Formulation of a newly developed shale-swelling model as a function of compaction pressure and temperature

One of the most critical problems in the oil and gas industry is the tendency of shale formation to swell in the presence of water-based mud. The diffusion of water molecules in the nanoplatelet of clay minerals is the main reason behind the wellbore instability issues. This interaction promotes some severe mechanical and physical problems, which eventually minimize the integrity of the wellbore. In the laboratory, shale swelling is experimentally investigated through linear dynamic swell meter (LDSM). In this study, we modified our scaling model developed in 2022 with the addition of compaction pressure. This parameter along with temperature is the critical features responsible for the hydro-mechanical characteristics of a material. The newly proposed model was used to validate the LDSM experimental result. The result of the study shows that the new model effectively models LDSM swelling results. The performance of the model was compared with the help of statistical error sources namely mean absolute error, root mean squared error and average absolute deviation (AAD %). The shrinkage of all these error sources below 1% clearly demonstrates the efficacy of the newly pressure model. In addition, the ANOVA analysis was also used to prove the efficiency of the model. Based on the results, F_calculated < F_crit and \(p{\text{-value}} >0.05\) $p\text{-value}>0.05$ , it can be concluded that the null hypothesis was failed to reject and there was no substantial change between the model and the experimental result. In addition, the newly developed model was also used to model Ranikhot shale formation experimental data. The investigation shows the high efficacy of the model as it demonstrated absolute error well below 0.2%. All these examinations give the conclusive idea that the newly proposed pressure model is a useful tool for the validation of experimental swelling results.