Interpretation of Steady Linear Visco-Inertial Gas Flow Data

Abstract

Abstract When laboratory gas flow data are presented on a Klinkenberg plot, the points trace a path which curves downward in the region of high mean pressure. Recent work has shown that this departure from linearity is due to visco-inertial flow. Consequently, it has been suggested that if flow measurements are restricted to the viscous region the resulting points must fall on a straight line, in which case an unbiased estimate of the true linear relationship may be obtained by the method of least squares. In the case of flow measurements taken in the visco-inertial flow region, theory suggests that the resulting data may be plotted in such a manner as to yield a straight line with a slope equal to the inertial resistance coefficient, β, and an intercept equal to the inverse of the permeability, K. In practice, however, when such a plot is made, the points invariably trace a path which curves downward in the region of low flow rates. Although it has been recognized that the departure from linearity was due to slip at the gas-solid interface, a criterion for the delineation of the linear region of the plot was unavailable. The present work offers such a criterion and demonstrates its validity by applying it to a set of laboratory data.