Feed tray location optimization

Finally, the case of easy separation between the heavy reactant and the heavy product is explored. The relative volatilities are ac = 16, ua = 8, as = 4, and ao = 1- Feed tray location optimization gives Nf a = 9 and Nps = 12. In this case, 14.7% energy can be saved (from 0.0365 to 0.0311 kmol/s Table 18.3). Once again heuristic H2 applies, and the percentage of energy saved is also similar to the high activation energy counterpart (Table 18.2). 

The solution to the RD problems results in the optimum number of trays, the optimal feed tray location, reflux ratio, condenser and reboiler duties and liquid hold-ups on each tray. Since the model contains both continuous e.g. temperature and composition) and discrete i.e. number of trays) design variables, it should be solved by MINLP optimization technique. 

Ciric and Gu (1994) present a MINLP-based approach for the design of RD columns for systems where multiple reactions take place and/or where reactive equilibrium or thermal neutrality caimot be assured. This method is based on the combination of a rigorous tray-by-tray model and kinetic-rate-based expressions to give basic constraints of an optimization model that minimizes the total annual cost. The major variables are the number of trays in the column, the feed tray location, the temperature and composition profiles within the column, the reflux ratio, the internal flows within the column and the column diameter. 

State the feasible splits for the equimolar mixture of acetone(l), benzene(2), chlo-roform(3), and toluene(4). For each spht, determine the necessary tray numbers and liquid and vapor flow rates in the top and bottom sections of the column at optimal location of the feed tray and optimal distribution of the component and reflux excess coefficients and product purities as in item 1. 

In all three MIDO iterations the primal problem resulted in a positive definite matrix Q indicating that both outputs are participating in the optimal control structure. In the process structure there are 30 possible feed tray locations and for the feed located on tray k there are 31 —k) alternatives for the reflux tray locations. Hence the total number of discrete alternatives is XI (31 — fc) = 465. Despite this large number of alternative discrete decisions the algorithm... 

Since there is no recycle flow back to the first preconcentrator column, this standalone column can be optimized first with two product specifications and two design variables of the total number of stages and feed tray location. One of the product specifications is the selection of the XDl composition by varying the reflux ratio. The other product specification is the bottoms water composition at 0.999 by varying the reboiler duty. 

Kirkbride s method is used to find the optimal feed tray location Np. 

The lower right graph in Figure 6.19 shows that there is an optimal feed tray location. Figure 6.21 shows the effect of feed tray locations on temperature and composition profiles. This optimum location is the top of the reactive section. Above this point, the effect of the rectifying section to keep the reactant in the reactive sections is lessened, and below this point there is an effect similar to reducing the number of reactive trays. Either position will increase the vapor boHup. 

TABLE 16.2 Results for Reactive Distillation Columns with Optimized Feed Tray Location... 

Finding the optimal feed locations can be formulated as an optimization problem in which the vapor rate is minimized by varying the feed tray locations. 

Figure 18.4 Feed tray locations and corresponding energy consumption (compared to base case) from optimization results.

Second, the optimization is carried out for a 40% decrease in the feed flowrate. The optimal feed trays become Npjs, = 12 and Nf,b = 15, and a 9% savings in the vapor rate is observed. As pointed out earlier, this has the same effect as that from reaction rate increases, and we should move the feed trays closer to each other. The results clearly indicate that we should change the feed tray locations as the production rate changes because 9% or 28% energy can be saved by simply moving the feed trays. The next question then becomes, how can we implement such a control strategy The coordinated control of Doukas and Luyben shed some light in this direction. ... 

The results presented in this section clearly show that the concept of optimal feed tray location can be carried over to process operation and control. With a simple modification in the control structure, improved closed-loop performance can be achieved while realizing substantial energy savings at the same time. 

In summary, for the system with relative volatilities of ac/aA/otB/cto = 8/4/2/1, we should move the feed locations of the heavy reactant downward and the light reactant upward. In terms of the search space for the optimal feed trays, we have the following heuristic ... 

Only one specific example has been explored thus far. It is interesting to see whether the results can be extended to different cases (e.g., different relative volatilities) and how this vapor-liquid equilibrium change will impact the location of optimal feed trays and the percentage of energy savings. Note that for every case studied, the column is redesigned using the procedure in Section 18.1. This means the columns may have different Nr, Ns, and Nrx and the location of the feed trays are described in terms of their relative position in the reactive zone. 

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