Competitive-consecutive reaction scheme

The accuracy of low-dimensional models derived using the L S method has been tested for isothermal tubular reactors for specific kinetics by comparing the solution of the full CDR equation [Eq. (117)] with that of the averaged models (Chakraborty and Balakotaiah, 2002a). For example, for the case of a single second order reaction, the two-mode model predicts the exit conversion to three decimal accuracy when for (j>2(— pDa) 1, and the maximum error is below 6% for 4>2 20, where 2(= pDd) is the local Damkohler number of the reaction. Such accuracy tests have also been performed for competitive-consecutive reaction schemes and the truncated two-mode models have been found to be very accurate within their region of convergence (discussed below). 

Consider the series-parallel reaction scheme, also referred to as the competitive consecutive reaction scheme, discussed earlier. The desired product R continues to react with the initial reactant B to produce the undesired product S. Usually the reaction conditions (temperature or catalyst) are arranged such that is much faster than 2- The selectivity, is defined as... 

The role of mixing has been studied in systems with more complex reaction schemes or considering more complex fluid-dynamical properties, and in the context of chemical engineering or microfluidic applications (for reviews on microfluidics see e.g. Squires (2005) or Ottino and Wiggins (2004)). Muzzio and Liu (1996) studied bi-molecular and so-called competitive-consecutive reactions with multiple timescales in chaotic flows. Reduced models that predict the global behavior of the competitive-consecutive reaction scheme were introduced by Cox (2004) and by Vikhansky and Cox (2006), and a method for statistical description of reactive flows based on a con-... 

From this example of a fast, competitive consecutive reaction scheme we can see that nonideal mixing can cause a decrease in selectivity in both continuous and semibatch reactors. Residence time distribution issues can cause a reduction in yield and selectivity for both slow and fast reactions (see Chapter 1), but for fast reactions, the decrease in selectivity and yield due to inefficient local mixing can be greater than that caused by RTD issues alone. In semibatch reactors, poor bulk mixing can also cause these reductions (see Example 13-3). 

Selectivity (alternative) selectivity as used by Baldyga and Bourne for the competitive-consecutive reaction scheme described in Section 13-1.2, Xs = 2S/(2S-HR)... 

Kinetic results for the reaction of tetramethyl-lead with perdeuterioacetic acid have been used to exemplify the method for determining the concentrations of various intermediate species in a competitive, consecutive reaction scheme. ... 

More complicated reactions schemes, including first-order reversible consecutive processes and competitive consecutive reactions, are considered in a textbook by Irwin [89]. Professor Irwin s textbook also includes computer programs written in the BASIC language. These programs can be used to fit data to the models described. 

Scheme 6.1 Competitive parallel reactions and competitive consecutive reactions...

Let us focus on the competitive consecutive reaction shown in Scheme 6.2. In the first step, compound A reacts with compound B to give a first product, PI. In the second step, PI reacts with another molecule of A to give a second product, P2. 

Control of molecular weight and molecular weight distribution in polymerization can be seen as control of competitive consecutive reactions as shown in Scheme 4, where A is an initiator and B is a monomer. 

The two reactions of vinylsilanes with cycloalkenes and alkadienes discussed above compete with ROMP and ADMET polymerization of the organic parent substances. Scheme 1 has been proposed to combine all the competitive/consecutive reactions. The successful formation of silyldiene and bis(silyl)diene occurs exclusively when n = 4 (see Scheme 1). 

The use of a single reaction requires the online measurement of the local species concentration along the flow. With such systems, one experiences the main drawback of physical methods with the local measurement and the influence of the probe size on the mixing quality estimation. For that reason, the so-called test reactions are very attractive. Two main systems, based on competitive chemical reactions, have been proposed for the investigation of mixing effects, that is, the competitive consecutive reaction system (Scheme 6.1) and the competitive parallel reaction system (Scheme 6.2). Let us consider the following simplest reactions schemes which do not exactly match the published real systems, but which facilitate the comparison ... 

Mixing-Kinetic Problem. The reaction scheme that has received the most attention in both theoretical and experimental investigations of the effects of mixing on selectivity is the competitive-consecutive reaction. In addition, the parallel reaction system is receiving attention for its importance in reactions and pH adjustments. These systems are discussed in Chapter 13 and highlighted here because of their fundamental importance in the fine chemicals and pharmaceutical industries. The reaction scheme is as follows ... 

Fig. 7.2 A scheme for a competitive consecutive reaction of A with B to give products PI and P2 in the case that the reaction is faster than mixing...

Reaction scheme, defined, 9 Reactions back, 26 branching, 189 chain, 181-182, 187-189 competition, 105. 106 concurrent, 58-64 consecutive, 70, 130 diffusion-controlled, 199-202 elementary, 2, 4, 5, 12, 55 exchange, kinetics of, 55-58, 176 induced, 102 opposing, 49-55 oscillating, 190-192 parallel, 58-64, 129 product-catalyzed, 36-37 reversible, 46-55 termination, 182 trapping, 2, 102, 126 Reactivity, 112 Reactivity pattern, 106 Reactivity-selectivity principle, 238 Relaxation kinetics, 52, 257 -260 Relaxation time, 257 Reorganization energy, 241 Reversible reactions, 46-55 concentration-jump technique for, 52-55... 

Looking back over the steps required to derive (5.290), it is immediately apparent that the same method can be applied to treat any reaction scheme for which only one reaction rate function is finite. The method has thus been extended by Baldyga (1994) to treat competitive-consecutive (see (5.181)) and parallel (see (5.211)) reactions in the limiting case where k -> oo.118 For both reaction systems, the conditional moments are formulated in terms of 72(X> and can be written as... 

Industrially relevant consecutive-competitive reaction schemes on metal catalysts were considered hydrogenation of citral, xylose and lactose. The first case study is relevant for perfumery industry, while the latter ones are used for the production of sweeteners. The catalysts deactivate during the process. The yields of the desired products are steered by mass transfer conditions and the concentration fronts move inside the particles due to catalyst deactivation. The reaction-deactivation-diffusion model was solved and the model was used to predict the behaviours of semi-batch reactors. Depending on the hydrogen concentration level on the catalyst surface, the product distribution can be steered towards isomerization or hydrogenation products. The tool developed in this work can be used for simulation and optimization of stirred tanks in laboratory and industrial scale. 

According to the works by Bourne et al. [162, 163], the azo coupling reactions between a-naphthol (A) and diazotized sulfanilic acid (B) to produce monoazo dye (R) and bisazo dye (S) are used as the competitive-consecutive (series-parallel) reaction scheme for the determination of micromixing, for which the rate constants have been determined [163], and their values at 298 K are... 

For pyrolysis of wood, models of different complexity have been proposed. Most of the models are based on schemes of competitive and consecutive reactions, through which the wood is converted into light gases, tars and char. Kinetic data for the different reactions vary over a wide range and no general model for the description of wood pyrolysis exists. At a certain temperature, denoted as isokinetic temperature, the different kinetic data lead to comparable pyrolysis rates, as shown by [10]. However, for particles sized between 5 and 25 mm the pyrolysis is determined by heat transfer over the particles. Even if in the outer part of the particle the temperature is close to the isokinetic temp ature, the pyrolysis rate for the Afferent kinetic data varies due to the non homogeneous temperature Astribution in the particle. 

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