Application of the effective diameters of porous media to the non-Darcy flow analyses

Non-Darcy flows are a vital event leading to the inaccuracy in flow performance evaluation, particularly in the fractured wells in shale gas and tight oil deposits. The internal flow commonly indicates high flow rates at the early period of production, owing to the large geometric size of hydraulic fracture and high porosity in proppant packs. After that, the production flow rate decays steeply until the Darcy flow regime is attained. Therefore, accurate porous flow analyses from the Darcy to Forchheimer and then turbulent flow regimes are essential for optimal facility designs and economic productions in the unconventional deposits. The Comiti capillary model is recognised as the leading non-Darcy flow correlation for simple packed beds comprising mono-size grains. However, in actual hydraulic fractures, various types of proppants are used simultaneously and generally combined with numerous soil grains of different sizes and shapes. In this study, the Comiti model is modified by incorporating the effective diameters of the porous media and then examined for mixed complex multi-size packs. Subsequently, a novel type of non-Darcy flow equation is presented according to the logarithmic turbulent friction factor based on the physical variables determined only in the Darcy flow regime. The new equation presents accurate results for all the types of proppant packs under wide porosity and permeability ranges. The generalised non-Darcy flow correlation, which can be extensively employed from the Darcy to non-Darcy flow analyses, particularly beyond the Forchheimer regime, is presented for the accurate flow evaluation of the fractured reservoirs.