Injection of colloids and suspensions in natural reservoirs accompanied with particle capture and external cake formation results in well injectivity decline. External filter cake build-up followed by stabilization is a well-known phenomenon in several engineering fields. Significant decline of the tangential rate along large intervals in long vertical wells yields non-uniform external filter cake profile. We derive the mechanical-equilibrium equations for the stabilized cake profile accounting for electrostatic particle-rock interaction and varying permeate factor. Torque balance is applied to cake equilibrium criterion and the lever-arm ratio is calculated 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 build-up correspond to low and high injection rates, respectively. If the rate is below the critical value, the external cake is built up in the overall injection interval. If the rate is above the critical value, there is no cake in the upper part of the wellbore; the cake starts at the depth where the tangential rate reaches the critical value. 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.

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