Evaluation of the Onda Correlations for Mass Transfer with Large

Environ. Sci. Technol. 1996, 30, 945-953

Evaluation of the Onda Correlations for Mass Transfer with Large Random Packings BRUCE I. DVORAK,† DESMOND F. LAWLER,* JAMES R. FAIR,‡ AND NEIL E. HANDLER§ University of Texas, Austin, Texas 78712

Although large (g5 cm) polypropylene packings are frequently used in air stripping towers for environmental applications, few fundamental studies of the mass transfer on these large packing designs have been performed. For small packings, previous research has verified that the Onda correlations are valid for environmental applications. In this research, experimental data for air stripping were obtained using a pilot-scale stripping tower, three test compounds, and four polypropylene packings. Results showed that, in general, Onda is a good predictor of mass transfer for large random packings. However, Onda tended to underpredict mass transfer, with 90% of the data falling between a 16.5% overprediction and a 34.0% underprediction of the observed mass transfer. The underpredictions tended to occur at high gas flow rates and when the gas-film resistance predicted by Onda is large. Further analysis revealed that the functionality of the volumetric gas loading rate is incorrect in the Onda correlations.

large (g5 cm) plastic packings of geometric shapes other than saddles or rings are used for environmental applications, though little investigation of the application of Onda to these larger packing designs has been performed. The few experimental results using g5-cm plastic packing materials (2, 3) show that Onda underpredicted the observed mass transfer. Two types of systematic errors in the Onda correlations, which could lead to an underprediction of mass transfer, have been suggested by other researchers. Several researchers (2-4) have suggested that the Onda correlations overstate the importance of the gas-film resistance to mass transfer. Another potential systematic error has been identified in distillation data by Bravo and Fair (5), who suggested that Onda does not correctly predict the effective wetted surface area. Since the Onda correlations are frequently used as a design tool, these issues are important in ensuring the most accurate mass transfer predictions. The objectives of this research were to investigate the applicability of the Onda correlations to modern packings that are quite different from those used to develop the correlations and to identify any systematic errors in the correlations. The research focused only on “random” packing materials, which are manufactured as individual pieces up to several centimeters in longest dimension and are placed randomly in gas transfer columns. “Structured” packings, which are manufactured in three-dimensional units up to 1 m or more in each dimension, were not included.

Review of Pertinent Literature Design Model. The theories of gas transfer and of packed tower aeration are well known and can be found in numerous places in the technical literature. Only a brief review of the relevant theory, terminology, and equations is given here. Henry’s Law describes the linear relationship between liquid and gas-phase concentrations for dilute solutions at equilibrium:

CG ) HCL

Introduction

(1)

The Onda correlations are commonly used for estimating mass transfer of volatile chemicals from water during air stripping with random packing. Prior research has verified the Onda correlations for some conditions, but questions about the range of applicability of the correlations have remained. The correlations of Onda et al. (1) were developed from a database of experiments with then current packing materials (primarily small ceramic rings, saddles, and spheres). In the interim, packing materials have changed dramatically and now are larger, more porous, more varied in shape, and made of plastics. Frequently,

where CG and CL are the gas and liquid-phase concentrations, respectively, and H is the Henry’s constant. If the concentrations in both phases are given in the same units (e.g., mg/m3), the Henry’s constant is often considered dimensionless, but more properly it has dimensions of volume of liquid per volume of air (e.g., m3 of liquid/m3 of air). On the basis of the two-film theory, the total resistance to mass transfer can be estimated by summing the individual resistance terms of the liquid and gas phases. The relationship is expressed as

* Corresponding author present address: Department of Civil Engineering, ECJ 8.6, University of Texas, Austin; telephone: (512) 471-4595 fax: (512) 471-5870; e-mail address: Des_Lawler.cemail@ cemailgate.ce.utexas.edu. † Present address: Department of Civil Engineering, University of Nebraska, Lincoln, NE. ‡ Present address: Department of Chemical Engineering, University of Texas, Austin. § Present address: U.S. Environmental Protection Agency, Region 1, J.F.K. Federal Building (HSV-CAN5), Boston, MA 02203-2211.

1 1 1 ) + KLa kLa HkGa

0013-936X/96/0930-0945$12.00/0

 1996 American Chemical Society

(2)

where KLa is the overall mass transfer rate coefficient based upon the liquid-phase driving force, kLa is the liquid-side mass transfer coefficient, and kGa is the gas-side mass transfer coefficient. More properly, KL, kL, and kG are the mass transfer coefficients, and a in each of these terms is the interfacial area per unit volume of the reactor, but the

VOL. 30, NO. 3, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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product of a with the true mass transfer coefficients is also often called a mass transfer coefficient. Each term in eq 2 represents a gas transfer resistance, so that, for example, 1/(kLa) represents the liquid-phase resistance. In many instances, one of the resistance terms on the right side of eq 2 dominates the equation, indicating that the overall gas transfer is controlled by that film (phase). Compounds that have high Henry’s law constants (oxygen, vinyl chloride) are controlled by the liquid film resistance and are easily stripped from water. Conversely, compounds that are fairly soluble in the liquid phase (ammonia) are controlled by the gas-film resistance and are more difficult to remove via stripping (but are more easily absorbed). The stripping factor (S), an important parameter to characterize operational conditions, is a dimensionless quantity defined as follows:

