Feasibility Study of a Moving-Bed Adsorption Process with Heat

Dec 9, 2014 - A high-efficiency heat integration scheme that recovers the heat of adsorption and reuses this energy as the heat of desorption was desi...
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Feasibility Study of a Moving-Bed Adsorption Process with Heat Integration for CO2 Capture through Energy Evaluation and Optimization Yongho Son, Kiwoong Kim, and Kwang Soon Lee* Department of Chemical and Biomolecular Engineering, Sogang University, 1-Shinsoodong, Mapogu, Seoul 121-742, Korea ABSTRACT: The feasibility of employing a moving-bed adsorption (MBA) process as a postcombustion carbon capture process was investigated using zeolite 13X as the adsorbent. The MBA process consists of an adsorption bed and two desorption beds, which are operated under different temperatures and pressures. Adsorbent particles circulate around the beds in a countercurrent direction to the gas flow in each bed. A high-efficiency heat integration scheme that recovers the heat of adsorption and reuses this energy as the heat of desorption was designed and implemented to minimize the energy requirements. A fixed-bed dehydration unit using MIL-101 (Cr) as the adsorbent was also designed for pretreatment of the flue gas and was incorporated as an integral part of the process. Models were established for predicting the operating energy for constituent process units from the dehydration to liquefaction stages, and the minimum energy requirement was calculated. The results indicated that the total energy demand per unit amount of CO2 removal in terms of the equivalent work was intermediate to those of the optimized piperazine- and monoethanolamine-based absorption processes. The regeneration energy, which accounts for only the capture process, except for the dehydration and liquefaction processes, was estimated to be less than half of those of the absorption processes. The sensitivity of the process performance to the CO2 selectivity and sorption capacity was also analyzed to investigate the potential improvement in the performance of the MBA process when using more efficient adsorbents.

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INTRODUCTION The greenhouse effect, which is caused by greenhouse gases in the atmosphere, is a major contributor to global warming, and it is perhaps the most important environmental issue worldwide, both currently and in the foreseeable future. Although other energy sources, such as nuclear energy and renewable energy, have been intensively studied as alternatives to fossil fuels, the energy from fossil fuels is the primary source for power generation, and this energy paradigm must be maintained for several more decades. Carbon capture and sequestration (CCS), which includes the entire process chain from CO2 capture to sequestration, has been recognized as the most feasible option for reducing greenhouse gases while maintaining fossil fuel consumption until clean energy sources are secured.1−3 To implement CCS technology, the overall CCS cost must be decreased below a certain level. With the current technologies, the cost of CO2 capture represents a large part of the overall CCS cost, and most CCS research efforts are dedicated to the development of new capture processes with enhanced energy efficiency.4 There are several possible approaches for capturing CO2 from power plants. These methods can be classified as absorption into a liquid, adsorption onto a solid sorbent, and gas separation using a membrane. Among these capture processes, amine-based absorption processes and their variants are currently considered the most feasible for commercialization. In fact, the amine-based process has a long history of commercialization for purposes other than CCS. For CO2 capture, these processes must be further developed prior to commercialization because of the costly energy requirements to regenerate CO2 from the solvent. In addition to the regeneration energy, the corrosion and degradation of the solvents must also be overcome.5−7 © 2014 American Chemical Society

Membrane separation provides some advantages over other conventional separation techniques. Membrane technology is considered to be a low-cost and compact technique for gas separation when a high-purity product stream is not vital.8−10 However, maintaining the high pressure difference across a membrane requires a significant amount of energy. In addition, polymer-based membrane materials can be easily damaged by contact with flue gas, which may also contain highly reactive impurities.11 Although membrane processes have considerable potential, these factors render the commercialization of membrane processes a remote possibility at present. Adsorption has been commercially used to separate CO2 from small- to medium-scale gas effluents with high CO2 contents, such as waste-gas separation from biological treatments and landfill sites.12−14 The processes currently available for capturing CO2 are primarily based on vacuum-swing adsorption (VSA) with zeolite 13X as the adsorbent in a fixed bed. In VSA, adsorption is conducted at atmospheric pressure and desorption occurs in a vacuum. Because of the limited selectivity of the adsorbents and expansion of the gas volume in a vacuum, the VSA process is inappropriate when high-purity CO2 separation is desired and the amount of flue gas is large, both of which are required in CCS. The temperature-swing adsorption (TSA) method can help the adsorption processes overcome such limitations. However, this method is difficult to apply to fixed-bed processes because of the substantial amounts of heating and cooling energy that must be alternately provided to each bed. Received: August 8, 2014 Revised: October 28, 2014 Published: December 9, 2014 7599

