Binary batch distillation column

Consider the binary batch distillation column, represented in Fig. 3.58, and based on that of Luyben (1973, 1990). The still contains Mb moles with liquid mole fraction composition xg. The liquid holdup on each plate n of the column is M with liquid composition x and a corresponding vapour phase composition y,. The liquid flow from plate to plate varies along the column with consequent variations in M . Overhead vapours are condensed in a total condenser and the condensate collected in a reflux drum with a liquid holdup volume Mg and liquid composition xq. From here part of the condensate is returned to the top plate of the column as reflux at the rate Lq and composition xq. Product is removed from the reflux drum at a composition xd and rate D which is controlled by a simple proportional controller acting on the reflux drum level and is proportional to Md-... 

CONSTANT HOLDUP BINARY BATCH DISTILLATION COLUMN EQUILIBRIUM PLATE BEHAVIOUR... 

Bubble Point Calculation Binary Batch Distillation Column... 

Process Modes for a Bioreactor 538 Binary Batch Distillation Column 490 Bubble Point Calculation for a Batch Distillation Column 504... 

Develop the state model for an ideal binary batch distillation column with N ideal plates (Figure PII. 12). At t = 0, the composition of the initial mixture is cA and cB (molar fractions), and its total mass is M (moles). 

Operation of a batch distillation is an unsteady state process whose mathematical formulation is in terms of differential equations since the compositions in the still and of the holdups on individual trays change with time. This problem and methods of solution are treated at length in the literature, for instance, by Holland and Liapis (Computer Methods for Solving Dynamic Separation Problems, 1983, pp. 177-213). In the present section, a simplified analysis will be made of batch distillation of binary mixtures in columns with negligible holdup on the trays. Two principal modes of operating batch distillation columns may be employed ... 

An extensive literature survey indicates that the role of column holdup on the performance of batch distillation has been the subject of some controversy until recently. The following paragraphs outline briefly the investigations carried out on column holdup since 1950. Most of the investigations were restricted to conventional batch distillation columns and binary mixtures. The readers are directed to the original work to develop further understanding of the topic. 

Domenech and Enjalbert (1974) carried out a series of experimental tests in a laboratory batch distillation column. A binary mixture of Cyclohexane and Toluene was considered for the purpose. The experimental equipment used was a perforated plate column, with 4 trays and a 60 litre reboiler heated with a heat transfer coefficient of 3 kw. The experimental results obtained by Domenech and Enjalbert together with column input data are presented in Table 4.5. 

Robinson (1969) considered the following example problem. A binary feed mixture with an initial amount of charge, B0 = 100 kmol and composition xB0 = <0.50, 0.50> molefraction, having constant relative volatility of 2.0 was to be processed in a batch distillation column with 8 theoretical stages. The aim was to produce 40 kmol of distillate product (D) with composition (xd) of 0.5 molefraction for component 1 in minimum time (tF) using optimal reflux ratio (/ ). 

Logsdon and Biegler (1993) considered a binary separation of cyclohexane-toluene mixture in a conventional batch distillation column. Maximum distillate problem was considered to maximise the amount of distillate with cyclohexane purity of 0.998 molefraction. The input data for the problem is given in Table 5.7. 

Single Separation Duty refers to the situation, where a single mixture (binary or multicomponent) is separated into several products using only one batch distillation column. Figures 7.1 and 7.2 show the operation sequences in STN form considered by Al-Tuwaim and Luyben (1991) for binary and ternary mixtures. 

Two binary mixtures are being processed in a batch distillation column with 15 plates and vapour boilup rate of 250 moles/hr following the operation sequence given in Figure 7.7. The amount of distillate, batch time and profit of the operation are shown in Table 7.6 (base case). The optimal reflux ratio profiles are shown in Figure 7.8. It is desired to simultaneously optimise the design (number of plates) and operation (reflux ratio and batch time) for this multiple separation duties. The column operates with the same boil up rate as the base case and the sales values of different products are given in Table 7.6. 

Sprensen and Skogestad (1996) compared the operation of regular (fig. la) and inverted (fig. lb) batch distillation columns for the separation of binary mixtures. In a later work Sprensen and Prenzler (1997) investigated the cyclic, or closed operation for the separation of binary mixtures. Warter et al. (2002) presented simulations and experimental results for the separation of ternary mixtures in the middle vessel column (fig. Ic). The cyclic operation was applied also in this case. Multicomponent mixtures can be separated in the multi-vessel distillation column. This might also be operated in closed operation (Wittgens et al. 1996). 

The column shown in figure Id can be visualised as an inverted batch distillation column placed on top of a regular batch column, the two being connected at the withdrawal stage. Hence, feasibility studies for the regular and inverted batch distillation columns may be applied to the novel process provided that the concentration of the withdrawal tray lies on the column s profile. Therefore, it is possible to obtain pure intermediate-boiling product b from an infinite column operated at infinite reflux ratios, only if the distillate and sump vessels contain the binary mixtures a-b (light-intermediate boilers) and b-c (intermediate-heavy boilers), respectively. 

The column liquid composition profile at the end of each operating step can be seen in Figure 13.13. Notice that there is no water in the upper rectifying section at the end of Step 1 (time = 0.96 h). This is due to the continuous feeding of the entrainer into the column to push the water down the column, and it is present only in the lower extractive section of the column. At the end of Step 2 (time = 3.19 h), the column composition profile has moved away from the IPA comer toward the water comer. The top liquid composition has moved close to the water comer at the end of Step 3 (time = 4.68 h). At this time, there is almost no IPA inside the column, so the separation is just a regular binary batch distillation. At the end of Step 4 (time = 7.92 h), the water purity in the P2 product tank can no longer be... 

Batch distillation from a pot will not provide a good separation unless the relative volatility is very high. In most cases, a rectifying column with reflux is added to the pot, as shown in Figure 14.7. The operation of a batch distillation can be analyzed for binary systems at a given instant in... 

During the batch distillation of a binary mixture in a packed column the product contained 0.60 mole fraction of the more volatile component when the concentration in the still was 0.40 mole fraction. If the reflux ratio used was 20 1, and the vapour composition y is related to the liquor composition x by the equation y = 1.035x over the range of... 

The nonlinear nature of these mixed-integer optimization problems may arise from (i) nonlinear relations in the integer domain exclusively (e.g., products of binary variables in the quadratic assignment model), (ii) nonlinear relations in the continuous domain only (e.g., complex nonlinear input-output model in a distillation column or reactor unit), (iii) nonlinear relations in the joint integer-continuous domain (e.g., products of continuous and binary variables in the schedul-ing/planning of batch processes, and retrofit of heat recovery systems). In this chapter, we will focus on nonlinearities due to relations (ii) and (iii). An excellent book that studies mixed-integer linear optimization, and nonlinear integer relationships in combinatorial optimization is the one by Nemhauser and Wolsey (1988). 

Converse and Huber (1965), Robinson (1970), Mayur and Jackson (1971), Luyben (1988) and Mujtaba (1997) used this model for simulation and optimisation of conventional batch distillation. Domenech and Enjalbert (1981) used similar model in their simulation study with the exception that they used temperature dependent phase equilibria instead of constant relative volatility. Christiansen et al. (1995) used this model (excluding column holdup) to study parametric sensitivity of ideal binary columns. 

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