S)

QGH QL

(3)

where QG and QL are the volumetric gas and liquid flow rates (vol/time), respectively. A design equation for countercurrent towers can be derived from a mass balance over a control volume (6). When the influent gas (air) does not contain the pollutant to be removed from the liquid phase, the design equation for tower height (hT) is

hT )

( ) {

)[

QL S 1 S - 1 CLI ln + KLaA S - 1 S S CLE

(

]}

(4)

where A is the cross-sectional area of the packed tower and the subscripts LI and LE refer to the liquid influent and effluent, respectively. Equation 4 for the height of the tower is often represented as the product of the height of a transfer unit (HTU) and the number of transfer units (NTU); HTU is the first fraction [HTU ) QL/KLaA)] on the right-hand side of eq 4, and the remainder of the right-hand side of eq 4 is the NTU. The air stripping model assumes ideal flow in packed columns. Predicting Mass Transfer Coefficients. In environmental engineering applications, two-resistance models are used almost universally for predicting mass transfer of dilute organic chemicals because both the gas and liquid side resistances have been shown to be significant (4). Of the many two-resistance models, the correlations developed by Onda et al. (1) have been found by other researchers (4, 7) to fit their experimental data best. On the basis of those studies, this research focused on the further verification of the Onda correlations. The correlations can be described by the following equations (1):

kL ) 0.0051

( )( ) ( )( )

kG ) 5.23

QLFL AaµL

2/3

QGFG AaTµG

µL FLDL

0.7

-0.5

µG FGDG

(aTdp)0.4 1/3

( ) FL µLg

-1/3

(aTdp)-2aTDG

(5)

(6)

a ) aT{1 - exp[-1.45(σC/σL)0.75Re0.1Fr-0.05We0.2]} (7) where the Reynolds (Re), Froude (Fr), and Weber (We) dimensionless numbers are defined as

Re )

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QLFL AaTµL

(8)

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 30, NO. 3, 1996

Fr )

We )

QL2aT A2g QL2FL A2σLaT

(9)

(10)

and at is the specific surface area of packing (m2/m3); dp is the diameter of packing (m); DL and DG are the diffusivity of solute in liquid and gas phases, respectively (m2/s); g is the gravitational constant (9.81 m/s2); QL and QG are the liquid and gas volumetric flow rates (m3/s); µL and µG are the viscosity of liquid and gaseous phases (Ns/m2); FL and FG are the density of liquid and gaseous phases (kg/m3); σL is the surface tension of liquid (N/m); and σC is the critical surface tension of packing material (N/m). In this research, the Wilke-Chang and the Fuller et al. methods were used to determine the diffusivity of the solute in the liquid and gas phases, respectively, based on the recommendations of Reid et al. (8). The other physical properties needed in eqs 5-10 to calculate the overall mass transfer coefficient (e.g., viscosity, density, surface tension) were obtained from interpolation of available data. A value of 0.033 N/m was used for the critical surface tension of the packing (9). Previous Research. Staudinger et al. (10) gave a complete summary and discussion of pertinent literature concerning recent research on the Onda correlations. Onda’s correlations have been used to fit many researchers’ data. Research of particular interest to the current study includes that by Roberts et al. (4), Gossett et al. (2), LaMarche and Droste (7), and Little and Selleck (3). Using a test data base of 10 investigations, Staudinger et al. (10) found the Onda correlations to have an average accuracy of (30% based on 90% confidence limits. In comparison to other models, Onda’s model clearly predicts most accurately mass transfer for new untested packing designs. Previous researchers have primarily studied smaller ceramic packing media (e2.5 cm); notable exceptions were Gossett et al. (2) and Little and Selleck (3). Gossett et al. (2) found that Onda consistently underpredicted mass transfer for 5-cm polypropylene Tri-Packs in countercurrent columns by an average of 15%. In a cross-flow column, Little and Selleck (3) found that Onda underpredicted mass transfer for polypropylene 5-cm Tri-Packs and 5-cm saddles. The existence of systematic errors in the Onda correlations has been suggested by several researchers, with primary focus on the gas-film resistance. Roberts et al. (4) suggested that the transition region, where both gas and liquid film resistance to mass transfer are important, might be smaller than that predicted by the Onda correlations. A smaller transition region could lead to an underestimation of mass transfer by Onda. Gossett et al. (2) found that mass transfer for some packing designs was underpredicted by Onda when the gas-film resistance was significant; for those packings, they found a correlation between the fraction of the total resistance in the gas film (% R) as predicted by Onda and the difference between experimentally determined and Onda-predicted mass transfer coefficients (% D). Staudinger et al.(10) did not observe the % D vs. % R relationship in their study and questioned the concern about Onda’s gas-film resistance correlation. Little and Selleck (3) stated that Onda’s gas-film resistance correlation overstates significantly the gas-side resistance

