Sand erosion with a porosity diffusion law

The computational formulation of a continuum theory for erosion in relation to the sand production problem in reservoir sandstones is presented. The erosion theory regards the continuum as a three-phase medium and establishes a set of mass balance equations for the various phases. The solution requires an additional equation in the form of a constitutive or evolution law, which here takes the form of a porosity diffusion type law and results in a sand rate that decreases over time. Erosion is coupled with the mechanical behavior of a sand-producing cavity and leads to the enlargement of the erosion zone with sand production.