Second-order Reaction Model

Similarly, the rate of second-order reaction in a grid also decreases as a- 1, and even faster. As a result, the choosing of Cc is more critical. Fig. 9 shows the effect of Cc on surface temperature and burning rate of HMX. Compared with the bum rates using the first-order reaction model, as shown in Fig. 8, the bum rates for second-order reaction are higher at low Cc values, (e.g., 5.5 cm/s for 

Finally we note that as expected, the ignition time is not sensitive to solid phase reaction models, because the surface structure does not change significantly during the initial heating period. 

The choice of reaction model does make a difference in the modeling of HMX combustion. Different reaction models generate different burning surface structure, surface temperature and as a result, the burning rate of energetic materials. A critical concentration is introduced to the model to deal with the special problem that first-order and second-order reaction have. The effect of choosing this critical concentration turns out to be a very important factor to determine how well the model can simulate the combustion. 

The use of grids in the solid phase is a simple and efficient way to model complicated burning surface structure. The limitations of this model, however, are also evident. It creates some inevitable artificial treatment of surface reaction and heat transfer. 

This research is supported by the Center for Simulation of Accidental Fires and Explosions (C-SAFE) at the University of Utah, under LLNL subcontract B341493. 

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The polymerization rate of several diphenoxide salts with 4,4 -di-chlorodiphenylsulfone has been measured in methyl sulfoxide and other solvents. The experimental data conforms to a second-order reaction model, which consists of a high reaction rate constant at the monomer stage, followed by a lower reaction rate constant at subsequent polymerization stages. Based on this kinetic model, the reaction rate constants and activation energies have been determined. 

Fig. 6. Arrhenius plot for the second order reaction model (basic system)...

Drug stability studies may require the use of zero-, first-, or second-order reaction models. Reaction rates may be measured as a function of pH and buffer concentrations to determine the influence of various catalysis possibilities. For example, the hydrolysis of a compound may be pseudo first-order, as shown in Eq. (7) ... 

A second order reaction model gave a good fit to the polymerization reaction in both the catalyzed formulations. In the case of the extended system, this was also confirmed by isothermal measurements at 32°C (Figure 4). The slope of the plot of log reaction rate vs log fraction remaining was 2.1 before the discontinuity and 2 afterwards. This implies that second order kinetics are still followed after the discontinuity which occurs between 55 and 60% reacted. 

The adsorption properties of natural clinoptilolite toward Co were investigated by batch equilibration technique [07S2], The kinetic data were fitted by pseudo-second-order reaction model, and the adsorption isotherms were defined by the Langmuir equation. The adsorption capacity of the natural clinoptilolite was decreased by the competition among the metal ions in solution. The adsorption capacity reached 2.34 mg/g for Co. The adsorption of Co was low, at low pH, but increased remarkably with increasing pH and precipitated at pH > 8. The presence of EDTA hindered the adsorption of Co on clinoptiloUte. 

Sometimes the effect of the detention time is so strong that the overflow rate can be ignored and the scale-up is based on the so-called second order test procedure (as the flocculation process usually follows a second order reaction model ). The required detention time is determined by testing the residual solids concentrations in the supernatant under the conditions of mild shear. 

To determine the reaction order we plot ln(%p-methoxyphenylacetylene) versus time for a first-order reaction, and (%p-methoxyphenylacetylene) versus time for a second-order reaction (Figure A5.1). Because the straight-line for the first-order plot fits the data nicely, we conclude that the reaction is first-order in p-methoxyphenylacetylene. Note that when plotted using the equation for a second-order reaction, the data show curvature that does not fit the straight-line model. 

FIG. 23-15 Chemical conversion by the dispersion model, (a) First-order reaction, volume relative to plug flow against residual concentration ratio, (h) Second-order reaction, residual concentration ratio against kC t. 

Slesser and Highet (S15) have proposed a theoretical model for the case of a second-order chemical reaction taking place in a slurry reactor. This model is based on concepts very similar to those employed by Sherwood and Farkas, apart from the obvious complications resulting when one treats a second-order reaction. 

