Application of smoothed particle hydrodynamics to the simulation of multiphase flow in complex fracture apertures

Smoothed particle hydrodynamics (SPH) models were used to simulate multiphase flow in fractures with complex geometries. SPH is a fully Lagrangian particle-based method that allows the dynamics of interfaces separating fluids to be modeled without employing complex front tracking schemes. In SPH simulations, the fluid density field is represented by a superposition of weighting functions centered on particles that represent the fluids. The pressure is related to the fluid density through an equation of state, and the particles move in response to the pressure gradient. SPH does not require the construction of grids that would otherwise introduce numerical dispersion. The model can be used to simulate complex multiphase flow phenomenon such as fluid-fluid displacement and phase separation. These processes are a severe challenge for grid-based methods. Surface tension and phase separation were simulated by using a van der Waals equation of state and a combination of short-range repulsive and longer-range attractive interactions between fluid particles. The wetting behavior was simulated using similar interactions between mobile fluid particles and stationary boundary particles. The fracture geometry was generated from self-affine fractal surfaces. The fractal model was based on a large body of experimental work, which indicates that fracture surfaces have a self-affine fractal geometry characterized by a material independent (universal) Hurst exponent of about 0.75. A detailed comparison between laboratory experiments and larger scale SPH simulations is needed to quantitatively validate the SPH models.