In the Laboratory
W
Dynamic and Equilibrium Adsorption Experiments Daniel L. A. Fernandes Departamento de Química, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal Ana M. R. B. Xavier QOPNA, Departamento de Química, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal Inês Portugal, Francisco A. Da Silva, and Carlos M. Silva* CICECO, Departamento de Química, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal; *
[email protected] www.JCE.DivCHED.org
•
study: Heterogeneous Catalysis, Separation Processes II, and Laboratory EQ4. Laboratory EQ4 is a weekly, six-hour laboratory where students are divided into groups of three. Each experiment lasts two weeks: in the first week students carry out the lab exercise and in the second week students do numerical calculations and simulations, which usually require computational support. Students assessment is based on an individual oral quiz and a report prepared by the student groups. In this article we present a low-cost experiment that illustrates the adsorption process from solution and its quantitative treatment. The system consists of glass microspheres, the adsorbent, and aqueous solutions of an organic dye, crystal violet (CV). The intense color of these solutions allows the students to visualize the propagation of the concentration profiles along the column. In previous articles (3–5) some authors selected the CV– sand system to illustrate, for instance, equilibrium and kinetic studies of adsorption and the determination of the specific surface area of adsorbents. Farooq (2) published breakthrough measurements for gas mixtures. As general reference we cite the book of Ruthven (1), which presents a summary and review of adsorption separations processes, covering both fundamental principles and industrial practice. The main objectives of this article are: (i) the determination of the adsorption isotherm, (ii) the measurement of the percolation parameters from the breakthrough curves, and (iii) the dynamic simulation of the column, using approximate and exact models. Theoretical Background
feed
0
Time
packed bed
efluent
Concentration
The partial differential equation representing the dynamic behavior of the column is obtained by a mass balance
Concentration
Adsorption, ion exchange, and chromatography are widespread operations in the chemical process industry, where some solutes are selectively transferred from the fluid phase to solid particles suspended in a vessel or packed in a column. This last arrangement is usually called percolation and produces a nearly solute-free effluent until the adsorbent in the bed approaches equilibrium and the solute breaks through the column (1). Adsorption processes have a wide range of applicabilities, from purifications to bulk separations. Their importance results partially from the capability adsorption beds have to incorporate large numbers of separation stages into modestsized equipment. Adsorption is particularly attractive to remove dilute components economically. In waste treatment and environmental applications the merits of adsorption processes rest on the ability to reduce the concentration of toxic solutes in effluent streams manyfold, sufficiently to permit release of the fluid, and upon their ability to concentrate the toxic materials to such a level that disposal, destruction, or subsequent use will be less costly. It is also an important alternative to distillation when the components have very close volatilities. For instance, the separation of propane and propylene can be accomplished by distillation, but at the expense of more than 100 trays and a reflux ratio of greater than 10. Some examples of commercial adsorption separations may be cited: (i) bulk gas separations (e.g., O2兾N2; hydrocarbons/vent streams), (ii) bulk liquid separations (e.g., normal paraffins兾 isoparaffins; fructose兾glucose; citric acid兾fermentation broth), (iii) gas purifications (e.g., SO 2 兾vent streams; sulfur compounds兾natural gas, hydrogen; odors兾air; hydrocarbons, halogenated materials, solvents兾vent streams), (iv) liquid purifications (e.g., dehydration of organics: H2O兾organics; water purification: organics兾H2O; decolorizing petroleum fractions, syrups, vegetable oil, etc.). The understanding of the dynamic behavior of a percolation column can be achieved following the chemical engineering approach, that is, solving conservation equations, equilibrium relations at the fluid–solid interface, kinetic laws of mass and heat transfer, and boundary and initial conditions (1, 2). Therefore it is possible to calculate bed profiles and breakthrough curves. The breakthrough curves refer to the response of an initially clean bed to a step change in the influent composition (Figure 1). When and how this breakthrough occurs is the focus of this article. Undergraduate students in the department of chemistry at University of Aveiro receive lectures on adsorption fundamentals and applications as part of three courses of their
0
Time
Figure 1. Input and output concentrations for a breakthrough experience.
