Design of a Pressure Swing Adsorption Process for Postcombustion

Article pubs.acs.org/IECR

Design of a Pressure Swing Adsorption Process for Postcombustion CO2 Capture Gerhard D. Pirngruber* and Damien Leinekugel-le-Cocq IFP Énergies nouvelles, Rond Point Échangeur de Solaize, 69360 Solaize, France S Supporting Information *

ABSTRACT: The adsorption processes for postcombustion CO2 capture are usually based on a temperature or vacuum swing (TSA or VSA). In the present contribution an alternative concept is presented, which is based on the regeneration of the solid sorbent (an immobilized amine) by a purge gas, low pressure vapor, under almost isothermal conditions. Because of the close to isothermal operation, the process consumes significantly less thermal and mechanical energy than conventional TSA and VSA processes, respectively. We present a rough design of such an isothermal concentration swing process based on a simplified, analytical model of a 2-step PSA (pressure swing adsorption) process. The analytical model allows a definition of the range of operating conditions that lead to the best compromise between energy consumption and productivity (size and number of the adsorbers). Moreover, it is possible to define the equilibrium and mass transfer properties of the ideal solid sorbent. The feasibility of the concentration swing process was finally validated by numerical simulations of a full PSA cycle under adiabatic conditions.

1. INTRODUCTION Carbon capture and storage (CCS) is part of the panel of solutions that will be required to limit the atmospheric CO2 concentration at an acceptable level of 450 ppm. Among the three main CCS routes, that is, oxy-combustion, precombustion CO2 capture, and postcombustion CO2 capture, the latter has the advantage that it can be most easily retrofitted to existing coal/petroleum firing power plants, refineries, etc., by adding a CO2 capture unit to the plant. Postcombustion CO2 capture acts on the flue gases produced by combustion. CO2 in these flue gases is diluted (10−15%) and at low pressure (total pressure is ∼1 bar), which makes CO2 removal difficult. The current state-of-the-art postcombustion capture technology is absorption of CO2 by an aqueous monoethanolamine (MEA) solution. MEA has a very strong affinity to CO2 and captures CO2 efficiently even at low partial pressure, but the regeneration of the solvent by heating requires a large amount of energy. Moreover, degradation of the amine by oxygen in the flue gas causes corrosion problems and leads to a high net consumption of solvent (>1.4 kg MEA/t CO2 captured, i.e., >4700 t per year for a 600 MW power plant). Therefore an intensive search for alternative solutions is going on.1 One of the options is to use pressure (or vacuum) swing adsorption (PSA or VSA) technology in combination with solid sorbents. PSA/VSA technology is proven and robust; it avoids the difficulties associated with the handling of liquids. However, the conditions of postcombustion CO2 capture are not very favorable for a PSA process. PSA exploits the difference of the partial pressure of CO2 between the adsorption and the desorption step. In conventional PSAs desorption is carried out at near ambient pressure. Since the objective is to recover a stream of pure CO2 (>95%), that is, the partial pressure of CO2 under desorption conditions is close to 1 bar, the partial pressure of CO2 in the feed must be higher than that. The molar concentration of CO2 in flue gases is typically 15%; the © 2013 American Chemical Society

pressure of the feed must, therefore, be at least 7 bar in order to have a positive partial pressure difference between adsorption and desorption. This strongly penalizes the cost and energy consumption of the capture process.2 Moreover, a weak partial pressure difference between adsorption and desorption will lead to a low recovery of CO2, that is, an inefficient separation. An alternative option is to desorb CO2 under vacuum, that is, to run a VSA process. On the one hand, this solution reduces the molar flow that needs to be treated by the vacuum pump (it does not treat the whole feed flow, but only the recovered CO2). Since the power consumption of a pump is directly proportional to the molar flow, the energy consumption decreases. On the other hand, the volume flow strongly increases under vacuum (the volume flow is inversely proportional to the pressure). The lower the pressure is, the more vacuum blower trains need to be installed in parallel and the more compression stages are needed to raise the pressure back to one atmosphere.2 Both factors strongly increase the capital expenses of the capture process. It is possible to combine adsorption at moderate pressure with desorption at a moderate vacuum level (VPSA), but also this option increases the capital cost because upstream compressors and vacuum blowers need to be installed. Most CO2 adsorbents that are considered for postcombustion CO2 capture have very steep isotherms that reach a plateau at very low partial pressures. From a point of view of adsorption thermodynamics it is therefore often more attractive to decrease the desorption pressure than to increase the adsorption pressure, because the former brings about a larger gain in the delta loading of the Received: Revised: Accepted: Published: 5985

January 2, 2013 April 2, 2013 April 3, 2013 April 3, 2013 dx.doi.org/10.1021/ie400015a | Ind. Eng. Chem. Res. 2013, 52, 5985−5996

Industrial & Engineering Chemistry Research

Article

this acid−base interaction.17−21 In some cases, the CO2 capacity is even enhanced in the presence of water.21,22 Water vapor was also reported to slow down the degradation of amines.23 Contrary to zeolites and MOFs, where desorption must be done under vacuum, it is possible to regenerate these adsorbents by a purge of water vapor. The purge gas has either the effect of stripping CO2 from the bed (dilution) or heating the bed or a combination of both. The possibility to regenerate by water vapor instead of using vacuum presents a huge advantage since thermal energy is cheaper than mechanical energy. We further have to take into consideration that vapor is more valuable the higher its temperature/pressure is. Low pressure vapor at a moderate temperature level is often abundantly available, sometimes as a waste product. It is, therefore, attractive to use this low pressure vapor for regeneration at a moderate temperature.24 We therefore envisaged to run the sorption swing process more or less isothermally, that is, with a desorption by water vapor at a temperature close to the adsorption temperature, using water vapor at subatmospheric pressure. Running the process without a temperature swing (except for the unavoidable temperature swing in the column due to the exothermic nature of adsorption and the endothermic nature of desorption) minimizes the energy that is wasted to heat and cool the solid sorbent, which presents a high auxiliary energy penalty.3 Vacuum is still necessary for regeneration, but only for avoiding the condensation of water. As a consequence, the desorption pressure can be much higher than in typical VSA processes. The optimal operating temperature is a compromise between the adsorption capacity of the sorbent, (decreases with temperature), the regenerability of the sorbent (increases with temperature), and the thermal stability (decreases with temperature). Figure 1 shows a simplified scheme of the capture process proposed in the previous section, with one column being in

