Dynamics—Binary Distillation

Continuous binary distillation is illustrated by the simulation example CON-STILL. Here the dynamic simulation example is seen as a valuable adjunct to steady state design calculations, since with MADONNA the most important column design parameters (total column plate number, feed plate location and reflux ratio) come under the direct control of the simulator as facilitated by the use of sliders. Provided that sufficient simulation time is allowed for the column conditions to reach steady state, the resultant steady state profiles of composition versus plate number are easily obtained. In this way, the effects of changes in reflux ratio or choice of the optimum plate location on the resultant steady state profiles become almost immediately apparent. 

Y.-L Hwang, On the nonlinear wave theory for dynamics of binary distillation columns. 

Nonequilibrium molecular dynamics simulations show that the assumption of local equilibrium in a column with heat and mass transfer is acceptable. The dissipation function in a binary distillation is (Ratkje et al., 1995 Sauar etal., 1997)... 

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 ... 

Do the same as in Problem III. 1 for the equations describing the dynamic and steady-state behavior of the binary distillation column modeled in Example 4.13. 

The analysis of nonlinear dynamics of chemical process systems has a long tradition. Most emphasis has been on chemical reactors initiated by the seminal work of Bilous and Amundson [10], van Heerden [109], and Aris and Amundson [3]. Comprehensive reviews have been given by Razon and Schmitz [86] or Elnashaie and Elshishini [19]. Multiplicity analysis of non-RD can be traced back to the paper of Rosenbrock [91] where stability and hence uniqueness of steady-states of a binary distillation column is demonstrated under quite general assumptions. 

Figure 21.2 shows the LV configuration for the two-point composition control of a binary distillation column discussed in Example 20.9. After assigning manipulated variables to regulate the vapor and liquid inventories, the boilup rate, V, and the reflux flow rate, L, remain available to control the distillate and bottoms product compositions, and Xg, respectively. To assess the controllability and resiliency of this configuration, the disturbances are taken to be the feed composition, Xp, and the flow rate, F. The column dynamics are approximated by a linear model in transfer function form (Sandelin et al., 1990) ... 

This section addresses the application of a dynamic optimization-based design approach to RD. The liquid-phase esterification reaction of C4 and methanol in the presence of inert nC4 in a staged RD column is used as tutorial example. Similar to the study on binary distillation (Bansal et al., 2000 Bansal, 2000) and on the synthesis of ethyl acetate by RD (Georgiadis et al, 2002), both spatial-related e.g. column diameter and heat exchanger areas) and control-related e.g. gain, set-point and reset time) design variables are optimized with respect to economic and dynamic performance in the presence of time-varying disturbances. 

A laboratory binary distillation column, consisting of five trays, a total condenser and a reboiler, has been studied by Hu and Ramirez (1972). They have shown that a linearized version of the model describes the process dynamics reasonably well. The linear model is... 

The first problem is taken from [28], and illustrates the use of controller parametrization within an optimization-based fiamework to assess the dynamic operability of processes exhibiting combinations of performance-limiting characteristics. The process considered is a binary distillation system analyzed in [7] represented by the transfer function model... 

Edwards, J.B. and Jassim, H.J. (1977) An analytical study of the dynamics of binary distillation columns. Transactions of the Institution of Chemical Engineers, 55,17-28. 

For a binary distillation column, convenient, compact representation of overall column composition dynamics in two equations has been suggested by Rippin and Lamb ... 

Signal flow diagram for Rippin-Lamb model for binary distillation column dynamics... 

A Theoretical Study of the Dynamics and Control of Binary Distillation, Bulletin, University of Delaware, 1960. 

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

TABLE 13-32 Initial and Fixed Conditions, Controller and Hydraulic Parameters, and Disturbance for Ideal Binary Dynamic-Distillation Example... 

DISTILLATION TABLE 13-33 Results for Ideal Binary Dynamic-Distillation Example of Table 13-32 ... 

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. 

The distillation column used in this example separated a binary mixture of propylene and propane. Because of the low relative volatility and large number of trays, the dominant time constant is very large (500 minutes). Despite this large time constant, a sampling period of 9.6 minutes gave poor results. The period had to be reduced to 1,8 minutes to get good identification, both dynamic and steadystate gain. 

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 ... 

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 single separation duty, Mujtaba and Macchietto (1993) proposed a method, based on extensions of the techniques of Mujtaba (1989) and Mujtaba and Macchietto (1988, 1989, 1991, 1992), to determine the optimal multiperiod operation policies for binary and general multicomponent batch distillation of a given feed mixture, with several main-cuts and off-cuts. A two level dynamic optimisation formulation was presented so as to maximise a general profit function for the multiperiod operation, subject to general constraints. The solution of this problem determines the optimal amount of each main and off cut, the optimal duration of each distillation task and the optimal reflux ratio profiles during each production period. The outer level optimisation maximises the profit function by... 

This section presents the dynamic optimisation problem formulation of Mujtaba (1989) and Mujtaba and Macchietto (1992) to obtain optimal recycle policies in multicomponent batch distillation. Some special cases were identified where the methods used for the binary case could be applied fairly easily to multicomponent mixtures. The previously mentioned measure q of the degree of difficulty of separation was used to identify those special cases. A new operational strategy regarding the order of off-cuts recycle in a multicomponent environment was discussed. The Benefits of recycling were correlated against the measure q. 

Also Mujtaba (1997) considered the separation of binary mixtures into one distillate product of specified purity. The objectives were to find out whether it was possible to replace conventional dynamic operation of batch columns by steady state operation using continuous columns for a comparable recovery, energy consumption, operation time, productivity, etc. and to obtain optimal operating policy in terms of reflux ratio. The following strategy was considered to compare the performances of the two types of operations ... 

Even in the first publications concerning the copolymerization theory [11, 12] their authors noticed a certain similarity between the processes of copolymerization and distillation of binary liquid mixtures since both of them are described by the same Lord Rayleigh s equations. The origin of the term azeotropic copolymerization comes just from this similarity, when the copolymer composition coincides with monomer feed composition and does not drift with conversion. Many years later the formal similarity in the mathematical description of copolymerization and distillation processes was used again in [13], the authors of which, for the first time, classified the processes of terpolymerization from the viewpoint of their dynamics. The principles on which such a classification for any monomer number m is based are presented in Sect. 5, where there is also demonstrated how these principles can be used for the copolymerization when m = 3 and m = 4. 

A deliberate mixture of the three binary xenon fluorides, dissolved in BrFs, was treated with an excess of AsFs. The BrFs and excess AsFs were vacuum distilled in a static vacuum at 0° to leave a mixture of XejFa+lAsFe]-, XeFs+[AsF6]-, and XeF,. The XeF, was recovered by sublimation at 20°, in a dynamic vacuum, to a trap at — 60° and was shown to be pure by its melting point, 117° (Schreiner, el al., give" 117.1°), X-ray powder photograph, and infrared spectrum. 

The distillation column used in this study is designed to separate a binary mixture of methanol and water, which enters as a feed stream with flow rate F oi and composition Xp between the rectifying and the stripping section, obtaining both a distillate product stream D oi with composition Ad and a bottom product stream 5vo/ with composition Ab. The column consists of 40 bubble cap trays. The overhead vapor is totally condensed in a water cooled condenser (tray 41) which is open at atmospheric pressure. The process inputs that are available for control purposes are the heat input to the boiler Q and the reflux flow rate L oi. Liquid heights in the column bottom and the receiver drum (tray 1) dynamics are not considered for control since flow dynamics are significantly faster than composition dynamics and pressure control is not necessary since the condenser is opened to atmospheric pressure. 

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