Section 5.1 shows how nonlinear regression analysis is used to model the temperature dependence of reaction rate constants. The functional form of the reaction rate was assumed e.g., St = kab for an irreversible, second-order reaction. The rate constant k was measured at several temperatures and was fit to an Arrhenius form, k = ko exp —Tact/T). This section expands the use of nonlinear regression to fit the compositional and temperature dependence of reaction rates. The general reaction is... 

Stepwise condensation polymerizations can be modeled as a second-order reaction of the functional groups. Let a be the concentration of functional groups so that = —ka - The following viscosity relationship... 

Determine the yield of a second-order reaction in an isothermal tubular reactor governed by the axial dispersion model with Pe = 16 and kt = 2. 

Some progress has been made in developing theoretical expressions for rj(6) for deactivation processes such as coking. Deactivation by loss of active sites can be modeled as a chemical reaction proceeding in parallel with the main reaction. It may be substantially independent of the main reaction. Site sintering, for example, will depend mainly on the reaction temperature. It is normally modeled as a second-order reaction ... 

The glycolysis of PETP was studied in a batch reactor at 265C. The reaction extent in the initial period was determined as a function of reaction time using a thermogravimetric technique. The rate data were shown to fit a second order kinetic model at small reaction times. An initial glycolysis rate was calculated from the model and was found to be over four times greater than the initial rate of hydrolysis under the same reaction conditions. 4 refs. 

Many, if not most, of the key reactions of chemistry are second-order reactions, and understanding this type of reaction is central to understanding chemical kinetics. Cellular automata models of second-order reactions are therefore very important they can illustrate the salient features of these reactions and greatly aid in this understanding. 

A second-order reaction takes place in a two-phase batch system. Reactant A is supplied by gas-liquid transfer and reactant B supplied by liquid feed. The model equations are... 

The model of a reactor consists of two equal sized CSTRs joined by a PFR whose residence time equals that of the combined CSTRs. A second order reaction with kC0t = 2 is to be studied by the maximum mixedness mechanism. More details of this problem are in problem P5.04.09 where the RTD is developed as... 

A second order reaction is to be conducted in a vessel whose RTD is an Erlang with n = 3. Find conversion with the dispersion and other models for... 

For complex chemical source terms, this expression generates new unclosed terms that are particularly difficult to model. Even for an isothermal, second-order reaction with... 

For non-linear chemical reactions, this term leads to new unclosed terms that are difficult to model. For example, even the isothermal second-order reaction, (3.142), where the joint dissipation chemical source term is given by... 

Very rarely are measurements themselves of much use or of great interest. The statement "the absorption of the solution increased from 0.6 to 0.9 in ten minutes", is of much less use than the statement, "the reaction has a half-life of 900 sec". The goal of model-based analysis methods presented in this chapter is to facilitate the above translation from original data to useful chemical information. The result of a model-based analysis is a set of values for the parameters that quantitatively describe the measurement, ideally within the limits of experimental noise. The most important prerequisite is the model, the physical-chemical, or other, description of the process under investigation. An example helps clarify the statement. The measurement is a series of absorption spectra of a reaction solution the spectra are recorded as a function of time. The model is a second order reaction A+B->C. The parameter of interest is the rate constant of the reaction. 

T.J. Thurston, R.G. Brererton, D.J. Foord, R.E.A. Escott, Monitoring of a second-order reaction by electronic absorption spectroscopy using combined chemometric and kinetic models, J. Chemom., 17, 313-322 (2003). 

The third chemical equation, involving nitric oxide, represents a termolecular reaction. Therefore, the overall order of the reaction is expected to exceed that of the second-order reaction generally assumed in the pre-mixed gas burning model. The high exothermicity accompanying the reduction of NO to N2 is responsible for the appearance of the luminous flame in the combustion of a double-base propellant, and hence the flame disappears when insufScient heat is produced in this way, i. e., during fizz burning. 

If Fig. 12 and Fig. 14 were laid on top of each other, then conditions of equivalence could be determined under which the performance of the tanks-in-series model with specified N would be the same as that of the recycle model, that is the value of R could be found which would result in the same conversion and V/Vpp ratio. Levenspiel [17] gives these values for a variety of conditions for both first- and second-order reactions. His data are reproduced in Table 8. 

Recycle ratio for equivalent performance of the recycle and tanks-in-series models at specified conversions for both first- and second-order reactions [17]. 

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