Optimization of One- and Two-Staged Kinetically Controlled CO2

Article pubs.acs.org/IECR

Optimization of One- and Two-Staged Kinetically Controlled CO2 Capture Processes from Postcombustion Flue Gas on a Carbon Molecular Sieve Reza Haghpanah,†,§ Arvind Rajendran,*,†,⊥ Shamsuzzaman Farooq,*,‡ and Iftekhar A. Karimi‡ †

School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, Singapore 637459 Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive, Singapore 117576

‡

S Supporting Information *

ABSTRACT: In this study, we systematically evaluate vacuum swing adsorption (VSA) processes for the kinetic separation of CO2/N2 from dry postcombustion flue gas on carbon molecular sieve by performing rigorous optimization. The synthesized VSA configurations are assessed first for their ability to produce high purity of CO2 at high recovery. A one-stage heavy reflux cycle and a two-stage process with an enriching VSA followed by a polishing VSA, both operated as basic four-step cycles with light product pressurization, are able to meet the purity-recovery constraints. These configurations are then optimized to minimize energy consumption and maximize productivity, and their energy-productivity Paretos are compared. General guidelines for purity-recovery targets in the first stage of a two-stage process are also discussed. The analysis also shows that the performance of zeolite 13X is superior to carbon molecular sieve.

1. INTRODUCTION In the past decade, a general consensus that global warming is real and there is a close correspondence between the increase in atmospheric CO2 and the global climate has been reached. Power plants that employ fossil fuels are the major sources of global CO2 emissions. There are several technical approaches toward mitigating and controlling the CO2 emissions from combustion of fossil fuels. The approaches can be broadly classified into two categories. The first category involves operations that continue to use fossil fuels but incorporate technologies that reduce the CO2 emitted per unit of electricity generated. This is achieved by either increasing the efficiency of the plant or by incorporating a CO2 capture unit. The second category of technologies focuses on replacing CO2 intensive fuels, e.g., coal, with less intensive ones, e.g., natural gas, or renewable resources. It is generally agreed that societies of the future will be powered chiefly by renewable sources. However, the current status of renewable energy systems, presence of fossil fuel based power plants, and the abundance of low cost fuel such as coal makes the large scale deployment of renewable energy sources an unlikely event in the near future.1 Hence, it is important to develop technologies that will allow the continued operation of fossil-fuel based power plants while reducing the amount of CO2 released to the atmosphere. Carbon capture and storage is a technology that seeks to separate CO2 from flue gas and sequester it permanently. The flue gas from postcombustion plants consists of predominantly N2 and CO2. It is important to separate and concentrate CO2 from this mixture for further sequestration. Recent studies have shown that vacuum swing adsorption (VSA) processes are promising options for CO2 capture with low power consumption.2−4 Conventional gas adsorption processes have been designed and optimized for the high purity and recovery of the light product (raffinate). However, in © 2013 American Chemical Society

CO2 capture, the challenge is to recover the heavier product (CO2) in high purity and recovery at the same time. In addition, low composition of the CO2 in flue gas (ca. 12−15 mol%) makes the separation of CO2/N2 difficult. Among the available commercial adsorbents that have received attention for VSA are 13X zeolite2,5,6 and inexpensive activated carbon7−10 from agricultural residue. However, it is worth noting that for the adsorbents with highly nonlinear CO2 isotherm, e.g. 13X zeolite, although the nonlinearity of the CO2 isotherm offers high selectivity, thereby allowing higher purity, it also causes the spread of the CO2 front in the desorption step which results in low CO2 recovery. Moreover, the presence of moisture poses a significant challenge, as most zeolitic commercial adsorbents adsorb water more strongly than CO2. In the context of these difficulties, another commercial adsorbent, carbon molecular sieve (CMS), that shows considerable kinetic selectivity for CO2/N2 separation also deserves attention. Carbon molecular sieves, unlike zeolites, are less sensitive to the presence of moisture due to the hydrophobic nature of the carbons.11 However, the downside of using carbons is the lower selectivity compared to 13X zeolite, hence making the high purity-recover requirements more challenging to attain. In equilibrium controlled separation like CO2/N2 separation on 13X zeolite, air separation for oxygen purification on LiLSX zeolite,12,13 etc., the separation is based on the difference in equilibrium affinity of the gases, and the mass transfer resistance plays a secondary role. In contrast, difference in Special Issue: Massimo Morbidelli Festschrift Received: Revised: Accepted: Published: 9186

September 22, 2013 December 19, 2013 December 19, 2013 December 19, 2013 dx.doi.org/10.1021/ie403143z | Ind. Eng. Chem. Res. 2014, 53, 9186−9198

Industrial & Engineering Chemistry Research

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Table 1. Equilibrium Isotherm and Transport Parameters for CO2 and N2 on BF CMS20 equilibrium parameters

kinetic parameters

adsorbate

b0 × 10 [m /mol]

−ΔUi [J/mol]

ai

qsci × 10 [mol/m ]

T [K]

D′c0/rc [s ]

−Ed [kJ/mol]

k′b0 [s−1]

−Eb [kJ/mol]

