Article pubs.acs.org/IECR
Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Mass Transfer Parameters for Packings: Effect of Viscosity Di Song,†,‡ A. Frank Seibert,‡ and Gary T. Rochelle*,† †
McKetta Department of Chemical Engineering, The University of Texas at Austin, 200 East Dean Keeton Street, C0400, Austin, Texas 78712, United States ‡ Separations Research Program, Pickle Research Campus, The University of Texas at Austin, 10100 Burnet Road, Austin, Texas 78758, United States S Supporting Information *
ABSTRACT: The effect of liquid viscosity (μL) on the effective mass transfer area (ae) and liquid film mass transfer coefficient (kL) of packing must be known to determine packing height. Most existing correlations are based on water and are not applicable to viscous systems. In this work, ae, kL, and gas film mass transfer coefficient (kG) were measured in a 0.43 m ID packed column with 0.5−3 m of packing. Liquid viscosity was varied from 0.8 to 70 mPa·s by adding glycerol to water. Liquid viscosity has an insignificant effect on ae over the range of μL investigated. The total dependence of kL on μL is −0.75, of which −0.35 is indirect influence through diffusivity, and −0.4 is direct influence through liquid turbulence. Universal mass transfer models for packing were developed as functions of packing geometry, operating condition, and fluid property.
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INTRODUCTION Many industrial applications require mass transfer in viscous liquid, such as electrolyte solutions, organic/polymer solutions, crude oil, and ionic liquids. The increase in μL can significantly decrease kL. In the case of postcombustion CO2 capture with aqueous amine, for example, the high solvent viscosity can cause slower diffusion of CO2 through the reactive boundary layer, slower diffusion of free amine from the bulk liquid to the gas−liquid interface (surface depletion of alkalinity), slower diffusion of loaded amine back to the bulk liquid (which affects equilibrium partial pressure of CO2 at the interface), and reduced liquid turbulence on the packing surface. Most of the existing kL (kLa) correlations investigate only water and thus provide unsatisfactory predictions for the influence of μL.1 Therefore, their application to amine solutions could lead to inefficient or insufficient column design, and a more systematic and reliable study on the effect of viscosity is needed. The SRP database for the air−water column contains valuable hydraulic and mass transfer data for structured, random, and hybrid packings. On the basis of the database, models of ae and kL have been developed previously by Tsai2 and Wang.3 The Tsai area model was developed seven years ago, and additional data with variable packing geometry have been generated. For the kL model developed by Wang, significant new data with water and aqueous glycerol were generated during the past two years. Therefore, it is necessary to validate or update both models with the expanded database. The model of kG was developed based on 20 packings in the SRP database. Compared to the Wang model,3 it is a simplified version applicable to structured, random, and hybrid packings © XXXX American Chemical Society
without incorporating the geometry-oriented dimensionless number, mixing-point density (Mi), which is different for different packing types.
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METHODS AND EQUIPMENT A systematic method for packing characterization with water has been developed at the Separations Research Program at the University of Texas at Austin. The method is based on the twofilm theory that describes interphase mass transfer resistance as a series of resistances (eq 1). 1 1 H 1 1 = + = + 0 K OG kG k k EkL G g′
(1a)
1 1 1 = + K OL Hk G EkL0
(1b)
The effective wetted area, ae, has been determined with chemical absorption of ambient CO2 into aqueous NaOH. The volumetric mass transfer coefficient for the caustic system, KOGae, is determined by measuring the CO2 in the inlet and outlet gas streams. The concentration of the NaOH was carefully chosen to make the system reaction film controlled. Therefore, the gas film (1/kG) and physical liquid film (1/kL0) mass transfer resistance become negligible;2 thus KOG is equal Received: Revised: Accepted: Published: A
October 23, 2017 December 6, 2017 December 21, 2017 December 21, 2017 DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research to kg′. ae can be determined by separating the kg′ from KOGae (≈ kg′ae) with kg′ calculated based on the well-established kinetics.4 The ae/aP measured using the method above becomes asymptotic to unity or slightly above unity at high liquid load, which is reasonable. The kL has been determined with air stripping of toluene from water. The volumetric overall mass transfer coefficient, KOLae, is determined by measuring the toluene in the inlet and outlet liquid streams. The system is controlled by liquid film resistance because of the limited solubility of the toluene in water (large H), so KOL ≈ kL. The kL is calculated by separating the ae from the KOLae (≈ kLae). For water-only experiments, the ae measured using the caustic scrubbing method for the same packing at the same operating condition is used. For aqueous glycerol