Sorption-enhanced reaction process with reactive regeneration

Chemical Engineering Science 57 (2002) 3893 – 3908

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Sorption-enhanced reaction process with reactive regeneration Guo-hua Xiua , Ping Lia; b , Alirio E. Rodriguesa;∗ a Laboratory

of Separation and Reaction Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s=n, 4200-465 Porto, Portugal b Department of Chemical Engineering, Shenyang Institute of Chemical Technology, Shenyang 110021, People’s Republic of China Received 10 October 2001; received in revised form 3 May 2002; accepted 17 May 2002

Abstract Sorption-enhanced reaction process with reactive regeneration of adsorbent was proposed where the purge step is performed at a ◦ ◦ low temperature of 400 C (compared with the reaction temperature of 450 C) with 10% H2 in nitrogen under atmospheric pressure. Hydrogen-enriched stream with traces of CO2 and CO can be produced by steam–methane reforming. A mathematical model taking into account multicomponent (six species) mass balances, overall mass balance, Ergun relation for the pressure drop, energy balance for the bed-volume element including the heat transfer to the column wall, and nonlinear adsorption equilibrium isotherm coupled with three main reactions was derived to describe this new cyclic process. The feasibility and e8ectiveness of this cyclic process is analyzed by numerical simulation. The results show that using either a 4 m or a 6 m long adsorptive reactor (depending on the operation time of the ;rst step), a product gas with above 88% hydrogen purity and traces of CO2 and CO (CO less than 30 ppm) can be continuously produced and directly used in the fuel cell applications. The validity of the model prediction was checked by comparing the simulated results with experimental data from the literature where the regeneration of adsorbent is carried out by steam purge at subatmospheric pressure. The model results qualitatively agree with experimental data. The package is needed to improve the design and analysis of sorption-enhanced reaction process. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Mathematical modelling; Reaction engineering; Reactive regeneration; Simulation; Sorption-enhanced reaction process; Steam–methane reforming

1. Introduction Separation-enhanced reaction processes have been widely investigated theoretically and experimentally (Roginskii, Yanovskii, & Graziev, 1962; Chu & Tsang, 1971; Takeuchi & Uraguchi, 1977; Cho, Aris, & Carr, 1980; Vaporciyan & Kadlec, 1987; Hsieh, 1989; Tsotsis, Champagnie, Vasileiadis, Zraka, & Minet, 1992; Lu & Rodrigues, 1994; Carvill, Hufton, Anand, & Sircar, 1996; Hufton, Mayorga, & Sircar, 1999; Ding & Alpay, 2000b; Waldron, Hufton, & Sircar, 2001; Xiu, Li, & Rodrigues, 2001; Xiu, Soares, Li, & Rodrigues, 2002b). The combination of reaction and separation in a single unit operation (such as adsorptive reactor, chromatographic reactor, membrane reactor, etc.) has advantages for achieving enhanced conversions and yields in catalyzed reversible reactions. ∗ Corresponding author. Tel.: +351-22-508-1671; fax: +351-22-508-1674. E-mail address: [email protected] (A. E. Rodrigues).

If an adsorbent selectively trapping the product is combined with the catalyst, conversion can almost run to completion; this type of adsorptive reactor has been demonstrated in the laboratory in particular for the production of hydrogen by steam–methane reforming (Hufton, Waldron, Weigel, Rao, & Sircar, 2000; Waldron, Hufton, & Sircar, 2001), and appears to be potentially a promising approach for further improving the eHciency of some industrial processes (Agar, 2000; Stankiewicz, 2000; Sircar, 2001). The operation of an adsorptive reactor is of discontinuous nature; on equilibrium of the adsorbent, the separation e8ect is lost and therefore periodic regeneration of the adsorbent is needed. For a practical process, the regeneration is often more important than adsorption. There are many methods developed to regenerate the adsorbent (see Ruthven, 1984; Yang, 1987; Suzuki, 1990), such as pressure swing, thermal swing, purge gas stripping, displacement desorption and reactive regeneration; all aim to decrease the equilibrium adsorbed amount. The choice of the regeneration

0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 2 ) 0 0 2 4 5 - 2

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process is mainly determined by the adsorption isotherm. In general, one single process could not eHciently accomplish the regeneration of adsorbent; hybrid regeneration processes are necessary as pressure swing coupled with intermediate purge. Since Skarstrom (1960) originally proposed the pressure swing adsorption (PSA) process, this technology is still more advantageous than traditional methods when high purities are required. The sorbent is periodically regenerated by using the principles of PSA in most of the published works (Vaporciyan & Kadlec, 1987, 1989; Lee & Kadlec, 1988; Alpay, Kenney, & Scott, 1993; Chatsiriwech, Alpay, Kershenbaum, & Kirkby, 1993; Alpay, Chatsiriwech, Kershenbaum, Hull, & Kirkby, 1994; Kirkby & Morgan, 1994; Carvill et al., 1996; Hufton, Mayorga, & Sircar, 1999; Ding & Alpay, 2000b; Hufton et al., 2000; Waldron, Hufton, & Sircar, 2001). In a previous work (Xiu et al., 2002b), a ;ve-step (high pressure reaction=adsorption, depressurization, low pressure purge with methane, low pressure purge with part of hydrogen product, and pressurization with part of hydrogen product) one-bed sorption-enhanced reaction process (proposed by Carvill et al., 1996) was theoretically analyzed for hydrogen production by steam–methane reforming; it was found that the regeneration process is not of high eHciency for strong favorable isotherms, especially for a long length of reactor. Recently, Hufton et al. (2000) developed a new four-step (Step 1: high pressure sorption reaction; Step 2: depressurization; Step 3: low pressure purge with a mixture of 5 – 10% H2 in steam to desorb CO2 ; Step 4: pressurization with a mixture of 5 –10% H2 in steam) one-bed process for the production of hydrogen. In fact, if the low pressure purge step (Step 3) is combined with thermal swing, it could be a better method to regenerate the adsorbent; in the following we call this reaction-enhanced desorption process a reactive regeneration (Xiu, Li, & Rodrigues, 2001). The three main chemical reactions in the cyclic process are described by the following equations (Xu & Froment, 1989): CH4 + H2 O
CO + 3H2 ; KH298 = 206:2 kJ=mol

(I);

CH4 + 2H2 O
CO2 + 4H2 ; KH298 = 164:9 kJ=mol

(II);

CO + H2 O
CO2 + H2 ; KH298 = −41:1 kJ=mol

(III): (1)

Reforming reactions (I) and (II) are strongly endothermic, so the forward reaction is favored by high temperatures, while the water–gas shift reaction (III) is moderately exothermic and is therefore favored by low temperatures. The reforming reactions will also be favored at low pressures, whereas the water–gas shift reaction is largely una8ected by changes in pressure. After depressurization (Step 2), the total pressure drops from high pressure to low

