Predicting Gas Apparent Permeability of Shale Samples: A Novel Analytical Approach

摘要

Natural gas production of the United States from shale resources increased from 4 percent of total gas production in 2005 to 40 percent in 2012. These resources are different from conventional hydrocarbon resources due to the presence of extremely tight organic pores and low permeabilities. Presence of the nanopores may cause rarefaction effects, especially in laboratory conditions, which increases the effects of temperature and pressure on the apparent permeability of shale samples. In order to determine the permeability of these resources, laboratory measured apparent permeabilities, if conducted in low pressure and temperature, need to be extrapolated to reservoir conditions. In addition, gas flow in low pressures has important applications in predicting the gas production rates from unconventional reservoirs. Analytical methods for estimating gas apparent permeability (AP) of shale have been already proposed, e.g. Navier-Stokes and Advective-Diffusive Models (ADM); however, they are valid for a limited range of Knudsen numbers (Kn 0.5) and they have oversimplifying assumptions that overestimate the mass flux (or permeability) of nanopores. In addition, their results do not show the effect of temperature and gas molecular weight on AP. The presented work aims to develop an analytical model for gas apparent permeability of nanopores which is valid for Knudsen number up to unity. Solutions to the Regularized 13 (R13)-moment equations (extension of Grad’s 13-moments equations) provide a reliable tool to derive an analytical model for gas AP in nanotubes. The novelty of this work is that we provide an analytical model for gas AP which is valid for higher range of Knudsen numbers (by comparing with the kinetic data) in contrast to the previously developed analytical models. The new model is used to predict the impact of controlling parameters such as temperature, pressure, molecular weight, pore size, and Tangential Momentum Accommodation Coefficient (TMAC) on gas AP. It is shown that the gas molecular weight and temperature have significant effect on gas apparent permeability at low pressures. The effect of adsorption on AP of nanotubes is studied by employing the experimental Langmuir isotherms of different shale samples. The bundle of tubes method is used to compare R13 AP model with the experimental data of a Marcellus shale core plug. The model’s AP results for Nitrogen and Carbon Dioxide agree with the experimental measurements.