experiments, which will be discussed in more detail later, the ae is calculated by the model. The kG has been determined with chemical absorption of injected trace SO2 from air by 0.1 M NaOH. The volumetric mass transfer coefficient, KOGee, is determined by measuring the SO2 in the inlet and outlet gas streams. This system is gas film controlled because of the instantaneous reaction (large E), so KOG ≈ kG. Similar to the kL method, the ae is taken the value measured by caustic scrubbing for the same packing at the same operating condition. Details of the experimental protocol can be found in Tsai2 and Wang.5 Glycerol was chosen to increase liquid viscosity because it dissolves readily in water, is relatively cheap, and provides Newtonian behavior. Liquid viscosities of approximately 1, 4, 15, and 65 mPa·s were obtained by adding 0, 44, 65, and 85 wt % glycerol to water. The reaction kinetics for CO2/NaOH/ H2O/glycerol were based on wetted-wall column data.6 Glycerol does not change the controlling mechanism for mass transfer. For air stripping of toluene, though the addition of glycerol decreases the infinite dilution activity coefficient of toluene, it will still be well above 100 at the highest proposed glycerol concentration,7,8 which ensures liquid film control. For the reactive system, the effect of physical liquid film mass transfer (i.e., surface depletion of alkalinity) has been corrected in the kinetic model and is believed not to be an issue for the packed column experiments considering the relatively low CO2 concentration and flux. Packed Column. Packing was characterized in a PVC column with a 0.43 m ID and a maximum packing height of 3 m (Figure 1). Liquid countercurrently contacted air supplied by
a 30 kW blower with a variable speed drive from a duct (0.2 m outside diameter) below the packing support. Up to 34 m3/h of liquid was delivered by a centrifugal pump with a variable speed drive from a 1.3 m3 storage tank. The liquid could either flow to the column top and be distributed by an F40 pressurized fractal distributor (430 drip points/m2) or flow back to the column sump and storage tank via a bag filter for the pump to operate in a more favorable drive-speed region. Above the distributor was a Trutna collector to knock out any liquid reaching the column exhaust. Typical liquid inventory was 1−1.2 m3. Typical gas and liquid rates were 0.5−1.5 m/s and 6−73 m3/m2·h, respectively. Approximately 3 m of packing was installed for a e measurement and kL measurement with aqueous glycerol. A shorter 1.8 m bed was used for kL measurement with water because of the difficulty of gas chromatograph (GC) analysis for the low outlet toluene concentration caused by high mass transfer efficiency. An even shorter bed (0.5−1 m) was used for kG measurement because of the extremely high absorption rate of SO2 with NaOH. Each packing element was installed with a 90° rotation to facilitate liquid distribution. Wiper bands have been arranged so that each element fits tight with the column wall. Samples of inlet liquid were collected at a sample valve between pump discharge and liquid distributor. Samples of outlet liquid were collected from a bayonet collector installed just below the packing. The sampling protocol minimized additional mass transfer.3 Wiper bands have been welded onto the bayonet to prevent collecting wall flow.9 Liquid samples at both inlet and outlet were collected at each operating condition for offline measurement of physical properties. The average value of physical properties was used for model development. Auxiliary Equipment. The CO2 in the inlet and outlet gas was measured online by a XStream CO2 IR analyzer (Rosemount). Inlet CO2 was ambient 370−400 ppmV, and outlet CO2 was 100−300 ppmV depending on the packing and gas flow rate. The SO2 concentration in the gas was measured online by a Thermo Scientific Model 43i SO2 analyzer. Typical inlet SO2 was 50−100 ppmV, and outlet SO2 500−10000 ppbV depending on the operating condition. Toluene in liquid samples was determined by FID gas chromatography (HewlettPackard 6890) with 1-bromo-4-fluorobenzene as the internal standard. Typical inlet toluene was 100−200 ppmw, and outlet was 0.5−50 ppmw depending on the liquid flow rate and viscosity. Liquid viscosity was measured by a TA Instrument AR-2000ex rheometer. Glycerol concentration was verified by density measurement with a Mettler Toledo DE40 densitometer. Details on the liquid property measurement for ae can be found in Song et al.9 Chemicals. NaOH pellets (Fisher) were used to prepare the caustic batch. The 0.1 N HCl and phenolphthalein used in titration were purchased from Sigma-Aldrich. The ultrapure nitrogen and 450 ppmV CO2 cylinders used for CO2 analyzer calibration were purchased from Praxair. The 90 ppmV SO2 cylinder used for SO2 analyzer calibration was from Praxair. The 2 vol % SO2 injected to the air in the kG experiments was from Praxair. USP-grade glycerol (99.7%) used to prepare the batch was purchased from Acme-Hardesty. The n-heptane and 1-bromo-4-fluorobenzene used in liquid sample extraction was purchased from Fisher and Aldrich Chemistry, respectively. Calculations. Liquid temperature was not controlled in the system, so the liquid properties vary with ambient temperature.
