Mass reactive systems

We have covered a body of material in this chapter that deals with movement of mass along gradients and between phases. We have examined the commonalities and differences between linear driving forces, net rates of adsorption, and permeation. Each has the common feature that reaction is not involved but does involve transport between apparently well-defined regions. We move now to chemically reactive systems in anticipation of eventually analyzing problems that involve mass transfer and reaction. 

The third term on the left side of the equation has significance in reactive systems only. It is used with a positive sign when material is produced as a net result of all chemical reactions a negative sign must precede this term if material is consumed by chemical reactions. The former situation corresponds to a source and the latter to a sink for the material under consideration. Since the total mass of reactants always equals the total mass of products in a chemical reaction, it is clear that the reaction (source/sink) term (R should appear explicitly in the equation for component material balances only. The overall material balance, which is equivalent to the algebraic sum of all of the component balance equations, will not contain any (R term. 

It must be kept in mind that the reaction term will not occur in the overall mass balance equations of reactive systems because S(R- = 0, i.e., there is no net mass gain or loss as a result of chemical reactions. 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

This section starts with some general remarks concerning scale-up of chemical reactors. Then the influence of chemical kinetics, heat transfer, and mass transfer on scale-up of reactive systems is discussed. Finally, scale-up from the results of calorimetric equipment, such as the ARC and VSP, is reviewed. 

Chemical or nuclear equilibrium of a reactive system is reached when there is no net transfer of mass and/or energy between the components... 

The development and application of a rigorous model for a chemically reactive system typically involves four steps (1) development of a thermodynamic model to describe the physical and chemical equilibrium (2) adoption and use of a modeling framework to describe the mass transfer and chemical reactions (3) parameterization of the mass-transfer and kinetic models based upon laboratory, pilot-plant, or commercial-plant data and (4) use of the integrated model to optimize the process and perform equipment design. 

A typical evolution of equilibrium mechanical properties during reaction is shown in Fig. 6.1. The initial reactive system has a steady shear viscosity that grows with reaction time as the mass-average molar mass, Mw, increases and it reaches to infinity at the gel point. Elastic properties, characterized by nonzero values of the equilibrium modulus, appear beyond the gel point. These quantities describe only either the liquid (pregel) or the solid (postgel) state of the material. Determination of the gel point requires extrapolation of viscosity to infinity or of the equilibrium modulus to zero. 

The field of chemical process miniaturization is growing at a rapid pace with promising improvements in process control, product quality, and safety, (1,2). Microreactors typically have fluidic conduits or channels on the order of tens to hundreds of micrometers. With large surface area-to-volume ratios, rapid heat and mass transfer can be accomplished with accompanying improvements in yield and selectivity in reactive systems. Microscale devices are also being examined as a platform for traditional unit operations such as membrane reactors in which a rapid removal of reaction-inhibiting products can significantly boost product yields (3-6). 

Another difficulty is related to the mass transfer by convection, as, by definition, the films are stagnant and hence, there should be no mass transport mechanism, except for molecular diffusion in the direction normal to the interface (Kenig, 2000). Nevertheless, convection in films is directly accounted for in correlations. Moreover, in case of reactive systems, the film thickness should depend on the reaction rate, which is beyond the two-film theory consideration. 

The film theory, once developed for equimolar binary mass transfer in non-reactive systems (Lewis and Whitman, 1924), was free from contradictions. Nowadays, it is widely applied for much more complicated processes, and therefore, additional assumptions have to be made. These assumptions are in some conflict with physical backgrounds, and thus, application of this theory becomes problematic (Kenig, 2000). 

Nonequilibrium Krishnamurthy and Taylor (88, 89) Mass-transfer-inhibited systems, replacement for use of efficiencies Highly nonideal and reactive systems Same as Naphtali-Sandholm... 

The heterogeneous reactors with supported porous catalysts are one of the driving forces of experimental research and simulations of chemically reactive systems in porous media. It is believed that the combination of theoretical methods and surface science approaches can shorten the time required for the development of a new catalyst and optimization of reaction conditions (Keil, 1996). The multiscale picture of heterogeneous catalytic processes has to be considered, with hydrodynamics and heat transfer playing an important role on the reactor (macro-)scale, significant mass transport resistances on the catalyst particle (meso-)scale and with reaction events restricted within the (micro-)scale on nanometer and sub-nanometer level (Lakatos, 2001 Mann, 1993 Tian et al., 2004). 

A typical example of nonequilibrium spatially homogeneous systems is an isotropic system where a chemical reaction occurs. The apphcation of nonequibbrium thermodynamics for the consideration of chemically reactive systems has a few peculiarities. Indeed, heat and mass transfer pro cesses are characterized usually by continuous variations in temperature and concentration (see Section 1.5). On the other hand, the chemical transformations imply transitions between the discrete states that pertain to the individual reaction groups. 

It is easy to demonstrate that in the reactive system with an arbitrary set of monomolecular (or reduced to monomolecular) reactions, the station ary state with respect to the intermediate concentration corresponds to the minimum in the value of functional (3.6) even under conditions that are far from equilibrium of the system. In other words, the functional 0( Ao( ) is, by definition, the Lyapunov function of this system. In fact, for a system that consists of monomolecular reactions in its stationary state, in respect to linearly independent (i.e., not related via mass balance with other intermediates) intermediate A , the following expression is valid ... 

Figure 26. Vehicular diffusivity of the proton which measures the movement of the centre of mass of the hydronium ion is given as a function of temperature — bold line, non-reactive system triangle, RSI square, RSII dot-dashed line, estimated using Eq. (13).

Two principal cases can be pointed out rheokinetics of production of linear or network polymers. In the first case, the viscosity variation of the reactive mass serves as a unified measure of conversion from the beginning to end of the process. In the second case, the reactive system becomes incapable of reversible deformations at a gelpoint, long before the curing is completed, i.e., the viscosity becomes indefinitely high but the process is continued. 

The dependence of viscosity on the degree of pol3mierization is also characterized by two linear portions (in log-log coordinates), and here the slope varies from 1 to 4.6 (Fig. 7). If the value of a = 1 is characteristic for a polymer with a low molecular mass, the value 4.6 exceeds the universal value of this exponent equal to 3.5. Considering the temperature dependence of viscosity of the reactive system, we see that Eqs. (4) and (5) are satisfied only if the exponent is equal to 4.6. Such a value of the exponent is not typical for linear polymers but usual for branched macromolecules. 

The establishment of a detailed kinetic model provides an opportunity for the numerical prediction of the behaviour of a chemical system under conditions that may not be accessible by experimental means. However, large-scale models with many variables may require considerable computer resource for their implementation, especially under non-isothermal conditions, for which stiffness of the system of differential equations for mass and energy to be integrated is a problem. Computation in a spatial domain, for which partial differential expressions are appropriate, becomes considerably more demanding. There are also many important fluid mechanical problems in reactive systems, the detailed kinetic representation of the chemistry for which would be highly desirable, but cannot yet be computed economically. In such circumstances there is a place for the use of reduced or simplified kinetic models, as discussed in Chapter 7. Thus,... 

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