ft
UILU-ENG 91-0107
HWRIC TR 006
APPLICATIONS OF SUPERCRITICAL FLUID
PROCESSING TO ENVIRONMENTAL
CONTROL
C. A. Eckert
G. W. Leman
D. L. Tomasko
Illinois Department of Energy and Natural Resources
Hazardous Waste Research and Information Center
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Advanced Eiivirtmmesilid Conlro! Techiiolosiy Mesesireh f:
^11
Hazardous Waste Research and information Center
Illinois Department of Energy and Natural Resources
One East Hazelwood Drive
I )(¦('('HllttT |«W1
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Final Report
ui'urvnovs 01 supercritical fluid processing
IO ENVIRONMENTAL CONTROL
Charles A. Eckerl*, Principal Investigator
Gregory W. Leman* Senior Investigator
David L. Tomasko
Department of Chemical Engineering
University of Illinois
Urbana, Illinois 61801
'Present address: School of Chemical Engineering, Georgia Institute of Technology, Atlanta, OA 30332-01(1)
~Present address: Cabot Corporation, P.O. Box 186, Tuscola, IL 61950
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iii
The information described in this report has been funded in part by the United States
Environmental Protection Agency under assistance agreement EPA Cooperative Agreement EPA
CR 812582 to the Advanced Environmental Control Technology Research Center. Additional fund-
ing was provided by the Illinois Hazardous Waste Research and Information Center. Although the
report has been reviewed internally with respect to its technical content, it has not been subjected
to either organization's required peer and administrative review. Therefore, it does not necessarily
reflect the views of the organizations and no official endorsement should be inferred. Mention of
trade names or commercial products does not constitute endorsement or recommendation for use.
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iv
ABSTRACT
Environmental control and waste remediation are of immediate technological and political
interest. One technology which has great potential is contaminant removal and separation with
supercritical fluids (SCF's) or supercritical fluid extraction (SFE). In order to take advantage of
this technology, both a fundamental understanding of phase equilibria and applicable engineering
design data are required. This report documents an extensive study into both aspects culminating
in the design and economic evaluation of a SCF regeneration process for granular activated carbon
(GAC).
We determined solubilities of relatively non-volatile solid compounds in supercritical fluid
solvents, exploring effects of solvent properties, solute properties, and the nature of the critical
region. Cosolvents added to an SCF were shown to enhance solubilities and increase selectivities
through specific intermolecular interactions. Vapor pressure measurements and spectroscopic
investigations also aided the understanding of solubility enhancement. The data were used to test
and develop equations of state for calculating phase equilibria in systems containing a supercritical
fluid.
The ability of supercritical C02 to remove model contaminant compounds from GAC and
subsequently drop out most of the contaminant in a liquid phase has been investigated in a pilot
scale apparatus. Typical desorption profiles indicate approximately 85% removal of contaminants
2-chlorophenol and toluene from the carbon. The presence of water on the GAC was shown to
inhibit slightly the efficiency of the desorption. The desorption results have been interpreted with
a generalized desorption-mass transfer model.
The results of the pilot scale studies have been applied to the design of a fixed-site GAC
regeneration unit consisting of a three element desorber with two stage flash separation. Optimiza-
tion of the process centers around minimizing the cost of recycling the SCF through an efficient
recompression scheme and regeneration cycle configuration in the desorber unit. An economic
evaluation shows a processing cost of 10.6e/lb GAC which compares favorably with thermal
regeneration and incineration. This non-destructive process allows re-use of the GAC while
maintaining a high adsorbate capacity, which reduces carbon replacement costs and significantly
decreases the need for carbon disposal by landfill or incineration.
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V
TABLE OF CONTENTS
Section Page
LIST OF TABLES vii
LIST OF FIGURES viii
I. INTRODUCTION 1
II. BENCH-SCALE SCF STUDIES 2
A. SUMMARY 2
B. RESULTS AND DISCUSSION 2
1. Solubility of Model Compounds 2
2. Cosolvent Effects on Solubility 6
3. Vapor Pressure Measurements 6
4. Spectroscopic Measurements 8
5. Models for SCF Phase Equilibria 9
C. CONCLUSIONS 9
III. PILOT-SCALE RESEARCH PROGRAM 9
A. SUMMARY 9
B. EXPERIMENTAL 10
C. RESULTS AND DISCUSSION 12
1. Adsorption/Desorption Studies 12
2. Near-Critical Gas/Liquid Separation 15
D. MODELING OF RATE PROCESSES 18
E. CONCLUSIONS 24
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vi
Page
IV. APPLICATION TO DESIGN OF TREATMENT FACILITIES 24
A. SUMMARY 24
B. DESIGN METHODOLOGY AND ASSUMPTIONS 24
1. Flowsheet Development 24
2. Regeneration Cycle Configuration 24
C. FINAL DESIGN AND ECONOMIC ESTIMATES 27
1. Flowsheet 27
2. Design Calculations 30
A. PRESSURE VESSELS (EXTRACTION UNITS AND FLASH SEPARATORS) 30
B. HEAT EXCHANGERS 30
C. INDUSTRIAL GAS COMPRESSORS 31
D. INDUSTRIAL REFRIGERATION 31
3. Economic Analysis 31
D. CONCLUSIONS 33
LITERATURE CITED 36
NOMENCLATURE 39
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vii
LIST OF TABLES
Table Page
1 Solid-SCF Systems Investigated 4
2 Summary of Vapor Pressure Studies 8
3 Summary of Investment Costs (M$, 1991) 32
4 Summary of Operating Costs (M$/YR, 1991) 34
5 Comparison of Operating Costs for Regeneration of GAC 35
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viii
LIST OF FIGURES
Figure Page
1 Enhancement Factors for Model Compounds in Supercritical C02
at 50° C 5
2 Selectivity for Acridine from an Acridine/Anthracene Mixture 7
3 Schematic of Pilot Plant for GAC Regeneration Process 11
4 Adsorption of 2-Chlorophenol from Supercritical C02 13
5 Desorption of Toluene with Supercritical C02, Symbols are Data
of Tan and Liou 14
6 Desorption of Toluene in the Presence (#8) and Absence (#5)
of Water 16
7 Vapor-Liquid Equilibria in the 2-Chlorophenol/C02 System 17
8 Model Correlation of Exit Concentration Data for 2-Chlorophenol 20
9 Model Correlation of Desorbed Fraction of 2-Chlorophenol 21
10 Calculated Exit Concentration Profile for Scaled-up Desorber 22
11 Calculated Desorbed Fraction Profile for Scaled-up Desorber 23
12 SCF Recycling Option 1 25
13 SCF Recycling Option 2 26
14 Desorber Regeneration Cycle Sequence 28
15 SCF Regeneration Process Simulation Flowsheet 29
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1
I. INTRODUCTION
Environmental control and waste remediation are of immediate technological and political
interest. The problem of removing potentially toxic compounds from waste streams or spill sites
is exacerbated by their low concentrations and even lower allowable limits, which for some
compounds is defined as zero. With legislative controls on emissions and liability for contamination,
the demand for economical treatment processes is growing stronger.
