Feed flow rate, optimization

The vertex of a separation region points out the better operating conditions, since it is the point where the purity criteria are fulfilled with a higher feed flow rate (and so lower eluent flow rate). Hence, in the operating conditions specified by the vertex point, both solvent consumption and adsorbent productivity are optimized. Comparing the vertex points obtained for the two values of mass transfer coefficient, we conclude that the mass transfer resistance influences the better SMB operating conditions. Moreover, this influence is emphasized when a higher purity requirement is desired [28]. 

Figure 11 Optimization of feed flow rate for catalytic hydrogenation using temporary on-line LC.

Optimisation may be used, for example, to minimise the cost of reactor operation or to maximise conversion. Having set up a mathematical model of a reactor system, it is only necessary to define a cost or profit function and then to minimise or maximise this by variation of the operational parameters, such as temperature, feed flow rate or coolant flow rate. The extremum can then be found either manually by trial and error or by the use of numerical optimisation algorithms. The first method is easily applied with MADONNA, or with any other simulation software, if only one operational parameter is allowed to vary at any one time. If two or more parameters are to be optimised this method becomes extremely cumbersome. To handle such problems, MADONNA has a built-in optimisation algorithm for the minimisation of a user-defined objective function. This can be activated by the OPTIMIZE command from the Parameter menu. In MADONNA the use of parametric plots for a single variable optimisation is easy and straight-forward. It often suffices to identify optimal conditions, as shown in Case A below. 

Remark 1 Since the light and heavy key recoveries of each column are treated explicitly as unknown optimization variables, then the cost of each nonsharp distillation column should be a function of its feed flow rate, feed composition, as well as the recoveries of the key components. 

Specification of the separation. A separation is specified by defining column feed flow rate and composition, overhead solute concentration (alternatively, solute recovery), and the concentration of solute (if any) in the lean solvent. If the purpose of absorption is to generate a specific solution, as in acid manufacture, the solution concentration completes the separation specification. For all other purposes, one specifying variable (e.g., rich solvent concentration or solvent flow rate) remains to be specified and is usually set by optimization as outlined below. 

Since the unit productivity is given by the product of the reactant feed concentration and the feed flow rate, the competing effect of an increasing reactant feed concentration and a decreasing feed flow rate, that is a decreasing difference rm-rm, leads to a problem of optimization. 

In all cases, using 5 colinnns, the optimal column configurations are found to be 1/2/1/1 and 1/1/1/2—I/I/2/1-1/1/2/1—1/2/1/1 for the SMB and 4 subinterval Varicol unit, respectively. It can be observed that for fixed purity specifications, both the SMB and the Varicol processes require to increase the eluent consumption in order to increase the feed flow rate. Secondly, the Varicol process consumes less eluent, D than the SMB process for the same feed flow rate, F or equivalently for the same eluent consumption, D, the Varicol process can treat more feed, F. However, the extent of improvement depends on the purity specifications. The more stringent the purity requirement, the larger the improvement achieved by Varicol over SMB. For example, at D = 5.6 ml/min, the improvement in production rate, F of Varicol over SMB is 10%, 25% and 127% for a purity requirement both in the extract and in the raffinate streams of 90%, 95% and 99%, respectively. Finally, it is seen from Figure 3 (for the case of purity requirement of 95%)... 

The separation problem examined in this case requires the simultaneous maximization of the raf ate (Pb) and the extract purity (Pe.) for a given feed flow rate, F, eluent flow rate, D and fixed configuration of the unit, for the same chiral separation considered in section 3.2. This optimization problem in the case of PowerFeed operation can be represented mathematically as follows ... 

We adopt the input/output data-based prediction model using the subspace identification technique. To find the correlation between the inputs and outputs, we need to obtain the input and output data. On the basis of the triangle Aeoiy[6], the optimal feed flow rate ratios at steady state are calculated. Then, the pseudo random binary input signal is generated on the basis of this optimal value. Figure 1 compares the output from the identified model (dot) with that from the first principles model (solid curve). Clearly, we observe that the identified model based on the subspace identification method shows an excellent prediction performance. The variance accounted for (VAF) indices for both outputs are higher than 99%. The detailed identification procedure can be founded in the literature [3,5,9,10]. 

For those cases where the permeability of reactant A is in between those of the two products, B and C, both the conversion and extent of separation increase with increasing permeation rate or permeation to reaction rate ratio (Table 11.9). The corresponding optimal compressor load (recycle flow rate to feed flow rate) also increases with the rate ratio. The top (permeate) stream is enriched with the most permeable product (i.e., B) while the bottom (retentate) stream is enriched with the least permeable product (i.e., C). It is noted from Table 11.9 that the optimal compressor loads for achieving the highest conversion and extents of separation can be quite different and a decision needs to be made for the overall objective. 

The model predictive control used includes all features of Quadratic Dynamic Matrix Control [19], furthermore it is able to take into account soft output constraints as a non linear optimization. The programs are written in C++ with Fortran libraries. The manipulated inputs (shown in cm Vs) calculated by predictive control are imposed to the full nonlinear model of the SMB. The control simulations were made to study the tracking of both purities and the influence of disturbances of feed flow rate or feed composition. Only partial results are shown. 

