Temperature Swing Adsorption Process with Indirect Cooling and

Temperature swing adsorption (TSA) processes are based on the periodic variation of the temperature of an adsorbent bed. The adsorption occurs at low ...
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Ind. Eng. Chem. Res. 2002, 41, 5802-5811

Temperature Swing Adsorption Process with Indirect Cooling and Heating Jocelyn Bonjour, Jean-Bertrand Chalfen,† and Francis Meunier* Laboratoire du Froid (E.A. 1408), CNAM, 292, rue St. Martin, 75141 Paris, Cedex 03, France

Experimental results for a new TSA process including a rapid heat exchanger for indirect cooling and heating are presented. Experiments were performed for the removal and recovery of ethane from a nitrogen stream (simulating a VOC in air). In addition, a simplified one-dimensional nonisothermal nonequilibrium model of the process was developed. As temperature swing is the driving force in the process, specific efforts were made to evaluate the heat-transfer coefficient between the heating or cooling medium and the gas stream. From the combination of the experimental and numerical results, the influence of some parameters (e.g., regeneration temperature, initial feed composition) on the process efficiency, analyzed in terms of both recovered mass and energy consumption, was determined. 1. Introduction Temperature swing adsorption (TSA) processes are based on the periodic variation of the temperature of an adsorbent bed. The adsorption occurs at low temperature, and the bed regeneration at high temperature. This kind of process is preferred to PSA (pressure swing adsorption) when strongly adsorbed species for which a simple variation of pressure is not efficient enough are involved. In addition, such processes are usually recommended for purification rather than bulk separation. Currently, TSA processes are commonly used for trace impurity removal from air in PPU (prepurification unit) systems, as well as for volatile organic compound (VOC) abatement from process air streams. TSA cycle times are usually quite long (several hours to several days), and TSA processes are characterized by two drawbacks: high energy consumption and large adsorbent inventories. If one wants to reduce the adsorbent inventory, a solution is to design rapid adsorbers so as to operate more cycles. The challenge is to be able to reduce the regeneration step time from about 1 h to a few minutes. The first innovation of the work presented herein is to use a rapid adsorber to reduce the time of the regeneration step. The second innovation of this work concerns the use of an indirect cooling and heating heat exchanger (HX). In fact, most of TSA processes use hot gas or steam for the regeneration phase. Nevertheless, in the case of direct heating by means of steam, the adsorbent must be dried after regeneration. Moreover, if the adsorbate is miscible with water, a secondary unit must be used to separate water. The hot gas technique leads to a dilute desorbed phase, and consequently, low condensation temperatures must be reached if the adsorbate is intended for reuse. That is the reason several alternative processes avoiding direct heating have been developed recently. These processes involve Joule heating through the electrical resistance of the adsorbent;1 microwaves;2 thermoelectric devices;3 or indirect heat* Corresponding author. Tel.: (+33) 1 40 27 22 11. Fax: (+33) 1 40 27 25 95. E-mail: meunierf @cnam.fr. † LIMSI, CNRS, UPR 3251 BP 133, 91403 Orsay Cedex, France.

ing,4 which is the heating mode of interest in the present study. However, the use of electric energy for heating purposes is generally not a good solution, and processes that allow for the use of waste heat should be preferred when they can be used, which is the case in the present study. For the adsorption phase, indirect cooling with a stream of cold water is required. The new TSA process presented herein offers the advantages of using an indirect heating and cooling HX and of using a rapid HX. In this article, the TSA process for VOC removal, recovery, and concentration from air streams is described. The adsorption of ethane in dry nitrogen (simulating air) on Ambersorb600 activated carbon is considered as an example for the purposes of this study. Ethane was chosen because it is not a very strongly adsorbed species, so that the regeneration is easier and adsorption should not take too long. This is the reason that the adsorption times presented in the experimental results below are quite short, which is not representative of actual TSA cycles. The geometry of the adsorption column and the experimental procedure are described first. Then, the mathematical model, including information concerning the heat transfer occurring in the column, and the experimental results are presented, compared, and discussed. 2. Experimental Study 2.1. Process Description. The process (Figure 1) is based on a vertical column of height H ) 1 m (Figure 2) made of stainless steel concentric tubes (outer diameter of the inner tube ) 19.05 mm, inner diameter of the outer tube ) 69.85 mm) that is heated during the regeneration step and cooled during the adsorption step. The outer surface of the outer tube is insulated to reduce the heat losses. Twelve stainless steel fins are located on the outer surface of the inner tube, with the geometry indicated in Figure 2. The adsorbent bed is made of small spheres (average diameter Dp ) 0.65 mm) and fills the annulus formed by the tubes, so that the mass of adsorbent reaches Mads ) 1.96 kg. The circulating gas can flow through the porous bed from the upper to the lower extremity of the column or in the opposite way. As explained above, a major goal of the process was to attain short cycle times (particularly short regenera-

10.1021/ie011011j CCC: $22.00 © 2002 American Chemical Society Published on Web 10/17/2002

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Figure 1. Schematic of the TSA cycle apparatus.

