Separative duty

Many of the above factors that affect column operation are due to vapor flow conditions being either excessive or too low. Vapor flow velocity is dependent on column diameter. Weeping determines the minimum vapor flow required while flooding determines the maximum vapor flow allowed, hence column capacity. Thus, if the column diameter is not sized properly, the column will not perform well. Not only will operational problems occur, the desired separation duties may not be achieved. 

The actual number of trays needed for a particular separation duty depends on the efficiency of the plate, and the packings if they are used. Thus, any factors that cause a decrease in tray efficiency will also change the performance of the colunm. Tray efficiencies are affected by such factors as fouling, wear and tear and corrosion, and the rates at which these occur depends on the properties of the liquids being processed. Thus the proper materials of construction must be selected for tray construction. 

However, a single mixture (binary or multicomponent) can be separated into several products (single separation duty) and multiple mixtures (binary or multicomponent) can be processed, each producing a number of products multiple separation duties) using only one CBD column (Logsdon et al., 1990 Mujtaba and Macchietto, 1996 Sharif et al., 1998). 

Figure 3.9. Multiple Separation Duties and Multiple Operational Alternatives...

Figure 3.10. STN with Two Separation Duties. [Mujtaba and Macchietto, 1996]...

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

For single separation duty, Farhat et al. (1990) considered the operation of an existing column for a fixed batch time and aimed at maximising (or minimising) the amount of main-cuts (or off-cuts) while using predefined reflux policies such as constant, linear (with positive slope) and exponential reflux ratio profile. They also considered a simple model with negligible liquid holdup, constant molar overflow and simple thermodynamics, but included detailed plate to plate calculations (similar to Type III model). 

For single separation duty, Al-Tuwaim and Luyben (1991) proposed a shortcut method to design and operate multicomponent batch distillation columns. Their method, however, required a great number of simulations, which must be computationally very expensive, before they could arrive at an optimum design and find an optimum reflux ratio. Further details are in Chapter 7. 

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. 

For single separation duty, Mujtaba and Macchietto (1993) proposed a method, based on extensions of the techniques of Mujtaba (1989) and Mujtaba and Macchietto (1988, 1989, 1991, 1992), to determine the optimal multiperiod operation policies for binary and general multicomponent batch distillation of a given feed mixture, with several main-cuts and off-cuts. A two level dynamic optimisation formulation was presented so as to maximise a general profit function for the multiperiod operation, subject to general constraints. The solution of this problem determines the optimal amount of each main and off cut, the optimal duration of each distillation task and the optimal reflux ratio profiles during each production period. The outer level optimisation maximises the profit function by... 

Mujtaba and Macchietto (1996) extended the work or Mujtaba and Macchietto (1993) to include multiple separation duties. Logsdon et al. (1990) also considered multiple separation duties using short-cut model. Some of these works are presented in Chapter 7. 

The dynamic optimisation problem formulation is illustrated for representative multiperiod operations. The STNs in Figures 6.1 and 6.2 for binary and ternary mixtures undergoing single separation duty describe the multiperiod operations (see Chapter 3). For other networks, mixtures with larger number of components and other constraints the problem formulation requires only simple modifications of that presented in this section. 

For single separation duty Farhat et al. (1990) presented multiple criteria decisionmaking (MCDM) NLP based problem formulations for multiperiod optimisation. This involves either maximisation (Problem 1) of specified products (main-cuts) or minimisation (Problem 2) of unspecified products (off-cuts) subject to interior point constraints. These two optimisation problems are described below. 

For single separation duties, Al-Tuwaim and Luyben (1991) provided a shortcut method for simultaneous optimisation of design and operation for binary and ternary separations. Using repetitive simulation strategy they have explained in detail the interaction between design and operation with an objective to maximise a capacity factor (total amount of specified products over unit time). 

Mujtaba and Macchietto (1996) presented a more general formulation for optimal design and operation, dealing in particular with multiple separation duties, multicomponent mixtures, more complex operations (involving off-cuts) and more general objective functions. The method utilises a dynamic model (Type IV, Chapter 4) of the column in the form of a generic system of DAEs. Models of various rigor (type III and V, etc. of Chapter 4) can therefore be used. 

In this chapter first, the optimisation method of Al-Tuwaim and Luyben (1991) for single separation duty is presented. Then the optimisation problem formulation and solution considered by Mujtaba and Macchietto (1996) is explained. Finally, the optimisation problem formulations considered by Logsdon et al. (1990) and Bonny et al. (1996) are presented. 

Design and Operation Optimisation for Single Separation Duty by Repetitive Simulation... 

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. 

Mujtaba and Macchietto (1996) presented a general design and operation optimisation problem formulation and solution for single and multiple separation duties. 

The multiple separation duty specifications can be made in several ways. Two of which are ... 

Having design parameters fixed in the outer problem and with a specific choice of D° (discussed in section 7.2) the inner loop optimisation can be partitioned into M independent sequences (one for each mixture) of NTm dynamic optimisation problems. This will result to a total of ND = 2 NTm problems. In each (one for each task) problem the control vector m for each task is optimised. This can be clearly explained with reference to Figure 7.3 which shows separation of M (=2) mixtures (mixture 1 = ternary and mixture 2 = binary) and number of tasks involved in each separation duty (3 tasks for mixture 1 and 2 tasks for mixture 2). Therefore, there are 5 (= ND) independent inner loop optimal control problems. In each task a parameterisation of the time varying control vector into a number of control intervals (typically 1-4) is used, so that a finite number of parameters is obtained to represent the control functions. Mujtaba and Macchietto (1996) used a piecewise constant approximation to the reflux ratio profile, yielding two optimisation parameters (a control level and interval length) for each control interval. For any task i in operation m the inner loop optimisation problem (problem Pl-i) can be stated as ... 

Reprinted from Journal of Process Control, 6, Mujtaba, I.M. and Macchietto, S., Simultaneous optimisation of design and operation of multicomponent batch distillation column-single and multiple separation duties, 27-36, Copyright (1996), with permission from Elsevier Science. ... 

Separation Duty 1 - Mixture 1 Separation Duty 2 - Mixture 2... 

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