Numerical Analysis on the Performance of the Three-Bed Temperature

Article pubs.acs.org/IECR

Numerical Analysis on the Performance of the Three-Bed Temperature Swing Adsorption Process for Air Prepurification Peikun Zhang†,‡ and Li Wang*,†,‡ †

School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China Beijing Engineering Research Center for Energy Saving and Environmental Protection, Beijing 100083, China".

‡

ABSTRACT: The three-bed temperature swing adsorption (TSA) air prepurification unit (APU) was proposed instead of the two-bed one. The three-bed TSA-APU can make energy savings of 29.5% by recovering and reusing the effluent purge gas. However, unlike the two-bed TSA-APU purged by clean gas, the impurities in the recovered gas may influence the bed performance. This study aimed to understand this influence by numerical simulation. Based on a nonequilibrium, nonisothermal, and nonadiabatic mathematic model, the breakthrough curves and bed profiles were obtained. The adsorption breakthrough curves show that the impurity contents in the product air of the three-bed TSA-APU are much lower than the typical tolerable limits. Thus, the energy savings of a TSA-APU were achieved by the three-bed design. The mechanisms that lead to this result were also discussed by analyzing the location and nature of the mass transfer and plateau zones, which were identified from the bed profiles.

1. INTRODUCTION China is the world’s largest producer of iron and steel. In 2007, the iron and steel sector energy use in China represented 9% of global industrial energy consumption,1 and this proportion is presently larger as China’s crude steel output exceeds 690 million tons. This makes it a pressing need to increase energy efficiency and to decrease emissions of the greenhouse gases in this energy-intensive sector. The iron or steel making process requires a supply of oxygen, and this may be supplied by cryogenic air separation units (ASU). The cryogenic air separation is achieved by taking large volumes of air from the atmosphere, which is then compressed, purified, cooled, and liquefied. Through a process of distillation the air is then separated into its major components. The air prepurification unit (APU) to remove impurities such as water vapor (H2O) and carbon dioxide (CO2) included in the atmosphere is essential in a cryogenic ASU, because the impurities solidify and plug the passages in the equipment.2 The typical specifications for H2O and CO2 levels in the compressed feed air are 0.1 ppm and 1.0 ppm, respectively.3 The industrial technique of choice for removing such impurities from air is adsorption, such as temperature swing adsorption (TSA) and pressure swing adsorption (PSA). In the iron and steel enterprise of China, the air prepurification of ASU is usually carried out by the TSA process. The TSA-APU consists of two or more beds of microporous adsorbent materials with a high affinity for the trace impurities to be separated. The two-bed process is most commonly used. The multibed process has also been used for special purposes such as energy conservation.4 The main source of energy consumption in TSA-APU is the thermal-pulse administered to the bed on regeneration (the heating step), which begins by introducing heated purge gas at the inlet of the bed which causes a heat pulse to form.5,6 The heat pulse is then pushed through the bed by supplying additional unheated purge gas (the cooling step). To maintain a high enough temperature © 2012 American Chemical Society

throughout the bed, a portion of heat in the pulse is vented from the bed as the used purge gas exits out of the outlet.6 Commonly, a heat wave with a temperature peak of about 120 °C is still remaining and swept at the end of regeneration. For the two-bed TSA process, this heat (contained in the effluent purge gas) is directly released into the atmosphere, because in this process one bed is on the adsorption step when the other is on regeneration, and so there is no saturated bed to consume the discharged heat opportunely. Moreover, since the heat over here is intermittent and at a low temperature of less than 200 °C, it is also difficult to utilize this heat effectively by conventional techniques. However, for the multibed TSA process, this heat can be reused without significant discharges to the atmosphere. By operating each bed in a well-defined sequence, it allows the purge gas being discharged from the bed on the cooling step to be reheated and used to hot purge the saturated bed and so on. Since there is no heat loss from the effluent purge gas, this process allows the TSA-APU to work at high energy efficiency. Presently, most of the TSA-APU in China uses the two-bed design. By moving to a multibed design, a significant energy savings is possible to be achieved, which can lead to an improvement in the overall energy efficiency of the iron and steel sector. However, one feature of the multibed process causes the consumers to worry about its product quality. The feature is that the effluent purge gas from the bed on cooling has been recovered and reused to hot purge a saturated bed. Since the effluent purge gas from the bed on cooling contains some impurities, such as H2O and CO2, it means that the multibed process uses a dirty gas to hot purge a bed countercurrent and some of the impurities would adsorb on Received: Revised: Accepted: Published: 885

August 12, 2012 November 28, 2012 December 17, 2012 December 17, 2012 dx.doi.org/10.1021/ie302166z | Ind. Eng. Chem. Res. 2013, 52, 885−898

Industrial & Engineering Chemistry Research

Article

Figure 1. The two-bed TSA-APU process.

