A Novel Rate of Penetration Prediction Model Integrating Log-Derived Geomechanical Properties and Physically Motivated Energy Parameters for Heterogeneous Formations

Accurate rate of penetration (ROP) prediction in heterogeneous formations remains a key challenge for drilling optimization, as existing empirical models rely on fixed-structure coefficients unable to adapt to rapid lithological transitions. This study presents a novel exponential-form ROP model integrating surface drilling parameters (weight on bit (W), rotary speed (N), torque (T), and standpipe pressure (SPP)), log-derived geomechanical properties (dynamic combined compressibility modulus for carbonates; total porosity for sandstones), and three physically motivated energy parameters: rotational mechanical power per unit bit area (Prot), axial crushing energy (AE/AEs), and hydraulic cleaning efficiency (Hce). Bit wear is quantified through a modified Hareland and Hoberock wear function requiring no laboratory measurements. Parameter selection used combined Pearson and Spearman correlation analysis across 16 candidate variables from a raw dataset of 9375 depth readings for Well A and 4443 for Well B (at 0.25 m intervals). The model was developed using nonlinear least squares regression (Levenberg–Marquardt algorithm) in MATLAB. Validated on two vertical wells penetrating mixed carbonate and clastic sequences in a Middle Eastern offshore field and benchmarked against four classical formulations, the model achieves R2 = 0.6568–0.6766 across full heterogeneous sections, improving on the best benchmark by margins of 0.36–0.46. Under lithology-specific calibration, R2 advances to 0.8239–0.9139, with MAPE reducing to 5.71%. The model is limited to two vertical wells in a single field; further field validation is recommended before broader deployment.