Chemical Engineering Science 113 (2014) 62–76
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Modeling of rapid temperature swing adsorption using hollow fiber sorbents Fateme Rezaei, Swernath Subramanian, Jayashree Kalyanaraman, Ryan P. Lively, Yoshiaki Kawajiri n, Matthew J. Realff n School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, GA 30332, United States
H I G H L I G H T S
The modeling of novel polymeric hollow fiber contactors loaded with CO2 adsorbents are reported. A four-step hollow fiber RTSA system is simulated by a single fiber model. Heat and mass balances are developed in different phases of the fiber. The sensitivity of the model to process parameters is evaluated. Hollow fiber RTSA system provides a novel cost-effective and scalable pathway for CO2 capture.
art ic l e i nf o
a b s t r a c t
Article history: Received 22 January 2014 Received in revised form 25 March 2014 Accepted 3 April 2014 Available online 13 April 2014
The use of novel polymeric hollow fiber contactors loaded with CO2 sorbents has been recently demonstrated experimentally as a new and scalable process configuration for post-combustion CO2 capture. The hollow fiber contactor allows coupling of efficient heat transfer and gas contacting, potentially yielding lower parasitic loads on host power plants compared to traditional contacting strategies using solid sorbents. In this study, a two dimensional mathematical model of a rapid temperature swing adsorption (RTSA) process is developed for the first time to predict polymersupported amine hollow fiber sorbent performance during post-combustion CO2 capture from flue gas. In particular, this work is focused on developing a single fiber model to simulate a four-step RTSA system accounting for adsorption, heating/desorption, heating/sweeping and cooling steps. The model is validated with experimental breakthrough data obtained from our RTSA system. The sensitivity of the model to parameter values such as gas and water velocity and initial temperatures are evaluated accordingly by considering the effect of these parameters on CO2 concentration and temperature profiles. Furthermore, the CO2 adsorption isotherms obtained experimentally were fitted with the Toth model. In addition, our model was validated against experimental breakthrough profiles. A good agreement was found between experimental and numerical data indicating that our proposed model can describe experimental observation very well. The numerical results obtained from RTSA cycle modeling indicate that under operating conditions considered here, it is possible to achieve high purity and recovery within a cycle time of shorter than 3 min. It was also found that there is a trade-off in cycle time, shorter for lower capital cost and longer to enable heat recovery for lower utility costs. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Hollow fiber sorbents CO2 capture Rapid temperature swing adsorption Coal-fired power plant Cyclic adsorption process
1. Introduction Emissions of greenhouse gases such as CO2 have increased over the past century and atmospheric concentrations surpassed 400 ppm at the Mauna Loa Observatory in Hawaii in May 2013
n
Corresponding authors. E-mail addresses:
[email protected] (Y. Kawajiri),
[email protected] (M.J. Realff). http://dx.doi.org/10.1016/j.ces.2014.04.002 0009-2509/& 2014 Elsevier Ltd. All rights reserved.
probably for the first time in 4 million years. Increased atmospheric CO2 concentrations have been associated with much warmer climate conditions in the geologic past and hence may pose a substantial risk to human development. The amount of CO2 produced from the combustion of fossil fuels in the United States exceeded 5.5 billion metric tons in 2010, with about 33% coming from the coal-fired electric power sector (U.S. Energy Information Administration, 2013). Coal-fired utility boilers generate nearly 50% of the electricity in the United States. The capacity of coal-fired power plants will increase from 313 GW to 325 GW by 2035 with
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only 5.7 GW of existing coal-fired plants being retired despite the recent developments in domestic shale gas supply and widespread use (U.S. Energy Information Administration, 2013). As stated in the annual energy outlook 2013 report: “in all the cases examined, new additions of coal-fired capacity from 2012 to 2040 total less than 15 gigawatts,” and thus coal use in the U.S. is unlikely to decline substantially over this period considering the electricity generation growth of 26% for the same period (0.9% annual growth). However, with strong economic growth and large coal reserves, the international growth in coal use will continue in the near future (U.S. Energy Information Administration, 2011). Therefore, for the foreseeable future coal will continue to play a critical role in powering the nation's and the world's electricity generation, especially for base-load generation (Davis et al., 2010). In order to address these issues, different types of post-combustion capture methods have been proposed to capture CO2 from coal-fired power plant flue gas in preparation for end use applications such as enhanced oil recovery or long term underground storage (sequestration) (Figueroa et al., 2008; Merel et al., 2008; Xiao et al., 2008). Such technologies include CO2 absorption by amine solutions as the most widely used technology, pressure/temperature swing adsorption (PSA/TSA) and membrane separation. Several new hybrid technologies have also gained attention in recent years (Esteves and Mota, 2002; Ritter et al., 2012). The use of a hollow fiber sorbent system operating in rapid thermal swing adsorption mode (RTSA) for CO2 capture has been described in Lively et al. (2009, 2012a, 2011). This work demonstrated the development of hollow fiber sorbent platform using a “proof-of-concept” sorbent, zeolite 13 , for the capture of CO2 from the flue gas. Unfortunately zeolite 13 demonstrates competitive adsorption behavior between CO2 and water and hence is not particularly suitable for moist flue gas streams. More recently, we proposed the use of supported amine materials as the sorbents in the hollow fiber, RTSA post-combustion CO2 capture system (Labreche et al., 2013; Rezaei et al., 2013). The new carbon capture system based on polymer-sorbent hollow fibers offers several advantages. First, with this hollow fiber configuration, it is possible to mitigate deleterious thermal effects typically associated with packed bed sorption (Pirngruber et al., 2013) and obtain higher sorption efficiencies through supplying cooling agents in the bore of the fiber during adsorption. The presence of the lumen layer (barrier layer) which allows for efficient heat transfer between the embedded solid sorbent particles and the heat transfer fluid without causing mass exchange, turns the hollow fiber configuration into “an adsorbing heat exchanger”. Second, the heat and mass transfer equilibration is very rapid due to the thin porous walls of the fiber sorbent which allows for more rapid thermal cycles and thereby reducing device volume. Third, pressure drops through hollow fiber bed is substantially lower than their traditional packed bed counterparts as a result of the structured packing of fiber-based sorbents. Previous work by Lively et al. (2009) showed that a lower energy cost for CO2 capture by hollow fiber sorbents can be achieved compared to the conventional absorption technology. Fiber sorbents can support submicron to micron (100 nm–5 μm) sized solid sorbents; therefore, rapid mass equilibration times are possible, which again allows for smaller device volumes and more efficient use of a given amount of sorbent. This efficient use of sorbent is enabled by rapid thermal equilibration times of the fiber sorbents. Essentially, each fiber acts as an individual packed bed with 400 μm-thick sorbent-laden walls rather than the traditional the 1–3 m diameters in industrial packed beds; this 2500–5,000 fold reduction in heat transfer distance allows for the fiber sorbents to be cycled very rapidly relative to normal packed beds.