adsorbent. The delta loading is the difference of adsorption capacity under adsorption and desorption conditions. Another challenge that fixed bed adsorption processes for postcombustion CO2 capture have to face is the huge amount of flue gas that has to be treated. The flue gas flow rate in a 600 MW power plant is on the order of 1.8 × 106 Nm3/h, which is six times higher than the amount that is treated by largest PSA plants for H2 purification that are currently in operation. To limit the size and number of the adsorption columns the gas velocity in the adsorbed has to be maximized. However, the gas velocity is limited by constraints of fluidization of the adsorbent particles, of mass transfer in the adsorbent particles, and of pressure drop. A high pressure drop in the bed requires compression of the feed, which increases cost and energy consumption. Lively et al. state that the pressure drop problem renders fixed bed PSA processes economically unviable and promotes structured adsorbent beds, where the adsorbents are packed into hollow fibers.3 It will, however, still take some years before this new technology can be proven on a medium or large scale.4 For our present analysis we therefore stick to traditional fixed bed adsorbers. The choice of appropriate adsorbents is another crucial issue. Several studies have analyzed the performance of zeolite NaX in postcombustion CO2 capture by a VPSA process.5,6 It was shown that NaX adsorbents achieve the desired purity (>95%) and recovery (>80%) of CO2 if either complex cycle is used,7 or in a two-stage PSA configuration where the extract stream of a first PSA unit is treated in a second PSA,8 or in modified dualreflux systems.9 The energy consumption of the VPSA was estimated to be very low, that is, between 0.4 (two-stage PSA)8 and 1.4 GJ/t,9 as compared to 4.3 GJ/t for the MEA process. However, for a fair comparison between the mechanical energy consumed by the VPSA and thermal energy (in the MEA process), a conversion factor of approximately 2.6 has to be applied to the former. Unfortunately, none of the above-mentioned studies gives sufficient information to scale up the VPSA process to the size required for a real power plant. We cannot, therefore, judge whether the size and number of columns are realistic and if the pressure drop is acceptable. Moreover, all the studies cited above have been carried out for a dry feed. In a humid feed (the water content of flue gases may be between 8 and 15%), the performance of NaX is heavily affected due to strong preferential adsorption of H2O by NaX.10 The cost of drying the flue gases upstream of the PSA process has not been reported, but is probably unacceptable. It is possible to run the VPSA with a two layer-adsorbent, that is, a first layer for the adsorption of H2O by, for example, alumina adsorbents followed by a second layer of NaX for the adsorption of NaX,11 but this will necessarily penalize the performance of the process in terms of purity, recovery, and energy consumption. It has recently been shown that some MOF adsorbents have very promising properties for postcombustion CO2 capture, but like NaX they also prefer the adsorption of H2O over CO2 and, therefore, require a dry feed.12−14 Another class of sorbents allows circumventing the problem of H2O in the flue gases: amines immobilized on solid supports. The immobilization may be carried out by grafting, by simple impregnation, or by an in situ surface polymerization.15,16 Solid amine sorbents mimic the chemistry of amine solvents. The acid−base interaction between amino groups and CO2 assures a very high selectivity (quasi-infinite) toward sorption of CO2. The presence of water in the flue gas does not interfere with

Figure 1. Simplified scheme of the partial pressure and vacuum swing adsorption process. One column (ADS) adsorbs CO2 from the flue gas, while the other is regenerated by steam under low pressure. The steam is separated from CO2 by condensation in the CO2 compression train (containing n compression stages) and is recycled after reheating.

adsorption mode, while the other is desorbed by flowing steam under low pressure. The steam is condensed in the CO2 compression train and can be recycled in a closed loop, after reheating to the required temperature. The process consumes mechanical energy, via the feed compressor, the CO 2 compressor train, and the vacuum blower, and thermal energy for reevaporating the condensed steam. 5986

dx.doi.org/10.1021/ie400015a | Ind. Eng. Chem. Res. 2013, 52, 5985−5996


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In this work, we pursue two objectives. First of all, we discuss the range of optimal operating conditions (column dimensions, gas velocities, pressure, etc.) for the concentration (or partial pressure and vacuum) swing process depicted in Figure 1 using a solid sorbent that was tested in our lab. We will show that the criterion of minimizing the energy consumption of the process has to be confronted with other constraints, like the cost of adsorbent and the spatial requirement (adsorber geometry). The second objective is to define the properties of the ideal solid sorbent, so as to define precise targets for the development of new, improved materials.

λ=

uA cA0tA ρ q *L

(1)

p 0

The concentration profile in the bed oscillates around an average concentration profile and can be mathematically described by a perturbation around this average profile. C = C(0) + λC(1) + λ 2C(2) + ... Q = Q(0) + λQ(1) + λ 2Q(2) + ...

(2)

C and Q are the (adimensionalized) concentrations in the gas and in the adsorbed phase, respectively. λ is the throughput ratio. The zero order terms C(0) and Q(0) represent the timeaveraged concentration profiles in the adsorption and desorption step. The higher order terms describe the concentration swing around these average profiles. For our purpose, which is to establish a mass balance of the PSA cycle, the analysis of the zero order term is sufficient. In Hirose’s model, the zero order terms can be calculated as a function of four dimensionless parameters: (i) the ratio of gas velocities in desorption and adsorption γ = uD/uA; (ii) the pressure ratio β = pD/pA; (iii) the nonlinearity of the adsorption isotherm. If a Langmuir isotherm model is used, the nonlinearity can be described by the parameter

2. METHODOLOGY Our ambition is to carry out the design of the adsorption swing process as a function of the adsorption and mass transfer properties of the sorbent. For this purpose, we have to find a model that links the performance of an adsorbent in a pressure swing process to its adsorption isotherm and its mass transfer properties. In general, PSA models involve numerous heavily coupled differential equations that require a numerical solution. It is therefore not straightforward to establish a direct link between the adsorption/transfer properties and the PSA performance, that is, the productivity and recovery. Surprisingly little research has been dedicated to the topic,25,26 with the exception of a series of excellent papers by Hirose and coworkers.27−29 In these papers simplified analytical or graphical solutions of a PSA cycle were established, which allow to define the optimum adsorption isotherm for a desired recovery. We have adapted Hirose’s analytical solution of simple two-step PSA to our problem and have used it for identifying the optimal operation conditions (velocity, ratio of step time) for a given solid amine sorbent. Then, in a second step, Hirose’s modified model is used for defining the equilibrium and mass transfer properties of the ideal solid sorbent.

r=

1 1 + bcA0

(3)

where b is the adsorption constant of the Langmuir model; (iv) the number of transfer units, NTU. NTU =

k(1 − ε)ρp Lq0* uA cA0

(4)

The parameter NTU is intimately related to the number of theoretical plates in a linear rate model. It quantifies the flux between the gas phase and the adsorbed phase, which depends on the mass transfer coefficient k, the contact time L/uA and the thermodynamic driving force: the ratio q*0 /cA0 can be considered as an equilibrium constant of adsorption (K = adsorbed phase concentration/gas phase concentration).

3. MODELING 3.1. Simplified PSA Model. Hirose’s analytical solution of an isothermal PSA cycle with only two steps (see Figure 2),

K=

qo*ρp cA0

(5)

The model implies that the kinetics of sorption is governed by mass transfer whereas the sorption step itself, i.e. the reaction between the solid and the adsorptive, is instantaneous. To simplify the problem mathematically, Hirose does not calculate the concentration profile as a function of NTU, but determines the value of NTU that is required to achieve a given concentration at the column exit cA1. To adapt Hirose’s model to our problem, we have introduced some modifications. The purge gas used for desorption is not recycled from the column effluent, but is pure water vapor. Therefore, the adsorptive concentration in the purge gas entering the column (cD1) is zero. As a consequence, the pressure level of the desorption step, which otherwise determines cD1, becomes irrelevant. We further drop the condition of equal half cycle times tA = tD and allow the desorption time to be longer than the adsorption time. Instead we impose the condition uD = uA = u so as to have approximately the same pressure drop in the bed during adsorption and desorption. We will see later that the pressure

Figure 2. Scheme of the two-step PSA cycle in (a) Hirose’s initial model and (b) in our modified model.

