Ideal Binary Distillation Column

Next to the ubiquitous CSTR, the distillation column is probably the most popular and important process studied in the chemical engineering literature. Distillation is used in many chemical processes for separating feed streams and for purification of final ami intermediate product streams. 

Most columns handle multicomponent feeds. But many can be approximated by binary or pseudobinary mixtures. For this example, however, we will make several additional assumptions and idealizations that are sometimes valid but more frequently are only cmde approximations. 

The purpose of studying this simplified ease first is to reduce the problem to its most elementary form so that the basie structure of the equations can be clearly seen. In the next example, a more realistic system will be modeled. 

We will assume a binary system (two components) with constant relative volatihty throughout the column and theoretical (100 percent efficient) trays, i.e., the vapor leaving the tray is in equilibrium with the liquid on the tray. This means the simple vapor-hquid equihbrium relationship can be used 

A single feed stream is fed as saturated liquid (at its bubblepoint) onto the feed tray N,. See Fig. 3.12. Feed flow rate is F (mol/min) and composition is z (mole fraction more volatile component). The overhead vapor is totally condensed in a condenser and flows into the reflux drum, whose holdup of hquid is Mj) (moles). The contents of the drum is assumed to be perfectly mixed with composition Xo The liquid in the drum is at its bubblepoint Reflux is pumped back to the top tray (iVj-) of the column at a rate R. Overhead distillate product is removed at a rate D. 

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Simulate the ideal binary distillation column of Sec. 5.4, using Euler and fourth-order Runge-Kutta and compare computation times. 

Example 4.13 Mathematical Model of an Ideal Binary Distillation Column... 

Return to the ideal binary distillation column (Figure 4.10). The system possesses six degrees of freedom (see Example 5.4), which are specified as follows ... 

Let us consider two processes we have already modeled the continuous stirred tank reactor and the ideal, binary distillation column. 

In an ideal binary distillation column the dynamics of each tray can be described by first-order systems. Are these capacities interacting or not What general types of responses would you expect for the overhead and bottoms compositions to a step change in the feed composition ... 

Consider the model for an ideal binary distillation column developed in Example 4.13. We have ... 

The number of degrees of freedom for the ideal binary distillation column is... 

Care must be exercised not to specify more control objectives than the available number of degrees of freedom. In such a case the system becomes overspecified and it is impossible to design a control system that satisfies all the desired control objectives. Thus it is impossible to design a control system for the ideal binary distillation column that can satisfy the following six operational (control) objectives ... 

Describe a procedure that would allow you to develop the input-output model for an ideal, binary distillation column. 

For an extensive discussion of the mathematical modeling of an ideal, binary distillation column and of a nonideal multicomponent column, the reader can consult the books by Douglas [Ref. 1], Luyben [Ref. 2], and Friedly [Ref. 3], An... 

Equimolar Counterdiffusion in Binary Cases. If the flux of A is balanced by an equal flux of B in the opposite direction (frequently encountered in binary distillation columns), there is no net flow through the film and like is directly given by Fick s law. In an ideal gas, where the diffusivity can be shown to be independent of concentration, integration of Fick s law leads to a linear concentration profile through the film and to the following expression where (P/RT)y is substituted for... 

Develop the state model for a multicomponent (C components) nonideal distillation column with N trays. Use the general nomenclature developed in Example 4.13 for the ideal binary distillation. 

FIG. 13-107 Binary distiUatio n column dynamic distillation of ideal binary mixture. 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

Example The location of the best temperature-control tray in a distillation column is a popular subject in the process-control literature. Ideally, the best location for controlling distillate composition xa with reflux flow by using a tray temperature would be at the top of the column for a binary system. See Fig. 8.9o. This is desirable dynamically because it keeps the measurement lags as small as possible. It is also desirable from a steadystate standpoint because it keeps the distillate composition constant at steadystate in a constant pressure, binary system. Holding a temperature on a tray farther down in the column does not guarantee that x will be constant, particularly when feed composition changes occur. 

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. 

Christiansen, A.C., Jacobsen, E.W., Perkins. J.D. and Skogestad, S., On the dynamics of batch distillation A study of parametric sensitivity in ideal binary columns. Presented at the AIChE Annual Meeting, Miami, USA, November, paper no. 184d, 1995. 

For example, suppose there is a stream in the process that is a binary mixture of chemical components A and B. If these components obey ideal vapor-liquid equilibrium behavior, we can use a single distillation column to separate them. If they form an azeotrope, we may have to use a two-column separation scheme. If the azeotropic composition... 

Operating Line and "Equilibrium" Curve. Both terms are of importance for the graphical solution of a separation problem, i.e., for the graphical determination of the number of stages of a cascade. This method has been developed for the design of distillation columns by MacCabe and Thiele and should be well known. For all cases, the operating line represents the mass and material balances. In distillation, the equilibrium curve represents the thermodynamical va-por/liquid equilibrium. For an ideal binary system, the equilibrium curve can be calculated from Raoult s law and the saturation-pressure curves of the pure components of the mixture. In all other cases, however, for example, for all membrane processes, the equilibrium curve does not represent a thermodynamical equilibrium at all but will represent the separation characteristics of the module or that of the stage. 

Develop the state model for an ideal binary batch distillation column with N ideal plates (Figure PII. 12). At t = 0, the composition of the initial mixture is cA and cB (molar fractions), and its total mass is M (moles). 

Disks, for digital computer, 555-56 Distillation batch binary, 108 degrees of freedom, 87-88 difficulties in modeling, 77 ideal binary, 70-74 modeling, 70-74 as a multicapacity process, 214 nonideal binary, 109 thermally coupled columns, 536 Distillation control adaptive, 442-43... 

Why have we neglected the energy balances for the binary ideal distillation column of Example 4.13 ... 

We notice that we have many more state variables than outputs. For such systems, the development of the input-output model is quite involved and difficult. Figure 5.4 depicts pictorially the input-output model that we would like to develop for the binary ideal distillation column. 

First, the role of reaction kinetics is analyzed considering RD processes for the simple reversible reaction Aj o Aj in an ideal binary mixture. The educt Aj is assumed to be the reaction component with the higher boiling point, so the product A2 is obtained in the distillate. The reaction can be carried out in an RD column sequence with an external recycling loop (Fig. 5.1), a non-RD column on top of a reactive reboiler (Fig. 5.2), or a full RD column (Fig. 5.3). More possible configurations are analyzed elsewhere [1]. 

In the example distillation system considered in Chapters 3 and 4, we studied the binary propane/isobutane separation in a single distillation column. This is a fairly ideal system from the standpoint of vapor-liquid equilibrium (VLE), and it has only two components, a single feed and two product streams. In this chapter, we will show that the steady-state simulation methods can be extended to multicomponent nonideal systems and to more complex column configurations. 

A continuous distillation column is essentially a binary separator that is, it separates a feed into two parts. For binary systems, both parts can be the desired pure products. However, for multiconponent systems, a sinple single column is unable to separate all the conponents. For ternary systems, two columns are required to produce pure products for four-conponent systems, three columns are required and so forth. There are many ways in which these multiple columns can be coupled together for multiconponent separations. The choice of cascade can have a large effect on both capital and operating costs. In this section we will briefly look at the coupling of columns for systems that are almost ideal. More detailed presentations are available in other books fBiegler et al.. 1997 Doher and Malone. 

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