Temperature control tray selection

If tray temperatures are to be used, the issue is the selection the best tray on which temperature should be held constant. This problem has been discussed in the distillation literature for over a half century, and several alternative methods have been proposed. All of these methods use steady-state simulations to assess some aspect of performance, given 

STEADY-STATE CALCULATIONS FOR CONTROL STRUCTURE SELECTION 

It is important to note that all of these methods use only steady-state information, so steady-state process simulators such as Aspen Plus can be easily used to perform the calculations. The methods all require that various variables are held constant, while other variables change. For example, two product compositions can be held constant, or a tray temperature and reflux flow rate may be held constant. The Design Spec/Vary feature in Aspen Plus is used to achieve the fixing of the desired independent variables and the calculation of all the remaining dependent variables. 

Invariant Temperature Criterion With Both the Distillate and Bottoms Purities Fixed, Change the Feed Composition Over the Expected Range of Values. Select the Tray Where the Temperature Does Not Change as Feed Composition Changes. The difficulty with this method is that there may be no constant-temperature tray for all feed compositions changes. This is particularly true in multicomponent systems where the amounts of the nonkey components can vary and significantly affect tray temperatures, especially near the two ends of the column. 

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. 

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Temperature Control Tray Selection. There are a number of methods for selecting the best tray for temperature control. The easiest and most frequently used is to simply look at the temperature profile and select a tray where temperamres are changing significantly from tray-to-tray. 

Criteria for selection of best temperature control tray... 

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. 

Figure 15.5 gives the temperature profile in the column at design feed flow rate conditions. Stage 35 is selected as the temperature control tray. Note that the reflux must come down 34 trays to affect this temperature. Column feed has to come down only 8 trays, so we expect the dynamics between feed and Stage 35 temperature to be faster than the dynamics between reflux and Stage 35 temperature. 

We have dealt with many of the problems that can arise with tray temperature control by selecting the optimum trays. There remain some other issues that we need to address with... 

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. 

Using the reflux ratio and vapor boilup as the manipulated variables, the two-temperature control structure is shown in Figure 12.80. Two temperature control trays, tray 85 and tray 5, are selected based on SVD analysis. Using relay-feedback tests, values of ultimate... 

Use the nonsquare relative gain (NRG) to select temperature control trays. The larger row sums of the NRG indicate a potential temperature control tray. Note that the temperatures with sign reversal (Fig. 13.3) cannot be used as controlled variables. 

In the previous section, two temperature control trays are selected from the NRG analysis. Because the bottoms product composition is one of the controlled variables, the other controlled variable is the temperature further away from the acetate withdrawal ends. The fourth column of Table 13.5 gives the steady-state gain matrices of these five 2x2 systems. One temperature and one composition are controlled with two manipulated variables heat input and feed ratio. 

But why is this a good way to select the best control tray It works because we want to find a tray where temperature is significantly affected by the compositions of the LK and HK components. Since temperature is also affected by other variables (pressure and other components), it is important that the effects of these variables are small compared with the effects of the compositions of the key components. 

However, sometimes selection of the appropriate controlled variable is not so easy. For example, in a distillation column it is frequently difficult and expensive to measure product compositions directly with sensors such as gas chromatographs. Instead, temperatures on various trays are controlled. The selection of the best control tray to use requires a considerable amount of knowledge about the column, its operation, and its performance. Varying amounts of non-key components in the feed can significantly affect the best choice of control trays. 

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. 

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). 

The flowsheet now has four controller face plates displayed, as shown in Figme 7.20. We have one more controller to add, a temperature controller that holds the temperature on a selected tray by adjusting the reboiler heat input. 

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