Figure 2. Schematic of the adsorption column.

tion times) and high adsorption capacities by means of indirect heating and cooling. This implied that high heat-transfer coefficients were to be sought for both heating and cooling periods. This necessity led to use the finned geometry described above in the bed to reduce the heat-transfer limitation on the porous bed side. In addition, for the heating periods of the cycles, it was decided to condense steam inside the inner tube with downward circulation. Indeed, steam condensation leads to very high heat-transfer coefficients (4000-7000 W/m2‚K, as measured by Mativet5 and Mativet et al.6) and consequently does not limit the heat transfer to the adsorbent. For the adsorption phase, the main parameters are the feed concentration and the adsorbate/ adsorbent characteristics, as well as the efficiency of the cooling, which is realized by the upward circulation of a volume flow of 400 L/h of cold water at 20 °C inside the inner tube. At the beginning of the cooling period, if the inner tube is at a temperature higher than 100 °C, the water is boiling and removes heat from the bed with a high heat-transfer coefficient (about 1000 W/m2‚

K). This lasts as long as the wall superheat is high enough to maintain bubble nucleation, but once this transient boiling period is finished, the heat transfer is due to single-phase convection. The two-phase heattransfer time was found to be much shorter (10-30 s for a bed initially at 150 °C) than the typical adsorption times, so it can be concluded that, because of the thermal performance of the column, a high temperature at the beginning of adsorption does not drastically limit the adsorption capacity of the bed. During the adsorption phase, all experiments involved the same feed flow rate (20 L/min NTP) of an ethane/ nitrogen mixture but two different mole fractions, namely, 10 and 1% (18 L/min NTP of nitrogen + 2 L/min NTP of ethane and 19.8 L/min of nitrogen + 0.2 L/min of ethane). These mole fractions correspond to 124.8 and 12.5 g/m3, respectively. The mixture was introduced at the top of the column. This operation lasted for 15 min for the 10% mixture and 45 min for the 1% mixture, while the column was cooled with cold water as explained previously. The adsorption times were chosen so as to avoid any detection of ethane at the column outlet, i.e., the nitrogen purity was higher than 99.995%, as the first ethane detection time (50 ppm) was typically about 20 min for the 10% feed and 65 min for the 1%. Then, the column was preheated for 10 min with a nitrogen flow of 0.2 L/min (NTP) by means of the downward circulation of steam in the inner tube. During this stage, the outlet stream was due to the gas thermal expansion in the column and the small flow of nitrogen, so that high outlet concentrations of ethane were reached. The preheating time was defined from the observation that the outlet concentration reached a maximum after about 10 min, so that heating was no longer efficient in regenerating the column. Then, a purge stream of pure nitrogen with a volumetric flow rate of 2 L/min (NTP) was introduced at the bottom of the column for 20 min. The purge time was chosen because it usually roughly corresponded to the time during which the outlet effluent concentration was higher than the feed concentration, which is an important feature in such a concentration process. These two

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stages constituted the regeneration period, during which the gas always circulated upward. Last, a precooling of the column was performed for 10 min by the same flow of cold water as during adsorption (20 °C, 400 L/h) with an upward circulation in the inner tube but also with a pure nitrogen flow of 0.2 L/min (NTP) introduced at the bottom of the column. 2.2. Instrumentation. Several parameters were measured during the experiments with various sensors, some of which are presented in Figure 1. Thermocouples, with an accuracy of about (1 K, were placed at five locations (called locations A, B, C, D, and E according to the notation in Figure 2) of three cross sections of the column (z ) 6, 50, and 95 cm) and at two locations (C and D) of two other cross sections (z ) 27.5 and 72.5 cm). Some thermocouples were also arranged along the inner tube. During the desorption phase, the condensed water was collected in a tank equipped with a level indicator, which allowed the steam consumption to be measured. A differential pressure gauge was used to measure the pressure drop through the porous bed. The gas mixture composition was determined at the outlet of the column by gas chromatography. The chromatograph was equipped with a thermal conductivity detector (TCD) and used nitrogen as the carrier gas; its detection limit was found to be 50 ppm. A statistical procedure showed that the relative uncertainty in the mixture composition measurement was about (15% at low ethane concentrations (100 ppm) but better than (1% at high concentrations (90%). However, it should be mentioned that a calibration of the chromatograph was necessary before each experiment. The inlet composition was fixed by the ratio of the flow rates of the gases, which were adjusted by mass-flow controllers (uncertainty of 1%). All of these instruments were connected to a PC equipped with a data-processing module. The outlet gas mass flow rate was measured by a flow meter with an accuracy of about 5%. 2.3. Heat-Transfer Analysis. In hot-gas TSA processes, the driving force is the temperature gradient between the adsorbent and the circulating gas, so that these temperatures must be evaluated separately. In contrast, in this indirect cooling and heating TSA process, the driving force is the temperature gradient between the heat-transfer fluid and the porous medium as a whole. The porous adsorbent and the gas can then be considered as homogeneous media in this case. This is the reason that local thermal equilibrium (LTE) is assumed to exist in the process modeling, so that the solid and the fluid are at the same temperature. The heat transferred from the heated inner column wall to the bed is thus described by means of a global wall/fluid heat-transfer coefficient, to which the process modeling is very sensitive. A small variation in the heattransfer coefficient leads to large variations in the predicted performance, breakthrough behavior, etc. Thus, the heat-transfer coefficient must be known as accurately as possible so that the heat- and masstransfer performances can be predicted correctly. A specific heat-transfer model was developed and preliminary experiments were performed to identify the heat-transfer coefficient. The validation of this model and the methodology for the identification of the heattransfer coefficient were discussed in detail previously,7 and it was found that the maximum difference between the calculated and measured temperatures throughout

