Three-dimensional modeling of particle transport in porous media considering accelerated effects

Based on a one-dimensional particle transport model, a theoretical model considering accelerated transport effects of particles is established. General solutions are derived with the help of the Laplace and Fourier transforms. According to the general solutions, specific solutions (instantaneously injected and periodically injected) are presented for point and areal inflow regions. The analytical solution for point source under instantaneous injection is taken as an example of specific solutions. A detailed discussion of the effect of time, distance, deposition and dispersion on particle transport is conducted. The studies show that the peak values of concentration decrease and the corresponding distance increases with the increasing time. Furthermore, the concentration contours exhibit ellipses on x-y plane, those near the particle inlet in the x-direction are arranged densely, and those far from the particle inlet are arranged sparsely. The range of low concentration contours increases and the range of high-concentration contours decreases with the increasing time. Besides, the concentration contours decrease with the increasing deposition rate. However, the range of concentration contours decreases with the increasing deposition rate. The contours in the x-direction increase and those in the y-direction decrease with the increasing D_x.