Distillation columns tray dynamics

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 ... 

Figure 4.5 Dynamic model for a distillation column Tray modelling...

Those controllers that should be reviewed include all level controllers, most temperature controllers (such as those on fired heaters, distillation column trays etc.) and any other controller where the process dynamics are relatively slow. Any controller identified by the process operator as problematic should also be addressed — whether or not important to the performance of MVC. This will help greatly with operator acceptance of the whole project. 

Wang XL, Liu CT, Yuan XG, Yu KT (2004) Computational fluid dynamics simulation of three-dimensional liquid flow and mass transfer on distillation column trays. Ind Eng Chem Res 43(10) 2556-2567... 

The state variables are the minimal set of dependent variables that are needed in order to describe fully the state of the system. The output vector represents normally a subset of the state variables or combinations of them that are measured. For example, if we consider the dynamics of a distillation column, in order to describe the condition of the column at any point in time we need to know the prevailing temperature and concentrations at each tray (the state variables). On the other hand, typically very few variables are measured, e.g., the concentration at the top and bottom of the column, the temperature in a few trays and in some occasions the concentrations at a particular tray where a side stream is taken. In other words, for this case the observation matrix C will have zeros everywhere except in very few locations where there will be 1 s indicating which state variables are being measured. 

You may wonder why we would ever be satisfied with anything less than a very accurate integration. The ODEs that make up the mathematical models of most practical chemical engineering systems usually represent a mixture of fast dynamics and slow dynamics. For example, in a distillation column the liquid flow or hydraulic dynamic response occurs fairly rapidly, of the order of a few seconds per tray. The composition dynamics, the rate of change of hquid mole fractions on the trays, are usually much slower—minutes or even hours for columns with many trays. Systems with this mixture of fast and slow ODEs are called stiff systems. 

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 ... 

The rate-based models suggested up to now do not take liquid back-mixing into consideration. The only exception is the nonequilibrium-cell model for multicomponent reactive distillation in tray columns presented in Ref. 169. In this work a single distillation tray is treated by a series of cells along the vapor and liquid flow paths, whereas each cell is described by the two-film model (see Section 2.3). Using different numbers of cells in both flow paths allows one to describe various flow patterns. However, a consistent experimental determination of necessary model parameters (e.g., cell film thickness) appears difficult, whereas the complex iterative character of the calculation procedure in the dynamic case limits the applicability of the nonequilibrium cell model. 

From a simulation viewpoint units SO, S6 and S7 may be considered blackboxes. On the contrary, SI to S5 are simulated by rigorous distillation columns, as sieve trays. In the steady state all the reactors can be described by a stoichiometric approach, but kinetic models are useful for Rl, R2 and R4 in dynamic simulation [7, 8]. As shown before, the reaction network should be formulated so as to use a minimum of representative chemical species, but respecting the atomic balance. This approach is necessary because yield reactors can misrepresent the process. 

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. 

This example is intended to demonstrate the process dynamics methodology as implemented on a single equilibrium stage. A stream of light hydrocarbons is sent to a distillation column where the C3 s and lighter components are separated from the C4 s. Since the feed composition fluctuates substantially, it is sent to a flash drum located upstream of the column in order to attenuate the composition fluctuations and thereby improve the column controllability. The vapor and liquid products from the flash drum are then sent to different trays in the column. 

Many industrial separation processes are based on phase equilibria. By this we mean that the various components of the mixtures present in the (vapor, liquid, solid) phases are in equilibriinn. This is a dynamic equilibriinn and equal mnnbers of components are being transferred continuously from one phase to the other thus the concentrations at equilibriinn do not change. To design the separation processes in industry, e.g., finding the height and number of trays of a distillation column, we need to know the concentrations at equilibrium at any temperature and pressure. 

A dynamic model of a distillation column can be assembled from simpler units, as trays, heat exchangers (condenser, reboiler), reflux drum, valves and pumps (Fig. 4.5). Tray modelling has to answer two issues (1) accurate description of material and energy holdup, and (2) accurate pressure drop calculation. 

