A homogenised model for a reactive filter

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