Aminosilica

Article pubs.acs.org/IECR

CO2 Sorption Performance of Composite Polymer/Aminosilica Hollow Fiber Sorbents: An Experimental and Modeling Study Yanfang Fan,† Jayashree Kalyanaraman,† Ying Labreche,† Fateme Rezaei,‡ Ryan P. Lively,† Matthew J. Realff,† William J. Koros,*,† Christopher W. Jones,*,† and Yoshiaki Kawajiri*,† †

School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, Georgia 30332, United States ‡ Department of Chemical & Biochemical Engineering, Missouri University of Science & Technology, 1101 East State Street, Rolla, Missouri 65409, United States S Supporting Information *

ABSTRACT: The dynamic CO2 sorption performance of polymer/silica supported polyethylenimine hollow fiber sorbents (CA-S-PEI), focusing on heat and mass transport effects, is investigated experimentally and computationally during sorption of CO2 from simulated, dry flue gases. The effect of the nonisothermality on the sorption performance is investigated by varying the module materials of construction. The heat effects are minimized by using a heat conductive module case with a diameter of 0.25 in., and, accordingly, the breakthrough capacities are increased by 30% over a similar module constructed from less conductive components, thereby improving fiber sorbents utilization efficiency. The sorption kinetics in CA-S-PEI hollow fiber sorbents are investigated in terms of flow rates, module packing fraction, module length, and silica particle size. A mathematical model developed previously is successfully utilized to predict various contributions to the overall mass transfer resistance. In fiber sorbents where the amine loading is high, such as those employed here, the sorption process is found to be controlled by intraparticle mass transfer resistances. Unlike fiber sorbents based on physisorbents, the external gas diffusion resistance has minimal effects on the breakthrough capacities, as evidenced with the negligible effects of the module packing fraction on the sorption capacities. Sorption capacities are found to increase with the fiber module length as a result of self-sharpening effects. The increase of particle size increases the mass transfer resistance of the fiber sorbents as illustrated by the more diffuse CO2 breakthrough fronts in fiber modules containing bigger silica particles. The capacities in fiber sorbents with the largest silica particles exhibit the lowest sorption capacity, as expected.

1. INTRODUCTION As global demand for coal- and gas-fired electricity remains strong across the world,1−3 fossil fuel consumption continues to rise, resulting in billions of tons of CO2 emission into the air every year.4,5 The atmospheric CO2 level has increased noticeably from approximately 250 to 400 ppm as a result of these CO2 emissions.6,7 As a major carbon mitigation option, CO2 capture and sequestration has attracted attention as a way to reduce the CO2 emissions from large-scale power plants and industrial facilities. In particular, the removal of CO2 from the flue gas of fossil fuel combustion processes is the subject of significant research and development activity on a global scale.8−16 Currently, a vast array of efforts are underway to develop a cost-effective capture technology. The benchmark mature technology of CO2 scrubbing using amine solutions suffers from a series of problems, including high energy use, degradation of the amine solution, and equipment corrosion issues.10,17,18 Solid sorbents have attracted significant attention, as they hold promise for achieving a high adsorption efficiency with less energy consumption.2,4,10,12,19−22 In contrast to aqueous amine-based CO2 capture systems, the regeneration energy consumed in processes using solid sorbents might be reduced dramatically due to the absence of large amounts of water.19,23 However, to make solid sorbents a viable industrial scale CO2 capture process for power plants, appropriate contactors for the © XXXX American Chemical Society

sorbents must be developed. Fixed beds, which are commonly studied on the laboratory scale,20,24 are impractical on flue gas scales due to the high pressure drops and poor heat transfer performance of these contactors. Polymeric hollow fibers imbedded solid sorbents have been developed as a novel gas−sorbent contacting configuration that can potentially be scaled to “mega” scale.25 For any practical sorbent system, there are several challenges that must be overcome, including achieving good sorption kinetics, managing heat effects, achieving a large sorption capacity at low temperature and CO2 partial pressure, and sufficient long-term sorbent stability, particularly in the presence of flue gas impurities such as O2, SOx, and NOx.26−30 Researchers continue to address these issues by developing novel sorption materials12,21,22,25,31−33 and optimizing the sorption−desorption processes.11,34−37 Hybrid hollow fiber sorbents composed of polymeric hollow fibers containing silica particles functionalized with amine groups31,38 are one type of new structured sorbent that has been successfully applied in rapid temperature swing adsorption processed (RTSA) for separation of simulated flue gases.11 In the RTSA process, flue gas containing CO2 flows over the shell Received: November 23, 2014 Revised: January 14, 2015 Accepted: January 23, 2015

A

DOI: 10.1021/ie504603h Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Schematic of RTSA system setup (left) and module configuration (right). MFC, mass flow controller; TC, thermocouple.

lab-scale fiber sorbent system with respect to the fiber sorbent’s sorption behavior needs to be better elucidated to allow for identification of the most efficient operating regimes for these structured sorbent materials. The focus of this work was to thoroughly quantify the performance of the fiber sorbents during CO2 sorption with regard to heat effects and the kinetic sorption behavior of the materials at the lab scale. The dynamic sorption capacities at varied simulated flue gas flow rates were investigated under dry conditions to understand the sorption kinetics of the CA-S-PEI fiber sorbents. In addition, a series of experiments were carried out to investigate the effects of the fiber module packing fraction and the module length on the overall dynamic sorption performance. On the basis of the mass and heat transfer model developed in our previous work,55 we were able to simulate the kinetics of the sorption process using the model, and we further discussed the kinetic sorption behavior of the CA-S-PEI fiber sorbents. This Article presents a systematic investigation of mass transfer kinetics and heat effects in polyethylenimine (PEI) impregnated hollow fiber sorbents. Specifically, the relative importance of heat transfer, external diffusion resistance, and internal diffusion resistance in the fiber sorbents was elucidated, which have not been reported earlier.