N2 CO2

0.804 0.078

19288.24 32133.12

3.36 2.99

6.20 6.96

302.15 303.15

83.94 0.50

30.62 14.51

121.61 4180.00

23.51 30.16

6

3

3

3

diffusional uptake rates of the mixture components into the adsorbent is exploited in kinetically controlled adsorption separation processes. Kinetically controlled adsorption separation processes may be broadly classified into three categories14 based on whether the equilibrium selectivity is neutral, favoring the faster component or favoring the slower component. Air separation for nitrogen production using carbon molecular sieves, an established industrial process, is an example where there is virtually no equilibrium selectivity.15 The equilibrium and kinetic effects reinforce when the equilibrium is also in favor of the faster component like CH4/N2 separation for natural gas upgrading on CMS. CO2/N2 separation on CMS also falls under the category where equilibrium favors the faster component (CO2) and reinforcing the kinetic effect. Air separation for nitrogen production on 4A zeolite is an example where equilibrium selectivity favors the slower-diffusing component.16 In a kinetic pressure swing adsorption (PSA) process, the duration of the adsorption and the desorption steps are critical design elements. On the one hand, the durations should be short enough to prevent the system from approaching equilibrium. On the other hand, they should be long enough to provide significant uptake of the components. Conventional kinetic PSA cycles, similar to those in the equilibrium PSA, have been developed for enrichment of the raffinate product.17 However, its use for recovering the extract product, e.g. CO2 capture, has been limited. In raffinate PSA cycles, during the adsorption step, the faster diffusing species is retained within the column and slower diffusing component is recovered at the high pressure product end as a raffinate product. Kinetic PSA on carbon molecular sieves for CO2 capture have been investigated in a few studies. Kikkindes et al. studied a four-bed, four-step VSA process to separate CO2 from a flue gas containing 17% CO2 in N2.10 A heavy reflux VSA configuration with the high pressure level (PH) of 1.2 atm and vacuum pressure of 0.1 atm yielded a CO2 purity of 90% with a modest recovery of 75% . Kapoor et al. considered a four-bed, seven-step PVSA cycle, operating between high pressure level (PH) of 15.8 atm and a vacuum pressure of 0.28 atm,18 to separate CO2 from a mixture containing 70% CO2 and the rest being N2. A purity of 98.3% and recovery of 65% were achieved. In the present study, we systematically evaluate the performances of a kinetically controlled VSA process for the separation of dry CO2/N2 on CMS by performing rigorous optimization of the configurations investigated. The goal is to develop a cycle which meets the target of 90/95% CO2 purity together with a 90% CO2 recovery with minimum energy consumption and maximum productivity.

2

−1

and N2 measured using volumetric technique at several temperatures from −10 to 70 °C. It was shown that the following multisite Langmuir isotherm model described the single component equilibrium data accurately: bici =

qc*i /qsci (1 − qc*i /qsci)ai

(1)

where bi = bi0e−ΔUi / R gT

(2)

In the above equations, qsi and bi are saturation capacity and equilibrium constant for component i, respectively, and ai is the adsorption sites occupied by each adsorbate molecule in the solid phase. The isotherm parameters corresponding to eq 1 are listed in Table 1. Equilibrium data for a ternary mixture containing 20% methane (CH4), 72% nitrogen (N2), and 8% carbon dioxide (CO2) at 30 °C were measured by differential adsorption bed method (DAB) in the same study, and the following multicomponent−multisite Langmuir isotherm, using pure component parameters, was shown to describe the mixture equilibrium reasonably well: bici =

qc*i /qsci n (1 − ∑i = 1 qc*i /qsci)ai

(3)

Therefore, the isotherm parameters given in Table 1 were retained in our simulations. Carbon molecular sieves are the class of adsorbents that are conventionally utilized in kinetically controlled PSA units.21 These adsorbents are heterogeneous particles which have a bidisperse pore structure with three distinguishable resistances to mass transfer: external film resistance around the particle, macropore resistance, and micropore resistance. However, the controlling resistance for the uptake of the sorbate is typically diffusion in micropores.20 In addition, the presence of restrictions at the pore mouth can also contribute to the transport resistance.20 The single component fractional uptakes in CMS were measured volumetrically by Qinglin et al.,19 simultaneously with equilibrium measurements. It was observed that CO2 diffused faster than N2. The authors considered a dual resistance model with concentration dependence of the transport parameters that took into account resistance at the pore mouth (barrier resistance) and that due to diffusion in the interior of the micropores. They had shown that the dual resistance model described the fractional uptakes of CO2 and N2 in the entire range. In the present study, to investigate the possibility of CO2 capture on CMS, the concentration dependence of the transport parameters were neglected. Instead, the barrier resistance at the micropore mouth and distributed micropore diffusional resistance were lumped into the overall mass transfer coefficient (k0) by the following equation:

2. EQUILIBRIUM AND KINETIC DATA The equilibrium and kinetic data for CO2 and N2 on Bergbau− Forschung GmbH (BF) CMS sample, reported in the literature by Qinglin et al.,19,20 were used in the present study. The authors reported pure component equilibrium data for CO2 9187

dx.doi.org/10.1021/ie403143z | Ind. Eng. Chem. Res. 2014, 53, 9186−9198

Industrial & Engineering Chemistry Research r2 1 1 = + c k0 k b0 15Dc0

Article

∂qi̅ ∂t

(4)

In the above equation, the first term on the right-hand side characterizes barrier resistance and second term represents the distributed pore diffusional resistance. The two transport parameters, kb0 and Dc0, were calculated from eqs 5 and 6 using the parameters listed in Table 1. k b0 = k b′0e

Dc0 rc 2

=

−E b / R g T

Dc′0 rc 2

e

= (1 − εp)

∂qci

∂t yP ∂T − εp i 2 RT ∂t

+ εp

y ∂P P ∂yi + εp i RT ∂t RT ∂t (8)

The mass transfer into the micropore, expressed by the LDF approximation, is given by:

∂qci ∂t

(5)

= k 0(qci* − qci)

(9)

The rest of the model equations are provided in the Supporting Information and the corresponding initial and boundary conditions are identical to our previous publications.3,4 For all of the VSA cycles in the present study, the bed is assumed to be saturated initially with pure N2 at 1 bar and 30 °C. To simulate a cyclic process, the final conditions of a particular step is used as the initial conditions for the next step. The PDEs and boundary conditions were nondimensionalized and discretized into 30 volume elements using high resolution finite volume technique and the resulting ordinary differential equations were solved using stiff solvers available in MATLAB such as ode23s. A mass balance error of less than 0.5% for five consecutive cycles was specified as the criteria for attainment of CSS. The number of cycles required to reach CSS varied between 80 and 120 cycles. It is important to note that in all VSA simulation, only one bed is employed. In an industrial multibed process all the beds undergo the same sequence of steps. Hence, for cycles constituting uncoupled steps, simulating one bed is adequate to fully capture the performance of a multibed process. For cycles involving steps where two more beds are coupled i.e., output from one bed is the input for another bed, data from such output streams are stored in data buffers and linear interpolation is implemented to obtain the data between two time steps while feeding these streams to another bed. Linear interpolation gives sufficient accuracy when very short time intervals are used for storing data. The parameters used in the VSA simulations are listed in Table 2.

