Mathematical models side reactions

Today contractors and licensors use sophisticated computerized mathematical models which take into account the many variables involved in the physical, chemical, geometrical and mechanical properties of the system. ICI, for example, was one of the first to develop a very versatile and effective model of the primary reformer. The program REFORM [361], [430], [439] can simulate all major types of reformers (see below) top-fired, side-fired, terraced-wall, concentric round configurations, the exchanger reformers (GHR, for example), and so on. The program is based on reaction kinetics, correlations with experimental heat transfer data, pressure drop functions, advanced furnace calculation methods, and a kinetic model of carbon formation [419],... 

Nonlinearity of a system is reflected in the right-hand sides of the differential equations forming the model corresponding to a reaction kinetics. These differential equations are the rate equations representing the mathematical model of a given chemical scheme. These equations not only incorporate the rate constants (k s) but also how each of the reacting elements enters into one or more reactions. Depending on the form of these interactions between the elements, the nonlinearity of the system can be determined. In turn, this nonlinearity leads to particular types of solutions with different oscillatory as well as nonoscillatory characteristics. 

The kinetic rate constants in Equations 7.23-725 depend on temperature and catalyst concentration. Since carboxyl groups can catalyze the reactions, the kinetic rate constants can also depend on the concentration of carboxyl groups (when TPA rather than DMT is used as a monomer) [ 17]. If mathematical models are required to predict the concentrations of cychc ohgomers, or the influence of high-temperature side reactions, then additional reactions and kinetic expressions are required for model development. 

The mathematical model developed widi the assumption of a simple kinetic scheme and estimated kinetic parameters is instrumental to understand and to predict effects of different operating conditions on the polymer properties. Though the model results differ from the experimental results in terms of the polymer MWDs measured by GPC, the model predicted average polymer properties are in fairly good agreement with the experimental values. To improve the model predictions a better understanding of possible side reactions is most likely needed. Finally, in contrast to earlier literature results [29], no dependence of the pol)mier properties on the reactor pressure and/or pressure reduction rate is found through both the model simulations and experiments. 

The solution of the left-hand side integral depends on the explicit expression of the function f(a) and is denoted as g(a) function. The formal expression of the g(a) function depends on the conversion mechanism and its mathematical model [2, 6]. The algebraic expression of functions of the most common reaction mechanisms operating in solid-state reactions are presented in Table 22.2. 

In this chapter, we have presented the kinetics of reversible step-growth polymerization based on the equal reactivity hypothesis. We have found that the polymerization consists of infinite elementary reactions that collapse into a single one involving reaction between flmctional groups. This kinetic model has been tested extensively against experimental data. It is found that in most of the systems involving step-growth polymerization, there are either side reactions or the equal reactivity hypothesis does not hold well. This chapter presents the details of chemistry for some industrially important systems motivated readers are referred to advanced texts for mathematical simulations. 

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

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