of the hollow fibers while cooling water flows through the bores of the fibers, allowing the fibers to operate as nanoscopic isothermal shell-and-tube heat exchangers. During desorption, heating fluids can be flowed through the fiber bore. Fiber sorbents containing silica-supported amines with a highly porous structure that allows for fast sorption kinetics and high capacity have been demonstrated.39 In that study, fiber sorbents composed of cellulose acetate (CA) polymer fibers containing silica particles impregnated with polyethylenimine (PEI), referred to as CA-S-PEI, were employed as solid CO2 chemisorbents. As compared to traditional physisorbents such as zeolites40,41 and activated carbon,42 the CA-S-PEI sorbents exhibited high CO2 capacity in the presence of water as well as good capacity at relatively elevated temperatures akin to those found in flue gases (55−75 °C). Moreover, the unique design of the porous hollow fiber sorbents allowed for the coupling of efficient heat transfer with effective gas contacting, essentially achieving a nearly isothermal sorption process along with a lower parasitic load as compared to traditional fixed bed adsorbers.11 On a laboratory scale, a hollow fiber module may contain a single fiber up to several dozen fibers, and have a module length of 10 in. to several feet in length. On a practical scale, each module may contain many millions of fibers that reach lengths of several meters. Similar to nonisothermal sorption processes in fixed bed adsorbers, thermal waves were observed in uncooled fiber sorbent modules (i.e., without internal cooling water fed in fiber bores) during the sorption step as a result of the release of adsorption enthalpy.39 Extensive theoretical and experimental studies on nonisothermal adsorption in fixed beds were performed by Amundson et al.,43−46 Basmadjian et al.,47 and other research groups.20,48−53 Earlier in 1965, Amundson et al.46 have developed an equilibrium theory for nonisothermal adsorption in fixed beds, showing that heat effects are of great importance in analyzing adsorber performance because adsorption isotherm is highly temperature dependent. In general, the heats released in adsorption process move as kinetic thermal waves in the axial direction. These thermal waves, referred to simply as heat effects in this study, affect the concentration front velocity, thereby increasing the dispersion of the mass-transfer zone and reducing the dynamic sorption capacities. The analysis of heat effects on adsorber performance is of interest in optimizing the adsorption process to develop a more efficient adsorption bed. Our previous studies31,39,54 have shown that in a lab-scale fiber sorbent module, a significant temperature rise in fiber sorbents occurs during the sorption process if no internal cooling water is used. The significance of the heat effects in a

2. EXPERIMENTAL SECTION 2.1. Hollow Fiber Fabrication and Fiber Module Preparation. Hollow fiber sorbents used in this work were spun and functionalized using the postspinning amine infusion techniques described in our previous work.31 The fiber sorbents were a hybrid matrix of CA (MW 50 000, Sigma-Aldrich) and commercial silica (C803, W.R. Grace), with a silica loading of 57 wt %. PEI (MW 800, Sigma-Aldrich) was used as the amine source in the postspinning amine infusion step. Multiple modules with different configurations, that is, module length L, packing fraction ϕ, and module case, were made using these hollow fiber sorbents. Temperature profiles during operation were measured by T-type thermocouples placed in the middle of the module, as shown in Figure 1. In addition, two other types of commercial silica ES757 (PQ Corp.) and CS 2129 (PQ Corp.) with varied particle size were used to make fiber sorbents to study particle size effects on the dynamic sorption performance. The majority of experiments were performed using fiber sorbents made with C803 silica, and this should be assumed unless otherwise noted. 2.2. CO2 Breakthrough Experiments. All CO2 adsorption measurements were performed with uncooled fibers at atmospheric pressure and 35 °C in a custom designed RTSA system. The RTSA system setup is shown in Figure 1. The B


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Figure 2. Schematic describing the mass transfer resistances and various interface concentrations in the fiber sorbents. Cg, Cms, and qms are the CO2 concentrations in the bulk gas phase, inside the fiber macropores and micropores, respectively. Cg0 and Cm0 are the interface CO2 concentrations in the bulk gas phase/macropore and the macropore/micropore interfaces, respectively.

packing fraction, fiber module length, and particle size of the silica support embedded in the fibers. The mass transfer resistance model developed was based on the assumption that the adsorption of CO2 in PEI impregnated silica sorbent occurred in two different types of amine sites, initially sites that were easily accessible, being available on the exposed surface of the sorbent pores (exposed PEI, red region in Figure 2), and then on ones that were confined within the bulk phase of the amino-polymer (bulk PEI, blue region in Figure 2) as reported in prior studies.24,55,56 The silica particle impregnated with PEI studied in this work has the measurable pore volume (see Supporting Information Table S1). This fact indicated that sorbents loaded with PEI have open pores that allow CO2 molecules to diffuse to react with amine groups as shown in Figure 2. The overall mass transfer resistances for adsorption on the exposed PEI (1/Kov,exposed) and for adsorption in the buried, bulk PEI (1/Kov,bulk) are defined, respectively, as follows.

simulated dry flue gas composition was 14% CO2, 14% inert tracer He, which has negligible adsorption capacity, with the balance N2. The simulated flue gas flow rate varied in a range of 30−250 sccm (standard cubic centimeters per minute, standard conditions: 101 kPa and 0 °C), and the corresponding gas hourly space velocity (GHSV) was in a range of 1000−6000 h−1. Prior to each adsorption experiment, the module was heated to 90 °C under flowing N2 at 80 sccm for 0.5 h to desorb adventitious CO2 and water, then cooled to 35 °C and exposed to simulated dry flue gas for the experimental sorption run. All CO2 adsorption measurements were performed at atmospheric pressure and 35 °C. The effluent composition exiting the fiber sorbent module was transiently measured by mass spectrometry (Pfeiffer, Omnistar Quadrupole mass spectrometer QMG 220). All experiments reported in this Article except those in section 4.1 were conducted using a copper module with an outer diameter of 0.25 in., housed with fibers of an inner diameter of 550 μm and outer diameter of 1305 μm, respectively. The module configuration, number of fibers loaded in the module, and length of the fiber used in each case were varied as described in the text.

1 Kov,exposed 1

3. KINECTIC MODEL The mass transfer characteristics of CO2 adsorption on supported amine hollow fiber sorbents that are highly loaded with amines are complex, exhibiting a characteristic shape in the breakthrough curve of a “long tail” after breakthrough, and the outlet concentration approaches the value of the feed gas asymptotically. Furthermore, a reversal of the trend in temperature dependency on breakthrough capacity was observed, where the breakthrough capacity increased with an increase of temperature.39 To understand these mechanisms, we employed a detailed mathematical model describing the diffusive mass transfer resistance of CO2 through the amine sorbents to investigate and understand the effect of mass and heat transfer kinetics on the CO2 sorption performance. In a previous work,55 we proposed a mass transfer resistance model, which included a first-principles model for each of the individual component diffusion resistances. The model was rigorously validated (see the Supporting Information) and shown to predict the experimental CO2 breakthrough curves sufficiently accurately under different operating conditions and module design parameters such as flue gas flow rate, module

Kov,bulk

=

=

1 1 1 + + Kg Km K s,exposed

1 1 1 1 + + + Kg Km K s,exposed K s,bulk

(1)

