Ind. Eng. Chem. Res. 2002, 41, 2305-2315
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Fractionation of Edible Oil Model Mixtures by Supercritical Carbon Dioxide in a Packed Column. 2. A Mass-Transfer Study Rui Ruivo, M. Joa˜ o Cebola, Pedro C. Simo˜ es,* and M. Nunes da Ponte Centro de Quı´mica Fina e Biotecnologia, Faculdade de Cieˆ ncias e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal
A mixture that partially resembles the distillates obtained from the deodorization process of olive oils was used as a case study to test and develop mass-transfer models valid for supercritical fluid processes. Such models are useful engineering tools that provide a theoretical background for the scale-up of industrial plants. In the first part of this series of papers, the fractionation performance of the model mixture squalene/methyl oleate by supercritical carbon dioxide in a countercurrent packed column containing a corrugated gauze-type structured packing was presented. This second part presents a general correlation for predicting the mass-transfer efficiency of the high-pressure packed column. Several correlations taken from the literature were used and their results compared with the experimentally determined mass-transfer coefficients and holdup. A model formerly developed for distillation columns was found to be valid for our high-pressure system. It was found that the area of the gauze packing effectively used for the mass transfer is important for the improvement of the accuracy of the model. Introduction
Table 1. Geometric Characteristics of Sulzer EX Gauze Packing Used in This Work
In the preceding paper,1 we present the experimental results obtained for the fractionation of a model mixture by supercritical carbon dioxide in a countercurrent laboratory-scale column filled with Sulzer EX packing (Table 1 lists the main characteristics of this packing). The mixture contains squalene, a long-chain hydrocarbon, and the fatty ester methyl oleate. The influence of the solvent to feed flow ratio, feed concentration, packing height, and reflux ratio was also discussed. The present work focuses on the mass-transfer performance of the structured gauze packing column with the purpose of developing a model able to adequately describe the hydrodynamic and mass-transfer phenomena of the packed column at supercritical conditions. Published data on the performance of packed columns applied to supercritical fluid extraction of liquid mixtures are limited, although this information is essential for a successful design and operation of such contactors. The studied systems ranged from those showing a low miscibility between the liquid phase and the dense gas phase (examples are the carbon dioxide extraction of alcohols from aqueous solutions2-4) to systems where a high solubility of the solutes in the supercritical solvent induces a nonnegligible miscibility of the two phases, such as the eucalyptus oil fractionation5 and the hydrocarbon processing by supercritical carbon dioxide.6 The fractionation of lipid mixtures, such as the one studied in this work, can be considered to be between those two cases. This is of importance when studying the mass-transfer phenomena because the physical and transport properties of the liquid phase can vary substantially with the solubilization of carbon dioxide at such high pressures. The fractionation of liquid mixtures by supercritical fluid solvents in countercurrent packed columns has * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: + 351 212 948 300. Fax: + 351 212 948 385.
packing type packing material height H1, mm diameter D1, mm surface area a, m2/m3 void fraction crimp height h, mm channel base 2b, mm side of corrugation s, mm channel flow angle from the horizontal θ, deg
Sulzer EX stainless steel 54 24 1710 0.86 1.6 4 2.9 45
some resemblance with extraction processes involving gas/liquid and liquid/liquid contact. On the one hand, supercritical fluids have gaslike transport properties but, on the other hand, because they are more dense than a gas, the density difference between the two contacting phases is lower, resulting in a process that acts like a liquid/liquid extraction. Mechanistically based models have been proposed during the past decades by several authors that describe the performance of packed columns containing structured packings; they were in most of the cases developed for conventional separation processes and only for a few cases applied to high-pressure conditions. The work developed by de Haan and de Graauw6 is one of these few cases. A mass-transfer model initially developed for structured packing distillation columns by Bravo et al.7 was applied to the supercritical carbon dioxide fractionation of hydrocarbons. The model proved to be useful in predicting the experimental results with a reasonable accuracy.6 The hydrodynamic and mass-transfer processes that occur in the packed column can be modeled and described by correlations that incorporate the parameters of liquid holdup, pressure drop, flooding, and masstransfer efficiencies and hydraulic and geometric characteristics of the packing as well as flow and physical property characteristics of the systems. As stated clearly by the work of Bravo et al.7 and later by Rocha et al.,8 the linking parameter for these model correlations
10.1021/ie0106579 CCC: $22.00 © 2002 American Chemical Society Published on Web 04/09/2002
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Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002
should be the holdup of the dispersed phase; this parameter relates with the effective interfacial area used for transport and ultimately with the masstransfer efficiency correlation. From the hydrodynamic point of view, the two basic approaches to describe the countercurrent flow of two phases in structured packed beds are the channel (or film) model and the particle (or drop) model. The latter considers that the continuous phase flows around discrete drops of the dispersed phase, while the former considers that the dispersed phase flows in a thin film wetting the corrugated channel walls of the packing. The film model approach will be used in this work because experimentally any formation of gas or liquid dispersed particles was not observed throughout the packing bed of our highpressure column during the supercritical fluid fractionation tests. Literature Survey. In 1993 Rocha et al.8 developed a model for predicting the holdup (as well as the pressure drop and flooding capacities) of distillation columns containing structured packings of the corrugated metal type, hereby called the RBF model, and based on the former investigations made by Bravo et al.7 Although the model was applied to a distillation process, the authors pointed out that the model could be also applied to absorption or stripping processes. Basically, it takes into consideration the interaction of a falling liquid film with the upstream vapor; the flow and physical characteristics of the system and the geometric properties of the packing are also taken into account to describe the hydrodynamics of the process. The liquid flow is considered to be dispersed in the form of thin films wetting the packing gauze surface (here, described as a series of parallel, inclined wetted wall columns), and no suspended liquid exists. The liquid holdup is directly related to the liquid film thickness and the effectively wetted surface area. The liquid film thickness under operating conditions was defined by a modification of the classical laminar falling film equation.9 The expression for the liquid holdup results as
