Abstract
Fluid flow in Fractures is the main transport and production mechanism in naturally and hydraulically fractured reservoirs. Thus, understanding the various non-Darcy flow regimes is critical for naturally fractured reservoirs, particularly for gas and near the wellbore. While the Forchheimer model for non- Darcy flow has been confirmed numerously, models describing flow behavior prior to the Forchheimer model are still controversial. Also, since the conductivity of a fracture network is dependent on the permeability of the individual fractures, the relationship between fracture transmissivity and morphology requires investigation.
In this paper, a systematic analysis of experimental data, spreading over a vast range of Reynolds number (Re), was carried out to assess the encountered flow regimes. The analysis was conducted using three diagnostic plots, which are: flow rate vs. pressure gradient and first and second derivatives of normalized permeability vs. Re. The analysis confirmed the Mei and Auriault (1993) and Forchheimer models during the weak and strong inertia regimes, respectively. Also, the Forchheimer dimensionless coefficient demonstrated an increasing trend when plotted against the Relative roughness, which was defined as the mean over the standard deviation of aperture. A universal correlation for the dimensionless Forchheimer coefficient could not be established from the plot. Therefore, we proposed investigating other geometrical parameters, which include contact areas, anisotropy, surface roughness, and aperture waviness to improve the correlation. Deriving a robust description of the Forchheimer dimensionless coefficient in terms of fracture relative roughness, will improve practices, such as well testing interpretation, history matching, and production forecasting of oil and gas.
