vacuum swing adsorption model for rapid adsorbent screening for CO2 capture applications

International Journal of Greenhouse Gas Control 15 (2013) 16–31

Contents lists available at SciVerse ScienceDirect

International Journal of Greenhouse Gas Control journal homepage: www.elsevier.com/locate/ijggc

A new simplified pressure/vacuum swing adsorption model for rapid adsorbent screening for CO2 capture applications Brian Joseph Maring, Paul A. Webley ∗ Cooperative Research Centre for Greenhouse Gas Technologies (CO2CRC), Department of Chemical and Biomolecular Engineering, University of Melbourne, Parkville, VIC 3010, Australia

a r t i c l e

i n f o

Article history: Received 17 May 2012 Received in revised form 18 December 2012 Accepted 6 January 2013 Available online 27 February 2013 Keywords: Adsorbent screening methodology CO2 capture Vacuum swing adsorption Ideal adsorbent

a b s t r a c t A large number of promising adsorbent materials for CO2 capture are reported almost daily. Unfortunately, the assessment of an adsorbent in a process is far more challenging. Statements on expected performance are usually confined to visual inspection of isotherms or calculations of pure component selectivities. These are poor indicators of performance in an actual capture process. We present here a new simplified pressure/vacuum swing adsorption model which can be used to quickly screen adsorbents for use in CO2 capture applications. The model strikes a balance between full adsorption simulation (which requires detailed knowledge of PSA operation and is time consuming) and simple visual inspection of isotherms and calculations of selectivities (which is incorrect and misleading in many cases). Our model has been validated against analytical PSA models, full adsorption numerical simulations, and experiments. Using post-combustion VSA as an example, we use the model to compare several types of adsorbents (zeolite 13X, Mg-MOF-74, Activated Carbon, PEI/MCF chemisorbent). Our analysis shows that 13X remains the best adsorbent in VSA applications (for dry flue gas of 12% composition) even though Mg-MOF-74 shows considerably higher CO2 capacity. We have also conducted a sensitivity study to determine which properties are most important to improving performance and we estimate the limits of PSA performance. Adsorbent selectivity and thermal effects have a more significant effect on the specific power consumption than does CO2 adsorption capacity. The optimal heat of adsorption of CO2 for PSA application is between 35 and 45 kJ/mol regardless of N2 heat of adsorption. Furthermore, continual increase in surface area is not necessarily beneficial to overall performance, becoming more detrimental as the heat of adsorption of N2 increases. As an estimate of an upper limit of material performance, a hypothetical material with the same surface area as MOF-177, no N2 adsorption, and a CO2 heat of adsorption of 35 kJ yields a 68% increase in working capacity and an increase in purity from 78% to 94% when compared to 13X. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction Anthropogenic CO2 emissions are a great threat to the environment because of their contribution to the greenhouse effect and global warming. One of the leading strategies considered to reduce emissions is carbon capture and sequestration. Cyclic adsorption processes such as pressure swing adsorption (PSA) and vacuum swing adsorption (VSA) are one of several separation methods being investigated to remove CO2 from the other components in flue gas, natural gas, and in IGCC processes so that it can be compressed and stored underground in geologic formations (D’Alessandro et al., 2010; Gielen, 2004). PSA is a widely used industrial unit operation for separating gas mixtures where one or more gases are preferentially adsorbed at high pressure and then

∗ Corresponding author. Tel.: +61 3 90357873. E-mail address: [email protected] (P.A. Webley). 1750-5836/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijggc.2013.01.009

desorbed at a lower pressure. Applications include air separation, drying, and hydrogen purification (Ruthven, 1984). The most important design decision when developing a PSA cycle is the choice of adsorbent (Kumar, 1994; Ruthven et al., 1994). However, it is still unclear how adsorbent properties such as capacity, selectivity, and heat of adsorption correspond to process performance which is measured by purity, recovery, specific power requirement, and throughput. Hundreds of materials have been studied as potential CO2 adsorbents (Choi et al., 2009), but there is still no well established rubric, such as the Robeson plot for membranes, for comparison and assessment of adsorbents, and to guide further adsorbent development. Adsorbent selection is often left up to ad hoc approaches or detailed simulation and there is no consistent benchmark against which adsorbent developers can evaluate their materials. Novel adsorbents are typically first synthesized in very small amounts where adsorption isotherms, porosity, density, and surface area can be measured. However, a much larger amount (several

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

Nomenclature m, b, d Cp k m N or n P R Q T or T TPDc V W y

isotherm parameters adsorbent heat capacity (J/kg K) ratio of heat capacities mass of adsorbent (kg) number of moles (gmol/kg) pressure (bar) ideal gas constant (J/gmol K) isosteric heat (J/gmol) temperature (K) or temperature change (K) tons per day of contained CO2 . For example, a stream of 100 TPD with 90 wt% CO2 has 90 TPDc CO2 volume (m3 ) work (kJ/kg) mole fraction

Greek letters ε void fraction  bed density (kg/m3 )  isentropic efficiency Subscripts 0 value from previous iteration A, B component A or B ads adsorbed phase atm atmospheric comp location after compressor/blower, before heat exchanger feed feed conditions in, out conditions at inlet and outlet of compressor high H L low RP repressurization step moles in both adsorbed and gas phase total

hundred grams) is required to perform breakthrough and lab scale PSA experiments and therefore computational modeling plays a critical role in adsorbent evaluation. Detailed PSA modeling has been well studied (Todd et al., 2001; Webley and He, 2000a,b) but is computationally intensive, requiring the solution of a series of coupled stiff PDEs with cyclic boundary conditions. Some of the complexity can be reduced by making assumptions, such as linear pressure profiles with respect to time (Rege and Yang, 1997). This type of model has been used (Chue et al., 1995) to compare activated carbon and zeolite 13X for post-combustion CO2 capture over a range of operating conditions. Even though the computation times can be made reasonable using this type of model, there are still many operating parameters and it is not known a priori under which conditions a cycle should be operated. Optimizing a cycle for a range of adsorbents over a range of process operating conditions is a daunting task making these models unsuitable for quick adsorbent screening. There are also several analytical solutions for isothermal PSA with linear adsorption isotherms (Ebner and Ritter, 2002, 2004; Knaebel and Hill, 1985) but these equations are not particularly useful for screening, especially for CO2 capture where the isotherms are highly nonlinear and thermal effects are significant. Several simplified methods in the literature have been reported for adsorbent comparison and while these methods all have merit and have been used successfully in certain cases, none of them include all of the key features affecting PSA performance and therefore give misleading results under certain circumstances.