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Among the above-mentioned alternative options, processes that use solid sorbents have recently attracted attention, primarily because they have a lower regeneration energy than the methods that use aqueous solvents.15−17 These processes eliminate the need for water evaporation and use sorbents with lower heat capacities, which is advantageous compared to liquid solvents.5,18 These characteristics can provide more salient advantages for physisorption sorbents if the sorbents have high CO2 sorption capacity and selectivity. Recently, Kim et al.19 proposed a moving-bed adsorption (MBA) process that consists of an adsorption bed and two desorption beds, around which adsorbent particles circulate countercurrent to the gas flow in each bed. The MBA process utilizes a combination of temperature- and pressure-swing desorption, and it has many advantages over other solid sorbent-based processes, which will be described in more detail in a later section. Kim et al.19 proposed a heat integration scheme, established a detailed mathematical model of the entire process, and performed numerical studies to evaluate the performance of the process. In this paper, we investigated the feasibility of employing the MBA process using zeolite 13X as a postcombustion carbon capture process from the perspective of energy efficiency. For this purpose, the original heat integration scheme19 was revised to be more efficient, a dehydration process using the metal− organic framework (MOF) MIL-101 (Cr) was designed and incorporated, and its performance was compared with those of representative absorption processes. The governing equations of the process are only presented in brief because a detailed description can be found elsewhere.19 Instead, models for the operating energies of the constituent main units from the dehydration to the liquefaction stages were established, and the minimum energy requirement was calculated through an optimization procedure. The total energy demand in terms of the equivalent work was compared with those of the optimized piperazine- and monoethanolamine-based absorption processes. The sensitivity of the process performance to variations in the CO2 selectivity and sorption capacity was also investigated.

Figure 1. Basic schematic of the heat-integrated moving bed adsorption process.

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MOVING BED ADSORPTION (MBA) PROCESS FOR CO2 CAPTURE A basic schematic of the MBA process is presented in Figure 1. The process consists of an adsorption bed (ADB) and two desorption beds (DEBs), and the adsorbent particles circulate around these beds. Continuous adsorption occurs in the ADB, which is operated at atmospheric pressure and ambient temperature because the adsorbent particles and the flue gas flow in a countercurrent direction. A heat exchanger is installed in the bed to remove the heat of adsorption and to shape the temperature profile that develops inside the bed. The discharged adsorbent particles are transferred to the atmospheric desorption bed (A-DEB), where high-temperature CO 2 desorption is performed, and subsequently moved to a vacuum desorption bed (V-DEB) for additional CO2 desorption under a vacuum. In this paper, we do not include a more detailed description of the MBA process because it has been intensively described in a previously published paper.19 Figure 2 shows a moving-bed vessel with embedded heat exchanger plates. The design of this vessel ensures a uniform downward solid flow and can be modified to increase or decrease the number of heat exchanger plates. This study assumed the moving-bed design shown in Figure 2, which

Figure 2. Schematic of MBA process embedded heat exchanger plates. This figure is borrowed from http://www.solexthermal.com and modified.

defines the notations used for the bed characteristics and for the heat exchanger. The MBA process possesses several advantages over the fixed-bed VSA process. First, because the operation is continuous, a higher product throughput is possible compared 7600

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∂Ts u ∂T 1 = s s + ∂t L ∂z cs

to an equivalent-sized VSA process. Additionally, each bed can have fixed operating conditions to realize the temperature swing and heat integration, which are difficult to achieve in the conventional VSA process. In the VSA process, the bed pressure widely varies during operation. Accordingly, the vacuum pump efficiency also fluctuates; however, the pumping cost dominates the operating cost. In contrast, in the MBA process, the desorption pressure can be maintained at a constant value when the pump efficiency is sufficiently high, which can reduce the pumping cost. The MBA process also has advantages over the fluidized-bed process. The countercurrent contact operation maximizes the driving force for mass transfer and uses the adsorbent capacity more efficiently than is possible in a fluidized-bed reactor.20 Liang-Shin Fan et al.21 showed that the theoretical solid conversion in a moving-bed reactor can be five times greater than that of a fluidized-bed reactor in the chemical looping system. The high solid conversion results in lower solid circulation rates and further reduces the energy requirement for solid sensible heat. The temperature profile formed by the countercurrent gas and solid flows enables more efficient heat integration than in a fluidized bed, which is isothermally operated. In this study, we selected zeolite 13X as the solid adsorbent because of its excellent CO2 adsorption capacity at low pressure, its high selectivity against N2, and the availability of reliable equilibrium adsorption and kinetic information for this adsorbent. Detailed information on this adsorbent is provided in Table 1.

