Batch distillation operating time

The shortcut model is developed based on the assumption that batch distillation operation can be represented by a series of continuous distillation operation of short duration and employs modified Fenske-Underwood-Gilliland (FUG) shortcut model of continuous distillation (Diwekar and Madhavan, 1991a,b Sundaram and Evans, 1993a,b). Starting with an initial charge (B0, xB0) at time f=fo and for a small interval of time At = t, - t0, the batch distillation column conditions at to and ts is schematically shown in Figure 4.1 (Galindez and Fredenslund, 1988). 

Robinson (1970) considered an industrial 10-component batch distillation operation. The feed condition is shown in Table 5.3. The distillation column was currently producing the desired product using constant reflux ratio scheme. Table 5.4 summarises the results of the application of minimum time problem using simple model with and without column holdup. 

For single separation duty, Bernot et al. (1991) presented a method to estimate batch sizes, operating times, utility loads, costs, etc. for multicomponent batch distillation. The approach is similar to that of Diwekar et al. (1989) in the sense that a simple short cut technique is used to avoid integration of a full column model. Their simple column model assumes negligible holdup and equimolal overflow. The authors design and, for a predefined reflux or reboil ratio, minimise the total annual cost to produce a number of product fractions of specified purity from a multicomponent mixture. 

The processes discussed so far in this book are all treated as continuous operations. Although dynamics were considered, for the most part those processes were considered as steady state, where the properties or state variables at any given point in the process are considered time invariant. An important separation process that differs in this respect is batch distillation, a time-dependent process. 

Optimizing batch distillation operations can have a significant economic impact, especially when the separation of high-value chemicals is involved. The control variable for optimizing a batch distillation product is the reflux ratio policy, i.e., the variation of the reflux ratio with time. As... 

Relaxation methods are not competitive with the steady-state methods in the use of computer time, because of slow convergence. However, because they model the actual operation of the column, convergence should be achieved for all practical problems. The method has the potential of development for the study of the transient behaviour of column designs, and for the analysis and design of batch distillation columns. 

Other synonyms for steady state are time-invariant, static, or stationary. These terms refer to a process in which the values of the dependent variables remain constant with respect to time. Unsteady state processes are also called nonsteady state, transient, or dynamic and represent the situation when the process-dependent variables change with time. A typical example of an unsteady state process is the operation of a batch distillation column, which would exhibit a time-varying product composition. A transient model reduces to a steady state model when d/dt = 0. Most optimization problems treated in this book are based on steady state models. Optimization problems involving dynamic models usually pertain to optimal control or real-time optimization problems (see Chapter 16)... 

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 ... 

Hence the reflux ratio, the amount of distillate, and the bottoms composition can be related to the fractional distillation time. This is done in Example 13.4, which studies batch distillations at constant overhead composition and also finds the suitable constant reflux ratio that enables meeting required overhead and residue specifications. Although the variable reflux operation is slightly more difficult to control, this example shows that it is substantially more efficient thermally—the average reflux ratio is much lower—than the other type of operation. 

This solvent was used for synthesis during a campaign in a pilot plant It was known to be contaminated with an alkyl bromide. Thus, it was submitted to chemical and thermal analysis, which defined safe conditions for its recovery, that is, a maximum heating medium temperature of 130 °C for batch distillation under vacuum. These conditions were established to ensure the required quality and safe operation. A second campaign, which was initially planned, was delayed and in the mean time the solvent was stored in drums. 

There can be several alternative STNs for multicomponent mixtures depending on the number of main-cuts and off-cuts to be produced. The two basic modules of Figures 3.2 and 3.3 can be combined as many times as required to describe the entire operation. A few alternative STNs for ternary batch distillation are given in Figures 3.5-3.7 as the combination of these two basic modules. 

The performance criteria of a batch distillation column can be measured in terms of maximum profit, maximum product or minimum time (Mujtaba, 1999). In distillation, whether batch, continuous or extractive, purity of the main products must be specified as it is driven by the customer demand and product prices. The amount of product and the operation time can be dictated by economics (maximum profit) or one of them can be fixed and the other is obtained (minimum time with fixed amount of product or maximum distillate with fixed operation time). The calculation of each of these will require formulation and solution of optimisation problems. A brief description of these optimisation problems is presented below. Further details will be provided in Chapter 5. 

Mujtaba and Macchietto (1988) used the measure, q, the degree of difficulty of separation (section 3.5.1) to correlate the extent of benefit of production and recycling of off-cuts for binary mixtures. It is reported that for some separations more than 70% batch time savings were possible when compared to no off-cut production and no recycle cases. Using the measure, q, the authors were also able to explain whether and when an initial total reflux operation was required in batch distillation. Further details are presented in Chapter 8. 

