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Ind. Eng. Chem. Res. 1996, 35, 2660-2671
SEPARATIONS Sieve Tray Performances for Steam Stripping Toluene from Water in a 4-ft Diameter Column John G. Kunesh,* Thomas P. Ognisty,† Michaharu Sakata,‡ and Guang X. Chen Fractionation Research, Inc., P.O. Box 2108, Stillwater, Oklahoma 74076
The liquid holdup, pressure drop, and mass transfer efficiency of sieve trays for the steam stripping trace toluene from water were measured from a 4-ft column at atmospheric pressure. The measured data were then compared with predictions from often-used models. It was found that the published efficiency models whether based on distillation or stripping systems are unable to predict both the trend and value of the measured efficiency. Since the 4-ft column owned by Fractionation Research, Inc. (FRI) can be considered as an industrial-scale column, the measured efficiency provides immediate design guidelines for such services. Introduction As the government regulations and industrial criteria become more stringent, air stripping for removal or reduction of chemical discharge to the environment is increasingly unable to give satisfactory results. This is because, for most cases, air stripping simply transfers the organic pollutants to air from water and the actual amount of chemical discharge to the environment is not reduced. In situations where low level heat is available, as it is in most refineries and chemical plants, steam stripping organic contaminants from effluent water becomes the most desirable method of treatment. The contaminant in steam stripping is recovered as a concentrated, immiscible liquid phase for recovery, recycle, or further treatment. However, there is a great deal of uncertainty in the design of such facilities, particularly when the tray efficiency is in question. Determination of the theoretical stage requirement based on laboratory data is straightforward because the concentration levels involved place the VLE in the Henry’s law regime (Hooper and Prausnitz, 1988). However, converting the theoretical stage requirement into actual installed stages is another matter. Columns designed for water cleanup service must meet design product specifications or the plant will be shut down. Therefore, all uncertainty must be covered by safety factors. However, unnecessary, non-productive investment is a direct charge against plant profitability. Additionally, excessive oversizing can be counterproductive, as it may cause a lessening of otherwise obtainable mass transfer performance. There are three principal reasons why the efficiency to be expected in the operation of these columns is an area of high uncertainty: 1. The concentration levels required (10-9) may be outside the range of validity of the mass transfer models. 2. Performance tests of operating commercial units are usually indeterminate. Successfully operating units † Present address: The M. W. Kellogg Co., 601 Jefferson Ave., Houston, TX 77210. ‡ Present address: The Ralph M. Parsons Co., 100 W. Walnut St., Pasadena, CA 91124.
normally produce a product which is at or below the limit of detection of the analytical equipment. Changing operating conditions to the point of reliable analytical detection could put the unit in violation of environmental regulations. Thus, the amount of overdesign is unknown. 3. Such systems are liquid-resistance controlled mass transfer systems. Very little data exist to validate predictive models for such systems (Huang et al., 1992). What data do exist have been obtained on laboratory scale columns. In view of the above, the study described in this paper was undertaken to satisfy both a short and long range objective: 1. Obtain immediate design guidelines for columns which must remove hydrocarbons from water. 2. Check the predictive models found in the literature. 3. Provide basic data to extend tray efficiency models to dilute, liquid-resistance controlled systems. Experimental Section Choice of Systems. Aromatic hydrocarbons have the highest solubility in water of the various hydrocarbon types and are the subject of the most stringent standards. A single compound available in high purity was required so that the program results could be utilized in modeling. Toluene was selected as representative of this class of materials. Its solubility and volatility data are well-known. Its toxicity is moderate. Its boiling point is such that the reboiler and condenser temperatures were easily within the utility system capabilities. Reliable analytical methods to concentrations of 10-9 were available with no interference from residuals of the paraffinic hydrocarbon test systems normally utilized in the equipment. VLE and Other Physical Properties. The validity of any conclusions regarding stage efficiency is totally dependent on the accuracy of the VLE data employed. A review of literature data with recommendations on the values to be used was commissioned and is available from FRI (Hooper and Prausnitz, 1988). Figure 1 presents the Henry’s constant for toluene in water as a function of temperature.
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Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2661
Figure 1. Henry’s constant.
Figure 3. Sieve tray dimensions. Table 1. Tray and Column Dimensions
Figure 2. Process flow diagram.
Choice of Flow Scheme. It is desired to recover toluene as a liquid, so that the need for further treatment of the overhead can be eliminated. Figure 2 is a simplified process flow diagram of the experimental unit as it was configured for this program. For all runs, the column was operated in a stripping mode. The liquid in the feed tank was pumped to the top of the column. A Milton Roy diaphragm pump, Model R151B, was used to inject a measured amount of pure toluene upstream of the feed pump. This allowed vigorous mixing of the charge from the feed tank and toluene being injected. To ensure additionally contacting between the hydrocarbon and water-rich phase, a static mixer, 2 ft (610 mm) in length, was installed downstream from the feed pump. The overhead vapor was totally condensed and routed through the reflux accumulator. Because of the low solubility of toluene in water at temperatures lower than column conditions, a water-rich phase and toluenerich phase existed in the accumulator. The hydrocarbonrich phase was decanted and recycled through the injection pump into the feed stream. The water-rich phase was cycled back to the feed tank. Choice of Hardware. Sieve trays have been in wide use in the petroleum and chemical industries since the 1950s and are the simplest cross flow trays. They are nonproprietary and inexpensive to fabricate. Six sieve trays having 12.7 mm diameter holes on 38.1 mm triangular centers were used in this study. The hole area was 7.5% of the bubbling area which was 0.86 m2.