∂t

=−

ug ∂yi L ∂z

U W (N + 1) ∂Th u ∂T (Ts − Th) = − h h + hs m m ∂t L ∂z ρh chAh

Mass transfer rate and adsorption equilibrium ri = kiL(qi* − qi) + kiQ |qi* − qi|(qi* − qi)/qi , i = N2 , CO2

∂t

(7)

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ENERGY MODELS The heat supply to the DEBs, vacuum pump, and blower operation and CO2 liquefaction are the major operations that consume energy. In addition, the dehydration of flue gas to prevent the sorbent from degrading should be considered. The cooling water and electric energy used to transport the sorbent particles also contribute to the operating cost. However, their contribution is very small and is neglected in this analysis. Work by Vacuum Pump and Blower. The operating conditions and associated efficiency of the vacuum pump cannot be fixed in advance and must be determined through optimization. We obtained a typical performance curve for a large-scale commercial vacuum pump from the World Wide Web. Figure 3 shows the efficiency chart of TRVK3003, which is a product of TRAVAINI Pump USA, Inc., for several suction pressures and volumetric flow rates, and it was revised to fit our design constraints. The work for the vacuum pump was computed using eq 8 with the corresponding efficiency in Figure 3. ⎤ ⎡⎛ ⎞(γ − 1)/ γ ⎛ kJ ⎞ 1 γ P 1 Wv − pump⎜ RT1⎢⎜ 2 ⎟ − 1⎥ ⎟= ⎥ ⎢⎝ P1 ⎠ η γ − 1 yCO ⎝ molCO2 ⎠ ⎦ ⎣ 2

∑ ri ,

i = N2 , CO2

i

(2)

us ∂qi + ri L ∂z

(8)

where η is the efficiency of the vacuum pump and yCO2 represents the mole fraction of CO2 in the gas. Equation 8 was also applied to calculate the blower energy required to overcome the pressure drop along the adsorption bed. We typically assumed a blower efficiency of 75%. Work for CO2 Liquefaction. The final state of liquid CO2 after liquefaction was assumed to be 150 bar and 40 °C. The energy for liquefying pure CO2 to the final state can be expressed as a function of the inlet gas pressure (Pin) and the final pressure (150 bar) as follows:

(1)

Component mass balance for the adsorbed phase

=

(6)

γ = c p/ c v

ρ1−ε (yi ∑ rj − ri) + s C ε j

∂qi

i

(5)

2 ⎞ Dax ⎛ ∂ yi ∂C ∂yi ∂ 2C ⎟ ⎜C 2 + y + i ∂z ∂z L2C ⎜⎝ ∂z 2 ∂z 2 ⎟⎠

+

∑ ri(−ΔHi)

Uhs (Tg − Ts) + (Th − Ts) + (1 − ε)ρs cs 2b(1 − ε)ρs cs

MATHEMATICAL MODEL We briefly present the unsteady one-dimensional conservation equations used to describe the process. Additional details on the model and solution method have been presented elsewhere.19 The countercurrent movements of the solid particles and gases require split boundary conditions. Although the steady-state conservation equations sometimes fail to yield a convergent solution, the unsteady model reliably produces a steady-state solution. Mass balance equations

∂yi

i

1 cs

hgsags

■

1 ∂(ugC) 1−ε ∂C − ρs =− L ∂z ∂t ε

∑ cg,irout,i(Tg − Ts) +

⎛ 150 ⎞ ⎛ kJ ⎞ Wcomp⎜ ⎟ − 4.096, ⎟ = 4.572 ln⎜ ⎝ Pin ⎠ ⎝ mol CO2 ⎠

(3)

Pin ≤ 4.56 bar

Energy balance equations

(9) 22

∂Tg ∂t

=−

ug ∂Tg L ∂z

+

2

+

λax ∂ Tg 2

cgρg L ∂z

2

+

(1 − ε)ρs ερg cg hgsags ερg cg

The above equation was proposed by V. Wagener et al. and obtained from a nonlinear regression of computational results from an ASPEN PLUS simulation of a series of compressor and cooler stages. Unlike in a chemisorption process, the CO2 product from the MBA process contains a non-negligible amount of N2 because of the limited selectivity of physisorption adsorbents. To remove the impurity from the liquefaction

∑ cg,irin,i(Ts − Tg) i

(Ts − Tg) (4) 7601

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a

Operating Variables with Nominal Values

Flue gas saturated with water at 40 °C before the dehydration unit. bMinimum temperature approach.

