Characterization of Reservoir Flow Units Based on a Power-Law Equation of Permeability Obtained from an Interacting Bundle of Leaky Tubes Model

Abstract

Abstract The conventional approach to flow units’ characterization according to Amaefule et al. (1993) is based on the Kozeny-Carman equation. Although, the Kozeny-Carman equation has been used widely for relating permeability to other properties of porous materials, it suffers from the assumption of non-interacting flow tubes. In this paper, the effects of pore connectivity, valve action of pore throats, and cementation factor are considered by an interacting bundle of tortuous leaky capillary-tubes model of porous media to derive an improved equation of permeability. The parameters of the power-law form of this equation are related to pore connectivity measured by the coordination number using the functional relationships derived from the phenomenological rate equations. The validity and accuracy of this approach is established by comparison with directly measured core data. This approach allows for incorporation of various data within a single, compact, and simple power-law equation over the full range of porosity and permeability. The power law exponent of the leaky-tubes model is shown to deviate significantly from the unity assumed in the Kozeny-Carman equation. While the Amaefule et al. (1993) approach characterizes the reservoir flow units solely based on a flow-zone indicator (FZI) parameter, the present improved approach adds a power-law exponent which allows for enhanced flow units’ characterization using two porosity dependent parameters. The analysis of the permeability vs. porosity data demonstrates that the power law flow units’ model alleviates the deficiencies of the classical Kozeny-Carman equation. This model adequately approximates the actual flow patterns in porous media because it allows interactions and cross-flow between the capillary hydraulic paths.