adsorption and desorption, relies on the short cycle time approximation. PSA operation is most efficient when the cycle time is short, that is, when the adsorbent bed is frequently switched between adsorption and desorption. Under these conditions the so-called throughput ratio λ, the ratio between the amount of adsorptive that enters the bed during a cycle and the maximum amount that the bed can adsorb at equilibrium, is small. 5987



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drop fixes the length of the bed. Since the relevant parameter is the amount of material entering the column, that is, the product u·t, the ratio φ = tD/tA in our modified model replaces the ratio γ = uD/uA in the initial model of Hirose. Our modified model is not a 2-column PSA any more. φ determines the ratio between the number of columns in desorption and the number of columns in adsorption mode. The expression for NTU in the modified model is (the derivation is provided in the Supporting Information):

K is the average slope of the isotherm, which we approximate by eq 5. Diffusion in macropores can be described as a mixture of molecular diffusion and Knudsen diffusion. For macropores in the micrometer range, the former mechanism dominates. Hence, the macropore diffusion coefficient Dmacro is given by the molecular diffusion coefficient Dm divided by the tortuosity of the particle τ. In the limiting case, where mass transport in the primary particles becomes fast compared to transport in the macropores, the expression for Dp becomes

⎡ 1 + φ (1 − r )2 ⎢ 1 (1 − CA12) ⎢ φ(φ − 1) r ⎣2

NTUA =

⎛ r φ ⎞ +⎜ (1 + φ) − CA1 ⎟(1 − CA1) φ − 1⎠ ⎝1 − r 2 ⎛ r φ − 1 + CA1 ⎤⎥ CA1 ⎞ + φ⎜ − ⎟ ln ⎥⎦ φ − 1⎠ CA1φ ⎝1 − r

Dp =

(6)

(1 − CA1)tA L

(1 − CA1)tA + (1 − yCO2 )ε u

A

(7)

3.2. Mass Transfer Considerations. Equation 6 was derived under the hypothesis that internal mass transfer in the adsorbent particle is governing the transport. We have verified that external mass transfer in the film surrounding the adsorbent particles is indeed very fast and not at all ratelimiting at the high gas velocities employed in CO2 capture. The mass transfer coefficient k can be assimilated to30

k=

Δpfluidization = (ρp − ρg )g (1 − ε)L

Δp = 0.75Δpfluidization = 0.75(ρp − ρg )g (1 − ε)L

(12)

Fixing the pressure drop, therefore, fixes the length of the bed. According to the Ergun equation, the pressure drop depends on u and dp:

(8.)

Dp is the diffusion coefficient in the particle and dp is the particle diameter. In section 5.2. we will consider an alternative scenario where the adsorbent particle has a hierarchical structure: small primary particles are agglomerated to a larger secondary particle. Diffusion from the external surface to the primary particles occurs via a macropore network. In that case, the relation for the mass transfer coefficient is31 2 d p2 Kd p2 d p,primary 1 = = + k 60Dp 60εpDmacro 60Dp,primary

(11)

We have decided to fix the actual pressure drop of the bed to 75% of the value that would lead to fluidization; that is,

60Dp d p2

(10)

τK

3.3. Application of the Simplified PSA Model to the CO2 Capture Process. As we have mentioned in the introduction, our objective is to minimize the energy consumption of the concentration swing process. The energy consumption depends on three parameters: • the amount of steam needed for regeneration; • the pressure level in the desorption step; • the inlet pressure of the flue gas, which must be sufficient to overcome the pressure drop in the column. The amount of steam needed for regeneration is proportional to φ (see Appendix). The desorption pressure is not a parameter of the simplified PSA model. We will ignore its influence until the last section of this paper where we will discuss the transition to real PSA cycles. The inlet pressure of the flue gas is also not a direct parameter of the simplified PSA model, although it slightly modifies the value of the nonlinearity parameter r (see eq 3) by changing the value of cA0. However, the pressure drop (which imposes the minimal inlet pressure) has a strong indirect impact on the hydrodynamic parameters of the bed, that is, on the values of L, u, and dp. The relationship between the bed length L, the gas velocity u, and the particle size dP is subject to two constraints: the acceptable pressure drop in the bed and the fluidization of the adsorbent particles, which must be avoided. Fluidization occurs when the upward force exerted on the bed by the pressure drop becomes higher than the weight of the bed. This condition can be mathematically expressed as

For a given ratio φ = tD/tA and a given nonlinearity of the isotherm we need the number of transfer units defined by eq 6 in order to achieve an average concentration CA1 = cA1/cA0 at the column exit. For our simulations, we require a CO2 capture rate of 90%; that is, CA1 = 0.1. The value of tA does not intervene in Hirose’s model equations, only the ratio tA/tD counts. The adsorption is, however, subjected to the constraint that the recovered CO2 must have a purity of more than 95%. The CO2 that is captured during each adsorption cycle is mixed with N2 present in the interstitial volume of the column. The longer the adsorption time, the higher is the amount of adsorbed CO2 compared to N2. Considering that the bulk phase at the end of the adsorption step is at the feed composition, and assuming that all the CO2 injected with feed during adsorption is equal to the working capacity of the adsorbent, the purity of CO2 can be approximated as pur =

εpDm

ρg u 2 1 − ε Δp 150μu (1 − ε)2 = + 1.75 L dP ε 3 dp2 ε3

(13)

uA and dp are antagonists in eq 13. To keep the pressure drop constant at a fixed value, the particle size must increase when the gas velocity increases. dp can be calculated as a function of uA or vice versa by solving the quadratic equation. In conclusion, fixing the pressure drop fixes the length of the bed (via the constraint of fluidization) and fixes a relationship between u and dp via the Ergun equation, that is, only one of the three parameters L, u, and dp remains a free variable.

(9) 5988



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3.4. Simulations of a Full PSA Cycle under Adiabatic Conditions. To validate the feasibility of the proposed concentration swing process, we have carried out simulations of a full PSA cycle, under adiabatic conditions. The model equations are provided in the Supporting Information. The pressure drop in the column was neglected in the simulations, but thermal effects were taken into account (in contrast to the simplified PSA model). A simple Skarstrom cycle was chosen, the only modification being that depressurization was carried out cocurrently (Figure 3). This modification significantly

amine was chosen so as to impregnate 70% of the mesopore volume of the adsorbent, which is 0.84 mL/g. The CO2 adsorption isotherm on this solid at 348 K can be represented by the Langmuir model (eq 14) with the parameters qsat = 2.13 mol/kg and b = 116 bar−1. The apparent density of the material is 1080 kg/m3. These parameters are compiled in Table 1. Table 1. Parameters of the Base Case Adsorbent b (348 K) qsat intraparticle diffusion coefficient ρp

