Bravo 1982

162 Ind. Eng Chem. Process Des. Dev. 1982, 21, 162-170

Generaiized Correlation for Mass Transfer in Packed Distillation Columns

Jose L. Bravo and James R. Fair Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712

An improved correlation of mass transfer rates for commercial-scale packed distillation columns has been developed. The correlation is based on effective area for mass transfer

a = 0.498a p($)(Ca ,Re,)0.392

where a e is effective area for transfer, a ,, is specific surface of the packing material, Z is height of packed bed (ft), u is surface tension (dynkm), and CaL and Re, are dimensionless liquid capillary number and gas Reynolds number, respectively. Packings represented are of the randomly arranged ring and saddle types. Basic data are from a bank of 231 evaluated runs covering eleven distillation systems. The correlation Is shown to be more reliable and more general than previously published models, with 96% of the calculated data falling within f20% of the observed values. For 95% confidence in design, a 1.6 safety factor is required.

Packed columns have been used extensively for distillation applications, especially those in which pressure drop is critical. The columns have usually been filled with randomly arranged packing elements of the ring or saddle type, and it is on these random packings that most experimental investigations of mass transfer rates have been made. While there is increasing interest in the so-called regular packings (mesh, grids, etc.), their applications tend to be limited by high cost and incomplete perform- ance documentation. These latter packings are normally handled on a proprietary basis through the experience of their vendors.

In 1979 Bolles and Fair described a large data base that they assembled from published tests of flooding, pressure drop, and mass transfer in columns containing random packings. They utilized the base to evaluate existing packed column models. They did not attempt to improve the existing models for flooding or pressure drop, but did develop a mass transfer model that was superior to those previously published. Their model generalized on fluid properties and flow rates, but required two inputs: prior validation for a specific packing type and size, and a consistent (if not completely reliable) method for predicting the flooding condition for the system and packing under scrutiny.

The present work represents an attempt to develop a general design model for distillation applications, a model that would not require previous validation for the packing type or size and which hopefully could be extended to the regular packings. Furthermore, the Bolles-Fair requirement of flooding knowledge was thought to be an encum- brance as well as a limitation on reliability, and it was hoped that such requirement would not be needed with a new model. The model, if successful, could then be applied to a variety of packing sizes and shapes while still being general with respect to properties and flow conditions; in view of the continuing development of packing types, such a model should be well received by process engineers and packing vendors alike. Previous Work

A vast amount of literature dealing with mass transfer in randomly packed columns is available. Studies have covered a wide variety of packing types and sizes ranging

from simple, naturally occurring materials, such as chunks of coke, to carefully fabricated geometric shapes such as metallic or ceramic saddles, and from tiny devices for laboratory use to large commercial packing elements with nominal sizes of 3 in. and larger.

An extensive review of earlier data pertinent to commercial operations was presented by Cornel1 et al. (1960a,b). These data are mainly from studies that used either Berl saddles or Raschig rings. Also, the data were obtained largely from tests with unidirectional mass transfer, gas-to-liquid or liquid-to-gas. A more recent paper by Charpentier (1976) presents a good general overview of additional data and of some of the approaches that investigators have used in dealing with the prediction and description of mass transfer in packed columns.

As noted earlier, the 1979 paper by Bolles and Fair included an extensive data bank for a wide range of packings, column sizes, and systems. Many of the data in this bank are for distillation conditions and include results of work done by Fractionation Research, Incorpo- rated (FRI). This data bank provided all of the model validation material for the present work. As is appropriate for differential contacting, the Bolles and Fair model utilizes the transfer unit approach, equivalent to the mass transfer coefficient approach

where the effective interfacial area a, may differ from the actual interfacial area.

The volumetric mass transfer coefficient KOGae in eq 1 may be divided into coefficient and area components for fundamental analysis, and this approach has been used by a number of workers (Shulman et al., 1955a-c; Yoshida and Koyanagi, 1954; Onda et al., 1968,1972; Hughmark, 1980). Most of the work was confined to Raschig ring and Berl saddle packings.

The work by Shulman can be considered as the basis for the present effort, as it has been for most other mass transfer efficiency studies that describe the transfer coefficient and the effective area.

