Ind. Eng. Chem. Res. 1997, 36, 1747-1757
1747
SEPARATIONS Design Method for Distillation Columns Filled with Metallic, Ceramic, or Plastic Structured Packings J. J. Gualito, F. J. Cerino, J. C. Cardenas, and J. A. Rocha*,† Chemical Engineering Department, Instituto Tecnolo´ gico de Celaya, Av. Tecnologico y A. G. Cubas, Celaya, Gto., C.P. 38010, Mexico
This work is a continuation and refinement of a general model developed at the Separations Research Program at The University of Texas at Austin (SRP II model) for the prediction of the height equivalent to a theoretical plate and pressure drop for distillation columns filled with metallic structured packings. It contains three parts. In the first part, the general model is briefly described and the participating equations are summarized. In the main part, the parameters needed for applying the general model for structured packings made of ceramic and plastic are presented and discussed. In the third part, we try to correct the model in order to get good predictions at low and high pressures. Introduction In the chemical and petrochemical industry, distillation is the most used separation process for the separation and purification of mixtures. In distillation operation, the operating conditions (pressure and temperature) must be chosen to assure that vapor and liquid phases coexist. The liquid flows down and the vapor flows up inside the columns or towers. The internal parts have the function of promoting the mass transfer process (passing the light material from the liquid to the gas phase and simultaneously passing the heavy components from the gas to the liquid phase). The internal parts of a distillation column include (1) plates (sieve, valves, and cups); (2) random packing; (3) structured packing. Table 1 presents the main characteristics and differences of the three different internals for distillation columns. It may be observed that apart from the possibility of plugging and the economic factor, structured packings have the following advantages: (A) higher efficiency; (B) lower pressure drop; (C) higher capacity. Because of these benefits, many new columns are designed with structured packings, and also numerous random packed and plate columns are being retrofitted with structured packings. This paper deals with the design and the analysis of distillation columns filled with structured packing made of metal, ceramic, and plastic. Previous Work Two Generations of Models for Metallic Structured Packings Applied in Distillation. The first kind of structured packings extensively used was the Sulzer BX packing, fabricated from metal gauze (woven wire cloth), but its price was too high; then several sheet †
Phone, (461) 1 78 02; fax, (461) 1 77 44; email, rocha@diq00. itcelaya.ciateq.mx. S0888-5885(96)00625-2 CCC: $14.00
metal structured packings (Mellapak, Glitsch, Flexipac, Intalox, Maxpak, Montz, etc.) entered the industrial market. In the actuality, the sheet metal structured packings are more used. One advantage of the Sulzer packing is that because of its woven wire cloth of construction, it gets almost complete wetting. Bravo et al. in 1985 assumed that the effective superficial area of the Sulzer packing was equal to the packing area and presented the first model for the analysis of mass transfer in structured packings. Their model proposed a correlation to predict the height equivalent to a theoretical plate (HETP), which allows the designer to specify the total height of the distillation column using eq 1.
Z ) Nt(HETP)
(1)
Fair and Bravo in 1990 proposed a method for the prediction of HETP for sheet metal packings based on the original 1985 model but using a factor for the partial wetting of the packing area. The other important parameter in the design is the column diameter, which may be calculated when the flooding velocity or the pressure drop at several operating velocities of the vapor phase is determined. Once the operational velocity of the gas phase is established, the column area (and from here the diameter) is calculated with eq 2 by knowing the volumetric flow rate of the gas phase QG.
Ac )
QG UG,oper
(2)
The same authors Bravo et al. in 1986 proposed a correlation to predict pressure drop below loading conditions. The proposed correlation seems to be valid for gauze and sheet metal structured packings. The combined models of Bravo et al. (1985, 1986) form the SRP model I for the prediction of efficiency and pressure drop for metallic structured packings. The development of the mass transfer model and the development of the hydraulic or pressure drop model © 1997 American Chemical Society
1748 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 Table 1. Comparison for Internals of Distillation Columnsa,b property
cup plates
sieve plates
valve plates
double-flow plates
random packings
structured packings
vapor capacity liquid capacity efficiency flexibility pressure drop cost capacity for dirty systems design reliability
3 4 4 5 2 3 3 4
4 4 3 3 3 5 3 4
4 4 4 5 3 4 3 3
5 5 3 1 3 5 4 2
5 5 4 4 4 2 2 3
5 5 5 5 5 1 1 3
a
5 ) excellent, 4 ) very good, 3 ) good, 2 ) regular, 1 ) bad. b Adapted from Fair (1965).
have been carried out in a form completely independent. In this paper we call this approach models of the first generation. Other authors that have proposed methods or correlations of the first generation for the prediction of HETP are Spiegel and Meir (1987) and Billet (1990). Other authors for the first generation of pressure drop predictions are Billet and Shultes (1991), Spiegel and Meir (1987), Stichlmair et al. (1989), and Robbins (1991). Generalized Model for Metallic Structured Packings It has been known that the closer the models represent the actual phenomena, the better the possibility of good predictions, but many times the complexity plays an important role in the result of the models, and these need to be simplified. In the operation of distillation columns of any type of internals, the hydraulic and the mass transfer process occur simultaneously. This is taken into account in the second generation model. For the authors, the liquid holdup is the linked parameter. For the hydraulic analysis, the increase in the velocity of any phase increases the thickness of the film and the liquid holdup of films and droplets, and this produces an increase in the pressure drop. For the mass transfer analysis, the increase in holdup produces an increase in interfacial area, and this gives higher mass transfer rates or efficiencies (lower values for HETP). Billet (1988) and Billet and Shultes (1992) mention the relationship between pressure drop and mass transfer. More recently Hanley et al. (1994a,b) do the same. The separations research program at The University of Texas at Austin and the Instituto Tecnologico de Celaya are doing cooperative work toward the development of correlations that allow the design of distillation columns filled with structured packing. In a sabbatical year (1989-1990) spent at SRP, the senior author together with Dr. James R. Fair and J. Luis Bravo developed a generalized model (called SRP II model) that links pressure drop and mass transfer with the use of liquid holdup. The results of this work have been presented in 1992 by Bravo et al. and by Rocha et al. (1993, 1996). Here in Tables 2 and 3 the main equations are presented. In 1990 when the SRP II model was developed, we did not have complete data (pressure drop and mass transfer) for ceramic, plastic structured packings, or metal at high pressures (more than 5 bar). We tried to get a generalized model that can handle structured packings of other materials, and for that effect we leave some parameters to be adjusted. The companies Koch and Sulzer make public, through commercial bulletins, information about pressure drop for packings made of
Table 2. Equations for HETP Prediction in Metallic Structured Packings
HETP ) HTU
kG ) 0.054
kL ) 2
UGe )
ULe )
[ ]
[ ] [ )( )
ln λ ln λ ) [HG + λHL] ) λ-1 λ-1 ULs ln λ UGS +λ kGae kLae λ - 1
( )(
DG (UGe + ULe)FGS S µG
0.8
µG DGFG
][ ]
(3)
0.33
x
DLULe πS
(4)
(5)
UGS
(6)
(1 - hL) sin θ ULs hL sin θ
(7)
ae 29.12(WeLFrL)0.15S0.359 ) FSE 0.2 0.6 ) FSEFt ap Re (1 - 0.93 cos γ)(sin θ)0.3
(8)
L
WeL )
2 ULs FLS σ
(9)
FrL )
2 ULs Sg
(10)
ReL )
ULsSFL µL
(11)
for metallic structured packing:
cos γ ) 0.90 cos γ ) 5.211 × 10
-16.835σ
for
σ e 0.055 N/m
(12)
for
σ > 0.055 N/m
(13)
for gauze metallic packing:
ae ) 0.65 ap a
(14)
Adapted from Bravo et al. (1992).
