Conversion and temperature profiles for complex reactions in laminar and plug flow

Abstract

An investigation of the mass and heat transfer equations describing radial and axial profiles for tubular reactors in laminar and plug flow is reported. Reactor conditions evaluated were isothermal, constant wall temperature, and adiabatic. Both diffusion and nondiffusion were considered. The reaction investigated was the demethylation of toluene in the presence of hydrogen.It was found that diffusion plays only a minor role in laminar flow for the conditions investigated. It was also found that isothermal and constant wall temperature reactor operation affected the temperature and concentration profiles very little when r / R was less than 0.6.In recent years, considerable research has been carried out in the analyses of tubular reactors considering both the radial velocity and temperature distributions. Much of this work has been applied to first-order reactions in order to simplify the analysis ( 3 , 4, 6, 8 ) ; however, the approach has been extended to photochemical reactions by Schecter*and Wissler (10) and to the treatment of a reversible homogeneous reaction (A 2 B ) by Rothenberg and Smith (9). Few, if any, commercially important reactions have been treated by these techniques. The demethylation of toluene was chosen as an example of a non firstorder reaction of considerable industrial significance. It was desired to calculate concentration and temperature profiles rigorously under several methods of reactor operation: isothermal, constant wall temperature, and adiabatic. It was hoped that these results would suggest the optimum method of reactor operation for this reaction. THEORETICAL DEVELOPMENTThe partial differential equation resulting from an energy balance for tube flow with chemical reaction is as follows:where M is defined by the velocity profile as( 2 ) In an analogous manner, a mass transfer equation is derived in which diffusion is only considered in the radial direction:R" The usual simplifying assumption of plug flow reduces Equations ( 1 ) and (3) torespectively. Equations (1) and ( 3 ) and the simplified Eqwtions ( 4 ) and (5) were solved by finite-difference techniques by using a Burroughs B5500 digital computer. Conversion of the partial differential equations to finite-difference equations was carried out by the method outlined by Jensen and Jeffreys ( 5 ) . Equation (1)

Mixing in Sub‐micron Ducts

“…The other limit with D t=R 2 ® ¥, gives piston flow behavior. Merill and Hamrin [1] concluded that the reactor behaves as a laminar flow reactor with no diffusion provided D t=R 2 < 3 Â 10 À3 , but we are interested in the opposite limit.…”

Study of fluid dynamic conditions in the selected static mixers part III—research of mixture homogeneity

“…In the literature, some relations that enable mixing efficiency estimations can be found . They are based on different measures, such as the number of layers into which the fluid stream is divided n’ , the coefficient of variation CoV, as well as different indexes of mixing effectiveness I m and ; however, their practical use may be difficult due to the limited number of constants available only for a few mixers’ geometries.…”

“…CoV correlations have a very general form (similar to those used in the dimensional analysis), which shows the parameters that may influence the CoV but does not give a direct formula applicable for engineering (practical) calculations.…”

THE LAMINAR FLOW TUBULAR REACTOR WITH HOMOGENEOUS AND HETEROGENEOUS REACTIONS I. Integral Equations for Diverse Reaction Rate Regimes

“…Laminar flow tubular reactors (LFTRs) have received special attention since the early studies of Bosworth in 1948. Design equations for LFTRs with homogeneous reactions have been numerically solved using finite differences (Cleland and Wilhlem, 1956), series expansions (Hsu, 1965), method of the moments (Aris, 1980), Galerkin's method in the Laplace transform domain (Nigam er ul., 1982), Green's functions (Arce er ul., 1988), among many other articles (Merril and Hamrin, 1970;Subramanian er ul., 1974;Nigam and Nigam, 1980;etc.). Also, LFTRs with heterogeneous -at the wallreactions have been analyzed in several contributions (Katz, 1959;Wissler and Schechter, 1962;Smith and Carberry, 1976;inoue and Funakoshi, 1981;Vi-Doung Dang, 1983;erc.).…”