Research on the Convection-Reaction-Diffusion Model of Contaminants in Fracturing Flowback Fluid in Non-Equidistant Artificial Fractures with Arbitrary Inclination in (3+1)-Dimensional Space-Time

[Image: see text] This paper extends the improved fracture equivalent method and then establishes (3+1)-dimensional convection-reaction-diffusion models of contaminants in fracturing flowback fluid in the i-th artificial fracture with arbitrary inclination by comprehensively analyzing the convection effect of fracturing flowback fluid during the flowback process, the diffusion effect of pollutants in fracturing flowback fluid, and the possible chemical reactions between the fracturing fluid and shale matrix. Next, we use a series of transformations and solving methods to solve the established model and obtain semi-analytical solutions of the (3+1)-dimensional convection-reaction-diffusion models. Finally, this paper takes chloride ions as an example to study the concentration changes of pollutants in fracturing flowback fluid in three-dimensional artificial fractures with arbitrary inclination and analyzes the influence of various main control factors on the chloride ion concentration at the inlet end of the i-th artificial fracture with arbitrary inclination.