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Preprint, 11th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems June 6-8, 2016. NTNU, Trondheim, Norway New Performance Indicators for Evaluation of Adsorbents for CO2 Capture with PSA processes Seongbin Ga*, Hong Jang*, Jay H. Lee* *Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea (e-mail: jayhlee@ kaist.ac.kr). Abstract: Pressure swing adsorption (PSA) process is one of the candidate processes for CO2 capture. The interest has led to the development of various adsorbents such as modified zeolite materials and metalorganic frameworks (MOFs). Performance of the developed adsorbents is evaluated through lab-scale methods based on simple measures like working capacity and selectivity. However, these performance indices are not entirely reflective of the performance in a PSA process. In this work, we propose new performance indices that are better reflective of actual process-level performance: efficiency and purity. Both are derived for an ideal PSA process, which means they serve as the limits of the best achievable performance of a PSA process with target adsorbents. For simple calculation and quick evaluation, the performance indices are derived as explicit analytical expressions. Case study involving the evaluation of zeolite 13X, activated carbon and Cu-BTC is presented to show the use of the new performance indicators, and the results are compared with rigorous simulation results. Keywords: Performance evaluation, Pressure swing adsorption, CO2 capture based on rigorous first-principle models may be needed. The simulation requires deep understandings in the underlying numerical methods for solving the differential equations, which in this case include heat, mass and momentum balances. Usual materials scientists do not have this background needed to carry out process simulation-based evaluations of their adsorbents. Dynamic simulation of the PSA process becomes further complicated due to the cyclic steady state (CSS) resulting from the periodic switching of the columns. Besides, there are many process-level parameters to decide and optimize. Thus, even with enough background to carry out the simulation, it may take too long to thoroughly evaluate a large number of candidate adsorbents. 1. INTRODUCTION CO2 capture has increasingly received attention from industry and academia due to the mounting concerns of climate change. Many efforts have been made to find a proper solution for this (Richardson et al., 2009). Pressure swing adsorption (PSA) process is one of leading candidates considered for CO2 capture because it has been widely used in various gas separation areas, especially in high purity gas production processes such as hydrogen separation. Due to this potential, many studies about the application of the PSA process to CO2 capture have been carried out (Sircar, Golden, & Rao, 1996; Zhao, Cui, Ma, & Li, 2007). Some of the studies have mainly focused on finding more efficient materials which have high capacity and selectivity for CO2. As a result of such efforts, a variety of materials are suggested as adsorbent candidates for CO2 capture, such as zeolite, activated carbons, and metal-organic frameworks. For the above-stated reasons, in this work, we present new performance indicators that will act as an intermediary between the laboratory-level evaluation and the process-level evaluation of adsorbents, especially for those adsorbents used in a PSA process with the aim of CO2 capture. Efficiency indicator and purity indicator are the measures we propose to use. They indicate the performance of an ideal PSA process with targeted adsorbents. The performance indicators are formulated such that simple and quick evaluation is feasible with the users simply putting certain parameter values that can be measured in the laboratory into explicit formulas. They do not require any other information or a priori knowledge about the process. Materials scientists who develop adsorbent materials tend to focus on the recipe of new adsorbents without considering the situation of practical application. After finding new adsorbents, the scientists evaluate their work by measuring physical properties such as selectivity (Goj, Sholl, Akten, & Kohen, 2002; Saha, Bao, Jia, & Deng, 2010). However, this evaluation method does not entirely