A theoretical model for gas adsorption-induced coal swelling

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Abstract

Swelling and shrinkage (volumetric change) of coal during adsorption and desorption of gas is a well-known phenomenon. For coalbed methane recovery and carbon sequestration in deep, unminable coal beds, adsorption-induced coal volumetric change may cause significant reservoir permeability change. In this work, a theoretical model is derived to describe adsorption-induced coal swelling at adsorption and strain equilibrium. This model applies an energy balance approach, which assumes that the surface energy change caused by adsorption is equal to the elastic energy change of the coal solid. The elastic modulus of the coal, gas adsorption isotherm, and other measurable parameters, including coal density and porosity, are required in this model. Results from the model agree well with experimental observations of swelling. It is shown that the model is able to describe the differences in swelling behaviour with respect to gas species and at very high gas pressures, where the coal swelling ratio reaches a maximum then decreases. Furthermore, this model can be used to describe mixed-gas adsorption induced-coal swelling, and can thus be applied to CO2-enhanced coalbed methane recovery.

Introduction

Coal swelling due to gas adsorption is a well-known phenomenon. Experiments using either strain gauges (Levine, 1996) or optical methods (Robertson and Christiansen, 2005) have shown that coal swells with adsorption of carbon dioxide (CO2), methane (CH4) and other gases. The observed swelling represents the difference between two opposing effects; volumetric expansion of the coal matrix due to the adsorption of gas and the matrix compression as a result of pore pressure. Observations show that swelling initially follows the form of the adsorption isotherm. But at high pressures, as the rate of change in adsorbed gas content becomes small, matrix compression dominates and can decrease the volumetric strain.

Adsorption-induced coal swelling is of great importance to coalbed methane (CBM) recovery and CO2 sequestration in coal reservoirs. Coal permeability is primarily determined by the cleat aperture, and in coal the aperture size is a function of effective stress; i.e., increased effective stress through decreased pore pressure leads to the cleats closing. Swelling and shrinkage of coal under a confining stress may also change the cleat aperture; some of the volume change has to be accommodated by the coal porosity, of which the cleat porosity makes up a significant component. Although volumetric strain as a result of gas adsorption and desorption is small with respect to the total volume (e.g., up to 4%), cleat porosity also tends to be small (e.g., 2%). Thus, the coal permeability is a function of both the effective stress and the coal swelling or shrinkage. In practice, significant permeability change has been observed during CBM production and CO2 injection (Pekot and Reeves, 2002).

Levine (1996) summarized a series of measurements of adsorption-induced coal swelling. These showed that the linear swelling ratio (or linear strain) of coal in CO2 was less than 0.6% at pressures up to 2.1 MPa. CH4 adsorption-induced coal swelling was smaller than CO2 at the same pressure. With these measurements, the coal linear strain was less than 0.3% with pressures up to 2.1 MPa Levine (1996) also measured the swelling ratio on a sample of bituminous coal from Illinois. Levine's measurements showed a linear swelling ratio in CO2 at 3.1 MPa of 0.41% and 0.18% in CH4 at 5.2 MPa. Levine (1996) found that the swelling behaviour followed the same form as the adsorption isotherm, in this case explained using a Langmuir-like equation.

Chikatamarla et al. (2004) measured H2S, CO2, CH4, and N2 induced swelling on four coal samples with pressures up to 5.0 MPa. Their measurements showed that the volumetric strain at 0.6 MPa is from 1.4% to 9.3% for H2S, from 0.26% to 0.66% for CO2, 0.09% to 0.30% for CH4, and from 0.004% to 0.026% for N2. Their measurements also showed that the volumetric strain and pressure can be described using a Langmuir-like equation and the volumetric strain is approximately linearly proportional to the amount of gas adsorbed.

Robertson and Christiansen (2005) found a linear strain of less than 1.0% for coal in CO2 at pressures up to 5.3 MPa and 0.2% for coal in CH4 at pressures up to 6.9 MPa. They also measured adsorption-induced coal swelling in CO2, CH4 and nitrogen (N2) on a bituminous and a sub-bituminous coal samples. Their results showed that linear strain caused by CO2 adsorption on the sub-bituminous coal was 2.1% and it was more than twice as much as the bituminous coal at 5.5 MPa; CH4-induced coal swelling for the two coal types was similar at about 0.5% at 6.9 MPa; N2-induced swelling was about 0.2% at 6.9 MPa.