( )( Ft s
ht ) 4
2/3
)
3µLuLS FL sin θgeff
1/3
(1)
where Ft (eq 2) is a correction factor for the holdup that accounts for the effective wetted area of packing and geff (eq 3) represents the “effective” gravity on the liquid phase, i.e., the result of the force balance acting on the liquid. An expression originally developed by Shi and
Ft )
29.12(WeLFrL)0.15s0.359 ReL0.20.6(1 - 0.93 cos γ)(sin θ)0.3
geff ) g
[(
)(
FL - FG ∆P/∆Z 1FL (∆P/∆Z)flood
)]
(2)
(3)
Mersmann10 to estimate the effective interfacial area of ceramic and plastic random packings was applied in the RBF model to evaluate the correction factor. The contact angle γ between the liquid and the specific packing surface accounts for the surface material wettability. The model has some limitations: experimental data are needed to obtain some packing coefficients on which the model depends, and a value for the pressure drop at flooding conditions is needed to estimate the liquid holdup.
Figure 1. Flow channel arrangement and geometry of the gauze packing.
In a subsequent paper,11 the same authors proposed a correlation for the mass-transfer efficiency in distillation columns containing structured packings. The gasphase-transfer coefficient is based on the classic “wetted wall” relationship that uses the dimensionless groups of Sherwood, Reynolds, and Schmidt (eq 4), and the liquid-phase mass-transfer coefficient is predicted by the penetration theory of Higbie (eq 5):
ShG ) C1ReGmScGn
(4)
kL ) 2(DLCEuLeff/πs)1/2
(5)
where CE is a correction factor for retarded surface renewal (≈0.9). The side dimension of the corrugation cross section of the structured packing, s, was taken as the characteristic length of the packing (see Figure 1). From the database available by the authors, they determined for eq 4 that C1 ) 0.054 and m ) 0.8, with n being taken as 0.333. Both equations use the effective velocities of the gas and liquid phases, ueff, which are a correction of the superficial velocities for the packing space that is occupied by the liquid. The effective velocities depend on the liquid holdup as well as the porosity, , and angle of corrugation of the packing, θ. For sheet metal structured packings, Rocha et al. estimated the effective interfacial area based on the expression developed by Shi and Mersmann.10 The mass-transfer model was validated for distillation systems with a variety of commercial structured packings. Olujic et al.12 introduced a corrugation geometry based model (the OKG model) to predict the masstransfer efficiency of structured distillation packing columns. The model, developed for corrugated sheet metal packings, considers the gas flow as a continuous zigzag flow through a triangular shape corrugation channel; the characteristic dimension of the packing flow channel is defined by the hydraulic diameter of the triangular gas channel. The respective expression includes explicitly the liquid film thickness, δ, defined as below. Assuming a well-distributed liquid phase, the liquid holdup follows simply from the product of the packing surface area and the mean liquid film thickness:
ht ) δa
(6)
This implies that the model is based on a complete wetting of the packing surface by the liquid phase. The mean liquid film thickness is estimated from the classical correlation for laminar falling films as adapted for inclined wetted walls:
δ)
(
)
3µLuLS FLga sin θ
1/3
(7)
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2307
The authors point out that the liquid film thickness can be calculated in the absence of countercurrent gas flow if the actual operating conditions in the column are in the preloading range. The mass-transfer expression for the gas-phase coefficient is divided into two individual laminar and turbulent flow contributions, both being dependent on the Sherwood, Reynolds, and Schmidt numbers.12 The mass-transfer resistance equation for the liquid phase uses the same definition as that proposed by Rocha et al.11 The effective interfacial area for mass transfer was estimated by assuming that all the packings studieds sheet metal packingsshad the same wetting behavior; an exponential expression was used to fit available experimental data as a function of the surface area texture and the liquid load:
1-Ω ae ) a 1 + 2.143 × 10-6/uLS1.5
(8)
where Ω stands for the fraction of the packing surface area that is occupied by holes. The authors pointed out that a reliable prediction of the effective surface area is a keynote to a better performance of the mass-transfer model. Billet and Schultes13 proposed a model to calculate the dispersed-phase holdup in gas/liquid countercurrent columns, filled with either random or structured packings (the BS model). The model assumes that the effective free volume of the packing is equivalent to a series of vertical flow channels, wherein the liquid trickles downward along the wall and the gas flows upward countercurrently. According to the authors, at operating conditions lower than the loading point of the column, the liquid holdup is a function of the liquid velocity only and the gas flow hardly exerts any influence. Aware of the fact that the packing surface may be incompletely wetted by the liquid phase, they proposed a correction factor based on a hydraulic area of packing per unit volume of packed bed, ah, which is different from the effective interfacial area of the packing used for the mass-transfer process. The hydraulic area was correlated for several packing geometries and sizes and was found to be dependent on the Reynolds and Froude numbers for the liquid phase as presented in eq 10. A slightly different definition for the Reynolds number was used by Billet and Schultes (ReL ) uLSFL/aµL).
