Mathematical modelling of surface tension of nanoparticles in electrolyte solutions

Abstract Nanoparticles (NPs) have been successfully applied to reservoirs for enhanced oil recovery and fines migration mitigation at laboratory scale. Despite the successful implementation at laboratory scale, it is rarely applied at field scale. One of the major reasons for the delay in implementation is the lack of an appropriate model to predict the fluid-particles behaviour in the reservoir. An accurate prediction of the surface tension of the fluid system is particularly important in field design and development in the petroleum sector. The surface tension of NPs in deionized water increases with increase in concentration of NPs. This study exploits the Debye-Huckel constants to calculate the mean activity coefficients of NPs in solution combined with the equation proposed by Li and Lu (2001) for single electrolyte solutions to estimate the change in surface tension. However, NPs behaviour in brine (electrolyte solution) is different from the behaviour of mixture of different electrolytes. In deionized water, the surface tension of the fluid increases with increase in the NPs concentration, but NPs in electrolyte solutions behave as surface active agent decreasing the surface tension with increase in NPs concentration. This work includes the dipole-dipole interaction and structural effects along with the equation developed by Borwankar and Wasan (1988) for surface excess adsorption. This surface excess adsorption is applied to Li and Lu's equation for mixed electrolyte solutions to estimate the change in surface tension. This study is able to model the surface tension of NPs with or without electrolyte. Here, the molecular interaction of NPs in deionized water and electrolyte solutions is considered to predict the fluid-surface tension. The free energy at the interface is affected by the intermolecular interaction of the NPs. This intermolecular interaction includes electrical double layer, dipole-dipole interaction, and structural effects. The proposed model shows a good agreement with the experimental data from previous studies.