Mathematical model for calculation of optimal temperature desublimation in metal fluorides and the number of desublimation stages has been developed; it permits achieving the degree of base product recovery from gas-vapour mixture nearly to 100 %. Experimental checking of modeling results at uranium hexafluoride desublimation shows a good correlation with the theoretical data

Buynovskiy, А. S.

Lazarchuk, V. V.

Matveev, А. А.

Smolkin, P. А.

Sofronov, V. L.

Electronic archive of Tomsk Polytechnic University

REFERENCES1. Petrov Yu.I. Clusters and minor particles. – Moscow: Nauka, 1986.– 368 p.2. Ilyin A.P., Tikhonov D.V., Tolbanova L.O., An V.V. Threshold phenomena in nanopowders // Isvestiya Vusov. Fizika. – 2006. – № 8(Appendix). – P. 550–552.3. Chemical Encyclopedia. V. 1. – Moscow: Sovetskaya Enziklopediya,1988. – 623 p.4. Ilyin A.P. The development of electroblasting technology of nanopowders obtaining in the RI of High Voltages at Tomsk PolytechnicUniversity // Bulletin of the Tomsk Polytechnic University. – 2003.– V. 306. – № 1. – P. 133–139.5. Godymchuk A.Yu., Ilyin A.P., Astankova A.P. Aluminum nanopowder oxidation in liquid water at heating // Bulletin of the TomskPolytechnic University. – 2007. – V. 310. – № 1. – P. 102–104.6. Ilyin A.P., Gromov A.A. Oxidation of aluminum and boron hyperfine powders. – Tomsk: Izdvo TPU, 1999. – 131 p.Received on 27.12.2006Chemistry69IntroductionSublimationdesublimation limit, being a refiningoperation is of great importance in technology of obtaining a number of pure substances and semiproductsincluding the technology of nuclear fuel.All existing desublimators may be divided into threegroups by the way of solid phase extraction from gasflow: surface, volumetric and mixed [1]. However, allthese apparatus have a significant disadvantage. It is alow yield of a main product into disublimate(80...90 %), the reason of which is aerosols formation atintense overcooling of desublimated substance vaporand their carryover from the system. In industry thedesublimation processes of ZrF4, TiF4, UF6, WF6, ReF6and other volatile metal fluorides are usually carried outat temperatures, which are considerably lower than actual temperatures of desublimation. The latter cause theformation of crystallization centers in apparatus volumeand as a result loss of the product in the form of aerosol.The investigations of the influence of apparatus surface temperature on desublimation process of titaniumtetrafluoride carried out before showed [2], that at desublimation temperature decrease lower than the actualone by 250 °С loose desublimate of pinfin type is formed; by 150 °С – the layer of friable product is formed;by 100 °С – solid vitreous product along the whole layer is formed. In this case products output losses fromdesublimator were 27, 12, and 5 wt. %, correspondingly.The most efficient way of organizing the desublimationprocess would be the way at which in the conditions of changing heating rate it could be possible to suppress the processof aerosols occurrence and control the desublimator layerrise ensuring apparatus maximal filling and its passability.1. Aerosol formation at vapor supersaturation The point of desublimation process is in product gaseous molecules delivery from gasvapor mixture volumeto the cold desublmator surface. As far as desublimationmay occur at high rate only fulfilling the condition [1](1)where S is the degree of gasvapor mixture supersaturation; Scr is the critical degree of supersaturation overwhich the formation process of solid phase nuclei in apparatus volume starts; Р, Р∞(Т) is the current gas pressurein the system and substance gas pressure over its desublimate at the given temperature; depending on theway of disublimation process organization various means of its behavior are possible.If Scr is obtained only on the surface of disublimatethen the whole product will settle on it. In this case thelower its temperature is the higher is the rate of desublimation process. However, it is stated experimentally [2]that in this case product yield into desublimate sharplydecreases due to its volumetric desublimation, alwaysoccurring there where Scr is obtained, the zone of whichwill transfer from the surface into the volume of gasvapor mixture (Fig. 1).If we denote the input temperature of gasvapormixture into desublimator by T1, temperature of coldsurface is denoted by T2, the distance which the gasvapor mixture will cover having been cooled from temperature T1 to T2 is L then assuming that as the distance xincreases from gas entry point into apparatus to its exitpoint the temperature of gasvapor mixture T will decrease linearly from T1 to T2 we obtain( ),êðTPS SP∞= ≤UDC 546.791.6’161MATHEMATICAL MODEL OF DESUBLIMATION PROCESS OF VOLATILE METAL FLUORIDESP.