Ind. Eng. Chem. Res. 1997, 36, 227-237
227
Mass Transfer in Beds of Modern, High-Efficiency Random Packings Ingo Wagner,† Johann Stichlmair,† and James R. Fair* Chemical Engineering Department, The University of Texas at Austin, Austin, Texas 78712
A new model has been developed for the prediction and correlation of mass-transfer rates in distillation columns containing random packings. Emphasis is placed on the characteristics of the newer “high-efficiency” random packings: IMTP, CMR, Fleximax, and Nutter. These packings are of the high void fraction, through-flow type and have become quite popular for new designs as well as for retrofits. In building the model use has been made of a large bank of experimental data from the laboratories of Fractionation Research, Inc., and the Separations Research Program (SRP) at The University of Texas at Austin. The model is based on an earlier SRP study of liquid holdup and gas pressure drop in beds of random or structured packing (Stichlmair et al. Gas Sep. Purif. 1989, 3, 19]. The only packing parameter needed is a “packing characteristic” which has a value of about 0.030 for a 2-in. Pall and Raschig rings and about 0.050 for the 2-in. nominal size of the high-efficiency packings listed above. The model was found to fit 95% of 326 experimental values of height equivalent to a theoretical plate (HETP) to within (25% and all values within (30%. Prediction of the mass-transfer efficiency of distillation columns containing random packings has long been considered a risky endeavor, primarily because of a lack of understanding of the complex two-phase flow that prevails in such packings. While reasonable masstransfer models have evolved for the older, bluff-body packings, such as Raschig rings and Berl saddles, the advent of newer, through-flow type metal random packings has left the existing models wanting. For one thing, there has been an insufficient amount of commercial-scale efficiency data published for these newer packings, certainly not enough data for preparing generalized models. For another, there is the problem of a different kind of surface generation in the newer packings, certainly a departure from the traditionally assumed liquid film flow and vapor channel flow approaches. Examples of the through-flow packings are IMTP (Norton Co.), Nutter rings (Nutter Engineering Co.), CMR (Glitsch, Inc.), and Fleximax (Koch Engineering Co.) and have registered trade names. The traditional metal Pall ring also can be classified as “through-flow”. The work described here has resulted from further investigations of the character of flow through the newer packings, particularly the work reported by Stichlmair et al. in 1989. In addition, a large amount of commercially important experimental data have become available in recent years, especially those from the Separations Research Program at The University of Texas at Austin (SRP) and from Fractionation Research, Inc. (FRI). With these sources coupled with pertinent previously published information, a data bank of 326 experimental efficiency points has been assembled. This bank comprises the basis for evaluating the model to be described below. The objective of the work was to develop a semiempirical model taking into account the effect of irrigated pressure drop and liquid holdup on mass transfer. * To whom correspondence should be addressed. E-mail:
[email protected]. † Present address: Technische Universita¨t Mu¨nchen, Mu¨nchen, Germany. S0888-5885(96)00019-X CCC: $14.00
Previous Work Generalized methods for predicting the mass-transfer performance of larger-scale packed distillation columns have been reviewed by Kister (1992). For random packings, only four methods have been thought to be general enough and reliable enough to merit serious consideration for commercial design. The method of Cornell et al. (1960) utilizes the two-film model and empirical parameters specific to each packing type and size. Its development was based on a rather limited data set and did not include the more modern, throughflow packings. Onda et al. (1968a,b) developed a random packing model based on a modest-sized data set, using the two-film model and covering traditional random packings such as ceramic rings and saddles. Bolles and Fair (1982) expanded the Cornell et al. data base and adapted the model to new experimental results taken at larger scales of operation. They included distillation results for a through-flow random packing, the Pall ring, in their analysis. Bravo and Fair (1982) used the Onda model plus the Bolles-Fair data base to provide a correlation for effective interfacial area in randomly-packed columns. These four approaches to predicting mass transfer purported to cover absorption/ stripping as well as distillation applications. A knowledge of fluid dynamic behavior is fundamental not only for column design but also for the prediction of mass transfer. It is well-known that there is a strong dependence on hydraulics of the effective interfacial area in a packed bed. Thus, in the present work it was necessary to consider pressure drop and liquid holdup effects in arriving at a suitable model for mass transfer. The pressure drop studies of Stichlmair et al. (1989) compared the behavior of packed columns with the experimental findings for a fluidized bed, with the result of a slight modification of the Ergun model for fixed beds of packing:
∆pd 3 1 - µV2 ) f0 4.65 FV Z 4 dp f0 )
C1 C2 + + C3 ReV Re 0.5 V
© 1997 American Chemical Society
(1)
(2)
228 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997
Figure 1. Dry and wet bed pressure drop for 25 mm Bialecki rings (Billet, 1995). Reprinted with permission from VCH Publishers. Copyright 1997 American Chemical Society.
