Chemical kinetics and transport processes

Here we focus on the issue of how to build computational models of biochemical reaction systems. The two foci of the chapter are on modeling chemical kinetics in well mixed systems using ordinary differential equations and on introducing the basic mathematics of the processes that transport material into and out of (and within) cells and tissues. The tools of chemical kinetics and mass transport are essential components in the toolbox for simulation and analysis of living biochemical systems. 

Instead of digging into the details of differential equations and numerical analysis, which we leave to specialized books on those topics, we show examples of how mathematical models may be simulated using tools such as Matlab, a high-level and easy-to-use programming environment. Thus our focus here is on building 

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Since chemical reaction engineering considerations apply to nondcterministic as well as deterministic methods they will be briefly dealt with separately. The interaction of chemical kinetics and transport processes and their effect on catalyst activity and selectivity in reaction networks will be emphasized. Some attention will be also paid to catalyst deactivation. 

It is, however, simpler to consider for the totality of chemical kinetic and transport processes that operate on different physical and time scales in the surficial environment three main classes of driving forces—physical, hydro-logical, and chemical—and responses to these forces in various physical, hydrological, and biogeochemical processes. This is illustrated schematically in Table 1, which gives a matrix of 3 x 3 couplings between physical, hydrological, and chemical forces and their environmental effects as far as these concern transport. 

BACKGROUND RATES OF CHEMICAL KINETIC AND TRANSPORT PROCESSES... 

Background rates of chemical kinetic and transport processes 511... 

Wilkinson, K. J. and Buffle, J. (2004). Critical evaluation of physicochemical parameters and processes for modelling the biological uptake of trace metals in environmental (aquatic) systems. In Physio chemical Kinetics and Transport at Biointerfaces, eds. van Leeuwen, H. P. and Koster, W., Vol. 9, IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, Series eds. Buffle, J. and van Leeuwen, H. P., John Wiley Sons, Ltd, Chichester, UK, pp. 445-533. 

Apparent rate laws include both chemical kinetics and transport-controlled processes. The apparent rate laws and rate coefficients indicate that diffusion and other microscopic transport processes affect the reaction rate. 

Understanding the kinetics of contaminant adsorption on the subsurface solid phase requires knowledge of both the differential rate law, explaining the reaction system, and the apparent rate law, which includes both chemical kinetics and transport-controlled processes. By studying the rates of chemical processes in the subsurface, we can predict the time necessary to reach equilibrium or quasi-state equilibrium and understand the reaction mechanism. The interested reader can find detailed explanations of subsurface kinetic processes in Sparks (1989) and Pignatello (1989). 

In Section 3.4.2, we introdnced the concept of chemical vapor infiltration, CVI, in which a chemical vapor deposition process is carried out in a porous preform to create a reinforced matrix material. In that section we also described the relative competition between the kinetic and transport processes in this processing technique. In this section we elaborate npon some of the common materials used in CVI processing, and we briefly describe two related processing techniques sol infiltration and polymer infiltration. 

Chemical Equilibrium. Although CVD is a nonequilibrium process controlled by chemical kinetics and transport phenomena, equilibrium analysis is usefiil in understanding the CVD process. The chemical reactions and phase equilibria determine the feasibility of a particular process and the final state attainable. Equilibrium computations with intentionally limited reactants can provide insights into reaction mechanisms, and equilibrium analysis can be used also to estimate the defect concentrations in the solid phase and the composition of multicomponent films. 

Thermodynamic analysis is a useful tool in understanding CVD processes but should be used with caution and careful attention to the assumptions underlying the application. Because CVD is a nonequilibrium process, the thermodynamic predictions are often only semiquantitative and mainly serve to provide insights into the process. Accurate process prediction must include chemical kinetics and transport rate considerations. 

Apparent rate laws include both chemical kinetics and transport-controlled processes. One can ascertain rate laws and rate constants using the previous techniques. However, one does not need to prove that only elementary reactions are being studied (Skopp, 1986). Apparent rate laws indicate that diffusion or other microscopic transport phenomena affect the rate law (Fokin and Chistova, 1967). Soil structure, stirring, mixing, and flow rate all affect the kinetic behavior when apparent rate laws are operational. 

As is evident from the examples we have cited, most environmental problems are highly complex and often ill-defined. At a minimum, they usually require a synthesis of virtually all elements of the chemical engineer s arsenal—thermodynamics, chemical kinetics, and transport phenomena at the most, an interdisciplinary team is required. An insufficient understanding of molecular-scale processes is frequently the key obstacle in developing innovative approaches to environmental protection. 

In the second half of the nineteenth century, physical chemistTy developed as a well-defined subject, consisting of thermodynamics, kinetics, and transport processes, and mainly dealing with bulk properties and continuum models. When quantum mechanics was discovered in 1925, paving the way for modem molecular physics, this subject was less well received by the chemists. Partly this was due to the morass of equations and calculations one sinks into, just to get insight into such a simple concept as the chemical bond. Application of quantum methods in chemistry was pioneered by people like Henry Eyring, Linus Pauling, Robert Mulliken, Per-Olov Lowdin, Bjorn Roos, and many others. Most of these scientists called themselves quantum chemists. ... 

When the rate of the process is determined both by chemical kinetics and transport phenomena, the necessary mathematical model becomes quite complicated, and the necessary parameters may be difficult to determine. It may be safer to take a more empiricd appoach, and measure the degree of conversion as a function of time, in a laboratory batch reactor, for well defined conditions. One will probably find that the apparent reaction order is betweeen 0 and 1. The results may be expressed as a conversion/time relation, that can be substituted in eq. (7.13b). Together with eq. (7.14) one finds a differential equation that can be solved numerically, or simply graphically. 

While physical modeling has been important historically, and is still a central part of chemical education and some investigations in stereochemistry, contemporary chemical models are almost always mathematical. Families of partially overlap>-ping, partially incompatible models such as the valence bond, molecular orbital, and semi-empirical models are used to explain and predict molecular structure and reactivity. Molecular mechanical models are used to explain some aspects of reaction kinetics and transport processes. And lattice models are use to explain thermodynamic properties such as phase. These and other mathematical models are ubiquitous in chemistry textbooks and articles, and chemists see them as central to chemical theory. 

Many factors affect the mechanisms and kinetics of sorption and transport processes. For instance, differences in the chemical stmcture and properties, ie, ionizahility, solubiUty in water, vapor pressure, and polarity, between pesticides affect their behavior in the environment through effects on sorption and transport processes. Differences in soil properties, ie, pH and percentage of organic carbon and clay contents, and soil conditions, ie, moisture content and landscape position climatic conditions, ie, temperature, precipitation, and radiation and cultural practices, ie, crop and tillage, can all modify the behavior of the pesticide in soils. Persistence of a pesticide in soil is a consequence of a complex interaction of processes. Because the persistence of a pesticide can govern its availabiUty and efficacy for pest control, as weU as its potential for adverse environmental impacts, knowledge of the basic processes is necessary if the benefits of the pesticide ate to be maximized. 

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