Column Holdup

Bogaid [Trans. Am. Inst. Chem. Eng., 33, 139 (1937)] developed the following equation for this situation with column holdup assumed to be negligible ... 

During their passage through the column, sample molecules spend part of the time in the mobile phase and part in the stationary phase. All molecules spend the same amount of time in the mobile phase. This time is called the column dead tine or holdup time (t.) and is equivalent to the tine required for an unretained solute to reach the detector frsolute retention time (t,) is the time between the instant of saiq>le introduction and when the detector senses the maximum of the retained peak. This value is greater than the column holdup time by the amount of time the solute spends in the stationary phase and is called the adjusted retention time (t, ). These values lead to the fundamental relationship, equation (1.1), describing retention in gas and liquid chromatography. 

Column Void Volume V. Retention volume corresponding to the column holdup time V. - V. 

Column Length (cm) Internal Diameter (- P u tlcle Size (F ) Column Efficiency (n) Column Holdup Volume ( 1) Peak Stemdard Deviation (Ml) k > 0 k - 5 ... 

Figur 4.31 Sequential, isocratic elution using a stepwise reduction in solvent strength to identify a binary solvent of acceptable strength for elution of a five ca x>nent mixture. In this example the column holdup time was 1 min.

With all the surface area of the packing, a lot of liquid is held up on it. This phenomenon is called column holdup, since it refers to the material retained in the column. Make sure you have enough compound to start with, or it will all be lost on the packing. 

The Claisen distillation head was filled with glass wool to avoid formation of foam. The checkers found that constant heating of the distillation apparatus with a heat gun greatly facilitates the rate of distillation and minimizes the column holdup. 

Vq is the column holdup volume (including the extra column breakthrough curve is the thick volume)... 

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. 

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. 

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. 

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. 

Figure 3.18a. Minimum Batch Time vs Column Holdup at different q...

However, for difficult separation (q > 0.60) this is reversed. Figures 3.18a and 3.18b clearly show that for q > 0.60 the column performance, in terms of minimum batch time, is improved significantly with decreasing plate holdup and suggests that for difficult separations the column holdup should be kept as minimum as possible. This is also clear from the results presented in Table 3.3 which show that for difficult separations optimum column holdup is very close to the minimum (Mujtaba and Macchietto, 1998 used 2% as the minimum column holdup). The minimum batch times for both cases (using minimum and optimum holdup) are almost alike and no time saving could be realized when compared to one another (last column of Table 3.3). The results discussed so far clearly show that holdup may have a dramatic effect on the operation. 

Figure 3.19a. Optimum Reflux Ratio vs Column Holdup at different qe...

The distillate accumulator, plate 1 (top) and the reboiler liquid composition (for benzene) profiles for case 3 are presented in Figures 3.20-3.22. Figure 3.23 presents the plate 1 liquid composition profile for case 4. Using these composition profiles Mujtaba and Macchietto (1998) made the following observations for better understanding of the role of column holdup. 

Note that Sundaram and Evans (1993a,b) used FUG method of continuous distillation directly and developed time explicit model, while Diwekar (1992) developed modified FUG method as described above and time implicit model for batch distillation. Sundaram and Evans used time as an independent variable of the model while Diwekar (1992) used reboiler composition as independent variable. Both models are based on zero column holdup and does not include plate-to-plate calculations. See the original references for further details. 

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. 

Nad and Spiegel (1987) carried out experimentation in a conventional packed batch distillation column using a cyclohexane-heptane-toluene mixture. The column consists of 20 theoretical stages (equivalent) including the condenser and reboiler. The feed to the column was 2.93 kmol of which 1.9% was total column holdup and 1.2% was condenser holdup. The column underwent an initial total reflux operation for about 2.54 hr before any product was collected. After then the mixture was separated into 3 main-cuts with 2 off-cuts in between, leaving a final product in the reboiler. 

The input data defining the column configurations, feed, feed composition, column holdup, etc. are given in Table 4.14. The reaction is modelled by simple rate equations (Table 4.14). The feed tank location was Np = 7 (stages numbered from the top down). The given batch time is 12 hrs. Conversion to product C was 70%. 

Depending on the numerical techniques available for integration of the model equations, model reformulation or simplified version of the original model has always been the first step. In the Sixties and Seventies simplified models as sets of ordinary differential equations (ODEs) were developed. Explicit Euler method or explicit Runge-Kutta method (Huckaba and Danly, 1960 Domenech and Enjalbert, 1981 Coward, 1967 Robinson, 1969, 1970 etc) were used to integrate such model equations. The ODE models ignored column holdup and therefore non-stiff integration techniques were suitable for those models. 

However, in batch distillation, the system is frequently very stiff, owing either to wide ranges in relative volatilities or large differences in tray and reboiler holdups. Therefore, if methods for non-stiff problems are applied to stiff problems (ODE models but having column holdup and/or energy balances), a very small integration step must be used to ensure that the solution remains stable (Meadow, 1963 Distefano, 1968 Boston et al., 1980 Holland and Liapis 1983, etc.). 

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