Clogging of Porous Column of Spheres by Sediment

When a sediment suspension moves downward at a constant laminar flow through a vertical porous column packed regularly with uniform spheres and having critical pores which permit passage of spheres smaller than 1/7-diam. of the matrix grain, sediment deposition takes place by a characteristic mechanism known as bridging. The critical parameter which controls the clogging of the matrix is the ratio of the pore size of the matrix to the sediment size. Sediment with diameters equal to or greater than half the critical pore diameter of the matrix will deposit and, in time, totally clog the matrix preventing further motion of sediment particles through the matrix. Sediment with diameters less than half the critical pore diameter will deposit only in the dead space of the matrix by the straining mechanism. Considering sediment deposition in a vertical porous column as a stochastic process of pure birth, the time and space variation of sediment accumulation in the column is described by a second-order partial differential equation which has a closed solution. The hydraulic resistance of a clogging matrix is represented by an equation similar to Kozeny-Carman equation for head loss in flow through porous media and was verified experimentally.