The mass transfer coefficient of the adsorbent was estimated from breakthrough experiments at different gas velocities and different particle sizes.32 The particle size had an influence on the shape of the breakthrough curve, which allowed estimation of an intraparticle diffusion coefficient of Dp = 5 × 10−11 m·s−2. For the smallest particle size (100−200 μm) that was tested in the above-mentioned study, this yields a characteristic time of diffusion of dp2/(60KDp) = 0.03 s. Although we cannot precisely estimate the role of the chemical reaction between CO2 and the amine in the adsorption kinetics, we can state that the characteristic time of the chemical reaction must be lower than the value of 0.03 s. 4.2. Application of the Simplified PSA Model to the Base Case Adsorbent. Our calculations were carried out for a CO2 concentration in the flue gas of 15%. The other flue gas components are considered as inert. We chose for a first calculation a pressure drop of 0.25 bar. On the one hand, higher pressure drops consume more energy and may also require a switch to a more expensive compressor technology. On the other hand, lower pressure drops may lead to an uneven distribution of the gas in the column (deviation from plug flow). The average pressure in the bed was, thus, 1.125 bar, which yields a nonlinearity parameter of the isotherm of r = 0.049 (since r depends on cA0 its value varies slightly with the pressure). Having fixed the pressure drop, the parameter that we need to optimize in order to minimize the energy consumption is φ. φ is proportional to the consumption steam in the regenration step (see Appendix). We have to aim for a low φ, that is, a short (and therefore incomplete) regeneration of the bed. Equation 6 calculates the relationship between NTU and φ. It is exemplified in Figure 4 for the nonlinearity parameter r of the base case adsorbent. Figure 4 shows that a shorter regeneration (lower φ) has to be

Figure 3. Skarstrom cycle used for the simulations of a “real” PSA system.

increased the CO2 capture rate. The durations of adsorption and the desorption steps were varied in order to reach the target purity and recovery of CO2. As in the simplified model the gas velocity in both steps was the same. The durations of the depressurization and pressurization steps were fixed at a fairly high value, in order to improve the numerical stability of the simulation. Therefore, the system is not optimized in terms of productivity, and productivity data will not be reported. The adsorption of CO2 on the solid sorbent was represented by a Langmuir isotherm q = qsat

bpCO

2

1 + bpCO

2

(14)

The temperature dependence of the adsorption constant b was described by a van’t Hoff equation

b = b0e−ΔHCO2 /(RT )

116 Pa−1 2.13 mol/kg 5 × 10−11 m2·s−1 1080 kg/m3

(15)

CO2 was considered to be the only adsorbable component in the feed, at a concentration of 15%. Making reference to Figure 1, we assumed that the flue gas arrived at a temperature of 313 K from upstream deNOx and deSOx treatment and was heated to the temperature of adsorption in the feed compressor. Adsorption temperature and pressure were, therefore, linked by the characteristics of the compressor.

4. ANALYSIS OF THE CONCENTRATION SWING PROCESS FOR A BASE CASE ADSORBENT 4.1. Description of the Base Case Adsorbent. The sorbent used for our case study was described in an earlier publication.32 It is tetraethylenepentamine (TEPA) impregnated on the mesoporous silica Grace X254. The amount of

Figure 4. Relationship between NTU and φ = tD/tA for an outlet concentration CA1 = 0.1 and a nonlinearity constant r = 0.049. 5989



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compensated by an increase in the number of transfer units. In other words, we can afford to spend less steam (less purge gas) for regeneration, if mass transfer is very fast (high k) and/or if the contact time L/u is very long (see eq 4). The mass transfer coefficient k can be increased by decreasing the particle size dp. The contact time L/u can be increased by decreasing the gas velocity (L being fixed by the pressure drop). Note that increasing the contact time means decreasing the productivity of the process (the amount of flue gas that can be treated by a given amout of sorbent). We have seen in section 3.3 that the particle diameter and the gas velocity are not independent parameters. The Ergun equation gives the smallest possible value of dp for a given gas velocity. If we inject all that information into the expression for NTU (eq 4), we can calculate NTU as a function of the gas velocity: NTU = =

60Dp 2

[d p(u)]

(1 − ε)K

Figure 6. Evolution of φ and of the total mass of adsorbent as a function of the gas velocity. Numbers were calculated for the base case adsorbent with a pressure drop of 0.25 bar and a feed flow rate of 1.76 × 106 Nm3/h.

L u

60Dp

Δp K [d p(u)] 0.75(ρp − ρg )g u 2

(16)

velocities, the mass of sorbent is high because the contact time is large. At high velocities, the contact time is low, but there are many beds in desorption for one bed in adsorption. Hence, the total mass increases. The sorbent mass is minimized at intermediate gas velocities (see Figure 6). A similar result is obtained for the total cross section of the beds (adsorbers and desorbers). The economic optimum depends on how the capital costs, mass of sorbent and number and size of columns, are weighed against the operating costs, the vapor consumption for regeneration, which is proportional to φ. To give an example, at u = 0.20 m/s, φ = 1.8 and the mass of sorbent is still close to its minimum value. At this velocity, the total mass of sorbent is 26 500 tons, the total cross section of the beds is 7800 m2 and the particle size is 1.1 mm. For the chosen pressure drop of 0.25 bar, the length of the bed is 5.0 m. Sorbent mass and cross section are huge. It will be necessary to use new, innovative bed geometries that allow achieving these enormous cross sections without occupying too much space. For the calculations above we had arbitrarily fixed the pressure drop to 0.25 bar. The pressure is a very important parameter because it determines the energy consumption of the feed compressor. If our objective is to minimize the energy consumption of the process we have to minimize at the same time the pressure drop and the vapor consumption for regeneration (Δp and φ). To perform this exercise at equal sorbent cost, we have looked for couples of Δp and φ that lead to the same total mass of sorbent. This exercise can be realized as follows: fixing the mass of solid fixes the ratio L/u*(1 + φ). L (1 + φ) = const (17) u

The plot of NTU as a function of the gas velocity is shown in Figure 5. The number of transfer units rapidly decreases with

Figure 5. Relationship between NTU and the gas velocity uA: ε = 0.37, ρp = 1080 kg/m3, Dp = 5 × 10−11 m·s−2, Δp = 0.25 bar, K = 375.

increasing gas velocity. Increasing the gas velocity has a double impact on NTU, first via decreasing the contact time L/u and second because it requires an increase of the particle size dp(u) in order to keep the pressure drop constant. As a next step we link the information of Figure 4 and Figure 5, in order to establish a relationship between φ (the desorption time ≡ the steam consumption) and the gas velocity u. For this purpose, the curve in Figure 4 was fitted by a power function and combined with eq 16. The result is shown in Figure 6: the ratio between the desorption and adsorption time steeply increases with increasing gas velocity. Higher gas velocities lower the number of transfer units, and this has to be compensated by a higher steam consumption in the desorption step. If our sole objective is the minimize the steam consumption it would be best to run the process at the lowest possible gas velocity. A low gas velocity, however, means a low productivity: the contact time and, therefore, the bed volume, that is, the mass of sorbent, is large. The total mass of adsorbent depends on two factors: (i) it is proportional to the contact time; (ii) it depends on the number of beds in desorption for one bed in adsorption, that is, φ. The total mass of adsorbent is therefore roughly proportional to L/u*(1 + φ). We have added a plot of the mass of adsorbent to Figure 6. The numbers are valid for a feed volume of 1.76 × 106 Nm3/h, which is the flue gas volume produced by a 600 MW power plant.33 At very low

We arbitrarily choose a value of φ and calculate the corresponding NTU via eq 6. The parameters L, u, dp, and Δp are then determined by solving the system of equations given by eq 16, 17, the Ergun equation (eq 13) and fluidization condition (eq 12). The results are shown in Table 2, for a constant mass of sorbent of 30000 t. If we increase φ, that is, if we increase the amount of steam spent for regeneration, we can afford to decrease the number of transfer units, that is, we can raise the gas velocity. At constant mass of adsorbent, raising the gas velocity means decreasing the cross section of the adsorption columns, while increasing their length. As a consequence, the pressure drop increases. 5990



