Modeling and parameter estimation for a fixed-bed adsorption process for CO2 capture using zeolite 13X
Highlights
► Accurate numerical model for an adsorption process for CO2 capture using zeolite 13X. ► A new mass transfer rate model and associated parameter estimation techniques. ► Numerical technique to efficiently integrate stiff PDEs. ► The proposed model was validated through experiments.
Introduction
Pressure–temperature-swing adsorption (PTSA) is a potentially viable technology for CO2 capture from large CO2 sources [1], [2]. The operation of a PTSA process involves a number of complicated steps, and numerical studies can play a crucial role in finding new operating conditions that improve the feasibility of the process [3], [4]. To this end, an accurate numerical model that replaces or minimizes experimental studies should be available.
The numerical modeling and analysis of adsorption processes has a long history and a large body of results is available [5], [6], [7]. Recently, numerical studies focusing on CO2 capture have also been presented by many research groups. Park et al. [1] performed economic assessment of a one-stage pressure-swing adsorption (PSA) process for recovering CO2 from flue gas using a numerical model. Ko et al. [4] and Choi et al. [8] studied the optimization of PSA operation using a process model. Chang et al. [9] researched a robust numerical simulation strategy for the PSA process, and Chue et al. [10] conducted a comparison study using zeolite 13X and activated carbon for the recovery of high-purity CO2 through PSA cycle simulations. In most such studies, standard adsorption process models have been employed with typical parameter values. For example, the LDF (linear driving force) equation has been adopted, simply for convenience, as the mass transfer rate model in most adsorber simulation studies for CO2 capture. Similarly, the Ergun equation has been used as a universal rule to describe the pressure drop in an adsorption bed in which strong pore diffusion occurs along with bulk flow. The evidence from this study, however, suggests that an improved mass transfer rate expression other than the LDF equation is necessary for rigorous simulation of an adsorption unit for CO2/N2 separation using zeolite 13X, and the porosity value in the Ergun equation may differ when the bed is packed with a porous material. The numerical model should be accurate if the goal is to analyze or optimize a specific, practical PTSA process.
On the basis of the above considerations, the objective of this study was to provide a comprehensive procedure for developing an accurately tuned numerical model of a fixed-bed adsorption process for CO2 capture using zeolite 13X through parameter estimation. In this method, the coefficients of the Langmuir isotherm equation, the bed porosity, the average particle size, the heat transfer coefficients, and the mass transfer rate coefficients are determined using experimental data from a series of separately designed experiments. Special attention was paid to the mass transfer rate expression, and an empirical model was proposed by combining the driving forces of the LDF and QDF (quadratic driving force) models. To estimate the coefficients associated with the proposed model, we measured the transient responses of the CO2 mole fraction, gas velocity at the bed outlet, and bed temperatures to random binary changes in the feed concentration. During the mass transfer rate estimation, we found that the porosity estimate from a preliminary experiment should be revised to account for the interferences in bulk flow due to the effects of adsorption and desorption. In addition, heat transfer coefficients distributed along the axial direction were introduced to accommodate the effects due to the geometry of the adsorption bed in a simplified dynamic model of wall temperature. To ensure a numerically stable and fast calculation, the so-called gradient-directed adaptive predictive collocation was adopted, in combination with a cubic spline interpolation function [11] and far-side boundary conditions [12].The performance of the adsorption bed model and the proposed mass transfer rate equation were experimentally validated.
Section snippets
Mathematical model of an adsorption bed
A non-isothermal dynamic model of an adsorption bed is considered in this study. Major assumptions in the model include the following:
- (i)
The radial concentration and temperature distributions are negligible.
- (ii)
The ideal gas law holds in the bulk gas phase.
- (iii)
Thermal equilibrium between the adsorbent and bulk gas is assumed.
- (iv)
Thermal conduction inside the column wall along the axial direction is negligible.
The mass balance for component i, where i = CO2, N2, in the bulk phase is given by
Experimental fixed-bed adsorption system
A schematic diagram of the fixed-bed adsorption experimental apparatus is shown in Fig. 1. The adsorption column is made of SUS316 with a height of 90 cm and an inner diameter of 2.54 cm; the middle 70 cm is packed with zeolite 13X (Z10-02NDmanufactured by Zeochem Co., Switzerland, spherical beads with dp = 0.16–0.26 cm). The remaining sections at each end of the column are filled with glass mesh to ensure uniform gas distribution and also to prevent the carryover of adsorbent particles. An electric
Sensitivity of wave fronts to parameter changes
The most important information in PTSA dynamics is the time-dependent shape and position of the concentration and temperature wave fronts. Among the various parameters, the mass transfer rate coefficients and the bed porosity may have the most significant effects on the wave front. The bed porosity defines the adsorbed amount in a unit bed volume and thus determines the speed of the wave front, whereas the mass transfer rate has a role similar to the concentration dispersion [5] and determines
Parameter estimation
The mathematical model can be upgraded to a process simulator through model tuning, which is normally performed by estimating key parameters using experimental data. In this study, isotherm parameters, particle size (as a single value), bed porosity, heat transfer coefficients, and mass transfer rate coefficients were estimated through a series of experiments, and the resulting tuned model was appraised using validation data.
The measured data from each experiment were pretreated with outlier
Adsorption isotherms
The equilibrium adsorption data for CO2 and N2 on zeolite 13X at 298, 323, and 373 K over the pressure range of 4–120 kPa were provided by the adsorbent manufacturer [26]. The data were fit to Langmuir isotherms and the parameter values were obtained as shown in Table 2. Fig. 5 shows the pure component equilibrium data and the corresponding simulated values according to the estimated parameters. It is evident that the CO2 and N2 isotherms are of the favorable type (concave downward), and CO2 is
Conclusions
Developing economically feasible process for capturing CO2 capture from large CO2 sources is a competitive research area worldwide, and PTSA is a potentially viable option. Although a significant portion of the studies have been devoted to developing new adsorbents, the discovery of new operating modes and optimum operating conditions is indispensable and equally important. Such process studies are normally conducted by experiment, but they can be greatly facilitated by an accurate and reliable
Acknowledgments
This work was supported by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea Government Ministry of Knowledge Economy (No. 20094010100160). K. S. Lee would like to acknowledge the financial support from NRF grant funded by the MEST through Mid-career Researcher Program (No. 20110000243). W. Won would like to appreciate Prof. Suh in the Department of Chemical Engineering at Hongik University, Seoul, Korea for his
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