ceramic and plastic, respectively. Also here at Instituto Tecnologico de Celaya (ITC), we have experimentally tested two sizes of a ceramic and one size of a plastic structured packing for distillation at total reflux and atmospheric pressure. Experimental Work The experimentation of this work was carried out in a stainless steel distillation column, with an internal diameter of 0.245 m and height of packing of 2.75 m. Figure 1 shows the basic equipment. Binary distillation
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1749 Table 3. Hydraulic Parameters Calculationa 1. Get FL, FG, µL, µG, S, , θ, ULS, UGS 2. Estimate dry pressure drop:
∆P (∆Z )
0.1775FG )
2
dry
S (sin θ)
2 UGS +
2
88.774µG UGSs s2 sin θ
(15)
3. Calculate the correction factor for total holdup:
29.12(WeLFrL)0.15S0.359
Ft )
(16)
0.6 0.3 Re0.2 L (1 - 0.93 cos γ)(sin θ)
4. Set initial conditions for iterations:
∆P (∆Z )
) new
∆P (∆Z )
(17)
dry
5. Execute iteration process:
hL )
[ ] 4Ft S
2/3
{
[(
3µLULs
)(
(∆P/∆Z)new FL - FG FL sin θg 1FL (∆P/∆z)flood
}
)]
1/3
∆P ∆P ∆Z dry ) ∆Z [1 - (0.614 + 71.35S)h ]5 L
( )
(18)
Model Development
(19)
6. Check for convergence:
if
∆P ∆P * ∆Z ∆Z
new
if
∆P ∆P ≈ ∆Z ∆Z
new
( ) ( )
a
then
∆P (∆Z )
) new
then STOP
∆P (∆Z );
go to step 5
(2) Start the flow of cooling water (3) Start the flow of heating steam to the reboiler. (4) Reach hydraulic steady state. (5) Wait 1.5-2 h to get mass transfer steady state. (6) Register the value for operational parameters (7) Take samples from liquid entering and leaving the packing bed. (8) Analyze samples by refraction index or gas chromatography. (9) Calculate the number of theoretical stages with equilibrium diagram or Fenske equation. (10) Calculate HETP with eq 1. The details and specific information of the experimental runs are given by Cerino (1995), Cerino and Rocha (1995), and Gualito (1996), but Table 6 shows a summary. Kunesh and Shariat (1993) provide an excellent report on the testing method for distillation columns, for efficiency and pressure drop.
(20) (21)
Adapted from Rocha et al. (1993).
Generalized Model for Ceramic and Plastic Structured Packings. The structured packing Flexeramic made from ceramic and the Mellapak 250Y made from poly(propylene) were used to extend the general model to these materials. We believe that the hydraulic and the mass transfer process in distillation is carried out by the same mechanism and will depend on the real or effective contact area between liquid and vapor phase, but the packing material may affect the fraction and the form in which the liquid phase wets the solid surface of the packing. Then the main contribution of this paper is the proposition of a general model for designing distillation columns filled with structured packings made of metal, ceramic, or plastic. The model is a generalization of Tables 2 and 3, but specifying the parameters that are different for each different packing as: used for calculation of:
symbol A1 and A2
Ft ae/ap
B1, B2, and σref cos(γ) C1 and C2 D1 and D2
Figure 1. Distillation column.
was carried out at total reflux and atmospheric pressure using the system cyclohexane/n-heptane for the plastic structured packing and cyclohexane/n-heptane and methanol/ethanol for the ceramic packing. The characteristics of the packings and the physical properties for the mentioned systems and those for the air-water system are shown in Tables 4 and 5. The procedure to perform the distillation runs at total reflux is summarized as follows: (1) Feed the column with an approximately equimolar mixture of c6/n-c7 or methanol/ethanol.
