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Experiment and prediction of breakthrough curves for packed bed adsorption of water vapor on cornmeal
Chemical Engineering and Processing 45 (2006) 747–754
Experiment and prediction of breakthrough curves for packed bed adsorption of water vapor on cornmeal Hua Chang, Xi-Gang Yuan ∗ , Hua Tian, Ai-Wu Zeng State Key Laboratory of Chemical Engineering, Chemical Engineering Research Center, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, PR China Received 16 November 2005; accepted 5 March 2006 Available online 10 March 2006
Abstract The adsorption isotherms of water vapor on cornmeal and the breakthrough curves at 82–100 ◦ C were measured in a fixed-bed apparatus for ethanol dehydration. Using the water isotherms measured and fitting the experimental data to fixed-bed model for breakthrough curve, the effective diffusivity of water was obtained. The effective diffusivity was estimated and used to predict breakthrough curves at other adsorption conditions. The controlling factor for mass-transfer resistance was discussed. © 2006 Elsevier B.V. All rights reserved. Keywords: Adsorption isotherm; Effective diffusivity; Ethanol dehydration; Breakthrough curve; Adsorption model
1. Introduction Starchy materials can adsorb and remove water from alcohol vapors to dry fuel grade ethanol in an energy-efficient manner [1–4]. The adsorption and desorption of water on starchy materials, especially, i.e. cornmeal, corn grits and pure starch, for ethanol dehydration have been extensively studied [1–16]. The success of this dehydration method seems related to the differences in the rate of adsorption, as well as differences in the strength of interaction between each species and the adsorbent. Compounds which exhibit either weak interactions or slow rates of adsorption are expected to be readily separated from those that exhibit strong, relatively fast interactions with the adsorbent [13,17]. Due to strong polar attraction between water molecules and the hydroxyl groups of the adsorbent, water can adsorb on the adsorbent faster and stronger than ethanol, which is known as major mechanism for the selective adsorption of water [9,13]. Corn grits have been used in large-scale fermentation alcohol plants producing fuel-grade ethanol [18–21]. Works on modified-starch material as desiccant for industrial applica-
Abbreviations: ads., adsorbent; concentr., concentration; Temp., temperature ∗ Corresponding author. Tel.: +86 22 27404732; fax: +86 22 27404496. E-mail address: [email protected] (X.-G. Yuan). 0255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2006.03.001
tions in drying air using PSA (pressure swing adsorption) can also be found recently [17–20,22]. A number of studies have been published concerning the adsorption behavior of water vapor on starchy material, including the measurement of equilibrium isotherms and breakthrough curves [2,4,8,13,16]. However, there has been little attempt to correlate them with equilibrium and kinetic information except work of Hills and Pirzada [23] for prediction of breakthrough curves on steamed and flaked cornmeal. Our aim is to measure the water isotherms in bench-scale apparatus and apply it to process model for breakthrough curve prediction. By fitting the experimental data to model of breakthrough curve, the effective diffusivity of water was estimated and validated by predicting breakthrough curves at some other operation conditions. 2. Experimental The corn meals used as adsorbents are from Wuqing County in north China, with a granularity of <0.45 mm. All the adsorbents were dried for 8 h in air-convection oven at 105 ◦ C. One hundred and twenty grams of dried cornmeal were used in all runs. To provide vapor feeds with different concentrations, water–ethanol mixtures with different concentrations were prepared by mixing anhydrous ethanol and water. Fig. 1 is the experimental apparatus used in this work. In Fig. 1a, a transparent column of 0.9 m long and 0.025 m i.d.
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Fig. 1. Diagram of experimental apparatus for fixed-bed adsorption: (1) adsorber; (2) adsorbent; (3) support packing; (4) oil bath; (5) kettle and electro-heater; (6) and (7) condenser; (8) voltage controller; (9) gas blowout; (10) cold trap; (11) cooling water; (12) rotameter.
with oil bath jacket was used as adsorber and packed with cornmeal, which is supported from the bottom and covered from the top by a layer of random packing, respectively. Thermopoints are arranged along the axial direction of the column with intervals of 0.1 m to measure the temperatures of the bed at the corresponding positions. The kettle was heated by electro-heater to provide the ethanol–water vapor feed. The superficial velocity of vapor in the adsorber was controlled through regulating the voltage on the electro-heater with a voltage controller. The temperatures were monitored by multi-road heat resistance contact thermometer, the compositions of samples were analyzed by HP5890 gas chromatogram workstation, and the mass of the material was weighed by Mettler AE163 electrical scale with the precision of 0.0001 g. The temperature of the adsorber was kept well above the dew point of the vapor feed to avoid condensing. The experiment was divided into two steps, the adsorption step (Fig. 1a) and the desorption step (Fig. 1b). Using the apparatus of Fig. 1a, 120 g adsorbent was packed in the adsorber and the vapor feed went through the adsorber and the ethanol rich product was collected at the outlet end of condenser 7. The adsorber was operated for 300 min and the breakthrough curves can be obtained by measuring the concentration of outlet solution at intervals of set time. When the adsorption operation had finished, the experiment passed to step 2 where the adsorber was flushed by 106 ◦ C nitrogen gas for 240 min using the same apparatus but configured as Fig. 1b. The desorbed material was collected in the cold trap that was cooled by liquid nitrogen, weighed by Mettler AE163 and analyzed by gas chromatogram. At the moment when the adsorption operation stopped, the void spaces in the system including those within the bed and in the pipelines were supposed to be full of vapor feed, which could be flushed to the cold trap during the desorption operation, and then, should be subtracted from
the desorbate to correct the experimental data, assuming that the ideal gas condition holds. Note that we assumed that quantities of water and ethanol sorbed on the inner surface of the shells of the column and tubes and on the support packing are negligible compared to those collected in the cold trap. With the assumption that the adsorbed ethanol and water at the first phase almost completely desorbed at the second phase, the equilibrium amount of water and ethanol adsorbed can be determined by the quantity and the concentration of the desorbate. The pipelines the vapor went through were heated by heat tape to avoid condensing and the pipelines above the adsorber were kept at little high temperature to prevent condensation back to adsorber. 3. Models considered in this work 3.1. Linear adsorption isotherm Assuming linear adsorption according to Henry’s law for dilute concentration of water, the adsorption isotherm for water can be correlated as a linear adsorption isotherm, which is given by q = Kc
(1)
where K is the adsorption equilibrium constant for a linear adsorption isotherm and q denotes the mass of water adsorbed in mol m−3 adsorbent and c is the concentration of water in mol m−3 . 3.2. Model for breakthrough curves The aim of the experiments was to attempt to predict masstransfer diffusivity and breakthrough curves from the measured
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adsorption isotherm. In the case of isothermal adsorption, the differential equations can be written as follows [24].
