Influence of Capillary Pressure on Sand Production in Unconsolidated Sand Formation: Implications for Capillarity Strength Via Experimental and Mathematical Modeling

Source abstract

Abstract This study investigates the significant increase in sand production during water injection into unconsolidated sandstone formations, which is associated with increased water saturation. While sand production rates are primarily governed by changes in rock strength, this research focuses on quantifying the role of capillary pressure in modulating capillary strength. By integrating experimental and mathematical modeling approaches, the work aims to advance the understanding of sand detachment dynamics and formation instability under varying saturation conditions. A comprehensive mathematical model was developed to delineate the relationship between capillary pressure and capillary strength as a function of water saturation in unconsolidated sand formations. The model incorporates particle size effects and dual-particle interactions. Experimental capillary pressure data, obtained via AutoPore IV Mercury Porosimeter measurements, were integrated into the mathematical model. The combined approach enabled a systematic analysis of how water saturation alters capillary strength, specifically emphasising the initial conditions for particle detachment. Sensitivity studies on particle size further elucidated the mechanical contributions of fine versus coarse particles to formation stability. Results demonstrate a direct correlation between capillary pressure and capillarity strength, with both parameters peaking under initial water saturation conditions (0.05 MPa capillarity strength at 9 psi capillary pressure). Increasing water saturation reduced capillary pressure, weakened interparticle cohesion, and triggered sand detachment. The model predicts a critical threshold where capillarity strength declines by ∼90% at high water saturation, culminating in formation failure. Particle size significantly influenced stability: fine-grained sands exhibited higher capillarity strength due to enhanced surface interactions, whereas coarser sands showed accelerated destabilization. These findings underscore that water saturation not only governs capillary pressure but also acts as a key destabilizing factor in unconsolidated formations. The study concludes that maintaining capillary pressure above critical thresholds, through controlled injection rates, can mitigate sand production risks during waterflooding operations. This study introduces a novel perspective that links capillary pressure dynamics to sand production mechanisms in unconsolidated formations, particularly during post-water-breakthrough scenarios. By quantifying the dual roles of water saturation and particle size, the study offers actionable insights for optimizing injection strategies and formation stabilization in sandstone reservoirs.