TADB(bottom) (K) = 298, PADB(top) (bar) = 1, PA−DEB(top) (bar) = 1 TCW,in (K) = 284, conditions for liquefied CO2: 313 K, 150 bar ṁ s = 300000 (kg/h), ṁ CW = 400000 (kg/h)

37

εDax/Dm = 20 + 0.5Re Sc, λax/kg = 7 + 0.5Pr Re38 −dP/dz = 150.0((1 − ε)2)/(ε2) μ/(d2p)(ug + us) + 1.75 × 10−4(1 − ε)/ε (ρg)/(dp)(ug + us)|ug + us|39

Supplementary Equations

ags = 1.5 dp, ΔTmin(MTAb, K) = 10 Nuh = 0.023 Re0.8Prn, n = 0.4 for heating, 0.3 for cooling34 hh (J/cm2 K s) = 6 for steam, ags(cm2/cm3) = 6/dp20 19 Nugs = 2.0 + 1.1Pr1/3Re0.6,20 Uhs = 1/hs + 1/hh, hs ≈ −(2ke)/b ((∂2Ts/∂x2)/(Tw − Tavg s )) 35,36 ke/kg = 0.0935 + 0.9065 [2/(1 − kg/ks)][(ks)/(ks − kg) (lnks/kg) − 1] + 0.11RepPr

Heat Transfer Parameters

L (cm) = 300, W (cm) = 1190 2b (cm) = 3, plate thickness (cm) = 1.2

Bed Dimensions (Applied to All Beds)

tcycle (h) = 8, ug,dehy (cm/s) = 63,33 Ldehy(cm) = 400

ΔHH2O (kJ/mol) = −44.5,30 cs (J/g K) = 1.25,32 dp,dehy (cm) = 0.5

MIL-101 (Cr) Properties and Dehydation Process

ρs (g/cm3) = 0.65, cs (J/g K) = 1.07, dp (cm) = 0.342, ε = 0.31, ks (J/m K s) = 0.0173 parameters for adsorption isotherm, heat of adsorption and mass transfer rates were borrowed from ref 31

Adsorbent (Zeolite 13X) and Bed Characteristics

Tfeed (K) = 298, cg (J/(mol K) s) = ∑iciyi, μ (g/m s) = ∑iμiyi, kg (J/m K s) = ∑ikiyi, i = CO2, N2

Qfeed (mol/s) = 3055, yCO2(%) = 12.3, yN2(%) = 80.7, yH2Oa (%) = 7

Feed Gas Conditions and Properties (before the Capture Unit)

Table 1. Model Parameters and Nominal Operating Conditions

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Figure 3. Efficiency curves of a vacuum pump, model TRVK3003, from TRAVAINI Pump USA, Inc. Each number at the lines indicates the efficiency of a vacuum pump at that condition.

Figure 4. Effect of adsorbed water on CO2 adsorption capacity of zeolite 13X at 40 °C.

stage, we added a distillation column to the compression stage, as proposed in ref 23. N2 was removed at the top of the distillation column with some CO2, and pure liquid CO2 was obtained from the distillation bottom product at 60 bar and 20 °C. The CO2 was further compressed to 150 bar using a liquid pump. The compressor efficiency was assumed to be 82%. The energy penalty to separate the impurity gas was estimated to be 0.95 (kJ/mol CO) per mole% of N2. The energy penalty is reflected in the overall liquefaction energy for the MBA process such that

the MBA process using zeolite 13X, a pretreatment process to remove the water vapor is required before the capture unit.27,28 The dehydration energy is not small and should be considered in the energy evaluation when it is included. Figure 4 shows the effect of water on the CO2 adsorption capacity of zeolite 13X at 40 °C, which was derived by fitting experimental data29 to the competitive binary isotherm model. As shown in this figure, 0.5 mol/kg of H2O reduces the CO2 adsorption capacity by approximately 20% from the water-free adsorption capacity. There are various process options for dehydration. In this study, a fixed-bed TSA process based on MIL-101 (Cr) was considered. MIL-101 (Cr) is a metal−organic framework (MOF) sorbent for dehydration, and it has a higher water sorption capacity than widely used dehydration adsorbents, such as SAPO-34, NaX, and silica gel, and features reversible sorption.30 MIL-101 (Cr) can be regenerated at approximately 70 °C using a modest amount of desorption energy. The assumed TSA process, which is shown in Figure 5, is composed of two beds

⎛ kJ ⎞ Wliqf = Wcomp + Wpenalty , Wpenalty ⎜ ⎟ = 0.95yNprod 2 ⎝ mol CO2 ⎠ (10)

yprod N2

where denotes the mole fraction of N2 in the CO2 product gas from the MBA process. Equivalent Work for Steam and Total Work. Steam is used for the regenerator operation shown in Figure 1. The thermal energy of the steam was converted to the equivalent work (EW) and added to the electric energy to obtain the total energy demand in the form of work. The EW is defined as the amount of mechanical energy that can be extracted from a certain source of thermal energy, and it directly represents a penalty on power generation when the steam is drawn from a power plant. The EW for steam can be computed as follows:24 ⎛ kJ ⎞ Tstm, i − Tsink Wstm, i⎜ ⎟ = ηQ Tstm, i ⎝ mol CO2 ⎠