Table 1. Typical Identified Wall/Fluid Heat-Transfer Coefficients and Finned-Surface Efficiencies gas flow rate (L/min)

interstitial velocity at 293 K (m/s)

hη (W/m2‚K)

0.2 2 20

0.002 0.024 0.237

5.5 12 48

Table 2. Typical Values of Material Propertiesa property F

material

typical value

(m3/kg)

ethane nitrogen adsorbent

1.270 1.133 500

cp (J/kg‚K)

ethane nitrogen adsorbent

2070 1100 850

 ∆H (kJ/kg) K (m2) µn (Pa‚s) λeff (W/m‚K)

bed ethane/Ambersorb bed nitrogen bed

0.37 1000 3.47 × 10-10 200 × 10-7 0.29b

a At NTP conditions for gases. b This is the effective conductivity for the bed in which some gas circulates under a pressure close to atmospheric pressure. Thus, it is higher than values usually obtained under low pressure. However, it is in accordance with typical measurements performed by Gurgel8 or Gurgel and Grenier.9

the entire column was 4 K. It was also noticed that the axial temperature gradient was usually lower than 5 K/m. The product of the heat-transfer coefficient and fin efficiency, hη, varies strongly with the gas velocity, as can be seen from typical values of the product hη given in Table 1. 3. Process Modeling Both periods of the cycle (adsorption and desorption) are described with the same set of equations, but the boundary and initial conditions are different. The model is one-dimensional and includes axial dispersion. The gases are assumed to behave as ideal gases under a Darcy flow, giving the pressure profile as

∂P µu )∂z K

(1)

The thermophysical properties of the solid and the bed porosity ( ) 0.37) are fixed at constant values. In contrast, the gas properties and the heat of adsorption were calculated with a dependency on the temperature and/or the pressure. A typical set of the material properties, not showing the pressure or temperature dependency, is given in Table 2. The heat transfer is taken into account through the heat-transfer coefficient, and the fin efficiency is determined from the heattransfer analysis (section 2.3). The outer tube is modeled as adiabatic, and the wall temperature of the inner tube is set to the steam saturating temperature during the heating phase and to the mean water temperature during the cooling phase. The assumption of an isothermal wall was checked via experimental observations. Initial and boundary conditions (i.e., initial temperature, velocity field, gas- and adsorbed-phase concentration fields, inlet temperature and mass flow rate for both species, outlet pressure) were set to the experimental values. The process model is based on the following equations, whose unknown variables, depending on the position

Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5805 Table 3. Experimental Conditions and Main Results of the Various Tested Configurations experiment no. parameter

Figure 3. Isotherms of adsorption of ethane on Ambersorb600.

and time, are the gas-phase concentration C, the interstitial velocity u, the adsorbed-phase concentration q, and the bed temperature T. The nitrogen mass balance can be written as

∂Fn ∂(Fnu) + )0 ∂t ∂z

(2)

The adsorbate mass balance is written as

∂(uC) 1 -  ∂C ∂q ∂2C )Fads + Dz 2 ∂t ∂z  ∂t ∂z

(3)

The energy balance is written as

(1 - )Fadscp,ads

∂(Fgucp,gT) ∂T ) - + ηhΣ(Tw - T) + ∂t ∂z ∂q (4) (1 - )Fads∆H ∂t

In eq 9, the product of the fin efficiency and heattransfer coefficient is based on the nitrogen flow rate (Table 1). Its value is identified from the heat-transfer model or preliminary experiments as described above. The axial heat conduction was neglected in the heat balance because of the low axial temperature gradients observed during these experiments and simulations. The mass transfer is accounted for by the linear driving force (LDF) approximation

∂q ) k(q* - q) ∂t

(5)

The isotherms of adsorption q* ) f(T,C) were measured during specific experiments with a microbalance. They are presented in the form q* ) f(T,P) with C ) MP/RT in Figure 3. The isotherms were found to be properly fitted by a Toth equation. Finally, these coupled equations were solved using the SIMPLE algorithm.10 4. Results and Discussion 4.1. Experimental Results. The main features of three typical experiments are summarized in Table 3. This table includes the operating parameters of the experiment, the amount of ethane processed per cycle, and some information concerning the energy consumption, as well as other results. These values were obtained from averages over a few successive cycles after a cyclic steady state had been reached. It is worth noting that the steady cyclic behavior was obtained after only

mass of adsorbent regeneration temperature initial feed composition cycle characteristic times preheating regeneration precooling adsorption characteristic flow rates preheating (N2) regeneration (N2) pre-cooling (N2) adsorption (N2+C2H6) average concentration during desorption nitrogen recovery amount of processed ethane energy consumption steam consumption energy consumption (total) heat losses active carbon heating inner tube heating outer tube heating fins heating nitrogen heating desorption heat temperature front velocity length of unused bed

units kg °C % min

L/min (NTP)