A liquid binary mixture with B0 = 10 kmol (Hc) and xB0 = <0.6, 0.4> (xj) molefraction is subject to inverted batch distillation shown in Figure 4.12. The relative volatility of the mixture over the operating temperature range is assumed constant with a value of (a-) 2. The number of plates is, N= 10. The vapour boilup rate is, V = 10.0 kmol/hr. The total plate holdup is 0.3 kmol and the reboiler holdup is 0.1 kmol. The total batch time of operation is 4 hr with two time intervals. The first interval is of duration 1 hr and the column is operated with a reboil ratio of 0.8. The second interval is of duration 3 hrs when the column is operated with a reboil ratio of 0.9. The column operation is simulated with the type III model (section 4.3.2.1). 

The optimal control of a process can be defined as a control sequence in time, which when applied to the process over a specified control interval, will cause it to operate in some optimal manner. The criterion for optimality is defined in terms of an objective function and constraints and the process is characterised by a dynamic model. The optimality criterion in batch distillation may have a number of forms, maximising a profit function, maximising the amount of product, minimising the batch time, etc. subject to any constraints on the system. The most common constraints in batch distillation are on the amount and on the purity of the product at the end of the process or at some intermediate point in time. The most common control variable of the process is the reflux ratio for a conventional column and reboil ratio for an inverted column and both for an MVC column. 

The minimum time problem is also known as the time optimal control problem. Coward (1967), Hansen and Jorgensen (1986), Robinson (1970), Mayur et al. (1970), Mayur and Jackson (1971), Mujtaba (1989) and Mujtaba and Macchietto (1992, 1993, 1996, 1998) all minimised the batch time to yield a given amount and composition of distillate using conventional batch distillation columns. The time optimal operation is often desirable when the amount of product and its purity are specified a priori and a reduction in batch time can produce either savings in the operating costs of the column itself or permit improved scheduling of other batch operations elsewhere in a process. Mathematically the problem can be written as ... 

Table 4.6 in Chapter 4 presents the simulation results for a quaternary batch distillation. The amount of product and the composition of key component of each cut were used by Mujtaba (1989) to formulate and solve a minimum time problem for each cut. Optimal reflux ratio in each operation step is obtained independently of other step with the final state of each step being the initial state of the next step. 

In batch distillation, as the overhead composition varies during operation, a number of main-cuts and off-cuts are made at the end of various distillation tasks or periods (see Chapter 3). Purities of the main-cuts are usually determined by the market or downstream process requirements but the amounts recovered must be selected based on the economic trade off between longer distillation times (hence productivity), reflux ratio levels (hence energy costs), product values, etc. Increasing the recovery of a particular species in a particular cut may have strong effects on the recovery of other species in subsequent cuts or, in fact, on the ability to achieve at all the required purity specifications in subsequent cuts. The profitable operation of such processes therefore requires consideration of the whole (multiperiod) operation. 

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. 

Note that for a fixed operation time, t in Equation 9.1, the profit will increase with the increase in the distillate amount and a maximum profit optimisation problem will translate into a maximum distillate optimisation problem (Mujtaba and Macchietto, 1993 Diwekar, 1992). However, for any reaction scheme (some presented in Table 9.1) where one of the reaction products is the lightest in the mixture (and therefore suitable for distillation) the maximum conversion of the limiting reactant will always produce the highest achievable amount of distillate for a given purity and vice versa. This is true for reversible or irreversible reaction scheme and is already explained in the introduction section. Note for batch reactive distillation the maximum conversion problem and the maximum distillate problem can be interchangeably used in the maximum profit problem for fixed batch time. For non-reactive distillation system, of course, the maximum distillate problem has to be solved. 

As presented in the earlier chapters, the operating policy for a batch distillation column can be determined in terms of reflux ratio, product recoveries and vapour boilup rate as a function of time (open-loop control). Under nominal conditions, the optimal operating policy may be specified equivalently in terms of a set-point trajectory for controllers manipulating these inputs. In the presence of uncertainty, these specifications for the optimal operating policy are no longer equivalent and it is important to evaluate and compare their performance. 

The initial state of Task 2 is the final state of Task 1. Therefore, Hyt of Task 1 becomes the initial feed amount B, for Task 2 (Figure 10.6). The distillate compositions for all cases of Task 2 are close to that of the feed mixture and therefore the distillate can be stored, recycled and reprocessed in subsequent batches. In this Task, in fact, the distillate could be obtained at purity higher than 0.5 molefraction in acetone. But re-mixing of this Task with a fresh feed mixture in the next batch would not be a thermodynamically sensible option (Mujtaba, 1989 Quintero-Marmol and Luyben, 1990 Mujtaba and Macchietto, 1992) as explained in Chapter 8. The recovery of Acetone (can be calculated using Equation 10.11) decreases with increasing B0 in Task 1 (Table 10.10). Therefore the amount of distillate in Task 2 increases with B0 for a given recovery (98%) of Acetone in Task 2 and so does the operation time. 

Also Mujtaba (1997) considered the separation of binary mixtures into one distillate product of specified purity. The objectives were to find out whether it was possible to replace conventional dynamic operation of batch columns by steady state operation using continuous columns for a comparable recovery, energy consumption, operation time, productivity, etc. and to obtain optimal operating policy in terms of reflux ratio. The following strategy was considered to compare the performances of the two types of operations ... 

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