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

We present a novel computationally efficient approach for investigating the effect of surface roughness on the fluid flow in discrete fracture networks at low Reynolds number. The effect of parallel and series fracture arrangements on the flow rate and hydraulic resistance was studied numerically by patching Hele-Shaw (HS) cells to represent the network. In this analysis, the impact of surface roughness was studied in different arrangements of the network. For this aim, four models with different sequences of fracture connections were studied. The validity of the models was assessed by comparing the results with solutions of the full Navier-Stokes equations (NSE). The approximate hydraulic resistance and flow rate calculated by the HS method were found to be in good agreement with the NSE (less than 7% deviation). Results suggest a quadratic relationship between the network hydraulic resistance and the joint roughness coefficient (JRC). Notably, an increase in surface roughness caused a growth in hydraulic resistance and a fall in flow rate. Further insight was provided by drawing an analogy between resistors in electrical circuits and fractures in networks.