Modelling mass transfer in a rotating disk reaction vessel

Abstract

A rotating disk apparatus is commonly used to study kinetics of heterogeneous reactions such as calcite dissolution by acid. The apparatus consists of a rock disk attached to a rotating shaft; the rock is submerged in a solution of reactant which is transferred to the disk surface by convection and molecular diffusion. The former due to the rotation of the disk, and the latter due to the concentration gradient of the reactant between the bulk fluid and the rock surface.

Schlumberger is interested in determining how to use the rotating disk experiments to extract parameters that govern the reaction rate between the acid and carbonate rock. For mass transfer limited reactions these include (i) the diffusion rate across the boundary layer, and (ii) the thickness of the boundary layer. For a reaction that is surface limited, (i) the reaction rate and, (ii) the reaction order are of paramount interest.

The Study Group began by reanalyzing the solution by Levitch coupled with numerical solutions of the flow in the hope that it would lead to a deeper understanding of the fluid dynamics in the neighbourhood of the rock. In particular, how the fluid flow changes as the Reynolds number is increased and how this might indicate the most ideal location to measure the calcium in the reaction vessel.

The modelling looked not only at the coupling of the fluid flow with the diffusion equation for the ions but also a preliminary Stefan problem for the dissolving rock.