Ind. Eng. Chem. Res. 2000, 39, 2427-2433
2427
SEPARATIONS Development of Fixed-Bed Adsorber Correlation Models V. K. C. Lee, J. F. Porter, and G. McKay* Department of Chemical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China
The adsorption of three single-component acid dyes onto activated carbon has been studied using fixed-bed adsorption. Conventional simplified design methods, namely, bed depth service time (BDST) and empty-bed residence time (EBRT) models, were applied to the experimental breakthrough curve data but failed to correlate these data. Consequently, modifications have been developed that enable modified BDST and EBRT models to be applied and to correlate the experimental data very accurately. The modification is based on an expression to correlate the residence time in the adsorption bed with the time-dependent fraction degree of saturation of the bed. This model is particularly suited to predicting the performance of fixed-bed adsorbers when the system requires a long period of time to reach equilibrium or when several fixed-bed adsorbers are used in series. Introduction Increasing government legislative requirements for effluent discharges emphasize the need for effective treatment methods. Colored organic compounds generally impact only a small fraction of the total organic load in wastewaters; however, their high degree of color is easily detectable and detracts from the aesthetic value of rivers and receiving waters. In addition, the presence of color reduces photosynthetic processes and some dyestuffs, particularly, metal-containing dyes, are toxic. Large volumes of aqueous effluent are discharged by the clothing sector, including textiles, leather, and dyeing. Additional sources of colored effluent include the food, pharmaceutical, and several chemical processing industries. Adsorption is gaining prominence as an effective and cost-effective method for the removal of pollutants from wastewaters. The mechanism is based on the ability of porous solids, adsorbents, to concentrate and hold solute molecules, such as dyestuffs, on their surfaces. The properties of porous solids that render them useful for water treatment include high porosity and surface area as well as the physical and chemical nature of the internal adsorptive surface.1 In the past 30 years, but particularly in the last 10 years, extensive research has been undertaken to identify suitable adsorbents for dyes. These include basic dyes on carbon,2-4 peat,5-7 wood,8-10 and Fuller’s earth.11 More recent studies involve the adsorption of cationic dyes on sulfonated coal,12 mordant dye on China clay,13 chrome dye on fly ash12 and direct dye 12 by biogas residual slurry.14 A number of pith-based materials have been tested, such as waste orange peel15 and waste sugar cane bagasse pith.16 However, the major problem in all these previous studies is that they are * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: (852) 2358 7133. Fax: (852) 2358 0054.
equilibrium or batch contact systems. There are only limited fixed-bed data available for the adsorption of dyes on which to base column design models and none have been applied using activated carbon as the adsorbent. Furthermore, the application of batch experimental data is often difficult to apply to fixed-bed adsorbers because isotherms cannot give accurate scale-up data in fixed-bed systems because a flow column is not at equilibrium; uneven flow patterns occur in fixed beds and the problems of recycling and regeneration cannot be studied. Consequently, it is necessary to carry out flow tests using columns prior to obtaining design models. The problem in designing columns is to predict how long they will last before regeneration or replacement becomes necessary. The most widely applied simplified design model for this purpose is the bed depth service time (BDST) and this can be extended into an optimization model based on empty-bed residence time (EBRT) and the adsorbent exhaustion rate. However, there is still only limited literature on the application of these simplified column design models. These models are based on a model developed for gas adsorption on carbon17 or phenol on carbon18,19 or dyestuffs onto carbon,20,21 peat,22,23 and wood.24 Most of these models applied the conventional BDST model modification and only two papers demonstrated a graphical optimization procedure to predict the carbon exhaustion rate. No predictive equations were developed or applied to analyze the fixed-bed applications except for metal ion sorption on bone char.25 The fixed-bed biosorption of copper ions onto Rhizopus arrhizus and Mucor miehei has been studied.26 However, only a simplified two-parameter mathematical fitting model was applied to a very limited quantity of experimental data. There are few applications of fixed-bed modeling studies for the sorption of dyes. In the present paper the single-component adsorption of Acid Blue 80 (AB80), Acid Yellow 117 (AY117), and
10.1021/ie000017q CCC: $19.00 © 2000 American Chemical Society Published on Web 06/17/2000
2428 Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000
Acid Red 114 (AR114) dyes onto activated carbon has been studied. The system variables include flow rate, initial dye concentration, and particle size. A modified BDST and modified EBRT optimization model has been applied to the data and predictive correlations have been derived for the three process variables. The predictive correlations incorporate a time-dependent relationship that compensates for the time required for beds to achieve or not achieve, as the case may be, equilibrium sorption capacity. In this manner, the models can be used for multiple fixed beds in series or single shortadsorption columns. Figure 1. BDST plot of the variation in liquid flow rate in the AB80 adsorption system (C0 ) 100 ppm, 500-710 µm).
