Comparison of gas, Klinkenberg, and liquid permeability of sandstone: Flow regime and pore size

Abstract

Liquid permeability of sedimentary rocks is relevant in several contexts, but gas permeability is easier to measure, so liquid permeability is typically estimated from gas permeability via empirical or semiempirical correction procedures. A frequently used and trusted procedure is the well-known Klinkenberg correction, which is based on the pressure dependence of gas permeability. However, from gaseous and liquid flow-through experiments on a series of Fontainebleau, Castlegate, Bentheim, and Obernkirchen sandstones, this study indicates that the equivalent liquid permeability derived from gas permeability via the Klinkenberg correction only compares with liquid permeability, when the gaseous flow adheres to Darcy’s law. The lower and upper limits to Darcy flow are defined by the Knudsen and Reynolds numbers, respectively. Both numbers can be estimated from porosity and pore-throat distribution, so from these properties, it is possible to assess the flow and pressure limits for the applicability of the Klinkenberg correction. For the studied sandstones, non-Darcy flow is indicated for the largest pores with diameters above approximately 10 μm, causing an erroneous Klinkenberg correction. Knudsen diffusion takes place in pores smaller than approximately 0.1 μm, but the contribution to the overall gas permeability of these small pores is, however, insignificant in these sandstones. Liquid permeability modeled from contributions from each pore size by using Kozeny’s equation and surface relaxation times from nuclear magnetic resonance data shows that the largest pores have no positive effect on permeability because of the existence of pore throats; instead, they may have a negative effect on permeability because of turbulence.