Upscaling of Stochastic Micro Model for Suspension Transport in Porous Media

Abstract

Micro scale population balance equations of suspension transport in porous media with several particle capture mechanisms are derived, taking into account the particle capture by accessible pores, that were cut off the flux due to pore plugging. The main purpose of the article is to prove that the micro scale equations allow for exact upscaling (averaging) in case of filtration of mono dispersed suspensions. The averaged upper scale equations generalise the classical deep bed filtration model and its latter modifications.

Modeling of Fine Migration in a Porous Medium

“…During long-time filtration the number of free small pores is significantly reduced, and the porosity and permeability of the porous medium are changed. To take into account this phenomenon, in contrast to the classical equations of filtration the dependence of coefficients of the mass balance equation on deposit concentration ( , ) S x t is introduced [7]. It is assumed that the deposit growth is proportional to the concentration ( , ) C x t of suspended particles.…”

Improved population balance model for straining-dominant deep bed filtration using network calculations

“…The dynamics of natural pore throat and particle size distributions during flow and capture is described by population balance models [15][16][17][18][19][20][21][22]. Papers [15,16] present mass balance of suspended and captured particles with kinetic rate equations for different particle capture mechanisms; the capture system dispersivity (correlation length) is assumed to be equal to an effective pore length.…”

“…Both features are reflected in the geometrical porous media model of parallel tubes with mixing chambers (further in the text called by its abbreviation PTMC), see [17][18][19][20][21]. Both processes occur in real rocks simultaneously while they are separated in PTMC model: the particle straining occurs at the chamber exits only, while the particle motion in capillaries occurs between the chambers.…”

“…A major constituting parameter in these equations is the correlation mixing length that is equal to the distance between the mixing chambers. The system allows for exact upscaling from the pore scale to the core scale only in the case of mono dispersed filtration [19]. The upscaling for poly-disperse suspensions results in a separate system of partial differential equations for each particle size [22].…”

Critical analysis of uncertainties during particle filtration

“…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.…”