(∆P/∆Z)dry (∆P/∆Z)
correction factor for holdup ratio of interfacial to packing area humectant capacity of packing dry pressure drop irrigated pressure drop
eq no. 16 8 13 15 19
Pressure drop data was obtained for Flexeramic 28, 48, and 88 using Koch Bulletin KCP-1 (1989) and the Bulletin Separation Columns for Distillation and Absorption from Sulzer Chemtech for poly(propylene) structured packings. For both structured packings the system was air-water at atmospheric pressure. One of the problems we found when trying to use the general model was the value for the pressure drop at flooding. In Bravo et al. (1992) it is established that most of the reported values lie between 900 and 1200 Pa/m. When the lower value is used, the curving of holdup is more pronounced and the prediction of holdup, pressure drop, and maximum capacity seems to be better; one problem with fixing the numerical value of the pressure droop at flooding in the low range is that some of the points that were in the operating range will be taken as inoperable. On the other hand, if we assign a high value to the term (∆P/∆Z)flood, then the capacity of the packing is extended and the curving will come later than the actual. Uresti and Rocha (1993) had the
1750 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 Table 4. Dimensions for Metallic, Ceramic, and Poly(propylene) Structured Packings
packing surface ap (m2/m3) channel side S (m) void fraction of packing (dimensionless) angle of channel θ (deg)
Flexipac 2 FL 2
Flexeramic 28 F-28
Flexeramic 48 F-48
Flexeramic 88 F-88
poly(propylene) Mellapak 250Y PPM250Y
233.0
282.15
157.5
101.7
250.0
0.018
0.0120
0.022
0.044
0.0135
0.95
0.70
0.74
0.85
0.92
45
45
45
45
45
Table 5. Physical Properties for the Systems Used system
P (bar)
FL (kg/m3)
FG (kg/m3)
µL (kg/m/s)
µG (kg/m/s)
DL (m2/s)
DG (m2/s)
σ (N/m)
λ
chlorobenzene/ethylbenzene chlorobenzene/ethylbenzene chlorobenzene/ethylbenzene chlorobenzene/ethylbenzene methanol/ethanol air/water cyclohexane/n-heptane isobutane/n-butane isobutane/n-butane isobutane/n-butane isobutane/n-butane
0.05 0.10 0.40 0.96 1.00 1.00 1.00 6.90 11.4 20.7 27.2
925.0 927.0 905.0 858.0 756.0 1000.0 625.0 523.0 487.0 426.0 383.0
0.35 0.39 2.00 3.26 1.20 1.30 3.36 17.0 30.0 58.0 85.0
4.11e-4a 4.01e-4 3.2e-4 2.50e-4 4.50e-4 1.0e-3 3.01e-4 11e-5 8.8e-5 6.2e-5 4.9e-5
7.6e-6 7.82e-6 8.5e-6 9.37e-6 8.5e-6 18.0e-6 7.58e-6 8.4e-6 9.0e-6 9.8e-6 10.2e-6
4.33e-9 4.42e-9 6.0e-9 7.55e-9 4.0e-9
28.0e-6 27.33e-6 15.0e-6 4.09e-6 9.10e-6
0.027 0.026 0.022 0.018 0.031 0.072 0.014 0.0073 0.0048 0.0021 0.0011
1.05 1.05 1.04 1.04 1.1
a
4.9e-9 1.05e-8 1.38e-8 2.08e-8 2.68e-8
4.30e-6 0.797e-6 0.549e-6 0.356e-6 0.291e-6
0.978 1.3 1.23 1.15 1.10
Read as 4.11 × 10-4.
Table 6. Experimental Data for Total Reflux Distillation with Flexeramic and Poly(propylene) Mellapak 250Y no.
Fs
system
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4
0.55 0.77 0.99 1.22 0.61 0.73 0.85 1.05 0.29 0.46 0.81 2.32 0.31 0.46 0.55 0.69
methanol/ethanol methanol/ethanol methanol/ethanol methanol/ethanol methanol/ethanol methanol/ethanol methanol/ethanol methanol/ethanol C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7 C6/C7
E1 E2 E3 E4 E5
0.36 0.54 0.66 0.74 1.97
packing
HETP
HETP calc
% error
F-28 F-28 F-28 F-28 F-48 F-48 F-48 F-48 F-28 F-28 F-28 F-28 F-48 F-48 F-48 F-48
0.6230 0.5956 0.5956 0.5222 1.0280 1.1000 0.6530 0.8960 0.4370 0.5144 0.5610 0.6221 0.9042 0.8904 0.8904 0.8164
0.6921 0.6705 0.6560 0.6458 1.3213 1.3024 1.2869 1.2672 0.4696 0.4651 0.4601 0.4917 0.8643 0.8684 0.8697 0.8712
11.1 12.6 10.1 23.70 28.5 18.4 97.1 41.4 07.5 09.6 18.0 21.0 04.4 02.5 02.3 06.7
averages: C6/C7 C6/C7 C6/C7 C6/C7 C6/C7
Flexeramic PP-M250Y PP-M250Y PP-M250Y PP-M250Y PP-M250Y
0.7397 0.6541 0.7000 0.9359 0.7159
0.6782 0.6739 0.6715 0.6700 0.6668
19.68 08.3 03.0 04.1 28.4 06.9
averages:
PP-M250Y
same problem; they chose a value of 2050 Pa/m (2.5 in. of liquid/ft of packing). Gualito (1996) observed from the reported pressure drop for Flexeramic, poly(propylene), and Flexipac that for most of the plots of irrigated pressure drop versus Fs factor, the runs at higher liquid volumetric flows needed higher (∆P/∆Z)flood values. That is evident from most of the plots, by the fact that the slope of the irrigated pressure at low liquid volumetric flows is vertical in the low range (about 900-1600 Pa/m), but the irrigated pressure drop for the high liquid flow rates are still far from vertical at 1600-2000 Pa/m. McNulty and Hsieh (1982) in an excellent report provide values for pressure drop and holdup, for four sizes of Flexipac; for high liquid flow rate they report values larger than 3000 Pa/m without reaching flooding. Gualito observed from the McNulty and Hsieh data that a linear relationship exists between superficial
10.14
velocity of the liquid phase and the value for (∆P/∆Z)flood. This observation is opposite to comments of Fair and Bravo (1990) for pressure drop at the flooding point using the Stichlmair et al. model (1989). Using the mentioned data he correlated and proposed eq 22:
∆P (∆Z )
flood
) 1500 + 65 000ULS
(22)
when this equation is applied, the values for (∆P/∆Z)flood range between 1540 and 3300 Pa/m. One important consideration in the general model was the use of the correction factor Ft given by eq E-16 that was adapted from the work of Shi and Mersmann (1985).
