A Capillary Flow Model for Filtration

"Darcy’s law has been used extensively to model cake filtration. It is a macroscopic model, in which particle size dominates the kinetics and cake moisture. In the present work, a capillary flow model has been developed from first principles to study the effects of microscopic parameters such as capillary radius, boundary layer slip, disjoining pressure, and surface tension that may be important for dewatering ultrafine particles. Laboratory-scale pressure filtration tests show that dewatering kinetics is strongly dependent on capillary radius, which in turn is influenced by surface hydrophobicity, surface charge, and length scales of particles. The model parameters determined from laboratory-scale filtration tests show that use of a hydrophobizing reagent can greatly improve fine particle filtration due to increased slip and decreased capillary pressure. The kinetics of dewatering kaolin clay is fastest at a pH where the layer-structured particles coagulate with a face-to-edge orientation. The capillary flow model developed in the present work may be useful for designing filters and optimizing operating conditions.INTRODUCTIONIn 2014, Canada produced 2.2 million barrels per day of crude oil from the oil sands resources in Alberta, which is expected to grow to 3.2–4.0 million barrels per day by 2030 (CAPP, 2013). One of the challenges to meeting these projections is the tailings management. At present, the industry uses ?77 km2 of the lands to construct tailings ponds. Significant amounts of the tailings disposed to the ponds are silts and clays that are slow to settle and consolidate, creating problems for reclamation. It is, therefore, the objective of the present work to develop a filtration model that may be useful for developing advanced dewatering technologies that can address the tailings management issues.Darcy’s equation is the governing law for filtration. It was derived as an empirical model by H. Darcy in 1856 while he was studying fluid flow in sand filters (Hall, 1956). Since then, many investigators derived it from first principles. It relates superficial fluid velocity to the pressure drop across a porous medium of known permeability. In filtration, the latter can be related empirically to particle size using the Kozney equation (Yoon, 2005)."