Optimization maximum production rate

Process Reliability Simulation VIP The process reliability simulation VIP is the use of reliability, availability, and maintainability (RAM) computer simulation modeling of the process and the mechanical reliability of the facility. A principal goal is to optimize the engineering design in terms of life cycle cost, thereby maximizing the project s potential profitability. The objective is to determine the optimum relationships between maximum production rates and design and operational factors. Process reliability simulation is also applied for safety purposes, since it considers the consequences of specific equipment failures and failure modes. 

Preparative HPLC optimization goals which ultimately lead to a product with a given minimum purity may include the maximum amount of the purified material per weight unit of stationary phase per time unit (g/kg/day), the maximum amount of the purified material per mobile phase unit per time unit (g/L/day), the maximum production rate (g/day), the lowest cost ( /kg), the maximum recovery (%), and the maximum production rate with maximum recovery. Regardless of the differences in application, it is important to be aware of the following parameters that may affect the purity and recovery of the product as well as the time and cost required for the separation ... 

In the last part of this book, we apply the different models discussed earlier, particularly the ideal model and the equilibrium-dispersive model, to the investigation of the properties of simulated moving bed chromatography (Chapter 17) and we discuss the optimization of the batch processes used in preparative chromatography (Chapter 18). Of central importance is the optimization of the column operating and design parameters for maximum production rate, minimum solvent use, or minimum production cost. Also critical is the comparison between the performance of the different modes of chromatography. 

Jandera et al. [35] measured by frontal analysis the competitive isotherms of the enantiomers of mandeHc acid, phenyl-glycine and tryptophan on the glyco-peptide Teicoplanin, in water/methanol or ethanol solutions. The less retained L enantiomers of the two amino acids follow Langmuir isotherm behavior while the D isomers foUow bi-Langmuir behavior. The enantiomeric separation factors increase with increasing alcohol concentration while the solubilities of these com-poimds decrease. Similar results were reported by Loukih et al. [36] for the separation of the enantiomers of tryptophan on a teicoplanin- based CSR The authors insisted on the importance of the nature of the ions in a supporting salt. Optimization of the experimental conditions for maximum production rate must take this effect into account. 

Figure 18.5 shows the results calculated with the ideal model for the combined objective function of production rate and recovery yield. When the separation of the less retained component is optimized, the ideal model fails to identify an optimum value of the loading factor for maximum production rate. The production rate increases monotonously with increasing loading factor while the recovery... 

Golshan-Shirazi and Guiochon have investigated the optimization of the experimental conditions using the analytical solution of the ideal model [20-24]. In the case of touching bands, the recovery yield is practically total ( 100%). Therefore, the same experimental conditions assure the maximum production rate for both components. Their assumptions are limited to the following two ... 

Finally, the dependence of the production rate on the separation factor is complex since No, 7, x, and X depend on a, [21]. x varies rapidly with a when the relative concentration of the second component is large, and the displacement effect is dominant [2], Nevertheless, it can be shown that at constant pressure AP, the maximum production rate obtained with an optimized column is approximately proportional to [(a — l)/a] [28]. For a given i.e., nonoptimized) column, the production rate is proportional to [(a - T)/ ]y, with y between 2 and 3, depending on the importance of the difference between the given and the optimum columns [28]. 

Since the recovery yield achieved rmder the experimental conditions giving the maximum production rate is of the order of 60%, a first-order approximation of the loading factor giving a recovery yield Y is Lf = 0.6L /Y. Then the column efficiency is adjusted to achieve the required recovery yield. This method has been adopted because the results of numerical optimization suggest that there is a quasi-linear relationship between the recovery 5deld and both the mobile phase velocity and the loading factor [7]. 

Figure 18.11 Plot of the maximum production rate in elution versus the retention factor of the less retained component of a binary mixture. Separation factor 1.2. Each data point gives the maximum production rate after optimization of the mobile phase velocity, the sample size, the particle size, and the column length. Reproduced with permission from A. Felinger and G. Guiochon,. Chromatogr., 591 (1992) 31 (Fig. 12).

Top part, optimization for maximiun production rate of the first component. Bottom part, optimization for maximum production rate of the second component. k = 4. N, optimum plate number Ly, optimum loading factor m, optimum reduced or apparent sample size (Eq. 10.15c) Pr, maximum production rate. 