% % g/cycle kJ/cycle g/cycle kJ/cycle

1

2

3

1.96 150 10

1.96 150 1

1.96 135 1

10 20 10 15

10 20 10 45

10 20 10 45

0.2 2 2 18 + 2 42.9

0.2 2 2 19.8 + 0.2 17.6

0.2 2 2 19.8 + 0.2 17.6

93.5 12.05 900 400 900 315 173 78 160 151 5 18 1.0 51.2

93.5 12.05 705.8 315 705.8 215 143 66 132 127 4.8 18 1.2 51.2

81.3 40.2 838 373 838 299 151 70 134 135 5 44 cm/min 4.5 % 39.5

one or two cycles. It is considered typical that the cyclic steady behavior was obtained quickly,11 and it should be emphasized that this constitutes an advantage of this kind of process when compared to PSA cycles. Indeed, a large number of cycles must be performed with PSA systems to reach steady-state cyclic behavior. To make the presentation of the results clearer, some terminology is first defined. The performance of the process can be measured by the following parameters, among which some refer to nitrogen, if the process goal is to purify this gas, or to ethane, if the aim is to recover this pollutant: (1) The purity applies to nitrogen and represents the volume-averaged nitrogen mole fraction in the purified gas obtained during the adsorption stage. (2) The nitrogen recovery is the ratio of the amount of recovered pure nitrogen during adsorption to the amount of nitrogen used for the process (during all stages of the cycle). (3) The average desorbed ethane concentration is defined as the ratio of the total amount of ethane desorbed to the total amount of gaseous effluent during the preheating and regeneration periods. (4) The enrichment ratio is the average desorbed ethane concentration divided by the ethane feed concentration. (5) The process productivity applies to ethane and represents the amount of ethane processed divided by the mass of adsorbent per cycle or per unit of time. 4.1.1. Influence of the Feed Concentration. The numerical values discussed in this section correspond to the experiments numbered 1 and 2 in Table 3 (steam temperature of 150 °C with 10 and 1% initial feed concentrations, respectively). Figure 4 shows typical evolutions of the gas-phase ethane mole fraction at the column outlet for a few cycles. Time t ) 0 corresponds to the beginning of the preheating stage after the column has been previously saturated by a 1 or 10% ethane concentration feed. After a cyclic steady state is obtained (i.e., after the first cycle), when the feed is 1%, the maximum concentration reaches 25% (312 g/m3),

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Figure 4. Experimental outlet ethane concentration vs time for a few cycles (regeneration temperature ) 150 °C).

Figure 5. Breakthrough curves.

whereas for the 10% feed, the maximum concentration is 90% (1.12 kg/m3). In addition to the maximum concentration, the average desorbed ethane concentration must also be considered; it was found to be 42.9% (535.3 g/m3) for the 10% experiment and 17.6% (219.6 g/m3) for the 1% experiment. The corresponding enrichment ratios are thus 4.3 and 18, respectively. The difference is due to the favorable shape of the isotherms (Figure 3), from which the ratio of the adsorbed-phase concentration between 25 and 150 °C ranges from 13.5 for a 10% mixture to 100 for a 1% mixture. Linked to the isotherms shape is also the amount of ethane processed per cycle once the cyclic steady state is obtained: 30 L (NTP) for the 10% initial feed (i.e., 40.2 g) but only 9 L (NTP) (i.e., 12.05 g) for the 1% initial feed. Thus, the productivity of the process is 20.5 g/kg‚ cycle (22.4 g/kg‚h) for the 10% feed and 6.15 g/kg‚cycle (4.4 g/kg‚h) for the 1% feed. For the purpose of comparing these values, it should be recalled that one cycle lasts 55 min for the 10% experiment but 85 min for the 1% experiment. The purity of the recovered nitrogen exiting the column during the adsorption phase can be observed in Figure 5, which shows the outlet stream gas-phase ethane concentration as a function of time during breakthrough experiments for the 10 and 1% feeds. From these graphs, it appears that the recovered nitrogen purity is higher than 99.995% (the ethane mole fraction is lower than the chromatograph detection limit, which corresponds to less than 62.4 mg/m3) for 22 min for the 10% feed and for 63 min for the 1% feed. With the characteristic times and mass flow rates for the cycles, the nitrogen recovery is 81.3% for the 10%

feed and 93.5% for the 1% mixture. These values can be compared, for instance, to typical performances of a PSA process described by Yang,11 who noticed that the nitrogen recovery is about 50% and its purity is 9599.9%. The energy efficiency is analyzed in terms of raw energy consumption per cycle (which is deduced from the measurements of the amount of steam used during the regeneration period, assuming a latent heat of vaporization for water of 2250 kJ/kg) and the ratio of the mass of recovered ethane to the energy consumption per cycle. Considering the uncertainties, the steam consumption is identical for both feeds and equals 373400 g/cycle, which represents 838-900 kJ/cycle. Thus, the relative steam consumption is 33.2 kg of steam/kg of ethane for the 1% feed and 9.3 kg/kg for the 10% feed. The 10% value lies in the range of values reported by LeVan and Schweiger12 in their literature review of direct heating processes (0.77-20 kg of steam/kg of solvent, depending on the solvent), but the 1% value is noticeably higher. From the results in Table 3, calculated from the temperature variations experienced by the various elements of the column and an energy balance, it appears that the heat losses represent 35% of the supplied energy. It can be concluded that the thermal insulation might be a limiting parameter in such a process. The energy used for heating the adsorbent (151-173 kJ), heating the external tube of the column (134-160 kJ), and the heat of desorption (18 kJ for the 1% feed and 44 kJ for the 10% feed) would also be used in a direct heating process, but the energy corresponding to heating of the inner tube and the fins (205-229 kJ, i.e., one-fourth of the total energy) represents the excess energy consumption due to the choice of indirect heating. The relatively low contribution of the heat used to actually desorb the adsorbate was already pointed out by Schweiger and LeVan13 in their study of the steam regeneration of an activated carbon bed, as they found that only 26% of the energy was used for that purpose. In our case, this part of the energy consumption is only 2% (experiment number 2) to 5.3% (experiment number 1). If the heat losses are excluded (assuming that the insulation could be drastically enhanced), these ratios reach 3 and 8%, respectively, which are still very low values. Nevertheless, as stated by Basmadjian et al.,14 a larger bed for an industrial application would help to reduce the effect of heat leaks, which would lead to a lower energy consumption and, thus, to an increased energy ratio. During the adsorption step of the cycles, traveling thermal waves are observed. Figure 6 shows the thermal waves observed at various heights in the column during the adsorption stage for experiments 1 and 2. The temperature evolution is not plotted for the lower part of the column because no temperature peak could be measured. The origin of the abscissa corresponds to the beginning of the precooling, which lasts for 10 min and is followed by the actual adsorption period (15 min for the 10% and 45 min during the 1% experiment). The thermal effect of adsorption is analyzed from the temperature overshoot, i.e., the difference between the maximum temperature during a peak and the temperature at the beginning of the peak. From Figure 6, it appears that the temperature overshoot decreases and the peak broadens as the wave travels along the column. The thermal waves resulting from the adsorption in the column depend on several factors, of which the feed