where ξ = (kKZ/u) ((1 − εb )/εb ) is the dimensionless distance coordinate, τ = k(t−(Z/u)) the dimensionless time coordinate, and erf(x) is the error function that is defined as
3.2.1. Mass balance on water on an element of column A mass balance on the solute for the flow of fluid through a differential adsorption-bed length, dZ over a differential time duration, dt, gives:
erf(−x) = −erf(x) x 2 2 erf(x) = √ e−η dη π 0
−DL
∂2 c ∂(uc) ∂c (1 − εb ) ∂¯q + + + =0 ∂Z2 ∂Z ∂t εb ∂t
(2)
where the first term accounts for axial dispersion with eddy diffusivity DL , the second term permits an axial variation in fluid velocity, and the fourth term that is based on q¯ , the mass-average adsorbate loading per unit mass accounts for the variation of q throughout the adsorbent particle. Eq. (2) gives the concentration of solute in the bulk fluid as a function of time and location in the bed. 3.2.2. Linear driving force model for mass transfer [24] ∂¯q = k(q∗ − q¯ ) = kK(c − c∗ ) ∂t
(3)
where q* is the adsorbate loading in equilibrium with the solute concentration c, in the bulk fluid. c* is the concentration in equilibrium with average loading q¯ ; k is the overall mass-transfer coefficient in s−1 , which includes both external and internal transport resistances; and K is the adsorption equilibrium constant for a linear adsorption isotherm in Eq. (1). 3.2.3. Relationship for the factor Kk [24] R2p Rp 1 + = 15De kK 3kc
ξ and τ coordinate transformations for Z and t, convert the equations to a much simpler form of erf(x). The approximation given by Eq. (6) is known to be acceptable and the error could be within 0.6% for ξ > 2.0. Klinkenberg model [24,25] has also included the following approximate solution for the profiles of solute concentration in equilibrium with the average sorbent loading: √ c∗ q¯ 1 1 1 = ∗ ≈ τ− ξ− √ − √ 1 + erf (9) cF qF 2 8 τ 8 ξ where c∗ = q¯ /K and c∗ /cF = q¯ /qF∗ , where qF∗ is the loading in equilibrium with cF . The simple model of Klinkenberg, giving c/cF as a function of dimensionless time τ, and dimensionless bed length ξ, was not worse than more sophisticated models, and could be known as adequate for preliminary design purpose [26]. The equilibrium constant K for a given temperature can be correlated by experimental data. By fitting the experimental breakthrough curves to Eq. (6), the overall mass-transfer coefficient k can be estimated. Then by Eqs. (4) and (5), the effective diffusivity De can be evaluated. In addition, the breakthrough curves at various conditions can be predicted by De which has been obtained. 4. Results and discussion
3.2.4. The correlation for external mass-transfer coefficient The external transport coefficient of particles in fixed-bed can be correlated by [24]: 1/3
(8)
(4)
where kc is the external mass-transfer coefficient in m/s, De is effective diffusivity in m2 /s and Rp is adsorbent particle radius in m. The first term in Eq. (4) is the overall mass-transfer resistances, the second and third term is external one and internal one, respectively.
Sh = 2 + 1.1Re0.6 Sci
(7)
(5)
where Sh = Shrewoodnumber = Kc Dp /Di , Re = Reynolds number = Dp G/µ, and Sci = Schmidt number = µ/ρDi . By Eq. (5), external mass-transfer coefficient kc can be estimated from Sh. The analytical solution of a simplified form of Eq. (2), in which negligible axial dispersion, constant fluid velocity u, and the linear driving force mass-transfer model were assumed, was summarized by Ruthven and discussed in detail by Klinkenberg [25]. An adopted approximate solution is that of Klinkenberg [24]: √ c 1 1 1 ≈ 1 + erf (6) τ− ξ+ √ + √ cF 2 8 τ 8 ξ
All the results of the experiment were listed in Table 1. From the data in Table 1, considerable ethanol was also adsorbed on the cornmeal in all runs, which must be recovered by recycling to a distillation stage if it is used for the separation process. 4.1. Linear model of adsorption isotherm for water The adsorption isotherms of water are shown in Fig. 2. By fitting the experimental results of adsorption isotherm to the linear isotherm represented by Eq. (1), the adsorption equilibrium constant at different temperatures was correlated and listed in Table 2. From Fig. 2, it can be seen that the linear correlation represent the isotherm fairly well with the value of the correlation coefficient R2 as 0.9666 for 91 ◦ C at dilute concentration of water. The linear adsorption isotherms for water were used in the prediction of breakthrough curves in after mentioned section. 4.2. Prediction of effective diffusivity By least square correlation: 2 ci ci min f (k) = − cF cF experimental result
(10)
7.47 7.01 3.01 3.18 2.52 2.73 2.77 1.56 1.59 1.89 4.11 1.74 2.80 2.92 4.50 5.60 1.35 2.59
A fitted value of parameter k can be obtained as (ci /cF ) in Eq. (6) is only a function of overall mass-transfer coefficient k at the condition that other variables such as bed depth Z, equilibrium isotherm constant K, the bed void fraction εb , and constant velocity u, are known. The error for the model prediction with optimum k can be expressed by
0.858 0.764 0.596 0.563 0.547 0.504 0.477 0.446 0.410 Note: temp.: temperature; ads.: adsorbent; concentr.: concentration.