pressure, then purging the ;xed bed at low pressure with a mixture of 5 –10% hydrogen in steam, the desorption of CO2 from adsorbent could be enhanced because the reaction of hydrogen with CO2 is expected to occur according to the reversible reactions of reactions II and III. Due to a large amount of steam (it is also a product of the reversible reactions of reactions II and III) being introduced to the reactor, the enhancement is not obvious. Whereas the limitation of the concentration of hydrogen in the purge gas mixture and the reaction is an exothermic reaction, we improve the regeneration process (Step 3) with 5 –10% hydrogen in N2 at lower temperature. The choice of the optimum purge temperature depends on the methanation and reverse water–gas shift reactions and the adsorption isotherm. In this paper, a four-step one-bed sorption-enhanced reaction process (Step 1: high pressure reaction=adsorption at high temperature; Step 2: depressurization; Step 3: low pressure reactive regeneration with a mixture of 10% H2 in N2 at low temperature and purge with steam at high temperature; Step 4: pressurization with steam at high temperature) for hydrogen production by steam–methane reforming was theoretically analyzed. For comparison, the case with constant wall and feed gas temperatures was also presented where purge is carried out by steam at atmospheric pressure. The simulation results for the ;rst step use data from the papers of Hufton et al. (2000) and Ding and Alpay (2000a). A model taking into account multicomponent (six species) mass balances, overall mass balance, Ergun relation (Ergun, 1952) for the pressure drop, energy balance for the bed-volume element including heat transfer to the column wall, and nonlinear adsorption equilibrium isotherm coupled with three main reactions was derived to describe the cyclic process. The linear driving-force (LDF) model was adopted to describe the mass-transfer rate of CO2 to the adsorbent (Ding & Alpay, 2000a). Numerical solution of model equations for the cyclic process was obtained by using the method of orthogonal collocation (Malek & Farooq, 1997). The purpose of this work is to ;nd suitable operating conditions that allow the combination of suHciently high purity of hydrogen (average purity over 80%) with traces of CO2 and CO (CO less than 30 ppm for fuel cell applications), over 50% methane conversion, fast reactive regeneration of adsorbent, and cyclic steady state operation.

2. Process description The reaction kinetic model of Xu and Froment (1989) (Eq. (1)) can be summarized as
 PH3 2 PCO k1 1 RI = PCH4 PH2 O − ; (1a) KI (DEN)2 PH2:52 k2 1 RII = (DEN)2 PH3:52




P 4 PCO2 PCH4 PH2 2 O − H2 KII

 ;

(1b)

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Table 1 Parameters used in Eq. (1) (Xu & Froment, 1989; Twigg, 1989)

1 atm2a , KII = KI KIII exp (0:2513Z 4 − 0:3665Z 3 − 0:58101Z 2 + 27:1337Z − 3:2770) 1000 KIII = exp (−0:29353Z 3 + 0:63508Z 2 + 4:1778Z + 0:31688)a , where Z = −1 T    240 100 1 1 k1 = 1:842 × 10−4 exp − − kmol bar 0:5 =kgcat h R T 648 KI =



k2 = 2:193 × 10−5 exp − 

67 130 R

k3 = 7:558 exp −



KCH4 = 0:179 exp 

KCO = 40:91 exp



38 280 R

70 650 R

243 900 R

1 1 − T 648







1 1 − T 648

kmol bar 0:5 =kgcat h



kmol=kgcat h bar

1 1 − T 823

1 1 − T 648









bar −1 ; KH2 O = 0:4152 exp − bar −1 ; KH2 = 0:0296 exp



88 680 R

82 900 R





1 1 − T 823

1 1 − T 648





bar −1

a Taken from Twigg (1989). The data of Xu and Froment (1989) are as follows: K = 4:707 × 1012 exp(−224 000=RT ) bar 2 ; K = 1:142 × I III 10−2 exp(37 300=RT ) (for T = 948 K).

k3 1 RIII = 2 (DEN) PH2



PH PCO2 PCO PH2 O − 2 KIII

 ;

(1c)

where DEN = 1 + KCO PCO + KH2 PH2 + KCH4 PCH4 + KH2 O PH2 O =PH2 , with Pi = yi P (i = H2 O; CH4 ; H2 ; CO2 , and CO, P is the local total pressure, and yi is the gas-phase mole fraction of component i). For the expressions of k1 ; k2 ; k3 ; KCO ; KH2 ; KCH4 ; KH2 O and KI ; KII , and KIII , see Table 1. The equilibrium data KI ; KII , and KIII are the key parameters for the simulation. There are two sources to obtain their expressions, as listed in Table 1; for present work, we take the results of Twigg (1989). The formation or consumption rate of component i; ri , was then calculated by using Eqs. (1a) – (1c) as follows: ri =

III 

vij Rj

(i = 1 − 5);

(2)

j=I

where vij is the stoichiometric coeHcient of component i. If i refers to a reactant, vij is negative, and for a product vij is positive. Thus we have rCH4 = −RI − RII ;

(2a)

rH2 O = −RI − 2RII − RIII ;

(2b)

rH2 = 3RI + 4RII + RIII ;

(2c)

rCO = RI − RIII ;

(2d)

rCO2 = RII + RIII :

(2e)

The operation scheme of the four-step one-bed sorptionenhanced reaction process is shown in Fig. 1.

Case 1: Pressure swing cyclic process Step 1: High pressure reaction=adsorption step. Feed a stoichiometric mixture of H2 O and CH4 at Tf = TH and PH through the regenerated reactor that has been previously saturated with steam at TH and PH . An eOuent stream containing essentially component H2 is produced from the reactor at pressure PH , the wall temperature is also kept with Tw = TH . The step is continued until near the breakthrough point of CO2 (ppm level). Step 2: Countercurrent depressurization step. Depressurize the reactor to a lower pressure level of PL countercurrent to that of the reactant-feed gas Pow. A gas stream containing all components of the system exits the reactor. It consists of interparticle void gas in the column as well as some adsorbed gases present in the reactor at the end of Step 1. In the countercurrent blowdown step, the reaction and desorption of CO2 should take place. Step 3: Low pressure countercurrent purge step. Introduce steam to the reactor at Tf = TH and PL in the direction countercurrent to that of the reactant-feed gase Pow, the wall temperature Tw = TH . Step 4: Countercurrent repressurization step. Pressurize the reactor from PL to PH by countercurrently introducing steam at Tf = TH , the wall temperature Tw = TH . Case 2: Pressure swing cyclic process coupled with thermal swing (reactive regeneration) Step 1: High pressure reaction=adsorption step. Same as the ;rst step in Case 1. Step 2: Countercurrent depressurization step. Depressurize the reactor to a lower pressure level of PL countercurrent to that of the reactant-feed gas Pow with Tw = TL . In the countercurrent blowdown step, the reaction and desorption of CO2 should take place.

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Fig. 1. (a) Flow direction for four-step one-bed sorption-enhanced reaction process (↓ adsorption, ↑ desorption) for Case 1. (b) Flow direction for four-step one-bed sorption-enhanced reaction process (↓ adsorption, ↑ desorption) for Case 2.

Step 3: Low pressure countercurrent purge and reactive regeneration step. Introduce the mixture of 10% H2 in N2 to the reactor at Tf = TL and PL in the direction countercurrent to that of the reactant-feed gase Pow, the wall temperature is kept with Tw = TL . Then, purge with steam at Tf = Tw = TH in order to remove the remaining N2 in the reactor and increase the wall temperature of the reactor. At this step, the adsorbent is regenerated e8ectively. Step 4. Countercurrent repressurization step. Same as the fourth step in Case 1. In the following discussion, we set CH4 =H2 O = 6; TH = ◦ ◦ 450 C; TL = 400 C; PH = 445:7 kPa, and PL = 125:7 kPa.

