Predicting CH4 adsorption capacity of microporous carbon using N2 isotherm and a new analytical model (1998)

A new analytical pore size distribution (PSD) model was developed to predict CHI adsorption (storage) capacity of microporous adsorbent carbon. The model is based on a 3-D adsorption isotherm equation, derived from statistical mechanical principles. Least squares error minimization is used to solve the PSD without any pre-assumed distribution function. In comparison with several well-accepted analytical methods from the literature, this 3-D model offers relatively realistic PSD description for select reference materials, including activated carbon fibers. N2 and CH4 adsorption data were correlated using the 3-D model for commercial carbons BPL and AX-21. Predicted C h adsorption isotherms, based on N2 adsorption at 77 K, were in reasonable agreement with the experimental CH4 isotherms. Modeling results indicate that not all the pores contribute the same percentage VmNs for CH, storage due to different adsorbed CH4 densities. Pores near 8-9 A shows higher VmNs on the equivalent volume basis than does larger pores. INTRODUCTION Activated carbon usually has a heterogeneous pore structure due to the structural complexity and randomness.' The distribution of pore sizes is a critical parameter for characterizing the adsorbent, when the adsorption potential is a dominant factor. Adsorption density is strongly dependent on the adsorbent's pore size (w). For instance, adsorption is enhanced in micropores (w 500 A) volume and maximum micropore volume. In particular, w for micropores should be near 8 A; the optimal pore size for CH4 adsorption.2 In this study w is defined as the distance between the edges of the carbon atoms in opposite pore walls. The pores are modeled as slits consisting of two infinite graphite planes. A number of PSD models have been developed on the basis of N2 adsorption at 77 K. Although the models provide great insights, there is apparent lack of consistency in the modeled PSD results' due to their different theoretical foundations and assumptions. Well-accepted PSD characterization methods include MP; DRS? JC,6 HK' and, more recently, SNAPss9 and DFT. SNAP is one of the latest PSD methods based on numerical results from Mean-Field Density Functional Theory (MFT).8,9 SNAP uses a pre-assumed log normal distribution function to model NZ adsorption at 77 K. DFT (Micromeritics) is one of the latest PSD methods based on Non-local MFT. DFT employs a Regularization technique to solve the generalized adsorption isotherm (GAI)8' I ' which results in a discrete PSD. Another version of DFT (Quantachrome) is based on Local MFT, which neglects the adsorbate-adsorbate interactions. The objective of this study is to model and correlate N2 and CH4 adsorption on microporous carbon through an analytical approach. A PSD model is developed on the basis of a 3-D isotherm equation without pre-assumed distribution functions. Prediction of CH4 adsorption isotherm is canied out by correlating the N2 and CH4 adsorption for select adsorbents. , MODEL DESCRIPTION Taking an approach similar to Chen and Yan 's 2 D adsorption isotherm equation,I2 a 3-D adsolption isotherm equation w i s develoDed. 73 for a given pore size and geometxy.(slits), with a mean force field 0. The classical DubininStoeckli (DS) inverse relati~nship, '~ is used for its simplicity to evaluate the mean force field as a function of pore size. p and p' are volume number densities of the gas and adsorbed phases,