Heat and Mass Transport Characteristics of Pressure Swing

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Separations

Heat and mass transport characteristics of pressure swing adsorption for the removal of high-level moisture along with CO2 from air Yun Fei Shi, and Xiang Jun Liu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00601 • Publication Date (Web): 20 Apr 2018 Downloaded from http://pubs.acs.org on April 20, 2018

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Industrial & Engineering Chemistry Research

Heat and Mass Transport Characteristics of Pressure Swing Adsorption for the Removal of High-Level Moisture along with CO2 from Air Yun Fei Shi, Xiang Jun Liu* School of Energy and Environmental Engineering, University of Science & Technology Beijing, Beijing 100083, China

Abstract High-level moisture removal is often encountered in the pressure swing adsorption (PSA) for air prepurification. The effects of high-concentration water vapor adsorption on the heat and mass transport characteristics of PSA should be described in detail for further design and optimization of air prepurification processes. In this work, a mathematical model of an alumina/13X-layered two-bed Skarstrom-type PSA cycle for the removal of high-level moisture along with CO2 from air is established to study the heat and mass transport characteristics during the process. The maximum increase and decrease in temperature are related to the water vapor concentration in the feed air, and two simplified formulas are proposed to estimate their magnitudes. The mass transport characteristics, especially the penetration depths of the two impurities, are examined under different inlet temperatures, adsorption pressures, purge-to-adsorption flow rate ratios, inlet flow rates, and cycle times. A relation between the penetration depth of water vapor and the five operating parameters is developed and can be readily used to predict the location of the water vapor adsorption front in the PSA design for air

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prepurification and other purification processes involving high-level moisture. Keywords: transport characteristics; water vapor adsorption; air prepurification; pressure swing adsorption; binary adsorption; layered bed

1. INTRODUCTION Prepurification is an important step in industrial cryogenic air separation systems. Trace impurities, such as H2O, CO2, NOx, and light hydrocarbons, in air should be removed before air liquefaction to prevent pipe blockage and potential explosion hazard. Adsorption-based technologies, including temperature swing adsorption (TSA) and pressure swing adsorption (PSA), which are the two major options, have been primarily used for this purpose in recent time. PSA is generally preferred to TSA due to its lower energy and equipment costs. To improve the design of PSA systems for air prepurification, especially the removal of two major impurities, namely, H2O and CO2, studies on the characteristics of PSA were carried out. Chihara and Suzuki1,2 modeled non-isothermal PSA for air drying and discussed the effects of heat loss from the wall, bed length and operating parameters including cycle time and purge-to-feed ratio on the process. Their results were limited to very-low-concentrated H2O removal as their model assumed a linear isotherm for water vapor adsorption. Farooq et al.3 simulated adiabatic PSA processes for the removal of H2O from air by activated alumina and showed the non-uniqueness of the cyclic steady state and its dependence on the initial conditions of the bed due to the thermal effects and the nonlinearity of the isotherm. Their results were obtained in the low humidity range in which the isotherm can be characterized by the Langmuir


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equation. Rege et al.4 established an equilibrium-based non-isothermal PSA model for the trace removal of H2O and CO2 from air that uses single-layer beds with one type of sorbent and two-layer beds with two different sorbents (alumina/zeolite), respectively. Optimized layering of the beds was given for certain operating conditions. Other researchers claimed some patents5–10 of PSA designs for the removal of H2O and CO2 from air using single- or multi-layer beds. Layered beds with alumina/zeolite were preferred, in which the first layer removes all H2O content and some CO2 content, and the second layer eliminates the remaining CO2 and other impurities. Some researchers studied the PSA characteristics from a universal perspective. LeVan11 analytically determined the cyclic steady state of a PSA system for both favorable and unfavorable isotherms based on an isothermal and local equilibrium model. Pigorini and LeVan12–15 serially investigated PSA for purification and enrichment in layered beds, for two-tracecomponent separation and purification and related optimizations, and for multicomponent adsorption with equilibrium theory. They derived periodic concentration profiles and discussed the effects of isotherm shapes, bed layering, and operating conditions on the periodic state. Glover and LeVan16 examined the sensitivity of the breakthrough of adsorption beds to system parameters and the impact of mass and energy transfer effects and adsorbent layer thicknesses, and then applied the sensitivity data to determine the optimum bed layering of a two-layer, two-bed PSA system. Although various aspects of PSA for air prepurification have been studied, the removal of high-level moisture, which is often encountered in industrial practices17, has



