Modeling of Aggregation and Gelation of Nanoparticles Using Quadrature Method of Moments

Applications of Nanotechnology are growing significantly in the petroleum industry such as oil recovery, and well stimulation. In aqueous media, silica nanoparticles aggregate if there is sufficient attractive energy between nanoparticles. Aggregate size distribution evolves as aggregation continues, and once it spans the space, it forms a gel. The objective of this study is to study the aggregatio n and gelation kinetics in the batch. Population Balance equation (PBE) is used to model the kinetics of aggregation. Quadrature method of moments (QMOM) is used to convert the PBE with continuous distribution of nanoparticle size into a set of moment equa tions for efficient computation. The closure problem for moment transport equation is resolved using Gaussian Quadrature that requires estimation of roots orthogonal polynomials. Wheeler algorithm is then used for calculation of the coefficients of the rec ursive formula of the orthogonal polynomials. This study shows that the PBE and the QMOM along with the effective medium theory can be used to model the aggregation and gelation of nanoparticles at different conditions of salinity and concentration. The mo deled developed in this study is used to compare between the kinetics of aggregation and gelation of fumed silica and colloidal silica nanoparticles at the same conditions. The case studies presented show the unique behavior of fumed silica over colloidal silica nanoparticles for forming a gel network at significantly low concentration. This is basically due to the fractal structure of the fumed silica nanoparticles that has higher effective volume than the spherical particles of colloida l silica of the sam e size. The model also shows that there is a critical concentration of salt and nanoparticles above which the viscosity increase, and the gel network can be formed. The model developed in this study can be coupled with a transport model to simulate nanopar ticles transport aggregation and in situ gelation in porous media.