Exact solutions to the deep bed filtration problem for low-concentration suspension

For deep bed filtration equations, exact solutions are constructed that describe typical laboratory experiments (injection of a suspension into a porous sample). In case of the kinetic equation with an arbitrary dependence of the clogging rate on the retention (volume of deposited particles per unit filter volume), the solution is obtained in quadratures. In special case of linear dependence of clogging rate on retained particles volume, an analytical solution is given. For the axisymmetric flows of suspensions (injection into a porous bed through a well), the solution is given in terms of the solution to a system of ordinary differential equations.