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The four step RTSA cycle is illustrated in Fig. 1a. In adsorption and cooling, cold fluid is passed through the bore of a fiber to remove the heat of adsorption and sensible heat of the fiber respectively. In adsorption, the CO2 is removed from the flue gas and an adsorption wave develops in the fiber whilst the cooling fluid keeps the thermal front ahead of the adsorption wave to maximize the fiber capacity. After adsorption, the fiber module is cycled to desorption mode and the CO2 is released from the fibers by passing heating fluid through the bore of the fibers, as shown in the Heating steps of Fig. 1a. An integral mechanism for producing a highly concentrated CO2 product involves configuring the fiber sorbent bed such that the CO2 outlet is placed at the top of the bed, while the heating agent (ideally hot water) for desorption is fed from the bottom. This essentially drives the CO2 out of the sorbents held within the fibers, displacing the interstitial gas in plug flow fashion, thereby ideally generating near-pure “waves” of CO2 that can then be sent to the compression station. Provided that the water is sufficiently high in temperature (100–120 1C), CO2 desorption will readily occur (stronger CO2 desorption fronts are obtained with higher water temperatures). Nitrogen can be used to push out the interstitially held CO2 during the sweeping step and as the bed cools down. The single fiber can be bundled and housed in a shell as shown in Fig. 1c. As can be seen in this Figure, this configuration is similar to a shell-and-tube heat exchanger, which allows effective heat transfer between the gas and the water in the bore. In a large-scale industrial operation, the replacement of sorbents in the bundle of hollow fibers could be done by simply replacing one canister without shutting the whole system down. Moreover, the sorbent fibers that have lost their amine species via leaching or degradation after use could be recharged (Labreche et al., 2013). In this study, we carry out all analyses considering a single fiber inside a module, which can be scaled up linearly if there is no significant radial gas distribution in the shell. This hollow fiber RTSA system can also be beneficial in terms of energy recovery through the collection of heat by water and use of it as “preheating water” in the power plant. This can be done through heat integration of the adsorption and cooling steps with the heating steps which further improves the energy efficiency of the whole CO2 capture system. A conceptual CO2 capture system with such heat recovery capability is shown in Fig. 2. Recently, Determan et al. (2012) investigated the heat and mass transfer kinetic of a zeolite-loaded hollow fiber system used in rapid temperature swing adsorption mode (RTSA). The authors analyzed the influences of fiber geometry and internal and external heat- and mass-transfer resistances. However, they looked at adsorption step solely and did not study the performance of hollow fiber sorbents in multiple steps. In addition, their analysis was confined to the radial direction of the fiber. To the best of our knowledge, there have not been any studies on the numerical simulation of cyclic RTSA hollow fiber sorbents, unlike the conventional TSA processes or other advanced contactors whose cyclic performance has been studied in detail by many researchers (Bonjour et al., 2002; Bonnissel et al., 2001; Clausse et al., 2004; Moate and LeVan, 2010; Ribeiro et al., 2013). The overall objective of this paper is to propose a model to numerically simulate the performance of a hollow fiber sorbent loaded with aminosilica materials in post-combustion CO2 capture from flue gas. The other objective is to fit the CO2 adsorption isotherms and to validate the model predictions against experimental breakthrough data. The outcome of this modeling effort is used to help scale up the bench-scale RTSA system and guide the experimental team in the development of the fiber properties as well as optimizing the RTSA operation conditions. In the present work a set of numerical models for a four-step RTSA process are developed and used for comparison and to illustrate how the
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Fig. 1. Illustration of (a) four-step RTSA process and (b) a typical module containing hollow fiber sorbents.
hollow fiber configuration facilitates the heat removal and hence impacts the overall purity and recovery of the final product. The effect of gas and water velocity and initial temperatures on adsorbate transport, cycle time and temperature profiles in RTSA CO2 capture system are evaluated accordingly.
2. Process description and model We consider an RTSA cycle with aminosilica loaded fiber as a sorbent and operated with four steps: adsorption, heating/desorption, heating/sweeping and cooling, as shown in Fig. 1. During the adsorption step, feed gas consisting of 87% N2 and 13% CO2 at 35 1C and 1 atm pressure is supplied to the shell side of the fiber (the low pressure drops required to effect flow through the fiber module are not considered in this analysis), while the water is supplied to the bore of the fiber at 35 1C allowing for isothermal operation. As CO2 is adsorbed by aminosilica particles, nitrogen is obtained as an exhaust stream at the other side of the fiber module. During the heating/desorption step, hot water is run through the bores at 120 1C to heat up the bed with the bed gas feed closed, which allows desorbing CO2 to create a local high pressure zone, thereby displacing downstream interstitial gas. Shortly after this, a N2 sweep is used to help push the desorbing CO2 out of the bed. In this way, a plug of high purity CO2 is obtained. After the desorption step, clean flue gas pushes
interstitial CO2 out of the bed and then the fiber sorbents are returned to the sorption temperature via cooling water. 2.1. Heat and mass transfer model equations A mathematical model was developed to simulate the hollow fiber sorbent behavior consisting of time varying temperature and concentration profiles in both the radial and longitudinal fiber directions under different RTSA operating conditions. The following assumptions were made for the gas phase: ideal gas law and ideal mixture are assumed, with a constant gas phase pressure; diffusion and heat conduction in the axial direction of bulk gas flow are neglected; temperature and concentration in the bulk gas phase is uniform in the radial direction. For the lumen layer and water in the bore, the following assumptions were made: mass transfer between the lumen layer and the fiber/sorbent is neglected (Fan et al., 2014); this is based on the fact that lumen layer is non-permeable to mass; heat transfer resistance within the lumen layer is equal to the heat transfer resistance in the polymer sorbent porous matrix
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Fig. 2. Conceptual overview of a CO2 capture system with heat recovery.
(this is a conservative assumption which underestimates heat transfer rate); the heat capacity of the lumen layer is negligible; gas components do not penetrate into the lumen layer; temperature of hot/cold water in the bulk water phase in the fiber bore is uniform in the radial direction. Finally, for the fiber-sorbent, the following assumptions were made: bulk diffusion and convection in the axial direction of the fiber phase is neglected; adsorption of N2 can be neglected; adsorption of CO2 by the polymer fiber material can be neglected; the polymer fiber, sorbent particles, and intrafiber gas are considered to reach thermal equilibrium very rapidly at any point in the radial and axial direction and hence the fiber temperature can be represented by a single variable Tf (r,z). Fig. 3 represents the schematic representation of a single hollow fiber sorbent with corresponding temperature and concentration variables in different phases (i.e., free space around the fiber, polymer/sorbent solid phase and fiber bore). 2.1.1. Mass balance equations Based on the above assumptions, the differential mass balance for the components in the gas phase flowing parallel to the water bore is: ∂ci;g ∂ci;g ∂ug þug þ ci;g ¼ kg AO ðci;g ci;p jr ¼ rOD Þ þ AO εf ucp jrOD ci;p jrOD ∂t ∂z ∂z
ð1Þ
Given that the pressure is constant, if there is a change in the number of moles at any point in the module, this necessitates a change in gas volume in order to satisfy the equation of state, the ideal gas law in our case. This change in gas volume is translated to a convective term. Hence there is a change in velocity within the entire module, depending on the change in mass flow. For the bulk gas phase, this is captured by the interstitial velocity given by ug which can vary along the axial direction. To account for a change in number of moles within the fiber, a convective pore velocity in radial direction denoted as ucp is defined. This convective pore velocity accounts for the bulk transfer of the components between the pores of the fiber and the bulk gas phase. The axial component of ucp is ignored in the model equations described here since the both ends (z¼0 and z¼L) of the fiber are sealed. This term is usually ignored in conventional packed-bed systems mainly because, unlike hollow fiber configuration in which the fast change in temperature
Fig. 3. A schematic representation of a single hollow fiber sorbent.