2.3169 5.1122 2.1978 3.9232 4.9922 7.3120 9.1567 2.1142 5.0116 1 2 3 4 5 6 7 8 9
82 82 91 91 91 91 91 100 100
97.4 93.8 97.4 95.2 93.8 90.5 87.8 97.5 93.8
0.133 0.294 0.091 0.163 0.208 0.304 0.381 0.065 0.153
ethanol adsorption capacity (g/g ads. × 102 ) Water adsorption capacity (g/g ads. × 102 ) The relative humidity of ethanol, Pi /Pis Water concentration, c (mol H2 O/m3 )
The relative humidity of water, Pi /Pis
Fig. 2. Adsorption isotherm for water and its linear model (solid line).
Sy =
Vapor feed concentr. of ethanol (%) Bed temp. (◦ C) Run no.
Table 1 Run conditions and results
888.8398 1938.1697 817.5243 1318.8561 1374.6437 2118.8588 2636.8131 637.1892 1219.7844
H. Chang et al. / Chemical Engineering and Processing 45 (2006) 747–754 Water adsorption capacity q (mol H2 O/m3 ads.)
750
n ((ci /cF ) − (ci /cF )experimental result )2 i=1 n−1
(11)
where Sy is standard deviation for the prediction to experimental result. The smaller the value of Sy , the better the effect of prediction. Changing the value of k to minimize Eq. (10), the optimal k is obtained as 2.7813 × 10−3 s−1 with Sy being 0.101 for the operation condition of bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 1.64 cm/s and 6.2 wt.% water concentration feed. The comparison of correlation breakthrough curve and experimental one is shown in Fig. 3. The deviation from zero for experimental result at low τ can be explained by the measurement error from the humidity of air. Using the same method, the overall mass-transfer coefficient k at different temperature can be estimated, and it was found that the values so obtained for k almost keeps constant at 2.7813 × 10−3 s−1 , with Sy being 0.057 and 0.086 for 82 and 100 ◦ C, respectively. The breakthrough curves for the other two temperatures of 82 and 100 ◦ C are shown in Figs. 4 and 5.
Table 2 Adsorption equilibrium constant in linear adsorption isotherms for water on cornmeal Temperature (◦ C)
K
82 91 100
379.89 293.07 252.15
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Fig. 3. Comparison of breakthrough curves between experimental results (() points) and Klinkenberg’s model (solid line) (bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 1.64 cm/s, water concentration feed of 6.2 wt.%).
Fig. 4. Comparison of breakthrough curves between experimental results (() points) and Klinkenberg’s model (solid line) (bed temperature of 82 ◦ C, bed depth 43 cm, superficial velocity of 1.26 cm/s, water concentration feed of 6.2 wt.%).
Fig. 5. Comparison of breakthrough curves between experimental results (() points) and Klinkenberg’s model (solid line) (bed temperature of 100 ◦ C, bed depth 43 cm, superficial velocity of 1.70 cm/s, water concentration feed of 6.2 wt.%).
751
Fig. 6. Prediction of breakthrough curves for different bed depths (solid line) and comparison with experimental results (points) (bed temperature of 91 ◦ C, superficial velocity is 1.60 cm/s, water concentration feed of 6.2 wt.%).
4.3. Predictions of breakthrough curves and comparison with experimental results Generally, Klinkenberg’s [24] models, Eqs. (6) and (9), could be used respectively to predict the breakthrough curves and profiles of solute concentration in equilibrium with the average sorbent loading for different bed depth at same other operational conditions. In this paper, we try to predict the breakthrough curves for different bed depth, as well as different velocity and different water vapor concentration by using the value of k obtained in the foregoing section. The breakthrough curve predictions for different bed depths and the comparison with experimental data are shown in Fig. 6. From Fig. 6, it can be seen that with the value of k as 2.7813 × 10−3 s−1 , the breakthrough curves for similar velocity but different bed depth can be well predicted with the calculated Sy from Eq. (11) being 0.052, 0.046, 0.045 and 0.051 for 22, 28, 43 and 46 cm bed depths, respectively. This indicates that Klinkenberg’s [24] model is quite adequate for our experimental conditions, and that it is valuable for industrial applications. The profiles of solute concentrations in equilibrium with the average sorbent loading for different bed depths are shown in Fig. 7. The shapes of the profiles of solute concentration in the bed for different bed depths are similar with those of breakthrough curves. The breakthrough curve for large superficial velocity of 4.31 cm/s at 91 ◦ C was predicted in Fig. 8, and different water concentration of vapor feed in Fig. 9. As seen from Fig. 8, the model of Klinkenberg [24] gives a good fit to the experimental points with Sy of 0.060 for the same concentration of vapor feed but a different superficial velocity. Thus, in spite of the sweeping assumption involved in Klinkenberg’s [24] model, direct measurement on a small sample can be used to predict the breakthrough curves of a larger adsorber by means of the numerical solution of the model. However, from Fig. 9, Klinkenberg’s [24] model cannot give perfect fit for different vapor concentration. The corresponding values of Sy are 0.141, 0.143, and 0.242 for 9.5, 12, and 20 wt.% water concentration feed, respectively. This indicates that with the water concentra-
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Fig. 7. Prediction of profiles of solute concentration in equilibrium with the average sorbent loading for different bed depths (bed temperature of 91 ◦ C, superficial velocity is 1.60 cm/s, water concentration feed of 6.2 wt.%).
Fig. 8. Prediction of breakthrough curves for large velocity (solid line) and comparison with experimental results (() points) (bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 4.31 cm/s, water concentration feed of 6.2 wt.%).
