Modeling gas-solid non-catalytic reaction

I am working on gasification of biomass. In this, char (a solid phase) reacts with carbon dioxide (gas phase) to form carbon monoxide (gas phase). I need to model this system in a plug flow reactor, in which the solid char will be entering from one inlet with some velocity and a side injection of CO2 will be provided.

If anybody can help in this regard that would be a great help.

Thanks