Mathematical modelling reliable process

In contrast to fluid process technologies such as distillation, absorption, and extraction, mechanical processes are only accessible to a limited extent to mathematical modeling, and process design is dependent on experiment. However, only a few experimental techniques that allow reliable scale-up to be performed are available. 

Identification of a process involves formulating a mathematical model which properly describes the characteristics of the real system. Initial model forms are developed from first principles and a priori knowledge of the system. Model parameters are typically estimated in accordance with experimental observations. The method in which these parameters are evaluated is critical in judging the reliability and accuracy of the model. 

A universal method of handling the problem is mathematical modelling, i.e., a quantitative description by means of a set of equations of the whole complex of interrelated chemical, physical, fluiddynamic, and thermal processes taking place concurrently or consecutively in a reactor. Constants of these equations are determined in laboratory experiments. If the range of determining factors (reactive mass compositions, temperature, reaction rates, and so on) in an actual process lie within or only slightly outside the limits studied in laboratory experiments, the solution of the determining set of equations provides a reliable idea of the process operation. 

Approaches based on parameter estimation assume that the faults lead to detectable changes of physical system parameters. Therefore, FD can be pursued by comparing the estimates of the system parameters with the nominal values obtained in healthy conditions. The operative procedure, originally established in [23], requires an accurate model of the process (including a reliable nominal estimate of the model parameters) and the determination of the relationship between model parameters and physical parameters. Then, an online estimation of the process parameters is performed on the basis of available measures. This approach, of course, might reveal ineffective when the parameter estimation technique requires solution to a nonlinear optimization problem. In such cases, reduced-order or simplified mathematical models may be used, at the expense of accuracy and robustness. Moreover, fault isolation could be difficult to achieve, since model parameters cannot always be converted back into corresponding physical parameters, and thus the influence of each physical parameters on the residuals could not be easily determined. 

The control of a fed-batch alcoholic fermentation process can be obtained by controlling the substrate concentration in the medium by manipulation of the feed flow. The fermentation process presents complicated kinetic mechanisms. In addition, there is the absence of accurate and reliable mathematical models as well as the difficulty of obtaining direct measurements of the process variables owing to a lack of appropriate on-line analyzers and sensors. Control systems are formed by a set of instruments and control mechanisms connected through electrical signals in the... 

Both the need to reduce experimental costs and increasing reUabiUty of mathematical modeling have led to growing acceptance of computer-aided process analysis and simulation, although modeling should not be considered a substitute for either practical experience or reliable experimental data. 

It is also worth mentioning that mathematical modeling of the process and combustion chamber was so reliable that it could be employed as a powerful design tool to optimize the combustion system avoiding expensive trials (Figure 23.23). Then modeling could be used in conjunction with experiments in a unified strategy for... 

The lack of robustness can be corrected by adjustments in the operational and control parameters of the process when fluctuations occur. To accomplish this, it is important that a mathematical model be available to aid in the decision making, mainly when the difficulties of monitoring the key process variables are taken into account. Care has to be taken with the values of the model parameters, especially the kinetic ones so that reliable predictions can be made. 

Mathematical models, especially when coupled with computer techniques, are a very effective tool in searching for optimal operating conditions in the design, operation and control of enzyme reactors. The study of a reliable model for the enzyme reaction system is of significant importance for the industrial application of the biocatalyst. The model has to be effective in a wide range of values of the process variables. 

A mathematical model with which the dryer and process parameters can be studied is of extreme utility to the industry. A reliable model often will prevent or minimize costly mistakes in prototype development. The model also can be utilized for the control of process, specifically in adaptive and feed-forward control strategies. With the proliferation of low cost and powerful computers, the simulation models are useful. In this chapter, the emphasis is on the presentation of formulas and equations rather than the conventional charts and graphs in drying calculations. 

However, in spite of the known advantages and applications of liquid membrane separation processes in hollow-fiber contactors, there are scarce examples of industrial application. The industrial application of a new technology requires a reliable mathematical model and parameters that serve for design, cost estimation, and optimization purposes allowing to accurate process scale-up. " The mathematical modeling of liquid membrane separation processes in HFC is divided into two steps (1) the description of the diffusive mass transport rate and (2) the development of the solute mass balances to the flowing phases. 

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