Modeling Coupled Transport, Aggregation, and In Situ Gelation of Nanoparticles in Porous Media
Authors: Abdelfatah Elsayed , Pournik Maysam , Shiau Bor-Jier Ben , Harwell Jeffrey 
Published: October 2017

Abstract
Applications of Nanotechnology are growing significantly in the petroleum industry such as oil recovery, and well stimulation. In aqueous media, fumed 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 evolution of nanoparticle size distribution during transport in porous media, including the aggregation, deposition, straining and initiation of gelation. Population Balance equation (PBE) was used to model the growth of aggregates and the interaction between aggregates and porous media. Quadrature method of moments (QMOM) was used to convert the PBE with continuous distribution of nanoparticle size into moment transport equations for efficient computation. The closure problem for moment transport equation was resolved using Gaussian Quadrature that requires estimation of roots orthogonal polynomials. Wheeler algorithm was used for calculation of the coefficients of the recursive formula of the orthogonal polynomials. Finite volume method was used for discretization of mass transport equations, continuity equation and Darcy law. Changes in nanoparticle size and shape due to inter–particle interactions (i.e., aggregation) can significantly affect particle mobility and retention in porous media. To date, however, few modeling studies have considered the coupling of transport and particle aggregation processes. Model sensitivity analysis explained the influence of particle concentration, and interstitial velocity gradient on particle–particle, and, consequently, particle–collector interactions. Model simulations demonstrate that, when environmental conditions can promote inter–particle interactions, neglecting aggregation effects can lead to over-estimation of nanoparticle mobility. Results also suggest that the extent to which higher order inter–particle collisions influence aggregation kinetics will increase with the volume fraction of primary particles. The model shows that when nanoparticles dispersions are injected into free media like large pores or fractures that the effect of filtration is negligible, the gelation can be achieved but after longer time compared to the batch experiments. However, when including the effect of filtration, the viscosity of the does not increase due to exclusion of larger aggregates once they are formed. This prevents the growth of the gel network. The model developed in this work accurately captures aggregation and initiation of gelation of silica in porous media. This work demonstrates the potential importance of time-dependent aggregation processes on nanoparticle mobility and provides a numerical model capable of capturing/describing these interactions in water-saturated porous media. This modeling study attempts to answer the critical questions pertaining the coupling of aggregation and in situ gelation on the nanoparticles transport in porous media.