17

Adsorption capacity, which is the amount of gas adsorbed at the feed condition, is the most common measurement that material developers use to demonstrate the potential of new materials (Yazaydın et al., 2009). While a material must adsorb a significant amount of CO2 to be useful in a capture process, it is more important that it can be regenerated. To account for this, the concept of working capacity has been developed, which is the difference between the amount adsorbed at the adsorption and desorption pressures. Pure gas working capacity has been used to assess adsorbents for CO2 capture (Harlick and Tezel, 2004, 2005). While this can be a good indicator of performance, mixed gas working capacity is much different than for pure gases. Furthermore, because desorption is endothermic, the bed temperature decreases as the pressure decreases, shifting the adsorption isotherm and decreasing the working capacity. Because CO2 typically has a large heat of adsorption it is especially critical to consider thermal effects when analyzing CO2 capture. Fig. 1 demonstrates the adsorption capacity and working capacity for a pressure swing between a CO2 partial pressure of 0.15 bar (typical feed conditions) and 0.01 bar (typical conditions at the end of blow down). The starting temperature is 320 K and the final temperature is 300 K. It is clear that the actual working capacity obtained in practice (A = adiabatic working capacity) is lower than the apparent isothermal working capacity (A + B) and significantly lower than the absolute capacity (A + B + C). Selectivity is also very important in assessing an adsorbent and has been defined in several ways in the literature. The term (nA,ads /yA )(yB /nB,ads ), where yA and yB represent mole fractions of A and B in the feed gas and nA,ads and nB,ads their corresponding solid loadings, is analogous to relative volatility in a distillation column and is probably the most popular version of adsorbent selectivity used. Despite its popularity, it has little direct relevance to a PSA process because PSA is a transient process where the separation occurs between two distinct states (high pressure and low pressure) as compared to distillation which is steady state and the separation occurs at one distinct condition. Selectivity has also been defined as the ratio of adsorption capacities nA,ads /nB,ads (Krishna and van Baten, 2012) which is misleading because it also does not consider regeneration. A lumped parameter, the product of kinetic and equilibrium selectivities, has also been used to screen adsorbents for air separation (Jain et al., 2003). While these are both important characteristics, this term is ad hoc, equilibrium characteristics tend to be more important than kinetics for PSA, and kinetic data is typically not available for new materials. In general, screening by selectivity alone is misleading because good selectivity is not a sufficient condition for a good adsorbent. As will be demonstrated in Section 3.1, there are chemisorbents which only adsorb CO2 and therefore have infinite selectivity but do not yield the best performance because of poor working capacity. In order to balance capacity and selectivity, many researchers have used the product of working selectivity and working capacity also known as the adsorption figure of merit (AFM) for screening purposes (Ackley et al., 2000; Rege and Yang, 2001). While this term has been shown to strongly correspond to process performance, it is ad hoc and can result in misleading conclusions because it does not account for the work required to achieve a given separation. Breakthrough time has been used in order to screen MOFs for various CO2 capture applications (Krishna and Long, 2011). Although column breakthrough time is an important characteristic for process performance, regeneration is especially important for CO2 capture because the product is produced in the regeneration step. Adsorbents have also been screened based on a variety of metrics, including the simulation of a breakthrough experiment, selectivity and working capacity, without lumping them into a single parameter (Krishna and van Baten, 2012). While this strategy is useful, it is also important to determine how much each of these characteristics alone corresponds to process performance.

18

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

Fig. 1. Demonstration of capacity and working capacity for pressure swing on a typical adsorbent (assuming 20 K temperature swing during blow down).

Our aim in this study is to build on these existing methods and develop a screening methodology that is simple to implement, robust, and can directly relate adsorbent properties to PSA performance without much computational complexity. It is important in any simple model to capture the first order effects which are important in PSA behavior. These are the adsorbent working capacity for the product to be recovered, the selectivity between A and B, and the thermal effects accompanying the pressure swing. Other effects such as mass transfer and convective heat transfer will all influence the outcome but are regarded as second order. We also wanted to be able to screen adsorbents and obtain an approximation of the performance of these adsorbents without the need for cycle design. We confine our analysis here to equilibrium separations only which cover the vast majority of adsorption applications. While a single PSA simulation can be run on a desktop PC in a matter of seconds, the major advantage of our model is that it dramatically reduces the level of complexity of the simulation, especially in the number of process variables and removes the need for specifying cycle, steps times, etc. which are difficult for the non-PSA expert. Even if one simulation can be run quickly, comparing two adsorbents when there are dozens of process variables for a PSA cycle is an exhaustive and complex task.

In this study, we present a new, simple PSA model which contains only the essential features of the process and can be used to estimate performance data and predict trends. Our model can accommodate any adsorption isotherm equations, so long as they are continuous functions of partial pressure and temperature. Using this model, we demonstrate a methodology for screening adsorbents, using post-combustion CO2 capture VSA as an example, and also determine the optimal operating conditions and the adsorbent properties most important to process performance. This analysis is general to any pressure or vacuum (VSA) swing process even though the example used in the case study is VSA for CO2 capture. Other cyclic adsorption processes such as temperature swing adsorption (TSA) will require a different analysis and will be examined in a future work. 2. Model development, validation and application 2.1. PSA model development As shown in Fig. 2 the PSA model consists of three steps: blow down from an initial condition in which the bed is saturated with feed at PH to a final pressure of PL ; repressurization by feed from

Fig. 2. Simple model diagram of PSA process.

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

PL to PH ; and feed at PH until breakthrough. The equations presented are general to a binary mixture of gas species A and B where A is preferentially adsorbed over B and will be applied to the case of post-combustion CO2 capture by VSA. Typically CO2 will be adsorbed preferentially to other gases such as N2 , CH4 , and H2 . A brief description of the model is provided below with detailed derivations included in Appendix. The adsorbed phase is always at equilibrium with the gas phase and the mass balances in Eqs. (1) and (2) apply at all times in the cycle. nA,ads and nB,ads are isotherm equations which can be any continuous function of partial pressure and temperature, and V is the total void volume which requires knowledge of the voidage of the adsorbent. The total moles of A and B in the system at any time are calculated from: nA,total = nA,ads (PA , PB , T ) + nB,total

PyA V RT

PyB V = nB,ads (PA , PB , T ) + RT

(1) (2)

The temperature change in the bed can be calculated from the following simplified energy balance. mCp T = QA nA,ads + QB nB,ads

(3)

The bed is assumed to be adiabatic (which closely represents industrial practice) and the isosteric heats are calculated using the Clausius–Clapyron equation shown below.



∂ ln Pi ∂T



= ni,j

−Qi RT 2

(4)

The energy equation for the system is used to solve for the temperature changes during adsorption and desorption. Only the specific heat of the solid adsorbent is considered because it is much larger than the specific heat of the gas. The temperature changes during the pressure swing are therefore tracked and their effect on performance is included. The bed is arbitrarily sized by setting the mass of adsorbent at 1 kg and the corresponding bed volume is calculated using the void volume and the bed density. 2.1.1. Initial condition The feed is available at a specified temperature, pressure and composition and compressed adiabatically to the adsorption pressure, PH with an isentropic efficiency of 75%. The temperature of the gas increases as it is compressed. The gas is then passed through a heat exchanger where the temperature can be increased or decreased to the adsorption temperature. The initial bed condition is the bed saturated with feed after breakthrough at the adsorption temperature and pressure. These conditions are known a priori and therefore cyclic steady state can be achieved in just one cycle – this is an important feature of the model and greatly reduces computation time. The bed temperature after a breakthrough experiment is much higher than the starting bed temperature because of the heat of adsorption. Our model specifies this initial condition as the “end-of-feed” temperature. The bed temperature at the start of feed is much lower (corresponds to the end of repressurization). Using any other initial temperature in our model would increase the complexity needlessly. In addition, the performance of the PSA is much less sensitive to small changes in the absolute feed temperature than it is to the magnitude of the temperature swing during a cycle. We note that the actual detailed steady state temperature profiles generated in a multilayer, non-isothermal cyclic adsorption system are very complicated with a “cold spot” often developing after several hundred cycles (Li et al., 2008). It is not our aim in this model to capture these detailed profiles – rather, we aim to capture the essential features of an adiabatic temperature swing accompanying the pressure swing.