FIGURE 1. Schematic of air stripping system.

to mass transfer in cross-flow air stripping using 5-cm packings. The effective wetted surface area has also been cited as a possible cause of error in the Onda correlations. In a model for packed distillation columns, Bravo and Fair (5) modified Onda’s effective wetted surface area correlation to incorporate the gas flow rate. This modification was made on the belief that a correspondence between the liquid holdup and effective transfer area could be expected with gas and liquid in counterflow. The gas kinetic energy could affect mass transfer by causing film surface rippling, liquid droplet dispersion, and the occurrence of gas bubbles in liquid puddles. Bravo and Fair’s modified effective wetted surface area term improved the predictions of the Onda correlations for distillation but not for stripping and absorption (5).

Experimental Methods The experimental pilot-scale air stripping system (shown in Figure 1) consists primarily of a feed tank, pump, packed column, and blower. The locations of sampling ports are shown, but for simplicity, temperature probes, pressure

sensors, and flow meters are not shown. The chemicals used for this study were chloroform (CHCl3), trichloroethylene (TCE), and perchloroethylene (PCE). The Henry’s constants of CHCl3, TCE, and PCE at 20 °C are 0.12, 0.32, and 0.59 (m3 of liquid/m3 of air), respectively. The Henry’s constant and temperature dependence relationships found by Munz and Roberts (11) were used in this research for the three test compounds. The experimental tower has a packing height of 3.05 m and an inside diameter of 42.9 cm. Influent water distribution is accomplished through the use of a lateral pipe distributor having a pour point density of 430 points/m2. A 23-m3 fiberglass tank was used to provide a contaminated water source. In the analysis of the results, end effects were assumed to be negligible in the tower because of the excellent water distribution at the top of the tower and the relatively open mesh support system at the bottom. The contaminated water was prepared by adding a known mass of chemical into approximately 100 mL of methanol, adding the mixture to the City of Austin tap water in the feed tank, and then mixing with a recirculating pump for a period of 15-18 h. An ambient CHCl3 concentration of approximately 5 µg/L was found in the tap water. Since the tap water was used to make standards, an additional 5 µg/L was added to all samples with calculated CHCl3 concentrations greater than the background level. Samples with concentrations less than background levels were calculated with an external calibration curve prepared with reagent water, since some effluent samples were stripped to below background levels of CHCl3. The influent and effluent water temperatures were measured, and the average was used for the data analysis. The influent water temperatures varied among the experiments between 18.6 and 30.0 °C. The effluent temperature was found consistently to be 2.8 °C higher than the influent. The air temperature was also measured and varied between 28.9 and 39.4 °C in different experiments. The liquid and gas flow rates were measured through the use of turbine flow meters whose signal outputs are linked to a computer console. The liquid and gas loadings used in this study are listed in Table 1, and the corresponding stripping factors ranged between 2 and 560. The pressure drop through the tower was monitored. The types and characteristics of the four packing materials tested are included in Table 1. These packings

TABLE 1

Experimental Overview packing description (material)

specific surface areaa (m2/m3)

void fractiona

nominal diametera (cm)

Pall rings (polypropylene)

206.6

0.90

2.5

Snowflake (polypropylene)

91.8

0.95

9.4

Cascade Mini-rings 2A (polypropylene)

141.0

0.94

Nor-Pac 2 (polypropylene)

101.7

5.1

a

Information provided by vendors of the individual packings.

influent concn (µg/L)

liquid loading rate -3 (10 m3/m2 s)

air loading rate 3 (m /m2 s)

TCE

200-800

4.4, 8.7, 17.5, 26.2

0.245-4.17

TCE

500-750

4.4, 8.7, 17.5, 26.2

0.245-4.91

6.6b

TCE TCE, PCE, and CHCl3

400-750 500-850 230-500 450-750

4.4, 8.7, 17.5, 26.2 4.4, 8.7, 17.5, 26.2

0.245-4.91 0.245-4.91

0.94

TCE PCE CHCl3 TCE, PCE, and CHCl3

400-700 400-1300 700-1850 950-1450 700-800 1200-1750

4.4, 8.7, 26.2 8.7, 17.5 8.7, 17.5 8.7, 17.5

0.245-4.91 0.245-4.91 0.245-4.91 0.245-4.91

b

compd(s) studied

Average diameter of upper and lower surfaces.


