Response surface modeling of oxidized polyethylene drag reduction for hydraulic fracturing

Abstract Hydraulic fracturing operations require precise control of friction-reducer dosage to minimize pumping costs, yet the nonlinear coupling between polymer concentration, flow rate, and drag reduction (DR) efficiency remains difficult to predict quantitatively. To address this gap, the present study develops a predictive Response Surface Methodology (RSM) framework for optimizing the DR performance of oxidized polyethylene (1 MDa) in aqueous fracturing fluids. Using a closed-loop pipe flow system (inner diameter 3 cm, test length 10 m), a central composite design (CCD) was executed over the parameter space of polymer concentration (200–600 ppm) and volumetric flow rate (10–50 L/min) at 20 ± 0.5 °C. The resulting quadratic regression model correlating DR% with the two factors is statistically highly significant ( p < 0.01, R 2 = 0.985, Adj. R 2 = 0.961). The RSM model predicts an optimum DR% of ~ 69.3% at a polymer concentration of ~ 376 ppm and a flow rate of ~ 33 L/min (Re ≈ 35 000), which is experimentally bracketed by the center-point confirmation run (400 ppm, 30 L/min, measured DR% = 69.0%). Validation experiments confirm a prediction error below 2%, and scale-up analysis via empirical scaling laws projects a DR% of 59% under field-relevant conditions (Re = 100 000, large-diameter pipe). Furthermore, temporal degradation tests reveal that DR performance decays exponentially under continuous circulation (first-order rate constant k = 0.045 min −1 ), declining from 70% to 45% within 20 min. These findings provide a reproducible, data-driven basis for real-time dosage optimization and operational fluid management in hydraulic fracturing.