The optimum reflux ratio and the minimum batch time for separation task 1 are 3 and 80.62 min (Table 3.1). The separation task 2 could be achieved using 3 different reflux ratio (Table 3.2) but however, /?exp= 2 gives the true minimum batch time which is about 40% lower than the batch time that would be required to achieve the same separation with Rexp = 4.
The main advantage of the algorithm is that for a given reflux ratio it will estimate the duration of the batch. However, the major disadvantage of this approach is that a time consuming experiment is to be carried out for each new value of the Rexp until the given separation task can be achieved in minimum time.
Note to avoid abortion of batches during trial experiments (if carried out in an actual plant with large throughput) it is recommended to stop the batch when the distillate composition drops below or the top tray temperature goes above the specification. This will avoid any possible loss of revenue. Also note that, whether it leads to optimal operation or not, the industrial operators decides the cut time based on the above criteria.
In a steady state continuous distillation with the assumption of a well mixed liquid and vapour on the plates, the holdup has no effect on the analysis (modelling of such columns does not usually include column holdup) since any quantity of liquid holdup in the system has no effect on the mass flows in the system (Rose, 1985). Batch distillation however is inherently an unsteady state process and the liquid holdup in the system become sinks (accumulators) of material which affect the rate of change of flows and hence the whole dynamic response of the system.
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.
Rose et al. (1950) and Rose and O'Brien (1952) studied the effect of holdup for binary and ternary mixtures in a laboratory batch column. They qualitatively defined the term sharpness of separation as the sharpness in the break between successive components in the graph of instantaneous distillate composition against percentage distilled. They showed that an increase in column holdup enhanced the sharpness of separation at low reflux ratio but did not have any effect at a very high reflux ratio.
For binary mixtures Converse and Huber (1965) found that in all cases studied, column holdup causes a decrease in the amount of maximum distillate obtained for a fixed time of operation. In another way, for a fixed amount of distillate and purity of the lighter component, higher column holdup increased the batch time. The authors concluded that the presence of significant holdup is bad anyway.
Using binary mixtures, Luyben (1971) studied the effects of holdup, number of plates, relative volatility, etc. on the capacity (total products/hr). For an arbitrarily assumed constant reflux ratio the author observed both positive and negative effects of tray holdup on the capacity for columns with larger number of plates, while only negative effects were observed for columns with smaller number of plates. It is apparent that these observations are related to the degree of difficulty of separation.
Mayur and Jackson (1971) simulated the effect of holdup in a three-plate column for a binary mixture, having about 13% of the initial charge distributed as plate holdup and no condenser holdup. They found that for both constant reflux and optimal reflux operation, the batch time was about 15-20% higher for the holdup case compared to the negligible holdup case. Rose (1985) drew similar conclusion about column holdup but mentioned that the adverse effects of column holdup depends entirely on the system, on the performance required (amount of product, purity), and on the amount of holdup. Logsdon (1990) found that column holdup had a small but positive effect on their column operation.
Using binary mixtures, Mujtaba and Macchietto (1998) carried out further investigation to explain the effect of holdup qualitatively or quantitatively and to correlate the facts observed in the past. The goal was to provide a technique for helping in the selection of proper column holdup at the design stage.
The approach used by Mujtaba and Macchietto was to independently (a) characterise the column for a given number plates, mixture and separation, (b) fix the mode of operation which will measure the performance of the column for a given column holdup.
3.5.1. Column Characterisation- the Degree of Difficulty of Separation Referring to Figure 3.1 for a binary mixture and given:
• the number of plates (NT) of a batch column
• the type of mixture to be handled (thermodynamic and physical properties)
• an initial charge composition (xB0) and
• a desired distillate product purity (x D)
Christensen and Jorgensen (1987) proposed a measure q, the degree of difficulty of separation to characterise the column separation task.
Here, xBf is the final bottom product composition and xB is a reboiler composition intermediate between xBF and xB0.
This measure was based upon the ratio of the minimum necessary number of plates, A^^ (averaged over the reboiler composition) in a column to the actual number of plates in the given column, NT. Christensen and Jorgensen assumed that the mixture has a constant relative volatility a and the column operates at total reflux using constant distillate composition (x*D) strategy (section 3.3.2) and evaluated Nm\n using the Fenske equation:
Since the relative volatility changes considerably as batch distillation progresses Mujtaba and Macchietto (1998) suggested that a values should be estimated at the top and bottom of the column using rigorous vapour liquid equilibrium model and geometric average a be used in Equation 3.8 as xB changes.
The measure q reflects in a single number the column used, the type of mixture and the separation requirements. The value of q increases with decreasing relative volatility, increasing distillate purity demands and decreasing number of stages in excess of the minimum. Its value is independent of the amount charged. It ranges from 0 (infinite number of stages) to 1 (minimum number of stages). Typical values are q < 0.60 for an easy separation and q > 0.6 for a difficult one (Christensen and Jorgensen, 1987). Also this measure is very useful as q does not only measure how close the boiling points of the components are, it also measures the extent a given column is oversized for the purpose.
Mujtaba and Macchietto (1998) chose the minimum time as the most suitable performance measure, because the separation requirements (e.g. product purities) are fixed and quantitative measure, q could be easily used.
The effects of column holdup can be easily correlated in terms of q and of the minimum batch time required to achieve a given separation task.
A summary of several example cases illustrated in Mujtaba and Macchietto (1998) is presented below. Instead of carrying out the investigation in a pilot-plant batch distillation column, a rigorous mathematical model (Chapter 4) for a conventional column was developed and incorporated into the minimum time optimisation problem which was numerically solved. Further details on optimisation techniques are presented in later chapters.
Three typical binary mixtures were considered. The mixtures were: 1. Benzene-Toluene, 2. Cyclohexane-Toluene and 3. Butane-Pentane. Some of the results were presented graphically to show the role of holdup in terms of the degree of difficulty of separation and minimum time operation.
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