The work by Onda and co-workers is based on the concept of wetted packing area, as opposed to interfacial

0196-4305/82/1121-0162$01.25/0 0 1981 American Chemical Society

area. The work draws on the earlier efforts by Yoshida and co-workers and uses the wetted area as a geometric parameter in determining the Reynolds number for the liquid.

The Onda and Shulman models, which form a part of the basis for the present model, will be described fully in the next section. Model Development

The two-film mass transfer model as well as the concept of the transfer unit provide the basis for this work. Al- ternate maw transfer models based on the penetration and surface renewal theories may provide a more realistic physical description of the mass transfer mechanisms, but a t the present stage of development they have not changed significantly the mass transfer relationships based on the film model.

An exception to the above may be found in the value for the exponent affecting the diffusion coefficient in the general flux equation. The two-film theory predicts an exponent of unity whereas the penetration theory predicts a value of one-half. The applicable mass transfer coefficient correlations, especially the two used in the present work (by Shulman and by Onda), show a dependence on the diffusivity intermediate between film and penetration predictions: a two-thirds exponent for the gas side and a one-half exponent for the liquid side.

Using the two-film model, and allowing for significant resistance to mass transfer in both phases, the overall transfer unit height results from individual phase transfer unit heights

(2) where X = mGMLM, or the ratio of slopes of the equilibrium and operating lines.

The integration of the general flux equation, coupled with the definition of the number of transfer units, leads to defining expressions for the heights of individual transfer units

HOG = HG + AH,

HG = G / ( ~ G ~ ~ ' M G ) (3)

HL = L/ @ L ~ , P L ) (4) where a, is the effective interfacial mass transfer area.

At this point it is important to note that the value for a, in a given system is considered equal for the gas and liquid phases, since it consists of the area through which mass transfer occurs a t the interface. I t is also to be observed that the value of a, is composed not only by the wetted area over the packing but also by the area provided by suspended and falling droplets, gas bubbles within liquid puddles, ripples on the liquid film surface, and any contribution from film falling on the walls of the column.

(5) A combination of eq 2, 3, and 4 gives

a, = ( a 3 G + XaaL)/HOG Thus, an effective area can be calculated from available mass transfer coefficients kG and kL, themselves based on known values of G , L, MG, ML, P, and pL.

Clearly, the selection of a specific mass transfer coefficient correlation is critical to the present work. The correlations by Onda and co-workers (1968,1972) and by Shulman and co-workers (1955a-c) were selected for our analysis because they conform to the commonly accepted functionalities

k$MG/G = QReG'ScG" (6)

kLC&lL/L = Q'ReLrScLs (7)

and

Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 1, 1982 163

Both correlations for the individual mass transfer coefficients show the same type of dependence on key variables such as diffusivity and velocity.

The equations describing kL and kG in the Shulman model are

0.45

kLdp/DL = 25.1[ z ] (SC~)O.~O (9) In eq 8 and 9 d , is the diameter of a sphere having the same surface area as an element of packing under consideration.

On the other hand, the model developed by Onda is described as follows

[ kL( gPL pL )"'I = 0.0051( %PL ) 3 ( S c L ) - 1 / 2 ( a p d (11)

(12)

where L

RetL = - U p P L

aPL2 FrL = - gPL2

L2 WeL = -

apWL

(13)

(14)

and u,, a critic& surface tension, = 61 Ljm/cm for ceramic packings, 75 dyn/cm for steel packings, and 33 dyn/cm for polyethylene packings.

The data bank provided input variables to enable calculation of effective areas by the Shulman and Onda models. These areas were compared with the known specific areas of the packings used.

The Onda correlation gave more moderate a, values than the Shulman correlation (a, values never greatly above the value for the specific area, a,, of the packing under consideration) and also covered a wider range of packing types and sizes as well as test systems. Therefore, it was selected as a source of kL and kG values. I t was recognized that future work leading to improved methods for predicting kL and kG could lead to improvements in the present work.

