Correlation-Based Approach to the Optimization of Fixed-Bed Sorption

Nov 6, 1999 - The effects of process variables such as bed height, flow rate, initial concentration, ... height, and particle size on a fixed-bed bone...
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Ind. Eng. Chem. Res. 1999, 38, 4868-4877

Correlation-Based Approach to the Optimization of Fixed-Bed Sorption Units Danny C. K. Ko, John F. Porter, and Gordon McKay* Department of Chemical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

The sorption of copper, zinc, and cadmium ions onto bone char in fixed-bed columns has been studied. The effects of process variables such as bed height, flow rate, initial concentration, percentage breakthrough, and particle size have been investigated. The results have been used to predict the effect of parameter changes on the system by using the bed depth service time (BDST) approach. After the BDST results are obtained, the system variables can further be optimized based on the adsorbent exhaustion rate and the empty bed residence time (EBRT). The correlations for operating lines of the EBRT plot have been proposed and tested on three metal ion sorption systems. The mechanism of the metal ion sorption on bone char was also investigated. Introduction One of the byproducts of modernization is pollution. Numerous industrial processes1 produce enormous amounts of aqueous effluents containing toxic and poorly degradable compounds. Scientists and engineers are working hard to keep pace with the ever-increasing legislative standards. Heavy metal ions, because of their toxicity and cumulative effects on living organisms, arouse lots of environmental concerns. The most common methods of removal of metals from industrial effluents include chemical precipitation, reverse osmosis, ion-exchange resins, and adsorption. Precipitation is one of the most traditional treatment methods employed to remove heavy metals. A common hindrance to effective precipitation is the formation of soluble metal complexes with chelating agents. Maintenance of pH throughout the precipitation reaction and subsequent settling is essential, thus slowing down the time for the treatment process and making the process less flexible. Ion exchange is another method used to treat metalcontaining effluents. Cation-exchange resins are used to replace the positively charged metal ions by hydrogen ions. However, each ion-exchange resin is characterized by a selectivity series which has a specific action for selected metal ions. Compared with the above methods, adsorption has demonstrated efficiency and economic feasibility as a wastewater treatment operation. Three types of contacting systems of adsorption are usually encountered, which are the batch, fixed-bed, and fluidized-bed processes.2 Batch-type processes are usually limited to the treatment of small volumes of effluent, whereas the bed-column systems have an advantage of continuous operation. Fluidized beds for effluent treatment can have high mass-transfer rates but suffer from relatively short residence times, leading to rapid breakthrough. Because fixed-bed processes can provide continuous treatment with a long breakthrough time, they are widely used in wastewater treatment processes. The design of industrial adsorption towers requires substantial quantities of information, and usually all * To whom correspondence should be addressed. E-mail: [email protected]. Phone: (852)23587133. Fax: (852)23580054.

of the preliminary design information is gathered in an extensive series of pilot-plant experiments that are timeconsuming and expensive. The purpose of conducting pilot-scale column runs is to predict what will happen in a full-scale column with various design and operating parameters. These parameters include linear flow rate, feed and product concentrations, bed height, particle size, type of adsorbents, pH, temperature, and viscosity. With varyiation of the above parameters, the optimum conditions for the column operation can be predicted through different design methods. Several models based on fundamental mass transport mechanisms, including external film, pore, and surface diffusion, have been proposed3-10 but require the solution of a number of differential equations. In addition, these solutions also require accurate correlations for mass-transfer parameters11-15 to describe external film, internal pore diffusion and the equilibrium relationship between sorbate and sorbent. There are several simplified design models available16,17 which are based on general assumptions and lumped mass-transfer parameters. The use of simplified design models has been the basis for the present work. The bed depth service time (BDST) model18,19 and the empty bed residence time (EBRT) model3,20 are two common design approaches selected in this work which are used to predict and optimize the fixed-bed column operation, respectively. By using these short-cut models, pilot-plant testing could be used largely for verification rather than information gathering, saving time and money. In this paper, three metal ion systems, namely, copper(II), zinc(II), and cadmium(II), were studied, and the effects of linear flow rate, solute concentration, bed height, and particle size on a fixed-bed bone char column were presented in this paper using the BDST and EBRT models. Mathematical equations for the operating line of the EBRT optimization model will be postulated, and the mechanism of the metal ion sorption on bone char will be discussed. Experimental Section As example systems, the sorption of three metal ions onto bone char was studied. Copper (Cu2+), cadmium

10.1021/ie9902784 CCC: $18.00 © 1999 American Chemical Society Published on Web 11/06/1999

Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4869 Table 1. Properties of Bone Char (Source: Tate and Lyle Ltd.) carbon (%) acid-insoluble ash (% max) moisture (% max) hydroxyapatite (%) calcium carbonate (%) calcium sulfate (%) iron(III) oxide (% max) total surface area (m2/g) carbon surface area (m2/g) pore size distribution (nm) pore volume (cm3/g) bulk density (dry) (kg/m3)

9-11 3 5 70-76 7-9 0.1-0.2 0.3 100 50 7.5-60 000 0.225 640

∂C/∂Z ) -(k/v)qC

(2)

