Mass kinetics modeling

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

The failure to identify the necessary authigenic silicate phases in sufficient quantities in marine sediments has led oceanographers to consider different approaches. The current models for seawater composition emphasize the dominant role played by the balance between the various inputs and outputs from the ocean. Mass balance calculations have become more important than solubility relationships in explaining oceanic chemistry. The difference between the equilibrium and mass balance points of view is not just a matter of mathematical and chemical formalism. In the equilibrium case, one would expect a very constant composition of the ocean and its sediments over geological time. In the other case, historical variations in the rates of input and removal should be reflected by changes in ocean composition and may be preserved in the sedimentary record. Models that emphasize the role of kinetic and material balance considerations are called kinetic models of seawater. This reasoning was pulled together by Broecker (1971) in a paper called "A kinetic model for the chemical composition of sea water."... 

Minimizing the cycle time in filament wound composites can be critical to the economic success of the process. The process parameters that influence the cycle time are winding speed, molding temperature and polymer formulation. To optimize the process, a finite element analysis (FEA) was used to characterize the effect of each process parameter on the cycle time. The FEA simultaneously solved equations of mass and energy which were coupled through the temperature and conversion dependent reaction rate. The rate expression accounting for polymer cure rate was derived from a mechanistic kinetic model. 

In this work, the MeOH kinetic model of Lee et al. [9] is adopted for the micro-channel fluid dynamics analysis. Pressure and concentration distributions are investigated and represented to provide the physico-chemical insight on the transport phenomena in the microscale flow chamber. The mass, momentum, and species equations were employed with kinetic equations that describe the chemical reaction characteristics to solve flow-field, methanol conversion rate, and species concentration variations along the micro-reformer channel. 

OS 63] ]R 27] ]P 46] Experimental results were compared with a kinetic model taking into account liquid/liquid mass transfer resistance [117]. Calculated and experimental conversions were plotted versus residence time the corresponding dependence of the mass-transfer coefficient k,a is also given as well (Figure 4.78). 

Main axis experimental conversions ( ) intrinsic kinetic model (solid line) kinetic model + mass transfer kinetics (dashed line). Secondary axis variation of computed k,o with flow rate. 

This system displays a two-enzyme kinetic model in which bioconversion is controlled by the interaction between the two reactions and the mass transfer. This situation offers a more realistic model for the conditions occurring in vivo, in which some pathways of intermediary metabolism consist of linear sequences of reactions. These pathways take place in highly organized compartments. 

Beginning in the late 1980s, a number of groups have worked to develop reactive transport models of geochemical reaction in systems open to groundwater flow. As models of this class have become more sophisticated, reliable, and accessible, they have assumed increased importance in the geosciences (e.g., Steefel et al., 2005). The models are a natural marriage (Rubin, 1983 Bahr and Rubin, 1987) of the local equilibrium and kinetic models already discussed with the mass transport... 

In the next chapter (Chapter 27) we show calculations of this type can be integrated into mass transport models to produce models of weathering in soils and sediments open to groundwater flow. In later chapters, we consider redox kinetics in geochemical systems in which a mineral surface or enzyme acts as a catalyst (Chapter 28), and those in which the reactions are catalyzed by microbial populations (Chapter 33). 

As shown in Example 22-3, for solid particles of the same size in BMF, the form of the reactor model resulting from equation 22.2-13 depends on the kinetics model used for a single particle. For the SCM, this, in turn, depends on particle shape and the relative magnitudes of gas-film mass transfer resistance, ash-layer diffusion resistance and surface reaction rate. In some cases, as illustrated for cylindrical particles in Example 22-3(a) and (b), the reactor model can be expressed in explicit analytical form additional results are given for spherical particles by Levenspiel(1972, pp. 384-5). In other f l cases, it is convenient or even necessary, as in Example 22-3(c), to use a numerical pro-... 

A unified gas hydrate kinetic model (developed at ARC) coupled with a thermal reservoir simulator (CMG STARS) was applied to simulate the dynamics of CH4 production and C02 sequestration processes in the Mallik geological zones. The kinetic model contains two mass transfer equations one equation transfers gas and water into hydrate, and a decomposition equation transfers hydrate into gas and water (Uddin etal. 2008a). 

Similar to generalized mass-action models, lin-log kinetics provide a concise description of biochemical networks and are amenable to an analytic solution, albeit without sacrificing the interpretability of parameters. Note that lin-log kinetics are already written in term of a reference state v° and S°. To obtain an approximate kinetic model, it is thus sometimes suggested to choose the reference elasticities according to simple heuristic principles [85, 89]. For example, Visser et al. [85] report acceptable result also for the power-law formalism when setting the elasticities (kinetic orders) equal to the stoichiometric coefficients and fitting the values for allosteric effectors to experimental data. 

Evaluating the structural kinetic model, we first consider the possibility of sustained oscillations. Starting with the simplest scenario, all saturation parameters are set to unity, corresponding to bilinear mass-action kinetics and... 

The construction of the structural kinetic model proceeds as described in Section VIII.E. Note that in contrast to previous work [84], no simplifying assumptions were used the model is a full implementation of the model described in Refs. [113, 331]. The model consists of m = 18 metabolites and r = 20 reactions. The rank of the stoichiometric matrix is rank (N) = 16, owing to the conservation of ATP and total inorganic phosphate. The steady-state flux distribution is fully characterized by four parameters, chosen to be triosephosphate export reactions and starch synthesis. Following the models of Petterson and Ryde-Petterson [113] and Poolman et al. [124, 125, 331], 11 of the 20 reactions were modeled as rapid equilibrium reactions assuming bilinear mass-action kinetics (see Table VIII) and saturation parameters O1 1. 

The two-phase kinetic model developed by Karickhoff (65) is capable of fitting either the sorption or desorption of a sorbing solute. For linear isotherms, the mathematical description given by Karickhoff (1) and others (67, 70, 71) is virtually identical to that of a mass transfer process (72). 

Behr and Obendorf [21] proposed a step-wise reaction model, according to which diethers are formed from monoether and isobutene and triether is formed from diethers and isobutene. In the simplified kinetic model no difference was considered between the two monoethers and the two diethers, and disproportion reactions and all side reactions were neglected (Fig. 10.6). The conversion rate was modeled without taking into account any mass transfer processes and phase... 

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