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were conditioned for at least 1 week by operating the packed experimental tower for approximately 2 h each day at high liquid loading rates and by filling the packed section of the tower with water overnight. This process removes any film left on the packing material during the manufacturing process and roughens the surfaces; both can affect the interfacial area. Billet et al. (12) demonstrated that conditioning new packing can minimize changes in the interfacial area. During this conditioning period, the tower was operated under a wide range of liquid and gas loading rates to find the limits of those rates for reasonable operation; this extensive operation, which included extreme conditions, also ensured that any instability in the packing arrangement would be eliminated prior to actual use. The set of tests on each packing material was performed over a period of several days. The experiments were conducted by holding the liquid loading rate constant for several hours and incrementally increasing the gas flow rate to obtain each successive data point. One or two liquid loading rates were done each day of experimentation. Throughout the experimentation with each packing material, no shift or slumping of the packing occurred; any changes in the void volume would have been evident in the viewing window at the top of the column. Headspace free samples were obtained by filling sample bottles from the waste line at a low flow rate, minimizing stripping losses and the entrainment of air bubbles. Samples were logged and put on ice until later analysis; all analyses were performed within 24 h of sampling. A standard protocol for headspace analysis with gas chromatography to analyze the VOCs was developed and used in this research. The analytical equipment (all manufactured by Hewlett-Packard) consisted of a 19395A headspace sampler, a 5890A gas chromatograph (GC), and a 5895A computer workstation. The method detection limit (MDL) is defined as the minimum concentration of a substance that can be measured and reported with 99% confidence that the value is above zero (13). A value of 1 µg/L was established as the MDL for all compounds in this study.

Results For each set of experimental conditions, the amount of mass transfer was calculated from the compound’s Henry’s constant, monitored gas and liquid flow rates, and influent and effluent concentrations. After calculation of S, as defined in eq 3, the overall mass transfer coefficient KLa was determined as the only unknown in eq 4. Because the data for KLa in this research were to be used to evaluate the accuracy of the Onda correlations, it was critical to understand the potential for error in the values obtained with the method described above. The evaluation of KLa is very sensitive to experimental errors or limitations in two regions, as indicated in Figure 2 and explained subsequently. The curved line in Figure 2 indicates the calculated removal efficiency in a tower of a particular height, cross-sectional area, and mass transfer coefficient; these calculations are an application of eq 4 (rearranged). The trends of this line at low stripping factors and very high removal efficiencies are what is important here. At the low values of the stripping factor (S < 2), a small error in the magnitude of the calculated stripping factor can produce a large error in the calculated overall mass transfer coefficient; Roberts et al. (4) have a good discussion of this type of error. The magnitude of the calculated stripping factor can be easily affected by small errors

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FIGURE 2. Conditions where the calculated overall mass transfer coefficient is sensitive to experimental error. (The line depicts representative predicted removal efficiency within the tower at a specified overall mass transfer coefficient.)

associated with the measurement of the volumetric air and water flow rates, the temperature of the water in the column, or the value of Henry’s constant. In turn, the S/(S - 1) term before the logarithmic term in eq 4 as well as the logarithmic term itself create significant error in the calculation of KLa when S < 2. The steep reduction in removal efficiency as S decreases below 2 shown in Figure 2 is suggestive of the sensitivity of this equation in this region. The second region of sensitivity to experimental error occurs when the effluent concentration is near the method detection limit (MDL) and the fractional removal efficiency is high. In this research, KLa was determined using only one set of influent and effluent concentration values for each condition; with this method, small analytical errors in determining the effluent concentration when it is small can lead to larger errors in the value of the ratio CLI/CLE in eq 4 and, thus, can lead to large errors in the calculated KLa. In terms of Figure 2, this region coincides with a high removal efficiency (near unity). The asymptotic approach of the removal efficiency to 100% at high stripping factors in Figure 2 is suggestive of this type of error; in this region, wide variations of KLa lead to minor changes in removal efficiency and, conversely, minor changes in removal efficiency cause wide variations in the calculated KLa. In light of the sensitivity in these two regions and the need for ideal flow to meet the assumptions of the model, data were not used in the subsequent analysis if the conditions violated any of the following criteria: if flooding was observed in the column, if the stripping factor was less than 2.0, if the effluent concentration was less than 1.0 µg/L, or if removal efficiency was greater than 99.5% and the effluent concentration was less than 7.0 µg/L. Of the 230 data points obtained experimentally, 53 data points were omitted because of these criteria. Overall Fit to Onda Correlations. The relationship between the predicted and observed values of KLa are shown on parity plots in Figure 3 for each packing tested. Overall, the Onda predictions result in a good fit to most of the experimental mass transfer coefficients. All the data points are within (30% of the Onda predicted value, except 13%

FIGURE 3. Parity plots for the mass transfer coefficients of the four packing types tested. TABLE 2

Experimental Results: Deviations from Onda Correlations

packing type 2.5-cm Pall rings Snowflake CMR 2A Nor Pac 2 all packings

% of data % of data % of data underwithin within no. of predicted (30% (20% av points by Ondaa of Onda of Onda APEb 12 18 64 83 177

100 89 23 86 64

100 94 100 87 93

67 78 94 66 77

17.5 11.6 10.1 15.1 13.1

a Percent of data that Onda’s mass transfer predictions are less than experimental mass transfer coefficient. b Absolute percent error (APE) ) |KLapred - KLaobsd/KLaobsd| × 100%.

