Clogging at pore scale and pressure-induced erosion

Introducing a model to study deposition and erosion of single particles at microscopic scale, we investigate the clogging and erosive processes in a pore. The particle diameter, concentration, and adhesive forces rule the way particles are deposited and, therefore, characterize the clogging process. We study the hydraulic pressure that induces erosive bursts and conclude that this pressure depends linearly on the deposited volume and inversely on the pores' diameter. While cohesion does not play an important role for erosive bursts, the adhesion is the main force initiating clogging, and when overcome by the hydraulic pressure, erosive bursts are triggered. Finally, we show how the magnitude of erosive bursts depends on the pore length, particle diameter, and pore size.

Figure 1

Setup for the simulations: in the inlet region (I) particles are inserted until a certain inlet particle concentration $C_{\text{in}}\sim C_0$ is reached. When particles leave the outlet region (II) they are disregarded. The particles flow freely through region (III) and reach the pore structure (IV), which in this case is a simple constriction with the shape of a cylinder.

Figure 2

The experimental data stem from Ref. [3] and show a jump in pressure loss caused by an erosive burst. Data from our previous model reproducing erosive bursts are shown by the continuous line, and data from the model presented here are shown by the dashed red line. Pressure and time are rescaled for all three curves by the respective jump size $\left(\tilde{P}=P/\mathrm{\Delta }P\right)$ and jump duration $\left(\tilde{t}=t/\mathrm{\Delta }t\right)$.

Figure 3

Three snapshots of a simulation are shown; the numbers of the snapshots relate to time and pressure shown in the graph. The first snapshot (1) shows a state before any deposition has taken place, in the second (2) the deposition and pressure loss has reached a local maximum (peak pressure), and in the third (3) an erosive burst has unclogged the pore space. The particle colors from blue to yellow indicate the experienced fluid drag per mass for each particle (from low to high). The rainbow colors indicate the flow speed of the fluid.

Figure 4

Pressure loss peaks $P$ are plotted versus the deposited volume $V_{\text{dep}}$ from 100 simulations with different random seeds. The dashed line is a linear fit with slope 1.15(1), and the Pearson correlation coefficient 0.71(1) suggests positive correlation.

Figure 5

Twelve simulations were run for different pore lengths $L=\{0.14,...,7.75\}$ (see Sec. pp1-s1a) and constant pore diameter $D=3.52$. The lengths are given in dimensionless units by dividing by the particle diameter $d$. The pressure peaks show an approximate linear correlation against the deposited length $L_{\text{dep}}$. The Pearson correlation coefficient is 0.91(1). The dashed line is a linear fit over all data points with coefficient 0.27(1).

Figure 6

A set of simulations was run for different pore diameters $D=\{1.76,...,7.04\}$ (see Sec. pp1-s1b) and constant pore length $L=4.22$. The pressure peaks are plotted against $L_{\text{dep}}/D$. Smaller pore diameters exhibit larger critical pressures; the same adhesive coefficient was used for all simulations. The dashed line is the graph of Eq. (15).

Figure 7

Parameter phase space diagram for adhesive $k_a$ and cohesive $k_c$ coefficients. The circles represent data from simulations, the data in between are interpolated. The pore length is $L=6.45$, and the pore diameter $D=3.52$.

Figure 8

Parameter phase space diagram for adhesive coefficient $k_a$ and particle diameter $d$. The circles represent data from simulations, the data in between are interpolated. Since we change the particle diameter here, lengths are given in units of the pore diameter $D$, and the pore length is $L=1.2\left[D\right]$.

Figure 9

At the inlet different particle concentrations are set $C_{\text{in}}=0,...,0.1$. The average pressure loss jump is measured for all simulations. The pore length is $L=4.23d$, and the pore diameter $D=3.52d$. For low concentrations (range I) there is no clogging, while for higher concentrations (range II) there is severe clogging.

Figure 10

For a constant pressure loss we measure average particle ${\overline{\mathrm{\Phi }}}_{\text{particle}}$ and fluid flux ${\overline{\mathrm{\Phi }}}_{\text{fluid}}$, normalized by the total flux. Up to a certain pressure $\left(P\sim 0.35\right)$ particles are only deposited, and there is no particle flux through the pore; above this pressure there is erosion of particles and a finite particle flux is measured at the outlet. The adhesion coefficient is $k_a=0.05$.