A Homogenized Model for a Reactive Filter

Abstract

Many chemical filters contain reactive components where harmful substances are 4 removed or transformed. In this paper, we derive a homogenised model for a flue-gas filter that con5 verts sulphur dioxide into liquid sulphuric acid. We consider a microscale domain, focused on a single 6 catalytic pellet, and homogenise over both the gaseous and the liquid phase to obtain macroscale 7 equations for the concentration of sulphur dioxide and the thickness of the liquid sulphuric acid layer 8 that grows around the pellets. We explore two interesting limits of the homogenised model, in which 9 the reaction rate at the pellet surface is small, and where the mass transfer across the gas–liquid 10 interface is small, respectively. We then couple the macroscale equations to an equation governing 11 the external gas flow through the filter. We solve the resulting model and consider asymptotic re12 ductions based on the filter geometry. We consider two distinguished limits and, for one of them, 13 obtain an explicit solution for the sulphur dioxide concentration and the void fraction in the filter. 14 We vary parameters such as the gas speed and establish the operating regimes for effective cleansing 15 of flue gas. 16