ht )
(
)()
12µLa2uLS FLg
1/3
ah a
2/3
(9)
ReL < 5: ah/a ) ChReL0.15FrL0.1 ReL > 5: ah/a ) 0.85ChReL0.25FrL0.1
(10)
The parameter Ch is characteristic of each packing geometry. The mass-transfer process was described in terms of the packing geometry and the physical properties influencing the gas/liquid or vapor/liquid systems in absorption and desorption. Both expressions for the gas and liquid mass-transfer coefficients were developed from the original formulation of Higbie:
( )( )
kL ) CL × 121/16
uLS ht
1/2
DL lτ
1/2
(11)
where lτ represents the length of a flow path (characteristic dimension) defined as 4/a:
() ( ) ( ) 1/2
1 a k G ) CG 1/2 l ( - ht) τ
DG
uGS aµG
3/4
1/3
µG DG
(12)
CL and CG are parameters that depend on the packing type. Billet and Schultes estimated the effective interfacial area for mass transfer by regressing the experimental data in the form
( ) (
ae uLSlτ ) 1.5(alτ)-1/2 a µL
-0.2
) ( )
uLS2FLlτ µL
0.75
uLS2 glτ
-0.45
(13)
For gas/liquid absorption processes with structured packings, Suess et al.14 proposed an empirical correlation for the liquid holdup:
ht ) Ca0.83(3600uLS)m
( ) µL
µ20°C water
0.25
(14)
where
{
C ) 16.9 × 10-5m ) 0.37 C ) 7.5 × 10-5m ) 0.59
if uLS < 0.011 m/s if uLS > 0.011 m/s
Lately this correlation was successfully applied by Brunnazi et al.15 in the absorption of 1,1,1-trichloroethane with a mixture of poly(ethylene glycol) dimethyl ethers. Results and Discussion The usefulness of the models described in the former section to describe the mass-transfer efficiency of structured packing columns at high-pressure conditions was tested by using experimental results obtained in our countercurrent supercritical extraction packed column of 2 m height and 2.4 cm internal diameter. A description of this apparatus was given in the first paper of this series.1 The chosen case study was the fractionation of the mixture squalene/methyl oleate by supercritical carbon dioxide; two feed mixtures were studied with different initial squalene contents: one with 40 wt % squalene and the other with 70 wt % squalene. The pressure and temperature conditions of the fractionation tests were set at a constant value of 11.5 MPa and 313 K, respectively. The experimental apparatus was equipped with several sapphire windows in the extraction column. These windows allowed the direct visualization of the dispersed phase during a fractionation run. The reasonably dense laboratory-scale packing used in this work did not allow a clear visual observation of an oil film wetting the packing surface; however, no oil droplets were observed during the countercurrent contact of the two phases. It was assumed that the oil-rich phase was dispersed as a thin film layer over the packing surface. This consideration was decisive to the choice of the models used in this work, as was already mentioned.
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Table 2. Physical Properties and Equilibrium Partition Coefficient Used in This Work density (kg/m3) viscosity (mPa s) diffusion coefficients (109 m2/s)
continuous gas phase dispersed liquid phase continuous gas phase dispersed liquid phase
722.3 911.7 0.061 1.025 1.490 6.672 1.284 2.80 0.103
40% by weight squalene 70% by weight squalene
continuous gas phase dispersed liquid phase
surface tension (mN/m) equilibrium partition coefficient
Figure 2. Experimental holdup for different extraction conditions as a function of the gas flow factor.
Experimental liquid holdup and mass-transfer efficiency were determined and compared with the values estimated by the mass-transfer models. The required physical properties of the two phases were determined at the operating conditions of pressure, temperature, and composition as follows: the densities of the liquid and gas phases were experimentally measured in our column; the other physical properties were estimated when no experimental data was available in the literature. The viscosity of pure carbon dioxide was taken from Stephan and Lucas.16 The viscosity of the liquid phase was estimated by the method of Grunberg and Nissan17 as modified by Kashulines et al.18 The viscosity of pure liquid squalene was taken from Kuss and Golly19 and the viscosity of pure methyl oleate from Kashulines et al.18 and extrapolated using the Bridgman correlation17 for pure lipid compounds. The diffusion coefficient of methyl oleate in the liquid phase was estimated by the WilkeChang equation,17 whereas for the vapor phase we used the experimental data given by Tuan et al.20 The experimental surface tension of an olive oil/supercritical carbon dioxide system21 was taken as the value of the surface tension of our system. The physical property data of the two phases are given in Table 2. Liquid Holdup. The experimental liquid holdup was measured by the volumetric technique; at the end of each fractionation run, the liquid feed flow rate was stopped and the amount of liquid drained from the packed column measured. The experimental holdup measured for the different extraction conditions is shown in Figure 2 as a function of the gas flow factor, usGFG1/2. The liquid holdup rises with the increasing liquid phase load, as expected. As the flow of the gas phase increases, hardly any effect can be noticed on the holdup. As pointed out by other authors,12,13 the dispersed-phase holdup is reasonably not influenced by the gas load until the loading point is reached, at which point the liquid flow actually starts to “feel” the gas
Figure 3. Comparison of measured and calculated values of liquid holdup.