Because the volumetric sorption capacity is given by N0 ) qe, after integration of eqs 1 and 2, the proposed relationship between bed depth, Z, and service time, t, in terms of process concentrations and sorption parameters is shown by eq 3,

ln(C0/Cb - 1) ) ln(ekN0Z/v - 1) - kC0t

(Cd2+), and zinc (Zn2+), were used as single-component sorbates from the salt solutions: copper sulfate, cadmium sulfate, and zinc sulfate with deionized water. The bone char was provided by Brimac (Tate and Lyle Ltd.) and was derived from charred animal bones at 500-600 °C. The properties of the bone char are given in Table 1. The bone char was sieved into discrete particle size ranges, and the ranges of 355-500, 500710, and 710-1000 µm were used in the experiments. The adsorber beds were made of Perspex tubes of 4.5 cm internal diameter and 25 cm height. An adsorbentretaining sieve of 65 mesh size was fixed in the lower part of the column, and then 2 mm diameter ballotini balls were placed at the column base in order to provide a uniform inlet flow of solution into the column. A weighed amount of adsorbent was tapped well within the column, and then an upper retaining sieve of 65 mesh size was inserted on top of the bed and firmly secured in place by a 2 mm diameter ballotini, followed by larger ballotini on top of a retaining screen. The metal ion salts to be contacted with the adsorbent were weighed out, added to the water tanks, and mixed well. The metal ion solution could then be pumped vertically upward inside the column to avoid channeling due to gravity and to enhance uniform distribution of solution throughout the column. Rotameters were calibrated to give the correct flow rate which was maintained constant during each experiment. Periodic flow rate checks were carried out by physically collecting samples of solution at the outlet for a given time and weighing the amount collected. Sample points were located at 5 (point A), 10 (point B), 15 (point C), 20 (point D), and 25 cm (point E) height in the column enabling a series of 10 cm3 sample syringes to be used to withdraw samples from the center point of the bed for analysis. Samples were taken at time intervals ranging from 15 min to 0.5 h until the metal ion concentration was at the breakthrough point at the top of the bed. The metal ion concentrations were determined using inductively coupled plasma atomic emission spectrophotometry (ICP-AES) at wavelengths corresponding to the maximum sensitivity for each metal ion. This procedure enabled the breakthrough curves to be obtained. Theoretical Background The data were analyzed using a model originally proposed by Bohart and Adams21 for the adsorption of chlorine and hydrogen chloride on carbon. Considering a given portion of adsorbing material, its adsorption capacity diminishes at a rate given by

∂q/∂t ) -kqC

Considering the solute phases, the solute concentration is diminishing at a rate given by

(1)

(3)

Because the exponential term, ekN0Z/v, is usually much higher than unity, the unity term within the brackets on the right-hand side of eq 3 is often neglected. A linear relationship between the bed depth and service time can be written as

t)

(

)

C0 N0Z 1 ln -1 C0v kC0 Cb

(4)

For the current system, the critical bed depth, Z0, is the theoretical depth of bone char sufficient to prevent the solute concentration from exceeding the Cb value at t ) 0. By letting t ) 0 in eq 4, Z0 is obtained:

Z0 )

(

)

C0 v ln -1 kN0 Cb

(5)

According to eq 4, the service time, t, and the bed depth, Z, can be correlated with the process parameters: the initial solute concentration, the solution flow rate, the adsorption capacity, and the adsorption rate constant. Equation 4 is the BDST equation with the form of straight line t ) mZ + b, as suggested by Hutchins.18 Thus, the slope of the BDST plot, which equals N0/C0v, is the time required to exhaust a unit length of the sorbent in the column under the test condition. The intercept on the ordinate, called b, is the time required for the adsorption wave front to pass through the critical bed depth and is given by

b)

( ) (

C0 -1 ln -1 kC0 Cb

)

(6)

Results and Discussion Column Operation. Inside the column, it is assumed that there is no variation of the axial liquid velocity and solute concentration in the radial direction. Cooney19 suggested that the column diameter to the particle diameter ratio should be on the order of 20 or higher, such that the effects of channeling at the wall and random variations in the interstitial velocity within the bed become negligible. The column diameter to the particle diameter ratio for this experiment ranges between 53 and 105, which is far above the requirement. The Reynolds number based on an empty column for the largest flow rate used is 45, which ensures the flow is laminar inside the column. The general range of metal ions selected for study is that found in the medium concentration range in the PCB electronics and electroplating industries; these require relatively large amounts of chemicals but relatively low concentration for conventional electrolytic recovery.

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Figure 1. Breakthrough curves for a bone char column (500-710 µm) with 4 mmol/L CdSO4 flowing at 50 mL/min.

Figure 2. BDST plot for three metal ions at 50% breakthrough. Table 2. Change of Sorbate for C0 ) 3 mmol/L, Mean dp ) 605 µm, and Flow Rate ) 50 mL/min at 50% Breakthrough metal ion

slope m (min/cm)

y intercept b (min)

x intercept Z0 (cm)

correlation coefficient (r2)

N0 × 104 (mg/L)

BDST capacity (mg/g)

k × 10-3 (L/mg‚h)

min EBRT R (s)

min ads. exhaustion rate, β (g/dm3)