(2)

where the gas phase and fiber macropore (interparticle) diffusion resistances are represented by 1/Kg and 1/Km, respectively, as shown in Figure 2. Here 1/Ks,exposed represents the sorbent or the intraparticle resistance with respect to diffusion of CO2 to the exposed PEI sites. On the other hand, 1/Ks,bulk represents the intraparticle resistance with respect to the diffusion of CO2 to the bulk PEI. Thus, the overall diffusion resistance for adsorption on accessible PEI (1/Kov,exposed) is governed by the combined resistances of the gas film, and interparticle and intraparticle diffusion to the exposed PEI (eq 1). The overall diffusion resistance for adsorption on the bulk PEI (eq 2) is governed by the intraparticle diffusion within the bulk PEI region in addition to the combined diffusion resistances encountered during adsorption on more exposed PEI (gas, interparticle, and intraparticle diffusion to the more accessible PEI). Resistances corresponding to gas film diffusion (1/Kg) and the interparticle diffusion (1/Km) are represented by eqs 3 and 4. C


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Industrial & Engineering Chemistry Research 2kg εf ro

Kg =

within the bulk PEI reduces the available free volume. Additionally, the Arrhenius relation in the above equation, including the activation energy E, defines the temperature dependency of the amino-polymer diffusivity. The CO2 accumulation in the fiber sorbent (in both sites) is modeled using the Linear Driving Force (LDF) model as follows:

∂qeq

(ro2 − ri2) ∂C (1 − εf )ρf g

Km =

(3)

8ro2Df,pεf ∂qeq

(ro2 − ri2)2 ∂C (1 − εs)(1 − εf )ρf g

∂qexposed

(4)

∂t

where Kg is the convective mass transfer coefficient of the gas and Df,p is the CO2 diffusivity in the fiber macropores. Additionally, the models for the intraparticle sorbent resistance with respect to diffusion to the exposed PEI (1/Ks,exposed) and bulk PEI sites (1/Ks,bulk) are given as follows: K s,exposed =

∂t

∂qeq

rs2 ∂C ψ (1 − εs)ρs

(5)

15Dpεs ∂qeq

rs2 ∂C (1 − ψ )ρs g

(6)

where Dp,exposed is the Knudsen diffusivity based on the sorbent pore diameter (as the mean free path = 100 nm > ds,pore = 20 nm) and Dp is the diffusivity of CO2 in the amino-polymer phase of the sorbent. Here, ψ represents the ratio of the amine sites available on the exposed, accessible PEI layer to the total amine sites available in a unit weight of the sorbent, that is, the percentage of PEI represented by the red region in Figure 2. The estimation of ψ is performed on the basis of the assumption that the surface area lost upon impregnating PEI in silica particle is occupied by exposed PEI, which leads to the following equation: ψ=

Ab − Al Spw

= Kov,bulk((1 − ψ )qeq − qbulk )

(10)

(7) Figure 3. Average mass transfer resistance components of the exposed PEI and bulk PEI sites at the normalized time instant τ = 60. The inset shows a zoomed view of the y-axis from 0 to 0.5.

Here, Ab and Al are the surface areas of bare silica particle and PEI impregnated silica, respectively. Sp is the surface area occupied by a unit weight of exposed PEI, and w is PEI weight percent loading in the silica. The value of Sp is estimated on the basis of the known fraction of exposed PEI sites in PEI impregnated SBA-15 silica (ψSBA‑15 = 0.64), as reported by Wang et al.56 using temperature-programmed desorption experiment. The value of Sp is accordingly estimated to be 2719 m2/g-exposed PEI (see the Supporting Information) from eq 7. Assuming that the value of Sp does not depend on the silica particle, the value of ψ for the silica sorbent of interest, C803, can be estimated using the same equation as ψC803 = 0.16 using the following values: AC803 = 209 m2/g and AC803 = 37 b l 2 C803 m /g, and w = 39%. This ratio indicates that approximately 16 wt % of PEI loaded in C803 type of silica sorbents is available as exposed PEI. It should finally be noted that this estimation method for ψ is based on a very simple and crude calculation. To calculate Dp, a model analogous to the free volume theory model of polymers57 was proposed and rigorously validated in our earlier work.55 The amino-polymer diffusivity, Dp, is given by eq 8. Dp = Dp0 e−αqbulk e−E / RTg

(9)

In the above, qexposed is the CO2 concentration in the exposed PEI layer of the sorbent, and qbulk is the CO2 concentration in the bulk PEI of the sorbent. The total CO2 sorbent loading is thus calculated as q = qexposed + qbulk. More details on the model formulation can be found elsewhere55 and are not repeated here for the sake of brevity. The sorption isotherm of this material (Supporting Information Figure S1) and a short discussion of the key model equations were included in the Supporting Information. Figure 3 shows the distribution of the different component mass transfer diffusion resistances spatially averaged at a given

15Dp,exposed εs g

K s,bulk =

∂qbulk

= Kov,exposed(ψqeq − qexposed)

normalized time instant, τ. Here, we define the normalized time as τ = t/tres, where tres is the residence time of the flue gas. The spatial average of the mass transfer resistance, 1/Kg, for example, is obtained as follows: 1 2 = 2 Kg (ro − ri2)L

L

∫0 ∫r

i

ro

⎛1 ⎞ r ⎜⎜ (r , z)⎟⎟ dr dz ⎝Kg ⎠

(11)

where ri, ro, and L are the inner radius, outer radius, and length of the fiber, respectively. As seen in Figure 3, diffusion in the bulk PEI (1/Ks,bulk) is the dominant resistance followed by diffusion in the macropore (1/Km) and gas film (1/Kg). On the basis of the relative orders of magnitude, we can infer that the adsorption in the accessible PEI sites (1/Kov,exposed in eq 1) is controlled by the diffusion resistances of both the gas (1/Kg) and the interparticle resistances (1/K m ), whereas the adsorption within the bulk PEI sites (1/Kov,bulk in eq 2) is controlled solely by the intraparticle diffusion resistance (1/ Ks,bulk) within the bulk PEI. The detailed analysis of this behavior has been reported in our previous work,55 where the developed model has already been validated (see Supporting Information Figures S2−S4) against the different parametric module design and operating conditions studied in this Article.

(8)

where qbulk is the CO2 concentration in the bulk PEI phase of the sorbent and α defines the rate at which CO2 adsorption D


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Industrial & Engineering Chemistry Research Thus, the model is used in this work to analyze and make inferences on the process behavior under different parametric conditions.