of the Nor Pac data points and one Snowflake point. The data shown in Figure 3 are summarized in Table 2 with statistics about each packing and the overall data set. If a line 17% greater than parity (observed equals predicted mass transfer) is constructed on a parity plot containing all of the data, then 95% of the data lies below. A line on the same parity plot that is 35% less than parity would result in 95% of the data being situated above the line. Thus, 90% of the mass transfer data falls between a 17% overprediction and a 35% underprediction by Onda of the mass transfer. On a parity plot that excludes the Nor

Pac data, 90% of the remaining mass transfer data falls between a 18.0% overprediction and a 23.0% underprediction. Snowflake and 2.5-cm Pall rings were tested with TCE as the only contaminant; the Onda correlations underpredicted nearly all of the experimental data points. Both single and multiple component experiments were performed using the Cascade Mini-rings (CMR) and Nor Pac brands. No systematic deviation between the Onda predictions and experimental values related to the volatility (different compounds) was detected; like Munz and Roberts (11), no multiple component effects on mass transfer were detected at the concentrations studied. Mass transfer for the CMR packing material was predicted quite well by Onda, better than the other three packings in this study. Taken together, these results show that the Onda correlations can predict reasonably well the mass transfer of volatile compounds of typical environmental concentrations in stripping towers using large random packing materials, although an appropriate safety factor should be used in design to account for the deviation between the predicted and observed mass transfer coefficients. Critical Surface Tension. The value for the critical surface tension that was used in this study was 0.033 N/m, but this value is not known with certainty. Increasing the critical surface tension to 0.040 N/m, a value in the range suggested by Little and Selleck (3), increased the Onda


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predicted values of mass transfer by 1-6% depending upon the packing, temperature, and liquid flow rate and, therefore, reduced the tendency for underprediction. The increased critical surface tension improved the general fit of Onda to the Nor Pac, Snowflake, and 2.5-cm Pall Ring data in this study. To minimize the Onda prediction deviations from the experimentally determined mass transfer data by increasing the surface tension, an unrealistic value of 0.090 N/m would be required. The sensitivity of the critical surface tension might be masked by the other deficiencies in the Onda correlation. Deviations from the Onda Predictions. A closer inspection of the data reveals a trend in the deviations from the Onda predictions. The data in the plots in Figure 3 are clustered in four groups for each packing, although some of these clusters are more obvious than others. For three of the four packing materials, each group of data points appears as an “L” rotated 90° clockwise in Figure 3. The L-shape is not apparent for the 2.5-cm Pall rings, possibly because of the limited data. Each group represents a different liquid loading rate (QL/A). Within each liquid loading rate group, each data point represents a different gas loading rate (QG/A), and a systematic pattern of deviation from Onda occurs. The vertical section of the rotated L occurs at low gas flow rates; the experimental results for KLa are less sensitive to changes in gas flow rate than Onda predicts. The horizontal section occurs at high gas loading rates, and here the sensitivity of KLa to gas flow rate is higher than Onda predicts. This rotated L can also be observed in data of Mertooetomo et al. (14). Varying the surface tension of the packing does not affect the L-shape on the parity plots, only the magnitude of their deviations from the Onda predicted mass transfer coefficients. These trends in the data are not related to the order of the experiments. While Onda yields an overall good fit, clearly there appears to be some systematic error(s). Thus, the question to investigate is: where are the errors and what can be learned about these errors from the data in this research? To investigate the Onda correlations for systematic errors, four techniques were used. The first two techniques isolate the relationship between the overall mass transfer coefficient and two individual independent parameters: volumetric liquid (QL/A) and gas (QG/A) flow rates, respectively. By examining the fit of relationships between these independent parameters and the mass transfer, significant systematic errors might be detected. The third technique concerns the identification of any trends between errors in the transfer rate prediction and the volumetric gas flow rate. The fourth technique involves identification of a relationship between transfer rate prediction errors and the relative contribution of Onda’s gas-film correlation to the overall mass transfer resistance. Validity of the Functionality of Liquid Loading Rate. To quantify directly the effect of varying the liquid volumetric loading rate on the overall mass transfer coefficient is complex and requires several assumptions. According to eqs 5 and 7, the Onda correlations predict that an increase in the liquid velocity will affect both the individual liquid film transfer coefficient (kL) and the specific wetted area (a). The general trend expected is that the overall mass transfer coefficient will increase. In an attempt to quantify the relationship of the specific wetted area to the liquid loading rate, described exactly in eq 7, the following simplification is assumed:

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a ) k′

( ) QL A

p

(11)

where k′ is the constant describing all terms independent of the liquid loading rate in eq 7, and p is some exponential power describing the relationship of a to QL/A. The relationship of the liquid loading rate to the specific wetted areas (calculated from eq 7) was evaluated using eq 11 for the four packing materials tested in this research. A linear regression of the log transformed data (a vs QL/A) resulted in excellent fit, with an R2 value greater than 0.99 for each type of packing. The value of p found ranged between 0.255 and 0.284, with the average being 0.269 for the packings tested. According to these results, a is the product of (QL/A)0.27 and some constant k′. This value can be substituted into eq 5 to determine the relationship of the individual liquid transfer coefficient and the liquid velocity. The result is that kL is equal to the product of (QL/A))0.49 and some constant k′′. If a and kL are expressed in terms of QL/A, eq 2 can be rewritten as

