Testing kinetic models

Testing kinetic models involves the following procedures  

Propose possible mechanisms involving elementary steps. 

Assume that the rate equations for each elementary step can be written by inspection of the stoichiometric equation  

Assume that after a short initial period that the rates of concentration change of all active centers are zero. For example  

From the above assumption, (-rB )net = 0, steady state approximation. 

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Obtaining Kinetic Samples for Reactive Extrusion. To develop and test kinetic models, homogeneous samples with a well defined temperature-time history are required. Temperature history does not necessarily need to be isothermal. In fact, well defined nonisothermal histories can provide very good test data for models. However, isothermal data is very desirable at the initial stages of model building to simplify both model selection and parameter estimation problems. 

M. Greenfeld described unique laboratory experiments designed to stimulate and understand the complex chemistry of in-situ coal gasification. Developed at the Alberta Research Council, the gasification simulator was heavily instrumented with calorimeters and gas chromatographs to determine the enthalpy, composition, and kinetics of formation of the product gases. Computer techniques were used to calculate mass and heat balances and to test kinetic models. 

Most experimental kinetic curves are rather smooth, i.e, the concentration of adsorbate in solution monotonically decreases, but some kinetic curves reported in the literature have multiple minima and maxima, which are rather unlikely to be reproducible. Such minima and maxima represent probably the scatter of results due to insufficient control over the experimental conditions. For instance use of a specific type of shaker or stirrer at constant speed and amplitude does not necessarily assure reproducible conditions of mass transfer. Some publications report only kinetic data—results of experiments aimed merely at establishing the sufficient equilibration time in equilibrium experiments. Other authors studied adherence of the experimentally observed kinetic behavior to theoretical kinetic equations derived from different models describing the transport of the adsorbate. Design of a kinetic experiment aimed at testing kinetic models is much more demanding, and full control over all parameters that potentially affect the sorption kinetics is hardly possible. 

In today s competitive climate, investigators cannot spend much time on the clarification of the kinetics for a new process. At Union Carbide Corporation in the 1970s the study to replace the old and not very efficient butyraldehyde hydrogenation was done in three months. In another three months a kinetic model was developed and simultaneously tested in an existing single tube in a pilot-plant (Cropley et al,1984). Seldom is a completely new process studied for which no similar example exists in the industry. 

Some authors have not only given advice but have created methods to execute experiments to generate kinetic models. The Heuristic Approach to Complex Kinetics of Cropley (1978) which is well tested, is one that will be described next. Then, other recommendations will be discussed briefly. 

Remarks The aim here was not the description of the mechanism of the real methanol synthesis, where CO2 may have a significant role. Here we created the simplest mechanistic scheme requiring only that it should represent the known laws of thermodynamics, kinetics in general, and mathematics in exact form without approximations. This was done for the purpose of testing our own skills in kinetic modeling and reactor design on an exact mathematical description of a reaction rate that does not even invoke the rate-limiting step assumption. 

Studying the effects of such variations can be most helpful in designing the next round of kinetics experiments, to test the model under conditions where its validity can be confirmed or denied. Different models can be compared to be certain that the... 

The semibatch model GASPP is consistent with most of the data published by Wisseroth on gas phase propylene polymerization. The data are too scattered to make quantitative statements about the model discrepancies. There are essentially three catalysts used in his tests. These BASF catalysts are characterized by the parameters listed in Table I. The high solubles for BASF are expected at 80 C and without modifiers in the recipe. The fact that the BASF catalyst parameters are so similar to those evaluated earlier in slurry systems lends credence to the kinetic model. 

The kinetic model predicted the observed reaction rates, pressures, rates of pressure rise and temperature rise within order-of-magnitude accuracies. The accuracy of the kinetic model was better for the large-scale tests. 

We computed the percentage errors between the reaction rate computations based on the experiments with those based on the kinetic model. Note that, like the pressure and temperature comparisons, the accuracy of the calculations for reaction rates decreases as we compare Test 1 with Test 2 and Test 3- In Test 1 the error ranges from 3 to 21, in Test 2 it was 10 to 21, in Test 3 it ranged from 5 to 36. ... 