4. RESULTS AND DISCUSSION 4.1. Role of Heat Transfer in the Sorption Process. Like any exothermic process, adsorption is thermodynamically favored by heat removal, which results in an increase of the sorption capacity. In the proposed RTSA configuration,58,59 the heat of adsorption is removed by the cooling water flow through the bore of the fibers, which are coated with a water impermeable lumen layer, making the fibers nanoscopic shelland-tube heat exchangers.60 In the case of the CA-S-PEI fiber sorbent studied in this work, the formation of distinct thermal waves in the sorption process has been characterized in our early study.39 It should be noted that the total heat of adsorption released even with complete saturation in a lab-scale module with six fibers is not significant (the product of heat of adsorption ΔH with pseudoequilibrium capacity, qpe, in such as case is approximately 65 J). As the heat capacity of the module wall is significant, the majority of the sorption enthalpy gets rapidly lost. Thus, the rate of the heat removal from the fibers at the lab scale could be tailored by using highly heat conductive module cases in the module construction to reduce the heat transfer resistance in lab-scale dry CO2 sorption experiments. Two different module cases made of stainless steel and copper tubing with different thermal conductivities were used to make fiber sorbent modules. Both modules were of diameter 0.25 in. and loaded with six fibers of length 10 in. Copper, with a thermal conductivity of 401 W/(m·K), acts as a much better heat conductor as compared to stainless steel, which has a thermal conductivity of 16 W/(m·K).61 Thus, more heat is expected to be removed during the adsorption process in the copper module. The effect of the heat of adsorption on the sorption performance is referred to as heat effects in the subsequent discussion. Figure 4 shows the breakthrough curve obtained using both the uncooled copper module and the uncooled stainless steel module at a flue gas flow rate of 80 sccm, along with the respective fiber temperature profiles. As is seen clearly from the breakthrough curves, the copper module results in a higher breakthrough capacity than the stainless steel module at a given flow rate, as CO2 breaks through the module much later in the copper module as compared to the stainless steel module. Also, the stainless steel module resulted in a higher temperature rise than the copper module, indicating a lower heat removal rate with the stainless steel as compared to the copper module. Several important parameters tb, qb, and qpe and the fractional length of unused bed (LUB) were derived from the breakthrough curves. The breakthrough time, tb, in this work was defined as the time corresponding to Cbr/Co = 0.05, where Cbr is CO2 concentration at breakthrough and Co is the inlet CO2 concentration of simulated flue gas. The CO2 breakthrough capacity, qb, was the capacity corresponding to tb. The pseudoequilibrium adsorption capacity, qpe, was defined as the capacity obtained after 500 s of gas exposure, a point where the module had reached a pseudosaturation state. Both qb and qpe were determined by utilizing a method similar to that reported in our previous work,39 that is, integrating the area bounded by the He and CO2 breakthrough curves within tb and 500 s, respectively. Here, He acts as the inert tracer to capture the background flow information, and CO2 is the adsorbate of

Figure 4. Breakthrough curves (top) and temperature profiles (bottom) of CA-S-PEI fibers mounted in different module cases. Qfluegas = 80 sccm. ΔT: Tfiber − Texp, Tfiber is the fiber temperature and Texp is the experimental temperature of 35 °C.

interest. The fractional length of unused bed (LUB) is defined as follows:62 t ⎞ ⎛ LUB = ⎜1 − b ⎟ ⎝ t̅ ⎠

(12)

where t ̅ is the stoichiometric breakthrough time (i.e., t ̅ is calculated on the basis of t ̅ = ((sorbent weight × qeq)/ (QfluegasC0))), tb is the experimental breakthrough time, and L is the adsorber bed length. Figure 5 compares the breakthrough capacity qb, LUB, and the maximum thermal peak intensity of the CA-S-PEI fiber sorbents within different module cases. The fiber module with the copper case exhibited a much higher breakthrough capacity, especially at higher flow rates, where approximately 30% higher capacity was achieved as compared to that with stainless steel module. The high gas flow rates yield a higher heat delivery rate in the sorption process, and the heat effects in the sorption process seem to be more prominent at higher flow rates. In effect, the copper module with the higher heat conductivity as compared to that of the stainless steel module case yields significantly higher sorption capacities than the latter, especially at higher flow rates (Figure 5). We have observed a similar phenomenon when comparing water-cooled fibers at the lab scale and fibers not actively cooled with water. Moreover, the fiber module with the copper case exhibited a lower LUB as compared to the stainless steel module case, indicating improved fiber sorbent utilization efficiency as a result of the efficient heat removal. This result is consistent with our expectation that reduced heat effects occur in the copper fiber module as a result of better heat transfer through the copper case surface. Accordingly, the fiber temperature in the copper module is much lower than in the stainless steel module during sorption, as shown in Figure 5 (bottom). This result E


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case, the sorbent temperature sharply rises to approximately 42 °C, and CO2 had a much earlier breakthrough as compared to the isothermal case. Although thermal waves still occur in the fibers contained in the copper module and heat effects are not completely eliminated, the sorption behavior is nearly the same as the calculated isothermal sorption performance. To determine the reason for the near identical breakthrough capacities of the copper module and the modeled isothermal conditions, the relative movement of the thermal and concentration fronts in the fiber is analyzed using the model, as shown in Supporting Information Figure S5. As the thermal front propagates ahead of the mass transfer zone, the concentration front is not influenced significantly by the minimal fiber temperature rise (5−10 °C) occurring in the adsorption zone and in the downstream region. Plotting the concentration and thermal front velocities that are estimated using the model in Supporting Information Figure S6 shows that the thermal front moves faster than the concentration front by nearly 20% across different flue gas flow rates. It should be also noted that while the temperature increase in the stainless steel module may have increased the diffusion rate of the gas, it did not overcome the decrease in the equilibrium capacity, and thus resulted in a lower breakthrough capacity. In our previous study using a copper module, we reported that a higher temperature in a certain temperature range (between 35 and 55 °C) improved the breakthrough capacity due to faster gas diffusion yielding better access to buried PEI sites.55 Because the maximum temperature rise of the stainless module (approximately 6 °C in Figure 4) is higher than that of the copper module (approximately 4 °C in the same figure), the diffusion rate in the stainless module may be faster. Nevertheless, qb of stainless steel module shows a lower value than that of copper module (Figure 5, top). This can be explained by assuming that this temperature rise occurs only locally and temporarily in the fiber module in such a way that the equilibrium capacity was decreased without improving the diffusion rate significantly. Further quantitative analysis would require modeling of the sorption dynamics and complex interactions between the diffusion rate and equilibrium capacity in the stainless steel module, which was not carried out in this work. In the experiments below, the copper module is used to study the mass transfer kinetics while avoiding the influence of the heat transfer as the insignificant temperature rise observed in copper module does not significantly interfere in CO2 breakthrough profiles. 4.2. Role of Mass Transfer Kinetics in Sorption Process. The kinetics of the CO2 sorption process in PEI