reflect the performance of adsorbents when used in the PSA process. Because of this problem, many adsorbents that are reported to be great improvements often turn out not to improve the performance of the PSA process by much if at all. This indicates that evaluation methods of adsorbents reflecting the PSA process and its operation would be more valuable than the current evaluation method used by the material scientists. The rest of the article is organized as follows. Section 2 explains the existing performance indices used by adsorbent developers for evaluation of their adsorbents. In Section 3, the dynamic simulation of PSA processes is explained as it can provide a reference to other simpler evaluation methods. Section 4 provides the assumptions for the idealized PSA process which serves as the basis for new performance However, detailed process-level evaluation is timeconsuming and challenging. For this, full dynamic simulation Copyright © 2016 IFAC 651 IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway indicators, and explicit formulas for the new indicators are derived on the basis of the assumptions. Section 5 gives an evaluation example to show how the new indices can be used. Finally, some conclusion is drawn in the last section. component of the operating cost of a PSA system. Therefore, the working capacity is not able to show the economic efficiency of a corresponding PSA process. 4) 2. EXISTING PERFORMANCE INDICES In the materials engineering area, the main interest is the development of a new recipe for synthesizing new adsorbents with improved physical properties. Therefore, these studies tend to report representative physical properties as measures of the developed materials’ performance (Sircar, et al., 1996; Zhao, et al., 2007). Among the properties, isotherm curve is the most commonly reported. The points in the isotherm curve are obtained by measuring the number of adsorbed gas molecules at a given temperature with increasing pressure. The measured data can be fitted with various isotherm models such as the Langmuir isotherm model and Freundlich isotherm model. 3. OPERATION AND SIMULATION OF PSA PROCESS In order for the practical evaluation of a new adsorbent, the adsorbent should be evaluated with the operation data from a PSA process using the adsorbent, rather than the lab-scale data. However, there are too many options to consider in the operation of a PSA system. Based on the isotherm curve, two performance indices for the adsorbent are commonly reported: working capacity and selectivity. Working capacity is the difference in the amounts of adsorbed gas molecules at high pressure and at low pressure. The two pressures are designated by some prior knowledge about the pressure range of the intended PSA operation. Selectivity is also defined on the basis of the isotherm curve but needs multiple isotherm curves with respect to multiple gas components. At some chosen pressure, the ratio of the amount of one component adsorbed that of the other components is defined as selectivity. In Fig. 1, for example, the working capacity can be expressed as the difference between A and B, and the selectivity of CO2 over N2 is proportional to the ratio of A to C. With the two performance indices, the materials scientists report how much they have improved the adsorbents. Fig. 1. Isotherm curves for two gas components However, the working capacity and selectivity do not reflect the performance of adsorbents when they are applied to the actual PSA process. The reasons for that are listed below. 1) Each adsorbent has a different optimal operating pressure range due to the differences in the physical properties. 2) Operating pressure is the overall pressure of the mixed gas, but the isotherm data are based on partial pressures of the components. 