gradient results in rapid sorption and therefore movement of gas on a short time scale, temperature gradients change less rapidly and hence adsorption proceeds more slowly. In the above equation, Ao is an external specific surface area of the hollow fiber which is defined as the external surface area per free space volume and is calculated based on the equation provided in Appendix A. Here free space is defined as the space allocated to each fiber in a hollow fiber module as illustrated by dash lines around the fiber in Fig. 3. As experimentally shown by Lively et al. (2009) in a proof-ofconcept study, the pressure drop for hollow fiber sorbents is negligible for the RTSA system with only 10–20% decrease in pressure. Therefore, the assumption of constant pressure is justified here. Similarly, the differential mass balance for the components inside the solid phase (fiber/sorbent) is given by: ! ð1 εf Þ ∂qi ∂ci;p ucp ci;p ∂ci;p ∂2 ci;p 1 ∂ci;p ∂ucp þ ρf þ þ ci;p þ ucp Def f ¼ εf ∂t r ∂r ∂r ∂t r ∂r ∂r 2 ð2Þ Analogous to the bulk gas phase, the total pressure is assumed constant within the fiber as well. This assumption is supported by
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experimental observations that the fiber permeance is high and the thin polymer matrix contains large pores resulting in high porosity (Labreche et al., 2013; Lively et al., 2009; Rezaei et al., 2013). The water phase mass balance is ignored and only heat transfer from water and phases are considered. The overall mass balance equations for the gas and fiber phases in the RTSA system are: ! Z rOD ucp cTp ∂cTp ∂2 cTp 1 ∂cTp ð1 εf Þ ∂ucp ∂q þ cTp þucp Def f þ ρ ∑ i ¼ f εf r ∂r ∂r ∂t ∂r 2 r ∂r r ID ð3Þ ug
∂cTg ∂z
þ cTg
Ncp Ncp ∂ug ¼ ∑ kg AO εf ðci;g ci;p jrOD Þ þ ∑ AO εf ucp jrOD ci;p jrOD ∂z i¼1 i¼1
ð4Þ
where ks0 and α (coverage factor) are estimated by fitting our numerical results to experimental breakthrough data. This equation implies that ks varies with coverage and exponentially decays with surface coverage, as opposed to models for physisorbents where the mass transfer coefficient is not a function of adsorbate coverage. It should be noted here that the sorbent mass transfer equation (Eq. (8)) is a purely empirical correlation and the choice of this modified equation will be further justified in Section 3.1. 2.1.2. Heat balance equations For our non-isothermal system, the differential energy balance for the fiber phase (polymer matrix loaded with sorbent particles) gives: ! ∂T f λf ∂2 T f 1 ∂T f ∂2 T f ∂q ρf C pf þ ð9Þ þ ¼ ρf ΔH ads i ∂t ð1 εf Þ ∂r 2 r ∂r ∂t ∂z2
In the models described here, CO2 is the only component that adsorbs and N2 adsorption is negligible. The rate of adsorption of CO2 is approximated by the linear driving force model (LDF):
The following equation is used to describe the water energy balance in the fiber bore:
∂qi ¼ ks ðqeq i qi Þ ∂t
ρw C pw
ð5Þ
A Toth isotherm equation is used to represent adsorption equilibrium: qi eq ¼
qs bP i
ð6Þ
n 1=n
ð1 þ ðbP i Þ Þ
where the temperature dependent saturated capacity and affinity constant are estimated by: T ΔH T0 ; 1 ; b ¼ b0 exp qs ¼ qs0 exp η 1 T0 RT 0 T T0 n ¼ AþB 1 T In the above equations, η is a non-dimensional parameter that defines the dependency of maximum sorption capacity to the temperature. kg and ks are external and sorbent mass transfer coefficients respectively, estimated by kg ¼
Sh:Dm dO
ð7Þ
For amine sorbents, Bollini et al. (2012a, 2012b) reported a “long tail” in the breakthrough curve where the CO2 concentration in the gas increases very slowly after breakthrough. They hypothesized that the captured CO2 on the surface inhibits further diffusion of CO2 molecules in the pores resulting in a very slow mass transfer rate. In their “Heterogeneous Treatment” model, the mass transfer rate is modeled using three parameters: two mass transfer coefficients and another parameter that represents the available adsorption sites. In this study, we consider the dependence of the mass transfer coefficient ks on the adsorbed CO2 coverage θ ¼ qi =qeq using the following empirical model that i involves only two parameters: ks ¼ ks0 expð αθÞ
ð8Þ
∂T w ∂T w þ ρw C pw uw ¼ AI hw ðT w T f jr ¼ rID Þ ∂t ∂z
ð10Þ
The bulk gas temperature balance in the fiber shell can be written as: ρg C pg
∂T g ∂T g þ ρg C pg ug ¼ AO hg ðT f jr ¼ rOD T g Þ ∂t ∂z
ð11Þ
The initial and boundary conditions applied to above equations for the RTSA operation (individual steps) are listed in Tables 1 and 2. For the adsorption step simulation, we start with a clean bed (i.e., CO2 concentration is initially zero, cCO2 ;g ðzÞjt ¼ 0 ¼ cCO2 ;p ðr; zÞjt ¼ 0 ¼ 0). Also, at the beginning of the cooling step, we assume that the N2 sweep has completely swept through the bed and therefore for this step the initial CO2 concentration is zero as well (cCO2 ;g ðzÞjt ¼ 0 ¼ cCO2 ;p ðr; zÞjt ¼ 0 ¼ 0). The complete cycle consists of these four individual steps (i.e., adsorption, heating/desorption, heating/sweeping and cooling), and the purity and recovery of CO2 obtained from RTSA cycle simulation can be estimated by: R tcycle I 1 ug jz ¼ L cCO2 ;g jz ¼ L dt ð12Þ PurityCO2 ¼ 0R cycle t I 1 ug jz ¼ L cTg jz ¼ L dt 0 R tcycle RecoveryCO2 ¼
0
I 1 ug jz ¼ L cCO2 ;g jz ¼ L dt R tcycle ads ug;i cCO2 ;in dt 0
ð13Þ
In the above equations, tcycle is cycle time and is calculated as the sum of individual steps (i.e., adsorption, heating/desorption, heating/sweeping and cooling) and I 1 ðtÞ is a binary variable. When I 1 ðtÞ ¼ 0, the gas from the outlet is released to the atmosphere, and when I 1 ðtÞ ¼ 1, the gas is collected as the CO2 product. This timevarying binary parameter is chosen so that the required purity and recovery are achieved. In this study, this parameter is chosen as follows: in the adsorption step, I 1 ðtÞ is fixed a priori to 0.0 which requires the entire outlet stream be released to the atmosphere.