3. Theoretical model The theoretical model adopted for the PSA reactor process is a non-isothermal, non-adiabatic, and non-isobaric operation, developed to describe both steam–methane reforming (SMR) and sorption-enhanced SMR (SE-SMR) processes. A Langmuir model was used to describe the adsorption equilibria of CO2 , and an LDF model for the intraparticle mass transfer of the adsorbent. The model assumptions adopted are summarized below (Malek & Farooq, 1997; Silva & Rodrigues, 1998; Da Silva & Rodrigues, 2001; Xiu et al., 2002b): (1) The Pow is represented by an axial-dispersed plug-Pow model. Mass dispersion in the axial direction is considered, with negligible radial gradients. The axial dispersion coeHcient was estimated from the correlation

of Edwards and Richardson (1968), as shown in Table 2. Change of Pow due to sorption and reactions, as determined by the overall material balance, is taken into account. The gas is assumed to be ideal. (2) Pressure distribution in the packed-bed reactor was described by the mechanical energy equation. (3) The system is non-isothermal. The column wall and the feed stream are maintained at the same constant temperature (TH or TL ). Thermal dispersion in the Pow direction is considered, with negligible radial gradients. Axial thermal conductivity is estimated using the empirical correlation given by Yagi, Kunii, and Wakao (1960), as reproduced in Table 2. For a bed packed with spherical particles, the wall– bed heat transfer coeHcient, U is given by Li and Finlayson (1977) and De Wash and Froment (1972). The gas-phase and the catalyst=adsorbent particle are assumed to be in local thermal equilibrium at all times. (4) There exist ;ve components (CH4 ; H2 ; CO2 , CO, and H2 O) in an inert carrier (N2 ). The Langmuir model is adopted to describe the adsorption equilibrium for component CO2 . Hufton, Mayorga, and Sircar (1999) and Ding and Alpay (2000a) reported signi;cant e8ect of steam on the adsorption behavior of CO2 . In this paper, we operated at the wet (all steps for Case 1, and Steps 1, 2, and 4 for Case 2) and dry (Step 3 for Case 2) conditions. (5) The LDF model is used to represent the transport in the adsorbent. Table 2 also shows the correlation to evaluate the value of the LDF mass-transfer coeHcient (Ding & Alpay, 2000a). From the above assumptions, we can derive the following governing equations and the corresponding initial conditions and general boundary conditions for the four steps.

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Table 2 Parameters for the governing equations

Semi-empirical relationships for KD and KV (Ergun, 1952) 150(1 − b )2 1:75(1 − b ) PM (N s=m4 ); KV = KD = (N s2 =m5 ), in which M ≈ 0:018 kg=mol RT d2p b3 dp b3 Axial dispersion coeHcient DL (Edwards & Richardson, 1968) 0:5udp DL = 0:73Dm + (m2 =s), in which Dm = 1:6 × 10−5 m2 =s for PH and Tf , and Dm = 5:6 × 10−5 m2 =s for PL and Tf (Reid, 1 + 9:49Dm =(udp ) Prausnitz, & Poling, 1988) Langmuir isotherm (Ding & Alpay, 2000a) 

mCO2 bCO2 PCO2 17 000 , where mCO2 = 0:65 mol=kg and bCO2 = 2:36 × 10−4 exp 1 + bCO2 PCO2 R    10 000 1 1 and bCO2 = 1:69 × 10−4 exp − Pa−1 (dry condition) R T 673 ∗ = qCO 2



1 1 − T 673



Pa−1 (wet condition), mCO2 = 0:63 mol=kg

Mass transfer coeHcient (Ding & Alpay, 2000a) kCO2 =

15 p D p , in which p = 1300 kg=m3 ; Dp = 1:1 × 10−6 m2 =s ∗ =@P rp2 p + p RT (@qCO CO2 ) 2

Bed e8ective conductivity kz (Yagi, Kunii, & Wakao, 1960; Malek & Farooq, 1997) Cpg  kz k0 k0 1 − t , Pr = = z + 0:75(Pr)(Rep ), where z = t + , and kg kg kg 0:139t − 0:0339 + 2=3(kg =kp ) kg g ut dp Rep = , in which kp = 1 × 10−2 J=cm s K and kg = 2:5 × 10−4 J=cm s K (Eucken formula, in Bird, Stewart, & Lightfoot, 1960)  Wall–bed heat-transfer coeHcient, U (Li & Finlayson, 1977) 

2UR0 3dp = 2:03Rep0:8 exp − kg R0



(Rep = 20–7600,

dp k0 = 0:05– 0.3), and U = 6:15 z as 2R0 2R0

Rep → 0 (De Wash & Froment, 1972)

Based on Eq. (2), the actual rates (ri )obv (i = CH4 ; H2 O; H2 ; CO2 , and CO) can be expressed as

(4)

by ad = 'b; ad =(1 + ') and cat = b; cat =(1 + '), where ' is the mass ratio of adsorbent and catalyst in the packed bed. The kinetic energy change is neglected in the mechanical energy balance; then we have (Sereno & Rodrigues, 1993) @P @ (5) (g u) = − − KD u − KV u|u|; @t @z where g is the gas-phase density, KD and KV are parameters corresponding to the viscous and kinetic pressure loss terms (see Table 2). For component i (qRi = 0 unless for i = CO2 ), the mass balance for the packed-bed reactor can be written as III  @Ci @qR @(uCi ) vij &j Rj t + + ad i − cat @t @z @t j=I   @ @yi DL C ; (6) =b @z @z

where C is the total molar concentration in the bulk phase, t is the total porosity of the packed bed, u is the super;cial velocity, qRCO2 is the solid-phase concentration for CO2 (average over an adsorbent particle), ad is the mass of adsorbent per bed volume, and cat is the mass of catalyst per bed volume. These densities of ad and cat are related with the bulk densities of the individual materials b; ad and b; cat

where Ci is the molar concentration of gas-phase component i (Ci = yi C); b is the voidage of the bed, and DL is the axial dispersion coeHcient. The LDF model is adopted to describe the mass-transfer rate of CO2 to the adsorbent, @qRCO2 ∗ − qRCO2 ); (7) = kCO2 (qCO 2 @t

(ri )obv =

III 

vij &j Rj

(i = 1 − 5);

(3)

j=I

where &j is the e8ectiveness factor for reaction j (j = I; II; III). Thus, the overall mass balance equation is t

@qR @C @(uC) + + ad CO2 − cat @t @z @t 5  III  × vij &j Rj = 0 i=1 j=I

(i = CH4 ; H2 O; H2 ; CO2 ; CO);

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∗ where kCO2 is the LDF mass-transfer coeHcient and qCO 2 is the equilibrium solid-phase concentration, which are respectively evaluated by the correlation given by Ding and Alpay (2000a) and the Langmuir isotherm; see Table 2. The energy balance for the bed-volume element that includes the heat transfer to the column wall is described as (Kikkinides, Yang, & Cho, 1993)

@T @t n 

[t CCvg + (ad + cat )Cps ] + CCpg u

@T − ad @z

−KHadi

i=1 5

@qRi @t

=

@ @z

kz

@T @z





z=0

= *7 ;

@T @z

 z=L

= *8 ;

(9d)

in which the expressions of * for four steps are listed in Table 3. Although the above model is a simpli;cation of the real situation, it allows investigating the whole cyclic process for ;ne catalyst/adsorbent particles packed in the adsorptive reactor with small diameter. 3.1. Simpli9cation of governing equations

III

i=1



@T @z



 2U − (Tw − T ) − cat vij &j Rj KHRj R0 j=I 



;

(8)

where Cpg and Cps are the gas-and solid-phase heat capacity, respectively, Cvg is the heat capacity of gas phase at constant volume, kz is the e8ective thermal conductivity, −KHadi is the adsorption heat of component i (i.e., CO2 ), KHRj is the reaction heat of reaction j; U is the overall bed–wall heat-transfer coeHcient, and R0 is the inner radius of the reactor. Initial conditions: T = Tf ; u = 0; qi = 0; yH2 = 1; yi = 0; PH2 = PH ; Pi = 0 (i = CO; CO2 ; H2 O; CH4 ; N2 ) at t = 0: The ;nal distributions of concentrations, temperature, and pressure along the reactor column for one step are the initial conditions for the next step. General boundary conditions for four steps:     @yi @yi = *1 ; = *2 ; (9a) @z z=0 @z z=L  (u)z=0 (for Steps 1; 4)     = *3 ; @u (for Steps 2; 3)   @z z=0    @u  (for Steps 1; 4)  @z z=L (9b) = *4 ;   (u)z=L (for Steps 2; 3)  (P)z=0 (for Steps 1; 2)     = *5 ; @P (for Steps 3; 4)   @z z=0    @P  (for Steps 1; 2)  @z z=L (9c) = *6 ;   (P)z=L (for Steps 3; 4)

