Patching Hele-Shaw cells to investigate the flow at low Reynolds number in fracture networks

TL;DR

This paper introduces a computationally efficient method using Hele-Shaw cells to model low Reynolds number flow in fracture networks, accurately capturing pressure and flow characteristics with minimal error.

Contribution

The study presents a novel Hele-Shaw based modeling approach that simplifies flow simulation in fracture networks while maintaining high accuracy compared to full Navier-Stokes solutions.

Findings

Hydraulic resistance increases linearly with intersection length.

Flow rate increases with intersection length, decreasing pressure along the intersection.

Hele-Shaw approximation error is less than 2% compared to Navier-Stokes solutions.

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.