Numerical investigation of the effects of Fluid Inertia on Sand Production in Cased-Perforated Oil Wells

Sand production by eroding downhole and surface equipment, production loss, and some other impacts can greatly increase hydrocarbon recovery and operational costs. Prediction of sand production in oil wells is generally conducted by using linear Darcy’s law as the constitutive equation for oil flow. This simple law does not include the contribution of fluid inertial in pressure drop and therefore is valid when the flow velocity is low. In petroleum engineering, deviation from Darcian trend is ordinarily considered important for gas wells, however in a perforated oil well considerable flow convergence occurs near the perforation tunnels, which makes it susceptible to inertia effects. In this paper, impacts of flow inertia on sand production from vertical cased-and-perforated oil wells are numerically analyzed. In this regard, 3D coupled, poro-elastoplastic finite element methods with arbitrary Lagrangian-Eulerian adaptive mesh approach are employed. Forchheimer’s law is utilized to account for high velocity flow effects in the analysis. A pressure gradient-based erosion law is adapted for use as the sanding criterion. The helical symmetry of the perforations, generally the case in practice, is utilized to achieve a more realistic but efficient simulation. Sanding response modifications due to inertia effects are presented for the considered range of parameters. The results indicate that high velocity flow leads to an increase in hydrodynamic forces around the perforation tunnels, which in turn can lead to more sand production. It is shown that ignoring the effects of inertia in perforated oil wells can lead to significantly lower predictions of both amount and rate of sand production.