In the work of St. George and Barakat (2001), volumetric strains were measured for adsorption at 4.0 MPa for CO2, CH4, N2 and Helium on a coal sample from New Zealand. The volumetric strain was 2.1% for CO2, 0.4% for CH4, and 0.2% for N2. Moffat and Weale (1955) measured coal swelling in CH4 with pressures up to 70.0 MPa. Although the magnitude of swelling was different for different coal types, the swelling isotherms showed similar trends with a maximum at around 15.0 MPa.

Levine (1996) used a Langmuir form of equation to describe the swelling and achieved good agreement with the experimental measurements. Palmer and Mansoori (1998) applied this model to describe the change in cleat porosity for coal. Pekot and Reeves (2002) used an equation in which the swelling ratio is proportional to the quantity of gas adsorbed. Pekot and Reeves (2002) also introduced an extra parameter to represent the differential swelling behaviour resulting from different gas species, using Levine's experimental results. However, these purely empirical models can describe the swelling behaviour at low and moderate pressures, and require observations of swelling. An additional complication is relating the laboratory swelling data to the situation in the field where coal is under stress. In practice, the parameters describing swelling/shrinkage as it affects the reservoir permeability can only be determined through history matching. However, discerning the effects of this process requires long periods of gas production or CO2 injection, making prediction of reservoir processes difficult.

In this paper the authors propose a model, based on an energy balance approach, to describe adsorption-induced volumetric changes as a first step in describing the effects of shrinkage/swelling on permeability. The developed model assumes that the surface energy change caused by adsorption is equal to the change in elastic energy of the coal solid. The model is tested by application to published experimental measurements of gas adsorption-induced coal swelling.

Section snippets

Model development

A porous body dilates when its surface energy changes, either by adsorption of a gas or by immersion in a liquid (Scherer, 1986). If the specific surface energy (γ) of a body changes by adsorption of a vapour or immersion in a liquid, there is a consequent dilatation of the body; if γ increases, the body shrinks to reduce its surface area, and vice versa (Scherer, 1986). Scherer (1986) and Bentz et al. (1998) applied this approach to model the dilation of porous glass with water vapour

Results

With a Langmuir adsorption isotherm model:na=LBP1+BPand assuming the fugacity is equal to pressure for calculation simplicity, the surface potential can be calculated asΦ=0PVadPRToP(i=1Cniadlnfi)=0PVadPRT0PLB1+BPdP=0PVadPRTLln(1+BP)However, fugacity differs with pressure for non-ideal gases, such as CO2 at high pressures, for example, near or high than its critical pressure, 7.4 MPa. Nevertheless, for CO2 at low pressure and CH4 at all pressures, fugacity equal to pressure is a

Swelling for mixed gas adsorption

This model can be readily extended to describe the swelling behaviour caused by mixed-gas adsorption. A multi-component adsorption model is required, and for example, the extended Langmuir model can be used:nia=LiBiPyi1+BiPyiand assuming that the gas fugacity is equal to pressure, the surface potential can be derived asΦ=0PVadPRTi=1CLiln(1+BiyiP).

Adsorption model

The Langmuir model is a relatively simple adsorption model that can describe low-pressure adsorption behaviour with reasonable accuracy. However,

Conclusions

This paper has presented a theoretical model to describe adsorption-induced coal swelling. Previous procedures have been empirical. This new model is based on an energy balance between changes in the surface potential energy caused by gas adsorption and the elastic energy change caused by solid volume change. All parameters in this model have physical meanings. This provides a predictive basis for shrinkage/swelling behaviour with gas adsorption.

The parameters used in the presented model are

Acknowledgements

The financial support of CSIRO Energy Transformed Flagship is gratefully acknowledged. The authors are also grateful to Dr. A. L. Myers of the University of Pennsylvania for his helpful discussion on thermodynamics of adsorption in porous materials.

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