Model development for the gas transport through nanopores

  • Li, Jun (PI)

Project: Research

Project Details


The gas transport mechanism changes with the Knudsen number (), which is the ratio of the molecular mean free path to the flow characteristic size (i.e., the dominant pore size in our study) and equivalent to the frequency ratio of the molecular collisions with the wall surface and the intermolecular collisions. The usual gas transport at small is a collective behavior of a large number of molecules that interact with each other and move together through intermolecular collisions, which can be characterized by the viscosity and described by the traditional Navier-Stokes equation. With the increase of (e.g., due to the decrease of the pore size from the conventional reservoirs to unconventional ones), the frequency of molecular collisions with the wall surface is increased and will finally become higher than that of the intermolecular collisions that depends mainly on the given pore pressure. In this case, molecules move independently with negligible intermolecular collisions and the gas transport becomes a diffusion process, which can be described by the Boltzmann-like equation without the intermolecular collision term. Most gas transport processes at the nanoscale are subjected to both mechanisms, namely the viscous transport at 0 and the diffusion transport at . Empirical transport models have been proposed in literature using a weighted superposition of the analytical models obtained in simplified channel-like geometries at 0 and , respectively, and are then extended to irregular porous media by adding correction coefficients for porosity, tortuosity, ect. The previous derivation of the analytical model at is not rigorous and we propose to obtain the model coefficient by using the probability distribution function of the reflected molecular velocity. This fundamental derivation from scratch involves a multivariable integral with respect to the reflected molecular velocity, which might need numerical integration if elegant analytical solution is impossible. The derived models are usually valid for simplified geometries but the practical validity should be verified in porous media applications. Since the experimental measurement of gas transport through tight rocks is still subjected to large error/uncertainty due to very low permeability, we will use the pore- scale molecular simulation inside representative rock samples to get the reference data for the model validation. A small sample size will be used such that fine discretization grids/cells can be afforded to contain the numerical error that depends mainly on the grid resolution and is the only error source. The developed transport model, after comprehensive validations, will be the basis for the accurate reservoir simulation to evaluate the reservoir quality and predict the production performance.
Effective start/end date1/09/2131/08/22


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