Modelling and Performance Analyses of Annular Equivalent Circulation Density in Extended Reach Wells Using Response Surface Methodology

Abstract

This study presents a rigorous investigation into the modeling and optimization of annular equivalent circulating density (AECD) in extended reach wells (ERWs) using a hybrid approach that integrates physics-based simulation from Landmark Well Plan with statistical modeling via response surface methodology (RSM). This approach quantitatively assesses the influence of critical operational parameters-including pump rate (200–300 gal/min), rate of penetration (ROP: 25–45 ft/h), rotary speed (20–40 rpm), and cuttings density (2.1–2.16 sg)-on AECD variation and interactions in a 35,017 ft measured depth of an 8½-in wellbore drilled with water-based mud. Sensitivity analysis conducted in Well Plan showed that increasing the pump rate from 200 to 300 gal/min resulted in a reduction of AECD from 18.91 to 14.94 ppg, a 21% decrease attributed to the increase in annular velocity and the corresponding improvement in cuttings transport. Meanwhile, raising the ROP from 25 to 50 ft/h led to an increase in AECD of 0.87 ppg, due to elevated cuttings concentration and frictional pressure loss. Increasing rotary speed from 60 to 200 rpm reduced AECD by 0.79 ppg, demonstrating enhanced cuttings agitation and reduced solids bed accumulation. Conversely, cuttings density exhibited a strong positive effect on AECD, with values rising from 16.97 to 17.64 ppg across the density range of 2.1 to 2.16 sg. A second-order quadratic RSM model was developed to capture the nonlinear and interaction effects of these parameters on AECD, achieving an R² of 0.9630, an adjusted R² of 0.9259, and a predicted R² of 0.7866. The model also demonstrated a low coefficient of variation (CV = 1.7%) and a standard deviation of 0.0142 ppg, confirming its excellent predictive capability. Analysis of variance (ANOVA) validated the statistical significance of the model, with a model F-value of 38.41 and p-values < 0.0001 for all linear, interaction, and quadratic terms. Contour plots illustrated strong synergistic interactions, particularly between ROP and cuttings density, where combined increases caused AECD to approach formation fracture thresholds unless mitigated by higher pump rates and rotary speeds. The study demonstrates that the integrated Well Plan–RSM framework offers a high-resolution predictive tool for AECD management in ERWs, facilitating real-time hydraulic optimization and operational decision-making. This, in turn, improves wellbore integrity and reduces non-productive time by up to 12%, representing a significant advancement in drilling hydraulics design, particularly for complex extended reach trajectories.