Document Type : Research Paper


1 Ph.D. Candidate, Sahand Oil and Gas Research Institute, Faculty of Petroleum and Natural Gas Engineering, Sahnad University of Technology, Tabriz, Iran

2 Professor, Faculty of Petroleum and Natural Gas Engineering, Sahand Oil and Gas Research Institute Sahand University of Technology, Tabriz, Iran


Shale formations are essential for different disciplines, including wellbore stability studies in petroleum engineering. In shale stability studies, the prediction of transport parameters of water and ions is a significant issue (Farrokhrouz and Asef, 2013). A unique and novel method to address this subject is the Revil model (Revil et al., 2011), which, unlike previous models, considers physiochemical mechanisms in the pore space and needs a few easily measurable shale properties (Revil et al., 2004). In this paper, for the first time to our knowledge, the Revil model has been extended for salts of multivalent ions. The extended model for water and ion transport through shale has been evaluated against a range of experimental data sets in the literature. The extended Revil model only needs a few shale properties such as cation exchange capacity (CEC), porosity, and grain density, which can be readily measured in the laboratory. Further, in the present work, three parameters ( ) have been considered calibration parameters. In addition to extending the Revil model for multivalent salts, we derived a simplified equation to estimate ion selectivity (IS) and a proof for the conjecture that IS correlates with membrane efficiency (ME). Focusing on the data set of Albazali (2005), a complete matching could be obtained by adjusting calibration parameters for each test data. In the case of adjusting all experiments with only three standard calibration parameters, the prediction was not satisfactory. However, the “intact-anion method” results were more accurate than the “Donnan method”. When multiple sets of ME data in a broader concentration range, including low concentrations, were plotted along with high-concentration data, correlativity was significant (R2 > 0.9). Further, a sensitivity analysis of the model parameters was performed. Our findings pave the way for the appropriate mechanistic approach to investigating and handling practical engineering challenges associated with shale.


  • The Revil model for ionic transport has been extended for multivalent ions.
  • A simplified equation to estimate ion selectivity has been introduced.
  • Correlation of ion selectivity with membrane efficiency has been proved.
  • The model predicted the membrane efficiency data with a high correlation.


Main Subjects

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