Effect of nanoparticle behaviour on mud cake buildup for directional and horizontal wells: mathematical modelling and experimental study

The present study examined the effect of nanoparticle size and geometry on filter cake buildup during dynamic filtration using experimental and modeling approaches. A dynamic filtration setup was proposed and designed to test cross-flow circulation against a synthetic core at a constant differential pressure. The proposed mathematical model considers the critical deposition boundary of the porous media for particles along with drag, lift, friction, buoyancy, permeate, and electrostatic forces. The comprehensive model response allowed investigation of the aggregation and shape of nanoparticles at different cross-flow inclinations. The drag and lift force coefficients and moment of inertia of the nanoparticles were determined using cluster structures of nanoparticles identified using dynamic light scattering (DLS) and fractal theory. The deposition and erosion intensity index of all solid particles were experimentally determined and used in the model. Electronic microscope images of the mud cake surface confirmed the proposed cluster structure of the aggregated particles. The mud cake thickness measured by dynamic filtration tests and the nanoparticle-bentonite weight ratio acquired by DLS showed good agreement with the mathematical model results. The proposed approach allows selection of the optimum shape and size of the nano-solid particles as additives to minimize mud cake buildup along the borehole.