Table 1 Initial conditions for adsorption, heating/desorption, heating/sweeping and cooling steps ð 8 r A ½r ID ; r OD 8 z A ½0; LÞ. Adsorption
Heating/desorption and heating/sweepinga
Cooling
T f jt ¼ 0 ¼ T w jt ¼ 0 ¼ T g jt ¼ 0 ¼ T ads 0 qi ðr; zÞjt ¼ 0 ¼ 0 cCO2 ;g ðzÞjt ¼ 0 ¼ cCO2 ;p ðr; zÞjt ¼ 0 ¼ 0
T f jt ¼ 0 ¼ T w jt ¼ 0 ¼ T g jt ¼ 0 ¼ T des 0 (step 2) qi ðr; zÞjt ¼ 0 ¼ qi eq (step 2) cCO2 ;g ðzÞjt ¼ 0 ¼ cCO2 ;p ðr; zÞjt ¼ 0 ¼ cdes CO2 ;0
T f jt ¼ 0 ¼ T w jt ¼ 0 ¼ T g jt ¼ 0 ¼ T cool 0 qi ðr; zÞjt ¼ 0 ¼ 0 cCO2 ;g ðzÞjt ¼ 0 ¼ cCO2 ;p ðr; zÞjt ¼ 0 ¼ 0
cN2 ;g ðzÞjt ¼ 0 ¼ cN2 ;p ðr; zÞjt ¼ 0 ¼ cads N 2 ;0
cN2 ;g ðzÞjt ¼ 0 ¼ cN2 ;p ðr; zÞjt ¼ 0 ¼ cdes N 2 ;0
cN2 ;g ðzÞjt ¼ 0 ¼ cN2 ;p ðr; zÞjt ¼ 0 ¼ ccool N 2 ;0
a
We sequentially run steps 2 and 3 and do not reinitialize the step 3.
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Table 2 Boundary conditions for adsorption, heating/desorption, heating/sweeping and cooling steps ð 8 r A ½r ID ; r OD 8 z A ½0; LÞ. Adsorption
Heating/desorption
Heating/sweeping
Cooling
∂T w T w jz ¼ 0 ¼ T ads w;in ; ∂z z ¼ L ¼ 0 ∂T g T g jz ¼ 0 ¼ T ads ¼0 g;in ; ∂z z¼L ∂T ∂T f ∂T f λf : ∂rf ¼ hw ðT f T w Þ ¼ ¼ 0 ∂z z ¼ 0 ∂z z ¼ L r ¼ r ID ∂T f ¼ hg ðT f T g Þ λf : ∂r
∂T w T w jz ¼ 0 ¼ T des w;i ; ∂z z ¼ L ¼ 0
; ∂T∂zw z ¼ L ¼ 0 T w jz ¼ 0 ¼ T sweep w;i
T w jz ¼ 0 ¼ T cool w;i ;
r ¼ rOD
∂T f ∂z z ¼ 0
¼
∂T f ∂z z ¼ L
∂T ¼ 0 λf : ∂rf
r ¼ r ID
¼ hw ðT f T w Þ ∂T ¼ hg ðT f T g Þ λf : ∂rf r ¼ rOD
cCO2 ;g ðtÞjz ¼ 0 ¼ cads CO2 ;in
∂ci;p ðr;tÞ ∂z z ¼ 0
∂ci;p ðr;tÞ ∂z z ¼ L ¼ 0 ∂ci;p ðz;tÞ ¼ 0 Def f : ∂r r ¼ r OD
¼
∂ci;p ðz;tÞ ∂r r ¼ r ID
cN2 ;g ðtÞjz ¼ 0 ¼ cads N 2 ;in
¼ kg :ðci;g ðz; tÞ ci;p;r ¼ rOD ðz; tÞÞ ug ðtÞjz ¼ 0 ¼ uads g;in
cCO2 ;g ðtÞjz ¼ 0 ¼ 0 cN2 ;g ðtÞjz ¼ 0 ¼ 0
∂ci;p ðr;tÞ ∂z z ¼ 0
∂ci;p ðz;tÞ ∂r r ¼ r ID
∂ci;p ðr;tÞ ∂z z ¼ L ¼ 0 ∂ci;p ðz;tÞ ¼ 0 Def f : ∂r r ¼ r OD
¼
¼ kg :ðci;g ðz; tÞ ci;p;r ¼ rOD ðz; tÞÞ ug ðtÞjz ¼ 0 ¼ 0
Table 3 System parameters for RTSA CO2 capture.
∂T f ∂z z ¼ 0
¼ ∂T f λf : ∂r
∂T f ∂z z ¼ L
r ¼ rOD
∂T f ¼ 0 λf : ∂r r ¼ r ¼ hw ðT f T w Þ ID
∂ci;p ðz;tÞ ∂r r ¼ r ID
∂T f ∂z z ¼ L
∂T ¼ 0 λf : ∂rf
r ¼ r ID
r ¼ rOD
cCO2 ;g ðtÞjz ¼ 0 ¼ 0 cN2 ;g ðtÞjz ¼ 0 ¼ ccool N 2 ;in ∂ci;p ðr;tÞ ∂ci;p ðr;tÞ ∂z z ¼ 0 ¼ ∂z z ¼ L ¼ 0 ∂ci;p ðz;tÞ ∂ci;p ðz;tÞ ¼ 0 Def f : ∂r
∂ci;p ðr;tÞ ∂z z ¼ L ¼ 0 ∂ci;p ðz;tÞ ¼ 0 Def f : ∂r r ¼ r OD
¼
¼
¼0
¼ hw ðT f T w Þ ∂T ¼ hg ðT f T g Þ λf : ∂rf
¼ hg ðT f T g Þ
cCO2 ;g ðtÞjz ¼ 0 ¼ 0 cN2 ;g ðtÞjz ¼ 0 ¼ csweep N 2 ;in ∂ci;p ðr;tÞ ∂z z ¼ 0
∂T f ∂z z ¼ 0
∂T w ∂z z ¼ L
∂r
r ¼ r ID
r ¼ rOD
¼ kg :ðci;g ðz; tÞ ci;p;r ¼ rOD ðz; tÞÞ
¼ kg :ðci;g ðz; tÞ ci;p;r ¼ rOD ðz; tÞÞ
ug ðtÞjz ¼ 0 ¼ usweep g;in
ug ðtÞjz ¼ 0 ¼ ucool g;in
Table 4 Mass and heat transfer properties.
Name
Symbol
Value
Parameter
Value
Flue gas thermal conductivity [W/m K] Flue gas heat capacity [J/kg K] Flue gas density [kg/m3] Flue gas viscosity [g/cm s] Water thermal conductivity [W/m K] Water heat capacity [J/kg K] Water density [kg/m3] Water viscosity [g/cm s] Fiber outer diameter [mm] Fiber inner diameter [mm] Fiber pore diameter [nm] Fiber length [m] Fiber porosity Fiber tortuosity Fiber sorbent loading [volsorbent/volpolymer] Fiber thermal conductivity [W/m K] Fiber heat capacity [J/kg K] Fiber density [kg/m3]
λg Cpg ρg mg λw Cpw ρw mw dO dI rpore L εf τf νs λf Cpf ρf
0.06 1094 1.3 10 3 2.0 10 4 0.64 4178 1000 0.01 1200 320 200 3 0.44 2 50 0.05 1000 960
hw [W/m2 K] hg [W/m2 K] kg [m/s] Dm [m2/s] Deff [m2/s] Ds [m2/s] T0 [K] b0 [1/pa] qs0 [mol/kg] ΔH [kJ/mol] η A,B AI [m2/m3] AO [m2/m3]
7268 185 0.008 1.64 10 6 3.49 10 6 1.70 10 10 298 0.80 1.29 112 1.26 0.28, 1.32 12,500 5003
Capacity (mmol CO2/g)
In the sweeping step I 1 ðtÞ is fixed at 1.0 requiring that the entire outlet stream be recovered as purified CO2. In the other two steps, I 1 ðtÞ switches between 0 and 1. The design specifications and model parameters used for the simulation of RTSA for post-combustion CO2 capture from flue gas are tabulated below (Table 3).
