Enrichment Of Heavy Water Research Articles

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.

Improvement in deuterium recovery from water–isotope mixture by thermal diffusion in the device of branch columns

Deuterium recovery from water–isotopes mixture using thermal diffusion can be improved by employing the branch column device, instead of single column devices, with the same total column length. The remixing effect due to convection currents in a thermal diffusion column for heavy water enrichment is thus reduced and separation improvement increases when the flow rate or the total column length increases. The improvement in separation can reach about 50% for the numerical example given.

Conjugated mass transfer in an inclined thermal-diffusion column for heavy water enrichment with plate aspect ratio variations

A two-dimensional mathematical model was developed theoretically to predict the degree of separation of heavy water in an inclined flat-plate thermal-diffusion column. An orthogonal expansion technique for solving separation problems of heavy water enrichment under plate aspect ratio and inclination angle variations was carried out analytically. The effects of plate aspect ratio and inclination angle on the degree of separation have been investigated with a consideration of a fixed operating expense. Considerable improvements in device performance are obtained if the thermal-diffusion columns are inclined at the optimal angles as compared to the vertical orientation. Further improvement can be achieved if the flow-rate fractions of top and bottom products are suitably adjusted.

Modified Separation Theory of Heavy Water Enrichment by Thermal Diffusion in the Cocurrent-Flow Frazier Schemes

The separation theory for heavy water enrichment from water-isotope mixture in the cocurrent-flow Frazier scheme of thermal diffusion columns, has been modified with the values of pseudo product form of concentration determined by the method of least squares method, instead of simply taking the concentration in the product form as the feed concentration performed in previous works. The results indicate that serious errors occurred for the estimation of heavy water enrichment in the previous works, especially for employing the Frazier scheme with a larger number of thermal diffusion columns.

The analytical study on heavy water enrichment in concentric circular thermal-diffusion columns with optimal plate spacing for improved performance

A two-dimensional mathematical model was developed theoretically to predict the degree of separation of heavy water in concentric circular thermal-diffusion columns with total fixed expense and with plate spacing variations. An orthogonal expansion technique for solving separation problems of heavy water enrichment to estimate optimal plate spacing for maximum separation has been developed analytically. Considerable improvements in device performance were obtained when the thermal-diffusion column with optimal plate spacing were used. The effects of plate spacing and mass flow rate and on the degree of separation have been investigated with a consideration of the fixed total expense. Further improvement can be achieved if the feed position and flow-rate fractions of top and bottom products are suitably adjusted.

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

AbstractThis 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

Performance analysis for an inclined thermal diffusion column with side-stream operation for heavy water enrichment

Heavy water enrichment using an inclined Clusius–Dickel thermal diffusion column with side-stream operation has been investigated theoretically. The mathematical model to determine the separation efficiency and the best inclination angle have been developed. Significant improvement in heavy water enrichment can be obtained relative to a classic, vertical without side-stream, design. The study of the effects of design and operating variables points out the design provides greater improvement for lower feed flow rate and higher top and side product ratios.

Further study on heavy water enrichment by thermal diffusion in the countercurrent-flow Frazier scheme

The separation theory for heavy water enrichment from water–isotope mixture in the countercurrent-flow Frazier scheme of thermal diffusion columns has been modified by the method of least squares. The results show that if the degree of separation is calculated from the modified separation equation, a serious error will be prevented, especially for employing the Frazier scheme with larger number of thermal diffusion columns.

The optimal column number for the improvement in heavy water removal rate from water-isotopes mixture by thermal diffusion in the countercurrent-flow Frazier scheme with the total sum of column heights fixed

The effect of column number on the enrichment of heavy water from water–isotope mixture in the countercurrent-flow Frazier scheme with total sum of column heights L fixed, has been investigated. The equations, which may be employed to predict the optimal column numbers for maximum performances, have been derived. Considerable improvement in removal rate is obtainable if the scheme is constructed with the optimal column number of thermal diffusion columns, especially for larger flow rate with smaller L, or smaller flow rate with larger L.

Modeling of mass transfer Graetz problems in flat-plate thermal-diffusion columns for heavy water enrichment

The mass transfer Graetz problem of flat-plate thermal-diffusion columns for heavy water enrichment was investigated. An orthogonal expansion technique was used to solve the laminar counter-current flat-plate thermal-diffusion column separation problems under flow-rate fraction variations and feed position. The present theoretical predictions for the degree of separation were solved based on the separation variable method. Positive and negative eigen-values are needed for the enriching and stripping sections, respectively, during the calculation procedure. The results show that the degree of separation increases with decreasing the feed flow rate and the maximum degree of separation is obtained for feed positions δ = 0.5 and feed concentration C F = 0.385. Moreover, the theoretical predictions are in better agreement with the experimental results than those predicted using the transport equation in the previous works.