(11)

where η was assigned as a turbine effective efficiency of 75% and assumes steam condensation Tsink at 313 K and Q represents the thermal energy consumed for one mole of CO2. When steams at different temperatures are supplied through the regeneration component, the total equivalent work for steam is as follows: Wstm =

∑ Wstm,i i

(12)

Energy to Remove Water Vapor in a Flue Gas. Flue gas from typical power plants contains a significant amount of water vapor (approximately 3−8% depending on the site). The water vapor is detrimental to the CO2 adsorption capacity of polar adsorbents such as zeolite 13X.25,26 To properly operate

Figure 5. Schematic of the dehydration process. 7603

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Figure 6. MBA process with an improved heat integration scheme. The stream values are optimized with MTA = 10 K except for HE1 (MTA = 30 K) due to poor gas transfer coefficient on gas side.

60% of the minimum fluidization velocity, which is 2.08 m/s at 298 K and 1 bar. In addition, the bed dimensions and conditions for the dehydration process are listed with the relevant properties and specifications of the dehydration sorbent MIL-101 (Cr). The flow rates for the cooling water will be provided in the new heat integration scheme. The operating variables without fixed nominal values were selected as the decision variables for optimization. The adsorption isotherm parameters, heats of adsorption, and mass-transfer rates were adopted from ref 31 and are not presented here. The initial flue gas contains CO2, N2, O2, and water. Water was removed during the pretreatment dehydration process. Additionally, the feed gas was assumed to contain no O2 because O2 is known to negligibly affect the CO2 adsorption equilibrium.40 Thus, the capture unit only handles the binary mixture of CO2 and N2. The three beds were assumed to have the same dimensions.

that periodically alternate: one for adsorption at 40 °C and one for desorption at 70 °C. The dimensions and operating conditions of the TSA beds were determined such that the dried flue gas contained virtually no water vapor, and desorption was conducted using the exhaust gas from the ADB. The exhaust gas lost its thermal energy at heat exchanger HE1 (see Figure 6) and must be reheated for the desorption operation of the dehydration beds. This energy can be supplied by the hot CO2 product gas from the A-DEB and V-DEB. In the energy evaluation, we considered the major energy terms for dehydration, including the heat of desorption, sensible heat for the sorbent bed, and blower work. The total operation energy for the MBA process is computed as the sum of the individual energy terms described above. ⎛ kJ ⎞ Wtotal ⎜ ⎟ = Wv ‐ pump + Wliqf + Wstm + Wdehy ⎝ mol CO2 ⎠

■

■

(13)

THE MBA PROCESS WITH A REVISED HEAT INTEGRATION SCHEME Heat Integration Scheme. Heat integration is essential for enhancing the energy efficiency of the proposed CO2 capture process. The heat integration scheme shown in Figure 1 and originally proposed by Kim et al.19 can be further improved. In the basic scheme in Figure 1, the CW flow rate significantly affects the adsorption performances, particularly the CO2

MODEL PARAMETERS AND COST DATA Table 1 lists the feed gas conditions, properties, bed dimensions, adsorbent properties, adsorption characteristics, heatand mass-transfer parameters, and operating variables with their nominal values or ranges. The bed size for the MBA process was determined such that the gas velocity was approximately 7604

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recovery and the degree of heat integration (DHI), which is defined as follows:

Table 2. Optimization Results of the MBA Process operating work (kJ/molCO2)

reused thermal energy through heat integration DHI (%) = × 100 total thermal energy demands in two DEBs

PV−DEB(bar) = 0.42, ṁ s(kg/h) = 307290 ṁ CW(kg/h) = 429210, TDEB(K) = 473 ṁ CW R2(kg/h) = 102480, LADB−HE(m) = 1.43 DHI (%) = 61 CO2 purity (%) = 98.2, CO2 recovery (%) = 81.5

