Lattice Boltzmann based simulation of gas flow regimes in low permeability porous media: Klinkenberg’s region and beyond

Abstract

Tight gas reservoirs are of prominent importance among unconventional petroleum reservoirs. Due to the complicated flow dynamics of gas in tight porous media and compressibility effects, corrections have to be applied to the Darcy equation so that it can properly predict gas flow dynamics. As the mean pore diameter of tight rocks (e.g. shales) decreases, the ratio of the mean free path to the pore diameter, known as the non-dimensional Knudsen number, rises, the gas rarefaction effects becomes important, and the condition of no-slip on the pore surface is violated. Proper treatments of these complexities have been attempted by using classical continuum fluid mechanics and kinetic theory of gases approaches. The most well-known slip condition correction was presented by Klinkenberg in 1941. Many researchers have tried to correct and extend Klinkenberg's model beyond the slip flow regime. In this research the slip condition of the rarefied gas in low permeability simple porous media is studied by the lattice Boltzmann method and new corrections to Klinkenberg's coefficients are investigated. These corrections allow the extension of Klinkenberg model to higher ranges of Knudsen numbers. All the simulations in this work were performed by codes developed by the authors.