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Figure 6. Time evolution of the bed temperature at various heights during the adsorption period (experiments 1 and 2, Table 3).

Figure 7. Experimental ethane concentration and recovered mass of ethane vs time for two regeneration temperatures (initial feed ) 1%).

concentration is of the highest importance.15 This is the reason the temperature overshoot is higher and stiffer for the 10% than for the 1% initial feed composition. For example, for z ) 95 cm, the temperature increases by 18.1 K in 36 s in the former case and by 5.38 K in 264 s in the latter. Indeed, the adsorption rate is higher when the initial feed increases, so that the energy release due to adsorption is higher, and the temperature overshoot consequently increases. The temperature front velocity can also be estimated from Figure 6 as the ratio of the distance between the thermocouples to the time for the temperature peak to travel between these locations. For the 10% experiment, the front velocity is 4.5 cm/min, but it is only 1.0 cm/min for the 1% experiment, which shows that front propagation depends on adsorption phenomena. 4.1.2. Influence of the Regeneration Temperature. The influence of the regeneration temperature is revealed by experiments 2 and 3 in Table 3 (1% initial feed with 150 or 135 °C as the regeneration temperature). As is typical for TSA processes,16 reducing the regeneration temperature shifts the regeneration profile (Figure 7) toward longer times, but it is noticeable that the maximum outlet concentration is about the same for both regeneration temperatures, at about 25%. The mass of recovered ethane during the preheating stage is higher for the higher regeneration temperature. In fact, during preheating, the temperature increase is slower for the 135 °C experiment than for the 150 °C experiment, so that lower concentrations and flow rates

are reached. In contrast, during the regeneration step, the slope of the curve representing the mass of recovered ethane is higher for 135 °C than for 150 °C, so that after 20 min, the desorbed masses of ethane are similar for the two regeneration temperatures. This is the reason the average desorbed ethane concentration is the same for both temperatures, namely, 17.6%. In fact, the average desorbed ethane concentration is obtained from the mass flow rates and process times, provided that breakthrough does not occur during the adsorption step. With these temperatures, mass flow rates, and adsorption durations, the process allows almost the same amount of ethane to be treated for both temperatures (about 12 g, i.e., 9 L NTP) because, from the isotherms of adsorption (Figure 3), for T ) 150 and 135 °C, the adsorbed-phase concentrations in equilibrium with a 1% gas are both small (0.11 and 0.24 g/kg, respectively) when compared with the value for ambient temperature (12.6 g/kg). From these values, the productivity and enrichment ratio are almost the same for the two temperatures. This is an interesting conclusion because the energy consumption will obviously be lower for 135 °C than for 150 °C for the same process performance. Decreasing the regeneration temperature from 150 to 135 °C reduces the energy consumption by 21% (from 900 to 705.8 kJ). This decrease is mainly due to the decrease in the heat losses through the thermal insulation (-34%) because, for T ) 135 °C, the temperature gradient through the insulation is lower than it is for T ) 150 °C. Because the temperature variations experienced by all of the materials are also lower, the energy used to heat the metallic parts of the column, the adsorbent, and the nitrogen also decrease by about 13%. Thus, for T ) 135 °C, the relative steam consumption reaches 26.1 kg of steam/kg of ethane, which is close to the highest values observed by LeVan and Schweiger.12 Such a low steam temperature application is attractive for environmental purposes. It should allow the use of waste heat and the possibility that TSA processes (either for PPU systems or for VOC abatement) can be implemented in low-CO2-emissions integrated systems.17 4.2. Numerical Simulation. 4.2.1. Model MassTransfer Parameters. The model includes two masstransfer parameters, namely, the axial dispersion coefficient Dz and the overall pellet mass-transfer coefficient k. The overall pellet mass-transfer coefficient was measured for the ethane/adsorbent pair using the apparatus specifically built by Bourdin et al.18 for such a purpose. This method is based on temperature infrared measurements and on single-step or thermal frequency response (TFR) analysis. The experiments performed19 gave a numerical value for k of 0.1 s-1. For the dispersion coefficient, a correlation given by Ruthven20 is written as

Dz ) 0.7Dm + Dpu/2

(6)

where Dm is the molecular dispersion, Dp is the pellet diameter, and u is the fluid velocity. The molecular dispersion can be estimated from several correlations such as that proposed by Ranz and Marshall (cited by Yang11)

( )( )

kDp µ ) 2 + 0.6 Dm FDm

1/3

FuDp µ

1/2

(7)

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Figure 8. Gas-phase outlet mole fraction vs time for various mass-transfer parameters during a regenration experiment (column initially saturated with a 10% feed).

