Equimolal overflow

A useful method for a binary mixture employs an analysis based on the McCabe-Thiele graphical method. In addition to the usual assumptions of adiabatic column and equimolal overflow on the trays, the following procedure assumes neghgible holdup of hquid on the trays, in the column, and in the condenser. 

Enthalpy, Btu/unit flow 2,901.076 lb = 31.48 Feed temperature 90°F, liquid at stage 5 from top, Equimolal overflow not assumed Column Pressure 0.39 (top) to 0.86 (bottom) psia, distributed uniformly to each tray... 

Remember these V s are not necessarily constant with time. The vapor boilup can be manipulated dynamically. The mathematical effect of assuming equimolal overflow is that we do not need an energy equation for each tray. This- is quite a significant simplification. 

Theoretical trays, equimolal overflow, and constant relative volatilities are assumed. The total amount of material charged to the column is M q (moles). This material ean be fresh feed with composition Zj or a mixture of fresh feed and the slop cuts. The composition in the still pot at the begiiming of the batch is Xgoj. The composition in the still pot at any point in time is Xgj. The instantaneous holdup in the still pot is Mg. Tray liquid holdup and reflux drum holdup are assumed constant. The vapor boilup rate is constant at V (moles per hour). The reflux drum, eolumn trays, and still pot are all initially filled with material of eomposition Xg j. 

The digital simulation of a distillation column is fairly straightforward. The main complication is the large number of ODEs and algebraic equations that must be solved. We will illustrate the procedure first with the simplified binary distillation column for which we developed the equations in Chap. 3 (Sec. 3.11). Equimolal overflow, constant relative volatility, and theoretical plates have been assumed. There are two ODEs per tray (a total continuity equation and a light component continuity equation) and two algebraic equations per tray (a vapor-liquid phase equilibrium relationship and a liquid-hydraulic relationship). 

ASSUMPTIONS CONSTANT RELATIVE VOLATILITY, EQUIMOLAL OVERFLOW, THEORETICAL TRAYS, SIMPLE LIQUID TRAY HYDRAULICS... 

Une energy balance per tray must be included if equimolal overflow cannot be assumed. 

The model of a multicomponent batch distillation column was derived in Sec. 3.13. For a simulation example, let us consider a ternary mixture. Three products will be produced and two slop cuts may also be produced. Constant relative volatility, equimolal overflow, constant tray holdup, and ideal trays are assumed. 

Example 12.6. Let us consider a much more complex system where the advantages of frequencynlomain solution will be apparent. Rippin and Lamb showed how a frequency-domain stepping technique could be used to find the frequency response of a binary, equimolal-overflow distillation column. The column has many trays and therefore the system is of very high order. 

The dynamic model of the stripping column consists of one ordinary differential equation per tray if equimolal overflow, constant liquid holdups on the trays, and instantaneous... 

Referring to Figure 4.2 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... 

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. 

Both the steady state and dynamic column models (for CBD only) used by Mujtaba (1997) are based on the assumptions of constant relative volatility and equimolal overflow and include detailed plate-to-plate calculations. This will allow a direct comparison between CBD and continuous column operation. The continuous column model is presented in section 4.3.1 and the CBD model (Type III) is presented in section 4.2.3. Some of the modelling assumptions, for example, constant molar holdup, constant pressure, equimolal overflow, etc., can be relaxed, if needed, by replacing them with more realistic assumptions and therefore by adding the relevant equations (as presented in Chapter 4). 

So we must pay particular attention to the effects of the reaction section on the separation section. In this chapter we strip away all of the confusing factors associated with complex physical properties and phase equilibrium so that we can concentrate on the fundamental effects of flowsheet topology and reaction stoichiometry. Therefore, in the processes studied here, we use such simplifying assumptions as constant relative volatilities, equimolal overflow, and constant densities. 

Let s finish the problem by determining the flowrates. Once again, all the flowrates can be deduced from the equimolal overflow assumption and the reboil fraction. All the liquid flowrates correspond to the flowrate of the liquid fed to the top ... 

The second graph on the right above is what would be predicted by making the equimolal overflow assumption. We forced Chemsep to make the equimolal overflow assumption by altering slightly the thermodynamic model. Navigating back to the... 