Because of the nature of the hydraulics and geometry of packed beds with gas and liquid in counterflow, a cor- respondence between liquid holdup and effective transfer area is to be expected; thus, the trends observed in liquid holdup behavior at varying loading conditions should apply for effective area. Also, an added gas kinetic energy effect should be included for the area analysis because of its influence on film surface rippling, liquid droplet dispersion, and the occurrence of gas bubbling in puddles. It can be reasoned that the behavior of liquid holdup for different flow conditions should be similar to that of the interfacial area, the latter possibly showing a greater influence from

164

gas velocity and density. Accordingly, a significant gas effect was included in the present work since it is generally practical to operate commercial packed columns a t high gas loadings and relatively close to flooding conditions.

In analyzing the various forces acting in such systems, it was concluded that an improved correlation should be able to deal with the following considerations. (a) The effective transfer area should be proportional to the liquid rate since increased liquid velocities would provide a better wetting of the packing, rippling of the film surface, and a more effective renewal of the liquid in the puddles. (b) Systems with low surface tensions should provide increased wettability as well as smaller droplets yielding in this sense more interfacial area. On the other hand, a lower surface tension would make the liquid separate more easily from the packing at high gas rates, thus reducing the effectiveness of the packing. (c) Increased kinetic energy of the gas should tend to increase the effective area. (d) A packing with a high specific surface should yield a relatively high value for the net interfacial area under similar flow conditions. (e) A correlation for liquid maldistribution due to column height and diameter should be expected.

With these considerations in mind, and after different schemes were tried unsuccessfully, the following functionality was proposed

aep /ap = f(L,G,ZPc,u) (16)

The values for asp (the effective mass transfer area for the packing alone) were obtained by correcting the total effective area (a,) for column wall effects

uep = U, - CY~/D, (17)

The factor a allows for wall blockage by packing elements and should not exceed unity. For the present work a value of a = 1.0 was assumed, since for large columns the wall correction essentially disappears.

Modification of the fmdings of Cornell et al. (196Oa) and of Fair and Moczek (1964) led to a corrected effective packing area

a* = a,J04/&5 (18)

where a* is an adjusted effective area suitable for analysis or design of commercial equipment. Equation 20 proved to be a good choice since all of the available data grouped very nicely when the adjustment, combined with the previously mentioned diameter correction, was applied. It should be noted that eq 18 is dimensional, although it could be made dimensionless by using height and surface tension ratio to base values (e.g., 2 = 10 ft and a, = surface tension of water = 72 dyn/cm). As used in this work, 2 has units of feet and u has units of dyn/cm.

In order to incorporate the liquid and gas rate effects as well as the contributions from the viscous forces within the liquid, the following dependence was then proposed

Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 1, 1982

a*/ap = f ( C a ~ , R e d (19)

CUL = NLL/(PLugc) (20) In eq 19, CuL is the dimensionless capillary number

which provides the ratio of viscous forces to surface tension forces. The dimensionless Reynolds number ReG is defined as

ReG = ~ G / ( ~ , , P G ) (21)

which in turn provides the ratio of inertial forces to viscous forces in the gas. Note that the length criterion is the diameter of a sphere having the same surface to volume ratio as the packing element under consideration.

Table I. Symbols for Figures 1-17

A Cyclohexane/n-Heptane 5.0 p s i a

X Cyclohexane/n-Heptane 24.0 p s i a

+ n -But ane/i-But ane 165.0 p s i a 0 %Pro panol/wat e r 14.7 ps ia

X Sthylbenzene/Styrrne 2.0 p s i a

m Methanol/Ethanol 14.7 ps ia 0 Ethanol/water 1L.7 ps ia

23 Ethylbenzene/Styrene 1.0 p s i a

1L.7 p i a X n-Heptane/Toluene

Y NHg/H2Q/air 1L.7 ps ia

X o2/H20/air 1L.7 p s i a

+ Benzene/Dichloroethane lL.7 ps ia .%p 1-Oct ane/Toluene 20.0 p s i a

Various combinations of these dimensionless groups were tried in searching for the best grouping of the data. Most combinations showed a very significant packing size/type dependence, and in most instances, the trends followed by the correlating coefficients were not distin- guishable among the different packings and were highly random. For these cases, it was impossible to establish a relationship between the variation in the value of the correlating coefficients with the differences in packing size and type.

To circumvent this problem, a function of the type (22)

was used, and ita application showed all the data for either distillation or absorption (each operation independently) in what appeared to be one single group, regardless of packing size or type. This finding led us to the proposal of one single correlation for all of the packings studied.

