Novel Thermal Swing Adsorption Process with a Cooling Jacket for

Ind. Eng. Chem. Res. 2001, 40, 4973-4982

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Novel Thermal Swing Adsorption Process with a Cooling Jacket for Benzene-Toluene-p-Xylene Purification Daeho Ko,† Mikyung Kim,‡ and Il Moon* Department of Chemical Engineering, Yonsei University, Seoul 120-749, Korea

Dae-ki Choi§ Environment & Process Technology Division, Korea Institute of Science & Technology, Seoul 130-650, Korea

This paper proposes a novel design of a thermal swing adsorption (TSA) system with a cooling jacket and compares it with conventional TSA processes by cyclic simulations. The purposes are to increase the adsorption efficiency and to find a suitable condition for its application to a two-bed TSA system for continuous operation. These processes purify the ternary mixtures consisting of benzene, toluene, and p-xylene. The models are based on nonequilibrium, nonisothermal, and nonadiabatic conditions. The breakthrough curves of our simulation model are compared with that of Yun’s experiments (Ph.D. Thesis, Korea University, 1999). As a result of the continuous simulation from startup to the cyclic steady state (CSS), the augmented ratio of the amount adsorbed of jacketed TSA system to the conventional one at CSS is 20.3% for a two-step operation and 6.3% for a three-step operation, respectively. 1. Introduction Chemical industries have widely used the periodic adsorption processes such as thermal swing adsorption (TSA) and pressure swing adsorption (PSA) for purification and separations, respectively. TSA has not been conventional for the bulk separation processes but has been more preferable than PSA for solvent recovery, purification, and drying.1-4 Especially, a fixed bed of TSA has been one of the most conventional cyclic processes including adsorption and desorption steps for purifying strong adsorbates. As for a part of the experimental and theoretical studies, the effects of the thermal wave were reported5 and the discussions of a cooling step were addressed.6-9 The extended researches about the regeneration were carried out.10-19 Adsorption equilibrium data were presented for some chlorinated organic solvents (dichloromethane, 1,1,1-trichloroethane, and trichloroethylene) on activated carbon at various temperatures.20,21 Adsorption isotherms were obtained for binary component systems such as benzenemethylbenzene vapors on activated carbon22 and benzene-toluene vapors on activated carbon fiber23 by experimental and theoretical study. In view of mathematical modeling, lots of fixed-bed models have been developed using many simplifying assumptions. The simplest models are the dilute single-component systems whose condition is isothermal. Very little was been published about nonisothermal conditions of multicomponent systems before 1970 because of their numerical complexity. Cooney and Strusi24 and Thomas and Lombardi25 studied multicomponent isothermal adsorption in fixed beds. Basmadjian and Wright26 performed the experimental nonisothermal desorption for a multicom* To whom correspondence should be addressed. E-mail: [email protected]. Fax: +82 2 312 6401. † Present address: Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA. ‡ Present address: Department of Chemical Engineering, Yonsei University, Seoul, Korea. § Present address: Environment and Process Technology Division, KIST, Seoul, Korea.

ponent system without modeling. Even though a noble theory for nonisothermal adsorption has been developed by Rhee and Amudson27 and Pan and Basmadjian,5 there has also been little previous work on the analysis of cyclic behaviors. Davis et al.28 performed a theoretical study on the cyclic TSA of two components. Huang and Fair29 applied the Flory-Huggins form of the vacancy solution model (VSM) to predict a two-adsorbate system from pure-component isotherms and studied design and operating parameters on the regeneration (1989). Nagel et al.30 introduced an orthogonal collocation method (OCM) for solving partial differential equations, developed by Villadsen et al.31-34 and Finlayson.35 Even though there have been many theoretical and experimental studies on TSA as described above, little has been published about the cyclic simulation of nonisothermal and nonequilibrium TSA systems to purify more than ternary components. In addition, there have also been few studies of the TSA system with a cooling jacket. Therefore, this paper proposes the novel cyclic TSA system in which the operating temperature of the adsorption is maintained closely to the desired adsorption temperature by the cooling jacket surrounding the bed in nonisothermal and nonequilibrium conditions. This target process purifies the ternary mixtures consisting of benzene, toluene, and p-xylene (BTX). We performed rigorous and robust dynamic simulations of these nonisothermal multicomponent cyclic TSA models by computing the variables representing the highly nonlinear dynamic behaviors involving the exponential terms. The main objectives of this study are not only to develop a dynamic model of the multicomponent cyclic TSA process but also to introduce the new jacketed TSA system as well as to find a suitable operating condition for the application to two-bed operation. In the following sections, target processes are described, mathematical models are formulated, and the methodology of simulation is explained. The adsorption breakthrough curves of simulation for a conventional TSA without a jacket show a good agreement of those of Yun’s experiments.21 The newly designed TSA with

10.1021/ie000515z CCC: $20.00 © 2001 American Chemical Society Published on Web 10/09/2001

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Figure 2. Two- or three-step operation of a jacketed TSA process. Figure 1. Two- or three-step operation of a conventional TSA process.