Fig. 10. Comparison of breakthrough curves between experimental results (() points) and Klinkenberg’s model (solid line) with the updated k value (bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 1.76 cm/s, water concentration feed of 20 wt.%).
tion increases, the prediction is getting worse. If we assumed that Sy larger than 0.11 is unacceptable, it can be concluded that the value of k as 2.7813 × 10−3 s−1 cannot be applied to predict the breakthrough curves for different vapor concentrations. A larger slope in the beginning of S-shape breakthrough curves suggests a much larger mass-transfer rate than that in the end. While at the end of the breakthrough curves, the small slope in the end of S-shape breakthrough curves indicates that adsorption rate becomes very small when adsorbent approaching to equilibrium. In fact, the breakthrough curve prediction from Klinkenberg model [24] is symmetrical. Even with an updated value of k, which was obtained as 1.1125 × 10−3 s−1 by re-minimize the criterion of Eq. (10) with the experimental results for 20 wt.% water concentration feed, the value of Sy was as high as 0.177. The key here is that, the breakthrough curve demonstrated under relative higher water concentration are becoming far from being symmetric and cannot be predicted well with Klinkenberg model [24], as seen in Fig. 10. 4.4. Analysis of mass-transfer resistance
Fig. 9. Prediction of breakthrough curves for different water concentrations (solid line) and comparison with experimental results (() points) (bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 1.80 cm/s).
According to Eq. (5), the external mass-transfer coefficient for different operation conditions can be estimated. The estimation results are listed in Table 3. From Table 3, the overall mass-transfer resistance 1/kK increases with the increasing of temperature, and the internal mass-transfer resistance is controlling factor due to (R2p /15De ) ≈ (1/kK) (Rp /3kc ) even for large velocity at the end of breakthrough curves. This is consistent with the fact that the overall mass-transfer coefficient obtained at low superficial velocity can be used to predict well the breakthrough curves for large superficial velocity, that is, the overall mass-transfer coefficient is similar for both low velocity and high velocity due to the fact that internal mass-transfer is controlling factor. As a result, the estimated value for De is in the order of 2.5 × 10−9 m2 s−1 .
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Table 3 Values of parameters for different operation conditions T (◦ C)
K
k (× 103 s−1 )
u0 (× 102 m/s)
εb
u (× 102 m/s)
Rp (× 106 m)
ρ (kg/m3 )
µ (× 105 Pa s)
Di (× 105 m2 /s)
82 91 91 100
379.89 293.07 293.07 252.15
2.7813 2.7813 2.7813 2.7813
1.26 1.64 4.31 1.70
0.3 0.3 0.3 0.3
4.20 5.47 14.37 5.67
225 225 225 225
1.486 1.443 1.443 1.421
1.085 1.111 1.111 1.137
1.642 1.736 1.736 1.809
T (◦ C)
Re
Sci
Sh
kc (m/s)
1/kK
Rp /3kc (× 104 )
R2p /15De
De (× 109 m2 /s)
82 91 91 100
2.589 3.194 8.395 3.186
0.445 0.444 0.444 0.443
3.486 3.684 5.007 3.680
0.127 0.142 0.193 0.148
0.946 1.227 1.227 1.426
5.898 5.278 3.883 5.071
0.946 1.226 1.226 1.425
3.568 2.752 2.752 2.368
5. Conclusions The adsorption isotherms for water at 82–100 ◦ C was measured in a fixed-bed apparatus. The water isotherms were linearized and applied to the prediction of breakthrough curves. By fitting the experimental results of breakthrough curves to the model of Klinkenberg, the overall mass-transfer coefficient was estimated as 2.7813 × 10−3 s−1 and successfully used for the prediction of breakthrough curves at different superficial velocity and different bed depth, but cannot predict well the breakthrough curves for different vapor concentration. The simple model of Klinkenberg, giving c/cF as a function of dimensionless time τ, and dimensionless bed length ξ, was not worse than the more sophisticated model, and could be known as adequate for preliminary design purpose. The analysis of mass-transfer resistance indicated that water adsorption on cornmeal was controlled by the internal mass-transfer resistance for both the low and high velocity at the end of the breakthrough curves. Appendix A. Nomenclature
c cF c* Di Dp erf(x) G k kc K Pi Pis Pi /Pis q q¯ q*
concentration of water (mol m−3 ) concentration of water in feed vapor (mol m−3 ) concentration in equilibrium with average loading q¯ (mol m−3 ) molecular diffusivity (m2 s−1 ) diameter of adsorbent (m) error function mass velocity of vapor (kg m−2 s−1 ) overall mass-transfer coefficient (s−1 ) external mass-transfer coefficient (m/s) adsorption equilibrium constant for water in a linear adsorption isotherm partial pressure for component i at the adsorption temperature (Pa) vapor pressure for component i at the adsorption temperature (Pa) the relative humidity for component i water adsorption capacity (mol m−3 ) average loading of adsorbent for water (mol m−3 ) adsorbate loading in equilibrium with the solute concentration c in the bulk fluid (mol m−3 )
Re Rp Sy Sci Sh u u0
Reynolds number = Dp G/µ radius of adsorbent (m) standard deviation for the prediction Schmidt number = µ/ρDi Sherwood number = kc Dp /Di effective velocity of vapor (m/s) superficial velocity of vapor (m/s)
Greek letters µ viscosity of vapor (Pa s) ξ dimensionless distance coordinate ρ density of vapor (kg m−3 ) τ dimensionless time coordinate corrected for displacement εb bed void fraction References [1] M.R. Ladisch, K. Dyck, Dehydration of ethanol: new approach gives positive energy balance, Science 205 (1979) 898–900. [2] M.R. Ladisch, M. Voloch, J. Hong, P. Bienkowski, G.T. Tsao, Cornmeal adsorber for dehydrating ethanol vapors, Ind. Eng. Chem. Process Des. Dev. 23 (3) (1984) 437–443. [3] P.R. Bienkowski, A. Barthe, M. Voloch, R.N. Neuman, M.R. Ladisch, Breakthrough behavior of 17.5 mol% water in methanol, ethanol, isopropanol, and T-butanol vapors passed over corn grits, Biotechnol. Bioeng. 28 (7) (1986) 960–964. [4] A.A. Hassaballah, J.H. Hills, Drying of ethanol vapors by adsorption on corn meal, Biotechnol. Bioeng. 35 (6) (1990) 598–608. [5] G.H. Robertson, L.R. Doyle, A.E. Pavlath, Intensive use of biomass feedstock in ethanol conversion: the alcohol–water, vapor-phase separation, Biotechnol. Bioeng. 25 (12) (1983) 3133–3148. [6] J. Hong, M. Voloch, M.R. Ladisch, G.T. Tsao, Adsorption of ethanol–water mixtures by biomass materials, Biotechnol. Bioeng. 24 (3) (1982) 725–730. [7] V. Rebar, E.R. Fischbach, D. Apostolopoulos, J.L. Kokini, Thermodynamics of water and ethanol adsorption on four starches as model biomass separation systems, Biotechnol. Bioeng. 26 (5) (1984) 513–517. [8] R. Neuman, M. Voloch, P. Bienkowski, M.R. Ladisch, Water sorption properties of a polysaccharide adsorbent, Ind. Eng. Chem. Fundam. 25 (1986) 422–425. [9] J.Y. Lee, M.R. Ladisch, Polysaccharides as Adsorbents: an Update on Fundamental Properties and Commercial Prospects, Henniker, NH, USA, Acad of Sciences, New York, USA, 1987, pp. 492–498. [10] A. Ostroff, E. Hatzidimitriu, J.L. Kokini, Thermodynamics of water and ethanol adsorption on model biomass systems, Biotechnol. Bioeng. 31 (8) (1988) 880–884.