Figure 2. A typical operation schedule for the two-bed TSA-APU.

adsorption. (2) Depressurization. When the bed is saturated, the adsorber is removed from service and slowly vented until atmospheric pressure is reached in the vessel. The depressurization flow direction is counter current to the adsorption flow. (3) Heating. The temperature of the bed is raised to a level such that the adsorbed impurities are desorbed from the bed. This step is carried out by flowing a preheated clean purge gas in a direction counter current to the adsorption flow. (4) Cooling. The temperature of the bed returns to near adsorption temperatures before it is placed back online. This step is carried out by flowing a cold clean purge gas in a direction opposite to the adsorption flow. (5) Pressurization. The adsorber vessel is repressurized to the operating pressure of the adsorption step by using the clean product air generated by the online bed. The pressurization flow direction is counter current to the adsorption flow. In addition, because the pressurization gas flow only occupies a small portion (1−2%) of the product air flow, the TSA process can be continuous with a constant feed rate of air. Furthermore, to completely describe the two-bed process, a typical operation schedule (with 4 h adsorption duration) is shown in Figure 2, and the cyclic operation schematics associated with the schedule are depicted in Figure 3. The main consumption of energy of TSA-APU is the thermal-pulse administered to the adsorber during the regeneration step. In this step, the purge gas is sent through the bed and removes the trace contaminants and then is vented to the atmosphere (shown in Figure 3). The purge gas is hot for a period of time, followed by a cooling flow to return the bed to near feed temperature before it is placed back online. Thus, a thermal-pulse has been created at the purge gas inlet (port A in Figure 1) of the bed, desorbing the adsorbates until it reaches the purge gas outlet (port B in Figure 1), resulting in heat front proceeds through the bed as an S-shape wave. To maintain a high enough temperature throughout the bed, some of the thermal pulse remaining at the end of the regeneration step is lost as it exits out of the bed bottom. A typical set of

the designed unused-portion of the bed as a result. These impurities may have some influence on the product quality. The purpose of this study is to understand the influence of these impurities on the thermal regeneration and the subsequent adsorption. The adsorption and thermal regeneration characteristics for the multibed TSA-APU are compared with those for the two-bed one by numerical simulation. The reminder of this paper proceeds as follow. First, the two-bed TSA-APU with a thermal-pulse type of regeneration and its energy-saving potential are analyzed in Section 2.1. Taking the three-bed process as a special case of the multibed process, the details of the three-bed TSA-APU cycle are described in Section 2.2. After that, in Section 3, a nonequilibrium, nonisothermal, and nonadiabatic dynamic model is proposed to simulate the TSA process. Finally in Section 4, the comparative analysis of a single bed of the two- and the three-bed TSA processes is accomplished as follows. In Section 4.1, the energy saving rate and the impurity characters in effluent purge gas for the three-bed TSA process are illustrated by the regeneration effluent curves. In Section 4.2 the purification performance of the three-bed TSA process is obtained from the adsorption breakthrough curves. To account for the resulting breakthrough curves, the bed profiles of the regeneration and the adsorption steps are also analyzed in Section 4.3 and Section 4.4, respectively.

2. PROCESS DESCRIPTION 2.1. The Two-Bed TSA-APU and Its Energy-Saving Potential. As shown in Figure 1, a typical TSA-APU consists of two adsorber beds which are alternately online and offline: the online bed is for adsorption, whereas the offline bed is used for regeneration. Each bed operates with five main steps strictly: (1) Adsorption. The online bed is with air passing through the bed, which is packed with layers of two different adsorbents, with activated alumina to remove H2O in the upstream side of the bed and zeolite to remove CO2 in the downstream side of the bed. Trace impurities are removed by 886

dx.doi.org/10.1021/ie302166z | Ind. Eng. Chem. Res. 2013, 52, 885−898


Article

Figure 3. Cyclic operation schematics for the two-bed TSA-APU.

