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Two-Dimensional Equation-of-State Modeling of Adsorption of Coalbed Methane Gases

Sayeed Mohammad1, Zhejun Pan1, R.L. Robinson1, and K. a. M. Gasem2. (1) Chemical Engineering, Oklahoma State Univ., Stillwater, OK 74078, (2) School of Chemical Engineering, Oklahoma State University, 423 Engineering North, Stillwater, OK 74078

Adsorption equilibrium models are essential for optimizing coalbed methane (CBM) production and carbon dioxide (CO2) sequestration processes. Although a number of frameworks are available for describing the adsorption phenomenon, two-dimensional (2-D) equations of state (EOS) offer distinct advantages in modeling supercritical, high-pressure adsorption systems.

Current applications of 2-D EOS typically involve regressions of data on individual adsorption isotherms to determine the temperature-dependent EOS parameters (, ", k). For the EOS to have maximum utility, generalized correlations for these parameters are needed. Such generalizations would facilitate (a) correlation of adsorption data over a range of operating temperatures, and (b) a priori predictions of adsorption behavior. Accordingly, we have focused on developing new correlations for the 2-D EOS parameters that yield precise representations and accurate predictions of high-pressure, supercritical, pure-gas adsorption encountered in CBM recovery and CO2 sequestration. Further, we have extended the 2D-EOS to adsorption from gas mixtures by incorporating "mixing rules" to describe the composition dependence of the model parameters.

In this work, we have used the 2-D Peng-Robinson (PR) EOS to illustrate the proposed method for determining the EOS pure-fluid parameters and to demonstrate the 2-D EOS capability to represent and predict pure-gas adsorption of CBM gases (CH4, CO2, and N2) on carbon adsorbents. Experimental adsorption measurements, including both activated carbons and coals (both dry and wet), were used to evaluate the efficacy of this approach.

The new correlations for the 2-D EOS parameters appear effective in modeling pure-gas adsorption on carbon matrices at supercritical and near-critical conditions. The 2-D PR EOS, using the new parameter correlations, can represent adsorption on activated carbon and coals within their expected experimental uncertainties. Specifically, the 2-D EOS parameter correlations can represent the pure-gas adsorption over a range of temperature with 2.4% absolute average deviation (AAD) for activated carbons and 4.4% AAD for coals. Further, the new correlations, which are generalized in terms of accessible adsorbate and adsorbent properties, can predict (a) pure-gas adsorption on activated carbons with 9% AAD (within three times the expected experimental uncertainties), and (b) binary and ternary gas adsorption within three times the experimental uncertainties, on average.