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Experiment and prediction of breakthrough curves for packed bed adsorption of water vapor on cornmeal Hua Chang, Xi-Gang Yuan ∗ , Hua Tian, Ai-Wu Zeng State Key Laboratory of Chemical Engineering, Chemical Engineering Research Center, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, PR China Received 16 November 2005; accepted 5 March 2006 Available online 10 March 2006
Abstract The adsorption isotherms of water vapor on cornmeal and the breakthrough curves at 82–100 ◦ C were measured in a fixed-bed apparatus for ethanol dehydration. Using the water isotherms measured and fitting the experimental data to fixed-bed model for breakthrough curve, the effective diffusivity of water was obtained. The effective diffusivity was estimated and used to predict breakthrough curves at other adsorption conditions. The controlling factor for mass-transfer resistance was discussed. © 2006 Elsevier B.V. All rights reserved. Keywords: Adsorption isotherm; Effective diffusivity; Ethanol dehydration; Breakthrough curve; Adsorption model
1. Introduction Starchy materials can adsorb and remove water from alcohol vapors to dry fuel grade ethanol in an energy-efficient manner [1–4]. The adsorption and desorption of water on starchy materials, especially, i.e. cornmeal, corn grits and pure starch, for ethanol dehydration have been extensively studied [1–16]. The success of this dehydration method seems related to the differences in the rate of adsorption, as well as differences in the strength of interaction between each species and the adsorbent. Compounds which exhibit either weak interactions or slow rates of adsorption are expected to be readily separated from those that exhibit strong, relatively fast interactions with the adsorbent [13,17]. Due to strong polar attraction between water molecules and the hydroxyl groups of the adsorbent, water can adsorb on the adsorbent faster and stronger than ethanol, which is known as major mechanism for the selective adsorption of water [9,13]. Corn grits have been used in large-scale fermentation alcohol plants producing fuel-grade ethanol [18–21]. Works on modified-starch material as desiccant for industrial applica-
Abbreviations: ads., adsorbent; concentr., concentration; Temp., temperature ∗ Corresponding author. Tel.: +86 22 27404732; fax: +86 22 27404496. E-mail address: [email protected] (X.-G. Yuan). 0255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2006.03.001
tions in drying air using PSA (pressure swing adsorption) can also be found recently [17–20,22]. A number of studies have been published concerning the adsorption behavior of water vapor on starchy material, including the measurement of equilibrium isotherms and breakthrough curves [2,4,8,13,16]. However, there has been little attempt to correlate them with equilibrium and kinetic information except work of Hills and Pirzada [23] for prediction of breakthrough curves on steamed and flaked cornmeal. Our aim is to measure the water isotherms in bench-scale apparatus and apply it to process model for breakthrough curve prediction. By fitting the experimental data to model of breakthrough curve, the effective diffusivity of water was estimated and validated by predicting breakthrough curves at some other operation conditions. 2. Experimental The corn meals used as adsorbents are from Wuqing County in north China, with a granularity of <0.45 mm. All the adsorbents were dried for 8 h in air-convection oven at 105 ◦ C. One hundred and twenty grams of dried cornmeal were used in all runs. To provide vapor feeds with different concentrations, water–ethanol mixtures with different concentrations were prepared by mixing anhydrous ethanol and water. Fig. 1 is the experimental apparatus used in this work. In Fig. 1a, a transparent column of 0.9 m long and 0.025 m i.d.
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Fig. 1. Diagram of experimental apparatus for fixed-bed adsorption: (1) adsorber; (2) adsorbent; (3) support packing; (4) oil bath; (5) kettle and electro-heater; (6) and (7) condenser; (8) voltage controller; (9) gas blowout; (10) cold trap; (11) cooling water; (12) rotameter.
