Numerical simulation of recovered water flow and contaminants diffusion in the wellbore of shale gas horizontal wells

On the basis of momentum conservation and mass conservation theory, this paper proposes mathematical model to investigate recovered water flow and contaminant diffusion in the wellbore of shale gas horizontal wells. Two significant improvements are made to conventional models. One is that the quality and velocity flow of each cluster are considered as dynamic parameters in equation of flow, and another one is that source terms and reaction terms are considered as dynamic parameters in equation of contaminant diffusion. The validity of the model of recovered water flow and contaminants diffusion is verified by comparing the predicted results with the actual production data and the experimental data in the literature. Then main factors affecting the concentration of contaminants in horizontal wells are studied systematically. It can be shown that the concentration of contaminants at wellhead increases linearly with the linear increase of the initial concentration, boundary concentration and the source term in the whole time period. The concentration of contaminants increases nonlinearly with the linear increase of the length of horizontal wellbore and flow-back average velocity of recovered water in different time periods. The research of this paper provides guidance for the control of recovered water.