Figure 1. Packed column experimental system. B
DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 2. Comparison of measured and calculated area from eq 9 for water
asecondary = a top + a wall + abottom ≈ a wall
Average system temperature (eq 2) has been used for kinetics in the calculation of ae. Tsystem = ((Tgas,in + Tgas,out)/2 + Tliquid,in)/2
The top area includes area generated by the liquid streams from distributor to packing top (both stream peripheral and impact area). Similarly, the bottom correction includes the area generated by the liquid streams from packing bottom to sump. It is demonstrated in a later section that wall area is always dominant in asecondary. The correction for secondary effects is a worst-case scenario. The wall area includes that in the packing section and in the section between packing bottom and liquid sump:
(2)
This practice was found to do a better job of reconciling the data for ae at ambient temperature extremes (summer and winter) than did simply using the liquid temperature.2 The difference between the system temperature and liquid inlet temperature is typically within 3 °C. The total mass transfer area in the column, ae,total, was determined experimentally by eq 3, which is derived from differential mass balance across phases for plug flow along the column. kg′ for aqueous NaOH was calculated using the model of Pohorecki and Moniuk.4 kg′ for caustic glycerol solutions was calculated from a model developed based on the wetted-wall column data. 6 The k L a e and k G a e were determined experimentally by eqs 4 and 5. ae,total =
⎛ CCO ,in ⎞ K OGae K a uL 2 ⎟ ≈ OG e = ln⎜⎜ K OG kg′ kg′ZRT ⎝ CCO2,out ⎟⎠
kLae,total =
k Gae,total
uL ⎛ C toluene,in ⎞ ⎟⎟ ln⎜⎜ Z ⎝ C toluene,out ⎠
⎛ CSO ,in ⎞ u 2 ⎟ = G ln⎜⎜ Z ⎝ CSO2,out ⎟⎠
a wall = πDcolumn (Zpacking + Zauxiliary )
(8)
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MODEL OF MASS TRANSFER AREA (AE) A model representing ae,packing was developed (eq 9) based on measurements with water and aqueous glycerol reported here and on data for water, surfactant liquid, and solutions of polyethylene glycol (PEG) measured by previous researchers2,5,11 using the same equipment. Thirty-nine structured, random, hybrid, and gauze packings are included. ae,packing = 1.16η(We Fr −1/2)0.138 aP
(3)
(4)
⎡⎛ ρ ⎞ ⎤0.138 = 1.16η⎢⎜ L ⎟ g1/2uLaP−3/2 ⎥ ⎣⎝ σ ⎠ ⎦ (5)
(9)
Figure 2 compares the measured and calculated area for water. Empirical correction factors are included in the model to account for deviation of random/hybrid packings, plastic packings, and data measured at the loading zone (eq 10 and Table 1). The packing type correction is a linear function of aP to optimize the overall fitting of the 16 random/hybrid packings in the database. The model works surprisingly well for the one gauze packing in the database without correction. The correction for plastic packing is obtained by comparing the data for two packings of which both the stainless steel and plastic versions were measured (PR 1.0 and CMR 2A). Besides the area measured at the preloading zone (ΔP < 400 Pa/m) for all
Physical properties (density, viscosity, surface tension, diffusivity, and Henry’s constant of CO2) of the aqueous glycerol were calculated using models developed previously.1,9 Density of air was calculated from temperature and pressure based on the ideal gas law. Diffusivity of SO2 in air was calculated from the Fuller equation.10 Secondary effects (end and wall effects) on mass transfer area (asecondary) have been subtracted to give the effective mass transfer area of the packing surface (ae,packing): ae,total = ae,packing + asecondary
(7)
(6) C
DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research Table 1. Packing Correction Factor in Equation 9 ηtype ηmaterial ηloading
structured
random/hybrid
1.0
1.34 − 0.26
stainless steel 1.0 preloading zone (ΔP < 400 Pa/m) 1.0
plastic 0.62 loading zone (ΔP ≥ 400 Pa/m) 1.15
( 250a ) P
39 packings, area at the loading zone (ΔP = 400 Pa/m) was investigated for one structured packing (B1 250), three random packings (IMTP 25, PR 2.0 and 1.0), and one gauze packing (A3 500X). A constant 15% increase in the area was seen for the five packings regardless of packing type or liquid load (Figure 3). For 39 packings with drastically different geometry, the model shows an average absolute deviation (AAD) of only 8.9%. η = ηtypeηmaterial ηloading (10)
Figure 5. Relative error of eq 9 with variable viscosity.
surface tension varied from 72 to 30 mN/m with the addition of a surfactant (TERGITOL NP-7). No systematic bias of the model was found as a function of surface tension. In fact, the model does a slightly better job for surfactant liquid than water. Figure 5 shows the relative error of the model as a function of liquid viscosity. Neither the PEG data (1−15 mPa·s) from Tsai,2 nor the glycerol data (1−50 mPa·s) reported here show that ae,packing is affected by μL in the range investigated. The average dependence of ae,packing on μL for the six investigated packings in Figure 5 is −0.007 ± 0.022, which is insignificant compared to other factors in the area model (eq 9). It is also small compared to the dependence of kL on μL, which is −0.75 as shown in Figure 13. Therefore, it is concluded that μL does not have significant effect on ae in the μL range investigated in this work for both polymer (PEG) and small molecule (glycerol). The relative error of the model is mostly within 10% for viscous liquids. Because of the partly shared database, the form of the model (eq 9) is similar to that of Tsai12 (eq 11) with the same dimensionless groups. However, this new model uses an expanded database and includes the correction for the secondary area, which makes it more widely applicable to variable packing sizes. ae,packing = 1.34(We Fr −1/3)0.116 aP
Figure 3. Comparison of ae at loading (ΔP = 400 pa/cm) and preloading (ΔP < 400 Pa/cm) zone.
