Analytical Modelling and Upscaling of Multicomponent Suspension-Colloidal Transport in Porous Media

Abstract

Hereby I present a PhD thesis by publications. The thesis includes seven journal papers, from which five have already been published, one has been submitted for publication and is presently under review, and another one is under final preparation to be submitted. The journal publications include high-impact-factor academic journals, e.g., Chemical Engineering Journal, Water Resources Research, Journal of Hydrology, and Transport in Porous Media, which are the major academic journals in transport in porous media. Besides that, during the PhD candidature, I have published an extended abstract in the International Journal of Chemical and Molecular Engineering, and a shared conference paper at The APPEA Journal. The thesis presents new mathematical models for transport and cotransport of colloidal and nano-particles flow in porous media. The novelties in this thesis are the development of new systems of equations, able to model phenomena that differ from the classical deep bed filtration theory, as breakthrough curves that asymptotically increase until stabilising at a lower limit than the injected concentration; prediction of non-exponential retention profiles (hyper-exponential and non-monotonic retention profiles); and the development of a new uspcaled procedure able to predict the behaviour of micro-scale particle populations. The application of colloids, engineered nano-particles, and suspension, in general, has been rapidly growing in the last two decades. The demand for these particles in several industries and processes has increased the disposal of these particles in subterranean aquifers and reservoirs. Therefore, understanding and modelling of the phenomena of particles flow through porous media have gained a lot of attention recently. In order to explain, model and predict the behaviour of the colloidal suspension and nano-particles disposal into porous structures, this thesis presents mathematical models and new physical-explanation for different phenomena that occur in porous media. Firstly, the thesis explain the transport of a single particle population that shows breakthrough curves that increase asymptotically and tends to a stabilization at a value lower than the injected concentration by two-particle capture mechanisms, where one mechanism is attachment-based on Langmuir’s blocking function, and the other mechanism is straining or size-exclusion based on constant filtration function. Secondly, the thesis proposes a new mathematical model for cotransport of a binary colloidal-species that accounts for the same two capture mechanisms previously mentioned; however, these mechanisms are applied for each particle population. The thesis also presents a new exact averaging (upscaling) procedure that results in a largescale system of equations, which significantly differs from the traditional deep bed filtration model. The proposed upscaled model is based on the average concentrations of suspended and retained particles and also includes a new site-occupation kinetic equation. Sequentially, the thesis introduces a new and simple mathematical model based on mass activity law accounting separately for single and two particles capture mechanisms, able to predict hyper-exponential retention profiles. Finally, the thesis proposes an original explanation for non-monotonic retention profiles based on a mathematical model that accounts for binary colloidal populations. This mathematical model is upscaled in radial coordinates and the behaviour non-monotonic retention profiles are predicted in reservoir-scale along with formation damage prediction. All mathematical models developed in this thesis are applicable for different areas and industrial processes and they are useful for successfully close matching of several laboratory data available in the contemporaneous literature.