Description of the Model

To model multiphase reactors, the molar balance by phase can be written as (Gunjal and Ranade, 2007) 

Equation 9.1 is a balance that takes into account unsteady-state variations (dldti Cf)), the convective flux V -zUCf), the diffusive flux V - zCUDVf), and the term of gen-eration/disappearance of any compound ( S). This equation allows for modeling the performance of fixed-bed reactors, taking the catalyst as the solid phase, and liquid and gas as fluid phases. 

In Equation 9.1, k is any phase, / is the component in the mixture, Q is the total concentration in k phase, A, is the molar fraction of i compound in k phase, is the molecular velocity or average true velocity for averaged models of k phase, is the diffusivity of compounds, and is the term of generation/disapparition (source) for i species. 

Assuming steady-state and concentration variations only in the main direction of flow (z) in cylindrical coordinates. Equation 9.1 reduces to 

Taking the phase fraction and phase velocity as constant. Equation 9.2 becomes 

Desert woody shrub Tundra woody shrub -5 -45 0 500 400 10 

mean temperalure of llie coldest monlh in °C absolute minimum temperature in °C GDD5, growing degree-days on a S C base Sd, the minimum survivable wdnter snowpack in cm. 

Recently, an increasing number of studies have evaluated the CO2 exchange of terrestrial ecosystems, applying the experimental methods outlined above. Results for 51 different forest and 

Latitudinal averages of flux-weighted A, estimates display a tri-modal distribution with A, values being greatest in the boreal zones of both hemispheres and the humid tropics (Fig. 4). Due to large longitudinal variations within a latitudinal band of 0.5°, the moist, highly productive tropical rain forests (between 10° N and 

FIGURE 3 Modeled ecosystem carbon-isotope discrimination. See Sec. 3 for details on B10ME3.5. 

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In appendix, a formal description of the model can be found, using the Express language, based on the STEP (STandard for the Exchange of Product model data) standardized approach (ISO 10303). 

D. J. Greenwood and T. V. Karpinets, Dynamic model for the effects of K-fertilizer on crop growth, K-uptake and soil-K in arable cropping I. Description of the model. Soil Use Mift. i34 19, (1997). 

ICRP (1989) Americium Biokinetics Model Description of the model. 

Description of the model. The Leggett Model includes a central compartment, 15 peripheral body compartments, and 3 elimination pools, as illustrated in Figure 2-9. Transport of lead between... 

The complete description of the model is beyond the scope of the paper. In Figure 5 it is shown that at low attachment rates the deposition rate of the unattached daughters ( un) can be evaluated and at high attachment rates the ventilation rate. 

Given the understanding that our description of molecular transport junctions is based on a description of the model that we build, we can proceed to some of the concepts that characterize the mechanistic behaviors. 

Majone B, Bertagnoli A, Beilin A, Botter G, Settin T, Marani M, Rinaldo A (2005) Structure of the modeling system with detailed description of the models. AquaTerra Deliverable C3.2. 

Description of the model. The Perbellini model has eight compartments (See Figure 2-5) ... 

Description of the Model Reesterification Reaction within the Framework of a Strange Diffusion Concept... 

Description of the model. Benzene and its metabolites (phenol, catechol, and hydroquinone) were assumed to compete for the same reaction site on the enzyme cytochrome P-450 2E1. In addition, phenol can undergo both oxidation and conjugation, although the enzymes for each of these reactions are localized in different compartments of the liver, and competition between them is thereby regulated. 

The detailed description of the models currently being used to describe tunneling in enzyme-catalyzed reactions will be undertaken in a later part of our treatment in which theoretical studies will be reviewed and ideas about the role of protein motions will be a focus. At this point, we will briefly sketch the most commonly used ideas. 

With this description of the model we have adjusted the two dielectric constants D( = 55 and Dj. = 78 to compute the correlation functions of the three model compounds. 

Description of the Model. The Corley chloroform PBPK model was based on an earlier PBPK model developed by Ramsey and Andersen (1984) to describe the disposition of styrene exposure in rats, mice, and humans. A schematic representation of the Corley model (taken from Corley et al. 1990) is shown in Figure 2-5 with oral, inhalation, and intraperitoneal routes represented. The dermal route of exposure is not represented in this model however, others have modified the Corley model to include this route of exposure (see below). Liver and kidney are represented as separate compartments since both are target organs for chloroform. 

Description of the Model. The McKone (1993) PBPK model addressed potential exposure to chloroform by the inhalation and dermal routes. McKone revised existing shower-compartment, dermal uptake and PBPK models to produce a revised PBPK model for simulating chloroform breath levels in persons exposed in showers by the inhalation route only and by the inhalation and dermal routes combined. Parameters used by this model were taken primarily from two main sources, Jo et al. (1990a) and Corley et al. (1990). 

A full description of the modelling and control of multicomponent polymerisations is beyond the scope of this presentation since there are many exceptions to the above simplistic model hence details will be described elsewhere (9). 

Kinetic modeling of the transient absorption spectra is necessary in order to obtain estimates of the lifetimes and rate constants associated with the evolution of the intermediates observed during the dissociation. A detailed description of the modeling may be found in our work on the picosecond photodissociation of the natural car-boxy- and oxy- heme complexes (3,4). The model is designed to treat the dissociation as a series of first or second order steps indicated in pathways I and II, ones that are consistent with the transient absorption data and with arguments based on bottlenecks... 

The released U(VI) from the U()2 matrix will continue to be dissolved until saturation with secondary U(VI) solid phases is reached. The observations from both laboratory and natural systems would indicate that the kinetically preferred phase is hydrated schoepite. This will be denoted as U02(0H)2(s) for the sake of description of the model, although the correct notation would be U03-xH20, with x oscillating between 0 and 2. Depending on the presence of carbonates in the contacting solution, the reactions can be described as ... 

The description of the model up to this point is analogous to a description of a chromatographic model which incorporates the concept of the theoretical plate ( 5). ... 

Steady-state modeling calculations were performed to examine how congener-specific properties (such as sediment-water partition coefficients, Henry s law constants, and molecular diffusion rates) affect the transport and fate of PCBs. A basic description of the model, along with modeling results, is presented here to further explain the importance of physiochemical weathering processes in controlling the fate and distribution of PCB congeners in Twelve Mile Creek and the upper portion of Lake Hartwell. 

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