γ

Cu Zn Cd

67.8 49.7 42.8

72.0 56.5 66.0

1.06 1.14 1.54

0.9997 0.9996 0.9997

4.06 3.07 4.54

46.1 34.9 51.6

15.8 19.7 11.3

40 40 40

4.1 5.2 6.7

80 160 190

Figure 1 is a typical plot of data obtained for the sorption of cadmium ions onto bone char for the five bed heights 5, 10, 15, 20, and 25 cm at a flow rate of 50 mL/min. BDST Model.2,18,19,22 Figure 2 shows the BDST plots for three metal ions with a concentration of 3 mmol/L, a flow rate of 50 mL/min, and a breakthrough of 50% for different bed heights. The variations of the curves and constants demonstrate that the three metal ions have different sorption capacities. The coefficients N0 and k for different systems can be calculated based on eq 6. The slopes and intercepts for the BDST plots for different process variables are shown in Tables 2-6. Critical Bed Depth. Critical bed depth Z0 is defined

as the minimum depth for obtaining satisfactory effluent at time zero under the test operating conditions.18 Z0 can be found by setting t ) 0 in the eq 4, and the resulting equation is shown in eq 5. Thus, Z0 can be read directly from the BDST plot as the intercept on the bed depth (x) axis. From the experimental data in Table 3, it is found that Z0 is directly proportional to the linear flow rate v, as predicted from eq 5. Doubling the flow rate will increase Z0 by approximately 3 times for both copper and zinc ions and 2.5 times for the cadmium ion. Because for a large linear flow rate the amount of time available for adsorption to take place is less, the residence time for adsorption is also smaller. Thus, a large Z0 results.

Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4871 Table 3. Change of Volumetric Flow Rate for C0 ) 3 mmol/L and Mean dp ) 605 µm at 50% Breakthrough metal ion

vol. flow rate (mL/min)

slope m (min/cm)

y intercept b (min)

x intercept Z0 (cm)

correlation coefficient (r2)

N0 × 104 (mg/L)

k × 10-3 (L/mg‚h)

min EBRT R (s)

min ads. exhaustion rate, β (g/dm3)

γ

Cu Cu Cu Cu Zn Zn Zn Zn Cd Cd Cd Cd

50 75 100 125 25 50 75 100 25 50 75 100

67.8 45.8 33.8 26.6 110 49.7 32.8 23.4 87.5 42.8 26.7 19.7

72.0 93.0 116 163 43.0 56.5 66.0 73.0 55.5 66.0 67.5 77.5

1.06 2.03 3.43 6.13 0.39 1.14 2.01 3.12 0.63 1.54 2.53 3.93

0.9997 0.999 0.9958 0.9974 0.9997 0.9996 0.9994 0.9986 0.9997 0.9997 0.9991 0.9989

4.06 4.11 4.05 3.98 3.38 3.07 3.03 2.89 4.64 4.54 4.25 4.18

15.8 12.2 9.81 6.98 25.9 19.7 16.9 15.3 13.4 11.3 11.0 9.63

40 27 20 16 80 40 27 20 80 40 27 20

4.1 4.1 4.1 4.1 5.2 5.2 5.2 5.2 6.7 6.7 6.7 6.7

80 120 160 200 80 160 240 320 95 190 285 380

Table 4. Change of C0 for Mean dp ) 605 µm and Flow Rate ) 50 mL/min at 50% Breakthrough metal ion

C0 (mmol/L)

slope m (min/cm)

y intercept b (min)

z intercept Z0 (cm)

correlation coefficient (r2)

N0 × 104 (mg/L)

k × 10-3 (L/mg‚h)

min EBRT R (s)

min ads. exhaustion rate, β (g/dm3)

γ

Cu Cu Cu Cd Cd Cd

2 3 4 2 3 4

90.0 67.8 52.2 60.6 42.8 30.9

56.0 72.0 94.0 89.0 66.0 65.5

0.62 1.06 1.80 1.47 1.54 2.12

0.9996 0.9997 0.9993 0.9994 0.9997 0.9999

3.59 4.06 4.17 4.28 4.54 4.37

26.9 15.8 9.82 11.4 11.3 9.14

40 40 40 40 40 40

2.7 4.1 5.5 4.5 6.7 9.0

53 80 107 175 260 350

Table 5. Change of Particle Sizes for C0 ) 4 mmol/L and Flow Rate ) 50 mL/min at 50% Breakthrough metal ion

dp (µm)

slope m (min/cm)

y intercept b (min)

x intercept Z0 (cm)

correlation coefficient (r2)

N0 × 10 (mg/L)

k × 10-3 (L/mg‚h)

min EBRT R (s)

min ads. exhaustion rate, β (g/dm3)

γ

Cu Cu Cu Cd Cd Cd

427.5 605 855 427.5 605 855

52.6 52.2 51.8 31.4 30.9 30.3

73.0 94.0 107 62.0 65.5 71.5

1.39 1.80 2.07 1.97 2.12 2.36

0.9982 0.9993 0.9999 0.9999 0.9999 0.9993

4.20 4.17 4.14 4.44 4.37 4.28

12.6 9.82 8.63 9.66 9.14 8.38

40 40 40 40 40 40

5.5 5.5 5.5 9.0 9.0 9.0

85 107 135 280 350 440

Table 6. Change of Percentage Breakthrough for C0 ) 3 mmol/L and dp ) 605 µm metal ion

vol. flow rate (mL/min)

percentage breakthrough

slope m (min/cm)

y intercept b (min)

x intercept Z0 (cm)

correlation coefficient (r2)

N0 × 104 (mg/L)

k × 10-3 (L/mg‚h)

