Modeling transport of soft particles in porous media

Flow-driven transport of soft particles in porous media is ubiquitous in many natural and engineering processes, such as the gel treatment for enhanced oil recovery. In many of these processes, injected deformable particles block the pores and thus increase the overall pressure drop and reduce the permeability of the particle-resided region. The change of macroscopic properties (e.g., pressure drop and permeability) is an important indicator of the system performance, yet sometimes impossible to be measured. Therefore, it is desirable to correlate these macroscopic properties with the measurable or controllable properties. In this work, we study flow-driven transport of soft particles in porous media using a generalized capillary bundle model. By modeling a homogeneous porous medium as parallel capillaries along the flow direction with periodically distributed constrictions, we first build a governing differential equation for pressure. Solving this equation gives a quantitative correlation between the total pressure drop and measurable parameters, including concentration and stiffness of particles, size ratio of particle to pore throat, and flow rate. The resultant permeability reduction is also obtained. Our results show that the total pressure drop and permeability reduction are both exponentially dependent on the particle concentration and the size ratio of particles to pore throat. With no more than two fitting parameters, our model shows excellent agreements with several reported experiments. The work not only sheds light on understanding transport of soft particles in porous media but also provides important guidance for choosing the optimal parameters in the relevant industrial processes.

Figure 1

Illustration of (a) homogeneous porous medium; (b) generalized capillary bundle model; (c) microgel suspension flowing in capillary. $L_P$ is the distance between two successive deformed microgels in throats. Inset: a deformed microgel marked with the contact length and the pressures at upstream and downstream side of the microgel.

Figure 2

Comparisons between model prediction and experimental results for the variation of (a) total pressure drop; and (b) permeability reduction with microgel concentration [14].

Figure 3

Comparisons between model prediction and experimental results for the variation of (a) total pressure drop with position when $L/\tilde{L}$ is small; and (b) pressure gradient with the ratio of gel to throat diameter [12].

Figure 4

Comparison between model prediction and experimental results for the variations of (a) residual resistance factor; (b) pressure drop as a function of Darcy flux. Red error bars and circles are experimental data from Ref. [8]; green crosses are experimental data from Ref. [14].

Figure 5

Illustration of distance between two microgels in capillary: $L_0$.

Figure 6

Illustration of β: scaled by the length ratio.

Figure 7

Comparisons between model prediction and experimental results in Ref. [12] for the variation of normalized pressure gradient by Darcy's law with the ratio of gel to throat diameter.