column diameter, m column cross-sectional area, m2 tray spacing, m flow path length, m outlet weir height, m outlet weir length, m tray thickness, mm hole diameter, mm hole spacing, mm downcomer area at top, m2 downcomer area at bottom, m2 downcomer clearance, mm free area, m2 bubbling area, m2 number of holes per tray hole area, m2 hole area, percent of bubbling area perforated sheet edge of hole facing vapor flow downcomer type number of trays
1.22 1.17 0.686 0.762 0.0508 0.94 1.6 12.7 38.1 0.14 0.14 38.1 1.01 0.86 508 0.0644 7.5 stainless steel sharp straight 6
The vertically straight downcomers occupied 13% of the tower area. The downcomer exit clearance was 38 mm. Outlet weirs were 50.8 mm high by 940 mm long. Tray spacing was set at 686 mm to allow a higher upper operating region for the efficiency measurements. Tray design details are given in Figure 3 and Table 1. This tray design was also used in a previously published study utilizing conventional hydrocarbon systems (Sakata and Yanagi, 1979). In that study this tray demonstrated overall efficiency on the order of 70%-80%. Liquid sampler and thermocouple locations are shown in Figure 4. A view port was located between trays 3 and 4 for visual observations. Pressure drops across trays 1-6, 1-3, and 4-6 were monitored and measured. Two bubblers were installed on tray 3, one at the center of the tray and the other near the outlet weir, so that liquid holdups at these two locations could be obtained and compared. Analytical Details. The solubility of toluene in water at 100 °C is approximately 0.0003 mole fraction or 1500 mg/L (Hooper and Prausnitz, 1988). Stripping
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2662 Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996
Figure 6. Gas chromatography calibration curve.
Figure 4. Probe locations.
Figure 5. McCabe-Thiele diagram.
removes toluene from this maximum possible concentration level to succeedingly lower values depending upon the efficiency of the tray. A McCabe-Thiele diagram which illustrates the relationship between the equilibrium curve and operating line is shown for the toluene/water system in Figure 5. The equilibrium curve is essentially a straight line, because the system obeys the Henry’s law relationship, ye = 2300x at 1 atm (Hooper and Prausnitz, 1988). After fewer than three theoretical stages the liquid composition falls well below 1 × 10-9 mole fraction, or about 1 part per billion. At these extremely low concentration levels it was necessary to obtain a very sensitive analytical device. To measure low concentrations of toluene in water, a Hewlett Packard 5890 gas chromatograph equipped with an HP 3393A integrator and a photoionization detector (PID), Model PI-52-02A manufactured by HNU Systems, Inc., was used. A head space sampler was obtained but was not needed. The HP 5890 gas chromatograph was fitted with a 6-ft 1/8-in. diameter stainless steel packed column. The column packing used was 5% SP-1200/1.75% Bentone 34 on a 100/120 Supelcoport. The SP-1200 is a low
polarity ester type stationary phase, and the gelled adsorbent Bentone 34 is a montmorillonite treated with amine. This column is recommended by the Environmental Protection Agency, as outlined in Method 602 (EPA, 1984) for analyzing purgeable aromatics in water. The gas chromatograph was operated at 90 °C with a helium carrier gas flow rate of 30 mL/min. The photoionization detector, PID, ionizes a vapor sample with ultraviolet light. The current produced by the ion flow is measured and is proportional to the concentration within a particular range. The PID detects organic and some inorganic chemicals in the picogram to microgram range, with ionization potentials less than the UV source (in this case 10.2 eV). The PID detector has a wider linear concentration range and is much simpler to operate than the commonly used flame ionization detector (FID). The correlation between the response curves recorded by the integrator and the toluene concentration were determined by calibration. As recommended in the EPA methods (EPA, 1984), 10-mL stock standard solutions were prepared by adding a carefully measured amount of toluene to methanol and then successively diluting portions of this mixture to obtain several secondary dilutions called calibration standards. At the lowest toluene levels (picograms) the dilution factor was more than 1 million. Initially, the dilutions were made with distilled water, but the samples yielded a scattered integrator response with no consistent trend. The calibration solutions were then prepared by diluting with pure methanol to give an improved and repeatable linear response upon integration. Other investigators (API, 1985) have found unsatisfactory results when diluting gasoline with water and have used carbon disulfide for preparing calibration standards. The toluene-in-water dilutions were retried to simulate the actual experimental samples. By carefully preventing toluene from being stripped when transferring between storage flasks and allowing sufficient time for maximum absorption to occur (overnight) between dilutions, comparable results to the methanol calibration standards were obtained. Varying liquid sample sizes with several different calibration standards were then analyzed to obtain the calibration curve given in Figure 6. Measuring errors were more apparent at the very small sample sizes, so a 2-µL standard injection size was established. Several water sources were used to make certain the toluene integration peaks were not obscured by unexpected contaminants. The toluene calibration was not repro-
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Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2663
Figure 8. Composition profiles. Figure 7. Operation diagram.