The experimental reaction rate computations based on equation (4) are primarily functions of the computed average solution temperature (T ). The kinetic model rate computations based on equation (1) or (2) are primarily functions of both "T " as well as the estimated conversion(s). Earlier we explained why we expected decreasing accuracies of estimating both the conversions and the average solution temperature in Tests 1, 2 and 3 respectively. 

Computer simulations have been useful for validating a kinetic model that Is not easily tested. The model was equally capable of describing multi-site polymerizations which can undergo either first or second order deactivation. The model parameters provided reasonably accurate kinetic information about the Initial active site distribution. Simulation results were also used as aids for Interpretation of experimental data with encouraging results. 

Recently a kinetic model was developed to describe the reactions occurring in the extruder (1). However, thorough testing and further development of this model was limited mainly because only samples of feed and extrudate could be obtained (2.31. Reacted samples with reaction times less than the minimum residence time of the extruder were not available. This minimum time was approximately 2.8 min. All reactions were generally completed within that time. Thus,this work had two primary objectives ... 

Finally, the constructed micro-kinetic model must of course be tested against measurements performed with real catalysts. Figure 7.23 shows a plot of the calculated output from the reactor against experimental values. Apparently, the micro-kinetic model describes the situation very well. This does not prove that the model is correct since models based on another series of elementary steps might also work. 

If a reliable kinetic model and data on cooling capacity are at hand, runaway scenarios can be examined by computer simulations and only final findings have to be tested experimentally. Such an approach has been presented, e.g. by Zaldivar et al. (1992). However, the detailed reaction mechanism and reaction kinetics are rarely known. Therefore, thermokinetic methods with gross (macro-)kinetics dominate among methods for data... 

Statistical testing of model adequacy and significance of parameter estimates is a very important part of kinetic modelling. Only those models with a positive evaluation in statistical analysis should be applied in reactor scale-up. The statistical analysis presented below is restricted to linear regression and normal or Gaussian distribution of experimental errors. If the experimental error has a zero mean, constant variance and is independently distributed, its variance can be evaluated by dividing SSres by the number of degrees of freedom, i.e. 

The simplest kinetic model applied to describe lipase catalyzed reactions is based on the classic Michaelis-Menten mechanism [10] (Table 3). To test this model Belafi-Bakd et al. [58] studied kinetics of lipase-catalyzed hydrolysis of tri-, di-, and mono-olein separately. All these reactions were found to obey the Michaelis-Menten model. The apparent parameters (K and V ) were determined for global hydrolysis. 

Timm, Gilbert, Ko, and Simmons O) presented a dynamic model for an isothermal, continuous, well-mixed polystyrene reactor. This model was in turn based upon the kinetic model developed by Timm and co-workers (2-4) based on steady state data. The process was simulated using the model and a simple steady state optimization and decoupling algorithm was tested. The results showed that steady state decoupling was adequate for molecular weight control, but not for the control of production rate. In the latter case the transient fluctuations were excessive. 

A network structure model has been developed from which a parameter that correlates well with physical measures of paint cure can be calculated. This model together with a kinetic model of crosslinking as a function of time and temperature has been used to evaluate the cure response of enamels in automotive assembly bake ovens. It is found that cure quality (as measured by the number and severity of under and overbakes) is good for a conventional low solids enamel. These results are in agreement with physical test results. Use of paints with narrower cure windows is predicted to result in numerous, severe under and over bakes. Optimization studies using SIMPLEX revealed that narrow cure window paints can be acceptably cured only if the bake time is increased or if the minimum heating rate on the car body is increased. 

The kinetic model simulations described above reveal straightforward methods of determining reversibility in chain transfer. In the cases simulated above, a reduction inM in connection with narrowing of the distribution such thatM IM < 2.0 indicates reversible chain transfer. These criteria provide a test for finding suitable combinations of catalyst and chain transfer agent for use in our two-catalyst system. 

The autoxidation of 3,5-di-terf-butylcatechol (H2DTBC) was frequently used to test the catalytic activity of various metal complexes. Speier studied the reaction with [Cu(PY)Cl] (PY = pyridine) in CH2C12 and CHCI3, and reported second-, first- and zeroth-order dependence with respect to Cu(I), 02 and substrate concentrations, respectively (41). The results are consistent with a kinetic model in which the rate determining oxidation of Cu(I) is followed by fast reduction of Cu(II) by H2DTBC. 

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