Figure 2. Liquid holdup for 25 mm Bialecki rings with the airwater system (Billet, 1995). Reprinted with permission from VCH Publishers. Copyright 1997 American Chemical Society.
where calculation of the dry bed pressure drop ∆pd requires the use of friction factor f0, itself a function of vapor flow and packing device geometry. Values of the constants C1, C2, and C3 for many packings are given in the Stichlmair et al. paper. Correlations similar to that of eqs 1 and 2 have been presented by Kast (1964) and Billet et al. (1989). Determination of the irrigated pressure drop takes into account the rise in interstitial gas velocity with diminished flow area due to the presence of the flowing liquid. A representative set of irrigated pressure drop data is shown in Figure 1, where it may be observed that above the loading point the liquid flow lines curve away from the dry pressure drop line. Several authors have presented models for irrigated pressure drop (Billet et al., 1989; Billet and Schultes, 1993; Kolev, 1976; Mackowiak, 1991; Reichelt and Blass, 1971; Robbins, 1991). For the present work, the model of Stichlmair et al. (1989) was used; it was considered by Kister (1992) to be the most fundamental model available, and, importantly, it includes the determination of liquid holdup both below and above the loading point. The model is as follows:
In the loading zone, however, holdup increases as vapor velocity approaches the flooding point. The holdup relationship of Stichlmair et al. (1989) does not account for physical properties and has been validated for air/water systems only, but it was shown that the equation is applicable for liquid viscosities up to 5 × 10-3 Pa‚s. This can be explained by the moderate influence of viscosity and surface tension on liquid holdup (Strigle, 1987). The equation is similar to that of Billet and Mackowiak (1988) but does not include a constant that depends on the packing type:
∆pirr 1 - + h (2+c)/3 4.65 ) ∆pd 1- -h
(
)
(
)
(3)
with friction factor f0 taken from eq 2 and
(
c) -
)
C1 C2 f -1 ReV (2Re )0.5 0 V
(4)
The liquid holdup in a packed column is defined as the volume of liquid held under operating conditions per volume of packed bed. This holdup can be divided into two components, the static and the dynamic (or operating) holdup. The static holdup consists of the liquid kept in the voids or dead spaces of the packing, while the dynamic portion flows down the column. The static holdup is influenced by the physical properties of the liquid and the packing surface but is independent of the liquid load (Jesser and Elgin, 1943). The static holdup is normally of no great significance in packed columns (Strigle, 1987). The dynamic holdup is primarily a function of the liquid velocity. Figure 2, from Billet (1995), shows the typical behavior of the holdup as a function of vapor velocity in a packed column, for various liquid loads. It is clear that the holdup below the loading point is independent of the vapor velocity.
( )
h0 ) 0.555
apuL2
1/3
(5)
g4.65
Above the loading point, the correlation for liquid holdup of Stichlmair et al. is dependent on the irrigated pressure drop:
[
( )]
h ) h0 1 + 20
∆pirr ZFLg
2
(6)
A disadvantage of eq 6 is that the irrigated pressure drop must be known in order to determine the holdup in the loading region. Since the calculation of the irrigated pressure drop by eq 3 requires a value of holdup, an iteration is necessary. The amount of the existing effective vapor-liquid interfacial area in randomly-packed distillation or absorption columns is a basic factor that affects the mass transfer. It has been found that the area is smaller than the total vapor-liquid surface area (Davidson, 1959; Hanley et al., 1994a; Weiland et al., 1993). This, among other things, is caused by negligible liquid flow through thin liquid films, making the wetted surface largely ineffective for mass transfer. The effective interfacial area is also reduced because of a “shielding” effect (Hanley et al., 1994a,b). This means that a part of the vapor flow cannot interact with the liquid because of gas maldistribution caused by liquid-filled voids which block the vapor flow. This phenomenon will have a great influence on mass transfer as the flooding point is approached because of the rapidly increasing holdup. Several investigators have proposed that a large part of the effective interfacial area results from liquid drops generated in the packed column (Bornhu¨tter, 1991a,b; Fair and Bravo, 1987). Bornhu¨tter found that the amount of drop flow is about 5-45% of the total liquid flow depending on packing type and liquid properties, and thus the effect of drop flow on mass transfer cannot