The form of the equation selected meets all of the re- quirements outlined above with the added advantage of generality toward packing size/ type. Nevertheless, this form has some limitations, particularly in distillation using low reflux ratios. These limitations are discussed in the Conclusions section and some recommendations are also made. Data Presentation and Correlation

The functional relationship of eq 22 is shown in Figure 1 through 13 (see Table I for symbols) for the packings listed in Table 11 and the systems listed in Table III. The values of a*/ap were obtained from the Bolles-Fair data bank by using physical properties a t the experimental conditions, the geometric parameters of the experimental column and packing, mass transfer coefficients computed by the Onda model, and the reported equilibrium and HETP or Hm data. The systems analyzed, as well as their important physical properties, are shown in Table 111.

An inspection of Figures 1-13 shows clearly that the functionality of eq 22 holds regardless of the system and

u*/u, = A(CUL X ReG)b


O N ,. a

0- al

a. \ a

0-

0 m

6-

0 0

0

VI 1 " C E R R M I C 8. S. -1

a N I

0 m 0-

e \ a

2: &-

0 m 0-

a 1 " C E R R M I C R . R. VI

-1 a N

d

0 al

0

e \ a

:: 0

I I I I

f

I I I

I I

I /

Master co r re l a t ion /

\y/ /

Master co r re l a t ion

Yb d ' I b O ' """" I b l ' ' """ 1 b2 ' 1 b3 1b4 C F I L s R E G s l E 03

Figure 4. Area ratio for 1-in. ceramic Raschig rings. Figure 1. Area ratio for 1-in. ceramic Berl saddles.

0 VI 1. 5 ' ' C E R R M I C R . R . 0 VI 1 / 2 ' 'CERFIM I C R. R. 'I

I I

I

I I I

/I I ;

/ Master co r re l a t ion

Master co r re l a t ion d / /.

/ /

/

a VI 3 " C E R F i M I C R . R

X

0

Ln 3 / 4 ' ' C E R F I M I C R. R. 7 '1 I

X X I I i

I I / d I x ! I

x// /

/ x / /

/

a. a Master co r re l a t ion 1 \'

/ /

/ /

/

/' X

/,/

/ Master co r re l a t ion

0 a 3- //' C F I L s R E G s l E 03

Figure 6. Area ratio for 3-in. ceramic Raschig rings. Figure 3. Area ratio for 3/r-in. ceramic Raschig rings.

166 Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 1, 1982

0 Lo

-1 1 ' ' M E T i l i 8. R. 0 Lo

5 / 8 ' ' M E T R L P. R.

/ I

I I

I

0

L a

/

I 0

& I \ / /

/ /

/ /

/

0 In

-1 1. 5 ' ' M E T F I L R . R .

/ I I

I I

/ /

I I I I

/

..

O m 0-

Q

\ a

E: 0-

/ M a s t e r correlation / v !?aster c o r r e l a t i o n \i

I /

d pi

Figure 11. Area ratio for 1-in. metal Pall rings. 0 Ln

1. 5 ' ' M E T R L P. R. 0 m 2 ' ' M E T i i i R. F. '1

F i -1 I I I

I I I

I I

i

Figure 9. Area ratio for 2-in. metal Raschig rings.


- c

a N -

0 In

0

2 ' ' M E T R L P. R.

+ rf i

/

i / +

Figure 13. Area ratio for 2-in. metal Pall rings.

Table 11. Packings Included in Data Bank and Used in the Present Work

SP nominal surface,

size, void a , packing type in. material fraction ftzf)ft3 Berl saddles 1 ceramic 0.68 76 Raschig rings ceramic 0.64 112 Raschig rings 'I4 ceramic 0.72 74 Raschig rings 1 ceramic 0.74 58 Raschig rings 111, ceramic 0.73 37 Raschig rings 2 ceramic 0.74 28 Raschig rings 3 ceramic 0.75 1 9 Raschig rings 1 steel 0.86 56

Raschig rings 2 steel 0.92 29 Pall ringsa =is steel 0.93 104 Pall rings 1 steel 0.94 63 Pall rings 2 steel 0.96 31

This packing type is marketed under the names of Pall rings, Flexirings, and Ballast rings.

experimental conditions under consideration. The data also line up very nicely when values for different packings are plotted together. Thus, for a given value of CaL X ReG the corresponding value for a*/ap appears to be the same for different systems and/or packing type or size.