been rarely explored. The adsorption of water vapor in a high-humidity range differs a lot from that in a low-humidity range as capillary condensation is involved, and the isotherm shapes distinctively. Since the high-concentration water vapor adsorption produces a considerable amount of heat and remarkably affects the adsorption of other adsorptive components, the heat and mass transport characteristics of the process can be complicated. These characteristics are very important to the design and optimization of air prepurification. As such, their behavior in the presence of high-concentration water vapor adsorption should be analyzed in detail. In this work, a mathematical model of an alumina/13X-layered two-bed Skarstromtype PSA cycle for the removal of high-level moisture along with CO2 from air is established to study the heat and mass transport characteristics during the process. The bed temperature profiles are analyzed, and the factors that affect the maximum increase and decrease in temperature are revealed by two proposed formulas. The mass transport characteristics, especially the penetration depths of the two impurities, are examined under different inlet temperatures, adsorption pressures, purge-to-adsorption flow rate ratios, inlet flow rates, and cycle times. A relation between the penetration depth of water vapor and the five operating parameters is developed and can be readily used to predict the location of the water vapor adsorption front in the PSA design for air prepurification and other purification processes that involve high-level moisture.

2. MODELS AND METHODS 2.1. PSA model A two-bed Skarstrom-type PSA cycle was applied to simulate air prepurification. The


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cycle consisted of four sequential steps: (I) pressurization, (II) adsorption, (III) blowdown, and (IV) purge. The variation in the bed pressure during pressurization and blowdown can be characterized by the following equation: P  Pend  ( Pstart  Pend )(1  t / t d ) 2 ,

(1)

where td is the duration of the pressure changing steps. In this study, td was set to 2 min. The bed pressure was kept steady at the atmospheric level during purge and at several times higher during adsorption. Two impurities were considered to be present in the feed air, namely, H2O (100% relative humidity) and CO2 (375 ppm). The cleaned air was regarded as a mixture of 78% N2, 21% O2, and 1% Ar. The bed was packed with 70 vol.% activated alumina F200 as the bottom layer and 30 vol.% zeolite 13X as the top layer. The detailed characteristics of the bed, adsorbents, and adsorbates are given in Table 1. The PSA model was established on the following assumptions: the bed is adiabatic; the adsorbents are identical spheres; the gas flow is uniformly distributed along radial directions so that the radial dispersion can be neglected; axial pressure drop is neglected; all the gas components obey the ideal gas law; the adsorption of N2, O2, and Ar is neglected; the heat transfer resistance between the gas and solid phases is neglected; the gas flow and adsorbents have constant specific heat capacities; and the axial dispersion coefficient and thermal conductivity are constant. The mass balance equation for component i is written as18 q j qi  yi y  2 y  RT   u i  Dax 2i  b   yi  ,  P  j t t  t x x

(2)

where y is the molar fraction, u is the interstitial velocity, R is the universal gas constant,



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T is the temperature, and q is the adsorbed amount (mol/kg). With the overall mass balance equation, the velocity of the gas flow can be calculated19:

T

q j (u / T )  ln( P / T ) b RT   .   P j t x t

(3)

(The detailed derivations of Equations (2) and (3) are provided in Derivations S1 and S2 in Supporting Information.) The heat balance equations for the gas and solid phases may be written as

 (  g cvgTg ) t

b c ps



 (u  g c pg Tg ) t

 ax

 2Tg x

2



v (T  T ) ,  s g

(4)

q j Ts  b  H j   v (Tg  Ts ) , t t j

(5)

where αv is the volumetric heat transfer coefficient between the gas and solid phases (W·m−3·K−1). Neglecting the heat transfer resistance and noting that

