PB87-102273
Correlations for the Determination of
Surface Diffusivities of Organic Chemicals
Adsorbed onto Granular Activated Carbon
Michigan Technological Univ., Houghton
Prepared for
Environmental Protection Agency, Cincinnati, OH
Sep 86
U:S. DepariRtaat tf Commerce
focfe»c3l Information Service
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TECHNICAL REPORT OATA v I
Illrtir rrad Intlrui I;I>H\ IHI Ilir rrirrii' N !<>rr < «mp/f imgl \
i REPORT NO i
EPA/600/2-86/082
4. TITLE AND SUBTITLE
CORRELATIONS FOR THE DETERMINATION OF SURFACE DIF-
FUSIVITIES OF ORGANIC CHEMICALS ADSORBED ONTO GRANULAR
ACTIVATED CARBON
». AUTHORIS)
Mark Dobrzelewski
9 PERFORMING ORGANIZATION NAME AND ADDRESS
Michigan Technological University
Houghton, Michigan 49931
12. SPONSORING AGENCY NAMS AND ADDRESS
Water Engineering Research Laboratory- Cincinnati, OH
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, OH 45268
RICIPIINTS ACCESSION NO 1
r-Joi ,. .- ..2:?3/AS
REPORT DATE 1
September 1986 I
6. PERfORMING ORGANIZATION CODE 1
8. PERFORMING ORGANIZATION REPORT NO I
• 1
10. PROGRAM ELEMENT NO. 1
11. CONTRACT/GRANT NO. 1
CR 811150 by-product
13. TYPE OF REPORT AND.PERIOD COVERED 1
Published Paper
14. SPONSORING AGENCY CODE 1
:PA/600/14 1
IS SUPPLEMENTARY NOTES 1
Project Officer: B. Lykins, (513/569-7460)
Master of Science in Chemical Engineering Thesis
16. ABSTRACT
Differential column batch reactor (DCBR) experiments in organic-free water were
conducted for the following volatile organic compounds (VOCs): trichloroethene,
tetrachloroethene, cis-1,2 dichlorethene, and toluene. Surface diffusion was required
to explain the rate of uptake for the VOCs, and the contribution of pore diffusion was
determined to be negligible. Since considerable time is required to conduct a DCBR
study, a correlation was developed for the surface diffusion based on the liquid
diffusivity of the adsorbates and the physical properties of the activated carbon.
The correlation can be used to calculate the surface diffusivities of halogenaterf one-
and two-carbon molecules and some aromatic substituted organic compounds for two types
of carbons. The significance of this correlation is that it can be used to calculate
the mass transfer zone lengths of VOCs in a fixed-bed adsorber with a fair amount of
precision.
17. KEY WORDS AND DOCUMENT ANALYSIS |
1. DESCRIPTORS
•
ifl- DISTRIBUTION STATEMENT
RELEASE TQ PUBLIC
b.lOENTIFIERS/OPEN ENDED TERMS
19 SECURITY CLASS iTIlll Rrporl}
UNCLASSIFIED
2O SECURITY CLASS iTlHipatei
UNCLASSIFIED
c. COSATI Field/Group 1
21. NO OF PAGES
162
22. PRICE
FWIM 2220-1 (R»». 4-77) PUCVIDU* COITION is OBIOLCTC
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PB87-102273
EPA/600/2-86/082
September 1986
CORRELATIONS FOR THE DETERMINATION OF SURFACE DIFFUSIVITIES OF
ORGANIC CHEMICALS ADSORBED ONTO GRANULAR ACTIVATED CARBON
by
Mark Dobrzelewski
Michigan Technological University
Houghton, Michigan 49931
Cooperative Agreement CR 811150
Project Officer
Benjamin Lykins
Drinking Water Research Division
Water Engineering Research Laboratory
Cincinnati, Ohio 45268
WATER ENGINEERING RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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DISCLAIMER
Although the research described in this article has been funded wholly or
in part by the United States Environmental Protection Agency, it has not been
subjected to the Agency's peer and administrative review and therefore may not
necessarily reflect the views of the Agency and no official endorsement should
be inferred.
ii
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FOREWORD
The U.S. Environmental Protection Agency is charged by Congress with
protecting the Nation's land, air, and water systems. Under a mandate of
national environmental laws, the agency strives to formulate and implement .
actions leading to a compatible balance between human activities and the
ability of natural systems to support and nurture life. The Clean Water Act,
the Safe Drinking Water Act, and the Toxics Substances Control Act are three
of the major congressional laws that provide the framework for restoring and
maintaining the integrity of our Nation's water, for preserving and enhancing
the water we drink, and for protecting the environment from toxic substances.
These laws direct the EPA to perform research to define our environmental
problems, measure the impacts, and search for solutions.
The Water Engineering Research Laboratory is that component of EPA's
Research and Development program concerned with preventing, treating, and
managing municipal and industrial wastewater discharges; establishing
practices to control and remove contaminants from drinking water and to
prevent its deterioration during storage and distribution; and assessing the
nature and controllability of releases of toxic substances to the air, water,
and land from manufacturing processes and subsequent product uses. This
publication is one of the products of that research and provides a vital
communication link between the researcher and the user community.
In treating drinking water to remove synthetic organic chemicals., granular
activated carbon is used, the research reported here considers the surface
diffusivities of organic chemicals adsorbed onto granular activated carbon.
francis T. Mayo, Director
Water Engineering Research Laboratory
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ABSTRACT
Differential column batch reactor (DCBR) experiments in organic-free water
were conducted for the following volatile organic compounds (VOCs):
trichloroethene, tetrachlcroethene, cis-1,2 dichlorethene, and toluene.
Surface diffusion was required to explain the rate of uptake for the VOCs, and
the contribution of pore diffusion was determined to be negligible. Since
considerable time is required to conduct a DCBR study, a correlation was
developed for the surface diffusion based on the liquid diffusivity of the
adsorbates and the physical properties of the activated carbon. The
correlation can be used to calculate the surface diffusivities of halogenated
one- and two-carbon molecules and some aromatic substituted organic compounds
for two types of carbons. The significance of this correlation is that it can
be used to calculate the mass transfer zone lenghts of VOCs in a fixed-bed
adsorber with a fair amount of precision.
This research work was supported by U.S. Environmental Protection Agency
cooperative agreement CR 811150-01-0.
iv
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TABLE OP CONTENTS
page
TABLE OF CONTENTS V
LIST OF TABLES 1x
LIST OF FIGURES xi
I. INTRODUCTION 1
II. EXPERIMENTAL PROCEDURES 4
A. Chemicals Used in Experiments 4
B. Carbons Used in Experiments 4
C. Water Matrices Used in Experiments 4
D. Carbon Preparation and Characterization 5
E. Chemical Analysis 6
;F. Eqn il ibr ium I sotherm P-roc-edur-e..-, ..; 7
G. Differential Column Batch Reactor Procedure 7
1. Previous Designs 7
2. Chosen Design to Conduct Kinetic Studies 7
III. MODEL FRAMEWORK FOR THE BATCH HOMOGENEOUS SURFACE
DIFFUSION MODEL 10
A. Previous Work 10
B. Model Mechanisms and Assumptions , 12
C. Equations Describing the Mult icomponent BHSDM 12
D. Dimensionless Groups Which Describe th«
Mnlticomponent BHSDM . 15
IV. MODEL FRAMEWORK FOR THE BATCH PORE AND SURFACE
DIFFUSION MODEL 17
A. Previous Work 17
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B. Model Mechanisms and Assumptions 17
C, Equations Describing the Mult icomponent BPSDM 18
D. Dimensionless Groups Which Describe the
Mult icomponent BPSDM 21
V. PRELIMINARY CALCULATIONS AND CRITERIA NEEDED CONDUCT A
SUCCESSFUL DIFFERENTIAL COLUMN BATCH REACTOR STUDY 23
A. Representative Sample from the B&tch Reactor 23
B. Obtaining a Representative Carbon Sample 24
C. Temperature Dependence of Equilibrium and
Kinetic Parameters 24
D. Effect of the Liquid-Phase Mass Transfer Rr;ce 24
E. Calculation of the Concentration Gradient Across the
Differential Carbon Column 25
VI. COMPARISON OF THE MATHEMATICAL MODELS USED TO SIMULATE THE
DIFFERENTIAL COLUMN BATCH REACTOR 28
A. Single Solute Batch Rate Results 28
B. Equilibrium Times and Concentrations for the Differential
Column Batch Reactor Studies...... 39
C. Multicoijponent Results for the Wansau Water Matrix 41
1. Batch Rate Results Using Thawed
Wausau Water Matrix 41
2. Multicomponent Results Using Fresh
Wausau Water Matrix 45
3. Degradation Results of the Wausau Water Matrix 46
VII. SENSITIVITY ANALYSIS OF THE PARAMETERS WHICH CHARACTERIZE
THE SOLUTIONS TO THE DIFFERENTIAL COLUMN BATCH REACTOR 50
A. Sensitivity Analysis of the Liquid-Phase Mass Transfer
Rate and the Intraparticle Diffusion Pate in the
Determination of the Surface Diffusion Rate 50
B. Sensitivity Analysis of the Frenndlich Isotherm
Parameters K and 1/n in the Determination of the
Surface Diffusion Rate 59
VIII. CORRELATIONS FOR THE DETERMINATION OF
SURFACE DIFFUSIVITIES 66
A. Correlation Based on the Boiling Point of the Adsorbates 66
VI
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B. Correlation Based on the Liquid Diffusivity and the
Partitioning Evaluated at the Initial Concentration
of the Adscrbates.. 66
C. Correlation Based on the Liqnid Diffusivity and the
Average Driving Force of the Adsorbates 69
D. Correlation Based on the Self-Diffnsivity and the
Partitioning Evaluated at the Initial Concentration
of the Adsorbates 70
E. Results and Discussion 71
IX. CONCLUSIONS AND RECOMMENDATIONS 81
A. Conclusions 81
B. Recommendations for Future Work....' 83
APPENDIX 1. REFERENCES 85
APPENDIX 2. NOMENCLATURE 88
APPENDIX 3. TRACE ORGANICS RESEARCH EQUIPMENT CLEANING
PROCEDURE 92
A. Glassware 92
B. Teflon 93
C. Rubber Septa 94
-ID. -Stainless Steel 94
APPENDIX ,4. CARBON PREPARATION AND CHARACTERIZATION 95
A. Procedure for Obtaining a Representative Sample of GAC.. 95
1. Carbon Splitting Procedure 95
B. Procedure for Washing the GAC 96
C. Procedure to Determine the Particle
Size Distribution 96
D. Procedure to Determine Grain Shape and Shape
Variation of the GAC 97
E. Procedure to Determine th;. Bulk Density of the GAC 97
F. Calculation of the Apparent Density 103
G. Calculation of the Intrapart icle Void Fraction 106
B. Preparation of Powered and Ground Activated Carbon 106
vii
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1. Procedure for Obtaining Powdered and Ground
Activated Carbon...... 106
2. Procedure to Clean the Ground and Powdered
Activated Carbon 107
APPENDIX 5. PROCEDURE FOR THE DIFFERENTIAL COLUMN
BATCH REACTOR 108
A. General Operation of the Differential Column
Column Batch Reactor 108
B. Selecting the Proper Column 108
C. Selecting the Proper Carbon Dosage 112
D. Packing the Differential Carbon Column 112
E. Measuring the Flow Rate of the DCBR 114
F. Spiking the Reactor with a VOC 114
G. Sampling from the Differential Column Batch Reactor.... 114
1. Sampling for the Liquid-Liquid Extraction Technique 115
2. Sampling for the Purge and Trap Technique 115
APPENDIX 6. DIFFERENTIAL COLUMN BATCH REACTOR DATA 113
APPENDIX 7. MULTICOMPONENT DIFFERENTIAL COLUMN
-BATCH REACTOR DATA -AND RESULTS................. 13 6
APPENDIX B. 'SAMPLE INPUT AND OUTPUT FILES FOR USE WITH
fME BHSDM AND THE ;BPSDM. 141
A. The BHSDM Sample Run 141
1. Mapping Routine 141
2. Input Data File 141
3. Program Run stream 142
4. Output File 143
B. ihe BPSDM Sample Run 145
1. Mapping Routine 145
2. Input Data File 145
3 . Program Runstream 145
4. Output File 146
vili
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Table
LIST OF TABLES
page
VI-1 Single Solute Freundlich Isotherm Constants Dsed in the
BHSDM and the BPSDM Calculations 29
VI-2 Surface Diffnsivities and Film Transfer Coefficients
Determined by Fitting Experimental Data Using the
BflSDM and the BPSDM 37
