Comparison of adsorption models in reservoir simulation of enhanced coalbed methane recovery and CO2 sequestration in coal
Introduction
CO2 sequestration in unminable coal is a potential management option for greenhouse gas emissions. The feasibility of this process will be determined by various factors including the gas storage capacity of the coal, the rate of injection and the long-term behaviour of the sequestered CO2. To investigate these questions, representative models for the reservoir behaviour of the CO2 in coal and reliable experimental data are required. One important process in determining the reservoir behaviour is adsorption of CO2 with simultaneous desorption of methane in a migrating front of mixed gas within the coal seam. This requires mixed-gas adsorption to be represented. Furthermore, the impact of the adsorption models in the simulation is not only on storage capacity, but also on the fluid flow behaviour due to adsorption-induced swelling. Adsorption-induced coal swelling tends to reduce the cleat porosity and thus the permeability under reservoir conditions. It is commonly assumed to be proportional to the amount of adsorbed gas and has been explicitly represented in existing coal reservoir permeability models (Sawyer et al., 1990, Pekot and Reeves, 2002, Shi and Durucan, 2005). Recently, a theoretical model has been developed to demonstrate that a linear relationship between swelling strain and the amount of adsorbed gas may be valid under certain pressure ranges (Pan and Connell, 2007). In the reservoir simulations presented in this paper, adsorption models were used to determine the amount of adsorbed gas, and permeability then modified for the associated adsorption strain.
Existing coal reservoir simulators are based on similar descriptions of the physical processes, such as Langmuir and Extended Langmuir models (ELM) for pure- and mixed-gas adsorption (Law et al., 2002), and the Warren and Root model for the role of dual-porosity (Young, 1998). In a recent model intercomparison study using a broad range of coal gas simulators, results were very similar (Law et al., 2002). However, a key question is how well the simulators replicate the various processes operating under actual reservoir conditions. If these inaccuracies introduce systematic bias to the simulation results then the reliability of the model predictions can be questioned (Reeves, 2004).
Adsorption models have been studied for mixed-gas adsorption on coals under reservoir conditions (DeGance, 1992, Zhou et al., 1994, Clarkson and Bustin, 2000, Fitzgerald et al., 2005). Although these studies have found that adsorption models, such as the Two-Dimensional Equation of State (2D EOS) and IAS model, in conjunction with Dubinin–Astakhov (D–A) pore filling single component model, have greater accuracy in predicting the mixed-gas adsorption than the Extended Langmuir model, most of the reservoir simulators used for CO2 sequestration in coal implement the Langmuir model and ELM for pure- and mixed-gas adsorption, respectively. Since the Extended Langmuir model is not always thermodynamically correct and subject to large errors for mixed-gas adsorption (Do, 1998), the Ideal Adsorbed Solution (IAS) model has been implemented in several simulators (i.e. SIMED II). However, the Ideal Adsorbed Solution model is for mixed-gas adsorption only and requires a pure-gas adsorption model. Hence, the inaccuracy of the pure-gas adsorption model propagates to the mixed-gas adsorption calculation and thus the IAS model predictions are strongly dependent upon the choice of the pure-gas adsorption model (Clarkson and Bustin, 2000).
Furthermore, not all adsorption models are appropriate for implementation into reservoir simulators. Some adsorption models such as IAS with D–A (Clarkson and Bustin, 2000) and Simplified Local Density model (Fitzgerald et al., 2003) require numerical integration in the adsorption calculation. Appling these models may significantly prolong the computer time required to carry out a simulation since the adsorption calculation will be called at every time step and for each grid block where gas is present.
To investigate the impact of adsorption modeling on reservoir simulation, this paper considers three approaches, the ELM, IAS with the Langmuir model, and 2D EOS. These models do not require numerical integration for the adsorption calculation and thus can be efficiently implemented into reservoir simulators. The coal gas reservoir simulator SIMED II (Spencer et al., 1987, Stevenson and Pinczewski, 1995, Stevenson, 1997) is used as the basis for this work with the ELM and IAS with Langmuir model already part of this simulator. For this study the 2D EOS adsorption model was also implemented in SIMED II. Measurements of mixed-gas adsorption for two coal types, Fruitland coal from USA and Bulli coal from Australia, were used to estimate the parameters of the adsorption models. These were then used in hypothetical simulation studies to investigate the impact of the adsorption modeling on reservoir simulation results.
Section snippets
Langmuir and Extended Langmuir model
The Langmuir model assumes that adsorption occurs on a flat surface. At equilibrium, a continual process of bombardment of molecules onto the surface and a corresponding evaporation of molecules from the surface maintain a net zero rate of accumulation at the surface. The Langmuir model further assumes that the surface is homogeneous, that is, the adsorption energy is constant over all sites. Furthermore it implies that the adsorption on the surface is localized, which means that the atoms or
Adsorption algorithms
For mixed-gas adsorption calculation, it is a set of coupled equations to be solved simultaneously. Thus, an efficient mixed-gas adsorption algorithm is important in reservoir simulation. For the Extended Langmuir model, adsorption is explicit for each gas component as described in Eq. (2). Therefore the mixed-gas adsorption algorithm is straightforward. In this new work, an iterative method was applied for the 2D EOS. This method is similar to that used in vapor–liquid equilibrium calculations
Simulation results and discussion
Hypothetical enhanced CBM recovery through CO2 injection simulation studies were developed to illustrate how the different adsorption models affect the reservoir simulation results using the adsorption data presented above for Fruitland coal and Bulli coal. In the simulation studies, a CO2 injection well is located in a corner of a 200 m × 200 m field and a CH4 recovery well is located in the opposite corner. For Fruitland coal, the initial reservoir pressure was set at 8.8 MPa, corresponding to
Conclusions
This paper has investigated the representation of adsorption behaviour in reservoir simulation of CO2 sequestration and enhanced coal seam methane recovery. Gas adsorption is a key process in coal seam reservoirs since it determines the quantity of gas in place within the reservoir and also affects the permeability through changes in porosity as the coal matrix shrinks and swells with changes in gas content.
Three adsorption isotherm models were considered; two existing approaches, the Ideal
Acknowledgements
Financial support for this work was provided, in part, by the CSIRO Energy Transformed Flagship. The authors are grateful to the anonymous reviewers for their thoughtful suggestions.
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