Patching Hele-Shaw Cells to Investigate the Flow at Low Reynolds Number in Fracture Networks

Abstract

This research has found a novel computational efficient method of modelling flow at low Reynolds number through fracture networks. The numerical analysis was performed by connecting Hele-Shaw cells to investigate the effect of the intersection to the pressure field and hydraulic resistance for given inlet and outlet pressure values. In this analysis, the impact of intersecting length, intersecting angle and fracture aperture on the fluid flow was studied. For this purpose, two models with different topologies were established. The Hele-Shaw simulation results for hydraulic resistance, pressure and velocity agreed well with results obtained by solving the full Navier-Stokes equations (NSE). The results indicated an approximately linear relationship between intersection length and hydraulic resistance. Specifically, an increase in the intersection length increases the flow rate and as a result, the pressure along the intersection length decreases. The error associated with employing the Hele-Shaw approximation in comparison with NSE is less than 2%. All Investigations were performed in the Reynolds Number range of 1-10.

The effects of surface roughness on the flow in multiple connected fractures

“…On account of the fact that the computational cost of applying rough texture on rock fractures is high, most earlier studies have simplified the problem by considering smooth parallel surfaces (Lemieux and Sudicky 2010, Wu et al 2018, Aghajannezhad et al 2020. The fluid flow behaviour in a single natural fracture has been thoroughly investigated in the last two decades solving the full NSE and Reynolds equation (Zou et al 2015, 2017a, Lee and Babadagli 2021.…”