VI-3 Comparison of the Model Equilibrium Times and
Concentrations to the Final Observed
Concentrations and Times for the Differential
Column Bctch Reactor Studies 40
VI-4 Biological. Organic, and Inorganic Analysis of Wausau Well
#4 Water Matrix Collected on February 20, 1984 42
VI-3 Degradation Study of the Vrausau Water Matrix 43
VIII-1 Data for the Correlation Eased on the Boiling
Points of the Adsorbates 72
VIII-2 Comparison of Calculated and Observed Surface
Diffusivities Based on the Liquid Diffusivity
and the Partitioning Evaluated at the Initial
Concentration of the Adsorbates 74-5
VIII-3. Comparison of Calculated and Observed Surface
'Diffusivities Based on the Liquid Diffusivity
and on the Average Driving Force of the Adsorbates 78
VIII-4 Comparison of Calculated and Observed Surface
Diffusivities Based on the Self-Diffusivity
and the Partitioning Evaluated at the Initial
Concentration of the Adsorbates 80
4-1 Results of the Sieve Analysis for the
F-400 and WV-G Carbons 98
4-2 Sieve Size and Percent Carbon Passing a Given Sieve
for the F-400 and WV-G Carbons 98
4-3 Data Collected From the Bulk Density Experiment
for (12x40) Mesh F-400 and WV-G Carbons 104
5-1 Equipnent List for the Differential
Column Batch Reactor 110
6-1 Batch Kinetic Data for Trichloroethene and
(12x40) F-400 Carbon Using Thawed Wausau Water 118
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6-2 Batch Kinetic Data for Trichloroetbene and
(12x40) WV-G Carbon Using Thawed Wausau Water... 120
6-3 Batch Kinetic Data for Trichloroethene and
(12x40) F-400 Carbon Using Milli-Q Water 122
6-4 Batch Kinetic Data for Tetrachloroethene and
(12x40) F-400Carbon Using Milli-Q Water 124
6-5 Batch Kinetic Data for Trichloroethene and
(60x80) F-400 Carbon Using Milli-Q Water 126
$-6 Batch Kinetic Data for Tetrachloroethene and
(60r80) F-400 Carbon Using Milli-Q Water 128
6~7 Batch kinetic Data for Trichloroethene and
(12x40) V'V-G Carbon Dsing Milli-Q Water 130
6-8 Batch Kinetic Data for cis-1,2 dichloroethene and
(12x40) F-400 Carbon Using Milli-Q Water 132
(>-9 Batch Kinetic Data for Toluene and
(12r40) F-400 Carbon Using Milli-Q Water 134
7—1 Batch Kinetic Data for the Mul t icomponent Run and
(12x40) F-400 Carbon Using Fresh Wausan Water 137
"—2 Component and System Parameters for the Multi-
Component Fresh Wausau Water Run Using (12x40)
F-400 Carbon 138
7-3 Comparison of the Multicomponent Fresh Wansau
Water Data and the Predicted BPSDM Model 139
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LIST OF FIGURES
Figure page
II-l Basic Design for the Differential Column Batch Reactor 9
III-l Mechanisms and Assumptions that are Incorporated into
the BHSDM and BPSDM 11
VI-1 BHSDM and BPSDM Simulations for Trichloroethene ia
Milli-Q Water and (12x40) F-400 Carbon:
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VII-4 BIISDM Sensitivity Analysis of +/- 50% kf for
Toluene in Milli-Q Water and (12x40)
F-400 Carbon (Bi=133.5; CD = 372.4 ug/L). ............ 54
VII-5 BHSDM Sensitivity Analysis of +/- 50% D for
Trichloroethene in Milli-Q Water and (12x40)
F-400 Carbon (Bi=18.1 ; CQ = 1322.7 ng/L) ............. 55
VII-6 BDSDM Sensitivity Analysis of +/- 50% DS for
cis-1,2 Dichloroethene in Milli-Q Water and (12x40)
F-400 Carbon (Bi=28.7 ; CG = 507.0 ug/L) .............. 56
VII-7 BHSDM Sensitivity Analysis of +/- 50% D$ for
Trichloroethene in Thawed Wansau Water and (12x40)
F-400 Carbon (Bi=75.8 ; CQ = 1441.6 ug/L) ............. 57
VII-8 BHSDM Sensitivity Analysis of +/- 50% DS for
Toluene in Milli-Q Water and (12x40)
F-400 Carbon (Bi=133.5; C = 372.4 tig/L) ............. 58
VII-9 BHSDM Sensitivity Analysis of +/- 95% Confidence
Interval for the Freundlich K for Trichloroethene
in Milli-Q Water and (12x40) F-400 Carbon
(Bi = 18.1 ; CQ = 1322.7 fjg/L) ........................ 60
VII-10 BHSDM Sensitivity Analysis of +/- 95% Confidence
Interval for the Freundl ich K for Tetrachloroethene
in MUli-Q Water and (12x40) F-400 Carbon
(Bi = 46.8 ; CQ = 1438.4 ug/L) ........................ 61
VII-11 BHSDM Sensitivity Analysis of +/- 95% Confidence
Interval for the Freundlich K for Toluene
in Milli-Q Water and (12x40) F-400 Carbon
4Bi = 133.5 ; C = 372.4 ng/L) ........................ 62
VII-12 BHSDM Sensitivity Analysis of +/- 95% Confidence
Interval for the Freundlich 1/n for Trichloroethene
in Milli-Q Water and (12x40) F-400 Carbon
(Bi = 18.1 ; CQ = 1322.7 ug/L) ........................ 63
VII-13 BHSDM Sensitivity Analysis of +/- 95% Confidence
Interval for the Freundlich 1/n for Tetrachloroethene
in Milli-Q Water and (12x40) F-400 Carbon (Bi=46.8)...
(Bi = 46.8 ; C0 = 1438.4 (ig/L) ........................ 64
VII-14 BHSDM Sensitivity Analysis of +/- 95% Confidence
Interval for the Frenndl ich 1/n for Toluene
in Milli-Q Water and (12x40) F-400 Carbon „
(Bi = 133.5 ; CQ = 372.4 ug/L) ........................ 65
VIII-1 Comparison Between the Measured Surface Dif fusivities
and the Pore Diffusion Flux Contribution Using the
Liquid Diffusivity Correlation. Carbon Type and Mesh Size
is Indicated ............................. T.... ........ 76
xii
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4-1 Percent Carbon (by weight) Passing a Given Sieve Size
Versus the Log of the Size of Separation for
WV-G Carbon 99
4-2 Percent Carbon (by weight) Passing a Given Sieve Size
Versus the Log of the Size of Separation for
F-400 Carbon 100
4-3 Shape Factors of Granular Materials and Typical
Porosities Associated with them (Fair et. al.. 1971).. 101
4-4 Relationship Between the Bed Void Fraction and the
Particle Shape 102
4-5 Determination of the Bulk Density of F-400 and WV-G
Carbons Using a Dry Weight of Carbon Versus the Volume
Occupied by Hilli-Q Water 105
5-1 Basic Design for the Differential Column Batch Reactor 109
5-2 Schematic of the Ports for the Differential Column
Batch Reactor Ill
5-3 Schematic of the Packed Differential Carbon Column... 113
5-4 Design of the Sampling and Injection Ports for the
Differential Column Batch Reactor 116
xiii
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ACKNOWLEDGMENTS
I would like to tuank my advisor, Dr. John C. Crittenden, for
sharing his knowledge with me over the past 2 years. Special thanks
go to David Hand (Research Engineer), for his innovative ideas and
to David Perram (Assistant Research Scientist) for his invaluable
knowledge in the laboratory.
xiv
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I. INTRODUCTION
Treatment with granular activated carbon (GAC) is a useful, but expensive
technique for removal of synthetic organic chemicals (SOCS) found in drinking
water sources. A properly designed fixed-bed adsorption is required in order
to reduce the cost of using GAC. A pilot investigation and a predictive model
can be used to design a fixed-bed process. A pilot investigation is only valid
for the duration of the study. A predictive model and a pilot investigation,
however, allows a user to design fixed-bed adsorbers for treatment conditions
other than the original pilot investigation. The HSDM (Homogeneous Surface
Diffusion Model) has been shown to succe ssful ly predict fixed-bed adsorber
dynamics for a ntunber of adsorbate—adsorbent systems (Crittenden, 1978; Lee,
1980; Thacker, 1983; and Pirbazari, 1981). The important kinetic parameters
in the HSDM are the liquid—phase mass transfer coefficients and the
intraparticle diffusion coefficients. The liquid-phase mass transfer
coefficients are estimated using various correlations (Williamson e_t_._
a 1 ..3>63; Wilson and Geankoplis, 1966). The Intraparticle diffusion
coefiicients are determined from differential column batch reactor (DCBR)
studies. The DCBR studies, however, are difficult to conduct. Therefore, a
correlation which was based on the liquid diffusivity and the physical
properties of the carbon, was developed.
A correlation, which is based on the liquid diffusivities of the
adsorbates and the void fraction of the activated carbons, can be used to
estimate surface diffusion diffusivities of halogenated, one and two carbon
molecules, and some aromatic substituted organic compounds. The correlation,
however, is only valid for several macroporous activated carbons. The
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correlation can be used in conjunction with Hand et. al. .• 1984 to calculate
the mass transfer zone lengths (MTZL) for these types of compounds and
activated carbons. To make conservative estimates for fixed-bed design.
Equation VIII-12 may be used to estimate the surface diffusivity of a variety
of adsorbates. Equation VIII-13 either predicts the surface diffusivity with
reasonable precision or a lower surface diffusivity for some compounds.
Consequently, the calculated surface diffusivity can br used to make a
conservative estimate of the mass transfer zone lengths in a fixed-bed. This
estimate would be conservative, because the surface diffusivity would either
be correct or underestimated such that there would not be premature
breakthrough of the solute in the fixed-bed.
Single-solute intraparticle diffusion coefficients for trichloroethene,
tetrachloroethene, toluene, and cis-1,2 dichloroethene in organic-free water,
along with single—solute trichloroethene in a Tjackground water matrix of total
organic carbon (TOO were measured. Surface diffusion was found to be the
.most important latrapa-rticle mass transfer mechanism for .s in.gl e-solutes in
organic-free water. Pore difftision was slower than surface diffusion and did
not predict the experimental data. The uptake rates for trichloroethene in
the background water matrix and the organic-free water were the same, so
competitive effects from the background water matrix were not observed.
A multicomponent batch rate study was attempted, but problems with
degradation of the aromatic compounds occurred. Also, selection of a proper
carbon dosage to determine surface diffusivities was not possible. If a high
carbon dosage was chosen to observe the concentration history profile of the
weakly adsorbing solute, it would result in a film transfer limited case for
the strongly adsorbing solute. If a low carbon dosage was chosen to observe
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the concentration history profile of the strongly adsorbing solute, the
concentration history for the weakly adsorbing solute would not be
significantly depressed enough to see a profile and measurement of the
intraparticle surface diffusion coefficient for the weakly adsorbing solute
would not be possible.
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II. EXPERIMENTAL PROCEDURES
A. Chemicals Used in Experiments
All chemicals used in single solntt experiments were reagent grade or
better. 1.1.1-tr ichloroethene, stabilized, (lot number 004411) and
tetrachloroethene, (PCE), (Photrex), (lot nunber 2-9218) were obtained from
J.T. Baker Chemical Company, Phi 11ipsburg. New Jersey. 2,2,4-
trimethylpentane, trihalouethane grade, (lot number AK716), trichloroethene,
(TCE). (lot number AE777). and methyl alcohol, trihalomethane grade (lot
number AL065) were obtained from Burdick and Jackson, Muskegon, Michigan.
Cis-1,2 dichloroethene 97%,(DCE), (lot number 8409PK) and Toluene, 99%, (lot
number P115TH) were obtained from Aldrich Chemical Company, Milwaukee,
Wisconsin.
B. Carbons Used in Experiments
Two granular activated carbons were used in the studies: Calgon
Corporation's Filtrasorb 400 (F-400) (lot number 52095) Pittsburgh,
Pennsylvania, and Westvaco's WV-G (lot number 39815) Covington, 'Virginia.
were used. Both carbons were originally 12x40 mesh. Ground Granular
Activated Carbon (60 x 80 mesh) ras also studied. For the (60 x 80 mesh)
carbon, (12 x 40 mesh) carbon was ground until all of the original sample
passed the 60 mesh size.
