An improved Klinkenberg permeability model for tight reservoir cores: Effects of non-linear gas slippage to real gases

Abstract

Absolute permeability is one of the most fundamental reservoir-rock properties required for reservoir simulation models. Most research studies are focused on the Klinkenberg gas slippage, considering the ideal behavior of the flowing gas under first- and second-order slippage conditions. This paper assesses the non-linear slippage of real gas through the low permeability reservoir rock samples. The cubic equation of state (van der Waals/Soave-Redlich-Kwong/Peng-Robinson), coupled with Taylor series-based non-linear slippage, predicts the apparent permeability for the non-Darcy gas flow in tight reservoir rock. The novelty of the present contribution is to develop a comprehensive mathematical model to describe the temperature- and pressure-dependent non-linear slippage effect accounting for the real gas behavior, which is based on the fundamental principle of momentum balance. The thirty-nine sets of experimental results of different authors using different core samples (e.g., coal seams, tight sandstones, tight carbonates, gas-shale reservoirs) and gases (Air, H2, He, N2, CH4, C2H6, and CO2) are used to authenticate the proposed non-linear slip model for real gases. Results show that (a) the proposed model correctly predicts infinite permeability and non-linear slippage coefficients of eight-tests non-ideal gases with an average absolute deviation of ≤9.69%, (b) non-linear slippage dominates for the core samples having permeability <1.5 mD, and (c) the first- and second-order slippage coefficients vary from 0.76 to 6.22 atm and 0.15–9.30 atm2, respectively. The proposed model is simple and may readily be applied for the reservoir simulation of coal seams, tight sandstones, tight carbonates, gas-shale reservoirs, etc., for reservoir characterization, forecasting future natural gas production, decision-making, and efficient reservoir management practices for enhanced production efficiency and sustainability.