10
35 oC
1
55 oC 0.1
80 oC
0.01 120 oC
2.2. Numerical solution The above described RTSA models have been implemented in gPROMSs version 3.5 released by Process Systems Enterprise Limited in 2011 (Process Systems Enterprise, 2011). The models were solved by the method of lines, discretizing the axial and radial domains using the second-order centered finite difference method (CFDM). For all simulation runs, a tolerance value equal to 10 5 was fixed while DASOLV integrator was used to integrate ordinary differential and algebraic equations over time. The number of points was increased until no further change is observed in the numerical results which resulted in 750 and 10 points in the axial and radial domains, respectively. In addition, the parameter estimation and model validation were performed in gPROMS to determine mass transfer parameters and to fit the experimental data.
0.001 0.001
0.01
0.1
1
PCO2 (bar) Fig. 4. CO2 adsorption isotherms for APS/silica/CA hollow fiber sorbent obtained at 35, 55, 80 and 120 1C. Points are experimental data and lines are fitted model.
3. Results and discussion 3.1. Isotherm parameters and mass transfer coefficients estimation Typically, for the numerical simulation of the single hollow fiber sorbent, a simulated dry flue gas containing 13 vol% CO2 in N2 is considered as a feed stream at 35 1C and 1 atm. In addition, the corresponding heat and mass transfer coefficients, estimated from
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F. Rezaei et al. / Chemical Engineering Science 113 (2014) 62–76
Fig. 5. Comparison of experimental and simulated breakthrough profiles obtained using (a) conventional constant ks model and (b) the modified model (c), (d) and (e) present the modified model validation against experimental data obtained at different temperatures and gas flow rates.
F. Rezaei et al. / Chemical Engineering Science 113 (2014) 62–76
related correlations presented in Appendix A, are presented in Table 4. The experimental data from isotherm measurements of 3-aminopropyltrimethoxysilane (APS)/silica/polymer hollow fibers were used to estimate the parameters for CO2 adsorption using the temperature-dependent Toth isotherm model (Fig. 4). More information on how the hollow fiber sorbent was prepared and isotherm measurements were performed can be found in Rezaei et al. (2013). The Figure demonstrates that good agreement between model predictions and experimental data was achieved, both at low (inset) and high partial pressures, and at all temperatures studied between 35 and 120 1C. The estimated Toth model parameters are presented in Table 4. To estimate the mass transfer coefficient, the model equations described above were fitted to experimental breakthrough data obtained from our fiber sorbent experimental setup that has been described in previous studies (Labreche et al., 2013; Rezaei et al., 2013). The experimental and fitted curves are shown in Fig. 5a and b and the estimated mass transfer coefficients are presented in Table 4. The experimental breakthrough curve shows a “long tail” where the CO2 concentration increases slowly after breakthrough, which is consistent with the result reported in Bollini et al. (2012a, 2012b). This experiment was carried out using a single hollow fiber sorbent without water in the bore but in a copper shell which has a large heat capacity to absorb the heat of adsorption. We assume isothermal conditions, and fit the model only to the concentration profiles. Fig. 5a shows the simulated data obtained using conventional model in which mass transfer coefficient is not a function of surface coverage. As can be seen, the conventional model fails to describe the experimental trend using both low and high values of mass transfer coefficient. On the other hand, our empirical model (Eq. (8)) shows an excellent fit to the data obtained experimentally as can be seen in Fig. 5b. To obtain the fit, three sets of experimental data at 35, 55 and 75 1C were used to fit the curves and another two sets of data at 45 and 65 1C, all obtained using a simulated flue gas at 40 mL/min, were used to validate the model (as shown in Fig. 5c and d). The mass transfer parameters estimated from curve fitting, ks0 and α, were appeared to be 0.165 s 1 and 1.31, respectively, which indicates that ks decreases by 73% when θ changes from 0.0 to 1.0. Furthermore, the model was validated against another set of experimental data at 80 mL/min and the corresponding profiles are shown in Fig. 5e. As can be seen from this Figure, a good match was observed which further confirms that the model can predict the experimental observations very well. This good match between the breakthrough profiles of the empirical model (Eq. (8)) and experimental data may support our hypothesis that for the chemisorbent material considered in this work, amine functionalized fiber sorbents, surface coverage decreases the adsorption rate. Although this hypothesis was successfully tested for our hollow fiber sorbents, it should also be noted that there is a lack of consensus in the literature on the factors that contribute to the slow mass transfer rate in the aminebased sorbent materials. For instance, Jones and co-workers related the broad breakthrough profile of APS functionalized SBA-15 to the diffusion resistance introduced by the aminopolymer (Bollini et al., 2012a). We employed the same hypothesis using a simpler empirical mass transfer model (Eq. (8)). On the other hand, Ritter and co-workers considered the chemisorption reaction between amine moieties and physisorbed CO2 molecules into their model in order to fit the experimental breakthrough profiles (Ebner et al., 2011). It may also be attributed to another potential mechanism of mass transfer slow-down where polymer chain reacted with CO2 may occupy the pore volume. More investigation however needs to be done in order to verify the contributing factors to the slow adsorption rate. The numerical values of initial and boundary conditions corresponding to each individual step are also given in Table 5.
