Klinkenberg Effect and Effective Pressure for Gas Permeability of Tight Sandstones

Abstract

Gas permeability kg of tight sandstones was measured while cycling pore pressure, Pf, and confining pressure, Pc, using two different procedures. First, we cycled the pore pressure from a minimum value close to atmospheric pressure to a maximum one slightly lower than Pc, while keeping the Pc constant. Second, Pf and Pc were simultaneously varied so as to keep the difference, Pc − Pf, constant. Significant effects owing to slip flow were observed when the gas pressure was lower than about 5 MPa. Klinkenberg plots showed that, under constant Pc, gas permeability kg decreased linearly for high values of 1/Pf, reached a minimum and then sharply increased as 1/Pf approached zero. Under constant Pc − Pf, kg again decreased linearly in the high limit of 1/Pf and showed additional decrease in the low 1/Pf limit. The linear segments in both procedures indicate that kg in tight sandstones was subject to slip flow at low values of Pf, while the curved segments revealed the sensitivity of permeability to effective pressure when Pf became comparable in magnitude to confining pressure. The effective pressure coefficient α was estimated and generally appeared to be a well‐defined decreasing function of the pressure difference Pc − Pf. We modified the Walsh permeability model for fissured rocks to include slip flow effects and obtained satisfactory fits to the experimental data for the samples with the lowest porosities and the highest pressure sensitivities. This observation suggests that the intrinsic permeability of these rocks was controlled by intergranular and/or intragranular crack‐like pores.

Experimental Investigation about Gas Transport in Tight Shales: An Improved Relationship between Gas Slippage and Petrophysical Properties

“…Al Ismail and Zoback measured the gas permeability of Utica and Permian shales using argon, but they did not provide any model for the Klinkenberg effect. Xiao et al developed an empirical correlation for the gas slippage factors of tight sandstone reservoirs, which is analogous to the Jones and Owens correlation. Furthermore, second-order slip laws were recently developed to model apparent gas flow in nanopores of shales. , However, the expressions of first-order coefficient (Klinkenberg slippage factor) and second-order coefficient are quite different in these works. − …”

Viscous Dissipation and Apparent Permeability of Gas Flow in Nanoporous Media

“…This correlation was further modified in other studies under different conditions (Jones & Owens, ; Sampath & Keighin, ; Ziarani & Aguilera, ). Due to the simple format, the Klinkenberg model was widely used in shale gas permeability measurements (Liang et al, ; Xiao et al, ) and macroscale shale gas reservoir simulations (Wu et al, ; Wu & Pruess, ).…”

“…This correlation was further modified in other studies under different conditions (Jones & Owens, 1980;Sampath & Keighin, 1982;Ziarani & Aguilera, 2012). Due to the simple format, the Klinkenberg model was widely used in shale gas permeability measurements (Liang et al, 2001;Xiao et al, 2019) and macroscale shale gas reservoir simulations (Wu et al, 2014;Wu & Pruess, 1998). Beskok and Karniadakis (1999) developed a second-order slip boundary condition based on a Hagen-Poiseuille-type equation to describe gas flow in micro channels and nanochannels or capillaries.…”

Role of Pore-Size Distribution in Coals to Govern the Klinkenberg Coefficient and Intrinsic Permeability

“…The effective stress is defined as where P c and P p are confining and pore pressures, respectively, and χ is the effective stress coefficient, which varies as a function of the gas pressure . χ is determined via experiments with certain assumptions ,,, and also with numerical models. , Characterization of gas permeability evolution as a function of pressure in the laboratory using eq is a common practice . However, experimental or real field gas permeability in tight reservoirs is better estimated if the slippage or slip effect is considered along with the effective stress changes. ,− The slippage effect describes the permeability enhancement associated with gas flow in microporous conduits due to the acceleration of the nonstationary layer of gas molecules in contact with the pore capillary walls (see Figure of Letham and Bustin).…”

“…The Klinkenberg corrected permeability in tight reservoir rocks have been studied through state-of-the-art novel experiments ,,,− and also by numerical and analytical models. ,− , The studies were mostly focused on the variation of the Klinkenberg coefficient as a function of stress and demonstrate that permeability evaluation of tight reservoirs, such as coal seams at depth, should consider the role of effective stress and the Klinkenberg coefficient. They showed that the Klinkenberg coefficient increases with pore pressure at constant effective stress for an adsorbing gas. , Initially, the Klinkenberg coefficient increases with increasing pore pressure at constant confining stress; however, at even higher pore pressures, the Klinkenberg coefficient may continue to rise or decrease .…”