Swelling of shale potentially occurs when it is exposed to water-based drilling fluid. The migration of hydrogen ions (H⁺) in the nano-interlayered platelets of the shale rock is utterly responsible for the swelling behavior in the shale. Conventionally, swelling behavior of any shale formation can be experimentally determined by linear dynamic swell meter. However, it is extremely important to validate these experimental results; hence, this research study aims in conducting a comparative performance analysis for different kinetic models, namely Peleg’s model, first-order exponential association equation and pseudo-second-order kinetic model, and a newly developed scaling swelling model in estimating the experimental results of three different shale samples, namely Talhar, Ranikot and Murree, obtained from different regions of Pakistan. It was found that the performance of the scaling swelling model was the most accurate in predicting the experimental swelling results with accuracy greater than 95% in all the three samples. Peleg’s model is found to be the most inaccurate with $$p \mathrm{values}< \alpha (0.05)$$p values < α ( 0.05 ) in all the three formations. The equilibrium state in all the three samples was unable to attain by the use of this model. This clearly shows that the transient states continue throughout the course of experimentation, thus demonstrating a higher water activity in the shale samples. Moreover, when comparison was made between the two remaining kinetic adsorption models, it was perceived that pseudo-second-order kinetic was far superior to first-order exponential association equation with $${\mathrm{mean}}_{\mathrm{model}}\simeq {\mathrm{mean}}_{\mathrm{experiment}}$$mean model ≃ mean experiment and less dispersion in the dataset. Nevertheless, the performance of this model also suffers with the increase in clay content. Furthermore, all these analyses were further validated by different statistical error analysis that includes MAE, APRE% and ANOVA.

One of the most significant problems in oil and gas sector is the swelling of shale when it comes in contact with water. The migration of hydrogen ions (H⁺) from the water-based drilling fluid into the platelets of shale formation causes it to swell, which eventually increases the size of the shale sample and makes it structure weak. This contact results in the wellbore instability problem that ultimately reduces the integrity of a wellbore. In this study, the swelling of a shale formation was modeled using the potential of first order kinetic equation. Later, to minimize its shortcoming, a new proposed model was formulated. The new model is based on developing a third degree polynomial equation that is used to model the swelling percentages obtained through linear dynamic swell meter experiment performed on a shale formation when it comes in contact with a drilling fluid. These percentages indicate the hourly change in sample size during the contact. The variables of polynomial equation are dependent on the time of contact between the mud and the shale sample, temperature of the environment, clay content in shale and experimental swelling percentages. Furthermore, the equation also comprises of adjustable parameters that are fine-tuned in such a way that the polynomial function is best fitted to the experimental datasets. The MAE (mean absolute error) of the present model, namely Scaling swelling equation was found to be 2.75%, and the results indicate that the Scaling Swelling equation has the better performance than the first order kinetics in terms of swelling predication. Moreover, the proposed model equation is also helpful in predicting the swelling onset time when the mud and shale comes in direct contact with each other. In both the cases, the percentage deviation in predicting the swelling initiation time is close to 10%. This information will be extremely helpful in forecasting the swelling tendency of shale sample in a particular mud. Also, it helps in validating the experimental results obtained from linear dynamic swell meter.

The 3DOM LSC exhibited a better catalytic performance than Powder LSC and improved the reversibility of the O₂ electrode.