Vol. 82 No. 6 June 2005
•
Journal of Chemical Education
919
In the Laboratory
on the solute for the fluid flow through a differential adsorption bed length, dz, over a differential time duration, dt. Assuming: (i) plug flow of the fluid (no axial dispersion) with constant interstitial velocity, u, (ii) instantaneous equilibrium of the solute at solid–liquid interface, and (iii) isothermal operation, the governing equation is u
∂ C ∂ C 1 − ε ∂ q + + = 0 ∂ z ∂ t ε ∂ t
(1)
where C is the solute concentration in the bulk liquid, q is the loading per unit volume of adsorbent in the bed, and ε is the bed porosity. There is an external or film resistance to mass transfer surrounding each glass microsphere. This gives rise to a concentration driving force, C − Cs, where Cs is the solute concentration at the interface, which generates a molar flux of solute, NA, calculated by
NA = kc (C − C s )
(2)
where kc is the convective mass transfer coefficient, estimated by correlations involving dimensionless groups (i.e., Sherwood, Reynolds, and Schmidt numbers). The accumulation of CV on the glass spheres may be now written as
∂ q = kc av (C − C s ) ∂ t
q max
t = 0 ⇒ C = q = 0 for z > 0
The simultaneous solution of eqs 1, 3, 4, and 5 gives the solute concentration profiles for both the fluid and adsorbent phases as function of position and time; that is, C = C(t, z) and q = q(t, z). Note that the breakthrough curves correspond to profiles at column exit (z = L):C = C(t, z = L). In this experiment, the solution is obtained by numerical integration using the method of lines (6). The z coordinate is divided into N increments or N + 1 grid points evenly spaced. Therefore the problem reduces to a set of ordinary differential equations of the initial-value type with time as an independent variable. The finite-difference approach has been adopted with central differences of second order. For the particular case of linear isotherm, q = mCs, and constant interstitial velocity, u, there exists an exact analytical solution in terms of Bessel functions owing to Anzelius. A useful approximation is that of Klinkenberg (7) C 1 = 1 + erf C0 2
KCs = 1 + KCs
MTZ
C /C0
t3
t4
tbp
t5
0 0
L
Distance, z
C /C0
1
area 2
C /C0 = 0.05
area 1
0
ξ ≡
tbp
tst
t
τ ≡
8 τ
+
1 8 ξ
(6)
kc av u
1− ε z ε
(7a)
kc av z t − m u
(7b)
∞
Figure 2. Movement of solute wave front: concentration–distance profiles and corresponding breakthrough curve: MTZ is the mass transfer zone, tbp is the breakthrough point, and tst is the stoichiometric time.
Journal of Chemical Education
1
Equation 6 is accurate to less than 0.6% error for ξ > 2.0. Figure 2 shows typical solute concentration profiles for the fluid as a function of distance through the bed at increasing times t1, t2, t3, and so forth. The corresponding breakthrough curve is also represented. From this experiment it is possible to determine important percolation parameters, such as the breakthrough point, stoichiometric time, length of unused bed, and width of the mass transfer zone (MTZ). The breakthrough point, tbp, identifies the moment at which the exit concentration reaches a predefined small value, for example 0.05C0. Hence, C (t = tbp, z = L) = 0.05C0. The stoichiometric time, tst, corresponds to the mean residence time obtained by numerical integration of the breakthrough curve
Time, t
920
ξ +
(4)
1
t2
τ −
where erf(x) denotes the error function; ξ and τ are the dimensionless distance coordinate and the dimensionless time coordinate corrected for displacement, respectively,
where K is the adsorption equilibrium constant and qmax is
t1
(5)
z = 0 ⇒ C = C 0 for t ≥ 0
(3)
where av = 6兾Dp is the external surface area兾volume of the particle and Dp is the particle diameter. For this system the equilibrium found between q and Cs is well represented by a Langmuir isotherm (5) q
the maximum loading corresponding to complete surface coverage by CV. The initial and boundary conditions of the problem are
•
t st =
1 − 0
C dt C0
(8)
It is graphically determined in Figure 2 by positioning the
Vol. 82 No. 6 June 2005
•
www.JCE.DivCHED.org
In the Laboratory
breakthrough curve for equal areas; that is, area 1 is equal to area 2. The experimental value should be compared with the theoretical prevision given by material balance over an ideal equilibrated bed according to
purge line
peristaltic pump
tst
L 1 − ε q0 =
1 + u ε C0
(9)