Assuming ideal-gas law C =P=RT , the following equation can be derived from Eq. (6):   @yi b DL @2 yi 1 @T @yi 1 @P @yi = − + @t t L2 @+2 P @+ @+ T @+ @+   1 @yi @u uyi @P uyi @T − u + yi + − t L @+ @+ P @+ T @+ −

III ad RT @qRi cat RT  vij &j Rj + t P @t t P j=I

−

yi @P yi @T ; + P @t T @t

(10a)

where + = z=L; i denotes CH4 ; H2 O; H2 ; CO2 , CO, and the inert gas N2 . The term @qRi =@t equals zero except for i =CO2 ; @qRCO2 =@t is calculated by Eq. (7). The Pow velocity is derived from the overall material balance (Eq. (4)) u @T u @P ad RTL @qRCO2 @u = − − @+ T @+ P @+ P @t +

2cat RTL (&I RI + &II RII ) P

−

t L @P t L @T + : P @t T @t

(10b)

The interbed pressure dynamics for the variable pressure steps are estimated using a linear dynamic pressure (Sereno & Rodrigues, 1993; Malek & Farooq, 1997):  0 (for Step 1);      −(PH − PL )=t2 (for Step 2); @P = (10c)  @t 0 (for Step 3);     (PH − PL )=t4 (for Step 4): The mechanical energy balance (Eq. (5)) is changed as (Ergun equation) @P = L(−KD u − KV u|u|): @+

(10d)

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Table 3 Values of * for the four steps of the PSAR cycle

Step

*1

1

−

2

0

3

0

4

0

u10 (yfi − yi ) b D L

*2

*3

*4

*5

*6

*7

0

u10

0

PH

0

−

0

0

P(t)a

0

0

0

−u30

0

PL

0

0

0

0

P(t)a

0

0 u30 (yfi − yi ) b D L u40 (yfi − yi ) b D L

*8 u10 CCpg (Tf − T ) kz

0 0 u30 CCpg (Tf − T ) kz u40 CCpg (Tf − T ) kz

Note: All velocities uk0 (k = 1; 2; : : : ; 4) are taken as positive number, whatever the Pow direction. The index k stands for the step number and the index 0 stands for the feed side in Steps 1, 3, and 4 and outlet for Step 2. a Eq. (10c) was used (linear ramp).

Based on Eq. (8), the energy balance for the bed-volume element that includes the heat transfer to the column wall is described as 1 @T =  C P @t t vg + (ad + cat )Cps ] [ RT   @qRCO2 kz @2 T Cpg Pu @T +  − (−KH ) ad adCO 2   L2 @+2 RTL @+ @t : ×   2U + 2cat (&I RI KHRI + &II RII KHRII ) + (Tw − T ) R0 (10e) 3.2. Numerical method The model equations were solved by the orthogonal collocation method for the continuous hydrogen production in the PSA reactor. Because of the presence of steep composition gradients within the bed and the periodic reversal in the direction of gas Pow, in this simulation, 31 axial collocation points for the ;xed-bed reactor were selected in order to obtain the stable numerical solution. At all collocation points, Eqs. (10b) and (10d) are discretized into a set of linear algebraic equations that are solved numerically by the Gauss method in order to obtain the velocity and pressure distributions along the reactor. Eqs. (10a) and (10e) are discretized into a set of ordinary di8erential equations with initial value which are integrated in the time domain using Gear’s sti8 variable step integration routine in order to obtain the eOuent mole fraction/concentration and temperature histories and the mole fraction/concentration and temperature pro;les along the reactor. The sequence in solving numerically the PSA reactor at each step is as follows: (1) calculate the reaction rates using Eqs. (1a) – (1c); (2) calculate the pressure derivative using the linear dynamic model Eq. (10c); (3) calculate the adsorptive loading derivative by Eq. (7); (4) solve Eq. (10b) for the velocity;

(5) (6) (7) (8)

solve Eq. (10d) for the pressure; solve Eqs. (9a) and (9d) for the boundary conditions; solve Eq. (10a) for the species mole fraction derivative; solve Eq. (10e) for the temperature derivative.

At the end of each step, the gas-and solid-phase component concentrations (or mole fractions), temperature, and pressure were stored and used as the initial conditions for the next step in the cycle. The criteria to switch from one step to the next are: the average purity of hydrogen product for Step 1 is over 80% and the concentration of CO is small (for example, below 30 ppm for fuel cell applications), and the exit mole fraction of CO2 for Step 3 should be lower than 1:0×10−2 . The time durations of Steps 2 and 4 were set to be 150 and 100 s, respectively. The criterion for cyclic steady state operation was based on the average purity of hydrogen product and the concentration of CO (¡ 30 ppm for fuel cell applications). 4. Results and discussion 4.1. Checking the validity of the model prediction Typical eOuent mole fractions for high pressure reaction/adsorption step (Step 1) are shown in Fig. 2 at the following conditions: reactor length L = 2 m, reactor radius R0 = 12:5 mm, mass of adsorbent per bed volume ad = 466:6 kg=m3 , mass of catalyst per bed volume cat = 233:3 kg=m3 , particle diameter dp =1 mm, wall temperature ◦ Tw = 450 C, feed gas velocity u1 = 0:08 m=s, feed gas tem◦ perature Tf = 450 C, and feed gas pressure PH = 445:7 kPa, the mole ratio of steam to methane (H2 O=CH4 ) is 6. The other conditions are listed in Table 4. It should be noted that we assumed that &j be the same for di8erent reactions. It is evident from Fig. 2 that the whole region can be divided into three zones according to the adsorption behavior of CO2 : (I) the adsorption-enhanced reaction zone, where the eOuent mole fraction of CO2 is lower (molar fraction is about 9:4 × 10−3 ), adsorption enhances the conversion of methane, and the eOuent mole fraction of hydrogen at the exit is higher; (II) the breakthrough zone of CO2 , where

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G.-h. Xiu et al. / Chemical Engineering Science 57 (2002) 3893–3908

III

II

I 1.0 0.8

H2O

yj

0.6 0.4

H2

0.2

CO2 CO, N2

CH4

0.0 0

300

600

900

1200

1500

t,s Fig. 2. Typical eOuent mole fractions at high pressure adsorption and ◦ reaction step for PH = 445:7 kPa; Tf = Tw = 450 C; L = 2 m; u10 = 0:08 m=s; H2 O=CH4 = 6.

reaches the equilibrium value. In the adsorption-enhanced reaction zone (zone I), because of the adsorbent selectively removing CO2 from the product mixture, the conversion of methane is enhanced up to 55%, which is higher than that at the equilibrium state (about 25%), the purity of hydrogen at the exit of the reactor is also higher than that at the equilibrium state (about 54%, dry basis). For example, if the reaction time is controlled at t1 = 500 s, the average purity of hydrogen can reach yH2 (ave)=84:2%, and the average mole of H2 product per gram of solid is up to 0:73 mol=kg-solid. The conversion of methane XCH4 , the average purity of hydrogen (dry basis) yH2 (ave); yi (dry basis), and the average mole of H2 product per gram of solid are respectively de;ned as XCH4 feed of CH4 (mol=s) − eOuent of CH4 (mol=s) feed of CH4 (mol=s)     RTf uPyCH4 =1 − ; (11a) u10 PH yCH4 feed RT outlet