Theory Existing BDST Model. The objective of fixed-beds operations is to reduce the concentration in the effluent so that it does not exceed a predefined breakthrough value (Cb). The original work on the BDST model was carried out by Bohart and Adams17 who proposed a relationship between bed depth (Z) and the time taken for breakthrough to occur. The service time (t) was related to the process conditions and operating parameters:
ln
(
)
C0 - 1 ) ln(eKaNtZF - 1) - KaC0t Cb
(1)
Hutchins18 proposed a linear relationship between the bed depth and service time:
t)
(
Nt C0 1 Zln -1 C0u KaC0 Cb
)
(2)
The critical bed depth (Z0) is the theoretical depth of adsorbent sufficient to prevent the adsorbate concentration from exceeding Cb at t ) 0. By letting t ) 0, Z0 is obtained from eq 1 by solving Z. Because the exponential term is usually much larger than unity, the unity term within the brackets in the right-hand side of eq 1 is often neglected, leaving
Z0 )
( ) (
C0 u ln -1 KaNt Cb
)
(3)
Equation 2 enables the service time (t) of an adsorption bed to be determined by a specified bed depth (Z) of adsorbent. The values of t and Z are correlated with the process parameters and initial dye concentration, solution flow rate, and the adsorption capacity. Equation 2 has the form of a straight line
t ) mZ + b
(4)
with the slope of this equation
m)
Nt C0u
(5)
and the intercept of this equation represents
b)-
(
)
C0 1 ln -1 KaC0 Cb
(6)
Modified BDST Models. Figure 1 shows a BDST plot of variation of liquid flow rate in the AB80 adsorption system with constant initial concentration and
Figure 2. Modified BDST plot of the variation in liquid flow rate in the AB80 adsorption system (C0 ) 100 ppm, 500-710 µm).
adsorbent particle size. The experimental points are not well fitted in the BDST plots, which means the relationship between the service time of the column and the bed depth is not purely linear. The problem is significantly demonstrated in the BDST plot with a 30 mL/ min liquid flow rate. The gradient of the BDST plot is gradually increasing with increasing bed depth (or service time). Equation 5 shows that the slope of the BDST plot is dependent on three parameters: bed capacity, initial concentration, and liquid linear flow velocity inside the bed during operation. If the BDST plot is a linear relationship, the slope of the BDST plot has to be a constant value throughout all bed depth values. However, as mentioned before, the gradient is increasing with the increase of bed depth, even when the initial concentration is kept constant throughout the experiments. As the cross sectional area of the columns are constant throughout all experiments and the liquid linear flow velocities are constant for a particular flow rate, then the only cause of the change in slope is due to the bed capacity term changing during the experiment. The curves in Figure 2 illustrate that the bed capacity is increasing as the service time of the bed increases. In previous work25 this effect was not so pronounced. However, in this case, there is a major difference in the time taken to reach equilibrium between the metal ions/bone char system, which takes 5 days, and the acid dye/carbon system, which takes 21 days. To investigate the phenomenon in Figure 2, it was decided to develop a correlation to predict the effect of solid phase dye uptake with time. Because the process is largely diffusion controlled, a correlation with a square root of time was selected. The relationship between the bed capacity and the service time of the bed can be described by an equation of the following type:
Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2429
Nt ) N0(1 - exp(-axt))
(7)
This modification for variation in bed capacity at different bed service times was then implemented into the existing BDST models by replacing the term of constant bed capacity. The normal BDST model represented by eq 2 is modified to
t)
(
)
N0(1 - exp(-axt)) C0 1 Zln -1 C0u KaC0 Cb
(8)
Equation 8 can be rearranged into
t ) m′(1 - exp(-axt))Z + b′
(9)
The modified BDST slope and intercept parameters are now given by
m′ )
N0 C0u
(
C0 1 ln -1 b′ ) KaC0 Cb
(10)
)
t - b′ m′(1 - exp(-axt))
(11)
(12)
The modified BDST plot is plotted as the bed depth (Z) versus the service time (t). The modified BDST slope parameter, m′, and modified BDST intercept, b′, are found from a trial-and-error method incorporating a minimum sum of the error-squared method by minimizing the following terms:
SSE )
∑(tcal - texp)2
volume of carbon inside the fixed bed, dm3 volumetric flow rate of liquid, dm3 s-1 (15)
For a given system to achieve a given performance, there is a single line relating these two variables that is called the operating line. The operating line concept can be used to optimize the basic design to achieve the lowest cost or other objectives. The operating line approaches minimum on both axes. The minimum exhaustion rate for a given adsorption duty is that which is achieved when the exhausted carbon is in equilibrium with the influent liquid, and the minimum retention time represents the minimum volume of carbon necessary to achieve the desired effluent purity at infinitely high carbon exhaustion rates. Once the operating line is established, it is possible to select the combination of the carbon exhaustion rate and liquid retention time, which gives the optimum or lowest cost design. Experimental Section
The term m′ does not represent the slope of the modified BDST plot because the equation is no longer linear (the slope of modified BDST plot is m′(1 - exp(-axt))). This slope parameter, m′, represents the slope of the BDST plot when the bed capacity has reached equilibrium capacity value. After eq 9 is rearranged, the modified BDST can be represented as the following equation:
Z)
EBRT )
(13)
The improvement by the use of the modified BDST model is also demonstrated by using this SSE equation. Empty Bed Residence Time Model (EBRT). McKay and Bino19 suggested that the capital and operating costs are basically a function of two variables in a fixed-bed adsorption system, namely, carbon exhaustion rate and EBRT. The carbon exhaustion rate is referred to as the “burn rate” or “carbon dosage”. This is usually expressed as mass of carbon deactivated per volume of liquid treated:
carbon exhaustion rate ) mass of carbon, g (14) volume of liquid treated, dm3 EBRT is the time that the liquid would take to fill the volume of the carbon bed and is a direct function of liquid flow rate and carbon volume:
The adsorbent used in the research is granular activated carbon F400 (GAC) supplied by Chemviron Ltd. The GAC was crushed by using a hammer mill and sieved into several discrete particle size ranges: 355500, 500-710, and 710-1000 µm. It was washed by deionized water to remove fines. It was then dried under 110 °C in an oven for 24 h. The dyestuffs used as the adsorbates were Polar Blue RAWL (Acid Blue 80, AB80), Acid Red 114 (AR114), and Polar Yellow (Acid Yellow 117, AY117). The concentration of dyestuffs was measured by a Varian Cary 1E UV-vis spectrophotometer at specific wavelengths for each dyestuff at which maximum absorption of light occurs, λmax. The wavelengths, λmax, for each dyestuff are listed in Table 1. The deionized water used is piped to the adsorption pilot plant at the top and it is fed into a 50-dm3 plastic container (item 1). A known amount of dye salt is added to another plastic container (item 2) with a batch of 50 dm3 of water from item 1 and it is kept under continuous stirring by means of recirculation agitation (item 4). The solution is then transferred into another similar tank (item 3). Samples are taken from a sampling point (item 6) to record the value of the initial concentration used in each test run. Influent to the adsorption beds is pumped via item 5 and a three-way valve (item 8) served to control the recycle feedback to the constant head tank (item 3). Calibrated rotameters (item 9) are used to control the flow rate through the columns (item 11). Sample points are located at various heights (item 10), 0.05 m apart, on the adsorbent column (item 11), and 10-cm3 syringes and stainless steel needles are used to obtain samples of solutions from the adsorption beds. If necessary, the pH of the effluent from the columns can be measured by collecting effluent from the discharge outlet (item 12). Finally, the effluent is discharged into the drain. Results and Discussion A summary of bed performance using the original BDST analysis model in the form of eq 4 is shown in Table 3. The error analysis in the form of the sum of the errors squared as shown in eq 13 has been calculated and the values are shown in the final column. The
2430 Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 Table 1. λMax Values for Each Acid Dye
Table 4
abbreviation
λmax (nm)
AB80 AR114 AY117
626 522 438
Acid Blue 80 Acid Red 114 Acid Yellow 117
A. Summary of BDST Parameters Using Modified Model C 0, ppm
F, mL/ min
dp, µm
m′, h/m
b′, h
a, h-0.5
AB80
100 100 100 100 50 100 150 50 50 50
30 40 60 80 30 30 30 30 30 30
605 605 605 605 605 605 605 427.5 605 855
498.1 351.1 249.1 181.1 930.2 498.1 329.4 911.1 930.2 941.1
-0.148 -0.107 0.121 0.142 -0.213 -0.148 -0.038 -0.271 -0.213 -0.056
0.0420 0.0420 0.0420 0.0420 0.0273 0.0420 0.0577 0.0346 0.0273 0.0215
AY117
100 100 100 100
30 40 60 80
605 605 605 605
700.9 464.2 287.2 238.1
-0.067 0.032 0.068 0.084
0.0334 0.0334 0.0334 0.0334
AR114
100 100 100 100
30 40 60 80
605 605 605 605
458.2 340.5 228.2 178.5
-0.224 -0.210 -0.065 -0.030
0.0489 0.0489 0.0489 0.0489
dye
Table 2. Equipment Specification for an Adsorption Column Pilot Plant item number 1 2
description
specification
50-dm3
11
plastic container 50-dm3 plastic containers with recirculation agitation 100-dm3 plastic containers with recirculation agitation centrifugal pump 1/6 hp ac motors sampling points to check on initial influent concentration three-way valve connected to recirculate solution rotameter sampling points subar-seals for syringes (10 cm3) perspex columns
12
effluent collection vessel
3 4 and 5 6 7 and 8 9 10
i.d. ) 0.045 m length ) 0.5 m
B. Comparison of Old BDST and Modified BDST Model dye
Table 3. Summary of BDST Parameters Using the Existing Model
AB80
C0, F, mL/ ppm min
dp, µm
N 0, kg/m3
SSE
SSE before SSEold/ modification SSEnew
100 100 100 100 50 100 150 50 50 50
30 40 60 80 30 30 30 30 30 30
605 605 605 605 605 605 605 427.5 605 855
56.4 56.0 56.4 56.6 55.9 56.4 57.6 51.6 55.9 58.3