a jacket is compared with the previous two-step and three-step operating TSAs without jackets by cyclic simulations. Finally, the newly developed TSA system is proven to have a better adsorption efficiency over the previous TSA processes. Computations are performed on a SUN SPARC 3000 server with four 168 MHz CPUs and 512 MRAM. 2. Process Models A typical TSA operation consists of two steps (adsorption and regeneration) or three steps (adsorption, regeneration, and cooling), as shown in Figure 1. The feed gas is supplied to the column at ambient temperature during the adsorption (feeding) step. The hot gas flows in a countercurrent or cocurrent direction during the regeneration (heating) step. Because the performance of the countercurrent regeneration is generally better than that of the cocurrent one, the countercurrent one is adopted in this study. The adsorbate-free gas at ambient temperature is used in the same direction as that for the heating, if the cooling step is adopted after the regeneration step. Nitrogen is used as not only a carrier gas of the feeding step but also a hot purge gas of the regeneration step as well as a cooling gas of the cooling step. Desirable operations of the TSA process are to reduce the heat loss and to increase the amount adsorbed and regenerated. Especially for the two-bed TSA system, the adsorption time should be greater than or at least equal to the sum of the regeneration time and the cooling time for the continuous operation. The adsorbent is chosen as an activated carbon (Sorbonorit B4, 12-14 mesh), which is good at purifying BTX. The design specifications are listed in Table 1. The integrated system of the adsorption bed and the jacket is shown in Figure 2. including a bed surrounded by a cooling jacket that controls the bed temperature during the feeding step. In this integrated system, the bed wall and the jacket are nonadiabatic and the jacket and the air outside of the system are adiabatic. The jacket uses water as a coolant to maintain the bed at a desired adsorption temperature during adsorption. When cooling the bed with the jacket during the feeding step, the coolant at atmospheric temperature, which is the same as the feed gas temperature, flows into the jacket and flows out of the jacket at a little higher temperature than that of the inlet coolant stream. Consequently, the

Table 1. Properties of a TSA Bed param

value

Dp [cm] Fp [g/cm3] p  Lt [cm] L [cm] Dinside bed [cm] Doutside bed [cm] Fw [g/cm3] Cps [J/g/K] Cpw [J/g/K] hw [J/cm2/s/K] hs [J/cm2/s/K] Uair [J/cm2/s/K] Ujacket [J/cm2/s/K] R [J/mol/K] Ei [J/mol]

0.154 0.714 0.67 0.44 40.0 25.5 2.20 3.20 7.80 0.47 0.34 6.0 × 10-3 1.0 × 10-2 1.6 × 10-4 4.0 × 10-3 8.314 14 000

temperature within the bed comes to the desired operating temperatures faster and is maintained more closely to those temperatures than any other processes during the adsorption step. The adsorption amount and time increase in this advanced system. The jacket discharges the coolant just before the regeneration step begins, so that there is no cooling water but stagnant air at atmospheric temperature within the jacket during the regeneration step. 3. Mathematical Formulations 3.1. General Material and Energy Balances of a Conventional TSA Model. The following model equations describe the nonisothermal and nonadiabatic operation of the systems based on nonequilibrium models. The system also assumes that the heat-transfer mechanism is included in the following steps: (1) heat transfer from the particle to the bulk gas phase (hs), (2) heat transfer from the bulk gas phase to the column wall (hw), and (3) heat transfer from the column wall to the outside of the bed (Uair). The solid temperature is considered as a function of time and the axial bed position without any temperature gradient within a particle. Because the temperature within the particle is assumed as uniform and the radial temperature gradient in the bed is neglected, hw in this study represents an effective lumped transfer coefficient. This value includes the resistance within the bed as well as the column wall. Resistance to heat transfer from the exterior of the column wall and to the atmosphere is lumped into the overall heat-transfer coef-

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ficient (Uair). All coefficients of the heat-transfer rate (hs, hw, and Uair) are determined from experimental nitrogen heating data at steady state.21 Furthermore, the system is treated as dilute. Additional assumptions are as follows: (1) The gases follow an ideal gas law. (2) The system is a multiple adsorbate. (3) The velocity of the gas is constant through the bed. (4) The pressure gradient across the bed is neglected. (5) Radial temperature, concentrations, and velocity gradients within the bed are negligible. (6) The mass-transfer rate is represented by a linear driving force expression. (7) The multicomponent adsorption equilibrium is represented by the temperature-dependent extended Langmuir equation. (8) The physical properties of the gas phase are those of the feed gas. (9) The physical properties of the adsorbent and the column wall are assumed to be constant. With these considerations, the material balance for any component i is written as

(

) (

)

[

KL ∂2Tgas ∂Tgas as(1 - ) ∂Tgas ) - hs -u (Tgas 2 ∂t CpgFp ∂z ∂z CpgFg 2 (T - Twall) (2) Tsolid) - hw RbCpgFg gas where KL is the axial thermal dispersion coefficient [cm2/ s], Cpg the heat capacity of gas [J/mol/K], Twall the wall temperature [K], Fg the gas density [mol/cm3], Tsolid the solid temperature [K], Rb the bed radius [cm], and as the particle external surface area-to-volume ratio [1/cm] defined as

as ) 6/Dp

aair aw ∂Twall (T - Twall) - U (T - Tair) ) hw ∂t CpwFw gas CpwFw wall (7) where aw is the ratio of the internal surface area to the volume of the column wall [1/cm], aair is the ratio of the log mean surface area of the insulation to the volume of the column wall [1/cm], Cpw is the heat capacity of the column [J/g/K], Fw is the column density [g/cm3], and Tair is the ambient temperature. aw and aair are defined as

aw )