= the molar fraction of CO2 increases from 9:4 × 10−3 to 3:8 × 10−2 , the adsorbent is nearly saturated by CO2 in the operation zone of the reactor, the enhancement is not evident, the purity of hydrogen at the exit drops rapidly; (III) the equilibrium state zone, where the adsorbent is saturated almost entirely by CO2 , the operation mode is the same as the conventional one, i.e., the steam–methane reforming reaches a steady state, and the conversion of methane

1

yH2 (ave) =  t1

Pu(1−yH2 O ) [ ]outlet RT 0



×

0

t1 

PuyH2 RT

dt



outlet

dt;

(11b)

Table 4 Reference parameter values used in the simulations for Step 1 Parameters (constants) a

bCO2 Cpg a Cps a dp b DL c R0 a KD c KV c kz a KHadCO2 a mCO2 a PH a PL b Tf a Tw b Uc b a p a (for adsorbent) t a a ad b cat b &j d a Data

from Ding and Alpay (2000b). work. c Data evaluated from Table 2. d Xiu, Li, and Rodrigues (2002a). b Present

Values 2:36 × 10−4 Pa−1 (wet condition) 42 J=mol K 850 J=kg K 1 × 10−3 m 5:0 × 10−4 m2 =s 0:0125 m 10 526 N s=m4 12 734 N s2 =m5 0:29 J=m s K −17 000 J=mol 0:65 mol=kg (wet condition) 445:7 kPa 125:7 kPa 723 K 723 K 50J=m2 K 0.48 0.24 0.64 2:87 × 10−5 Pa s 467 kg=m3 233 kg=m3 0.8

Change with Constant Constant Constant Change with Constant Constant Change with Change with Constant Constant Constant Constant Constant Constant Change with Constant Constant Constant Constant Constant Constant Constant

T

u T; P u

u

G.-h. Xiu et al. / Chemical Engineering Science 57 (2002) 3893–3908

1.0 yj (dry basis)

0.8 0.6

H2 6m

4m

L=2m

0.4

CH4

0.2 0.0 0

2700

1800 t,s

900

CO2 CO ,N2 3600

Fig. 3. The e8ect of the length of colunm on the hydrogen purity in exit ◦ gas for PH =445:7 kPa; Tf =Tw =450 C; u10 =0:08 m=s; H2 O=CH4 =6.

yi (dry basis) =

yi ; 1 − yH2 O

mol H2 =g-solid 1 = AL(ad + cat )

 0

t1



(11c)

PuyH2 RT

3901

saturated with CO2 (Waldron, Hufton, & Sircar, 2001; Xiu et al., 2002b). Waldron, Hufton, and Sircar (2001) proposed a new regeneration method with purge by steam at subatmospheric pressure (70 –35 kPa) for the continuous production of high purity hydrogen with low concentrations of CO and CO2 . The comparison between the experimental data and simulation results is shown in Table 5. It should be noted that the model predictions are only qualitative. For example, the di8erences between the experimental and the estimated H2 product and CH4 to H2 conversion are ∼ 25%. This is in part because due to the lack of adsorption data at ◦ ◦ 490 C, we used the available data at 400 C in the simulation (Hufton, Mayorga, & Sircar, 1999). In addition, the adsorption isotherm used was based on data from the adsorption of CO2 at relatively high concentrations, which may in part be responsible for the di8erences between the experimental data and simulation results for the concentrations of CO and CO2 in the product, which are very low and no experimental adsorption data were available in that range.

 outlet

A dt;

(11d)

where A is the cross-sectional area of the reactor. Considering the characteristics of the reversible reactions and the adsorbent capacity for adsorption of CO2 , a longer length of reactor will favor the conversion of methane. A higher purity of hydrogen in the adsorption-enhanced reaction zone can thus be obtained, and the eOuent mole fractions of CO and CO2 are also lower, as shown in Fig. 3, where the length of reactor L was selected as 2, 4, and 6 m, the other conditions being the same as those in Fig. 2. Waldron, Hufton, and Sircar (2001) reported that if L = 6 m, 88–95% H2 with methane as the primary impurity can be directly produced, the concentration of CO2 impurity in the product gas was less than 130 ppm and the concentration of CO in the product gas was not detectable (below 50 ppm) by controlling the operating conditions. For a long reactor, it is diHcult to e8ectively regenerate the adsorbent

4.2. Reactive regeneration (reaction-enhanced desorption process) A new reactive regeneration of adsorbent process (i.e., the reaction-enhanced desorption process) was proposed based on the work of Hufton et al. (2000). In the new process, the gas mixture of 10% hydrogen in nitrogen was used to purge the adsorptive reactor at Step 3. Hydrogen in the purge gas reacts with carbon dioxide in the bulk phase to form methane, and enhance the desorption of carbon dioxide from the adsorbent. The choice of the regeneration temperature is a rather critical parameter as a compromise between the extent of the methanation reaction and the CO2 adsorption equilibrium. This methanation reaction is an exothermic reaction; purge at low temperature will favor the methane formation. However, when decreasing the purge temperature, the desorption of carbon dioxide from the adsorbent will decrease from the point of view of the adsorption isotherm;

Table 5 Comparison between the experimental data (Waldron, Hufton, & Sircar, 2001) and the simulated results Feed press. (kPa)

Gas quantities (mol/kg solid in reactor/cycle)

Hydrogen product (dry)

Feed

H2 (%)

CH4 (%)

CO2 (ppm)

CO (ppm)

88.7

11.3

136

ND

54

90.1

9.8

685

71

68

88.5

11.4

627

63

66

86.8

12.1

587

50

63

Purge steam

Hydrogen product

Methane conv. to hydrogen (%)

◦

Waldron, Hufton, and Sircar (2001) (490 C) 458.2 0.54 0.77 0.16 ◦ Simulation results (490 C) 458.2 0.54 0.77 0.201 ◦ Simulation results (480 C) 458.2 0.54 0.77 0.194 ◦ Simulation results (470 C) 458.2 0.54 0.77 0.181 kg=m3 ;

kg=m3 ;

Note: reactor L = 6 m; R0 = 12:5 mm; ad = 610:0 cat = 305:0 dp = 3 mm; total cycle operating time 856 s (reaction time 289 s, depressurizing time 60 s, steam purge time 447 s, and pressuring time 60 s); adsorption isotherm: mCO2 = 0:919 − 0:0728N + 0:00339N 2 mol=kg for N 6 10 and mCO2 = 0:5 mol=kg for N ¿ 10 (wet condition; Hufton, Mayorga, & Sircar, 1999), bCO2 = 3:94 × 10−4 exp[(17 000=R)(1=T − 1=673)] Pa−1 (wet condition; Hufton, Mayorga, & Sircar, 1999; Ding & Alpay, 2000a); other parameter, &j = 0:6 (Xiu, Li, & Rodrigues, 2002a).

