A Stochastic Model for Particulate Suspension Flow in Porous Media

Abstract

Abstract. A population balance model for a particulate suspension transport with size 6 exclusion capture of particles by porous rock is derived. The model accounts for particle 7 flux reduction and pore space accessibility due to restriction for large particles to move 8 through smaller pores -a particle is captured by a smaller pore and passes through a 9 larger pore. Analytical solutions are obtained for a uniform pore size medium, and also 10 for a medium with small pore size variation. For both cases, the equations for averaged 11 concentrations significantly differ from the classical deep bed filtration model. 12

Critical analysis of uncertainties during particle filtration

“…This parameter can be evaluated by fitting Eq. (13) to experimental data, with obtained results in Figure 5 showing a gradual increase in the internal cake thickness accompanied with an increase in critical retention particle concentration. changes from 0 to 6.6 × 10 −4 m/s.…”

“…(13) and (14). In order to evaluate uncertainties in the values of critical retention concentrations derived from the models (13) and (14), u(σ model cr ), it is necessary to know uncertainties in the parameters of these models.…”

“…Applying formula (3) to (17) Table III). Model (14) represents experimental σ cr = σ cr (U)-data less accurately than model (13) due to the presence in Eq. (14) of the attractive electrostatic force, whose value and uncertainty cannot be reliably established due to unavailability of dielectric data.…”

“…Theoretical models for different particle capture mechanisms have been developed and represent the respective experimental data with various degrees of agreement. [12][13][14][15] However, according to Al-Abduwani et al, 16 validation of such models via different experimental methods is limited. Additionally, unavailability of uncertainty analyses for models describing suspension transport in porous media and limited information about uncertainties for the respective experimental data makes validation of such models difficult.…”

Modeling of filtration of 2-types particles suspension in a porous medium

“…The coefficient of proportionality in the kinetic equation is called the filtration coefficient. Modern models take into account the dependence of the porosity and permeability of a porous medium on the deposit size and various mechanisms of particle capture [6][7][8][9].…”