A 3D tortuous fracture network construction approach to analyze proppant distribution in post-fractured shale

To reveal the proppant transport in the tortuous fracture network, a method introducing the normal distribution random function into the quartet structure generation set was proposed to construct the three-dimensional tortuous fracture networks. The tortuosity can be controlled by the variance of random function. And then, the proppant distribution in the tortuous fracture network was simulated with the consideration of the interact between slurry, fracture surface and proppants. Finally, effects of velocity and viscosity of slurry and the density and particle size of proppants on the proppant distribution in three different fracture networks were investigated. The accuracy of this model was verified by the experiment. The simulation reveals that besides the velocity decrease due to the fluid split, the slurry velocity also fluctuates because of the fracture width variation. The transport distance of proppants in tortuous fracture is about 10.7% shorter than that in the smooth fracture, while the distribution height is increased in the tortuous fracture network. Instead of forming the regular sand dune, the proppant is dispersively distributed in the tortuous fracture network. The proppant density and the slurry velocity are the main factors influencing the proppant distribution, followed by the slurry viscosity and proppant size. Proppant with smaller particle size can enter the area with narrow fracture width, so that the distribution of proppant in the fracture is more uniform. The research results can provide some guidance for the optimal design of slurry and pumping schedule in the hydaulic fracturing operation.