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 229 Table 1. Equations for the Liquid-Side Mass-Transfer Coefficient
( )( ) ( )( )( ) ( ) ( ) ( )( ) ( ) () ( ) ( ) DL 4
0.5
Billet (1993)
kL ) C
Onda (1968b)
kL ) 0.0051
Schultes (1990)
kL ) C
Shi and Mersmann (1964)
kL ) 0.91
FLg µL
FLg µL
µLg FL
1/3
µL1/3
1/3
uLFL aeµL
apDL 4
1/6
6DL πdn
0.5
0.5
kL ) 25.1
van Krevelen (1942)
kL ) 0.015
Zech (1987)
kL ) C
uL uL ap ap
0.5
(apdn)0.4
1/3
uL0.19g0.220.2FL0.23 σ FL µ 0.23a 0.4 L
0.5
µL FLDL
2/3
(1 - 0.93 cos θ)1/3
FL2g
1/3
µL F L DL
µL2
DLap
6(1 - )
( )( )( ) uLFL aeµL
0.05
p
0.45
6(1 - )uLFL apµL
Shulman et al. (1955)
DL F L µL
2/3
DL
( ) ( )( ) FLgdn2 σ
-0.15
uLgdn 3
1/6
6DL πda
0.5
Table 2. Exponents Used in Correlations for the Liquid-Side Mass-Transfer Coefficient author
uL
DL
FL
µL
Billet (1993) Schultes (1990) Shi and Mersmann (1964) Shulman et al. (1955) Zech (1978) new model
0.33 0.33 0.19 0.45 0.167 0.167
0.5 0.5 0.5 0.5 0.5 0.5
0.33 0.167 0.23 -0.05 -0.15
-0.33 -0.167 -0.23 0.05
σ
g 0.33
0.05 0.15
0.22 -0.017 0.167
Table 3. Summary of Equations for the Vapor-Side Mass-Transfer Coefficienta
a
( )
DV uVFv dn apµv
0.8
ScV1/3
van Krevelen and Hoftijzer (1948)
kV ) 0.20
Shulman and de Gouff (1952)
kV ) 0.0137(uVFV)0.65
Onda et al. (1968b)
kV ) 5.23DVap
Zech and Mersmann (1979)
kV ) C
Billet (1993)
ap DV FVuV kV ) C (4)0.5 ( - h)0.5 apµV
Cornell et al. (1960)
HV )
( ) 1 ScV
( ) FVuV apµV
(
2/3
0.7
ScV1/3(apdn)-2
)
2 2 + 0.012 (1 - )DV uV FV µVdn
( )
1/3
0.75
ScV1/3
( )( )
uV Dc C ) Sc 0.5 kVae (3600F u f f f )q V 3.66 L L 1 2 3
n
Z 3.05
1/3
ScV ) µV/FVDV.
be neglected. It is also important to note that the amount of effective interfacial area in a given system is the same for vapor- and liquid-side mass transfer (Bravo and Fair, 1982). It is clear that the interfacial area in a packed column is closely related to the hydrodynamics. The fluid conditions are mainly described through irrigated pressure drop and holdup. Previous workers have concluded that the amount of vapor-liquid surface area is directly linked to the operating holdup (Bravo and Fair, 1982; Martin et al., 1988; Puranik and Vogelpohl, 1974; Rocha et al., 1993; Yilmaz, 1973). Relationships between effective interfacial area and actual packing surface have been developed by a number of researchers (Onda et al., 1968a,b; Billet and Schultes, 1993; Kolev, 1976; Bravo and Fair, 1982; Zech, 1978; Shi and Mersmann, 1984). The ratio of ae/ap was determined in various ways, but not for any of the newer through-flow random packings.
In distillation applications the liquid-side masstransfer resistance normally has a minor effect on masstransfer rate, unlike absorption and desorption applications which may be dominated by the liquid-side mass-transfer resistance. However, the liquid-side resistance in distillation is still significant enough to merit attention by the present work. A summary of the equations for the liquid-side mass-transfer coefficient contributed by other authors is given in Table 1. A summary of the exponential relationships for the various parameters is given in Table 2. The only consistency is the 0.5 exponent on the diffusion coefficient, as predicted by the penetration model of Higbie (1935). The vapor-side mass-transfer coefficient has been the subject of much experimental and theoretical study. A summary of the various published correlating equations for the vapor side is given in Table 3, with the exponents of the principal parameters given in Table 4. The variations of the exponents for the vapor side are less
230 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997
The same process for the gas phase leads to
Table 4. Exponents Used in Correlations for the Vapor-Side Mass-Transfer Coefficient author
uV
DV
Billet (1993) Mersmann and Deixler (1986) Onda et al. (1968b) Shulman et al. (1955) van Krevelen (1948) Zech and Mersmann (1979) new model
0.75 0.66 0.7 0.65 0.8 0.66 0.5
0.66 0.66 0.66 0.66 0.66 0.66 0.5
µV
FV
σ
g
-0.416 0.416 - -0.33 0.33 - -0.367 0.367 - 0.65 - -0.467 0.467 - -0.33 0.33 - -
than those for the liquid side, but it is notable that the variation of the diffusion coefficient is to the 0.66 power, which is not predicted by the penetration model. However, that model was developed primarily for the liquid phase.