Figure 5. Heat effects on the breakthrough capacity, qb, and LUB in the CA-S-PEI fibers at various flow rates (top); and maximum fiber temperature rise during sorption at various flow rates (bottom). ΔT: Tfiber,max − Texp, Tfiber,max is the maximum fiber temperature in sorption process and Texp is the experimental temperature of 35 °C.

demonstrates that heat effects reduced the sorbent capacity in normal operation without heat removal as a result of the exothermic nature of the sorption process. To further quantify the impact of the extent of heat removal on the sorption performance, we considered two extreme cases using the mathematical model: CO2 breakthrough under isothermal and adiabatic conditions. The breakthrough curves under these two extreme conditions are compared to experimental data from the copper module. Figure 6 (left) compares the experimental breakthrough curves obtained in the copper module along with the extreme cases of isothermal and adiabatic adsorption for a flue gas flow rate of 80 sccm, whereas Figure 6 (right) shows the temperature profiles for the respective cases. We found that the experimental breakthrough curve corresponding to the copper module was nearly identical to that predicted by the isothermal model even though a temperature rise of 3 °C was observed under the experimental conditions. On the other hand, for the adiabatic adsorption

Figure 6. Breakthrough curves (left) and temperature profiles (right) of experimental results versus model prediction at 80 sccm. F


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sharpened with an increase in the flow rate, that occurred because the external gas film resistance, which was an important diffusion resistance in that study, was reduced by an increase of the gas flow rate. We also show that the influence of flow rate on the broadening of the breakthrough profile cannot be explained by axial dispersion. Axial dispersion of concentration profile is due to the combined effects of radial diffusion, which reduces the concentration front velocity, and axial convection, which leads to the increase of concentration front velocity.66 The axial dispersion effect on the breakthrough profiles was investigated experimentally using the He breakthrough profiles, which were obtained by flowing a He/N2 gas mixture through a module initially filled with N2. The gas mixture was of composition containing 14% He and 86% N2. Figure 8 shows the He

impregnated porous fiber sorbents are postulated to be controlled by one or a combination of the following mechanisms:55,62 (1) external gas diffusion resistance, that is, transport of CO2 (adsorbate) from the bulk gas phase to the outer surface of fiber sorbent; (2) interparticle diffusion resistance, that is, transport of adsorbate through the macropores within the polymeric matrix of fiber; (3) intraparticle diffusion resistance, that is, transport of adsorbate through the PEI-filled micro and mesopores of the silica particles; and finally (4) reaction of the CO2 with the amines. As the CO2 reaction rate with amines is typically on the order of 200−3000 s−1,63 it is assumed that reaction rate is not a controlling step in the CO2 sorption process. The CO2 breakthrough experiments were carried out with varied conditions such as the flue gas flow rate, fiber packing fraction, fiber module length, and particle size of the support silica to investigate the effect of various components of mass transfer kinetics on the sorption performance. 4.2.1. Effect of Flue Gas Flow Rate on Sorption Kinetics. Among the different factors controlling the CO2 adsorption rate, the external diffusion resistance is determined by the external boundary layer thickness, which is inversely proportional to the square root of the flue gas flow rates.64 The effect of the external diffusion resistance can therefore be studied by varying the flue gas flow rates. The increase of the flue gas flow rate is expected to reduce the external gas diffusion resistance. Figure 7 illustrates the experimental CO2 concentration profiles

Figure 8. Experimental He breakthrough profiles at various flow rates in a 17 in. fiber module.

breakthrough profiles at various gas flow rates plotted against the normalized time, τ. Because He is an inert gas and does not adsorb in the amine sorbents, it can be assumed that the change in shape or breakthrough time of the He concentration profiles with flow rate is solely due to the effects of axial dispersion without being influenced by mass transfer resistances. As observed in Figure 8, the He breakthrough profiles did not change significantly with the increase in flow rate, which implies that the effect of axial dispersion is not significant in the labscale modules tested in this work. Therefore, it can be concluded that the broadening (nonsharpening) of the CO2 breakthrough profiles observed with the increase in flow rate in the amine sorbents is mainly due to the impact of intraparticle diffusion mass transfer resistances, rather than axial dispersion. Model analysis of the behavior of the gas film resistance (1/ Kg) with the increase in flow rate is performed as shown in Supporting Information Figure S7 to determine if the increase in flow rate reduces the gas film resistance, as expected. As observed, the gas film resistance indeed decreases with the increase in flow rate. However, the gas diffusion resistance is only one of the controlling resistances for adsorption on the accessible PEI sites (Figure 3), which accounts for only a small fraction of the total adsorption amine sites (ψ = 0.16, see the Supporting Information). Therefore, the decrease in gas film resistance with the increase of flow rate did not have a significant overall impact on the CO2 breakthrough profiles and the breakthrough capacity. 4.2.2. Effect of Packing Fraction of the Fiber Module on Sorption Kinetics. The fiber packing fraction, ϕ, based on the number of fibers in a module with a given diameter, di,mod, is another important parameter influencing the mass transfer

Figure 7. Experimental CO2 concentration profiles at various flow rates against normalized time, τ. τ = t/tres, where tres is residence time.

with respect to the normalized time, τ, at various flow rates. Earlier, Lively et al.65 reported that the increase in flue gas flow rate sharpens the breakthrough profiles due to the improved mass transfer kinetics of CO2 in hollow fibers loaded with zeolite 13X. In contrast, in the hollow fiber loaded with the silica particles impregnated with PEI, the concentration front becomes less sharpened with the increase of flow rate in the PEI impregnated fiber sorbents, as shown in Figure 7. The above observation that the breakthrough profile broadens with the increase in flow rate can be explained by the significantly slower internal (intraparticle) diffusion resistance of the amine sorbent relative to zeolite 13X. In our previous study on the same amine sorbents, we found that the mass transfer rate from gas phase to the adsorbed phase was controlled by internal (intraparticle) diffusion resistances.55 While the residence time of the bulk gas flow reduces with the increase of flow rate, the time for CO2 to diffuse into the particles remains the same, causing a broader breakthrough profile. On the other hand, the opposite trend was obtained in the study of Lively et al.,65 where the breakthrough profile G


