Insight into Debye H\xfcckel length (\u03ba\u22121): smart gravimetric and swelling techniques reveals discrepancy of diffuse double layer theory at high ionic concentrations

Abstract

Smart gravimetric and swelling techniques were utilized in this work to examine the validity of the Debye Hückel length (κ−1) equation when shale interacts with highly concentrated salt solutions. The swelling and shrinkage behavior of two different shales, when exposed to monovalent and divalent ionic solutions (NaCl, KCl and CaCl2) at concentrations ranging from 2 to 22%w/w was observed and measured. Shale swelling and shrinkage results show that Debye Hückel length (κ−1) equation seems to work adequately at low ionic concentrations where osmotic water flow out of shale plays a major role in decreasing the diffuse double layer thickness by withdrawing water out and thereby shrinking κ−1. At high ionic concentration levels, the flow of associated water into the diffuse double layer negates the withdrawal of osmotic water out of the diffuse double layer which could maintain κ−1 or possibly increase it. Data on measured ionic uptake into shale suggests that excessive ionic diffusion into shale, especially at high concentrations, leads to higher electrical repulsion between alike ions in the diffuse layer which could lead to the expansion of the diffuse double layer thickness. Furthermore, swelling and shrinkage data analysis for shale suggests the existence of a ‘critical concentration’ below which the Debye Hückel length equation works. Above the critical concentration, the validity of the Debye Hückel length equation might be in question. The critical concentration is different for all ions and depends on ionic valence, hydrated ion diameter, and clay type.