Model Development Height Equivalent to a Theoretical Plate (HETP). The HETP is used extensively for characterizing the mass-transfer capability of a packed bed. It suffers, however, from not being fundamentally-based with respect to interphase transport. Rather, the height of an overall transfer unit, Hov, is more appropriate in that it includes individual phase mass-transfer coefficients and concentration driving forces. Well-known theory leads to the following representation of Hov:
Hov )
(
)
uV FVMLkV 1+m kVae FLMVkL
(7)
The second term on the right represents the additional transfer resistance of the liquid phase. As can be seen, this relationship includes three unknowns: the liquidand vapor-side mass-transfer coefficients kL and kV and the effective interfacial area ae. Mass-Transfer Rate. The penetration theory of Higbie (1935) was extended by Lockett and Placka (1983), who introduced an enhancement factor φ to account for turbulent diffusion and multiple surface renewals. This leads to equations for the liquid- and vapor-side mass-transfer coefficients:
kL ) kV )
( ) ( ) 4φLDL πτL
0.5
4φVDV πτV
0.5
kL ) kV )
(
)
4φLDLuL πhχ
(
4φVDVuV
0.5
(14)
)
0.5
(15)
π( - h)χ
One should note that the exposure times for liquid, τL, and vapor, τv, are different, which is in agreement with the findings of Chen and Chuang (1994). Looking at eqs 14 and 15, one can see that there are now three instead of two unknown factors, the liquid and gas phase enhancement factors φL and φV as well as the characteristic length χ. At operating conditions the enhancement factors can approximately be set equal to unity, so that only the value of the characteristic length χ must be determined in order to calculate the masstransfer coefficients. It may be pointed out that use of the penetration model for determining the gas-phase coefficient in packed columns is not common. For sieve trays, on the other hand, the penetration model is used to predict both the liquid- and vapor-side mass-transfer coefficients, and there are investigators who have proposed an exponent of 0.5 for the vapor diffusion coefficient in packed columns, according to penetration theory (Cornell et al., 1960; Lynch and Wilke, 1955; Vidwans and Sharma, 1967). It seemed reasonable in the present study to utilize the penetration model as an approximate representation of the physical mechanisms involved in phase contacting in random packings. Effective Interfacial Area. As mentioned earlier, the effective interfacial area is closely related to the hydrodynamics in the column. Considering the pressure drop model of Stichlmair et al. (1989), eqs 1 and 3, the particle diameter dp can be replaced by its definition:
dp )
6(1 - ) ap
(16)
(9)
∆pd 3 ap ) f0 4.65FVuV2 Z 4 6
(10)
(17)
Thus, the dry pressure drop is proportional to the packing surface area. The basic idea now is that the irrigated pressure drop as well is directly dependent on the total surface area in the wetted packing. The Stichlmair equation for the irrigated pressure drop becomes
∆pirr 3 atot ) f0 F u 2 Z 4 6( - h)4.65 V V
(18)
(11) This can be transformed, using eq 17, into
so that time τ can be written as:
τL ) χh/uL
Dovetailing eqs 12 and 13 into eqs 8 and 9 results in:
which leads to the following expression for the dry pressure drop:
The effective velocity can be determined by using the liquid holdup:
uLeff ) uL/h
(13)
(8)
The time the liquid is in contact with the gas phase can be expressed through the effective liquid velocity uLeff and a characteristic length χ:
τL ) χ/uLeff
τV ) χ( - h)/uV
(12)
∆pirr f0′ atot 4.65 ) ∆pd f0 a p - h
(
)
(19)
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 231 Table 5. Physical Properties of the Test Systems system
FL (kg/m3)
p (kPa)
cyclohexane/n-heptane
33.3 165.5 413.7 1160.0 13.3 6.7 100.0 100.0
i-butane/n-butane ethylbenzene/styrene ethanol/water methanol/ethanol
656.7 608.7 560.6 493.6 829.7 842.5 760.9 752.8
FV (kg/m3)
µL (Pa‚s)
σ (N/m)
DL (m2/s)
DV (m2/s)
1.18 5.45 13.14 28.37 0.48 0.26 1.44 1.20
0.43 × 0.23 × 10-3 0.16 × 10-3 0.97 × 10-4 0.39 × 10-3 0.47 × 10-3 0.50 × 10-3 0.45 × 10-3
17 × 12 × 10-3 8 × 10-3 6.2 × 10-3 26 × 10-3 27 × 10-3 2 × 10-3 19 × 10-3
2.7 × 6.2 × 10-9 9.3 × 10-9 1.35 × 10-8 3.0 × 10-9 2.7 × 10-9 6.2 × 10-9 3.6 × 10-9
1.1 × 10-3 2.9 × 10-4 1.4 × 10-4 5.6 × 10-7 2.4 × 10-3 3.8 × 10-3 1.5 × 10-3 1.0 × 10-5
where, according to Stichlmair et al., the ratio of wet and dry friction factors is
f0′ 1 - + h c/3 ) f0 1-
(
)
(20)
A comparison of eq 3 with eqs 19 and 20 shows that the total interfacial area in a wetted packing can be determined by
atot 1 - + h 2/3 ) ap 1-
