Column deadtime

We will neglect any delay time (deadtime) in the vapor line from the top of the column to the reflux drum and in the reflux line back to the top tray (in industrial-scale columns this is usually a good assumption, but not in small-scale laboratory columns). Notice that y T is not equal, dynamically, to x. The two... 

The procedure has been tested primarily on realistic distillation column models. This choice was deliberate because most industrial processes have similar gain, deadtime, and lag transfer functions. Undoubtedly some pathological transfer functions can be found that the procedure cannot handle. But we are interested in a practical engineering tool, not elegant, rigorous all-inclusive mathematical theorems. 

Column base level (or reboiler level in a kettle reboiler) can be held by the flowrate of the bottoms, the vapor boilup, or the feed (if the feed is partially liquid and the stripping section does not contain too many trays). Since the typical hydraulic lag is 3 to 6 seconds per tray, a 20-tray stripping section introduces a deadtime of 1 to 2 minutes in the feed-to-base-level loop. Because of these hydraulic lags, reflux is only very7 rarely used to control base level. For this loop to work successfully, the column must be relatively short (less than 30 trays) and the holdup in the base must be large (more than 10 minutes). 

However, very few distillation columns use this ideal dual-composition control stmcture. There are a number of practical reasons for this. Composition analyzers are often expensive to purchase and have high maintenance costs. Their reliability is sometimes inadequate for on-line continuous control. They also introduce deadtime into the control loop if chromatographic methods are used. 

The program is run to make sure everything works okay without a lag or a deadtime in the loop. Now we back up and insert a deadtime element on the flowsheet between the column and the temperature controller. The reason for installing the controller initially without the deadtime element is to avoid initialization problems that sometime crop up if you attempt to install the deadtime and the controller all in one shot. 

The equations derived above are implemented in Aspen Dynamics using Flowsheet Equations. Figure 16.7 shows the syntax required to use the measured pressure and temperature on Stage 55 to estimate the C4 composition on Stage 55. This calculated variable is the input signal to the deadtime block. The control signal line from the column icon to the deadtime block is deleted on the process flowsheet diagram. 

Composition measurements often involve the use of a chromatographic column, and these devices exhibit significant deadtimes because of both sample-line and column-cycle... 

Figure 5.8 shows the control structure developed for this system. Conventional PI controllers are used for all flows, pressures, and temperatures. Proportional controllers are used for all liquid levels. Relay-feedback tests are run on the two temperature controllers to determine ultimate gains and periods, and Tyreus-Luyben tuning is used. Each temperature controller has a 1-min deadtime in the loop. Reflux ratios are held constant in each column (2.84 in the low-pressure column and 3.11 in the high-pressure column). 

Both the temperature on Stage 9 and the column pressure are used to calculate Tpc, which is the process variable signal fed to the TC2 temperature controller. In Aspen Dynamics, this is easily achieved by using flowsheet equations, as shown in Figure 6.27. The last equation calculates the signal fed to the deadtime element in the TC2 loop. Figure 6.28 gives the control structure. 

All level controllers are proportional only with a gain of 2. The trays selected for temperature control are located near the bottom of the columns, where the temperatures are changing the most rapidly from tray to tray (see Figure 7.9). A 1-min deadtime is inserted in each temperature loop. Relay-feedback tests and Tyreus-Luyben tuning are used to obtaining... 

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. 

The Aspen Plus file of this extractive distillation system is exported to Aspen Dynamics after dynamic parameters are specified (equipment sizes). Figure 11.8 shows the control stmcture developed for this system, which is based on the extractive distillation control structure proposed by Grassi. Relay-feedback testing and Tyreus-Luyben tuning of the temperature loops give the controller parameters given in Table 11.2. The temperature controllers have 1 min deadtimes in the loops. Reflux ratios are held constant in each column (3.44 in the extractive column and 1.61 in the methanol column). 

Tray temperatures are controlled in both columns. A 1 min deadtime is included in the temperature loops. In the water system, a single temperature in the methanol column is controlled. In the DMSO and chlorobenzene systems, an average temperature is controlled because of the sharp temperature profile. 

It is often said that derivative action should only be used in temperature controllers. It is true that temperatures, such as those on the outlet of fired heater and on distillation column trays, will often exhibit significantly more deadtime than measurements such as flow, level and pressure. However this is not universally the case, as illustrated in Figure 3.7. Manipulating the bypass of the stream on which we wish to install a temperature controller, in this case around the tube side of the exchanger, will provide an almost immediate response. Indeed, if accurate control of temperature is a priority, this would be preferred to the alternative configuration of bypassing the shell side. 

There are level controllers that have substantial deadtimes. Consider the process in Figure 4.19. Level in the base of the distillation column is controlled by manipulating the reboiler duty. Unlike most level controllers it would be difficult (and probably umeliable) to predict the relationship between F Vand MV. Further the reboiler introduces a large lag. The only practical way of identifying the process dynamics would be a plant test, as described in Chapter 2. The controller would then be tuned by applying one of the methods described in Chapter 3. This, unlike most level controllers, is likely to benefit from the use of derivative action. 

Figure 9.2 shows the potential economic beneht. Point A represents a typical benchmark with a 6/x ratio of 4. This might be from a process lag of 5 minutes and a deadtime of 20 minutes - both quite reasonable dynamics for a process such as a distillation column with a chromatograph on the distillate product rundown. In these circumstances an inferential could be expected to reduce the deadtime by at least 10 minutes (point B). Doing so would allow the controller to be tuned more quickly and would result in a reduction by about 33 % in off-spec production. 

Dynamic compensation is likely to be necessary to ensure that the reflux and steam flows are adjusted at the right time. The method for tuning these deadtime/lead-lag algorithms is described in Chapter 6. Part of this procedure involves steptesting the DV, in this case feed rate, to obtain the dynamic response of the PV, in this case tray temperature. This can present a problem on some columns. 

Success was claimed for a similar scheme based on on-stream analysers (Reference 3). Here the PV controlled by reboiler duty was defined as (HKj — LK/,) while that controlled by distillate flow was defined as the average of HKj and LKh- It is likely that analyser deadtime was large compared to the dynamics of the process and masked any differences between top and bottom of the column. 

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