Abstract
AbstractSwelling 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.
Highlights
Shale is basically defined as a clay-rich non-clastic sedimentary rock, which primarily comprises silts, clays and mud in varying proportions (Gholami et al 2018)
The instability problems mainly arise by the presence of clay minerals in the shale formation (Aftab et al 2017; Lal 1999)
The purpose of this study is to investigate in detail using graphical and statistical approaches through already established kinetic and scaling swelling models for the validation of the shale swelling experimental results obtained from linear dynamic swell meter (LDSM)
Summary
Shale is basically defined as a clay-rich non-clastic sedimentary rock, which primarily comprises silts, clays and mud in varying proportions (Gholami et al 2018) These formations are utterly responsible for causing over 70% of the wellbore instability problems (Gholami et al 2018; Aftab et al 2017). These clay minerals are classified into three distinct categories, namely kaolinite, montmorillonite and illite (Aftab et al 2017 , 2017; Lal 1999) Out of these three categories, montmorillonite demonstrates strong affinity to water, as swelling starts to occur once the rock fluid interaction is established (Khodja et al 2010; Salles et al 2008). The difference in concentration of the cations that are present in clay mineral and surrounding water gives rise to different forces that are eventually the main source of this type of swelling (Oort 2003; Nehdi 2014; Hashmi et al 2012)
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