At a high CW flow rate, the average ADB temperature is reduced, which enhances adsorption in this unit operation. However, the DHI deteriorates because the CW exits the ADB in a cooler state than that at a low CW flow rate. Thus, a large amount of steam is required at HE2 to sufficiently raise the temperature of the CW discharged from ADB to heat the A-DEB. At a low CW flow rate, the opposite result occurs. The CO2 recovery is reduced, and the steam demand at HE2 is decreased. To enhance the DHI and to minimize the reduction in the CO2 recovery, a new scheme is presented in Figure 6. The ADB heat exchanger is divided into two sections such that the CW flow rate in each section can be individually determined. In the lower section heat exchanger, a high CW flow rate is provided to ensure high CO2 recovery. In the upper section, the CW flow rate is decreased to obtain a high CW exit temperature. The high-temperature CW exit stream is further heated at HE2 to the A-DEB target temperature, whereas the low-temperature CW exit stream is heated at HE1 and HE3 after a fraction of the stream is returned to the cooling tower. This proposed scheme is a revision of the previously proposed scheme,19 which is the same scheme as in Figure 1 except for the CWR branching before HE1. Optimization. For the MBA process with the new heat integration scheme, the operating conditions and CW branching position for the ADB heat exchanger were optimized to minimize the total work. The decision variables to minimize the total work include the desorption temperature (TDEB) and pressure (PV‑DEB), the solid circulation rate (ṁ s), the CW inlet flow rate (ṁ CW), the CW return flow rate from the heat exchanger branching point (ṁ CW R2), and the length of the lower portion of the ADB heat exchanger (LADB−HE). The optimization problem can be stated as

PZa

MEAb

Wstm

11.0

23

21.5

Wcpump Wliqf

0.5 20.5

3 7

0.5 16.1

Wdehy Wblower

3.4 1.0

0.6

0.8

Wtotal

36.4

33.6

38.9

a

Rochelle et al.41 Blower energy is added to the original result. b Rochelle et al.22 Blower energy is added to the original result. cWpump represents work for the vacuum pump in the MBA process and work for liquid pumping in absorption processes.

with a standard stripper,22 are listed together with the respective optimum operating conditions. The regeneration energy of the PZ process is approximately 2.6 GJ/ton CO2 at a regeneration pressure and temperature of 15−17 bar and 150 °C, respectively, whereas that of the MEA process is 3.55 GJ/ton CO2 at 2 bar and 100 °C. For the CO2 capture stage only, the optimum regeneration work of the MBA process was 11 kJ/mol CO2, which is less than half of those of the absorption processes. The lower amount of required work is attributed to the improved heat integration scheme. The DHI was enhanced from 57% with the original scheme19 to 61% with the new heat integration scheme in this study. The liquefaction energy of the MBA process is the highest among the three, primarily because the MBA process produces CO2 at 1 bar, whereas the MEA- and PZ-based processes produce CO2 at 2 and 15 bar, respectively. In addition, the CO2 product from the MBA process contains 1.8% N2, which increases the liquefaction energy for its separation. The blower work in Table 2 refers to the energy to feed the flue gas to the main CO2 capture units. Because the blower energy for the absorption processes is not provided in the cited references, we computed and added it by assuming a 20-m-high bed, Sulzer Mellapak 250X structured packing, and operating conditions of 75% of the flooding point. The dehydration energy for the MBA process accounts for approximately 9% of the total operating work. The relatively low energy requirement is due in part to the plausible performance of MIL-101 (Cr) and the reuse of high-temperature waste energy of the product gas to regenerate the dehydration bed. The estimated total required work of the MBA process is 36.4 kJ/molCO2, which is slightly higher than that of the PZ process but considerably lower than that of the MEA process. The capital cost is not a concern of this study. Considering that the absorption column is usually at least approximately 20 m in height, whereas the adsorption bed is only 3 m in height, the MBA process could be more energy efficient than the absorption process. Effects of Operating Conditions on the MBA Performance. Figure 7 shows the sensitivity of Wtotal to the four selected operating variables in this optimization. Because the optimum conditions are considered the base, Wtotal increases for both positive and negative changes of the operating variables, except TDEB, which hits the upper constraint limit. The MBA performance is clearly most sensitive to the desorption temperature TDEB and thus ṁ s.

min Wtotal(X ) X

subject to [T P]liquid CO = [288 150] 2

CO2 purity ≥ 0.96, CO 2 recovery ≥ 0.80 X min ≤ X ≤ X max LADB ‐ HE] ̇ where X = [TDEBPV − DEBm ṡ ṁ CW m CWR2 X min = [400 0.1 230440 100000 0 0] X max = [473 0.5 460870 600000 600000 3]

MBA

operating conditions and results

(14)

All units are in K, bar, kg, h, and m in the written sequence. The constrained optimization problem was solved after scaling using the fmincon.m (interior-point method) in MATLAB (R2010a).