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and φ. It depends on the nonlinearity of the isotherm. Highly nonlinear isotherms (very low values of r) are difficult to regenerate. This has to be compensated by an increase in NTU (faster mass transfer, longer contact time, or higher capacity) or by raising the time spent for regeneration (φ). A completely linear isotherm (r = 1) is optimal for regeneration, but does not have any compressive effect on the breakthrough front and leads to more dispersed concentration profiles. To define the optimal nonlinearity of the isotherm we have plotted the evolution of NTU as a function of r for three fixed values of φ in Figure 7. Figure 7 shows that the required number of transfer units first decreases with increasing r and then remains almost stable. Since we authorize a rather high average CO 2 concentration in the raffinate stream (CA1 = 0.1), the positive effect of a more linear isotherm on regeneration dominates over the negative effect of dispersing the concentration profiles. The minimal NTU values are obtained when r is between 0.3 and 0.6. The lower is the value of φ, the higher is the optimum value of r. This makes sense. The less energy we want to spend for regeneration, the more linear the optimal isotherm should be. NTU depends on mass transfer, contact time, and the adsorption capacity q0*. If we assume that the adsorption capacity and the mass transfer coefficient are independent of r, NTU is a measure of the contact time, that is, it is proportional to the mass of adsorbent. In the above reasoning we assumed that the adsorption capacity q0* remains constant when the isotherm becomes more linear. This assumption is not realistic because it implies that the adsorption capacity at saturation qsat increases when r increases, as we can see from the relation between q0*, qsat, and r (obtained by injecting eq 3 into eq 14):

Table 2. Gas Velocity, φ, Particle Diameter, Length of Bed, Total Cross Section of the Beds and Number of Transfer Units as a Function of the Pressure for a Fixed Total Mass of Sorbent (30 000 t) φ

Δp (bar)

uA (m/s)

dp (mm)

L (m)

Stot (m2)

NTU

1.05 1.1 1.2 1.5 2.0 2.5

0.14 0.17 0.22 0.30 0.35 0.33

0.08 0.09 0.12 0.19 0.25 0.32

0.57 0.63 0.74 0.96 1.19 1.43

2.8 3.4 4.3 6.1 6.9 6.5

15660 13000 10160 7300 6350 6760

85 67 47 24 13 9

Summing up the reasoning above, at constant total mass of solid sorbent, when φ increases, the pressure drop also increases. Increasing φ and Δp increases the energy consumption and is, therefore, undesirable. The best solution is obviously to run the process at a very low pressure drop, that is, at very low gas velocity. However, under these conditions, the total cross section of the beds is enormous, while the length of the bed is only a couple of meters. At higher gas velocities, the adsorbers become taller sizes (bed length of 6−7 m) and their cross section decreases, but the energy consumption of the process rises (because Δp and φ increase). If we took a column diameter of 8 m, more than 100 columns would be needed to generate the cross section of 6350 m2, which is the smallest value in Table 2, achieved for unfavorable values in terms of energy consumption (φ = 2, Δp = 0.35 bar). Decreasing the steam consumption and the pressure drop by roughly a factor of 2 (φ = 1.1, Δp = 0.17 bar), almost doubles the total cross section of the columns. These data demonstrate the need for new adsorber geometries that allow creating huge cross sections in combination with low bed lengths, so as to be able the put into practice energetically favorable process designs with a very low pressure drop. We further note that for values of φ > 2 (last entry in Table 2), the total cross section rises again because the number of columns in regeneration mode increases.

qsat =

q0* 1−r

(18)

Instead, it makes more sense to assume that the adsorption capacity at saturation qsat is constant, because it is limited, for example, by the pore volume available for the impregnation of an amine. In that case, q*0 decreases when the isotherm becomes more linear: q0* = qsat(1 − r). To account for this loss of capacity when the isotherm becomes more linear, we have to look at the evolution of NTU/(1 − r) as a function of r (see eq 4). At constant qsat and constant mass transfer, NTU/(1 − r) is proportional to the contact time. Figure 7b shows that if we take into account the capacity effect, the minimum of r

5. STUDY OF THE IDEAL ADSORBENT 5.1. The Optimal Nonlinearity of the Adsorption Isotherm. A very attractive feature of Hirose’s PSA model is that it can be used to determine the properties of the adsorbent that will lead to the best process performance under isothermal conditions. Equation 6 shows the relationship between NTU

Figure 7. Relationship between NTU and the nonlinearity of the isotherm (r) for different values of φ, (a) with the assumption of constant q*0 (b) with the assumption of constant qsat. 5991



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10−6 m2/s for Dmεp/τ vs DpK = 1.5 × 10−8 m2/s for our base case adsorbent, an improvement of 2 orders of magnitude. Since the effective diffusion coefficient in the hierarchical particle is very high, we can increase the gas velocity, while still maintaining the value of NTU high, that is, we can increase the productivity without sacrificing the quality of separation. In this scenario of very fast transport, there is a risk that the chemical kinetics of adsorption may become the limiting factor. We, therefore, verified, whether the characteristic time of mass transport was still higher than the upper limit of the characteristic time of the chemical reaction that we had estimated in section 4.1, that is, 0.03 s. For the optimal solutions that will be discussed in the next section, the hypothesis of chemical kinetics not being limited was always valid. 5.3. The Optimal Solid Sorbent. As explained above, the optimal solid sorbent displays a hierarchical pore structure, where transport is limited by molecular diffusion in the macropores. Its isotherm is characterized by a nonlinearity parameter of r = 0.2 − 0.6. r = 0.22 was chosen as a realistically attainable value (vide supra). Finally, we suppose that it should be possible to improve the saturation capacity of the sorbents. For example, our base case amine sorbent has an amine loading of ∼8 mol N/kg, but its saturation capacity is only ∼2 mol/kg, which is only 50% of the theoretical maximum of 4 mol/kg. It has recently been shown that advanced preparation methods lead to a better dispersion of the polyamine and hence a better accessibility of the amine groups.34 We, therefore, postulate that a saturation capacity of 4 mol/kg should be within reach, either by increasing the accessibility and/or the amine loading. To evaluate the gain that can be achieved by improving either the nonlinearity of the isotherm, the saturation capacity or mass transfer, we compared our base case adsorbent (i) with a hypothetical sorbent with improved nonlinearity (r = 0.22), but the same saturation capacity and (ii) with another hypothetical sorbent with improved nonlinearity and improved capacity (qsat = 4 mol/kg). Concerning mass transfer, two different assumptions were compared. In the first case, mass transfer takes place in the amine phase throughout the whole sorbent particle. The diffusion coefficient was supposed to be identical to the one found for our base case sorbent (Dc = 5 × 10−11 m2/s). For the second case, we considered sorbent particles with a hierarchical pore structure where the active amine phase is confined to small primary particles that are alimented with CO2 via a macropore network. The primary particles are supposed to be sufficiently small so that their mass transfer resistance is negligible. Mass transfer resistance is therefore entirely confined to the macropores. The hierarchical pore structure was accounted for in the density of the material, which was corrected by a factor (1 − εp). To compare the six hypothetical materials at constant energy consumption, we arbitrarily fixed φ to 1.5 and Δp to 0.25 bar. For each case, NTU was calculated as a function of φ and r via eq 6. The length of the bed was determined from the pressure drop and density of the adsorbent (eq 12). The gas velocity u could then be calculated from eq 16 (mass transfer in adsorbed phase) or eq 20 (mass transfer in macropores). The particle diameter dp results from the Ergun equation (eq 13). The total cross section of the adsorbers is given by

becomes a lot more pronounced. Compared to Figure 7a, the optimal r values are shifted to lower values because higher nonlinearity improves capacity. The r-value of our base case adsorbent is ∼0.05. The nonlinearity depends on the magnitude of the adsorption constant b.