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1751
ae (WeLFrL)0.150.76f ) Ft ) 0.2 0.6 ) ap Re (1 - 0.93 cos γ)(sin θ)0.3 L
(WeLFrL)0.15A1SA2 0.6 0.3 Re0.2 L (1 - 0.93 cos γ)(sin θ)
(23)
This factor is an important parameter for the determination of liquid holdup with eq 18 and also is relevant for the calculation of the interfacial area through eq 8. Shi and Mershmann say that the values of A1 and A2 are functions of the packing material; by example they report values for ceramic and plastic random packings. In this work the values of A1 and A2 were backcalculated from the reported pressure drop data and mass transfer experimentation carried out by Uresti (1993) and Cerino (1995) for ceramic structured packings and Gualito (1996) for poly(propylene) structured packing. Table 6 shows a summary of the mass transfer data obtained experimentally at ITC. For this model and for those called II generation models, the mass transfer parameters are linked to the hydraulic factors. Then, before or simultaneously to the calculation of A1 and A2, it is necessary to determine the dry pressure drop, the irrigated pressure drop, and total liquid holdup. Tables 7 and 8 present the required equations to apply the general model. Equations EGM1-EGM19 present the general model together with the corresponding values for the constants A-D for the sheet metal, ceramic, and poly(propylene) structured packings. Results and Discussion The application of the general model may be partially seen by observing Figures 2-4, which show the experimental and predicted values for HETP for metallic, ceramic, and poly(propylene) structured packings. The metallic structured packing gives a regular efficiency, and the efficiency improves as the pressure goes up. It is clear that the ceramic packing with more area (Flexeramic 28) provides about the same efficiency but with 20% more packing area. For Flexeramic 48 with a 0.56 packing area of F28, the HETP values are 83% higher. The poly(propylene) structured packing due to the low capacity of the plastic to be wet by the liquid phase presents the lowest efficiency for unit of packing area. For this plastic structured packing, we must say that, although the temperature of the liquid never exceeded 195 °F in either of the runs, the poly(propylene) structured packing was partially destroyed after several runs carried out on three different days. We believe that the damage was due to the changes in temperature when the distillation column was started and shot down. Then the use of poly(propylene) structured packing should be restricted to temperatures below 150 °F. Figure 5 shows that the model predicts mass transfer efficiency very well as the HETP for different sizes of metallic packing. Comparative Values for Some Parameters for Metallic, Ceramic, and Plastic Ordered Packing. The correction factor for liquid holdup Ft given by eq 16 is the main parameter for the different ratios of ae/ ap that affect the efficiency values in the expected and measured way.
If we apply the equations of the general model to total reflux distillation hypothetical runs, with the organic system c6/n-c7 at atmospheric pressure using the same Fs factor of 1.0 over the structured packings Flexipac 2, Flexeramic 28 and 48, and PP-Mellapak- 250Y, we obtain the comparative values show in Table 9. We observe that for dry pressure drop, the metallic packing has the lowest value while the ceramic F28 shows the highest value. For liquid holdup, Flexeramic 48 presents the lowest value, and the metallic packing the highest. For irrigated pressure drop, the plastic packing has the lowest value, while the small ceramic packing presents the highest value. Again the plastic packing has the lowest value of Ft, and the metallic has the highest value. For the effective interfacial area, the metallic packing shows the highest value, while the ceramic F48 shows the lowest. It is observed that the metallic packing does not have the highest values for effective velocities, nor for the mass transfer coefficients. Then the influence of effective interfacial area is more important, because if the efficiency of the metallic structured packing is fixed at a value of 1.0, then the small Flexeramic 28 packing provides 0.83 the efficiency of the metallic; the plastic structured packing presents 0.57 the efficiency of the metallic; the large ceramic F48 provides only 0.43 the efficiency of the metallic structured packing. Model Development Generalized Model at High Operating Pressures. At the 1995 AIChE Spring Meeting in Houston, TX, Fitz, Shariat, and Spiegel presented the paper Performance of Structured Packing at High Pressure. In their Figures 20 and 21, the SRP II model predicts very poorly the pressure drop at operating pressures of 6.8-27.2 bar. It was said that the SRP II model was developed using data from 0.05-4.14 bar. The Fitz et al. data (1995) is the first series of data available for the authors of this paper on pressure drop and efficiency for metallic structured packings operating at high pressure. Using these data, in the next section we try to correct the model for high operating pressure. We would like to apply a more in depth analysis, but if we do that, this paper and the contribution of the general model for metallic, ceramic, and plastic structured packing would be delayed. We will instead present some crude corrections that could enable the possibility of applying the general model for low and high operating pressures. Pressure Drop at High Operating Pressure. Part of the data for the high pressure column, from Figures 10-18 of the paper of Fitz et al. (1995), was read and put in tabular form. The SRP II model was applied to the data to try to detect the cause of the underprediction in pressure drop and to suggest the modification to get a good prediction. A similar analysis was done for the prediction of HETP. It has been observed by several researchers that the efficiency gets better (lower HETP) the higher the operating pressures; see, for example, Figure 2 of this paper and the data reported by Sakata (1972). The analysis showed that the dry pressure drop predicted was very low and about the same for the four operating pressure: 6.8 bar (100 psia), 11.2 bar (165 psia), 20.7 bar (300 psia), and 27.2 bar (400 psia) reported in the Fitz et al. paper. Also the analysis
