Throughput parameter

Two dimensionless variables play key roles in the analysis of single transition systems (and some multiple transition systems). These are the throughput parameter [see Eq. (16-129)] and the number of transfer units (see Table 16-13). The former is time made dimensionless so that it is equal to unity at the stoichiometric center of a breakthrough cui ve. The latter is, as in packed tower calculations, a measure of mass-transfer resistance. 

The variable Ti defined by Eq. (16-127) or (16-129) is a throughput parameter, equal to unity (hence, the I subscript) at the time when the stoichiometric center of the concentration wave leaves the bed. This important group, in essence a dimensionless time variable, essentially determines the location of the stoichiometric center of the transition in the bed at any time. 

The integration of Eq. (16-140) or (16-141) as an indefinite integral will give an integration constant that must be evaluated to center the transition properly. The material balance depicted in Fig. 16-26 is used. The two shaded regions must be of equal area if the stoichiometric center of the transition is located where the throughput parameter is unity. Thus, we have... 

The throughput parameter Q (Eq. 15.3) describes the dimensionless throughput, parameter K (Eq. 15.4) describes pressure build-up, and the PI parameter (Eq. 15.5) describes energy conversion. 

The adsorption equilibrium constant is K, with K = k Jk a-The dimensionless throughput parameter is defined as... 

Optimization of an existing SMBR system Maximizing the purity of a fraction and the yield of a compormd and minimizing the solvent consumption are chosen as the three objective functions. Six decision variables were used in this optimization study, the switching time (fj), the number of columns in sections II, III, and IV, the amormt of raffinate produced, and the eluent consumed. Since the optimization of an existing system is considered, the number of columns, their lengths and their diameters were kept fixed, but the sensitivity of the results to the number of columns on the Pareto shift was studied. The flow rate in section II and the temperature of the columns were also kept constant in order to allow a comparison of the optimum results at constant operation cost. Of the two throughput parameters, the raffinate flow rate (j3) was selected as a decision variable, in order to determine the optimum raffinate flow rate for a constant feed flow rate. 

The number of column void-volumes of fluid that have passed through the column, divided by the distribution ratio, also gives the throughput parameter ... 

Fig. 5 shows the volumetric efficiency t1v x), throughput parameter Nq(x) and gradient Nq (x) for the case of yc/H = 0.1 and Ce = 0.5. The full lines for Nq(x) and Nq (x) correspond to the optimum divergence angle X = 1.54° and, as shown, the gradient Nq (x) is virtually constant indicating uniform draw-down in the hopper. The volumetric efficiency decreases from the rear to the front of the feeder as is expected. 

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