(
)
(
)
10-9
substituted into eq 7. Further, it was assumed that for all test systems the average slope of the equilibrium line was approximately unity. Under this assumption, and operating with total reflux (L/V ) 1), the HETP is equal to the height of an overall vapor transfer unit Hov. This leads to:
HETP )
(
)[ (
π( - h)uV 4DV
0.5
1+
hDVMLFV
)]
( - h)DLMVFL
0.5
χ0.5 ae (23)
(21)
The total surface area in the irrigated column is expected to be greater than the effective area for mass transfer; thus
ae 1-+h ) -R ap 1-
10-3
10-3
(22)
The term R takes into account the dry or ineffective part of the total surface area in the wetted packing and can be deduced from experimental data. Adjusting the Model Parameters. To adjust the missing parameters for the new model developed earlier, experimental data taken from the Separations Research Program (SRP) and Fractionation Research, Inc. (FRI; 1986), as well as from the investigations of Billet (1979) and Kirschbaum (1969) were used. These data include several types of metal random packings tested with aqueous and nonaqueous systems under various conditions. Table 5 shows physical properties for the test systems. The FRI information for Pall rings is included in a paper by Shariat and Kunesh (1995); the SRP data are new, and the research facility and experimental methods have been described by Fair and Bravo (1990) and by Rocha et al. (1993). The different experimental conditions and the column geometries for all packings tested are listed in Table 6. For the experiments of the SRP a perforated pipe type distributor with feed reservoir and 430 pour points/m2 of bed cross section was used. The distributor of FRI was a tubed drip pan device with 5 mm tubes and 120 pour points/m2. Billet used a drip-tube/riser distributor with 246 nozzles of 3 mm diameter in a column of 0.8 m diameter and in other work in a 0.5 m column, a special orifice-riser type distributor with liquid under pressure, with the 108 orifices being extended 2 mm nozzles. Kirschbaum used a rotating perforated pipe distributor in his experiments. All of these distributors provided a very good initial liquid distribution. It can be seen from Table 6 that the experiments cover a wide range of physical properties, packing geometries, and operating pressures. To determine the two missing parameters in the newly developed mass-transfer model, the characteristic length, χ, and the ineffective part of the total surface area, R, in the wetted packing, eqs 14 and 15 for the liquid- and vapor-phase mass-transfer coefficients were
Equation 23 can be rearranged to
ae ) χ0.5 π( - h)uV 4DV
(
)[ ( 0.5
1+
hDVMLFV
)]
V ( - h)DLMVFL L
0.5
1 (24) HETP
The value of holdup was calculated by means of the correlation of Stichlmair et al. (1989), i.e., eqs 5 and 6. The relationships do not take into account physical properties, since the interfacial area was based on the Stichlmair et al. holdup correlation. The experimental results for HETP now can be inserted into eq 24. In Figures 3 and 4 the values of ae/χ0.5 are plotted against holdup for IMTP No. 40, Fleximax 300, CMR No. 2, and 50 mm Pall rings. It is clear that all the curves begin at the origin. Further, it can be concluded that physical properties have little or no effect on the term ae/χ0.5, while the packing height seems to have a significant influence on the mass transfer (Figure 4). Those data points that are out of line are based on conditions close to flooding, where HETP rises rapidly with increasing loading. By eq 24, high values of HETP imply low values for the effective interfacial area. This means that the effective interfacial area decreases as the flooding point is approached. Since operation in this region is of no commercial interest, these data points were excluded from further work. Characteristic Length. The observation that the packing height has a significant influence on mass transfer leads to the assumption that the characteristic length χ can be expressed by
χ ) Cpk2Z
(25)
where Cpk is a dimensionsless packing characteristic and Z is the bed height. Figure 5 shows the results of the Z0.5 assumption for 50 mm Pall rings. The results for the different packing heights are in good agreement, especially since three different systems in a pressure range from 13.3-413.7 kPa are compared in the plot. This seems to prove the hypothesis that increasing bed height causes a decrease in the overall mass transfer. This fact was observed earlier by other investigators, and the exponent of 0.5 used for the packing height is close to the value 0.4 proposed by Bravo and Fair (1982).