b1 = b2

1 − r1 r1 1 − r2 r2

(19)

To pass from r = 0.05 to, for example, r = 0.33, b has to decrease by a factor of 10. This can be achieved by increasing the temperature of the process. A recent paper reported that the heat of sorption of a TEPA-impregnated solid is −50 kJ/ mol.17 Applying the van’t Hoff equation (eq 15), we calculate that an increase of the adsorption temperature from 348 to ∼400 K would bring about the desired decrease of b by a factor of 10. At 400 K, however, the thermal stability of impregnated amines is insufficient and they degrade and/or volatilize quite rapidly. The adsorption constant b can also be changed by modifying b0 and/or the heat of adsorption. A decrease of b by a factor of 10 corresponds to a decrease of the heat of sorption by 6.7 kJ/ mol. We judged that a decrease of the heat of adsorption of 5 kJ/mol should be feasible. This corresponds to a reduction of b by a factor of 5.6 and leads to a value of r = 0.22, which is sufficiently close to the minima in Figure 7. 5.2. Improving Mass Transfer. Mass transfer in our base case adsorbent is rather slow, which presents an important handicap for its performance. Mass transfer is slow not because of the small diffusion coefficient, but because the diffusion pathway to penetrate into the center of the millimeter sized particle is long. Mass transfer could be improved by reducing the particle size, but a lower limit is imposed by the constraints of pressure drop and fluidization. Zeolite adsorbents like NaX (13X) have much lower intracrystalline diffusion coefficients than our impregnated amine. Mass transfer in NaX is faster because the crystal size is only a few micrometers. Transport from the outer particle surface to the crystals takes place through mesopores/macropores where the diffusion coefficient is high. By adopting suitable synthesis and shaping methods, it should be possible to transpose this hierarchical pore structure to amine support materials. The objective is to prepare small mesoporous silica particles in the submillimeter range, which are impregnated by an amine. These small primary particles are aggregated to larger secondary particles via a macropore network that is, in the ideal case, free of amine. If the primary particles are sufficiently small, their transport resistance becomes negligible compared to the diffusion in the macropores. In that case, the intraparticle diffusion coefficient is given by eq 10 and the expression for NTU becomes NTU =

60 εpDm L (1 − ε) 2 u τ dp

(20)

Under the assumption that mass transfer is limited by the diffusion in the macropores, NTU does not depend on the adsorption capacity of the solid any more. The relation between NTU and the gas velocity is analogous to eq 16, but the term DpK is replaced by Dmεp/τ. For a 15% CO2/N2 mixture at 348 K, the molecular diffusion coefficient of CO2 is 2 × 10−5 m2/s. Typical values of the particle porosity εp and of the tortuosity τ are 0.3 and 2.0, respectively. We, thus, obtain a value of ∼3 ×

Stot =

Ffeed (1 + φ) u

(21)

and the total mass is calculated from 5992



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Table 3. Effect of the Nonlinearity of the Isotherm (r), the Adsorption Capacity qsat, and the Type of Diffusion Resistance on the Total Mass and the Total Cross Section of Sorbenta r 0.05 0.22 0.22 0.05 0.22 0.22 a

qsat (mol/kg) 2.13 2.13 4 2.13 2.13 4

K 375 307 575 263 215 403

diffusion limitation adsorbed phase adsorbed phase adsorbed phase macropore macropore macropore

Dmεp/τ or DpK (m2 s−1) 1.9 1.5 2.9 3.1 3.1 3.1

× × × × × ×

−8

10 10−8 10−8 10−6 10−6 10−6

dp (mm)

φ

u (m/s)

mtot (103 t)

L (m)

Stot (m2)

0.9 1.2 1.5 6 9 9

1.5 1.5 1.5 1.5 1.5 1.5

0.17 0.25 0.32 0.91 1.16 1.16

27.0 18.5 14.5 5.2 4.0 4.0

5.0 5.0 5.0 7.1 7.1 7.1

8000 5450 4300 1530 1200 1200

Values obtained at a constant pressure drop of Δp = 0.25 bar.

mtot = StotLρp (1 − ε)

Table 4. Parameters of the Solid Sorbent Used for the Simulations of a Full PSA Cycle under Adiabatic Conditions

(22)

All these parameters are compiled in Table 3 for each of the six hypothetical materials mentioned above. Table 3 shows that improving the nonlinearity of the isotherm or improving the sorption capacity (to a lesser extent) both help to reduce the total mass of sorbent (for a fixed value of φ). The most dramatic increase is achieved, however, by shifting the mass transfer resistance from the primary particles to the connecting macropore network. Under these conditions the sorbent mass decreases to less than 5000 t and the total cross section of the adsorbers is in the order of ∼1000 m2. These values become reasonable. Hirose’s model, therefore, suggests that it is more important to work on mass transfer than to improve the regenerability or the capacity of the adsorbents.

−50 kJ/mol

b0 qsat diffusion coefficient in the adsorbed phase porosity of the particles εp ρp Cp dp diameter of the primary particles τ

6.5 × 10−12 Pa−1 2 mol/kg 5 × 10−11 m2·s−1 0.35 750 kg/m3 1300 J·kg−1·K−1 3 × 10−3 m 10 × 10−6 m 2

estimated by summing the heat capacities of silica and of the amine. A first round of simulations was carried out for a base process temperature of 343 K (see Table 5). The simulations confirm that it is possible to achieve the target purity (>95%) and recovery (>90%) of CO2. The consumption of steam (per CO2 recovered) is comparable to the values obtained in the simplified PSA model. The temperature swing in the column is −13 K in desorption and approximately +30 K in adsorption. By applying rule 23, we can deduce the highest possible desorption pressure that will avoid condensation of vapor in the column. It is 0.2 bar. This desorption pressure is significantly higher than in pure VSA processes where the vacuum level is at least a factor of 4 lower,36,37 but for economic reasons (capital expenses for the CO2 compression train), it would be attractive to further increase the desorption pressure. This is only possible by increasing the temperature in the adsorption columns. We have, therefore, carried out a second round of simulations at a higher process temperature of 363 K. This allows raising the desorption pressure to 0.5 bar. Since regeneration becomes easier at the higher temperature, we can also decrease the value of φ compared to the simulations at 343 K. Yet, since the desorption pressure is higher, we actually spend a larger amount of H2O for regeneration than at 343 K (see eq 26). Moreover, the maximum temperature in the bed during adsorption rises to 385 K, which is a range where the thermal stability of the amine becomes critical. Hence, the potential for improving the process economics by increasing the operating temperature is rather limited.