temperature data from the purge gas inlet and outlet (ports A and B in Figure 1, respectively) of an industrial scale TSA-APU on regeneration is shown in Figure 4. As can be seen in Figure 4, a square heat wave is introduced into the bed by purge gas, resulting in a curving breakthrough curve with a peak temperature of about 120 °C. The coolingtemperature-peak during the cooling step indicates that plenty of residual heat is contained in the effluent gas. For the two-bed process, this effluent is vented to the atmosphere as waste. Although the amount of waste heat is enough large, it is difficult to effectively utilize this heat by conventional techniques, because the heat over here is intermittent and at a low temperature of less than 200 °C. However, the three-bed process can accomplish heat recovery and reuse, giving a high level of energy efficiency. 2.2. The Three-Bed TSA-APU. In this process, three adsorber beds are used with one always undergoing adsorption, one on heating, and one on cooling. As shown in Figure 5, the

Figure 4. Typical temperature curves of single bed from an industrial scale TSA-APU on regeneration.

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shortening its adsorbent service life. For a fair comparison, the limiting case is that the adsorbent service life of the three-bed process is reduced to equal the two-bed process, which resulted in an identical cycle period for the two processes. That is to say, the cycle period of the three-bed process is adjusted from 12 to 8 h (adsorption and regeneration periods are 2.67 and 5.33 h, respectively). Then, since the adsorption period is shorter, the bed length of the three-bed process can be reduced to decrease the adsorbent amount without affecting system performance. However, as shown in Figures 5 and 7, since the resulting hot purge gas from the heater is essentially the effluent of Bed A2 on cooling, the impurities in the effluent gas will be introduced into Bed A3. In this manner, some of these impurities will adsorb on the designed unused portion of Bed A3 as a result. Such impurities may have an influence on the regeneration and the following adsorption steps, which is different from the twobed TSA-APU purged by clean purge gas. To specifically analyze the impurity character in the recovered effluent purge gas and to quantify the influence of these impurities on the TSA performance, a mathematic model is proposed to simulate the TSA process in the next section.

Figure 5. Three-bed TSA-APU process with heat recovery during regeneration.

purge gas is used in a series first to cool Bed A2 just heated and then to heat Bed A3 to be desorbed. Thus, most of the heat swept from Bed A2 can be recovered to reduce the heating requirement. Since an additional bed is employed, the ratio of the regeneration time and the adsorption time for the three-bed process is two times that of the two-bed process. To make three beds operating sequentially and allow the effluent gas from cooling to be used to hot purge the saturated bed correctly, each bed has to be operating in a well-defined sequence. It is possible to achieve the timing to recover the whole coolingtemperature-peak by adjusting the duration of the heating step. With the fixed regeneration temperature and total heat amount selected, the heating duration changes with the flow rate of purge gas. In this study, by simulating the TSA process at various flow rates of purge gas, it is found that, for the three-bed process, the whole cooling-temperature-peak can be recovered when the flow rate is 55% of the two-bed process. The operation schedule of the resulting design for the three-bed TSA-APU process is shown in Figure 6, and the cyclic operation schematics are also depicted in Figure 7. Compared with the two-bed process, this three-bed process has a similar but a little bit smaller time ratio of heating and cooling. In this study, for the convenience of comparison, the three-bed process has the same bed length and adsorption period as the two-bed process. Since one more bed is employed, the adsorbent amount and the cycle period of the three-bed process are both 50% more than the two-bed process. The longer cycle period means the three-bed process has a longer adsorbent service life than the two-bed process, because for the adsorbent with fixed-maximum times of alternate adsorption and regeneration, the service life is linearly increased with an increasing cycle period. Therefore, it is possible to reduce the adsorbent requirement of the three-bed process by

3. MATHEMATIC MODEL AND SIMULATION A realistic model of adsorption and thermal regeneration is necessary to obtain a better understanding of the TSA process, because the validity of the conclusions made is limited by the adequacy of the model used. The reported efforts toward the modeling of the TSA process for air prepurification7−10 and others such as volatile organic compounds (VOC) removal11−13 and air-drying14,15 can serve as a helpful guide for precisely modeling the prepurification processes. Early, Carter and Husain7 studied the simultaneous adsorption of CO2 and H2O by fixed beds of 4A molecular sieve, but no theoretical analyses have been done on regeneration. In the work of Schoofs and Petit,8 the pressurization and adsorption steps of TSA-APU upstream of a cryogenic ASU was analyzed with a one-dimensional equilibrium stage model. To minimize thermal pulse during the feed step, Kumar and co-workers9 used a nonequilibrium and nonisothermal mathematical model to simulate the TSA-APU process. More recent work is the study by Urakami and co-workers.10 The adsorption bed is treated as a nonisothermal nonadiabatic system. They developed an airpurification TSA simulator for cryogenic ASU on the basis of the following equations: a linear driving force (LDF) equation, a polynomial equation for the equilibrium relationship of H2O on activated alumina, and a dual-site Langmuir equation for multicomponent adsorption on zeolite. Besides, in the works of Yun et al.11 and Ko et al.,12 single- and multicomponent VOC removal TSA processes were treated and modeled as dilute systems, and the model was found to provide an acceptable fit to the experimental data. Furthermore, Ahn and Lee14 studied