−Ed / R gT

(6)

It is worth noting that, by neglecting the concentration dependence of the transport parameters, we are indeed underestimating the value of k0 and the results obtained typically underestimate the performance of the process.

3. MODELING OF ADSORPTION COLUMN DYNAMICS The following assumptions are used to derive the model equations: • An axially dispersed plug flow model represents the flow of the bulk fluid in the adsorber packed with adsorbent particles. • The gas phase obeys ideal gas law. • The interphase mass transfer rate is described by the linear driving force (LDF) model with the overall mass transfer coefficient computed as shown in eq 4. • The pressure drop along the column is described by the classical Darcy’s equation. The use of the Ergun equation, although accurate in the description of the pressure drop, was found to have a minor effect on the energy consumption calculation in a VSA process. • Thermal equilibrium between the gas and solid phases is established instantaneously. Except for high flow rates in an adiabatic separation, this is a good approximation.22 • No concentration, temperature, and pressure gradients in the radial direction. Farooq and Ruthven23 have experimentally shown that although there is radial temperature gradient in the column, the inside wall film heat transfer resistance dominates, and hence a onedimensional heat transfer model with a lumped coefficient confined at the wall adequately represents the heat transfer of the adsorber with the surrounding in a laboratory scale adsorption process. For pilot to industrial scale operations, the column is practically adiabatic. As noted in the previous section, the linear driving force (LDF) approximation is used to describe the mass transfer from the fluid to the solid phase. In addition, it is assumed that the macropore voids have the same gas as in the bulk phase. Thus, the equilibrium adsorbed concentration per unit micropore volume, qci, is related to the adsorbed concentration per unit macroparticle volume, qi̅ by the following equation: qi̅ = (1 − εp)qci + εpci (7)

4. OPTIMIZATION 4.1. Maximization of Purity and Recovery. Our robust and rapid PSA/VSA simulator and its use in detailed stochastic optimization have been discussed in two previous publications.3,4 With that resource at hand, we first perform multiobjective optimization to maximize CO2 purity and recovery, in order to evaluate the potential of a synthesized VSA cycle for CO2 capture. The optimum Pareto front from this optimization provides the best possible purity and recovery that can be obtained from the synthesized cycle. Hence, one can clearly assess if the cycle is able to meet the desired purityrecovery requirements for CO2 capture. We use the nondominated sorting genetic algorithm II (NSGA-II) proposed by Deb et al.,24 available in the MATLAB global optimization toolbox, for the multiobjective optimization. In all the optimization problems, we have used 60 generations and a population of 10 times of decision variables in each generation. Despite its limitations and lack of convergence guarantee, GA have been extensively and fruitfully applied in many practical systems of interest such as pressure swing adsorption,25,26 simulated moving bed chromatography (SMB),27,28 etc. For optimization problems such as this, it also offers the possibility to parallelize the calculations thereby offering significant reduction in computational time.

where ci is the gas phase concentration of component i and εp is the macropore voidage. The differential form of eq 7 is as follows: 9188



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adsorption step, CO2, which is the faster diffusing component, is rapidly adsorbed by CMS and hence the slower diffusing N2 is collected as raffinate from the product end. Higher equilibrium capacity of CO2 helps to elevate the driving force for diffusion. During the forward blowdown step, the feed end is closed and the column pressure is reduced from atmospheric pressure to an intermediate vacuum pressure (PI) in order to desorb N2 as much as possible. In the evacuation step, enriched CO2 is recovered at the feed end while the column pressure is decreased from intermediate pressure to vacuum pressure (PL). The performance of the cycle is determined by calculating the CO2 purity and CO2 recovery at the cyclic steady state condition. Since the product is collected only in the evacuation step, CO2 purity and recovery can be calculated by the following equations:

Table 2. Parameters Used in VSA Simulations parameter

value

column properties column length, L [m] inner column radius, rin [m] outer column radius, rout [m] column void fraction, ε [−] particle voidage, εp [−] particle radius, rp [m] properties and constants flue gas pressure Pf [bar] adsorbent density, ρs [kg m−3] column wall density, ρw [kg m−3] specific heat capacity of fluid, Cpg [J mol−1 K−1] specific heat capacity of adsorbed phase, Cpa [J mol−1 K−1] specific heat capacity of adsorbent, Cps [J kg−1 K−1] specific heat capacity of column wall, Cpw [J kg−1 K−1] fluid viscosity, μ [kg m−1 s−1] molecular diffusivity, Dm [m2 s−1] adiabatic constant, γ thermal conductivity of column, Kz [J m−1 K−1 s−1] thermal conductivity of column wall, Kw [J m−1 K−1 s−1] inside heat transfer coefficient, hin [J m−2 K−1 s−1] outside heat transfer coefficient, hout [J m−2 K−1 s−1] universal gas constant, R [m3 Pa mol−1 K−1] compression/evacuation efficiency, η

1 0.1445 0.1620 0.37 0.33 1.5 × 10−3 1 980 7800 30.7 30.7 960 502 1.72 × 10−5 1.6 × 10−5 1.4 0.0903 16 8.6 2.5 8.314 0.72

Purity Pu =

moleout,CO2 moleout,CO2 + moleout,N2

× 100% (10)

evac

Recovery Re =

moleout,CO2|evac mole in,CO2|press + mole in,CO2|ads

× 100% (11)

In the optimization problem, the duration of the adsorption (tads), blow down (tbd), and evacuation (tevac) steps, the intermediate pressure (PI), low pressure (PL), and feed velocity during adsorption step (vfeed) are considered as decision variables. The duration of the pressurization step, tpress, and its pressure limit, PH, are fixed at 20 s and 1 bar (postcombustion flue gas pressure), respectively. The lower bounds and upper bounds for the decision variables are listed in Table 3. In

