# FISH Seminar: Wenlian Xiao (MIT)

**Nonlinear Effective Pressure Law in Tight Rocks**

The concept of effective pressure Peff first introduced by Terzaghi[1925] is commonly used in problems involving porous rock and pore pressure Pf . Terzaghi’ effective pressure is defined as Peff = Pc - Pf, where Pc 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 written in the form, Peff = Pc - αPf, 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 Pc and Pf (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 Pc - Pf cycles and constant Pc cycles respectively. The observations indicate that the gas permeability in tight sandstones is affected by the Klinkenberg effect at low values of Pf and by the effective pressure as Pf is increased. 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(Pc - Pf). Finally, I will discuss the pressure dependence of permeability using these accurately determined EPLs.

**Prior knowledge:** Rock physics, Geomechanics, Multi-phase flow

**About the Speaker**

Wenlian Xiao is an Associate Professor at the College of Petroleum Engineering, Southwest Petroleum University, China. His research interests include petrophysical properties of rocks, and oil and gas production. Xiao is currently at MIT as a Visiting Scientist in the Earth Resources Laboratory.

**About the Series**

The Friday Informal Seminar Hour [FISH, Earth Resources Laboratory] is a postdoc-run weekly seminar series within the ERL. Topics include research relating to geophysics, and in particular seismology, with applications in Earth resources exploration such as e.g. seismics exploration, microseismicity, earthquake physics, and Earth imaging techniques. The seminars usually take place on **Fridays at 12 noon in 54-209** (term-time only).