232 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 Table 6. Test Systems, Packing Types, and Bed Geometries source SRP
system
packing type
cyclohexane/n-heptane
1.0 in Pall rings 1.5 in. Pall rings 2.0 in. Pall rings IMTP No. 40 CMR No. 2 Fleximax 30
FRI
5/ in. Pall rings 8 1.0 in. Pall rings
cyclohexane/n-heptane
2.0 in. Pall rings CMR No. 3 Fleximax 300 FRI
5/ in. Pall rings 8 1.0 in. Pall rings
cyclohexane/n-heptane
2.0 in. Pall rings 3.5 in. Pall rings Nutter rings No. 2 Billet
methanol/ethanol
15 mm Pall rings 25 mm Pall rings 35 mm Pall rings 50 mm Pall rings 50 mm Raschig rings 15 mm Pall rings 25 mm Pall rings 35 mm Pall rings 50 mm Pall rings 15 mm Raschig rings 25 mm Raschig rings 35 mm Raschig rings 50 mm Raschig rings
ethylbenzene/styrene
Kirschbaum
ethanol/water
25 mm Pall rings
Ineffective Part of the Total Surface. As mentioned before all the curves in Figures 3-5 appear to begin at the origin. Accordingly, for a value of holdup equal to zero, the effective interfacial area must be zero. This leads to a value of R ) 1 in eq 22, so that the effective interfacial area can finally be expressed by:
ae )
[(1 -1 - + 0) - R]a
p
(26)
Keeping the value of R constant for all liquid loads means that the amount of the dry surface area is ineffective during operation under countercurrent liquid/ vapor flow conditions. An explanation can be found in a poorly wetted metal surface leading to drop flow and low liquid velocities in the thin film on the packing surface. A part of the packing is wetted but is ineffective or only very slightly effective for mass transfer, because of the small mass flow and long exposure time. Figure 6 shows comparisons between the measured and calculated effective interfacial areas for some of the packings, assuming arbitrarily a packing characteristic of 0.061.
pressure (kPa)
column diameter (m)
bed height (m)
33.3 165.5 413.7 33.3 165.5 413.7 33.3 165.5 413.7 33.3 165.5 413.7 33.3 165.5 413.7 33.3 165.5 413.7 34.0 34.0 165.0 34.0
0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 1.22 1.22 1.22 1.22 1.22 0.425 0.425 0.425 0.425 0.425 0.425 1.22 1.22 1.22 1.22 1.22 1.22 1.22 0.5 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3
3.12 3.12 3.12 3.16 3.16 3.16 3.16 3.16 3.16 3.09 3.09 3.09 3.16 3.16 3.16 3.07 3.07 3.07 3.66 3.66 3.66 3.66 3.66 3.16 3.16 3.16 3.07 3.07 3.07 3.66 3.66 3.66 3.66 3.66 4.30 4.30 1.50 2.00 2.00 2.00 2.00 2.00 1.50 2.00 2.00 1.33 1.50 2.00 2.00 2.00 2.00 2.00
33.3 165.5 413.7 33.3 165.5 413.7 34.0 34.0 165.0 34.0 34.0 34.0 165.0 100.0 100.0 100.0 100.0 100.0 100.0 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 6.7 100.0
Packing Characteristic. The last unknown factor resulting from the substitution for the characteristic length χ using eq 25 is Cpk, which must be determined from experimental results. It was found that Cpk can be expressed as a constant for each packing. Final Model. For distillation columns filled with random packing and on the basis of the development outlined above, the design correlation becomes
(
) ) ][(
0.5
Z0.5 π( - h)uV × HETP ) Cpk ap 4DV hDVMLFV V 0.5 1 - + h 1+ 1- ( - h)DLMVFL L
[ (
) ] 2/3
-1
-1
(27)
Results and Discussion The model has been applied to the experiments listed in Table 6. The values predicted by the new model were compared with 326 experimental data points. The packing characteristic Cpk was evaluated for each packing type (Figure 7). Table 7 includes values for Cpk as
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 233
a
b
Figure 4. Plot of the ae/χ0.5 function against liquid holdup at several bed heights. Packing ) 50 mm Pall rings. Systems: cyclohexane/n-heptane, methanol/ethanol, ethylbenzene/styrene, all at total reflux. Pressure range; 13.3-413.7 kPa.
c Figure 5. Plot of the function ae/Cpk vs liquid holdup, with packing heights normalized by Z0.5. Pall rings, 50 mm; height range ) 1.33-3.66 m.