3) Selectivity only considers the adsorption phenomena, even though the swing of the pressure involves both adsorption and desorption of gas components. Above all, theoretical and empirical knowledge about the PSA process operation is required. In the operation, there is a "step", which is one part of an operation cycle. As the operation switches from one step to another, operating condition needs to be changed. The operating condition is changed mainly by manipulating the valves connected to the PSA column. Several steps comprise one cycle and the cycle is repeated until the end of operation. Various steps can be roughly classified into two types: adsorption(saturation) step and desorption(desaturation) step. During an adsorption step, the pressure of an adsorption column increases because gas is injected into the column. This drives more gas molecules to be adsorbed on the adsorbents packed in the column. On the other hand, during the desorption step, the pressure goes down, and the decreased pressure causes the gas molecules to detach from the surface of the adsorbents. This desorption step regenerates the adsorbents to be used in the next cycle again, but some amount of gas remain on the surface of the regenerated adsorbents. For a practical evaluation of adsorbents in connection to the PSA process, a rigorous simulation of the PSA operation is one option. In the area of systems engineering, there have been numerous studies on the simulation of a PSA system. Some studies suggested ways to choose the model parameters to be consistent with experimental data, and also ways to obtain optimal design and operation of a PSA process to maximize the product purity or recovery (Ko, Siriwardane, & Biegler, 2005; Kvamsdal & Hertzberg, 1997). Other studies focused on the numerical methods to shorten the computation time because the cyclic steady state (CSS) in the simulation causes high computation time (Biegler, Jiang, & Fox, 2005). Although several innovative methods have been suggested to reduce the computational cost significantly, most commercial simulators still rely on the successive substitution method, which accompanies high computation time. In this work, rigorous dynamic simulation of a PSA process for CO2 capture is carried out only as a reference. The model is constructed based on a previous work (Won & Lee, 2011). Details of the parameters and equations including mass, energy and momentum balance with constitutive equations can be found in (Won & Lee, 2011). To solve the system equations which include partial differential equations (PDEs), the cubic spline collocation method is used to convert the PDEs into the form of ordinary differential equations (ODEs). The converted equations are Working capacity does not consider the energy consumed for the pressure swing, which is the main 652 IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway solved by using ode15s solver, which is available in MATLAB. The boundary condition for the PDEs switches from step to step, and the sequence of the boundary conditions is repeated in a cyclic way. The CSS of the process is also obtained by the successive substitution method. and operating condition for each adsorbent, the comparison of different adsorbents becomes meaningful. Moreover, the above assumptions decrease the number of required parameters to evaluate adsorbents. For the evaluation, there is limited information about the process operation at the materials development stage. Because the focus of the adsorbent development is the properties of adsorbents, other physical parameters related with the operation are usually not measured, although many parameters are required to develop a model of a PSA process such as the mass and heat transfer coefficients, void fraction, conductivity, heat capacity, particle diameter. However, the idealization process ignores the non-ideal phenomena causing the loss of performance so that these parameters are no longer required. 4. NEW PERFORMANCE INDICATORS 4.1 Idealization of a PSA process for the evaluation The issues discussed in the previous section act as obstacles in the use of the simulation as a practical evaluation of adsorbents in a PSA system. To reduce the complexity of the evaluation without losing the practical considerations completely, we idealize the PSA process. The list of assumptions for the idealized PSA process is as below. 1) The cycle of a PSA process consists of an ideal adsorption (saturation) step and an ideal desorption (desaturation) step. 2) During the ideal adsorption step, the packed column contains two regions: a saturated region and an unsaturated region. The adsorbents in the saturated region are in equilibrium with the flue gas, while those in the unsaturated region have the same loading as in the ideal desorption step. 3) During the ideal desorption step, the produced gas is in equilibrium with the adsorbents in the column. 