Two semi-analytic models, SLAM and SPAM, are proposed to study the amount and rate of sand production in the context of hollow cylinder tests in a Mohr-Coulomb material. Yielding of the material is a prerequisite for sand production. Sand production is predicted to occur when the local fluid pressure gradient is higher than a local, strength-dependent critical value, which is also a function of grain size. The models use Darcy's law and an analytical expression for specific discharge that is applicable for gas, water, or oil. The models rely on geometry changes to reflect the erosion process. In the SLAM model, sand is produced as a combination of superficial volumetric erosion and macroscopic surface erosion. Volumetric erosion occurs in a boundary layer. As sand is being produced, the porosity of the boundary layer increases to a critical value. When the critical porosity is reached, collapse occurs, and the material remaining in the boundary layer is produced at once in the form of sand. The SPAM model can be viewed as a limiting case of SLAM in which sand production occurs as a result of surface erosion. The conditions for initiation of sanding and stabilization of the erosion mechanism are predicted analytically for SLAM and SPAM. The logic for the models has been implemented numerically, and sanding curves are produced for both models.
