Volume reaction model

These models are also grouped from a different point of view as grain models, pore models, volume reaction models and deactivation models. In number of these models, changes in pore structure during the reaction and variations in diffusion and reaction parameters are considered. 

The shrinking core and the volume-reaction models have been examined to interpret the conversion-time data of combustion and steam gasification of the gingko nut shell char [4]. The shrinking core model provides the better agreement with the experimental data. With the shrinking core model, the relationship between [1-(1-X) ] and the reaction time t at 350°C -... 

Scientists of the Institute of Science and Technology of UMIST (Manchester, UK) and collaborating laboratories have developed a network-of-zones model (Mann et al, 1981 Mann and Knysh, 1984 Mann and El-Hamouz, 1992, 1995 Mann et al, 1995 Nienow et al, 1992 Togatorop et al, 1994 and Wang and Mann, 1990, 1992). According to this model a reaction volume is represented by an assembly of backmixed zones, each of equal volume. The liquid... 

Here the first term arises from the diffusive approach of reactants A into trapping spheres around B s it is nothing but the standard expression (8.2.14). The second term arises due to the direct production of particles A inside the reaction spheres (the forbidden for A s fraction of the system s volume). Unlike the Lotka-Volterra model, the reaction rate is defined by an approximate expression (due to use of the Kirkwood superposition approximation), therefore first equations (8.3.9) and (8.3.10) of a set are also approximate. 

For this reason, several mathematical models consider reactions (3.15) and (3.16) confined at the electrode-electrolyte interface (e.g. [6, 33, 34]). This simplification is introduced in Section 3.4, while in the present section the reaction zone is considered as a finite volume. 

The above kinetic models are based on the surface action law that is absolutely analogous to the mass action law for volume reactions in ideal systems. In this case a model of "an ideal adsorbed layer acts, which is valid under the following assumptions ... 

Many methods have been used to size relief systems area/volume scaling, mathematical modeling using reaction parameters and flow theory, and empirical methods by the Factory Insurance Association (FIA). The Design Institute for Emergency Relief Systems (DIERS) of the AIChE has performed studies of sizing reactors undergoing runaway reactions. Intricate laboratory instruments as described earlier have resulted in better vent sizes. 

Several models that describe gas-solid noncatalytic reactions are summarized in Table 7-7. The first two, the sharp interface and volume reaction models, are pseudo-homogeneous, form part of the class of shrinking core models, and can be treated by using the Thiele modulus and effectiveness factor concept. The last three are heterogeneous models. 

Volume reaction model Grain model Reacting solid is also porous. Reaction occurs everywhere in the particle. Particle is divided into identical solid spherical... 

FIG 7-12 Typical concentration profiles for the volume reaction model. [From Wen, Noncatalytic Heterogeneous Solid-Fluid Reaction Models, Ind. Eng. Chem. 60(9) 34-54 (1968), Fig. 3.]... 

Volume Reaction Model A typical concentration profile for the volume reaction model is shown in Fig. 7-12. 

The final elements of the mass balances are the adsorption equilibria or the adsorption kinetics. According to Eqs. 6.5 and 6.6, adsorption and desorption steps are modeled as reactions with finite rate. The volumetric reaction rate based on the solid volume of all particles (Eq. 6.20) in the volume element is... 

Values of reaction orders (Table 3) and competitive sorption effects mentioned in Section 3.3 could be quantified more satisfactorily using a adsorption kinetic model. The model was derived under the assumptions of constant volume reaction, nitrous oxide reacting from the gas phase (because of the small influence of nitrous oxide feed concentration on phenol selectivity), three times higher phenol sorption constant than benzene sorption constant (Kc6H5oh 3 Kc6H6, 3s derived from sorption simulation calculations), but without considering the dependency on temperature (reaction temperature 400°C) [5,7]. 

The general conservation equations for the solid and reactant species for the volume reaction model in dimensionless form are as follows ... 

A general mathematical formulation that is applicable to most models described in the earlier sections begins with the volume reaction model described by Equations (11.69) through (11.72). Then, for a reaction first order in the gaseous component, we recast these equations as... 

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