Uses of Mathematical Models

Without doubt, the most important result of developing a mathematical model of a chemical engineering system is the understanding that is gained of what really makes the process tick. This insight enables you to strip away from the problem the many extraneous confusion factors and to get to the core of the system. You can see more clearly the cause-and-effect relationships between the variables. 

Mathematical models can be usefiil in all phases of chemical engineering, from research and development to plant operations, and even in business and economic studies. 

Research and development determining chemical kinetic mechanisms and parameters from laboratory or pilot-plant reaction data exploring the effects of different operating conditions for optimization and control studies aiding in scale-up calculations. 

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Y. S. Sedunov, V. A. Borzilov, and N. V. Klepikova, Use of Mathematical Modeling to Estimate Formation of Contaminated Areas Resultingfrom Nuclear Accident, IAEA-SM-306/114, IAEA, Vienna, Austria, 1990. 

On a prospective basis, an agency can project its source composition and location and their emissions into the future and by the use of mathematical models and statishcal techniques determine what control steps have to be taken now to establish future air quality levels. Since the future involves a mix of existing and new sources, decisions must be made about the control levels required for both categories and whether these levels should be the same or different. 

R. Schuster and H. G. Holzhiitter, Use of mathematical models for predicting the metabolic effect of large scale enzyme activity alterations. Application to enzyme deficiencies of red blood cells. Eur. J. Biochem. 229(2), 403 418 (1995). 

Prasarma et al. [185] were also able to observe an optimum thickness of DLs for fuel cells experimentally. They demonstrated that the thicker DLs experience severe flooding at intermediate current densities (i.e., ohmic region) due to low gas permeation and to possible condensation of water in the pores as the thickness of the DL increases. On the other hand, as the thickness of the DL decreases, the mass transport losses, contact resistance, and mechanical weakness increase significantly [113,185]. Through the use of mathematical modeling, different research groups have reported similar conclusions regarding the effect of DL thickness on fuel cell performance [186-189]. 

The petroleum refining industry provides many opportunities for the use of mathematical models in process simulation. Although it is generally known in the industry that widespread interest exists in this application of computers, there have been few literature references to this work (A6, H2, Ul).2 These published remarks have been quite brief and vague. It is probably worth while to consider here, however, some of the reasons for the interest of the refining industry in mathematical models on computers, as it may serve to indicate the desirability of similar applications in other areas. 

Successful construction and use of mathematical models for individual processes soon leads to more ambitious projects. It has already been mentioned, for example, that in petroleum refining most processes cannot be regarded as separate entities because they consume products of other processes and supply raw materials for still other operations. If one tries, however, to construct a mathematical model which will directly represent the operations of an entire refinery, the task can become overwhelming. The size of the model, when looked at in its entirety, is simply too large for a proper perspective. 

Models have been developed to predict cat cracker yields based on operating parameters and feedstock properties (34) These have aided in application and evaluation of metals passivation benefits. Miller and Pawloski (35) reported the use of mathematical models to calculate the benefits of vanadium passivation, and Teran (27) reported the need for FCCU hydrogen modeling and metals tracking to optimize passivation benefits. 

The term chemometrics was hrst coined in 1971 to describe the growing use of mathematical models, statistical principles, and other logic-based methods in the held of chemistry and, in particular, the held of analytical chemistry. Chemometrics is an interdisciplinary held that involves multivariate statistics, mathematical modeling, computer science, and analytical chemistry. Some major application areas of chemometrics include (1) calibration, validation, and signihcance testing (2) optimization of chemical measurements and experimental procedures and (3) the extraction of the maximum of chemical information from analytical data. 

The designing of hydride reactors is an intricate versatile thermophysical problem. It can be solved by complex approach to designing with use of mathematical modelling, technological and experimental elaboration of separate units (especially, characteristics of hydride beds). In general, the improvement of MHHP parameters may be expected after substantial improvement of hydrogen capacity of hydrides. 

Laurence, W.H., Bas, G.E., Purcell, W.P., Autian, J. (1972) Use of mathematical models in the study of structure-toxicity relationships of dental compounds I. Esters of acrylic and methylacrylic acids. J. Dent. Res. 51, 526-535. 

Finally, this study provides an extensive set of data on thick wood pyrolysis which can be better interpreted and generalized by the use of mathematical models taking into account the effects of transport phenomena and chemical reactions. Models including such features are already available in the literature (for instance, see References 23,24) and have proven to give quantitative predictions of temperature dynamics, but product yield predictions are still unacceptable, mainly because of unreliable kinetic constants. Therefore, this issue deserves further investigation before extensive computer simulation and/or development of more advanced physical models of thick wood pyrolysis are proposed. 

How has the use of mathematical models for predicting dispersion of compounds in water systems developed after 1900 ... 

The interaction of waste with geological media involves complex and interacting processes. One important use of mathematical models is the integration of data, concepts, and processes that are from different disciplines. There is no better way to understand them than to construct geochemical and hydrological models, and the art of... 

Glaser D, Bridges TS. 2007. Separating the wheat from the chaff the effective use of mathematical models as decision tools. Integr Environ Assess Manage 3 442 -49. 

Tannenbaum LV. 2007. And so we model the ineffective use of mathematical models in ecological risk assessments. Integr Environ Assess Manage 3 473 4-75. 

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