A simple model for desulphurisation of flue gas using reactive filters

Desulphurisation of flue gas is essential before it can be released safely into the atmosphere. One way of removing sulphur dioxide is to use a purification device incorporating a reactive filter, in which the flue gas stream passes in front of a porous-catalyst-filled structure which converts the gaseous sulphur dioxide into liquid sulphuric acid. In this paper, we build and solve a simple mathematical model to describe the operation of a paradigm reactive filter. Our model captures the transport of sulphur dioxide through the device via advection in the main "outer" flow and diffusion through the catalyst structure along with the production of sulphuric acid. This sulphuric acid gradually accumulates in the filter rendering it less efficient. We determine the clogging time for an individual channel (that is, the time at which the entrance to the channel becomes completely filled with liquid) and explore how the concentrations of sulphur dioxide and oxygen and the thickness of the sulphuric acid layer change as the key dimensionless parameters are varied, comparing numerical and asymptotic results where appropriate. We then turn our attention to the device scale and solve our model numerically to determine the overall lifetime of the device. We vary the key dimensionless parameters and explore how they affect the efficiency of the device. In the physically relevant parameter regime, we find an explicit solution to the outer flow problem which agrees well with numerical solutions and provides a formula for the lifetime of the device. Finally, we propose a formula for determining the catalyst reaction rate, given data on the concentration of sulphur dioxide exiting the device.