Assessing Sand Production Risks: A Sensitivity Analysis Using Analytical Models

Abstract The primary objective of this paper is to conduct analytical sensitivity models for predicting the initial stage of sand dislodgement in oil and gas wells. Using the methodologies and equations developed by Papamichos and Furui, the study is to evaluate effects of several critical variables on sand production risks. The scope includes both the Mohr-Coulomb (MC) and Drucker-Prager (DP) failure criteria to provide a comprehensive understanding of the factors influencing sand disintegration. The research employs analytical models based on hole failure criteria, considering tangential, axial, and shear stresses, implemented in MATLAB. Sensitivity analysis is conducted for key parameters affecting sand production, including unconfined compressive strength (UCS), perforation hole diameters, reservoir pressures (both initial and depleted), water saturation, borehole deviation angles, and perforation orientations relative to horizontal stress directions. The study applies both the MC and DP failure criteria to evaluate critical bottom hole pressure (CBHP) under varying conditions. The findings demonstrate that higher UCS values result in lower CBHP, which lessens the possibility of sand production. CBHP is strongly impacted by perforation hole diameter, with larger tunnels translating into higher CBHP, thus reducing the duration of sand-free production. Perforations aligned with the minimum horizontal stress are more likely to produce sand in a normal faulting system due to their influence on CBHP. Well deviation angles have a pronounced effect, with highly deviated wellbore leading to lower CBHP that can considerably prolong the well production life. Additionally, water saturation (Sw) levels keep as essential role on the UCS, as higher Sw causes rising CBHP, making formations more susceptible to sand production. The DP criterion generally predicts higher CBHP compared to the MC’s, suggesting a more conservative approach. These results highlight the importance of considering multiple parameters and their interactions in forecasting sand production onset and optimizing well design and completion techniques. This paper presents fresh insights by integrating a thorough sensitivity analysis on both MC and DP failure criteria. It offers practical recommendations for well planning and perforation strategies, contributing valuable information to the existing body of literature on sand production prediction and management, ultimately benefiting engineers in optimizing wellbore stability and minimizing sand production risks.