Cpg ) 31.15 - 1.357 × 10-2Tgas + 2.68 ×

∂Tsolid ∂t

as

1 (Tgas - Tsolid) ) hs CpsFp Cps

(

∑i ∆Hi

)

∂ni ∂t

(5)

where Cps is the heat capacity of the solid [J/mol/K]. Equation 5 includes the heat generated by adsorption of adsorbates. The isosteric heat of adsorption, -∆H, is defined by an equation of the Clausius-Clapeyron type36

(8)

∆Xw(Dinside bed + ∆Xw)

(

aair )

)

Doutside bed Dinside bed

∆Xw(Dinside bed + ∆Xw)

(9)

where Dinside bed and Doutside bed are the diameters of the inside and the outside of the bed, respectively, and ∆Xw is the wall thickness [cm]. The mass-transfer rate of the gas and solid phases is formulated by a linear driving force (LDF) approximation model.37

∂ni ) ki(n/i - ni) ∂t

(10)

where n/i is the moles adsorbed at equilibrium with y* and ki. The overall mass transfer follows the following four-step mechanism: (1) fluid film transfer, (2) pore diffusion, (3) adhesion on the surface, and (4) surface diffusion. Because the Reynolds number is in the low range, the film mass-transfer coefficient, kfi, is formulated by the correlation of Petrovic and Thodos.38

kfi )

0.357 0.64 0.33DiM Re Sc  Dp

(11)

where the Re is the Reynolds number, Sc is the Schmidt number, and DiM is the molecular diffusion coefficient [cm2/s] calculated by the following equation:39

10-5Tgas2 - 1.168 × 10-8Tgas3 (4) The energy balance around the solid phase is expressed as

Dinside bed

(Doutside bed - Dinside bed)/ln

(3)

where Dp is the particle diameter [cm]. The heat capacity of gas is

(6)

N

where Pi is the adsorbate partial pressure [Pa]. The energy balance around the wall describing the heat transfer from the gas phase to the atmosphere is written as

yi ∂Tgas yi ∂2Tgas ∂yi ∂2yi ∂yi ) DLi 2 -u + 2 ∂t T ∂z T ∂z gas ∂z gas ∂z yi ∂Tgas RTgas 1 -  ∂ni F (1) Tgas ∂t P  p ∂t where yi is the mole fraction of component i, DLi the axial dispersion coefficient [cm2/s], Tgas the gas temperature within the bed [K], u the interstitial bulk fluid velocity [cm/s], R the gas constant [J/mol/K],  the bed void fraction, Fp the particle density [g/cm3], and n the moles adsorbed [mol/g]. The energy balance around the gas phase in the packed bed includes heat transfer to the solid phase and to the wall as well as the axial conduction as

]

∂ ln Pi -∆H ) 2 ∂T RT

DiM )

1.0 × 102Tgas1.75x(Mw,i + Mw,N2)/Mw,iMw,N2 P{(Dv,i)1/3 + (Dv,N2)1/3}2

(12)

where Dv is the diffusion volume.40 Pore diffusion may be explained by ordinary molecular and Knudsen diffusion in a porous solid. In a large pore, the molecular diffusion dominates the process for diffusion. In contrast, for a micropore adsorbent the Knudsen diffusion has a more significant influence on the flux through the pores than the ordinary molecular diffusion.4,9,17,19 The Knudsen diffusion coefficient is

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Table 2. Isotherm Constants for a Temperature-Dependent Langmuir Equation

Table 3. Basic Conditions of the TSA Process for Simulations

adsorbate

M0 [mol/g]

M1 [K]

B0 [1/Pa]

B1 [K]

benzene toluene p-xylene

2.889 × 10-3 1.828 × 10-3 3.061 × 10-3

79.11 254.10 55.10

5.429 × 10-10 1.626 × 10-8 1.400 × 10-8

5292 4818 5173

given by the following equation:41

re DKi ) 9.7 × 10-13 τp

x

T Mw,i

(13)

where re is the mean pore radius, τp is the pore tortuosity factor, and Mw is the molecular weight. This model assumed a local equilibrium between the gas phase and the solid phase because the surface adhesion step arises instantaneously. The surface diffusion coefficient, DS, is expressed by the following Arrhenius-type equation:9,17,19,21,42

DSi ) DS0i exp(-Ei/RT)

(14)

In addition, the coefficient of the pore diffusion and surface diffusion is related through the equilibrium isotherm and combined into an effective diffusion coefficient, Dei.17,18

pFg ∂y/i Dei ) DSi + DKi Fp ∂ni

(15)

Therefore, the effective overall mass-transfer coefficient, ki, is

Fp n/i Dp 1 ) + ki kfiFgas yi 10Deias

(16)

For the extended Langmuir isotherm, the analytical form of the derivative is obtained as follows:

∂y/i ∂ni

ni(1 + )

bjPy/j ) ∑ j)1,j*i

(mi - ni)2biP

1+ +

bjPy/j ∑ j)1,j*i

(mi - ni)biP

(17)

The following temperature-dependent extended Langmuir equation explains the equilibrium isotherm of the multicomponent adsorption system:

n/i )

mi(Tsolid)bi(Tsolid)Pyi 1+

(18)

∑i bi(Tsolid)Pyi

where

m(T) ) M0 exp(M1/T)

(19)

b(T) ) B0 exp(B1/T)

(20)

The values of the parameters of Langmuir isotherms are listed in Table 2.21 We derived the analytical form of the isosteric heat of adsorption equation from the Clausius-Clapeyron equation and the above Langmuir isotherms.

-∆H )

(

nB1 Rm(T) M + B1 m(T) - n 1 m(T)

)

(21)

param

adsorption model

regeneration model

yf,1 yf,2 yf,3 Tfeed [K] Tsolid,0 [K] Tgas,0 [K] Twall,0 [K] Tair [K] Tregeneration [K]

2.8369 × 10-3 2.2161 × 10-3 1.9693 × 10-3 294.05 293.15 293.15 296.55 294.05 see eq 38

291.35 291.35 291.65 295.65

cyclic operation model 2.8369 × 10-3 2.2161 × 10-3 1.9693 × 10-3 293.15 293.15 293.15 293.15 293.15 533.15

3.2. Boundary Conditions and Initial Conditions. 3.2.1. Feeding Step. The boundary conditions at z ) 0 and z ) L for the mole fraction of component i are written as

yi|z)0 ) yf,i ∂yi ∂z

|

z)L

)0

(22) (23)

Here, z means the axial position and L is packing bed length. The temperature conditions are

Ti|z)0 ) Tfeed

|

∂Tgas ∂z

z)L

)0

(24) (25)

3.2.2. Regeneration Step. As for the countercurrent regeneration case, the boundary conditions of mole fraction are

|

∂yi )0 ) 0 ∂z z

(26)

yi|z)L ) 0

(27)

Those of the temperature are

|

∂Tgas )0 ) 0 ∂z z

(28)

Tgas|z)L ) Tregeneration

(29)

All of the above boundary conditions are for t > 0 and z ) 0 or z ) L. The initial conditions associated with the boundary conditions are

yi|i)0 ) 0

(30)

ni|t)0 ) 0

(31)

Tgas|t)0 ) Tgas,0

(32)

Tsolid|t)0 ) Tsolid,0

(33)

Twall|t)0 ) Twall,0

(34)

All of the above initial conditions are for 0 < z < L and t ) 0. Values of these operating conditions are listed in Table 3. 3.3. Cyclic Steady-State (CSS) Conditions. A general CSS condition is defined by

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yi|t)0 ) yi|t)tcycle

(35)

ni|t)0 ) ni|t)tcycle

(36)

where ni is the amount adsorbed [mol/g] of component i as a distributed variable over the bed length. In this research, the conditions for the change of the step are as follows: (i) The adsorption step is finished when the outlet concentration is 1% of the feed concentration. (ii) The regeneration step is ended when the outlet concentration is 1% of the feed concentration. Therefore, the following equation is used to determine the CSS condition in this study.

QA,i,nc-1 ) QA,i,nc

(37)

where subscript nc means the number of cycles and QA,i,nc denotes the total amount adsorbed at the nc-th cycle. That is to say, the above CSS condition means that the total amount adsorbed of the nc-th cycle is the same as that of the (nc - 1)th cycle. The total amount adsorbed is obtained from

QA,i )

∫0Lni dz

(38)

3.4. Energy Balance of a Temperature-Controlling Jacket Model. The following equation describes the energy balance of the jacket.

∂Tjacket V˙ jacket ) (T - Tjacket) ∂t Vjacket jacket,inlet ajacket (T - Twall) (39) Ujacket CpgFg jacket where Tjacket is the coolant temperature within the jacket, Tjacket,inlet is the inlet temperature in the jacket, V˙ jacket is the volume flow rate of the coolant, Vjacket is the volume inside the jacket, Ujacket is the overall heattransfer coefficient from the exterior of the column wall to the coolant within the jacket,43,44 and ajacket is the specific parameter used in the model defined as

ajacket )

(Djacket - Doutside bed)/ln(Djacket/Doutside bed) ∆Xjacket(Doutside bed + ∆Xjacket)

(40)

where ∆Xjacket is the thickness of the jacket and Djacket is the inside diameter of the jacket. The value of Djacket is 4.2 cm, that of V˙ jacket is 100 cm3/s, and that of Tjacket,inlet is 293.15 K, in this model. The jacketed TSA is operated as follows: (1) The jacket uses the water as the coolant whose temperature is the same as the feed temperature during the feeding step. (2) There are no more heat losses than a conventional TSA because no heating medium but air at ambient temperature within the jacket exists during the regeneration step. (3) The coolant is also used during the cooling step if the cooling step is needed. The desirable operation of this process is to increase the adsorption efficiency as well as to make the operating time suitable for continuous two-bed operation. 4. Simulation Methodology The numerical procedure to solve this model is very complex for the following reasons:

Figure 3. Breakthrough curves of concentration and temperature at the adsorption step.

