Distillation columns model assumptions

It has been shown (Popken et al, 2001 BeRling et al, 1998) that the first model usually provides the highest deviations between calculation results and the behavior of real reactive distillation columns. The assumption that chemical equilibrium is reached is not adequate for most of the chemical reactions of commercial interest. Changes in composition and heat are taken into account by using the equilibrium constant K and the heat of reaction. The second model caimot be recommended because chemical reactions are slower than the time needed to reach VLE. Therefore, it makes no sense to assume kinetic limitations for the distillation part but to neglect the reaction kinetics. 

With this assumption, and using a modified Neumann model for HI/I2/H20 mixtures description, CEA (Leybros, 2009) devised a flow sheet for the iodine section which decomposes almost all incoming HI and therefore returns relatively pure products (the iodine return flow contains only 4 molar% water and less than. 3 molar% HI) to the Bunsen section, an important feature for the counter-current reactor. Secondary helium heat is provided to the boiler of the column (235 kj/mol), whereas all other heat needs are fulfilled through internal heat recovery, with the help of a heat pump which transfers heat from the products of the distillation column to its feed. Mainly because of the presence of this heat pump, the iodine section uses 60 kj/mol of electric power on top of the helium heat. 

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. 

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). 

Referring to Figure 4.10 of a continuous distillation column the model is developed based on the assumptions of constant relative volatility and equimolal overflow and include detailed plate-to-plate calculations. Further assumptions are listed below ... 

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... 

Distillation columns are made to separate at least two different components. There are several different types of columns. The assumption of equilibrium between the liquid and vapour that leave each tray is still in common use to model tray distillation. The work of Krishna and Wesselingh shows, however, that non-equilibrium models give results that are very different from those obtained with the equilibrium assumption. 

At this point, we are not concerned with the developing methods for rigorous solution of the above system of equations. Discussion on computational methods for the general case of multi-component systems is covered in Chapter 13. This chapter considers a simplified model that lends itself to graphical solution and provides a tool for qualitative understanding of the operation of a distillation column. The model has a relatively low level of complexity because of its binary nature and also because of other simplifying assumptions. 

The rigorous solution of batch distillation columns carries an extra dimension of complexity over continuous steady-state distillation because it is inherently a transient operation. The basic assumption of steady-state operation in the continuous column model obviously does not apply for batch distillation. The only possible steady-state operation in batch distillation is at total reflux, which is commonly used as the initial condition for the dynamic solution of the column. 

The modeling steps outlined above indicate that the overall procedure may be tedious and full of simplifying assumptions. At times the resulting model is overwhelming in size and the solution of the corresponding equations may be cumbersome. For the binary distillation column we have to solve a system of... 

Here we are interested in modeling a typical tray in a binary distillation column, as shown in Figure 5.14. The major assumption we usually make for binary distillation is that of equal-molar overflow, namely that the molar vapor flow rate entering the tray is equal to the molar vapor flow rate leaving the tray, Vn+i = K-... 

Chien and Fruehauf with the assumption of integrating plus deadtime model form for the initial dynamic response. The results of those calculations are Kc = 1.54 and tj = 7.5 min for the tray temperature loop in the extractive distillation column and Kc = 1.72 and Tj = 13.75 min for the tray temperature loop in the entrainer recovery column. 

As a more realistic distillation example, let us now develop a mathematical model for a multicomponent, nonideal column with NC components, nonequimolal overflow, and inefficient trays. The assumptions that we will make are ... 

Stirred tanks are usually modeled assuming both phases are well mixed. See Section 1.5 for conditions under which this assumption is reasonable. Tray columns are usually modeled as well mixed on each tray so that the overall column is modeled as a series of two-phase stirred tanks. (Distillation trays with tray efficiencies greater than 100% have some progressive flow within a tray.) When reaction is confined fo a single well-mixed phase, the flow regime for the other phase makes little difference but when the reacting phase approximates piston flow, the flow regime in the other phase becomes important. The important cases are where both phases approximate piston flow, either countercurrent or cocurrent. 

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