Figure 3. Plot of the ae/χ0.5 function against liquid holdup for distillation tests at 33, 165, and 413 kPa: (a) IMTP No. 40, (b) Fleximax 300, (c) CMR No. 2. Source: SRP data for the cyclohexane/n-heptane system at total reflux.
well as the main packing specifications, void fraction , and surface area ap. Figure 8 comprises parity plots for calculated vs measured HETP, for all sizes of Pall rings, Raschig rings, and the “high-efficiency packings”, IMTP No. 40 (Norton Co.), Fleximax 300 (Koch Engineering Co.), CMR No. 2 (Glitsch, Inc.), and Nutter rings No. 2 (Nutter Engineering Co.). The best agreement was found for the high efficiency packings, but only one organic test system and a constant bed height were used. For these packings, 90% of the analyzed data show a deviation of less that 10%. By way of contrast the data for metal Raschig rings and Pall rings cover a wide range of physical properties, packing height, and pressure, with aqueous and nonaqueous systems. The agreement between model predictions and experimental data is quite reasonable. Most of the calculated values are in a range of (25%. Over half of the calculated values (56%) for Pall rings vary less than 10% from the
Figure 6. Representative plot of the effective interfacial area as a function of liquid holdup. Packing, IMTP No. 40; packing characteristic Cpk, 0.061.
experimental values. For metal Raschig rings the maximum error was 28.5% for the 50 mm size, primarily at very low mass flow rates. Figure 9 presents all calculated vs measured HETP values; 94.8% of the data points are in a (25% range, and no deviations over 33% were observed. Using the new model, 218 (66.9%) of the 326 experimental data points could be predicted with less than 10% error, with only 1.8% (6 data points) showing a deviation of more than (30%. It must be mentioned that the model tends to predict lower values for the HETP compared to the experimental results, at low pressure and with the ethylbenzene/styrene system. Comparison of this method with generalized approaches discussed earlier is not straightforward be-
234 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 Table 7. Summary of Packing Specifications packing type
void fraction (m3/m3)
surface area (m2/m3)
particle diameter (mm)
packing characteristic
in. Pall rings 1.0 in. Pall rings 1.5 in. Pall rings 2.0 in. Pall rings 3.5 in. Pall rings 15 mm Pall rings 25 mm Pall rings 35 mm Pall rings 50 mm Pall rings 15 mm Raschig rings 25 mm Raschig rings 35 mm Raschig rings 50 mm Raschig rings Nutter rings No. 2 IMTP No. 40 CMR No. 2 Fleximax 300
0.93 0.94 0.95 0.96 0.97 0.93 0.94 0.95 0.96 0.92 0.93 0.94 0.95 0.98 0.97 0.97 0.97
341 207 128 102 66 360 207 145 102 350 220 150 110 96 170 144 144
1.23 1.74 2.34 2.35 2.73 1.17 1.74 2.07 2.35 1.37 1.91 2.40 2.73 1.25 1.06 1.25 1.25
0.060 0.034 0.030 0.032 0.034 0.057 0.036 0.030 0.031 0.067 0.037 0.028 0.030 0.047 0.061 0.052 0.050
5/
8
a
Figure 7. Representative plot of packing characteristic Cpk as a function of liquid holdup, based on experimental conditions. Packing ) IMTP No. 40.
cause of the makeup of the data base. Only the Bolles/ Fair and Bravo/Fair methods included a modern, through-flow packing, the Pall ring. For both methods, 85% of the data were within the (35% parity range. Both used the same data set, which included ceramic rings and saddles. As discussed by Bolles and Fair (1982), deviations from a composite data base are expected to be significant because of experimental variations in such factors as bed uniformity, liquid distribution, and sampling technique. The present method appears to be an improvement in data fit for the more traditional packings, and no comparison is possible with the newer packings. Besides the accuracy of the new model, an important concern is how the model tracks the trend of HETP with loading. Figure 10 shows comparisons between experimental and calculated values at a range of superficial vapor velocities. The agreement is excellent. As pointed out earlier, no attempt has been made to model HETP values in the vicinity of the flood point. For predictions above the loading point, it is necessary to determine liquid holdup using eq 6. For operation below the loading point the simpler form, eq 5, can be used. If used above the loading point, eq 5 leads to conservative values. It must be pointed out that according to the new model the only system property influencing mass transfer is the diffusion coefficient. This fact seems to be unusual, but it has been shown that in the range of properties tested, and for metal packings, surface tension and density have little or no effect on mass-transfer
b
c
Figure 8. Parity plots for several packing types, measured vs predicted values of HETP: (a) Pall rings, all sizes; (b) Raschig rings, all sizes; (c) IMTP No. 40, CMR No. 2, Fleximax 300, Nutter rings.
rate. The effect of liquid viscosity is found in its influence on the liquid diffusion coefficient. A broader
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 235
Figure 9. Parity plots for all packings tested.
a
Figure 11. Comparison between measured and predicted HETP values for 50 mm metal Pall rings. Isobutane/n-butane system at 1160 kPa and total reflux, 1.22 m diameter column. The top curve is based on data by Billet (1967) and the bottom curve on data by Shariat and Kunesh (1995).