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G.-h. Xiu et al. / Chemical Engineering Science 57 (2002) 3893–3908

0.6

0.4 0.3 0.2

0.10

0.02

0.0 0.0

0.00 1.0 z,m

1.5

2.0

2

RII +RIII , mol/(kg (cat).s)

0.0 −3.0×10 −4 −6.0×10 −4 −9.0×10 −4 −1.5×10 −3 0.0

100 s 300 s

R II+R III 0.5

CH 4 0

100

CO 200

300

400

t,s

dqCO2 /dt

−1.2×10 −3

H2

H2 O

0.04

Fig. 4. Axial pro;les of carbon dioxide solid-phase concentration after regeneration of adsorbent by di8erent purge method for L = 2 m; u10 = 0:08 m=s; u30 = 0:3 m=s; t1 = 500 s; t2 = 150 s; t3 = 400 s.

dqCO /dt , mol/(kg (ad).s)

0.06

0.1 0.5

CO 2

0.08 yj

0.5 qCO2 , mol/kg (ad)

0.12

Step 2 Step 1 steam at 723K 10% H2 in N2 at 623K 10% H2 in N2 at 673K 10% H2 in N2 at 723K

1.0 z,m

1.5

2.0

Fig. 5. Comparison between the CO2 desorption rate and methanezation ◦ rate at 400 C by 10% H2 in nitrogen purge, other conditions same as Fig. 4.

therefore, there exists an optimum purge temperature at which the regeneration of adsorbent can be carried out most e8ectively. Fig. 4 presents the comparison of the process purged by steam with that purged by 10% hydrogen in nitrogen at different temperatures; the other conditions are kept the same: Step 1 for 500 s, Step 2 for 150 s, Step 3 for 400 s (the purge velocity is the same u30 = 0:3 m=s). It is evident that the reaction of H2 with CO2 in the bulk phase enhances the desorption of CO2 from the adsorbent. After regeneration, the remaining concentration of carbon dioxide in the adsorbent ◦ is lower than that for steam purge; 400 C is an optimal temperature for the regeneration. In the following section, we ◦ take the purge process at 400 C, and analyze the feasibility and e8ectiveness of the process purge with 10% hydrogen in nitrogen. Fig. 5 shows the reactive rate of hydrogen with CO2 (i.e., RII + RIII ; RII  RIII ) and the desorption rate of CO2 (i.e., dqCO2 =dt). At the inlet part of the reactor (about 0 –0:75 m), the desorption rate of CO2 is higher. But at the outlet part of the reactor (about 1–2 m), because the concentration of CO2 in the adsorbent is small, the desorption rate is slow; it is diHcult to desorb CO2 from the adsorbent. The reaction rate of hydrogen with CO2 in the bulk phase is higher at 1–2 m if adopting the countercurrent purge with 10% H2 in

◦

Fig. 6. EOuent mole fractions at 10% H2 in nitrogen purge step at 400 C, other conditions same as Fig. 4.

nitrogen; the low concentration of CO2 in the adsorbent can be e8ectively removed due to the methanation and reverse water–gas shift reactions decreasing the concentration of CO2 in the bulk phase. Fig. 6 shows the eOuent mole fractions with time for ◦ purge step (Step 3) with 10% H2 in nitrogen at 400 C; about 60 –80% hydrogen in the purge gas reacts with CO2 (the mole fraction of hydrogen changes from 0.1 to 0.02 at t ≈ 0 s and 0.04 at t = 400 s). This part of hydrogen that reacts with low concentration CO2 enhances the regeneration of the adsorbent; this will be signi;cant for a long length of reactor, as discussed in the later part. Now, we evaluate the feasibility and e8ectiveness of the reactive regeneration cyclic process for the continuous production of high purity hydrogen with traces of CO and CO2 . Two processes are involved: Case 1, the regeneration of ◦ adsorbent is carried out by steam purge at 450 C at atmospheric pressure, this is a common cyclic process; Case 2, the reactive regeneration of adsorbent is carried out by 10% ◦ hydrogen in nitrogen purge at 400 C at atmospheric pressure. It should be noted that for Case 2 cyclic process, after carrying out the purge with 10% hydrogen in nitrogen, the purge with steam should be added in order to remove nitrogen in the reactor, the additional purge time is short (50 s as given in Table 6). In practice, the nitrogen is recycled after clean-up. The main operation conditions for each step are listed in Table 6 for Cases 1 and 2 cyclic processes. Fig. 7 shows the changes of pressure P (Fig. 7a), temperature T (Fig. 7b), and velocity u (Fig. 7c) with time at the middle of the reactor for a whole process at the 15th cycle. The changes of pressure and velocity present almost the same tendencies for Cases 1 and 2, as shown in Figs. 7a and c, where the negative velocity in Fig. 7c denotes the gas Pow direction is opposite to the axial direction of the reactor. The temperature changes appear to be di8erent due to the decrease of the wall temperature in Step 2, to the lower feed temperature in Step 3, and continuing to increase the wall temperature in Step 4 for Case 2. In Fig. 7, we take the length of reactor L = 2 m with inner radius R0 = 12:5 mm as an example.

G.-h. Xiu et al. / Chemical Engineering Science 57 (2002) 3893–3908

3903

Table 6 Main operating conditions for Cases 1 and 2

Step mode

Step 1, Step 2 high-pressure countercurrent reaction/adsorption depressurization

Step 3 countercurrent reaction and purge

Step 4 countercurrent pressurization

Case 1

H2 O=CH4 = 6; u10 = 0:08m=s; PH = 445:7 kPa; ◦ Tf = Tw = 450 C; t1 = 500 s

Depressurize from 445.7 to 125:7 kPa; ◦ Tw = 450 C; t2 = 150 s

Purge with steam u30 = 0:3 m=s; PL = 125:7 kPa; Tf = ◦ Tw = 450 C, t3 = 450 s

Steam pressurize from 125.7 to 455:7 kPa; Tw = ◦ 450 C; t4 = 100 s

Case 2

Same as Case 1

Depressurize from 445.7 to 125:7 kPa; ◦ Tw = 400 C; t2 = 150 s

(1) Purge with 10% H2 in nitrogen, u30 = 0:3 m=s; PL = 125:7 kPa; Tf = ◦ Tw = 400 C; t31 = 400 s

Same as Case 1

740

480

Case 1

400

720

320

T,K

P, kPa

(2) Purge with steam u30 = 0:3 m=s; PL = 125:7 kPa; Tf = Tw = ◦ 450 C; t32 = 50s

240

Cases 1 and 2

160

700

660

80 0

300

600

900

1200

t,s

(a)

Case 2

680

0

300

600

900

1200

t,s

(b)

0.1

u , m/s

0.0 −0.1

Case 1 Case 2

−0.2 −0.3 −0.4

0

300

(c)

600 t,s

900

1200

Fig. 7. (a) Pressure swing in the middle of reactor at the 15th cycles for Cases 1 and 2 at L = 2 m adsorptive reactor. (b) Temperature swing in the middle of reactor at the 15th cycles for Cases 1 and 2 at L = 2 m adsorptive reactor. (c) Velocity swing in the middle of reactor at the 15th cycles for Cases 1 and 2 at L = 2 m adsorptive reactor.

