A new approach for estimating sand production through gravel packs is presented in this paper. The approach involves two steps: (a) evaluating the pore throat size distribution (PoSD) of a gravel pack and (b) estimating sand production through the gravel pack using an analytical model. Results of the analytical model are compared with sand production data obtained from lab experiments and Monte Carlo simulations.

The PoSD of a gravel pack is evaluated using the discrete element method (DEM). The process includes generating a random close packing of gravel based on the gravel particle size distribution (PSD) and evaluating the pore throat size distribution (PoSD) in each layer of the gravel pack. The evaluated gravel pack PoSD is then used to compute the filter efficiency of the pack for various formation sand sizes. Sand production through the gravel pack is predicted analytically by applying the filter efficiency data to any given formation PSD under the assumption that straining is the dominant sand-retention mechanism for a gravel pack.

Results from DEM simulations show that the smallest and largest pore throats in a gravel pack are typically sized around 1/9 and 1/4.8 to 1/5.5 of the effective gravel diameter (D_eff), respectively. These observations suggest that any formation sand grains larger than 1/5.5 D_eff will be retained near the sand-gravel interface, i.e. within 10 layers of gravel from the sand-gravel interface. Furthermore, the gravel pack alone cannot retain any formation sand smaller than 1/9 D_eff for a typical thickness of the gravel pack. A secondary pack formed by retained formation sand is essential for effective sand retention in such cases. Increasing gravel packing thickness primarily improves the retention of sand sized between 1/5.5 to 1/9 D_eff, and the effect is insignificant for sand out of this size range. Finally, the analytically estimated sand production using DEM-evaluated PoSDs agrees reasonably well with sand production data obtained from lab experiments and Monte Carlo simulations.

The proposed approach provides a time and cost-efficient way to predict the effectiveness of a gravel pack for any given formation sand size distribution. The approach accounts for the gravel particle size distribution and the thickness of the annular gravel pack. Application of this new approach can improve the reliability of sand control completions by better justifying a gravel design, specifically in reservoir sands with poor uniformity (i.e., high-fines).