Although removal of contaminants from waste streams is often considered an economic
liability, these problems have several potential solutions, some of which can be profitable. For
instance, DuPont is recycling the wastes from their acrylonitrile and adipic acid processes to recover
dibasic ester, 2-methylpentamethylenediamine, and acetonitrile which will yield an estimated $70
million in profits for 1990 (Reisch, 1990). This solution shows a creative yet serious response to
a problem which, until recently, has been ignored by industry and the government. Other wastes
may not be amenable to such a solution but the renewed commitment to clean-up is motivation for
development of separation and treatment technologies.
One technology which has great potential is contaminant removal and separation with
supercritical fluids (SCF's) or supercritical fluid extraction (SFE). In this process, a gaseous
component is compressed and heated to a pressure and temperature above its critical point where
it has a substantial density and high compressibility. The density of the SCF is intermediate
between that of a gas and a liquid, allowing the dissolution of non-volatile solid compounds up to
1-2 mole percent. The high compressibility in the supercritical region gives substantial changes in
density with small changes in pressure or temperature, allowing the solvent power of the fluid to
be "tuned" so that contaminant mixtures may be separated in a series of steps. The thrust of this
project has been to investigate experimentally and theoretically the solubility enhancement of non-
volatile model contaminant compounds in pure SCF's and cosolvent/SCF mixtures. Using a well
defined progression of experiments, we have developed a basic understanding of the physico-
chemical properties that influence phase behavior in supercritical systems.
Detoxification of soils, sludges and adsorbents such as granular activated carbon (GAC)
appear amenable to SCF extraction. Detoxification processes will primarily be batch operations
with widely varying feedstocks, a situation that demands a flexible separation strategy. Supercritical
fluid extraction and separation may prove economically viable in such circumstances as indicated
by model compound solubility studies and laboratory scale feasibility studies demonstrating its use
for the regeneration of GAC.
Supercritical fluid regeneration of GAC was first investigated by DeFilippi and co-workers
(1980,1983) using pesticides from industrial wastewaters and model compounds (DeFilippi, et al.,
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2
1980; DeFilippi and Robey, 1983). Regeneration with C02 maintained a stable working carbon
capacity after 31 cycles while thermal regeneration typically reduces capacity 5-10% per cycle. An
economic analysis showed that the processing costs depend predominantly on the specific waste
properties and the regeneration throughput. These costs were competitive with thermal
regeneration. All of their regeneration experiments, however, were performed at either 120° C or
225° C, which corresponds to reduced temperatures of 1.29 and 1.64, respectively. The reduced
temperature is the operating temperature divided by the critical temperature of the solvent. Most
of the unique characteristics of these fluids, such has high compressibility and high diffusivities,
appear in the region of reduced temperature between 1.01 and 1.1 and many workers have since
demonstrated the ability to extract contaminants from GAC and soil at these conditions (Brady, et
al., 1987; Dooley, et al., 1987; Tan and Liou, 1988,1989a, 1989b; Hess, et al., 1991). We demonstrate
here a pilot scale study of the SCF regeneration of GAC at 40° C (Tr = 1.03). The data obtained
from this study are coupled with economic analyses and computer aided design packages to produce
a scaled up design of a fixed-site unit to carry out this process.
II. BENCH-SCALE SCF STUDIES
A. SUMMARY
We undertook a concerted effort to understand the phase behavior in solid-SCF systems.
We determined solubilities of relatively non-volatile solid compounds in pure and cosolvent-
modified supercritical fluid solvents. Cosolvents (typically 1-5 mole percent of a small polar
compound) added to an SCF were shown to enhance solubilities and increase selectivities through
specific cosolvent-solute interactions. Vapor pressure measurements of several solutes were
determined to help isolate the effect of solute properties on the phase equilibria. Spectroscopic
investigations also aided the understanding of solubility enhancement by giving information about
the local environment around a solute in solution. Correlation of the solubility data has shown that
although cubic equations of state are very popular for calculating phase equilibria, they do not
completely describe the solid-SCF system due to the molecular asymmetry of size and energy.
B. RESULTS AND DISCUSSION
1. Solubility of Model Compounds
To establish a database suitable for correlation, interpolation and/or prediction of
solubilities, it was necessary to measure first the solubilities of a variety of solutes in several
supercritical fluids. We made measurements using a gravimetric, dynamic flow technique in several
apparatuses capable of operating in different temperature ranges (Johnston and Eckert, 1981). This
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3
arrangement allowed the study of near room temperature fluids (Carbon Dioxide, Ethane, Ethylene,
Fluoroform, Sulfur Hexafluoride), moderately high temperature fluids (Ammonia, Butane), and a
very high temperature fluid (Ethanol). Solubilities were measured for 21 solid compounds in one
or more of the solvents as shown in Table 1. In general, the solutes were chosen to exhibit a variety
of physical and chemical properties such as molecular size, polarity, acidity, basicity, and hydrogen
bonding ability. The matrix of solubilities is not full due to either immeasurable solubility in a
given solvent or the probable formation of a liquid phase in the system.
In terms of the absolute magnitude of solubility, the solvent power for the non-polar room
temperature fluids appears to increase in the order SF6 < C02 < C2H6 < C2H4. Solubilities are
generally higher in the moderate temperature fluids ammonia and butane than in ethane. The
solvent power of fluoroform increases with the dipole moment and is a better solvent for polar
solutes but not as good as carbon dioxide for non-polar compounds. For solutes of low volatility,
the absolute solubility will depend greatly on the choice of solvent since solubility always increases
with temperature at constant density. This indicates that although carbon dioxide is a convenient
solvent because it is non-flammable and non-toxic, butane (Tc = 152° C) may be a better choice for
many environmental applications.
The effect of solute properties on solubility is essentially two-fold: solubility depends on the
solute's volatility or vapor pressure and also on the strength of solute-solvent intermolecular forces.