(1) The mathematical model consists of integrated partial differential-algebraic equations (IPDAEs). (2) The boundary conditions at the end of the bed change abruptly when operating steps change. (3) The favorable isotherms of the multicomponent are highly nonlinear. (4) These models involve the exponential terms of the Langmuir isotherm and effective diffusion coefficient. Model simulation is carried out in the gPROMS modeling tool.45-47 The method of lines48 adopted consists of two steps: (1) the discretization of the continuous spatial domains into finite grid of points, thus reducing PDAEs to differential-algebraic equations (DAEs) and (2) integration of the DAEs over time by employing an integrator, called a DASOLV code,49 based on backward differentiation formulas (BDF). The main advantage of this method is to minimize an integral error efficiently by this DAE integration technique. A centered finite difference method (CFDM) in the context of the MOL is used for the discretization. The spatial domain is approximated by second-order and 20 elements. 5. Results and Discussion 5.1. Reliability of This Conventional TSA Model. The simulation results are compared with the experimental data for the conventional TSA system to examine the feasibility of this model. Adsorption breakthrough curves of the simulations agree well with those of Yun’s experiments21 as shown in Figure 3. During

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Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001 Table 4. Operating Conditions of Cyclic TSA Processes Obtained from Computations operating variables tA [min] tR [min] tC [min] tcycle [min] uR ()uC) [cm/s]

typical TSA jacketed TSA typical TSA jacketed TSA two-step two-step three-step three-step operation operation operation operation 39.3 39.3 0.0 78.6 113.0

41.9 41.8 0.0 83.7 110.0

39.3 15.3 24.0 78.6 251.0

41.9 25.3 16.6 83.8 168.0

Table 5. Amount Adsorbed of Each Species [mol/g] Computed by Dynamic Simulations process

species

1st cycle

CSS cycle

two-step operating conventional TSA

benzene toluene p-xylene benzene toluene p-xylene benzene toluene p-xylene benzene toluene p-xylene

2.86 × 10-2 2.62 × 10-2 2.76 × 10-2 3.03 × 10-2 2.79 × 10-2 2.94 × 10-2 2.86 × 10-2 2.62 × 10-2 2.76 × 10-2 3.03 × 10-2 2.79 × 10-2 2.94 × 10-2

1.91 × 10-2 2.58 × 10-2 2.80 × 10-2 2.95 × 10-2 2.84 × 10-2 2.98 × 10-2 2.86 × 10-2 2.62 × 10-2 2.76 × 10-2 3.03 × 10-2 2.79 × 10-2 2.94 × 10-2

two-step operating jacketed TSA three-step operating conventional TSA three-step operating jacketed TSA

Figure 4. Breakthrough curves of concentration and temperature at the desorption step.

the regeneration step, the time-varying experimental data of the inlet temperature of experiments are expressed as the following equation by nonlinear regression programming in this study. -2

Tregeneration ) 352 + 222.2(1 - e-2.756×10 t) (41) Here, t is the elapsed time from the starting time point of the regeneration step. In this breakthrough curve simulation, the linear bulk fluid velocity of the feeding step is 45.2 cm/s, and that of the regeneration step is 50.0 cm/s, which are the same as the conditions of the experiments.21 Desorption breakthrough curves of the simulation are also compared with those of the experimental data, as shown in Figure 4. The effluent gas temperature profile of the simulation shows a good agreement with that of the experiment. The predicted concentration roll-up height of toluene is higher than that of the experiment, and that calculated for p-xylene occurs a little slower than that of the experiment. In view of experimental breakthrough curve of toluene, the amount regenerated is much smaller than the amount adsorbed according to Figures 3 and 4. This is because the toluene regenerated partly escapes when its concentration is measured at each 5-min interval. Though there are some inconsistencies between the simulation and the experiment in concentration depletion curves, the simulated amounts of adsorption and regeneration are exactly the same and the predicted regeneration time of p-xylene is almost the same as the real one. In addition, the operating step change of cyclic simulations follows the conditions described in section 3.3. Therefore, these models are reliable for the analysis of the dynamic behaviors of the cyclic TSA processes.

