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Batch Processing 4 Batch Distillation CONTENTS 4.1 Early Theoretical Analysis ........................................... 43 4.1.1 Simple Distillation ............................................. 45 4.1.2Copyrighted Operating Modes ............................................... 46 4.2 Hierarchy of Models .................................................. 53 4.2.1 Rigorous Model ................................................ 53 4.2.2 Low Holdup Semirigorous Model .............................. 53 4.3 Shortcut Model ........................................................ 55 4.4 Optimization and Optimal Control ................................... 58 4.5 Complex Systems ...................................................... 59 4.5.1 Azeotropic Distillation ......................................... 60 4.5.2 Reactive DistillationMaterial........................................... 61 4.6 Computer Aided Design Software ..................................... 62 4.7 Summary .............................................................. 63 Notations .............................................................. 63 - Batch distillation1 is the oldest separation processTaylor and the most widely used unit operation in pharmaceutical and specialty chemical industries. The most outstanding feature of batch distillation is its flexibility. This flexibility allows one to deal with uncertainties in feed stock or product specification. In the distillation process, it is assumed that the vapor& formed within a short pe- riod is in thermodynamic equilibrium with the liquid. Hence,Francis the vapor composition y is related to the liquid composition x by an equilibrium relation of the functional form y = f(x). The exact relationship for a particular mixture may be obtained from a thermodynamic analysis and is also dependent upon temperature and pres- sure. Figure 4.1 shows an example equilibrium curve for a system consisting of CS2 and CCl4 at 1 atmosphere pressure. Simple distillation is the simplest form of batch distillation. In this type of dis- tillation, a still is initially filled with a feed mixture, which evaporates after heating and leaves the still in the vapor form. This vapor which is richer in the more volatile component is collected in the condenser at the top. This simple distillation is often referred to as Rayleigh distillation because of Rayleigh’s pioneering theoretical work [35]. The concept of reflux and the use of accessories such as plates and packing ma- terials to increase the mass transfer converts this simple still into a batch distillation column as shown in Figure 4.2a. Because this batch column essentially performs the rectifying operation, it is often called a batch rectifier. The basic difference between batch distillation (rectifier) and continuous distilla- 1This chapter is based on the book by [7]. 41 42 Batch Processes: Modeling and Design 1 1 0.8 0.8 0.6 0.6 y 0.4 0.4 0.2 0.2 0 0 0 0.2 0.4 0.6 0.8 1 Copyrighted x FIGURE 4.1 Equilibrium curve for the CS2 and CCl4 mixture at 1 atmosphere pressure tion is that in continuous distillation (Figure 4.2b) the feed is continuously entering the column, while in batch distillationMaterial the feed is charged into the reboiler at the beginning of the operation. This feed is heated to form vapor. This vapor is passed through packing or plates where it meets the liquid coming from top (refluxed back) from the condenser at the top. Mass transfer takes place in contact and one gets a distillate which is richer in the more volatile component. The reboiler in batch dis- tillation gets depleted over time. The process- has an unsteady-state nature. Reflux ratio, which is a ratio of liquid reflux to distillateTaylor is an important operating parame- ter on which operating condition depends. If reflux ratio is kept constant throughout the operation this results in variable product composition. On the other hand, in order to keep the key composition constant, reflux ratio needs to be varied. There is a third policy of operation known as the optimal reflux& policy that is neither the constant reflux policy nor the variable reflux policy. Instead,Francis this operating policy exploits the difference between the two operating modes. Thus, the optimal reflux policy is essentially a trade-off between the two operating modes, and is based on the ability of the process to yield the most profitable operation. Thus, there are three operating conditions for batch distillation. Constant reflux and variable product composition, • Variable reflux and constant product composition of the key component, and • Optimal reflux and optimal product composition. • The flexible and transient nature of batch distillation allows to configure the column in a number of different ways, some of which are shown in