Network model for deep bed filtration

We study deep bed filtration, where particles suspended in a fluid are trapped while passing through a porous medium, using numerical simulations in various network models for flow in the bed. We first consider cellular automata models, where filtrate particles move in a fixed background flow field, with either no-mixing or complete-mixing rules for motion at a flow junction. The steady-state and time-dependent properties of the trapped particle density and filter efficiency are studied. The complete mixing version displays a phase transition from open to clogged states as a function of the mean particle size, while such a transition is absent in the (more relevant) no-mixing version. The concept of a trapping zone is found to be useful in understanding the time-dependent properties. We next consider a more realistic hydrodynamic network model, where the motion of the fluid and suspended particles is determined from approximate solutions of the time-dependent Stokes equation, so that the pressure field constantly changes with particle movement. We find that the steady-state and time-dependent behavior of the network model is similar to that of the corresponding cellular automata model, but the long computation times necessary for the simulations make a quantitative comparison difficult. Furthermore, the detailed behavior is extremely sensitive to the shape of the pore size distribution, making experimental comparisons subtle.