The number of variables for these breakthrough curve simulations is 1061. The total CPU times for these simulations are 44.77 s for the adsorption model and 54.37 s for the regeneration model, respectively. 5.2. Comparison of a Conventional TSA and a New Jacketed One. General TSA operations are in three steps (adsorption, regeneration, and cooling) and in two steps (adsorption and regeneration). This study did cyclic simulations of the two- and three-step operating TSA processes with nonisothermal conditions based on nonequilibrium theory, to check their dynamic phenomena. As a result of the continuous dynamic simulations of two-step operating TSA processes from startup to CSS, the CSS converges at the 4th cycle for the conventional process and at the 3rd cycle for the new jacketed process. As for the cyclic simulation of the three-step operating TSA, the CSS appears at the 3rd cycle for both the conventional and the new jacketed processes. Table 4 describes operating step times and suitable bulk fluid velocities of the regeneration step determined by dynamic simulations to satisfy the conditions of the continuous two-bed cyclic processes, when the bulk fluid velocity of the feeding step is set to 45.2 cm/s. According to Table 4, the bulk fluid velocity of the jacketed process is a little less than that of the typical one in the case of the two-step operation, and especially for the three-step operation, that of jacketed one is much less than that of the typical one. Because the high velocity requires lots of energy and the coolant velocity is just 17.2 cm/s, the jacketed TSA may be a more energy-saving process than the previous one. Though a cost evaluation is necessary in the future, this study focuses on the analysis of the dynamic phenomena and adsorption efficiency of these processes. The total CPU times and numbers of variables for the cyclic simulations are 480.1 s and 1128 for a two-step operating conventional model, 241.0 s and 1151 for a two-step operating jacketed one, 469.3 s and 1129 for a threestep operating conventional one, and 390.5 s and 1152 for a three-step operating jacketed one, respectively. The amounts adsorbed of each species for these processes are shown in Table 5. The adsorption for a

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Figure 5. Temperature distribution of a two-step operation for a conventional TSA process.

Figure 6. Temperature distribution of a two-step operation for a jacketed TSA process.

two-step operation becomes a little inactive from the 2nd cycle relative to the 1st cycle especially for benzene. This is because of the high bed temperature after the regeneration step. The temperature distributions of a two-step operation are shown in Figures 5 and 6. As for the three-step operation, the amounts adsorbed of each cycle are almost the same because of the cooling step. The temperature distributions such as those in Figures 7 and 8 explain these phenomena. So, the threestep operation is preferable in these cases in view of adsorption ability. The augmented ratio of the amount adsorbed of the jacketed bed to the conventional one at

CSS is 20.3% for a two-step operation and 6.3% for a three-step operation. 6. Conclusions This study performed the following main works: (1) cyclic simulations of nonisothermal multicomponent TSA processes with and without a jacket for BTX purification, (2) verification of the simulation model by comparing breakthrough curves of the simulation with those of Yun’s experiment,21 (3) comparison of the new jacketed TSA model with the conventional one, and (4) calculation of apt conditions such as each operating step

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Figure 7. Temperature distribution of a three-step operation for a conventional TSA process.

Figure 8. Temperature distribution of a three-step operation for a jacketed TSA process.

time and the bulk fluid velocity during the regeneration and the cooling step for running the two-bed TSA system. It is necessary that the economic analysis of these models should be performed in order to find optimal tradeoff in the future, but this paper focuses on the introduction of the new jacketed TSA and the comparison of the new one and the previous one. As a result of the dynamic simulations, we conclude the following facts: (i) Three-step operation is better than two-step operation in view of adsorption ability. (ii) Bulk fluid velocity during the regeneration and cooling steps of the conventional one should be faster

than that of the new jacketed one to meet the continuous two-bed TSA operating conditions. (iii) The new jacketed TSA system proposed in this study has enhanced adsorption efficiency compared with previous TSA beds without jackets. Acknowledgment This work was supported by the Korea Science and Engineering Foundation. Nomenclature ajacket ) ratio of the log mean surface area of the jacket to the volume of the jacket [1/cm]

Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001 4981 aw ) ratio of the internal surface area to the volume of the column wall [1/cm] aair ) ratio of the log mean surface area of the insulation to the volume of the column wall [1/cm] as ) particle external surface area-to-volume ratio [1/cm] C ) gas concentration [ppm] C0 ) adsorbate concentration in the feed [ppm] Cpg ) heat capacity of gas [J/mol/K] Cpw ) heat capacity of column [J/g/K] Cps ) heat capacity of solid [J/mol/K] Dei ) effective diffusion coefficient [cm2/s] Dp ) particle diameter [cm] DiM ) molecular diffusion coefficient [cm2/s] Djacket ) diameter of the jacket [cm] Dinside bed ) diameter of the inside of the bed [cm] Doutside bed ) diameter of the outside of the bed [cm] DL ) axial dispersion coefficient [cm2/s] DS ) surface diffusion coefficient [cm2/s] DS0 ) preexponential factor in the surface diffusion equation [cm2/s] Dv ) diffusion volume Ei ) activation energy in the surface diffusion equation [kJ/ mol] hs ) heat transfer from the particle to the bulk gas phase [J/cm2/s/K] hw ) heat transfer from the bulk gas phase to the column wall [J/cm2/s/K] i ) component of adsorbates (i ) 1 for benzene, i ) 2 for toluene, i ) 3 for p-xylene) KL ) axial thermal dispersion coefficient [cm2/s] ki ) overall mass-transfer coefficient [1/s] kf ) film mass-transfer coefficient [cm/s] L ) packing bed length [cm] Lt ) total bed length [cm] Mw ) molecular weight [g/mol] n ) moles adsorbed [mol/g] ni,0 ) initial moles adsorbed of component i [mol/g] n/i ) moles adsorbed at equilibrium with y* [mol/g] nc ) number of cycles Pi ) adsorbate partial pressure [Pa] QA,i ) total amount adsorbed of component i [mol/g] QR,i ) total amount adsorbed of component i [mol/g] R ) universal gas constant [J/mol/K] Rb ) bed radius [cm] Re ) Reynolds number Sc ) Schmidt number T ) temperature [K] Tgas ) gas temperature within the bed [K] Tgas,0 ) initial gas temperature within the bed [K] Tjacket,inlet ) inlet temperature of the cooling-heating medium into the jacket Tjacket ) temperature of the cooling-heating medium within the jacket Tfeed ) feed temperature [K] Tgeneration ) regeneration temperature [K] Tair ) ambient temperature [K] Twall ) wall temperature [K] Twall,0 ) initial wall temperature [K] Tsolid ) solid temperature [K] Tsolid,0 ) initial solid temperature [K] t ) time [min or s] tA ) adsorption time [min or s] tR ) regeneration time [min or s] tC ) cooling time [min or s] tcycle ) cycle time [min or s] Uair ) overall heat transfer from the column wall to the atmosphere outside of the bed [J/cm2/s/K] Ujacket ) overall heat transfer from the column wall to the coolant within the jacket [J/cm2/s/K] u ) interstitial bulk fluid velocity [cm/s]