As the first case study, a single-bed, four-step VSA cycle, shown in Figure 1, was chosen. The four-step cycle has the following steps: feed pressurization (step 1), high pressure adsorption (step 2), forward blowdown (step 3), and reverse evacuation (step 4). During the pressurization step the feed, 15 mol % CO2 in N2 at 1 bar and 30 °C, is supplied to the column and the bed is pressurized to atmospheric pressure (PH). In the

Figure 1. Basic four-step VSA cycle. 9189



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Table 3. Decision Variables and Corresponding Lower and Upper Bounds Provided to the Optimizer for Each Cycle cycle

tads [s]

tbd [s]

tHR [s]

θ [−]

tevac [s]

PI [bar]

PL [bar]

vfeed [m s−1]

basic four-step five-step with HR five-step with HR and LPP four-step VSA with LPP (stage 1) four-step VSA with LPP (stage 2)

20−200 20−200 20−200 20−200

30−200 30−200 30−200 30−200

30−250 30−250

0.2−0.9 0.2−0.9

30−250 30−250 30−250 30−250

0.05−0.5 0.05−0.5 0.05−0.5 0.03−0.8

0.01−0.5 0.01−0.5 0.01−0.5 0.01−0.5

0.1−1.5 0.1−1.5 0.1−1.5 0.1−1.5

15−200

15−200

15−250

0.03−0.8

0.01−0.5

0.1−1.5

addition, the following constraint is imposed to ensure that PI is greater than PL.

PI ≥ PL + 0.01[bar]

is 0.01 bar. All the points hit the lower bound of the evacuation pressure in order to maximize the purity-recovery of CO2. The same behavior is observed for the other two cases, i.e. for PL = 0.03 and 0.05 bar. It is further observed from Figure 3 that the decision variables PI and tbd are populated at the lower bound and upper bound, respectively. As already mentioned, the main role of forward blowdown step is to remove as much N2 as possible in order to prevent the contamination of the CO2 product during the evacuation step. Since N2 is the slower component, the optimizer tries to increase CO2 purity by choosing a combination of longer blowdown step and low intermediate pressure. However, very low intermediate pressure also results in loss of CO2 in the blowdown step thereby reducing CO2 recovery. It is important to note that although very high recovery is attainable from the basic four-step VSA cycle, it is not possible to get high CO2 purity and recovery at the same time even at PL = 0.01 bar due to the fact the conditions to conserve CO2 in the adsorbed phase do not allow sufficient removal of N2 from the bed in the blowdown step. Figure 4 shows the CO2 gas and solid phase column profiles at the end of each step for a point on the optimal Pareto front for the four-step VSA cycle with 90% recovery and 78% purity where the lower bound of the evacuation pressure is 0.01 bar. The operating conditions for this point are provided in the figure caption. The gas phase composition profile at the end of the blowdown step clearly shows that significant amount of N2 is present at the feed end which is collected along with CO2 during the evacuation step thus reducing CO2 purity. One way to improve CO2 purity is to return a portion of CO2 to the column, a step commonly referred to as heavy reflux (HR). The main idea of adding the HR step is to enrich the feed end with CO2 by displacing the lighter component toward the product end prior to the evacuation step. Hence, we have added the heavy reflux (HR) step, to the basic four-step VSA cycle as shown in Figure 5a and call it a “five-step VSA cycle with HR”. In the five-step VSA cycle with HR step, a fraction of the product stream, θ, from the evacuation step is collected in a tank and refluxed back into the column during the HR step at the intermediate pressure. Of course, in order to maintain the column pressure at PI during the HR step, an additional vacuum pump is required at the exit of the column. In a separate study, that is not detailed here we considered a configuration where the HR step was performed prior to the blowdown step at high pressure. It was noted that performing blowdown after the HR step resulted in significant loss of CO2 during the blowdown, resulting in lower recovery. For the fivestep VSA with HR the duration of the HR step, tHR, and reflux ratio, θ, are considered as additional decision variables and the corresponding lower bounds and upper bounds are also given in Table 3. An additional constraint tHR ≤ tevac was imposed. The inlet velocity to this step is calculated from the following mass balance equation:

(12)

The effect of evacuation pressure is investigated by systematically changing the lower bound of PL from 0.05 to 0.01 bar. The Pareto curves for CO2 purity and recovery for three lower bounds of the evacuation pressure are shown in Figure 2. It is clear that lower evacuation pressure pushes the

Figure 2. (a) Purity-recovery Pareto fronts for the VSA cycles explored in this study. (b) Zoomed version of part a.

Pareto front toward the high purity-recovery zone, i.e., to the top right corner of the figure. It is worth noting that even with a very low vacuum level of 0.01 bar, the process does not satisfy the expected purity-recovery values. This is in contrast to the early study of an identical process employing zeolite 13X, where purity and recovery greater than 90% were achievable with PL = 0.02 bar, a direct result of the high selectivity offered by 13X.3 Figure 3 shows the decision variables corresponding to the Pareto points for the case where the evacuation pressure 9190



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Figure 3. Decision variables corresponding to the Pareto front of basic four-step VSA with lower bound of evacuation PL = 0.01 bar shown in Figure 2. Note that range of the x-axis corresponds to the lower and upper bounds of the decision variables.

