Introduction. The problem of reducing CO₂ emissions in industrial production (the problem of creating low CO₂ emission industries) can be solved in different ways. One of them is the capture of carbon dioxide from the gas emissions of enterprises. The technology we offer is completely safe and relatively compact & energy-efficient.
The extraction of carbon dioxide from a gas mixture is carried out during a vapor-solid phase change so the final product is dry ice, which must be disposed of in one way or another. For example, it can be safely buried, or it can be to injected into an oil well for enhanced oil recovery (EOR) or CO₂ can be sold (there is a big market for dry ice and CO₂ gaseous worldwide).
The supercooling/supersaturation necessary for initiating a phase change is created when the mixture expands in a supersonic nozzle. As the flow accelerates and supercooling increases, the probability of homogeneous nucleation increases, which, if it occurred, would lead to avalanche-like, uncontrollable vapor-solid phase change. As a result, only a relatively small fraction of the CO₂ would have passed into the solid phase, but the supercooling would nevertheless have been exhausted. To avoid this and to realize controlled crystallization providing the desired degree of CO₂ removal, it is proposed to introduce a solid particle into the gas stream, on the surface of which the phase change vapor-solid will take place. The size of the solid particles can be chosen to be easily separated from the gas phase in cyclones. As the removal of carbon dioxide from the air mixture is possible at rather low temperatures of 210 -150 K, there is a need to pre-cool the initial gas mixture. In addition to using external energy sources, it is proposed to use purified gas mixture as a cooling agent in the heat exchanger. This would reduce the cost of CO₂capture.
EU patent No. EP3912703 is granted. Invention patent RU2757240 has been granted in Russia.

Method description. In the proposed method, the extraction of CO₂ occurs during of vapor – solid phase changes. Figure 1 shows a state diagram in the P (pressure) -T (temperature) coordinates.

The curve below the triple point represents the equilibrium line of the vapor-solid. In order phase changes from the vapor to the solid body to become possible, it is necessary to provide in the vapor-gas medium a certain deviation from the equilibrium state, that is, to move the gas to some unstable state, which is indicated by the "A" point on the diagram. The degree of deviation from the state of equilibrium is possible to characterize by supercooling ΔΤ = (Ts-Tg) or by supersaturation ε_p = Pv/Ps, for example. Here Tg is the temperature of the vapor-gas medium, Pv is the partial pressure of the extracted component; Ts = Ts(P =Pv) and Ps = Ps (T = Tg) are the temperature and pressure on the equilibrium line (see Figure). Its essence is to achieve a nonequilibrium gaseous state in the process of expanding (acceleration) the gas flow in a supersonic nozzle. In this way it is easy to get virtually any supercooling/supersaturation.
Figure 2 shows typical dependence of supercooling from the Mach number M for the cases of extraction CO₂ from the air.

Here the Mach number M is the ratio of the flow velocity at a given point of the gas flow to the local velocity of sound propagation in a moving medium. The calculations are performed for the cases when the pressure P₀ and temperature T₀ of the air at the input to the supersonic nozzle are equal P₀ = 1 bar (10⁵ Pa), T₀ =200 K. It can be seen that the large values of the supercooling ΔΤ necessary for intensive vapor condensation are attained only at M ≥ 1. In other words, they arise only as the flow approaches to the critical cross-section of the nozzle and in its supersonic part.
However, for complete extraction of CO₂, achieving only a big supercooling is not enough. The great supercooling will lead to an avalanche-like homogeneous nucleation, in so-called condensation shocks arisen in the flow. It is known that in condensation shocks can be extracted only about 25%-30% of the supercooled component. Thus, condensation jumps must be avoided. This means that the process of phase changes itself should be made manageable: the place (cross-section, in which they start) and time of their occurrence are to be under control. The last is made possible due to condensation on solid particles of a preselected size introduced in the gas flow in the right places.
The process described above is shown in Figure 3.

The initial gas mixture cooled to low temperature enters to supersonic nozzle. In it during expansion of mixture, the supercooling is created, sufficient to extract CO₂ from gas emissions. The extraction of carbon dioxide from the gas phase (desublimation) occurs on the surface of solid particles introduced in the Working section/Extraction Chamber which is located just behind the nozzle. It is advisable to use dry ice itself as material for solid particles. The solid particles are necessary then to separate from gas medium. It is possible to do for example in cyclone. The costs of CO₂ capture are significantly dependent on the energy costs (electricity). They can be considerably reduced by using the output gases as a coolant.

Experimental confirmation. The possibility of extracting one of the components forming (making up) the gas mixture has been confirmed experimentally.
Figure 4 shows the scheme of an experimental plant. Atmospheric air was compressed in a pump, then heated in a heat exchanger and passed through a melt layer of succinic anhydrides. The resulting vapor-gas mixture with a volumetric concentration of succinic anhydride C = 0.5-1.0% was supplied to the input of the Laval nozzle, in which it expanded (accelerated). The diameters of input, critical and output cross-sections were equal 13.6, 1.95 and 14,6 mm, respectively. Directly after the output cross-section of the nozzle, a “working section (chamber) was installed. It was a cylindrical section of the 15 mm long and an expanding section of 63 mm long.

The cylindrical section had holes in the side wall through which solid particles of succinic anhydride were supplied by means of a gas transport. The diameter of the particles was equal 20 -30 microns. After the separation of solid particles from a gas in the cyclone, the gas flow passed through the tissue filter, and then through a layer of an aqueous solution of alkali. At the exit cyclone in the gas phase succinic anhydride was absent. Thus, its extraction was complete.

By estimating of CO₂-quota market was taken into account that CO₂ emissions in the EU must be reduced by 600 million tonnes by 2030. Currently, the price per ton is around €90 and rising, hence the minimum size of the quoted market by 2030 will be around €50 -55 billion.
Market size value of liquid CO₂ used for enhanced oil recovery is about $42 billion in 2022 and will be around $78 billion in 2030 (Global Enhanced Oil Recovery Market Size Report, 2030). Thus, significant part of the captured CO₂ would be buried in oil wells. The sizes of CO₂-gaseous & dry ice markets were taken from literature.