Step 3 Algorithmic Development The mathematical model (7.1), which describes all process alternatives embedded in the superstructure, is studied with respect to the theoretical properties that the objective function and constraints may satisfy. Subsequently, efficient algorithms are utilized for its solution which extracts from the superstructure the optimal process structure(s). [Pg.234]

A mathematical model was found for each studied response. From the models, the contoured curves and the response surfaces were plotted, and the optimal points were sought and confirmed. [Pg.57]

In this study, we focused our attention on investigating the adsorption dynamics in column packed with activated carbon fiber. By optimizing the breakthrough curve data with a mathematical model, effective overall mass transfer coefficient was obtained. And it can be given reasonable predictions compared with the experimental data of breakthrough curve. [Pg.484]

The coefficient of correlation values (R2) were quite low for the estimated friability mathematical models. It seems that this response was independent of the studied parameters and their levels and, in our case, friability was not an important response to be optimized. This response could only be an evaluated property. Lindberg and Holmsquist [6] had also obtained low R2 values for this response (R2=0.57 and 0.68). [Pg.59]

Reaction mechanism of azo dyes removal Limited study has focused on the reaction mechanism of azo dyes removal. The research of mechanistic and mathematical models to optimize the integrated process and to characterize the interaction between the reactant and azo dyes should be carried out in the future. [Pg.150]

Thus, expectedly no rigorous mathematical models are available that can accurately describe the detailed flow behavior of the fluid streams in a membrane separation process or membrane reactor process. Recent advances in computational fluid dynamics (CFD), however, have made this type of problem amenable to detailed simulation studies which will assist in efficient design of optimal membrane filtration equipment and membrane reactors. [Pg.488]

Another study was performed on a catalytic hydrogenation of 1,3,5-trimethyl-benzene to 1,3,4-trimethylcyclohexane, which is a typical first-order reversible reaction [168]. By optimizing various operating conditions it was possible to achieve a product purity of 96% and a reactant conversion of 0.83 compared to a thermodynamic equilibrium conversion of only 0.4. The results were successfully described with a mathematical model derived by the same authors [169]. Comparison to a real countercurrent moving bed chromatographic reactor yielded very similar results for both types [170]. [Pg.196]

If the behaviour of complex chemical (in our case catalytic) reactions is known, it will be clear in what way these reactions can be carried out under optimal conditions. The results of studying kinetic models must be used as a basis for the mathematical modelling of chemical reactors to perform processes with probable non trivial kinetic behaviour. It is real systems that can appear to show such behaviour first far from equilibrium, second nonlinear, and third multi dimensional. One can hardly believe that their associated difficulties will be overcome completely, but it is necessary to approach an effective theory accounting for several important problems and first of all provide fundamentals to interpret the dependence between the type of observed kinetic relationships and the mechanism structure. [Pg.385]

It was estimated that, if all the Surfmers contributed to stabilization, the surface coverage would be close to 20% at the end of the process. When Surfmer burial is considered, the minimum surface coverage is in the region of 14.7-15.0 % [35]. The authors have also studied the influence of the addition procedure on the evolution of the Surfmer conversion and concluded that, despite the low reactivity due to the presence of the alkenyl double bond, the incorporation could be increased to 72% from the original 58% obtained with a constant feeding rate. A mathematical model able to describe Surfmer polymerization was used in the optimization process [36]. [Pg.221]

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