The optimal Pareto curves for five-step VSA cycle with HR step for lower bounds of 0.03 and 0.01 bar for PL have been added to Figure 2 for easy comparison. Clearly, the HR step has resulted in a significant increase in CO2 purity compared to the Paretos of the basic four-step cycle. With HR and the lower bound of PL = 0.01 bar, it is now possible to reach 90% CO2 purity (but not 95%) and 90% CO2 recovery simultaneously at the following operating conditions: tpress = 20 s, tads = 35.32 s, tbd = 37.26 s, tevac = 196.97 s, tHR = 111.43 s, θ = 0.86, PI = 0.44 bar, PL = 0.013 bar, and vfeed = 0.3 m s−1. The decision variables corresponding to this optimal Pareto are shown in Figure 6. Increase in CO2 purity has resulted from refluxing 60−90% of the evacuation stream. In addition, it is worth noting that the decision variables PI and tbd are populated closer to the upper and lower bounds respectively, which show the opposite trend compared to the basic four-step VSA cycle. In other words, the optimizer tries to reduce the loss of CO2 during the blowdown step by shortening its duration and choosing a high intermediate pressure. The column profiles at the end of each step for a point on the Pareto with CO2 purity and recovery of 90% are compared in Figure 4 with the column profiles for the basic four-step cycle discussed earlier. This figure demonstrates how the optimizer has chosen the decision variables to control the position of the CO2 front inside the column at each step in order to improve both CO2 purity and recovery. In addition, the column profile at the end of the HR step shows the enrichment of CO2 at the feed end prior to the evacuation step, which results in high CO2 purity. To further improve the performance of the five-step VSA cycle with HR, we have considered the light product pressurization (LPP) step as it was very effective in the equilibrium controlled CO2 capture and concentration on 13X zeolite discussed in our pervious study.4 In LPP, the effluent from the high pressure adsorption step is used to pressurize the column. The same idea has been implemented here to improve the purity and recovery performance of the cycle. Hence, the feed pressurization step in the basic five-step VSA cycle with HR is substituted with the LPP step (Figure 5b). The effluent

Figure 4. Gas (yCO2) and solid phase (xCO2) CO2 concentration profiles along the column length. Solid lines are for the basic four-step cycle at Pu = 78% and Re = 90%. The operating conditions are tpress = 20 s, tads = 70.67 s, tbd = 177.12 s, tevac = 141.3 s, PI = 0.107 bar, PL = 0.011 bar, and vfeed = 0.27 m s−1. The broken lines are for the five-step with HR cycle for Pu = 90% and Re = 90%. The operating conditions are tpress = 20 s, tads = 35.32 s, tbd = 37.26 s, tevac = 196.97 s, tHR = 111.43 s, θ = 0.86, PI = 0.44 bar, PL = 0.013 bar, and vfeed = 0.3 m s−1.

vHR =

θ × moleout|evac t HR Aε

P|z = 0 RT0

(13)

The extract product steams and feed steams, which have been used in calculations of the performance indicators, i.e., purity and recovery, are shown in the schematic of the synthesized cycles by P and F, respectively. The CO2 recovery for the five-step VSA cycle with HR is calculated from the following equation: Recovery Re =

(1 − θ )moleout,CO2|evac mole in,CO2|press + mole in,CO2|ads

× 100% (14) 9191



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Figure 5. Schematics of various VSA cycles analyzed for postcombustion CO2 capture. F and P refer to the feed and product streams.

partial pressurization with flue gas) is calculated from the following equation:

from the adsorption step is used to pressurize the column. The time dependent values of composition and temperature of the pressurization gas used in the LPP step come from the effluent of the previous adsorption step, which are stored in a data buffer. The duration of this step is determined by the time necessary for the column pressure to reach PH. Hence, the maximum possible duration of this step is set to be equal to the adsorption step. If the stream is not sufficient to pressurize the column from low pressure (PL) to high pressure (PH) even after the light product has been used up, the flue gas pressurization step is added to pressurize the column from the pressure attained, P*, to PH. The aim of the LPP step is to push the CO2 front toward the feed end and reduce the loss of CO2 during the adsorption and blowdown steps. The lower and upper bounds for the decision variables in the optimization problem for this cycle are also listed in Table 3. The CO2 recovery for the five-step VSA cycle with HR and LPP (without the need for

Recovery Re =

(1 − θ )moleout,CO2|evac mole in,CO2|ads

× 100% (15)

In case partial pressurization with flue gas is necessary, the recovery calculation is adjusted accordingly by falling back to eq 14. The optimal Pareto curve for five-step VSA cycle with HR and LPP for the cases where 0.03 and 0.01 bar are lower bounds of PL are also shown in Figure 2. It is obvious that by adding the LPP step to the five-step VSA cycle with HR the optimal Pareto has moved toward the top right corner. In addition, for the case where the lower bound of evacuation pressure is 0.01 bar, CO2 purity, and recovery well above 90% is achievable. The LPP step improves the CO2 purity because by pressurizing in the reverse direction with a stream that is richer 9192



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Figure 6. Decision variables corresponding to the Pareto front of a five-step VSA cycle with HR cycle with lower bound of evacuation PL = 0.01 bar shown in Figure 2.

in N2 than the feed, the CO2 front is pushed back into column. This allows the optimizer to choose a lower blowdown pressure compared to the five-step VSA cycle with HR and feed pressurization steps to remove more N2 during the blowdown step without losing CO2. Comparing the optimization study of zeolite 13X, it is also clear that in order to achieve high purity and recovery with CMS, an HR step is rather unavoidable. This is consistent with the lower selectivity of CMS. In order to understand what level of kinetic selectivity will be required to reach the target purity/recovery requirements, an optimization run was performed by increasing the value of kCO2 by 2 orders of magnitude. All other parameters, including the isotherm and the kinetic parameters of N2 were kept constant. The resulting Pareto is shown in Figure 2. The optimization results clearly show that both purity and recovery improve with increasing kinetic selectivity and it is possible to reach a purity/ recovery of 90/90 only if CO2 resistance is reduced by two orders of magnitude. 4.2. Minimization of Energy Consumption and Maximization of Productivity. Having identified the cycles that are able to provide 90% CO2 purity and recovery, the next task is to rank these cycles further according to their energy demand. The energy consumption of the CO2 capture and concentration unit is a parasitic energy loss for the power plant and should be minimized. On the other hand, the productivity of the capture unit, which is inversely related to the plant size and hence the capital cost, must be maximized. Therefore, in this section we investigate the energy-productivity Pareto fronts of the prospective cycles. The objectives are to minimize the energy consumption and maximize productivity while ensuring 90% purity and recovery. The same bounds for the decision variables for the five-step VSA cycle with HR and LPP given in Table 3 are used. The energy consumptions for the blowers and vacuum pumps in this cycle are calculated from the following equations based on the assumption of isentropic compression/ evacuation with an inherent efficiency of η = 72%:

