Summary
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.
Introduction
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.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
28 August 2006
- Meeting paper published:
11 October 2006
- Revised manuscript received:
5 November 2007
- Manuscript approved:
12 November 2007
- Version of record:
20 September 2008
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