Modeling Deep Bed Filtration Considering Limited Particle Retention

Abstract

The classic deep bed filtration model (CDBFM) has been widely used for predicting transport and retention of particulate suspensions in porous media. In the CDBFM, the filtration coefficient function is assumed to be dependent of the retained particle concentration, and the boundary conditions are fixed at the porous media inlet cross section. However, if particle retention is limited, no more retention occurs (filtration coefficient equals zero) in regions where maximum retention (jamming limit) is reached. In this article, a model for deep bed filtration considering limited retention is proposed and analytical solutions are obtained. In cases where jamming limit is reached, the well-known CDBFM and the proposed model significantly differ from each other. Contrary to the CDBFM solutions, the obtained solutions show that concentrations along porous media are highly influenced by maximum retention front, which propagates with velocity independent of filtration coefficient.

Study on the Plugging Performance of Bilayer-Coating Microspheres for In-Depth Conformance Control: Experimental Study and Mathematical Modeling

“…Numerous experimental studies have shown either an early breakthrough of particles , or a significant delay. , Yang and Bedrikovetsky introduced a drift delay factor α in order to characterize the velocity difference between particles and fluid. “Faster” particle migration, i.e., α > 1, is explained by the division of porous space into fractions that are accessible and inaccessible to finite-size (nonzero) particles. , While “slower” particle movement, i.e., α < 1, is attributed to the tortuosity of pores, the rolling or sliding of particles near the rock surface is where the velocity is lower compared with the average fluid velocity. , …”

“…32,33 While "slower" particle movement, i.e., α < 1, is attributed to the tortuosity of pores, 32 the rolling or sliding of particles near the rock surface is where the velocity is lower compared with the average fluid velocity. 34,35 Another assumption of the classic model is that the retained particle volume is negligible compared to the pore volume, i.e., low retention concentration, and therefore, the maximum retention concentration is never reached. The latter is questionable in the case of limited particle retention.…”

Numerical and Asymptotic Modeling of a Filtration Problem With the Initial Deposit

“…During the filtration of the suspension in the porous medium some of the fine particles pass through the pores, and part of them is stuck in a porous medium and forms a deposit [1][2][3][4]. Different physical models are used for description of the filtration depending on the properties of the suspension and the porous medium and the nature of their interaction [5][6][7][8][9][10][11][12]. In this paper the filtration of a suspension in a porous medium with an initial deposit is considered.…”