19

2.1.2. Blow down step In the blow down step, moles of gas are removed from the bed decreasing the bed pressure, and increasing the concentration of species A. In order to achieve desorption pressures less than one atmosphere, a vacuum pump is required. The instantaneous vacuum work is calculated using the isentropic compression equation (Eq. (5)) assuming a constant isentropic efficiency of 75%. Although the efficiency of an actual pump varies with the sorption pressure and flow rate, accounting for this in the calculation requires detailed knowledge of the pump that will be used. This is beyond the scope of this study and therefore the specific power calculations from this model should not be taken as precise estimates of process performance and should only be used to analyze trends. A variable efficiency can be added to the equations if the details of the pump are known. This equation is integrated over the duration of the blow down to determine the total vacuum work. 1 kRTin W=  k−1

 P

out

(k−1)/k

Pin



−1

(5)

The temperature change during desorption is calculated solving the energy equation and calculating the isosteric heat as the desorption proceeds (see Appendix for further details). 2.1.3. Repressurization by feed The repressurization by feed step is modeled as a “well-mixed” process. Feed is added to the bed in small steps until the desired pressure is reached. In reality, a complicated shock-front would appear in the bed (Knaebel and Hill, 1985), however, this well mixed assumption has been used effectively in the past and dramatically simplifies the analysis (Zhang and Webley, 2007). Feed is added to the bed in small increments until the pressure reaches the adsorption pressure. Heats of adsorption are calculated numerically after each step. The specific blower work for this step is calculated using the isentropic compression equations assuming an efficiency of 75% and a specific heat ratio of 1.4, total blower work is calculated by multiplying the moles of feed required for repressurization by the specific work. The gas temperature is increased in the compression stage (as shown in Eq. (6)), but can be increased or decreased afterwards using a heat exchanger as discussed earlier. Tcomp = Tfeed ×

 P (k−1)/k H Pfeed

(6)

2.1.4. Feed step After the repressurization step has been completed, the gas composition of A in the bed is lower than that of the feed, which is the required condition to produce a shock-wave during the feed step. To avoid calculating the concentration profile during the feed step, it is assumed that enough feed is provided for a complete breakthrough. A mass balance is performed to determine the amount of gas that enters and leaves the bed in order to reach the initial condition. An energy balance is guaranteed because the amounts of adsorbed components are the same at the beginning and end of the cycle and the total heat of adsorption and desorption are the same. Purity, recovery and working capacity are calculated from the mole balances while the specific blower work is calculated in the same manner as the feed step. Purity =

moles A product moles A product + moles B product

Recovery =

moles A product moles A feed + moles A repressurization

Working capacity = moles A product

(7) (8) (9)

The model was implemented in MATLAB and solves in less than 2 s to give expected performance data as a function of isotherm

20

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

Fig. 3. Comparison of simple PSA model with binary linear isotherm (BLI) analytic solutions.

parameters (A and B), adsorbent physical properties, feed conditions (T, P, and y) and composition, and process conditions (T and P). The model is an equilibrium one, i.e. there is no cycle time and therefore throughput results are expressed as per kg of adsorbent per cycle. The selection of an appropriate cycle time is clearly different for different adsorbents based on their kinetic performance and will directly affect the throughput. In our analysis and comparison, we assume equal cycle time for all adsorbents so that working capacity expressed on a unit mass of adsorbent is a proxy for throughput and therefore vessel size. 2.2. Model validation It is important to note that the cycle on which our model is based is a simple three step process so is not intended to provide quantitative agreement with more detailed cycles and models. Instead, our model is sufficiently complex to capture the essential features of the adsorbent which dominate its performance in a cyclic system and to provide a screening tool to assess the relative merits of different adsorbents. Therefore a moderate amount of discrepancy between this simple model and detailed simulation and/or experimental data is acceptable. Regardless of its simplicity, we show below that this simple model is capable of remarkably good agreement with more complex models and data. To gain confidence in the predictions of our model therefore and understand the limitations, we sought to test the simple model against analytic PSA solutions, detailed PSA computer simulations, and experimental data. We chose two semi-analytical PSA models (Chiang, 1996; Knaebel and Hill, 1985) for “analytical” validation of our model. These PSA models apply basic conservation of mass for a binary system (A and B) with linear adsorption isotherms to several different PSA cycles to predict purity and recovery. We tested our model with the same linear isotherms and isothermal conditions against their analytical solutions. Fig. 3 shows the effect of pressure ratio (feed pressure/blow down pressure) on recovery of the heavy component (CO2 in our case) for three different selective adsorbents. As seen in Fig. 3, there is reasonably good agreement in terms of CO2 purity between the analytical expressions and our simple model

particularly at higher pressure ratios, and the trends are correctly predicted with respect to selectivity. Both of the analytical models include a light purge step to achieve complete CO2 recovery and Chiang’s model includes a pressure equalization step, neither of which are included in our simple model explaining the discrepancy in purities at low pressure ratios. In spite of this difference, the match is acceptable and demonstrates the validity of the blow down calculation where the CO2 purity is determined. Our model predicts a lower purity than the analytical equations because our model does not have an axial concentration profile, nor light purge or pressure equalization steps. All three models converge to the same values at high pressure ratios because the purity at a complete blow down is determined by the initial bed loadings. Our model can also be used to calculate the specific work requirement which is essential for understanding the effect of the operating conditions. The specific work requirement for a postcombustion CO2 capture VSA from our model was compared to experimental data over a range of desorption pressures for 13X adsorbent (Chaffee et al., 2007). As seen in Fig. 4, our model predicts the same trend as in literature where the minimum specific work occurs at deep vacuum. Although the absolute values differ, a range of specific powers from 5 to 13 kW/TPDc (TPDc denotes) have been reported in literature (Zhang and Webley, 2007; Zhang et al., 2008b) and our model falls within this range at deep vacuum. Given the absence of more sophisticated “energy-saving” steps in our model (such as pressure equalization), it is reasonable that the specific power predicted by our model falls within the top end of this range. Finally, we compared our model to published results both from our group’s detailed numerical simulator MINSA (Todd et al., 2001) and several experiments. The results are shown in Table 1. The data covers a large range in operating temperature, pressure, and feed composition and a satisfactory match is obtained in all cases. Again, the model gave lower purities than reported in literature because of reasons articulated earlier. It is possible that additional process steps not included in this model such as purge, rinse, pressure equalization, and pressurization with light gas could affect the choice of adsorbent. However, such an effect is of second order and likely to come into play only

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

21

Fig. 4. Comparison of model and experimental power requirement.

for adsorbents which give very similar performance after initial screening. In addition, previous studies in which two adsorbents have been considered have always shown that one adsorbent has yielded consistently better performance over a range of conditions (Chue et al., 1995; Dasgupta et al., 2012; Kikkinides et al., 1993; Rege and Yang, 1997, 2001), regardless of the cycle used. Fig. 2 also shows that although Knaebel and Hill’s 4-step Skarstrom cycle and Chiang’s 8-step cycle which includes pressure equalization are quite different, our model is able to capture the major effects. Therefore it is likely that an adsorbent which gives the best performance in our model will be the best adsorbent regardless of the cycle configuration utilized. 2.3. Case study: post-combustion CO2 capture A very large number of adsorbents have recently been considered for CO2 capture, thus using this as a case study is particularly timely. In this case study, we will compare potential adsorbents for post-combustion capture, optimize operating parameters, and determine the adsorbent properties most important to improving performance. All flue gas in this study has a composition of 12% CO2 and 88% N2 and we will not consider other species present in flue gas such as water, SOx or NOx . The flue gas is considered to be available at 1 atm pressure and 30 ◦ C and pressurized to 1.2 bar in all studies. There are four main categories of adsorbents currently considered for the post-combustion adsorption of CO2 : zeolites, activated carbons, metal-organic frameworks (MOFs) and chemisorbents (Choi et al., 2009). Most zeolites have a very strong adsorption affinity for CO2 and therefore have nonlinear isotherms and relatively high adsorption at low partial pressure. In this study, we will use zeolite 13X as a representative of the zeolite family as it is the current benchmark for CO2 capture. The adsorption isotherms for CO2 and N2 are routinely measured in our laboratory and in this case