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Industrial & Engineering Chemistry Research kinetics of the sorption process. This parameter is defined as follows: ϕ=

Nfibersro2 2 d i,mod

(13)

where Nfibers is the number of fibers within the module and ro is the outer diameter of the fiber. For a given flow rate, a highly packed module has a lower interstitial space for gas flow and therefore a thinner gas diffusion boundary layer than a loosely packed module. A series of experiments were carried out to investigate the effects of packing fraction on the dynamic sorption performance of the CA-S-PEI fibers. Two modules with different packing fractions (ϕ = 0.69 and ϕ = 0.46) were constructed and tested in the RTSA system. As the comparison is between two modules having different number of fibers, the flue gas flow rate is normalized with respect to the volume of fibers for comparison at a common gas hourly space velocity (GHSV), which is defined as follows: GHSV =

Figure 10. Comparison of experimental breakthrough profiles in two modules with a packing fraction of 46% (ϕ = 0.46) and 69% (ϕ = 0.69) at GHSV = 4200 h−1.

was found that all of the component mass transfer resistances for the different packing fractions (Supporting Information Figure S8) are nearly the same except the gas diffusion resistance, 1/Kg, which was reduced significantly (approximately by 70%) with the increase in fiber packing fraction, as expected. Similar to the case study presented above for increasing the flow rate, the gas diffusion resistance reduction does not impact the overall breakthrough behavior and the resulting sorption capacity significantly, as it is one of the controlling resistances for only a small fraction of the adsorption sites (i.e., around ψ = 0.16 of the amine sites in PEI). 4.2.3. Effect of Fiber Module Length on Sorption Kinetics. To maximize the fiber sorbent utilization efficiency, the length of the fiber module is another critical parameter for consideration. The breakthrough front cannot be fully developed in a module that is too short. On the other hand, a module that is too long would increase the equipment cost and pressure drop on both the shell side and the lumen side. The effect of the fiber module length on the dynamic sorption performance was analyzed with the fixed module diameter of 0.25 in. and module packing fraction of 69% but with varying module length of 10, 17, and 34 in. Figure 11 shows the effect of the fiber length on the breakthrough capacity, qb, at the different flue gas flow rates. It

Q fluegas π (ro2

− ri2)LNfibers

(14)

where ro, ri, and L represent the outside, inner diameter, and length of the fiber, respectively. Figure 9 depicts the packing

Figure 9. Packing fraction effects on the experimental breakthrough capacity, qb, in CA-S-PEI hollow fibers.

fraction effects on the breakthrough capacity at various GHSVs. It can be seen that the loosely packed module with a packing fraction of 0.46 showed only slightly lower qb (around 5%) as compared to the tightly packed module (ϕ = 0.69). Furthermore, comparison of the breakthrough curves in Figure 10 for both packing fractions at GHSV = 4200 h−1 shows a similar breakthrough curve profile. This result indicates that the shell-side gas flow behavior did not significantly influence the mass transfer performance in the fiber sorbent module for the range of packing fractions examined in this study. Therefore, no significant enhancement of the breakthrough capacity is observed in a module with high fiber packing fraction at a constant space velocity (GHSV). This further demonstrates the importance of the internal diffusion resistance on the gas sorption. The nearly identical breakthrough curves may indicate that the overall mass transfer resistance remains nearly constant in the fiber modules with different packing fractions. To verify this hypothesis, model analysis was performed to compare the different components of the mass transfer coefficients in these two modules at a normalized flow rate of GHSV = 4200 h−1. It

Figure 11. Experimental breakthrough capacity, qb, in CA-S-PEI fibers for different fiber lengths for various gas flow rates.

can be observed that qb is consistently higher with a longer module than with a shorter module across the various flue gas flow rates tested. The higher breakthrough capacity for a longer module can be explained by the self-sharpening effect, which is well-known for the Langmuir-type isotherm, where the slope of H


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Industrial & Engineering Chemistry Research the isotherm decreases with increasing adsorbate concentration, resulting in an increase of the concentration wave velocity at higher adsorbate concentrations.67 This will ultimately lead to “self-sharpening” effects, where the concentration profile sharpens as it moves down the length of module until it attains a constant pattern. To confirm this hypothesis, propagation of the concentration front along the longest fiber (L = 34 in.) is plotted in Supporting Information Figure S9 (top) using the model. As seen in the figure, the concentration front continues to sharpen until the front reaches the length of 30 in., where it appears to have reached a constant pattern that continues in the remaining length of the module. Replotting the concentration fronts against a normalized length scale z′ = z/ zbreak in Supporting Information Figure S9 (bottom) clearly reveals that the front is continuously sharpened until the time t = 236 s (i.e., when the concentration front reaches a length of 30 in.). Here, zbreak is the length at which the concentration front has reached the breakthrough concentration, Cbr, at a given time instant. We also confirm that the lower breakthrough capacities for shorter modules are not due to module entrance effects. Entrance effects refer to the phenomena where the gas flow requires a certain distance from the inlet to achieve a fully developed profile.68 The entrance effects can be confirmed to be insignificant in our modules, because our model, which ignores the entrance effects, predicts the experimental breakthrough curves accurately for all of the modules of different fiber lengths, as shown in Figure 12. Here, the breakthrough

Table 1. Physicochemical Properties of Silica Supports with Various Particle Sizes material code name

avg particle size (μm)

surface areaa (m2/g)

pore volumea (cm3/g)

estimated ratio of exposed to bulk PEI ψ

amine loadingc (mmol N/g)

C803 ES757 CS2129

3.8 25 100

210 295 290

2.0 1.6 2.5

0.16b 0.22b

5.2 6.0 5.5

a

The surface area and pore volume were calculated from the nitrogen isotherm data at 77 K using the Brunauer−Emmett−Teller and Barrett−Joyner−Halenda (BJH) methods, respectively. bThe estimation of this value is described in the Supporting Information. cThis is the amine loading of fiber sorbents.

Figure 13 shows the effect of particle size on the breakthrough capacity at different flue gas flow rates, plotted

Figure 13. Silica particle size effects on the breakthrough capacity, qb, using CA-S-PEI fiber sorbents at different WHSVs.

as the WHSV (weight hourly space velocity). Here, all of the modules were made using copper and were packed with fibers with a consistent volume and fiber length (i.e., packing fraction ϕ is 0.69 and fiber length L is 17 in.). The flow rate is normalized against the amine sorbent loading weight rather than the volume of fibers, because the amine loading varies slightly among the different fiber sorbents that are used in the analysis. WHSV is defined as follows:

Figure 12. Comparison of experimental CO2 concentration profiles with model predictions for different module lengths at 80 sccm.