In order to compare the latter effects, a dimensionless enhancement factor is used which is defined
as the ratio of a solute's partial pressure in the supercritical phase to its ideal gas partial pressure
or vapor pressure (Eq. 1).
By factoring out the solute's volatility, the enhancement factor allows comparison of solvent and
secondary solute effects. Empirically, there is a linear relation between the log of the enhancement
factor and solvent density. In fact, for the non-polar and polar solutes shown in Fig. 1 in
supercritical C02, the enhancement factor plots almost coincide indicating that differences in
solubility are due primarily to vapor pressure differences. Non-linear behavior is noted for high
solubilities (lO'MO1 mole fraction) as in the case of naphthalene in supercritical ethylene. The
enhancement in pure fluids is relatively independent of solute structure but is sensitive to solvent
polarity and density.
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Table 1. Solid-SCF Systems Investigal
Temperatures (C) for which Solubility Data hav
ed
e been taken
Solute
co2
CjH6
c2h4
CHF3d
SF6d
c4h10
NHje
CH3OHe
Naphthalene
45a
20,25,35,45b
25,45,50c
50
Anthracene
30,50,70b
30,35,50,70b
50,70,85°
162,182e
142,162
Phenanthrene
30,50,70b
30,40,60b
25,45,70b,c
30,50
Fluorene
30,35,50,70b
25,45,70b
Pyrene
35,50,70b
45,75b
Acridine
35,50,70d
35,50d
50
Phenazine
50*
Dibenzofuran
35,50,70d
35,50d
30,50
50
Thianthrene
50,70e
9-Fluorenone
35,50d
35,50"
30,50
Dibenzothiophene
35,50,70®
Hexamethylbenzene
30,50,70b
25,45,70b
Carbon Tetrabromide
35d
12,25d
Triphenylene
142
Dodecahydrotri-
phenylene
162,182
Xanthone
157
Thioxanthone
162,182
Anthraquinone
155,165
175,185'
5,6 Dimethyl-
benzimidazole
155,165
175,185'
9,10 Phenanthrene-
quinone
165,175'
6,13 Dihydro-
dibenzo[b,i] phenazine
275
"Ziger, 1983; "Johnston, et aL, 1982; 'Johnston and Eckert, 1981; dEckert, et al., 1985; eHess, 1987;
'Alferi, 1989; «Van Alsten, 1986
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FLUORENONE
rACRIDINE
DIBENZOFURAN
PHENANTHRENE
1
I
0.004
0.014
DENSITY (MOL/CC)
0.024
Figure 1. Enhancement Factors for Model Compounds in Supercritical C02 at 50°C
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6
2. Cosolvent Effects on Solubility
In pursuit of further solubility enhancements and solute selectivities, cosolvents (also known
as entrainers) may be added to an SCF. Cosolvents are normally used at concentrations of 1-5
mole percent with methanol and acetone being typical examples. In the case of a non-polar solute
containing no functional groups, the cosolvent induced solubility enhancement is quite similar for
all cosolvents and depends only on the concentration of cosolvent. This type of enhancement
apparently results from alteration of the solvent properties rather than any specific interaction.
In the case of a polar or heterocyclic solute, the nature of the cosolvent does become
important in the magnitude of the enhancement factor. If the solute is capable of participating in
hydrogen bonding or dipole-dipole interactions, a complementary cosolvent can be chosen to take
advantage of this property. This has been demonstrated in the case of 9-fluorenone/C02/MeOH
and Acridine/C02/MeOH (Van Alsten, 1986). It is these types of specific interactions that allow
one to tailor a solvent/cosolvent mixture to enhance the solubility of a particular solute. The
preferential enhancement of one solute from a mixture of solutes then leads to novel separation
process. The selectivity for acridine from a mixture of acridine and anthracene is shown in Fig. 2
(selectivity = solubility of acridine/solubility of anthracene). The addition of 1% methanol as a
cosolvent in supercritical C02 yields a substantial increase in the selectivity of acridine. This
enhancement is due presumably to a specific hydrogen bonding interaction between the hydroxylic
proton in methanol and the unpaired electrons on the amine nitrogen in acridine whereas
anthracene is not capable of participating in such an interaction.
3. Vapor Pressure Measurements
As mentioned previously, the volatility of a solute is the primary physical property that
determines its solubility in an SCF and is a necessary piece of information for calculating the
enhancement factor. Therefore, previously undetermined vapor pressures of model compounds
used in the solubility studies were measured. Vapor pressures were measured for 10 compounds
using a transpiration technique which allowed accurate measurements down to 5 millipascals.
Measurements were obtained for temperature ranges of interest for SCF processes as long as the
solute exhibited a pressure of a few mPa. The data have been recently published so only a summary
of the compounds and temperatures studied is given in Table 2 (Hansen and Eckert, 1986; Alferi,
1989). These data also provide a good measure of the heat of sublimation which can be used to
correlate energy parameters for equations of state. This property will always be a critical factor in
process design and feasibility studies for proposed SCF processes.
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PRESSURE (BAR)
Figure 2. Selectivity for Acridine from an Acridine/Anthracene Mixture
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Table 2. Summary of Vapor Pressure Studies
Compound
Range of Temperature (C)
Anthracene
40-90
Carbazole
110-180
Dibenzofuran
30-70
Dibenzothiophene
30-75
5,6-Dimethylbenzimidazole
110-180
9-Fluorenone
25-70
9,10-Phenanthrenequinone
140-190
Thianthrene
45-110
Triphenylmethane
30-85
Xanthone
110-160
4. Spectroscopic Measurements
Of the possible mechanisms for solubility enhancement, that of solvent "clustering" has
recently been given much attention. Measurements of the partial molar volume at infinite dilution
for four solutes in supercritical COa show a large negative dip in the near-critical region where the
isothermal compressibility of the solvent diverges to positive infinity. This was originally interpreted
in terms of the solvent clustering about the solute molecule and therefore reducing the total volume
of the solution (Eckert, et al., 1983,1986b). A solvent cluster of about 100 solvent molecules was
put forward although at present this number seems excessive. Recent spectroscopic measurements
in our laboratories and others (Brennecke, et al., 1990; Kim and Johnston, 1987; Yonker and Smith,
1988; Kajimoto, et al., 1988) have probed the local environment around a solute in the same highly
compressible region and do indeed indicate an excess number of solvent molecules near the solute
over what would be determined from the bulk density. This local density reaches approximately 3-4
times the bulk density in the region where the fluid has a high compressibility. Hence, there is now
a substantial body of experimental evidence for the idea of clustering which would help explain
enhancement factors for solutes in pure supercritical fluids.