6. FROM THE SIMPLIFIED TOWARD A REAL SYSTEM: TAKING INTO ACCOUNT HEAT EFFECTS IN A FULL PSA SIMULATION All the calculations in the previous sections were carried out under the assumption that the column is isothermal. This is a very strong hypothesis since it is well-known that thermal effects have a large impact on the performance of an adsorption process.7 The temperature rise during adsorption and the temperature drop during desorption diminish the cyclic adsorption capacity of the bed compared to isothermal operation. In the simplified PSA model, this effect could, in first approximation, be taken into account by replacing the adsorption isotherm by an adiabate.35 Yet, for our specific system, which uses steam as the purge gas used for desorption, an additional factor has to be taken into account, which cannot be evaluated in the simplified model. If the temperature in the column drops during desorption, steam may condense. The desorption pressure must, therefore, be chosen as a function of the lowest temperature that may occur in the column, in order to avoid the risk of condensation. We applied the following rule to fix the desorption pressure: pD = pvap,H2O (Tmin ,col − 10K )

ΔHCO2

(23)

The desorption pressure is set to the vapor pressure of water at the lowest temperature in the column (Tmin,col) during the cycle, with a security margin of 10 K. To obtain the value of Tmin,col, simulations of a full PSA cycle under adiabatic conditions were carried out. The parameters of the solid sorbent used for the simulations are compiled in Table 4. It has a Langmuir adsorption constant that is 5.6 times smaller than that of our base case sorbent, a heat of adsorption of −50 kJ/ mol, and a hierarchical porosity with small primary particles, so as to ensure a fast mass transport. The heat capacity Cp was

7. CONCENTRATION SWING ADSORPTION PROCESS VS MEA We have carried out a technico-economic analysis to confront the proposed concentration swing adsorption with a reference MEA process, for the case of a 630 MWe power plant. The high temperature option (operating temperature of 363 K) of the preceding section was used for this exercise. According to the 5993



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Table 5. Key Input Parameters and Results of the Simulations of an Adiabatic PSA Cycle base temperature (K)

pA (bar)

pD (bar)

purity CO2

recovery CO2

nH2O/nCO2

φ

Tmin (K)

Tmax (K)

343 363

1.43 1.67

0.2 0.5

99.5% 95.7%

98.7% 98.2%

1.54 2.10

1.65 1.05

331 355

372 385

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process simulation, the “isothermal” adsorption process withdraws 10 times less steam from the power plant than the MEA process, because a large fraction of the low pressure steam needed for regeneration of the solid sorbent can be generated by heat integration with the CO2 compression train and other low temperature heat sources. On the other hand, the consumption of electrical power is much higher, due to the additional compressors upstream and downstream of the sorption process. Overall, the two processes are comparable in terms of energy consumption and capital expenses and the choice between the two processes will subtly depend on factors like the operating conditions, the possibilities for heat integration and the size of the installation.

APPENDIX

Relationship between φ and the Energy Consumption for Regeneration

The energy consumption for regeneration of the sorbent is proportional to the amount of vapor needed in the desorption step. This vapor is condensed at low temperature at the column exit in order to separate it from CO2 before entering into the CO2 compression train and its energy content is thereby lost. The molar amount of vapor consumed for regeneration is p nH2O = FH2O D t D (24) RT The relevant figure is the amount of vapor consumed per amount of CO2 capture. The molar amount of CO2 captured in the adsorption step is, for a capture rate of 90%: p nCO2 = yCO2 Ffeed A tA 0.9 (25) RT

8. CONCLUSIONS Most studies on solid amine sorbents for postcombustion CO2 capture consider temperature and/or vacuum swing sorption processes. Temperature swing has the disadvantage that considerable amounts of sensible heat are wasted in heating and cooling the solid between adsorption and desorption. Vacuum swing processes, on the other hand, are penalized by the very low pressure levels required for efficient regeneration. In this work we present an alternative solution, that is, a close to isothermal concentration swing process, which relies on the use of purge gas (low pressure vapor) to regenerate the solid sorbent. The design of the fixed bed process was optimized based on a simplified analytical solution of a PSA process. The calculations show that the overall energy consumption of the process (energy of upstream compression of the feed and thermal energy of the purge gas vapor) is minimized when the system is operated at a very low gas velocity and a low pressure drop. However, low gas velocities mean huge cross sections of the adsorbers. The estimations of the required cross sections are utopist and ask for significant improvements of the solid sorbent and/or for radically new adsorber designs. We have, therefore, used the simplified analytical PSA model in order to define target properties of an ideal solid sorbent, in terms of equilibrium and mass transfer properties. The surprising conclusion is that the biggest gain can be achieved by improving mass transport. The mass transport coefficient could be increased by several orders of magnitude by using a support material, which has a hierarchical structure where the active amine phase is confined to small primary particles that are alimented with CO2 via a macropore network. In this configuration, the diffusion in the adsorbed phase is not rate limiting any more. A surprising consequence of such a configuration is that the capacity of the solid becomes irrelevant for the process performance, at least in the simplified, isothermal PSA model: NTU does not depend on q*0 any more. Only the nonlinearity of the isotherm counts. The optimal adsorption isotherms are characterized by a nonlinearity parameter r = 0.2−0.6. Values close to r = 0.2 are probably attainable by improving current solid amine sorbents. The feasibility of the concentration (partial pressure and vacuum) swing process was proven by simulations of a full PSA cycle under adiabatic conditions.

The ratio between the two molar amounts is uDpD t D nH2O 1 1 = = γφβ nCO2 yCO2 uA pA tA 0.9 yCO2 0.9

(26)

Equation 26 shows that the energy consumption is directly proportional to φ. Verification of the Short Cycle Time Approximation

Hirose’s analytical PSA model is strongly based on the short cycle time approximation, that is, on the condition that the throughput ratio must be fairly low. According to Hirose and Minoda,27 the simplified PSA model agrees well with a full numerical simulation if the throughput ratio is less than 0.5. The throughput ratio can be expressed as the ratio of the adsorption time tA and the retention time L/u, divided by the adsorption constant K = ρpq*0 /cA0. t 1 λ= A tc (1 − ε)K (27) From the condition pur = 0.95 and eq 6, we can calculate the required ratio tA/tc; tA/tc must be higher than 44 in order to assure the required purity. To fulfill the condition λ < 0.5, the adsorption constant K must be K>

44 = 140 0.5(1 − ε)

This was the case for all the materials discussed in this study. Symbols

b = adsorption constant of the Langmuir isotherm [m3 mol−1 or bar−1] b0 = pre-exponential factor of the adsorption constant [m3 mol−1 or bar−1] c = gas phase concentration of the adsorptive [mol/m3] C = normalized gas phase concentration (with respect to c0) c0 = concentration of the adsorptive in the feed [mol/m3] Dm = molecular diffusion coefficient [m2 s−1] Dp = diffusion coefficient in the particle [m2 s−1] dp = particle diameter [m]

