A New Method for Determining the Non-Linear Effective Pressure

Tuesday, 16 December 2014
Wenlian Xiao1, Ling Li1, Yves Bernabe2, Jinzhou Zhao1 and Min Li1, (1)SWPU Southwest Petroleum University, State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu, China, (2)M I T, Cambridge, MA, United States
The physical properties (for example, permeability k) of linear elastic materials usually obey a simple effective pressure law (EPL), peff= pcpf (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=pcs(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).