An analytical solution for the radial flow of variable density grout in rock fractures

We present below an analytical solution to model the radial transient flow of polymer grout with variable density in a planar fracture. The flow of polymer grout mainly depends on the secondary pressurization caused by its own expansion, which is different from the diffusion mechanism of the grout with constant density driven by constant pressure. The diffusion process of polymer grout in the fracture can be divided into two stages: static-pressure injection phase and self-expansion phase. In the self-expansion phase where the external grouting pressure has been removed, the polymer grout is idealized as a self-expanding Newtonian fluid whose density decreases over time with the negative exponential law. Base on the theory of viscous fluid mechanics, the analytical expressions of the diffusion radius, radial velocity and pressure distribution over time between the fracture walls in this phase were derived. Furthermore, two typical cases were numerically simulated by commercial CFD code Fluent to validate the analytical solution. Then, the diffusion characteristics of the expansible grout were briefly analyzed and summarized. The aim of the present study is to provide a theoretical method for studying the diffusion mechanism of the polymer grout with a feature of self-expansion in the rock fracture. (C) 2019 Elsevier Ltd. All rights reserved.