogen begins when its pressure drops by ~30 times, i.e. at 6-7 atm. In total, the pressure is relieved to 1 atm, while a significant part of the hydrogen passes into the liquid state. The remaining hydrogen gas in the saturated vapor state is fed to the cryogenic liquefier, where it is completely condensed. Since the released heat will enter the radiator with an estimated temperature of 240 K after a few steps, then the total cooling capacity of the liquefaction process will be k=0.09, power consumption is not more than 2.3 kW, you will need an additional 14.5 m2 of heat-emitting surface.
   The actual performance of the hydrogen liquefaction plant will differ from the classical one due to a specific quantum effect. There are two modifications of hydrogen: orthohydrogen and parahydrogen. They differ in the mutual orientation of the nuclear spins. In orthohydrogen, they have the same direction, and in parahydrogen , they have the opposite direction. At normal temperature, hydrogen is a mixture of 75% orthohydrogen and 25% parahydrogen. As the temperature decreases under equilibrium conditions, the fraction of parahydrogen increases, reaching in liquid hydrogen at T = 20.4 K to 98.8%, i.e., the equilibrium liquid hydrogen is practically parahydrogen. The process of converting orthohydrogen to parahydrogen is called ortho-paraconversion. When hydrogen is liquefied without the use of special methods , ortho-paraconversion does not occur, the composition of the mixture is preserved. The conversion occurs spontaneously already in nonequilibrium liquid hydrogen: after 100 hours , 59.5% of parahydrogen is formed, after 1000 hours - 92%. At full conversion , heat is released - 525 kJ per 1 kg of the initial mixture of ortho-parahydrogen, therefore, the hydrogen must all boil off. To reduce the loss of liquid hydrogen during storage, accelerated hydrogen conversion is carried out in the presence of catalysts at the liquefaction stage. For the hydrogen liquefaction process, the heat of conversion is ballast, since it is diverted directly into the hydrogen stream, and as a result, the performance of the liquefier is significantly reduced, usually by 3040%. Taking the maximum value for the calculation, we get the total energy consumption of a cryogenic hydrogen plant of 6.3 kW, and the area of the radiator 55 m
2.
   Oxygen from the primary radiator enters the oxygen expander, where adiabatic expansion takes place in several stages. The condensation of oxygen begins when its pressure drops by ~4 times, i.e. at ~25 atm. Total pressure is relieved to 1 atm, while most of the oxygen passes into the liquid state. The remaining insignificant part of the oxygen gas in the saturated vapor state is fed to the refrigerator, where it is completely liquefied. This will require energy consumption of no more than 0.3 kW, and the increase in the radiator area will be no more than 2 m
2.
   In total, the ideal required power is 4.1 kW, and the surface area of the radiators is 57 m
2.
   The results obtained do not take into account all possible losses in the production of fuel, but suggest that the real energy consumption for the liquefaction of components will be a small fraction of the energy consumption for their production from water. When calculating the total energy consumption, it should be taken into account that electrolysis at high pressure will also be accompanied by increased energy consumption, somewhat greater than the work on isothermal gas compression (1.1 MJ per kilogram of decomposition products). Then the energy of the electrolysis unit should be amended:
- energy consumption for water decomposition - 20 MJ/kg;
- the cost of electricity to produce 1 kg of gaseous fuel components at a ratio of 1:6-25.7 MJ/kg;
- power of the electrolysis plant - 92.5 kW;
- the total energy consumption of fuel production is about 100 kW.

   The area of solar panels for the needs of fuel production, with their efficiency of 150 W / m2, it will be 670 m2. In an orbit with an inclination of 51, their average midsection area at the solar orientation will be about 450 m2, together with the radiator ~ 510 m2. To compensate for the aerodynamic drag at an altitude of 400 km when using a remote control unit running on compressed oxygen and hydrogen, it will take about 1 ton of fuel per year. Each tonne of payload produced annually on the GSO should be provided with 30 m2 solar panels. Their total mass will be 3350 kg with a specific mass of 5 kg/m2 , and the cost is $20.1 million with a unit cost of $30,000/m2. Considering that the initial efficiency of modern solar panels is 250 W/m2 and more, and the average degradation is no more than 5-7% per year, it is realistic to expect from them a 10-year guaranteed service life, i.e. to maintain the required capacity, you can plan an annual replacement of 67 m2. Then the cost of removing one kilogram of cargo to the GSO should include $100 of the cost of producing the solar panels. In addition, the delivery of the solar panels itself (15 kg/t of the cargo displayed on the GSO) it will also require expenses of $75 at the cost of delivery to the OS of $5000/kg. Taking into account the deployment work, the total annual cost of replacing the solar panels can be estimated at $200 per kg of cargo output to the GSO, which corresponds to ~1% of the withdrawal cost.