C. Vater Matrices Used in Experiments
Two water matrices were used in these studies: Organic-free water was
obtained from the Millipore system and raw water from well number four in
Wausan, Wisconsin was the source of the other water matrix. The Millipore
system consisted of a mi Hip or a Super-C cartridge, two ION-EX cartridges, and
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an Organex-Q cartridge in series. Finally, & Twin-90, 0.22pm, filter unit
was used to eliminate microorganisms. To obtain organic-free water the Milli-Q
water was purged. The city of Wausan, Wisconsin's well number 4 contained a
mixture of various (VOCS) and total organic carbou (TOO found in their
drinking water source.
D. Carbon Preparation and Characterization
The granular activated carbons from the two manufacturers were obtained
in two 50 pound bags. A representative sample was obtained by splitting the
carbon. Both carbons were washed with purged Mil 1 i-Q water to remove any
fine carbon particulate matter. The washings were continued until the
supernatant was clear. The carbon was placed in an oven at 105°C for 12
hours. Finally, the carbon was placed in clean, brown, borosilicate bottles,
»
with teflon liners, and stored in a dessicator. 'Appendix 4 contains the
procedure for splitting and washing the carbon.
Both powdered granular activated carbon (PGAC), and ground granular
activated carbon (GAC), were prepared by using a mortar and pestle to reduce
the carbon particle size. The PGAC was used in the isotherm equilibrium
studies and the GAC was used in the differential column batch rate studies.
The carbon was placed in centrifuge bottles which were filled two-thirds full
of purged Mil i i-Q water and capped. The bottles were shook and placed in a
centrifuge. Again, the washings were continued until the supernatant was
clear. The carbon was placed in an oven at 105°C for 16 hours. Finally, the
carbon was placed in clean, brown, borosilicate bottles with teflon liners in
the caps and stored in a dessicator. Appendix 4 contains the procedure for
crushing and cleaning the carbon.
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B. Chemical Analysis
Chemical analyses were made using the following instruments: 1) the
Hewlett-Packard 5830A Gas Chromatograph upgraded to a 5840A with an electron
capture detector 2) the Hewlett-Packard 5830A Gas Chromatograph with a flame
ionization detector coupled with a Hewlett-Packard 7675A Purge and Trap
Sampler. The columns which were used on the 5840A were either the 80/100
Carbopack B/0.1% SP-1000 or the 60/80 Carbopack C/0.2% Carbowax C. The column
which was used on the 5830A was ths 60/80 Carbopack B/l.0% SP-1000. All
columns were 10 feet in length.
There were two analytical techniques which were used to measure the VOC
samples. The first technique involved liquid-liquid extraction, using 2,2,4-
trimethylpentane (Isooctane) which contained an internal standard (1,1,1-
trichloroethene). The procedure for extracting the sample was similar to the
procedure which was described by Mieure (1977). Trichloroethene and
tetrachloroethene were the compounds analyzed from the aqueous phase using
this procedure. Once the VOC had been extracted with isooctane from the
aqueous phase, the organic layer was injected into the Hewlett-Packard 5840A.
The area ratios (sample area divided by the internal standard area), were used
t; determine the concentration. The determination of the correct extraction
ratio was important to insure that a representative sample which can be
accurately measured on the gas chromatograph. A sample calculation for the
correct extraction ratio was shown by Johnson (1984).
The second technique used was the Purge and Trap. This technique was used
for compounds that had poor response factors on the electron capture detector.
The internal standard was 1,2 dichloropropane. A 10 ml aliquot of a water
sample and a 5 ml aliquot of an internal standard were placed in a purge
vessel which was attached to the Purge and Trap Sampler. The area ratios
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(sample area divided by the internal standard area), were used to determine
the concentration.
F. Equilibrium Isotherm Procedure
The equilibrium studies which were performed used the bottle point
procedure by Luft (1984). Serum bottles with various amounts of PGAC were
allowed to come into contact with water containing the VOCS. Once equilibrium
was attained, the serum bottle was centrifuged to separate the PGAC from the
liquid. The liquid-phase concentration was determined by the liquid—liquid
extraction technique.
G. Differential Colum Batch Reactor Procedure
i. Previous Designs
Hand (1982) presented three possible experimental apparatus which could
be used to measure the surface diffusivities of VOCS: the completely mixed
batch reactor (CMBR), the Carberry reactor ,\nd the differential column batch
reactor (DCBE). The CMBR consists of the GAC being dispersed in the aqueous
phase. A motor controls a stirrer which agitates the 1iquid. The Carberry
reactor is a modification of the CMBR. In this design, the carbon is fixed in
a spinning basket. A motor rotates the basket in the fluid. The DCBR
consists of a large reservoir, a pump, and a column packed with a
differential height of carbon. The water from the reservoir is pumped through
the fixed-bed of carbon and recycled into the reservoir.
2. Chosen Design to Conduct Kinetic Studies
The CMBR design does not work '.'or soft carbons, sAnce the impeller blades
can cause attrition of the carbon particles and the smaller carbon particles
would increase the adsorption rate. The Carberry reactor is a possible choice,
but the user would have to use a large carbon dosage in this reactor.
-------
However, the carbon dosages were small for the adsorbates of interest in this
study. Therefore, the DCBR was chosen to conduct the experiments.
The procedure for the DCBR is presented in Appendix 5. The apparatus was
constructed using glass, teflon, and stainless steel materials. These
materials are chemically inert and therefore reduce the possibility of biased
results due to system leaching and adsorption. A continuously mixed glass
reaction vessel was completely filled with a water matrix and run at
isothermal conditions. See Figure II-l for the systen: design. For the single-
solute runs in Mill i-Q water, a pH of 6.0 was controlled using a phosphate
buffer. The raw Wausau water matrix was not buffered, but the value of the pH
was recorded and did not change during the experiment.
A high flowrate in the DCBR insured a minimum amount of liquid-phase mass
transfer resistance. This allowed for better estimates of the surface
diffusion coefficient -for « jg'iven adsorbent-adsorbate system.
The liquid-phase concentrations at various times were measured and a
.concentration history profile for a given solute was obtained. The
experimental data were compared -to the mathematical models which characterize
the process. The equations vhich describe the models are presented in
sections III and IV.
Preliminary calculations and the criteria for t'ne DCBR are contained in
section V. This section allows a potential user to correctly perform the
necessary calculations and to insure the experiment will yield a good
estimate of the surface diffusion coefficient.
-------
SYRINGES
VO
BYPASS
LOOP *-->^
]
OAC
GLASS ^"-"
COLUMN
I
^
*
T
\
|
V-
ST1RBAR >
4ou
•*^.
'
I.
~**«
«-=«
I
*i
0.
'*
ib.
*—
^O
p.
s
1
•cr
•i^tt^u
SI
.p.
3
^ —
uO-»
l.p.
*A~-
/
\^^
GLASS
x REACTION
VESSEL
•
MAGNETIC
STIRRER
PUMP
D.P. - DISCHARGE PORT SU.P. - SUCTION PORT
I.P. - INJECTION POUT S.P. - SAMPLING PORT
g - HitlTEf REGULATING VALVE
Figure II-l. Basic Design for the Cllferential Column Batch Reactor,
-------
III. MODEL FRAMEWORK FOR THE BATCH HOMOGENEOUS SURFACE DIFFUSION MODEL
As shown in Figure III-l, a three step mechanism iias been proposed to
describe the adsorption of volatile organic compounds from solution into
porous adsorbents such as granular activated carbon (GAC) (Weber et. a 1..
1963). The first step is the transport of the VOC from the liquid-phase to
the exterior surface of the adsorbent.- The second step is the diffusion of
the VOC into the pores of the adsorbent and is comprised of both pore and
surface diffusion. Finally, the third step are the local elementary reaction
steps which are involved in the adsorption of VOCS. In the batch homogeneous
surface diffusion model (BHSDM), the pore diffusion mechanism is nr.glected.
A. Previous Voxk
Several researchers have studied adsorption kinetics in batch reactors.
Crittenden and Weber (1978). have independently measured intrapartic1e
diffusion coefficients of phenol, -p—toluene sulfonate, p-bromopheaol, and
dodecyl benr.ene sulfonate for model calibration and were able to predict
adsorption column performance. Hand, Crittenden, and Thacker (1983), have
provided user-orientated solutions to the batch homogeneous surface diffusion
model which can be used to determine the surface diffusivity from
differential column batch reactor stv,-:;. T i. Suzuki and Kawazoe (1975) measured
the single-solute adsorption rate from batch experiments of 15 volatile
organic chemicals on coconut based carbon. Suzuki and Kawazoe (1974) also
provided graphical solutions for batch reactors assuming that both pore or
.surface diffusion could describe the intraparticle mass transfer rate. van
Lier (1983) conducted kinetic adsorption experiment; with nitrobenzene on
various types of carbon. He found that surface diffusion was the most
important intraparticle diff us ion mechanism. Sabi.1 (1981) conducted kinetic
10
-------
MODEL MECHANISMS DIFFUSION MECHANISMS
I.OCAJ. t-n'JI.KHlllJM 03-
1WUUII rtUHJ I'llASU AUD
AU'JOtlUUHl I'HABU
ponr.
uirrusioN
DUIK I
GOLUTION
ADSORBEHT
VOID
FHACTION
' . Cn
rLUID-PIIACG
ADnoilllGMI PHASE
a Z-R DPSDM
ruw-'Psft BHSDM
Figure II1-1. Meclinnismn and Asutimptlono that are Incorporated Into the
IMS KM nncl !ll\SI)M,
-------
adsorption experiments on two microporous carbons, HD-3000 and HD-4000, with
chloroform and found that the surface diffnsivities for the microporous
carbons were lower than surface diffnsivities for the macroporons carbon, F-
400. See Table VIII-2 for the comparison.
B. Model Mechanisms and Assumptions
The multicomponent batch homogeneous surface diffusion model (BHSDH),
includes the following transport mechanisms: 1) mass transfer from the bulk
of the solution onto the outer surface of the particles, and 2) diffusion of
molecules in the adsorbed state by surface diffusion. The BHSDH also includes
the following assumptions: 1) the transport of adsorbate from the bulk
solution to the exterior of the adsorbent particle is described by the linear
driving force approximation, 2) at the exterior of the adsorbent particle,
local equilibrium exists with the liquid-phase, 3) mnlticomponent adsorption
equilibrium is described by ideal adsorbed solution theory (IAST, Radke and
Pransnitz, 1972), while single—solute adsorption equilibrium is described by
the Freundlich isotherm equation, 4) the intraparticle mass flux is described
by Pick's law and bulk flow due to diffusion is neglected by assuming dilute
solutions (Weber and Chakravorti, 1974), 5} surface diffusion describes the
intraparticle mass fl'ix, and 6) there are no solute-solute interactions in
the diffusion process.
C. Equations Describing the Mul tic opponent BHSDM
Equations III-l to III-7 describe the spatial and temporal variation of
an adsorbate within the adsorbent and the liquid-phase. The derivation of
these equations and their conversion into diaensionless form was presented by
Friedman (1984). The following set of equations are required for obtaining
solutions to the BHSDM:
12
-------
The overall mass balance is:
0 -
«cl(t§)
3t
3Dg
s J
'
r»dr
(III-l)
where:
M1
— ,
at. Jn
dCi(ts) Mass of Adsorbate i
_ • Accumulated in
dt the Liquid Phase
__ _ Total Mass of
r*dr - Adsorbate i in
the Particle
The initial conditions for equation III-l are:
= 0)
0)
(III-3)
The intraparticle phase mass balance is:
s.i _
T - aqi(r.ts)
s.max
]
(III-4)
where:
-Ds j 1 3 j" _ aq^r.tj) 1
' — -^r- — — I r» - _ -- I
r*drl dr J
s.mai
Mass of Adsorbate i
Transferred Away from
the Exterior Surface by
Surface Diffusion
9qi(r,tg)
dt
Mass of Adsorbate i
Accumulated within the
Adsorbent Particle
The initial condition for Equation III— 4 is:
0)
(III-5)
13
-------
The boundary conditions for Equation III-4 are:
a
dr
0,ts)
(III-6)
— f-cr-f
a_ J qi(r.ts
) rldr
Bi
s.i
s,max
For multicomponent mixtures, the nonlinear equation which couples
Equations III-l through III-7 is the IAST equation. Luft (1984) found that
the IAST equation described competition for multicomponent mixtures. The IAST
equation written in terms of i components and in dimecsionless variables is:
qii
m
lj(r=1't,s)^.j
k=l
(III-8)
For single solutes, the Frenndlich -isotherm equation was used to relate the
liquid-phase concentration at the exterior of the adsorbent to the adsorbent
phase concentration.