А. Smolkin, А.S. Buynovskiy, V.V. Lazarchuk, А.А. Matveev, V.L. SofronovSeversk State Technological AcademyEmail: spanet@mail.ru, sofronov@ssti.ruMathematical model for calculation of optimal temperature desublimation in metal fluorides and the number of desublimation stageshas been developed; it permits achieving the degree of base product recovery from gasvapour mixture nearly to 100 %. Experimentalchecking of modeling results at uranium hexafluoride desublimation shows a good correlation with the theoretical data.(2)Then pressure P will also change similarly(3)Using the equations (1)–(3) the equation for determining the values of gas supersaturation degree at thepreset desublimator temperature may be derivedIn desublimators operating in working conditionsgas temperatures and pressures equalizing occurs owingto turbulent and molecular diffusion and product heatconductivity. That is the processes of mass and heatexchange – gas cooling and gas molecules carryover todesublimation surface occur simultaneously. The scheme of supersaturated vapor formation at motion of turbulent flow of gasvapor mixture in the tube cooled outside is shown in Fig. 1 [3].The ratio of mass and heat exchange rates is so thatvapor supersaturation at the beginning increases obtaining maximal value and then decreases. In the areawhere it increases the critical value (shaded region) there is volumetric desublimation.Fig. 1. Change of vapor flow supersaturation degree when moving along the tubeAt homogeneous desublimation it is meant by critical supersaturation Scr such supersaturation at whichthe rate of nuclei formation capable of further growthequals to a unity that is I=1 cm–3.s–1 The similar assumption is certainly conventional as nuclei formation occurs also at I<1 but the rate of such process is low. Taking into consideration strong dependence of nucleiformation rate on vapor supersaturation [1, 3] the valueof vapor critical supersaturation at its homogeneousdesublimation may be calculated by the equation, taking I=1 and S=Scr [3]where М is the molecular weight of desublimated substance, g/mole; ρ is the density of desublimate, kg/m3;Т is the temperature in the system, K; σ is the surfacetension, J/cm2; K is the kinetic coefficient calculated bythe formulaκ is Boltzmann constant equal to 1,38.10–23 J/K; γ is thecoefficient of desublimation expressing a part of vapormolecule staying on desublimator solid surface owing tocollisions (depending on desublimated substance nature, the degree of its contamination, absence of inert gasmolecules and some other factors its value γ may varyfrom 0 to 1,0); m is the vapor molecule weight of desublimated substance, kg.Surface stress σ is solved from the equation [3]:where ΔH is the enthalpy change at evaporation,kJ/mole; R is the universal gas constant, equal to8,314 J/(mole.K); n is the coordination number; Δn isthe number of missing neighbors of crystal lattice in surface layer; h is the thickness of molecule monolayer (forfluorides it is 0,2...0,3 nm), m; V0 is the molar volume ofsolid substance, cm3/mole, equal toCertain critical size of particles meets supersaturation existing in the system at every time moment. Theradius of critical spherical nucleus rcr is defined fromThomson equation [3, 4]:When achieving a certain critical size (10–4...10–3)mkm, the nucleus stabilizes and becomes the centre ofcrystallization trending to unrestricted growth [3, 4].Mass concentration of fog G, g/m3, appearing in thiscase may be calculated by the equation [3]The question of the fact where desublimation of theproduct takes place – on the surface of desublimator or inthe volume of gasvapor mixture, is