Rg  c pg  cvg ,

(6)

we can obtain the overall heat balance equation:

q j dP b  T T  2T b     c c u c      H j  c pg MT  , g pg ax  g pg  ps  t 2  j x x t dt  





(7)

where M is the molar mass of the gas phase. The linear driving force (LDF) model20 was used to determine the adsorption rate: qi  ki ( qi*  qi ) , t

(8)

where q* is the equilibrium adsorbed amount, which can be directly obtained from the isotherm model. The mass transfer rate coefficient k can be estimated from21

ki 

60 p De ,i d p2

.

(9)

The boundary conditions for each step of the PSA cycle are listed in Table 2.


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A cyclic steady state was considered to be reached when the difference between the total uptakes at the ends of two adjacent cycles for each component was less than 1% of the total feed amount in each cycle. Table 1. Characteristics of the bed, adsorbents and adsorbates for PSA modelling. Item

Symbol

Height of the bed

L

Value

Unit

2000

-

Diameter of the bed

db

200

mm

Adsorbent diameter

dp

2

mm

Porosity of the bed

ε εp

600

b

Height of each layer

Porosity of the pellet

1400

mm

a

0.37 0.5

mm

-

a

b

-

b

kg·m–3

0.5

a

Bulk density

ρb

870

Specific heat capacity of the adsorbents

cps

800a

Specific heat capacity of air

cpg

Isosteric heat of adsorption of H2O

ΔH1

50.0a

62.7b

kJ·mol–1

Isosteric heat of adsorption of CO2

ΔH2

29.8a

34.2b

kJ·mol–1

Effective intrapellet diffusivity of H2Oc

De,1

3.0e-10a

3.0e-10b

m2·s–1

Effective intrapellet diffusivity of CO2c

De,2

1.0e-10a

3.0e-10b

m2·s–1

Axial dispersion coefficientc

Dax

4.0e-4

Axial thermal conductivityc

λax

0.75

690

920b

J·kg–1·K–1 J·kg–1·K–1

1005

m2·s–1 W·m–1·K–1

a

For the Al2O3 layer;

b

For the 13X layer.

c

Estimations of these properties are provided in Figure S1 and Table S1 in Supporting Information.

Table 2. Boundary conditions for each step of the Skarstrom-type PSA cycle. Step

Boundary at the bottom

Boundary at the top

Pressurization

yi=yfeed,i

T=Tfeed

∂yi/∂x=0

∂T/∂x=0

Adsorption

yi=yfeed,i

T=Tfeed

∂yi/∂x=0

∂T/∂x=0

Blowdown

∂yi/∂x=0

∂T/∂x=0

∂yi/∂x=0

∂T/∂x=0

Purge

∂yi/∂x=0

∂T/∂x=0

yi=ypurge,i

T=Tpurge

2.2. Isotherm models 2.2.1. Binary isotherm model

The adsorption of H2O and CO2 on alumina or 13X can be interpreted as competitive



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adsorption in accordance with micropore volume filling theory22. However, this theory has two major deficiencies: (1) Each component has its maximum available pore volume for filling, thereby obtaining unreasonable results when the partial pressure of the strongly adsorptive component approaches its saturated vapor pressure; (2) the isotherm equation for each component is limited to the Dubinin–Astakhov equation23. Liu et al.24 extended the application range of this theory by assuming the same maximum available pore volume for each component and generalizing the forms of the isotherm equations. The resulting two-component isotherm model is expressed as q1*  q1*, single

1  A2 , 1  A1 A2

(10)

q2*  q2*, single

1  A1 , 1  A1 A2

(11)

where

A1  q1,* single / qs1 ,

(12)

A2  q2,* single / qs 2 .

