On a multiscale approach for filter efficiency simulations

Abstract

Filtration in general, and the dead end depth filtration of solid particles out of fluid in particular, is intrinsic multiscale problem. The deposition (capturing of particles) essentially depends on local velocity, on microgeometry (pore scale geometry) of the filtering medium and on the diameter distribution of the particles. The deposited (captured) particles change the microstructure of the porous media what leads to change of permeability. The changed permeability directly influences the velocity field and pressure distribution inside the filter element. To close the loop, we mention that the velocity influences the transport and deposition of particles. In certain cases one can evaluate the filtration efficiency considering only microscale or only macroscale models, but in general an accurate prediction of the filtration efficiency requires multiscale models and algorithms. This paper discusses the single scale and the multiscale models, and presents a fractional time step discretization algorithm for the multiscale problem. The velocity within the filter element is computed at macroscale, and is used as input for the solution of microscale problems at selected locations of the porous medium. The microscale problem is solved with respect to transport and capturing of individual particles, and its solution is postprocessed to provide permeability values for macroscale computations. Results from computational experiments with an oil filter are presented and discussed

The influence of porous-medium microstructure on filtration

“…But since the model is derived from a microscale model, its parameters bear a direct relation to the microscale features (Hornung, 1996). For these reasons, multiscale models have become a popular tool in mathematical modeling (see for example Allaire et al, 2014;Iliev et al, 2014;Ray et al, 2015;Schmuck and Bazant, 2015;Dalwadi et al, 2016).…”

“…Let us discuss three studies using the multiscale approach that are the most relevant to the work in this paper. Iliev et al (2014) use a volume averaging approach, which yields the macroscopic equations via local averages in the form of volume integrals. The proposed model accounts for the microscale features of the filtration while modelling a whole filter element, that is, a casing for the filter medium with an inlet for the contaminated fluid and an outlet for the filtered fluid.…”

Homogenization of Brinkman flows in heterogeneous dynamic media

“…In this figure, we depict a filter element and particle deposition process (following [15]). The particle deposition changes the microscale geometry of the filter and thus can greatly affect its macroscopic properties that are used in simulations [16,15]. The change due to particle deposition is described by Stochastic Differential Equations (SDEs) [15] where the particles' mean velocities are affected by the fluid velocity.…”

“…The particle deposition changes the microscale geometry of the filter and thus can greatly affect its macroscopic properties that are used in simulations [16,15]. The change due to particle deposition is described by Stochastic Differential Equations (SDEs) [15] where the particles' mean velocities are affected by the fluid velocity. Thus, the modified effective properties strongly depend on particle dynamics and deriving and understanding these effective properties are essential for many of these applications.…”

“…Motivated by this application, we consider a Brinkman model (cf. [15,16]) where the permeability changes due to particle dynamics that are driven by the fluid flow.…”