Cd Cd Cd Cd Cd Cd

25 25 25 100 100 100

20 40 60 20 40 60

82.4 86.6 93.8 11.7 16.3 22.5

247 139 21.0 51.0 66.5 65.5

3.00 1.61 0.22 4.36 4.08 2.91

0.9993 0.9997 0.9996 0.9975 0.9984 0.9995

4.37 4.59 4.97 2.48 3.46 4.77

3.02 5.37 35.5 14.6 11.2 11.4

Change of Solute Content. In this experiment, three metal ions are being tested. For the same number of moles of metal ions, the slope of the BDST plots is inversely proportional to the ionic radii of the metal ions. The larger the ionic radii of the metal ion, the smaller the slope, which means a higher bone char exhaustion rate. From the isotherm studies, the equilibrium adsorption capacity (in terms of gram of solute per gram of solid) for copper, zinc, and cadmium are 50, 37, and 64 mg/g, respectively. The BDST capacities for these three metal ions, which is calculated from the quotient of the corresponding bed adsorption capacity N0 by the bed density, equal 46.1, 34.9, and 51.6 mg/g, respectively. These bed adsorption capacities found from the experiments also match the equilibrium isotherm data. For fixed-system operating parameters, the y intercept, which is related to the rate constant k, depends on the physical and chemical properties of the solute. For instance, the ionic radii, the electronegativity, and the affinity of the solute ion onto the sorption site are some determining factors which affect the sorption rate. All of these inter-related factors, where some of them have an opposite effect on each other,

make the prediction of the y intercept or the k value becomes difficult. Change of Linear Velocity v. It is obvious that the breakthrough time increases with decreasing flow rate. Thus, the service time for small flow rates will be longer and the slope of the BDST plot will be higher. Hutchins18 suggested that the new slope of the BDST plot be equal to the original slope multiplied by the ratio of the original and new flow rates. Numerically,

new slope ) old slope × (vold/vnew)

(7)

Table 3 gives the experimental data for cadmium removal at volumetric flow rates of 25 and 50 mL/min. In both cases, the initial cadmium concentration was 3 mmol/L. The slope of the BDST plot for 50 mL/min calculated from data at 25 mL/min is 43.8 min/cm. The new actual slope found in the experiment (42.8 min/cm) is only 2% less than predicted. The above correlation also works well in other flow rates for the three metal ion sorption systems in this study. The underlying reason is that when v increases, the residence time for adsorption is decreased and the concentration profile

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becomes broader. As a result, at column breakthrough, the bed utilization is reduced, the resulting value for the bed adsorption capacity N0 will be smaller, and the slope (N0/C0v) decreases. The effect of the change of v on the y intercept (-1/ kC0) ln(C0/Cb - 1) will be determined by the variation of k subject to changes in v. The rate parameter k is dependent on the effect of both external film diffusional mass transport, which varies with fluid velocity, and intraparticle diffusion which is independent of fluid velocity. The experimental result shows that the slope changes with flow rate, but the significance of this dependence varies from system to system. The dependence demonstrates that both intraparticle diffusion and external film diffusion are important rate-determining factors in the metal ion adsorption system, and therefore the k value and the y intercept will be affected by a change in v. If k is independent of v (for instance, the intraparticle diffusion is the dominant rate-controlling factor), then the y intercept will be independent of changes in v. Change of Feed Concentration C0. Altering C0 will change both the slope and the intercept of the BDST plot as indicated in eq 6. At a fixed breakthrough and defined operating conditions, the critical bed height will increase when C0 increases, which agrees with the experimental results. Hutchins18 also proposed the new slope for a higher concentration could be estimated by multiplying the old slope by the ratio of the two feed concentrations, i.e.

new slope ) old slope ×

( ) C0,old C0,new

(8)

And the new intercept will be

new intercept ) old intercept × C0,old ln[(C0,new/Cb) - 1] (9) C0,new ln[(C0,old/Cb) - 1]

( )

From Table 4, when C0 of the cadmium ion is changed from 2 to 4 mmol/L, the calculated slope is 60.6 × 2/4 ) 30.3 min/cm, where the actual slope computed from experiment is 30.9 min/cm. Using the criterion Cb ) 5 ppm, the estimated new y intercept for the Cd ion at 3 mmol/L calculated from those at 2 mmol/L is 65.8 min where the y intercept found from the experiment is 66 min. However, the prediction on the y intercept for the copper ion does not work well. The variation may suggest that the assumption for eq 9 in which k is constant with the change of C0 is not totally valid for all systems. Experiments23 have demonstrated that the contribution of surface diffusion as well as the effective pore diffusion coefficient decreases as the concentration increases. The experimental k values for all systems also decrease with increasing concentration, but the extent of change is different for different systems. This helps to explain why the correlation for predicting the intercept works for one case but not the other. In addition, the small deviation from prediction may be caused by the fact that the BDST theory is based on the Bohart/Adams equation which assumes a rectangular isotherm. The isotherms for the selected three metal ions are curved, not step function in shape. Thus, for the selected C0, the corresponding adsorption capacity q is less than the constant value of qs at the