WHSV =

curves are plotted against a normalized time, θ = t/tb, where tb is the breakthrough time for a flue gas flow rate of 80 sccm. From the figures, it can be seen that the CO2 concentration front is much sharper with a longer module than with a shorter module at its breakthrough. 4.2.4. Effect of Silica Particle Size on Sorption Kinetics. The above results demonstrate that the intraparticle diffusion resistance is by far the controlling diffusion resistance for CO2 sorption in the majority of the PEI sites, that is, in the bulk PEI layer (1 − ψ = 0.84). The intraparticle diffusion resistance, 1/Ks,bulk, represented by eq 6, is inversely proportional to the particle size, which is a measure of the diffusion length scale. Thus, the particle size is a crucial parameter to impact mass transfer kinetics, and the reduction of particle size is expected to significantly improve the breakthrough capacity. The effect of particle size on the sorption performance was therefore investigated by using three fiber sorbents loaded with silica supports of different particle sizes. The characteristics of the different silica supports are listed in Table 1.

=

gas weight per hour amine weight in fiber module ρg Q fluegas π (ro2 − ri2)ρf L(1 − εf )ws

(15)

In the above equation, ρg and ρf are the gas and the fiber densities, respectively. Additionally, ws is the amine loading of the fibers expressed as a weight percent, εf is the fiber porosity, and Qfluegas is the volumetric gas flow rate. It can be seen that the increase in particle size from 3.8 to 25 μm did not significantly impact the breakthrough capacity, whereas the increase of particle size further to 100 μm resulted in a dramatic decrease of the breakthrough capacity, as expected for the effect of increased particle size. Figure 14 compares the experimental breakthrough profiles in the three fiber sorbents with various particle sizes at a given WHSV. The CO2 breakthrough front was much sharper in the fiber sorbents with smaller particles, due to lower overall mass transfer resistance associated with the smaller particles as compared to the larger particles (eq 6). The module with the largest CS2129 particles exhibited the most I


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accessible PEI sites in ES757 enhances the rate of adsorption, while at the same time it is countered by the increased mass transfer resistance reducing the adsorption rate significantly in the bulk PEI sites. Figure 15 show the comparison of the sorbent loading concentration front in the exposed PEI (top) and bulk PEI sites

Figure 14. Comparison of experimental breakthrough profiles in three fiber sorbents with various silica particle sizes at a fixed WHSV of 33 h−1.

diffuse breakthrough front, indicating the slowest mass transfer kinetics among the three cases. The experimental trend of the particle size impact on the breakthrough capacity is consistent with expectations, based on the analysis that the mass transfer resistance is controlled by the intraparticle diffusion and hence is inversely proportional to the particle size. However, the impact of particle size on qb is insignificant with the increase of its size from the 3.8 to 25 μm. This trend was not expected, and the cause is not immediately clear and therefore model analysis was used to probe this issue further. To that end, the overall mass transfer resistances of both the bulk PEI and accessible PEI adsorption sites are compared for both of the silica particle sizes at a constant WHSV = 32 h−1, in Supporting Information Figure S10. The overall mass transfer resistance, 1/Kov‑bulk, for adsorption in the bulk PEI is significantly reduced (approximately 56%) with a decrease in particle size from 25 to 3.8 μm, which is in accordance with the expected impact of particle size on the mass transfer kinetics in the fibers. However, the overall mass transfer resistance for adsorption in the exposed PEI, 1/ Kov‑exposed (inset figure), decreased by only about 22% with the decrease in particle size. This is because the intraparticle resistance is not one of the controlling resistances for the adsorption on exposed PEI sites, as mentioned above, and the observed reduction is perhaps due to the effect of the temperature increase on the overall mass transfer resistance resulting from increased adsorption at a given location. The insignificant influence of the increased particle size from 3.8 to 25 μm on the breakthrough capacity can be explained by the interplay between two factors: (i) the ratio of accessible PEI sites to the bulk PEI sites and (ii) the mass transfer resistances. The fraction of the accessible PEI sites available in ES757 (25 μm) was estimated to be 22%, and that of C803 (3.8 μm) was estimated to be 16% using the surface area values of the respective silica particle before and after the amine loading (Table 1).55 As the specific surface area available for ES757 is higher than that of C803,31 the fraction of exposed PEI sites available is accordingly higher for ES757 as compared to that of C803 sorbent. While the smaller particle size reduces the overall mass transfer resistance, the reduction in the ratio of the exposed PEI sites offsets the advantage. It is to be noted that the adsorption on the exposed PEI sites experiences a much smaller overall mass transfer resistance as compared to those experienced on bulk PEI sites with the value of exposed PEI adsorption resistance nearly about 1% of bulk PEI adsorption resistance, as can be seen in Supporting Information Figure S10. Accordingly, we find that the increased availability of

Figure 15. Model analysis: sorbent loading profile along the length of the fiber module in (top) exposed PEI, qexposed, and (bottom) in bulk PEI sites, qbulk, at t = 28 s.

(bottom) at WHSV = 32 h−1, respectively. It can be clearly seen in Figure 15 (top) that the amount of sorbent loading in the exposed PEI sites, qexposed, is increased significantly in ES757 (25 μm) by the increased availability of accessible PEI sites offering a low overall mass transfer resistance. We also find in Figure 15 (bottom) that the amount of sorbent loading in the bulk PEI sites, qbulk, is indeed reduced in ES757 due to the impact of the higher overall mass transfer resistance (in bulk PEI) as compared to C803. In other words, the advantage of reduced intraparticle diffusion resistance gained by the reduction of particle size from 25 to 3.8 μm is offset by the reduced easily accessible PEI sites in the smaller particles causing a minor impact of the particle size reduction on qb when moving from ES757 to C803 supports.