1752 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 Table 7. Equations for HETP Prediction for Metallic, Ceramic, and Poly(propylene) Structured Packings
[ ] ( )(
HETP ) HTU
kG ) 0.054
kL ) 2
UGe )
[ ] [ )( )
][ ]
ULS ln λ UGS ln λ ln λ ) [HG + λHL] ) +λ λ-1 λ-1 kGae kLae λ - 1
DG (UGe + ULe)FGS S µG
0.8
µG DGFG
(EGM1)
0.33
(EGM2)
x
DLULe πS
(EGM3)
UGS
(EGM4)
(1 - hL) sin θ ULS hL sin θ
ULe )
(EGM5)
[
]
(WeLFrL)0.15A1SA2FSE ae 1.2 ) 0.2 0.6 ap Re (1 - 0.93 cos γ)(sin θ)0.3 1 + 0.2e30(ULS/2UGS) L WeL )
(EGM6)
2 ULS FLS σ
(EGM7)
FrL )
2 ULS Sg
(EGM8)
ReL )
ULSSFL µL
(EGM9)
for metallic, ceramic, and plastic structured packing:
cos γ ) 0.90 cos γ ) B1 × 10 material
B2σ
for
σ < σref N/m
(EGM10)
for
σ > σref N/m
(EGM11)
A1
A2
B1
B2
σref
C1
C2
D1
D2
FSE
sheet metal
29.12
0.36
5.21
-16.83
0.045
0.177
88.77
0.614
71.35
ceramic
11.54
0.36
1.52
-3.51
0.065
0.244
0.0
0.532
92.22
poly(propylene)
21.67
0.13
5.58
-25.17
0.035
0.134
44.06
0.633
130.94
0.35 Flexipac 0.46 Flexeramic 0.46 PPMellapak
showed that each set of dry pressure drop should be multiplied by a factor whose value increases as the operating pressure increases. Analyzing the physical properties to try to get a correction factor, we found that the gas viscosity and density increase with the increase in operating pressure. It was the gas density that has a more clear increase in its value with the increment in pressure. On the other hand, we made a revision of several papers and reports looking for data at different pressures. It was found that also at low operating pressure, the pressure drop was higher the bigger the operating pressure or the higher the value of the density. This was clear from Figure 7 of Meier et al. (1979) for the chlorobenzene/ethylbenzene system at 0.05, 0.10, 0.40, and 1.0 bar. Figure 5 in the paper of Stephan and Mayinger (1992) shows the total pressure drop as formed of two parts: a contribution from hydrostatic pressure (equal to FGg), and a the contribution due to the flow of both phases. In this case, the operating pressures are 10-20 bar and the gas densities range from 38 to 75 kg/m3. For these cases the contribution of hydrostatic pressure drop is about half of the total pressure drop. In the cases of isobutane/n-butane system used by Fitz et al., the reported operating pressures are 6.9,
11.4, 20.7, and 27.6 bar. The contribution of hydrostatic pressure drop should be in the range of 171-833 Pa/m. However, the reported pressure drop ranges from 16 to 1200 Pa/m. The experimental data reported by Fitz and Shariat (1995) was carried out at Fractionation Research Institute (FRI), and we were informed that FRI deducts the hydrostatic pressure drop from the measured data, trying to report only the pressure drop due to the packing. Equation 24 shows the relationship between these terms
∆Pexp.meas ) ∆Ppacking + hsc
(24)
where ∆Pexp.meas is the experimentally measured pressure drop, ∆Ppacking is the pressure drop due to the packing itself, and hsc is the vapor static head in the column. When we developed the first model, we used only low operating pressures and the vapor static head was not taken into account, but we have seen that for moderate and high operating pressure, the static pressure drop is very important. Also, it should be noted that some researchers (such as Stephan and Mayinger, 1992) report the experimental measured total pressure drop (packing and static pressure), while others like FRI deduct the static pressure drop and report only the
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1753 Table 8. Hydraulic Parameters Calculation 1. Get: FL, FG, µL, µG, S, , θ, ULS, UGS 2. Estimate dry pressure drop:
( ) ( )( 0.4
∆P ∆Z
FG
2 C1FGUGS
)
Fair,1bar
dry
2
S (sin θ)
C2µGUGS 2
+
S2 sin θ
)
(EGM12)
3. Calculate the correction factor for total holdup:
ae (WeLFrL)0.15A1SA2 ) 0.2 0.6 ap Re (1 - 0.93 cos γ)(sin θ)0.3
Ft )
(EGM14)
L
4. Set initial conditions for iterations:
∆P (∆Z )
) new
∆P (∆Z )
(EGM15)
dry
5. Execute iteration process:
hL )
[ ] 4Ft S
2/3
{
FL sin θg
[(
3µLULs
)(
(∆P/∆Z)new FL - FG 1FL (∆P/∆Z)flood
}
)]
1/3
(EGM16)
∆P ∆P ∆Z dry ) ∆Z [1 - (D + D S)h ]5 1 2 L
( )
(EGM17)
6. Check for convergence:
material
if
∆P ∆P * ∆Z ∆Z
new
if
∆P ∆P ≈ ∆Z ∆Z
new
( ) ( )
then
∆P (∆Z )
)
new
∆P (∆Z );
go to step 5
(EGM18)
then STOP
(EGM19)
A1
A2
B1
B2
σref
C1
C2
D1
D2
FSE
sheet metal
29.12
0.36
5.21
-16.83
0.045
0.177
88.77
0.614
71.35
ceramic
11.54
0.36
1.52
-3.51
0.065
0.244
0.0
0.532
92.22
poly(propylene)
21.67
0.13
10.88
-30.92
0.035
0.134
44.06
0.633
130.94
0.35 Flexipac 0.46 Flexeramic 0.46 PPMellapak
Figure 3. Comparison of experimental and calculated HETP for Flexeramic 28 and 48, using cyclohexane/n-heptane at total reflux and atmospheric pressure. Figure 2. Comparison of experimental and calculated HETP at different pressures, for Flexipac 2, using cyclohexane/n-heptane at total reflux.
pressure drop due to the packing. In this paper and in
the future we are going to adopt the way that FRI reports pressure drop. Rigorously, the hydrostatic pressure drop neglected in the determination of the dry pressure drop by the SRP model should add a term to the equation, but in
1754 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997
Figure 4. Comparison of experimental and calculated HETP for poly(propylene) 250Y Mellapak, using cyclohexane/n-heptane at total reflux and atmospheric pressure.