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5. Models for SCF Phase Equilibria
The most widely used method for calculating high pressure gas phase thermodynamic
properties is the cubic equation of state (e.g., van der Waals, Soave-Redlich-Kwon, Peng-Robinson).
Various attempts have been made to modify the molecular interactions in these models to describe
more accurately the phase equilibria in the asymmetric solid-SCF system. Examples of this are the
Carnahan-Starling van der Waals equation (Johnston and Eckert, 1981) and the Augmented van der
Waals equation (Johnston, et al., 1982). It is also possible to adapt lattice theories which impose
a certain structure on the solution since the SCF is quite dense. An example of this is the
decorated lattice gas (Gilbert and Eckert, 1986). These models have had limited success in
correlating the solubilities or enhancement factors but are not yet predictive and do not correlate
cosolvent effects very well.
An approach for including cosolvent effects which appears promising is to treat the
cosolvent-solute interaction by the law of mass action with an equilibrium constant and couple this
chemical equilibrium with an equation of state that handles the physical interactions. These so
called chemical-physical models are very versatile but suffer from too large a number of adjustable
parameters. It may be possible to reduce the number of adjustable parameters, however, by
measuring equilibrium constants spectroscopically (Eckert, et al., 1986a). It is likely that the most
profitable applications of SCF technology will need to make use of cosolvent effects to "tailor" a
solvent for a particular solute and this type of model will likely be useful in the development of
these applications.
C. CONCLUSIONS
A substantial body of good experimental data for solubilities in pure and mixed SCF's over
a wide range of temperature has been established. This database along with vapor pressure
measurements has provided a proving ground for equation of state development. Spectroscopic
measurements have shown detailed molecular interactions of solutes in SCF's which can be used
to explain enhanced solubility and lead to further development of models. As a result of this work,
we can estimate from limited data the feasibility of applying SCF processing to a given separation.
III. PILOT-SCALE RESEARCH PROGRAM
A. SUMMARY
The ability of supercritical C02 to remove model contaminant compounds from GAC and
subsequently drop out most of the contaminant in a liquid phase has been investigated in a pilot
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10
scale apparatus. Model compounds, 2-chlorophenol and toluene, were chosen to represent common
features of hazardous waste chemicals such as aromaticity, acidity, and chlorination. Contaminants
were adsorbed onto GAC through either direct contact or by entrainment in a gas stream. Typical
desorption profiles indicate an 85% removal of the compound from the carbon. The presence of
water on the GAC was shown to inhibit slightly the efficiency of the desorption. Methanol was used
as a cosolvent for a desorption of 2-chlorophenol in which the carbon showed a net weight gain.
This indicates that although methanol can enhance the solubility of model compounds in an SCF
the GAC has a strong affinity for methanol which competes with the solvation process. The
desorption results have been interpreted with a generalized desorption-mass transfer model.
A series of near-Hxitical vapor-liquid equilibrium measurements have been carried out on
the 2-chlorophenol/C02 system. The effects of the presence of water as an impurity and methanol
as a cosolvent were also investigated.
B. EXPERIMENTAL
The pilot plant is a two-part apparatus designed to carry out SCF regeneration of GAC and
near-critical gas/liquid separations on a scale such that the data may be used directly in design
calculations for a detoxification unit with reasonable scale-up factors (Fig. 3). The two units are
a GAC regeneration or desorption bed and a contaminant separation flash vessel, which may be
operated separately or together. In addition to the pilot plant, another apparatus was constructed
similar to that used by Tan and Liou (1989a) for preparing "contaminated" GAC by adsorbing the
model compound onto the GAC from a nitrogen stream.
For GAC regeneration, liquid COz was pumped to operating pressure and brought to
temperature in a series of steam and cooling water heat exchangers. The system temperature and
pressure were monitored with a thermistor probe (OMEGA OL-703) and pressure transducer
(OMEGA PX302-3 KGV), respectively. Methanol was injected during the heat up stage by means
of a high pressure syringe pump (ISCO (iLC-500). The GAC bed consisted of an 18" long 3/8" OD
x 0.305" ID piece of stainless steel tubing which was loaded with a preweighed sample of
contaminated GAC. Glass wool plugs held the GAC in place during operation. An in-line high
pressure UV monitor (Milton Roy Critical Extraction Monitor) was located downstream of the
GAC bed to determine the concentration of contaminant in the SCF as a function of time. The
output from the UV had to be back calibrated from the final contaminant concentration determined
gravimetrically due to instrument deficiencies. Finally, the fluid mixture was flashed to atmospheric
pressure through a micrometering valve where the contaminant dropped out of solution and was
collected in a cold trap. The gas flow rate was monitored with a wet test meter.
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GAS CYLINDERS
rS
7S
¦?
STEAM
COMPRESSOR
-&
ENTRAIN ER
PUMP
r-Kt
TO GC
01
uu
CONTAMINANT
PUMP
~ COMPRESSOR
SWITCHING
VALVE
TO VENT
—
SWITCHING
VALVE
yl
COLDTRAP
TO GC
SWITCHING
VALVE
Figure 3. Schematic of Pilot Plant for GAC Regeneration Process
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12
The GAC was Calgon F-400 and was washed with distilled water once to remove fines, dried
under vacuum, then kept in a desiccator until ready for use. No screening for particle size was
carried out. Carbon dioxide was bone dry grade (99.0%) from Linde. The 2-chlorophenol (99 + %),
methanol (99.9%), toluene (99 + %), and water (HPLC grade) were obtained from Aldrich Chemical
Company and were used as received.
For near-critical vapor-liquid separation, C02 was pumped through the heat exchangers and
flashed through a micrometering valve into a separation vessel at a lower, but still elevated pressure.
The gas phase from the separation vessel was recompressed and recycled to provide a recirculating
flow while the liquid phase was pumped back to the top of the vessel to wash the gas stream. Once
the desired conditions stabilized, the contaminant was injected into the stream and allowed to
distribute between the two phases in the separation vessel. The vapor phase was then sampled and
analyzed by gas chromatography. When water or methanol was used, it was added before the
contaminant, and analysis was carried out before the contaminant was introduced.
C. RESULTS AND DISCUSSION
1. Adsorption/Desorption Studies
Regeneration experiments with C02 were carried out for 2-chlorophenol, 2-chlorophenol
with methanol cosolvent, toluene, and toluene in the presence of water at 40° C and 104 bar. Since
the temperature and pressure effects could be nominally predicted, these studies concentrated on
flow rate effects and desorption profiles.