were taken from (Xiao et al., 2008). Activated carbons typically have lower CO2 adsorption and poorer selectivity than zeolites but are tolerant to humidity which is beneficial when working with wet flue gas. Adsorption isotherms for CO2 and N2 on activated carbon were taken from (Xu et al., 2011). Metal organic frameworks (MOFs) have also been considered for CO2 capture because of their high surface area and corresponding high capacity for CO2 adsorption. However, many MOFs, such as CuBTC, have very low CO2 affinities and therefore large adsorption capacity is only reached at high pressure. Mg-MOF-74 has received attention recently because it has both a high capacity and adsorption affinity and will be analyzed in this study (Mason et al., 2011). The adsorption mechanism for these first three classes of adsorbents is physisorption where there is an interaction between the quadrupole moment of the gas and the polar adsorbent (D’Alessandro et al., 2010). CO2 has a strong quadrupole moment while N2 has a smaller but still significant quadrupole moment and therefore any physisorbent which adsorbs CO2 will also adsorb significant amounts of N2 . The fourth class of adsorbent (chemisorbents) involves a reaction between the CO2 and the surface (often a functional group tethered to the surface). These show complete selectivity of CO2 over N2 . They typically have very large heats of adsorption and correspondingly strong adsorption at low partial pressures. However, this also leads to large thermal effects and poor desorption under pressure swing conditions. For this reason, TSA is considered more promising for these adsorbents. The chemisorbent used in this study is PEI impregnated MCF/y.2500 (Subagyono et al., 2011). There are clearly advantages and disadvantages with each of these materials. Fig. 5 shows the isotherms for the three physisorbents at 25, 50 and 75 ◦ C. The chemisorbent isotherm is not shown at low temperatures (25 and 50 ◦ C) because of low kinetic performance making reliable measurements at these temperatures impractical. The chemisorbent is included in the isotherm plot at 75 ◦ C. Chemisorbents are typically proposed as TSA materials with a

Table 1 Comparison of simple PSA model to empirical data and rigorous MINSA simulations. Process conditions

Measure

Literature

Model

Source

15%CO2 /85%N2 PH = 7.2 bar; PL = 5–10 kPa; T = 120 ◦ C, 200 ◦ C 12%CO2 /88%N2 PH = 1.2 bar; PL = 5 kPa; T = 40 ◦ C 12.5%CO2 /87.5%(N2 + O2 ) PH = 1.2 bar; PL = 2–10 kPa; T = 45 ◦ C

Purity (%CO2 ) Recovery (%) Purity (%CO2 ) Recovery (%) Purity (%CO2 ) Recovery (%)

81, 69 88, 86 85.7 77.6 92–78 90–20

71–75, 62–64 88–93, 84–90 67 75 83–46 84–28

Zhang and Webley (2007) Xiao et al. (2008)

Lee et al. (2011)

22

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

Fig. 5. CO2 and N2 isotherms of a variety of adsorbents at several temperatures.

relatively the large heat of adsorption as opposed to PSA/VSA where it is a disadvantage. Our goal by including a chemisorbent in our study is to demonstrate how we can quickly screen materials based on their isotherms alone, without resorting to heuristics, and regardless of whether they are chemisorbents or physisorbents. Although we did not expect that tethered amines with heats of adsorption around 90 kJ/mol would perform better than 13X, the line between chemisorbents and physisorbents is somewhat blurred and it is possible that a chemisorbent with a more moderate heat of adsorption could give better results or indeed a higher operating temperature may favor the use of chemisorbents over physisorbents even in PSA/VSA mode. Visual inspection of the isotherms shown in Fig. 5 may suggest that Mg-MOF-74 is superior given its high apparent CO2 capacity. However, the nitrogen capacity is similarly elevated and it is unclear initially which adsorbent would be best for this separation. We have therefore used our simple model to estimate process performance using each of these four materials to objectively compare them. Adsorption isotherm data for these 4 adsorbents were fit to either dual site or single site Langmuir isotherm models. The isotherm constants are shown in Tables 2a and 2b, for the general

dual site Langmuir model as shown in Eq. (4) below. In order to fit this equation to experimental data, isotherms must be measured at several temperatures as done in Li et al. (2009). Nads,i =

m1 bi Pi m2 di Pi + 1 + bi Pi 1 + di Pi

bi = b0i exp di = d0i exp

(10)

Q  1

(11)

RT

Q  2

(12)

RT

The other physical properties required for this model (or almost any process model) are void fraction, density, and heat capacity. The void fraction and density can be calculated from Eqs. (13) and (14) (Duong, 1998). εtotal = εbed + (1 − εbed )εpellet

(13)

bed = (1 − εbed )ppellet

(14)

The bed void was assumed to be 0.37 (randomly packed spherical beads), while the particle void varies based on the adsorbent. We

Table 2a Adsorbent isotherm parameters. Terms

m1 (gmol/kg) m2 (gmol/kg) b0i (1/bar) Q1 (J/gmol) d0i (1/bar) Q2 (J/gmol) a b c d

Zeolite 13Xa

Activated carbonb

Mg-MOF-74c

Chemisorbentd

CO2

N2

CO2

N2

CO2

N2

CO2

N2

2.808 2.4975 4.37–05 32,194.30 3.30E−06 32,176

2.019 – 2.04E−04 14,875 – –

0.5914 7.5055 4.05E−05 31,400 1.68E−04 19,800

0.1553 41.3 8.34E−03 14,300 7.98E−12 50,000

6.8 9.9 2.44E−06 42,000 1.39E−05 24,000

14 – 4.96E−10 18,000 – –

3.82 – 1.22E−14 100,000 – –

– – – – – –

Xiao et al. (2008). Xu et al. (2011). Mason et al. (2011). Subagyono et al. (2011).

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

23

Table 2b Adsorbent physical properties. Adsorbent

Density (kg/m3 )

Total void

Heat capacity (J/kg K)

Zeolite 13X Activated carbon Mg-MOF-74 Chemisorbent

750a 480.5a 572.7b 230c

0.71d 0.69e 0.72b 0.37

920a 1050a 800b 1600f

a b c d e f

Chue et al. (1995). Wu et al. (2009). Zhang et al. (2012). Cavenati et al. (2004). Shen et al. (2010). Ciferno et al. (2011).

assumed that there is no particle void in the chemisorbent because the mesopores are completely filled with PEI. 3. Results and discussion 3.1. Adsorbent comparison and analysis of operating conditions Using the simple model, VSA performance was evaluated over a range of desorption pressures for each of the categories of adsorbent. We chose an adsorption temperature of 75 ◦ C so the chemisorbent could be included in the analysis. As seen in Fig. 6, zeolite 13X yielded the highest purity followed by the chemisorbent, Mg-MOF-74, and activated carbon, over the full range of vacuum pressure. The chemisorbent did not have the best performance even though it has “perfect” selectivity because the strong thermal effects lead to poor CO2 working capacity. Even though there is no N2 on the surface of the adsorbent, there is still a significant amount of N2 in the void and therefore a significant amount of CO2 must be released in the blow down to dilute the N2 and achieve a high purity product. The value of the relative volatility analog (nA,ads /yB )(yB /nB,ads ), commonly used to compare adsorbents, is infinite for this material despite its limited performance demonstrating the limitations of using this term for adsorbent selection. Mg-MOF-74, while showing higher working capacity than the other adsorbents (Fig. 6(d)) requires considerably more specific

power and produces a lower purity product due to significant N2 adsorption and poor CO2 desorption. The shape of the specific power curve and location of the minimum as a function of vacuum pressure is discussed in Section 3.2. Recovery is not very dependent on the adsorbent used (Fig. 6(b)), but is very sensitive to the blow down pressure. We will provide an explanation for this trend later in Section 3.2. This analysis was repeated under isothermal conditions, simulated by setting the adsorbent heat capacity to infinity, to demonstrate the importance of thermal effects. As can be seen in Fig. 7, the performance of all adsorbents was significantly improved, especially for Mg-MOF-74 and the chemisorbent because they have the largest thermal effects. For example, at a desorption pressure of 0.05 bar, the working capacity of Mg-MOF-74 increased from the adiabatic (more realistic) value of ∼0.4 mol/kg (Fig. 6(d)) to ∼1.5 mol/kg when isothermal conditions are assumed. More importantly, the ranking of adsorbents has completely changed from the more realistic adiabatic case shown in Fig. 6 where 13X was the preferred material. Mg-MOF-74 and the chemisorbent now appear to be superior to 13X adsorbent especially in regards to working capacity but even for CO2 purity. Under isothermal conditions, Mg-MOF-74 has a much greater working capacity than 13X. However, the working capacities are similar when thermal effects are considered. Furthermore, under adiabatic conditions, Mg-MOF-74 produces a much lower purity than 13X even though the selectivities, defined

Fig. 6. Adiabatic VSA simulations at different vacuum pressures at 75 ◦ C.