69
Table 5 Numerical values for initial and inlet conditions for individual steps. Operating parameter
Value
uads g;in [m/s]
4.4
[m/s] usweep g;in
0.2
ucool g;in [m/s]
1.0
uads w [m/s]
0.2
udes w [m/s] [m/s] usweep w [m/s] ucool w T ads g;in [1C] T ads w;in [1C] T des w;in [1C] T sweep w;in [1C] T cool w;in [1C] T ads [1C] 0 T des [1C] 0 [1C] T sweep 0 T cool [1C] 0 3 cads N 2 ; 0 [mol/m ] 3 [mol/m ] cdes N2 ; 0 3 [mol/m ] cdes CO2 ; 0 3 ccool N 2 ; 0 [mol/m ] 3 cads CO2 ; in [mol/m ] 3 [mol/m ] cads N 2 ; in 3 csweep N 2 ; in [mol/m ] 3 ccool N 2 ; in [mol/m ]
1.0 1.0 0.3 35 35 120 120 35 35 35 120 120 39.03 33.95 5.07 39.03 5.07 33.95 39.03 39.03
3.2. Adsorption step 3.2.1. Effect of cooling water on CO2 concentration and temperature Profiles Simulated breakthrough and adsorbed phase concentration fronts, temperature profiles and CO2 mole fraction for uncooled and cooled fibers at fiber outlet are presented in Fig. 6a–d. As can be seen from Fig. 6a, without cooling water, the fiber sorbent bed will lose capacity and results in earlier breakthrough, which is qualitatively consistent with the experimental observations for zeolite 13 hollow fiber sorbents (Lively et al., 2012b). It should also be noted that the breakthrough profile of the uncooled fiber is slightly sharper. This is most likely due to the “thermal self-sharpening effect”; as the breakthrough occurs, the fiber temperature increases due to the heat of adsorption and thus the adsorption capacity decreases rapidly. As a result, the adsorbent get saturated quickly after the breakthrough. This effect is not observed for the cooled fiber where the heat of adsorption is removed effectively to maintain the adsorption capacity. Comparing the normalized adsorbed phase concentration for uncooled and cooled fibers (shown in Fig. 6b), it can clearly be seen that without cooling water fiber will lose capacity and result in earlier CO2 breakthrough as compared with cooled fiber. In this RL Rr Figure, qave is defined as qave ¼ 2 0 rIDOD rqCO2 ðr; zÞdrdz=ðr 2OD r 2ID ÞL. Fig. 6c demonstrates temperature profiles of uncooled and cooled fiber beds during the adsorption step of RTSA cycle. Under the operating conditions listed in Table 4, the temperature rises to 76 1C for the case of uncooled fibers and remains constant until the end of the adsorption step. It rises to 53 1C for the case of cooled fibers and starts to decrease, after hitting the maximum value, as a result of heat transfer into the water stream running through the fiber bores. This enables the cooled fiber bed to achieve a higher CO2 adsorption capacity as shown in the previous section. These profiles clearly demonstrate the advantage of running water through the bore of fibers and therefore reducing the fiber bed
70
F. Rezaei et al. / Chemical Engineering Science 113 (2014) 62–76
Uncooled Fiber
1
1.0
0.8
0.8
qave/qeq
CadsCO2,g|z=L/ CadsCO2,in
Cooled Fiber
0.6
0.6
0.4
0.4
0.2
0.2 Uncooled Fiber Cooled Fiber
0
0.0 0
50
100
150
200
0
50
100
150
200
Time (sec.)
Time (sec.)
0.14
80 Uncooled Fiber Cooled Fiber
0.12
70
yg,CO2|t=40 s
Tf |z=L,r=rOD (oC)
0.1 60
50
0.08 0.06 0.04 Uncooled Fiber
40 0.02 30 0
50
100
150
200
Cooled Fiber
0 0
0.5
Time (sec.)
1
1.5
2
2.5
3
Axial Position (m)
Fig. 6. (a) CO2 breakthrough profiles, (b) normalized adsorbed concentration, (c) temperature profiles and (d) CO2 mole fraction for uncooled and cooled fiber sorbents at the end of fiber (z¼ 3 m) during the adsorption step with operating condition in Table 5.
3.2.2. Effect of gas flow rate on CO2 breakthrough capacity The effect of interstitial gas velocity on breakthrough capacity of hollow fiber sorbents was evaluated and the results are displayed in Fig. 7. It shows the normalized breakthrough
2,in
1 0.8 0.6
2
C adsCO ,b/C adsCO
temperature and making the bed condition closer to isothermal. It should also be noted here that the simulated temperature front for uncooled fiber does not show slow cooling as usually expected in conventional fixed bed systems due to the temperature of the feed gas (Bonjour et al., 2002). Fig. 6d demonstrates CO2 mole fraction profiles for uncooled and cooled fiber sorbents at 40 s. Ideally, once the fibers are actively cooled with cooling water, the CO2 front velocity will be slowed due to the increase in capacity as a result of the fibers being closer to isothermal. The model can capture this by demonstrating the difference in front velocity for both cooled and uncooled fibers. Based on the experimental results obtained by Lively et al. (2012b) on zeolite 13 hollow fiber sorbents, an average of a 34% reduction in front velocity was recorded for cooled fibers as compared to uncooled fiber. Our numerical results for aminosilica hollow fiber sorbents indicate a 30% reduction in front velocity when it is cooled. These results clearly show that cooling water is necessary to achieve one of the main advantages of fiber sorbents which is the retention of adsorption capacity at high CO2 flow rates, thus allowing for rapid cycles and concomitant minimization of the CO2 capture system size.
0.4 Uncooled Fiber
0.2
Cooled Fiber 0
1
2
3 4 5 6 7 Interstitial gas velocity (m/s)
8
Fig. 7. CO2 normalized breakthrough capacity as a function of interstitial gas velocity for uncooled and cooled fiber sorbents at the end of fiber (z¼ 3 m) during the adsorption step with operating condition in Table 5.
ads capacities ðcads CO2 ;b =cCO2 ;in Þ for uncooled and cooled fibers in the gas
velocity range from 2.5 to 7.5 m/s. The breakthrough capacity is dynamic adsorption capacity of the hollow fiber bed calculated as R tb ads ads 2 2 cads CO2 ;b ¼ Af s :ug 0 ðcCO2 ;in cCO2 jz ¼ L Þdt=ðπðr OD r ID ÞLÞ where tb is the
F. Rezaei et al. / Chemical Engineering Science 113 (2014) 62–76
1.2
uw= 0.05 m/s uw= 0.1 m/s uw= 0.2 m/s uw= 1 m/s
60 55 ave
Tw (oC)
69
uw=0.05 m/s uw=1.0 m/s uw=0.05 m/s uw=1.0 m/s
1
CadsCO2,b/CadsCO2,in| t=20
65
50 45 40
64 59
0.8
54 0.6 49 0.4 44 0.2
35 30 0
0.5 1 1.5 2 2.5 Cumulative Water Volume (cm3)
3
Tw |t=20 (oC)
70
71
39 34
0 0
0.5
1
1.5
2
2.5
3
Axial Position (m)
Fig. 8. (a) Water temperature profiles versus cumulative water volume and (b) CO2 concentration and water temperature profiles of cooled fiber sorbents along fiber length at different water velocities during the adsorption step.
breakthrough time at which 0.5% of initial CO2 concentration breaks through the fiber bed. As can be seen, in the case of uncooled fibers, increasing gas velocity decreases the breakthrough capacity dramatically, whereas in the case of cooled fibers, breakthrough capacity remains almost unchanged with increased velocity. The dramatic decrease in CO2 capacity for the uncooled fiber can be attributed to the increased temperature of the fiber due to the heat released during adsorption step. At lower velocities, the fiber bed operates almost isothermally and the rate of heat release is minimal, therefore, the uncooled fiber exhibits a comparable capacity with the cooled fiber. When the velocity increases, the rate of release of the heat of adsorption becomes important which make the fiber bed highly non-isothermal, hence reducing the CO2 breakthrough capacity for the uncooled fiber. On the other hand, in the presence of bore-side cooling water, the hollow fiber sorbent is operated under isothermal conditions at all gas velocities, and therefore displays very little change in the capacity. These observations clearly emphasize the importance of hollow fiber configuration which acts as a heat exchanger during adsorption and transfers the heat very efficiently to the water in the bore. The experimental observations reported earlier by Lively et al. qualitatively agree with these findings (Lively et al., 2012b).
