Temperature control tray selection 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. 

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. 

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. 

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. 

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. 

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). 

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. 

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... 

The maximum and the minimum of this function as suggested by Mooie are selected as the two tray locations for the temperature control points. For an example, Figure 9.10 shows the Z, for the Inventory Strategy 1 with two manipulated variables of aqueous reflux and reboiler duty. From this figure, temperatures at Stage 6 and Stage 16 are selected as the two controlled... 

The typical procedure for selecting which tray to control is to look at the steady-state temperature profile in the column at the base-case conditions, as illustrated in Fig. 6.10. We look for a location in the column where there are large temperature changes from tray to tray. In Fig. 6.10, the slope of the temperature profile is the steepest in the... 

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