Adsorption equilibrium models are essential for optimizing coalbed methane (CBM) production and carbon dioxide (CO₂) sequestration processes. Although numerous 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 (1) correlation of adsorption data over a range of operating temperatures and (2) 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 supercritical, pure-gas adsorption encountered in CBM recovery and CO₂ sequestration. Furthermore, we have extended the 2-D 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 (methane, nitrogen, and CO₂) 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. Using the new parameter correlations, the 2-D PR EOS 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 temperatures with an average absolute deviation (AAD) of 2.4% for activated carbons and an AAD of 4.4% for coals. Furthermore, the new generalized parameter correlations, expressed in terms of accessible adsorbate and adsorbent properties, can predict (1) pure-gas adsorption on activated carbons with an AAD of 9% (within three times the expected experimental uncertainties) and (2) binary and ternary gas adsorption within three times the experimental uncertainties, on average.