Numerical modeling of onset and rate of sand production in perforated wells

Shear-type failure at a wellbore or perforation is typically characterized by damage to the formation rock. For example during drilling, wellbore failure may occur with rock fragments breaking off from the wellbore wall, and for producing wells, the applied drawdown pressure can result in sanding. Perforations are more susceptible to such failures because, in general, they become less stable as the reservoir depletes. In this paper, a damage model using the Mohr-Coulomb failure criterion is formulated to better describe the failure of porous granular material. The damage variable is assumed to be related to the increase in porosity resulting from the loss of mass from the formation rock matrix. The comparisons of numerical predictions and triaxial compression tests data show that the model can accurately reproduce the mechanical behavior of sand materials. Numerical simulation of a sand production test on a perforated cylindrical specimen is performed. The proposed model demonstrated its capability to predict the accumulated sand mass and rate produced throughout the entire experiment. A threshold of equivalent plastic shear strain has been quantified to determine the onset of sand production in perforated wells; this threshold can be used for field application of sand production analysis on similar sand material. An application on a vertical well with horizontal perforations has been simulated numerically. The key objectives are to examine the critical drawdown pressure for different reservoir depletions and produced sand volume for different drawdown pressures. The critical drawdown window plot was generated and can be used to estimate the allowable drawdown pressure for different reservoir depletions. In addition, it was shown that the produced sand volume and sand mass rate increase with increase of drawdown pressure.