An analytical model to predict the volume of sand during drilling and production

Sand production is an undesired phenomenon occurring in unconsolidated formations due to shear failure and hydrodynamic forces. There have been many approaches developed to predict sand production and prevent it by changing drilling or production strategies. However, assumptions involved in these approaches have limited their applications to very specific scenarios. In this paper, an elliptical model based on the borehole shape is presented to predict the volume of sand produced during the drilling and depletion stages of oil and gas reservoirs. A shape factor parameter is introduced to estimate the changes in the geometry of the borehole as a result of shear failure. A carbonate reservoir from the south of Iran with a solid production history is used to show the application of the developed methodology. Deriving mathematical equations for determination of the shape factor based on different failure criteria indicate that the effect of the intermediate principal stress should be taken into account to achieve an accurate result. However, it should be noticed that the methodology presented can only be used when geomechanical parameters are accurately estimated prior to the production stage when using wells and field data.