horizontal part of the adsorption isotherm which is assumed to be constant for any concentration. Thus, the overall theoretical adsorption capacity of the bed N0 is overestimated, and the estimated slope and intercept may have some small inconsistencies. Change of the Particle Size of the Adsorbent dp. Bone char with particle sizes ranging from 355 to 500, 500 to 710, and 710 to 1000 µm was studied for the case of copper and cadmium ion adsorption. On the basis of the experimental results, the slope of the BDST plot will have a small decrease with an increase of the particle size. For the change of the particle size, a smaller particle size will have a faster pore diffusion rate because the diffusion path is shorter and the diffusion resistance is smaller. This correlated well with the results from the batch kinetic studies, which show the adsorption rate is higher with smaller particle size. From the isotherm studies, the adsorption capacities of these three metal ions for different particle sizes are similar because the change of the particle size will not have a significant change of the surface area for metal ion sorption to occur. The particle sizes ranging from 355 to 500 µm have a mere 2% increase in adsorption capacity compared with those ranging from 710 to 1000 µm, but the shape of the isotherm for smaller particle sizes is more rectangular. On the basis of the fact that a smaller particle size will have a higher rate of adsorption, the slope of the breakthrough curve for smaller particle size is higher. Therefore, because the adsorption capacity of bone char will have a small increase as the particle size decreases, the total volume treated at breakthrough will be higher for bone char with smaller particle sizes at a fixed operating condition, and the slope will be slightly higher as well. The y intercept shows an increase with increased particle size. The results again correlate well with the batch kinetic results, which show an increase in diffusivity in large adsorbent particles, but the degree of change is different for different metal ions. However, to a certain extent, the variation of the result may be caused by the change of the void fraction of the bed because of the change of the particle size. The above results suggest that using a finer particle size range would give a more efficient use of the bed, and more effluent solution will be treated before breakthrough; however, the pressure drop due to the smaller particle size will be more significant as shown by the Ergun equation, which is

(

)

dP v(1 - ) 150(1 - )µ + 1.75Fv ) dZ dp d 3 p

(10)

As predicted from eq 10, the finer particle size ranges will have a larger pressure loss, thus increasing the flow resistance of the bed, and the cost for the pumping system will increase accordingly. Change of Percentage Breakthrough. The prime objective of the fixed-bed column adsorption system is to reduce the solute concentration, and the degree of reduction in solute concentration is called the percentage breakthrough value. A small breakthrough value would mean having a small solute concentration in the effluent. Thus, as Cb increases, the volume of liquid treated would be larger and the adsorber would run longer. Theoretically, the value of Cb should not affect the slope of the BDST plots. This will happen when the breakthrough curves are steep and the mass-transfer zone is very short. However, practically, the slope of the

Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4873

breakthrough curves will change with the operating parameters. For example, when the flow rate is large, the mass-transfer zone will be large and the resulting breakthrough curve will be less steep. As a result, a change in percentage breakthrough will have a significant effect on the breakthrough time; thus, the slope of the BDST plots for different percentage breakthroughs at higher flow rates will have a larger variation than those at lower flow rates. In addition, the change of the slope for the BDST plot will be influenced by the “tailing effect” of the breakthrough curve when the breakthrough concentration is large. Cooney19 has demonstrated that the prediction for the BDST equation for the effect of different particle sizes is poor. The reason for the lack of agreement can also be described by the violation of the assumption of the BDST equation which assumes a rectangular isotherm. The lower the Cb value, the larger the discrepancy for the experimental and theoretical constant q value, and a larger error results. The result shows that the BDST theory is not accurate in predicting the effect of changes in percentage breakthrough. Therefore, the BDST result for the different percentage breakthroughs cannot be used in the EBRT model. EBRT Model.2,19,20,22 The EBRT model, or sometimes referred to as the empty bed contact time (EBCT), is a design procedure used to determine the optimum adsorbent usage in the fixed-bed adsorption column. McKay et al.2,20 proposed that the capital and operating costs of the adsorption system are almost entirely dependent on these two primary variables for a fixed liquid flow rate, impurity concentrations, and adsorbent characteristics. (i) The EBRT is the time required for the liquid to fill the column, on the basis that the column contains no adsorbent packing, and is a direct function of liquid flow rate and column volume.

EBRT (s) )

bed volume (11) volumetric flow rate of the liquid

(ii) The adsorbent exhaustion rate is the weight of adsorbent used in the column per volume of liquid treated at the time breakthrough occurs. That is

adsorbent exhaustion rate (g/dm3) ) mass of adsorbent used (12) volume of liquid treated at breakthrough These two variables were determined for both the copper and cadmium ion removal systems under different test conditions. Data used for the EBRT model can be obtained from the BDST analysis. Once a breakthrough percentage is specified, the service time for the column before breakthrough can be found and thus the adsorbent exhaustion rate and the EBRT at various adsorbent bed heights can be obtained. Then the adsorbent exhaustion rates are plotted against the EBRT values, and a single line relating these two variables is called the operating line. The minimum retention time and the minimum adsorbent exhaustion rate are obtained from the asymptotes of the operating lines. It is clear that when the EBRT increases with a fixed flow rate and mass of adsorbent used, the bed volume will have to be larger, thus allowing more solution to be treated and resulting in a lower adsorbent exhaustion rate. However, if the EBRT becomes larger (i.e., the