It is well known that a packed column loading/flooding condition can be approached by increasing either gas rate

Raschig rings 11/, steel 0.90 39

MQSTER C O R R E L R T I O N FOR D I S T I L L R T I C I N 0 m

I a i P '

X + I

x x + / i I

x / +

C R L r R E G s l E 03 Figure 14. Master correlation for distillation.

or liquid rate or both. Thus, the product Ca$eG can be viewed as a loading parameter, but no effort here has been made to generalize it in terms of experimental observations of loading and/or flooding.

Figures 1-13 do not include flooding conditions, but they do include experiments under high loadings. The increase in the slope of the curve, at high values of CaL X ReG and a* /a is in accordance with the well known behavior of HEgP at higher loadings.

Figure 14 shows all of the distillation data in one single plot combining all of the test systems and packings used in the correlation. The relationship that best describes these data is

a*/ap = 0.498(CaL x ReG)0.392 (23)

The fit of this equation to the data is discussed in the following section. Equation 23 is presented in Figures 1 to 14 as a dashed line for comparison. No data are shown for distillation in 2-in. ceramic Raschig rings because the data bank does not include distillation runs for this packing. After analyzing the fit for the other packings, especially for 1 and 1.5-in. ceramic Raschig rings it was concluded that the correlation should include 2-in. ceramic Raschig rings. The same reasoning was applied to Berl saddles in the range of 1 to 2 in.

The proposed correlation fits the individual data for each packing very well except for the case of 3-in. ceramic

Table 111. Test Systems Considered in the Present Work surface

pressure, gas density, liquid density, tension, re1 system psia lb/ft' lb/ft3 dynlcm volatility

cyclohexane/n-hept ane 5.0 0.06 44 20 1.9 cyclohexaneln-heptane 24.0 0.30 42 1 5 1.6 n- bu t an el iso bu tane 165.0 1.76 3 1 6 1.3 2-propanol/water 14.7 0.11 47 17 1.6 ethylbenzenelstyrene 1.0 0.016 52 27 1.4 ethylbenzene/styrene 2.0 0.03 52 26 1.3 methanol/ethanol 14.7 0.08 47 1 9 1.7 ethanollwater 14.7 0.09 48 22 1.4 n-heptane/toluene 14.7 0.20 4 1 1 5 1.3 benzeneldichloroethane 14.7 0.20 63 22 1.1 isooctane 1 toluene 20.0 0.28 4 1 14 1.2 NH,/H,O/air 14.7 0.08 62 74 a 0 ,/H,O /air 14.7 0.07 62.3 73 a

a These are absorption systems; all others are distillations.

168 Ind. Eng. Chem. Process Des. Dev., Vol. 21,

MASTER P L U T FUR A B S U R P T I U N 0 YI

No. 1. 1982

P A R I T Y PLOT D I S T I L L A T I O N

1 I I

I I /

a 0

/ /

/ /

/

..

Figure 15. Master plot for absorption.

Raschig rings with cyclohexaneln-heptane at 24 psia as the test system. This same system also falls somewhat out of line for 3/rin. ceramic h c h i g rings as shown in Figure 3. Figure 5 indicates that a t low loadings the iso- octaneltoluene system does not correlate very well. These deviations could not be explained when analyzing the data. Nevertheless, we do not think they seriously affect the fit of the overall correlation due to the large number of points (the deviated ones included) taken into consideration.

The absorption data as shown in Figure 15 also group adequately when plotting a* /ap vs. CaL X ReG. These data show lower values of effective area when compared to distillation data under similar conditions. This marked difference could not be readily explained, but may be due to the existence of vapor condensation simultaneous with liquid bubbling under distillation conditions. These two phenomena occurring at the same time should provide added mass transfer surface within the bulk of each phase. This added surface could account for part of the difference between absorption and distillation effective areas.

On the other hand, factors influencing the mass transfer coefficients and the use of a characteristic value for the slope of the equilibrium line in distillation could also in- tervene in explaining this difference in the deduced values for a,.

