Heavy water enrichment by thermal diffusion in the flat‐plate frazier scheme with column heights increased at a constant ratio for improved performance

This study investigates heavy water enrichment using the Frazier scheme of flat‐plate thermal diffusion columns with the column number adjusted and the column heights varied at a constant ratio with the total sum of column heights fixed. The equations for predicting the best number of columns and the best column‐height ratio for maximum separation are derived. Considerable improvement in performance is obtainable if the column‐height ratio and/or column number in a modified Frazier scheme are properly assigned, instead of using the conventional Frazier scheme of uniform column height with the same total sum of column heights. © 2013 Canadian Society for Chemical Engineering     

Enrichment of heavy water in flat‐plate thermal diffusion columns of the frazier scheme with the optimal plate aspect ratio for best performance

The solutions of the optimum plate aspect ratio as well as the corresponding maximum separation, maximum production rate and minimum plate surface area in thermal diffusion columns of the Frazier scheme for enrichment of heavy water have been obtained, analogous to those obtained in the previous work for separation of a binary system. It was found that all the optimum plate aspect ratios do not depend on feed concentration, while the corresponding best performances do. It is found that considerable improvement in performance is obtained when the operation is carried out with the optimal plate aspect ratio.     

Optimum Plate-Spacing for the Best Performance of the Enrichment of Heavy Water in Flat-Plate Thermal-Diffusion Columns of the Frazier Scheme

Abstract

The effect of plate spacing on the degree of separation and production rate for the enrichment of heavy water in flat-plate thermal diffusion columns of the Frazier scheme with fixed operating expense has been investigated. The equations for estimating optimum plate-spacing for maximum separation and for maximum production rate have been developed. Considerable improvement in performance is obtainable when thermal diffusion columns with optimum plate-spacing are employed for operation.     

Enrichment of Heavy Water by Thermal Diffusion in the Frazier Schemes with Column Heights Varied at a Constant Increment for Improved Performance

The improvement of heavy water enrichment by thermal diffusion in the Frazier scheme with column heights varied at a constant increment and with the total sum of column heights fixed, has been investigated. The equations, which may be employed to predict the optimal column number and the optimal column-height increment for maximum separation, have been derived. Considerable improvement in heavy water enrichment is obtainable if the column number and column-height increment in a modified Frazier scheme with the total sum of column heights fixed, are property assigned under certain flow-rate operation, instead of using the conventional scheme of uniform column height.     

OPTIMAL PLATE ASPECT RATIO FOR THE BEST PERFORMANCE OF THE ENRICHMENT OF HEAVY WATER IN THERMAL-DIFFUSION COLUMNS OF A COUNTERCURRENT-FLOW FRAZIER SCHEME

The effect of plate aspect ratio on the performance of enrichment of heavy water in thermal-diffusion columns of a countercurrent-flow Frazier scheme was investigated. The equation for the optimal plate aspect ratios and the corresponding best performance were derived. Considerable improvement in performance is obtained when thermal-diffusion columns are operated at the optimal plate aspect ratio. Further improvement can be achieved if the scheme is connected and operated in countercurrent flow, instead of concurrent flow.     

OPTIMAL PLATE ASPECT RATIO FOR THE BEST PERFORMANCE OF THE ENRICHMENT OF HEAVY WATER IN THERMAL-DIFFUSION COLUMNS OF A COUNTERCURRENT-FLOW FRAZIER SCHEME

The effect of plate aspect ratio on the performance of enrichment of heavy water in thermal-diffusion columns of a countercurrent-flow Frazier scheme was investigated. The equation for the optimal plate aspect ratios and the corresponding best performance were derived. Considerable improvement in performance is obtained when thermal-diffusion columns are operated at the optimal plate aspect ratio. Further improvement can be achieved if the scheme is connected and operated in countercurrent flow, instead of concurrent flow.     