Equations III-l through III-8 contain two independent dimensionless
variables: time, t , and radial position, r, and three dependent variables:
liquid-phase concentration, C^,(ts), the solid phase concentration, qi(r,ts>,
and the liquid phase concentration at the exterior of the adsorbent
C (r=l,t ), These equations were solved by Friedman (1984) and his computer
algorithms were used to determine the surface diffnsivities.
14
-------
D. Diaensionless Groups Which Describe the Multicoisponent BHSDK
There are four independent dimensionless groups which characterize the
solution to the BSSDH and determine if surface diffusion is the controlling
mechanics in the differential column batch reactor study. The four
independent dimensionless groups appearing in Equations III-l to III-8 are:
(a) Dgg ^ , which is the surface solute distribution parameter for component
i based on surface diffusivity, (b) D, {/D. „..,, which is the ratio of the
s , i s ,max
surface diffusivity for component i to the surface diffusivity of the fastest
diffusing component, (c) 1/n^, which is a Freundlich isotherm constant for
component i. and (d) Bi$ ^, which is the Bict number for component i is
based on surface diffusivity. The surface solute distribution parameter
which is based on surface diffusivity, Dg£ ^, and the Biot number which is
based on surface diffusivity are defined as:
P.q. j(l-e)
Dgs £ - -^ii =
kf jRU-e)
Bis,i * "~: (111-10)
The surface solute distribution parameter, Dg£ ^, is the ratio of the
mass of adsorbate i in the solid phase to the mass in the liquid-phase under
equilibrium conditions. It was based on a single solute capacity and evaluated
at the initial concentration of the batch reactor. As Dg£ ^ increases, fie
amount of adsorbate on the adsorbent increases. The surface Biot number,
Bi 4, is the ratio of the liquid—phase mass transfer rate to the
intraparticle phase mass transfer rate and has the greatest impact on the
design of the DCBR. Hand, Crittenden, and Thacker (1984), have shown that for
a Bi( ^ greater than 30, the intraparticle phase jaass transfer rate controls
15
-------
the mass transfer rate in fixed-beds. Therefore, it is possible to obtain
better estimates of the surface diffusivity in a differential column batch
reactor when the Bi$ ^ is greater than 30.
-------
IV. MODEL FRAMEWOtt FOR IBB BATCH POKE AMD SURFACE DIFFUSION MODEL
For a multicomponent mixture, the BBSDM may not predict the adsorption
rate of both strongly and weakly adsorbing solutes. Both strongly and weakly
adsorbing solutes cen diffuse by two kinetic mechanisms: they can travel
along the interior surface of the adsorbent or within the fluid contained in
the void of the adsorbent. These two kinetic mechanisms are known as surface
diffusion and pore diffusion, respectively. In the case of weakly adsorbing
solutes, many of the active sites on the carbon walls are occupied by
strongly adsorbing solutes and pore diffusion allows the weakly adsorbing
solutes to continue to diffuse into the carbon particle. See Figure III—1.
Therefore, a model incorporating both surface and pore diffusion as the
intraparticle diffusion mechanism was developed by Friedman, (1984) and used
in this study.
A. Previous Work
Several researchers have studied the combination of surface and pore
diffusion. Suzuki and Kawazoe, 1974. have provided graphical solutions
assuming both pore and surface diffusion could describe the intraparticle mass
transfer rate. van Lier, 1983, conducted batch—wise experiments with a
nitrobenzene/water/activated carbon system and tested several mathematical
models. Fritz et. al.. (1980) conducted competitive adsorption of p-
nitrophenol/p-chlorophenol/activated carbon and p-nitrophenol/phenol/activated
carbon systems. He found that the BPSDH predicted slightly better results
than the BHSDM.
B. Model Mechanises and Assumptions
The multicomponent batch pore and surface diffusion model (BPSDH)
17
-------
includes the following transport mechanisms: 1) BS.SS transfer from the bulk
solution onto the outer surface of the adsorbent particles, 2) diffusion of
molecules in the adsorbed state known as surface diffusion, and 3) diffusion
of molecules in the liquid filled pores known as pore diffusion. The BPSDM
also includes the following assumptions: 1) transport of adsorbate from the
bulk solution to the exterior of the adsorbent particle is described by the
linear driving force approximation, 2) local equilibrium at a particular
radial position is assumed throughout the adsorbent particle, 3) ideal
adsorbed solution theory (Radke and Pransnitz, 1972; Luft, 1984) is used to
describe the multicomponent equilibrium interactions, while single-solute
adsorption equilibrium is described by the Freundlich isotherm equation 4)
the intraparticle mass flux is described by Pick's law and bulk flow due to
diffusion is neglected by assuming dilute solutions (Weber and Chakravorti,
1974), 5) surface and pore diffusion describes the intraparticle mass flux,
and 6) there are no solute-solute interactions in the diffusion process.
C. Equations Describing the Hulticomponent BPSDM
Equations IV-1 to IV-8 describe the spatial and temporal variation of an
adsorbate within the adsorbent and the 1 iqnid—phase. To simplify the
development of the equations for the BPSDM, the total loading of the particle.
T{ is expressed as the sum of the surface loading, q.i and the liquid-phase
concentration in the pores, C £ (Neretnieks. 1976; Fritz et. al.. 1980).
Yi(r.t) •= q^r.t) + —2- Cp>i(r.t) (IV-1)
Pa
The derivation of these equations and their conversion into dimensionless form
was presented by Friedman (1984). The following set of equations are required
to obtain solutions to the BPSDM:
18
-------
The overall mass balance is:
0 -
at
3Dgi~
L(r.tp)
(IV-2)
where:
at.
' -f
at^ Jn
•V
Mass of Adsorbate i
Accumulated in
the Liquid Phase
Total Mass of
Adsozbate in
the Particle-
The initial, conditions for Equation IV-2 are:
0) - 1
(IV-3)
0)
The intraparticle phase mass balance is:
i d
r» dr
aiiU.t )
i
dr
•
., . is.i«''S»
1 ar
•
WiCr.t >
as
(IV-5)
where:
1 3
r* 3r
r* Xi —X _ P + r* Zj
dr
dr
Mass of Adsorbate i
Transferred Away from
« the Exterior Surface
by Pore and Surface
Diffusion
Mass of Adsorbate i
Accunulated within
the adsorbent
particle
19
-------
Tie initial condition for the intraparticle phase mass balance is:
0)
(IV-6)
The boundary conditions for the intraparticle phase macs balance are:
r^r o o.t )
dr
3 f1
-=- V*'
3t^ JO
tp)
Bi
c>. C±(tp) - Cpa
(IV-7)
(rv-8)
For multicomponent mixtures, the nonlinear equation which couples
Equations IV-2 through IV-8 is the IAST eq -ition. Luft (1984) found that the
IAST equation described competition for multicomponent mixtures. The IAST
equation written in. terms of i components and in dimensionless variables is:
-2-c
Pa
o.i
Pa
(IV-9)
m
I
k=l
e
Pa
> m
*i*i
For vingle-solutes, the Freundlich isotherm was used to relate the liquid-
phase concentration at the exterior of the adsorbent to the adsorbent phase
concentration.
Equations IV-2 through IV-9 contain two independent dimensionless
20
-------
variables: time, ts. and radial position, r. and three dspendent variables:
liquid phase concentration, (^.(tg), the solid phase concentration. qjCr.tg),
and the liquid phase concentration at the exterior and interior of the
adsorbent Cp(r,ts). These equations were solved by Friedman (1984) and his
computer algorithms were used to determine the surface diffusivities.
D. DiBensioaless Groups Which Describe the Multiccnponent BPSDN
Th« solutions to the BPSDM are characterized by the following
dimensionless groups and are being investigated, since they have an impect on
the design and operation of the DCBR:
8Co,i
gp*1-') Mep
D*p,i " - - -
e eV
D«s.i + D8p.i
k R (1-e
Ds.i
(IV-10)
(IV-15)
The surface solute distribution parameter, Dgs i§ is defined in Section
III-D. The pore solute distribution parameter, Dg ^, is the mass of
adsorbate _1 in the adsorbent pores divided by the mass of adsorbate i in the
21
-------
liquid-phase under equilibrium conditions. This dimensionless group will be
the seme for all solutes in a given system, since it is a function of the
porosity of the reactor, t, and the adsorbent void fraction, e .
The total adsorbent equilibrium capacity, Dg^, is the sun of the surface
solute distribution parameter. Dg$ ^, and the pore solute distribution
parameter, Dg ^. As shown in Eqt-tion IV-12, it is based on the single
solute capacity evaluated at the initial concentration of the batch reactor.
The Biot number, Bic £, includes a combined surface and pore diffusivity.
It compares the liquid-phase mass transfer rate to the total intraparticle
phase mass transfer rate. A combined Biot number greater than 30 would insure
an intr&particle controlled process and would insure a good determination of
the surface diffusivity.
The dimensionless group, X^, is the ratio of the rate of pore diffusion
»
to the combined rate of pore and surface diffusion. The diaensionless group,
Z^, . has no physical meaning.
The conversion to dimensionless variables reduces the number of
independent parameters to seven dimensionless groups: 1/nj, DgSj£> Dgp> j,
Dg^, Bic £, Xj, and Z^. Of the seven dimensionless groups, only the six
dimensioaless groups act independently: 1/n^ Dg£>i, Dgp,j» Bic,i' x*' and
22
-------
T. PRELIMINARY CALCULATIONS AND rgTTRBTA HEEDED TO CONDUCT A SUCCESSFUL
DIFFERENTIAL COLUMN BATCH REACTOR STUDY :>
It is important to minimize the effect of the liquid-phase mass transfer
resistance in the differential column batch reactor (DCBR) such that the
surface diffusivity can be estimated accurately. Presented below are the
preliminary calculations and criteria needed to conduct a successful
differential column batch reactor study.
A. Representative Sample from the Batch Reactor
The hydraulic retention time, Tr, is an important consideration in the
design of the DCBR. It is defined as the time needed to circulate one
reactor volume of water through the reactor and is related to the rate at
which *u tcr is passed through the differential carbon column. If the
hydraulic retention time is low enough, then there will be no concentration
gradient across the differential carbon bed (See Section V-E for more
discussion). The hydraulic retention time is calculated by the following
equation:
Tr «= - (V-l)
where V is the volume of the reactor* and Q is the volumetric flow rate
through the packed column. The hydraulic retention time is only a qualitative
criteria and can not be used to quantitatively select the proper flow rate
and velocity through the column.
The liquid-phase samples which are collected during a DCBR experiment are
used to determine the concentration history profile for a given solute.
However, the total sample volume removed should not be more than 5% of the
reactor volume.
23.
-------
B. Obtaining a Representative Carbon Sample
The carbon dosage, DQ, is another important design consideration,
because a representative sample of the carbon mast be taken. A large dosage of
activated carbon was used such that the isotherm capacity observed in the OCBE
would be the same as the capacity observed in the isotherm experiment. It was
assumed that at least 80 particles were a representative sample of the carbon.
The equilibrium capacities that were obtained from the batch rate studies were
similar to the capacities obtained from the isotherm studies; consequently, a
large enough carbon dosage was selected to give the same equilibrium capacity
as the iiothcrm experiments. See Section VI-B for further discussion.
C. Temperature Dependence of Equilibrium and Kinetic Parameters
The differential column batch reactor was conducted at the same
temperature as the isotherm study,-because both equilibrium and diffusion rate
are temperature dependent.
Since a high flow rate may cause heating of the water from the pump, the
the temperature inside the reactor was monitored. However, the temperature
inside the reactor was the same as the laboratory. Consequently, no
additional cooling of the DCBR was required.
D. Effect of the Liquid-Phase Mas* Transfer Kate
For Biot numbers greater than 30, it was found that surface diffusion was
required to explain the rate of uptake for the VOCS and the contribution of
pore diffusion was determined to be negligible. Therefore, the Biot number
which was based on the surface was used to determine the effect of the liquid-
phase mass transfer resistance. See Section III-D for further discussion.
The Biot number, which is based on the surface diffusivity of a given
24
-------
adsorbent, is defined by Equation 111-10.