4) The adsorption phenomena in the system follow the extended Langmuir isotherm. 5) Efficiency loss and purity loss due to dispersion and bed void are ignored. 6) The process is optimized to make the amount of injected feed gas equal to the full capacity of adsorbents so that adsorbents packed in the PSA column are fully used. 7) The pressure of a PSA column switches as a step change. 8) The spatial distribution of pressure in the PSA column is uniform. 9) The PSA is operated isothermally. Furthermore, the idealization simplifies the calculation. As mentioned above, the test of adsorbent using the simulation is highly complex and takes a long time. A series of PDEs should be solved with boundary conditions varying in a cyclic way. To find the best design and operating condition, optimization problem should be solved with various decision variables composed of design parameters and operating condition variables. However, the idealized process ignores the diverse factors causing the process to be less efficient. Owing to this, simple algebraic calculations instead of solutions of the complicated PDEs are needed. Based on the above assumptions, new performance indicators for the evaluation of adsorbents are suggested in the following two sub-sections. The first indicator is efficiency, and the second one is purity. Both are defined based on the above assumptions so that they represent the best achievable performance of an adsorbent in an ideal PSA process. Efficiency indicator indicates the efficiency of the ideal process, and purity indicator indicates the purity of CO2 in the gas produced from the ideal process. Such indicators provide quantitative measures for a lab-scale evaluation of adsorbents with consideration given to their end use in the PSA process. 4.2 Efficiency In order to consider how efficient the process is, we have to first think of what the objective of this process is and what the cost for the objective is. In the PSA process for CO2 capture, the objective is to separate CO2 molecules mixed in the flue gas, while energy is the cost to be minimized. Efficiency can thus be defined by the ratio of the amount of captured CO2 to the amount of consumed energy. The conceptual equation of efficiency is (1). 10) The pressure at the desorption step is 1 bar. 11) An ideal compressor is used to increase the gas pressure and the energy is solely consumed by the compressor. These idealized assumptions make the PSA process to provide the limit of achievable performance for each adsorbent. This is an important aspect because this ideal PSA process gives a fair comparison between adsorbents having different optimal designs and operating conditions. When two adsorbents are compared by rigorous simulations, for instance, testing with the same design and operating condition biases the evaluation one way or the other. One operating condition may be better for one adsorbent, another condition gives for another adsorbent. Therefore, the best performance with the best design and operating condition for each adsorbent should be compared for a fair comparison. Because the above assumptions consider the optimal design h= Dq ( Phigh , x) E ( Phigh ) (1) h , Dq, and E indicate efficiency, the amount of captured CO2 and energy consumed by the process, respectively. From the idealization assumptions, the gas phase and the solid phase are in equilibrium at the end of the adsorption step and desorption step, and the equilibrium is assumed to follow the 653 IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway extended Langmuir isotherm model. This leads the following equations. Namely, the efficiency is not dependent on the quantitative mass or volume of the process. Dq ( Phigh , x ) = ( q1 ( Phigh , y ) - q1 ( Plow , x ))(1 - e ) r sV (2) 4.3 Purity zP q1 ( P, z ) = qm ,1b1 2 . The purity of the product is one of the most important considerations. For the same separation system, efficiency varies with target purity. Furthermore, purity can provide a basis for quick screening of adsorbent candidates when a specific target value of purity should be met. (3) (1 + å bi pi ) j =1 In (3), z can be the CO2 mole fraction of the inlet flow or produced gas, indicating that the loading of CO2 is a function of pressure and mole fraction. Thus, q1 ( Phigh , y ) and