Dispersion models of unsteady tubular reactors

Abstract

Axial dispersion in time‐variable laminar flow in a tubular reactor is analyzed using an exact procedure for the case of a homogenous first‐order reaction. For the first time since the Taylor Dispersion model was originally introduced for the modeling of reactors, its validity is examined over a wide range of the reaction rate parameter by comparison against an exact analysis. It is shown that a constant coefficient dispersion model can be obtained from first principles for large values of time only for initial distribution problems; however, this simple approximate model also is reasonably good for describing concentration distributions for the present inlet distribution problem for slow reactions and for axial locations sufficiently far away from the inlet. For rapid reactions, while the dispersion model is inaccurate in describing axial concentration distributions, it is surprisingly good for predicting the reactor length required for complete conversion. In contrast to the conclusion of a recent article, it will be shown that the dispersion coefficient is independent of the reaction rate constant.

Dispersion, mass transfer and chemical reaction in multiphase contactors: Part II: Numerical examples

“…At the high reaction rates, where the solute is depleted rapidly by the chemical reaction, there can be essentially no reverse mass transfer, and the absorption process can be described simply as a first-order, irreversible removal of the solute from the y-phase, i.e., the presence of the second phase can be ignored. As shown by Subramanian et al (1974), a homogeneous, irreversible chemical reaction has no effect whatsoever on the dispersion characteristics of the reactive solute, and hence, for rapid reactions, the intraphase results for the y-phase should be recovered, as indeed they are. The effect of the reaction term on the x-phase dispersion characteristics is entirely different.…”

Wave model for longitudinal dispersion: Application to the laminar‐flow tubular reactor

“…Thus, the application of the SDM is burdened with the uncertainty of choosing the reactor length L. Different recommendations are known at this point. To be concrete we will assume the reactor is infinitely long as often recommended-see, for example, Wissler (1969) and Subramanian et al (1974)-so L +m.…”

“…For the solution of linear problems with other initial and boundary conditions different variants of the superposition technique have been developed using the solution of the basic equation Eq. 6 (Gill and Sankarasubramanian, 1972;Subramanian et al, 1974).…”

“…The dispersion flux is related to the concentration by j = -D,d?/dx. The G-S theory is applicable only for a first-order reaction with q = k,c and is described by Subramanian et al (1974). In this case the two coefficients K , ( t ) and K,(t) of Eq.…”

“…Numerical solutions of the same problem have been utilized by Ananthakrishnan et al (19651, Gill and Ananthakrishnan (1967), Mayock et al (1980), Yu (1981), Stewart (1983, 1989) and Takahashi et al (1990). Dynamic behavior of a tubular reactor with a first-order reaction has been analyzed by Subramanian et al (1974) and Nigam and Vasudeva (1976). The laminar-flow tubular reactor with a first-order homogeneous reaction was used as an example to examine the applicability of the SDM to the otherwise two-dimensional situation by a number of investigators (Bischoff, 1968;Wissler, 1969;Mashelkar, 1973;Kulkarni and Vasudeva, 1976;Carbonell and McCoy, 1978).…”