Figure 4.3 [36]. The column in Figure 4.3a, as explained, is a conventional batch distillation column with the reboiler at the bottom and the condenser at the top. A single column can be used to separate several products using the multi-fraction operation of batch distillation presented in Figure 4.3b. Some cuts may be desired and others may be intermediate products. These intermediate fractions can be recycled to maximize profits and/or minimize waste generation. Figure 4.3c shows a periodic operation Batch Distillation 43 (a) condenser (b) condenser distillate distillate reflux reflux section rectifying feed rectifying section reboil section stripping stripping Copyrighted bottom product reboiler reboiler FIGURE 4.2 Types of distillation processes:Material (a) batch distillation and (b) continuous dis- tillation. in which each charge consists of a fresh feed- stock mixed with the recycled off- specification material from the previous charge.Taylor Figure 4.3d represents a stripping column for separating a heavy component as the bottom product where the liquid feed is initially charged into the top. In 1994, Davidyan et al. [37] presented a batch distillation column that has both stripping and rectifying& sections embedded in it (Figure 4.3e). This column is called the middle vessel column. Although this column has not been investigated completely, recent studies demonstratedFrancis that it provides added flexibility for the batch distillation operation. Recently [38] described a new column configuration called a multivessel column (Figure 4.3f) and showed that the column can obtain purer products at the end of a total reflux operation. These emerging column designs play an important role in separation of complex systems such as azeotropic, extractive, and reactive batch distillation systems. Although all these column configurations are important, we will focus on the conventional batch column in this chapter. 4.1 Early Theoretical Analysis This section presents early theoretical analysis of simple distillation, which was first analyzed by [35]. 44 Batch Processes: Modeling and Design 2 3 2 3 Copyrighted 1 1 (a) (b) (c) Material - Taylor & Francis (d) (e) (f) FIGURE 4.3 Various configurations of batch distillation column. Batch Distillation 45 4.1.1 Simple Distillation The analysis of simple distillation presented by Rayleigh in 1902 marks the earliest theoretical work on batch distillation. Simple distillation, also called Rayleigh distil- lation or differential distillation, is the most elementary example of batch distillation. In this distillation system, the vapor is removed from the still during each time in- terval and is condensed in the condenser. The vapor is richer in the more volatile component than the liquid remaining in the still. Over time, the liquid remaining in the still begins to experience a decline in the concentration of the more volatile component, while the distillate collected in the condenser becomes enriched in the more volatile component. No reflux is returned to the still, and no plates or packing materials are provided inside the column. Therefore, various operating policies are not applicable to this distillation system. The earlyCopyrighted analysis of this process for a binary system, proposed by Rayleigh, is given below. Let F be the initial binary feed to the still (moles), and xF be the mole fraction of the more volatile component A in the feed. Let B be the amount of compounds remaining in the still, xB the mole fraction of component A in the still, and xD the mole fraction of component A in the vapor phase. The differential material balance for component A can then be written as: xD dB = d(B xB ) = B dxB + xB dB, (4.1) Material giving: B dB xB dx = B , (4.2) B xD xB ZF ZxF − or: B xB dx ln = - B . (4.3) F xTaylorD xB ZxF − In this simple distillation process, it is assumed that the vapor formed within a short period is in thermodynamic equilibrium with the liquid. Hence, the vapor composition xD is related to the liquid composition xB&by an equilibrium relation of the form xD = f(xB ). The exact relationship for a particular mixture may be obtained from a thermodynamic analysis depending on temperatureFrancis and pressure. For a system following the ideal behavior given by Raoult’s law, the equilibrium relationship between the vapor composition y (or xD) and liquid composition x (or xB ) of the more volatile component in a binary mixture can be approximated using the concept of constant relative volatility (α), and is given by: αx y = (4.4) ()α 1 x + 1 − Substitution of the above equation in Equation 4.3 results in: B 1 xB (1 xF ) 1 xF ln = ln − + ln − (4.5) F α 1 x1F ( xB ) 1 xB − − − Although the analysis of simple distillation historically represents the theoret- ical start of batch distillation
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