Recent studies have developed various adsorbents for $CO_2$ capture from flue gas. For simulation of adsorption process using a new adsorbent, the mathematical modeling has to consider the properties of the adsorbent. This study proposed the mathematical model including pore diffusion mass transfer rate model for simulation of PSA process. Activated carbon and zeolite 13X are used as an adsorbent for the experiment. The breakthrough experiments were conducted using a fixed-bed at two initial concentrations $(CO_2 : 40sccm/N_2 : 160sccm and CO_2 : 40sccm/N_2 : 80sccm)$, three pressures (1.5, 3 and 5 bars) and three temperatures (303.15, 323.15 and 343.15K). We found that the results of dynamic simulation were determined by the sub models of mass and energy balances such as estimation models for equilibrium gas uptake, mass transfer coefficients and heat transfer coefficients. The sub models were developed by comparing simulation results with experimental data as follows. 1) For estimation of equilibrium gas uptake, the Langmuir-Freundlich model was selected as the best model during several isotherm model. 2) A model for predicting the mass transfer coefficient is derived from the Glueckauf approximation equation which calculates the mass transfer coefficient when the adsorption rate is proportional to the linear driving force. In the adsorption process, the mass transfer rate is assumed to be determined by diffusion in the pores. The tortuosity, which is the difference between the gas movement inside and outside the adsorbent, and the Nussen diffusivity, which is influenced by the pore size, are reflected in the model. As a result, the predictive model of mass transfer coefficient is influenced by the structural properties of adsorbents such as particle size, pore diameter, porosity and tortuosity as well as the physical properties of the adsorbent such as equilibrium adsorption amount and heat capacity. 3) Kunii and Levenspiel and Bennett and Myer proposed the estimation model for inner and outer heat transfer coefficients, respectively. The methods were found in good performance for heat transfer coefficient estimation through comparing between the calculated and measured temperature profile. Many previous studies used a constant mass transfer coefficient but the variable mass transfer coefficient model can reflect the change of operating conditions such as $CO_2$ concentration and pressure, is proposed in this study. As a result of the adsorption experiment after complete desorption, it was confirmed that the mass transfer coefficient changes with the change of the carbon dioxide composition over time. Next, adsorption rate and adsorption amount were measured by partial desorption after desorption pressure (0.05, 0.1 and 0.2 bar) was changed. The simulation results using the constant mass transfer coefficient were significantly different from the experimental results, while the new mass transfer coefficient model accurately simulated the carbon dioxide breakthrough curve results such as adsorption amount and adsorption rate.
The PSA process consists of several steps including high pressure adsorption, low pressure desorption. The PSA process, which aims to separate carbon dioxide from the post-combustion gas, requires that the process be designed to maximize $CO_2$ recovery because the carbon dioxide content of the combustion gas is low. For this purpose, the PSA design of Reynolds was adopted as the basic model, which consists of pressure rise with $N_2$ -rich gas, high pressure adsorption, purification through light reflux, low pressure desorption, and heavy reflux purge.
The PSA process was simulated by varying the amount of low-molecular-weight reflux (0 to 35% of the flue gas flow rate), the individual step size (500, 1000 and 1500 sec) and the desorption pressure (0.1 and 0.2 bar).
When the constant mass transfer coefficient and the variable mass transfer model are applied, there is a difference in the adsorption amount or the desorption amount in each step. The operating conditions such as carbon dioxide composition and pressure are very different in each step, and therefore the magnitude of the relationship between the two mass transfer coefficients is also different for each step. As a result, the variable mass transfer coefficient model, which reflects the adsorption and desorption experiment results with varying pressure and carbon dioxide composition, proves to be a reliable model.
The PSA performance changes for the operating conditions were analyzed in terms of mass transfer rate. First, as the light reflux rate is increased, the PSA performance is improved and then decreased. That is, there is an optimum value of the light reflux rate. When the desorption pressure decreased, the optimum value also decreased. Next, as the time of the unit process becomes shorter, the $CO_2$ recovery increases but the purity decreases. However, when the desorption pressure is lowered to 0.1 bar, the mass transfer rate becomes a limiting condition for determining the performance of the process. Therefore, even if the step size is short, the increase of the $CO_2$ recovery is very small. If the order of the individual processes is maintained and the number of connected beds is varied, there is no significant performance difference between the different PSA designs when the desorption pressure is 0.2 bar. However, when the desorption pressure is 0.1 bar, the 4-bed 8-step design is expected to have better performance than other designs.