ducible below 30 pg, or liquid mole fraction levels below 3 × 10-9. Estimated error margins range from (30% at the lower concentrations to (10% at the higher values. The primary sources of analysis error at the low concentrations were the inability of the integrator to distinguish between normal noise levels and the extremely low response values of toluene in this region, and problems with handling the dilution of the mixture without allowing toluene to strip away. The sample analysis was conducted in order of ascending toluene concentrations (eg. bottoms, tray 1, tray 2, etc.) to minimize sample to sample contamination. The injection syringes were flushed several times with water and cleaned with syringe cleaner between each sample. Between run sample sets, water blanks were injected to flush the gas chromatograph of excess toluene and contaminants accumulated at the high concentration levels. The solubility limit of toluene in water at ambient conditions was also determined experimentally by testing a mixture of excess toluene in water left to equilibrate over several days. This sample was then used to periodically check the sensitivity of the analytical equipment at the higher toluene concentrations. The trace toluene in water analysis covered several orders of magnitude in concentration range and was a severe test of analytical technique. Experimental Range. A matrix of vapor and liquid rates was used to study the tray efficiency by operating the column as a stripping section of a tower. The following procedure was employed to obtain the combination of vapor and liquid rates: 1. The internal liquid rate was selected. 2. The feed rate to the column top was made equivalent to the liquid rate. 3. Several reboiler steam rates were selected to obtain vapor rates within a minimal entrainment and minimal weeping region. 4. The column condition for each combination of a vapor and liquid rate was maintained for approximately 2 h before pressure drop and other measurements were recorded and samples were taken. A duplicate sample set was obtained after 30 min for most runs. The combination of run conditions actually obtained is illustrated in the operation diagram shown in Figure 7. Four liquid rates were investigated at varying vapor rates that allowed liquid-to-vapor flow rate ratios to vary from about 1.0 to 20. Data Analysis Liquid Composition Profiles. The liquid compositions for the top inlet downcomer and subsequent outlet
downcomers are plotted for the 333 gpm (75.6 m3/h) liquid rate runs in Figure 8. In most cases replicate samples can be reproduced one another closely. For the dilute toluene concentrations encountered in these tests, the liquid composition profiles should be linear, as shown later. The expected linearity of the profiles allows screening of the data in the final efficiency determination. The lines drawn through the data were used to evaluate efficiencies for each run. Murphree Vapor Tray Efficiency (EMV). Several types of efficiencies can be obtained from the composition profiles shown in Figure 8. The Murphree vapor tray efficiency is usually expressed in terms of vapor compositions
EMV )
yn - yn-1 yn* - yn-1
(1)
where yn is the vapor composition of the light component leaving tray n, yn-1 is the vapor composition of the light component entering tray n, yn* is the vapor composition of light component in equilibrium with liquid leaving tray n. By material balance and the equilibrium relationship, eq 1 can be expressed in liquid compositions for the stripping section of a tower as follows:
EMV )
(L/V)(xn+1 - xn) L L - 1 x1 Kxn - xn V V
[
(
) ]
(2)
where K is the equilibrium ratio for the light component, L/V is the liquid to vapor rate ratio, x1 is the liquid composition of the light component leaving the column, xn is the liquid composition of light component leaving tray n, and xn+1 is the liquid composition of light component entering tray n. Because the liquid composition leaving the column is much less than the liquid composition for the trays above, eq 2 can be simplified without loss of precision to
EMV )
xn+1 - xn KV - 1 xn L
(
)
(3)
Murphree Liquid Tray Efficiency (EML). For liquid phase controlled mass transfer systems, the Murphree liquid tray efficiency is sometimes preferred and is expressed in terms of liquid compositions
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2664 Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996
EML )
xn+1 - xn xn+1 - xn ) xn+1 - xn* xn+1 - yn/m
(4)
where xn and xn+1 are the same as previous definitions and xn* is the liquid composition of light component in equilibrium with vapor leaving tray n, that is, xn* ) yn/ m. A mass balance between the tray n and the column bottom yields
V(yn - y0) ) L(xn+1 - x1)
L L yn ) xn+1 - x1 + y0 V V
(6)
Substituting yn into eq 4 gives
xn+1 - xn xn+1 x1 y0 + xn+1 λ λ m
(7)
where λ ) KV/L ) mV/L. If y0 ) 0 and x1 is much smaller than xn+1, eq 7 becomes
EML )
xn+1 - xn xn+1 - xn ) 1 xn+1 xn+1 1 xn+1 λ λ
(
)
(8)
If the λ is large (>100, e.g., in this study), eq 8 can be simplified as
xn EML ) 1 xn+1
(9)
Rearranging eq 14 gives the number of trays required for a specific separation at a given liquid tray efficiency
ln nactual )
( ) xexit xin
(17)
ln (1 - EML)
(1 - EML)xn+1 ) xn
(10)
Applying eq 10 for each tray gives
(1 - EML)x2 ) x1
(11)
(1 - EML)x3 ) x2
(12)
l (1 - EML)xn+1 ) xn
(13)
Multiplying the above equations both sides, respectively, produces