Figure 9. Model sensitivity to the mass-transfer coefficient during a breakthrough experiment with a 10% feed.

or that given by Wakao and Funazkri21

( )( )

kDp µ ) 2 + 1.1 Dm FDm

1/3

FuDp µ

0.6

(8)

The Wakao and Funazkri correlation has been shown to be valid for Reynolds numbers lower than 10, whereas that of Ranz and Marshall appears to be more general. For the lower velocities encountered in the process studied here (about 0.05 m/s), depending on the choice of the correlation, the axial dispersion coefficient ranges from 2.8 × 10-5 to 3.2 × 10-5 m2/s. For the higher velocities (e.g., 0.25 m/s), Dz ) (8.7-9.3) × 10-5 m2/s, which shows that the dispersion coefficient values obtained with the two correlation are consistent. The results of a study of the sensitivity of the outlet gas-phase composition and the temperatures at various locations in the bed to the mass-transfer parameters are depicted in Figures 8-10. This sensitivity study was performed not for cycles but for adsorption or desorption periods to start from a well-defined initial state that is easily obtained during the experiments, i.e., completely regenerated or saturated adsorbent, with a 10% initial gas concentration. Figure 8 shows that the outlet gas-phase mole fraction during the regeneration stage depends on k only for global pellet mass-transfer coefficients lower than 0.01 s-1. This is because the cycle times are long, particularly with respect to PSA cycles, for which the sensitivity to global pellet mass transfer is usually much stronger. The same results stand for the adsorption stage, as shown from the breakthrough curves plotted in Figure 9: the effect of the dispersion coefficient is negligible, and that of the mass-transfer coefficient is noticeable only for extremely low values. Such a negligible sensitivity to the dispersion coefficient and moderate sensitivity to the mass-transfer coefficient was also described by Kumar and Dissinger22 in their parametric study of thermal desorption by hot purge. Finally, a limitation of the model also appears in this graph because, although the breakthrough time is correctly predicted, the model does not correctly fit the experimental breakthrough curve. The traveling thermal waves are much more sensitive to the k value, as shown in Figure 10. In this graph are plotted the experimental thermal waves observed at three locations (close to the inlet at z ) 6 cm and outlet at z ) 95 cm and at the mid-height of the column z ) 50 cm) during a breakthrough experiment. The numer-

Figure 10. Comparison between the experimental and predicted traveling thermal waves for various mass-transfer coefficients during breakthrough (Dz ) 5 × 10-5 m2/s).

ical waves are plotted for z ) 6 cm and z ) 50 cm with k ) 0.1 s-1 and Dz ) 5 × 10-5 m2/s and for z ) 95 cm with Dz ) 5 × 10-5 m2/s and k ) 0.5, 0.1, and 0.005 s-1. As can be seen in Figure 10, for z ) 95 cm, as the value of k increases, the thermal wave occurs later, and its amplitude increases. The best agreement between the numerical and experimental waves is obtained for k ) 0.1 s-1 and Dz ) 5 × 10-5 m2/s. It should be noted that the shapes of the waves observed in Figures 10 and 6 are not the same because the initial conditions are different: Figure 10 represents the thermal waves occurring during a breakthrough experiment starting with a column at a uniform low temperature (25 °C), whereas for Figure 6, the waves are observed during the adsorption stage of a cycle, after the regeneration step at a high temperature (150 °C). Last, with the identified value of the dispersion coefficient, the experimental and numerical time evolutions of the temperature are compared in Figure 11 for the preheating and regeneration stages at z ) 95 cm and z ) 6 cm (gas outlet and inlet, respectively). The agreement between the numerical and experimental values is satisfactory. In addition, this graph is useful to show that the temperature field is quite homogeneous (axial temperature gradient lower than 4 K) when the column is heated. From all of these comparisons, it appears that, even though the model achieves a good qualitative agreement with the experiments, some quantitative discrepancies occur, particularly for the breakthrough curve. Several reasons for these discrepancies can be mentioned: (1) First, the one-dimensional model oversimplifies the

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Figure 11. Time evolution of the bed temperature (mean temeprature at z ) 95 and 6 cm) during a desorption period.

