A three-dimensional numerical model was developed to simulate the stability of wellbore and perforation tunnels completed in weak sandstone formations. Post-yield mechanical behavior of granular materials is incorporated in the model to study the mechanical instabilities associated with such completions. Fluid flow calculations are also incorporated in which they are computationally coupled with the mechanical calculations to generate pore pressure and stress distribution in the sand matrix. In addition, the presented model extends the use of the sand erosion criterion developed by Kim (2010) in order to compute the mass of the produced sand.
It has been shown through field experience that sanding is influenced by several factors such as completion geometry, wellbore inclination, perforation orientation, and in-situ stress anisotropy. The developed model is capable of simulating the impact of these factors and assessing their sanding risk through advanced modeling and meshing techniques. The model can be utilized accordingly to design a wellbore completion that maximizes the mechanical stability and reduces the sand production rate. Different production and operational conditions can also be simulated to determine the onset of sand production and the critical drawdown pressure.
Results obtained from the model shows that vertical wellbores produce less sand sands in regions where the overburden stress is the maximum in-situ stress. In horizontal wellbores, vertically oriented perforations are more stable than horizontally oriented perforations and can withstand higher drawdown before sand is produced. A wellbore model with multiple perforations was also constructed to investigate the effect of mechanical and hydraulic interference from adjacent perforations on the evolution of plastic strain. It was shown that perforation spacing has an influence on both the magnitude the spatial spread of the plastified zone. By combining the effects of phasing angle, perforation density, and wellbore diameter, the presented model is capable of determining the completion configuration with the least sanding risk.