Figure 2 shows that there is no systematic relative error of the model as a function of packing geometry, aP. Though a slight overprediction is observed for the finest packings (aP = 350−500 m2/m3), the relative error is still close to 20%, which is acceptable. Per the model, surface tension affects ae,packing, but viscosity does not. This is confirmed by Figures 4 and 5, where relative errors of eq 9 as a function of liquid properties are plotted. Figure 4 shows the data measured by Tsai,2 where the
4/3⎤0.116 ⎡ ρ ⎛ L ⎞ 1/3⎛ uL ⎞ ⎥ ⎢ = 1.34 ⎜ ⎟g ⎜ ⎟ ⎢⎣⎝ σ ⎠ ⎝ aP ⎠ ⎥⎦
(11)
asecondary is deducted from ae,total to give ae,packing (eq 6). With the 0.43 m ID column in this work, the secondary area is not significant for normal to fine packings (aP > 200 m2/m3), but it starts to play an important role for coarse packings (Figure 6). Since the wall area is dominant in the secondary area for the whole spectrum of packing aP, the top and bottom areas are omitted in the future correction of secondary effect for simplification. As expected, the column diameter will greatly affect the asecondary (Figure 7). For columns with ID greater than 0.5 m with M 250Y as an internal, the secondary area is less than 7%. Therefore, this correction to area measured in a pilotscale column will enable wider application of the model to columns of greater sizes where asecondary is negligible. The overall secondary area is a weak function of liquid load because the increase in top/bottom area and decrease in wall area offset each other as liquid load increases (Figure 8).
Figure 4. Relative error of eq 9 with variable surface tension. D
DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 6. Effect of aP on asecondary. Figure 9. Packing area regimes of MG 64Y.
Figure 7. Effect of column size on asecondary.
Figure 10. Comparison of kL measured with 3 and 1.8 m packing.
initially used. The height was then reduced to 1.8 m to get more precise measurement because the low outlet toluene concentration is close to the detection limit of the GC. Theoretically, kL should not be affected by packing height when there is no issue with liquid distribution and GC detection. However, greater kL was consistently observed with the shorter bed. The variation of kL with bed height could be caused by poor liquid distribution or effective axial mixing of the liquid. The effect of packing height on the mass transfer efficiency was observed in previous studies.13−15 Though the dependence varies from −0.06 to −0.4 in different works, a shorter bed always gave greater efficiency. In this work, the effect of packing height is included in the kL model (eq 12) with a dependence
Figure 8. Effect of liquid load on asecondary.
Different regimes of packing area are shown in Figure 9. The coarsest packing (MG 64Y) has been used for illustration. The correction of secondary area effectively shifts the area down proportionally since secondary area is a weak function of liquid load. The wetted packing area below unity results from the liquid film on the surface of packing metal, and the part above unity is from the satellite droplets in the corrugation channel and the mass transfer happening at packing element junctions. The latter part becomes less significant when the aP increases.
(
ln(1.32 / 1)
)
of −0.54 = ln(1.8 / 3.0) . Billet16 performed extensive studies on the effect of packing height on the mass transfer efficiency with different liquid distributor densities. The variation of efficiency was attributed to the difference in the “entrance effect” of the initial liquid distribution at the inlet of the packing bed. An empirical correlation was developed to calculate the optimum distributor density, above which the increase in distribution point no longer facilitates mass transfer. This “entrance effect”, however, is different from the kL variation seen in Figure 10, which is caused by the “self-deterioration” of liquid distribution along the packing bed. The liquid distribution is worsened
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MODEL OF LIQUID FILM MASS TRANSFER COEFFICIENT (KL) Effect of Packing Height. The experimental results suggest that the liquid film mass transfer coefficient, kL, is 1.32 times greater with a 1.8 m bed than that with a 3 m bed (Figure 10). The experimental protocol for kL measurement at SRP has changed over time. A total of 3 m of packing was E
DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research when packing height increases for a variety of reasons such as increase in wall flows, formation of large rivulets that may cause partial dryness of the packing surface, or effective axial mixing when liquid rivulets different in velocity and composition mix with each other. The distributor density (430 points/m2) in this work, though below the optimum value (∼1200 points/m2) calculated by the Billet correlation, is believed to be sufficient to avoid initial liquid maldistribution and other undesirable effects. This has been demonstrated by past distributor studies performed in the SRP, which was discussed by Tsai.2 Effect of aP. The average kL of structured, random, and hybrid packings at 1 m/s gas rate and 24, 37, and 49 m3/m2·h liquid load is plotted against aP (Figure 11). Because of the
Figure 12. Comparison of measured kL and kL calculated by eq 12.
kL model gives an AAD of 24% for all 20 packings, compared to an AAD of 8.9% for the area model. Unlike the area model, the kL model does not require a correction for packing type or material. The model assumes square root dependence on diffusivity (and thus Sc) in accordance with penetration theory.17 Dimensionless groups (Re, Ga) were selected with combined consideration of results in the least-squares fitting and physical significance in the mass transfer process. Since surface tension was not significantly varied in the experiment and is not believed to be affecting kL, dimensionless groups that contain surface tension (such as We or Ca) were excluded in the regression. The liquid film mass transfer depends on packing geometry (aP), liquid properties (μL, D, and ρL), liquid flow (uL), and gravity (g).
