Analytical solution of three-dimensional particle transport in porous media considering a dual deposition mode

Based on the classical one-dimensional particle transport model, a three-dimensional particle transport model with a dual deposition mode considering sieving and adsorption effects was established. Through Laplace and Fourier transforms, general solutions for particle transport in saturated semi-infinite porous media under one-dimensional seepage and three-dimensional dispersion conditions were derived. According to the basic solution in the case of a point source injection on the surface of a semi-infinite body, the analytical expression in the case of a circular surface source injection was obtained by the integration method. The analytical solution is verified using two well-established numerical simulation solvers. The influence of parameters such as the hydrodynamic dispersion coefficient, sieving coefficient, adsorption coefficient, and desorption coefficient, on the mechanism of the particle transport process was analyzed under the conditions of constant concentration and circulating concentration injection of the circular surface source. The results showed that the hydrodynamic dispersion effect accelerated the transport of particles, shortened the breakthrough time, and increased the peak concentration. Moreover, a larger sieving coefficient and particle adsorption coefficient meant a smaller particle release coefficient, and more particles deposited on the solid matrix with a smaller peak particle concentration in the pores.