1 1 1 + ) KLa k′′′(Q /A)0.76 k Hk′(Q /A)0.27 L G L

(12)

where k′′′ is the overall constant combining the terms k′ and k′′. The second term on the right-hand side of eq 12 represents the gas-film resistance. If the gas-film resistance is assumed to be negligible, then eq 12 can be rewritten as

1 1 ) KLa k′′′(Q /A)0.76

(13)

L

After inversion, eq 13 predicts that that a log-log plot of the mass transfer coefficient and the liquid velocity should be linear with a slope equal to 0.76. If the assumptions that the gas-film resistance is negligible and that the wetted area can reasonably be represented by eq 11 are correct, the plotting of experimental data in this fashion should yield lines whose slopes are equal to 0.76. When experimental data were analyzed in this fashion, a linear relationship was observed, and the slopes of the lines were all quite close to 0.76, as shown in Figure 4. These results confirm that the Onda correlations are essentially correct in predicting the effect of liquid flow rate on gas transfer. The slight deviations from the expected slope are also insightful. The greatest deviation from the expected slope was seen at the lowest gas velocity (Figure 4A) where it is expected that the gas-film resistance plays a more significant role in mass transfer and might not be negligible as assumed in this analysis. At the lowest gas velocity (0.24 m3/m2 s, Figure 4A) and highest liquid velocity (26.3 × 10-3 m3/m2 s), the gas-film resistance ranges between 19% and 51% of the overall resistance to mass transfer according to the Onda correlations for PCE and CHCl3, respectively. On the contrary, at the highest gas velocity (1.97 m3/m2 s, Figure 4C) and highest liquid loading (26.3 × 10-3 m3/m2 s), the range was between 4% and 16%. Although the gas-film resistance theoretically should be small, the slopes on Figure 4 became larger as the gas loading rate increased above 1.0 m3/m2 s (Figure 4, parts B and C). Also, close inspection of all three parts of Figure 4 reveals that the highest liquid loading rate tends to increase the slope. The greater than expected slope is believed to be due to an error in Onda’s wetted surface area correlation (eq 7) at larger gas and liquid loadings. This error is

FIGURE 4. Effects of increasing liquid flow on the overall mass transfer coefficient. (results shown are from Cascade Mini-ring packing.)

discussed subsequently. Overall, this analysis confirms that the Onda correlations correctly predict the effect of the liquid flow rate on the overall mass transfer coefficient; however, minor deviations from the theoretical result do occur, especially at extreme loading rates. Validity of the Functionality of Gas Flow Rate. Isolating the relationship in the Onda correlations between the overall mass transfer coefficient and the gas flow rate is simpler than for the liquid flow rate. The gas flow rate is a parameter only of the gas-film transfer coefficient (kG); as shown in eq 6, kG is proportional to the gas loading rate (QG/A) to the 0.7th power. The least volatile chemicals (CHCl3 in this research) should show the most pronounced effect as the superficial gas velocity is varied, because of the increased importance of the gas-film resistance. According to eq 2, the importance of the gas-film resistance increases as the product of the individual gas-film transfer coefficient and Henry’s constant decreases. Therefore, the compound with the smallest Henry’s constant should exhibit the greatest gas-film resistance effects, especially at the lower superficial gas velocities. The effects of changing the gas loading rate on the gasfilm resistance should also be evident on the overall liquid film mass transfer coefficient (KLa). According to eq 2, a linear relationship exists between the total resistance (1/ KLa) and the gas-film resistance (1/kGaH). Substituting the relationship that the gas-film resistance is proportional to the gas loading rate to the 0.7th power into eq 2 suggests that there should be a linear relationship between the total

FIGURE 5. Effects of the gas flow rate on the overall mass transfer coefficient. (Results shown are from Nor Pac 2 packing.)

resistance and the reciprocal of the gas loading rate to the 0.7th power. The intercept of such a line is equal to the liquid film resistance (1/kLa) and the slope is the reciprocal of the product of Henry’s constant and the specific interfacial area. The slope of the experimental results should increase as the Henry’s constant is decreased in this study. Data from this research are plotted as suggested above in Figure 5, with separate parts of the figure for each compound and separate lines for different liquid loading rates. The data for the different compounds were obtained in the same multicomponent experiment. Obviously, the data in Figure 5 are not linear; the nonlinearity suggests that Onda’s gas resistance correlation does not correctly predict the relationship between KLa and the gas flow rate. All three compounds shown have very similar trends on this figure. Similar results were observed for all of the multicomponent experiments. Systematic errors in the Onda correlations can be examined better by explicitly viewing deviations from the Onda predictions as a function of the gas loading rate. In Figure 6, the fractional difference (i.e., relative error) between the predicted and observed mass transfer coefficient is shown plotted against the gas velocity for the four packing materials used in this study. The figure is divided into two parts for clarity. Three of the four packings in this study have a checkmark or U-shaped trend in Figure 6, with the change of slope occurring at approximately 1.0


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FIGURE 7. Relationship between deviations from onda and the importance of the gas-film resistance. (Data from CMR and Snowflake packings. Only data for gas loading rates below 1 m3/m2 s are shown. % R and % D are explained in the text.)

