On the Klinkenberg Effect of Multicomponent Gases

Abstract In unconventional gas formations, due to the narrow pore size, gas molecules slip at the wall of the pore, known as the Klinkenberg effect. Although the Klinkenberg effect of single component gas has been thoroughly investigated, an accurate correlation for Klinkenberg effects on multicomponent gas flow has not been formulated so far. In this paper, we aim to quantify the multicomponent gas Klinkenberg effect by deriving a non-empirical correlation that can be directly used in reservoir engineering applications. 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 molecule 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 permeability (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. We have brought out a second-order non-empirical gas slippage correlation for the multicomponent Klinkenberg effect problem. Our model well captures the mass transfer mechanism of gas mixtures. The accuracy of our model has been compared to and validated by both molecular dynamics simulation and physical experimental (tube-flooding). We have also investigated the effect of wall roughness on the reflection of gas molecules, which fundamentally reveals the origin of gas slippage effect. Our correlation can be readily implemented in compositional reservoir simulators to investigate gas flow in unconventional formations, such as shale and tight sandstone. Compared to existing approaches, our approach has several novelties and advantages. First, our approach is a non-empirical gas slippage correlation for gas mixtures. The model is based on the kinetic theory of gasses, originating from the first principals. Secondly, our model is capable of handling a wide range of Knudsen numbers. Last, compared to Direct Simulation Monte Carlo (DSMC) and Lattice Boltzmann Method (LBM), our approach requires much less computing resources.