Fig. 8 shows the comparison of the average purity of hydrogen in the product gas that is directly produced from Cases 1 and 2 cyclic processes (where L=2 m). For the ;rst cycle, the average purity of H2 in the product gas yH2 (ave) is higher than that for the next cycle since the ;rst cycle uses the fresh adsorbent. After regeneration, the adsorption capacity of the adsorbent will decrease slightly due to the remaining CO2 in the adsorbent; therefore, the average purity of hydrogen will decrease. After 15 cycles, the cyclic operation almost reaches the cyclic steady state. In Case 1, 78.1% purity hydrogen can be continuously produced under

the cyclic steady state, while in Case 2, 80.5% purity hydrogen can be directly obtained due to the fact that methanation and reverse water–gas shift reactions enhanced the desorption of CO2 from the adsorbent at the purge step. The corresponding eOuent mole fractions with time at Step 1 for Cases 1 and 2 cyclic processes are shown in Fig. 9; the curves of the ;rst cycle and 15th cycle between two cyclic processes are compared. For the ;rst cycle, the efPuent mole fraction curves are the same for Cases 1 and 2. But after regeneration of adsorbent, the eOuent mole fraction of hydrogen for Case 2 is higher than that for Case 1,

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G.-h. Xiu et al. / Chemical Engineering Science 57 (2002) 3893–3908

0.90

1.0

0.85 y (dry)

Case 2

j

0.80

2

yH (ave)

H2

0.8

Case 1

0.75

1st cycle

0.6

15th cycle of Case 2

0.4

15th cycle of Case 1

CO , CO2 , N2

0.0

0.70

0

4

CH4

0.2

8 12 cycle number , N

0

16

100

200

300

400

500

t,s

Fig. 8. Comparison of hydrogen average purity in product gas between Cases 1 and 2 cyclic processes at L = 2 m adsorptive reactor.

which means that a more eHcient regeneration is performed for Case 2. The eOuent mole fractions of CO and CO2 at Step 1 are very low because the reaction is controlled at the adsorption-enhanced reaction zone (Zone I), the average concentrations of CO and CO2 in the product gas for Case 1 are evidently higher than those for Case 2, as shown in Table 7.

Fig. 9. Comparison of eOuent mole fractions between Cases 1 and 2 cyclic process processes at L = 2 m adsorptive reactor.

In Fig. 10, the solid-phase CO2 concentration distributions along the reactor for four steps (solid lines for the ;rst cycle, dashed lines for the 15th cycle) are demonstrated. By comparing Fig. 10a (Case 1) with Fig. 10b (Case 2), it is evident that the remaining concentration of CO2 in the adsorbent for Case 2 is lower than that for Case 1 after the purge step due to the methanation and reverse water–gas

Table 7 Gas quantities and hydrogen product purity at steady cycle processes for Cases 1 and 2 No. Time t1 (s)

Mode

Hydrogen product purity (dry) H2 (%)

CH4 (%)

CO2 (ppm)

CO (ppm)

Methane conv. to hydrogen(%)

Gas quantities (mol/kg solid in reactor/cycle) Feed

Purge gas

Hydrogen product in Step 1

Hydrogen used in Step 3

Net hydrogen product per cyclea

L=2m 1 500 2 500

Case 1 Case 2

78.12 80.50

21.56 19.29

3182 2044

152 109

47.51 51.14

2.118 2.118

2.016 2.154

0.563 0.604

No 0.193

0.563 0.411

L=4m 3 500 4 500

Case 1 Case 2

80.23 84.54

19.56 15.36

2112 979

116 64

50.88 58.22

1.059 1.059

1.008 1.072

0.297 0.338

No 0.096

0.297 0.242

L=6m 5 500 6 500

Case 1 Case 2

82.41 86.40

17.29 13.53

2965 704

177 48

54.72 61.89

0.706 0.706

0.672 0.714

0.206 0.232

No 0.064

0.206 0.168

L=4m 7 300 8 150 9 300 10 250

Case Case Case Case

1 1 2 2

83.58 87.06 87.54 87.91

16.31 12.90 12.42 12.09

925 388 422 338

62 33 34 28

56.44 63.17 64.14 65.0

0.635 0.318 0.635 0.529

1.008 1.008 1.072 1.072

0.187 0.093 0.212 0.176

No No 0.096 0.096

0.187 0.093 0.116 0.080

L=6m 11 400 12 250 13 400 14 400 15 350

Case Case Case Case Case

1 1 2 2b 2

83.85 86.03 87.93 87.21 88.80

15.95 13.91 12.03 12.74 11.15

1254 546 436 498 336

82 42 33 38 28

56.55 61.05 67.45 63.51 67.01

0.565 0.353 0.565 0.565 0.494

0.672 0.672 0.714 0.714 0.714

0.166 0.103 0.191 0.186 0.173

No No 0.064 0.051 0.064

0.166 0.103 0.127 0.135 0.109

a Net

hydrogen product per cycle = hydrogen product in Step 1 − hydrogen used in Step 3. with 8% hydrogen in nitrogen.

b Purge

G.-h. Xiu et al. / Chemical Engineering Science 57 (2002) 3893–3908

0.6

qCO , mol/kg (ad)

Case 1 Step 2

0.3

Step 1

0.2

2

2

qCO , mol/kg (ad)

1st cycle 0.5

15th cycle

0.4

0.1 0.0

(a)

0.6

1st cycle

0.5

3905

15th cycle Step 2

0.4

Case 2

Step 1

0.3

Steps 3 and 4

0.2 0.1

Steps 3 and 4 0.0

0.5

1.0 z,m

1.5

0.0 0.0

2.0

0.5

1.0 z ,m

(b)

1.5

2.0

Fig. 10. (a) Axial pro;les of carbon dioxide solid-phase concentration at the end of each step for Case 1 cycle process at L = 2 m adsorptive reactor. (b) Axial pro;les of carbon dioxide solid-phase concentration at the end of each step for Case 2 cycle process at L = 2 m adsorptive reactor.

0.96

2

yH (ave)

0.92 Case 2

0.88 0.84

Case 1

0.80 0.76

0

4

8

12

16

cycle number , N Fig. 11. Comparison of hydrogen average purity in product gas between Cases 1 and 2 cyclic process at L = 6 m adsorptive reactor.

1.0

H2

0.8

yj (dry)

shift reactions enhancing the desorption of CO2 , so the hydrogen average purity in the product gas at Step 1 for Case 2 is higher than that for Case 1 when carrying out the next cycle. At the cyclic steady state (for example, about the 15th cycle), the remaining concentration of CO2 in the adsorbent for Case 1 is evidently higher than that for Case 2 after the purge step. Figs. 11–13 show the simulation results for adsorptive reactor with L = 6 m in Cases 1 and 2 cyclic processes. The purge operation is near the atmospheric pressure where the input pressure is 125:7 kPa and the output pressure is about 101 kPa, instead of the subatmospheric pressure suggested by Waldron, Hufton, and Sircar (2001) (70 –35 kPa). All the operating conditions are the same as those of L = 2 m, only changing the reactor length to 6 m. By comparing Figs. 11 and 12 with Figs. 8 and 9 respectively, it is evident that the hydrogen average purity of product gas is increased due to increase in the length of the reactor. For Case 1, the hydrogen average purity is increased from 78.1% (L = 2 m) to 82.4% (L = 6 m), while for Case 2, from 80.5% (L = 2 m) to 86.4% (L = 6 m) under the cyclic steady state; the increase of hydrogen average purity in the product gas for Case 2 is more apparent than that for Case 1 due to the proposed reaction-enhanced regeneration method. In addition, the concentrations of CO and CO2 in the product gas obtained from Case 2 are also very low as shown in Table 7; the concentration of CO, lower at 48 ppm, nearly satis;es the standard of fuel cell applications (Hufton et al. (2000) reported that impure H2 50 –90% is acceptable with fuel cell applications as long as the CO level is kept below 30 ppm). For the adsorptive reactor with L = 6 m, after carrying out Step 1, the concentration of CO2 in the adsorbent is high only at the inlet part of the reactor (0 –2 m); it is lower for CO2 at the outlet part (2–6 m), as shown in Fig. 13. After the purge step, the remaining CO2 in adsorbent is higher at 2–6 m, as shown in Fig. 13a. While by purge with 10% H2 in nitrogen (Case 2), the methanation and reverse water–gas shift reactions enhance the desorption of CO2 from the adsorbent, then the low concentration of CO2 in the adsorbent can be desorbed well; the remaining CO2 in

1st cycle 15th cycle of Case 2 15th cycle of Case 1

0.6 0.4

CO , CO2 , N2

0.2

CH4

0.0 0

100

200

300

400

500

t,s Fig. 12. Comparison of eOuent mole fractions between Cases 1 and 2 cyclic process at L = 6 m adsorptive reactor.