FIGURE 6. Impact of gas flow rate upon relative errors in the mass transfer coefficients predicted by onda correlations. (Lines drawn between average values at each condition.)

m3/m2 s. The checkmark-shaped trend is more evident for NorPac and Snowflake than for CMR at gas flow rates below 2.8 m3/m2 s. No trend was identified in the 2.5-cm Pall Ring data from this research, possibly because of the small number of data points. The data of Gossett et al. (2) for two packing materials (Tri-Pack and 2.5-cm Pall Rings) were also plotted on a similar graph, but the data range was too small to see fully the same effect; all of Gossett's data were at low gas loading rates. The right-hand section of the checkmark-shaped trend in Figure 6 for CMR, Snowflake, and Nor Pac is the same as the horizontal section of the rotated L of Figure 3; both representations mean that KLa is more sensitive to gas velocity in this range than Onda predicts. As the gas loading increases in this range, mass transfer for these packing materials tend to be underpredicted by Onda. At high gas flows, the Onda correlations predict that the liquid film resistance accounts for nearly all mass transfer resistance. Thus, only eqs 5 and 7, Onda’s liquid film resistance, and specific wetted area equations, respectively, are needed to model mass transfer; both of these parameters, at least according to those equations, are independent of the gas loading rate. The experimental results shown in Figure 6 contradict the assumption of independence of the specific surface area and liquid film resistance from the gas velocity. The low value of the calculated mass transfer coefficients at the higher gas velocities may be due to an error in Onda’s specific wetted surface area term (eq 7), which is assumed to be proportional to the specific interfacial area of the packing. Potentially, at higher gas velocities, film surface rippling, liquid droplet dispersion, and the occurrence of gas bubbles in liquid puddles contribute more to removal than expected. The gas velocity is a parameter in the specific wetted surface area determination in the Shulman mass transfer correlation (15) and in Bravo and Fair's (5) specific

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wetted area term for distillation towers. The gas loading rate may influence the specific wetted surface area for large packing, particularly at gas velocities above the upper limit used in Onda’s original data set, 1.5 m3/m2 s. Data reported by Gossett et al. (2) for a smaller, more dense packing (2.5-cm Pall rings) exhibit the same trend of an increasing underprediction of mass transfer by Onda as the gas flux increased. Because of the smaller size of the packing, these results were evident at lower gas flow rates but similar pressure drops as in the experiments performed in this research. Gossett’s 2.5-cm Flexisaddles also exhibited similar behavior. However, for two other packing materials (5-cm and 1.5-cm Pall rings) investigated by Gossett, errors in the Onda predictions were not a function of gas flow rate; it is possible that trends are not apparent because of the limited range of gas and liquid loadings examined. The left-hand section of the checkmark-shaped trend in Figure 6 for CMR, Snowflake, and Nor Pac is the same as the vertical section of the rotated L of Figure 3, which represents less sensitivity to KLa than Onda predicts. As gas loading decreased below 1.0 m3/m2 s, mass transfer for these packings tended to be underpredicted by Onda; the 5-cm Tri-Pack data from Gossett et al. (2) also show this trend. Gas-film resistance is the most significant at the lowest gas flow rates. Roberts et al. (4), Gossett et al. (2), and Little and Selleck (3) all have suggested that the Onda correlations overestimate the gas-film resistance to mass transfer, resulting in an underestimation of mass transfer. An error in the gas-film resistance correlation may be the explanation for the overestimation of the gas-film resistance to mass transfer at low gas loading rates. If an error in Onda’s gas-film resistance correlation exists, then a relationship should exist at the lowest gas flow rates between the percent difference between experimentally determined and Onda predicted mass transfer coefficients [termed % D by Gossett et al. (2)] and the fraction of the total resistance in the gas-film (% R by Gossett) as predicted by Onda. A relationship between % D and % R was found in the data for the CMR and Snowflake packing, as illustrated in Figure 7. The CMR and Snowflake brands show a tendency for a larger underprediction of mass transfer as

the importance of the gas-film resistance increases. The trend in Figure 7 is similar to that observed by Gossett et al. (2) for the 5-cm Tri-Pack data. Like in Gossett’s research, the trend is only obvious when a significant quantity of data has a % R of more than 20%; in this research, none of the data for Nor Pac and 2.5-cm Pall rings had a % R greater than 20%. In Gossett’s study, only for 5-cm TriPacks did a large quantity of the data have more than 20% gas-film resistance. Thus, the Onda correlations tend to underpredict mass transfer as the importance of the gasfilm resistance increases for three packing materials: CMR and Snowflake of this research and 5-cm Tri-Pack of Gossett et al. (2). The data used by Onda et al. (1) to develop the gas-film resistance correlation contains significant scatter, as shown on the correlation plot of the original paper. A range of constants and exponents on the dimensionless terms in the correlation conceivably could fit Onda’s original data. Onda recommended different coefficients in the gas-film resistance correlation (eq 6) for “small” and “large” packing. A value of 2.0 is recommended for packing smaller than 1.5 cm, such as Raschig rings and Berl saddles. A coefficient of 5.23 is recommended for packing greater than 1.5 cm. Only 2 out of 25 packing materials in the data set available to Onda et al. had diameters greater than 2.5 cm. As shown herein, when the gas-film resistance is significant, application of Onda’s original gas-film resistance correlation to large random packing materials appears to result in significant prediction errors. Further study is needed to identify suitable alternatives. Potentially, a new (larger) coefficient and a different exponent on the gas Reynolds number term could enable Onda’s gas-film resistance equation to yield a better fit to large packing data.