upflow and holdup in the bed. The holdup increases with the gas-phase velocities until a maximum is reached at flooding conditions. Stockfleth and Brunner22 have recently presented some holdup data for Sulzer EX packing at supercritical conditions. They have shown that the loading region for their system was very small and not detectable, by either holdup or pressure drop measurements. It is possible that this same behavior occurs with our system. However, because of the limitation of the capacity of our pumps, it was impossible to increase further the gas or liquid load in this work. Based on the dependency of the holdup with the superficial velocity of the liquid phase (in the region below the loading point), a power-type equation was fitted to our experimental results to check such a dependence. The hydrodynamic models described in the former section were then applied to our results and the correlation parameters, if existing, adjusted for our gauze packing data. Figure 3 shows the comparison between our experimental holdup data and the predicted values according with the hydrodynamic models. Table 3 presents the adjustable parameters for the holdup correlations. The correction factor in eq 2 of the RBF model8 was adjusted to our high-pressure data by fitting the respective constant parameter. Because no pressure drop data were measured in this work, it was necessary to estimate such values in order to calculate the effective gravity factor, geff (in eq 3). The pressure drop at operating conditions was estimated from the model developed by Stichlmair et al.23 as modified by Stockfleth and Brunner:24
{[1 - (1 - ht/)]/(1 - )} ∆P ) ∆Pdry (1 - /h )4.65
(2+c)/3
(15)
t
with c ) (-C1/ReG)/ψ where ψ is the friction factor for flow through a packed bed which would result if no
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2309 Table 3. Holdup Model Equations after Adjustment to This Work proposed model RBF8 BS13
adjusted equation 0.15 m
Ft ) ah a
SS14
C(WeLFrL)
s
n 0.6
ReL (1 - 0.93 cos γ)(sin θ)
) ChReLmFrLn
0.3
(2) (10)
( )
ht ) Ca0.83(3600uLS)m
µL
0.25
20°C µwater
liquid flow existed in the bed; i.e., it is a dry-bed friction factor. C1 is a constant parameter from the dry friction factor expression and is dependent on the packing type; the pressure drop data obtained by Stockfleth and Brunner24 for the countercurrent extraction of olive oil deodorizer distillate by supercritical carbon dioxide in a Sulzer EX packing column were used to estimate the pressure drop of our system. It should be noted that the mixture squalene/methyl oleate partially resembles the residues obtained from the deodorization of olive oil.1 The pressure drop at flooding conditions, ∆Pflood (eq 3), was also obtained from the experimental data measured by Stockfleth and Brunner.24 The RBF model was able to describe quite well our experimental data within a (8% confidence interval. The use of the effective liquid velocity concept and the effective gravity concept may explain the ability of the model to fit the experimental data. The former accounts for the space occupied by the liquid holdup and the angle of inclination of the corrugation channels in the structured packing. The effective gravity term, geff (see eq 3), accounts for the liquid buoyancy force opposing the gravity force and the drag force on the liquid film by the gas phase. For high-pressure systems such as ours, the buoyancy term is of importance because the density difference between the two coexisting phases is much smaller than that found in distillation or absorption processes. Because the operating conditions of our countercurrent column were always far away from the flooding point, the pressure drop effect on the effective gravity is negligible. However, the usefulness of the RBF model has a limitation in that a corresponding values of the pressure drop at the actual operating conditions and at flooding conditions are needed to calculate the effective gravity term (eq 3). In the absence of experimental data, it is required to have an accurate prediction method for the pressure drop. In this work we decided to use the original formulation of Stichlmair et al.23 and later modified by Stockfleth and Brunner.24 The main reason was the similarity between the system studied by Stockfleth and Brunnersthe olive oil deodorizer distillate/supercritical carbon dioxidesand our system. Obviously, at conditions near the flooding point, a much closer look has to be made on the pressure drop term of eq 3. The classical equation for the liquid film thickness at the laminar regime as proposed by Olujic et al.12 clearly underpredicts our experimental holdup data, even at the lower liquid loads used in this work. The OKG model for the holdup is based on a complete wetting of the packing surface and does not take into account the liquid buoyancy effect on the film thickness expression. The high pressures involved in our system and the relatively high surface area available by Sulzer EX packing would explain the underestimation of the liquid holdup by this model.