determined by ratesratio of mass and heat exchange of desublimated product which may be estimated by Lewis number Le [4, 5]:where α is the coefficient of heat transfer, Wt/(m2.K); βis the coefficient of mass transfer m/s; cр is the specificgas heat capacity at constant pressure, J/(kg.K).If Le>1 at the given conditions then heat exchange intensity is higher than mass transfer intensity. As a result there is not enough time for desublimating product to be delivered to desublimator surface in the form of vapor and theprocess of volumetric desublimation is the dominant one.Le = ,pcαρβ( ) ( 1).TMPG SRT∞= −2 .lncrMrRT Sσρ=0 .MV ρ=0 ,H RT n hV nσ Δ − Δ=22 ,m PKTγ σρ π κ⎛ ⎞= ⎜ ⎟⎝ ⎠321,44lg ,lgcrMSK Tσρ⎛ ⎞= ⎜ ⎟⎝ ⎠Supersaturation S, ScrTube length L2 1 2 21 2 ( ) ( ).T TT T P P PST T P P∞ ∞− −= +−1 22 .P PP P xL−= +1 22 .T TT T xL−= +Bulletin of the Томsк Pоlytеchnic University. 2007. V. 310. № 3702. Desublimation process modeling On the basis of above mentioned equations themathematical model of desublimation process of metalvolatile fluorides allowing us to calculate the multistagedesublimation process and to bring the extraction ratioof target product from gasvapor mixture almost to100 % was developed. The mathematical model allowsdetermining the number of desublimation stages, optimal temperature of desublimating surface at each stageexcluding aerosols formation at maximal rate of desublimation process.The results of mathematical modeling of UF6 desublimation process are presented lower, Fig. 2, 3, as anexample. So for the most complete UF6 catching fromprocess gas obtained at fluorination of uranium oxidesthe model indicated the necessity of four desublimationstages organization at 288, 267, 246 and 224 K (at thesetemperatures the condition S=Scr is fulfilled). In thiscase the outlet residual pressure of UF6 in gas mixturefrom each stage is equal to 7,37.103; 1,38.103; 1,86.102and 13,3 Pa, and its collection efficiencies at each stageare 76,05; 19,51; 3,9 and 0,5 %, correspondingly. Thus,the collection efficiency of UF6 after four stages of desublimation forms not less than 99,96 %.Fig. 2. The degree of supersaturation and critical degree of supersaturation at different temperatures of desublimator wallAt the outlet from each stage of desublimation gascontaining residual pressure of UF6 and formed aerosolsis directed through the heated pipelines to the next stage of desublimation. And at organization of one stage ofdesublimation the degree of vapor supersaturation attemperature 224 K the degree of UF6 supersaturation is2,3.103 (dashdot line in Fig. 2).Fig. 3. The dependence of the mass of UF6 formed aerosols onthe temperature of desublimator wallConclusionThe mathematical model for calculating the efficient temperature of substances desublimation has beendeveloped. It allows revealing those parameters of theprocess at which the maximal rate of surface desublimation process is achieved and the process of aerosols formation in the volume of the apparatus is minimized.The suggested technique of calculation of desublimation process parameters is checked while determining the optimal conditions of UF6 and TiF4 desublimation processes and may be applied for the similar calculations of desublimation (condensation) processes ofother metal volatile fluorides supporting maximal efficiency of the process.Temperature T, KMass of formed aerosols G, kgTemperature T,KSupersaturation SChemistry71REFERENCES1. Grin H., Lein V. Aerosols – dusts, smokes and fogs. – Leningrad:Khimiya, 1969. – 428 p.2. Sofronov V.L., Buinovskiy A.S., Vasiliev K.F. On sublimation purification of titanium tetrafluoride / VII AllUSSR symposium on chemistry of inorganic fluorides: Theses of reports. – Moscow: Nauka,1984. – P. 73.3. Amelin A.G. Theoretical basis of fog formation at vapor condensation. – Moscow: Khimiya, 1972. – 304 p.4. Gorelik A.G., Amitin A.V. Desublimation in chemical industry. –Moscow: Khimiya, 1986. – 272 p.5. Raist P. Aerosols. Introduction into theory. – Moscow: Mir, 1987. –320 p.Received on 28.11.2006

Mathematical model of desublimation process of volatile metal fluorides

Abstract

Similar works

Full text

Available Versions

Electronic archive of Tomsk Polytechnic University