volumetric flow rate decreases), then the adsorbent will have more time to contact with the solution. When the EBRT value is so large that exhausted adsorbent is in equilibrium with the influent, the total volume of liquid treated at breakthrough will not increase with an increase of EBRT, and a constant EBRT, which corresponds to the minimum adsorbent exhaustion rate, will be obtained. On the other hand, the minimum retention time represents the minimum volume of adsorbent required to achieve the desired effluent concentration at infinitely high adsorbent exhaustion rate. For the adsorber system with fixed liquid flow rate, impurity concentration, and adsorbent characteristics, the total cost will mainly depend on the adsorbent exhaustion rate and the EBRT, which contribute to the operating cost and the fixed capital cost, respectively.20 It can be predicted that the lower the adsorbent exhaustion rate, the longer the EBRT and the smaller the amount of adsorbent needed per unit volume of feed treated, which implies a lower operating cost; however, a larger column will have to be used. In contrast, if the adsorbent exhaustion rate is large, the EBRT will be smaller and a small column is needed, which means a lower capital investment; nevertheless, the amount of adsorbent used will increase, which requires a higher operating cost. This economic tradeoff between the capital investment on the larger column and the savings on the adsorbent cost may be used to determine the size of the adsorption column. To select the optimum combination of adsorbent exhaustion rate and the liquid retention time, the operating line should first be established. However, there is no mathematical interpretation for the construction of the operating line and, needless to say, no predictive relationship of the operating line for different system variables found in the literature. In this paper, the method to obtain a mathematical equation for the operating line is presented, and the relationship with the equation variables and operating parameters will be postulated. On the basis of the fact that the operating line will approach a minimum at both axes and the relationship between the adsorbent exhaustion rate and the liquid retention time is inversely proportional, the following mathematical form of equation for the operating line is assumed:

(x - R)(y - β) ) γ

(13)

where x is the liquid retention time EBRT (s), y is the adsorbent exhaustion rate (g/dm3), R is the minimum liquid retention time (s), β is the minimum adsorbent exhaustion rate (g/dm3), and γ is a constant (s‚g/dm3). After rearrangement,

y)

γ +β x -R

(14)

On the basis of the experimental data set for x and y, the constants R, β, and γ are found by minimizing the sum of error squares for the predicted and the experimental value, ∑(ycal - yexp)2. After the constants are obtained, the operating line, which is the best-fit line for the experimental data following the pattern of eq 13, can be constructed. As suggested by eqs 13 and 14, the constant R is a function of column dimension and solute volumetric velocity and β, which occurs at infinite EBRT, is

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Figure 3. Effect of flow rate on the bone char exhaustion rate for cadmium ion removal. C0 ) 3 mmol/L; average dp ) 605 µm; 50% breakthrough.

determined by the quantity of adsorbent, the adsorption capacity of the adsorbent, and the concentration of the solute solution. The constant γ is a system parameter which changes with the system conditions. The experimental values for constant R, β, and γ are shown in Tables 2-5. Change of Linear Velocity v. The change of v will have an immediate effect on the EBRT, because the time required to fill up the column will be smaller for a large flow rate at a fixed-bed volume. A higher flow rate, which decreases the residence time in the bed, will result in lower bed utilization, thus a faster breakthrough will be attained and the volume of liquid treated will be smaller. As a result, the adsorbent exhaustion rate is higher for high flow rates. However, at any flow rate, an infinitely high EBRT corresponds to the infinite time required to fill up the column. This will allow the exhausted adsorbent to attain equilibrium with the influent liquid, and the corresponding minimum adsorbent exhaustion rate, β, should be independent of v. For the minimum EBRT, a larger flow rate will have a lower minimum EBRT, as predicted from eq 11. The change of constants with v is estimated by

( ) ( )

Rnew ) Rold

vold vnew

(15)

γnew ) γold

vnew vold

(16)

Figure 3 shows the EBRT plot for various flow rates of the cadmium ion solution. The solid operating line is constructed from the experimental data for a flow rate at 50 mL/min based on eq 13. The dotted lines are the predicted operating lines based on eqs 15 and 16 for flow rates 25, 75, and 100 mL/min. The predicted operating lines agree well with the experimental data, and similar agreement was also obtained for both the copper and zinc systems.

Change of C0. The EBRT is independent of the solute concentration; thus, at an infinite adsorbent exhaustion rate, the minimum EBRT, R, for all concentrations should be the same. However, the volume of liquid treated will be smaller for higher solute concentration, thus having a larger adsorbent exhaustion rate. For infinite EBRT, the minimum bone char exhaustion rate will depend on the equilibrium sorption capacity of the bed, which is a function of the solute concentration. Therefore, the proposed relationships for change of C0 are

( ) ( )

βnew ) βold

C0,new C0,old

(17)

γnew ) γold

C0,new C0,old

(18)

Figure 4 shows the EBRT plot for various concentrations of the copper ion solution. The solid operating line is constructed from the experimental data for concentration of 3 mmol/L based on eq 13. The dotted lines are the predicted operating lines based on eqs 17 and 18 for concentrations of 2 and 4 mmol/L. The predicted operating lines agree well with the experimental data for all concentrations, and similar agreement was also obtained for the cadmium system. Change of dp. The volume of liquid treated at breakthrough is about the same for different particle size ranges because their adsorption capacities for metal ions are similar. Thus, their minimum adsorbent exhaustion rate for different particle sizes is also about the same. Similarly, the minimum EBRT will not be affected by the change of particle sizes because EBRT is not a function of the adsorbent. However, the rate of achieving the minimum bone char exhaustion rate is different. Bone char with a smaller particle size attains the minimum exhaustion rate faster than fixed beds with larger particle size. Because the bed capacity is

Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4875

Figure 4. Effect of C0 on bone char exhaustion rate for copper ion removal. Flow rate ) 50 mL/min; average dp ) 605 µm; 50% breakthrough.

about the same, the different rate of attaining a minimum exhaustion rate would be due to the difference in time to reach saturation, which will be a function of the external film mass-transfer rate. The external masstransfer coefficient for a particle Reynolds number of the three different particle size ranges can be estimated using the correlation of Wilson and Geankoplis11 for a Reynolds number range of 0.0016-55 and a Schmidt number (NSc ) µ/FDAB) range of 165-70600:

1.09 NRe-2/3 JD ) 

(19)

where JD is the mass-transfer coefficient factor for flow outside the solid particle surface,  is the void fraction of the bed, NRe is the Reynolds number which equals Fv′dp/µ, v′ is the superficial velocity in the empty bed without packing, and µ is the viscosity of solute solution ) 1.005 × 10-3 N s m-2 for water at 20 °C. The diffusivity DAB of dilute solutes in liquids is expressed by24

T DAB ) 1.173 × 10-16(φBMB)1/2 µBVA0.6

(20)

where subscript A is the solute and B is the solvent, which is water in this case, MB is the molecular weight of solvent ) 18, φB is an “association parameter” of solvent ) 2.6 for water, T is the operating temperature ) 293 K, and VA is the solute molar volume at its normal boiling point25 in m3/kg‚mol (for water, VA ) 18.8 × 10-3 m3/kg‚mol). Assuming these dilute metal ion solutions have the same molar volume as water, the diffusivity equals 2.54 × 10-9 m2/s and NSc ) 396.6. For the mean particle diameters 427.5, 605, and 855 µm, the Reynolds number is equal to 0.223, 0.315, and 0.446, respectively, for a

flow rate of 50 mL/min. Thus, the influence of dp on the EBRT plot would be expressed as a function of particle NRe-2/3. The proposed relationship for constant γ is given as

( )

γnew ) γold

dp,new dp,old

2/3

(21)

Figure 5 shows the EBRT plot for various particle sizes of the cadmium ion solution. The solid operating line is constructed from the experimental data for bone char particle size ranging from 500 to 710 µm based on eq 13. The dotted lines are the predicted operating lines based on eq 21 for particle sizes ranging from 355 to 500 and 710 to 1000 µm. The predicted operating lines agree well with the experimental data for all selected particle size ranges, and similar good correlations were also obtained for the copper system. After the operating line is obtained, the next step will be finding the optimum point on the operating line. One useful way to obtain the optimum condition is by finding the EBRT which corresponds to the maximum adsorbent utilization rate in terms of the weight of pollutant removed per weight of adsorbent. Figure 6 shows that for a fixed operating condition such as flow rate and pollutant initial concentration, the bone char usage rate reaches an optimum high value which corresponds to an optimum EBRT. By taking the derivative of the equation of the best-fitted line, the optimum EBRT for the system can be determined. On the basis of this EBRT value, the dimensions of the column bed can be fixed accordingly. Mechanism of Metal Ion Sorption on Bone Char. Before the sorption mechanism is studied, the nature of the bone char has to be understood. The bone structure is very complex, and bone growth involves the initial formation of amorphous material and the sub-

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Figure 5. Effect of particle size on the bone char exhaustion rate for cadmium ion removal. C0 ) 4 mmol/L; flow rate ) 25 mL/min; 50% breakthrough.

Figure 6. Effect of EBRT on the bone char usage rate at fixed breakthrough for cadmium ion removal. C0 ) 2 mmol/L ) 224.8 mg/L; flow rate ) 50 mL/min; 50% breakthrough.

sequent crystallization of hydroxyapatite within the collagen fibers (bone mineralization).26 Bone char is obtained by the thermal destruction of bones at temperatures up to 900 °C. A typical bone char sample will have around 10% carbon content, and most of the rest will be the calcium-based salt. Tricalcium phosphate (a phosphate-based hydroxyapatite), which occupies more than 70 wt %, is the major composition of the bone char. The bone char has a rich surface of heterogeneous

components, allowing physisorption, chemisorption, or ion exchange to occur. The carbon surface of the bone char is capable of physical sorption of metal ions, the significant amount of calcium ions can be used in ion exchange, and the hydroxyapatite lattice structure provides a source of hydroxyl hydrogen which could provide exchange sites or attract the metal ions for loose physical sorption. The combination of all characteristics makes the bone char have the highest metal uptake capacity among other carbon-based adsorbents such as activated carbon and peat.27 Studies28 show that the kinetics of PO44- and Ca2+ ion exchange with hydroxyapatite is described as a rapid exchange with the hydration shell (1-2 min), an intermediate rate associated with the surface ion exchange (30 min), and a very slow process of incorporation of the ions into the crystals, primarily due to recrystallization. The nature of the apatite structure renders it particularly prone to substitution,26 and the possible substitutions on apatite for the Ca2+ ions are numerous and complex. The metal ions could be adsorbed onto the surface by the formation of complexes with the hydroxyl group or participated in ion-exchange reactions by binding metal ions with the release of Ca2+ ions.29 Above all, it is fairly clear that chemisorption can occur through the polar functional group in the hydroxyapatite surface site, but a common viewpoint on the exact mechanism of metal ion sorption on bone char is yet to be reached. Conclusion The sorption of copper, zinc, and cadmium ions by bone char in a fixed-bed column was studied. The experimental results showed that the bone char column removed the metal ions effectively and the effect of changing the column operating parameters, such as flow rate and initial concentration, can be predicted by the BDST model. The EBRT model was applied to optimize