complexity of the 3D heat exchanger. Important radial temperature gradients, not taken into account in the model, are observed. In fact, the experiments showed that the temperature difference between the heated wall and the inner wall of the outer tube can reach 70 K at the beginning of the desorption step. Nevertheless, after a few minutes of heating, this difference is only a few Kelvin. (2) A constant heat-transfer coefficient is used in the process modeling, whereas its value depends on the gas velocity, which varies during both the adsorption and desorption periods. The present model actually allows for the evaluation of the gas velocity, but it does not take its effect on the heat-transfer coefficient into account. A constant heat-transfer coefficient is an approximation that could be avoided in future simulations. (3) Even though the mean particle size of Ambersorb600 adsorbent is small (0.65 mm) when compared to the column and the geometric dimensions of the fins, a channeling flow along the column wall (which is not taken into account in the model) might have occurred during the experiments. The occurrence of this phenomenon could not be proven experimentally. 4.2.2. Numerical Simulation: Adsorbed-Phase Concentration Profiles. From the sensitivity study and the comparisons between the numerical and experimental results presented in the preceding section, the values of k and Dz were fixed to 0.1 s-1 and to 5 × 10-5 m2/s, respectively, and kept constant for the following simulations. The developed model allows for an analysis of the adsorbed-phase concentration profiles along the column axis, which cannot be measured directly. Figure 12 shows these profiles at various times during experiment 1 in Table 3. Time t ) 0 corresponds to the end of the adsorption phase and the beginning of the preheating phase. The precooling and adsorption stages are plotted in Figure 13, with time t ) 0 corresponding to the end of the adsorption stage. The shape of the profiles during cyclic column behavior is different from that observed during direct heating (with hot gas or steam) and cooling TSA processes described in the literature14,16,22 because the heat and mass transfer differ. In Figures 12 and 13, it can be observed that, at the end of the regeneration period, the bed is well regenerated because the adsorbed-phase concentration is very flat. These profiles also confirm the importance of changing the mass flow direction at the end of the precooling stage before the adsorption phase starts. Owing to this change, the lower part of the column (i.e., the outlet during the adsorption phase) is always kept as clean as possible. In contrast, the adsorbed-phase

Figure 12. Adsorbed-phase concentration axial profiles during preheating and regeneration (simulation, feed mole fraction ) 10%).

Figure 13. Adsorbed-phase concentration axial profiles during precooling and adsorption (simulation, feed mole fraction ) 10%).

concentration profile at the end of the adsorption step shows an elongated mass-transfer zone along the column. This means that the bed remains widely unsaturated, which reduces the column efficiency. In longer columns used in industrial operations, however, this effect would be of lower importance because, as stated by Basmadjian et al.,14 the transfer zone would occupy a proportionately smaller fraction of the bed length. The impact of this phenomenon can be quantified by computing the LUB (length of unused bed) from these simulated profiles. This parameter relates the actual amount of processed ethane to the maximum theoretical amount that would be processed if the adsorption step were performed until the saturation of the bed, if the temperatures were homogeneous, and if the bed could be completely regenerated. It is hence calculated from the equation

(

LUB ) 100 × 1 -

)

∫0H[qmax(z) - qmin(z)] dz q*H

(9)

where qmax and qmin refer to the maximum and minimum adsorbed-phase concentrations, i.e., the concentrations at the ends of the adsorption and regeneration phases, respectively, and q* refers to the equilibrium adsorbed-phase concentration for a bed at the coolingwater temperature. Thus, the integral in eq 14 represents the amount of ethane processed per cycle. Under the tested conditions (10% feed), the LUB equals 39.5%, and the simulation for the 1% experiments yielded an

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LUB of 51.2% for both regeneration temperatures (135 and 150 °C). It is remarkable that the same LUBs and process performances are obtained for both temperatures when the energy consumption has been shown to be noticeably lower for the lower regeneration temperature. However, if the regeneration temperature decreases too much, the efficiency of the regeneration step decreases, so that the LUB or the nitrogen purity is also reduced. Hence, there must be a tradeoff between energy consumption and process performance, which, in other words, means that an optimal regeneration temperature can be found for a given process performance. Such an optimal regeneration temperature was also shown to exist in hot-gas purge regeneration TSA cycles by Kumar and Dissinger.22 5. Conclusion The aim of the present work was to study the performance of and model a new TSA process for VOC capture with indirect cooling and heating. From the experimental results, it can be concluded that the indirect heat-transfer process used here is very effective because small axial temperature gradients are observed and the regeneration step is reasonably short (30 min). The TSA process yields good performances regarding the purity (typically higher than 99.995%, which corresponds to less than 62.4 mg/m3) or product recovery. The maximum and average concentrations of the recovered effluent are high because of the indirect mode of heating and cooling. To model this process, one difficulty lies in the evaluation of the heat-transfer coefficient from the heated/cooled wall to the fluid flowing through the active carbon bed. Specific experiments were performed, and a heat-transfer model was developed to obtain this heattransfer coefficient. The model developed for the process fits well with the available experimental results and was used to further investigate the column behavior. Two drawbacks of this process can be mentioned. First, the internal heat exchanger structure of the column induces some investment costs that must be compared to the costs of the burner or of a more common heat exchanger in classical TSA process. Second, the energy consumption remains too high at the moment. This is not too much a problem if waste heat is to be used, in which case the operating costs should be analogous to those of a direct TSA process. This is why this work is the first step of a study that will include at least three other steps to improve the process in terms of efficiency: (1) A first step is to use the model to define optimal operating conditions for higher energetic efficiency. (2) A second step will consist in optimizing the heat exchanger structure design so as to improve its efficiency.23 (3) A further step will be to design a multibed process so as to obtain a high working capacity as compared to that of a single-bed process. Nomenclature C ) gas-phase concentration (kg/m3) cp ) heat capacity (J/kg‚K) Dp ) particle diameter (m) Dm ) molecular dispersion (m2/s) Dz ) axial mass-diffusion coefficient (m2/s) H ) column height (m) h ) heat-transfer coefficient (W/m2‚K) K ) permeability (m2)

