Optimization ideal model

THE OPTIMIZED PAMPA MODEL FOR THE GUT 7.8.1 Components of the Ideal GIT Model... 

For the simulation of SMB-separations efficient software packages,based on the Triangle-Theory, are commercially available. The number of columns, the column dimensions, the theoretical number of plates in the columns, the feed concentration, the bi-Langmuir adsorption isotherm parameters and the number of cycles need to be defined by the user. Then the separation is simulated and values for the flow rate ratios, the flow rates, the switching time and the quality of the separation, purity and yield, are calculated. Based on these values an actual separation can be performed. However, some optimization/further development is usually necessary, since the simulations are based on an ideal model and the derived parameters and results therefore can only be taken as indications for the test runs. 

Given the limitations of the above systems, it is apparent that the optimal peptide model of a p-sheet (and a p-turn) should be as analagous to the monomeric helix models as possible. In particular, the ideal p-sheet model should be small (< 20 residues), monomeric, water-soluble, pure (composed of only p-sheets and p-turns), amphipathic (to investigate sidedness), reversibly denaturable, composed of only natural amino acids, easily synthesized and easily characterized by standard spectroscopic techniques. We believe that we have developed such a peptide model. It is based on the naturally occurring cyclic peptide gramicidin S, an antibiotic produced by the bacterium bacillus brevis (12). The schematic structure of gramicidin S as determined by X-ray and NMR studies (13, 14) is shown in Figure 1. 

Due to the simplifying assumptions made for the TMB approaches, accurate design and optimization of SMB processes is not possible. Several approaches based on SMB models have been suggested to improve the prediction and optimization of the SMB operation. Zhong and Guiochon (1996) have presented an analytical solution for an ideal SMB model and linear isotherms. The results of this ideal model are... 

Guiochon, G., Golshan-Shirazi, S. Theory of optimizing of the experimental conditions of preparative elution using the ideal model of liquid chromatography, Anal. Chem., 1989a,... 

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. 

In spite of some awkwardness in its formulation, the forward-backward scheme of numerical integration of the ideal model (Eq. 10.79) seems the most efficient way of calculating the band profiles of the equilibrium-dispersive model. It is particularly effective in terms of use of CPU time and is especially suitable for theoretical investigations of optimization strategies [10]. The best alternative procedure is not another finite difference scheme but one using orthogonal collocation on finite elements [9]. This procedure is more accurate but requires a much longer... 

Optimization for Touching Bands Using the Ideal Model.871... 

Simultaneous Optimization of the Production Rate and Recovery Yield using the Ideal Model... 

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... 

Knox and Pyper [17] made the first systematic study of the optimization of the experimental conditions in preparative liquid chromatography based on the use of a simple chromatographic model. They considered touching band separation (i.e., in the ideal model, tR 2 — 1e (Figure 8.6), or approximately a imit resolution between the two bands) with the following assumptions ... 

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 ... 

The optimization of the experimental conditions in displacement chromatography for maximiun production rate has been studied less than the optimization of overloaded elution, reflecting the lesser importance of this method in industrial practice. Frenz et al [52] performed an experimental study of the dependence of the throughput on the operational parameters in reversed-phase displacement systems. They demonstrated that both the nature and the concentration of the displacer must be appropriately selected to optimize the throughput. Jen and Pinto [53] have used the ideal model, and the fe-transform approach to maximize... 

This model is very often used to design and optimize chromatographic systems (e.g., Guiochon et al, 2006). Compared with the ideal model (Equation 6.39) a term describing axial dispersion (Equation 6.22) is included in the mass balance of the mobile phase ... 

The first term is a measure of the average log-goodness of fit of the model class Cj. It accounts for the log-goodness of fit for different combinations of the parameters, weighted by the posterior PDF, instead of the optimal parameters alone. An ideal model class should fit the data well even with a reasonably small perturbation of the parameters from their optimal values. In the special case if the likelihood function is of the Gaussian type and the prior PDF is relatively flat, the posterior PDF is approximately Gaussian and the log-likelihood function takes the following form ... 

More provocative is Strevens claim that [a]n idealizing explanation is in one important respect explanatorily optimal it cannot be further improved (ibid). Idealized models explicitly communicate the idea that certain features of a system do not make a difference to the causal entadment of the explanandum. Compare idealized models to what Strevens calls a canonical model , which is a causal model that has been subject to the kairetic procedure of optimization and cmitains... 

On average, the RUMBLE model overestimates the actual timing improvement by about 15 %. This makes sense since it assumes an optimal ideal buffering will be achievable, but this is not always the case, especially for multi-sink nets. 

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