Using the experimental data of Fitz and Shariat, for the range of Fs values from 0.6 to 0.8 (m/s)(kg/m3)0.5, we obtain the information show in Table 10. It is observed that for a range of operational pressure below 10 bar, the efficiency of the structured packing gets better with the increment in pressure; for a range from 10 to 15 bar, probably the efficiency is not affected with the pressure, but for pressure above 15 bar, the efficiency of the structured packing deteriorates. From the numerical data of Table 10, we observe that the resistance of the liquid phase to the mass transfer increases in importance. For vacuum or atmospheric pressure, the contribution of the liquid to the total resistance lies between 10 and 25%, and for this reason some times is neglected (Spiegel and Meier, 1987). But it should be clear that the liquid phase resistance becomes important for medium and high-pressure distillation. From the last paragraphs, we believe that at high pressures the backmixing is severe and the assumption of the plug flow is not longer valid. Then in analogous form to the calculation of rotating disk contactors for liquid-liquid extraction (Kosters, 1983) and also in distillation columns (Zuiderweg and Nutter, 1992), the height of the overall transfer unit could be corrected by the addition of a term due to axial mixing. This term could be the liquid height of a transfer unit (HL), or the correction factor could be applied to the effective interfacial area. In any case the correction factor for backmixing should be connected with the Peclet number (PeZ) or the axial dispersion coefficient (EZ). According to Sherwood et al. (1975) and Cussler (1984), these two term are related by eq 26:
PeZ )
ULSS )2 EZ
(26)
Then the coefficient for axial mixing is
EZ ) Figure 5. Comparison of experimental and predicted HETP for several sizes of Mellapak, using chlorobenzene/ethylbenzene at total reflux and 0.96 bar.
this case we use the multiplying factor of eq 25:
( ) ∆P ∆Z
dry,new
( )( 0.4
FG
)
Fair,1bar
C1FGU2GS 2
)
C2 µGUGS 2
S (sin θ)
+
S2 sin θ (25)
With this factor, the pressure drop at low pressures and gas densities remains near the calculated values, but at high operating pressure and gas densities, the correlating equations for irrigated pressure drop are very close to the experimental values, as is shown in Figure 6. The comparative results are encouraging and give the possibility of good prediction for other systems at high pressure. HETP at High Operating Pressure, Postulating Backmixing. As may be observed at the range of 0.33-4.14 bar, from Figure 2 the higher the operating pressure, the lower the experimental and predicted HETP. Then by extrapolating the general model, it will underpredict the HETP values for the runs reported by Fitz et al. (1995) at 6.8, 11.2, 20.4, and 27.2 bar.
ULSS 2
(27)
In order to have a dimensionless parameter, we divide this axial mixing coefficient by the superficial velocity of the gas phase times the size of the packing corrugation S, and we have the parameter (ULS/2UGS). Zuiderweg and Nutter (1992) have proposed the ratio (ULS/ UGS) for vapor backmixing in random packing. It should be noted that the correlating parameter ULS/(2UGS) is related to FG/FL. Postulating Backmixing and Correcting by Decreasing the Effective Interfacial Area. From the calculated ae/ap ratio at high pressures show in Table 10, it is seen that the effective area of the packing exceeds the packing area. While this may be explained by the formation of waves and liquid drops dispersed in the gas phase, the mathematical equation for the model considers that liquid flows down the column only as films over the packing sheets. Using the Fitz et al. data for the separation of butane and isobutane, we insert a correction factor that will decrease the value ae/ap, but only at high pressures. For the development of the correction factor, we use the ratio of superficial velocities of the liquid and gas phase; this relation came from backmixing considerations and the fact that the Peclet number for flow through packed beds is very close to 2.0.
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1755 Table 9. Relative Values of Some Important Parameters When Metallic Structured Packing Is Compared with a Size of Plastic Structured Packing and Two Sizes of a Ceramic Structured Packing packing
∆Pdry
hL
∆P
Ft
ae
ULe
UGe
KG
KL
HETP
FL2 F28 F48 PPM250
0.28 1.00 0.49 0.30
1.00 0.73 0.49 0.57
0.34 1.00 0.50 0.31
1.00 0.34 0.36 0.31
1.00 0.55 0.33 0.46
0.39 0.67 1.00 0.67
0.75 1.00 0.94 0.75
0.72 1.00 0.89 0.78
0.59 1.00 0.86 0.93
0.43 0.52 1.00 0.75
Figure 6. Parity plot for pressure drop at different operating pressures, for Mellapak 250Y, using c4/i-c4 at total reflux and data of Fitz et al. (1995). Table 10. Numerical Values for Several Parameters When the General Model of Tables 7 and 8 Is Applied to the Fitz et al. (1995) Data pressure (bar)
averaged HETP (m)
HL/HTU
ae/ap
ULS/(2UGS)
6.8 11.4 20.7 27.2
0.30 0.28 0.40 0.60
0.29 0.36 0.46 0.54
0.88 1.00 1.27 1.47
0.0162 0.0308 0.0681 0.1110
Using the cited consideration, the correction factor for the effective interfacial area to packing area ratio is introduced in eq EGM6 as
(
ae 1.2 ) FtFSE ap 1 + 0.2e30(ULS/2UGS)
)
(28)
The addition of the correction factor does not affect much the calculated values of ae/ap at low pressures where the values for (ULS/2UGS) range between 0.0002 and 0.0020 m/s. When the corrected ae/ap is applied to eq EGM1, the results shown in Figure 7 are obtained. It is observed that the method provides the inflection on HETP at operating pressures above 15 bar. Effect of Variation on Physical Properties. Because the HETP is a kind of averaged mass transfer efficiency of the packing, most of the time only a set of physical properties is used for the calculations, and sometimes these properties are fixed at an averaged temperature and also an averaged composition between the top and bottom of the packed bed. Other authors prefer to fix the temperature of the bottom to calculate (at this temperature) the physical properties of a mixture with an average composition. For some researchers the question of the variation on HETP with the temperature along the position in the distillation column is of importance; if the answer to the mentioned question is important, the computer tools available today may be used to estimate the height
Figure 7. Comparison of experimental and calculated HETP using the correction factor for ae given by eq 28. The system is c4/i-c4, at different pressures for Mellapak 250Y, at total reflux.