with oil bath jacket was used as adsorber and packed with cornmeal, which is supported from the bottom and covered from the top by a layer of random packing, respectively. Thermopoints are arranged along the axial direction of the column with intervals of 0.1 m to measure the temperatures of the bed at the corresponding positions. The kettle was heated by electro-heater to provide the ethanol–water vapor feed. The superficial velocity of vapor in the adsorber was controlled through regulating the voltage on the electro-heater with a voltage controller. The temperatures were monitored by multi-road heat resistance contact thermometer, the compositions of samples were analyzed by HP5890 gas chromatogram workstation, and the mass of the material was weighed by Mettler AE163 electrical scale with the precision of 0.0001 g. The temperature of the adsorber was kept well above the dew point of the vapor feed to avoid condensing. The experiment was divided into two steps, the adsorption step (Fig. 1a) and the desorption step (Fig. 1b). Using the apparatus of Fig. 1a, 120 g adsorbent was packed in the adsorber and the vapor feed went through the adsorber and the ethanol rich product was collected at the outlet end of condenser 7. The adsorber was operated for 300 min and the breakthrough curves can be obtained by measuring the concentration of outlet solution at intervals of set time. When the adsorption operation had finished, the experiment passed to step 2 where the adsorber was flushed by 106 ◦ C nitrogen gas for 240 min using the same apparatus but configured as Fig. 1b. The desorbed material was collected in the cold trap that was cooled by liquid nitrogen, weighed by Mettler AE163 and analyzed by gas chromatogram. At the moment when the adsorption operation stopped, the void spaces in the system including those within the bed and in the pipelines were supposed to be full of vapor feed, which could be flushed to the cold trap during the desorption operation, and then, should be subtracted from
the desorbate to correct the experimental data, assuming that the ideal gas condition holds. Note that we assumed that quantities of water and ethanol sorbed on the inner surface of the shells of the column and tubes and on the support packing are negligible compared to those collected in the cold trap. With the assumption that the adsorbed ethanol and water at the first phase almost completely desorbed at the second phase, the equilibrium amount of water and ethanol adsorbed can be determined by the quantity and the concentration of the desorbate. The pipelines the vapor went through were heated by heat tape to avoid condensing and the pipelines above the adsorber were kept at little high temperature to prevent condensation back to adsorber. 3. Models considered in this work 3.1. Linear adsorption isotherm Assuming linear adsorption according to Henry’s law for dilute concentration of water, the adsorption isotherm for water can be correlated as a linear adsorption isotherm, which is given by q = Kc
(1)
where K is the adsorption equilibrium constant for a linear adsorption isotherm and q denotes the mass of water adsorbed in mol m−3 adsorbent and c is the concentration of water in mol m−3 . 3.2. Model for breakthrough curves The aim of the experiments was to attempt to predict masstransfer diffusivity and breakthrough curves from the measured
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adsorption isotherm. In the case of isothermal adsorption, the differential equations can be written as follows [24].
where ξ = (kKZ/u) ((1 − εb )/εb ) is the dimensionless distance coordinate, τ = k(t−(Z/u)) the dimensionless time coordinate, and erf(x) is the error function that is defined as
3.2.1. Mass balance on water on an element of column A mass balance on the solute for the flow of fluid through a differential adsorption-bed length, dZ over a differential time duration, dt, gives:
erf(−x) = −erf(x) x 2 2 erf(x) = √ e−η dη π 0
−DL
∂2 c ∂(uc) ∂c (1 − εb ) ∂¯q + + + =0 ∂Z2 ∂Z ∂t εb ∂t
(2)
where the first term accounts for axial dispersion with eddy diffusivity DL , the second term permits an axial variation in fluid velocity, and the fourth term that is based on q¯ , the mass-average adsorbate loading per unit mass accounts for the variation of q throughout the adsorbent particle. Eq. (2) gives the concentration of solute in the bulk fluid as a function of time and location in the bed. 3.2.2. Linear driving force model for mass transfer [24] ∂¯q = k(q∗ − q¯ ) = kK(c − c∗ ) ∂t
(3)
where q* is the adsorbate loading in equilibrium with the solute concentration c, in the bulk fluid. c* is the concentration in equilibrium with average loading q¯ ; k is the overall mass-transfer coefficient in s−1 , which includes both external and internal transport resistances; and K is the adsorption equilibrium constant for a linear adsorption isotherm in Eq. (1). 3.2.3. Relationship for the factor Kk [24] R2p Rp 1 + = 15De kK 3kc
ξ and τ coordinate transformations for Z and t, convert the equations to a much simpler form of erf(x). The approximation given by Eq. (6) is known to be acceptable and the error could be within 0.6% for ξ > 2.0. Klinkenberg model [24,25] has also included the following approximate solution for the profiles of solute concentration in equilibrium with the average sorbent loading: √ c∗ q¯ 1 1 1 = ∗ ≈ τ− ξ− √ − √ 1 + erf (9) cF qF 2 8 τ 8 ξ where c∗ = q¯ /K and c∗ /cF = q¯ /qF∗ , where qF∗ is the loading in equilibrium with cF . The simple model of Klinkenberg, giving c/cF as a function of dimensionless time τ, and dimensionless bed length ξ, was not worse than more sophisticated models, and could be known as adequate for preliminary design purpose [26]. The equilibrium constant K for a given temperature can be correlated by experimental data. By fitting the experimental breakthrough curves to Eq. (6), the overall mass-transfer coefficient k can be estimated. Then by Eqs. (4) and (5), the effective diffusivity De can be evaluated. In addition, the breakthrough curves at various conditions can be predicted by De which has been obtained. 4. Results and discussion
3.2.4. The correlation for external mass-transfer coefficient The external transport coefficient of particles in fixed-bed can be correlated by [24]: 1/3
(8)
(4)
where kc is the external mass-transfer coefficient in m/s, De is effective diffusivity in m2 /s and Rp is adsorbent particle radius in m. The first term in Eq. (4) is the overall mass-transfer resistances, the second and third term is external one and internal one, respectively.
