A New Method for Determining the Non-Linear Effective Pressure
Tuesday, 16 December 2014
The physical properties (for example, permeability k) of linear elastic materials usually obey a simple effective pressure law (EPL), peff= pc-αpf (peff: effective pressure; pc: confining pressure; pf: pore fluid pressure), where α is a constant, often taken to be equal to 1 in the well-known Terzaghi' law, peff=pc-pf. However, non-linear EPL's, peff=pc-αs(pf, pc)pf, where the secant coefficient αs(pf, pc) is a function of pc and pf, should be expected in non-linear elastic rocks [Robin, 1978] and have been previously reported for permeability in low-permeability sandstones [Li et al, 2009, 2014]. A new method for experimentally determining non-linear EPL's for permeability was tested on low-permeability sandstones from reservoirs in China. The permeability of these low-permeability sandstones was measured while simultaneously cycling pf and pc (with 0 ≤ pf < pc). Based on the analysis of the experimental data using the Response Surface Method [Box and Draper, 1987], a contour map of permeability was drawn in the plane [pf, pc], from which the secant coefficient αs(pf, pc) and the effective pressure peff(pf, pc) were calculated. We found that αs(pf, pc) varied in the entire theoretically allowed range, φ ≤ αs(pf, pc) ≤ 1, where φ is the porosity. It is most interesting that αs(pf, pc) could be approximately described as a decreasing function αs(pc-pf) of Terzaghi’s differential pressure. Moreover, the non-linear EPL determined using the new method allowed a better estimation of the pressure dependence of permeability, k(peff), than classic Terzaghi' law, k(pc-pf).