The best column number for enrichment of heavy water in thermal-diffusion columns of countercurrent-flow Frazier scheme with total sum of column height fixed

The effect of column number N and the same column height h of each thermal-diffusion column, on the Frazier scheme performance with total sum of column height ( L = Nh) fixed, has been investigated. The equations, which may be employed to predict the optimal number of columns (generally not integers) for the maximum performance are derived. Accordingly, the best number of columns, which are the integers nearest to, and small than the optimal column numbers, are obtained for practical applications. Considerable improvement in performance is obtainable if the scheme is constructed with the best number of thermal-diffusion columns, instead of using a single column with column height L ( N = 1, h = L). This is because that increasing column height in a thermal-diffusion column, though increasing the performance, will decrease the increment in performance, and finally the performance reaches a limiting value.

Enrichment of heavy water in thermal-diffusion columns connected in series

The separation equations for enrichment of heavy water from water isotope mixture by thermal diffusion in multiple columns connected in series, have been derived based on one column design developed in previous work. The improvement in separation is achievable by operating in a double-column device, instead of in a single-column device, with the same total column length. It is also found that further improvement in separation is obtainable if a triple-column device is employed, except for operating under small total column length and low flow rate.

The optimum number of columns for enrichment of heavy water by thermal diffusion in the Frazier scheme at fixed sum of column heights

The effect of the number of columns on the enrichment of heavy water from water isotope mixture by thermal diffusion in the Frazier scheme at fixed sum of column heights has been investigated. The equations for predicting the optimum number of columns and the corresponding maximum separation have been derived. Considerable enrichment in separation is obtainable if the number of columns, as well as the column height, in a Frazier scheme is properly assigned for a certain flow-rate operation.

Enrichment of heavy water in flat-plate thermal-diffusion columns with optimal plate aspect ratio

The optimum plate aspect ratios for maximum separation of heavy water, maximum production rate and minimum plate surface area in flat-plate thermal-diffusion column with plate surface area fixed, have been determined. Essential improvement in performance is obtainable if the column is constructed with the best plate aspect ratio, so that the desirable cascading effect can be enhanced, while the undesirable remixing effect can be properly reduced. The maximum separation and maximum production rate are achieved without changing any total expense, while the design with minimum plate surface area results in minimizing the total expense.

The improvement of the heavy water enrichment under countercurrent-flow Frazier scheme and flow-rate fraction variations

The desirable cascading effect and undesirable remixing effect are the two conflicting effects produced in a thermogravitational thermal-diffusion column. A new design is proposed in the present study to obtain equilibrium separation efficiency improvement associated with a remixing-effect suppression and cascading effect enhancement. The separation equation for the heavy water enrichment by inclined thermal-diffusion columns in countercurrent-flow Frazier schemes under flow-rate fraction variations has been developed theoretically. The concentration-product term in the transport equation is treated in the enriching and stripping sections separately for more accurate analysis. It was found that the undesirable disadvantage of the remixing effect could be reduced effectively by suitably tilting the column and controlling the flow-rate fraction at both top and bottom product streams, leading to a considerable separation efficiency improvement. Numerical examples were given to illustrate the best inclination angle and flow-rate fraction on separation efficiencies for H 2O–HDO–D 2O system.

Optimal plate aspect ratio for the enrichment of heavy water from water–isotope mixture in a flat-plate thermal diffusion column with transverse sampling streams

Suitably adjusting the plate aspect ratio in a flat-plate thermal diffusion column is one of the flexible ways of properly controlling the convective strength, resulting in reducing the remixing effect while still preserving the effectively cascading effect, and thereby leading to improved separation. The optimal plate aspect ratios for the performances of the separation of heavy water from water–isotope mixture in flat-plate thermal diffusion columns with transverse sampling streams have been determined. The maximum separation and maximum production rate are achieved without changing the total expenditure, while the design with minimum plate surface area results in minimizing the total expenditure.

Effects of design parameters on enrichment of heavy water in batch-type flat-plate thermal diffusion columns

The influences of inclination angle, plate-spacing and plate aspect-ratio changes on the performance of batch-type flat-plate thermal diffusion columns that are used for the enrichment of heavy water from water–isotope mixtures have been investigated, while the total expense was kept unchanged. Considerable improvement in the performance is achievable if operation is carried out by increasing plate aspect ratio, and/or properly increasing the inclination angle and/or properly decreasing plate spacing. The temperature differences between hot and cold plates, needed for keeping the operating expense unchanged, are also described.

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.

Theoretical and experimental studies on the heavy water enrichment in concentric-tube Frazier-scheme thermal-diffusion columns under flow-rate fraction and plate spacing variations

An influence of plate spacing on heavy water enrichment in continuous concentric-tube Frazier-scheme thermal-diffusion columns at fixed operational expense has been investigated, both theoretically and experimentally, under flow-rate fraction variations. The analytical predictions are represented graphically and compared with those of a classical Frazier-scheme having the same column length and flow-rate fraction at both the top and the bottom of the column. Considerable improvement in the separation efficiency of the heavy water in thermal-diffusion columns of the same working dimensions is achieved by employing a Frazier-scheme with optimal plate spacing ( 2 w ) ∗ and flow-rate fraction variations. Experimental work was conducted to confirm the quantitative agreement with the theoretical prediction of the separation efficiency and the proposed separation theory. The effects of the plate spacing and flow-rate fraction on the separation efficiency of heavy water enhancement in the Frazier-scheme thermal-diffusion column with the column number, feed fraction concentration and feed mass flow rate have also been discussed.

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

ABSTRACT 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.