Comparative Evaluation of Different Kinetic and Diffusible Models to Identify the MostAccurate Predictor of Shale Swelling Behavior

Shale formation contains clay minerals that readily absorb water, which leads to swelling when exposed to water-based drilling fluid (WBDF).This study focuseson analyzing the swelling characteristics of shalecollected from Murree, located in northern Pakistan,and identifying the most appropriate kinetic and diffusible models topredictswelling behavior by comparing the experimental swelling with model-predicted swelling. Additionally, QXRD and SEM analyses were conducted to determine the mineralogical composition and microstructural features of the Murree shale formation. Experimental swelling percentages were measured using a linear dynamic swelling meter (LDSM). Swelling was continuously monitored in LDSM for 24 hours with data recorded at 30-second intervals. Five kinetic and diffusible models, namely, the first-order exponential association model, the pseudo-2nd-order kinetic model, Peleg's model, Higuchi model, and Peppas model, were applied to predict the swelling behavior. Statistical analysis, including absolute error, percentage relative error, mean absolute error (MAE), and absolute percentage relative error (APRE),was conducted to evaluate model performance. The results showed that the pseudo-2nd-order kinetic modelperformed the best withthe lowest MAE of 0.291% and the highest accuracy 96%, whilethe Higuchi modelperformed the poorest,with the highest MAEof 1.116% and a lower accuracy of 84%. The first-order exponential association model, Peleg's model, and the Peppas model exhibited moderate performance. However,Peppas' model performed slightly better than the first-order exponential association model and Peleg's model.Furthermore,the analysis plotted a cross-plot between experimental swelling and predicted swelling.This model-based approach offers a reliable tool for anticipating shale swelling and supports improved decision-making for managing wellbore instability during drilling operations.