Document Type : Research Paper
Authors
1 Nuclear Fuel Cycle Research School, Nuclear Science and Technology Research Institute, AEOI, P.O.Box:11365-8486, Tehran-Iran
2 Advanced Technologies Company of Iran, AEOI, P.O. Box: 14399-55431, Tehran - Iran
Abstract
In this research, the analytical and numerical comparison of the R model cascade with Q and QI model cascades for stable isotope separation has been done. In this regard, the numerical codes for the design of the R and QI model cascade for comparison to the analytical Q model cascade have been written in MATLAB software. The results show that for two components k1 and k2, a few R-cascades are special states of the QI cascade for the k1 component. Also, the findings show that the sum of the partial cut values for two components k1 and k2 in the cascade R is always equal to one (θk1,s+ θk2,s=1). Based on the results, if the parameter M* in the Q model is equal to the mean value of the two components, k1, and k2, in the R model, these two models are the same. Therefore, the R cascade is a special case of QI and Q cascades. The QI cascade encompasses a wide range of cascades, and by choosing the right cut in it, optimal relations can be achieved. For example, the results for isotopes 4 and 9 of Xe show that the total flow rate is optimal for the QI cascade. This is compared to the Q and R models.
Highlights
- M. Ragheb, Isotopic separation and enrichment, University of Illinois, Urbana- Champaign Course Materials (2012).
- K. Cohen, The Theory of Isotope Separation as Applied to the Large-Scale Production of U 235, National Nuclear Energy Series, Division III, Vol. IB, New York (1951).
- A.G. Kudziev, Production and application of stable enriched isotopes in the USSR, Nuclear Instruments and Methods in Physics Research, 282, 1 (1989).
- A. De la Garza, G.A. Garret, J.E. Murphy, Multicomponent isotope separation in cascade, Chem. Eng. Sci., 15, 188 (1961).
- A. De la Garza, A generalization of the matched abundance-ratio cascade for multicomponent isotope separation, Chem. Eng. Sci., 18, 73 (1963).
- R.Ya. Kucherov, V.P. Minenko, Theory of cascade for separating multi-component isotope mixtures, At. Energy., 19, 4 (1965).
- N.A. Kolokol’tsov, et al., Design of cascades for separating isotope mixtures, At. Energy., 29, 6 (1970).
- A. Apelblat, Y. Ilamed-Lehrer, The theory of a real isotope enriching cascade, Nucl. Energy., 22, 1 (1968).
- S. Zeng, Y. Cheng, A numerical method of cascade analysis and design for multicomponent isotope separation, Chem. Eng. Res. Des., 92, 2649 (2013).
- I. Yamamoto, Simple formulae for analyzing match abundance ratio cascade with constant separation factors for multicomponent isotope separation, Nucl. Sci. Technol., 24 (1987).
- S. Zeng, et al., The Q Cascade Explanation, Sep. Sci. Tech., 47, 1591(2012).
- G.A. Sulaberidze, V.D. Borisevich, X. Quanxin, Quasi-Ideal Cascades with an Additional Flow for Separation of Multicomponent Isotope Mixtures, Theo. Found. Chem. Eng., 40, 5 (2005).
- R.C. Raichura, M.A.M. AI-Janabi, G.M. Langbein, The effect of the 'KEY' molar mass on the design of a cascade handling a multi-isotopic mixture, Annals. Nucl. Energy., 18, 327 (1991).
- S. Zeng, Y. Chuntong, A method of separating a middle component in multicomponent isotope mixtures by gas centrifuge cascades, Sep. Sci. Tech., 35, 2173 (2000).
- A.Y. Smirnov, G.A. Sulaberidze, Features of mass transfer of intermediate components in square gas centrifuge cascade for separating multicomponent mixtures, Theo. Found. Chem. Eng., 48, 629 (2014).
- S. Khooshechin, et al., Optimization of flexible square cascade for high separation of stable isotopes using enhanced PSO algorithm, Prog. Nucl. Energy., 140 (2021).
- T.E. Azizov, A.Y. Smirnov, G.A. Sulaberidze, Optimization of a square cascade of centrifuges for separation of multicomponent mixtures of stable isotopes, At. Energy., 128, 291 (2020).
- G.A. Sulaberidze, V.D. Borisevich, Q. Xie, Comparison of optimal and model cascades for the separation of multicomponent mixtures at arbitrary stage numbers, Theo. Found. Chem. Eng., 42, 347 (2008).
- V.D. Borisevich, S. Zeng, G.A. Sulaberidze, New approach to optimize Q cascades, Chem. Eng. Sci., 66, 393 (2011).
- T. Song, et al., Comparative study of the model and optimum cascades for multicomponent isotope separation, Sep. Sci. Tech., 45, 2113 (2010).
