Nonuniform External Filter Cake in Long Injection Wells

Buildup and stabilization of external filter cake is a well-known phenomenon in several environmental and industrial applications. Significant decline of the tangential rate along thick intervals in lengthy vertical wells yields a nonuniform external filter cake profile. We derive the mechanical equilibrium equations for the stabilized cake profile accounting for electrostatic particle–rock interaction, varying permeate factor, applying the torque balance to describe cake equilibrium, and calculating the lever arm ratio using Hertz’s theory for contact deformation of cake and particles. An implicit formula for the cake thickness along the well is derived. Two regimes of the stabilized cake buildup correspond to low rates, where the cake starts from the reservoir top, and for high rates, where the cake is formed in the lower well section only. The sensitivity analysis shows that the drag and permeate forces are the competitive factors affecting cake thickness under varying Young’s modulus, rate, and salinity. The main parameters defining external cake profile are injection rate, cake porosity, water salinity, and Young’s modulus