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.