- F. Mansourzadeh, et al., Utilization of harmony search algorithm to optimize a cascade for separating multicomponent mixtures, Prog. Nucl. Energy., 111, 165 (2019).
- G.A. Sulaberidze, et al., Classification of model cascades for separation of multicomponent isotope mixtures, Sep. Sci. Tech., 56, 1060 (2020).
- Y. Lehrer-Ilamd, On the Value Function for Multicomponent Isotope Separation, Nucl. Energy., 23, 559 (1969).
- F. Mansourzadeh, et al., Performance comparison of match abundance ratio cascade with optimal conditions for the separation of stable xenon isotopes, Nucl. Scie. Tech., 94, 4 (2021).
Keywords
- M. Ragheb, Isotopic separation and enrichment, University of Illinois, Urbana- Champaign Course Materials (2012).
- K. Cohen, The Theory of Isotope Separation as Applied to the Large-Scale Production of U 235, National Nuclear Energy Series, Division III, Vol. IB, New York (1951).
- A.G. Kudziev, Production and application of stable enriched isotopes in the USSR, Nuclear Instruments and Methods in Physics Research, 282, 1 (1989).
- A. De la Garza, G.A. Garret, J.E. Murphy, Multicomponent isotope separation in cascade, Chem. Eng. Sci., 15, 188 (1961).
- A. De la Garza, A generalization of the matched abundance-ratio cascade for multicomponent isotope separation, Chem. Eng. Sci., 18, 73 (1963).
- R.Ya. Kucherov, V.P. Minenko, Theory of cascade for separating multi-component isotope mixtures, At. Energy., 19, 4 (1965).
- N.A. Kolokol’tsov, et al., Design of cascades for separating isotope mixtures, At. Energy., 29, 6 (1970).
- A. Apelblat, Y. Ilamed-Lehrer, The theory of a real isotope enriching cascade, Nucl. Energy., 22, 1 (1968).
- S. Zeng, Y. Cheng, A numerical method of cascade analysis and design for multicomponent isotope separation, Chem. Eng. Res. Des., 92, 2649 (2013).
- I. Yamamoto, Simple formulae for analyzing match abundance ratio cascade with constant separation factors for multicomponent isotope separation, Nucl. Sci. Technol., 24 (1987).
- S. Zeng, et al., The Q Cascade Explanation, Sep. Sci. Tech., 47, 1591(2012).
- G.A. Sulaberidze, V.D. Borisevich, X. Quanxin, Quasi-Ideal Cascades with an Additional Flow for Separation of Multicomponent Isotope Mixtures, Theo. Found. Chem. Eng., 40, 5 (2005).
- R.C. Raichura, M.A.M. AI-Janabi, G.M. Langbein, The effect of the 'KEY' molar mass on the design of a cascade handling a multi-isotopic mixture, Annals. Nucl. Energy., 18, 327 (1991).
- S. Zeng, Y. Chuntong, A method of separating a middle component in multicomponent isotope mixtures by gas centrifuge cascades, Sep. Sci. Tech., 35, 2173 (2000).
- A.Y. Smirnov, G.A. Sulaberidze, Features of mass transfer of intermediate components in square gas centrifuge cascade for separating multicomponent mixtures, Theo. Found. Chem. Eng., 48, 629 (2014).
- S. Khooshechin, et al., Optimization of flexible square cascade for high separation of stable isotopes using enhanced PSO algorithm, Prog. Nucl. Energy., 140 (2021).
- T.E. Azizov, A.Y. Smirnov, G.A. Sulaberidze, Optimization of a square cascade of centrifuges for separation of multicomponent mixtures of stable isotopes, At. Energy., 128, 291 (2020).
- G.A. Sulaberidze, V.D. Borisevich, Q. Xie, Comparison of optimal and model cascades for the separation of multicomponent mixtures at arbitrary stage numbers, Theo. Found. Chem. Eng., 42, 347 (2008).
- V.D. Borisevich, S. Zeng, G.A. Sulaberidze, New approach to optimize Q cascades, Chem. Eng. Sci., 66, 393 (2011).
- T. Song, et al., Comparative study of the model and optimum cascades for multicomponent isotope separation, Sep. Sci. Tech., 45, 2113 (2010).
- F. Mansourzadeh, et al., Utilization of harmony search algorithm to optimize a cascade for separating multicomponent mixtures, Prog. Nucl. Energy., 111, 165 (2019).
- G.A. Sulaberidze, et al., Classification of model cascades for separation of multicomponent isotope mixtures, Sep. Sci. Tech., 56, 1060 (2020).
- Y. Lehrer-Ilamd, On the Value Function for Multicomponent Isotope Separation, Nucl. Energy., 23, 559 (1969).
- F. Mansourzadeh, et al., Performance comparison of match abundance ratio cascade with optimal conditions for the separation of stable xenon isotopes, Nucl. Scie. Tech., 94, 4 (2021).