Dr. Wenlian Xiao, Professor at Southwestern Petroleum University and Visiting Scientist at MIT, presents "Nonlinear Effective Pressure Law in Tight Rocks."

"The concept of effective pressure P_eff was firstly introduced by Terzaghi[1925], and it’s commonly used in the problems where porous rock and pore pressure P_f are involved. Terzaghi’ effective pressure is defined by P_eff = P_c - P_f, where P_c is confining pressure, and its simplicity made it very popular. However, it has been shown both theoretically and experimentally that this law does not always hold. The effective pressure law (EPL) is generally written in the form, P_eff = P_c - αP_f, where the EPL coefficient α is usually taken to be constant, yielding a linear expression for effective pressure. Actually, the coefficient α has been observed to be a function of P_c and P_f (i.e., Non-linear EPL) for permeability and velocity in low-permeability or low-porosity rocks [Bernabé, 1986; Li et al., 2014].

In this presentation, I will focus on the laboratory determination of non-linear EPL for permeability. Firstly, I will introduce briefly the background and motivation. Then, I will present the experimental procedures and gas permeability measurements in tight sandstones. Two different experimental procedures in extended pore pressure ranges are run under constant P_c - P_f cycles and constant P_c cycles respectively. The observations indicate that the gas permeability in tight sandstones is affected by the Klinkenberg effect at low values of P_f while controlled by effective pressure as P_f is greater than a few atm. What’s more, a new method to estimate the non-linear EPL coefficient α will be proposed, and the calculated coefficient α appears to be a well-defined decreasing function of Terzaghi’s differential pressure α(P_c - P_f). Finally, I will discuss the pressure dependence of permeability using these accurately determined EPLs."