Modified Particle Detachment Model for Colloidal Transport in Porous Media

Abstract

Particle detachment from the rock during suspension transport in porous media was widely observed in laboratory corefloods and for flows in natural reservoirs. A new mathematical model for detachment of particles is based on mechanical equilibrium of a particle positioned on the internal cake or matrix surface in the pore space. The torque balance of drag, electrostatic, lifting and gravity forces, acting on the particle from the matrix and the moving fluid, is considered. The torque balance determines maximum retention concentration during the particle capture. The particle torque equilibrium is determined by the dimensionless ratio between the drag and normal forces acting on the particle. The maximum retention function of the dimensionless ratio (dislodging number) closes system of governing equations for colloid transport with particle release. One-dimensional problem of coreflooding by suspension accounting for limited particle retention, controlled by the torque sum, allows for exact solution under the assumptions of constant filtration coefficient and porosity. The explicit formulae permit the calculation of the model parameters (maximum retention concentration, filtration and formation damage coefficients) from the history of the pressure drop across the core during suspension injection. The values for maximum retention concentration, as obtained from two coreflood tests, have been matched with those calculated by the torque balance on the micro scale.

New Approach to Modelling Sand Filter Clogging by Septic Tank Effluent

“…• microscopic approach (microscopic trajectory analysis) -where the filter coefficient reflects the total collection efficiency as a summary result of Brownian diffusion, interception and settling [Fallah et al 2012]; • probabilistic approach -where the filter coefficient is changeable along filter depth due to particle capture probability [Bedrikovetsky et al 2011]. …”

Critical analysis of uncertainties during particle filtration

“…A detailed analysis of physical processes governing particle attachment/detachment in porous media at various flowrates was carried out by Bedrikovetsky et al 25,26 resulting in the mathematical model for the critical retention concentration as a function of velocity,…”

“…According to our calculations, h c varies from 1.3 × 10 −5 to 0 m when fluid velocity changes from 0 to its maximum value of 6.60 × 10 −4 m/s, corresponding to the condition 25 parameter x is the ratio between the drag and electrostatic forces, with the drag force determined according to the following formula:…”

“…Equation (8) is a simple representation of the two more complex expressions for the critical retention concentration: 25 σ model…”

“…where h c is a cake thickness, which is a function of velocity, m; H is thickness of a rectangular pore channel adopted as 2r p = 1.3 × 10 −5 m; F e -is the total electrostatic force calculated as the sum of attractive London-van der Waals (LvdW) and electric double layer repulsive (DLR), and Born repulsive (BR) forces according to Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, 19 N; x is the ratio between the drag and electrostatic forces; 25 and φ c is porosity of the cake formed on the internal surface of the borosilicate filter due to colloidal particle deposition.…”