Figure 11. Average kL as a function of aP.
more stable flow pattern, kL measured at medium liquid loads (24−49 gpm/ft2) has greater reproducibility compared to that at low or high loads. Therefore, the average value at medium liquid loads for each packing is for comparison. The lines in the figure are a quadratic fit for the same type of packing. A previous theory of mixing points3 suggests that kL should increase with increasing aP because there are more opportunities for mixing of the liquid film. However, Figure 11 shows an opposite trend for structured and hybrid packings, with kL decreasing with increasing aP. This might be caused by the greater liquid flow per channel at the same liquid load (and thus greater turbulence and Re) on the surface of coarse packings. Another explanation is that the dominant liquid flow pattern in coarse packings is large and thick liquid streams, which are believed to contribute to greater mass transfer efficiency than the spread-out and thin liquid films that are more common in fine packings. If the average kL is compared at the same flooding fraction instead of liquid load, then this trend will be more pronounced due to the greater capacity of coarse packings. The Y packing does not consistently out-perform X/Z packing in the same family, so the corrugation angle does not have a clear effect on kL. For random packing, the trend is not monotonic. The average kL first decreases, then increases with increasing aP. No systematic trend is found for random packing, probably because of the limited data for this type. Model for kL. A model of kL (eq 12a) was developed based on data from 20 structured, random, and hybrid packings. Glycerol tests were performed with 9 of the 20 packings. The kL used to develop the model is calculated from the experimental kLa by using measured area rather than area calculated from a model. Figure 12 compares the model and experimental kL. The
⎛ Z ⎞−0.54 ShL = 0.12Sc L0.5 ReL0.565 GaL1/6⎜ ⎟ ⎝ 1.8 ⎠
(12a)
⎛ μ ⎞−0.4 ⎛ Z ⎞−0.54 kL = 0.12uL0.565⎜⎜ L ⎟⎟ DL0.5g 1/6aP−0.065⎜ ⎟ ⎝ 1.8 ⎠ ⎝ ρL ⎠
(12b)
Effect of μL. The overall dependence on μL of kL predicted by eq 12b is −0.75, of which −0.35 is from the indirect influence of μL through diffusivity (Dtoluene ∝ μ−0.7 in aqueous L glycerol),9 and −0.4 is from the direct influence of μL on kL through liquid turbulence. The indirect part is believed to be system-dependent and requires knowledge on the D−μ relationship. The direct part is universally applicable to all Newtonian liquids. Figure 13 shows the dependence of kL normalized by other factors (liquid load, density, gravity, and aP) on μL. The slope (−0.75) is the same for structured, random, and hybrid packings. Figures 14 and 15 show the relative error of eq 11 as a function of aP and μL, respectively. The model underpredicts kL for coarse packings in Figure 14. No systematic bias of the model as a function of μL is apparent in Figure 14. Comparison to Other Work. The kLa of M 250Y measured by other researchers via oxygen desorption18,19 together with the data reported here are compared with various literature models18,20−22 in Figure 16. In the figure, the F
DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 16. Comparison of kLa models in the literature for M 250Y with experimental data for water (“Billet”,20 “Rocha”,21 “Delft”,22 “Valenz”,18 and “Laso”).19 Figure 13. Total dependence on μL of kL.
the Billet model20 predict the kLa for water reasonably well. The models of Delft22 and Valenz18 overpredict kLa, and the Rocha model21 underpredicts it. For aqueous glycerol, however, only the model developed here works. The other models fail to correctly predict the kLa of the viscous liquid (above 100% relative error) because they either do not include18 or underestimate20−22 the effect of μL on kLa. Another advantage of the model reported here is its simplicity; it does not require a packing-specific constant or detailed packing geometry (b, s, h).
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GAS FILM MASS TRANSFER COEFFICIENT (KG) Effect of aP. kG for structured packings increases with packing aP. The average kG for different packings at liquid load of 24 or 37 m3/m2·h and gas rates at 0.6, 1, and 1.5 m/s is plotted against aP in Figure 17. Y packings perform better at gas
Figure 14. Relative error of eq 12 with packing geometry.
Figure 17. Average kG as a function of aP.
film mass transfer than X/Z packings. The trend in aP is not monotonic for random packings, while the kG for hybrid packings remains unchanged as aP varies. The nonsystematic behavior of kG for random and hybrid packings probably results from the open geometry of these packings. Figure 18 compares the experimental and calculated kG from the model (eq 13). The model shows an AAD of 21% for all 20 structured, random, and hybrid packings (compared to 8.9% for the area model). It is notable that there was no significant change in the gas properties (μG, ρG, or DSO2) other than those
Figure 15. Relative error of eq 12 with variable viscosity.
experimental data from different sources with different systems are close to each other after normalization with diffusivity. It is notable that the data measured with shorter beds are consistently greater than those measured with taller beds. This agrees with the “maldistribution” effect of packing bed height on kL seen in Figure 10. Both the model in this work and G
DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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αeffective = 45°
(for random and hybrid packings)
(13c)
DISCUSSION For many industrial applications, it is the volumetric mass transfer coefficient (kLae) instead of individual mass transfer property that matters. For these cases, the recommended combined forms of kL·ae,packing and kG·ae,packing are kLae,packing = 0.14ηaP0.73uL0.7g 0.24 μL−0.4 DL0.5ρL0.54 σ −0.14 ⎛ Z ⎞−0.54 ⎜ ⎟ ⎝ 1.8 ⎠
(14)
k Gae,packing = 0.325ηuL0.14uG0.62aP1.17(sin 2α)0.65 DG0.5 −0.12 ⎡ ρL 1/2 ⎤0.14 ⎛ μG ⎞ g ⎥ ⎜⎜ ⎟⎟ ⎣⎢ σ ⎦ ⎝ρ ⎠ G
Figure 18. Comparison of measured and calculated kG from eq 13.
