A Permeability Model for Coal and Other Fractured, Sorptive-Elastic Media

Abstract

This paper describes the derivation of a new equation that can be used to model the permeability behavior of a fractured, sorptive-elastic media, such as coal, under variable stress conditions commonly used during measurement of permeability data in the laboratory. The model is derived for cubic geometry under biaxial or hydrostatic confining pressures. The model is also designed to handle changes in permeability caused by adsorption and desorption of gases from the matrix blocks. The model equations can be used to calculate permeability changes caused by the production of methane from coal as well as the injection of gases, such as carbon dioxide, for sequestration in coal. Sensitivity analysis of the model found that each of the input variables can have a significant impact on the outcome of the permeability forecast as a function of changing pore pressure; thus, accurate input data are essential. The permeability model can also be used as a tool to determine input parameters for field simulations by curve-fitting laboratory-generated permeability data. The new model is compared to two other widely used coal permeability models using a hypothetical coal with average properties. IntroductionDuring gas production from a coal seam, as reservoir (pore) pressure is lowered, gas molecules, such as methane, are desorbed from the matrix and travel by diffusion to the cleat (natural fracture) system where they are conveyed to producing wells. Fluid movement in coal is controlled by slow diffusion within the coal matrix and described by Darcy flow within the fracture system, which is much faster than the contribution of diffusion. A coal formation is typically treated as a fractured reservoir with respect to fluid flow; meaning that the sole contributor to the overall permeability of the reservoir is the fracture system and the contribution of diffusion through the matrix to total flow is neglected. Coalbeds are unlike other non-reactive fractured reservoirs because of their ability to adsorb (or desorb) large amounts of gas, which causes swelling (or shrinkage) of the matrix blocks.Coal has the capacity to adsorb large amounts of gases because of their typically large internal surface area, which can range from 30 m

Influence of the effective stress coefficient and sorption-induced strain on the evolution of coal permeability: Model development and analysis

“…Other stressbased coal permeability models include Harpalani and Chen (1997), Gilman and Beckie (2000), Shi and Durucan (S-D) (2004), and Cui and Bustin (C-B) (2005). Based on cubic geometry, Robertson and Christiansen (2006) described the derivation of a new equation that can be used to model the permeability behavior of a fractured, sorptive-elastic medium, such as coal, under variable stress conditions. Ma et al (2011) proposed a permeability model based on the volumetric balance between the bulk coal, solid grains and pores, using the constant volume theory proposed by Massarotto et al (2009).…”

The impact of effective stress and gas slippage on coal permeability under cyclic loading

“…They simplified the cleat system with cubic matrix blocks and considered the following three factors as contributors to changes in cleat width and matrix block size when different stresses were applied to coal: (1) pore volume compressibility; (2) matrix compressibility governed by mechanical elastic moduli; and (3) sorption-induced strain (Robertson and Christiansen, 2006).…”

“…Poisson's ratio is 0.31, and the Langmuir volume P L ¼ 2.86 MPa, which was obtained by sorption tests. Robertson, (2005Robertson, ( , 2006 obtained Langmuir strains of Anderson and Gilson coals tested by N 2 , which are extremely small, and the average value is as low as 0.0025. They also obtained the average compressibility change rate a ¼ 0.44 MPa À1 combining the study of McKee et al (1988).…”

A simplified permeability model for coalbed methane reservoirs based on matchstick strain and constant volume theory

“…A sensitivity study showed that permeability, cleat spacing and in situ stresses had a significant influence on CBM production, whereas Young's modulus, Poisson's ratio and Langmuir pressure were found to have a small impact. Robertson and Christiansen (2008) proposed a permeability model for coal and other fractured sorptive-elastic media. The cubic geometry model was used as the basis instead of the matchstick model.…”