Wads

γ 1 = πrin 2εv0 η γ−1

t = tads

∫t =0

γ − 1/ γ ⎡⎛ ⎤ P(t ) ⎞ ⎢ ⎜ ⎟ P(t )⎢⎜ − 1⎥⎥ dt ⎟ P ⎣⎝ f ⎠ ⎦

(16)

Wbd,HR,evac =

t = tbd,HR,evac γ 1 2 v(t )P(t ) πrinε η γ − 1 t=0 ⎡⎛ ⎤ ⎞γ − 1/ γ ⎢⎜ Patm ⎟ − 1⎥ dt ⎢⎣⎝ P(t ) ⎠ ⎥⎦

∫

(17)

Total energy E = Wads + Wbd,HR,evac

(18)

where Pf and Patm are the flue gas and atmospheric pressure, respectively. The flue gas pressure is taken as 1 bar in all energy calculations in this section. The productivity is calculated from the following equation: Productivity Pr =

total moles of CO2 in extract product(s) (total volume of the adsorbent) × (cycle time) (19)

Note that η = 72% is consistently used in the PSA literature and is retained in this study. However, in our recent pilot plant studies, we had noticed that at low vacuum levels the vacuum pump efficiencies drop to ≈30%.29 The constraints on purity and recovery are incorporated as penalties to productivity and energy consumption. The optimum Pareto curves for this constrained multiobjective optimization are shown in Figure 7. As expected there is tradeoff between energy consumption and productivity. The minimum energy consumption for the five-step VSA cycle with HR and LPP steps is 600 kW h/tonne CO2 captured with a productivity of Pr = 0.109 mol m−3 s−1 under the following operating conditions: tpress = 20 s, tads = 35.3 s, tbd = 30.12 s, tevac = 193.3 s, tHR = 189.0 s, θ = 0.64, PI = 0.13 bar, PL = 0.013 bar, 9193



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energy and productivity for this case. The energy consumption for this point is 1411 kW h/tonne CO2 captured which is significantly higher than the minimum energy consumption for the five-step cycle with HR and LPP. The introduction of LPP step makes it possible to attain high purity and recovery at a lower reflux ratio compared to the cycle without LPP, which has contributed to the reduction in energy consumption.

5. TWO-STAGE OPERATION Although the introduction of LPP step has led to a significant reduction in energy consumption compared to the cycle without LPP, the energy penalty of the five-step VSA cycle with HR and LPP is still 45% (based on 10 000 tonne of CO2 per day emitted from a coal fired 500 MW power plant), which is unacceptably high. Moreover, energy consumption increases very rapidly for a small increase in productivity. In order to reduce the energy penalty, one option is to consider a two-stage VSA cycle. The idea is to use the first stage to enrich the CO2 composition from 15% to a certain intermediate value and then we use the second stage to concentrate it up to 90%. This configuration has been studied by other researchers, both theoretically using 5A zeolite30 and experimentally using zeolite 13X and activated carbon as adsorbents.31 Since HR step significantly adds to the energy consumption and also reduces the productivity, a two-stage cycle will be advantageous if it can achieve 90% purity-recovery without resorting to this step. Therefore, in our two-stage investigation, we have considered a four-step VSA cycle with LPP for both stages as shown in Figure 8. We have assumed that the product of the first stage is collected in a tank, which acts as a buffer in order to maintain the constant molar flow rate to the second stage. While in principle, the volume of the buffer tank can be very high, we do not take that into account for the present study. However, in a real process, operating scheme needs to be developed to avoid the buffer tank. Hence, the average CO2 purity of the first stage is considered as the CO2 feed composition to the second stage. The length of the columns in the two stages are equal. Since the optimizer uses interstitial feed velocity as a decision variable, the diameter and the number of parallel units will depend on the flow rate requirement.

Figure 7. (a) Energy productivity Paretos for different processes subject to the constraint Re ≥ 90%. (b) Comparison of CMS and zeolite 13X energy-productivity Paretos. The adsorbent volume and energy penalty are calculated assuming a 500 MW power plant that produces 10000 tonne day−1. To convert the energy consumption from kilowatt hours per tonne CO2 captured to kilowatt hours per tonne CO2 avoided use the following formula: EkW h/tonne CO2 avoided = EkW h/tonne CO2 captured/(0.9 − 0.833 × 10−3EkW h/tonne CO2 captured).

and vfeed = 0.38 m s−1. For the five-step VSA cycle with HR, there are barely one or two points on the purity-recovery Pareto in Figure 2 where the 90% purity-recovery requirements are met. Hence, there is negligible room to further optimize the