Figure 6. The operation schedule for the three-bed TSA-APU. 888



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Figure 7. Cyclic operation schematics for the three-bed TSA-APU.

isothermal and nonadiabatic conditions. They15 also obtain that desorption dynamics of H2O should be predicted by using the

the adsorption and desorption dynamics of H2O and developed a nonequilibrium mathematical model that considers non889



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conductivity coefficient (KL) is included in the model equation. With three heat transfer coefficients of gas−solid (hs), gasvessel (hw), and vessel-atmosphere (Uair), the heat transfer mechanisms considered include the following: forced heat convection between particles and the bulk gas phase, forced heat convection between the bulk gas phase and the vessel wall, and natural heat convection between the vessel wall and the atmosphere, respectively. With the above considerations, the mass balance equation to a fixed bed for any component i is written as

isotherm model with its consideration of capillary condensation (type II isotherm according to the Brunauer classification). To simultaneously predict the adsorption of H2O and CO2, Zhang and Wang16 proposed a modified Langmuir equation. This equation performs well in numerical calculations as well as its ability to fit experimental data of type I and type II isotherms. Then based on this isothermal equation, we have developed a nonequilibrium, nonisothermal, and nonadiabatic dynamic model. This work adopted this model to simulate the TSAAPU process. Then the cyclic steady-state (CSS) cycles are obtained for both the two-bed and three-bed processes by cyclic simulation. 3.1. Conservation Equations. For the sake of simplicity, only three steps were considered to be modeled in the cycle, namely, the adsorption, heating, and cooling steps. The pressurization and depressurization steps were neglected, because there is no H2O and CO2 that would be adsorbed on the bed during these two steps. During the pressurization step, bed pressurization is carried out by flowing a clean product air in a direction opposite to the adsorption flow, so there is no H2O and CO2 would be brought in and adsorbed on the bed. During the depressurization step, because the pressure is reduced, some H2O and CO2 would be desorbed from the bed and then vented to the atmosphere with the depressurization flow whose direction is cocurrent to the purge flow. Thus, we believe that the TSA-PPU performance on the purification of H2O and CO2 would not be overestimated by the model which neglects the pressurization and depressurization steps. Moreover, since the residual water wave on the designed unused-portion will be pushed back more or less toward the inlet of feed air by the counter-current flow during the pressurization and depressurization steps, the calculated performance given by this model is more conservative for the three-bed process. In this study, the horizontal type adsorption bed is chosen for simulation. Because the adsorption capacity of H2O and CO2 in adsorbents was incomparably greater than that of air as a carrier gas, the contribution of nitrogen to the total adsorption dynamics could be negligible.14,15 Therefore, the TSA-PPU system is treated as dilute where CO2 and H2O are considered with air as carrier gas. The model is developed together with a set of additional assumptions, which are accepted by several previous studies8−15,17 on TSA modeling: (1) The gas phase follows ideal gas law since the compressibility factor of air is very close to 1 at the highest pressure and lowest temperature involved herein.8 (2) Pressure drops inside the bed are taken to be negligible because they are much smaller than the operating pressure.8 (3) The velocity of the gas is treated as constant through the bed.11−13 A general TSA process is much more strongly influenced by temperature than pressure, so the gas velocity through the bed can be assumed to be constant at each step.13 (4) The adsorption of carrier gas is negligible.15 (5) Radial temperature, concentrations, and velocity gradients in the bed are negligible.15 (6) The mass transfer rate can be represented by a LDF rate expression.18 (7) The gas and solid are assumed to have constant physical properties.11 Furthermore, the combined effects of axial mass dispersion and mass-transfer resistances are represented by modified LDF mass transfer coefficients.19 Also, according to Kumar and Dissinger20 who pointed out that the axial thermal conductivity affects the shape of the transfer fronts strongly, as well as the consideration that the model with the second derivatives can give more stable numerical results,11 the axial thermal