24

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

Fig. 7. VSA simulations under isothermal conditions at 75 ◦ C.

as nCO2 ,ads /nN2 ,ads , are on the same order of magnitude (13.5 for 13X and 8.1 for Mg-MOF-74). This demonstrates the futility of this measure of selectivity in screening adsorbents. N2 almost completely desorbs during the blow down step regardless of adsorbent but there is much more residual CO2 on Mg-MOF-74 than 13X because the Mg-MOF-74 isotherm is more non-linear. Any meaningful measure of selectivity must include the non-isothermal working capacities of both species as opposed to simply adsorbed capacities. After compression, the temperature of the gas can be increased or decreased using a heat exchanger in order to improve

performance. Increasing the temperature decreases the adsorption capacity, but also decreases the steepness of the adsorption isotherm and leading to a larger percentage of CO2 being desorbed. Fig. 8 shows that there are optimal temperatures for both purity and specific work, both around 50 ◦ C for zeolite 13X used in this study. Working capacity and recovery both decrease with increasing temperature while the optimal desorption pressure increases. The optimal desorption pressure is taken as that which minimizes specific power. This optimal temperature coincides closely with our experience in operating VSA systems for CO2 capture using zeolite

Fig. 8. Effect of adsorption temperature on process performance (zeolite 13X adsorbent, PH = 1.2 bar, desorption pressure optimized to minimize specific work for each process).

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

25

Fig. 9. Comparison of specific work and adsorption figure of merit (Ackley et al., 2000) for 13X and PEI chemisorbent at 75 ◦ C.

13X in which we have obtained best performance between 45 and 60 ◦ C in terms of purity and working capacity. The optimum for specific power is at a lower temperature because of the increase costs of pumping hot gasses. The optimal temperature for activated carbon is approximately 25 ◦ C and approximately 100 ◦ C for Mg-MOF-74 in terms of purity, recovery, and specific power. Activated carbon has a lower optimal temperature because its isotherm is less steep than 13X, while Mg-MOF-74 has a higher optimal temperature because its isotherm is more steep. As mentioned earlier, “adsorption figure of merit” has been suggested as a predictor of adsorbent performance. Our model offers an improvement over a lumped figure of merit parameter because the outputs from our model can be used to determine operating conditions. Furthermore, as seen in Fig. 9, there is no desorption pressure which maximizes AFM because both purity and recovery increase with decreasing vacuum pressure. However, the improved separation requires higher vacuum costs and the trade-off between power consumption and recovery leads to an optimal specific power. Furthermore, specific power can be used to estimate the operating costs while AFM has no physical meaning. Because there is a vacuum pressure for each of the adsorbents to minimize specific work requirement while purity, recovery, and working capacity all increase monotonically with the depth of vacuum, the ideal operating vacuum level is either at or deeper than the level which minimizes specific work. Determining this optimal level is complicated and requires knowing the detailed capital and operating costs of the system. Economic analysis of CO2 capture by VSA will be the focus of future work and in this study the optimal vacuum pressure will be assumed to be the pressure which minimizes specific work. The working capacity and specific work, which serve as analogs for capital and operating costs respectively, were calculated at the optimal desorption pressure for several adsorbents and shown in Fig. 10. The top left hand corner of the graph represents the best adsorbents (low specific power, high working capacity). The chabazite isotherms (denoted MCHA where M indicates the exchangeable cation) were from Zhang (Zhang et al., 2008a) and the physical properties were assumed to be identical to 13X. The CuBTC isotherm data was from Liang (Liang et al., 2009) and the physical properties were assumed to be the same as Mg-MOF74. Since overall capture cost (dictated by working capacity and

specific power) decreases as the top left corner of the graph is approached, it is clear that zeolite 13X remains the standard to which other adsorbents should be compared. Mg-MOF-74 had the highest working capacity, but most of the CO2 is removed at a deeper vacuum level because of strong thermal effects and very nonlinear isotherm and therefore the specific power requirement is very high. The chabazite materials have similar working capacities to 13X, but have higher power requirements for the same reason as Mg-MOF-74. These materials also all have poorer working selectivities resulting in lower purities. CuBTC yielded such poor performance because it does not adsorb much CO2 at the feed condition. More detailed analysis of the relative contributions of working capacity and specific power to the overall capture cost are needed before contours of constant capture cost can be drawn in Fig. 10. However, Fig. 10 remains a useful reference chart to which new adsorbents can be added once their isotherms and physical properties are determined. Although it would be useful to make a simple comparison plot similar to the Robeson plot for membranes, we believe this would be inappropriate for adsorption. There is no physical reason (and this is borne out by experience) why the working capacity and the working selectivity of an adsorbent should be inversely related as is usually the case for membranes. In fact, working selectivity often increases as working capacity increases. Secondly, an adsorption process is much more complicated than a membrane process because it is run under dynamic conditions at cyclic steady state and the choice of operating conditions directly impacts on the capacity and selectivity of the material. While a membrane has a fixed permeability, the adsorbents capacity and selectivity is directly a function of adsorbent and operating conditions (since the isotherms are non-linear). Therefore, we believe a single benchmark is probably insufficient to screen adsorbents and a plot such as the one shown in Fig. 6 (in which we compare adsorbents over a range of conditions) or Fig. 10 (in which we compare adsorbents each operating at their “optimal” condition) is more appropriate for adsorbent comparison. We assumed the flue gas to be dry for our analysis; however, actual flue gas emitted from power plants contains a considerable amount of water. Water saturates hydrophilic adsorbents, such as zeolites and MOFs, preventing them from adsorbing CO2 and therefore a pre-layer is required to protect these adsorbents from the humidity. This reduces the percentage of the bed containing the CO2 adsorbent and additional

26

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

Fig. 10. VSA simulations at different vacuum pressures at 75 ◦ C.

vacuum work is required to regenerate the pre-layer. Far less water adsorbs to hydrophobic materials, such as activated carbon or PEIimpregnated chemisorbents, and therefore humid flue gas can be processed without much additional cost. Detailed analysis of the costs differences between hydrophilic and hydrophobic adsorbents will be included in future work on economic evaluation of PSA. 3.2. Theoretical explanation of operating condition trends The screening conducted above suggests that very low vacuum levels are optimal for CO2 capture by VSA. The need to produce these deep vacuums at a very large scale is of concern. It would be advantageous to develop a process where the optimal specific power is reached at a milder vacuum, but this seems unlikely (in a single VSA stage) based on the four categories of adsorbents we have examined in this study. This can be explained using the theoretical limit (Subramanian and Ritter, 1997) where the enrichment ratio for a stripping cycle cannot exceed the pressure

ratio. Recovery is determined by the change in CO2 partial pressure as the bed goes from high pressure to low pressure in the blow down. CO2 partial pressure decreases with total pressure, with the effect somewhat counteracted by the increase in CO2 composition. It can be shown that for a perfect adsorbent (which has a linear CO2 isotherm with an infinite capacity, no N2 adsorption, and no thermal effects) that the enrichment is equal to the pressure ratio (until the purity approaches 100%), and there is no recovery until the pressure ratio has exceeded the reciprocal of the feed composition, as seen in Fig. 11. The adsorbents considered for VSA are relatively close to an ideal adsorbent and therefore for a feed of 12% CO2 , recovery and therefore low specific work will only be achieved below 10 kPa vacuum. One might consider increasing the adsorption pressure as a means to reduce the required vacuum depth. However, this requires performing significant compression work on an entire feed gas stream, which dramatically increases the total specific work required. Fig. 12 shows that the specific work requirement more

Fig. 11. Purity and recovery for an ideal linear adsorbent.

