고효율 증류탑의 설계와 운전

함 태원, 김 영한

동아대학교 화학공학과

Design and Operation of Fully Thermally Coupled Distillation Columns

Tae Won Ham and Young Han Kim

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

INTRODUCTION

Though the design of operational information, such as the minimum reflux flow rate, in a fully thermally coupled distillation has widely been investigated, the structural design of the distillation column was rarely examined before. Since the fully thermally coupled distillation column, also known as the Petlyuk column has interlinking between a prefractionator and a main column, usual multi-component design procedures are not applicable to it without the information of the interlinking streams.

A design procedure to utilize the three column model was introduced by Triantafyllou and Smith [1]. Separating the main column of the fully thermally coupled distillation system into two columns makes the system three separate continuous distillation columns to which the short-cut design equations for the multi-component distillation design can be applied. Though the design procedure gives easily the tray numbers of the three separate columns, matching the compositions of interlinking streams requires an adjustment and iterative calculation.

On the other hand, using only the operation condition without the structural information in the design leads to tedious iterative simulation in order to find a proper structure of the column. This problem also applies to the commercial design program, e.g. HYSYS. Often times, an inadequate structure does not give a converged solution in the process of the simulation.

Wolff and Skogestad [2] examined possible control schemes of the column and suggested that controlling the tray temperature close to the most critical composition measurement gives better performance than the direct composition control.

In this study, a structural design method for fully thermally coupled distillation columns is explained with three example systems having three different feed compositions. The effect of the mixing in feed tray and the remixing of middle component in a prefractionator is investigated using the liquid composition profiles. In addition, an operation scheme is proposed for the operation of the column and possible solutions for the problems associated with the column operation.

STRUCTURAL DESIGN

Since there are interlinking streams between a prefractionator and a main column, the conventional multi-component column design procedure is not directly implemented. Using the three column model [1], a short-cut design procedure for the conventional multi-component distillation can be utilized. But it is required to match the compositions entering and leaving streams of the bottom tray of upper section and the top tray of lower section of two separate columns of a main column, which leads to tedious iterative adjustment. Also, an ideal equilibrium is assumed, and the design outcome is not accurate enough to implement as the initial condition in a rigorous simulation.

Unlike a binary system, in a ternary distillation there are many distillation lines to connect the same composition of overhead and bottom products depending upon vapor boilup rate, and the composition in the middle of the lines is quite different from one to another. Therefore the design of a ternary distillation column is easy when a composition in the middle of the distillation line is given. In a main column of a fully thermally coupled distillation, the composition of side product has to be same to the composition of the stage of the side product. As a result, the composition profile of the column with total reflux is readily obtained using the stage-to-stage computation. Starting at the stage of side product with the composition of the product, the liquid composition at one stage above the product stage is computed using an equilibrium relation with total reflux and the assumption of ideal tray efficiency. This procedure continues until the tray composition meets the specification of overhead product. The trays below the side product stage are found in the same way. Note that the distillation line is for a packed column while tie lines are for a tray column. The equal procedure is applied to a prefractionator with the assumption that the feed stage has the same composition as feed. Now the interlinking stages between the main column and prefractionator are yielded by matching their composition profiles. The location of feed and side product stages is also obtained from the previous tray calculation.

The resulted design gives the minimum numbers of trays, since the computation is conducted at total reflux. In many field applications, twice the minimum number is employed as an actual tray number. The actual locations of feed and side product stages and interlinking stages are also determined by taking twice the stage numbers of the minimum design.

EXAMPLE SYSTEMS

The proposed design procedure of this study does not utilize short-cut design equations, so a generalized design outcome of ideal ternary systems having an equilibrium relation with relative volatility is not delivered here. Instead three real systems having non-ideal equilibrium relation are examined for three different feed compositions. The systems are ternary systems of s-butanol-i-butanol-n-butanol(I), cyclohexane-heptane-toluene(II) and methanol-ethanol-water(III). Three different feed materials are an equi-molar mixture(F1) and two mixtures of mole fractions of 0.75-0.125-0.125(F2) and 0.125-0.75-0.125(F3).

The design specification of products in systems I and II is set to 0.9 of mole fraction of the middle component in side product, 0.95 of the lightest component in overhead product and 0.95 of the heaviest component in bottom product. Since the system III has azeotrope near the side product composition of systems I and II, the specification of side product is adjusted to 0.8 of mole fraction of the middle component in order to evade the azeotrope composition and 0.9 for overhead and bottom products.

DESIGN RESULTS

The design outcome of the example systems using the proposed procedures is listed in Table 1. The liquid composition in trays for the system I with equi-molar feed is illustrated in Figure 1. The numbers in the figure are tray numbers, and the mid-section means the trays between interlinking stages of a main column. The circles are of a main column and the plus symbols are of a prefractionator. Note that the distance between the point F and the closest point, feed tray composition, denotes mixing at the feed tray and has the most significant effect on the thermodynamic efficiency of the system. In addition, the decrease of the concentration of intermediate component in the lower section of the prefractionator demonstrated by the curvature between the feed tray and lower interlinking tray indicates the remixing of the component and reduces the efficiency.

COLUMN OPERATION

The most likely controlled variables in the operation of a fully thermally coupled distillation column are the compositions of overhead, bottom and side products. Especially, the concentration of the lightest component in the overhead product, the heaviest component in the bottom product and the intermediate component in the side product are the most convenient set of the controlled variables.

A complete search for the possible 3 x 3 control schemes is conducted by Mizsey et al. [3] by comparing various controllability indices for multivariable systems. A regulatory control with changes of feed flow rate and feed composition is applied to examine the control performances of the possible control schemes, and it is found that the nput set of L-S-B gives the best control.

A D-V-S structure is implemented here since the structure gives positive elements of the RGA and positive Niederlinski index. The diagonal elements are 1.01, 1.09 and 0.87 and the NI is 0.90.

The conventional PID control can be implemented in the investigation of the performance of the proposed control scheme, but an advanced control, the quadratic dynamic matrix control is utilized in order to obtain improved performance. It is widely known that the control of the Petlyuk column has been one of major obstacles in its application.

The set-point changes of three components are imposed separately and the response is shown in Figure 2. The control performance of the set-point tracking in all three products is satisfactory, since no significant deviation from the set point is developed though the response is slow. A regulatory performance is examined by changing feed flow rate and feed composition as given in Figure 3. The effect of a two percent change of feed flow rate is not significant, but the impact of the change of feed composition is much greater. Since the lightest component has the largest change in composition, its deviation is the highest among three components.

CONCLUSION

A structural design procedure for fully thermally coupled distillation columns is proposed and exercised to three different systems having different compositions of feed. Also, other design considerations, such as mixing in feed tray, dividing wall structure and interlinking streams, are discussed.

For the column operation, a 3 x 3 control scheme is proposed and its performance of set-point tracking and regulation is investigated to result in satisfactory outcome.

ACKNOWLEDGMENT

Financial support from the Korea Science and Engineering Foundation through the CIIPMS, Dong-A University 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. Wolff, E. A., Skogestad, S. Operation of Integrated Three-Product (Petlyuk) Distillation Columns. Ind. Eng. Chem. Res. 1995; 34; 2094-2103.

3. Mizsey, P. Hau, N. T., Benko, N., Kalmar, I, Fonyo, Z. Process control for energy integrated distillation schemes. Comp. chem. Engng.; 1998; 22; S427-S434.