where q0 is the equilibrium adsorbed quantity corresponding to feed concentration C0. The MTZ of the bed is also represented in Figure 2. It is the region where concentration is changing and thus mass transfer is occurring. The zone is somewhat arbitrarily defined, since it is hard to tell exactly where it starts and ends. In this experiment the width of the MTZ is calculated for a range of C兾C0 from 0.95 to 0.05. Owing to the span of the concentration front, not all adsorbent is in equilibrium with the feed stream along the bed. There is a length of unused bed (LUB) for the separation, which is approximately one half of the MTZ, and can be determined as
LUB =
t st − t bp t st
L
A
30 °C
jacketed adsorption column
microsphere packed bed
) + (1.0906 × 10 A)
2
−2
mol m3
(11)
Breakthrough Curves The experimental apparatus for breakthrough measurement is shown in Figure 3. It consists of a jacketed glass column packed with the adsorbent and a variable-speed peristaltic pump to feed the pre-thermostatized CV solution. The absorbance of the effluent stream is measured at 590 nm. The column is kept at 30 ⬚C with a thermostatic water bath. When the column achieves equilibrium at the feed concentration, the feed is changed to ethanol兾water (1:1) for desorption. The CV solutions are prepared with previously deaerated distilled water to protect column from gas-bubble formation. The experimental conditions for the breakthrough measurement are listed in Table 1. www.JCE.DivCHED.org
feed tank
spectrophotometer
efluent
Adsorption Isotherms Different precise volumes of a CV stock solution are added to four flasks and filled to 500 cm3 with distilled water, resulting in concentrations in the range 1.2 × 10᎑3–1.2 × 10 ᎑2 mol兾m 3 . Accurately weighted samples of glass microspheres (∼100 g) are then added to each flask. The capped flasks are placed in a thermostatic water bath at 30 ⬚C with mechanical shaking during 24 hours to reach equilibrium. After this period, the absorbance of the supernatant solutions is measured at the λmax of the dye (590 nm); the calibration curve of the spectrophotometer at 30 ⬚C is:
(4.3119 × 10
thermostatic bath
(10)
Chemicals, Adsorbent, and Equipment The chemicals, materials, and relevant characteristics of the equipment used are found in List 1.
C =
feed
water flow for jacket
Experimental Procedure
−3
buffer tank
•
Figure 3. Schematic of the experimental setup. List 1. Chemicals, Materials, and Equipment Used in the Experiment Chemicals Crystal violet (CV) Ethanol Deaerated distilled water Adsorbent Characteristics of Glass Microspheres Averaged diameter/m 3
0.925 x 10᎑3
Density/(kg/m )
2460
External surface area/(m2/m3)
6486.5
Bed porosity
0.367
Equipment Jacketed adsorption column
Made in glass shop
Column internal diameter/m
0.0195
Column length/m
0.4
Peristaltic pump
Gilson – Minipuls 3
Thermostatic water bath
J. P. Selecta – Digiterm 100
Spectrophotometer
Jenway 6300
Table 1. Experimental Conditions for the Breakthrough Measurement Condition
Magnitude
CV feed concentration/(mol/m3)
0.0025
Temperature/K
303.15
Adsorbent load/kg
0.186
Volumetric flow rate/(m3/s)
6.102 ⫻ 10᎑7
Vol. 82 No. 6 June 2005
•
Journal of Chemical Education
921
q / (10ⴚ3 mol/m3)
In the Laboratory 40
Hazards
35
Crystal Violet is toxic and irritating to the respiratory system and skin, as well as dangerous for the environment. Proper attention and caution should be taken when handling ethanol, as it is flammable and irritating to eyes, respiratory system, and skin. Gloves and safety glasses are needed during the lab exercise. Students must review the Materials Safety Data Sheet for each chemical before starting the experiment and are instructed to collect wastes in specific tanks to be subsequently treated by the department of chemistry.
30 25 20 15 10
Results and Discussion
5 0 0
4
2
6
ⴚ3
C / (10
8
10
3
mol / m )
Figure 4. Adsorption isotherm of Crystal Violet on glass microspheres at 30 ºC. The line represents the fitted Langmuir isotherm.
1.0
0.8
C /C0
0.6
0.4
0.2
0.0 1000
0
2000
3000
4000
Time / s Figure 5. Experimental and simulated breakthrough curves: 䊊 experimental data; ___ proposed model; — - - Klinkenberg model; - - ideal breakthrough at t = tst.
Table 2. Results and Data Needed for the Calculations Quantity
Magnitude
Molecular weight of CV/(g/mol)
407.996
Binary diffusion coefficienta/(m2/s)
4.6 x 10᎑10
Mass transfer coefficient /(m/s)
1.205 x 10᎑5
Experimental stoichiometric time/s
1237
Theoretical stoichiometric time/s
1228
Breakthrough point/s
684
b
Length of unused bed/m
0.179
Width of mass transfer zone/m
0.4031
a
Estimated by Wilke–Chang equation (9).
b
Estimated by Wakao–Funazkri correlation (10).