Figure 8. Schematic of the two-stage VSA process. 9194



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s−1. The operating conditions for this point on the Pareto are tads1 = 108.08 s, tbd1 = 149.30 s, tevac1 = 165.53 s, PI1 = 0.39 bar, PL1 = 0.041 bar, vfeed1 = 0.21 m s−1 and tads2 = 152.61 s, tbd2 = 89.99 s, tevac2 = 149.21 s, PI2 = 0.53 bar, PL2 = 0.067 bar, vfeed2 = 0.12 m s−1. In the first stage, CO2 is enriched to 63.8% with 91.4% recovery, at the expense of 171.33 kW h/tonne CO2 captured and productivity of 0.197 mol m−3 s−1. In the second stage, CO2 purity and recovery are 90% and 98.4% respectively with energy consumption of 93.72 kWh/tonne CO2 captured and productivity of 0.7 mol m−3 s−1. The significant reduction in the overall energy consumption has resulted from the elimination of the heavy reflux step and increase in the evacuation pressure. Moreover, the productivity of the two-stage VSA operation with LPP corresponding to the minimum energy consumption is higher than the productivity of the single five-step VSA cycle with HR and LPP steps. This is expected since in the single stage VSA cycle high reflux ratio is required in order to get 90% purity and recovery which causes lower productivity. Furthermore, the energy-productivity Pareto for the two-stage optimization suggests that the productivity may be increased by nearly 50% for a modest increase in energy consumption by ∼20%. However, it should be noted that although more stages has the potential to further reduce energy consumption, it will come at the expense of reduced productivity. In order to evaluate the potential of the two-stage with LPP VSA cycle for higher purities, the optimization procedure was repeated with constraints of Pu ≥ 95% while maintaining the constraint of Re ≥ 90%. The Pareto front for this study is shown in Figure 7. Both minimum energy consumption and the corresponding productivity values worsen with increased purity requirement. Finally, the Pareto curve that we obtained for zeolite 13X from our previous publication is also included for comparison in Figure 7b. The minimum energy consumption using zeolite 13 X is 131 kW h/tonne CO2 captured compared to 275 kWh/tonne CO2 for CMS and the maximum productivity using zeolite 13X is 0.22 mol m−3 s−1 compared 1 mol m−3 s−1 for CMS. Hence, zeolite 13X owing to its superior CO2/N2 selectivity and faster kinetics performs significantly compared to CMS, both in terms of energy consumption and productivity. 5.2. Analysis of the Two-Stage Process. In the previous section, the multiobjective optimization of the two stage process has been considered. The results in Figure 9 indicate that the CO2 purity and recovery from stage 1 fall within a narrow band of values. In this section, we seek to understand the reasons for this result. Accordingly, we consider the stages as two independent VSA units running the same cycle, i.e., fourstep VSA with LPP. For stage 1, multiobjective optimization with the aim to maximize recovery and minimize energy consumption is performed. The product purity, Pu1, is used as a constraint and the optimization is repeated for Pu1 = 40, 50, 60, and 67%. The Paretos from the optimization are shown in Figure 10a. It is clear that by relaxing the purity requirement the process achieves a lower energy consumption for a given recovery. It can also be seen that the energy consumption increases rapidly with Re1. Moreover, the maximum achievable recovery decreases with increasing product purity. For Pu1 = 40%, very high recoveries (∼99%) are achievable, while for Pu1 = 67%, the recovery is limited to 90%. It is worth noting that for a two-stage process, minimum recovery in any one stage must be at least 90% for effective recovery of 90% to be mathematically possible. The Paretos reveal that targeting stage

5.1. Optimization of Two-Stage VSA. The bounds for optimization of the two-stage VSA process are also listed in Table 3. In total 12 decision variables are specified for the energy-productivity optimizer with 60 generations and 120 populations in each generation. The lower bound of the evacuation pressure in both stages is set at an industrially achievable value of 0.03 bar. The total energy consumption, productivity, and recovery of the two-stage process are calculated from the following equations: Effective recovery Re = Re1 × Re2

(20)

Total energy

E=

E1 + E2 Re2

(21)

Effective productivity Pr =

Pr1Pr2Re2 Pr2 + Pr1Re2

(22)

where the subscript refers to the stage number. The objective is to maximize effective productivity and minimize total energy consumption while maintaining the purity of the product from the second stage, Pu2, and effective recovery, Re, at least 90%. Since, information about purity and recovery are only available after CSS is reached, the objective functions are formulated by penalty function methods. It is important to note that in order to have effective recovery ≥90%, the recovery of the first stage, Re1, has to be at least ≥90%. Therefore, if this condition is not satisfied the second stage simulation is eliminated and the energy consumption and productivity terms in the objective function are penalized. The optimal Pareto front of the two-stage VSA thus obtained is compared with five-step VSA cycle with HR and LPP steps in Figure 7. It is indeed encouraging to see that the energy consumption is reduced significantly by performing a two-stage separation while satisfying the purity-recovery requirements. The purity and recovery of the first stage corresponding to the Pareto points are shown in Figure 9. It is clear from this figure that CO2 should be enriched up to 58−64% in the first stage with recovery of 91−95%, in order to achieve 90% purity from the second stage with 90% effective recovery. The minimum energy consumption for the two-stage VSA with LPP is 267 kW h/tonne CO2 captured with a productivity of 0.147 mol m−3

Figure 9. Purity and recovery of the stage one corresponding to the Pareto front of two-stage process (Pu2 ≥ 90). 9195



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The above equation also suggests that in order to minimize E, we need to target a lower value of Re1. These results differ from some studies that suggest operating stage 1 at the highest possible recovery.30

6. CONCLUSIONS In this work, we systematically evaluated the performance of kinetically controlled VSA cycles for BF CMS as adsorbent to separate CO2 from dry flue gas. A genetic algorithm (GA) based multiobjective optimization study of various VSA processes is considered. The synthesized VSA configurations are assessed first for their ability to produce high purity of CO2 at high recovery simultaneously. The roles of heavy reflux and light product pressurization steps and operating conditions on the performance of the VSA process are investigated. It is shown that the five-step VSA with HR cycle and five-step VSA with HR and LPP both are able to enrich CO2 to 90% purity with 90% recovery but a very low vacuum level, i.e., 0.01 bar, is required in the evacuation step. However, the heavy reflux step significantly increases the energy consumption and lowers the productivity. Although, the introduction of the LPP step reduces the energy consumption somewhat, it is still very high to prompt further exploration. Therefore, in order to further reduce the energy penalty, a two-stage VSA configuration is studied. In both stages, four-step VSA cycle with LPP is considered. It is shown that the energy consumption is significantly decreased in a 2-stage VSA due to the elimination of the heavy reflux step and increase in the evacuation pressure. By analyzing the performance of the two-stage process, we observe that the total energy is minimized by operating the first-stage at a lower recovery, while purity in the first stage is determined by the constraint on the overall recovery. Most adsorption-based studies in the literature have thus far focused on CO2 capture from dry postcombustion flue gas using zeolite based materials. It is well-known that industrial flue gas is saturated with moisture which is detrimental to most zeolite-based adsorbents. It is important to consider materials that are relatively more tolerant to moisture, e.g. carbon based materials. Hence, in this study we chose CMS, where the separation is kinetically controlled. While it would have been more pertinent to study capture from a wet flue gas, data related to the adsorption equilibria and kinetics of water on CMS is rare. In the absence of such data, we embarked on identifying the energy-productivity trade-offs for the case of dry flue gas. Note that capture from wet flue gas, using any material on which CO2 and H2O compete for adsorption sites, will invariably provide a worse energy-productivity Pareto curve compared to the dry case. Performing optimization studies on dry flue gas capture provides important information. On the one hand, if this trade-off is very favorable (compared to other processes), then it provides the motivation to perform the laborious characterization of water adsorption and then proceed to perform process-scale studies. On the other hand if this trade-off is unfavorable, then it will suggest that further studies must be carefully evaluated. Unfortunately, in the case of CMS, we believe we fall in the second category for the following two reasons: the selectivity of CMS does not allow meeting purityrecovery targets in a single stage and a two-stage process, even for dry flue gas, has an unfavorable energy-productivity trade-off compared to 13X zeolite.