the collection of same water volume at lower temperature – is obtained. On the other hand, although a low water velocity gives rise to better heat recovery, it can be insufficient to remove the heat of adsorption, in agreement with the profiles shown in Fig. 6c. Fig. 8b presents the CO2 concentration and water temperature profiles as a function of fiber length during adsorption, at 20 s with the water velocities of 0.05 and 0.2 m/s. In agreement with Fig. 8a, running water at a lower velocity gives rise to higher bed temperature resulting in the broader front, although the heat recovery is better. On the other hand, the concentration profile is sharper at the higher water velocity due to the lower bed temperature. Moreover, with the higher water velocity, the water temperature front is ahead of the concentration front which implies an isothermal bed during adsorption. As the cooling water flow increases, it keeps the fibers close to isothermal condition, resulting in the equilibrium CO2 capacity being maintained. In order to maintain a good CO2 capacity for hollow fiber sorbents, the water velocity should be optimized by taking into account the competing factors discussed above. Finally, it should be noted that the pumping cost for the water in the bore of the hollow fiber sorbents should be considered when designing the module dimension and selecting water velocity since the pressure drop is proportional to L, 1=r 2ID , and uw .
3.2.3. Effect of water flow rate on heat recovery As stated before, one of the advantages of hollow fiber configuration is to efficiently dissipate the heat of adsorption by running cold water through the fiber bore. This implies that a higher water velocity is favored in this regard, resulting in a more uniform bed temperature. However, from the economic point of view this implies higher operating costs (utility costs) and forgoes the opportunity to recover the heat released during adsorption. To evaluate this trade-off, water velocity during adsorption (uads w ) was varied from a minimum value of 0.05 m/s to a maximum value of 1.0 m/s. Fig. 8a displays the average temperature of water Rt accumulated at the end of fiber bed, T ave w ¼ 0 T w jz ¼ L dt=t versus 2 ads 2 cumulative water volume, uads w U πr ID Ut. Here, note that uw U πr ID U t and T ave represent the cumulative volume of the water and its w temperature to be supplied to the “Warm Water Tank” shown in Fig. 2. As this Figure shows, although running water with higher velocity results in lower bed temperature and hence higher capacity, an undesirable decrease in heat recovery – indicated by
3.3. Heating/desorption and heating/sweeping steps To demonstrate the time required to heat the hollow fiber bed to the desorption temperature, the fiber temperature profile as a function of time during heating/desorption and heating/sweeping steps is shown in Fig. 9. Fig. 9a demonstrates it is possible to heat up the entire fiber bed within only 25 s. using a hot water stream of 1.0 m/s at 120 1C. During the heating/desorption step, there is no inlet nitrogen flow and CO2 is released through the fiber bed due to the heating. Fig. 9b and c shows the CO2 mole fraction and normalized adsorbed concentration during these two steps respectively. As can be seen in Fig. 9b, the mole fraction of CO2, yg;CO2 reaches nearly 1.0 between t ¼ 40 and t ¼ 120 (s). The splitting of the outlet gas can be performed accordingly to recover this pure gas fraction by selecting the binary parameter I 1 , which will be discussed more in detail in Section 3.5. A nitrogen flow with the velocity of 1.0 m/s is used to sweep the bed during heating/sweeping step.
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F. Rezaei et al. / Chemical Engineering Science 113 (2014) 62–76
130 1 110
yg,CO2|z=L
Tf |z=L,r=rOD (oC)
0.8 90
70
50
0.6
0.4
0.2
30
0 0
20
40
60
80
100
120
0
Time (sec.)
40
60
80
100
120
Time (sec.)
1.1
1.1
1
Tw= 80oC Tw= 90oC Tw= 100oC Tw= 110oC Tw= 120oC
1
0.9
0.9
qave/qeq
qave/qeq
20
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5 0
20
40
60
80
100
120
Time (sec.)
0
50
100
Time (sec.)
Fig. 9. (a) fiber temperature, (b) CO2 mole fraction, (c) normalized adsorbed concentration of hollow fiber sorbents at the end of fiber (z¼ 3 m) and outer surface (r ¼600 mm) and (d) normalized CO2 uptake (qave/qeq) profiles for different values of Tdes w during the heating/desorption and heating/sweeping steps with operating condition in Table 5.
To investigate the impact of hot water temperature used during heating and desorption steps on step time and swing capacity for regenerating the hollow fiber sorbents, simulation runs were implemented by varying the water temperature while keeping all other operating parameters constant. Here, desorption capacity is defined as the amount desorbed during desorption step. In Fig. 9d, the normalized CO2 capacities obtained at different hot water temperature versus step time are shown. It was found that using a hot water stream at 120 1C gives rise to a 0.45 normalized desorption capacity (qave/qeq) at 120 s, whereas decreasing water temperature from 120 to 80 1C significantly decreases the normalized desorption capacity to 0.10 for the same duration. However, it is possible to increase the swing capacity using the lower temperature water stream at the price of a longer step time. 3.4. Cooling step Once the hollow fiber sorbent is regenerated by a hot water stream at 120 1C and the desorbing CO2 is swept by N2 out of the bed,
a cold water stream is used to bring the fiber bed temperature down to 35 1C. To evaluate the time required to cool down the fiber under the operating condition in Table 4, fiber temperature profile as a function of time during cooling step is shown in Fig. 10a. The temperature profiles for two other water velocities (ucool w ) are also presented in this Figure. It is evident from this Figure that cooling time is very fast in the case of 1.0 m/s and it takes only 10 s for the entire fiber to cool down. With the water velocity of 0.3 and 0.1 m/s, cooling time increases to 30 and 80 s, respectively. Obviously, the higher the water velocity, the shorter the cooling time becomes which translates to a shorter cycle time and hence a lower capital cost. This is a major advantage of this RTSA hollow fiber configuration over the traditional TSA systems, which exhibit long cooling steps that limit their use in bulk gas separation applications. Similarly to the discussion in Section 3.2.2 for the adsorption step, in terms of heat recovery, a higher water velocity results in lower heat recovery (higher utility demand), as demonstrated in Fig. 10b. By considering this trade-off between cooling step time and heat recovery, a water velocity of 0.3 m/s was chosen for cooling step.
F. Rezaei et al. / Chemical Engineering Science 113 (2014) 62–76
73
130
130
uw= 0.1 m/s uw= 0.3 m/s
110
110
T wave ( o C)
T f | z=L,r=rOD (oC)
uw= 1 m/s 90
70
uw= 0.1 m/s uw= 0.3 m/s uw= 1 m/s
50
20
40
60
70
50
30 0
90
80
100
30 0.03
0.05
0.07
0.09
Cumulative Water Volume (cm3)
Time (sec.)
Fig. 10. Temperature profile of (a) hollow fiber sorbent at the end of fiber (z¼ 3 m) and outer surface (r¼ 600 mm) during the cooling step and (b) water temperature profiles versus cumulative water volume at different water velocities.