Yoshida and Koyanagi (1962) and Onda et al. (1968) also observed the difference between distillation and absorption effective mass transfer areas. Yoshida and Koyanagi offer, a qualitative explanation of this difference through surface tension effects since the absorption data they used had water as the irrigating liquid, and the distillation data they analyzed were for organic liquids. In the present work, even though the ethanol/water system is included in the correlation, the surface tensions for the liquids in the distillation data are lower than the surface tension in the absorption systems. Thus, surface tension of the irrigating liquid could also account for the difference between the effective interfacial areas in distillation and absorption.

Figures 16 and 17 show a parity plot for the distillation data using the deduced values for a*/a , and the calculated ones from eq 23 with Figure 17 representing an expanded section of Figure 16. The degree of scatter shown in these plots does not seem to vary with the value of a*/a,; thus the degree of loading or approach to flood does not appear to influence the fit of eq 23.

+/ x x / x

%:oo o : r o o:ao 1: 20 1:60 2: 00 b / R P I B B S V l

Figure 16. Parity plot for distillation.

P Q R I T Y P L U T D I S T I L L f l T I U N

0 m

-r W

0 01

=: I /

Figure 17. Parity plot for distillation (expanded lower region).

Reliability and Comparison with Other Correlations

In this section reference is made to observed and calculated values for the ratio a*/u,. The observed values are obtained from data bank values plus the Onda correlation for masa tranfer coefficients. The calculated values are obtained by the use of the equation

(23)

The statistical analysis of the correlation can be described as follows. (a) The total number of data points used in the correlation is 231, with 11 different systems included. (b) The average absolute deviation was found to be 22% av abs dev = Cabs [l - (a*/ap)~cd/(u*/up)o~sdllOO/n

( c ) The average ratio ( a * / a , ) ~ , d / ( u * / u p ) o ~ was equal to

(a*/a,)CdCd = 0.498(CuL X ReG)0.392

Ind. Eng. Chem. Process Des, Dev., Vol. 21, No. 1, 1982 169

the present time, such an extension is not recommended. Conclusions and Recommendations

The independent treatment of the individual mass transfer coefficients and the effective interfacial area for mass transfer appears to provide a logical and fundamental approach to the description of mass transfer in counterflow gas-liquid packed column. Transfer rates within a single phase should depend on the available concentration gra- dient, the degree of turbulence in that phase, and on the physical properties of the fluid. The bulk-to-interface transfer rates (or the individual mass transfer Coefficients) should be much more heavily dependent on the system itself than on the geometric characteristics of the packing.

On the other hand, the effective interfacial area for mass transfer a t any given point in the bed should depend only on the relative kinetic energy of the phases, the geometry of the packing, the wettability of the packing surface, and the tendency toward rippling and/or droplet formation in the liquid. The extrapolation of this point area to a complete column should be some function of the overall dimensions of the bed.

The product of the capillary number for the liquid (which accounts for the liquid viscous and surface tension forces) and the Reynolds number for the gas (which describes the inertial and viscous forces in the gas) seems to provide an appropriate parameter for describing effective areas.

Through the course of this work it was observed that for similar flow conditions the available area for mass transfer was substantially higher in distillation systems than in absorption systems. The increased area in distillation could be explained by the existence of simultaneous and significant boiling in the liquid phase with condensation in the vapor phase. These two effects are thought to provide a continuous formation of interfacial area within each phase, thus providing an increased net effective area.

Most of the distillation data used in the correlation were reported under total reflux conditions. Thus, a separation of the liquid and gas velocity effects could not be studied from the available data. The work of Clump (1953), while not conclusive, indicated little effect of liquid/vapor ratio on measured Hoc values. The work of Eckert and Walter (1964) showed that for the rectifying section a decrease in liquid/vapor ratio (operation at fiiite reflux) the measured HETP decreased. An analysis of the effects of varying liquid and vapor rates, according to the models presented here, indicates compensating effects in the rectifying and stripping sections of a distillation column such that the predicted total reflux Hoc should be satisfactory for finite reflux operation, being somewhat conservative.