The decision variables used for the optimization of the reactor must be selected among the operating ones. After considering industry requirements, the effect of each of the operating variables on the objective function and the easiness of how these variables can be changed in the plant, the feed flow rate of hydrogen (FAo) and the reactor feed temperature (Tfo) were chosen as the decision ones. Thus the optimization routine searches for the values of FAo and Tfo that, with the current value of o-cresol flow rate, lead to maximal reactor profit. 

Since the feed flow rate of hydrogen and the reactants temperature are searched for, the upper and lower bounds stipulated for these variables in the optimization algorithms were selected according to the hydrogenation reaction stoichiometry and practical possible temperatures. For the optimizations here accomplished, the o-cresol feed rate was considered to be 1.29 kmol/h. In this way. Table 1 shows the lower and upper bounds of the considered decision variables. 

Where S, G, X, E and Enz are respectively the starch, glucose, cells, ethanol and enzyme concentrations inside the reactor, Si is the starch concentration on the feed, F is the feed flow rate, V is the volume of hquid in the fermentor and (pi, (p2, (ps represent the reaction rates for starch degradation, cells growth and ethanol production, respectively. The unstructured model presented in (Ochoa et al., 2007) is used here as the real plant. The ki (for i=l to 4) kinetic parameters of the model for control were identified by an optimization procedure given in Mazouni et al. (2004), using as error index the mean square error between the state variables of the unstructured model and the model for control. 

The monitoring uses formulas that take into account feed flow rates, targets calculated by the optimization layer of multivariable control, controlled variables upper and lower limits and other parameters. The economic benefits are based on the degrees of freedom and the active constraints at the steady state predicted by the linear model embedded in the controller. In order to improve the current monitoring, parameters dealing with process variability will be incorporated in the formulas. By doing this, it will be also possible to quantify external disturbances that affect the performance of the advanced control systems and identify regulatory control problems. 

Only the desorption front of component B is influenced by the increased flow rate in section II - all other fronts are not influenced and remain at their initial position. The decrease in feed flow rate has an impact on the total height of the concentration plateaus, especially in section III. This procedure of shifting the fronts is also applicable for all other sections of the SMB process, to optimize the internal concentration profile according to Fig. 7.16 and improve the process performance with respect to purities, productivity and eluent consumption. 

Multiobjective optimization of the SMB and Varicol processes by a non-dominated sorting genetic algorithm (NSGA) which does not require any initial guess of the optimum solution was carried out by Zhang et al. [80] who used in that process an objective function that maximizes the feed flow rate (maximum throughput). 

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. 

For an ethylene plant, each reactor has three key operating variables outlet temperature, steam dilution, and feed flow rate. Plants have on the order of 24 parallel reactors (with several within each heater). In addition, the separation section has many variables that can be adjusted for optimization, including recycle compositions, distillation pressures, and refrigeration temperatures. Thus, a plant often has 100 variables or more for optimization. 

Terephthalic acid (TA) production Maximization of feed flow rate while minimizing concentration of 4-carboxy-benzaldehyde intermediate in the crude TA. NSGA-II and Neighborhood and Archived GA (NAGA) Mu et al. (2003) employed NSGA-II whereas Mu et al. (2004) used NAGA for four cases of operation optimization with 1 to 6 decision variables. Mu et al. (2003) Mu et al. (2004)... 

Enantioseparation of SB-553261 racemate using SMB technology Three cases (a) maximizing the purity and productivity of raffirrate stream, (b) maximization of purity and productivity of extract stream, and (c) maximization of feed flow rate and minimization of desorbent flow rate. NSGA-n-JG Both SMB and Varicol processes were optimized, and the study found that the latter has superior performance. Wongsoc/fll. (2004)... 

NAGA was used by Mu et al. (2004) to optimize the operahon of a paraxylene oxidahon process to give terephthalic acid. They consider two objectives minimization of the concentration of the undesirable 4-carboxy-benzaldehyde (4-CBA) in the product stream, and maximization of the feed flow rate of the paraxylene. They consider four ophmization problems using a different number of decision variables (1, 2, 4 and 6 variables). The problem has two constraints. The plot of the Pareto front obtained presented a convex and conhnuous curve. 

Yee et al. (2003) make use of the original NSGA (Srinivas and Deb, 1994) to optimize both adiabatic and steam-injected styrene reactors. A pseudo-homogeneous model was used to describe the reactor. This study maximizes three objectives the amount of styrene produced, the selectivity of styrene and the yield of styrene. Two- and three-objective optimization problems are studied using combinations from these objectives. The decision variables for the adiabatic configuration are the feed temperature of ethyl benzene, inlet pressure, molar ratio of steam to ethyl benzene and the feed flow rate of ethyl benzene. The problem considers three constraints related to temperatures which are handled... 

Hashemi and Epstein (1982) linearized the set of ordinary differential equations (ODEs) resulting from the application of the method of moments on an MSMPR crystallizer model and used singular value decomposition to define controllability and observability indices. These indices aid in selecting measurements and manipulated and control variables. Myerson et al. (1987) suggested the manipulation of the feed flow rate and the crystallizer temperature according to a nonlinear optimal stochastic control scheme with a nonlinear Kalman filter for state estimation. 

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