Model description and assumptions

The CFD simulation of the MREF can be run over by a commercial code, where appropriate user-defined routines need to be added in order to model chemical reactions and permeation mechanism. In this case we have adopted ANSYS Fluent version 6.3.26 (ANSYS Inc., 2010) the setup for the numerical model is 2D axisymmetric calculator, with double precision, pressure-based solver and steady-state condition. 

In this section, the mathematical model built behind the simulation is described, together with certain characteristics such as membrane permeance and catalyst load for a configuration set as base case. Further on, results are shown for different simulated scenarios in comparison to the defined base case. In all cases modelled, the fuel fed at the inlet of the system is assumed to be pure methane. The validation of the model, already discussed in Roses et al. (2010b), showed good agreement with experimental data and also compared with similar simulation work. 

The thermodynamic and physical properties of the gas mixture reacting in the fuel processor are described in detail because of the strong dependency of reaction kinetics on temperature and composition, hence linked to thermal conductivities and diffusion velocity. 

Specific heat capacity of the gas mixture is calculated as mass fraction average of pure species  

Density, thermal conductivity and dynamic viscosity properties for gas mixtures are calculated with the assumption of ideal gas mixing, expressed as follows  

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Recently, Pallares and Johnsson [106] presented an overview of the macroscopic semi-empirical models used for the description of the fluid dynamics of circulating fluidized bed combustion units. They summarized the basic modeling concepts and assumptions made for each model together with the major advantages and drawbacks. In order to make a structured analysis of the processes involved, the CFBC unit is often divided into 6 fluid dynamical zones like the bottom bed, freeboard, exit zone, exit duct, cyclone and downcomer and particle seal, which have been shown to exhibit different fluid dynamical behavior. 

These spreadsheets formed the basis for the model review with which reference to the model stractures in FT+ where required. It is desirable that all information regarding the event data (excluding the change history) should be held in the FT+ model. However, there are restrictions in terms of the number of notes fields available (8) and the size of those fields (255 characters). Also, some of these fields may be required for description and assumptions regarding the logic. 

Adequate support from the facility staff is absolutely essential. The facility staff must help the analysis team gather pertinent documents (e.g., PSilDs, procedures, software descriptions, material inventories, meteorological data, population data) and must describe current operating and maintenance practices. The facility staff must then critique the logic model(s) and calculation(s) to ensure that the assumptions are correct and that the results seem reasonable. The facility staff should also be involved in developing any recommendations to reduce risk so they will fully understand the rationale behind all proposed improvements and can help ensure that the proposed improvements are feasible. Table 12 summarizes the types of facility resources and personnel needed for a typical QRA. 

The key attribute of flows in micro devices is their laminar character, which stands in contrast to the mostly turbulent flows in macroscopic process equipment. Owing to this feature, micro flows are a priori much more accessible to a model description than macro flows and can be described by first-principle approaches without any further assumptions. In contrast, for the simulation of turbulent flows usually a number of semi-heuristic models are applied, and in many situations it is not clear which description is most adequate for the problem under investigation. As a result, it stands to reason to assume that a rational design of micro reactors... 

There are various parameters and assumptions defining radionuclide behavior that are frequently part of model descriptions that require constraints. While these must generally be determined for each particular site, laboratory experiments must also be conducted to further define the range of possibilities and the operation of particular mechanisms. These include the reversibility of adsorption, the relative rates of radionuclide leaching, the rates of irreversible incorporation of sorbed nuclides, and the rates of precipitation when concentrations are above Th or U mineral solubility limits. A key issue is whether the recoil rates of radionuclides can be clearly related to the release rates of Rn the models are most useful for providing precise values for parameters such as retardation factors, and many values rely on a reliable value for the recoil fluxes, and this is always obtained from Rn groundwater activities. These values are only as well constrained as this assumption, which therefore must be bolstered by clearer evidence. 

No explicit mathematical model of the method was presented. However, a short descriptive model was outlined For each run, the average ignition and combustion rate (expressed as weight of fuel ignited or burnt per unit bed area and unit time) were calculated by determining the time taken for the ignition front to pass down through the bed and the completion of burn-out, respectively. No discussion is presented about limitations and assumptions of the method. 

A short descriptive model showed how the combustion heat rate was calculated. No discussion is presented about limitations and assumptions of the method. 

Estimation of this radiation dose is sometimes accomplished by modeling the sequence of events involved in the acquisition, deposition, clearance, and decay of radium within the body. While based on the current understanding of experimental data on radium toxicokinetics, different models make different assumptions about these processes, thereby resulting in different estimates of dose and risk. These models are described in numerous reports including BEIR IV (1988), ICRP (1979), and Raabe et al. (1983). In this section, the toxicokinetics of radium are described based on the available experimental data rather than on descriptions derived from models. 

Taking into account the points describe above, in literature there are many models proposed to describe electrochemical-oxidation wastewater-treatment processes (Polcaro and Palmas 1997 Canizares et al. 1999 Panizza et al. 2001 etc.). They are based on many different description levels and assumptions. In this section, two... 

The constitutive equations of transport in porous media comprise both physical properties of components and pairs of components and simplifying assumptions about the geometrical characteristics of the porous medium. Two advanced effective-scale (i.e., space-averaged) models are commonly applied for description of combined bulk diffusion, Knudsen diffusion and permeation transport of multicomponent gas mixtures—Mean Transport-Pore Model (MTPM)—and Dusty Gas Model (DGM) cf. Mason and Malinauskas (1983), Schneider and Gelbin (1984), and Krishna and Wesseling (1997). The molar flux intensity of the z th component A) is the sum of the diffusion Nc- and permeation N contributions,... 

Figure 55 sketches the situation. The realistic potential includes lattice potential and interaction potential. Two functions are crucial in the description of the jump relaxation model, developed and refined by Funke et al.217"219 (i) the probability W(t) that no correlated backward jump has occurred at time t (-W being the backward jump rate) and (ii) g(t) describing the positional mismatch (-g measuring the stabilization rate). The basic assumption of the jump relaxation model is... 

The basic concept is that estimated results for pesticide movements and exposure levels vary greatly with the model types and modeling philosophy. Before con-dncting a model exercise, a conceptual check of the model is needed to ascertain if the model contains aU relevant routes of exposure. A simple model, such as SCIES, is based on worst-case assumptions, and may be sufficient for inhalation risk assessment. More complicated simulation models, such as CONSEXPO and InPest, provide information on the amounts of pesticides on the room materials, as well as the airborne concentration, and they are appropriate for risk assessment via aU routes. Even in complicated models, each mechanistic model contains assumptions to simplify the process description of the pesticide movement in the real world . The underlying assumptions for each of the models, and the relevant processes they implicate, are criteria to consider when selecting an appropriate model. Therefore, the validity of the assumptions used for the assessment should be considered before using the model, and they should be well documented. A simple phrase such as, we used model xx to estimate an exposure level of yy, is inadequate for documentation purposes. 

Equation (10-1) is based on the assumption of simple additivity of all interactions and a competitive nature of analyte/eluent interactions with the stationary phase. The paradox is that these assumptions are usually acceptable only as a first approximation, and their application in HPLC sometimes allows the description and prediction of the analyte retention versus the variation in elution composition or temperature. For most demanding separations where discrimination of related components is necessary, the accuracy of such prediction is not acceptable. It is obvious from the exponential nature of equation (10-1) that any minor errors in the estimation of interaction energy, or simple underestimation of mutual influence of molecular fragments (neglected in this model), will generate significant deviation from predicted retention factors. 

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