Numerical Solution of Chemical Transport Models

In this section we will discuss some aspects of numerical solution of chemical transport models. We do not attempt to specify which numerical method is best rather, we point out some considerations in assessing the adequacy and appropriateness of numerical methods for chemical transport models. Our treatment is, by necessity, brief. We refer the reader to Peyret and Taylor (1983) and Oran and Boris (1987) for more study in this area. 

Each of these operators is distinctly different in basic character, each usually requiring quite different numerical techniques to obtain numerical solutions. We should note that no single numerical method is uniformly best for all chemical transport models. The relative contributions of each of the operators to the overall solution as well as other considerations, such as boundary conditions and wind fields, can easily change from application to application, leading to different numerical requirements. 

The implicit numerical solution of the time-dependent conservation equations provides the most powerful general method of solving premixed laminar flame problems in systems of (in principle) arbitrary chemical complexity. Indeed, with the simultaneous development of improved diagnostic techniques for the measurement of flame profiles, the possibility of obtaining such solutions has opened the way to realistic studies of reaction mechanisms even in hydrocarbon flames. The choice of solution method and transport flux formulation involves compromise between precision and cost, which becomes a matter of considerable import when modeling hydrocarbon oxidation in flames, which may involve some 25 chemical species and 80 or so elementary reactions. 

Edward G. Jefferson, Future Opportunities in Chemical Engineering Eli Ruckenstein, Analysis of Transport Phenomena Using Scaling and Physical Models Rohit Khanna and John H. Seinfeld, Mathematical Modeling of Packed Bed Reactors Numerical Solutions and Control Model Development... 

In order to make design or operation decisions a process engineer uses a process model. A process model is a set of mathematical equations that allows one to predict the behavior of a chemical process system. Mathematical models can be fundamental, empirical, or (more often) a combination of the two. Fundamental models are based on known physical-chemical relationships, such as the conservation of mass and energy, as well as thermodynamic (phase equilibria, etc.) and transport phenomena and reaction kinetics. An empirical model is often a simple regression of dependent variables as a function of independent variables. In this section, we focus on the development of process models, while Section III focuses on their numerical solution. 

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