Kinetic modeling parameter

The first-order and fractional power kinetics were also used to describe the behavior of DEHP biodegradation in the thermophilic phase, including the initial mesophilic phases (phase I) and the phase thereafter (phase II), respectively [62]. The fractional power kinetic model parameters, i.e., K and N. were calculated by (l)-(3) and derived from a plot of log (C/Co) versus log(f). The half time (f0.s) of DEHP degradation in phases I and II was calculated using first-order and fractional power kinetic equations (3), respectively. 

Vollertsen, J. and T. Hvitved-Jacobsen (1999), Stoichiometric and kinetic model parameters for microbial transformations of suspended solids in combined sewer systems, Water Res., 33(14), 3127-3141. 

This equation imposes limitations on kinetic model parameters. Whence... 

L. L. Oliveira and E. Biscaia Catalytic cracking kinetic models. Parameter estimation and model evaluation. Industrial and Engineering Chemistry Research, 28, 264-271 (1989). 

Evaluation of the appropriate kinetic model parameter from kinetic measurement defines the degree of conversion as a function of time and temperature, a T, t). This relationship is then used together with chemoviscosity and gel effects to define the thermoset process. 

Espitalie J., Marquis F., Drouet S. (1993) Critical study of kinetic modelling parameters. In Basin Modelling Advances and Applications (ed. Dore A.G. et al.) Norwegian Petroleum Soc. Spec. Publn 3, 233—42.Amsterdam Elsevier. 

In the field of pharmacokinetics, there has been much recent work on developing methods for estimating interindividual variation in kinetic model parameters, particularly in sparse data situations where there are... 

Density data and crystallization kinetics model parameters for various iPPs... 

Figs. 17.a and b and 18.a and b show a comparison of the density dependence upon cooling rate for the iPP grades studied, whereas Table 2 reports the crystallization kinetics model parameters calculated by a best fitting procedure not only on the basis of the final monoclinic and mesomorphic content of the quenched samples, taken from the deconvolution of the WAXD patterns, but also accoimting for results which provide the time and the temperature at the maxima of the crystallization rate (isothermal tests and DSC measurements) respectively. For this purpose a mulfiobjecfive optimization code was adopted. 

Todic et al. [14] developed a comprehensive micro-kinetic model based on the carbide mechanism that predicts FT product distribution up to carbon number 15. This model explains the non-ASF product distribution using a carbon number dependent olefin formation rate (e term). The rate equations for the olefins and paraffins used in the model are shown in Figure 2. The derivation of the rate equations and physical meaning of the kinetic parameters, as well as their fitted values, can be found in Todic et al. [14]. In the current study, a MATLAB code which uses the Genetic Algorithm Toolbox has been developed, following the method of Todic et al. [14], to estimate the kinetic model parameters. In order to validate our code, model output from Todic et al. [14] was used as the input data to our code, and the kinetic parameter values were back-calculated and compared to the values fi om [14], as shown in Table 1. The model has 19 kinetic parameters that are to be estimated. The objective function to be minimized was defined as... 

Kavitha, D. and Namasivayam, C. 2008. Capacity of activated carbon in the removal of acid brilhant blue Determination of equilibrium and kinetic model parameters. Chem. Eng. J. 139 453-461. 

Kinetic model parameters were adjusted to find the best values fitting experimental data with simulation results. A multiparametric, non-linear regression based on Marquardt algorithm was employed. The agreement of adjustment for each model can be compared in Table 2 by means of the variance values ... 

Oliveira, L.L. and Biscaia, E.C., "Catalytic Cracking Kinetic Models. Parameter Estimation and Model Evaluation", Ind. Eng. Chem. Res., 28, 264-271 (1989). 

Experimental data extracted from different levels (batch reactor, pilot-plant, and industrial units) are extensive and the derived kinetic model parameters are indeed dependent on feed properties. Thus, using parameters determined for one feed to others is risky and can introduce more error in the prediction of product yields. This is one typical drawback of lumped-based models. Interestingly, only one model reported the calculation of activation energies and frequency factors as function of molecular weight of the lumps involved in the reaction scheme. The reported results... 

In the following sections, the simulation of hydrotreating of heavy petroleum carried out at moderate reaction conditions in a bench-scale reactor is performed by means of a heterogeneous model, particularly for removing sulfur, nickel, and vanadium. The capability of prediction of the reactor model is also tested under conditions different from those used to determine the model parameters. Experimental information about the effect of temperature, space velocity, and pressure in a wide range of values is used to develop the kinetic model parameters. Particular emphasis is given on detailed explanations of how to determine all the parameters of the developed model. 

This procedure can be applied for data at different temperatures and other variables such as type of catalyst, feed, pressure, etc., in order to establish the dependence of the kinetic model parameters on these variables for any particular hydrocracking process. This is mathematically possible although the final correlations could be applicable only for the specific ranges of conditions under which the parameter values are derived. 

First, Equation 11.55 was solved in order to find the hydrocracking kinetic model parameters a, Oq, a, 8, and Then, by using these values. Equation 11.71 was resolved and the parameters p, and were found. All routines were written in MATLAB software. The criterion of minimization of the sum of square errors (SSE) obtained from the difference of calculated and experimental points was employed to determine all model parameters. More details of numerical solution of Equation 11.55 can be found elsewhere (Elizalde and Ancheyta, 2011). 

---