Sh = 2 + 1.1Re0.6 Sci
(7)
(5)
where Sh = Shrewoodnumber = Kc Dp /Di , Re = Reynolds number = Dp G/µ, and Sci = Schmidt number = µ/ρDi . By Eq. (5), external mass-transfer coefficient kc can be estimated from Sh. The analytical solution of a simplified form of Eq. (2), in which negligible axial dispersion, constant fluid velocity u, and the linear driving force mass-transfer model were assumed, was summarized by Ruthven and discussed in detail by Klinkenberg [25]. An adopted approximate solution is that of Klinkenberg [24]: √ c 1 1 1 ≈ 1 + erf (6) τ− ξ+ √ + √ cF 2 8 τ 8 ξ
All the results of the experiment were listed in Table 1. From the data in Table 1, considerable ethanol was also adsorbed on the cornmeal in all runs, which must be recovered by recycling to a distillation stage if it is used for the separation process. 4.1. Linear model of adsorption isotherm for water The adsorption isotherms of water are shown in Fig. 2. By fitting the experimental results of adsorption isotherm to the linear isotherm represented by Eq. (1), the adsorption equilibrium constant at different temperatures was correlated and listed in Table 2. From Fig. 2, it can be seen that the linear correlation represent the isotherm fairly well with the value of the correlation coefficient R2 as 0.9666 for 91 ◦ C at dilute concentration of water. The linear adsorption isotherms for water were used in the prediction of breakthrough curves in after mentioned section. 4.2. Prediction of effective diffusivity By least square correlation: 2 ci ci min f (k) = − cF cF experimental result
(10)
7.47 7.01 3.01 3.18 2.52 2.73 2.77 1.56 1.59 1.89 4.11 1.74 2.80 2.92 4.50 5.60 1.35 2.59
A fitted value of parameter k can be obtained as (ci /cF ) in Eq. (6) is only a function of overall mass-transfer coefficient k at the condition that other variables such as bed depth Z, equilibrium isotherm constant K, the bed void fraction εb , and constant velocity u, are known. The error for the model prediction with optimum k can be expressed by
0.858 0.764 0.596 0.563 0.547 0.504 0.477 0.446 0.410 Note: temp.: temperature; ads.: adsorbent; concentr.: concentration.
2.3169 5.1122 2.1978 3.9232 4.9922 7.3120 9.1567 2.1142 5.0116 1 2 3 4 5 6 7 8 9
82 82 91 91 91 91 91 100 100
97.4 93.8 97.4 95.2 93.8 90.5 87.8 97.5 93.8
0.133 0.294 0.091 0.163 0.208 0.304 0.381 0.065 0.153
ethanol adsorption capacity (g/g ads. × 102 ) Water adsorption capacity (g/g ads. × 102 ) The relative humidity of ethanol, Pi /Pis Water concentration, c (mol H2 O/m3 )
The relative humidity of water, Pi /Pis
Fig. 2. Adsorption isotherm for water and its linear model (solid line).
Sy =
Vapor feed concentr. of ethanol (%) Bed temp. (◦ C) Run no.
Table 1 Run conditions and results
888.8398 1938.1697 817.5243 1318.8561 1374.6437 2118.8588 2636.8131 637.1892 1219.7844
H. Chang et al. / Chemical Engineering and Processing 45 (2006) 747–754 Water adsorption capacity q (mol H2 O/m3 ads.)
750
n ((ci /cF ) − (ci /cF )experimental result )2 i=1 n−1
(11)
where Sy is standard deviation for the prediction to experimental result. The smaller the value of Sy , the better the effect of prediction. Changing the value of k to minimize Eq. (10), the optimal k is obtained as 2.7813 × 10−3 s−1 with Sy being 0.101 for the operation condition of bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 1.64 cm/s and 6.2 wt.% water concentration feed. The comparison of correlation breakthrough curve and experimental one is shown in Fig. 3. The deviation from zero for experimental result at low τ can be explained by the measurement error from the humidity of air. Using the same method, the overall mass-transfer coefficient k at different temperature can be estimated, and it was found that the values so obtained for k almost keeps constant at 2.7813 × 10−3 s−1 , with Sy being 0.057 and 0.086 for 82 and 100 ◦ C, respectively. The breakthrough curves for the other two temperatures of 82 and 100 ◦ C are shown in Figs. 4 and 5.
Table 2 Adsorption equilibrium constant in linear adsorption isotherms for water on cornmeal Temperature (◦ C)
K
82 91 100
379.89 293.07 252.15
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Fig. 3. Comparison of breakthrough curves between experimental results (() points) and Klinkenberg’s model (solid line) (bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 1.64 cm/s, water concentration feed of 6.2 wt.%).
Fig. 4. Comparison of breakthrough curves between experimental results (() points) and Klinkenberg’s model (solid line) (bed temperature of 82 ◦ C, bed depth 43 cm, superficial velocity of 1.26 cm/s, water concentration feed of 6.2 wt.%).
Fig. 5. Comparison of breakthrough curves between experimental results (() points) and Klinkenberg’s model (solid line) (bed temperature of 100 ◦ C, bed depth 43 cm, superficial velocity of 1.70 cm/s, water concentration feed of 6.2 wt.%).
751
Fig. 6. Prediction of breakthrough curves for different bed depths (solid line) and comparison with experimental results (points) (bed temperature of 91 ◦ C, superficial velocity is 1.60 cm/s, water concentration feed of 6.2 wt.%).
4.3. Predictions of breakthrough curves and comparison with experimental results Generally, Klinkenberg’s [24] models, Eqs. (6) and (9), could be used respectively to predict the breakthrough curves and profiles of solute concentration in equilibrium with the average sorbent loading for different bed depth at same other operational conditions. In this paper, we try to predict the breakthrough curves for different bed depth, as well as different velocity and different water vapor concentration by using the value of k obtained in the foregoing section. The breakthrough curve predictions for different bed depths and the comparison with experimental data are shown in Fig. 6. From Fig. 6, it can be seen that with the value of k as 2.7813 × 10−3 s−1 , the breakthrough curves for similar velocity but different bed depth can be well predicted with the calculated Sy from Eq. (11) being 0.052, 0.046, 0.045 and 0.051 for 22, 28, 43 and 46 cm bed depths, respectively. This indicates that Klinkenberg’s [24] model is quite adequate for our experimental conditions, and that it is valuable for industrial applications. The profiles of solute concentrations in equilibrium with the average sorbent loading for different bed depths are shown in Fig. 7. The shapes of the profiles of solute concentration in the bed for different bed depths are similar with those of breakthrough curves. The breakthrough curve for large superficial velocity of 4.31 cm/s at 91 ◦ C was predicted in Fig. 8, and different water concentration of vapor feed in Fig. 9. As seen from Fig. 8, the model of Klinkenberg [24] gives a good fit to the experimental points with Sy of 0.060 for the same concentration of vapor feed but a different superficial velocity. Thus, in spite of the sweeping assumption involved in Klinkenberg’s [24] model, direct measurement on a small sample can be used to predict the breakthrough curves of a larger adsorber by means of the numerical solution of the model. However, from Fig. 9, Klinkenberg’s [24] model cannot give perfect fit for different vapor concentration. The corresponding values of Sy are 0.141, 0.143, and 0.242 for 9.5, 12, and 20 wt.% water concentration feed, respectively. This indicates that with the water concentra-
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Fig. 7. Prediction of profiles of solute concentration in equilibrium with the average sorbent loading for different bed depths (bed temperature of 91 ◦ C, superficial velocity is 1.60 cm/s, water concentration feed of 6.2 wt.%).