3.5. Cyclic simulation In previous sections, we presented the results for individual steps of the RTSA system. The cyclic performance of the hollow fiber RTSA system is provided in this section. To perform cyclic simulation, the hollow fiber RTSA cycle – comprising four steps (adsorption, heating/desorption, heating/sweeping and cooling steps) – was considered. The step times and water velocities corresponding to each step as well as cycle time are listed in Table 6. Fig. 11a–c shows the variation of temperature profile, CO2 mole fraction in the bulk gas and adsorbed phase concentration obtained from four-step RTSA simulation with the operating conditions listed in the above Table 6. The initial conditions considered for cyclic simulations are the same to those presented in Table 1 for adsorption step, and succeeding steps are simulated without reinitialization over multiple cycles. The fiber temperature and CO2 mole fraction profiles over 5 cycles are displayed in Fig. 11a and b. By switching the binary parameter I1(t), we fractionate the purified CO2 fraction selectively as the purified product, as shown in Fig. 11b. The RTSA hollow fiber system reaches cyclic steady state (CSS) after only three cycles. The CSS is defined when the conditions at the end of each cycle are identical to those at its start; in our numerical model it is determined when the difference between variables at the start and the end of each cycle is less than 0.1%. With this set of parameters, a CO2 product stream with purity of 90.53% and recovery of 81.62% is obtained within the cycle period of 167 s. The adsorbed phase concentration (qave) over 5 cycles shown in Fig. 11c implies a low swing capacity for our RTSA system (i.e., 0.25 mmol/g). This is because the adsorption step time is only 20 s during cyclic simulation. Such a short cycle time was chosen to increase recovery. It should be noted that the operating conditions considered in this work are preliminary and not optimized systematically.
4. Concluding remarks In this study, a numerical simulation was performed to study the performance of an RTSA system in a post-combustion CO2
Table 6 RTSA operating conditions. Operating parameter
Value
uads w [m/s]
1.0
udes w [m/s] [m/s] usweep w [m/s] ucool w
1.0 1.0 0.3
uads g;in [m/s]
4.4
ucool g;in [m/s]
0.2
[m/s] usweep g;in
0.2
t ads [s]
20
t des [s] t sweep [s]
100
t cool [s]
12 35
t cycle (¼ tads þ tdes þ tsweep þ tcool)[s] I1 (t)
1 in
167 t A ½39 þ ðn 1Þt cycle ; 142 þ ðn 1Þt cycle ½s 0 otherwise
capture process. We presented a set of mathematical models describing the mass and heat balances in a single hollow fiber sorbent. The effects of different operating conditions on CO2 sorption and desorption behavior of thermally cycled hollow fiber sorbent were investigated in individual steps as well as the whole RTSA cycle. Simulation results, based on experimental data for the adsorption behavior fitted to a Toth isotherm, indicate that the CO2 capacity of cooled fibers is significantly higher than that of uncooled fibers as a result of fibers being close to isothermal, while, without cooling, fibers lose capacity and earlier breakthrough will be observed. Under the assumptions and non-optimized conditions studied here, a CO2 product purity of 90.53% is achievable at 81.62% recovery by performing RTSA cycles with a total cycle time 3 min. Also, it was shown that a cooling time of 30 s will permit the entire fiber to return to the adsorption temperature. These results clearly show that it would be possible to operate a complete RSTA cycle in just a few minutes to allow a large quantity of CO2 captured and concentrated within a reasonable time frame.
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F. Rezaei et al. / Chemical Engineering Science 113 (2014) 62–76
1.2
130
CO2 product
CO2 CO2 product product
CO2 product
CO2 product
1.0 110
yCO2, g|z=L
Tf |z=L,r=rOD (oC)
0.8 90
70
0.6
0.4
50
0.2
0.0
30 0
200
400
600
0
800
200
400
600
800
Time (sec.)
Time (sec.) 1.0
qave (mmol/g-fiber)
0.9
0.8
0.7
0.6
0.5 0
200
400
600
800
Time (sec.) Fig. 11. (a) fiber temperature, (b) CO2 mole fraction and (c) adsorbed concentration of hollow fiber sorbents at the end of fiber (z¼ 3 m) and outer surface (r¼ 600 mm) over five RTSA cycles with operating condition in Table 6.
Finally, for future work, it is important to optimize the operating conditions in order to improve purity and recovery of the final product.
t T u y z
time, s temperature, K velocity, m s 1 mole fraction axial position, m
Nomenclature A c Cp d D k h L n ncycle P q qs r rs R
specific surface area, m2 m 3 concentration, mol m 3 specific heat capacity, J kg 1 K 1 fiber diameter, m diffusion coefficient, m2 s 1 mass transfer coefficient, s 1 heat transfer coefficient, W m 2 K 1 fiber length, m Toth isotherm parameter number of cycles pressure, atm average sorbent loading, mol kg 1 saturation capacity, mol kg 1 radial position, m sorbent particle radius, m gas constant, J mol 1 K 1
Greek symbols ΔH heat of adsorption, J mol 1 α surface coverage αg thermal conductivity, m2 s 1 ε total fiber/sorbent void fraction ρ density, kg m 3 m viscosity, kg m 1 s 1 λ thermal conductivity, W m 1 K 1 τ fiber tortuosity η non-dimensional isotherm parameter Subscripts 0 b c
initial state breakthrough cooling
F. Rezaei et al. / Chemical Engineering Science 113 (2014) 62–76
cp eff eq f fs g h i I in ID k m O OD p w s
where Dcombined is combined diffusivity estimated from:
convective pore effective equilibrium fiber free space gas heating gas components (CO2, N2) inner inlet inner diameter Knudsn module outer outer diameter pore water sorbent
1 1 1 ¼ þ Dcombined Dm Dk
sffiffiffiffiffiffiffiffiffiffiffi T Dk ¼ 9:7 10 r pore M CO2 3
Appendix A Heat and mass transfer coefficients To estimate the mass transfer coefficient of the flue gas, the same concept of a flow through a pipe is assumed and mass transfer coefficient through external film is estimated by (McCabe et al., 2011): 0
k g dO 1=3 ¼ 1:495 GzM Dm
ðA 1Þ
Similarly, with the same concept of a flow through a pipe, heat transfer coefficient through external film is predicted by (McCabe et al., 2011): hg dO 1=3 ¼ 1:845 GzH λg
ðA 2Þ
where 2
GzM ¼
dO ug ; Dm L
2
GzH ¼
dO ug αg L
ðA 3Þ
In the above equation, αg is thermal conductivity of gas which is calculated by αg ¼ λg =ρg Cpg . Internal and external heat transfer areas for fiber sorbent are (m2/m3): AI ¼
External surface area πdI L 4 ¼ 2 ¼ volume Fiber πd L dI
ðA 4Þ
I
AO ¼
External surface area πdO L 4dO ¼ ¼ 2 2 2 2 Free space volume πðd d ÞL d d fs
ðA 8Þ
References
This work has been financially supported by the US Department of Energy via Grant number DE-FE0007804.
Nu ¼
ðA 7Þ
The binary diffusion coefficient between CO2 and N2 is estimated by Chapman-Enskog formula whereas, Knudsen diffusivity is calculated from:
Acknowledgment
Sh ¼
75
O
fs
ðA 5Þ
O
where dfs is free space diameter calculated by considering a fiber module with the diameter of 1.0 m and length of 3.0 m and 60% fiber packing. The gas transport through fiber is described by both molecular diffusion and Knudsen diffusion. Therefore, the effective diffusivity is given by: εf Def f ¼ Dcombined ðA 6Þ τf
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