Image interpretation for kaolinite detachment from solid substrate: Type curves, stochastic model

Abstract

Kaolinite clays are the most widespread natural fines attached to the rock surface; they can be mobilised by the flow with further migration in porous spaces, straining in thin pore throats and causing significant decline in the rock permeability. We conducted mathematical and laboratory studies of kaolinite detachment from solid substrates in visualisation cells. The mechanical equilibrium of the attached particles in the creeping flow was described by the torque balance. For uniform particles and substrates, this model presents fines detachment using only two rates that correspond to particles in primary and secondary energy minima, i.e., the attached concentration versus velocity is a piecewise-constant function. To observe this maximum retention function, we saturated a single-channel micromodel visualisation cell with a transparent top with kaolinite particles; it was then subjected to a flow with a piecewise-constant increasing rate. Images of the remaining attached fines were filmed after each rate increase. All the tests exhibit gradual fines detachment. To explain the phenomenon, we assumed a probabilistic distribution of the properties of the particles and the substrate. For two-parametric probability distribution functions, it adds the standard deviations to the list of model parameters. The continuous fines detachment versus velocity was highly matched by the torque balance equation with probabilistically distributed coefficients. The match allowed restoring probabilistic distributions of the selected model parameters from the measured maximum retention function. The sensitivity of the detachment rate to properties follows a decreasing order: semi-major axis, aspect ratio, lever arm ratio, and zeta potential. This work fundamentally advances lab-based mathematical modelling of colloidal detachment from solid surfaces by developing stochastic torque-balance equation, where standard deviations of the model coefficients are tuning / matching parameters along with their mean values. This approach allows determining the probabilistic distributions of the model coefficients from the image processing, and also calculating the attached concentration variation within six standard deviations of each parameter, permitting placing the model parameters in the order of their effect on particle detachment.