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.

[1]  Luke D. Connell,et al.  Laboratory characterisation of coal reservoir permeability for primary and enhanced coalbed methane recovery , 2010 .

[2]  M. Biot.  THEORY OF ELASTICITY AND CONSOLIDATION FOR A POROUS ANISOTROPIC SOLID , 1955 .

[3]  Ian D. Palmer,et al.  How Permeability Depends on Stress and Pore Pressure in Coalbeds: A New Model , 1998 .

[4]  J. P. Seidle,et al.  Application of Matchstick Geometry To Stress Dependent Permeability in Coals , 1992 .

[5]  Olivier Coussy,et al.  Mechanics of porous continua , 1995 .

[6]  Luke D. Connell,et al.  Coupled flow and geomechanical processes during enhanced coal seam methane recovery through CO2 sequestration , 2009 .

[7]  S. Durucan,et al.  The effects of stress and fracturing on permeability of coal , 1986 .

[8]  I. Gray,et al.  Reservoir Engineering in Coal Seams: Part 1-The Physical Process of Gas Storage and Movement in Coal Seams , 1987 .

[9]  Jonny Rutqvist,et al.  A New Coal-Permeability Model: Internal Swelling Stress and Fracture–Matrix Interaction , 2010 .

[10]  J. C. Jaeger,et al.  Fundamentals of rock mechanics , 1969 .

[11]  L. Connell,et al.  A theoretical model for gas adsorption-induced coal swelling , 2007 .

[12]  A. C. Bumb,et al.  Stress-Dependent Permeability and Porosity of Coal , 1988 .

[13]  R. Marc Bustin,et al.  Volumetric strain associated with methane desorption and its impact on coalbed gas production from deep coal seams , 2005 .

[14]  Jeffrey R. Levine,et al.  Model study of the influence of matrix shrinkage on absolute permeability of coal bed reservoirs , 1996, Geological Society, London, Special Publications.

[15]  X. Miao,et al.  Evaluation of stress-controlled coal swelling processes , 2010 .

[16]  Ian Palmer,et al.  Permeability changes in coal: Analytical modeling , 2009 .

[17]  J. Rice,et al.  Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents , 1976 .

[18]  Sevket Durucan,et al.  Drawdown Induced Changes in Permeability of Coalbeds: A New Interpretation of the Reservoir Response to Primary Recovery , 2004 .

[19]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[20]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[21]  Roger Beckie,et al.  Flow of Coal-Bed Methane to a Gallery , 2000 .

[22]  Sevket Durucan,et al.  Exponential Growth in San Juan Basin Fruitland Coalbed Permeability With Reservoir Drawdown: Model Match and New Insights , 2010 .

[23]  Robert W. Zimmerman,et al.  Compressibility of porous rocks , 1986 .

[24]  Luke D. Connell,et al.  Coupled flow and geomechanical processes during gas production from coal seams , 2009 .

[25]  Sevket Durucan,et al.  A model for changes in coalbed permeability during primary and enhanced methane, recovery , 2005 .

[26]  John R. Seidle,et al.  Experimental Measurement of Coal Matrix Shrinkage Due to Gas Desorption and Implications for Cleat Permeability Increases , 1995 .