q1 ( Plow , x ) Purity of the ideal PSA process can be defined as the purity of CO2 in the purge gas as below: correspond to the amount of adsorbed CO2 during the adsorption step and during the desorption step and the difference between the two means the amount of captured CO2, as expressed in (2). Thus, variables y and x represent the CO2 mole fractions of the feed and the product gas (purge product), respectively. Partial pressure of a gas component (pi) should be used for the extended Langmuir isotherm model, and this also requires the mole fractions of CO2 during the adsorption and desorption steps. qm,i and bi represent the Langmuir isotherm parameters, where subscript i indicates gas components including CO2 and N2. pi , , and V are the partial pressure of component i, bed porosity, solid density and overall volume of a PSA column, respectively. Desorption pressure is assumed to be 1 bar. On the other hand, the amount of consumed energy can be calculated by using the assumption about the ideal compressor. The work for an ideal compressor is calculated by the following equation. g -1 é ù æ Phigh ö g g ê ún E ( Phigh ) = RT ç 1 ÷ ê ú inject g -1 Plow ø è úû ëê x= Dq1 ( P, x) Dq1 ( P, x) + Dq2 ( P, x) x is purity, and Dq1 , Dq2 are the amount of captured CO2 and N2, which are functions of P and x. From the assumption of the loss from the void of the packed bed, the amount of each captured component is equal to the difference in the isotherm values of each component at high pressure and at low pressure. Dq1 = qm,1b1 ( Dq2 = qm,2b2 yPhigh 1+ b1 yPhigh + b2 (1- y ) Phigh ( (4) q temperature, and the amount of injected feed gas. But the assumption about full capacity and the assumption about the loss from void lead the following relationship. é æ Phigh ö RT êç g -1 êè Plow ÷ø êë g ù - 1ú ú úû 1 low + b2 (1- x ) Plow b xP (10) b (1- x ) P m ,2 2 low qlow,2 = 1+b1xP low + b2 (1- x ) Plow (11) b( z ) = (b1 - b2 ) z + b2 (12) With the substitution, the rearrangement is expressed as, (5) q xqm,2 éêb2 (1 - y ) Phigh - qlow,2 {1 + b( y ) Phigh }ùú m ,2 ë û q = (1 - x)qm,1 éêb1 yPhigh - qlow,1 {1 + b( y ) Phigh }ùú m ,1 ë û In (1), the substitution using (2) and (4) leads to the final form of the efficiency indicator. With the relationship of (5), the final form becomes simpler as below: g -1 g (1- x ) Plow - 1+b xP ) (8) ) (9) qlow,1 = 1+b1xPlowm ,1+b1 2 (1low- x ) Plow ninject are the isentropic expansion factor, gas constant, feed y low + b2 (1- x ) Plow 1 Equations (7), (8), and (9) are rearranged in linear form with respect to the adsorption pressure (Phigh) so that the pressure can be expressed as a function of x . For easy rearrangement, the following substitutions are carried out: q h= (1- y ) Phigh 1+ b1 yPhigh + b2 (1- y ) Phigh xPlow - 1+b xP The above equation should include the partial pressure of each component, so the mole fraction of each component is used. The above equation is from the thermodynamics textbook written by (Abbott, Smith, & Van Ness, 2001). g , R, T , and y × ninject = Dq ( Phigh , x) (7) (13) [qm,2 xb2 (1 - y ) - qlow,2 xb( y )]Phigh (6) - qlow,2 x (14) = [qm,1 (1 - x)b1 y - qlow,1 (1 - x)b( y )]Phigh - qlow,1 (1 - x) This final equation shows that the efficiency of the ideal PSA process is intrinsic property rather than extrinsic property. Phigh = q 654 qlow ,1 (1- x ) - qlow ,2 x m ,1b1 (1- x ) y - qm ,2 b2 x (1- x ) - qlow ,1 (1- x ) b ( y ) + qlow ,2 b ( y ) (15) IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway Phigh ( x) = where, Plow (1+ b ( x ) Plow ) Rq -b ( y ) Plow Rq = Suppose there are three adsorbent candidates being considered for CO2 capture with a PSA process. The CO2 mole fraction of the feed gas is 0.15 and the target purity is 0.3. Measured Langmuir isotherm parameters are listed in Table 1. , qm ,1b1 (1- x ) y - qm ,2b2 x (1- y ) x (1- x )[1m ,1 ]b1 - qm ,2b2 (16) Equation (16) is the final form of the equation. This gives the solution in an explicit form. This equation can be evaluated just with the parameters typically measured by adsorbent developers. The equation shows the relationship between purity and the operating pressure of an ideal PSA process. Table 1. Adsorbent candidates Adsorbent Zeolite 13X Activated carbon Cu-BTC Because the purity value monotonically increases and asymptotically converges as the pressure goes