Modelling a single tray is similar with a dynamic flash discussed before. The solution of the assembly of trays, increased with condenser, flash drum and reboiler, is a much more difficult problem, however. The equations presented below (for notations see Fig. 4.6) are known as MESH equations for modelling distillation columns at steady state enlarged with left hand terms for accumulation. 

Dynamic simulation of distillation column needs also tray sizing. We considered sieve trays with 0.4 m diameter of and 0.05 m static liquid height. 

A steady-state Plant Simulation Model of an existing plant helped to calibrate the base-case model on a representative operating point. Some details of an industrial process were skipped, but the omission of these details does influence neither the plantwide material balance nor the process dynamics. The units SO, S6 and S7 may be considered black-boxes. Contrary, SI to S5 are rigorous distillation columns, modelled as sieve trays. In steady-state all the reactors are described by stoichiometric approach, but kinetic models are used for Rl and R4 in dynamic simulation. 

Ellingsen, W. R., "Diagnosing and Preventing Tray Damage in Distillation Columns, DYCORD 86, IF AC Proceedings of International Symposium on Dynamics and Control of Chemical Reactors and Distillation Columns, Bournemouth, U.K., Dec. 8-10, 1986. 

Kooijman, H.A. and R. Taylor, Nonequilibrium model for dynamic simulation of tray distillation columns. AIChE Journal, 1995, 41(8) 1852 1863. 

The improvement in control by the use of pressure compensation has been quantitatively demonstrated. The implementation of this type of structure in Aspen Dynamics has been outlined. A simple procedure for deriving the relationships between temperature, pressure, and composition has been illustrated. Pressure compensation should be considered in distillation columns where pressure changes at the control tray are significant. 

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... 

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. 

Similar equipment in series (for example extraction units in series) or chains of similar sections (for example trays in a distillation columns) or equipment in which variables are a function of time and location can be described dynamically by a section model in order to characterize the distributed character of the equipment. Typical dynamic behavior of a distributed system is ... 

The phenomenon of overshoot or inverse response results from the zero in the above example and will not occur for an overdamped second-order transfer function containing two poles but no zero. These features arise from competing dynamic effects that operate on two different time scales (ti and T2 in Example 6.2). For example, an inverse response can occur in a distillation column when the steam pressure to the reboiler is suddenly changed. An increase in steam pressure ultimately will decrease the reboiler level (in the absence of level control) by boihng off more of the liquid. However, the initial effect usually is to increase the amount of frothing on the trays immediately above the reboiler, causing a rapid spillover of liquid from these trays into the reboiler below. This initial increase in reboiler liquid level, is later overwhelmed by a decrease due to the increased vapor boil-up. See Buckley et al. (1985) for a detailed analysis of this phenomenon. 

There are also control implications. As we will see in later chapters, the dynamic controllability of a reactive distillation column is improved by adding more reactive trays. Thus, as is true in many chemical processes, there is a conflict between steady-state design and dynamic controllability. The column with 9 reactive trays is the steady-state economic optimum. However, as we will demonstrate in Chapter 10, a column with 13 reactive trays provides better dynamic performance in terms of the ability to maintain conversion and product purities in the face of disturbances in throughput and feed compositions. 

However, there are two parameters that give counterintuitive results. The most important of these is the number of reactive trays. More trays does not necessarily improve the steady-state economics of a reactive distillation column. However, the effect of more reactive trays on the dynamic performance of a reactive column is distinctly different, as we will demonstrate in Chapter 10. 

Despite clear economic incentives for reactive distillation systems, there are relatively few articles that study the dynamics and control of reactive distillation columns. Al-Arfaj and Luyben give a review of the literature dealing with the closed-loop control of reactive distillation systems. Several control structures for an ideal two-product reactive distillation system and real chemical systems " have been proposed. One important principle in the control of reactive distillation is that we need to control one intermediate composition (or tray temperature) in order to maintain the stoichiometric balance between the two reactant components. ... 

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