(13)

The variable q* with subscript “single” represents the equilibrium adsorbed amount obtained from the corresponding single-component isotherm equation. The saturated adsorbed amounts of H2O and CO2, denoted as qs1 and qs2, are assumed to have the following relationship:

V0  vm1qs1  vm 2 qs 2 ,

(14)

where vm is the molar volume, which is 18.78 mL/mol for H2O and 42.61 mL/mol for CO2 4.


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2.2.2. Isotherm models for H2O and CO2 on alumina F-200

Since the humidity of the feed air is high (100%) in this study, the hysteresis effect during the adsorption/desorption of water vapor on alumina was considered in the equilibrium model. The adsorption branch of the isotherm data obtained from Serbezov25 was fit by the F–G equation26 expressed as * qad  qm  kmT  qc erf (kcT 1 / ln  ) ,

(15)

where χ is the relative humidity of water vapor, p/ps. The saturated vapor pressure ps for H2O can be calculated with an IAPWS standard formula27. The desorption branch was fit by a similar equation expressed as * qde  qm , de 

 qc , de f (  ) ,

(16)

f (  )  exp[kc ,de (1   )nde ] .

(17)

k m,deT

where

The adsorption and desorption data were fit together to minimize the deviation of the model from the experimental data defined as follows:

sdev   j

1 Nj

 (q

* ad ,model ,i , j

* 2 * * 2  qad ,expt ,i , j )  (qde, model ,i , j  qde,expt ,i , j ) ,

(18)

i

where j = 1, 2, 3, 4 representing each group of data, and Nj refers to the number of data points in each group. The fitting result is shown in Figure 1a, and the fitting parameters * * are given in Table 3. qad and qde should be the same when water vapor reaches

saturation; that is,

qs1  qm  qc  qm,de  qc,de .

(19)

When desorption is performed from different states other than saturation, new branches of the desorption isotherm, or the so-called scanning curves28–31, should be



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determined. Various means of determining the equilibrium adsorbed amount within the hysteresis loop have been developed32–35. For simplicity, in this study each branch of the desorption isotherm is obtained by scaling the loading due to capillary evaporation and expressed as * qde ,i  qm , de 

km,deT



*  qad ( i )  qm,de i m ,de k

T

 ff (( )) ,

(20)

i

where χi is the local humidity when desorption begins. The detailed calculation of the equilibrium adsorbed amount under arbitrary state was demonstrated in our previous work36. The original isotherm data obtained by Serbezov25 exhibit some irreversible amounts as there remain significant amounts of H2O in the adsorbents after the bed is desorbed to 10–4 Pa (close to vacuum). Complete removal of this irreversible amount requires at least 290 °C. Since the focus of this study is on cyclic steady state behaviors, the irreversible amount should be taken out from the isotherm data. For the desorption branch, the irreversible amount can be directly deducted from the desorption data. For the adsorption branch, the irreversible amount may be characterized by the Langmuir equation and then deducted from the adsorption data as it accumulates from zero during the process. The irreversible amount during adsorption is expressed as

qir  qm,ir bp / (1  bp) ,

(21)

where b is obtained by minimizing the squared deviation between the amended adsorption and desorption data below the relative pressure of 0.3. (The parameter b for each group of the data is listed in Table S2 in Supporting Information.)


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The isotherm data of CO2 on alumina F-200 obtained by Li et al.37 can be described by the Freundlich model expressed as

q2,* single  qs 2 ( p / ps 2 )ksT ,

(22)

where ps2 (Pa) is correlated with temperature by

ln ps 2  b0  b1T .

(23)

The fitting result is shown in Figure 1b and the corresponding fitting parameters are given in Table 3.

Figure 1. Fitting results of isotherm data on alumina F-200: (a) H2O; (b) CO2.



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Table 3. Fitting parameters of isotherm models for H2O and CO2 on alumina F-200. Adsorbate

Branch

Parameters

adsorption H2O desorption CO2

qm [mol/kg]

qc [mol/kg]

km [K–1]

kc [K]

6.040

16.18

1.628e-3

38.08

–1

qm,de [mol/kg]

km,de [K ]

kc,de

nde

8.427

1.509e-3

8.545

2.680

-

–1

qs2 [mol/kg]

ks [K ]

b0

b1 [K–1]

9.793

1.319e-3

10.30

2.371e-2

2.2.3. Isotherm models for H2O and CO2 on zeolite 13X

The isotherm data of H2O on zeolite 13X obtained by Ahn and Lee19 can be characterized by the DMAP model38:

q1,* single  qm  kmT  (qs1  qm )  kcT .