The film transfer coefficient correlation, which was reported by Vakao
et. a},. 1978, was used in the DCBR calculations, because the Reynolds numbers
in differential column batch reactor studies were high and this correlation
was developed for higher Reynolds numbers:
D
£fi 2 R
iii [ 2 + 1.1 %e°.« NSCfil/3 ] (V-3)
in which, Dj j is the liquid diffusivity of the adsorbate in water; NRe is the
Reynolds number.* and Ngc ^ is the Schmidt number for a given adsorbate. These
dimensionless groups were defined by the following equations:
2 R pi v. s
NRe •= CV-4)
NSc.i
in which, v^ is the interstitial velocity, e is the void fraction of the
carbon bed, n is the viscosity of water, and pj is the density of water. The
liquid diffnsivity of the adsorbate in water, D^ ^ was calculated using the
fol loring equation (Hayduk and Laudie, 1974):
13.25 10~5
^.j
B. Calculation of the Concentration Gradient Across the
Differential Carbon Col mm
The final requirement of the DCBR is that the influent and effluent
concentration across the differential carbon column are approximately the
25
-------
same. The mechanisms, which are important in transporting the solute across
the bed. are advection and axial dispersion. A plug flow, fixed-bed model was
used to calculate the ratio of the effluent liquid-phase concentration leaving
the differential carbon column to the influent liquid-phase concentration
entering the differential carbon carbon, Ceff'^inf because if axial
dispersion was included, then a higher Ce£f/C. , would be determined.
Therefore, a design which is based a plug flow model would be more
conservative. The assumptions that are built into the following model
(Friedman, 1984) are: 1) there is no axial dispersion in the fixed-bed, 2) the
surface concentration is zero, and 3) the system is operating at steady
state. The final fora of the equation is:
Ceff/Cinf ' '~3Sti
The Stanton number, St^, is defined as:
Sti = kfti(l - e)t/R(e) (V-8)
in which, T is the packed bed contact time and is equal to the ratio of the
volume of the carbon bed to the volumetric flow rate through the carbon bed.
Equation V-7 can also be used to describe the concentration gradient in a
DCBR. Although Equation V-7 was developed for the steady-state operation of a
fixed-bed adsorber with a cc?*-tant influent concentration, it can be used to
estimate the required flow rate in a DCBR. In a DCBR, the liquid-phase
concentration decreases with time and the surface concentration increases with
time; consequently, the actual concentration gradient across the column for
the DCBR would be less than the concentration gradient which would be
calculated using Equation V-7. Therefore, the use of Equation V-7 to estimate
the proper flow rate would be conservative.
26
-------
The ratio of C^f/C^f that was greater than or equal to 0.95 was chosen
as that required to guarantee no concentration gradient across the DCBR. This
would require a Stanton number less than or equal to 0.017.
When the concentration gradient across the differential carbon column is
greater than or equal to 0.95, and the Stanton number is less than or equal
to 0.017, the concentration across the differencial column is the same as the
concentration in the DCBR reservoir.
The Stanton number is the ratio of tne rate of mass transfer due to film
transfer to the rate of mass transfer due to advection. If the Stanton
number is greater than 0.017, then it is necessary to increase the hydraulic
loading or decrease the hydraulic retention tine such that the the Stanton
number will be less than 0.017. For a given flow rate or hydraulic retention
time, the column diameter can be reduced such that the film transfer
coefficient and the Stanton number would increase.
27
-------
VI. COMPARISON OF TOE MATHEMATICAL MODELS USED TO SIMULATE THE DIFFERENTIAL
COLUMN BATCH REACTOR
Surface diffnsivities of various VOCS were determined by comparing batch
rate data to a mathematical model. Three models were used for this
comparison. They vere: (a) the batch homogeneous surface diffusion model
(BHSDM) which includes liquid-phase mass transfer and surface diffusion, (b)
batch pore surface diffusion model (BPSDM) which includes liquid-phase mass
transfer and surface and pore diffusion, and (c) the pore diffusion model
(BPDM) which includes liquid-phase mass transfer and pore diffusion. The
developments of the BHSDM and BPSDM were presented in Sections III and IV,
respectively. The BPDH may be derived from the BPSDM by setting the surface
flux equal to zero.
Presented below are the experimental results and analyses for the
determination of the intraparticle diffusion coefficients using the models
described above.
A. Single Solute Batch Bate Results
Seven single-solute rate studies were conducted on two granular activated
carbons in Milli-Q water with four volatile organic compounds. The four
compounds were the weakly-adsorbing cis-1,2 dichloroethene, the moderately-
adsorbing trichloroethene, and the strongly—adsorbing tetrachloroethene and
toluene. Appendix 6 contains the experimental data and the physical
characteristics of the system. Table VI-1 contains the single solute
Freundlich isotherm parameters for the components used in the models.
The BHSDM and BPSDM were the two models which were used to simulate the
single-solute concentration history profiles in the batch rate study. Figures
VI—1 through VI—6 contain the experimental data for trichloroethene,
tetrachloroethene. cii-1.2 dichlorottheno, and toluene along with the BHSDM
-------
Tibl. 71-1. Sm(it Fit
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{ TRICHLOROETHENE BATCH RATE STUDY
L MODEL COMPARISON
Y, CARBON TYPE: 12X40 F-400
*A LEGEND
Vf. «= EXPERIMENTAL DATA
' »»V ...... BHSDM SIMULATION DS=3.1E-10,DP-=0
\ \ — •— - PORE PREDICTION DS-O.DP^e^E-e
\ V "»- BPSDM SIMULATION DS=2.4E-10,DP=6.4E-6
°\ \
\ "X^
A ^^^^^
^ ^^^
'* ^x*>*.
'\* ^^"^^
• ^1^
*fcv4 ^^**"*— — ^,
***** • '"""— ^""~^^»
""*"•••
"""""""••• •
•^•••--.A.^.,^
•0 """""'•1>'»O)»1nn^f,(%
0.0
20.0
40.0 60.0 80.0
TIME, HOURS
100.0
120.0
140.0
Flgiire VI-1, B11SOM and BPSDM Simulations for Trlclilorocthene in Hllli-Q Water and (12x40) F-400
Carbon (C = 1322.7 JJg/L).
-------
I.U
o °-8
z
o
p
< 0.6
H
Z
111
O
z
O 0.4
o
Q
111
0
Q °'2
UJ
cc
On
• U
\. TETRACHLOROEiHENE BATCH RATE STUDY
t%, MODEL COMPARISON
1A CARBON TYPE: 12X40 F-400
t\ .
\* , LEGEND
' \\ *- EXPERIMENTAL DATA
» x . ..•> ni-iRnM ciuiii ATirtM nQn x nc-n nDe>n
• N, •••••™onOUIVIolMUl./\IIU(MWOI:I^.OC~l I.Ur^U
\ V —.—«> PORE PREDICTION DS=0,DP= 6.BE-6
\ \. -* BPSDM SIMULATION DS-=»3.1E-11,DP=6.8E-6
•. ^S.
•VH \
•** ^%**'**'1*»^
* *"*v ^^"fc**'<**^^
ml* ^*****t'**^^^
***** ^**>^"**^«.1
****•• *j '"* «»..^
•**'»,-•» '"""^^ ••«»»..,
• -.
••*-*-H.
•^^-*- g
1 ....I.. .._ 1. 1 1 1 1 1 1
0.0 20.0 40,0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 20
TIME, HOURS
Figure Vl-2. BUSDM and BPSDN Simulations for Tetracliloroetliene in Milli-Q Water and (12x40) F-AOO
Carbon C0 =
-------
10
N>
l.U
O
O
***% ft Q
0 °'8
^
Z
o
F
*> 08
cc 0>e
H"
z
111
O.
O 0.4
O
Hi
|I i
— ^
0 0.2
UJ
HI
UJ
rr
UM
On
.Q
SN
°\ '"v^
% ^ * ^^
\j ^.,
\ ^^**"**" -~..
O\ ~" ' **"' !•. . ^
\ '"-*—• "——..—»«„.,
% • "" "' •"•" •* —
^ ^* *-
* %*.
• **••* •
»*-.^. *
"
CIS 1,2-DICHLOROETHENE BATCH RATE STUDY
MODEL COMPARISON .
CARBON TYPE: 12X40 F-400
LEGEND
• - EXPERIMENTAL DATA
- BHSDM SIMULATION DS= 2.7E-9.DP-0
— .— o PORE PREDICTION DS=O.DP= 7.6E-6
— - BPSDM SIMULATION DS=- 2.4E-9,DP=7.6E-6
ii i i i
0.0 20.0 40.0 60.0 80.0 100.0 12
TIME, HOURS
Figure VI-3. B11SDM and BPSDM Simulations fot els-1,2 dichloroethene in Milli-Q Water and (12x40)
F-400 Csrbon (C - 507.0 pg/L).
-------
w
l.U
o
O
3 °-8
«
z
o
H*"™
..
2 0.6
Z
UJ
z
O °-4
o
Q
UJ
O
ID . „
Q °'2
UJ
cc
n n
X
\ TOLUENE BATCH RATE STUDY " * — " •
\ MODEL COMPARISON
\ CARBON TYPE: 12X40 F-400
\
- »\ LEGEND
Vt •- EXPERIMENTAL DATA
\ = BHSDM SIMULATION DS=> 1.BE-9.DP-0
•V PORE PREDICTION DS=G,DP= 6.5E-6
• V •-— BPSDM SIMULATION DS=> 1.BE-9,DP=6.6E-6
^-"'-.,
****"***•••»«•« a
1 - 1 -.. 1 1
0.0
20.0
80.0
Figure
40.0 60.0
TIME, HOURS
BlISDM and BPSDM Simulations for Toluene in Mllli-Q Water and (12x40) F-400 Carbon
(C0 - 372.4 IJg/I.),
100.0
-------
1.0
o
o
o
z
o
DC
UJ
O
z
o
o
D
UJ
O
ID
Q
UJ
CC
0.8
0.6
0.4
0.2
0.0
t
\
A
•\
\\
\ \x
t ^-s^
\ '^
%V
*%
*"*••
TRICHLOROETHENE BATCH RATE STUDY
MODEL COMPARISON
CARBON TYPE:
60X80 F-400
LEGEND
»•=• EXPERIMENTAL DATA
" BHSDM SIMULATION DS=4.3E-10,DP=0
*_.__= PORE PREDICTION DS=-0,DP=6.4E-6
—- BPSDM SIMULATION DS=3.7E-10,DP=6.4E-6
.
-^^
""^"^ -,.
•
*~ * — _ t __
^~~^ ' ~~~~" ' ~~— • — — . ,
• V.. •
• 0-
""**•••»*• • •
ii i
1 1 1 1 1
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 ?4.Q
TIME, HOURS
Figure VI-5. BHSDM and UPSDM Simulations for Trichloroethene in Milli-Q Water and (60x80) F-400
Carbon (C0 = 1329.8 jip,/ '
-------
CO
Ul
I.U
5 °-a
z"
o
p
< 06
CC °'8
H
Z
UJ
o
Z
0 0.4
O
Q
UJ
0
Q °'2
HI
DC
n n
TETRACHLOROETHENE BATCH RATE STUDY
'. MODEL COMPARISON
« CARBON TYPE: 60X80 F-400
A
« \ LEGEND
~\ \ .. - - «- EXPERIMENTAL DATA
•j X ....- BHSDM SIMULATION DS- 1.5E-10.DP-0
\ V — r— PORE PREDICTION DS=*0,DP- B.8E-0
• \ - BPSDM SIMULATION DS'='1.4E-10,DP=6.8E-e
» 'V.
t ^V^
• • ^S.
\ ^*****,t
\ **^**'
Of '"*""^^,(
f* "**^*^-^
\ ^"*~*~~*.
**«. ^'**~^*'«»«^^-._
•'o '^ — •— —
^'•«
*"+.^f
***"m* 9
~~'* •-*--..
•
i iii i i i i i i i
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0
TIME, HOURS
Figure Vl-f>. BHSDM and BPSDM Simulations for Tetrachloroethene in Milli-Q Water and (60x80) F-400
Carbon (Co = 150A.O
-------
and BPSDM simulations and a BPDM prediction. The best fit of the film
transfer coefficient, kf ^, and the surface diffnsivity, D •, were determined
by a two parameter search using the BHSDM. The best fit was determined by
minimizing the sum of the differences between measured and calculated
concentrations using the following equation:
1/2
S(min)
r i
(Cjdata - qmodel)2 /(Cjdatal2 (VI-1)
in which S(min) represents the minimum relative error between the model
calculated values and the data.
The 95% confidence intervals for kf and DS were calculated for the two
parameters using the equation presented by Draper and Smith (1981).
1/2
r p i
S(9) - S(min) 1 + - F(p,n-p,l-a) (VJ-2)
L n-p J
in which, S(G) is the relative error for a given confidence contour; p is the
number of parameters; (n - p) is the number of degrees of freedom; n is the
number of data points; a is the desired confidence contour and F is the
distribution function based on the number of degrees of freedom, the number of
data points, and the desired confidence limit.
Table VI-2 contains the 95% confidence intervals for kf i and D$ ^, the
Biot numbers which were based on the surface diffusivity and the Stanton
numbers.