(14)
fitted parameter
AD (%)
C ) 28.37 m ) 0.36 n ) 0.50 Ch ) 3.94 m ) 0.15 n ) 0.1 C )21.8 × 10-5 m ) 0.37
8.4 14.5 7.7
The correlation proposed by the BS model is not able to follow the experimentally observed trend of the holdup with the liquid load. Clearly, the influence of the gas-phase density on the buoyancy force acting against the gravity is of importance in supercritical fluid systems. Moreover, the equation proposed by Billet and Schultes13 for the hydraulic area (eq 10) was developed mainly from holdup data obtained with random-type packings. The empirical correlation proposed by Suess et al.14 was found to provide a very good fit of our holdup data. This result is rather surprising considering that eq 14 was originally developed from holdup tests in gas/liquid absorption processes with metal sheet packings. The good fitting of the Suess correlation may be explained by the similarity between the power exponent of the liquid superficial velocity in eq 14 and the experimental exponent obtained from the power regression of our holdup data. Effective Interfacial Area. Structured packings made of corrugation sheets (metal or gauze) have been applied successfully in separation processes during the past decades because of their high mass-transfer efficiency combined with a minimal energy consumption. These packings present a large void fraction and relatively high surface area per unit volume of packing bed, which promote the performance of the countercurrent extraction column. One way of characterizing the efficiency of a structured packing column is to quantify the packing fractional area effectively used for mass transfer, i.e., the ratio between the effective area and the specific surface area of the packing. The effective area of a corrugated packing can be taken as the fraction of geometrical area efficiently wetted by the liquid phase. This is the case when one is operating a column in the preloading region where ripples or waves are not likely to occur.25 The fractional wetted area of a packing will depend on the wetting characteristics of the packing surface (nature and texture of the surface) and the physical properties of the system, mainly the liquid viscosity and the surface tension.26 Therefore, estimating the effective interfacial area of a structured packing is of critical importance to develop an accurate model for the mass-transfer efficiency of packed columns. The number of studies dealing with this subject and reported in the literature is limited, especially those regarding corrugated gauze packings such as the one used in this work at ambient or high pressures. Some work has been done where the fluid dynamics of a falling liquid film is investigated at ambient pressure10,26,27 as well as at high-pressure conditions.28-32 At these conditions, the observations showed that the falling film of a liquid phase in compressed carbon dioxide was smooth or wavy and disintegrated into drops as a consequence of the fluid dynamics (increased liquid flow velocity) and the physical properties of the liquid phase (because of a
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interfacial area of sheet metal structured packings by introducing a correction factor that accounts for possible surface enhancement by texturing. Gauze surfaces were not considered in this case; instead, a different correlation was proposed for gauze packing wetting:
( )
ae uLS2 ) 1 - 1.203 a sg
Figure 4. Predicted effective surface area of Sulzer EX gauze packing at supercritical conditions.
decrease in the liquid viscosity and surface tension with increasing absorption of carbon dioxide in the liquid film). Jaeger and Eggers32 investigated the wetting characteristics of a corrugated gauze-type packing, Sulzer BX, by corn germ oil in compressed carbon dioxide in a countercurrent column. They were able to measure the contact angle of the oil phase in the gauze surface at 338 K and pressures in the range of 10-26 MPa. The measured contact angles were lower than 25°, indicating that a relatively homogeneous oil film could be assumed to cover partially the gauze packing surface.32 The fractional wetted area was linked to the mass of liquid within the column, i.e., the holdup, and the mass flow. By assuming a laminar falling film of constant thickness, they estimated a film thickness of ca. 0.2 mm; the corresponding wetted portion, assuming a homogeneous surface coverage, was in the range of 27-48% of the specific surface area of the gauze packing. Because the objective of this work was to develop a model able to predict the mass-transfer performance of the high-pressure packed column, it was necessary to estimate the actual fractional wetted area of the gauze packing because no method was available to experimentally measure it. Several correlations are available in the literature for predicting the interfacial area of packed columns.10-13,15 The majority were applied to sheet metal structured packings; as far as we know, only Rocha et al.11 have proposed a correlation specifically for corrugated gauze surfaces such as the one used in this work. The estimated effective surface area of our packing, expressed by the fractional ratio of effective area ae/a, is shown in Figure 4 as a function of the superficial liquid velocity. Equations 8 and 13 were used to calculate the effective surface area for the OKG and BS models, respectively. The well-known correlation of Onda et al.33 originally developed for the first generation of random packings was also applied to our system:
[
()
ae σ ) 1 - exp -1.45 a σc
-0.75
]
ReL0.1FrL-0.05WeL0.2 (16)
where σc is the critical superficial tension of the packing material. The original model proposed by Rocha et al.11 uses the expression formerly developed by Shi and Mersmann10 for random packings to estimate the effective
0.111
(17)
As can be seen from Figure 4, all of the correlations but eq 17 show an increase of the fractional wetted area with the liquid load. No experimental confirmation exists in the literature whether the effective area for gauze surfaces at high-pressure conditions should increase or decrease with the liquid rate. Billet34 mentions that the efficiency of metal gauze packing depends on the load; at low liquid loads, the gauze nature of the surface exerts a capillary action so that the small amounts of liquid are uniformly spread over its surface, thus giving rise to a higher efficiency. The liquid film thickness estimated by using the RBF model (eq 1) shows an increasing dependence with the liquid velocity; this is in some way in agreement with the decrease of the fractional wetted area with the liquid load. The OKG model was developed for sheet metal packing surfaces. Equation 8 as proposed by Olujic et al.12 uses two packing-specific constants; it is questionable that the values taken from their work should apply to our case; only by fitting eq 8 to experimental data of effective surface areas of gauze packings at highpressure conditions should it be possible to test their method. Furthermore, the observed increase of the fractional wetted area with the liquid load is to be expected; it is known from the literature that the surface of sheet metal packings is fully wetted only at relatively high liquid rates.7,12 The BS model and the correlation proposed by Onda et al.33 gave very different values of the effective area, although they were developed from experimental data obtained mainly with random packings. Clearly, only by understanding the wetting process of gauze corrugated packings at high-pressure conditions will it be possible to develop more accurate methods to estimate effective surface areas. This can be accomplished by evaluating the influence of the main operating parameters on the liquid holdup distribution through the packing surface; recently, work on nonintrusive methods for phase distribution quantification by X-ray tomography35 has provided some in situ images of the liquid flow in corrugated sheet packings. Mass-Transfer Coefficient. The experimental masstransfer efficiency of the packed column was evaluated by determining the overall mass-transfer coefficients, using the conventional definition of a transfer unit for countercurrent packed columns. The height of packing required to achieve a desired top product concentration is given by36
Z ) NTUOGHTUOG
(18)
Because the mass fractions of solute in the gas phase are normally very small, the number of transfer units based on the gas compositions, NTUOG, can be given by
NTUOG )
∫yy
1
2
dy y - y*
(19)
The integral is determined from a knowledge of the thermodynamic equilibrium of the system and of the
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2311 Table 4. Mass-Transfer Model Equations after Adjustment to This Work proposed model
adjusted equation
RBF11
m
fitted parameter
n
ShG ) C1ReG ScG
BS13
(4)
( )( ) () ( ) ( ) ) ( ) x( x
kL ) CL × 121/16
uLS ht
1 a kG ) C G ( - ht)1/2 lτ OKG12
kG )
ShG,lamDG dhG
1/2
DL lτ
1/2
DG
2
+
ReGrvmScG 1+C
uGS aµG
3/4
µG DG
ShG,turbDG dhG
ShG,lam ) CReGrvmScGn
ShG,turb )
1/2
(11)
1/3
(12)
x
φξGL (ScG2/3 - 1) 8
CL) 1.164
AD (%) 15.7
27.4
CG ) 0.201
17.1
2
(23)
dhG lG,pe
φξGL 8
C1 ) 4.68 × m ) 0.8 n ) 0.33
10-3
(24)
[ ( )] dhG 1+ lG,pe
C ) 0.0217 m ) 0.5 n ) 0.33 C ) 12.7 m ) 2.62
2/3
(25)
relative magnitude of the liquid and gas loads in the column, given respectively by the equilibrium and operating lines. For dilute solutions such as ours, it is admissible to assume the linearity of the equilibrium line; moreover, taking the low solubility of squalene and methyl oleate in supercritical carbon dioxide and the low solubility of carbon dioxide in the oil phase, the gas and liquid loads along the column are reasonably constant so that the operating line is also linear. The equilibrium data of the methyl oleate/squalene/carbon dioxide system at 313 K and 11.5 MPa were determined over the range of compositions found in the fractionation experiments.1 The integral term of eq 20 is then given by36
NTUOG )
[(
)(
)
]
meGm y1 - mex2 meGm 1 ln 1 + meGm/Lm - 1 Lm y2 - mex1 Lm (20)
Figure 5. Predicted liquid-phase mass-transfer coefficient.
The overall volumetric mass-transfer coefficient based on the gas-phase compositions, KOGae, is then calculated from the following relation:
KOGae )
uGS NTUOG ) uGS HTUOG Z
(21)
The relation between the overall mass-transfer coefficient and the individual film coefficients kG and kL, according with the two-film resistance theory, is given by
1 KOGae
)
me 1 + kGae kLae
(22)
The film coefficients and the effective area are calculated from the respective equations for each model (see Table 4). A comparison of the predicted film mass-transfer coefficients for the liquid and gas phases as a function of the superficial velocities is shown in Figures 5 and 6, respectively.
Figure 6. Predicted gas-phase mass-transfer coefficient.
