Abstract
A countercurrent gas–liquid flow through a fixed bed of spherical particles is examined numerically by solving the particle-scale equations governing the gas and liquid flows. The liquid is assumed to flow along the surface of the particles forming a thin film. The case of small gas flow rates is examined in detail first. In this limit the presence of the liquid film increases the gas pressure drop over its value for a dry bed by three mechanisms: The liquid film makes the apparent size of the particles larger, decreases the pore space for the gas flow, and, with its velocity pointing opposite to the mean gas flow, increases the apparent velocity of the gas compared with the particle surface. The excess pressure drop is determined for both periodic and random arrangements of particles. Next, the case of high gas flow rates where the traction exerted by the gas at the gas–liquid interface is comparable to the weight of the liquid film is examined. In this regime the liquid holdup increases with the gas flow rate and the pressure drop-gas velocity relation is nonlinear. The results of numerical simulations are compared with approximate models and it is shown that a simple capillary model yields reasonably accurate predictions for the liquid holdup and gas pressure drop.
Highlights
Fixed beds of particles are widely employed in chemical industry for absorption, stripping, distillation, and other separation processes, and as reactors to provide efficient contact between liquid and gasor vaporphases
An important problem in these processes is to predict the gas pressure drop across the bed and the liquid phase volume fractionholdupas functions of the gas and liquid flow rates and the particle volume fraction. Another problem of interest is the prediction of critical gas flow rate above which the liquid starts accumulating at the top of the bed, a condition known as the flooding
The first systematic approach was due to Carman1 who modeled the void space in the fixed bed by straight capillaries whose diameter is taken to be a function of the volume fraction of the particles and the size of particles
Summary
Fixed beds of particles are widely employed in chemical industry for absorption, stripping, distillation, and other separation processes, and as reactors to provide efficient contact between liquid and gasor vaporphases. An important problem in these processes is to predict the gas pressure drop across the bed and the liquid phase volume fractionholdupas functions of the gas and liquid flow rates and the particle volume fraction. The phenomenon of gas–liquid flows through a fixed bed of particles is influenced by a number of parameters even when the bed consists of equal-sized spheres and the Reynolds number based on the average gas velocity is small. We shall consider here the case of wetting liquids with low enough flow rates such that the liquid film around each particle can be regarded as small compared with the size of the particles. The preceding discussion applies to the low gas flow rates where the liquid flow and film thickness are governed by the gravity force acting on it and the viscous stresses at the solid–liquid interface.
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