For the pore and .surface model diffusion simulations, the pore
diffusivity, D ^, was a calculated value and did not add an additional
unknown to the system. The best fit kf j from the BHSDM and the calculated
-------
VI-2. tefdO* BUfutaitiM «d TO* Taattn Qxttiiiau Itumai*
BftU bat Of BBM nd tbr. VSH
OdVWrf T»i*l«l fftttT TJiVWCUB
"—— *— "™ fetrix
Oufeot
bt/L) PQ
eir-1.2 ticUocv- 5O7.0 KUli-0 13.0
•tko. F-tOb
(12x40)
^••^Tm^^M^tfrjgy 1434,4 HiU£^ 11*0
F-MO
(12>40>
ItdkcUctwcliBB 1304.0 KULli-Q 11.0
F-400
«CkJO>
Tolsn. JT3.4 KinHJ 13.0
F-400
(13z40)
T,.,).I~_-.>— 1332.7 KUlr-Q 11.0
F-WO
• Int FU »Mt FU
talu* SortM.
DUfMirity DiUuirltr
D^JO"
34.0
OJ1
",
LJ5
nj
2,45
O* C.L)
t^io«
Z7.0
(17.0-51.0)
0.41
(OJ3-0.45)
1.50
CU25-1.IO)
1S.O
Q5.0-2X5)
3JO
(2.5-3.1)
BHtFU
rUMttwutn
Ctefticiot
(5«CI.)
UM/>)
7.10
(.15-100.0)
•
7.10
(4J-100.0)
43.0
UXJ-SO.D)
700.0
(— )
4.51
(2. 1-10.0)
Bin SuauM
later >ater
(D^B£AifiBZ* •»)
2S.73 0.0244
4^. ft 0.02O2
U.07 0.0311
133.50 0,0154
11.14 O.CSU
(12x40)
1UU3 «B»> 11.0
*«•«
U2rW)
ira.i Kint-o 11.0
F-400
warn
VflBMB llvO
F-»oo
KO1J-Q 11-0
r»-e
U2HO)
1.M
15.4
SZ.03 0.0077
O.4-1.Z)
1.70 4JO
O.D4.5)
O-JJ-Ufl
2.30 3.JO
14.0 t~n
(O.N-3.50)
13.00
3 JO
75.C O.OOU
14.5 O.Q2Q9
37
-------
Dp,i were held constant while a search was done on the surface diffusivity
using the BPSDM. The porosity of the adsorbent, e , van accounted for in the
development of the BPSDM and the true pore diffusion coefficient incorporated
both the porosity and tortuosity of the adsorbent. See equation IV-1. The
following equation was used to determine the pore diffusivity:
Dp,i
Dl
'
in which, T is the tortuosity. It was set equal to 1.0, because it will give
the largest contribution of pore diffusion flux. Dj ^ is the liquid
diffusivity of adsorbate i which was calculated from Equation V-6.
As shown in Figures VI- 1 to VI-6, the BHSDM and the BPSDM simulations
produced nearly identical concentration profiles. In all cases, as shown in
Table VI-2, the D ^ which was determined using the BPSDM was slightly lower
than the D, ; which was determined in the BHSDM. The difference in the values
s, i
of D$ ^ from the two models reflected the contribution of the pore flux.
Therefore, the pore flux was negligible. This was further confirmed from the
BPDH predictions. Since the tortuosity was st>t equal to one in these
predictions, the largest flux due to the contribution of pore diffusion
coefficient would be observed. However, as shown in Figures VI-1 to VI-6, the
pore prediction did not predict any of the concentration profiles.
Accordingly, it can be concluded that surface diffusion was the controlling
soechanism. See Appendix 8 for a sample data file and a sample output file for
both the BHSDM and BPSDM.
Two single-solute rate studies were conducted in Milli-Q water with F-
'•00, 60x80 mesh carbon. The two compounds were the moderately— adsorbing
t richloroethene and the strongly-adsorbing tetrachloroethene. As shown in
Table VI-2, the D$ i which was determined using the BHSDM and BPSDM for the
• 38
-------
smaller carbon were larger than the DS i measured for the larger carbon
(12x40).
As discussed in Section V, the Biot and Stanton numbers may be used to
evaluate whether the concentration difference across the DCBR is negligible
and whether film transfer or surface diffusion controls the rate of
adsorption. Table VI-2 displays the values of the Biot and Stanton numbers.
Even though all of the Stanton numbers were not less than 0.017 (This would
indicate that effluent to influent concentration ratio was less than 0.95.)
the concentration gradient across the differential carbon column was not
large. Also, it was not always possible to obtain Biot numbers greater than
30 (This would guarantee surface diffusion controlled.), because the carbon
dosages which were required to guarantee a representative would cause the
experiment to become film transfer limited. See Section V-B for further
discussion. Eventually, larger batch reactors which contained similar carbon
dosages were used to resolve this problem.
B. Equilibrium Tine and Concentration for the Differential Column
Batch Reactor Studies
The equilibrium time and concentration of the DCBR were determined in
order to evaluate whether the capacity which was observed in the batch rate
study agreed with the bottle point isotherm. That is, if the DCBR was run for
a long length of time, the equilibrium concentrations would agree with the
isotherm capacities that are reported in Table VI-3. Moreover, it was
expected that the equilibration time would be longer for the larger carbon
particles (12x40), while the equilibration time would be shorter for the
smaller carbon particles (60x60). The equilibrium concentration was
determined by solving Equation 5-2 in Appendix 5 by trial and error. The
equilibration time was determined by: running the BE SDH until 105% of the
39
-------
bbl* YX-4. Ctapwrm of tit* Hpa4 fim»»rratlfiti t* tta Fa*!
Cbacrrcd GKMvtxmim tad Tiati for tb* Diflcxvu-ul QaJva L«ttA Jaartag Stadias
Cteooiiwi I&itlAl VciiW lbd>l £aul^rt4B «7f
Triddort»Un> 1141.3 1 DIM. TJJ 1C.4S 20B.4
TV-S
CUi40)
Tri£Mnn»tiK^ 132S.V ftillr-4) 141.4 1.W 1£3.9
UblO)
P-400
U2l40)
Tritilort«ti«» 1S12.« Kllli-Q 104.7 21.74 1M.7
(1^40)
Ft&il Cb*«r«vd
TIB a u> oca
Drr«
«
-
1.0
J.f!
J-K
J.11
0.71
S.O
12.12
-------
equilibrium concentration was attained. As shown in Table VI-3, the'
equilibrium concentration determined in the batch reactor appeared to be the
same as the equilibrium concentration determined from the equilibrium data
when the time to achieve equilibrium is considered. In other words, the
equilibrium concentration was 'less then the final concentration of the DCBR
when the model calculated equilibration time was greater than the time to
achieve equilibrium was considered and the equilibrium concentration in the
DCBR agreed with the equilibrium concentration if the DCBR study was run for
an adequate length of time.
C. Multicexponent Results for the Tansau Water Matrix
JL Batch Rate Results Using Thawed Wausau Water Matrix
The purpose of this experiment was to determine the effect of the
background material present in the Wausau water matrix on the adsorption rate
of the carbon. Two batch rate studies which were conducted with F-400 and WV-
G carbon used thawed Wausau water. This water was previously frozen so a
minimum of biodegradation of the background material would occur and the
concentration of trichloroethene was increased and used as a tracer to
determine the competitive interactions of the background material other than
the VOCS. An analysis of the Wausau water before and after freezing are shown
in Table VI-4. As shown in Table IV-4. the concentration of the VOCS decreased
and benzene appeared. Benzene was never found in the raw Wausau water matrix.
However, if the raw Wausau water was aged, benzene was found,- accordingly, it
was thought that some of the aromatic compounds degraded to form benzene in
the presence of the background Wausau water matrix.
The DCBR data for trichloroethene which was conducted in organic-free-
water and in thawed Wausau water matrix are displayed in Figures VI-7 and VI-8
41
-------
Table VI—4. Biological, Organic, and Inorganic Analysis of Wansau Veil
#4 Water Matrix Collected on February 20. 1984
Compound
cis-1.2 dichloroethene
Tr ichl oroe thene
Tetracaloroe thene
Benzene
Toluene
Ethylbenzene
o.p-Xylenc
m-Xylene
Raw
Water
Analysis
(3/15/84)
(ug/L)
213.2
193.5
128.8
RA.
59.1
N^.
29.5
20.8
Thawed
Water
Analysis
(8/23/84)
(MS/I-)
86.4
6.4
55.4
56.9
24.4
2.4
11.7
3.6
N.A. Not Analyzed
Samples were analyzed using a Hewlett-Packard 5S30A
Purge and Trap Gas chromatograph
Component Result
Total Organic Carbon (TOC) 8.4 mg/L
TOC after Purging 8.6 mg/L
Total Carbon (TC) 29.2 mg/L
TC after Purging 22.3 mg/L
Manganese 1.27 mg/L
Iron 5.3 mg/L
Fluoride 0.34 mg/L
Alkalinity 84.0 mg/L
pH 6.8
Color 64.0
Ames Test Negative
Standard Plate Count Negative
-------
o
o
*s.
O
+
z
o
<
DC
H-
III
O
z
o
o
Q
UJ
O
D
Q
UJ
tr
1.0
0.8
0.8
0.4
0.2
0.0
D
TRICHLOROETHENE BATCH RATE COMPARISON
CARBON TYPE: 12X40 F-400
PARAMETERS FOR THAWED WATER STUDY
Bl= 75.82; St= .0085; Co=1441.G ug/L
PARAMETERS FOR MILLI-G WATER STUDY
Bl~ 18.14; 8t° .0316; Co°1322.7 ug/L
LEGEND
• -THAWED WAUSAU WATER EXPERIMENTAL DATA
D- MILLI-Q WATER EXPERIMENTAL DATA
D D
a
n
a.
a
a
n.
•
0.0
20.0
40.0 60.0 00.0
TIME, HOURS
100.0
120.0
140.0
Figure VI-7. Comparison of tlie TrJchloroetlienu Batch Hate llut.n Collected in Mllll-Q Water and Thawed
Wausau Water on I'-'tOO. CVirUon (l)s for TrIcliloroethene in Thawed Wausau Water: 2.6 10-10cm2/s;
ns for Trichlorocthcne 'in Mllll-Q Water: 3,1 10-1° cm2/s).
-------
O
O
^x
O
«.
z
O
<
DC
h-
uJ
O
z
O
O
O
UJ
O
D
a
UJ
oc
i.o
0.8
0.6
0.4
0.2
0.0
a
a
TRICHLOROETHENE BATCH RATE COMPARISON
CARBON TYPE: 12X40 WV-G
PARAMETERS FOR THAWED WATER STUDY
Bl= 82.0 ; St= .0077; Co=1241.6 UQ/L
T-ARAMETERS FOR MILLI-Q WATER STUDY
Bl= 14.5 ; St= .0205; Co = 1318.6 ug/L
D
LEGEND
* => THAWED WAUSAU WATER EXPERIMENTAL DATA
a=MlLLI-Q WATER EXPERIMENTAL DATA
a
D
a
• • •
0.0
20.0
40.0 60.0 80.0
TIME, HOURS
100.0
120.0
140.0
Figure VI-8. Comparison of the Tr i cliloroctliono Hatch Rate Data Collected In Mllll-Q Water and Th;iwed
Wausau Water on WV-G Carbon
for Triclilorocthcne in Tliawed Waiisau Water: 2.8
03 for TrJeliloroethenc in MtlH-Q Water: 3.3 10
~10
2/s).
-------
for F-400 and WV-G carbons, respectively. The organic-free-water
trichloroethene data showed a slower approach to equilibrium than the
trichloroethene data which was collected in the thawed Wausau water matrix,
because it was conducted at a higher flow rate. However, the difference
between the organic-free-water results and the thawed Wausan water results was
due to the difference in the liquid-phase mass transfer rate. As shown in
Table VI-2, the surface diffusion coefficients for the trichloroethene in the
organic-free-water were within the experimental error of those which were
determined ?.n thawed Wausau water. Since most of the VOCS were lost when the
Wausan water was frozen, the background total organic carbon in the thawed
Wausau water had little effect on the adsorption rate and capacity for the
solute trichloroethene when its concentration was increased to approximately
1400 ug/L.
2. Multiconpoaent Results Using Fresh Wansau Water Matrix
The purpose of this experiment was to determine if a multicomponent batch
rate study would provide useful kinetic data on the components which were
found in the Wausau water matrix and whether the correlation presented in
Section VIII-D would allow the concentration history profiles to be predicted
using the the BPSDM. Appendix 7 contains the raw data along with the
operational parameters.
