Effect of radial velocities on laminar flow, tubular reactor models

Abstract

Existing models for laminar flow in tubular reactors neglect radial velocities in the momentum transport equation. The axial velocity distribution is calculated assuming fully developed flow wherein axial velocities are in local equilibrium with the radial viscosity profile. A test of this assumption has been devised using a representative model of the Newtonian viscosity, μ(r, z), and by reconstructing the radial velocity components using the continuity equation. The assumption of fully developed flow is shown to be a valid approximation for typical polymerization reactions. However, the fact that radial velocities are negligible with respect to momentum transport does not mean they are negligible with respect to convective diffusion of heat and mass. Radial convection is shown to be important for typical polymerization and heat transfer examples.

Simulação numérica aplicada para avaliar o efeito da pré-polimerização no comportamento de reatores tubulares

“…balanços das concentrações de monômero (C M -mol/l), iniciador (C I -mol/l) e solvente (C S -mol/l), além dos balanços para os momentos do polímero morto de ordem zero (µ 0 ), um (µ 1 ) e dois (µ 2 ) [5,14,19,20] : . As equações obtidas para os momentos do polímero vivo de ordem zero (λ 0 ), um (λ 1 ) e dois (λ 2 ) são apresentadas a seguir, respectivamente [20] :…”

“…Realizando um balanço de energia em um volume de controle do reator tubular e desenvolvendo os operadores matemáticos para um sistema em coordenadas cilíndricas, obteve-se a seguinte equação diferencial parcial para estimar a temperatura (T em Kelvin) ao longo do reator tubular [5,14,19,20] .…”

“…Aplicando as hipóteses mencionadas anteriormente nas equações da continuidade e Navier-Stokes, e considerando um fluxo mássico constante através do reator, obtêm-se, respectivamente, as seguintes equações para o cálculo da queda de pressão [14] e da velocidade axial do escoamento [5,14,19,20] …”

Anionic Polymerization of Styrene in a Tubular Reactor

“…We use what has become the standard transport model for a tubular polymerization reactor in laminar flow. ,, Axial diffusion and conduction are ignored. Thermal conductivity, heat capacity, and the heat of polymerization are treated as constants.…”

Thermal and mass transients in the developing region of a homogeneous tubular chemical reactor

“…In 1983, a convective diffusion non‐Newtonian tubular flow under developing flow conditions was investigated by Venkatsubramanian and Mashelkar 12. A year later, McLaughlin et al13 studied the effect of radial velocity in a tubular laminar flow reactor. They showed that the radial velocity should not be neglected when the convective diffusion of heat and mass is considered.…”