x1 xn+1
Overall Tray Efficiency (EO). An analytical method for obtaining the overall tray efficiency for very dilute systems is outlined below. It has the advantage of providing a method for smoothing the experimental data. Referring to Figure 9, line A is the equilibrium line, y ) KX ) mx. As noted previously, this is valid because the concentration level involved is in the Henry’s law region. The operating line has a slope of L/V. If the concentration at the column bottom is very small (undetectable), that is xbottom ) 0, ybottom ) 0, the operating line becomes y ) (L/V)x, shown as line B in Figure 9. Working through lines A and B, one can have the following: From x1 one obtains y1 by using y ) mx, y1 ) mx1; From y1 one obtains x2 by using y ) (L/V)x, x2 ) (V/ L)y1 ) (V/L)(mx1); From x2 one obtains y2 by using y ) mx, y2 ) mx2 ) m(v/L)(mx1) ) (V/L)m2x1; From y2 one obtains x3 by using y ) (L/V)x, x3 ) (V/ L)y2 ) (V/L)2m2x1 ) (mV/L)2x1; Generalizing for n theoretical stages: xn+1 ) (mV/ L)nx1 The following equation can then be obtained:
( )
xn+1 x1 ntheo ) ) EOnactual V ln m L ln
( )
Rearranging eq 9 yields
(1 - EML)n )
(16)
(5)
where y0 and x1 are mole fractions of the light component of entering gas and exiting liquid. Rearranging eq 5 produces
EML )
slope ) -log(1 - EML)
(14)
This procedure is also used to obtain the Fenske equation for total reflux. A semilogarithmic plot of the liquid compositions versus tray number should be linear for a constant mV/L and efficiency. The slope of the line gives the number of theoretical trays for the zone of trays (EO), as shown in Figure 10. This type of plot is useful to smooth the data and to screen questionable points. The overall tray efficiency can also be determined by using the McCabe-Thiele diagram. Interconversion of Tray Efficiencies. Based on their definitions, each of the three tray efficiencies described can be converted from one to another by
EMV ) EML )
and
-n log(1 - EML) ) log xn+1 - log x1
(15)
A semilogarithmic plot of the liquid compositions versus the tray number should be linear. The slope of this line can then be related to the liquid tray efficiency (EML) as
(18)
EML )
λEO - 1 λ-1
(19)
λEMV 1 + (λ - 1)EMV
( )( λ λ-1
)
λEO - 1 λEO
(20)
(21)
The magnitude of the various efficiencies can differ considerably, depending on the λ value. In this work, m ) 2300 and (L/V) varied from 1 to 20, resulting in λ values from 100 to over 2000. Thus, an overall tray
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Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2665
vertical direction. For most situations, the vapor is probably in plug flow with little back-mixing in the vertical direction because of high vapor velocity. However, the vapor back-mixing could be significant when the ratio of vapor density to liquid density, FG/FL, approaches 1, for example, at high-pressure conditions. The system used in this study has a very small density ratio, so that eq 22 may be used. It is extremely difficult to relate the Murphree tray efficiency (EMV) to the point efficiency (EOG) without knowing the exact liquid and vapor flow patterns on the tray. Although experimental measurements of liquid flow patterns on the tray have been made by many researchers, the prediction of such flow patterns by CFD is still difficult. Two ideal flow patterns, totally-mixed liquid and one-dimensional liquid flow with backmixing, are assumed for efficiency modeling in the literature. For totally mixed liquid on the tray, the Murphree tray efficiency is the same as the point efficiency without any efficiency enhancement
Figure 9. Diagram for determining overall tray efficiency.
EMV ) EOG
(25)
For the one-dimensional liquid flow with liquid backmixing, the Murphree tray efficiency can be related to the point efficiency by the AIChE model (AIChE, 1958)
EMV exp(η) - 1 1 - exp(-η - Pe) + ) EOG (η + Pe)(1 + (η + Pe)/η) η(1 + (η/(η + Pe))) (26) Figure 10. Graphic method for determining overall tray efficiency.
efficiency of 35% at λ ) 100 results in an EMV ) 4% and an EML ) 80%.
((
Relationship between NOG, EOG, and EMV. If it is assumed that the vapor is in plug flow through the froth and the liquid is completely mixed in the vertical direction, a steady state mass balance over an elemental strip of the froth gives
EOG ) 1 - e
(22)
-NOG
where NOG is the number of overall vapor phase mass transfer units and can be predicted by models found in the literature. If it is assumed that the vapor and the liquid are both completely mixed in the vertical direction, a similar mass balance gives
NOG 1 + NOG
(23)
Equations 22 and 23 represent two extreme cases of vapor plug flow and vapor completely-mixed situations. However, the real case is always between the two extreme cases discussed, which means that the vapor is always partially mixed in the vertical direction. If the froth is vertically divided into j cells and the vapor in each cell is completely mixed, then the following equation can be obtained
(
)
NOG EOG ) 1 - 1 + j
-j
(24)
where j is the number of vapor mixing cells in the
)
4λEOG Pe 1+ 2 Pe
Pe )
Tray Efficiency Models
EOG )
η)
0.5
)
-1
LFP2QL AbhclDe
(27)
(28)
where De is the eddy diffusivity and can be estimated from several empirical equations found in the literature. If there is no liquid back-mixing, eq 26 becomes
EMV )
eλEOG - 1 λ
(29)