These numerical procedures have been applied to the solution of practical problems of optimization of the experimental conditions of separations by overloaded elution. For example, they made possible the calculation of the maximum production rate under yield constraints of the components of several racemic mixtures. The results of this numerical optimization procedure were compared with experimental data [32,33]. Very good agreement between the two sets of results was reported in the two cases investigated. 

Figure 18.18 illustrates the shift of the position of the optimum experimental conditions when Pr is replaced by the Pr X Y objective function for the optimization. The maximum production rate is at point A, while Pr x Y reaches its maximum at point B. The contour lines clearly show that the production rate is hardly lower at the new optimum. On the other hand, the recovery yield is improved when the experimental conditions are shifted from point A to point B. The surface determined by Pr x Y exhibits a well defined maximum, which makes the numerical path toward optimization stable. 

Felinger and Guiochon used the equilibrium-dispersive model to study the effect of experimental conditions on the maximum production rate and Pr xY [40,41]. We have seen in Section 18.2.3 that in isocratic elution chromatography, the loading factor and the column efficiency are the critical parameters to be optimized for maximum production rate. In gradient elution there is an additional parameter, the gradient steepness... 

Felinger and Guiochon [54] carried out a systematic investigation of the optimization of the experimental conditions for maximum production rate, using the same model as for their similar study on the optimization of elution [4] (competitive Langmuir isotherm, equilibrium-dispersive model [24], Knox equation [25], and super-modified simplex algorithm [34]). Their main conclusions are the following. 

Figure 18.25 Comparison of experimental and theoretical results. Optimization of the dis-placer concentration for maximum production rate xmder isotachic train conditions, (a) Experimental results. Plot of the maximum production rate versus the normalized breakthrough time of the displacer, (b) Optimum calculated with the shock layer theory. F = 0.416 Dl = 0.000023 cm /s fcy = 0.33 s. Langmuir isotherm coefficients (and k values) k y = 1.5, = 2.5, k 2 = 4.0, = 6.0 k = 9.0 = 0.04 bz = 0.07 bg = 0.12 bi = 0.18 b =...

A more systematic investigation was done by Katti et al. [3]. Using the competitive Langmuir isotherm model, the equilibrium-dispersive model [24], and the Knox equation [25], these authors optimized the operating parameters of given columns for maximum production rate of either the first or the second component of binary mixtures with various separation factors (1.2 < a < 1.7) and composition. Constraints of purity (98%) and maximum inlet pressure (125 atm) were included, and also, in some cases, a recovery yield (60 or 90%) constraint. The maximum production rates achieved with the two modes are comparable when there is no yield constraint. However, the recovery yield is lower in displacement than in elution, because the maximum production rate is achieved imder non-... 

If the optimized columns are used, the recovery yields achieved at the maximum production rate with both modes are comparable, and aroimd 60%. 

The next step is the optimization of the column length and the particle size for maximum production rate. In practice, there is an optimum for the ratio dp/L but no separate optima for L and dp. A satisfactory approximation of the optimiun ratio dp/L can be obtained using the following equation, which is derived assuming a simple plate height equation and neglecting the effect of competition... 

In Chapter 17, we discussed the optimization of the flow rate ratios in the four zones of the SMB process and that of the switching time. The triangle theory allows the determination of the optimum conditions for maximum production rate and minimum eluent consumption. Due to the complexity of the simulated moving bed process, most current studies limit studies on the optimization of an SMB unit operation to investigating the influence of these parameters. Few data are available on the optimization of many other experimental parameters e.g., pressure drop, product purity) and column design conditions e.g., column length, particle size, efficiency) or on that of the column configuration (optimum number of columns in the individual zones). 

Optimization Search of the experimental conditions allowing the achievement of the best possible separation, e.g., maximum production rate, minimiun production cost. See Chapter 18. 

The reader will find here a complete mathematical development of the models of chromatography and other physical laws which direct the chemical engineer in the design and scale-up of chromatographic processes. For preparative chromatographic separations, our ultimate purpose is the optimization of the experimental conditions for maximum production rate, minimum solvent consumption, or minimum production cost, with or without constraints on the recovery yield. The considerable amormt of work done on this critical topic is presented in the... 

Let us return, however, to the problem of optimizing total conversion and selectivity. To begin with, it is important to note the relation between the two functions. For a single reaction there is no problem optimum operation is the maximum production rate of the product per unit mass of catalyst. For plug-flow reactions the mass balance of reactant is given by Eq. (12-1), which may be rearranged to the form... 

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