Models of kL/kG and ae from different sources should generally not be mixed, since kL and kG are usually determined from a kLa and kGa measurement. Equation 12a shares the form of the theoretical prediction of kL for a laminar falling film as in a wetted-wall column:17,23
caused by ambient temperature or operating condition changes. Therefore, the fewest possible dimensionless numbers are used in the model because of the relatively limited range of gas property variance. The effect of corrugation angle for structured packings is reflected in the term, sin(2α), which is fundamentally identical to the form of the mixing point density, Mi, of the Wang correlations.3 For structured Y packings, the angle correction is essentially one. Effective corrugation angle of 45° was assigned to random (RSR) and hybrid (RSP) packings for optimum fitting (eq 13c). The dependence on Sc was fixed to 0.5 to satisfy the penetration theory.17 Compared to the kL model, the kG model shows a positive dependence on aP, similar dependence on the fluid superficial velocity (0.62 compared to 0.565), and lower dependence on the kinematic viscosity (−0.14 compared to −0.4). The relative
Sh = 0.724Sc1/2 Re1/3 Ga1/6
⎛ μ ⎞−0.12 k G = 0.28uG0.62⎜⎜ G ⎟⎟ DG0.5aP0.38(sin 2α)0.65 ρ ⎝ G⎠
(16b) 24
Derivation of eq 16 can be found in Mshewa. Equations 12a and eq 16a have the same dependence on Sc and Ga, so they have identical predictions of the effect of gravity and diffusivity. However, because of the difference in Re dependence, eq 12 shows a greater effect of liquid load (0.565 compared to 1/3) and viscosity (−0.4 compared to −1/6) on kL compared to that of eq 16. The difference results from the turbulent nature of liquid flows in packings compared to the laminar flow of falling films described in eq 16. For the latter, the liquid load and μL only affect mass transfer via the change of film thickness (and thus surface velocity and contact time). Flow in packing, contrastively, is probably turbulent because of surface modification (embossing, perforation, etc.), gas−liquid friction in packing channels, or liquid mixing at packing joints. Both liquid load and μL will affect not only the film thickness but also the degree of liquid turbulence and thus the surface renewal and mass transfer rate in packing flows. This explains the greater dependence on Re in eq 12 compared to eq 16. The liquid flow in each triangular channel in the structured packings can be regarded as a tilted falling film as described in eq 16. The kL can be estimated by eqs 17−20: qchannel = Q column /nchannel
error of eq 13 is plotted against aP in Figure 19. No systematic bias of the model as a function of packing geometry is observed. ShG = 0.28ScG 0.5 ReG 0.62
(16a)
⎛ q1/3 ⎞⎛ g sin αρ ⎞1/6 1/2 kL0 = 1.15⎜⎜ 1/2 1/3 ⎟⎟⎜ ⎟ D μ ⎠ ⎝ l W ⎠⎝
Figure 19. Relative error of eq 13 with packing geometry.
⎛ sin 2α ⎞0.65 ⎜ ⎟ ⎝ sin(2 × 45°) ⎠
(15)
nchannel
A = column = achannel
ltotalmixing =
(13a)
(
(17)
π 2 D 4 column b h /2 sin α
)
b 2 sin α cos α
lnomixing = Hpackingelement /sin α (13b)
w = 2s H
(18)
(19a) (19b) (20) DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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falling film. Two assumptions may explain the abnormality: “no-mixing” or “big rivulet”. The first assumption is that no mixing (or only partial/ insignificant mixing) occurs between adjacent corrugation channels. On the basis of this assumption, eq 19b instead of eq 19a is used to calculate the length of the falling film, l. The significantly longer l makes the falling film kL for packing channels lower than the experimental kL, which itself lies below the falling film kL for wall flows (Figure 21). The experimental kL is closer to the falling film kL for packings than it is for the wall, which agrees with Figure 6 that shows secondary wall flow is relatively small for packings with aP of 250 m2/m3. The assumption of “no-mixing” also explains the trend shown in Figure 11. Because of the insignificant mixing, the flow path length, l, is only a weak function of aP but is dictated by Hpacking element, which does not vary significantly between packings (usually 20−25 cm). As a result, the increase in the liquid flow per channel in coarse packings due to the decrease in number of corrugation channels leads to greater kL compared to finer packings at the same liquid load. This effect becomes less and less significant when packing area (and thus number of corrugation channels) further increases, which explains the gradually flattened slope in Figure 11. Therefore, the theory of mixing point that is based on total mixing at joints of packing corrugation channels may not be valid for liquid film mass transfer.3 Another possible explanation of the unexpected low value of kL is “big rivulets”. The area measured using caustic scrubbing of CO2 may be significantly greater than the ae contributing to liquid film mass transfer in the toluene stripping experiment. Thus, a significantly smaller kL is obtained when separating it from experimental kLa using a significantly greater ae. Computational fluid dynamics (CFD) studies have suggested a lower area compared to the experimental data.26 The difference in the area for the two experiments results from the two regimes of liquid flow on the packing surface: big rivulets that contain the majority of volumetric liquid flow but cover a relatively small portion of the packing surface; spreadout thin films that cover most of the packing surface will have limited volume flow and turbulence. Both regimes contribute to ae in the CO2 scrubbing experiment because of the relative abundance of the NaOH. However, only the big rivulets contribute to ae in the toluene stripping experiment because of the fast depletion and slow renewal of toluene in the thin films. Moreover, due to the difference in the toluene concentration and fluid velocity of the two flow regimes, effective back-mixing