uA ) interstitial bulk fluid velocity during adsorption [cm/ s] uR ) interstitial bulk fluid velocity during regeneration [cm/s] uC ) interstitial bulk fluid velocity during cooling [cm/s] V˙ jacket ) volume flow rate of the cooling-heating medium within the jacket [cm3/min] Vjacket ) volume of the cooling-heating medium within the jacket [cm] yi ) mole fraction of component i yi,0 ) initial mole fraction of component i yf,i ) feed mole fraction of component i z ) axial distance coordinate [cm] Greek Letters Fg ) gas density [mmol/cm3] Fp ) particle density [g/cm3] Fw ) column density [g/cm3]  ) bed void fraction p ) particle porosity re ) mean pore radius [cm] τp ) pore tortuosity factor ∆Xjacket ) thickness of the jacket [cm] ∆Xw ) wall thickness [cm] -∆H ) isosteric heat of adsorption [J/mol]

Literature Cited (1) Lukchis, G. M. Adsorption systems. Part II: equipment design. Chem. Eng. 1973, July 9, 83. (2) Lukchis, G. M. Adsorption systems. Part III: adsorbent regeneration. Chem. Eng. 1973, August 6, 83. (3) Ruthven, D. M. Principles of adsorption and adsorption processes; Wiley: New York, 1984. (4) Yang, R. T. Gas separation by adsorption processes; Butterworth: Boston, 1987. (5) Pan, C. Y.; Basmadjian, D. An analysis of adiabatic sorption of single solutes in fixed beds: pure thermal wave formation and its practical implications. Chem. Eng. Sci. 1970, 25, 1653. (6) Basmadjian, D. On the possibility of omitting the cooling step in thermal gas adsorption cycles. Can. J. Chem. Eng. 1975, 53, 234. (7) Davis, M. M.; LeVan, M. D. Experiments on optimization of thermal swing adsorption. Ind. Eng. Chem. Res. 1989, 28 (6), 778. (8) Chen, A.-Q.; Wankat, P. C. Scaling rules and intensification of thermal swing adsorption. AIChE J. 1991, 37 (5), 785. (9) Hwang, K. S.; Choi, D.-K.; Gong, S. Y.; Cho, S. Y. Adsorption and thermal regeneration of methylene chloride vapor on an activated carbon bed. Chem. Eng. Sci. 1997, 52 (7), 1111. (10) Zwiebel, I.; Gariepy, R. L.; Schnitzer, J. J. Fixed bed desorption behavior of gases with non-linear equilibria: Part I. dilute, one component, isothermal systems. AIChE J. 1972, 18 (6), 1139. (11) Zwiebel, I.; Kralik, C. M.; Schnitzer, J. J. Fixed bed desorption behavior of gases with nonlinear equilibria: Part II. dilute, multicomponent, isothermal systems. AIChE J. 1974, 20 (5), 915. (12) Basmadjian, D.; Ha, K. D.; Pan, C.-Y. Nonisothermal desorption by gas purge of single solutes in fixed-bed adsorbers. I. equilibrium theory. Ind. Eng. Chem. Process Des. Dev. 1975, 14 (3), 328. (13) Friday, D. K.; LeVan, M. D. Solute condensation in adsorption beds during thermal regeneration. AIChE J. 1982, 28 (1), 86. (14) Friday, D. K.; LeVan, M. D. Thermal regeneration of adsorption beds: equilibrium theory for solute condensation. AIChE J. 1984, 30 (4), 679. (15) Friday, D. K.; LeVan, M. D. Hot purge gas regeneration of adsorption beds with solute condensation: experimental studies. AIChE J. 1985, 31 (8), 1322. (16) Kumar, R.; Dissinger, G. R. Nonequilibrium, nonisothermal desorption of single adsorbate by purge. Ind. Eng. Chem. Process Des. Dev. 1986, 25 (2), 456.