(24)

The isotherm data of CO2 on zeolite 13X obtained by Lee et al.39 can be described by the Freundlich model, which is given in Equations (22) and (23). The fitting results are shown in Figure 2, and the fitting parameters are listed in Table 4.


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Figure 2. Fitting results of the adsorption isotherm data on zeolite 13X: (a) H2O; (b) CO2.

Table 4. Fitting parameters of the isotherm models for H2O and CO2 on zeolite 13X. Adsorbate H2O CO2

Parameters qs1 [mol/kg]

qm [mol/kg]

km [K–1]

kc [K–1]

18.38

13.54

5.051e-4

2.181e-2

–1

qs2 [mol/kg]

ks [K ]

b0 [-]

b1 [K–1]

8.102

9.324e-4

3.800

3.434e-2

2.3. Numerical methods The first-order upwind scheme and the central difference scheme were used to discretize the first-order spatial derivatives and the second-order spatial derivatives, respectively. The governing equations (2), (3), (7), and (8) were discretized with the finite volume method, solved with the Tri-Diagonal Matrix Algorithm method separately, and coupled for an iterative solution. The simulation program was developed in MATLAB (numerical computing software developed by MathWorks).



3. RESULTS AND DISCUSSIONS 3.1. Basic transport characteristics and analysis of temperature variation A simulation case of PSA for air prepurification was conducted under an adsorption pressure PH of 10 bar, an inlet temperature Tin of 50 °C, an inlet flow rate QV of 140 Nm3/h, a flow rate ratio of purge to adsorption (P/A ratio) of 0.3, and a cycle time of 28 min (pressurization 2 min, adsorption 12 min, blowdown 2 min, and purge 12 min). The cyclic steady state was achieved after 100 h of operating time (Figure S2 in Supporting Information). The axial distributions of the concentrations and uptakes of H2O and CO2 and the bed temperature at the ends of the adsorption and purge steps under the cyclic steady state are shown in Figure 3. H2O is completely adsorbed by the Al2O3 layer and its mass transfer zone covers nearly the bottom half of the bed. The gap between the H2O uptake distributions at the ends of adsorption and purge shown in Figure 3b, which represents the total amount of H2O in the feed air during the adsorption step, indicates that the central area of the mass transfer zone has the highest throughput for H2O. The cause may be that, in the upper zone a relatively lower uptake occurs; thus, less amount is desorbed, while in the lower zone, though the uptake is higher, the H2O concentration of the local atmosphere is also high, thereby suppressing desorption. The uptake of CO2 is concentrated on the 13X layer, which takes 77.1% of its total amount fed into the system. The competitive adsorption between H2O and CO2 is reflected in the upstream area where the uptake of CO2 is remarkably reduced by the high-level adsorption of H2O (uptake over 15 mol/kg, Figure 3b). The bed temperature


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reaches the maximum increase at 20.7 °C outside the adsorption zone of H2O during adsorption and decreases by 26.7 °C within the H2O adsorption area during purge (Figure 3c). The falling edge of the temperature profile at the end of adsorption does not break through the bed. In other words, the heat produced during adsorption is preserved in the bed and can be reused for desorption during purge. The edge moves backward by 30% of the bed height during purge as the flow rate of purge is just 30% of that during adsorption. Note that the movement speed of heat is different from that of gas flow in that it also depends on the relative volumetric heat capacity of gas flow to adsorbents because heat is mainly stored in solid phase36. Thus, heat moves more slowly than gas flow. The 13X layer is covered in the movement range of heat, which is beneficial to the desorption of CO2.

