A network model for deep bed filtration processes

Abstract

Equations for the deep bed filtration problem are obtained as a special case of a general model formulated earlier. The filtration coefficient X is expressed as an explicit function of system parameters such as fluid flow rate, pore density, and pore size distribution. For a unimodal pore size distribution it is found that X remains constant both in space and time. In general, however, Xis shown to decrease. Explicit solutions to the problem, including particle density profiles and permeability, are obtained for the two cases of large values of the coordination number Z (capillary tube model), and for a bimodal pore size distribution with a finite coordination number.

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

“…The flow field in the network is determined by the numerical solution of the system of linear equations (16,17) with the boundary conditions of a given pressure drop across the flow domain in direction x (Fig. 2).…”

“…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.…”

“…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. Other approaches to pore and particle size distribution modelling during suspension transport in porous media include trajectory analysis [11,23,24], random walk models [22,[25][26][27][28][29] and mean-field description of the traps [30].…”

“…on the particle size. Yet, the current population balance models assume a constant mixing (correlation) length for different size particles [15][16][17][18][19][20][21]. Besides the correlation length, these models contain the empirical functions of accessible fractional flow and porosity as functions of the particle radius.…”

Size exclusion during particle suspension transport in porous media: stochastic and averaged equations

“…are responsible for the capture of suspended particles during ticle size distributions is also present in the literature. The population balance equations are derived in [20][21][22] from continuity equations for each particle size. The closed system of equations is presented.…”