A Smoothed Particle Hydrodynamics Approach for Modelling Meso-scale Fluid–Fracture Interaction

Abstract

The fluid–fracture interaction at meso-scale is vital in numerous applications and challenging for numerical studies. During this process, the solid deforms or even damages due to the force transmitted from the surrounding fluid, whereas the deformation and failure of the solid in turn change the flow behaviour. Besides, the surface tension and wettability at meso-scale can have considerable effects on fluid behaviour. As a particle-based approach, the smoothed particle hydrodynamics (SPH) has shown its capability in modelling the flow at multiscale and potential in reproducing the fracture. Therefore, to model the fluid–fracture interaction at meso-scale, this thesis aims to develop a modified SPH method considering the surface tension of fluid and the fracture propagation of solids at meso-scale. In this approach, an interparticle force that can provide repulsive force in a short-range and attractive force in a long-range is introduced to model the fluid–fluid and fluid–solid interactions. Compared to traditional methods modelling the surface tension and wettability, the proposed interparticle force can be employed in complex geometry without explicitly identifying the fluid–solid interface. The formation of a droplet with surface tension and the change of contact angles on fluid–solid interface demonstrate the capability in reproducing the mesoscopic effects. Moreover, this interparticle force can prevent the SPH particles from clustering when under great pressure. The compressibility of the pipe flow is consistent with the physical value of water without particle clustering. This interparticle force is then coupled with the no-slip boundary to expand its application range. The simulation results of the Couette flow and the Poiseuille flow are consistent with the analytical solution, showing the feasibility of using this approach in the pipe flow under a no-slip boundary. For the solid part, the Drucker–Prager (DP) model and the Grady–Kipp (GK) damage model are combined and implemented to describe the shear failure and tensile failure, respectively. A shear analytical model a biaxial compressive model and a uniaxial compressive experiment are simulated. The results show that the implemented DP model reproduces the shear failure well. After calibrating the GK damage model through the available uniaxial tensile test, the DP model is combined with the GK damage model. A Brazilian disc test is then simulated. The numerical results reproduce the fracture patterns consistent with the experimental ones, showing the feasibility of using this mixed solid model to express the complex fracture of rock-like material. Finally, by coupling the fluid model and the solid model, an SPH framework is formed to consider the surface tension and fracture of the solid. A process of hydraulic fracturing is simulated at the meso-scale with different in-situ stress conditions. Moreover, a pre-existing flaw is added in the solid domain to investigate the influence of natural fracture in hydraulic fracturing. The results suggest that tensile failure is the dominant failure type controlling the fracture pattern of hydraulic fracturing. Moreover, since the in-situ stress state and the pre-existing flaw have mutual effects, the hydraulic fracturing should be analysed comprehensively. All the results prove that this modified SPH method had considerable potential in modelling the fluid–fracture interaction with the consideration of the surface tension effects of fluid and the fracture propagation of solid.