Temperature control tray location

A final method for selecting a temperature control tray location is to use singular value decomposition (SVD) techniques. This approach was first presented by Downs and Moore and is summarized on p. 458 in Luyben and Luyben (1997). A steady-state rating program is used to obtain the gains between the two manipulated variables and the temperatures on all trays. The gain matrix is decomposed by using SVD to find the most sensitive tray locations. This method requires more computation than the others. 

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. 

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. 

Minimum Product Variability Criterion Choose the Tray that Produces the Smallest Changes in Product Purities When it is Held Constant in the Face of Feed Composition Disturbances. Several candidate tray locations are selected. The temperature on one specific tray is fixed, and a second control degree of freedom is fixed such as reflux ratio or reflux flow rate. Then the feed composition is changed over the expected range of values, and the resulting product compositions are calculated. The procedure is repeated for several control tray locations. The tray is selected that produces the smallest changes in product purities when it is held constant in the face of feed composition disturbances. 

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. 

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... 

When pressure is controlled at the temperature control tray, the speed of response of the temperature instrument can vary considerably with tray location, and is normally slower. 

A two-temperature control structure is considered first. Selecting the vapor boilup and reflux ratio as manipulated variables, the control problem then is to find the best locations for the two temperature control trays. Figure 12.50 shows the steady-state changes in tray temperatures throughout the column for several small changes in vapor boilup and reflux ratio. 

Column Bottom Temperature. The bottom temperature is often controlled on the reboiler outlet line with a control valve in the heating medium line. The control point can also be on a bottom section tray. Care must be exercised in location of the temperature control point. It is recommended, especially for large columns, that a cascade arrangement be used. The recommended scheme has a complete flow recorder/controller (FRC) in the heating medium line including orifice and control valve. The set point of this FRC is manipulated by the temperature recorder/controller (TRC). This eliminates the TRC from manipulating the control valve directly (recall that temperature is the most difficult parameter to control). This makes for smoother control for normal operations. Also, it is handy for startup to be able to uncouple the TRC and run the reboiler on FRC for a period. 

If the feed composition and the column pressure are constant, temperature can be used as an indirect measure of composition. When the bottom product composition is being controlled, the temperature sensor is located in the lower half of the column and when overhead composition is controlled, in the upper half of the column. The temperature sensor should be located on a tray that strongly reflects changes in composition (Figure 2.84). When two compounds of relatively close vapor pressures are to be separated, two temperatures or a temperature difference can be used instead of a single sensor. This configuration can also be used to eliminate the effects of column pressure variations. 

How do we sel ect the best tray location for this temperature control The next section outlines the normal procedure and illustrates its application with a specific example. 

Pressure variations can be compensated for by measuring both temperature and pressure at a tray location and computing a pseudocomposition signal. This computed composition signal (pressure-compensated temperature) can then be controlled ... 

It is advisable to use the plant set points in building a model. For example, it is possible that a column simulation might involve the specification of the reflux ratio and bottoms flow rate because such specifications are (relatively) easy to converge. It is quite likely that the column may be controlled by using the temperature at some specific location (e.g., the temperature of tray 48). This specification should be used in building the model. In this case we do not know the set points used for controlling the column, but we do have sufficient information to allow us to compute the reflux ratio from plant flow data R = 11.6). Finally, the bottom product flow is specified as equal to the adjusted value reported above (17,999 kg/h). 

A pilot-scale distillation column located at the University of Sydney, Australia is used as the case study [60]. The 12-tray distillation column separates a 36% mixture of ethanol and water. The following process variables are monitored temperatures at trays 12, 10, 8, 6, 4, and the reflux stream, bottom and top levels (condenser), and the flow rates of bottoms, feed, steam, distillate and reflux streams. The column is operated at atmospheric pressure using feedback control. Three variables are controlled during the operation top product temperature, condenser level, and bottom level. Temperature at tray 8 is considered as the inferential variable for top product composition. To maintain a desired product composition, PI controllers cascaded on flow were used to manipulate the reflux, top product and bottom product streams. 

Temperature control loops can be applied to control the temperature of a stream exiting a heat exchanger, of a tray in a distillation column, or of a CSTR. Figure 15.32 shows a schematic of a temperature controller applied to control the temperature of a process stream leaving a gas-fired heater. The sensor is an RTD element placed in a thermowell located in the line leaving the heater. 