Thermal diffusion in inclined flat-plate columns of the frazier scheme

The separation theory of thermal diffusion in inclined flat-plate columns of the Frazier scheme has been developed and investigated. The equations for the best angle of inclination and maximum separation have been derived. Considerable improvement in separation is obtained when thermal diffusion columns are operated at the best angle of inclination.     

THE OPTIMUM PLATE-SPACING FOR THE BEST PERFORMANCE IN FLAT-PLATE THERMAL DIFFUSION COLUMNS OF THE FRAZIER SCHEME

The effect of plate spacing on the degree of separation and production rate in flat-plate thermal diffusion columns of the Frazier scheme with fixed operating expense, has been investigated. The equations for estimating optimum plate-spacing for maximum separation and for maximum production rate have been developed. Considerable improvement in performance is obtainable when the thermal diffusion columns with optimum plate-spacing are employed for operation.     

Thermal diffusion in the modified Frazier schemes with column heights varied at a constant increment for improved performance

The effects of column number and column-height increment on the degree of separation in the modified Frazier scheme of thermal diffusion columns with the total sum of column heights fixed, has been investigated. The equations, which may be employed to predict the optimal column number and the optimal column-height increment for the maximum separation, have been derived. Considerable improvement in performance is obtainable if the column number and column-height increment in a modified Frazier scheme with the total sum of column heights fixed, are properly assigned under a certain flow-rate operation, instead of using the conventional Frazier scheme of constant column height with the same total sum of column heights.     

The Improvement of Thermal Diffusion Performance in the Modified Frazier Scheme by Increasing the Column Heights at a Constant Ratio

The effects of column number and the variation of column heights on thermal diffusion along the modified Frazier scheme, has been investigated with the total sum of column heights fixed. The equations, which may be employed to predict the optimal number of columns and the optimal column-height ratio for the maximum separation, have been derived. Considerable improvement in performance is obtainable if the column-height ratio and/or column number in a modified Frazier scheme with the total sum of column heights fixed are properly assigned for a certain flow-rate operation, instead of using the conventional Frazier scheme of uniform column height with the same total sum of column heights.     

Recovery of Deuterium from Water‐Isotopes Mixture in Flat‐Plate Thermal‐Diffusion Columns of the FRAZIER Scheme with Optimal Plate Aspect Ratio for Improved Performance

Abstract

The equations for estimating the optimal plate aspect ratio as well as the corresponding maximum recovery, maximum production rate, and minimum plate surface area for recovery of deuterium from water‐isotopes mixture in flat‐plate thermal diffusion columns of the Frazier scheme, have been derived. Considerable improvement in performance is obtainable if the operation is carried out with the optimal plate aspect ratio. It was found that all the optimal plate aspect ratios, as well as the improvements in performance, do not depend on feed concentration.     

The best performance of spiral wired thermal diffusion columns of the frazier scheme

Equations have been derived for the optimum wire angles of inclination for maximum separation, maximum production rate and minimum column height in the Frazier scheme of concentric‐tube thermal diffusion columns with a tight fitting wire spiral, having a diameter equal to the annular spacing, and wrapped on the entire inner tube. Considerable improvement in performance is obtained when a Frazier scheme is operated at the optimum corresponding wire angle of inclination, especially for the scheme of high column number.     

THE PROPER COLUMN NUMBER FOR BEST PERFORMANCE IN THERMAL DIFFUSION COLUMNS OF THE FRAZIER SCHEME WITH TOTAL SUM OF COLUMN HEIGHT FIXED

The effect of column number on the Frazier scheme performances with total sum of column heights fixed has been investigated. The equations that may be employed to predict the optimal number of columns (generally not integers) for the maximum performance are derived. Accordingly, the proper number of columns, which are the integers nearest to and smaller than the optimal column numbers, are obtained for practical applications. Considerable improvement in performance is obtainable if the scheme is constructed with the proper number of thermal diffusion columns, instead of using a single column, with the same total sum of column heights.     

