A Permeability Model for Coal and Other Fractured, Sorptive-Elastic Media
- Eric P. Robertson (Idaho National Laboratory) | Richard L. Christiansen (Wind River Resources Corp)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2008
- Document Type
- Journal Paper
- 314 - 324
- 2008. Society of Petroleum Engineers
- 5.3.2 Multiphase Flow, 4.1.2 Separation and Treating, 1.2.3 Rock properties, 5.10.1 CO2 Capture and Sequestration, 4.3.1 Hydrates, 5.8.3 Coal Seam Gas, 4.3.4 Scale, 5.5 Reservoir Simulation, 4.6 Natural Gas, 4.1.5 Processing Equipment, 1.6.9 Coring, Fishing, 5.5.1 Simulator Development
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This paper describes 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. The equation is applicable to confinement pressure schemes commonly used during the collection of permeability data in the laboratory. The model is derived for cubic geometry under biaxial or hydrostatic confining pressures. The model is designed to handle changes in permeability caused by adsorption and desorption of gases onto and from the matrix blocks in fractured media. The model equations can be used to calculate permeability changes caused by the production of methane (CH4) 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 also can 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.
During gas production from a coal seam, as reservoir (pore) pressure is lowered, gas molecules, such as CH4, 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 is described by Darcy flow within the fracture system, which is much faster than the contribution of diffusion. A coal formation typically is 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 nonreactive fractured reservoirs because of their ability to adsorb (or desorb) large amounts of gas, which causes swelling (or shrinkage) of the matrix blocks.
Coalbeds have the capacity to adsorb large amounts of gases because of their typically large internal-surface areas, which can range from 30 to 300 m2/g (Berkowitz 1985). Some gases, such as carbon dioxide, have a higher affinity for the coal surfaces than others, such as nitrogen (N2). 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 coalbeds, but also to the design and operation of projects to sequester greenhouse gases in coalbeds (RECOPOL 2005). 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 (1987), Sawyer et al. (1990), Seidle and Huitt (1995), Palmer and Mansoori (1998), Pekot and Reeves (2003), and Shi and Durucan (2003). These models were derived to mimic field conditions, and they assume a matrix-block geometry described as a bundle of vertical matchsticks under a uniaxial stress regime (Palmer and Mansoori 1998; Seidle et al. 1992).
However, in the laboratory, permeability typically is measured by use of hydrostatic (biaxial) core holders, which apply a single confining pressure to all external points of the core inside the holder. This is obviously different from the stress conditions encountered in the field, which typically are characterized as being under uniaxial stress as noted previously. Moreover, on a laboratory scale, coal matrix blocks may be approximated better by cubic instead of matchstick geometry, as will be discussed later in this paper. A recent study (Robertson and Christiansen 2005c) 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 match the data accurately. 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 medium, 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 contribute neither 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, respectively, and thus affect permeability.
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