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

27

Fig. 12. Specific work as function of adsorption pressure.

than doubles by increasing the adsorption pressure from 1.2 bar to 2 bar. This is consistent with current CO2 capture VSA designs where adsorption pressure is kept to a minimum. It is also possible to increase the product purity either with a product rinse step or by operating two PSA units in series and therefore reducing the need for a high pressure ratio while also reducing CO2 recovery. Dual reflux cycles have been studied (Ebner and Ritter, 2004; Kearns and Webley, 2006) in which significant amounts of product and waste purge are both used in order to achieve high purity and recovery. However, these cycles have high specific power requirements and low throughput because of the amount of recycling required.

3.3. Effect of improved adsorbent properties on process performance Much of the focus in materials development is on improving adsorption capacity even though this is not necessarily the most important property when selecting an adsorbent. We performed a sensitivity analysis to examine the effect that changes in CO2 capacity, N2 capacity, and heat capacity (thermal effects) have on the process purity and working capacity using 13X as a baseline. As can be seen in Fig. 13(a), improving the selectivity has a greater effect on CO2 purity than does CO2 capacity. Similarly, increasing the heat capacity of 13X has a greater effect on the working capacity than increasing the CO2 capacity

Fig. 13. Sensitivity analysis for theoretical adsorbent against 13X benchmark.

28

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

Fig. 14. Finding optimal surface area and heat of adsorption for VSA processes (contours correspond to purities).

(Fig. 13(b)). This suggests that there needs to be considerable focus on developing adsorbents which have good adsorption capacity without the strong thermal effects, i.e. many adsorption sites with moderate adsorption affinity. Furthermore, we suggest that the N2 adsorption isotherm has a more direct impact on the specific power consumption than the CO2 isotherm. Almost any adsorbent will be highly selective to CO2 over N2 because of the difference in interaction energy, but as mentioned earlier, defining selectivity as the ratio of adsorbed CO2 to adsorbed N2 is misleading because a large amount of CO2 will not desorb. Even a small amount of N2 adsorption significantly decreases the final product purity.

We performed a case study to determine the optimal surface area and CO2 heat of adsorption for an adsorbent. We assumed a general single site Langmuir isotherm for both N2 and CO2 . The b0 term for both CO2 and N2 was set to e−12 , the lower limit of Trouton’s law (Myers and Siperstein, 2001). Repeating the study at the upper limit of e−10 (not shown) yielded similar results. We performed case studies at three different heats of adsorption for N2 : 0 kJ, 17 kJ, and 23 kJ. In each case, we varied the CO2 heat of adsorption and the adsorption capacity (an analog for surface area, which is kept the same for CO2 and N2 to maintain thermodynamic consistency). As seen in Fig. 14, the optimal heat of adsorption for CO2 for all three cases is between 35 kJ/mol and 45 kJ/mol which

Fig. 15. Performance of theoretical material with adsorbent capacity of MOF-177.

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

is relatively mild because large heats of adsorption lead to strong thermal effects and can lower working capacity even though they increase adsorption capacity. Likewise, a large physisorbent surface area increases N2 capacity as well as CO2 capacity which can lower purity and increase the specific power requirement. Therefore, the optimum adsorbent capacity decreases with increasing N2 heat of adsorption. In order to test the realistic limits of an improved adsorbent, we performed a series of simulations with a hypothetical material assuming no N2 adsorption, and an adsorption capacity of 42 mol/kg, corresponding to the maximum capacity of MOF-177 (Mason et al., 2011). The CO2 heat of adsorption was varied and as shown in Fig. 15, a heat of adsorption of approximately 35 kJ/mol optimizes throughput, purity, and specific work (not shown). The corresponding values of 94% CO2 purity and 0.67 mol/kg working capacity respectively are significant improvements over what is achieved using 13X. Despite its capacity, MOF-177 is not a promising material for VSA because its CO2 heat of adsorption is only 14 kJ/mol. 4. Conclusions A new simple model was developed, validated, and used to approximate bulk PSA performance separations for adsorbent screening. The model is easy to use, can be quickly solved, and is flexible with the isotherm data that can be used. It is useful both for material developers who want to demonstrate the potential of a new adsorbent as well as process engineers who are selecting an adsorbent for a PSA process. We emphasize that studies reporting new adsorbents for CO2 capture should report isotherms at three temperatures (to permit evaluation of thermal effects) as well as N2 isotherms and material voidage. This set of data is sufficient to permit evaluation by the model described here. Our model has been used to screen adsorbents for CO2 capture from flue gas using vacuum swing adsorption, determine operating conditions, and make suggestions for material development with respect to post-combustion pressure swing adsorption. The following specific conclusions can be drawn: • Existing metrics for adsorbent performance based on selectivities and capacities are misleading – account must be taken of thermal effects and relative amounts of CO2 and N2 adsorbed over the pressure range of interest • A comparison of 13X, Mg-MOF-74, activated carbon, and a chemisorbent with our model showed that 13X remains the preferred adsorbent in a VSA configuration with a dry flue gas. The apparently higher CO2 capacity of Mg-MOF-74 is more than offset by its correspondingly higher N2 capacity and poor regenerability • The optimal temperature for CO2 capture with 13X adsorbent under VSA operation is ∼50 ◦ C • The feed gas (flue gas) to the adsorber should be kept to as close to 1 atm as possible. Compression of the flue gas to even 2 bar is not recommended with current adsorbents. • Materials development should focus on reductions in N2 capacity rather than increases in CO2 capacity as they have relatively a higher impact on purity • Adsorbent heat capacity has a significant effect on the performance of the process. Numerous approaches such as diluents, phase change materials etc. should be pursued to mitigate the thermal swing accompanying the pressure swing • The optimal heat of adsorption for CO2 appears to lie in the range 35–45 kJ/mol regardless of the N2 heat of adsorption in VSA applications. The optimal surface area decreases as the heat of adsorption of N2 increases and should not necessarily be increased without bound.