k ) mass-transfer coefficient (s-1) LUB ) length of unused bed (%) M ) mass (kg) M ) molar mass (kg/mol) P ) pressure (Pa) q ) adsorbed-phase concentration (kg/kg) q* ) maximum adsorbed-phase concentration (kg/kg) R ) molar universal gas constant (J/mol‚K) T ) temperature (K) t ) time (s) u ) interstitial velocity (m/s) z ) axial location from the bottom of the column (m) Greek Letters ∆H ) heat of desorption (J/kg)  ) bed porosity η ) fin efficiency µ ) kinematic viscosity (Pa‚s) F ) density (kg/m3) Σ ) heat-transfer surface per unit of column length (m2/ m) Subscripts ads ) adsorbent g ) gas n ) nitrogen w ) wall Abbreviation NTP ) normal temperature and pressure conditions (T ) 273 K and P ) 101 325 Pa)

Literature Cited (1) Baudu, M.; Le Cloirec, P.; Martin, G. Thermal regeneration by Joule effect of activated carbon used for air treatment. Environ. Technol. 1992, 13, 423. (2) Mezey, E. J.; Dinovo, S. T. Adsorbent regeneration and gas separation utilizing microwave heating. U.S. Patent 4,322,394, 1980. (3) Bonnissel, M.; Luo, L.; Tondeur, D. Fast thermal swing adsorption using thermoelectric devices and new adsorbent. In Proceedings of the 6th Conference on Fundamentals of Adsorption (FOA6); Elsevier: Paris, 1998; p 1065. (4) Salden, A.; Boger, T.; Eigenberger, G. A combined vacuum and temperature swing adsorption process for the removal and recovery of organic components from waste-air-systems. In Proceedings of the 6th Conference on Fundamentals of Adsorption (FOA6); Elsevier: Paris, 1998; p 915. (5) Mativet, A. Etude expe´rimentale d’un proce´de´ de chauffage et de refroidissement par changement de phase du fluide caloporteur. The`se de Doctorat, Universite´ Paris XI, Paris, France, 1997. (6) Mativet, A.; Meunier, F.; Chalfen, J. B.; Marvillet, C. Experimental study of heat transfer during film condensation in transient conditions in a vertical smooth tube. Exp. Heat Transfer 1999, 12, 247. (7) Bonjour, J.; Mativet, A.; Chalfen, J. B.; Meunier, F. Identification du coefficient de transfert de chaleur par convection a` travers un milieu poreux. In 3e` mes Journe´ es Tunisiennes sur les Ecoulements et les Transferts; Ste Tunisienne de Physique: Sfax, Tunisia, 2000; p 167. (8) Gurgel, J. M. Contribution a` l’e´tude expe´rimentale de la conductivite´ thermique de milieux granulaires. The`se de Doctorat, Universite´ Paris VI, Paris, France, 1989. (9) Gurgel, J. M.; Grenier, Ph. Mesure de la conductivite´ thermique du charbon actif AC-35 en pre´sence de gaz. Chem. Eng. J. 1990, 44, 43. (10) Patankar, S. V. Numerical Heat Transfer and Fluid Flow; Taylor & Francis: New York, 1980. (11) Yang, R. T. Gas Separation by Adsorption Processes; Imperial College Press: London, 1997. (12) LeVan, M. D.; Schweiger, T. A. J. Steam regeneration of adsorption beds: theory and experiments. In Proceedings of the 3rd Conference on Fundamentals of Adsorption; Engineering Foundation: New York, 1989; p 487.

Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5811 (13) Schweiger, T. A. J.; LeVan, M. D. Steam regeneration of solvent adsorbers. Ind. Eng. Chem. Res. 1993, 32, 2418. (14) Basmadjian, D.; Ha, K. D.; Proulx, D. P. Nonisothermal desorption by gas purge of single solutes from fixed-beds adsorbers. Part II. Experimental verification of equilibrium theory. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 340. (15) Delage, F.; Pre´, P.; Le Cloirec, P. Effect of moisture on warming of activated carbon bed during VOC adsorption. J. Environ. Eng. 1999, 125, 1160. (16) Basmadjian, D.; Ha, K. D.; Pan, C.-Y. Nonisothermal desorption by gas purge of single solutes from fixed-beds adsorbers. Part I Equilibrium theory. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 328. (17) Meunier, F. Adsorption for Environment. In Proceedings of the 7th Conference on Fundamentals of Adsorption (FOA7); Elsevier: Paris, 2001. (18) Bourdin, V.; Gray, P. G.; Grenier, Ph.; Terrier, M. F. An apparatus for adsorption dynamics studies using infrared measurement of the adsorbent temperature. Rev. Sci. Instrum. 1998, 69, 2130.

(19) Grenier, Ph., LIMIS-CNRS, Orsay, France. Personal communication, 2001. (20) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons: New York, 1984. (21) Wakao, N.; Funazkri, T. Effect of fluid dispersion coefficients on particle-to-fluid mass transfer coefficients in packed beds. Chem. Eng. Sci. 1978, 33, 1375. (22) Kumar, R.; Dissinger, G. R. Nonequilibrium, nonisothermal desorption of single adsorbate by purge. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 456. (23) Bejan, A.; Bonjour, J.; Meunier, F. Optimization of fin tree geometry in a coaxial two-stream heat exchanger, manuscript to be submitted.

Received for review December 17, 2001 Revised manuscript received August 22, 2002 Accepted August 28, 2002 IE011011J