Conclusions and Engineering Applications The Onda correlations generally provide good prediction of mass transfer for large (g5 cm) random packing materials. More than 95% of the data was within +17% and -35% of the Onda prediction. The Onda correlations can be used for design when an appropriate safety factor is applied. The functionality of the volumetric liquid loading rate (QL/ A) in the Onda correlations is correct. The functionality of the volumetric gas loading rate (QG/ A) in the Onda correlations is not correct, especially at extreme values. At both low and high gas flow rates, the Onda correlations tend to underpredict the mass transfer, although at intermediate flows they predict well. The sources of error appear to be in the wetted surface area and/or the gas-film resistance equations. The error distribution of the Onda correlations is dependent upon operating conditions for large (g5 cm) random packing frequently used for environmental ap-

plications. When air stripping is used to remove semivolatile compounds (such as DBCP and Bromoform), gas velocities of up to 2 m3/m2 s may be required. At such high gas flow rates, Onda apparently underpredicts mass transfer. Also, air pollution regulations frequently mandate off-gas treatment for air stripping towers. When off-gas treatment is required, minimal gas flow rates are often economically optimal (16); at low gas flow rates, the gas-film resistance contribution to the overall mass transfer resistance can be large, and Onda again tends to underpredict mass transfer. Increasingly air strippers are being designed to use large random packing materials at operating conditions where the Onda correlations tend to underpredict mass transfer. When designing for these operating conditions, the engineer could choose to reduce the safety factor on the mass transfer coefficient or to use the tendency for underprediction as an additional safety factor on the design.

Literature Cited (1) Onda, K.; Takeuchi, H.; Okumuto,Y. J. Chem. Eng. Jpn. 1968, 1 (1), 56. (2) Gossett, J. M.; et al. Air Force Engineering & Services Laboratory Report No. ESL-TR-85-18, June 1985, Tyndall Air Force Base, FL. (3) Little, J. C.; Selleck, R. E. J. Am. Water Works Assoc. 1991, 83 (6), 88. (4) Roberts, P. V.; Hopkins, G. D.; Munz, C., Riojas, A. H. Environ. Sci. Technol. 1985, 19 (2), 164. (5) Bravo, J. L.; Fair, J. R. Ind. Eng. Chem. Process Des. Dev. 1982, 29 (1), 162. (6) Hines, A. L.; Maddox, R. N. Mass Transfer Fundamentals and Applications; Prentice-Hall: Englewood Cliffs, NJ, 1985. (7) Lamarche, P.; Droste, D. L. J. Am. Water Works Assoc. 1989, 81 (1), 78. (8) Reid, R. C.; Prausnitz, J. M.; Polling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill Book Company: New York, 1987. (9) Fair, J. R.; Steinmeyer, D. E.; Penney, W. R.; Crocker, B. B. in Perry’s Chemical Engineers’ Handbook, 6th ed.; McGraw-Hill: New York, 1984; Section 18. (10) Staudinger, J.; Knocke, W. R.; Randall, C. W. J. Am. Water Works Assoc. 1990, 82 (1), 73. (11) Munz, C.; Roberts, P. V. J. Am. Water Works Assoc. 1987, 79 (5), 62. (12) Billet, R.; Mackowiak, J.; Koziol, A. Fette Seifen Anstrichm. 1985, 87 (5), 201. (13) U.S. EPA. Methods for Organic Chemical Analysis of Municipal and Industrial Wastewater; U.S. EPA: Washington, DC, 1984; 40 CFR, Part 136, Appendix A, Method 601. (14) Mertooetomo, E.; Valsaraj, K. T.; Wetzel, D. M.; Harrison, D. P. Water Res. 1993, 27 (7), 1139. (15) Treybal, R. E. Mass-Transfer Operations, 3rd ed.; McGraw-Hill Book Company: New York, 1980. (16) Dvorak, B. I.; Lawler, D. F.; Speitel, G. E., Jr.; Jones, D. L.; Boadway, D. A. Water Environ. Res. 1993, 65 (7), 827.

Received for review June 13, 1995. Revised manuscript received October 23, 1995. Accepted November 7, 1995.X ES950408+ X

Abstract published in Advance ACS Abstracts, January 15, 1996.


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Evaluation of the Onda Correlations for Mass Transfer with Large

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