On the DLVO Theory: Experimentally Measured Debye–Hückel Length

The validity of the theoretical Debye–Hückel length (${\kappa }^{-1}$), determined on the basis of the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, to characterize diffuse layer thickness has been experimentally challenged. A series of linear swelling tests using a LVDT apparatus was utilized to measure shale swelling as it interacted with various ionic solutions. A regression technique was employed to develop an empirical equation for an experimental Debye–Hückel length (${\kappa }_E^{-1}$) as a function of ionic strength ($I$) and swelling displacement ($\mathrm{\Delta }L$). Results showed that the measured ${\kappa }_E^{-1}$ is less than the predicted ${\kappa }^{-1}$ due to the physicochemical interactions of shale with the ionic solutions. Such discrepancy had a profound impact on the estimated electric potential ($\psi /{\psi }_0$) and total interaction energy ($V_T$) in the electrical diffuse double layer (EDDL). Moreover, the energy barrier was found to be smaller when ${\kappa }_E^{-1}$ is used as the diffuse layer’s thickness than when $\pm E^{-1}$ is used. Results also showed that increasing the ionic strength of the solution decreases the energy barrier and the distance ($x$) at which the energy barrier occurs (location). The blind reliance on theoretical (${\kappa }^{-1}$) may induce errors in characterizing clay behavior in the presence of ionic solutions, which could compromise the process of design and engineering, especially those related to wellbore stability problems.

Shale swelling is regarded to be one of the main causes of wellbore stability in shale formations drilled with water-based muds. The unfavorable exchange of water and ions between shale and water-based drilling muds may lead to the expansion or shrinkage of clay platelets. To avoid shale swelling, water extraction out of shale by means of chemical osmosis, through the addition of salts, is often adopted in order to reduce the amount of clay platelets separation between clays that make up shale formations. The separation distance between clay platelets is generally associated with the Debye–Hückel length, diffuse layer thickness. Therefore, many operators rely on theoretical Debye–Hückel length to get a first-hand estimate of the amount of shale swelling prior to the application of certain salt drilling muds. The blind reliance on theoretical Debye–Hückel length may underestimate the diffuse layer thickness and separation distance between clay platelets because it completely ignores the physicochemical interactions of clay with the ionic solutions. Such practice may induce errors in characterizing clay behavior in the presence of ionic solutions, which could compromise the process of design and engineering, especially those related to wellbore stability problems. This may eventually lead to wellbore collapse and loss of resources.