458 石 油 学 会 誌 Sekiyu Gakkaishi, 36, (6), 458-466 (1993) [Regular Paper] Minimum Reflux Calculations for Heterogeneous Azeotropic Distillation Processes Fang-Zhi LIU, Hideki MORI*, Setsuro HIRAOKA, and Ikuho YAMADA Dept. of Applied Chemistry, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466 (Received December 16, 1992) An algorithm is presented for solving operating type minimum reflux problems of heterogeneous azeotropic distillation processes, based on the concept of hypothetical pinch plate proposed by Yamada et al. The process discussed here is restricted to column sequence in which the entrainer recycle stream returns to the azeotropic column as a feed stream and which is favourable over the other sequences in respect to energy consumption. A design technique is also proposed to simultaneously calculate the inner and outer minimum reflux ratios of azeotropic column, the minimum reflux ratio of recovery column, and the optimal recycle flow rate. The algorithm and the design technique are illustrated by numerical examples of ethanol dehydration with benzene. 1. Introduction the pinch point in the stripping section; (2) one pure component is obtained in bottoms stream; The calculation of minimum ref lux ratios is an and (3) the mole fraction ratio of light and heavy important and extremely difficult problem in key components at the pinch point in the stripping calculations and design of distillations. Any section is equal to that in feed composition. Since excess ref lux will not only lead to an increased this method is simple and easy to use, and no other energy consumption but also larger column method is available, the graphical analysis method diameters and heat exchanger areas. The mini- has been used to estimate the minimum reflux in mum ref lux provides us a valuable piece of the design of azeotropic columns, though its information on the actual energy consumption of accuracy is sometimes not satisfactory. The columns. Columns can also be designed quickly boundary-value procedure5) is also based on the and with confidence when minimum reflux rates constant molar overflow assumption. This are known for given specifications. assumption is obviously incorrect for heteroge- Some important methods or procedures have neous azeotropic distillation systems. Further- been published in the area of minimum reflux more, the boundary-value procedure is based on calculations. They can be classified into two dew point calculations in rectifying section, but groups: shortcut methods and rigorous methods. dew point calculations often fail on top stages of a The well-known shortcut methods are the heterogeneous azeotropic column, when the vapor Underwood method or its relatives1)-3). Neverthe- compositions are close to the heterogeneous less, since these methods are based on the as- azeotrope. sumptions of constant relative volatility and The rigorous methods are based on the constant molar overflow, they are not suitable to characteristic of pinch points and the physical distillations of strongly nonideal mixtures. For connection between pinch points and column end determining the minimum reflux of heteroge- compositions. Typical methods of rigorous neous azeotropic columns, Yorizane et al.4) methods are those reported by McDonough and proposed a graphical analysis method and Pham et Holland6), Chien7), and Yamada and coworker8)-10). al.5) proposed a boundary-value procedure. The Except for Yamada's method, however, these graphical analysis method4) is limited to ternary methods were only tested on ideal mixtures. To systems and based on the assumptions of (1) our knowledge, no rigorous method has been constant molar overflow between the top stage and reported to calculate the minimum ref lux of heterogeneous azeotropic columns or processes, * To whom correspondence should be addressed. and because the assumption of constant molar 石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 459 overflow largely deviates from practice, a rigorous rate as stated by Doherty et al.11),12), they have method of minimum reflux calculation is neces- almost been replaced by the configuration shown sary for heterogeneous azeotropic distillation in Fig, 1c in practice. Our discussion here, columns. therefore, is restricted to the process shown in Fig. The literature contains many options of con- 1c. figurations for heterogeneous azeotropic distilla- In this work, we proposed a procedure for tion processes. These configurations generally solving the minimum reflux problem of hetero- consist of either two or three columns with various geneous azeotropic distillation systems based on options for handling the entrainer recycle stream. the hypothetical pinch plate model proposed by Several typical configurations are given in Figs. Yamada8). Furthermore, a design technique is 1a-1c. The earlierindustrial processes used to developed to determine simultaneously the inner employ the configurationsshown in Figs. 1a and and outer minimum reflux ratios of azeotropic 1b, i.e.the entrainerrecovery column only consists columns, the minimum reflux ratio of entrainer stripping section and the entrainer recycle stream recovery columns, and the optimal flow rate of the is returned directly to the decanter. Since these recycle stream based on the energy consumption kinds of configurations require a large recycle flow consideration for a given separation requirement. 