∂yi ∂t

+u

∂yi ∂z

+

ρp (1 − ε)RTg ∂q i εP

∂t

= 0,

i = 1,

2

(1)

The energy balance around gas phase with heat transfer to solid phase and to the vessel wall as well as axial conduction is as follows: −

2 ∂Tg ∂Tg a (1 − ε) KL ∂ Tg + +u + hs s (Tg − Ts) 2 Cpgρg ∂z ∂t ∂z Cpgρg ε

+

2(Da + La) hw (Tg − Tw ) Da La Cpgρg ε (2)

=0

The energy balance around the solid phase is written as ∂Ts ha − s s (Tg − Ts) + ∂t Cpsρp

2

∑ i=1

ΔHi ∂qi =0 Cps ∂t

(3)

The heat loss through the vessel wall and the heat accumulation in the wall were considered during the heating regeneration time. The outer wall of the bed could not be regarded as adiabatic condition although the wall was wrapped by the heat-insulating material. Therefore, the energy balance in the vessel wall is expressed as follows: Uair ∂Tw hw − (T g−Tw ) + (Tw − Tair) ∂t Cpwρw ΔX w Cpwρw ΔX w (4)

=0

3.2. Mass Transfer Calculations. The LDF model is used for the prediction of adsorption rate as follows:

∂qi ∂t

= kci(qi* − qi)

(5)

The combined effects of axial dispersion and mass-transfer resistances on the adsorption behavior of packed beds can be expressed approximately in terms of the modified LDF mass transfer coefficient kc:21 ρ D 1 1 = b 2L + 0 kc ε u kc (6) This equation extends the linear addition principle to combined axial dispersion and mass-transfer resistances. Even for a highly nonlinear isotherm, the linear addition principle expressed by this equation provides a useful approximation except in the extreme case of low mass-transfer resistance and large axial dispersion, when DLρbk0c /u2ε ≫ 5.21 The DL can be calculated by the following equations:22,23 DL = d pu(20/ReSc + 0.5) 890

(7)



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Table 1. Parameters for the Temperature-Dependent Modified-Langmuir Equation sorbates

sorbents

Q0 (mol/kg)

Q1 (K)

H2O H2O CO2 CO2

zeolite 13x activated alumina zeolite 13x activated alumina

2.296 0.0934 0.2202 1.31 × 10−4

433.92 1030.8 820.7 2604.5

Sc = ν /Dm

(9)

The unmodified LDF parameter following equation:21 Rp

k0c

is calculated from the

10−9 10−3 10−7 10−5

Ra = GrPr =

1 = + 3k f 15εpDp kc0

(10)

In this equation, the Knudsen diffusion diffusivity Dp should not be larger than molecular diffusion diffusivity Dm, which is calculated by the Chapman-Enskog equation.18,21 For the low Reynolds number region, the correlation of Wakao and Funazkri is adopted:23 D k f = (2.0 + 1.1Sc1/3Re 0.6) m , 3 < Re < 10000 2R p (12)

qi =

3.3. Heat Transfer Calculations. For the forced heat convection between the bulk gas and particles which has a circle cross section, the heat transfer coefficient can be given by

2,

(14)

4 < Re ≤ 40

Nu = 0.683Re 0.466Pr 1/3 ,

40 < Re < 4000

(15)

(16)

The Reynolds and Nusselt numbers can be obtained by the following equation:24

Re = uL/ν

(17)

Re < 5 × 105,

gβ(Tw − Tair)Da 3 ν2

Pr

(20)

(21)

1 + bi(Ts)Pi + bj(Ts)Pj i≠j

,

i = 1,

2,

j = 1, (22)

exp(Q 1/T )

(23)

b(T ) = B0

exp(B1/T )

(24)

n(T ) = N0

exp(N1/T )

(25)

and Ps is the saturated vapor pressure of H2O, which is only determined by temperature. In this equation, the exponential term is used to describe the H2O adsorption at a high relative humidity where capillary condensation was a dominant adsorption mechanism. While this equation is used to correlate the type I adsorption equilibrium of CO2, it reduces to the classical Langmuir equation for n = 0. The adsorption equilibrium data of H2O on the zeolite 13x and activated alumina come from Kim et al.25 The adsorption equilibrium data of CO2 on the zeolite 13x and activated alumina come from Lee et al.26 and Rege et al.,27 respectively. The model parameters obtained from the best fit to the equilibrium data are summarized in Table 1. 3.5. Initial Conditions, Boundary Conditions. The initial conditions of each step were the conditions at the end of the preceding step: for the adsorption step, the initial conditions are the bed conditions after regeneration; for the regeneration step, the initial conditions are the bed conditions after adsorption. Prior to the first cycle, the beds are initialized with a specified set of initial conditions.