922
Journal of Chemical Education
•
Adsorption Isotherm The adsorption isotherm at 30 ⬚C is shown in Figure 4. The points represent experimental data and the line is the fitted Langmuir isotherm, whose parameters are q m = 0.044511 mol兾m3 and K = 432.75 m3兾mol (see eq 4). The linearized isotherm to be used with the approximate model of Klinkenberg is q = 10.50C. It is regressed in the range (0:0.0025) mol兾m3 (i.e., from zero to the feed concentration). Breakthrough Curves The experimental breakthrough curve is shown in Figure 5, together with: (i) the ideal breakthrough, (ii) the approximate linear model by Klinkenberg (eqs 6 and 7), and (iii) the numerical solution of the proposed model (eqs 1– 5). The results and all data needed for the modeling calculations are listed in Table 2. The stoichiometric time obtained by numerical integration of experimental data (eq 8) is 1237 s and is almost coincident with that estimated by eq 9 (tst = 1228 s; 0.7% error). Both values are represented by dotted vertical line in Figure 5. The breakthrough point is 684 s and the length of unused bed 0.179 m, thus the column efficiency is 55.2%. The students are asked to interpret these results from a scale-up point of view. Isotherms that are convex upward are called favorable, since in the absence of dispersive phenomena (such as axial dispersion and resistance to mass transfer) the step-function feed propagates ideally without change along the adsorption bed and exits the column tst seconds later. Therefore, the ideal breakthrough is merely a displaced step signal: C = C0H(t − tst), where H(t) represents the Heaviside function. Accordingly, the doted line in Figure 5 identifies the ideal response of our column. The differences found between step output and experimental breakthrough curve suggest that mass transfer limitations occur in the system. The effect of axial dispersion may be completely neglected, as the axial Peclet number was estimated as 865 (8). The compressive character of the Langmuir isotherm is also shown in Figure 5, since the numerical solution of the proposed model is clearly sharper than the analytic solution by Klinkenberg. In fact, the unique difference between the two is the type of isotherm: Langmuir versus linear. The model proposed in this work accomplishes good approximation to the experimental data. It is important that the students understand that no parameters have been optimized. The model is purely predictive, as diffusivity and the convective mass transfer coefficient are estimated.
Vol. 82 No. 6 June 2005
•
www.JCE.DivCHED.org
In the Laboratory
Conclusions
the oral quiz, and the Matlab computer code, (version 6.1) to solve the proposed model.
The presented laboratory experiment introduces the students to the determination of a single component equilibrium isotherm and the study of the dynamic behavior of a percolation column. The most important parameters, breakthrough point, stoichiometric time, length of unused bed, and width of the mass transfer zone can be measured from the experimental breakthrough. Concerning modeling, a comparison is carried out between ideal, Klinkenberg, and exact models. Examining experimental results and theoretical previsions the students gain insight in this important process operation. Acknowledgment We thank António Morais, the technician responsible for the glass workshop. W
Supplemental Material
The following materials are available in this issue of JCE Online: experimental procedures for instructors, questions for
www.JCE.DivCHED.org
•
Literature Cited 1. Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons: New York, 1984. 2. Farooq, S. Chem. Eng. Educ. 1998, 32, 76–81. 3. Casado, J.; Salvador, F.; Rincón, S. J. Chem. Educ. 1985, 62, 800–801. 4. Brina, R.; De Battisti, A. J. Chem. Educ. 1987, 64, 175– 176. 5. Duff, D. G.; Ross, M. C.; Vaughan, D. M. J. Chem. Educ. 1988, 65, 815–816. 6. Schiesser, W. E. The Numerical Method of Lines; Academic Press: New York, 1991. 7. Klinkenberg, A. Ind. Eng. Chem. 1954, 46, 2285–2289. 8. Levenspiel, O. Chemical Reaction Engineering; John Wiley & Sons: New York, 1999. 9. Wilke, C. R.; Chang, P. AIChE J. 1955, 1, 264. 10. Wakao, N.; Funazkri, T. Chem. Eng. Sci. 1978, 33, 1375.
Vol. 82 No. 6 June 2005
•
Journal of Chemical Education
923