1.56 × 10-4 2.46 × 10-4 5.56 × 10-4 3.01 × 10-3 6.47 × 10-5 1.56 × 10-4 1.80 × 10-5 9.74 × 10-5 6.47 × 10-5 3.85 × 10-6
7.89 × 10-3 50.58 1.65 × 10-3 6.71 1.14 × 10-3 2.05 4.86 × 10-3 1.61 8.98 × 10-4 13.88 7.89 × 10-4 5.06 7.80 × 10-4 43.33 5.30 × 10-4 5.44 8.98 × 10-4 13.88 8.62 × 10-4 223.90
C 0, ppm
F, mL/min
dp, µm
m, h/m
b, h
SSE
100 100 100 100 50 100 150 50 50 50
30 40 60 80 30 30 30 30 30 30
605 605 605 605 605 605 605 427.5 605 855
104.2 59.15 31.81 19.71 165.1 104.2 86.73 236.8 165.1 110.8
-5.923 -3.789 -1.802 -1.255 -9.619 -5.923 -4.938 -12.69 -9.619 -6.362
7.89 × 10-3 1.65 × 10-3 1.14 × 10-3 4.86 × 10-3 8.98 × 10-4 7.89 × 10-4 7.80 × 10-4 5.30 × 10-4 8.98 × 10-4 8.62 × 10-4
AY117 100 100 100 100
30 40 60 80
605 605 605 605
69.3 70.1 70.0 71.9
2.53 × 10-4 3.15 × 10-4 3.96 × 10-4 1.55 × 10-3
1.12 × 10-3 2.56 × 10-3 1.97 × 10-3 4.48 × 10-3
4.43 8.13 4.97 2.89
AY117
100 100 100 100
30 40 60 80
605 605 605 605
165.1 63.07 24.72 20.36
-9.844 -3.165 -1.312 -1.128
1.12 × 10-3 2.56 × 10-3 1.97 × 10-3 4.48 × 10-3
AR114 100 100 100 100
30 40 60 80
605 605 605 605
51.9 51.4 51.6 51.9
1.98 × 10-4 5.62 × 10-4 2.39 × 10-4 1.14 × 10-4
9.75 × 10-4 1.87 × 10-3 1.84 × 10-3 9.87 × 10-4
4.92 3.33 7.70 8.66
AR114
100 100 100 100
30 40 60 80
605 605 605 605
120.9 73.79 34.40 21.01
-7.192 -4.995 -2.218 -1.285
9.75 × 10-4 1.87 × 10-3 1.84 × 10-3 9.87 × 10-4
dye AB80
performance of the bed is analyzed by studying the change in the BDST slope parameter defined in eqs 9 and 12. The results are shown in Table 4A. There is great improvement in the new model fitting by comparing the sum of error squared value from Table 3 with the values of the modified BDST in Table 4B. The ratio of the old error to new error is shown in the final column of Table 4B. Values greater than unity imply a better fit for the new modified BDST. Figure 2 also demonstrates the benefits of the modified BDST plot solidus curves of the variation of flow rate of AB80 adsorption with constant initial concentration and adsorbent particle size. The agreement between these curves and the experimental data points is excellent. The analysis can be divided into three sections, according to the variation of operation parameters: liquid flow rate, initial concentration, and mean particle size of the adsorbent. Another set of experimental data are compared with the model predictions using eq 12 in Figures 3 and 4 for the effect of initial dye concentration and mean particle size on the adsorption of AB80, respectively.
Figure 3. Modified BDST plot of the variation of initial concentration in the AB80 adsorption system (F ) 30 mL min-1, 500710 µm).
Bed Performance with Different Liquid Flow Rate. The rate parameter, a, in eq 7 demonstrates the extent of change in bed capacity with respect to the service time of the beds. A large value of the rate parameter indicates that the bed capacity will reach the equilibrium value faster. The liquid volumetric flow rate affects the rate of change in bed capacity with respect to the service time of the beds in two ways. A higher liquid volumetric flow rate decreases the external film
Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2431 Table 5. Summary of EBRT Error Analysis Using Both Models dye
Figure 4. Modified BDST plot of the variation of mean particle size in the AB80 adsorption system (F ) 30 mL min-1, C0 ) 50 ppm).
Figure 5. Curve of the percentage of bed saturation versus service time in the variation of liquid flow rate in the AB80 adsorption system (C0 ) 100 ppm, 500-710 µm).