When the system distilled is fairly uncommon, temperature measurement connections should be placed in locations that can serve as alternative control points in case the design control tray is not the best control tray (98). 

Mislocated temperature control point Often, the temperature control point is located on an incorrect tray, especially if the system distilled is uncommon. It is worthwhile to try hooking the controller to other temperature-measurement points and checking if this improves performance. Having a reasonable estimate of the expected temperatures at these other points is essential for the success of this technique. Further discussion is in Sec. 18.2. 

Another djmamic consideration is associated with the column feed. Glenerally, most disturbances enter the column at the feed. If the temperature controller is far from the feed, the disturbance may propagate a long way before the corrective action is taken. On the other hand, if the control tray is located near the feed, it will tend to take excessive corrective action and may be imstable. This consideration is most important when feed composition changes are frequent, and is detailed elsewhere (400). 

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. 

Figure 18.4 Effect of variation in control tray temperature on product composition with a correctly and an incorrectly located control tray. Same column as in Fig. 18.3a. (a) Overhead composition (6) bottom composition. (Reprinted by permission. Copyright Instrument Society of America 1980. From T. L. Tolliver and L. C. McCune, In Tech- ptember 1980.)...

In sharp splits such as that shown in Fig. 18.5, neither a top section temperature controller nor a bottom section temperature controller will be capable of adequately a controlling both product purities over the entire operating range. In most cases, one of the two products is selected as the more important, and the control tray is located in the section from which this product exits. The other product purity is allowed to vary. Alternatively, an average temperature control scheme can be used (58, 59, 68) and effectively overcome the problem. This is described in the next section. 

The effect of pressure on the control temperature can be minimized by adequate selection of the temperature control location. Generally, all column temperatures have a similar sensitivity to pressure, but the sensitivity of temperature to composition varies widely from tray to tray. Therefore, locating the control temperature in a region highly sensitive to composition reduces its relative sensitivity to pressure changes (see Fig. 18.4). 

A good knowledge of the column temperature profile, coupled with a good choice of control trays, can sometimes make the differential temperature control technique work even in the presence of nonkeys and when neither product is pure. Vermilion (411) made this system work in another deisobutanizer, the feed to which contained a substantial fraction of both light and heavy nonkeys. The bottom sections contained 40 trays Vermilion used tray 14 [from the bottom this is similar to Webber (418)] as the first temperature control location, and tray 34 as the second. In that case, composition and temperature variations near the feed were relatively small (411). Figure 18.8c demonstrates the importance of correctly choosing the differential temperature measurement location. 

Boyd (58, 59) applied a double differential temperature control to a column producing high-purity products. Although the main purpose of this system was to optimize the location of the control tray, it was also effective in compensating for both pressure and differential pressure variations. This system is described in detail in Sec. 18.5. 

A first control scheme proposed in [90] is shown in Fig. 10.26. In this scheme, product purities of methyl acetate (MeAC) and water (HjO) are inferred from temperatures on trays 3 and 12, respectively, and the feed rates of methanol (MeOH) and acetic acid (AcH) are used as manipulated variables. For this configuration, three different temperature profiles exist with identical temperature values at the sensor locations but different feed rates and completely different product compositions. The solid line in Fig. 10.26 represents the desired temperature profile with high conversion. This situation corresponds to input multiplicity as introduced at the beginning of section 10.2 on multiplicity and oscillations. Here, the same set of output variables (temperatures) is produced by (three) different sets of input variables (feed rates). Because the steady state values of the output variables are fixed by the given setpoint of the controllers, this input multiplicity will lead to steady state multiplicity of the closed loop system as illustrated in Fig. 10.27. 

Temperature profiles after a stepwise increase of the heating rate are shown on the right side of Eig. 10.29. These profiles show distinct nonlinear wave characteristics as discussed in the previous section. Therefore the process is sensitive to disturbances and composition control is required. Again focus is on an inferential control scheme. Measured variables are the temperatures on trays 4 and 60, which are located within the upper and the lower ware front. Hence, they show good sensitivity to disturbances. Manipulated variables are the heating rate and the reflux ratio. Eor this process neither input nor output multiplicities occur. 

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