Conclusions
b
c
This paper presents a new model for predicting mass transfer in randomly packed distillation columns. The model was developed theoretically using pressure drop and holdup to calculate the effective interfacial area. The model was then tested using 326 experimental data points taken with four different systems under various conditions. The data cover a pressure range from high vacuum (6.7 kPa) up to 413.7 kPa, a liquid viscosity range from 0.16 to 0.5 mPa‚s, a vapor density range from 0.48 to 13.13 kg/m3, and a surface tension range from 8 to 27.3 dyn/cm ()27.3 × 10-3 N/m). Although the model only takes into account the diffusion coefficient as a physical property, 95% of the predicted values showed a deviation of less than 25% from the experimental results. It must be pointed out that the physical properties do have an effect on mass transfer, but the influence seems to be small. An improvement of the model might be possible by using a modified holdup correlation that considers additional physical properties. This could make the model applicable to a wider range of systems and pressures without any fundamental changes. Further, it must be mentioned that the equation for determining the effective interfacial area is derived from the pressure drop model of Stichlmair et al. (1989) and therefore has the same limitations. Acknowledgment The senior author is grateful for receiving a travel and research grant from the Ernest-Solvay Foundation, Essen, Germany. All authors acknowledge the financial support of the Separations Research Program at The University of Texas at Austin. Addendum
Figure 10. Representative comparisons between measured and predicted HETP values, for varying superficial vapor velocities. (a) IMTP No. 40, (b) Fleximax 300, (c) CMR No. 2.
range of properties should be studied in order to validate the completely general nature of the new model.
Since the completion of the paper, additional data have become available for the distillation of isobutane/ n-butane at 1160 kPa, using 50 mm Pall rings in a 1.2 m column. This work was carried out in the facilities of Fractionation Research, Inc., and was recently published (Shariat and Kunesh, 1995). Properties of the test mixture are included in Table 5.
236 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997
The fit of the model with the new data is shown in Figure 11. Also shown in the figure are the earlier data of Billet (1967), for identical operating conditions except for the use of an inferior liquid distributor. The reasonable fit of the new model to this higher pressure operating data is encouraging. Nomenclature ae ) specific effective interfacial area (m2/m3) ap ) specific packing surface area (m2/m3) atot ) specific total surface area (m2/m3) C ) constant c ) exponent in eq 9 Cpk ) packing characteristic DL ) liquid diffusion coefficient (m2/s) dp ) particle diameter dp ) 6(1 - )ap-1 (m) DV ) vapor diffusion coefficient (m2/s) f ) Fanning friction factor in eq 10 f0 ) friction factor for flow past a single particle f0′ ) friction factor for flow past a single wetted particle g ) gravitational constant (m/s2) h ) operating holdup (m3/m3) h0 ) operating holdup under loading point (m3/m3) Hov ) height of a transfer unit based on overall vapor resistance (m) kL ) liquid-side mass-transfer coefficient (kmol/s‚m2) kV ) vapor-side mass-transfer coefficient (kmol/s‚m2) L ) molar liquid flow (kmol/s) m ) slope of equilibrium line ML ) molecular weight of liquid (kg/kmol) MV ) molecular weight of vapor (kg/kmol) n ) exponent ∆pd ) dry pressure drop (N/m2) ∆pirr ) irrigated pressure drop (N/m2) ReV ) vapor Reynolds number uL ) liquid velocity (m/s) uV ) vapor velocity (m/s) V ) molar vapor flow (kmol/s) x ) characteristic length (m) Z ) packed-bed height (m) Greek Letters R ) ineffective part of the total surface area in a wetted packing ) void fraction (m3/m3) µL ) liquid viscosity (Pa‚s) µV ) vapor viscosity (Pa‚s) FL ) liquid density (kg/m3) FV ) vapor density (kg/m3) τL ) exposure time of liquid element to vapor phase (s) τV ) exposure time of vapor element to liquid phase (s) φL ) liquid phase enhancement factor for turbulent diffusion φV ) vapor enhancement factor for turbulent diffusion χ ) characteristic length (m)
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Received for review January 19, 1996 Revised manuscript received September 10, 1996 Accepted September 18, 1996X IE9600194
X Abstract published in Advance ACS Abstracts, December 1, 1996.
