The contaminants

such as filtrate of waste landfill

intrusion seawater

nuclear waste

production sewage and living sewage

would threaten human survival when they migrate into groundwater system. Randomness of groundwater seepage makes the problem of solute transport more complicated. According to the characteristics of flow net

implicit difference scheme of the solution of unit solute concentration based on the principle of mass conservation with the stream tube element is solved by the streamline and equipotential lines. Based on the velocity distribution patterns of porous media

the Monte Carlo method is used to establish the flow rate field for simulating the process of migration of solute. The accuracy of the numerical simulation method is proved by the comparison of the simulation and model tests. In the numerical model the convection and diffusion have effect on the substance exchange along the direction of stream tube. However

only solute diffusion exists between stream tubes. In this model

the feasibility of dispersion coefficient and the limitation of feasibility are overcome. The method for determining flow rate with randomness can provide a new idea for research of advantage migration of contaminants in heterogeneous flow field.