Reaction-rate model

The reaction rate model is based on total enzyme, substrate and inhibitor concentrations. 

The kinetics of culture media sterilisation describe the rate of destruction of microorganisms by steam using a fust-order chemical reaction rate model. As the population of microorganisms (N) decreases with time, the rate is defined by the following equation ... 

A Langmuir-Hinshelwood reaction rate model for the reaction between an adsorbed nitric oxide molecule and one adjacently adsorbed hydrogen molecule is described by ... 

Furthermore, one often finds that best fits of data may give rise to negative adsorption equilibrium constants. This result is clearly impossible on the basis of physical arguments. Nonetheless, reaction rate models of this type may be entirely suitable for design purposes if they are not extrapolated out of the range of the experimental data on which they are based. 

Although the formulation of such a theory has never been achieved, Eyring s absolute reaction rate model [123] has several features in common with such theory. 

In the model-specification stage, we concentrate upon two types of reaction-rate models, the power-function model... 

The latter danger is, of course, potentially present any time any data interpretation is attempted, particularly if nature is assumed always to follow Eq. (1). The only course of action is to attempt to include as much theory in the model as possible, and to confirm any substantial extrapolation by experiment. It is erroneous, however, to presume that kinetic data will always be so imprecise as to be misleading. The use of computers and statistical analyses for any linear or nonlinear reaction rate model allows rather definite statements about the amount of information obtained from a set of data. Hence, although imprecision in analyses may exist, it need not go unrecognized and perhaps become misleading. 

The concept of the reaction-rate model should be considered to be more flexible than any mechanistically oriented view will allow. In particular, for any reacting system an entire spectrum of models is possible, each of which fits certain overlapping ranges of the experimental variables. This spectrum includes the purely empirical models, models accurately describing every detail of the reaction mechanism, and many models between these extremes. In most applications, we should proceed as far toward the theoretical extreme as is permitted by optimum use of our resources of time and money. For certain industrial applications, for example, the closer the model approaches... 

In reaction-rate modeling, precise parameter estimates are nearly as essential as the determination of the adequate functional form of the model. For example, in spite of imprecisely determined parameters, an adequate model will still predict the data well over the range that the data are taken,... 

The procedure to be followed, then, is to estimate the parameters K within each reaction-rate model by some appropriate technique (K8). The intrinsic parameter A can then be estimated by linear least squares. Owing to experimental error in the data, this estimate of A will typically be neither plus nor minus one-half. Hence the remaining portion of the analysis is to estimate the... 

An intrinsic parameter is one that is inherently present in or arises naturally from a reaction-rate model. These parameters, which are of a simpler functional form than the entire rate model, facilitate the experimenter s ability to test the adequacy of a proposed model. Using these intrinsic parameters, this section presents a method of preparing linear plots for high conversion data, which is entirely analogous to the method of the initial-rate plots discussed in Section II. Hence, these plots provide a visual indication of the ability of a model to fit the high conversion data and thus allow a more... 

The development of an adequate mathematical model representing a physical or chemical system is the object of a considerable effort in research and development activities. A technique has been formalized by Box and Hunter (B14) whereby the functional form of reaction-rate models may be exploited to lead the experimenter to an adequate representation of a given set of kinetic data. The procedure utilizes an analysis of the residuals of a diagnostic parameter to lead to an adequate model with a minimum number of parameters. The procedure is used in the building of a model representing the data rather than the postulation of a large number of possible models and the subsequent selection of one of these, as has been considered earlier. That is, the residual analysis of intrinsic parameters, such as Cx and C2, will not only indicate the inadequacy of a proposed model (if it exists) but also will indicate how the model might be modified to yield a more satisfactory theoretical model. 

Theory for the transformation of the dependent variable has been presented (Bll) and applied to reaction rate models (K4, K10, M8). In transforming the dependent variable of a model, we wish to obtain more perfectly (a) linearity of the model (b) constancy of error variance, (c) normality of error distribution and (d) independence of the observations to the extent that all are simultaneously possible. This transformation will also allow a simpler and more precise data analysis than would otherwise be possible. 

