Second-order gas slippage model for the Klinkenberg effect of multicomponent gas at finite Knudsen numbers up to 1

Abstract

Within microchannels, rarefied gas molecules frequently interact with the channel wall, resulting in non-zero velocity at the wall. This phenomenon is known as the gas slippage effect or Klinkenberg effect in porous media. Although the gas slippage effect of single component gas has been thoroughly investigated, an accurate correlation to account for the gas slippage effect in multicomponent gas flow has not been formulated so far. In this paper, we aim to quantify the multicomponent gas slippage effect by deriving a non-empirical second-order correlation.Our approach is based on kinetic theory. We calculate the mean free path of gas mixtures, and capture the loss of horizontal flux momentum of gas flux after the molecules diffusively reflect at the wall. The horizontal flux momentum acts as shear stress on gas flow. In this sense, the loss of momentum induces reduction of viscosity and enhancement of mass transfer. By quantifying the loss of horizontal momentum as well as the reduction of viscosity, we can solve the gas slippage coefficient for the multicomponent gas flow system.Our model captures the mass transfer mechanism of gas mixtures at low pressure (near-ideal condition). The accuracy of our model has been validated by both molecular-level simulation data and physical experimental data. The difference between our results and benchmark data is within 10% for Knudsen number up to 1.Our model can be readily applied to the numerical simulation of unconventional gas formations.