The predicted dependence of kL on the liquid load as well as the magnitude of the coefficients is similar for all of the models. The estimated values of kL by the OKG model lie above those calculated by the RBF model, although both models apply the penetration theory expression. In the OKG model, the characteristic dimension for the liquid path is considered to be equal to the equivalent diameter of a triangular flow channel,
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Figure 7. Comparison of measured and predicted overall masstransfer coefficients as a function of the gas flow factor, for a constant liquid load of 9 g/min.
dhG, which is slightly lower for Sulzer EX packing than the characteristic length taken by the RBF model, assumed to be the side length of the corrugation channel, s. The same trend was observed by Olujic et al.12 and Fair et al.37 for the distillation of cyclohexane/ n-heptane mixtures with sheet metal packings. The BS model (eq 12) estimates higher values for kG than the other two models; however, this difference is compensated at the end by the lower values estimated for the effective surface area (eq 13). The RBF model estimates a much lower dependence of the gas-phase coefficient kG with the gas load than that expected from the wetted wall column relationship, eq 4. In the original equation, the exponent of the gas Reynolds number is 0.8; however, the observed dependence of the estimated kG with the gas velocity is about half of it. The reason is that the gas-phase Reynolds number incorporates the relative effective velocities of the two phases; i.e., the velocity term is uLeff + uGeff. Because the liquid rates used in this work are lower than the corresponding gas flow rates, the resulting power exponent of the gas-side coefficient is lower than expected. All of the models predict a much higher resistance to mass transfer in the gas phase; the calculated liquid film resistance contributes with less than 2% to the total resistance to the mass-transfer process. Catchpole et al.38 for the shark liver oil/supercritical carbon dioxide system and de Haan and de Graauw6 for the system hexadecane/2-methylnaphthalene/supercritical carbon dioxide have reported the same trend. This behavior can be attributed to the low distribution coefficients (the slope of the equilibrium curve) normally observed in supercritical systems; the limiting step should be the solubilization and diffusion in the solvent phase and not its diffusion in the liquid phase. Moreover, as pointed out by others,7 the capillary action of the gauze nature of the packing and the thickness of the liquid film should enhance a Marangoni type of interfacial turbulence effect, allowing for a rapid mass transport process through the liquid film. A comparison of the predicted and measured overall mass-transfer coefficients, KOGae, is shown in Figure 7 as a function of the superficial gas velocity; in Figure 8 is shown a parity plot of all sets of values. Table 4 presents the adjustable parameters of the mass-transfer relationships for the BS, RBF, and OKG models. The original definition of the gas-phase Reynolds number by Bravo et al.7 (eq 4) was modified in this work so that
Figure 8. Parity plot of calculated and experimental overall masstransfer coefficients for several operating conditions.
the predicted dependence of the overall KOGae with the gas flow factor by the RBF model would follow the experimentally observed trend, that is
ReG ) sFGuGeff/µG
(26)
The modified RBF model (with the gas-phase Reynolds number defined as above) fits the experimental data with an average deviation of 15%; ca. 90% of the points fall within (25%. The BS model was able to predict with reasonably accuracy the experimentally observed behavior of the overall mass-transfer coefficient with the gas flow factor, although only around 60% of the points fall within (25% of the experimental data. This is quite interesting because this method was developed mainly from gas absorption data with random packings or sheet metal ordered packings. The original correlation of the OKG model overpredicted the masstransfer efficiency of our system; we were forced to modify the exponents of the gas-phase Reynolds number in the respective equation of the gas-phase coefficient (see Table 4) so that the calculated order of magnitude for the KOGae was equal to the experimental one. Some attempts were made to improve the accuracy of the mass-transfer models by considering other existing models available in the open literature. Theoretically based equations for holdup and liquid-phase masstransfer coefficients as recently proposed by Shetty and Cerro39 were applied to our high-pressure data. According to the authors, the corrugation base length of a packing channel was taken as the characteristic dimension, thus accounting explicitly for the liquid film thickness. Using their equations instead of the penetration theory based eq 5 did not result in any improvement of the modified RBF model. Taking the fact that the kL coefficient makes a minor contribution to the overall mass-transfer coefficient, it is doubtful that a theory other than the former should be necessary at the moment to improve the accuracy of mass-transfer models in supercritical systems. We also used other definitions for the characteristic dimension of the gas flow channel in our gauze packing than the corrugation side length, s, as proposed initially; using the general definition of the hydraulic diameter as introduced by Billet and Schultes13 or the hydraulic diameter of a triangular gas flow channel defined by Olujic et al.12 in the modified RBF model did not result in further improvement.
Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2313
Figure 9. Effect of the liquid-phase viscosity on the liquid holdup, with G ) 90 g/min (deviation: +20% µL ) 12.9%, -20% µL ) 13.8%).
The RBF model appears to be a reasonably good model for high-pressure extraction systems with corrugated gauze packing columns. It incorporates the key parameters for a correct description of a countercurrent packed column, that is, hydraulic parameters such as the holdup, pressure drop, and flooding capacity (although this was not used in this work) as well as masstransfer parameters such as the effective interfacial area and the mass-transfer coefficients. Although it requires the definition of some constant parameters dependent on the packing type to be used, these parameters are then conserved for other systems and operating conditions than this work, provided that the respective column uses gauze-type packing. Our future intention will be to test the model to other high-pressure systems with different physical properties than the lipid-like system used in this work. The physical properties required to perform the masstransfer calculations were, most of them, estimated for the squalene/methyl oleate/carbon dioxide system. The uncertainty in the estimation method may produce a nonnegligible influence on the accuracy of the calculated holdup and overall mass-transfer coefficient; thus, it is important to evaluate how the model depends on the physical properties and which ones are more important. A sensitivity analysis was performed by introducing finite perturbations on the estimated values of each physical property by amounts corresponding to likely uncertainty in the data; the corresponding variations in the calculated liquid holdup and overall masstransfer coefficient were then calculated. Figure 9 presents the deviation of the calculated holdup by the RBF model against a variation of (20% in the liquid viscosity. The sensitivity analysis showed that the liquid viscosity had the greatest impact on the holdup prediction. A variation of (20% in the liquid viscosity yielded an averaged deviation of (13% in the holdup. The surface tension of the liquid phase had a much lower impact on ht: an averaged deviation of (2% was determined. The overall mass-transfer coefficient was found to be dependent more strongly on the physical properties of the gas phase, which is not surprising because the fractionation of the oil mixture was a gasphase-controlled process. The gas-phase diffusivity and viscosity had the greatest impact on the estimation of KOGae (Figure 10). All of the other variables were found to not have a significant influence on the accuracy of the models.