For the forced heat convection between the bulk gas and the vessel walls which contact with adsorbents and are assumed as flat plates, the heat transfer coefficient can be obtained by

hw = kNu/L

(19)

ni(Ts)Pi / Psi(Ts) qmi(Ts)bi(Ts)Pe i

qm(T ) = Q 0

where Nu is the average Nusselt number for forced convection over circular in cross-flow, which can be expressed in terms of the Reynolds and Prandtl numbers in the form24

Nu = 0.911Re 0.385Pr 1/3 ,

−3446 −2987 0 0

where

(13)

Re = ud p/ν

N1 (K)

47784.2 40548.1 0 0

3.4. Adsorption Equilibrium Correlations. The H2O adsorption on zeolite 13x and activate alumina had a capillary condensation in the high relative humidity range, resulting in the adsorption equilibrium belonging to type II according to the Brunauer classification.15,25 An adsorption isotherm model considering capillary condensation is necessary to predict the adsorption and desorption dynamics of H2O.15 Therefore, a modified-Langmuir isotherm equation16 is extended to multicomponent form and applied to represent equilibrium relationships. The temperature-dependent form of this isotherm model is

(11)

hs = kNu/d p

N0

5189.3 490.85 1567.1 191.57

⎫2 ⎧ 0.387Ra1/6 ⎬ Nu = ⎨0.6 + (1 + (0.559/Pr )9/16 )8/27 ⎭ ⎩

For gas-phase diffusion in small pores at low pressure, the molecular mean free path may be larger than the pore diameter, giving rise to Knudsen diffusion. Satterfield gives the following expression for the pore diffusivity:21 −1 1/2 1 ⎡⎢ 3 ⎜⎛ πM ⎟⎞ 1 ⎤⎥ + Dp = τp ⎢⎣ 4rp ⎝ 2RT ⎠ Dm ⎥⎦

B1 (K)

Uair = kNu/Da

R p2

Nu = 0.664Re 0.5Pr1/3 ,

× × × ×

vessel which can be regarded as a horizontal cylinder, the heat transfer coefficient can be expressed by the following equation:24

(8)

Re = d pεu/ν

B0 (1/Pa) 4.191 7.504 9.169 5.762

Pr ≥ 0.6 (18)

The heat convection and thermal radiation between the exterior of the vessel wall and the atmosphere are lumped into the overall heat transfer coefficient Uair. For the natural heat convection between the atmosphere and the surface of the 891



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yi (z , 0) = yi0 (z)

(26)

Ti(z , 0) = Ti0(z)

(27)

qi(z , 0) = qi0(z)

Table 2. Specifications and Characteristics of the Adsorption Bed parameters

(28)

The boundary conditions for the adsorption step are inlet properties of adsorbates and for the regeneration step are inlet properties of purge gas. yi (0, t ) = yiInlet (t )

(29)

Ti(0, t ) = TiInlet(t )

(30)

∂yi (z , t ) ∂z

∂Ti(z , t ) ∂z

=0

4.2 25 1.29 0.018

ρw (kg/m3) Cpw (kJ/kg·K) Cpg (kJ/mol·K) KL (kJ/s·m·K) hs (kJ/s·m2·K) hw (kJ/s·m2·K) Uair (kJ/s·m2·K)

7800 0.5 0.029 1.38 × 10−3 0.072 8.56 × 10−3 3.53 × 10−3

(31)

z=L

simulations are presented in Tables 3 and 4, respectively. According to these given conditions, the mass transfer parameters are obtained and also summarized in Table 4.

=0 (32)

z=L

3.6. Cyclic Steady-State Conditions. The step changes of the cyclic operation are controlled by fixed times in this study. The adsorption step is finished after 4 h, and the regeneration step is set to terminate after 4 and 8 h for the two- and threebed processes, respectively. The general CSS condition is that the cycle state at the end of each cycle must be identical to this at the beginning. In this study, the following criterion12 is adopted to determine the CSS condition

∫0

values

Da (m) La (m) L (m) ΔXW (m)

L

qidz|(nc − 1)th cycle −

∫0

Table 3. Conditions of TSA Operations

L

qidz|(nc)th cycle

Numerical Analysis on the Performance of the Three-Bed Temperature

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