Feed Tray Dynamics

The feed tray differs from the basic tray in two ways (1) it has an additional flow, the feed flow and (2) the thermal condition of the feed may cause the vapor and liqtiid rates above the feed tray to be significantly different from those below Ae feed tray. Let us first write an equation for the summation of steady-state flows at the feed tray  

We can next write a material-balance equation fix the nwre volatile component (perfect mixing assumed)  

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The third factor is the simplified, steady-state treatment of the feed tray. For purposes of this chapter, we do not believe this introduces a seriotis error. Feed tray dynamics will be dealt with more rigorotisly in Chapter 18. 

In this numerical example, the temperature control tray is located in the lower section of the column, which results in slow dynamics between temperature and reflux. In other columns where the temperature control tray is high in the column, the use of reflux for temperature control should work better than in this example. The phase of the feed stream would also affect the dynamics between feed flow rate and tray temperature. A liquid feed is used in the numerical example, so it affects temperature below the feed tray fairly quickly. If the feed were vapor, it would not affect temperatures below the feed tray as quickly, but would affect temperatures above the feed tray very quickly. 

Distillation operation Feeding on the optimum feed tray minimizes energy consumption for a given desired separation. However, studies [4] have shown that feeding on a non-optimum feed tray produces better dynamic controllability. This... 

With all feed conditions and the column configuration specified (number of trays in each section, tray holdup in the reactive section, feed tray locations, pressure, and desired conversion), there is only one remaining degree of freedom. The reflux flowrate is selected. It is manipulated by a distillate composition controller to drive the distillate composition to 95 mol% C. The vapor boilup is manipulated to control the liquid level in the base. Note that the distillate and bottoms flowrates are known and fixed as the dynamic model is converged to the steady state that gives a distillate composition of 95 mol% C. The composition of the bottoms will be forced by the overall component balance to be 95 mol% D. 

The control structure with feed tray manipulation ( coordinated control ) gives fast dynamics in the product composition, as can be seen in Figure 18.14 (solid lines) where the top and bottoms compositions return to setpoint in less than lOh. In contrast, the conventional control strucmre shows a little slower dynamic response with the product compositions taking more than 10 h to return to their setpoints. Of more importance, the coordinated control stmcmre results in a 21% energy savings compared to the conventional control structure, which can be seen from the smaller vapor rate in Figure 18.14. 

FIG. 13-109ii Resp onses after a 30 percent increase in the feed flow rate for the nmlticomponent-dynamic-distillation example of Fig. 13-100. Alcohol mole fractions on several trays. (Frokopakis and Seider, Am. Inst, Chem. Eng. J., 29, 1017 (1983). ]... 

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. 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

Generally, trays work better in applications requiring high flows, because plate efficiencies increase with increased vapor velocities, and therefore increase the influence of the reflux to feed ratio on overhead composition. Column dynamics is a function of the number of trays, because the liquid on each tray must overflow its weir and work its way down the column. Therefore, a change in composition will not be seen at the bottoms of the tower until some time has passed. 

A dynamic simulation of this column using HYSYS was used to explore the dynamics of the process for the two cases where different tray temperatures are controlled. Either tray 6 or tray 14 temperature is controlled by manipulating reboiler heat input. Reflux flowTate is held constant. Disturbances are step changes at time equals 5 minutes in feed flowrate (25 percent increase) or feed composition. The feed composition disturbance is a drop in the HHK component in the feed (normal octane changed from 10 mol % to 0 mol % while normal pentane changed from 45 mol % to 55 mol %). 

Figure. 14 Dynamic response to HHK feed composition disturbance, (a) With control tray 6 (i) with control tray 14.

Pure component physical property data for the five species in our simulation of the HDA process were obtained from Chemical Engineering (1975) (liquid densities, heat capacities, vapor pressures, etc.). Vapor-liquid equilibrium behavior was assumed to be ideal. Much of the flowsheet and equipment design information was extracted from Douglas (1988). We have also determined certain design and control variables (e.g., column feed locations, temperature control trays, overhead receiver and column base liquid holdups.) that are not specified by Douglas. Tables 10.1 to 10.4 contain data for selected process streams. These data come from our TMODS dynamic simulation and not from a commercial steady-state simulation package. The corresponding stream numbers are shown in Fig. 10.1. In our simulation, the stabilizer column is modeled as a component splitter and tank. A heater is used to raise the temperature of the liquid feed stream to the product column. Table 10.5 presents equipment data and Table 10.6 compiles the heat transfer rates within process equipment. 

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. 

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 ... 

Now let us apply the capacity-based approach. Positive and negative 10 percent disturbances are made in the fresh feed flow rate Fg and in the fresh feed composition Zq. Dynamic simulations (confirmed by frequency-domain analysis, to be discussed in Chapter 10) show that the variability in product quality xb is decreased by increasing reactor volume or by decreasing the number of trays in the stripper. 

Figure 18.3 shows examples of applying this procedure to benzene-toluene columns with different feed points and different feed compositions. Accordingly, trays 7,10, and 5 or 10 are the best control trays in Fig. 18.3a, b, and c, respectively. Figure 18.4, based on the column in Fig. 18.3a, shows how a variation in control tray temperature affects product composition with a correctly located and an incorrectly located control tray. When the temperature variation is caused by a change of pressure or in the concentration of a nonkey component, it will produce a steady-state offset in product composition. A disturbance in the material or energy balance will cause a similar temperature variation until corrected by the control action in this case, the offset will only be temporary. Figure 18.4 shows that the offset in either case is minimized when the control tray is selected in accordance with Tolliver and McCune s procedure (403). A dynamic analysis by these authors (403) indicated that the control tray thus selected tends to have the fastest, most linear dynamics. 

Several of the control loops in Figure 21.35 are provided for inventory control, in three level-control loops and two pressure-control loops. Note, however, that the pressure in V-100 is assumed to be constant and loop PC-1 is not simulated by HYSYS.Plant. In contrast, pressure control is crucial to maintain stable internal flows in the column. Finally, because the feed flow rate and temperature controllers are decoupled from the rest of the process, they are not included in the C R analysis. Consequently, the interactions to be analyzed involve the four valves V-7, V-9, V-10, and V-12, and four controlled variables Xdj, JC/u (mole fractions of benzene in the distillate, MCB in the bottoms, and HCl in the absorber overhead stream, respectively) and Tg, the recycle temperature. Note that to improve the dynamic performance, the temperature of tray 4 is controlled rather than the distillate benzene mole fraction. 

AbSOrbBr. A column with 11 stages operates at 1 atm pressure at the top. A tray pressure drop of 0.2 psi is specified in order to satisfy the requirement that the specified pressure drop is greater than the pressme drop calculate from the hydraulics when exporting to Aspen Dynamics. The design feed gas is 13,100 kmol/h and is compressed to 1.136 atm and fed at the bottom of the absorber. The specified recovery of carbon dioxide is 90%, which corresponds to an absorber exit gas composition of 1.3 mol% CO2. 

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