Application of Response Surface Methodology and Box–Behnken Design for the Optimization of the Stability of Fibrous Dispersion Used in Drilling and Completion Operations

Fibers are extensively used as a fluid additive in the oil and gas industry to improve hole-cleaning performance, control fluid filtration loss, and enhance hydraulic fracturing effectiveness. Generally, a small amount of fiber is dispersed in the base fluid to achieve the desired results without increasing the viscosity of the base fluid. Nevertheless, sustaining a uniform fiber dispersion can be challenging under wellbore conditions, which is essential for fibers' functionality. Consequently, a better understanding of fiber suspension or stability in base fluids is necessary for their efficient utilization in drilling and completion operations. In this study, response surface methodology (RSM) and box-behnken design (BBD) are used to investigate the stability of fiber in polymeric base suspensions, including carboxy methyl cellulose (CMC), polyacrylamide (PAM), and xanthan gum (XG). The BBD of three factors was selected to observe the influence of polymer concentration, fiber concentration, and temperature on fibrous suspension stability, with three levels of design factors (low, mid, and high) and two fiber aspect ratios (3 and 12 mm fibers). The base fluid polymer concentration ranged from 1 to 8 vol %, fiber concentration ranged from 0.01 to 0.08 wt %, and the temperature was varied from 25 to 80 °C. The stability measurements were analyzed using Minitab, subsequently, evaluating the factors' impact and interactions and determining the optimum conditions for the stability of the fibrous suspensions. The results predicted by the developed model were in good agreement with the experimental results R2 ≥ 0.91-0.99. The sensitivity analysis showed that base fluid polymer concentration is the most significant factor affecting fibrous suspension stability. At high polymer concentrations, fiber concentration and temperature effects are minimal, while the temperature effect on the stability was observed at low concentrations (e.g., low suspension viscosities). The fiber aspect ratio indirectly affects system stability. Long fibers have a better tendency to entangle and form a structured network, which in turn hinders the buoyancy that induces individual fiber migration. On the contrary, short fibers do not form a network, allowing them to easily migrate to the surface and agglomerate at the top layer (unstable region). Optimization results revealed that suspensions with viscosities above 50 mPa·s are sufficient to maintain the stability of the suspensions at ambient (25 °C) and elevated (80 °C) temperatures.