Classic chemical engineering models

In this section the classical heat and mass transfer theories are examined. The singular surface jump conditions for the primitive quantities, as derived in the framework of the standard averaging procedures, are approximated by the classical chemical engineering stagnant film theory normally used in chemical reactor models. The relevant transport phenomena solutions and the classical theories on heat and mass transfer considering both low- and high mass transfer rates are summarized in the subsequent subsections. 

Classical chemical engineering has been intensively developed during the last century. Theoretical backgrounds of momentum, mass, energy balances, and equilibrium states are commonly used as well as chemical thermodynamics and kinetics. Physical and mathematical formalisms are related to heat, mass, and momentum transfer phenomena as well as to homogeneous and heterogeneous catalyses. Entire object models, continuum models, and constrained continuum models are frequently used for the description of the events, and for equipment designing. Usual, principal. 

The model can be used for process intensification, since it provides information about the effect of temperature, concentrations, and wood chip sizes on the cooking time required. A more comprehensive treatment can be found, for example, in Refs. [35,36]. As can be seen, classical chemical engineering concepts are applicable and can be successfully adapted in cases of very complex natural materials. The main challenge of the model development is the description of the chemical system. However, it is expected that the delignification reactors of future, the digesters, will be designed on the basis of rational chemical engineering principles. 

Many elements of a mathematical model of the catalytic converter are available in the classical chemical reactor engineering literature. There are also many novel features in the automotive catalytic converter that need further analysis or even new formulations the transient analysis of catalytic beds, the shallow pellet bed, the monolith and the stacked and rolled screens, the negative order kinetics of CO oxidation over platinum,... 

As already said, Taylor s effective model contains a contribution in the effective diffusion coefficient, which is proportional to the square of the transversal Peclet number. Frequently this term is more important than the original molecular diffusion. After his work, it is called Taylor s dispersion coefficient and it is generally accepted and used in chemical engineering numerical simulations. For the practical applications we refer to the classical paper (Rubin, 1983) by Rubin. The mathematical study of the models from Rubin (1983) was undertaken in Friedman and Knabner (1992). 

The ion exchanger is known to be in dimeric form in aliphatic diluents [30], and the stoichiometry in Eq. (7) was found with classical slope analysis at low concentrations and FTIR-analysis even at high concentrations [31, 32], A compilation of all thermodynamic parameters is given in http //dechema.de/Extraktion/, as this system is a recommended test system for reactive extraction studies by the European Federation of Chemical Engineering (EFCE). The predictability of the model is quite good, as is depicted in Fig. 10.10, where zinc extraction from chloride media is predicted from sulfate media [33],... 

At this time, only a small number of nanoscale processes are characterized with transport phenomena equations. Therefore, if, for example, a chemical reaction takes place in a nanoscale process, we cannot couple the elementary chemical reaction act with the classical transport phenomena equations. However, researchers have found the keys to attaching the molecular process modelling to the chemical engineering requirements. For example in the liquid-vapor equilibrium, the solid surface adsorption and the properties of very fine porous ceramics computed earlier using molecular modelling have been successfully integrated in modelling based on transport phenomena [4.14]. In the same class of limits we can include the validity limits of the transfer phenomena equations which are based on parameters of the thermodynamic state. It is known [3.15] that the flow equations and, consequently, the heat and mass transport equations, are valid only for the... 

In both models the only model parameter used is the mean residence time tpp and tpsR F gtire 6 shows the reactor dynamics of the PFR and the PSR in the normalised time and frequency domain (dimensionless time 0 = t/T, dimensionless frequency fg = l/2jt9). In the time domain the step response F(9) as well as the impulse response E(0) (which is the RTD) can be discussed. This type of data presentation is normally used in chemical engineering application. But the same data can also be presented in the frequency domain, the so called Bode plot. This type of presentation allows to identify effects which are not visible in the classical used plot in the time domain. The Bode plot consists of the magnitude Gj 030)1 and the phase arg G(jO)0). ... 

Wiley, New York, 1999. Smith, J. M., H. C. Van Ness, and M. M. Abbott, Introduction to Chemical Engineering Thermodynamics, 7th ed., McGraw-Hill, New York, 2005. Tester, J. W., and M. Modell, Thermodynamics and Its Applications, 3d ed., Prentice-Hall PTR, Upper Saddle River, N.J., 1997. Van Ness, H. C., and M. M. Abbott, Classical Thermodynamics of Nonelectrolyte Solutions With Applications to Phase Equilibria, McGraw-Hill, New York, 1982. 

H. F. Johnstone and M. Thring, Pilot Plants, Models and Scale-Up Methods in Chemical Engineering. New York McGraw Hill, 1957. A classic on how and what to consider. 

The revolution created in 1960 by the publication and widespread adoption of the textbook Transport Phenomena by Bird et al. ushered in a new era for chemical engineering. This book has nurtured several generations on the importance of problem formulation by elementary differential balances. Modeling (or idealization) of processes has now become standard operating procedure, but, unfortunately, the sophistication of the modeling exercise has not been matched by textbooks on the solution of such models in quantitative mathematical terms. Moreover, the widespread availability of computer software packages has weakened the generational skills in classical analysis. 

In many industrially important situations, it is impossible to maintain geometric, mechanical (kinematic/hydrodynamic and turbulence similarities), and thermal similarities simultaneously. Consider a stirred tank reactor with heat exchange only through a jacket on its external surface. The jacket heat transfer area to vessel volume ratio is proportional to (l/T). Evidently, with scale-up, this ratio decreases, and it is difficult to maintain the same heat transfer area per unit volume as in the small-scale unit. Additional heat transfer area is required to cater to the extra heat load resulting from increase in reactor volume. This area can be provided in the form of a coil inside the reactor or an external heat exchanger circuit. In both cases, the flow patterns are significantly different than the model contactor used in bench-scale studies and kinematic similarity is violated. This is the classic dilemma of a chemical engineer it is impossible to preserve the different types of similarities simultaneously. 

---