For the system and the 4-ft column used in this study with the eddy diffusivity calculated from various equations found in the literature, eq 26 gives a result very similar to that from eq 29 for most conditions. This means that these models indicate that the liquid on the 4-ft tray in this study is very close to the plug flow. Relationship between NOL and EML. In order to simplify the problem, some assumptions have to be made: (1) the liquid is completely mixed in the vertical direction; (2) the gas is completely mixed between trays. A steady state mass balance over an elemental strip of froth gives
-L dx ) KOL(x - x*)ahf dA
(30)
where x* is in equilibrium with the bulk gas above the tray. Rearranging eq 30 yields
KOLahf dA dx )x - x* L
(31)
If the liquid is in plug flow from the inlet weir to the outlet weir without back-mixing, integration of eq 31
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2666 Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996
from the inlet weir to the outlet weir provides
KOLahfAb xn - x* )Ln xn+1 - x* L
d32, the interfacial area (a) may be given by
The overall number of liquid phase mass transfer units (NOL) is defined as
KOLahfAb MLKOLahfAb ) NOL ≡ L FLQL
(33)
If the liquid on the tray is totally mixed, a steady state mass balance on the liquid for the whole tray gives
(35)
From eqs 4, 33, and 35, the EML can then be related to the NOL by
NOL 1 + NOL
EML )
(36)
Equations 34 and 36 represent two ideal extreme cases of liquid plug flow and liquid completely-mixed situations. However, the real cases are always between the above two cases and the liquid is always partiallymixed in the horizontal direction. For partially-mixed liquid, the froth is horizontally divided into i cells. Each cell has the same bubbling area of Ab/i. The froth height and the (KOLa) are assumed to be the same for all cells. If the overall number of mass transfer units for the whole tray is NOL, then for each cell it is NOL/i based on eq 33. The liquid flow is presumed to be one-dimensional and the liquid in each cell is assumed to be completely mixed. The gas between trays is also assumed to be completely mixed. A similar mass balance gives
(
EML ) 1 - 1 +
)
NOL i
-i
(37)
where i is the number of liquid mixing cells in the horizontal direction. For systems whose vapor phase mass transfer resistance is absent, e.g., when m or λ is large such as the system used in this study, KOL can be considered to equal kL. The penetration theory (Higbie, 1935) gives
kL ∝
FL 0.5 D ML L
(38)
Combining eqs 38 and 33 yields
ahfAbDL0.5 ahclAbDL0.5 atLDL0.5 (39) NOL ∝ ) ) QL RQL R where tL is the liquid resident time on the tray and defined as
tL )
hclAb QL
(41)
1 t D 0.5 ) t D 0.5 d32R L L d32 1 - L L
(42)
If the bubble size is assumed to be a constant for all stripping systems involved with water, eq 42 becomes
(34)
L(xn+1 - xn) ) KOL(xn - x*)ahfAb
6 d32
Substituting eq 41 into eq 39 produces
NOL ∝
Combining eqs 4, 32, and 33 gives
EML ) 1 - e-NOL
a)
(32)
(40)
If the froth is uniform with a Sauter-mean bubble size
NOL ∝
t D 0.5 1-L L
(43)
Experimental data such as provided in this study are required to determine the parameters for eq 43. AIChE Model (1958). The AIChE model was the first recognized and the most commonly accepted model in the literature. It is covered well in the standard chemical engineering texts (Lockett, 1986; Kister, 1992). The model is based on the results of the number of mass transfer units from experiments using single phase mass transfer resistance systems (absorption and stripping). It also provides empirical equations for the liquid holdup and eddy diffusivity. Chan and Fair (1984) modified the AIChE model to represent most of the efficiency data available for largescale sieve trays. However, they retained the same correlation for NL as the original AIChE model. Thus, Chan and Fair’s model will give the same prediction as the AIChE model for the system used in this study because of the large λ. The NG correlation has little effect on the NOG when λ is large. Zuiderweg’s Model (1982). Zuiderweg (1982) reviewed sieve tray performance and proposed a method of predicting point efficiencies based on the commercialscale experimental sieve tray efficiency data of Fractionation Research, Inc. reported by Yanagi and Sakata (1982) and Sakata and Yanagi (1979). Correlations for the mass transfer coefficients in the vapor and the liquid phases were developed. By use of the Weber number and taking into account the effect of surface tension, the interfacial area was correlated with reference to the flow regimes. Equations outlined by Zuiderweg (1982) were used to identify the flow regimes. The liquid holdup is evaluated by Hofhuis and Zuiderweg’s correlation (1979) as
(FPb)
hcl ) 0.6hw0.5p0.25
0.25
(44)
This correlation was suggested to be applicable to both the froth and spray regimes. The flow parameter (FP) is defined by
FP )
()
L FG V FL
0.5
(45)
The main difference between the AIChE and Zuiderweg efficiency models is that the AIChE model is based on the absorption and stripping systems whose mass transfer resistance is confined in either the liquid or vapor phase whereas Zuiderweg’s model is based on distillation systems whose mass transfer resistances in both liquid and vapor phases are significant. Since these two models can basically represent all other
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Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2667 Table 2. Run Conditions and Physical Properties run no.