Figure 10. Effect of the gas-phase diffusivity and viscosity on the overall mass-transfer coefficient, for a constant liquid load, with L ) 9 g/min (deviation: +20% DG ) 12.8%, -20% DG ) 13.7%; +20% µG ) 8.1%, -20% µG ) 10.9%).
Conclusions The mass-transfer performance of a structured gauze packing column for the fractionation of the system squalene/methyl oleate by supercritical carbon dioxide was evaluated and used as a case study to test available hydrodynamic and mass-transfer models for high-pressure conditions. Experimental data of liquid holdup and mass-transfer coefficients for the high-pressure system were compared with the values predicted by the different models. It was found that a model formerly developed for distillation columns containing structured packings of the corrugated metal type can be applied successfully to supercritical extraction processes as well. Although the method requires the use of packing-specific constants, it was possible to extend its validation to gauze-type structured packings such as the one used in this work. More work will be done to test the model for other highpressure systems. The effective area used for the mass transport was found to be essential in order to improve the accuracy of the model; it is necessary to understand the two-phase distribution along the packing surface at high-pressure conditions so that a correct prediction method for the fractional wetted area of a packing can be developed. Acknowledgment The authors are thankful for the financial support of Fundac¸ a˜o para a Cieˆncia e Tecnologia, under Grant PBIC/C/QUI/2364/95 and Ph.D. Grant PRAXIS XXI/BD/ 18296/98. Nomenclature a ) specific surface area of packing, m2/m3 ae ) effective surface area, m2/m3 ah ) hydraulic area of packing per unit volume of packed bed, m2/m3 b ) channel base of a packing element, mm C ) parameter fitted C1 ) constant parameter (eq 15) CE ) correction factor for surface renewal Ch ) hydraulic parameter characteristic of each packing geometry (eq 10) CL, CG ) mass-transfer parameter characteristics of a packing geometry (eqs 11 and 12)
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deq ) equivalent diameter, m D ) diffusion coefficient, m2/s D1 ) diameter of a packing element, mm Ft ) partial wetting correction factor (eq 2) geff ) effective gravity submitted by the liquid phase, m/s2 (eq 3) g ) gravity acceleration, m/s2 G ) gas mass flow, kg h-1 h ) crimp height of a packing element, mm ht ) total liquid holdup H1 ) height of a packing element, mm HTU ) height of a transfer unit, m k ) mass-transfer coefficient, m/s KO ) overall mass-transfer coefficient, m/s l ) characteristic dimension, m lτ ) length of the flow path (BS model, )4/a), m L ) liquid mass flow, kg h-1 m ) parameter fitted me ) slope of the equilibrium curve NTU ) number of transfer units s ) side dimension of corrugation, m S ) column cross-sectional area, m2 uS ) superficial velocity, m/s uGeff ) uGs/[(1 - ht)sin θ] ) effective gas velocity, m/s uLeff ) uLs/(ht sin θ) ) effective liquid velocity, m/s x ) mass fraction of methyl oleate in the liquid x* ) equilibrium liquid mass fraction y ) mass fraction of methyl oleate in the vapor y* ) equilibrium vapor mass fraction Z ) column height, m Greek Letters δ ) mean film thickness, m θ ) angle of corrugation, deg γ ) contact angle between the liquid and the packing surface, )30° (from Jaeger and Eggers32) ) packing porosity, m3/m3 µ ) viscosity, Pa s η ) kinematic viscosity, m2/s F ) density, kg/m3 σ ) surface tension of the liquid, N/m σc ) critical surface tension of the packing material (eq 16), )0.075 N/m (from Onda et al.33) Ω ) void fraction of the packing surface (eq 8, )0 for our packing) ψ ) friction factor for flow through a packed bed Dimensionless Groups FrL ) uL2/sg ) Froude number for the liquid ReL ) uLsFL/µL ) Reynolds number for the liquid ReG ) sFG(uGeff + uLeff)/µG ) Reynolds number for the gas ScG ) µG/FGDG ) Schmidt number for the gas ShG ) kGs/DG ) Sherwood number for the gas WeL ) uL2FLs/σ ) Weber number for the liquid Subscripts flood ) flooding conditions L ) liquid phase G ) gas phase O ) overall m ) average
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Received for review August 2, 2001 Revised manuscript received February 13, 2002 Accepted February 20, 2002 IE0106579