In order to model the rate of desorption it is also desirable to know the adsorption profile
to help establish the equilibrium. We carried out the adsorption of 2-chlorophenol from
supercritical C02 at 173 bar and 50° C. This adsorption profile resulted in a maximum loading of
0.80 g/g GAC and was modeled with a Toth isotherm which correlates the data very well (Fig. 4).
To expedite preparation, further samples of GAC for the regeneration studies were prepared in a
low pressure system using nitrogen as the carrier.
Using the nitrogen adsorption method, 2-chlorophenol showed a loading of 0.53 g/g GAC,
while toluene adsorbed at 0.37 g/g GAC. These loadings were reproducible to within 2%.
The regeneration efficiency of C02 is defined as the percent of the initial concentration
removed during regeneration. The desorption profile for toluene is shown in Fig. 5 along with
literature data for this system (Tan and Liou, 1989b). The data are plotted as a function of a
dimensionless volume (volume of fluid at bed conditions/volume of GAC) in order to compare
between our data and the literature data. There is quite good agreement with the literature despite
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13
O EXPT'L
TOTH ISOTHERM
So
so
o /
10 10 "5 10 -2 10
MOLE FRACTION 2-CHL0R0PHEN0L
Figure 4. Adsorption of 2-ChIorophenol from Supercritical C02
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14
100Q
a
•-B
$
CJ
8
a
a
a
80 ~
60-
40 *
O 318K 87atm
A 308K 87atm
• 318K 136atm
~ 308K 136atm
— 313K 101atm Ext. Run 5
Volume *
Figure 5. Desorption of Toluene with Supercritical C02, Symbols are Data of Tan and Liou
(Volume* = Dimensionless Volume Defined in Text)
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15
differences in temperature, flow rate, and GAC. Figure 6 shows the effect of water on the
desorption of toluene. The regeneration efficiency was 96% without water and 85% with water but
the initial rates of desorption (indicated by the slope of the desorption profile) are similar for both
cases. Water apparently has a shielding effect for low concentrations of toluene.
Efficiencies of 85% and 89% were observed for 2-chlorophenol. In early studies the flow
rate of C02 was varied to attempt to reach the mass transfer limit in terms of superficial velocity
of solvent. This is the point at which the solvent velocity is too fast for the concentrations in each
phase (adsorbed and SCF) to equilibrate. We were not able to attain velocities sufficiently large
to deviate from an equilibrium desorption process. Methanol was added as a cosolvent to try to
increase the regeneration efficiency but it appears to adsorb onto the carbon from the SCF phase
and does not help. The GAC actually gained weight during a desorption run using methanol as a
cosolvent.
The regeneration efficiency is apparently determined by two competing effects, solvation and
adsorption. The solvation is dictated by thermodynamic equilibrium and can be estimated using the
models described above for solid-SCF phase equilibria. Generally, high pressures will give higher
solubilities of contaminants. The adsorption is determined strongly by the characteristics of the
GAC which are by no means general. Such things as surface area per unit volume, heat treatment,
and particle size, affect the adsorption/desorption properties but little can be done to predict these
effects. Usually adsorption/desorption experiments must be carried out for compounds of interest
and the results fit to a model, as was shown above, which can then be extended in pressure and
temperature space for that compound only. Through repetitive cycles, other investigators have
demonstrated sufficiently that SCF regenerated carbon retains consistently higher adsorption
capacity than steam regenerated carbon (DeFilippi, et al., 1980; Tan and Liou, 1988).
2. Near-Critical Gas/Liquid Separation
The systems studied for separation include 2-chlorophenol/C02,2-chlorophenol/water/C02,
and 2-chlorophenol/methanol/C02. The concentrations of water and methanol were both 5 mole
percent. The results from these experiments are shown in Fig. 7 as vapor concentration vs. liquid
concentration. For a successful separation to occur, the contaminant must preferentially distribute
into one of the two phases leaving the other phase relatively pure. This distribution will show up
as a deviation of the data from the 45° line, which in the figure rises steeply away from the data
due to the scale of the axes. The data indicate that most of the contaminant is in the liquid phase
and that it would be possible to recycle the vapor phase as a solvent and concentrate the
contaminants in a liquid phase.
-------
16
100
o 4 1 —i 1 1 1 1 1
0 10000 20000 30000 40000
Volume*
Figure 6. Desorption of Toluene in the Presence (#8) and Absence (#5) of Water
(Volume* = Dimensionless Volume Defined in Text)
-------
4000
3000
a
0,
3.
~a
o
V3
PI
u
a
!>
2000 -
1000 -
/ 0
Run 5: 2-chlorophenol
I •
Run 6: 2-chlorophenol
1 n
Run 7: 2-chlorophenol / water (5%)
1 A
Run 8: 2-chlorophonol / MeOH (5%)
r~\l
•
Lit
-
-j
0 I
•
~
In
V_l
~
/
~
CI
/
•
/
~
1
•
1
O
1
O
1 • O ~
/
~
1 °
A A
A
A
n ¦ — 1 1 ¦ 1 ¦
10000 20000 30000
liquid Concentration (ppm)
40000
Figure 7. Vapor-Liquid Equilibria in the 2-ChIorophenoI/COz System
-------
18
D. MODELING OF RATE PROCESSES
Several recent publications discuss models for supercritical regeneration of GAC; Tan and
Liou (1988) present a model for the desorption of ethyl acetate which assumes no axial dispersion
and which approximates the desorption kinetics as being linearly related to the adsorbed
concentration. The resulting equation for desorption bed outlet concentration, C(L,t) is:
C(L,t) = C lex]
+H
aLjj-exp(-kl)
(2)
where k is defined as the kinetic desorption constant given by:
dC.