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RESULTS AND DISCUSSION Optimization Results. The optimized operating conditions and the required energy in terms of the equivalent work are summarized in Table 2. The associated heat and mass balance values are provided in Figure 6. For comparison, the performances of two absorption processes, one using 8 m piperazine (40 wt % PZ) with regeneration in heated two-stage flash units41 and one using 9 m monoethanolamine (35 wt % MEA) 7605

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selectivity and adsorption capacity of the adsorbent are enhanced from those of zeolite 13X, while the other properties remain unchanged. For each case, the operating conditions of the MBA process were optimized such that Wtotal is minimized. CO2 selectivity has rather minor effects on the considered performance items. Enhancing the CO2 purity by increasing the CO2 selectivity, although not significant, contributes to lowering Wtotal by reducing the cost penalty for the separation of nitrogen in the liquefaction stage. Increasing the adsorption capacity has a more salient effect on decreasing Wtotal despite its near-negligible effect on the CO2 purity and recovery. The major cause for this decrease is the reduction in the solid circulation rate and the subsequent decrease in the thermal energy demand from the DEBs.

Figure 7. Effects of individual operating variables on the total required work. Changes are made around the optimum values. Other variables such as ṁ CW R2 and LADB−HE are fixed at the optimum values.

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CONCLUSIONS The feasibility of employing a moving-bed adsorption process as a postcombustion CO2 capture process was investigated using zeolite 13X as the adsorbent, and the operating energy of this process was evaluated. The MBA process has many advantages over other conventional carbon capture processes. Compared with fixed-bed processes, the MBA process, as a continuous process, can accommodate temperature- and pressure-swing operations without difficulty. This process can have a lower solid circulation rate than the fluidized-bed process. The temperature profile formed by the countercurrent gas and solid flows enable more efficient heat integration than does an isothermally operated fluidized bed. Using zeolite 13X as the adsorbent, the estimated regeneration energy in terms of the equivalent work for the proposed MBA process was 11 kJ/mol CO2, which is less than half of the operating energy of the compared absorption processes. The estimated degree of heat integration was as high as 61% under the assumed MTAs. On the other hand, the estimated CO2 liquefaction energy was 20.5 kJ/mol CO2, which is nearly three times greater than the liquefaction energy for the PZ-based process, the product gas of which has a higher pressure and lower impurity contents. The estimated total operating energy of the entire MBA process from the dehydration to the liquefaction was 36.4 kJ/mol CO2, which is slightly higher than that of the PZ process but lower than that of the MEA process. Although it has not been quantitatively

TDEB has profound effects on the working capacity, which is defined as the amount of CO2 produced per unit mass of the adsorbent, and Wtotal. According to the isotherms for the zeolite 13X in this study, 11% of the CO2 that was adsorbed at the ADB remains undesorbed at PV‑DEB = 0.42 bar and 473 K. Figure 7 shows that if TDEB is higher than 473 K, it can further reduce Wtotal. This upper limit is imposed because of the uncertainty of the adsorbent isotherms in the high-temperature region, which were originally obtained using experimental data up to 393 K,31 and the increased pressure of the heat-transfer water. A lower PV‑DEB increases the working capacity but simultaneously increases the vacuum pump work. The opposing effects result in a low sensitivity of PV‑DEB to Wtotal. The solid circulation rate ṁ s is another critical factor that significantly affects Wtotal. When ṁ s is high, the adsorbent particles leave the ADB unsaturated with CO2, which is less than the equilibrium amount in the adsorption condition; however, the CO2 recovery can be high otherwise. In the opposite situation, the adsorbent particles can leave the ADB saturated with the adsorbed CO2; however, the CO2 recovery can be reduced. Figure 7 shows a consequence of this trend. The effects of the CW flow rates on Wtotal were discussed in the heat integration section and need not be repeated here. Effects of the Adsorbent Competency on the MBA Performance. Figure 8 shows the changes in the MBA performance under hypothetical situations in which the CO2

Figure 8. Effects of the selectivity and the adsorption capacity (AC) of the adsorbent on (a, b) the MBA performance and (c) the total required work. 7606

