Measured and modeled superficial flow profiles in packed beds with liquid flow

Abstract

Packed bed chemical reactors, adsorbers and heat exchangers are simulated by partial differential equations derived from energy and species balances. To solve these equations, an assumption has to be made with respect to the average flow distribution (superficial flow profile) over the cross section of the tubular packed bed. Commonly plug flow is assumed, although the real flow distributions exhibit near-wall flow maxima due to a higher porosity and the no-slip condition at the wall. To our knowledge, Saunders and Ford (1940) were the first to measure the uneven distribution of flow over the exit cross section of the packing. Since then, their observations have been confirmed by numerous authors employing different experimental techniques. An excellent summary of all this work is found in Ziolkowska and Ziolkowski (1988). Lerou and Froment (1977) evaluated the effect of different flow profiles on the performance of a wall-cooled chemical reactor. Fairly large differences between longitudinal temperature profiles were observed depending on whether the flow profiles were even or uneven. This work found support by Vortmeyer and coworkers (1980Vortmeyer and coworkers ( , 1981Vortmeyer and coworkers ( , 1991. In all cases a better simulation of the experimental results was obtained with unevenly distributed profiles. These findings were also observed by Daszkowski and Eigenberger (1992) and in a recent contribution by Papageorgiou and Froment (1995).A theory to compute superficial flow profiles within the packing was proposed by Vortmeyer and Schuster (1983). They extended the well-known Brinkman equation by the inertia Ergun pressure-loss term and replaced the constant average porosity E by a porosity function E(r), where r represents the radial position (m).The use of artificial flow profiles evaluated above the packed bed in the open tube is open to criticism, because one may argue that the profile over the bed is mainly shaped by the last one or two particle layers and that it is deformed by radial circumferential flow components (Drahos et al., 1982) which develop already within the last two particle layers. Price (1968) prevented this shift to a certain extent by fixing a honeycomb structure on top of the packed bed. In a recent work of Bey and Eigenberger (1997) the structure of the outlet flow is preserved by a monolith.In the past, the most successful attempts to measure velocities inside the packed bed involved the use of Laser-Dop- 484 February 1998pler-velocimetry with matched refraction indices of fluid and solid. Johnson and Dybbs (1975) and Dybbs and Edwards (1984) applied this method to packed beds consisting of Plexiglas spheres. The interest of Northrup et al. (1992) was the nature of flow within the voids of the bed. They obtained important results by the method of particle imaging. McGreavy et al. (1986) measured velocity profiles inside a packed bed having a ratio D/dp of about 3; because of this ratio, they could find passes for optical access. Another group of authors injected a tracer and a...

Numerical Generation of a Fixed Bed Structure

“…10 comparison with data of (Zhang et al, 2006) is shown for minimum and maximum density packing of cylinders (E1 and E2, respectively). Quantitative comparison with experimental data of (Giese et al, 1998) reveals good agreement near the container wall but, as the spatial scale of the oscillations is a little larger in the numerical simulation, discrepancies arise in the bed interior (Fig. 11).…”

“…11. Radial porosity profile -quantitative comparison with experimental data of Giese et al (1998) 4. CONCLUSIONS…”

Modeling of the Interactions Between Catalytic Surfaces and Gas-Phase

“…Thus the model cannot predict the velocity maximum in the vicinity of the wall observed experimentally for those reactors [56]. An averaged velocity with a radially varying axial component can be provided by a further modification of the momentum balance [56][57][58] as an improvement of the classical model. The reader is referred to the textbook by Keil [54] and references therein.…”

Computational Fluid Dynamics Simulation of Catalytic Reactors

“…An averaged velocity with a radial varying axial component can be provided by a further modification of the momentum balance [76][77][78] as improvement of the classical model.…”