QL, gpm
Fb, (m/s)(kg/m3)0.5
K or m
mea. EO, %
λ
DL × 10-9, m2/s
σ, N/s
FG, kg/m3
FL, kg/m3
16 533 16 534 16 535 16 536 16 537 16 538 16 543 16 544 16 545 16 546 16 547 16 548 16 549 16 550 16 551 16 552 16 553 16 554 16 555 16 556 16 557
161 162 81 83 21 162 88 167 170 86 24 23 24 27 337 336 305 87 167 167 167
1.4 1.7 1.4 1.7 1.6 1.7 1.1 1.1 2.2 2.2 1.1 1.3 1.7 2.2 2.2 1.8 1.4 1.8 1.7 0.9 2.5
2379 2355 2392 2359 2382 2368 2424 2424 2340 2344 2417 2407 2390 2350 2334 2367 2391 2375 2377 2424 2299
37 39 43 40 38 39 42 33 38 34 36 40 37 31 32 36 35 35 39 33 39
229.9 285.8 460.9 547.3 2036 282.9 341.9 177.1 351.4 697.6 1185 1533 1882 2196 178.9 142.4 120.2 542.2 278.7 148.4 392.3
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059 0.059
0.62 0.63 0.62 0.64 0.62 0.63 0.61 0.61 0.65 0.65 0.60 0.61 0.62 0.64 0.65 0.63 0.61 0.63 0.63 0.60 0.67
956 955 956 955 956 955 956 956 955 955 957 956 956 955 955 955 956 956 956 957 954
literature models, other efficiency models are not discussed and compared to the experimental data. Tray Hydraulic Models Liquid Holdup Models. Colwell (1981) developed a liquid holdup model based on theories only suitable to liquid phase continuous froth or emulsion regimes. Although its applicability to the gas phase continuous spray regime is uncertain, this model is the most-oftencited model in the literature and recommended by Lockett (1986), Kister (1992), and others. Both the Colwell model and eq 44 by Hofhuis and Zuiderweg (1979) are compared to the experimental liquid holdup obtained in this study. Pressure Drop Models. The total tray pressure drop can be approximately given by
∆p ) hDT + hcl + hR
(46)
where hDT can be considered as the dry tray pressure drop and is usually modeled by an orifice-type equation
ξFGuh2 hDT ) 2gFL
(47)
where ξ is the orifice coefficient. Many equations are available in the literature to estimate the orifice coefficient as reviewed by Lockett (1986). In this study, the equation of Cervenka and Kolar (1973) was chosen because of its analytical form
ξ)
0.94(1 - φ2)
(48)
φ0.2(t/dh)0.2
For comparison, the equation of Zuiderweg (1982) was also used
(
( ))
ξ ) 0.7 1 - 0.14
ghclFL uh2FG
2/3
(49)
The residual pressure drop, hR, in eq 46 has been modeled as the excess pressure required to overcome surface tension when bubbles are formed at the orifice (Fair, 1963).
Figure 11. Reproducibility of measured tray efficiency.
This term is significant only for systems having a large surface tension and with small hole size trays. Equation 44 was used with eq 49, while eq 48 is combined with the Colwell liquid holdup model, to predict the tray pressure drop through eq 46. Results and Discussion Reproducibility. The reproducibility of the data obtained during these studies is illustrated in Figure 11. Even at these low concentration levels of toluene, reproducible results were obtained at the same repeated column conditions for three runs recorded after switching back from other run conditions. The other measurements can also be reproduced within measurement errors. The measured efficiency is given in Table 2 together with all the physical properties used in the model predictions. Liquid Holdup. The bubbler measured liquid holdups at two locations are grouped by liquid rates and presented in Figure 12 together with those predicted from Colwell’s and Hofhuis and Zuiderweg’s correlations. The measured liquid holdup decreases as the vapor velocity increases at a constant liquid rate, which is as expected. The liquid holdup measured near the outlet weir is generally higher than that measured at the center of the tray. One possible reason may be that the liquid volume fraction at the center of the column is lower than that near the outlet weir. Figure 12 shows that Colwell’s correlations underestimated the liquid holdup at low liquid rates (23 and 83 gpm). This may
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Figure 12. Comparison of measured and predicted liquid holdups.
Figure 13. Comparison of measured and predicted pressure drops.
be partially due to the fact that Colwell’s correlations are based on experimental data mainly from rectangular trays and rectangular trays generally retain less liquid than round trays. At low liquids, a tray tends to operate in the spray regime. Colwell’s correlations are not designed to predict the liquid holdup for the spray regime. Hofhuis and Zuiderweg’s correlation, although more empirical, matched the experimental data quite well for this particular system, as shown in Figure 12. Pressure Drop. Pressure drop data were carefully measured across various trays and are shown in Figure 13. It was found that the pressure drop increases as the liquid rate increases at a fixed vapor rate. This is because the liquid holdup increases as the liquid rate increases. It was also found that both pressure drop models described in this study yield similar predictions. They predicted the measured pressure drops reasonably well at low vapor rates and overpredicted them at high vapor rates especially at the high liquid rate. Overall Tray Efficiency. The overall tray efficiency results are summarized in Figure 14 and also grouped by liquid rates. It can be seen that the measured overall tray efficiency is in a narrow range of 30-40%. However, the predicted efficiency from the AIChE model ranges from 96% to 33% and does not trend properly with liquid rates or λ. At the low liquid rate (23 gpm), the λ value is about 2000, the vapor tray efficiency enhancement from the point efficiency may be overestimated by the AIChE model. The overestimation of efficiency enhancement at low λ values (e.g., at 333 gpm) is not as significant as at high λ values. This may explain why the AIChE model predicted the efficiency quite well at low λ values (high liquid rates, 163 and 333 gpm).