occurs when the two regimes mix either at packing element joints or when big rivulets shift. The back-mixing is detrimental to mass transfer efficiency and will also lead to lower kL. Figure 22 shows the ratio of the experimental kL to calculated kL for falling film from eqs 16−20 with variable viscosity. The packing not only enhances mass transfer area, but also enhances kL because the ratio is mostly greater than unity at different viscosities. The ratio decreases with increasing μL, however, because eq 16 predicts significantly less dependence on μL (−1/6) compared to that with eq 12 (−0.4). This can be explained by the “big rivulet” assumption that when viscosity increases, depletion of toluene in the thin film becomes slower because of the decreased mass transfer efficiency, thus decreasing the difference in the area in the experiments of caustic scrubbing of CO2 and air stripping of toluene. The two assumptions to explain the difference between the experimental kL and calculated kL for falling films seen in Figure
In the calculation, liquid is assumed to be evenly distributed to each fully wetted channel, with no mixing at perforations, and no flow along the column wall. The length of the falling film, l, has a significant effect on kL.25 If complete mixing happens between two adjacent corrugation channels, the length can be calculated by eq 19a (sketched in Figure 20). If no mixing is
Figure 20. Length of falling film in packing channel if total mixing is assumed.
assumed, then l is related to the height of a packing element, which is 10−15 times longer and can be approximated by eq 19b. This is limiting calculation for the longest possible l, since in smaller columns the channel length is the shorter distance to the wall. Similar calculations can be done for the falling film along the column wall (eqs 16 and 21−23): qwall = Q column
(21)
l wall = Hpackingelement
(22)
wwall = πdcolumn
(23)
In this calculation, it is assumed that all the liquid flows along the wall instead of through the packing. Another assumption is that complete liquid mixing happens once in each packing element. This is a simplified assumption since elements for some packings have more than one wiper band, and whether complete liquid mixing happens at wiper bands is also arguable. Comparison of the falling film kL from eqs 16−23 and experimental kL for M 250Y is shown in Figure 21. If total mixing between adjacent corrugation channels is assumed, then falling film kL for both the wall and packing is significantly (more than two times) greater than the measured value. This is not reasonable because the kL of turbulent flows in the packings should be greater than the theoretical value for the laminar
Figure 21. Comparison of the theoretical kL from eqs 16−23 and experimental kL for M 250Y. I
DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 22. Ratio of experimental kL to falling film kL (no mixing) from eqs 16−20 with variable viscosity.
Figure 23. kL/kG with aP (kL is the average measured value at 6G = 1 m/s, L = 24, 37, and 49 m3/m2·h, normalized to 25 °C, with unit of m/s; kG is the average measured value at L = 24 or 37 m3/m2·h, G = 0.6, 1, 1.5 m/s, normalized to 25 °C, with unit of m/s).
21 are only qualitative ones. Either or both of them could be true. Rigorous quantitative study in this area is promising but is not within the scope of this work. Although asecondary has been deducted from the total area in the model, it is the measured total area, ae,total, that has been used to separate kL from the experimental kLae. This assumes that the liquid in the secondary area has the same kL as in the packing section, which is not true according to Figure 21. However, since the secondary area is less than 10% for higher area packings (aP > 200 m2/m3), this simplification is still valid for most of the packings. Differentiating and quantifying kL in different flow regimes would be a more rigorous way of modeling, but it is not within the scope of this work due to the limited data for coarse packings for which secondary flow is more significant. The operating conditions for ae and kL measurement in this work are well below the loading point (20−40% flooding for water), so the result may not be valid for operating conditions close to or above the loading zone, especially for viscous liquids that have drastically different hydraulic behavior than water. Caution should also be exercised when the conclusions about the viscosity effect on mass transfer are extrapolated beyond the μL range of this work (0.8−70 mPa·s). Due to different degrees of maldistribution, a systematic difference in kL with different packing height has been observed (Figure 10) and all kL has been normalized to the shorter bed (1.8 m). Therefore, error may arise when applying the models in this work to columns of different size and packing bed height (and thus different degree of liquid maldistribution). Many other factors that affect mass transfer efficiency will also be different from column to column, such as how tight the packing fits the column, the condition and number of wiper bands of packing elements, and the degree of packing damage due to (re)install. This is a universal and important problem for all models and requires systematic research in the future. Figure 23 shows the ratio of kL and kG (both in m/s unit) as a function of aP. The ratio decreases with aP for all packing types investigated, which implies that liquid film mass transfer resistance becomes more important for finer packings. This agrees with the previous analysis that kL decreases with increasing aP, while kG increases with aP. This analysis should provide qualitative guidance in column design but should not be used as a rigorous method. Figure 24 compares the results of this work and other kL (kLa) correlations in the literature. Details of the correlations in
Figure 24. Result of this work compared to literature correlations.