mass resistance at the surface of the adsorbents because of the additional velocity shear, thus reducing the film thickness. However, at the same moment, the residence time of the effluent inside the bed decreases with higher liquid volumetric flow rate. Then, the dye molecules have less time to penetrate and diffuse into the center of the adsorbents. Therefore, a high flow rate usually decreases the extent of change in bed capacity with respect to the service time of the beds because of this decreasing residence time effect. Figure 5 illustrates that the values of the rate parameter, a, are essentially unchanged with respect to the change in liquid flow rate in AB80, AY117, and AR114 adsorption systems. It means that the changes in the two effects are tending balance to each other. Hence, a constant value of a that is used for the investigation of the modified BDST analysis with the variation of flow rate and a single curve, based on eq 7, is used to correlate the data. Equation 10 shows that the term of the new BDST slope parameter is inversely proportional to the linear velocity of the liquid flow inside the fixed bed. The modified BDST slope parameter is inversely proportional to the liquid flow rate. Table 4A shows that the values of the BDST slope parameter in three dye adsorption systems, for fixed initial concentration and adsorbent mean particle diameters, decrease with the increase of liquid flowrate. The ratios of these slope parameters follow the inverse proportional relationship:
mF1′
F2 ) mF2′ F1
(16)
Bed Performance with Different Initial Concentrations. A comparison of the capacity values, N0, in
F, C 0, ppm mL/min
dp, µm
AB80
100 100 100 100 50 100 150 50 50 50
30 40 60 80 30 30 30 30 30 30
605 605 605 605 605 605 605 427.5 605 855
AY117
100 100 100 100
30 40 60 80
AR114
100 100 100 100
30 40 60 80
SSE using SSE using SSEold/ old model new model SSEnew 72 585 82 165 156 088 78 407 30 630 72 585 111 341 33 595 30 630 60 455
986 11 139 830 1 052 106 39 591 2 280 285 107 669
73.6 7.4 188.1 74.5 289.0 1.8 48.8 117.9 286.3 90.4
605 605 605 605
22 053 55 502 70 696 21 860
129 6 180 750 1 388
171.0 9.0 94.3 15.7
605 605 605 605
36 322 87 984 134 757 189 399
3 998 1084 10 627 16 138
9.1 81.2 12.7 11.7
Table 4B illustrates that the extent of change in bed capacity versus service time is increasing with the increase of initial concentration. It can be explained by using the governing mass-transfer equation. The masstransfer flux is dependent on the mass-transfer coefficient, area perpendicular to the mass flux, and the concentration gradient. Hence, a higher initial concentration leads to a higher concentration gradient. Thus, this high mass-transfer driving force gives a larger rate of change in bed capacity with respect to the service time of the beds. Hence, Table 4A shows that the value of a is increased with increasing initial dye concentration. It also found that the relationship between the rate parameters and the initial concentration can be described as
aC0,1 aC0,2
( ) C0,1 C0,2
≈
2/3
(17)
Table 4A shows that the values of the new BDST slope parameters in the AB80 adsorption systems decrease with increasing initial dye concentration in the liquid. Similar to the variation of liquid flow rate, the new slope parameters are inversely proportional to the initial concentration of the effluent. Hence, the relationship between the new BDST slope parameters and the initial concentration of the effluent is formulated as
mC0,1′ mC0,2′
)
C0,2 C0,1
(18)
Bed Performance with Different Mean Particle Size. Table 4A illustrates that the values of the rate parameter, a, increase with the decrease in the mean adsorbent particle size. The relationship between the value of a and the mean adsorbent particle size can be described by eq 19. The power of -2/3 can be explained
adp1 adp2
≈
( ) dp1 dp2
-2/3
(19)
by the correlations for film mass-transfer coefficients of liquids in packed beds. For a Reynolds number range of 0.0016-55, eq 20 is valid using the Wilson and
2432 Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000
Figure 6. Effect of liquid flow rate on the carbon exhaustion rate in the AB80 adsorption system (C0 ) 100 ppm, 500-710 µm).
Figure 8. Effect of liquid flow rate on the carbon exhaustion rate in the AR114 adsorption system (C0 ) 100 ppm, 500-710 µm).
Figure 7. Effect of liquid flow rate on the carbon exhaustion rate in the AY117 adsorption system (C0 ) 100 ppm, 500-710 µm).
Figure 9. Effect of initial concentration on the carbon exhaustion rate in the AB80 adsorption system (F ) 30 mL min-1, 500-710 µm).