The rate study was conducted for only four days, because the pxmp failed.
Only five data points were collected over the four day period and the problems
with the degradation of the aromatic compounds (See Section VI-C-3) made it
impossible to predict the data with ths BPSDM or to use it to determine the
surface diffusivities. In addition, the selection of a proper carbon dosage
was not possible for the determination of the surface diffusivities. If a
high carbon dosage was chosen to observe the concentration history profile of
45
-------
the weakly-adsorbing solute, it would result in a film transfer limited case
for the strongly-adsorbing solute. If a low carbon dosage was chosen to
observe the concentration history profile of the strongly-adsorbing solute,
the concentration history profile for the weakly-adsorbing solute would not be
significantly depressed enough to see a concentration profile and allow the
determination of the intraparticle surface diffusion coefficient. The model
prediction, using the calculated surface diffnsivities from equation VIII-13,
along with the raw data are displayed in Table 7-3.
3j_ Degradation Results o_f_ the Wausau Water Matrix
The purpose of this experiment was to determine if a 0.22(im Millipore
filter would eliminate microorganisms in the Vausan water well that may have
been responsible for the degradation of the aromatic compounds. The other
objective was to determine if the 0.22}im filter would adsorb any of the
volatile organic compounds found in the water matrix.
a. Experimental Plan for Degradation Experiments
(1) A 40 liter glass carboy was filled with water from Wausau
well #4. The water was spiked with toluene to an initial
concentration of 64 ug/L. The glass carboy was placed in a constant
temperature environment of 11°C. A magnetic stirxer was used to keep
the contents of the carboy well mixed.
(2) A pump and a 0.22|jm filter were placed in series. Sampling
ports were placed before and after the filter. Five liters of the
spiked water was initially flushed through the system to purge the
lines.
(3) Samples were taken before and after the 0.22+un filter. Two
46
-------
camples were taken immediately after purging the lines: aa influent
to the filter and an effluent to the filter. This would determine
whether any of the compounds present in the water matrix were
adsorbed onto the filter. Eight influent and effluent camples were
then collected during the first hour of the experiment in 45 ml
sample vials. The eight filtered and unfiltered camples were stored
in an isothermal environment of 11°C.
(4) A filtered and unfiltered sample was then analyzed using
the purge and trap method for an eight day period. Table VI-5
contains the raw data.
b. Results
Figure VI-9 shows the data for the degradation experiment. The
compounds of interest were trichlor^ethene, tetrachloroetheno, cis—
1,2 dichloroethene, end the spiked toluene. The influent and
effluent concentrations of the immediate samples showed that no
solutes adsorbed onto the 0.22(im filter. The eight day study
resulted in the same influent and effluent concentrations for the
cis-1.2 dichloroethene, trichloroethene, and tetrachloroethene.
However, both the influent and effluent concentration for toluene
showed that degradation was present. The 0.22jun filter will remove
any known organism that could cause degradation. Also, toluene in
oxganic-free-water showed no sign of degradation over a three week
period when used as a standard for the purge and trap analysis.
Therefore, toluene in the Wausau water matrix was degraded by some
other mechanism.
47
-------
Table VI-5. Degradation Study of the Wausan Water Ihtf ix
Day Influen^ Effluent
(concentration, jig/L)
cis-1.2 dichloroethene
Efftuefrfr foflpent
(concentration, |ig/L) (concentration, |ig/L)
Trichloroethcna Tetrochloroethere
Influent Effluent
(concentration. pg/L)
Toloena
00
74.0
74.0
74.0
76.0
72.0
68.0
74.0
70.0
76.0
72.0
71.0
68.0
68.0
62.0
52.0
52.0
50.0
54.0
48.0
42.0
50.0
49.0
55.0
48.0
48.0
48.0
42.0
45.0
36.0
38.0
36.0
38.0
34.0
29.0
32.0
38.0
36.0
32.0
31.0
33.0
29.0
26.0
64.0
54.0
43.0
37.0
22.0
62.0
62.0
42.0
49.0
24.0
22.0
-------
IO
D)
D
z
o
5
cc
UJ
o
z
o
o
1150.0
140.0
130.0
120.0
110.0
100.0
90.0
80.0
70.0
60.0
50.0
40.0
30.0
20.0
10.0
0.0
DEGUADATION STUDY ON THE
WAUSAU WATt-R MATRIX
o> = INFLUENT
a « EFFLUENT
• = INFLUENT
• = EFFLUENT
A-INFLUENT
*-EFFLUENT
0 = INFLUENT
P= EFFLUENT
LEGEND
CIS-1,2 DICHLOROETHENE
CIS-1,2 DICHLOROETHENE
TOLUENE
TOLUENE
TETRACHLOROETHENE
TETRACHLOROETHENE
TRICHLOROETHENE
TRICHLOROETHENE
0.0 1.0
2.0
3.0
7.0
Figure VI-
4.0 6.0 6.0
TIME, DAYS
9. Results of' the Oegrnd.ition Study on tlie Fresh Wnusau Water Matrix.
e.o
o.o
10.0
-------
TII. SBNsmvrrr ANALYSIS OF THE MODEL PARAMETERS WHICH CHARACTERIZE
THE SQLUnONS TO THE DIFFERENTIAL COLUMN BATCH REACTOR
In order to assess the impact of the model parameters on the
determination of the surface diffusivity, a sensitivity an&lysis was conducted
on all the parameters which affected the BHSDM calculations. These were the
isotherm and kinetic parameters. The Freundlich isotherm parameters, X and
1/n. were determined independently and were assumed to be correct within
experimental accuracy. Accordingly, the Freundl ich parameters, K and 1/n,
were varied plus or minus their 95% confidence interval in the sensitivity
analysis. The film transfer coefficient and the surface diffusion coefficient
were varied plus or minus 50% in the sensitivity analysis.
There are three important parameters to consider in the determination of
the surface diffusivity which were illustrated by the sensitivity analysis:
the Biot number and the Freundlich isotherm parameters K and 1/n. A high Biot
number is desirable (Hand et. al. ; 1984), because the intraparticle mass
transfer rate will control the adsorption rate and a good estimate of the
surface diffusivity may be determined.
A. Sensitivity Analysis of the Liquid Phase Mass Transfer Rate and the
Intraparticle Diffusion Rate in the Determination of the
Surface Diffusion Rate
The impact of the film transfer coefficient and the surface diffusion
coefficient on the DCBR study depends on the Biot number. The Biot numbers
which were observed in the DCBR experiments ranged from 18.1 to 133.5. See
Table VI-2. A sensitivity analysis, therefore, was conducted on Biot
numbers of 18.1, 28.7, 75.8, and 133.5.
As the Biot number increases, it was. expected that the effects of the
film transfer rate would be reduced. Figures V1I-1 to VII-8 display the
effect of the film transfer coefficient and the surface diffusivity on the
50
-------
o
O
O
o:
z
LU
O
z
o
o
Q
LU
O
D
Q
UJ
CC
MODEL PARAMETERS:
MIIII-Q Water ; Temp - 11.0 Deg.C
Carbon Typo: ROO 12x40 Mesh Rad=.06129 cm
Solute: Trlchloroethene
Bl « 18.1 ; St =» 0.0317 ; Tau = 86.7 m!n.
.6 {umol/g)(L/umo!)**1/n ; 1/n«0.4163
Do = 65.C mq/L : pH » 8.0
LEGEND:
— -BEST FIT In Kl Uulng the BHSDM
-•-+GO"/. Change In Kf Using the BHSDM
- 50% Change In Kf Using the BHSDM
0.0
20.0
40.0 60.0 80.0
TIME, HOURS
100.0
120.0
140.0
Figure VII-1. BHSDM Sensitivity Analysis of +/- 50% k, for Trichloroetliene in Milli-Q Water and
(12x40) F-400 Carbon (Bi - 18.1; C = 1322.7
-------
Ul
ro
O
O
^x
O
*
z
O
DC
UJ
O
z
O
O
Q
HI
O
13
Q
UJ
CC
0.2
0.0
0.0
MODEL PARAMETERS:
MIIII-Q Water ; Temp - 12.0 Deg.C
Carbon Type: F400 12x40 Mesh Rad=.05129 cm
Solute: cls-1.2 Dlchloroothone
B» - 28.7 ; SI = 0.0266 ; Tau = 19.0 mln.
K= 61.0 (umol/g)(L/umol)"1/N ; 1/n=0.5618
Do " 34.8 mg/L ; pH = 6.3
LEGEND:
-— BEST FIT In Kl Using the BHSDM
——+50Ve Change In Kl Using the BHSDM
--60% Change In Kf Using the BHSDM
20.0
40.0 60.0 80.0
TIME, HOURS
100.0
120.0
Figure VII-2. BHSDM Sensitivity Analysis of.-t-/- 50 "-f for cis-1,2 dicliloroethene in Milli-Q
Water and (12x40) F-400 Carbon (Bl=28.7 ; C0 - 507.0 ug/L)
to* '
-------
1.0
o
o
•«*
o
z"
g
5
DC
Z
LLJ
O
Z
o
o
Q
01
O
"D
Q
UJ
CC
O.S
0.6 -
0.4
0.2 -
0.0
LEGEND:
BEST FIT In Kl Using the BHSDM
460V* Change In Kl Using the BHSDM
50% Change ?n Kf U«ine ins 3H8DM
MODEL PARAMETERS:
Thawed Wauaau Water ; Tamp - 11.0 Dag.C
Carbon Type: F400 12x40 Mesh Rad-.061l29 cm
Solute: Trlohloroathene
Bl •* 76.8 ; St - 0.0085 ; Tau - 8.03 mln.
K-1B6.8 (umol/g)(L/umol)"1/n ; 1/n-0.41B3
Do - 60.7 mg/L ; pH - 8.93
0.0 20.0 40.0 80.0 80.0 100.0
TIME, HOURS
120.0
140.0
Figure VII-3. BHSDM Sensitivity Analysis of +/- SOX kf for Trichloroethene in Th«v*cl Wmts*u Water
and (12x40) F-AOO Carbon (Bi-75.8 ; CQ - UA1.6 yg/L).
-------
o
O
O
»
z
o
h-
<
DC
Z
-------
o
O
->.
O
•I
z
o
DC
Z
UJ
o
z
o
o
Q
UJ
O
D
Q
UJ
cc
0.8
0.2 -
MODEL PARAMETERS:
MIIII-Q Water ; Temp - 11.0 Deg.C
Carbon Type: F400 12x40 Meeh Rad-.06129 cm
Solute: Trlchloroelhene
Bl - 18.1 ; 3t - 0.0317 ; Tau - 85.7 mln.
K-198.8 (umol/g)(L/umol)"1/n ; 1/n-0.4163
Do • 56.6 mg/L ; pH - 8.0
LEGEND:
BEST FIT In Da Using the BH8DM
450V* Change In Da Using the BHSDM
-50% Change In Da Using the BHSDM
20.0
40.0 • 80.0 80.0
TIME, HOURS
100.0
120.0
140.0
Figure VI1-5 . BHSDM Sensitivity Analyaia of +/- 501 D for Trlchloroethen* in Mllli-^J Water and
(12x40) F-400 Carbon (Bi - 18.1; CQ - 1322.7
-------
o
o
«>»
o
MODEL PARAMETERS:
MI1II-Q Water ; Temp • 12.0 Deg.C
Carbon Type: F400 12x40 Mash Pad-.05129 cm
Solute: cla-1,2 Dlchloroethene
B! - 28.7 ; St - 0.0266 ; Tail « 10.0 mln.
K- 51.0 (umol/g)(L/umo!)"1/N ; 1/n-0.5616
Do - 34.B mg/L ; pH - 6.3
LEGEND:
BEST FIT In Da Using the BHSDM
(-60% Change In Da Using the BHSOM
Change In Da Using the BHSDM
LU
O
z
o
o
a
UJ
o
D
a
UJ
cc
0.0 20.0 40.0 80.0 80.0 100.0 120.0
TIME, HOURS
Figure VII- ft. BHSDM Sensitivity Analysis of +/- 50J D8 for; cls-1,2 dichloro«th«n« in Millt-<3
Water and (12x40) Carbon (Bi-28.7 ; Co - 507.0 Ug/L).
-------
o
o
"•x
o
»
z
o
UJ
O
Z
o
o
D
UU
O
D
Q
UJ
QC
0.8
0.2 -
MODEL PARAMETERS:
Thawed Wauaau Water; Temp - 11.0 Oeg.C
Carbon Type: F4DO 12x40 Mesh Rad-.06129 cm
Solute: Trlohloroelhene
Bl - 75.B ; St - 0.0085 ; Tau - 8.03 mln.