the figure can be found in previous work by this author.1 The direct dependence on μL of kL predicted in eq 12 (−0.4) is similar to the other four experiments on random packings with relatively large viscosity variance (the four solid circles in the figure). The end effects for ae and kL measurements are believed to be negligible since tall beds of 3 and 1.8 m of packing were used. The inlet and outlet sampling points are close to the packed bed to minimize the end effects. For kG measurement where a shorter bed (0.5 m) is used, the end effect between the gas inlet and packing bottom (mainly the column sump) has been corrected by measuring the SO2 both at the inlet gas duct and packing support right below the bed. Billet and Schultes20 extensively discussed the entrance effect where mass transfer efficiency of the top packing elements is different (either greater or smaller) from the rest of the column due to the different fluid hydraulics dictated by the distributor. The F40 fractal distributor used in this work has a drip point density (432 points/m2) higher than the typical value used in industrial-scale columns (∼ 100 points/m2), which will make the entrance effect more significant for the column used in this study. Due to the limited scope of this work, this entrance effect has not been corrected and the efficiency difference along the packed bed is assigned only to the “Z term” in the model of kL. J
DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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CONCLUSIONS Models of ae,packing, kL, and kG (eqs 9, 12, and 13) represent data with 39 packings of various type, aP, and materials. Increasing liquid viscosity from 0.8 to 70 mPa·s reduces kL with a total dependence of −0.75, of which −0.35 is from the indirect influence through diffusivity, and −0.4 is from the direct influence through liquid turbulence. Viscosity does not affect ae,packing in the range of μL investigated in this work, which was below the loading point. kL decreases with increasing aP for structured packings. Shorter packing height consistently shows greater kL than higher packing height. The experimental kL is significantly lower than the theoretical value for falling film on the packing surface.
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d = characteristic length in dimensionless groups (1/aP in this work, s in the RBF model), m g = gravitational acceleration, m/s2 H = packing element height, m h = packing crimp height, m kg′ = liquid film mass transfer coefficient with chemical reactions expressed in gas unit, mol/m2·Pa·s kL = liquid film mass transfer coefficient, m/s kG = gas film mass transfer coefficient expressed in liquid unit as driving force, m/s KOG = overall mass transfer coefficient expressed in gas unit as driving force, mol/m2·Pa·s l = length of falling film in eq 16b, m n = number of packing corrugation channels in the crosssectional area of the column Q or q = volumetric liquid flow rate, m3/s s = packing channel side, m u = superficial velocity, m/s W = wetting peripheral of falling film in eq 16b, m Z = packing height, m
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b04396. Packings in the SRP Air−Water Column database (Appendix I); literature kLa correlation in Figure 16 (Appendix II) (PDF)
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Greek Letters
α = corrugation angle of packing (degree) σ = surface tension, N/m ε = packing void fraction, m3/m3 η = correction factor in eq 8 (detail in eq 9 and Table 1) θ = opening angle of packing corrugation channel (= 90°) μ = viscosity, Pa·s (or mPa·s if noted) ρ = density, kg/m3 Φ = fractional area of packing (= ae/aP)
AUTHOR INFORMATION
Corresponding Author
*Tel.: +1-512-471-7230. E-mail:
[email protected]. Notes
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. The authors declare no competing financial interest.
Dimensionless Groups
Ca = capillary number, μu/σ Fr = Froude number, u2/gd Ga = Galilei number, gd3ρ2/μ2 Mi = mixing point density,
2
( ( )) sin( )
3 sin(2α) cos
θ 2
θ 2
32
Re = Reynolds number, duρ/μ Sc = Schmidt number, μ/ρD Sh = Sherwood number, kLd/D We = Webber number, ρu2d/σ Packing Names
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ACKNOWLEDGMENTS We acknowledge financial support provided by the Process Science and Technology Center of the University of Texas at Austin and by the U.S. Department of Energy, Office of Fossil Energy through the CCSI2 (Carbon Capture Simulation for Industry Impact) (subcontract 318779 with Los Alamos National Laboratory).
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NOMENCLATURE A = cross-sectional area of the column, m2 ae = effective area of mass transfer per volume of column, m2/m3 aP = specific area of packing per volume of column, m2/m3 b = packing channel base, m C = concentration, ppmV or ppmW D = diffusivity, m2/s Dcolumn = diameter of the column, m
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A3 = MONTZ-Pak Type A3 B1 = MONTZ-Pak Type B1 CMR = Cascade Mini-Rings F = Flexipac GTO = GT-OPTIMPAK GTP = GT-PAK HFP = Hiflow Plus IMTP = IMTP random packing M = MellaPak MG = MellaGrid PR = Pall Ring RSP = Raschig Super-Pak RSR = Raschig Super-Ring SB-2P = SuperBlend 2-Pac
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L
DOI: 10.1021/acs.iecr.7b04396 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
