Chemical mass balance modelling 446 Subject

The discussion above provides a brief qualitative introduction to the transport and fate of chemicals in the environment. The goal of most fate chemists and engineers is to translate this qualitative picture into a conceptual model and ultimately into a quantitative description that can be used to predict or reconstruct the fate of a chemical in the environment (Figure 27.1). This quantitative description usually takes the form of a mass balance model. The idea is to compartmentalize the environment into defined units (control volumes) and to write a mathematical expression for the mass balance within the compartment. As with pharmacokinetic models, transfer between compartments can be included as the complexity of the model increases. There is a great deal of subjectivity to assembling a mass balance model. However, each decision to include or exclude a process or compartment is based on one or more assumptions—most of which can be tested at some level. Over time the applicability of various assumptions for particular chemicals and environmental conditions become known and model standardization becomes possible. 

Trace element compositions of airborne particles are important for determining sources and behavior of regional aerosol, as emissions from major sources are characterized by their elemental composition patterns. We have investigated airborne trace elements in a complex regional environment through application of receptor models. A subset (200) of fine fraction samples collected by Shaw and Paur (1,2) in the Ohio River Valley (ORV) and analyzed by x-ray fluorescence (XRF) were re-analyzed by instrumental neutron activation analysis (INAA). The combined data set, XRF plus INAA, was subjected to receptor-model interpretations, including chemical mass balances (CMBs) and factor analysis (FA). Back trajectories of air masses were calculated for each sampling period and used with XRF data to select samples to be analyzed by INAA. 

Chemical mass balances use flux, the definitive term for chemical mobility, in their formulation (Bird et al., 2002). It simplifies, clarifies, and unifies the derivation procedure needed in this complex subject. Therefore, fluxes are imbedded in the CE. Decomposing Equation 2.1, as is done in the following paragraph, reveals the basic flux terms and provides an entrde to the ones used in chemodynamic modeling and the mass-transport processes covered in this book. By assuming steady-state, constant properties, no reaction, dilute solution (i.e., <5%) and focusing only on the z-dimension Equation 2.1 can be written as ... 

Models of BCR can be developed on the basis of various view points. The mathematical structure of the model equations is mainly determined by the residence time distribution of the phases, the reaction kinetics, the number of reactive species involved in the process, and the absorption-reaction regime (slow or fast reaction in comparison to mass transfer rate). One can anticipate that the gas phase as well as the liquid phase can be either completely backmixed (CSTR), partially mixed, as described by the axial dispersion model (ADM), or unmixed (PFR). Thus, it is possible to construct a model matrix as shown in Fig. 3. This matrix refers only to the gaseous key reactant (A) which is subjected to interphase mass transfer and undergoes chemical reaction in the liquid phase. The mass balances of the gaseous reactant A are the starting point of the model development. By solving the mass balances for A alone, it is often possible to calculate conversions and space-time-yields of the other reactive species which are only present in the liquid phase. Heat effects can be estimated, as well. It is, however, assumed that the temperature is constant throughout the reactor volume. Hence, isothermal models can be applied. 

The ultimate objective of this handbook is to enable the user to obtain numerical estimates of mass transport parameters for inclusion in quantitative models describing chemical fate. All quantitative models that address chemical fate derive their origin from the Lavoisier mass balance. On the subject of calcinations of metals (i.e., oxidation) he wrote I realize that the property of increasing weight by calcinations, which is simply a slower combustion, was not particular to metals, as has been thought, but that it was a general law in nature to which a large number of solid and liquid bodies... 

By adopting a system approach, the book deals with a wide range of subjects normally covered in a number of separate courses— mass and energy balances, transport phenomena, chemical reaction engineering, mathematical modeling, and process control. Students are thus enabled to address problems concerning physical systems, chemical reactors, and biochemical processes (in which microbial growth and enzymes play key roles). 

The equations presented so far for the multigrain model are mass- and energy-balance equations in a spherical catalyst particle used for conventional heterogeneously catalyzed reactions subjected to a moving boundary due to polymer formation. To predict polymer properties such as chain length and chemical composition, these monomer and temperature profiles must be coupled with an additional set of equations that describes polymerization and termination mechanisms... 

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