to infinity. Using this relationship, the upper bound of purity also can be derived. In order to make the pressure go to infinity, the denominator should be zero. This gives the following relationship: q m ,1 ( mol / kg ) q m ,2 ( mol / kg ) -1 -1 b1 ( bar ) b2 ( bar ) 4.83012 1.0691 10.576 0.89423 2.5 1.469 1.9090 0.16214 14.3 6.343 0.5544 0.04087 With some rearrangement of the equation, the equation can be express as a quadratic equation about x ; The above table is the information that is usually provided by the adsorbent developers. Only with this, the adsorbent candidates should be evaluated and this can be done using the new performance indicators. First, the target purity of this problem should be considered. Using (19), the upper bound of the achievable purity can be calculated and compared with the results from the rigorous dynamic simulation of a PSA process in Table 2. Ax 2 + Bx + C = 0 Table 2. Upper bound of purity (1 + b( x) Plow ) Rq - b( y ) Plow = 0 (17) where, Candidates A = (qm,1 - qm,2 )b1b2 Plow B = qm,1 ( b1 - b1 y ) + qm,2 ( b 2 - b2 (1 - y )) ) b1 = b1 (b1 - b2 ) + b1 b( y ) - b1b2 y Plow ( ) b 2 = - b2 2 + b2 b( y ) Plow The above equation can be solved easily by using the quadratic formula. xupper - B - B 2 - 4 AC = 2A Product purity from the rigorous simulation 0.1992 Zeolite 0.296 13X Activated 0.556 0.2601 carbon Cu-BTC 0.76 0.333 From the results of the upper bound calculation, the purity upper bound of zeolite 13X is smaller than our target purity, 0.3. This indicates that zeolite 13X cannot achieve the target purity even with the ideal PSA process. With this fact, zeolite 13X can be screened out. (18) C = (1 + b2 Plow )qm,1b1 y ( xupper Because the purity upper bound values represent the theoretically achievable maxima with the ideal PSA process, they are larger than the results from the rigorous simulation, where a variety of non-ideal factors are considered. Although the indicator values are not same as the rigorous simulation results, the trends are the same. Cu-BTC gives the highest purity, activated carbon the next, and zeolite 13X gives the lowest purity. (19) This provides an upper bound of purity, which is theoretically achievable in the ideal case; a given adsorbent cannot exceed the above value. 5. USE OF THE PERFORMANCE INDICATORS For the same adsorbents, selectivity and working capacity which have been widely used for the evaluation of adsorbents in the other studies(Liang, Marshall, & Chaffee, 2009; McEwen, Hayman, & Yazaydin, 2013) are calculated. The results are listed in Table 3. In this section, the use of the new performance indices is shown with an example problem. Results from the new performance indices are compared with the results from the rigorous dynamic simulation of a PSA process. The rigorous dynamic simulation takes the Skarstrom cycle composed of four steps: pressurization step, adsorption step, blowdown step, and purge step. The mass, energy and momentum balance equations and additional constitutive equations are solved with boundary conditions switching as step changes in a cyclic manner. The CSS solution is considered. The rigorous simulation considers various non-ideal aspects including dispersion, pressure drop, temperature effect, etc. These non-ideal aspects make the rigorous simulation closer to the real PSA process than the idealized PSA process. Table 3. Existing criteria of the adsorbent evaluation Candidates Selectivity Working capacity Zeolite 100~300 2.2mol/kg 13X Activated 20~26 0.95mol/kg carbon Cu-BTC 7~25 8.1mol/kg The above table shows that the evaluation method using selectivity and working capacity are not closely related to the 655 IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway performance of the PSA process obtained from the rigorous dynamic simulations. Note that Cu-BTC with the lowest selectivity value gives better purity in the simulation. However, a significant gap exists between values from the new performance indicators and rigorous simulations. The gap originates from the idealization assumptions. If the extent of the non-ideal property of a PSA process can be expressed in a simple way, modification factors may be included in the performance indices to predict the performance of a PSA process more accurately. This will make the use of the performance indicators more general. As a