An analytical coal permeability model for tri-axial strain and stress conditions

Coal permeability is sensitive to the effective stress and is therefore coupled to the geomechanical behaviour of the seam during gas migration. As coal shrinks with gas desorption and swells with adsorption, understanding this coupling to geomechanical behaviour is central to interpreting coal permeability. Existing coal permeability models, such as those proposed by Shi and Durucan (2004) and Palmer and Mansoori (1996), simplify the geomechanical processes by assuming uni-axial strain and constant vertical stress. However it is difficult to replicate these conditions in laboratory tri-axial permeability testing and during laboratory core flooding tests for enhanced coal bed methane. Often laboratory tests involve a hydrostatic stress state where the pressure in the confining fluid within the tri-axial cell is uniformly applied to the sample exterior. In this experimental arrangement the sample is allowed to undergo tri-axial strain. This paper presents two new analytical permeability model representations, derived from the general linear poroelastic constitutive law, that include the effects of tri-axial strain and stress for coal undergoing gas adsorption induced swelling. A novel approach is presented to the representation of the effect of coal sorption strain on cleat porosity and thus permeability. This involves distinguishing between the sorption strain of the coal matrix, the pores (or cleats) and the bulk coal. The developed model representations are applied to the results from a series of laboratory tests and it is shown that the models can predict the laboratory permeability data. As part of this characterisation the various sorption strains are identified and it is shown that the pore strain is significantly larger than (approximately 50 times) the bulk sorption strain. The models also provide further insight into how coal permeability varies with coal shrinkage and swelling and how the permeability rebound pressure depends upon the effective stress applied.

Research Highlights
► An improved theoretical interpretation of coal permeability behaviour during pressure and gas content changes that builds on the work of Shi and Durucan (2004) and Cui and Bustin (2005).
► A coal permeability model that is representative of hydrostatic tri-axial testing conditions.
► An improved representation of the role of coal matrix shrinkage/swelling as a result of changes in gas content by recognizing the distinct influence of pore volume sorption strain on coal permeability.
► Application of the developed hydrostatic permeability model to laboratory measurements of coal permeability with respect to pore and confining pressure and for a number of different gases.