The SGS turbulence model employed is the compressible form of the dynamic Smagorinsky model [17, 18]. The SGS combustion model involves a direct closure of the filtered reaction rate using the scale-similarity filtered reaction rate model. Derivation of the model starts with the reaction rate for the ith species, to i", which represents the volumetric rate of formation or consumption of a species due to chemical reaction and appears as a source term on the right hand side of the species conservation equations ... 

Fitting Reaction Rate Models to Rate Data... 

Investigation 9 dealt with reaction rate models for the catalytic hydrogenation of propylene over Pt-alumina. Computations via Eq. (7.1-15) were given for 15 reaction models, the best of which were constructed from evidence on multiple surface species along with the reactor data. 

The selectivity problem has hardly been treated by kinetic analysis. Recently Bourne published a detailed kinetic selectivity study on the aldehyde formation [106b]. The activation energy required for the formation of n- and isobutanal was determined to be 54 and 82 kJ/mol, respectively. The reaction rate models r and /"iso (eqs. (9) and (10)) explained the observed n/i ratios at different reaction conditions within 8 % standard deviation from the experimental results. 

NEB reaction rate model system containing sorbitol or no added plasticizer. Rate against moisture (a) and water activity (b) (Labuza et al., 1977). 

HIE) 1973 Eckert, E., Hlavacek, V., Marek, M. Catalytic Oxidation of CO on Cu0-A1203, I. Reaction Rate Model Discrimination, Chem. Eng. Comm. vol. 1, 89-94. II. Measurement and Description of Hysteresis and Oscillations in a Laboratory Catalytic Recycle Reactors Chem. Eng. Com. vol. 1, 95-102... 

The last mentioned assumption allows the use of separable kinetics. Thus the reaction rate model in a deactivating system may be written as two simultaneous equations ... 

The lack of data is obvious and surprising at a time when the Ruhrchemie/ Rhone-Poulenc process has been in operation for more than 20 years. A rigid reaction rate model, established under idealized conditions, becomes complex and complicated when it is transferred to the hydroformylation of lower olefins under conditions relevant to the industrial practice, as the mass transfer phenomena involved in a triphasic system (gas-liquid-liquid) in large reactors have to be taken... 

In terms of the reaction-rate model, the influence of the sign of the overpotential, r CT, on the dominance of the reaction components is illustrated by the curves of Fig. 3.8. When r CT = 0, the Gel versus distance curve represents the equilibrium condition and corresponds to the curve in Fig. 3.6. The activation energies for the oxidation and reduction components are equal, the oxidation and reduction rates are therefore equal, and the interface reaction is at equilibrium. If r CT is made positive by, for example, connecting the metal to the positive terminal of an external source as in Fig. 3.7, Gel M<> is raised relative to Gel Mm+, and net oxidation occurs. That is, the activation energy for the oxidation component has been reduced relative to the reduction component of the... 

Details of the kinetic parameters and reaction rate model are given in chapter 3. With reference to Figure 5.8, the mass and heat balance for the catalyst pellet surface can be written as ... 

Details of the kinetic parameters and reaction rate model are given in chapter 3. 

The mixed side-pore diffusion model also reasonably simulated the experimental data (Figures 5a and 5b). This model was slightly more accurate than the reaction-rate model in simulating breakthrough curves for a range of input concentrations (Figure 5a-5c) however, significant discrepancies also were observed between experimental data and model simulations at concentrations of less than 0.01 mmol/1 Mo(VI). 

The concept of Mo(VI) diffusion into and out of side pores that had an immobile-water phase resulted in a more accurate simulation of experimental breakthrough curves for a wider range of concentrations. The mixed side-pore diffusion model could be used to fit a particular experimental breakthrough curve with about the same degree of accuracy as the reaction rate model however, the mixed side-pore diffusion model was applicable for a wider range of concentrations. 

Figure 2 shows experimental data points for the catalyzed ABA homopolymer system at different temperatures and fitting curves according to equation 13. This figure also indicates that the reaction rate model is adequate. Rate constants and activation energies are listed in Table 1. It is obvious that the catalyst sodium acetate plays a very marginal role. Arrhenius plots for catalyzed and uncatalyzed ABA homopolyesterification reaction is indicated in Figure 3. Kinetics in systems comprising 80 to 90% of ABA were also studied and evaluated according to equation 13 both for uncatalyzed and catalyzed reactions.

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