When the correlation is applied to new designs, a question of limits on packed height can arise. The data bank included studies of mass transfer in heights up to 33 ft. However, prudent design often limits the height of an individual section of packing to about 20 ft. Thus, the height correction appears to be valid within the range of, practical application.

In conclusion, an improved mass transfer model has been developed for application to distillation in columns containing random packings. The model is more fundamental than those previously published and on the basis of testing against a large data bank is more reliable than those currently available. More work will be needed before the model can be extended to nondistillation systems and to nonrandom packings. Nomenclature A = coefficient in eq 22

Table Iv. Model Reliability Analysis and Comparison Bolles and Fair this work

0.323 0.286 0.042 -3.42 x 10-14 OF,

S F s (95% confidence) 1.70 1.60

1.042. (d) For the 231 points, 96% of the calculated values of Q* were within f20% of the observed values, 71% within &lo%, and 40% within f5%.

Bolles and Fair (1979) used and recommended a reliability analysis procedure based on a logaritmic ratio objective function, which in the case of this work is

OFi = In ((a*/Qp)obsd/(Q*/Qp)calcd) (24)

The lower bound of this objective function was selected to be the critical one since the conservative approach is to assume that the actual design value for the effective area will be smaller than the one obtained from the model. (For an HOG, objective function like the one proposed by Bolles and Far , the upper bound wil l be the critical one since the height of a transfer unit is inversely proportional to the effective area.)

Following the procedure presented by Bolles and Fair, the following expression for lower bound critical is obtained

where OF, = mean of the objective function = COFi/n, n = number of observations, OFi = objective function for the ith observation, S = standard deviation of the objective function = [C(OFi - - l)]0.5, and t = Students t for a certain degree of confidence.

The real measure of the reliability of the model is the standard deviation or scatter of the objective function. Thus the safety factor, Fs = ets, should provide the best reliability measure for the model for a certain percent confidence.

The analysis described above was applied to the present model for a 95% confidence (t = 1.645) and the results as well as a comparison with the Bolles and Fair model are presented in Table IV.

The present model appears to be slightly more reliable than the one by Bolles and Fair. These authors show in their paper an improvement over the models of Onda and Comell et al. Based on this comparison, the present model appears to be the most reliable of the four. I t should be noted, however, that the other three models are not spe- cifically for distillation as the present one is, so a greater scatter is present in those models that encompass different mass transfer operations in packed columns. Extension to Other Packings

The model described here is based on randomly arranged packing elements that can be characterized as having a nominal diameter d,,. This diameter is used in the calculation of phase transfer coefficients k, and k ~ . One would expect the model to apply to packings other than those tested so long as the packings have similar shapes and identifiable nominal diameters. For example, ceramic Intalox saddles were not included in the data bank and thus did not contribute to the general development of the model; however, they are similar to Berl saddles with about 12% higher specific surface up. The model would show that ceramic Intalox saddles would have a somewhat higher mass transfer efficiency than ceramic Berl saddles, for the same phase rates and system properties.

Extension of the model to the nonrandom packing materials would call for assumptions of equivalent diameter that could only be validated by considerable test data. At

170 Ind. Eng. Chem. Process Des. Dev. 1982, 21, 170-173

a* = corrected effective area, (ft2/ft3)(fto.4/ (dyn/~m)O.~) a, = effective interfacial area, ft2/ft3 aep = effective area provided by packing alone, ft2/ft3 a,, = specific surface of the packing, ft2/ft3 a, = wetted area, ft2/ft3 b = exponent in eq 22 CaL = capillary number for the liquid D, = column diameter, f t DG = diffusion coefficient for the gas DL = diffusion coefficient for the liquid d, = diameter of a sphere with the same surface area as one

d6 = nominal diameter of the packing element F, = safety factor for model reliability FrL = Froude number for the liquid G = gas superficial mass velocity G, = gas superficial molar mass velocity g = acceleration of gravity g, = force/mass conversion factor HG = height of a gas transfer unit, f t HL = height of a liquid transfer unit, f t HE = height of an overall gas transfer unit, f t HETP = height equivalent to a theoretical plate, f t kG = mass transfer coefficient for the gas phase kL = mass transfer coefficient for the liquid phase K O G = overall gas mass transfer coefficient, based on gas