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Q = consumed thermal energy (kJ/molCO2) Qfeed = molar flow rate of flue gas (mol/s) R = gas constant (= 8314.395), (kPa cm3/mol K) Re = Reynolds number (= ρsεudp/μ) Sc = Schmidt number (= μ/ρD) T = temperature (K) TDEB = desorption temperature (K) Tfeed = feed gas temperature (K) Tg = gas temperature (K) ΔTmin = minimum temperature approach (K) Uhs = overall heat transfer coefficient between heating medium and solid (W/cm2 K) W = length of bed (cm) Wtotal = total equivalent work (kJ/mol CO2) Wm = length of unit module of bed (cm) ags = the heat transfer area between the gas and solid phases per unit volume (cm2/cm3) b = half distance between plates (cm) bi = Langmuir constant of component i (1/kPa) cg = specific heat capacity of gas (J/g K) cs = specific heat capacity of adsorbent (J/g K) dp = particle diameter (cm) dp,dehy = particle diameter for dehydration process (cm) hgs = heat transfer coefficient between gas and solid phase (W/cm2 K) hh = heat transfer coefficient of heating medium side (W/cm2 K) hs = heat transfer coefficient of solid side (W/cm2 K) ke = effective thermal conductivity (W/cm K) kg = thermal conductivity of gas (W/cm K) ks = thermal conductivity of solid (W/cm K) ki = thermal conductivity of component i (W/cm K) kLi = coefficient of linear mass transfer model for component i (1/s) kQi = coefficient of quadratic mass transfer model for component i (1/s) m = molar flow rate (mol/sec) ṁ CW = mass flow rate for cooling water (kg/h) ṁ s = mass flow rate for solid (kg/h) ṁ CW R2 = mass flow rate for CWR2 stream (kg/h) qi = amount adsorbed of component i (mol/g-ads) q*i = equilibrium adsorbed phase concentration (mol/g-ads) qi = amount adsorbed of component i (mol/g-ads) q m,i = maximum amount adsorbed of component i (mol/g-ads) ri = mass transfer rate of component i from bulk gas to adsorbed phase (mol/g-ads.s) rin,i = a positive mass transfer rate from the solid to the gas phase (mol/g-ads.s) rout,i = a positive mass transfer rate to the reverse direction (mol/g-ads.s) tcycle = dehydration adsorption time (h) ug = interstitial linear velocity of gas (cm/s) ug,dehy = interstitial linear velocity of gas in dehydration unit (cm/s) uh = interstitial linear velocity of heating medium (cm/s) us = interstitial linear velocity of solid (cm/s) yi = mole fraction of component i yfeed = feed mole fraction of component i i

evaluated and compared, the proposed MBA process could be advantageous over the absorption process from a capitalinvestment perspective. The required bed height for the ADB is only approximately 3 m, whereas the absorption column is usually at least approximately 20 m in height. The economic feasibility of the MBA process in terms of CAPEX and OPEX is a subject of future research. There are various opportunities to improve the energy efficiency of the proposed MBA process. The largest improvement can be achieved using a novel solid sorbent that can offer a higher CO2 sorption capacity with a lower heat of adsorption. MOFs or amine-grafted silica gel (A-SiG) are potential candidates for this purpose. The A-SiG sorbent does not require water removal or a vacuum desorption stage, and the overall energy can be further enhanced. Heat integration extended between the liquefaction stage and the carbon capture unit can markedly reduce the thermal energy requirement. In addition, the heat integration scheme in Figure 6 can be further refined to yield a better DHI. One of the hurdles for commercially implementing the MBA process is the attrition problem with large sorbent particles. To properly operate a moving bed, the particle size should be at least a few mm, and the attrition problem can be severe even under gentle movement of particles. Methods to alleviate the attrition problem have been proposed at the level of equipment design.42 However, truly overcoming this problem requires the development of sorbent manufacturing and binding techniques that ensure high mechanical strength.43

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], Phone: +8210 4871 8477. Fax: +822 3272 0319. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Energy Resource R&D program (2010T10 0100913) under the Ministry of Knowledge Economy and the Korea CCS R&D Center (KCRC) grant funded by the Korean government (Ministry of Education, Science and Technology, No. 2012-0008886). K.S.L. acknowledges the Korean Institute of Energy Research (KIER) grant funded by the Korean government (Ministry of Science, ICT & Future Planning).

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NOMENCLATURE Ah = cross-sectional area of heating medium channel (cm2) C = concentration in gas phase (mol/cm3) Ci = concentration of component i in gas phase (mol/cm3) Dax = mass axial dispersion coefficient (cm2/s) Dm = mass axial dispersion coefficient (cm2/s) ΔHi = average isosteric heat of adsorption for component i (J/mol) L = bed height (cm) Ldehy = bed height of dehydration unit (cm) LHE1 = HE1 height (m) Nuh = Nusselt number of heating medium (= hL/k) Nm = number of modules P = pressure (kPa) PV−DEB = pressure in V-DEB (bar) Pr = Prandtl number (= cμ/k)

Greek letters

λax = effective axial thermal conductivity of gas (W/cm K) μ = gas viscosity (kPa s) ρg = gas density (g/cm3)

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ρs = bulk adsorbent density (g/cm3) ε = bed porosity η = efficiency γ = heat capacity ratio (= cp/cv)

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Subscripts

ADB = adsorption bed A-DEB = atmospheric desorption bed CW = cooling water V-DEB = vacuum desorption bed avg = average blower = blower comp = compression dehy = dehydration feed = feed g = gas h = heat transfer medium in = input liqf = liquefaction m = module penalty = penalty s = solid stm = steam sink = sink v-pump = vacuum pump w = wall (plate) Superscripts

prod = production avg = average

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