5. CONCLUSIONS A mathematical model, which was experimentally validated earlier,55 has been used to study the impact of different module design parameters and operating conditions on the sorption kinetics of CA-S-PEI hollow fiber sorbents. The impact of “heat effects” on the sorption performance was studied using modules constructed of two materials with the varied thermal conductivities. The sorption performance obtained using a highly heat conductive copper module case nearly approached isothermal sorption behavior, as predicted and verified by the mathematical model. The breakthrough capacity increased around 30% in the CA-S-PEI fibers contained within the copper J


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Industrial & Engineering Chemistry Research module case as compared to the fibers contained within the stainless steel module case as a result of rapid heat removal. Individual mass transfer resistance components in the CA-SPEI fiber sorbents were analyzed using the model to understand the impact of different parameters, such as flue gas flow rate, module packing fraction, fiber length, and sorbent particle size, on the breakthrough capacity. Increase in the flue gas flow rate was found to negatively impact the sorption kinetics due to the dominant intraparticle diffusion limitations of the highly loaded amine sorbents, in contrast to the earlier observed CO2 sorption kinetic limitations in fibers containing zeolite 13X.60 It was also found that the module packing fraction did not show a significant effect on the sorption capacity, indicating again that the external gas diffusion resistance in the CA-S-PEI fibers with high amine loadings has a negligible effect on the sorption kinetic performance. In addition, longer fiber modules exhibited higher sorption capacities than the shorter module due to the effect of self-sharpening, which attains a constant pattern beyond a fiber length of 30 in. Finally, the experimental study of the breakthrough capacity with varying silica particle size confirms the modeling analysis that the sorption in the CA-SPEI fiber sorbents is limited by intraparticle diffusion. Furthermore, the model investigation of the results using C803 and ES757 supports indicated that the increased availability of easily accessible PEI sites resulting from a higher surface area can offset the negative impact of the intraparticle diffusion resistance of modestly larger sorbent particles. The collected results affirm that the most effective pathway to achieve improved performance using the CA-S-PEI fiber sorbents is to reduce the internal diffusion resistances within the PEI phase in the sorbents.

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physical properties of silica supports after impregnating PEI. Table S2 shows all parameters for estimation of ψ. All of this information is cited from ref 55. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the DOE-NETL under contract DEFE0007804 for financial support. However, any opinions, findings, conclusions, or recommendations expressed herein are those of the author(s) and do not necessarily reflect the views of the DOE.

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ASSOCIATED CONTENT

* Supporting Information S

Figure S1 shows model prediction of CO2 isotherm profiles based on Toth adsorption isothermal model. Model equations including mass balance equations and energy balance equations are included in pp S2−S5. Figure S2 shows CO2 breakthrough profiles (left) and fiber temperature profiles (right) at different flue gas flow rates; solid line without marker is the model prediction. Figure S3 presents CO2 breakthrough profiles at different packing fractions for Qfluegas = 80 sccm, and temperature profile at ϕ = 0.69; solid line without marker is the model prediction. Figure S4 shows CO2 breakthrough profiles (left) at different particle sizes and temperature profiles (right) at a particle size = 25 μm; solid line without marker is the model prediction. Figure S5 model analysis: Profiles of concentration and temperature along the length of the fiber module at time t1 and t2 at 80 sccm. Figure S6 displays model prediction of the front velocity as a function of the flue gas velocity. Figure S7 shows model analysis showing the effect of flue gas flow rate on 1/Kg at τ = 70. Figure S8 is model analysis: mass transfer resistance components of bulk PEI sites (1/ Kov,bulk) for the fiber modules with packing fraction of ϕ = 0.46 and ϕ = 0.69 at τ = 40. The inset shows a zoomed view of the y-axis from 0 to 1.0. Figure S9 shows model analysis of (top) propagation of the concentration front along the 34 in. fiber length and (bottom) concentration front plotted against the normalized length scale, z′ = z/zbreak. Figure S10 compares overall mass transfer resistances in the different silica sorbents at t = 28 s. Overall resistance comparison for bulk PEI 1/Kov,bulk is plotted in the main figure and for the exposed PEI 1/ Kov,exposed is plotted in the inset figure. Table S1 shows the K

NOMENCLATURE Cg = gas-phase concentration [mol/m3] Cms = CO2 concentration in the fiber macropores [mol/m3] Cm0 = CO2 concentration at macropore/micropore interface [mol/m3] Cbr = CO2 concentration at breakthrough point [mol/m3] Co = gas-phase inlet concentration [mol/m3] Cp = specific heat capacity [J/kg·K] d = diameter [m] Df,p = macropore gas diffusivity [m2/s] Dg = bulk gas diffusivity [m2/s] Dp = sorbent polymer diffusivity [m2/s] Dp,k = Knudsen diffusivity in the sorbent micropore [m2/s] Dpo = maximum sorbent polymer diffusivity at zero loading [i.e., at infinite temperature] [m2/s] E = activation energy for diffusion [J/mol] hg = flue gas convective heat transfer coefficient [W/m2·K] ht = convective heat transfer coefficient between thermocouple and module [W/m2·K] kg = flue gas convective mass transfer coefficient [m2/s] LUB = length of unused bed L = fiber module length [m] Pe = Peclet number Qflue gas = volumetric gas flow rate (sccm) q = average CO2 loading in sorbent [mmol/g] qb = breakthrough capacity [mmol/g] qpe = pseudoequilibrium capacity [mmol/g] qeq = CO2 loading at equilibrium [mmol/g] qm = maximum possible CO2 loading at a given temperature [mmol/g] qexposed = CO2 loading in sorbent within the exposed PEI sites [mmol/g] qbulk = CO2 loading in sorbent within the bulk PEI sites[mmol/g] rfs = free surface radius around a fiber [μm] ro = outside diameter of fiber sorbent [μm] ri = inside diameter of fiber sorbent [μm] rs = silica particle diameter [μm] R = gas constant [J/mol·K] Sp = surface area occupied by a gram of exposed PEI [m2/gexposed PEI] T = temperature [K] DOI: 10.1021/ie504603h Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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ug = bulk gas velocity [m/s] ugm = maximum gas velocity [m/s] U = overall heat transfer coefficient of the module [W/m2·K] w = weight percent loading of amine in silica sorbents 1/Ks,exposed = sorbent phase mass transfer resistance for the exposed PEI sites [s−1] 1/Ks,bulk = sorbent phase mass transfer resistance for the bulk PEI sites [s−1] 1/Km = fiber macropore phase mass transfer resistance [s−1] 1/Kg = gas-phase mass transfer resistance [s−1] z′ = normalized fiber length Greek Symbols

ΔHads = average heat of adsorption [J/mol] ΔH0 = isosteric heat of adsorption at zero loading [J/mol] α = parameter related to rate of PEI free volume reduction with CO2 adsorption [kg-fiber/mol] ε = porosity ρ = density [kg/m3] λ = thermal conductivity [W/m·K] τt = normalized time (t/tres) ϕ = packing fraction ψ = fraction of total exposed amine sites [g exposed PEI/g total PEI] η = parameter defining the temperature dependency of maximum sorption capacity ζ = fiber phase concentration [mol/kg fiber] Subscripts

s = sorbent f = fiber g = gas m = fiber membrane br = breakthrough res = residence

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