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

Abstract

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. Introduction During 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 m2/g to 300 m2/g.[i] Some gases, such as carbon dioxide, have a higher affinity for the coal surfaces than others, such as nitrogen. Knowledge of how the adsorption or desorption of gases affects coal permeability is important not only to operations involving the production of natural gas from coal beds, but also to the design and operation of projects to sequester greenhouse gases in coal beds.[ii] Laboratory measurements of permeability using coal samples can be used to gain insight into field-scale permeability changes and to determine key coal property values necessary for field-scale simulation. A number of permeability models derived for sorptive-elastic media such as coals have been detailed in the literature and include those proposed by: Gray in 1987, Sawyer et al. in 1990, Seidle and Huitt in 1995, Palmer and Mansoori in 1998, Pekot and Reeves in 2003, and Shi and Durucan in 2003. These models were derived to mimic field conditions and assume a matrix-block geometry described as a bundle of vertical matchsticks under a uniaxial stress regime.6, However, in the laboratory, permeability is typically measured using hydrostatic (biaxial) core holders, which apply a single confining pressure to all external points of the core inside the holder. This is obviously different than the stress conditions encountered in the field, which are typically characterized as being under uniaxial stress. Moreover, on a bench-scale, coal matrix blocks may be better approximated by cubic instead of matchstick geometry as will be discussed later in this paper. A recent study compared the accuracy of three field-permeability models when applied to laboratory-generated, sorption-affected permeability data and found that none of the three was able to accurately match the data. A model specifically derived for laboratory coreflooding conditions would be expected to provide a more reasonable match of permeability results. This paper describes the derivation of a new model that describes the permeability behavior of a fractured, sorptive-elastic media, such as coal, under typical laboratory conditions where common radial and axial pressures are applied to a core sample during permeability measurements. The new model can be applied to fractured rock formations where the matrix blocks do not contribute to the porosity nor to the permeability of the overall system, but where adsorption and desorption of gases by the matrix blocks cause measurable swelling and shrinkage and thus affect permeability.