Nonlinear effective pressure law for permeability

Abstract

The permeability k of porous rocks is known to vary with confining pressure pc and pore fluid pressure pf. But it is, in principle, possible to replace the two‐variable function k(pf, pc) by a function k(peff) of a single variable, peff(pf, pc), called the effective pressure. Our goal in this paper is to establish an experimental method for determining a possibly nonlinear, effective pressure law (EPL) for permeability, i.e., find the function κs(pf, pc) such that the effective pressure is given by peff = pc − κs(pf, pc) pf. We applied this method to a set of 26 sandstone cores from various hydrocarbon reservoirs in China. We found that κs greatly varied, from sample to sample, in magnitude and range, sometimes even reaching theoretically prohibited values (i.e., greater than 1 or lower than porosity). One interesting feature of κs(pf, pc) is that it could be approximately described in all rocks but one as a decreasing function κs(pc − pf) of Terzaghi's differential pressure. We also investigated the dependence of permeability on peff for each of our samples. Three models from the literature, i.e., exponential (E), power law (P), and the Walsh model (W), were tested. The (W) model was more likely to fit the experimental data of cores with a high pressure dependence of permeability whereas (E) occurred more frequently in low‐pressure‐sensitive rocks. Finally, we made various types of two‐ and three‐dimensional microstructural observations that generally supported the trend mentioned above.

Klinkenberg Effect and Effective Pressure for Gas Permeability of Tight Sandstones

“…Here, we have enough information to use equation . Li et al () estimated h / a ref for 22 sandstones from the same reservoirs investigated in the present paper, and found values very similar to those given in Table , even though they used a smaller reference pressure (20 MPa).…”

“…Among our samples and those of Li et al (), we distinguished the ones reasonably consistent with the Walsh model from the others. The distinction is clearer in this study than in Li et al (), where most samples verified multiple models equally well. Data points consistent with the Walsh model tend to be located in the upper‐left quadrant of Figure , suggesting that microcracks and/or crack‐like pores may plausibly be considered to control the permeability of low‐porosity rocks (ϕ < 0.1) with pressure sensitivities γ higher than about 0.02 MPa −1 (yellow region).…”

“…Values for α are plotted against the pressure difference P c − P f in Figure . In general, the observed EPLs were nonlinear, and α appeared to be a well‐defined decreasing function of P c − P f (Li et al, ). Values of α fell within the theoretically allowed range, ϕ < α < 1 (see Table and Berryman, ), except for samples 9‐1, 6‐16, and 56‐2, for which α was smaller than porosity.…”

“…It is therefore obvious that α is constant (linear EPL) when the iso‐ k lines are straight (e.g., blue line M′N′ in Figure ), but is a function of P c and P f (nonlinear EPL) when iso‐ k lines are curved (e.g., green line in Figure ). Nonlinear EPLs are expected in nonlinear elastic rocks (Robin, ) and have been reported for permeability in granites, limestones, and low‐permeability sandstones (Bernabé, , , ; Ghabezloo et al, ; Li et al, , ; Warpinski & Teufel, ; Xiao et al, ).…”

Effect of pore and confining pressure on the supercritical CO2 permeability of sandstone: Implications for the effective pressure law

“…Likewise, Li et al . [, ] and Bernabe [, ] also reported that there was a discrepancy in the coefficient caused by loading hysteresis and path.…”