Figure 14 shows clearly that Zuiderweg’s model significantly underestimated the efficiency at all conditions. His model was developed on the basis of the data for distillation systems. Chen and Chuang (1995) have given the reasons why efficiency models developed on the basis of distillation systems will underpredict the efficiency for stripping systems. One other reason may be that Zuiderweg’s model overestimates the liquid phase mass transfer resistance. The measured efficiencies are also compared with the two model predictions when totally-mixed liquid was assumed on the tray and eq 25 was used, which is shown in Figure 15. In that case, the AIChE model matches the measured efficiency at the low liquid rate and underpredicts it at the high liquid rate. Of course, Zuiderweg’s model predicts even lower efficiencies. From these results, it can be concluded that the current efficiency models in the literature whether based on distillation or stripping systems are unable to predict the efficiency for stripping systems with a high λ value. The experimental results from this study can serve as a basis for remodeling the efficiency for liquid phase controlled systems. Liquid and Vapor Tray Efficiency. Liquid and vapor tray efficiencies can be obtained both from the measured composition profiles and from eqs 19 and 20. The results are given in Figure 16 as a function of λ. It can be seen that the liquid tray efficiency increases with increasing λ and the vapor tray efficiency decreases with increasing λ, while the overall tray efficiency is relatively independent of λ. The increase in λ is mainly a result of the decrease in the liquid rate for this system. Thus, liquid tray efficiency increases as the liquid rate decreases, which is consistent with what eq 39 or 43
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Figure 14. Comparison of measured and predicted overall tray efficiency.
shows. In general, the measured liquid tray efficiency is in the range of 80-95% for this system. Choices of Efficiencies in Design. From eqs 19 and 20, the EMV and EO can be calculated as a function of λ with a fixed EML as a parameter. The results so obtained are shown in Figures 17 and 18. It can be seen that the EMV and EO decrease significantly with λ even though the EML remains constant. Since λ is a primary variable and varies significantly with liquid and vapor rates and from system to system in this type of operation, the EMV and EO can also change substantially from one application to another. This may cause difficulties and confusions in selection of a tray efficiency in the design. In addition, the physical meanings of EMV and EO for stripping systems are not as clear and straightforward as for distillation systems. Since distillation systems have a small and quite constant λ, the EMV and EO are usually modeled and used in design. Nevertheless, they are not the wise choice for stripping systems. Since stripping systems usually have a large m, the assumption made for eq 42 that gas phase resistance is negligible may not introduce a big error. The obtained eq 42 based on this assumption then indicates that the EML is independent of m or λ, which is unlike the EMV and EO. This implies that it should be easier to model EML than to model EMV for stripping systems. Furthermore, the EML can be directly related to the number of trays required for a specified separation, as suggested by eq 17. Its physical meaning is also very clear and easy to be understood. It represents the fractional removal rate of the light component for each tray shown by eq 9. The only physical property which has a major effect on the EML is the liquid diffusivity, as indicated by eq
Figure 15. Comparison of measured and predicted overall tray efficiency (totally mixed liquid assumed).
Figure 16. Comparison of measured various tray efficiencies as a function of λ.
42. The liquid diffusivity is mainly determined by the properties of the liquid phase (water phase in the case of this study). As a result, all the stripping systems should have a similar EML at similar liquid and vapor
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Figure 17. Vapor tray efficiency as a function of λ at fixed liquid tray efficiencies.
Figure 19. Total number of trays required as a function of liquid tray efficiency when (xexit/xin) ) 10-20.
12.5 to 8.75. This suggests that an extra two or three trays installed in the column will be safe enough to compensate for the efficiency estimation error. Conclusions
Figure 18. Overall tray efficiency as a function of λ at fixed liquid tray efficiencies.
rates. This explains why most strippers have a similar tray efficiency. This characteristic is different from the distillation systems whose efficiency mainly depends on m and physical properties, not the operating conditions. Steam stripping systems should have a higher EML than air stripping systems due to a larger liquid diffusivity resulting from a higher temperature. Design Guidelines. The procedure for determining the actual tray number for a specified separation by stripping is outlined in the following list of steps: a. Calculate the vapor fraction () and liquid holdup for the system used in this study and the system to be designed. b. Select a liquid flow pattern on the tray, e.g., for totally-mixed liquid, i ) 1, for plug flow liquid, i ) ∞, or something in between. c. Determine eq 42 or 43 on the basis of experimental data given in this study. d. Use the determined eq 42 or 43 to estimate the liquid tray efficiency. e. Obtain the number of actual trays needed from eq 17 for the design system. On the basis of experimental data in this study, a liquid tray efficiency of higher than 95% is not recommended in design. Given the separation xexit/xin ) 10-20 in eq 17, the total number of actual trays (n) needed for this separation can be calculated as a function of EML from eq 17. The results, shown in Figure 19, indicate that an increase of liquid tray efficiency from 0.8 to 0.9 reduces the total number of trays by 30% from
