Comparative performance analysis of different swelling kinetic models for the evaluation of shale swelling
Shaine Mohammadali Lalji, Syed Imran Ali, Rafiq Ahmed, Saud Hashmi, Awan Zahoor
Abstract
Abstract 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 $$p \mathrm{values}< \alpha (0.05)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mi>values</mml:mi> <mml:mo><</mml:mo> <mml:mi>α</mml:mi> <mml:mo>(</mml:mo> <mml:mn>0.05</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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 $${\mathrm{mean}}_{\mathrm{model}}\simeq {\mathrm{mean}}_{\mathrm{experiment}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>mean</mml:mi> <mml:mi>model</mml:mi> </mml:msub> <mml:mo>≃</mml:mo> <mml:msub> <mml:mi>mean</mml:mi> <mml:mi>experiment</mml:mi> </mml:msub> </mml:mrow> </mml:math> 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.