The optimum plate aspect ratio for the best performance in a flat-plate thermal diffusion column of the frazier scheme

The effects of plate aspect ratio on the degree of separation, production rate and plate surface area in a flat-plate thermal diffusion column of the Frazier scheme, have been investigated. Theoretical considerations show that when the thermal diffusion columns of the Frazier scheme are constructed with the best plate aspect ratio, maximum separation, maximum production rate or minimum plate surface area can be obtained. The optimum plate aspect ratio for maximum separation is obtained with given production rate and plate surface area, while that for maximum production rate is determined with the degree of separation and plate surface area fixed, and that for minimum plate surface area is estimated with known degree of separation and production rate. It is interesting that the optimum plate aspect ratio for maximum separation is exactly the same as that for minimum plate surface area. The maximum separation and maximum production rate are achieved without changing any total expenditure, while the design with minimum plate surface area results in minimizing the total expense.     

The Optimum Column Number for the Best Performance of Thermal Diffusion in the Frazier Scheme with the Total Sum of Column Height Fixed

The effect of column number N, as well as the column height h of thermal diffusion columns, on the degree of separation in the Frazier scheme with the total sum of the column height L (=Nh) fixed, has been investigated. The equations, which may be employed to predict the optimum column number N* for the maximum separation Δ _N,max, have been derived. Considerable performance in separation is obtainable if the column number, as well as the column height, in a Frazier scheme with the total sum of the column height fixed is properly assigned for a certain flow-rate operation.     

Enrichment of heavy water in rotated wired concentric-tube thermal diffusion columns

The enrichment performances of heavy water in various concentric-tube thermal diffusion columns, such as open, wired and rotated wired devices, have been compared with different flow-rate range operations. It was found that the operation with a wire spiral inserted in the annular spacing and with tubes rotated in opposite directions will reduce the remixing effect and enhance the cascading effect, respectively, resulting in improved the separation.     

The generalised equation of separation in thermal diffusion columns by linear approximation

A generalised equation of separation applicable to the whole range of concentration in flat-plate thermal diffusion columns has been derived. The improvement in theoretical analysis was obtained by replacing the product form of the concentration dependence with a linear approximation instead of a constant.     

The best performance of inclined thermal diffusion columns of the frazier scheme

The equations for the best angles of inclination for maximum separation, maximum production rate and minimum column length in inclined flat-plate thermal-diffusion columns of the Frazier scheme, have been derived. Considerable improvement in performance is obtained when a Frazier scheme is operated at the best corresponding angle of inclination, especially for the schemes of high column number.     

MASS TRANSFER IN LAMINAR FLOW IN CONCENTRIC-TUBE THERMAL-DIFFUSION COLUMNS FOR HEAVY WATER ENRICHMENT UNDER THE EFFECTS OF FLOW-RATE FRACTIONS AND RECYCLES

An orthogonal expansion technique for solving separation problems in laminar countercurrent concentric circular thermal-diffusion columns under flow-rate fraction variations is developed analytically and applied to heavy water enrichment. Experimental work for the H₂O–HDO–D₂O system has been also conducted. The present theoretical predictions are based on Sturmian theory, and positive and negative eigenvalues are needed for enriching and stripping sections, respectively, during the calculation procedure. The results show that the theoretical predictions are in better agreement with the experimental results than those predicted in previous works by using the transport equation.     

Separation of Heavy Water by Vapor-Phase Thermal Diffusion Coupled with Distillation and Condensation

Abstract

A study on the enrichment of heavy water in a vapor-phase thermal-diffusion column has been conducted. With the combination of the effects of distillation, vapor-phase thermal diffusion, and partial condensation, considerable improvement in the degree of enrichment has been achieved in a vapor-phase column rather than in a liquid-phase column. It was also found that even the part of enrichment contributed only by vapor-phase thermal-diffusion effect is much higher than that obtained by liquid-phase thermal diffusion.