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the operating system conditions. New mathematical correlations have been postulated to construct the operating line of the EBRT plot, and optimum conditions can be obtained by maximizing the adsorbent utilization rate. Finally, the sorption mechanism of metal ion onto bone char was previewed, suggesting that physisorption, ion exchange, and chemisorption would occur simultaneously within the bone char particle, and this explains why bone char is a very effective adsorbent compared with other carbon-based adsorbents used for metal ion sorption. Nomenclature  ) void fraction of the bed F ) solute density (kg/dm3) φB ) “association parameter” of the solvent µ ) viscosity of the solute solution (N s m-2) b ) intercept on the ordinate of the BDST plot (min) Cb ) breakthrough solute concentration (mmol/L) C0 ) initial solute concentration (mmol/L) Ct ) solute concentration at time t (mmol/L) DAB ) molecular diffusivity (m2/s) dp ) mean adsorbent particle diameter (µm) F ) volumetric flow rate (mL/min) JD ) mass-transfer coefficient factor k ) kinetic rate parameter (L/mg‚h) m ) slope of the BDST plot (min/cm) MB ) molar mass of solvent N0 ) volumetric sorption capacity of bed (mg/L) NRe ) Reynolds number NSc ) Schmidt number q ) adsorption capacity (mmol/g) S ) cross-sectional area of the adsorption bed (cm2) T ) operating temperature (K) t ) service time/operating time of the bed (min) v ) linear velocity (cm/s) v′ ) superficial velocity based on the cross section of an empty bed (m/s) VA ) solute molar volume (m3/kg‚mol) w ) adsorbent usage rate (g of pollutant/g of adsorbent) x ) liquid retention time EBRT (s) y ) adsorbent exhaustion rate (g/dm3) Z ) bed depth (cm) Z0 ) critical bed depth (cm)

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(6) Cooper, R. S. Slow Particle Diffusion in Ion Exchange Columns. Ind. Eng. Chem. Fundam. 1965, 4, 308. (7) Cooper, R. S.; Liberman, D. A. Fixed Bed Adsorption Kinetics with Pore Diffusion Control. Ind. Eng. Chem. Fundam. 1970, 9, 620. (8) Weber, T. W.; Chakravorti, R. K. Pore and Solid Diffusion Models for Fixed Bed Adsorbers. AIChE J. 1974, 20, 228. (9) Rice, R. G. Approximate Solutions for Batch, Packed Tube, and Radical Flow AdsorberssComparisons with Experiment. Chem. Eng. Sci. 1982, 37, 83. (10) Cooney, D. O. External Film and Particle Phase Control of Adsorber Breakthrough Behavior. AIChE J. 1990, 36, 1430. (11) Wilson, E. J.; Geankoplis, C. J. Liquid Mass Transfer at Very Low Reynolds Number in Packed Beds. Ind. Eng. Chem. Fundam. 1966, 5, 9. (12) 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. (13) Liu, K. T.; Weber, W. J., Jr. Characterization of Mass Transfer Parameters for Adsorber Modeling and Design. J. Water Pollut. Control Fed. 1981, 53, 1541. (14) Traegner, U. K.; Suidan, M. T. Evaluation of Surface and Film Diffusion Coefficients for Carbon Adsorption. Water Res. 1989, 23, 267. (15) Cooney, D. O. Determining External Film Mass Transfer Coefficients for Adsorption Columns. AIChE J. 1991, 37, 1270. (16) Michael, A. S. Simplified Method for Interpreting Data in Fixed-bed Ion Exchange. Ind. Eng. Chem. 1952, 44, 1922. (17) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley & Sons: New York, 1984. (18) Hutchins, R. A. New Method Simplifies Design of Activated Carbon Systems. Chem. Eng. 1973, Aug 20, 133-138. (19) Cooney, D. O. Adsorption Design for Wastewater Treatment; Lewis Publishers: Boca Raton, FL, 1998. (20) McKay, G.; Bino, M. J. Simplified Optimization Procedure for Fixed Bed Adsorption Systems. Water, Air, Soil Pollut. 1990, 51, 33-41. (21) Bohart, G. S.; Adams, E. Q. Some Aspects of the behavior of charcoal with respect to chlorine. J. Chem. Soc. 1920, 42, 523. (22) Wase, J.; Forster, C. Biosorbents for Metal Ions; Taylor & Francis Publishers: London, 1997. (23) McKay, G.; Al-Duri, B. Study of the Mechanism of Pore Diffusion in Batch Adsorption Systems. J. Chem. Technol. Biotechnol. 1990, 48, 269-285. (24) Wilke, C. R.; Chang, P. I. N. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, 1, 264. (25) Le Bas, G. The Molecular Volumes of Liquid Chemical Compounds; David McKay Co., Inc.: New York, 1915. (26) Corbridge, D. E. C. Studies in inorganic chemistry 20; Elsevier Press: Amsterdam, The Netherlands, 1995. (27) Brown, P.; Flynn, O.; McKay, G.; Allen, S. J. The Evaluation of Various Sorbents for the Removal of Heavy Metals from Wastewaters. Int. Chem. Eng. Res. Conf. Proc. 1992, 152-154. (28) Elliott, J. C. Studies in Inorganic Chemistry 18; Elsevier Press: Amsterdam, The Netherlands, 1994. (29) Abe, M.; Kataoka, T.; Suzuki, T. New developments in ion exchange: materials, fundamentals, and applications: proceedings of the International Conference on Ion Exchange; ICIE ’91, Tokyo, Japan, Oct 2-4, 1991; Elsevier: Tokyo, 1991; pp 401-406.

Received for review April 20, 1999 Revised manuscript received September 2, 1999 Accepted September 2, 1999 IE9902784