2. Modeling 2.1. Inner Reflux and Outer Reflux To design the distillation process shown in Fig. 1c, determination of three reflux ratios: inner reflux ratio Ri, outer reflux ratio Ro, and reflux ratio of recovery column R', as defined below are required. (1) Fig. 1a A Two-column Process with a Recycle Stream to the Decanter (2) (3) The relationship between Ri, Ro, and an overall reflux ratio of the azeotropic column R is as follows. (4) The feed rate of the recovery column, D, is Fig. 1b A Three-column Process usually much smaller than the flow rates of aqueous phase in the decanter if all the overhead vapor V1 is condensed and subcooled, and then put into the decanter. Furthermore, the decanter temperature is much lower than the saturated temperature of the reflux liquid. Therefore, the introduction of inner reflux LiR can not only reduce energy consumption but also improve the sepa- ration of the azeotropic column. 2.2. Pinch Points and Decomposition Strategy When a column is operated at minimum reflux, the number of stages in the rectifying and stripping sections should be infinite to satisfy separation Fig. 1c A Two-column Process with a Recycle Stream requirements. Under this condition, there will be to the Azeotropic Column two pinch points, one is between the feed stage and 石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 460 the top stage and one between the feed stage and the 2.3. Decanter (#1) reboiler, no matter whether or not all components The isothermal liquid-liquid equilibrium in are distributed to the top and bottom products. the decanter can be described by the following This is also true for the columns of the azeotropic equations, supposing complete separation of two distillation process under consideration. liquid phases in it. Since a recycle stream is included in the azeotropic distillation process, the whole process L0=LI+LII (5) shown in Fig. 1c has to be modeled in order to solve rigorously the minimum reflux problem of the L0y1i=LIxIi+LIIχIIi (6) process. To model the process, it is decomposed into two xIi=KLixIIi (7) columns by breaking up the recycle stream and each column is further decomposed into several (8) sections as shown in Figs. 2a and 2b. In the following discussion, the theoretical stage and the 2.4. Top Section of Azeotropic Column (#2) adiabatic column assumptions are used. At the hypothetical pinch plate, the downcom- ing liquid and the upflowing vapor streams are in equilibrium. For the upper hypothetical pinch plate (HI) of the azeotropic column, the following equation is obtained. yHI,i=KHI,iχHI,i (9) (10) Besides, the top section of the azeotropic column as shown in Fig. 2a can be described by the following balance equations. VHI+LoR=LHI+L0 (11) VHIyHI,i+LoRχoRi=LHIxHI,i+L0y1i (12) VHIHHI+LoRhoR=LHIhHI+L0h0+Ｑc (13) Fig. 2a An Azeotropic Column at Minimum Reflux 2.5. Bottom Section of Azeotropic Column (#3) Similar to the top section, the section below the lower hypothetical pinch plate (HII) can be described by the following equations. (14) (15) (16) (17) (18) 2.6. Middle Section of Azeotropic Column (#4) As is proposed by Yamada et al.9), the number of stages between the two hypothetical pinch plates is assigned to an arbitrary finite number which can satisfy Eqs. (9) and (14). For this section, input Fig. 2b A Recovery Column at Minimum Reflux streams are Ft, VHIIand LHI and output streams are 石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 461 VHI and LHII. It can be dealt with as a column Since the reflux to the azeotropic column without condenser and reboiler. Any one stage of consists of inner reflux and outer reflux, one this section can be described by the MESH more degree of freedom remains. Here, β is (Material balance, Equilibrium, Summation of specified and it is defined as follows. mole fraction, and Heat balance) equations. 2.7. Entrainer Recovery Column φ=LI/LII (29) The recovery column is decomposed into three sections as shown in Fig. 2b. Similar to the Romin=βφ azeotropic column, the middle section between the β≧1} (30) two hypothetical pinch plates is also dealt with as a column with a finite number of stages. The top Where φ is the relative proportion of the flow rates and bottom sections are described by the following of two liquid phases in the decanter. equations. Since β≧1, the distillate D consists of only the For the top section (#5): phase II. Thus, y'HI,i=K'HI,ix'HI,i (19) xDi=xIIi (31) L0=(1+βφ)D=(1+βφ)(B'+D') (32) (20) V'HI=L'HI+D' (21) (33) V'HIy'HI,i=L'HIx',HI,i+D'x'Di (22) 3.2.