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Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001

(17) Schork, J. M. Thermal regeneration of fixed adsorption beds. Ph.D. Thesis, University of Texas at Austin, Austin, TX, 1986. (18) Schork, J. M.; Fair, J. R. Parametric analysis of thermal regeneration of adsorption beds. Ind. Eng. Chem. Res. 1988, 27, 457. (19) Huang, C.-C.; Fair, J. R. Study of the adsorption and desorption of multiple adsorbates in a fixed bed. AIChE J. 1988, 34 (11), 1861. (20) Yun, J.-H.; Choi, D.-K.; Kim, S.-H. Adsorption equilibria of chlorinated organic solvents onto activated carbon. Ind. Eng. Chem. Res. 1998, 37 (4), 1422. (21) Yun, J.-H. Multicomponent adsorption of VOCs and thermal regeneration of fixed beds. Ph.D. Thesis, Korea University, 1999. (22) Yun, J.-H.; Choi, D.-K. Adsorption isotherms of benzene and methylbenzene vapors on activated carbon. J. Chem. Eng. Data 1997, 42 (5), 894. (23) Yun, J.-H.; Hwang, K.-Y.; Choi, D.-K. Adsorption of benzene and toluene vapors on activated carbon fiber at 198, 323, and 348 K. J. Chem. Eng. Data 1998, 43 (5), 843. (24) Cooney, D. O.; Strusi, F. P. Analytical description of fixedbed sorption of two Langmuir solutes under nonequilibrium conditions. Ind. Eng. Chem. Fundam. 1972, 11 (1), 123. (25) Thomas, W. J.; Lombardi, J. L. Binary adsorption of benzene-toluene mixtures. Trans. Inst. Chem. Eng. 1971, 49, 240. (26) Basmadjian, D.; Wright, D. W. Nonisothermal sorption of ethane-carbon dioxide mixtures in beds of 5A molecular sieves. Chem. Eng. Sci. 1981, 36, 937. (27) Rhee, H.-K.; Amundson, N. R. An analysis of an adiabatic column: Part I. theoretical development. Chem. Eng. J. 1970, 1, 241. (28) Davis, M. M.; McAvoy, R. L.; LeVan, M. D. Periodic states for thermal swing adsorption of gas mixtures. Ind. Eng. Chem. Res. 1988, 27 (7), 1229. (29) Huang, C. C.; Fair, J. R. Parametric analysis of thermal swing cycles for multicomponent adsorption. AIChE J. 1989, 35 (10), 1667. (30) Nagel, G.; Kluge, G.; Flock, W. Modelling of non-isothermal multi-component adsorption in adiabatic fixed bedssI. the numerical solution of the parallel diffusion model. Chem. Eng. Sci. 1987, 42 (1), 143. (31) Villadsen, J.; Stewart, W. E. Solution of boundary-value problems by orthogonal collocation. Chem. Eng. Sci. 1967, 22, 1483. (32) Villadsen, J.; Sørensen, J. P. Solution of parabolic partial differential equations by a double collocation method. Chem. Eng. Sci. 1969, 24, 1337.

(33) Michelsen, M. L.; Villadsen, J. A convenient computational procedure for collocation constants. Chem. Eng. J. 1972, 4, 64. (34) Villadsen, J.; Michelsen, M. L. Solution of differentrial equation models by polynomial approximation; Prentice-Hall: Englewood Cliffs: NJ, 1978. (35) Finlayson, B. A. Packed bed reactor analysis by orthogonal collocation. Chem. Eng. Sci. 1971, 26, 1081. (36) Hill, T. L. Statistical mechanics of adsorption. V. Thermodynamics and heat of adsorption. J. Chem. Phys. 1949, 17, 520. (37) Glueckauf, E.; Coates, J. I. Theory of chromatography: Part IV. The influence of incomplete equilibrium on the front boundary of chromatograms and on the effectiveness of separation. J. Chem. Soc. 1947, 1315. (38) Petrovic, L. J.; Thodos, G. Mass transfer in the flow of gases through packed beds. Ind. Eng. Chem. Fundam. 1968, 7, 274 (39) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases & liquids; McGraw-Hill: New York, 1988. (40) Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H. Handbook of chemical property estimation methods; McGraw-Hill: New York, 1982. (41) Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; R. E. Krieger Publishing Co.: Huntington, NY, 1980. (42) Smith, J. M. Chemical engineering kinetics; McGrawHill: New York, 1981. (43) Kern, D. Q. Process Heat Transfer; McGraw-Hill: New York, 1990. (44) McAdams, W. H. Heat Transmission, 3rd ed.; McGrawHill: New York, 1954. (45) PSE Ltd. gPROMS Introductory User Guide, Release 1.7; 1999. (46) Barton, P. I. The modelling and simulation of combined discrete/continuous processes. Ph.D. Thesis, Imperial College of Science, Technology and Medicine, London, 1992. (47) Oh, M. Modelling and simulation of combined lumped and distributed processes. Ph.D. Thesis, Imperial College of Science, Technology and Medicine, London, 1995. (48) Schiesser, W. E. The numerical method of lines; Academic Press: New York, 1991. (49) Jarvis, R. B. Robust dynamic simulation of chemical engineering processes. Ph.D. Thesis, Imperial College of Science, Technology and Medicine, London, 1993.

Received for review May 23, 2000 Accepted March 15, 2001 IE000515Z