Figure 3. Distributions of concentrations, uptakes, and temperature along the dimensionless height at the ends of the adsorption and purge steps under cyclic steady state: (a) concentration; (b) uptake; is for CO2. The solid lines represent the (c) temperature. Color is for H2O, color distributions at the end of the adsorption step, the dashed lines represent the distributions at the end of the purge step. Dimensionless height range of 0–0.7 is the Al2O3 layer; the rest is the 13X layer.



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Figure 4 shows the variations in temperatures at the two ends of the bed within a complete cycle. The crest of the top-end temperature originates from the breakthrough of the remaining heat as indicated by the bumped dash line in Figure 3c. The trough of the bottom-end temperature is the outcome of H2O desorption. A considerable amount of heat is needed for desorption in the bottom area since the area is concentrated with H2O. However, the bottom area cannot be fueled by the remaining heat of adsorption because the P/A ratio is less than 1. Thus, the temperature decreases in each cycle until a steady state is achieved. Since the adsorption of H2O is the major source of heat in the bed, the maximum temperature increase can be readily calculated by using the coherence condition40 for the H2O concentration wave and the temperature wave and neglecting any mass and heat transfer resistances:

 s dq* dc



Cs H  s dq*  , Cf C f dT

(25)

where ρs is the pellet density, c is the molar concentration, and Cs and Cf are the volumetric heat capacities of solid and fluid (J·m–3·K–1), respectively. For a steep adsorption front, we have

s

H ql*  qr* ql*  qr* Cs   s , cl  cr C f C f Tl  Tr

(26)

where subscripts l and r represent the values on the two sides of the front. For the H2O front in this case,

 s qin* cin



Cs H  s qin*  . Cf C f Tin  Tmax

(27)

For the adsorption of H2O with a high concentration, normally


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 s qin* cin



Cs . Cf

(28)

Thus, H cin Tmax  Tin  Cf

 C s cin  1  *  C f  s qin

1

 H cin H ps .    Cf Mc pg P 

(29)

Therefore, the temperature increase during adsorption can be estimated as follows: Tmax  Tin 

H ps (Tin ) 50 103 12236   C  21.0 C , 3 Mc pg PH 29 10 1005 10 105

(30)

which is 0.3 °C higher than the simulated result. For the temperature decrease during purge, supposing that the bed is desorbed from saturation, we may use the following estimation: Tin  Tmin 

H ps (Tmin ) , Mc pg PL

(31)

which provides a maximum temperature decrease of 32.8 °C. This value is 6.1 °C higher than the simulated result, which may be due to the partially saturated bed and < 100% desorbed gas humidity.

Figure 4. Variations in the temperatures at the top and bottom ends of the bed and the bed pressure



within a complete cycle (I: pressurization; II: adsorption; III: blowdown; IV: purge).

Figure 5. Variations in the CO2 concentration and bed temperature at the Al2O3/13X interface within a complete cycle (I: pressurization; II: adsorption; III: blowdown; IV: purge).

Figure 6. Variations in the H2O concentration (presented in dew point) and bed temperature at the dimensionless height of 0.4 within a complete cycle (I: pressurization; II: adsorption; III: blowdown; IV: purge).

Figure 5 shows the variations in the CO2 concentration and bed temperature at the Al2O3/13X interface. The trends of these two lines are consistent during adsorption and purge, thereby manifesting the strong effect of temperature on the adsorption of CO2. When the temperature increases, more CO2 is desorbed from the bed, thus the CO2


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concentration increases. When the temperature decreases, the adsorption capability of the bed for CO2 is enhanced, and the CO2 concentration consequently decreases. The first temperature crest is caused by the remaining heat from the last cycle, whereas the second crest results from the newly produced heat by H2O adsorption. The trough between them is developed from the low-temperature level zone that forms at the bottom during the purge step of the last cycle. Likewise, the H2O concentration is significantly influenced by the bed temperature (Figure 6).

