The use of statistical methods to build mathematical models of chemical reacting systems

Reilly, Park M.; Blau, Gary

doi:10.1002/cjce.5450520301

Cited by 64 publications

(28 citation statements)

References 32 publications

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“…( 1963a, b) and an older model due to Temkin and Pyzhev (1940). However, a statitical test following the procedure of Reilly and Blau (1974) failed to distinguish among these models. Ferraris et al (1974) were also unable to distinguish among a similar set of competing models using steady-state data.…”

Section: Effect Of Temperaturementioning

confidence: 97%

Influence of forced feed composition cycling on the rate of ammonia synthesis over an industrial iron catalyst part I — Effect of cycling parameters and mean composition

1983

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Studies have been carried out at 2.38 MPa total pressure and at 360 and 400°C of the synthesis of ammonia over a triply‐promoted iron catalyst (United Catalysts Inc.). Runs were carried out using a gradientless reactor in steady‐state and periodic modes, the latter employing forced composition cycling. The catalyst had a particle diameter of 0.30 mm; the resulting reaction rates were free from transport intrusions. The range of mean compositions for steady‐state measurements was from 0.1 to 0.9 mole fraction of hydrogen and for periodic operation from 0.5 to 0.9. The cycle‐split ratio (used to describe non‐uniform cycling) varied from 0.2 to 0.85. Effects of cycle period, mean composition, cycle‐split, and temperature were investigated. Instantaneous rate variations within the cycle are reported. Results showed that the cycling mode of operation results in an improvement in the time‐average rate of ammonia formation of up to 30%, depending upon the choice of operating parameters. Some implications for the mechanism of ammonia synthesis under periodic operation are presented.

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Section: Effect Of Temperaturementioning

confidence: 97%

Influence of forced feed composition cycling on the rate of ammonia synthesis over an industrial iron catalyst part I — Effect of cycling parameters and mean composition

1983

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“…rameter estimation, i.e., the experimental errors were assumed to be normally distributed. The maximum likelihood function was used to provide a general formulation for the objective function (Biegler et al, 1986;Reilly, 1970;Reilly and Blau, 1974) and the optimization was carried out by generalized reduced gradient (GRG) method. The model equations were integrated numerically using Gear's method.…”

Section: Literature Value Based On Total Biomass Concentration Wasmentioning

confidence: 99%

A structured model for hyphal differentiation and penicillin production using Penicillium chrysogenum

Paul

Thomas

2000

Biotechnol. Bioeng.

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A structured kinetic model describing growth, differentiation, and penicillin production in submerged Penicillium chrysogenum fermentations is reported. The filamentous hyphae are divided into four distinct regions on the basis of the activities and structure of hyphal compartments, viz., actively growing (mainly apical) regions, nongrowing or penicillin producing regions, vacuoles, and degenerated or metabolically inactive regions. A mechanistic approach is taken to give quantitative descriptions of differentiation and degeneration as a consequence of vacuolation. The growth and degeneration of vacuoles are expressed in the form of a population balance. The model assumes that newly generated vacuoles appear by differentiation of healthy regions, grow in size with limitation of available substrate, and eventually give rise to empty hyphal compartments. In the model the penicillin production is related to the amounts of the nongrowing regions of the hyphae. The model is used for successful predictions of the amounts of the four hyphal regions and the penicillin G production rate throughout the fed‐batch fermentations of an industrial P. chrysogenum strain under different glucose feeding regimes. Quantitative information on proportions of the hyphal regions was obtained from image analysis measurements and the parameters of the kinetic model were identified. When the glucose feed rate to the production culture is switched between a high and a low value, the model can successfully predict the dynamic changes of differentiation and the resulting penicillin production caused by the variations in the nutrient conditions. The use of image analysis to characterize differentiation as a basis for structured modeling of the penicillin fermentation appears to be very powerful, and the method has great potential for use in process simulation and control of antibiotic fermentations. © 1996 John Wiley & Sons, Inc.

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“…After a step-by-step demonstration of the Bayesian approach, several case studies from complex polymerization scenarios have shown that what is novel in the Bayesian approach is the simplicity and the natural way it follows the logic of sequential model building paradigm [9,16]. The most distinguishing feature of the Bayesian method is that it takes full advantage of the researcher's expertise and information (knowledge about process/product) prior to the design.…”

Section: Discussionmentioning

confidence: 96%

A Sequential Iterative Scheme for Design of Experiments in Complex Polymerizations

et al. 2010

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The Bayesian design approach is an experimental design technique which has many advantages over standard experimental designs. It incorporates prior knowledge about the process into the design to suggest a set of future experiments in an optimal, sequential, and iterative fashion. Since for many complex polymerizations prior information is available, either in the form of experimental data or mathematical models, the use of Bayesian design methodology could be beneficial. Exploiting this technique in complex polymerizations could hopefully lead to optimal performance in fewer trials, thus saving time and money. Advantages of the Bayesian design approach are illustrated via case studies drawn from the nitroxide-mediated radical polymerization as an example. However, since this technique is perfectly general, it can be potentially applied to other polymerization variants. IntroductionFor many complex polymerizations some sort of experimental information might be available (even in preliminary form) either from industrial or exploratory laboratory work. In addition, mathematical models (of different level of detail, empirical, or semi-mechanistic) usually do exist, albeit with unreliable and/or highly correlated parameters and sometimes even unverified mechanistic bases. Hence, ideas from the modelbased design of experiments applied as early as possible (in the design/brainstorming stage) can be very beneficial for the clarification of polymerization kinetics.Standard experimental design methods, e.g., (fractional) factorial designs, have been employed extensively and are useful in optimizing a wide variety of systems. However, these designs usually suffer from several limitations and cannot handle certain situations, as listed in Tab. 1. In addition, these approaches do not take direct advantage of the considerable prior knowledge that is available about the reaction system to design experiments. As prior information is already available within existing data, it is logical that it should be used in order to contribute to the optimality of the designed experiments, and hence to improved models and performance of the process in question.Although some of the issues with standard designs cited in Tab. 1 have solutions, these are usually known only to experts in the design of experiments. Hence, it often happens that the practicing scientist or engineer is not aware of the solutions, cannot easily handle the issues faced, and gives up on the use of statistical designs altogether. Using more efficient experimental designs which can accommodate these restrictions could lead to optimal performance in fewer trials, thus saving time and money.Such efficient designs can be found in the family of Bayesian approaches. The Bayesian design is a powerful and in the poly- [9]. The common characteristic of all these Bayesian framework applications (including the ones mentioned above as well as others from the scientific literature not cited herein for the sake of brevity), to a split of about 7 or 8 to 2, is that they are concern...

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The use of statistical methods to build mathematical models of chemical reacting systems

Cited by 64 publications

References 32 publications

Influence of forced feed composition cycling on the rate of ammonia synthesis over an industrial iron catalyst part I — Effect of cycling parameters and mean composition

Influence of forced feed composition cycling on the rate of ammonia synthesis over an industrial iron catalyst part I — Effect of cycling parameters and mean composition

A structured model for hyphal differentiation and penicillin production using Penicillium chrysogenum

A Sequential Iterative Scheme for Design of Experiments in Complex Polymerizations

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