Sand deposition is also considered in some models [28]
It is assumed that the sand in place is fully degraded from the beginning and the production is only due to the hydrodynamic forces. Equilibrium eqn. for solid phase is often ignored To initiate the process a very small solid concentration is given as a boundary condition. The results are insensitive to this value as long as it is small
if , else pore collapse or sudden element removal.
Later models defined as a function of stresses (Wang and Xue [32]). Critical plastic strain was later linked to the state of zero cohesion (Azadbakht et al. [39])
Porosity is assumed to increase until it reaches unity. Usually, it is assumed that eroded elements collapse once their porosities reach a critical level less than unity (say 0.5)
After failure, new material properties are assigned to the failed material (such as zero cohesion). The infill is assumed to behave as a Poiseuille fluid with a viscosity depending on the sand concentration
Some models consider sand production from elements whose cohesion is already reduced but not equal to zero yet (Detournay et al. [11]):
(2) Tensile criterion
Vaziri et al. [10], Nouri et al. [12], Nouri et al. [13], Vaziri et al. [14]
Complete degradation ( and tensile failure
Tensile failure has been replaced by either tensile effective stress or tensile mean effective stress, assuming cohesionless sand has no tensile strength A more comprehensive one is: shear-failed element with zero cohesion falls in tension or sand fails in tension (Nouri et al. [12])
The element that satisfies sanding criteria is removed from the mesh (assuming cavity can grow adjacent to the wellbore)
For illustration purposes the boundary is shown from 0 to in all directions. This can be considered as an elaboration of tensile criterion considering the effect of friction coefficient
The element is removed suddenly without allowing the porosity to grow gradually