3.2. Heat and mass transport characteristics under different operating conditions 3.2.1. Inlet temperature

The distributions of the H2O and CO2 concentrations and the temperatures at the ends of adsorption and purge under different inlet temperatures are shown in Figure 7. Other operating conditions are as follows: the adsorption pressure is 10 bar, the P/A ratio is 0.3, the inlet flow rate is 140 Nm3/h, and the cycle time is 28 min. The initial bed temperature, the same as the inlet temperature, is denoted by T0. The inlet humidity is kept at 100%. Consequently, the inlet concentration of H2O increases as inlet temperature increases. As shown in Figure 7a, the adsorption fronts of H2O and CO2 are pushed forward further at high inlet temperature. When high amounts of H2O are fed in, a wide adsorption zone is needed to accommodate the increment. For CO2, the inlet concentration remains unchanged, but the adsorption capability is weakened as temperature increases. Furthermore, the adsorption of H2O causes CO2 to move from the Al2O3 layer to the 13X layer. Thus, the adsorption front of CO2 is close to



breakthrough as the inlet temperature increases.

Figure 7. Distributions of the concentrations and temperatures along the dimensionless height under different inlet temperatures: (a) concentrations of H2O and CO2 at the end of adsorption; (b) temperature increments at the ends of adsorption and purge.

Figure 7b shows that a high inlet temperature leads to a large temperature change. In Equations (30) and (31), one can easily derive that the maximum rise and decline in the bed temperature increase with the inlet temperature. The underlying cause is that, when the inlet temperature is lifted, the amount of H2O to be dealt with in each cycle is increased and the amount of heat produced during adsorption or consumed during


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desorption is thereby also increased. 3.2.2. Adsorption pressure

Figure 8 shows the distributions of the H2O and CO2 concentrations at the end of adsorption and the temperatures at the ends of adsorption and purge under different adsorption pressures. Other operating conditions include inlet temperature of 30 °C, P/A ratio of 0.4, inlet flow rate of 140 Nm3/h, and cycle time of 28 min. Both the adsorption fronts of H2O and CO2 are pushed backward as adsorption pressure increases, and the effect becomes insignificant. The causes are similar to inlet temperature conditions. As adsorption pressure increases, the feed-in amount of H2O decreases, whereas the adsorption capability of the bed for CO2 is enhanced. Figure 8b reveals that the maximum increase in temperature decreases with the adsorption pressure, and this observation can be verified by Equation (30). For the maximum temperature decline, the temperature decrease at the bottom during purge is less than that predicted by Equation (31) because the bed is far from saturation as the adsorption pressure increases.



Figure 8. Distributions of the concentrations and temperatures along the dimensionless height under different adsorption pressures: (a) concentrations of H2O and CO2 at the end of adsorption; (b) temperature increments at the ends of adsorption and purge.

3.2.3. P/A ratio

Figure 9 illustrates the distributions of the concentrations and temperatures under different P/A ratios. Other operating conditions include inlet temperature of 30 °C, adsorption pressure of 10 bar, inlet flow rate of 140 Nm3/h, and cycle time of 28 min. Figure 9a shows that the effect of P/A ratio on the positions of the adsorption fronts is less significant as the P/A ratio exceeds 0.3. Figure 9b indicates that the bottom area of the bed approaches saturation at low P/A ratios, thereby causing a large temperature decline during purge.


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Figure 9. Distributions of the concentrations and temperatures along the dimensionless height under different P/A ratios: (a) concentrations of H2O and CO2 at the end of adsorption; (b) temperature increments at the ends of adsorption and purge.