29

Future work will include developing a more advanced capital costing model as well as the inclusion of temperature swing adsorption into the model (in which chemisorbents are expected to be the preferred option) and a methodology for inclusion of the effect of water. Acknowledgements The authors acknowledge financial support for this work from the Cooperative Research Centre for Greenhouse Technologies (COCRC), which is established and supported under the Australian Government’s Cooperative Research Centre Program. Appendix A. Appendix In this, we provide a detailed description of how the calculations were performed. These equations can be evaluated in any programming language; however MATLAB was used in this study to make use of the existing mathematical libraries. The equations below are for a general separation on a binary gas mixture where species A is preferentially adsorbed over species B. All gasses are assumed to be ideal and the gas phase is always in thermal and mass equilibrium with the adsorbed phase. A.1. Initial conditions The initial condition is a bed fully saturated with feed, where the bed composition and temperature are the same as the feed and the bed is at the adsorption pressure (Eqs. (A1)–(A3)). The breakthrough loadings are calculated from the isotherm equations which are functions of the gas partial pressures and the temperature (Eqs. (A5) and (A6)). The system is given an arbitrary size by setting the mass of adsorbent to 1 kg. The void volume, which is occupied by the gas phase, is calculated using the total bed void fraction and density (A4). yA,initial = yA,feed

(A1)

Tinitial = Tfeed

(A2)

Pinitial = PH

(A3)

Vinitial

1 kg × ε = 

(A4)

nads,A = f (PA , PB , T )

(A5)

nads,B = f (PA , PB , T )

(A6)

A.2. Blow down In the blow down step, the pressure is decreased in small increments. Before each step, the heat of adsorption for each component at the loading and temperature is calculated using the Clausius–Clapyron equation ((A7) and (A8)). The isotherm derivatives with respect to temperature and pressure are calculated numerically. Then Eqs. (A9)–(A11) are solved simultaneously for the three variables: temperature, moles of gas removed, and gas composition. Initial conditions from the previous step are denoted with a subscript “0”. The specific work for each step is calculated using the isentropic compression equation. QA =

QB =

RT 2 (∂nA,ads /∂PB )(∂nB,ads /∂T ) − (∂nA,ads /∂T )(∂nB,ads /∂PB ) PA (∂nA,ads /∂PA )(∂nB,ads /∂PB ) − (∂nA,ads /∂PB )(∂nB,ads /∂PA ) (A7) RT 2 (∂nB,ads /∂PA )(∂nA,ads /∂T ) − (∂nB,ads /∂T )(∂nA,ads /∂PA ) PB (∂nB,ads /∂PB )(∂nA,ads /∂PA ) − (∂nB,ads /∂PA )(∂nA,ads /∂PB ) (A8)

30

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31

If we assume that the adsorption of A and B are independent, i.e. (∂nB,ads /∂PA ) = (∂nA,ads /∂PB ) = 0, the equations reduce to

T − T0 =

QA (P, yA , T ) − NA,0 ) (n Cp × m A,ads +

QB (P, (1 − yA ), T ) − NB,0 ) (n Cp × m B,ads

(A22)

RT 2 ∂nA,ads /∂T QA = PA ∂nA,ads /∂PA

(A9)

RT 2 ∂nB,ads /∂T PB ∂nB,ads /∂PB

(A10)

After the repressurization step has completed, the composition of A in gas phase of the bed will be less than the feed which is the condition for a shock-wave through the bed.

QB =

NA,total = nA,ads (P, yA , T ) × m +

yA PV RT

(A11)

A.4. Feed

NB,total = nB,ads (P, yA , T ) × m +

yB PV RT

(A12)

The feed is assumed to produce a perfect shock-wave through the bed until there is a complete breakthrough. This means that the flow out of the bed is bed composition at the end of the repressurization step. A mass balance is performed to determine the moles of feed and product needed to reach cyclic steady state.

(A13)

NA,initial = NA,RP + Nfeed × yA,feed − Nwaste × yA

(A23)

NB,initial = NB,RP + Nfeed × yB,feed − Nwaste × yB

(A24)

T − T0 =

QA (P, yA , T ) − NA,0 ) (n Cp × m A,ads QB (P, (1 − yA ), T ) − NB,0 ) (n Cp × m B,ads

+

  ⎧  k   Patm (k−1)/k ⎨ N × 1 Tfeed − 1 , if P < Patm  k−1 P Wi,vacuum = ⎩ 0,

if

In this study, the blow down was calculated in 100 steps. The moles of gas removed in this step are the heavy product (CO2 product) from this separation. The moles of product and total vacuum work are calculated by taking a summation of the moles removed and vacuum work in each step ((A15)–(A17)). At the beginning of the blow down step, where the pressure is still above atmospheric, it is assumed that no vacuum work is required to remove the gas.



iblow down

NA,product =

(A15)

yA N

1



Wvacuum =



(1 − yA )N

(A16)

 k  k−1

Wi,vacuum

PH Pfeed

(k−1)/k



−1

(A17) A.5. Process performance

RT 2 (∂nA,ads /∂PB )(∂nB,ads /∂T ) − (∂nA,ads /∂T )(∂nB,ads /∂PB ) PA (∂nA,ads /∂PA )(∂nB,ads /∂PB ) − (∂nA,ads /∂PB )(∂nB,ads /∂PA ) (A18)

RT 2 (∂nB,ads /∂PA )(∂nA,ads /∂T ) − (∂nB,ads /∂T )(∂nA,ads /∂PA ) PB (∂nB,ads /∂PB )(∂nA,ads /∂PA ) − (∂nB,ads /∂PA )(∂nA,ads /∂PB ) (A19)

NA,total + N × yA,feed = nA,ads (P, yA , T ) × m +



Tfeed

(A26)

The repressurization also proceeds incrementally. In each step, a small amount of feed is added to the bed where it mixes completely with the gas already in the bed. As with the previous step, the pressure is increased gradually from desorption to adsorption level and at each pressure, the temperature, gas composition, and number of moles of feed required are calculated to achieve mass and energy balances ((A20)–(A22)).

QB =

1 

1

A.3. Repressurization

QA =

Nfeed and Nwaste are the only two unknowns in these two linear equations (A23) and (A24). The combined number of moles entering the bed in the feed and repressurization steps is multiplied by the isothermal specific compression work in order to determine the blower work (A26). In a VSA process, the flue gas is provided at atmospheric pressure and must be pressurized slightly. However, in many cases the feed is supplied at elevated pressure and no blower is required. Wblower = (NRP + Nfeed ) ×

iblow down

NB,product =

(A14)

P > Patm

yA PV RT

NA,total + N × (1 − yA,feed ) = nA,ads (P, yA , T ) × m +

(A20) yA PV RT

(A21)

Once the cycle has been simulated, the following process parameters can be calculated. Purity =

NA,product (NB,product + NA,product )

Recovery =

NA,product yA,feed × (NRP + Nfeed )

Specific work =

Wvacuum + Wblower NA,product

(A28)

(A29) (A30)

References Ackley, M.W., Stewart, A.B., Leavitt, F.W., Notaro, F., Kane, M.S., 2000. PSA apparatus and process using adsorbent mixtures. Praxair Technology, Inc., United States Patent 6027548. Cavenati, S., Grande, C.A., Rodrigues, A.E., 2004. Adsorption equilibrium of methane, carbon dioxide, and nitrogen on zeolite 13X at high pressures. Journal of Chemical & Engineering Data 49, 1095–1101. Chaffee, A.L., Knowles, G.P., Liang, Z., Zhang, J., Xiao, P., Webley, P.A., 2007. CO2 capture by adsorption: materials and process development. International Journal of Greenhouse Gas Control 1, 11–18. Chiang, A.S.T., 1996. An analytical solution to equilibrium PSA cycles. Chemical Engineering Science 51, 207–216. Choi, S., Drese, J.H., Jones, C.W., 2009. Adsorbent materials for carbon dioxide capture from large anthropogenic point sources. ChemSusChem 2, 796–854.

