Research on convection-reaction-diffusion model of contaminants in fracturing flowback fluid in non-equidistant fractures with arbitrary inclination of shale gas development

Abstract

The large-scale hydraulic fracturing technology used in shale gas development will cause major environmental pollution problems. Therefore, determining the concentration of contaminants in the fracturing flowback fluid to reduce surface water pollution caused by shale gas development is one of the main tasks facing shale gas development. This paper mainly studies the convection, reaction and diffusion process of contaminants in fracturing flowback fluid in non-equidistant fractures with arbitrary inclination. Firstly, based on the convection-reaction-diffusion model of fluid and combined with the fracture morphology, the convection-reaction-diffusion model of contaminants in fracturing flowback fluid in non-equidistant fractures with arbitrary inclination is established. Secondly, in order to solve the established model, an improved fracture equivalent method is proposed, which fully considers all the distributions of the left and right wings of the fractures. Thirdly, the convection-reaction-diffusion model is solved by using coordinate transformation, the Laplace transform method, the characteristic root method, and the Gaver-Stehfest numerical inversion method. Then the concentration of contaminants at the port of the left and right wings of each fracture near the horizontal wellbore in real space is obtained. Finally, taking the chloride ion in the fracturing flowback fluid as an example, the influence of the main controlling factors on its concentration is studied. The results show that the chloride ion concentration increases nonlinearly with the linear increase of backflow velocity and molecular diffusion coefficients, and decreases nonlinearly with the linear increase of rate coefficients and the length of the fracture. This research provides a theoretical basis for the research on the flowback pollution of fracturing flowback fluid. • Convection-reaction-diffusion model of contaminants in flowback fluid in non-isometric fractures is established. • This paper proposes the improved fracture equivalent method. • The model is solved by using coordinate transformation, characteristic root method, Laplace transform and its inversion-. • The methods to solve the model are simple and effective for solving convection-reaction-diffusion model. • By the sensitivity analysis, we know that varies nonlinearly with the linear increase of ς f i l , v f i l , D and L f i l .