Deterministic and Stochastic Modelling of Fines Attachment and Detachment during Colloidal Flows

Abstract

Hereby I present a PhD thesis by publication. This thesis includes seven journal publications, four of which have been published, two have been accepted for publication, and one which has been submitted for publication. This thesis is focussed on using mathematical techniques alongside laboratory tests to improve the modelling of microscale processes in porous media. Both deterministic and stochastic processes are used in order to most accurately model these processes. The laboratory tests are largely centred around investigating particle detachment. By developing a methodology to produce artificial sand-kaolinite cores with uniform and reproducible properties including clay content, the impact of clay content on low-salinity water induced permeability decline is investigated. It is found that above a certain clay threshold, between 1-3% total mass content, particle detachment and straining manifest in similar ways, evidenced by the measured drop in permeability. It also shown that only a fraction of clay particle can be potentially detached. Additional laboratory tests investigate in more detail the process by which changing the fluid salinity results in particle detachment. In both a single-phase environment and in the presence of residual oil, it is shown that when using calcium ions in the injected water, reduction of the fluid salinity does not detach particles. The opposite is found to be true for sodium ions. Investigations around these laboratory tests are presented, and a tentative conclusion is drawn that calcium ions adsorb on the clay surface with significant hysteresis during the loading and unloading stages. Novel analytical solutions are presented for fines migration accounting for the delay in particle detachment observed in experimental studies in the literature. Both the linear case and axi-symmetric flow cases are presented, and analytical solutions are given for the suspended and strained particle concentrations and the pressure drop. The solutions highlight the impact of the delay, which significantly affects the stabilisation time, but does not affect the stabilised strained particle profile or the final pressure profile. The thesis also presents three models derived using Boltzmann’s kinetic equation applied to colloidal flows in porous media. The model allows for coupling of a distribution of particle velocities and a particle velocity dependent capture. The models are upscaled using Fourier transforms and Hilbert space projection operators. First, the base model is presented, compared with laboratory data, and investigated, revealing inherent relationships between the model coefficients. The upscaled model exhibits delayed advective velocity for the particles compared with the fluid. Two generalisations of this model are presented, in the form of an arbitrary dependence of the capture on velocity, and the general 3-Dimensional anisotropic case. The former allows for investigation of emergent macroscale behaviour using various microscale models for capture, and the latter is capable of modelling the effects of transverse flow on capture, which is shown to be significant even in quasi- 1-Dimensional flows. The models presented in this work are relevant and applicable to many industries, including water management, environmental and chemical engineering, and energy-generation technologies. The use of more accurate models provides better predictions and allow operators to make more informed decisions. The key findings include a greater understanding of particle detachment, and new models for fines migration with delayed particle detachment, and particle flow in porous media with simultaneous capture and dispersion.