Fig. 8. Prediction of breakthrough curves for large velocity (solid line) and comparison with experimental results (() points) (bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 4.31 cm/s, water concentration feed of 6.2 wt.%).
Fig. 10. Comparison of breakthrough curves between experimental results (() points) and Klinkenberg’s model (solid line) with the updated k value (bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 1.76 cm/s, water concentration feed of 20 wt.%).
tion increases, the prediction is getting worse. If we assumed that Sy larger than 0.11 is unacceptable, it can be concluded that the value of k as 2.7813 × 10−3 s−1 cannot be applied to predict the breakthrough curves for different vapor concentrations. A larger slope in the beginning of S-shape breakthrough curves suggests a much larger mass-transfer rate than that in the end. While at the end of the breakthrough curves, the small slope in the end of S-shape breakthrough curves indicates that adsorption rate becomes very small when adsorbent approaching to equilibrium. In fact, the breakthrough curve prediction from Klinkenberg model [24] is symmetrical. Even with an updated value of k, which was obtained as 1.1125 × 10−3 s−1 by re-minimize the criterion of Eq. (10) with the experimental results for 20 wt.% water concentration feed, the value of Sy was as high as 0.177. The key here is that, the breakthrough curve demonstrated under relative higher water concentration are becoming far from being symmetric and cannot be predicted well with Klinkenberg model [24], as seen in Fig. 10. 4.4. Analysis of mass-transfer resistance
Fig. 9. Prediction of breakthrough curves for different water concentrations (solid line) and comparison with experimental results (() points) (bed temperature of 91 ◦ C, bed depth 43 cm, superficial velocity of 1.80 cm/s).
According to Eq. (5), the external mass-transfer coefficient for different operation conditions can be estimated. The estimation results are listed in Table 3. From Table 3, the overall mass-transfer resistance 1/kK increases with the increasing of temperature, and the internal mass-transfer resistance is controlling factor due to (R2p /15De ) ≈ (1/kK) (Rp /3kc ) even for large velocity at the end of breakthrough curves. This is consistent with the fact that the overall mass-transfer coefficient obtained at low superficial velocity can be used to predict well the breakthrough curves for large superficial velocity, that is, the overall mass-transfer coefficient is similar for both low velocity and high velocity due to the fact that internal mass-transfer is controlling factor. As a result, the estimated value for De is in the order of 2.5 × 10−9 m2 s−1 .
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Table 3 Values of parameters for different operation conditions T (◦ C)
K
k (× 103 s−1 )
u0 (× 102 m/s)
εb
u (× 102 m/s)
Rp (× 106 m)
ρ (kg/m3 )
µ (× 105 Pa s)
Di (× 105 m2 /s)
82 91 91 100
379.89 293.07 293.07 252.15
2.7813 2.7813 2.7813 2.7813
1.26 1.64 4.31 1.70
0.3 0.3 0.3 0.3
4.20 5.47 14.37 5.67
225 225 225 225
1.486 1.443 1.443 1.421
1.085 1.111 1.111 1.137
1.642 1.736 1.736 1.809
T (◦ C)
Re
Sci
Sh
kc (m/s)
1/kK
Rp /3kc (× 104 )
R2p /15De
De (× 109 m2 /s)
82 91 91 100
2.589 3.194 8.395 3.186
0.445 0.444 0.444 0.443
3.486 3.684 5.007 3.680
0.127 0.142 0.193 0.148
0.946 1.227 1.227 1.426
5.898 5.278 3.883 5.071
0.946 1.226 1.226 1.425
3.568 2.752 2.752 2.368
5. Conclusions The adsorption isotherms for water at 82–100 ◦ C was measured in a fixed-bed apparatus. The water isotherms were linearized and applied to the prediction of breakthrough curves. By fitting the experimental results of breakthrough curves to the model of Klinkenberg, the overall mass-transfer coefficient was estimated as 2.7813 × 10−3 s−1 and successfully used for the prediction of breakthrough curves at different superficial velocity and different bed depth, but cannot predict well the breakthrough curves for different vapor concentration. The simple model of Klinkenberg, giving c/cF as a function of dimensionless time τ, and dimensionless bed length ξ, was not worse than the more sophisticated model, and could be known as adequate for preliminary design purpose. The analysis of mass-transfer resistance indicated that water adsorption on cornmeal was controlled by the internal mass-transfer resistance for both the low and high velocity at the end of the breakthrough curves. Appendix A. Nomenclature
c cF c* Di Dp erf(x) G k kc K Pi Pis Pi /Pis q q¯ q*
concentration of water (mol m−3 ) concentration of water in feed vapor (mol m−3 ) concentration in equilibrium with average loading q¯ (mol m−3 ) molecular diffusivity (m2 s−1 ) diameter of adsorbent (m) error function mass velocity of vapor (kg m−2 s−1 ) overall mass-transfer coefficient (s−1 ) external mass-transfer coefficient (m/s) adsorption equilibrium constant for water in a linear adsorption isotherm partial pressure for component i at the adsorption temperature (Pa) vapor pressure for component i at the adsorption temperature (Pa) the relative humidity for component i water adsorption capacity (mol m−3 ) average loading of adsorbent for water (mol m−3 ) adsorbate loading in equilibrium with the solute concentration c in the bulk fluid (mol m−3 )
Re Rp Sy Sci Sh u u0
Reynolds number = Dp G/µ radius of adsorbent (m) standard deviation for the prediction Schmidt number = µ/ρDi Sherwood number = kc Dp /Di effective velocity of vapor (m/s) superficial velocity of vapor (m/s)
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