—^ = -kC,
a
(3)
Recasens, et al. (1989) improved upon this model by incorporating the solid-SCF equilibrium and
external mass transfer coefficient explicitly, assuming a parabolic concentration profile inside the
particles. Analytical solutions were developed for two cases: 1) where equilibrium desorption occurs
and is controlled by the external and intraparticle mass transfer rates and 2) where a first-order
irreversible desorption step is controlling. The first of these is found to effectively describe the
supercritical desorption of ethyl acetate. The solutions for exit concentration and desorbed fraction
from carbon with an initial concentration C„ are:
exp[-(b+b/)0][exp(b+b')-l]
CyK b+b
+ exp[-(b+b')(0-l)]]jn (-l)m+1
m-0
fb)mAm(b/) AJb'd-6)]
(4)
vb7/
(m^-
where
e = JL
L«
b- 3kPL«
r0(p +pK)u
b/ = 3(1'tt)kpL
r0u
(4a)
-------
19
and Am is related to the incomplete gamma function and is calculated from:
Aq = 1 - exp(-w); m=0
Am = Am-iCw) ~ wmexp(-w); mil
(5)
The equilibrium constant K rigorously denotes the equilibrium between adsorbed concentration and
concentration in the pore fluid:
c. = KC«»
• pore
(6)
The desorbed fraction is given by Eq. 7. We found the first four terms in the summation sufficient
to approximate the series.
F =
b+b'
j _ exp[-8(b + b0][exp(b + bQ -1]
b+b'
1 j; AJbO Am[b(0-1)]
b+b'm-o (ml):
b
(7)
(b+b^b
-/exp[-(b+b/)(0-l)]]C(-l)"*1
mm
^r^cbKlbd-e)]
kb'J (m!)2
In this work the data for SCF regeneration of GAC adsorbed with 2-chlorophenol has been
modeled with these equilibrium desorption/mass transfer equations. Optimal fits for the
equilibrium constant K and the overall mass transfer coefficient, kp, were obtained by visual
inspection using MathCAD software on a Compaq 286 computer. It is apparent the observed
desorbed fraction may be reasonably predicted for a range of K, kp combinations, but in order to
simultaneously model the exit concentration, the values are constrained to a single pair. Figures
8 and 9 display a series of data in comparison with predicted values. The fitted values for
equilibrium and mass transfer coefficients are 2.5 x 10"2 m3/kg and 5.7 x 10"7 m/s, respectively.
These were used in the design study to determine cycle times and regeneration effectiveness for
various fluid flow rates and bed lengths. Representative results for u = .05 m/s and 10 m bed
length are shown in Figs. 10 and 11.
-------
20
Concentration vs. Time
2-ChlorophenoI Extraction
Time, seconds
(Thousands)
¦*— Measurement —'— Model
Figure 8. Model Correlation of Exit Concentration Data for 2-Chlorophenol
-------
21
Desorbed Fraction vs. Time
2-Chlorophenol Extraction
Time, seconds
(Thousands)
Measurement —«— Model
Figure 9. Model Correlation of Desorbed Fraction of 2-Chlorophenol
-------
Concentration vs. Time
Plant Design Case
Time, seconds
(Thousands)
Figure 10. Calculated Exit Concentration Profile for Scaled-up Desorber
-------
Desorbed Fraction vs. Time
Plant Design Case
(Thousands)
Figure 11. Calculated Desorbed Fraction Profile for Scaled-up Desorber
-------
24
E. CONCLUSIONS
A pilot plant for the regeneration of GAC using supercritical fluids was constructed and
operated demonstrating the feasibility of this application. Several contaminants were investigated
including 2-chlorophenol which was deemed to represent a difficult desorption and provide a
conservative basis for design. Phase equilibria measurements were made on the systems
2-chlorophenol/C02 and 2-chlorophenol/methanol/C02 and equation of state parameters likely to
affect the regeneration process.
IV. APPLICATION TO DESIGN OF TREATMENT FACILITIES
A. SUMMARY
The results of the pilot plant studies have been applied to the design of a fixed-site GAC
regeneration unit consisting of a three element desorber with two stage flash separation.
Optimization of the process centers around minimizing the cost of recycling the SCF through an
efficient recompression scheme and cycle configuration in the desorber unit. An economic
evaluation shows a processing cost of 10.60/lb GAC. This non-destructive process allows re-use of
the GAC reducing carbon replacement costs and significantly decreases carbon disposal by landfill
or incineration.
B. DESIGN METHODOLOGY AND ASSUMPTIONS
1. Flowsheet Development
Previous studies and industrial practice has shown that direct recycling of vapors (via
recompression to supercritical pressure) is problematic in that demisting of the entrained solute is
difficult and costly due to high compression of large vapor flows. An alternative which is often
lower cost and is operationally superior is to condense the flashed vapors, pump the liquid phase
to the desired pressure, and then heat to operating temperature. These concepts denoted as
Options 1 and 2, respectively, are shown in Figs. 12 and 13. Each of these options has been
simulated with ChemCAD version 2.41 process simulation software.
2. Regeneration Cycle Configuration
The regeneration data for 2-chlorophenol indicates the mass transfer kinetics are limiting.
Thus the exit concentrations are not approaching the SCF solubility limits at any time, most
particularly during the last half of the desorption cycle time. Consequently, it is advantageous to
use a progressive sequence in which the SCF from a bed in the last half of its cycle is used to
-------
GAC
BED
AFTERCDDLER
FLASH
VESSEL
V/F NEAR
1.0
to
Lr\
\ RFMnVED \
7 SDLUTE /
~ PTIDN 1
Figure 12. SCF Recycling Option 1
-------
K)
~PTIDN 2' IMPRDVED FLOWSHEET
Figure 13. SCF Recycling Option 2
-------
27
accomplish the first half of the cycle of another bed. With three beds as a unit, the cycle sequence
is shown in Fig. 14.
The final flowsheet adopts this approach, minimizing cost of recycling the fluid and keeping
the exit concentration fairly stable as a function of time. It is an assumption of this configuration
that the individual regeneration vessels are being emptied of regenerated carbon and refilled during
the off-line time. One half of a complete regeneration cycle should be adequate for the solids
handling steps.
The model developed via analysis of the experimental data was used to examine the effects
of bed height and fluid velocity over practical ranges. The optimal superficial velocity was
determined by increasing the flow until further increments no longer result in decreased cycle time.
This limit exists because the mass transfer rate is the desorption rate limiting step. A superficial
velocity of 4.0 ft/min was found to be optimal and was adopted for the final flowsheet and economic
analysis.
The cost calculations and analyses were performed on a computer spreadsheet (Quattro
Pro). Cost/capacity relationships for major equipment inserted in the spreadsheet have been
derived from cost data presented in Peters and Timmerhaus (1980) and Guthrie (1974).
The chemical engineering cost index for CPI industry was used to convert purchased costs
to a 1991 basis. The Guthrie (1974) data includes ratios for total installed costs to purchased costs
for each type of equipment, and these are used to develop the Direct Capital Investment. Ratios
for Indirect Capital are taken from Peters and Timmerhaus (1980).