B.J. Maring, P.A. Webley / International Journal of Greenhouse Gas Control 15 (2013) 16–31 Chue, K.T., Kim, J.N., Yoo, Y.J., Cho, S.H., Yang, R.T., 1995. Comparison of activated carbon and zeolite 13X for CO2 recovery from flue gas by pressure swing adsorption. Industrial & Engineering Chemistry Research 34, 591–598. Ciferno, J.L.J., Brickett, L., Murphy, J., Munson, R., Zaremsky, C., Marano, J., Strock, J., 2011. DOE/NETL Advanced CO2 Capture R&D Program: Technology Update. NETL, pp. B-206. D’Alessandro, D.M., Smit, B., Long, J.R., 2010. Carbon dioxide capture: prospects for new materials. Angewandte Chemie International Edition 49, 6058–6082. Dasgupta, S., Biswas, N., Aarti, Gode, N.G., Divekar, S., Nanoti, A., Goswami, A.N., 2012. CO2 recovery from mixtures with nitrogen in a vacuum swing adsorber using metal organic framework adsorbent: a comparative study. International Journal of Greenhouse Gas Control 7, 225–229. Duong, D.D., 1998. Adsorption Analysis: Equilibria and Kinetics. Imperial College Press, London, UK. Ebner, A.D., Ritter, J.A., 2002. Equilibrium theory analysis of rectifying PSA for heavy component production. AIChE Journal 48, 1679–1691. Ebner, A.D., Ritter, J.A., 2004. Equilibrium theory analysis of dual reflux PSA for separation of a binary mixture. AIChE Journal 50, 2418–2429. Gielen, G.P.J., 2004. Prospects for CO2 Capture and Storage. International Energy Agency, IEA, Paris. Harlick, P.J.E., Tezel, F.H., 2004. An experimental adsorbent screening study for CO2 removal from N2. Microporous and Mesoporous Materials 76, 71–79. Harlick, P.J.E, Tezel, F.H., 2005. Equilibrium analysis of cyclic adsorption processes: CO2 working capacities with NaY. Separation Science and Technology 40, 2569–2591. Jain, S., Moharir, A.S., Li, P., Wozny, G., 2003. Heuristic design of pressure swing adsorption: a preliminary study. Separation and Purification Technology 33, 25–43. Kearns, D.T., Webley, P.A., 2006. Modelling and evaluation of dual-reflux pressure swing adsorption cycles: part I. Mathematical models. Chemical Engineering Science 61, 7223–7233. Kikkinides, E.S., Yang, R.T., Cho, S.H., 1993. Concentration and recovery of carbon dioxide from flue gas by pressure swing adsorption. Industrial & Engineering Chemistry Research 32, 2714–2720. Knaebel, K.S., Hill, F.B., 1985. Pressure swing adsorption: development of an equilibrium theory for gas separations. Chemical Engineering Science 40, 2351–2360. Krishna, R., Long, J.R., 2011. Screening metal–organic frameworks by analysis of transient breakthrough of gas mixtures in a fixed bed adsorber. The Journal of Physical Chemistry C 115, 12941–12950. Krishna, R., van Baten, J.M., 2012. A comparison of the CO2 capture characteristics of zeolites and metal–organic frameworks. Separation and Purification Technology 87, 120–126. Kumar, R., 1994. Pressure swing adsorption process: performance optimum and adsorbent selection. Industrial & Engineering Chemistry Research 33, 1600–1605. Lee, A., Xiao, G., Xiao, P., Joshi, K., Singh, R., Webley, P.A., 2011. High temperature adsorption materials and their performance for pre-combustion capture of carbon dioxide. Energy Procedia 4, 1199–1206. Li, G., Xiao, P., Webley, P., Zhang, J., Singh, R., Marshall, M., 2008. Capture of CO2 from high humidity flue gas by vacuum swing adsorption with zeolite 13X. Adsorption 14, 415–422. Li, G., Xiao, P., Webley, P.A., Zhang, J., Singh, R., 2009. Competition of CO2 /H2 O in adsorption based CO2 capture. Energy Procedia 1, 1123–1130. Liang, Z., Marshall, M., Chaffee, A.L., 2009. CO2 adsorption-based separation by metal organic framework (Cu-BTC) versus zeolite (13X). Energy & Fuels 23, 2785–2789. Mason, J.A., Sumida, K., Herm, Z.R., Krishna, R., Long, J.R., 2011. Evaluating metal-organic frameworks for post-combustion carbon dioxide capture via

31

temperature swing adsorption. Energy & Environmental Science 4, 3030– 3040. Myers, A.L., Siperstein, F., 2001. Characterization of adsorbents by energy profile of adsorbed molecules. Colloids and Surfaces A: Physicochemical and Engineering Aspects 187–188, 73–81. Rege, S.U., Yang, R.T., 1997. Limits for air separation by adsorption with LiX zeolite. Industrial & Engineering Chemistry Research 36, 5358–5365. Rege, S.U., Yang, R.T., 2001. A simple parameter for selecting an adsorbent for gas separation by pressure swing adsorption. Separation Science and Technology 36, 3355–3365. Ruthven, D.M., 1984. Principles of Adsorption and Adsorption Processes. WileyInterscience, New York. Ruthven, D.M., Farooq, S., Knaebel, K.S., 1994. Pressure Swing Adsorption. VCH Publishers, New York, NY. Shen, C., Grande, C.A., Li, P., Yu, J., Rodrigues, A.E., 2010. Adsorption equilibria and kinetics of CO2 and N2 on activated carbon beads. Chemical Engineering Journal 160, 398–407. Subagyono, D.J.N., Liang, Z., Knowles, G.P., Chaffee, A.L., 2011. Amine modified mesocellular siliceous foam (MCF) as a sorbent for CO2 . Chemical Engineering Research and Design 89, 1647–1657. Subramanian, D., Ritter, J.A., 1997. Equilibrium theory for solvent vapor recovery by pressure swing adsorption: analytical solution for process performance. Chemical Engineering Science 52, 3147–3160. Todd, R.S., He, J., Webley, P.A., Beh, C., Wilson, S., Lloyd, M.A., 2001. Fast finite-volume method for PSA/VSA cycle simulation experimental validation. Industrial & Engineering Chemistry Research 40, 3217–3224. Webley, P.A., He, J., 2000a. Fast solution-adaptive finite volume method for PSA/VSA cycle simulation; 1 single step simulation. Computers & Chemical Engineering 23, 1701–1712. Webley, P.A., He, J., 2000b. Introduction to the PSA Simulator MINSA. Department of Chemical Engineering, Monash University. Wu, H., Zhou, W., Yildirim, T., 2009. High-capacity methane storage in metal−organic frameworks M2(dhtp): the important role of open metal sites. Journal of the American Chemical Society 131, 4995–5000. Xiao, P., Zhang, J., Webley, P., Li, G., Singh, R., Todd, R., 2008. Capture of CO2 from flue gas streams with zeolite 13X by vacuum-pressure swing adsorption. Adsorption 14, 575–582. Xu, D., Zhang, J., Li, G., Xiao, P., Webley, P., Zhai, Y.-c., 2011. Effect of water vapor from power station flue gas on CO2 capture by vacuum swing adsorption with activated carbon. Journal of Fuel Chemistry and Technology 39, 169–174. Yazaydın, A.O.z.r., Snurr, R.Q., Park, T.-H., Koh, K., Liu, J., LeVan, M.D., Benin, A.I., Jakubczak, P., Lanuza, M., Galloway, D.B., Low, J.J., Willis, R.R., 2009. Screening of metal–organic frameworks for carbon dioxide capture from flue gas using a combined experimental and modeling approach. Journal of the American Chemical Society 131, 18198–18199. Zhang, J., Singh, R., Webley, P.A., 2008a. Alkali and alkaline-earth cation exchanged chabazite zeolites for adsorption based CO2 capture. Microporous and Mesoporous Materials 111, 478–487. Zhang, J., Webley, P.A., 2007. Cycle development and design for CO2 capture from flue gas by vacuum swing adsorption. Environmental Science & Technology 42, 563–569. Zhang, J., Webley, P.A., Xiao, P., 2008b. Effect of process parameters on power requirements of vacuum swing adsorption technology for CO2 capture from flue gas. Energy Conversion and Management 49, 346–356. Zhang, Z., Ma, X., Wang, D., Song, C., Wang, Y., 2012. Development of silica-gelsupported polyethylenimine sorbents for CO2 capture from flue gas. AIChE Journal 58, 2495–2502.