Geankoplis correlation.27 It is also found that the value
JD )
1.09 -2/3 Re
(20)
of the modified BDST slope parameter is increased with increasing particle size. Hence, the bed capacity is also increased with the increase in particle size. This is because the voidages of the adsorption beds with different particle size ranges are different. The column heights of adsorption beds made by the same mass of GAC (194 g) with mean particle size 427.5, 605, and 855 µm are 25.5, 25.0, and 24.7 cm, respectively. A large particle may give large interparticle voidage. However, in some cases, a small intraparticle voidage may be characteristic of a large adsorbent particle for certain adsorbents. Hence, for the same mass of adsorbent, the column packed with the large adsorbent particle size range gives a longer column than that packed with small diameter adsorbent particles. Therefore, 5 cm of packed beds of particle size ranges 355-500, 500-710, and 710-1000 µm are equivalent to 38, 38.8, and 39.25 g. Therefore, a higher bed capacity will occur in the dye adsorption systems using this activated carbon with a large adsorbent mean particle size. EBRT Analysis Using a New Model. Equation 14 shows that the carbon exhaustion rate is dependent on the mass of carbon inside the adsorption bed and the volume of liquid treated. The volume of liquid treated is the product of the volumetric flow rate during the adsorption operation and the service time of the bed. As the mass of carbon inside the bed and the volumetric flow rate of the liquid remain constant during the operation, the main cause of error between the experimental results and the modeling results are the error in the calculation of service time. The calculation of
Figure 10. Effect of mean particle size on the carbon exhaustion rate in the AB80 adsorption system (F ) 30 mL min-1, C0 ) 50 ppm).
service time can be performed by using the existing BDST model or the modified BDST model. The degree of improvement can be formulated by using a sum of the errors squared equation, eq 21. Table 5 shows the
SSE )
∑(CHRcal - CHRexp)2
(21)
ratio of the old sum of error squared to the new sum of error squared. The values greater than unity imply a better fit for the new modification. Figures 5-10 illustrate the experimental results are well fitted with the modified EBRT model. Hence, the EBRT model is a better fit to the experimental results with the modification of service time calculation using eq 7. Conclusions The BDST model has been modified because of the change in bed capacity with different service times of
Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2433
the beds when different operating conditions are considered. The modified model is useful in the case of adsorption bed operation in which a long period of equilibrium time is required. The prediction of the service time of the beds was improved and this was illustrated by comparing the sum of the errors squared showed in Table 4B. The performance of the adsorption beds under different operating conditions (liquid volumetric flow rate, initial concentration, and mean particle size) were studied. The BDST slope parameter decreased as the volumetric flow rate decreased. However, the BDST slope parameter was increased as the initial concentration and the mean particle size increased. The relationship between the BDST slope parameters and the operating parameters were reviewed. As the estimation of bed service time was improved, the EBRT analysis was also improved using the modified BDST model. This result was also demonstrated by comparing the sum of the errors squared using the existing model and new model. The sum of the errors squared in the new model was decreased. Acknowledgment One of the authors (V. K. C. Lee) would like to thank the Croucher Foundation of Hong Kong for providing support for this research. Nomenclature a ) rate parameter defined in eq 7 (hr-1/2) b ) intercept parameter of BDST plot (h) b′ ) new intercept parameter of BDST plot (h) C0 ) initial dye concentration (mg dm-3) Cb ) breakthrough dye concentration (mg dm-3) Ct ) dye concentration at time t (mg dm-3) CHR ) carbon exhaustion rate (g dm-3) dp ) mean particle size (µm) F ) volumetric flow rate (dm-3 min-1) JD ) mass-transfer factor (dimensionless) Ka ) BDST adsorption rate constant (m3 kg-1 s-1) m ) slope of BDST plot (h m-1) m′ ) new BDST slope parameter (h m-1) N0 ) saturated adsorption capacity in BDST model (kg m-3) Nt ) adsorption capacity in BDST model at service time t (kg m-3) Re ) Reynolds number (dimensionless) SSE ) sum of error squared t ) service time of the bed (h) u ) linear velocity (m s-1) Z ) bed height (m) Z0 ) critical bed height (m) Greek Letters e ) void fraction (dimensionless) λmax ) maximum absorption of light occurs
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Received for review January 6, 2000 Revised manuscript received April 18, 2000 Accepted April 25, 2000 IE000017Q
