Analytical models for sand onset under field conditions

Analytical sand onset models consider the tangential stress at the hole (wellbore or perforation) to compare with the strength of the formation. This simplified criterion does not consider the effect of axial and shear stress at the hole which in experiments have been shown to play a role. This paper presents the formulation of three analytical failure criteria for wellbore or perforation failure and sand onset under field conditions. The resulting analytical expressions are suitable for implementation in programs for sand onset and sand mass analyses. Expressions for critical formation strength, critical drawdown or critical depletion for sand onset are derived. The models can be calibrated on hollow cylinder hole failure strength data or eventually on the uniaxial compressive strength. The analytical model results are compared and validated on numerical simulations using a finite element program developed for sand production studies. The comparisons show that analytical models can reproduce satisfactory sand failure diagrams under various stress anisotropy and production conditions in the field. Finally, the effect of the wellbore on the perforation stresses is analyzed by comparing finite element and analytical results.