These variations in flowrate within a cascade stem from the fact that the enthalpy of saturated liquid is not independent of temperature or acetone content as is required for "equimolal overflow." The plot at right shows the liquid and vapor enthalpies, and the mole fraction of acetone in the liquid, versus stage number. ... 

For equimolal overflow, the enthalpy profiles should be two vertical lines. Clearly, they are not vertical lines. The departure arises because the heat of vaporization of acetone and methanol are not quite equal. The following values were read from the ChemSep library ... 

We assume constant density, equimolal overflow, theoretical trays, total condenser, partial reboiler, and five-minute holdups in the column base and the overhead receiver. Tray holdups and the liquid hydraulic constants are calculated from the Francis weir formula using a one-inch weir height. 

For the moment, let us assume that the pressure has been specified, so the VLE is fixed. Let us also assume that the reflux ratio has been specified, so the reflux flow rate can be calculated R = (RR) (D). The equimolal overflow assumption is usually made in the McCabe-Thiele method. The liquid and vapor flow rates are assumed to be constant in a given section of the column. For example, the liquid flow rate in the rectifying section Lr is equal to the reflux... 

In Fig. 11.4-4a the distillation tower section above the feed, the enriching section, is shown schematically. The vapor from the top tray having a compositionpasses to the condenser, where it is condensed so that the resulting liquid is at the boiling point. The reflux stream L mol/h and distillate D mol/h have the same composition, so y, = Xp. Since equimolal overflow is assumed, L = Lj = L and Kj = Kj = F), =... 

Note that in Example 11.6-2 in the stripping section, the vapor flow increases slightly from 125.0 to 126.5 in going from the reboiler to near the feed tray. These values are lower than the value of 133.0 obtained assuming equimolal overflow. Similar conclusions hold for the enriching section. The enthalpy-concentration method is useful in calculating the internal vapor and liquid flows at any point in the column. These data are then used in sizing the trays. Also, calculations of <7r used... 

What we have just derived is referred to as the principle of equimolal overflow and vaporization. 

In practice, the systems tend to be more complex than the simple binary example used here, and the computations are done using appropriate computer packages. Today, these packages are quite powerful and are able to handle mixtures of many components without recourse to the simplifying assumption of equimolal overflow and vaporization. The McCabe-Thiele diagram nevertheless remains a valuable tool for visualizing the principal features of the fractionation process and for providing the student an entry into the treatment of more complex systems. 

Column General Information Saturated liquid feed is to 12th stage (of 20) numbered from the top down. Equimolal overflow is assumed. A is the more volatile component assume equilibrium holds for each stage ... 

The vapor leaving the top of the column is larger than the vapor boilup, despite the fact that equimolal overflow has been assumed. This is due to the exothermic heat of reaction generating more vapor on the reactive trays. 

The chemical equilibrium constant at 366 K [(Feq)366] and the relative volatilities (constant or temperature dependent) are specified for each case. Equimolal overflow is assumed in the distillation columns, which means that neither energy balances nor total balances are needed on the trays for steady-state calculations. Other assumptions are isothermal operation of the reactor, theoretical trays, saturated hquid feed and reflux, total condensers, and partial reboilers in the columns. Additional assumptions and specifications are the following ... 

The steady-state vapor and liquid rates are constant through the stripping and rectilying sections because equimolal overflow is assumed. However, these rates change through the reactive zone because of the exothermic reaction. The heat of reaction vaporizes some liquid on each tray in that section therefore, the vapor rate increases up through the reactive trays and the liquid rate decreases down through the reactive trays. 

With the equimolal overflow assumption mentioned above, all of the vapor rales (Vn) throughout the stripping section are equal to V5, and all of the liquid rates (Z ) are equal to Ls- Analogously, all V beginning from the top feed tray throughout the rectifying section and total condenser are Vr, and all L are equal to Lr. 

The reactors are assumed to be adiabatic, and the holdups of each reactor are the same. We assume that the number of trays between each liquid trap-out tray is the same. Other assumptions are theoretical trays, equimolal overflow, saturated liquid feeds and reflux, total condenser, and partial reboiler. 

The liquid and vapor rates through the stripping and rectifying sections are calculated using Eq. (16.3) together with the equimolal overflow assumption. 

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