next step, by applying the target purity to (16), the pressure required can be obtained. Phigh (0.3) Actiated carbon = (20) Plow (1+ b ( x ) Plow ) Rq -b ( y ) Plow = 2.7187bar ACKNOWLEDGE The authors would like to acknowledge the financial support from the grant (G01160051) funded by Saudi AramcoKAIST CO2 management center. Phigh (0.3)Cu -BTC = Plow (1+ b ( x ) Plow ) Rq -b ( y ) Plow (21) = 2.219bar REFERENCES With above values, efficiency can be obtained by using (6). In the equation, isentropic expansion factor is set as 1.291. h ( Phigh , Activated carbon ) = Abbott, M. M., Smith, J. M., & Van Ness, H. C. (2001). Introduction to chemical engineering thermodynamics. McGraw-Hill. Biegler, L. T., Jiang, L., & Fox, V. G. (2005). Recent advances in simulation and optimal design of pressure swing adsorption systems. Separation & Purification Reviews, 33, 1-39. Goj, A., Sholl, D. S., Akten, E. D., & Kohen, D. (2002). Atomistic simulations of CO2 and N2 adsorption in silica zeolites: the impact of pore size and shape. The Journal of Physical Chemistry B, 106, 8367-8375. Ko, D., Siriwardane, R., & Biegler, L. T. (2005). Optimization of pressure swing adsorption and fractionated vacuum pressure swing adsorption processes for CO2 capture. Industrial & engineering chemistry research, 44, 8084-8094. Kvamsdal, H., & Hertzberg, T. (1997). Optimization of PSA systems—studies on cyclic steady state convergence. Computers & chemical engineering, 21, 819-832. Liang, Z., Marshall, M., & Chaffee, A. L. (2009). CO2 adsorption-based separation by metal organic framework (Cu-BTC) versus zeolite (13X). Energy & fuels, 23, 27852789. McEwen, J., Hayman, J.-D., & Yazaydin, A. O. (2013). A comparative study of CO 2, CH 4 and N 2 adsorption in ZIF8, zeolite-13X and BPL activated carbon. Chemical Physics, 412, 72-76. Richardson, K., Steffen, W., Schellnhuber, H. J., Alcamo, J., Barker, T., Kammen, D. M., Leemans, R., Liverman, D., Munasinghe, M., & Osman-Elasha, B. (2009). Climate change-global risks, challenges & decisions: synthesis report: Museum Tusculanum. Saha, D., Bao, Z., Jia, F., & Deng, S. (2010). Adsorption of CO2, CH4, N2O, and N2 on MOF-5, MOF-177, and zeolite 5A. Environmental science & technology, 44, 1820-1826. Sircar, S., Golden, T., & Rao, M. (1996). Activated carbon for gas separation and storage. Carbon, 34, 1-12. Won, W., & Lee, K. S. (2011). Adaptive predictive collocation with a cubic spline interpolation function for convection-dominant fixed-bed processes: Application to a fixed-bed adsorption process. Chemical Engineering Journal, 166, 240-248. Zhao, Z., Cui, X., Ma, J., & Li, R. (2007). Adsorption of carbon dioxide on alkali-modified zeolite 13X adsorbents. International Journal of Greenhouse Gas Control, 1, 355359. y g -1 é P æ high ö g RT êç ÷ g -1 êè Plow ø ë g ù - 1ú ú û (22) = 1.875 CO2 tonne / GJ h ( Phigh ,Cu - BTC ) = y éæ P ö high RT êç ÷ g -1 êëè Plow ø g g -1 g ù - 1ú úû (23) = 2.335 CO2 tonne / GJ In the simulation, the target purity was not achievable with activated carbon, and the efficiency of Cu-BTC was 0.481CO2 ton/GJ. 6. CONCLUSION The new performance indicators suggested in this work can be used for quick evaluation of newly developed adsorbents based on limited information about them. Still the new indicators consider the aspects that were ignored in the existing performance indices so that the users of the new indicators can obtain more practically relevant information from the same measurement. Furthermore, the idealization assumptions on which the new performance indicators are based enable the users to calculate the indicators without deeper understandings about process systems engineering tools and without the complicated and time-consuming computations. In the example tried, it took 579.534 seconds of CPU time to compute a single product purity value using the rigorous dynamic simulation, even with a reasonable initial guess (3405.560 sec with a poorer initial guess), whereas the presented formula took only 0.136 seconds for calculation. In addition, the indicators give the meaningful values taking account of the performance of the PSA process. Because the new indicators reflect the best achievable performance with an ideal PSA process, an adsorbent whose purity indicator does not reach the targeted value can be screened out before in-depth analysis. 656