Simplified analysis of the enrichment of heavy water in a batch thermal-diffusion column
Introduction
The first complete presentation of the separation theory of thermal diffusion in a thermogravitational column introduced by Clusius and Dickel [1], [2], was that of Furry and coworkers [3], [4]. Recently, the enrichment of heavy water in the Clusius–Dickel column was studied both theoretically and experimentally [5], [6], [7], [8], [9]. For the enrichment of heavy water in a batch-type thermal diffusion column, the separation theory is more complicated than that in continuous-type column owing to the time dependence of unsteady-state operations [5], [9]. The application of those results is limited to the range of low concentration [5] and, on account of the complicated forms of the separation equations [9], their use is still difficult for optimum design and operation. Though rather simpler equations of separation have been derived [8], they are applicable only for short-time operations. The purpose of this work is to derive simplified, but still precise, equations of separation for the whole range of concentrations, long-term operations, and easy treatment of optimum design and operations.
Section snippets
Separation theory
An analysis of the separation of the H2O–HDO–D2O system in a Clusius–Dickel thermal diffusion column was given by Yeh and Yang [5]. Fig. 1 illustrates the flows and fluxes presented in such a column. The column consists of two vertical plates separated by a small distance. One plate is heated and the other cooled, and the thermal diffusion effect causes heavy water in the water isotopic mixture to move toward the cold plate. At the same time the density gradient causes smooth laminar convection
Comparison of theoretical prediction with experimental results
The present theory for predicting the degree of separation in an unsteady-state batch-type thermal diffusion column will be compared with the experimental results obtained in previous studies. Yeh and coworkers [5], [8] employed a concentric-tube thermal diffusion column of column length L=144.78 cm to separate heavy water from water isotopes. The outside radius of the inner tube was 1.59 cm and the inside radius of the outer tube was 1.63 cm; thus, the annular space 2ω was 0.04 cm. Hot and cold
Conclusion
On the basis of the results of this study, the following conclusions were reached. A simpler equation of separation for the enrichment of heavy water in a batch-type thermal-diffusion column has been derived, as shown in , for steady and unsteady states respectively. Some graphical representations for Eq. (19) are given in Fig. 2. The most important assumptions in this work are that the concentrations are locally in equilibrium at every point in the column, and that the pseudoproduct form of
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