고효율 증류탑의 간이설계

장 태만, 김 영한

동아대학교 화학공학과

Approximate Design of a Fully Thermally Coupled Distillation Column

Tae Man Chang and Young Han Kim

Dept. of Chem. Eng., Dong-A University

INTRODUCTION

Though a fully thermally coupled distillation column shown in Figure 1, the Petlyuk column, has been introduced a half century ago, its commercial implementation has not been materialized until recently owing to the difficulty of its design and operation.

For the separation of ternary mixtures, the Petlyuk column requires less amount of energy compared with a conventional distillation system utilizing two distillation columns in various feed conditions. The energy saving in the Petlyuk column is from the elimination of the remixing of middle component in the first column and the reduction of mixing effect in the feed stage of a conventional distillation system.

Though the minimum reflux flow rates has been widely investigated, other design information, such as number of trays in a prefractionator and a main column and stages of feed, side product and connection between two columns, was rarely studied. A three-column model for the short-cut design of the Petlyuk column has been employed by Triantafyllou and Smith [1]. By separating the main column into two, the short-cut design equations for multicomponent distillation were applicable and the minimization of total cost including capital and energy costs was conducted to find an optimum design of the Petlyuk column. But, the linking the separated two columns requires an adjustment for the match of vapor flow rates of both columns to result in the recalculation of stage numbers. Also, the short-cut design leaves an accuracy problem.

In this study, a stage-to-stage design procedure to find the column size information, such as the number of trays of a prefractionator and a main column, feed and side product stages and connection locations between the prefractionator and main column in the Petlyuk column, is proposed and implemented to an example system of methanol-ethanol-water ternary mixture. The performance of the designed Petlyuk column is compared with a conventional two column system.

DESIGN VARIABLES

In a practical design of a distillation column, the number of trays is calculated using various design equations by setting a reflux flow rate at between 1.2 and 1.5 times the minimum reflux flow rate. Otherwise an optimization for the minimization of the total annual expense including capital cost and energy expense is conducted to find the optimum reflux flow rate.

In this study, the minimum number of trays of a prefractionator and a main column is computed first and all the tray related numbers are proportionally increased for a practical distillation column with varying reflux flow rate. Not only the total number of trays but also the stage locations of feed, side product and connection between a prefractionator and a main column are obtained from the stage-to-stage computation of the minimum number of trays in a total reflux condition.

Assuming that the feed stage has equal liquid composition to the composition of a saturated liquid feed and an ideal tray efficiency, one can calculate the liquid composition of  a stage above the feed stage with Eq. (1).

[eqn: {x}_{n+1,i}~ = { alpha }_{i } { x}_{n,i} ~ /~ SUM from { j } { alpha }_{j } { x}_{n,j }]                                 (1)

where the subscript n denotes the nth tray counted from the bottom and [eqn: alpha] is a relative volatility. The relative volatility is computed from experimental data. Similarly, the liquid composition of the trays below the feed stage is

[eqn: {x}_{n-1,i}~ =~ { x}_{n,i} ~ /~[ { alpha }_{i } ~ SUM from { j }~({ x}_{n,j }/ { alpha }_{j })]]                         (2)

This procedure is applied to a prefractionator of the Petlyuk system.

OPERATIONAL VARIABLES

There are four operational variables, reflux flow rate, vapor boilup rate, liquid split ratio and vapor split ratio. Among them, two are eliminated in a steady state operation. Namely, the vapor boilup rate is found from the reflux flow rate and overhead product rate.

Therefore, the only operational variable is the actual reflux flow rate. Since the tray number design of a column is found in the previous section, a steady state simulation is conducted  using material balance to find the reflux flow rate. A procedure [2] for the composition calculation of a multi-component distillation is modified for the Petlyuk column. In the simulation the reflux flow rate is varied until the composition of products meets the design specification listed in Table 1.

RESULTS AND DISCUSSION

The proposed design procedure is applied to a ternary system of methanol-ethanol-water mixture. As indicated in the section of design variables and the listed results in Table 1, the operational variable is found as 654 mol/h of vapor boilup rate and the liquid split ratio is 1:4.2. The variation of liquid composition is illustrated in Figure 2.

When the actual reflux flow rate is compared with the minimum reflux flow rate, it is found to be 1.5 times the minimum and it is in the range of common practice. Therefore, the tray number taken in this design, twice of the minimum number of trays, is quite reasonable. However, the actual liquid flow rate of a prefractionator is less than the predicted amount from the minimum reflux flow rate. It is because a large liquid flow deviates the liquid composition at feed tray from the feed composition and leads to a mismatch between the design and actual composition profile.

Unlike other design, the number (14) of trays of the prefractionator is different from the number (32) of trays between two connection stage of the main column. This prevents from the column construction in a divided wall structure, but since the equilibrium of a ternary mixture in quite different compositions does not guarantee an equal number of stages a separate prefractionator has to be built.

For the comparison with a conventional distillation system, a similar design procedure is applied to a direct sequence two column distillation system. In this case the liquid composition profile at the minimum number of trays does not include the feed composition of the second column, four extra stages are added to the first column for the compensation of feed composition mismatch. The liquid composition in an actual system is shown in Figure 3. The vapor boilup rate for the first column is 590 mol/h and 350 mol/h for the second column. Therefore, the conventional system requires 30.4 % more heat duty. Though the number of trays in the conventional system has 11 % less than the Petlyuk column, the cost of extra heat exchangers is much more than the extra tray cost.

A recent study [3] indicates that the thermodynamic efficiency of the Petlyuk column is lower than that of a direct sequence arrangement of conventional distillation system for the particular ternary system of this study. Though the reboiler temperature of the Petlyuk column is higher than that of the reboiler of the first column in the conventional direct sequence distillation by about 11□ in centigrade found from the boiling points of mixture, total energy cost of the Petlyuk column is less than the conventional system when it is counted that the low pressure steam costs 0.85% more per degree increased.

CONCLUSION

A stage-to-stage design procedure for a fully thermally coupled distillation system is proposed and implemented in an example ternary mixture. The procedure computes the minimum number of trays of a prefractionator and a main column using feed and side product compositions. The minimum reflux flow rate of the two columns is used to calculate liquid split ratio between two, and twice the minimum number of trays is applied in the simulation of liquid compositions for a given reflux flow rate to examine the compositions of products to meet a design specification.

The result of a design for the methanol-ethanol-water system indicates that the fully thermally coupled distillation column requires 30.4 % less heat duty than a conventional system. Even though the Petlyuk column needs higher temperature in a reboiler than the first reboiler of a conventional distillation system, the high-temperature compensated energy cost of the Petlyuk column is less than that of the conventional column. Also, the proposed design procedure is more accurate than the short-cut design with three column model.

ACKNOWLEDGMENT

Financial support from the Korea Science and Engineering Foundation through the Automation Research Center at POSTECH is gratefully acknowledged.

LITERATURE CITED

1. Triantafyllou C, Smith R. The design and optimisation of fully thermally coupled distillation columns. Trans. IChemE 1992; 70; Part A; 118-132.

2. Wang JC, Henke GE. Tridiagonal matrix for distillation. Hydrocarbon Process. 1966; 45(8); 155-163.

3. Agrawal R, Fidkowski ZT. Are thermally coupled distillation columns always thermodynamically more efficient for ternary distillation. Ind. Eng. Chem. Res. 1998; 37(8); 3444-3454.