Figure 10. Maximization of recovery and minimization of energy consumption for (a) stage one and (b) stage two for a two-stage VSA. Note that for part a the legend provides purity of the product from stage 1 while that in part b denotes the purity of the feed introduced to stage 2 and is expected to produce a minimum product purity of 90%.

1 to produce a purity higher than 67% will violate the requirement of Re ≥ 90%. Thus 67% is the upper limit of useful purity from stage 1. Since the product of stage 1 will be fed to stage 2, we consider the same optimization problem for the second stage with feed composition to be 40, 50, 60, and 67%, but now with a product purity constraint of Pu2 ≥ 90%. The results of this study are presented in Figure 10b. The trends of the Paretos resemble those in Figure 10a. Among the Paretos, shown in Figure 10b, there is a small window in the range 50 < Pu1 ≤ 67 where the recovery constraint, i.e., Re1Re2 ≥ 90% is satisfied. This explains the narrow band of purity and recovery values from stage 1 shown in Figure 9 for the Parerto points of the two-stage VSA process (Pu2 ≥ 90%) in Figure 7a. It is also clear from Figure 9 that for the Pareto points, recoveries in stage 1 are in the 91−95% range. Also the lower the recovery in stage 1, the lower the total energy consumption. Hence, as a guideline, it is recommended to keep the recovery from stage 1 closer to the lower limit necessary to achieve the effective recovery target. This can be also rationalized by observing the Paretos in Figure 10a, which indicate that E1 increases sharply with increasing recovery and, in general, E1 is significantly larger than E2. Further, by incorporating the constraint that Re2 = 0.9/Re1 into eq 22 we obtain E=

E1Re1 + E2 0.9

(23) 9196



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q*ci = equilibrium adsorbed amount based on microparticle volume, [mol m−3] qci = adsorbed amount based on microparticle volume, [mol m−3] qsci = saturation concentration in the microparticle [mol m−3] qi̅ = average adsorbate concentration in the macropore, [mol m−3] rc = microparticle radius [m] rin = column inner radius [m] rout = column outer radius [m] rp = particle radius [m] R = universal gas constant [Pa m3 mol−1 K−1] t = time [s] T = temperature [K] Ta = ambient temperature [K] Tw = column wall temperature [K] U = internal energy [J mol−1] v = interstitial velocity [m s−1] W = energy consumption of vacuum pump or compressor [J] x = dimensionless concentration in solid phase [−] y = composition in the fluid phase [−] z = axial coordinate [m]

ASSOCIATED CONTENT

S Supporting Information *

Table listing the complete model equations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +1.780.492.3912. Fax: +1.780.492.2881. E-mail: arvind. [email protected]. *Tel.: +65 6516 6545. Fax: +65 6779 1936. E-mail: chesf@nus. edu.sg. Present Addresses §

Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, CA 94305, USA. ⊥ Department of Chemical and Materials Engineering, University of Alberta, 7th Floor, Electrical & Computer Engineering Research Facility (ECERF), 9107 - 116 Street, Edmonton, Alberta, Canada T6G 2V4 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The work was carried out under the thematic strategic research program on carbon capture and utilization funded by A*STAR, Singapore. A.R. fondly recollects Massimo Morbidelli’s supervision during his graduate studies at ETH Zurich.

Greek Symbols

ε = bed voidage [−] εp = particle voidage [−] η = compression/evacuation efficiency [−] γ = adiabatic constant [−] μ = fluid viscosity [kg m−1 s−1] ρg = fluid density [kg m−3] ρs = adsorbent density [kg m−3] ρw = wall density [kg m−3]

■

NOMENCLATURE a = adsorption sites occupied by each adsorbate molecule in the adsorbed phase [−] A = cross-sectional area of the column [m2] b0 = parameter in multisite Langmuir isotherm [m3 mol−1] c = concentration in the fluid phase [mol m−3] Cpa = specific heat capacity of adsorbed component [J mol−1 K−1] Cpg = specific heat capacity of adsorbed component [J mol−1 K−1] Cps = specific heat capacity of solid phase [J kg−1 K−1] Cpw = specific heat capacity for column wall [J kg−1 K−1] dp = particle diameter [m] DL = axial dispersion [m2 s−1] Dm = molecular diffusivity [m2 s−1] Dc0 = limiting micropore diffusivity, [m2 s−1] Dc′0 = pre-exponential constant for temperature dependence of diffusivity, [m2 s−1] Eb = activation energy for diffusion across the barrier resistance at the pore mouth, [J mol−1] Ed = activation energy for diffusion in micropore interior, [J mol−1] hin = inside heat transfer coefficient [J m−2 K−1 s−1] hout = outside heat transfer coefficient [J m−2 K−1 s−1] H = enthalpy [J mol−1] kb0 = limiting barrier coefficient, [s−1] k′b0 = pre-exponential constant for temperature dependence of barrier resistance coefficient, [s−1] k0 = overall mass transfer coefficient, [s−1] Kw = thermal conductivity of column wall [J m−1 K−1 s−1] Kz = thermal conductivity of column [J m−1 K−1 s−1] L = column length [m] P = pressure [Pa] P* = final pressure of light product pressurization step [bar]

Subscripts

■

1,2 = stage number ads = adsorption step bd = blowdown step evac = evacuation step f = flue gas feed = feed condition H = high HR = heavy reflux step i = index of component I = intermediate L = low LPP = light product pressurization out = stream leaving a column press = pressurization step

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Optimization of One- and Two-Staged Kinetically Controlled CO2

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