International Journal of Greenhouse Gas Control 8 (2012) 101–110 Contents lists available at SciVerse ScienceDirect International Journal of Greenhouse Gas Control j ourna l ho mepage: www.elsevier.com/locate/ijggc Influence of the effective stress coefficient and sorption-induced strain on the evolution of coal permeability: Model development and analysis Zhongwei Chen a,b , Jishan Liu a,∗ , Zhejun Pan b , Luke D. Connell b , Derek Elsworth c a School of Mechanical and Chemical Engineering, The University of Western Australia, WA 6009, Australia b CSIRO Earth Science and Resource Engineering, Private Bag 10, Clayton South, Victoria 3169, Australia c Department of Energy and Mineral Engineering, Penn State University, PA 16802-5000, USA a r t i c l e i n f o Article history: Received 4 March 2011 Received in revised form 25 January 2012 Accepted 27 January 2012 Available online 12 March 2012 Keywords: Coal permeability Swelling strain Effective stress effect CO2 storage a b s t r a c t A series of coal permeability experiments was conducted for coal samples infiltrated both with non- adsorbing and adsorbing gases – all under conditions of constant pressure difference between the confining stress and the pore pressure. The experimental results show that even under controlled stress conditions, coal permeability decreases with respect to pore pressure during the injection of adsorb- ing gases. This conclusion is apparently not congruent with our conceptual understanding: when coal samples are free to swell/shrink then no effect of swelling/shrinkage strain should be apparent on the permeability under controlled stress conditions. In this study, we developed a phenomenological per- meability model to explain this enigmatic behavior of coal permeability evolution under the influence of gas sorption by combining the effect of swelling strain with that of the mechanical effective stress. For the mechanical effective stress effect, we use the concept of natural strain to define its impact on the change in fracture aperture; for the swelling strain effect, we introduce a partition ratio to define the contribution of swelling strain to the fracture aperture reduction. The resulting coal permeability model is defined as a function of both the effective stress and the swelling strain. Compared to other commonly used models under specific boundary conditions, such as Palmer–Mansoori (P–M), Shi–Durucan (S–D) and Cui–Bustin (C–B) models, our model results match the experimental measurements quite well. We match the experimental data with the model results for the correct reason, i.e. the model conditions are consistent with the experimental conditions (both are stress-controlled), while other models only match the data for a different reason (the model condition is uniaxial strain but the experimental condition is stress-controlled). We have also implemented our permeability model into a fully coupled coal defor- mation and gas transport finite element model to recover the important non-linear responses due to the effective stress effects where mechanical influences are rigorously coupled with the gas transport system. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction Coal Bed Methane (CBM) is naturally occurring methane gas (CH 4 ) in coal seams. Methane was long considered a major prob- lem in underground coal mining but now CBM is recognized as a valuable resource. Australia has vast reserves of coal-bed methane (about 310–410 trillion m 3 ) (White et al., 2005) and has attracted billions of dollars in foreign investment to develop this resource. CBM recovery triggers a series of coal–gas interactions. For gas pro- duction, the reduction of gas pressure increases effective stress which in turn closes fracture aperture and reduces the perme- ability (McKee et al., 1988; Seidle and Huitt, 1995; Palmer and Mansoori, 1996). As gas pressure reduces below the desorption ∗ Corresponding author. Tel.: +61 8 6488 7205; fax: +61 8 64881024. E-mail address: jishan@cyllene.uwa.edu.au (J. Liu). point, methane is released from coal matrix to the fracture net- work and coal matrix shrinks. As a direct consequence of this matrix shrinkage the fractures dilate and fracture permeability cor- respondingly increases (Harpalani and Schraufnagel, 1990). Thus a rapid initial reduction in fracture permeability (due to change in effective stress) is supplanted by a slow increase in permeability (with matrix shrinkage). Whether the ultimate, long-term, per- meability is greater or less than the initial permeability depends on the net influence of these dual competing mechanisms (Shi and Durucan, 2004; Chen et al., 2008; Connell, 2009). Therefore, understanding the transient characteristics of permeability evolu- tion in fractured coals is of fundamental importance to the CBM recovery and CO 2 storage in coal, which has dual and complemen- tary benefits: the enhanced production of methane and concurrent long-term storage of CO 2 . A broad variety of models have evolved to represent the effects of sorption, swelling and effective stresses on the dynamic 1750-5836/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijggc.2012.01.015