equivalent to a theoretical plate at any point in the column, this is to calculate punctual HETP values. In an attempt to gain better understanding of this matter, we have done some runs with the general model: (A) Use the general model to calculate the variation in HETP using Flexipac 2 metallic structured packing, for the system c6/n-c7, at total reflux with a pressure of 4.14 bar. The height of the packing was about 3.0 m, and the temperatures at the top and bottom of the column were 283 and 303 °F, respectively. With these temperatures we assume that at the top of the column the physical properties were those of a mixture with 0.99 mole fraction of c6 at 283 °F; the ratio of equilibrium to operating line (λ ) 0.753) was calculated from the equilibrium line diagram at a mole fraction of 0.8817 for cyclohexane.. Also it was assumed that at the bottom of the column the composition of the mixture was 0.99 mole fraction of c7 at 303 °F, with a value of λ ) 1.176. The HETP for each set of conditions was calculated, and the results are shown in Figure 8. It is observed that the HETP at the top is higher by about 10% than the HETP at the lower part of the column. The better efficiency at the bottom is probably due to the lower viscosity of the mixture. The range of the deviation is 0.14 for the runs with low Fs values and 0.07 for the runs at high Fs values. The deviation in the calculated HETP values is due in part to the change in physical properties, but it seems that the variation of λ is more important. (B) Use the general model to calculate the variation in HETP for the same system but for a column that will make an almost perfect separation between c6 and n-c7 at atmospheric pressure using the ceramic packing Flexeramic 28 (F28). In this case the variations in the
1756 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997
Figure 8. Effect of physical properties and equilibrium line variations on HETP.
temperatures are about 32 °F. This time the variation in HETP is about 0.25 if the ratio of slopes in equilibrium and operating lines are taken from the equilibrium diagram as 0.6 for the top and 1.66 for the bottom. The results of the calculated HETP with values for the top and bottom of the distillation column are shown in Figure 8. Then we see that the variation in the HETP with the physical properties is affected by the differences in temperature between the top and the bottom and also by the values of λ that depend on the equilibrium diagram. Then, for the analysis or design of distillation columns filled with structured packings, it is recommended to do several calculations for HETP. The number of calculations will depend on the differences in temperature between top and bottom and also in the position of the operating and equilibrium line, but at least should include one calculation for the top and one calculation for the bottom. Conclusion The mechanism of the diffusion process in distillation columns filled with structured packing made from different materials depends mainly on the interaction between the liquid and gas phase and on the interaction of the liquid and solid phase. By adapting to structured packings the correlation proposed by Shi and Mershmann (1985) for estimating the wetted packing area, it is possible to have the same model for the prediction of hydraulic and mass transfer parameters for distillation with structured packing made from metal, ceramic, or plastic. The general model uses the equations given in Table 7 and 8 plus the correction factor provided by eqs 28 and a set of nine constants that are specific for the packing material: (1) The parameters A1 and A2, to calculate the correction factor for holdup and the ratio of effective to packing area; (2) The parameters B1, B2, and σref, to calculate the contact angle between liquid and solid phases and the fractional wetted surface;
(3) The parameters C1 and C2, to determine the dry pressure drop; (4) The parameters D1 and D2, to estimate the irrigated pressure drop. The listed parameters have been backcalculated using reported data for pressure drop and experimentally measured HETP values. Using a set of reported data for pressure drop and HETP at medium and high-operating pressures (6.827.2 bar), the general model has been adapted to follow the tendency of decreasing the values of HETP when the operating pressures goes up to 10 bar, presenting a plane tendency and an inflection zone between 10-15 bar; above 15 bar, the HETP value augments (efficiency is deteriorated with the increment of operating pressure), probably due to backmixing. The pressure drop calculations have been adapted by applying a correction factor to the dry pressure drop and HETP at highoperating pressure by the use of a correction factor that decreases the effective interfacial area at high pressure or by the addition of a backmixing liquid height transfer unit HL;bm. For the more than 150 experimentally reported points of our data bank, the general model for metal, ceramic, and plastic corrected for high-operating pressure gives an average deviation of 19% for HETP and 25% for pressure drop. Acknowledgment The authors acknowledge the kind support from Sulzer Chemtech, Sulzer Hermanos S.A., Koch Engineering Co., The Separations Research Program at the University of Texas, and COSNET and CONACYT in Mexico. Nomenclature A, B, C, D ) constants for the generalized model Ac ) area of column, m2 ae ) effective packing area, m2/m3 ap ) packing surface, m2/m3 B ) channel base, m DG ) diffusion coefficient for gas, m2/s DL ) Diffusion coefficient for liquid, m2/s f ) Shi-Mersmann correction factor, dimensionless FS ) vapor flow parameter (FS ) UGSFG0.5), m/s (kg/m3)0.5 FSE ) factor for surface enhancement, dimensionless Ft ) correction factor for total holdup, dimensionless FrL ) Froude number for the liquid, dimensionless g ) acceleration of gravity, 9.81 m/s2 gc ) conversion factor, 1.0 for SI units geff ) effective gravity, m/s2 hL ) liquid holdup, dimensionless hsc ) pressure drop due to vapor static head in the column, Pa/m H ) height of an individual transfer unit, m HTU ) height of an overall phase transfer unit, m HETP ) height equivalent to theoretical plate, m kG ) gas phase mass transfer coefficient, m/s kL ) liquid phase mass transfer coefficient, m/s Nt ) number of theoretical plates, dimensionless P ) pressure, Pa and bar Q ) volumetric flow rate, m3/s ReL ) Reynolds number for liquid, dimensionless S ) side dimension of corrugation, m UGe ) effective gas velocity, m/s ULe ) effective liquid velocity, m/s UGS ) superficial velocity of gas, m/s ULS ) superficial velocity of liquid, m/s WeL ) Weber number for liquid, dimensionless