C. FINAL DESIGN AND ECONOMIC ESTIMATES
1. Flowsheet
The predominant factor determining operating feasibility and overall economy is the SCF
recycle efficiency. As discussed previously, the condensation of vapors from the first flash with a
liquid pump for recompression and a gas compressor from the secondary flash vapors is much more
economical than recompressing a vapor stream from a single flash. This scheme is more energy
efficient primarily because the operating temperature of the facility is not far removed from
ambient. This recycle scheme has been incorporated into a process simulation flowsheet along with
the 3-unit desorber described above. The flowsheet is shown in Fig. 15.
-------
K>
00
THIRD 1/2 CYCLE TIME
REGENERATION CYCLE CONFIGURATION
Figure 14. Uesorber Regeneration Cycle Sequence
-------
Figure 15. SCF Regeneration Process Simulation Flowsheet
-------
30
2. Design Calculations
For ease of use in the spreadsheet, all graphical data from various sources have been fit to
equations. Base cost is in the year given by Guthrie (1974) or Peters and Timmerhaus (1980) with
appropriate cost indices applied to determine costs in 1991 dollars.
A. PRESSURE VESSELS (EXTRACTION UNITS AND FLASH SEPARATORS)
Base cost in 1970 dollars for a vessel of diameter D (ft) operating at pressure P(psig):
C™ = 294 D1825 (8)
Cost factors for pressure (Fp) and internal support (Cint) are given by:
Fp = 0.057 P0625
C™ = 35.2 D137
For pressure vessels, the ratio of direct capital to purchased cost is 3.0 (Guthrie, 1974),- thus, the
total direct capital (DC^,) in 1991 dollars is:
DC^ = TiFp[C^+c^*3-0 (10)
No allowances were made for stainless steel or better alloys. If specific applications require alloy
construction, capital costs will increase accordingly.
B. HEAT EXCHANGERS
Base cost in 1979 dollars for an exchanger with surface area A (ft2):
c£= 547 A0M3 (11)
The cost factor for pressure in excess of 1000 psig is given by:
Fp = 0.575 + 4.14x10"4P
(12)
-------
31
The ratio of direct capital to purchased cost is 2.30 for heat exchangers giving a total direct capital
of:
= !||fpc£*2.30 (13)
C. INDUSTRIAL GAS COMPRESSORS
Costs for compressors, up to 3-stage with intercooling, are given by:
C£ = 2.59 q0317 (14)
where q is the intake flow in actual cubic feet per minute. The direct capital ratio is 1.57 and total
direct capital is then:
DCcmp = —-C™ *1.57 (15)
®p 230
D. INDUSTRIAL REFRIGERATION
The flowsheet includes condensation of C02 at 51°F, thus requiring an ammonia
refrigeration loop. The cost for this system and its operation costs are calculated as follows: the
unit cost, in 1979 dollars, for a QRF ton (1 ton = 12,000 BTU/hr) unit operating at 20° F, is:
c£ - 3.098 (16)
Operating costs are approximately $1.20/ton-day and the direct capital ratio is 3.46, therefore, the
total direct capital is:
DCS " (17)
3. Economic Analysis
The design presented is a fixed-site unit with a regeneration capacity of 24 tons of GAC per
day. The capital cost does not include equipment for steam generation and so assumes that the
plant is part of a larger industrial unit from which steam is supplied at $1.50/1000 lb and cooling
water at $1.00/10,000 gal. A summary of the direct capital investment costs is given in Table 3.
Indirect costs are estimated as 38% of direct costs, then fees and contingencies are 25% of direct
-------
32
Table 3. Summary of Investment Costs (M$, 1991)
Direct Capital Costs:
Extraction Vessels
345.7
Primary Flash Vessel
19.8
Reboiler for Primary Flash
42.1
Secondary Flash Vessel
3.8
Condenser
84.2
Refrigerated Condensate Loop
93.1
High P Liquid Pump
43.4
Heater for High P Liquid
49.2
Secondary Flash Recycle Compressor
93.1
After Cooler
72.6
Blowdown Recycle Compressor
49.2
After Cooler
1.8
Process Control/Instrumentation
250.0
Unlisted Equipment (35% of Total Dir.)
483.5
Total Direct Capital
1,631.5
Indirect Costs (0.38 x Direct Costs)
620.0
Fees and Contingency
(0.25 x Dir. + Ind.)
562.9
Working Capital (15% of Total Capital)
496.6
Total Capital Investment
3,310.9
-------
33
plus indirect costs. The total capital investment for the unit is 3.3 million dollars. Table 4 is a
summary of operating costs for the regeneration unit on the basis of one operator per shift (24 hr
operation), 0.5% loss rate for the SCF, and 4(t/lb replacement costs for COz, yielding a regeneration
cost of 10.6e/lb.
Table 5 lists our costs along with those reported by DeFilippi and co-workers (1980,1983)
for phenol, dinitrobutylphenol, atrazine, and an estimate for thermal regeneration. Comparisons
of treatment costs with thermal regeneration are favorable. In addition to maintaining a stable
capacity, SCF regeneration is consistently less expensive than thermal treatment. The final
alternatives are incineration or disposal by landfill. Incineration of soils containing hazardous
wastes is at least 20e/lb for a similar scale unit (EPA Engineering Bulletin, 1990). This process
compares favorably both economically and ecologically with the alternatives.
D. CONCLUSIONS
A 24 ton/day fixed-site regeneration plant has been designed and examined for economic
feasibility. The estimated capital and operating costs are valid within approximately 30%. If a
small, mobile unit were to be built, the operating costs would be somewhat higher due to an
economy of scaling which favors larger units and, the infeasibility of including a refrigeration system,
forcing the use of the high cost flowsheet option which requires only cooling water.
The cost of this process compares favorably with thermal regeneration, the most often
chosen alternative, but has the distinct advantage of maintaining a stable adsorbate capacity. This
many-cycle regenerative use reduces carbon replacement costs and avoids disposal of spent material.
-------
34
Table 4. Summary of Operating Costs (M$/YR, 1991)
Direct Production Costs:
Make-up C02
271.4
Operating Labor
200.0
Direct Supervision
40.0
Utilities: Electricity
Steam
Cooling Water
162.4
142.1
2.5
Maintenance (7% of T.C.I.)
231.8
Operating Supplies (15% of Maint.)
34.8
Laboratory Charges
(15% of Op. Labor)
30.0
Fixed Charges:
Depreciation
163.1
Taxes and Insurance
(3% of Fixed Cap.)