The tray performances including the liquid holdup, pressure drop, and mass transfer efficiency for the trace toluene/water steam stripping system were measured experimentally in a 4-ft industrial-scale column. The measured data indicate that the liquid tray efficiency or the removal rate of the light component for each tray is ranging from 80 to 95% for the system studied, depending on the liquid rate. Experimental results also show that liquid tray efficiency decreases as the liquid rate increases, which is consistent with the theory described in this study. The measured liquid holdup, pressure drop, and efficiency were compared with the predictions from commonly-used models. It was found that literature tray efficiency models based on distillation systems (Zuiderweg’s model) or stripping systems (AIChE model) are unable to predict the measured efficiency. Thus, an empirical method was provided in this study. It was also suggested that the liquid tray efficiency is easier to use in modeling and design than the vapor tray efficiency for stripping systems. Nomenclature Ab ) tray bubbling area, m2 a ) interfacial area, m2/m3 of froth b ) weir length per unit bubbling area, 1/m DG ) vapor molecular diffusion coefficient, m2/s DL ) liquid molecular diffusion coefficient, m2/s De ) eddy diffusivity, m2/s dh ) hole diameter, m EML ) Murphree liquid tray efficiency EMV ) Murphree vapor tray efficiency EO ) overall tray efficiency EOG ) Murphree vapor point efficiency Fb ) F-factor based on bubbling area, (m/s)(kg/m3)0.5 FP ) flow parameter g ) gravity acceleration, m/s2 hf ) froth height, m hcl ) liquid height, m hDT ) dry tray pressure drop, m of liquid hDT ) dry tray pressure drop, m of hot liquid hW ) outlet weir height, m i ) number of liquid mixing cells j ) number of vapor mixing cells K ) the equilibrium ratio for the light component kG ) vapor phase mass transfer coefficient, (kg mol)/(sm2)
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Ind. Eng. Chem. Res., Vol. 35, No. 8, 1996 2671 kL ) liquid phase mass transfer coefficient, (kg mol)/(sm2) KOG ) overall vapor phase mass transfer coefficient, (kg mol)/(sm2) L ) molar liquid flow rate, (kg mol)/s LW ) outlet weir length, m LFP ) flow path length, m m ) slope of the vapor-liquid equilibrium line MG ) vapor molecular weight ML ) liquid molecular weight n ) number of trays or tray number NG ) number of vapor phase mass transfer units NL ) number of liquid phase mass transfer units NOG ) number of overall vapor phase mass transfer units NOL ) number of overall liquid phase mass transfer units p ) hole pitch, m Pe ) Peclet number ∆p ) total tray pressure drop, m of liquid QL ) volumetric flow rate of clear liquid, m3/s (gpm) QV ) volumetric vapor flow rate, m3/s ub ) vapor velocity based on bubbling area, m/s uh ) vapor velocity though holes, m/s V ) molar gas flow rate, (kg mol)/s W ) outlet weir length, m xi ) mole fraction of the light component in liquid phase at various locations yi ) mole fraction of the light component in gas phase at various locations Greek Letters λ ) mV/L FG ) vapor density, kg/m3 FL ) liquid density, kg/m3 σ ) surface tension, N/m φ ) fractional open area ξ ) orifice coefficient R ) froth liquid volume fraction ) froth vapor volume fraction
Literature Cited AIChE Bubble Tray Design Manual; AIChE: New York, 1958. API Laboratory study on solubilities of petroleum hydrocarbons in ground water API Publication No. 4395; API: Washington, DC, August, 1985. Cervenka, J.; Kolar, V. Hydrodynamics of plate columns VIII. Czech. Chem. Commun. 1973, 38, 2891.
Chan, H,; Fair, J. R. Prediction of Point Efficiencies on Sieve Trays. Ind. Eng. Chem. Process Des. Dev. 1984, 23, 814. Chen, G. X.; Chuang, K. T. Liquid-Phase Resistance to Mass Transfer on Distillation Trays. Ind. Eng. Chem. Res. 1995, 34, 3078. Colwell, C. J. Clear Liquid Height and Froth Density on Sieve Trays. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 298. EPA Method 602. Appendix A to Part 136. Methods for organic chemical analysis of municipal and industrial waste water. Federal Register, Rules and Regulations, Friday, Oct. 26, 1984; Vol. 49, No. 209, pp 43272-43280. Fair, J. R. In Design of Equilibrium Stage Processes; Smith, B. D., Ed.; McGraw-Hill: New York, 1963. Higbie, R. The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans. Am. Inst. Chem. Eng. 1935, 31, 365. Hofhuis, P. A. M.; Zuiderweg, F. J. Sieve plates: dispersion density and flow regimes. Inst. Chem. Eng. Symp. Ser. 1979, No. 56, 2.2/1. Hooper, H.; Prausnitz, J. Vapor-liquid equilibria for toluene in water and for water in n-heptane or cyclohexane in the region 70-250 °F, FRI Topical Report No. 105, 1988 (available from Fractionation Research, Inc., P.O. Box 2108, Stillwater, OK 74076). Huang, Y-L.; Keller, G. E.; Olson, J. D. Steam Stripping for Removal of Organic Pollutants from Water. 1. Stripping Effectiveness and Stripper Design. Ind. Eng. Chem. Res. 1992, 31, 1753. Kister, H. Z. Distillation Design; MaGraw-Hill: New York, 1992. Lockett, M. J. Distillation Tray Fundamentals; Cambridge University Press: Cambridge, U.K., 1986. Sakata, M.; Yanagi, T. Performance of a commercial scale sieve tray. Inst. Chem. Eng. Symp. Ser. 1979, No. 56, 3.2/21. Yanagi, T.; Sakata, M. Performance of a Commercial-Scale 14% Hole Area Sieve Tray. Ind. Eng. Chem. Process Des. Dev. 1982, 21 (4), 712. Zuiderweg, F. J. Sieve tray, a view on the state of the art. Chem. Eng. Sci. 1982, 37 (10), 1441.
Received for review December 15, 1995 Revised manuscript received May 17, 1996 Accepted May 20, 1996X IE950760W
X Abstract published in Advance ACS Abstracts, July 1, 1996.