L = liquid superficial mass velocity L, = liquid superficial molar mass velocity m = slope of the equilibrium line M = molecular weight n = number of observations OFi = objective function for observation i OF, = mean of the objective function P = total pressure Q, Q = coefficients in eq 6 and 7 ReG = Reynolds number for the gas (= 6 G / ( a MG) ReL = Reynolds number for the liquid (= 6Lfia L) ReG = modified gas Reynolds number (= R e G / 8 ReL = modified liquid Reynolds number (= ReL/6) R = universal gas constant r , s = exponents in eq 7

packing element

concentration

S C ~ = Schmidt number for the gas ScL = Schmidt number for the liquid S = standard deviation T = absolute temperature t = Students t u, u = exponents in eq 6 WeL = Weber number for the liquid 2 = height of packing in column, f t Greek Symbols a = factor to correct for available column wall surface t = void fraction X = ratio of slopes (equil. line/operating line = mG,/L,) i . ~ = viscosity p = density (r = surface tension, dyn/cm a, = critical surface tension, dyn/cm Subscripts G = referred to the gas L = referred to the liquid GM = molar property for the gas

Li terature Cited Bolles. W. L.; Fair. J. R. Inst. Chem. Eng. Symp. Ser. 1979. 56 , 3/35. Charpentier, J. C. Chem. Eng. J . 1976, I f , 161. Clump. C. W. W.D. Dissertation, Carnegie Instltute of Technology, Pittsburgh,

Pa.. 1953. Cornell, D.; Knapp, W. G., Falr, J. R. Chem. Eng. Rog. 1960a, 56(8) 68. Cornell. D.; Knapp, W. G.; Close, H. J.; Falr, J. R. Chem. fng. Rog. 1960b,

Eckert, J. S.; Walter, L. F. ~&ocarbonRocess. 1964, 43, 107. Fair, J. R., Moczek, J. S., Presented at Les Vegas AICM Meeting, Aug 1964. Hughmark, G. A. Ind . Eng. Chem. Fundam. 1960, 79, 385. Onda, K.; Takeuchl. H.; Okumoto, Y. J . Chem. ng. Jpn. 1966, I , 56. Onda, K. Mem. Fac. Eng., Nagoya Unlv. 1972, 24(2) 164. Shulman, H. L.; Ullrlch. C. F.; Wells, N. AI& J . 1955a, 7 , 247. Shulman, H. L.; Ullrlch, C. F.; Proulx, A. 2.; flmmerman. J. 0. AIChE J .

Shulman, H. L.; Ullrlch, C. F.; Wells, N.; Proulx, A. 2. AICM J . 1955~ . I .

Yoshkla, F.; Koyanagi. T. Ind . Eng. Chem. 1954, 46, 1756. Yoshkla, F.; Koyanagi. T. AI&. J . 1962, 8 , 309.

56(6) 46.

1955b, I , 253.

259.

Receiued for review May 22, 1981 Accepted September 10, 1981

Upgrading of Recycle Solvent Used in the Direct Liquefaction of Wyodak Coal

Ronald L. Mlller and Howard F. Sliver Chemical Engineering Depaflment, University of Wyoming, Laramle, Wyoming 8207 1

Robert J. Hurtublse Chemishy Depaflmnt, University of Wyoming, Laramie, Wyoming 82071

Hydrogen donor characteristics are one of the most important properties of a coalderived recycle solvent used in the direct liquefaction of coal. This property can be modified by direct catalytic hydrogenation to increase the solvent hydrogen content. Results of this work using 22 solvents derived from three coals indicate that recycle solvent effectiveness goes through a maximum as the hydrogen content of the solvent increases. However, the solvent hydrogen content at which the observed maximum occurs differs for different solvents. Weight percent hydrogen in a solvent at observed maximum llquefaction effectiveness has been correlated as a linear function of a Watson-type characterization factor, K,.

In t roduc t ion The extent to which coal can be directly converted to

gases and benzene soluble liquids depends not only on the

coal dissolver reaction conditions but also on the quality of the recycle solvent used. A good recycle solvent must be physicallv compatible with the coal fragments formed

0196-4305/82/1121-0170$01.25/0 0 1981 Americar, Chemical Society

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Bravo 1982