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1757 XD ) mole fraction at top of packing, dimensionless XB ) mole fraction at bottom of packing, dimensionless Z ) height of packing, m Greek Letters γ ) contact angle between liquid and solid, deg ) void fraction of packing, dimensionless θ ) angle with horizontal for corrugation channel, deg µ ) viscosity, kg/(m s) F ) density, kg/m3 σ ) surface tension, N/m λ ) ratio of slopes, equilibrium line/operating line, dimensionless Subscripts B ) bottom D ) distillate eff ) effective exp ) experimental G ) gas phase L ) liquid phase m ) measured s ) superficial
Literature Cited Billet, R. Relationship between Residence Time, Fluid Dynamics and Efficiency in Countercurrent Flow Equipment. Chem. Eng. Technol. 1988, 11, 139. Billet, R. Contribution to Design and Scale-Up of Packed Columns. Fat Sci. Technol. 1990, 92 (9), 361. Billet, R.;. Shultes, M. Modeling of Pressure Drop in Packed Columns. Chem. Eng. Technol. 1991, 14, 89. Billet, R.; Shultes, M. Relationship between Pressure Drop and Mass Transfer in Two-Phase Countercurrent-Flow Columns. Fat Sci. Technol. 1992, 94 (4), 138. Bravo, J. L.; Rocha J. A.; Fair, J. R. Mass Transfer in Gauze Packings. Hydrocarbon Proc. 1985, 64 (1), 91. Bravo, J. L.; Rocha, J. A.; Fair, J. R. Pressure Drop in Structured Packings. Hydrocarbon Proc. 1986, 65 (3), 45. Bravo, J. L.; Rocha, J. A.; Fair J. R. A Comprehensive Model in the Performance of Columns Containing Structured Packings, Distillation and Absorption; Institution of Chemical Engineers Symposium Series 128; Institution of Chemical Engineers: London, 1992; Vol. 1, pp PA48-A507. Cerino-Cordoba, Felipe de J. Transferencia de Masa en Empaques estructurados de Ceramica. M.C. Thesis, Instituto Tecnologico de Celaya, Aug 1995. Cerino-Cordoba, F. J.; Rocha, J. A. Distillation with Ceramic Structured Packing. AIChE Spring Meeting, Houston, TX, March 1995; Paper 25f. Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems; Cambridge University Press: Cambridge, UK, 1984. Fair, J. R. Selecting Fractionating-Column Internals. Chem. Eng. 1965, July 5. Fair, J. R.; Bravo, J. L. Distillation Columns Containing Structured Packings. Chem. Eng. Prog. 1990, 82 (1), 19. Fitz, C. W.; Shariat, M.; Spiegel, L. Performance of Structured Packings at High Pressure. 1995 AIChE Spring National Meeting, Houston, TX, March 1995; Paper 25e. Gualito-Hernandez, J. J. Modelo Generalizado para Disen˜ar Columnas de Destilacion con Empaque Estructurado de Metal, Ceramica y Plastico. Reporte de Avance del Proyecto de Tesis de Maestria en Ciencias; Instituto Tecnologico de Celaya: Enero, 1996.
Hanley, B.; Dounbobbins, D.; Bennet, A Unified Model for Countercurrent Vapor/Liquid Packed Columns. 1. Pressure Drop. Ind. Eng. Chem. Res. 1994a, 33, 1208-1221. Hanley, B.; Dounbobbins, B.; Bennet, D. A Unified Model for Countercurrent Vapor/Liquid Packed Columns. 2. Equations for the Mass Transfer Coefficients, Mass Transfer Area, the HETP, and the Dynamic Liquid Holdup. Ind. Eng. Chem. Res. 1994b, 33, 1222-1230. Kosters, W. C. G. Rotating-Disk Contactor. In Handbook of Solvent Extraction; Lo, T. T., Baird, M. H. I., Hanson, C., Eds.; John Wiley & Sons: New York, 1983. Kunesh, J. G.; Shariat, A. Packing Efficiency on a Commercial Scale with Good Reflux Distribution. AIChE Spring National Meeting, Houston, TX, March 1993. McNulty, K.; Hsieh, C. L. Hydraulic Performance and Efficiency of Koch Flexipac Structured Packing. AIChE National Meeting, Los Angeles, CA, Nov, 1982. Meier, W.; Hunkeler, R.; Socker, D. Performance of the New Regular Tower Packing “MELLAPAK”. Inst. Chem. Eng. Symp. Ser. 1979, 56, 3.3/1-3.3/17. Robbins, L. A. Improve Pressure Drop Prediction with a New Correlation. Chem. Eng. Prog. 1991, 87 (5), 87. Rocha, J. A.; Bravo, J. L.; Fair J. R. Distillation Columns Containing Structured Packings: A Comprehensive Model for their Performance. 1. Hydraulic Models. Ind. Eng. Chem. Res. 1993, 32 (4), 641-651. Rocha, J. A.; Escamilla, E. M.; Martinez, G. Basic Design of Distillation Columns Filled with Metallic Structured Packings. Gas Sep. Purif. 1993, 7 (1), 57-61. Rocha, J. A.; Bravo, J. L.; Fair J. R. Distillation Columns Containing Structured Packings: A comprehensive Model for their Performance. 2. Mass Transfer Model. Ind. Eng. Chem. Res. 1996, 35 (5), 1660-1667. Sakata, M. Test of 1000, 250, and 70 mm diameter columns with Koch Sulzer packing. Plant test report No. 22; Fractionation Research Inc.: S. Pasadena, CA, Feb 15, 1972. Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer; McGraw-Hill: New York, 1975. Shi, M.; Mersmann, G. Effective Interfacial Areas in Packed Columns. Ger. Chem. Eng. 1985, 8, 87. Spigel, L.; Meier, W. Correlations of the Performance Characteristics of the Various Mellapak Types (Capacity, Pressure Drop, Efficiency). Inst. Chem. Eng. Symp. Ser. 1987, 104, A203. Stephan, M.; Mayinger, F. Experimental and Analytical Study of Countercurrent Flow Limitation in Vertical Gas/Liquid Flows. Chem. Eng. Technol. 1992, 15, 51-62. Stichlmair, J.; Bravo, J. L.; Fair, J. R. General Model for Prediction of Pressure Drop and Capacity of Countercurrent Gas/Liquid Packed Columns. Gas Sep. Purif. 1989, 3, 19. Uresti-Mele´ndez, J. Empaque Estructurado de Ceramica. M.S. Thesis, Instituto Tecnologico de Celaya, Mexico, April 1993. Uresti, M. J.; Rocha, J. A. Pressure Drop in Ceramic Structured Packings. Ind. Eng. Chem. Res. 1993, 32 (10), 2247-2253. Zuiderweg, F. J.; Nutter, D. E. Evidence of Vapor Backmixing in Packed Columns in the Case of High Pressure Distillation. In Distillation and Absorption 1992; Institution of Chemical Engineers Symposium Series 128; 1992; Paper 13, p A481.
Received for review October 7, 1996 Revised manuscript received January 21, 1997 Accepted January 22, 1997X IE960625Z X Abstract published in Advance ACS Abstracts, March 1, 1997.