67.5
Plant Overhead
(60% of Op. Lab. + Sup. + Maint.)
283.1
Administrative Costs
(15% of Op. Lab. + Sup. + Maint.)
70.8
Total Treatment Cost
1,699.4
Unit Treatment Cost
10.6 e/lb
-------
35
Table 5. Comparison of Operating Costs for Regeneration of GAC
Contaminant
Capacity/Throughput
(Ton/Day)
Reported Unit
Cost
(0/lb)
Adjusted Unit
Cost"
(*/lb)
2-Chlorophenol
24
10.6
10.6
Atrazine
2.5
14b
29
Dinitrobutylphenol
1
29b
46.2
Phenol
5
8.5°
16.1
Thermal Regeneration
29-36b
46-57
Incineration (From Data on Soils)
•o
00
1
00
20-53
"Adjusted to 1991 dollars assuming 6% inflation
b1983 dollars
c1980 dollars
d1989 dollars
-------
36
LITERATURE CITED
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Urbana, IL.
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Brennecke, J.F., Tomasko, D.L., Peshkin, J., and Eckert, C.A., "Fluorescence Spectroscopy of Dilute
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DeFilippi, R.P., Krukonis, V.J., Robey, R.J., and Modell, M., "Supercritical Fluid Regeneration of
Activated Carbon for Adsorption of Pesticides," EPA Report EPA-600/2-80-054, 1980,
United States Environmental Protection Agency, Washington, DC.
DeFilippi, R.P. and Robey, R.J., "Supercritical Fluid Regeneration of Adsorbents," EPA Report
EPA-600/2-83-038,1983, United States Environmental Protection Agency, Washington, DC.
Dooley, K.M., Kao, C-P., Gambrell, R.P., and Knopf, F.C., "The Use of Entrainers in the
Supercritical Extraction of Soils Contaminated with Hazardous Organics," I&EC Res., 1987,
26, 2058.
Eckert, C.A., Ziger, D.H., Johnston, K.P., and Ellison, T.K., "The Use of Partial Molal Volume Data
to Evaluate Equations of State for Supercritical Fluid Mixtures," Fl. Phase. Equil., 1983, 14,
167.
Eckert, C.A., Hansen, P.C., and Ellison, T.K., "Solute Enhancement Factors in Supercritical
Solutions," submitted to Fluid Phase Equilibria, 1985.
Eckert, C.A., McNiel, M.M., Scott, B.A., and Halas, L.A., "NMR Measurements of Chemical Theory
Equilibrium Constants for Hydrogen-Bonded Solutions," AIChE J., 1986a, 32(5), 820.
Eckert, C.A., Ziger, D.H., Johnston, K.P., and Kim S., "Solute Partial Molal Volumes in
Supercritical Fluids,"/. Phys. Chem., 1986b, 90, 2738.
Environmental Protection Agency, "Mobile/Transportable Incineration Treatment," Engineering
Bulletin, 1990, EPA/540/2-9/014, Office of Research and Development, Cincinnati, OH.
-------
37
Gilbert, S. and Eckert, C.A., "A Decorated Lattice-Gas Model of Supercritical Fluid Solubilities and
Partial Molar Volumes," Fl. Phase Equil., 1986, 30, 41.
Guthrie, K.M., Process Plant Estimating Evaluation and Control. Craftsman Book Company of
America, Solona Beach, CA, 1974.
Hansen, P.C. and Eckert, C.A., "An Improved Transpiration Method for the Measurement of Very
Low Vapor Pressures," / Chem. Eng. Data, 1986, 31, 1.
Hess, B.S., "Supercritical Fluids: Measurement and Correlation Studies of Model Coal Compound
Solubility and the Modeling of Solid-Liquid-Fluid Equilibria," PhD Thesis, 1987, University
of Illinois, Urbana, IL.
Hess, R.K., Erkey, C., and Akgerman, A., "Supercritical Extraction of Phenol from Soil," J.
Supercritical Fluids, 1991, 4, 47.
Johnston, K.P. and Eckert, C.A., "An Analytical Carnahan-Starling-van der Waals Model for
Solubility of Hydrocarbon Solids in Supercritical Fluids," AIChE J., 1981, 27(5), 773.
Johnston, K.P., Ziger, D.H., and Eckert, C.A., "Solubilities of Hydrocarbon Solids in Supercritical
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Kajimoto, O., Futakami, M., Kobayashi, T., and Yamasaki, K., "Charge-Transfer-State Formation
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1347.
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-------
38
Tan, C-S. and Liou, D-C., "Desorption of Ethyl Acetate from Activated Carbon by Supercritical
Carbon Dioxide," I&EC Res., 1988, 27, 988.
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Carbon Dioxide," Sep. Sci. Tech., 1989a, 24(1,2), 111.
Tan, C-S. and Liou, D-C., "Supercritical Regeneration of Activated Carbon Loaded with Benzene
and Toluene," I&EC Res., 1989b, 28, 1222.
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Supercritical Solvents," PhD Thesis, 1986, University of Illinois, Urbana, IL.
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Supercritical Fluids,"/. Phys. Chem., 1988, 92, 235.
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Molar Volumes and Solubilities," PhD Thesis, 1983, University of Illinois, Urbana, IL.
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39
NOMENCLATURE
Symbols
A - Heat transfer area
Am(w) - Incomplete gamma function
b,b' - Dimensionless groups defined in Eq. 4a
C - Concentration in SCF phase
C70 - Cost in 1970 dollars
C79 - Cost in 1979 dollars
D - Diameter
DC91 - Direct capital costs in 1991 dollars
E - Enhancement factor
F - Fraction desorbed
Fp - Cost factor for pressure
K - Adsorption equilibrium constant
k - Desorption rate constant
kp - Overall mass transfer coefficient
L - Length of carbon bed
P - Pressure
Q - Refrigeration system capacity
q - Compressor intake flow rate
rD - GAC particle radius
t - Time
u - Superficial velocity of fluid at T and P of bed
w - Dummy variable in incomplete gamma function
Superscripts
sat - Saturation (VLE or SVE boundaiy)
Subscripts
a
- Adsorbed phase
cmp
- Compressor
hx
• Heat exchanger
int
- Internal support
0
- Initial
pore
- Fluid in pore
rf
- Refrigeration system
vsl
- Pressure vessel
Greek
Symbols
a
- Void fraction of GAC bed
P
- Porosity of GAC particles
e
- Dimensionless time defined in Eq. 4a
p
- Density of GAC particles
------- |