Kinetically Limited Linear Driving Force Model for Diffusion-Based Adsorptive Separations

A new kinetically limited linear driving force (KLLDF) model, based on a modified extended Langmuir (EL) isotherm, was developed. This KLLDF model augments the equilibrium driving force in the LDF model in such a way that the equilibrium loading of each component in the LDF model depends on the actual, kinetically limited loading of the other components in a gas mixture, not their partial pressures. In contrast, the LDF model assumes that the presence of a slower diffusing adsorbate in a gas mixture affects the equilibrium of a faster diffusing adsorbate in a pore structure via its gas phase partial pressure even if this slower diffusing component has hardly entered the pore structure. This potentially erroneous assumption of the LDF model for severely diffusion limited separations is corrected with the new KLLDF model. The KLLDF driving force transitions continuously to the LDF driving force as the loading of the slower diffusing species increases inside the pore structure and is equivalent to the LDF driving force when the system is in equilibrium, leading to the same EL isotherm predictions. It is therefore just as applicable as the LDF model. The KLLDF model correlates well with binary gas mixture uptake experimental data in the literature for CO2-CH4 and O2-N2 on Takeda and Bergbau–Forschung carbon molecular sieves and for N2-CH4 on titanium silicate Ba-ETS-4. This includes predicting the intrinsic roll-up feature of the faster diffusing species even better than a more complicated barrier resistance model. The traditional LDF model failed to predict the behavior of the binary experimental data in the literature. With the KLLDF model exhibiting the smallest residual sum of the square errors (RSSEs), its validity and usefulness were established for extracting mass transfer parameters from diffusion limited adsorbate–adsorbent systems. Also, because this new KLLDF model requires just one fitting parameter for each component in the gas mixture, i.e., the mass transfer coefficient just like in the traditional LDF model, it should be very useful in an adsorption process simulator.