3.2.4. Inlet flow rate

Figure 10 shows the distributions of the concentrations and temperatures under different inlet flow rates. Other operating conditions include inlet temperature of 30 °C, adsorption pressure of 10 bar, P/A ratio of 0.3, and cycle time of 28 min. The positions of the adsorption fronts change linearly with the inlet flow rate. The maximum increase and decrease in temperature barely change with the inlet flow rate. However, the



distribution of the bed temperature exhibits a wave-like shape at low inlet flow rates. This is the result of the incomplete discharge of residual heat during adsorption. At the end of each purge step, a given volume of heat remains in the bed as the bed is not fully desorbed. This volume of heat is pushed downstream during the adsorption step of the next cycle (Figure S3 in Supporting Information). If the inlet flow rate is sufficiently high, the residual heat is completely discharged from the bed by the end of adsorption. However, when the inlet flow rate is low, heat is retained in the bed and indicated as a temperature crest because it cannot be vented out either during adsorption or during purge. As the flow rate of purge is lower than that of adsorption, the crest moves a certain distance toward the top end of the bed after each cycle. The crest is retained along with a newly formed temperature crest in the next cycle. Eventually a series of crests developed from different cycles appear in the bed temperature profile, thereby forming a wave-like shape.


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Figure 10. Distributions of the concentrations and temperatures along the dimensionless height under different inlet flow rates: (a) concentrations of H2O and CO2 at the end of adsorption; (b) temperature increments at the ends of adsorption and purge.

3.2.5. Cycle time

The distributions of the concentrations and temperatures for different cycle times are given in Figure 11. Other operating conditions include, inlet temperature of 30 °C, adsorption pressure of 10 bar, P/A ratio of 0.3, and inlet flow rate of 140 Nm3/h. The positions of the adsorption fronts barely change with the adsorption time. The temperature distribution for short cycle times indicates a wave-like shape, which is the same as that at low inlet flow rates. The reason is also the same. The newly generated heat cannot be vented out from either the bottom or the top of the bed within one cycle with short cycle times. Besides, the flow rate of purge is lower than that of adsorption. Thus, a series of temperature crests are formed after several cycles, which show up as a wave in the temperature profile. The maximum increase and decrease in temperature are scarcely influenced by cycle time.



Figure 11. Distributions of the concentrations and temperatures along the dimensionless height under different cycle times: (a) concentrations of H2O and CO2 at the end of adsorption; (b) temperature increments at the ends of adsorption and purge.

3.3. Location of the water vapor adsorption front Considering that water vapor adsorption/desorption causes a significant temperature change in the bed and affects the adsorption of CO2, we should know how the H2O adsorption front is affected by operating conditions, including inlet temperature, high and low-level pressures, P/A ratio, inlet flow rate, and cycle time. The front moves back and forth in the bed during the process but eventually converges to a certain position


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when a cyclic steady state is achieved. The location of the H2O adsorption front can be highly correlated with the five operating parameters. Assuming that the distribution of H2O uptake is a triangle shape (Figure 12), and that the adsorption front of H2O is pushed forward by distance Δx during the adsorption step of each cycle, through the mass balance of H2O adsorbed and fed in, we obtain

p (T ) 1  tad s in , qin b ac x  QV cair 2 PH

(32)

 is the molar concentration of air under the standard state (1 atm, 0 °C), Δtad where cair

is the duration of the adsorption step, qin is the uptake of H2O at the inlet, ac is the cross-sectional area of the bed, and ps(Tin) is the saturated vapor pressure of H2O at inlet temperature Tin. Thus, the location of the H2O adsorption front at the end of adsorption in the ith cycle is  x , i  1 . xi , ad    xi 1, de  x, i  1

(33)

Figure 12. Evolvement of the H2O adsorption front in the process of approaching cyclic steady state.

The location of the front at the end of desorption in the ith cycle can be determined by the mass balance of H2O desorbed and vented out:



p (T ) 1  tde s out , qin b ac ( xi ,de  xi ,ad )   QV cair 2 PL

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(34)

where γ is the P/A ratio, Δtde is the duration of the purge step, and φ is the saturation factor indicating the degree of saturation, which may be proportional to the width of the adsorption zone:



xi,ad x

.

(35)

Note that Δtad=Δtde, by defining

*  

ps (Tout ) , ps (Tin )

(36)

we can obtain  P  xi , de   1   * H  xi , ad . PL  

(37)

Therefore, i

 P  xn,de  1   * H  x . PL  i 1  n

(38)

When n→∞, by assuming that γβ*

Heat and Mass Transport Characteristics of Pressure Swing

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