Time, batch distillation

Although batch distillation is covered in a subsequent separate section, it is appropriate to consider the application of RCM and DRD to batch distulation at this time. With a conventional batch-rectification column, a charge of starting material is heated and fractionated, with a vapor product removed continuously. The composition of the vapor prodiic t changes continuously and at times drastically as the lighter component(s) are exhausted from the stiU. Between points of drastic change in the vapor composition, a cut is often made. Successive cuts can be removed until the still is nearly diy. The sequence, number, and limiting composition of each cut is dependent on the form of... 

Feed rate to tower, lb mols/hr or, mols of feed, (batch distillation) entering flash zone/time all components except non-condensable gases Factor for contribution of other feed flow to minimum reflux Mols of liquid feed Mols of vapor feed... 

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. 

There are two scaledown concepts that even experienced professionals relearn reactions take longer to run in the plant than lab, and batch distillation times are also noticeably longer in the plant compared with lab. 

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)... 

Three products (PI, P2, aod P3) and two slop cuts (SI and S2) are produced. The average composition of the products are 95 mole percent. The PI product is mostly the lightest component (component 1). The P2 product is mostly intermediate component (number 2) with some impurities of both the light and the heavy components. The final product P3 is what is left in the still pot and on the trays. The times to produce the various products and slop cuts are given in the results shown in Table 5.14. The total time for the batch distillation in this example is 6.4 hours. 

Processing. Early asphaltic crudes, such as Panuco (Mexican) and Heavy Californian, yielded up to 65% asphalt (4), and were fairly readily processed in horizontal, direct-fired batch stills as shown in Figure 2. Usually steam was introduced to assist in the vaporization of the volatile constituents. The temperature at the termination of the process varied between 600° and 750° F., and the time of distillation was between 12 and 36 hours. These batch stills were replaced by continuous stills of similar construction. The oil flows from one still to another, with each still producing a predetermined grade of distillate. 

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. 

To a batch of approximately 10 liters of filtered broth is added 150 grams of activated charcoal. The mixture is stirred continuously for about 5 minutes and is then filtered. The slightly yellowish (almost colorless) filtrate is discarded and the charcoal residue is washed several times with distilled water and finally with 95% ethanol. The washed material is then suspended in 1.5 liters of 95% ethanol, made 0.15 normal with hydrochloric acid. The suspension is stirred for about an hour and allowed to stand in the cold for about 10 hours more with occasional stirring. The suspension is then filtered, the charcoal residue discarded, and the yellowish clear filtrate thus obtained is poured into 10 liters of ether, with stirring. A brown-colored aqueous layer separates and is drawn off. 

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 duration of the first step can usually be considered negligible compared to the overall batch distillation time, whereas the duration of steps 2-5 is important and in some cases it may take a long time to reach a steady state or the desired initial distillate composition (Holland and Liapis, 1983 Nad and Spiegel, 1987 Ruiz, 1988 Logsdon and Biegler, 1993). 

Using the constant reflux operation strategy outlined in section 3.3.2 Greaves et al. (2001) carried out few experiments using different values of Rexp and different batch time. The accumulated distillate composition profiles as functions of batch time and distillate holdup are shown in Figures 3.13 and 3.14 respectively. Figure 3.15 shows the instant distillate composition profile for Rexp = 2. 

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. 

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. 

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. 

The Rayleigh model was developed for a single stage batch distillation-where a liquid mixture is charged in a still and a vapour is produced by heating the liquid. At any time, the vapour on top of the liquid is in equilibrium with the liquid left in the still. The vapour is removed as soon as it is produced but no part of the vapour is returned as reflux to the still after condensation. 

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). 

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. 

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). 

Rigorous and stiff batch distillation models considering mass and energy balances, column holdup and physical properties result in a coupled system of DAEs. Solution of such model equations without any reformulation was developed by Gear (1971) and Hindmarsh (1980) based on Backward Differentiation Formula (BDF). BDF methods are basically predictor-corrector methods. At each step a prediction is made of the differential variable at the next point in time. A correction procedure corrects the prediction. If the difference between the predicted and corrected states is less than the required local error, the step is accepted. Otherwise the step length is reduced and another attempt is made. The step length may also be increased if possible and the order of prediction is changed when this seems useful. 

With an example of batch distillation, Seader and Henley showed that the time step needed in implicit Euler s method was 200 times of that needed for explicit Euler s method. 

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 ... 

Application to Batch Distillation Minimum Time Problem... 

The application of Equations P.1-P.7 to batch distillation enables the solution of time optimal control problems. 

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 (/ ). 

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