adsorbent is small, as shown in Fig. 13b. After carrying out the next cycle process, the hydrogen average purity in the product increases and the concentrations of CO and CO2 in the product gas drop rapidly. By simulation for Case 2, we ;nd that for short length of adsorptive reactor (for example L = 2 m), the hydrogen average purity produced by the reactive regeneration process

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G.-h. Xiu et al. / Chemical Engineering Science 57 (2002) 3893–3908

0.6 Step 2

0.5

Step 1

0.4

Case 1

0.3

2

Steps 3 and 4

0.2 0.1 0.0

(a)

1st cycle 15th cycle

qCO , mol/kg (ad)

2

qCO , mol/kg (ad)

0.6

1st cycle

Step 2

0.5

15th cycle

Step 1

0.4

Case 2

0.3

Steps 3 and 4

0.2 0.1 0.0

0

1

2

3 z,m

4

5

0

6 (b)

1

2

3 z,m

4

5

6

Fig. 13. (a) Axial pro;les of carbon dioxide solid-phase concentration at the end of each step for Case 1 cyclic process at L = 6 m adsorptive reactor. (b) Axial pro;les of carbon dioxide solid-phase concentration at the end of each step for Case 2 cyclic process at L = 6 m adsorptive reactor.

reaches 80.5%, but the concentrations of CO and CO2 do not satisfy the industry standard; increasing the length of the reactor (where L = 4 and 6 m of adsorptive reactor are adopted as shown in Table 7), the hydrogen average purity in product gas increases, while the concentrations of CO and CO2 in product gas decrease rapidly. But for Case 2, part of hydrogen will be consumed in the purge step (Step 3). In Table 7, we evaluated the loss of hydrogen at the cyclic steady state; about 25 –33% hydrogen produced in Step 1 will be used in Step 3 if Case 2 cyclic process for 6 m length adsorptive reactor is adopted. However, it should be noted that the tolerance of CO impurity in H2 product is very stringent for industrial demands. Particularly, for a fuel cell application, the CO purity of more than 30 ppm is not acceptable. That is to say, the purity of hydrogen and the remaining concentration of CO are both important for the industry. As shown in Table 7, only the following simulation results satisfy the conditions of enriched hydrogen product gas with low CO concentration (less than 30 ppm for fuel cell applications): No. 10 (Case 2) for L = 4 m, No. 15 (Case 2) for L = 6 m. It was found that the total amount of hydrogen product which can satisfy the standard of fuel cell applications will increase if taking a longer adsorptive reactor, the net hydrogen productivity (mol/kg of solid per cycle) obtained from Case 2 cyclic process will increase 20 – 40% compared to Case 1 for 6 m adsorptive reactor. Therefore, even if the enhancement of CO2 desorption is at the expense of hydrogen consumption, the net e8ect is the improvement of H2 production through the proposed cyclic operation. 5. Conclusions An interesting modi;cation of the separation-enhanced reaction process for steam–methane reforming was theoretically investigated in which reactive regeneration (through methanation and reverse water–gas shift reactions) is used to improve CO2 desorption. In particular, the operating tem-

perature during the regeneration step is lowered to thermodynamically favor the methanation reaction. In doing so, it is shown that regeneration times can be considerably shortened whilst maintaining a high hydrogen purity and production rate, and thus practical operating cycles can be established. The proposed process is also a demonstration of how the in situ separation and reaction concept can be extended to possibly integrate sequential reaction systems involving simultaneous exothermic and endothermic reactions. High purity hydrogen product gas with low concentrations of CO and CO2 can be directly produced from the adsorptive reactor if a long reactor is used and the reaction time is controlled in the adsorption-enhanced reaction zone. For a longer adsorptive reactor, the regeneration of the adsorbent can be e8ectively carried out by steam purge at subatmospheric pressure as suggested by Waldron, Hufton, and Sircar (2001), or by 10% hydrogen in nitrogen purge ◦ at a slightly low temperature of 400 C (compared with ◦ the reaction temperature 450 C) and atmospheric pressure proposed in this paper (reactive regeneration), while the conventional steam purge at atmospheric pressure fails to e8ectively regenerate the adsorbent. For the reactive regeneration process, if a 6 m long reactor is used, above 88% hydrogen in product gas with low concentrations of CO and CO2 (CO less than 30 ppm) can be continuously produced which can be directly used in fuel cell applications. In this process, 10% H2 in N2 purge is used instead of steam for regeneration of the adsorbent; in practice, nitrogen should be recycled after clean-up. A mathematical model for this process has been developed. Numerical solution of the model equations for the cyclic process was obtained by the orthogonal collocation method. The accuracy of the model is evaluated by comparing the simulated results with the experimental data reported by Waldron, Hufton, and Sircar (2001); the model results qualitatively agree with experimental data. The package is needed to improve the design and analysis of sorption-enhanced reaction process.

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Notation A bCO2 C Cfi Ci Cpg Cps Cvg dp Dm Dp DL kCO2 kg ki kp kz KD KV L mCO2 M N P Pi PH PL qRi q∗ ri rp R R0 Rj t ti T Tf Tw u ui0 U yfi yi z

3907

Greek letters cross-sectional area of the reactor, m2 Langmuir model constant for component CO2 ; Pa−1 total molar concentration in the bulk phase, mol=m3 gas-phase concentration of component i in the feed, mol=m3 molar concentration of gas-phase component i, mol=m3 gas-phase heat capacity, J=mol K solid-phase heat capacity, J=kg K heat capacity of gas phase at constant volume, J=mol K particle diameter, m molecular di8usivity, m2 =s combination of molecular and Knudsen di8usivity, m2 =s axial dispersion coeHcient, m2 =s LDF mass transfer coeHcient, s−1 gas-phase thermal conductivity, J=m s K rate constant of reaction i; i = 1; 2: mol Pa0:5 = kg-cat s; i = 3: mol=kg-cat s particle thermal conductivity, J=m s K e8ective thermal conductivity, J=m s K Ergun equation coeHcient, N s=m4 Ergun equation coeHcient, N s2 =m5 reactor length, m Langmuir model constant for component CO2 ; mol=kg average molar weight of the gas mixture, kg=mol cycle number local total pressure, Pa partial pressure of gas-phase component i, Pa high pressure, Pa low pressure, Pa solid-phase concentration for component i (average over an adsorbent particle), mol=kg equilibrium solid-phase concentration, mol=kg formation or consumption rate of component i; mol=kg-cat s radius of the adsorbent, m universal gas constant, J=mol K inner radius of the reactor, m reaction rate de;ned by Eq. (1), mol=kg-cat s time, s operational time for step i, s temperature in bulk gas phase, K feed gas temperature, K wall temperature, K super;cial velocity, m/s initial super;cial velocity for step i; m=s overall bed–wall heat-transfer coeHcient, J=m2 K gas-phase mole fraction of component i in the feed gas-phase mole fraction of component i axial coordinate in bed, m

' −KHadi KHRi b p t + &j  ad cat b; ad b; cat g p

mass ratio of adsorbent and catalyst in the packed bed adsorption heat of component i (on the adsorbent surface), J=mol reaction heat of reaction i; J=mol bed porosity adsorbent porosity total bed porosity z=L catalyst e8ectiveness factor viscosity of Puid, kg=m s mass of adsorbent in the bed volume, kg=m3 mass of catalyst in the bed volume, kg=m3 bulk density of the adsorbent, kg=m3 bulk density of the catalyst, kg=m3 gas-phase density, kg=m3 adsorbent pellet density, kg=m3

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