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Ffeed = feed flow rate [m3 s−1] FH2O = flow rate of vapor during desorption [m3 s−1] K = dimensionless adsorption constant = ρp q0*/cA0 k = mass transfer coefficient [s−1] L = column length [m] nCO2 = amount of CO2 captured in one cycle [mol] nH2O = amount of vapor consumed for regeneration in one cycle [mol] NTU = number of transfer units p = pressure [bar] pur = purity of the recovered CO2 [%] q = adsorbed quantity [mol/kg] Q = normalized adsorbed phase concentration (with respect to q*0 ) q0* = adsorbed quantity at equilibrium with the feed [mol kg−1] qsat = adsorption capacity at saturation [mol kg−1] R = Boltzmann constant = 8.314 J mol−1 K−1 r = nonlinearity of the Langmuir isotherm =1/(1 + bc) T = temperature [K] tA = adsorption time [s] tc = contact time = L/u [s] tD = desorption time [s] u = superficial gas velocity [m s−1] yCO2 = mol fraction of CO2 in the feed β = pressure ratio = pD/pA γ = velocity ratio = uD/uA ΔH = heat of sorption [J mol−1] Δp = pressure drop [Pa] ε = porosity of the bed (fixed at 0.37 in this study) λ = throughput ratio = feed amount per cycle/capacity of the bed μ = viscosity of the gas [Pa s] ρg = gas density [kg m−3] ρp = density of the solid particle [kg m−3] τ = tortuosity φ = ratio between desorption and adsorption time = tD/tA

(2) Ho, M. T.; Allinson, G. W.; Wiley, D. E. Reducing the Cost of CO2 Capture from Flue Gases Using Pressure Swing Adsorption. Ind. Eng. Chem. Res. 2008, 47, 4883. (3) Lively, R. P.; Chance, R. R.; Koros, W. J. Enabling Low-Cost CO2 Capture via Heat Integration. Ind. Eng. Chem. Res. 2010, 49, 7550. (4) Lively, R. P.; Chance, R. R.; Kelley, B. T.; Deckman, H. W.; Drese, J. H.; Jones, C. W.; Koros, W. J. Hollow Fiber Adsorbents for CO2 Removal from Flue Gas. Ind. Eng. Chem. Res. 2009, 48, 7314. (5) Chue, K. T.; Kim, J. N.; Yoo, Y. J.; Cho, S. H.; Yang, R. T. Comparison of Activated Carbon and Zeolite 13X for CO2 Recovery from Flue-Gas by Pressure Swing Adsorption. Ind. Eng. Chem. Res. 1995, 34, 591. (6) Ko, D.; Siriwardane, R.; Biegler, L. T. Optimization of Pressure Swing Adsorption and Fractionated Vacuum Pressure Swing Adsorption Processes for CO2 Capture. Ind. Eng. Chem. Res. 2005, 44, 8084. (7) Zhang, J.; Webley, P. A. Cycle Development and Design for CO2 Capture from Flue Gas by Vacuum Swing Adsorption. Environ. Sci. Technol. 2008, 42, 563. (8) Cho, S.-H.; Park, J. H.; Beum, H. T.; Han, S.-S.; Kim, J.-N. A 2Stage PSA Process for the Recovery of CO2 from Flue Gas and its Power Consumption. Stud. Surf. Sci. Catal. 2004, 153, 405. (9) Sivakumar, S. V.; Rao, D. P. Modified Duplex PSA. 1. Sharp Separation and Process Intensification for CO2-N2-13X Zeolite System. Ind. Eng. Chem. Res. 2011, 50, 3426. (10) Li, G.; Xiao, P.; Webley, P.; Zhang, J.; Singh, R.; Marshall, M. Capture of CO2 from High Humidity Flue Gas by Vacuum Swing Adsorption with Zeolite 13X. Adsorption 2008, 14, 415. (11) Li, G.; Xiao, P.; Webley, P. A.; Zhang, J.; Singh, R. Competition of CO2/H2O in Adsorption Based CO2 Capture. Energy Procedia 2009, 1, 1123. (12) Liu, J.; Wang, Y.; Benin, A. I.; Jakubczak, P.; Willis, R. R.; Levan, M. D. CO2/H2O Adsorption Equilibrium and Rates on Metal− Organic Frameworks: HKUST-1 and Ni/DOBDC. Langmuir 2010, 26, 14301. (13) Liu, J.; Benin, A. I.; Furtado, A. M. B.; Jakubczak, P.; Willis, R. R.; LeVan, M. D. Stability Effects on CO2 Adsorption for the DOBDC Series of Metal Organic Frameworks. Langmuir 2011, 27, 11451. (14) Kizzie, A. C.; Wong-Foy, A. G.; Matzger, A. J. Effect of Humidity on the Performance of Microporous Coordination Polymers as Adsorbents for CO2 Capture. Langmuir 2011, 27, 6368. (15) Jones, C. W.; Maginn, E. J. Materials and Processes for Carbon Capture and Sequestration. Chemsuschem 2010, 3, 863. (16) Sayari, A.; Belmabkhout, Y.; Serna-Guerrero, R. Flue Gas Treatment via CO2 Adsorption. Chem. Eng. J. 2011, 171, 760. (17) Ebner, A. D.; Gray, M. L.; Chisholm, N. G.; Black, Q. T.; Mumford, D. D.; Nicholson, M. A.; Ritter, J. A. Suitability of a Solid Amine Sorbent for CO2 Capture by Pressure Swing Adsorption. Ind. Eng. Chem. Res. 2011, 50, 5634. (18) Lee, S.; Filburn, T. P.; Gray, M.; Park, J. W.; Song, H. J. Screening Test of Solid Amine Sorbents for CO2 Capture. Ind. Eng. Chem. Res. 2008, 47, 7419. (19) Gray, M. L.; Champagne, K. J.; Fauth, D.; Baltrus, J. P.; Pennline, H. Performance of Immobilized Tertiary Amine Solid Sorbents for the Capture of Carbon Dioxide. Int. J. Greenhouse Gas Control 2008, 2, 3. (20) Schladt, M. J.; Filburn, T. P.; Helble, J. J. Supported Amine Sorbents under Temperature Swing Absorption for CO2 and Moisture Capture. Ind. Eng. Chem. Res. 2007, 46, 1590. (21) Xu, X. C.; Song, C. S.; Miller, B. G.; Scaroni, A. W. Influence of Moisture on CO2 Separation from Gas Mixture by a Nanoporous Adsorbent Based on Polyethylenimine-Modified Molecular Sieve MCM-41. Ind. Eng. Chem. Res. 2005, 44, 8113. (22) Liu, S. H.; Wu, C. H.; Lee, H. K.; Liu, S. B. Highly Stable Amine-Modified Mesoporous Silica Materials for Efficient CO2 Capture. Topics Catal. 2010, 53, 210. (23) Sayari, A.; Belmabkhout, Y. Stabilization of Amine-Containing CO2 Adsorbents: Dramatic Effect of Water Vapor. J. Am. Chem. Soc. 2010, 132, 6312.

Indices

A = adsorption D = desorption 0 = feed end of the column 1 = feed outlet end of the column macro = macropore

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ASSOCIATED CONTENT

S Supporting Information *

Derivation of Hirose’s simplified PSA model and equations of the full PSA model. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +33 4 37 70 27 33. Fax: + 33 4 37 70 20 66. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Figueroa, J. D.; Fout, T.; Plasynski, S.; McIlvried, H.; Srivastava, R. D. Advances in CO2 Capture TechnologyThe U.S. Department of Energy’s Carbon Sequestration Program. Int. J. Greenhouse Gas Control 2008, 2, 9. 5995



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Design of a Pressure Swing Adsorption Process for Postcombustion

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