K-198.8 (umol/8)(L/umol)"1/n ; 1/n-0.4183
Do - 60.7 mg/L ; pH - 6.93
LEGEND:
BEST FIT In Da Uilng the BHSDM
-. — 450% Change In Da Using the BHSDM
50% Change In Da Ualngthe BHPDM
0.0 20.0 40.0 60.0 BO.O 100.0
TIME, HOURS
120.0
140.0
Figure VII-7. BHSDM Sensitivity Analysis of +/- 50Z Da for Trlchloroethene In Thawed Wausnu Water
and (12x40) F-400 Carbon (Bl • 75.8 ; CQ • 1441.6 Ug/U.
-------
O
o
^
O
•»
z
o
DC
HI
O
z
o
o
Q
LU
O
Z)
Q
UJ
MODEL PARAMETERS:
MIIII-Q Water ; Temp - 13.0 Deg.C
Carbon Type: F400 12x40 Mesh Rad-.05129 cm
Solute: Toluene
Bl - 133.5 ; St - 0.0134 ; Tau - 16.4 mln.
K-475.0 (umol/g)(L/umol)"1/N ; 1/n-0.32fl2
Do = 7.8 mg/L ; pH - 8.3
LEGEND:
BEST FIT In Ds Using the BHSDM
+50% Change in Ds Using tho BHSDM
60% Change In Da Using the BHSDM
20.0
80.0
40.0 80.0
TIME, HOURS
Figure VII-8. BHSDM Sensitivity Analysis of +/- 50Z D9 for Toluene In Hilli-q Water and (12*40)
F-400 Carbon (Bl - 133.5 ; C0 " 372.4 pg/L).
100.0
-------
i'l! SPM c«lculationi for varioosBiot cu=b«rt. At short tlmtt. Him transfer
1 tmUs the rste and the initial part of the curve ii acre impacted by film
tmnxftr. whjl« tb« «t longer tines, surface diffusion limits the rate and the
liter p«rt of the curve i* impacted by surface diffosivity. Figure* VII-1
through VII-4 display the sensitivity analysis for the film transfer
coefficient, and Figures VII-5 through VII-8 display the sensitivity analysis
for the surface diffusion coefficient. These figures demonstrated that for
Biot numbers greater than abont 30. film transfer had little impact on the
BHSDM calculations. It is likely that these results are only valid for the
particular Freundlich K's and 1/n's in this study.
B. Sensitivity Analysis of the Freundlich Isotherm Parameters K said I/a
in tbn Determination of the Surface Diffusion Bat*
The Freundlich isotherm parameters I and 1/n must also be well defined to
accurately estimate the surface diffnsivity. Table VI-1 displays the upper and
lower bounds of the 95% confidence limits. A sensitivity analysis of the
Freundlich isotherm parameters, K and 1/n. was performed using the 95%
confidence limits for trichjoroethene, tetrachloroethene. and toluene, and are
displayed in Figures VII-9 through V1I-14, respectively. As shown in Figures
VII-9. VII-10, and VII-11. calculations were sensitive to the 95% confidence
limits in the Freundlich isotherm parameter K for trichloroethene, while the
95% confidence limits in the Freundlich itotherm constant K tetrachloroethene
and toluene had less impact on BHSDM calculations. Although the 95%
confidence limits for the Freundlich isotherm parameter K have a significant
impact on the predictive profiles, the capacities observed in the DCBR studies
agreed fairly well with isotherm capacities as shown in Table VI-3.
As shown in Figures VII-12. VII-13. and VII-14. the Freundlich isotherm
parameter 1/n for tricbloroethene, tetrachloroethene. and toluene had little
impact on the BHSDM calculations.
59
-------
o
o
^»
o
•
z
o
z
Ul
O
Z
o
o
Q
Ul
C
D
Q
UJ
CC
0.8
0.8
MODEL PARAMETERS:
MIIII-Q Water ; Temp - 11.0 Deg.C
Carbon Type: F4CO 12x40 Mesh Rad-.06129 cm
Solute: Trlchloroethene
Bl - 18.1 ; St - 0.0317 ; Tau - 85.7 mln.
K-19B.8 (umol/g)(L/umol)"1/n ; 1/n-0.418J
Do - SS.5 mq/L ; pH - 8.0
LEGEND:
BEST FIT Freundlloh K Ualng BH3DM
— •— 495% C.I. Freundlloh K Using BH8DM
96% C.». Freundllch K Ualng BH8DM
20.0
40.0
100.0
120.0
Figure VI 1
60.0 80.0
TIME, HOURS
-9. BHSDM Sensitivity Analysis of +/- 95Z Confidence Interval for the Freundlich K
for Trlchloroethene in Mllli-Q Water and (12x40) Carbon (Bl-lB.l ; Co-1322.7
140.0
-------
1.0
o
O
-«.
O
z
g
LU
O
Z
o
o
o
uu
o
D
Q
LU
CC
0.8
0.6
0.4 I-
0.2 I-
0.0
0.0
MODEL PARAMETERS:
MIIII-Q Water ; Temp - 11.0 Deg.C
Carbon Type: F400 12x40 Mesh Rad-.06129 cm
Solute: Tetrachloroethene
Bl - 48.B ; 8t - 0.0202 ; Tau - 81.2 mln.
K-650.6 (umol/g)(L/umol)"1/n ; 1/n»0.4679
Do - 21.27 mg/L ; pH - 6.0
LEGEND:
-—BEST FIT Freundllch K Using BHSDM
-.-495% C.I. Freundlloh K Using BHSDM
96% C.I. Freundllch K Using BHSDM
20.0
40.0
60.0
80.0 100.0 12C.O 140.0 160.0 180.0 200.0
TIME, HOURS
Figure VII-IO. BHSDM Sensitivity Analysis of +/- 95X Confidence Interval for the Freundlich K for
Tetrachloroethene in Milli-Q Water and (12x40) F-400 Carbon (Bi-46.8 ; C0-1438.* V>g/U .
-------
MODEL PARAMETERS:
MIIII-Q Water ; Temp - 13.0 Deg.C
Carbon Type: F400 12x40 Mesh Rad-.05129 cm
Solute: Toluene
Bl - 133.5 ; 8t - 0.0134 ; Tau - 16.4 mln.
K-475.0 (umol'g)(L/umol)"1/N ; 1/n-0.3282
Do'- 7.6 mg/L ; pH « 6.3
LEGEND:
BEST FIT Freundllch K
+95% C.I. Freundllch K
-95% C.I. Freundllcn K
Using BHSDM
Using BHSDM
Using BHSDM
Figure VII-11
80.0
100.0
40.0 80.0
TIME, HOURS
BHSDM Sensitivity Analysis of +/- 95Z Confidence Interval for the Freundlich K for
Toluene in Milli-Q Water and (12x40) F-400 Carbon (Bi-133.5 ; Co- 372.4 yg/L).
-------
o
o
-X
o
DC
Z
LU
O
Z
o
o
0
UJ
o
D
Q
UJ
CC
MODEL PARAMETERS:
MIIII-Q Water ; Temp - 11.0 Deg.C
Carbon Type: F400 12x40 Mesh Rad-.05129 om
Solute: Trlohloroethene
Bl - 18.1 ; St - 0.0317 ; Tau - 85.7 mln.
K-198.8 (umol/g)(L/umol)**1/n ; 1/n-0.4163
Do - 65.6 mg/L : pH - 8.0
LEGEND:
BEST FIT Freundllch 1/n Using BHSDM
495V. C.I. Freundllch 1/n Using BHSDM
-96% C.I. Freundllch 1/n Using BHSDM
0.0
20.0
40.0 60.0 80.0
TIME, HOURS
100.0
120.0
140.0
Figure VII-12. BHSDM Sensitivity Analysis of +/- 95Z Confidence Interval for the Freundlich 1/n for
Trlchloroethene in Milli-Q Water and (12x40) F-400 Carbon (Bl-18.1 ; Co-1322.7 Ug/L).
-------
o
o
--.
o
»
z
o
r-
UJ
O
Z
o
o
Q
UJ
O
D
O
UJ
CC
MODEL PARAMETERS:
MIIII-Q Water ; Temp - 11.0 Deg.C
Carbon Type: F400 12x40 Meah Rad-.06129 om
Solute: Tetrachloroethena
Bl - 48.B ; St - 0.0202 ; Tau - 81.2 mln.
K-660.8 (umol/g)(L/urnol)"1/n ; 1/n-0.4679
Do - 21.27 mg/L : pH - 8.0
LEGEND:
BEST FIT Freundllch 1/n Using BHSDM
-• — f96% C.I. Freundllch 1/n Using BHSDM
95% C.I. Freundllch 1/n Uslno BHSDM
20.0
40.0
80.0
140.0 160.0 180.0 200.0
Figure VII-13.
80.0 100.0 120.0
TIME, HOURS
BHSDM Sensitivity Analysis of +/- 95X Confidence Interval for the Freundlich 1/n for
Tetrachloroethene in MlUi-Q Water and (12x40) F-400 Carbon (Bi-46.8 ; CQ-1A38.4 pg/L)
-------
o
o
^N,
O
g
<
cc
UJ
O
z
o
o
Q
UJ
O
Z>
Q
UJ
CC
MODEL PARAMETERS:
MIIII-Q Watar ; Temp - 13.0 Deg.C
Carbon Typo: F400 12x40 Mesh Rad-.05129 cm
Solute: Toluene
Bl - 133.5 ; St • 0.0134 ; Tau - 16.4 mln.
K-475.0 (umol/g)(L/umol)"1/N ; 1/n-0.32B2
Do *• 7.6 mg/L ; pH • 6.3
LEGEND:
BEST FIT Freundllch 1/n Using BHSDM
+95% C.I. Freundllch 1/n Using BHSDM
-96% C.I. Freundllch 1/n Ualng BH3PM
0.0
Figure VII-14,
20.0
40.0 60.0
TIME, HOURS
80.0
100.0
BHSDH Sensitivity Analysis of +/- 95Z Confidence Interval fgr the Fr;eundlich 1/n for
Toluene In Milli-Q Water and (12x40) F-400 Carbon (Bi - 133.5 ; Co m 372.4 Ug/L ).
-------
VUl. CORRK1.A1IONS FOR TBB DETEBM1NATION OP SUKFACE DIFFTJSIYITIBS
Correlations were developed to determine the surface diffusivities from
the physical properties of the adsorbent and the known chemical properties of
the adsorbates. The properties of adsorbates that where investigated for
possible correlation were: 1) the boiling point of the adsorbates. 2) the
liquid diffusivity of the adsorbates and the partitioning evaluated at the
initial concentration of the adsorbates 3) the liquid diffusivity and the
average driving force of the adsorbates and 4) the aelf-diffnsivity and the
partitioning evaluated at the initial concentration of the adsorbates.
A. Correlation Basod om th* Boil IAS; Foist of the Adsorbates
A net hod which was proposed by Suzuki et. al.. (1975), is given in the
following equation:
D, A exp1"8 Adaorbatea
The basis for this equation was to set the effective solid diffusion flux
e«.ual to a pore diffusion flux times a constant. This constant was defined as
the pore to surface diffusion flux ratio (PSDFR). The following equation was
developed from the total adsorbent phase mass flux. J^ot' l^Ten ^* F^-inra III-
1:
66
-------
*1 Dl «„ • <•'
Vt - P - - — — - *- (VJIJ-2J
The following equation it t t Inp 1 if ioat ion of Equation VJJI-2 wind
irj resents the total flax «> an effective solid diffusion flux:
Jtot " ~ D
r
where
Snrfsce Flux - - D$
Contribution 3i
D, « «C
Pore Flai - - - £- - -
Contribution T Si
Effective ( 3q
Solid Flux '
Contribution
The pore diffusion coefficient was given ••:
Dl
Dp •= - (VIII-4)
Value* for the tortuosity, r range between 2 and 6. A value of 1.0 was
chosen for ; , because it would give the largest flux due to the contribution
of pore diffusion. However, this was not important, because the effect* of T
were taken into account in the pore to surface diffusion flux ratio, PSDFR.
Settinc the Equation VIII-2 equal to Equation VIII-3 yields the following
eqoat ion :
67
-------
r,, «r »r
Reariinning Equation V1I1-5 and using th* chain rule results IB Equation
Vlll-6:
-D
(VIIJ-6)
«r
Setting the turftoe diffniion coefficient. D(, »qnil to the pore
diffusion flax tines • con»t«nt (PSDFR - 1) yield*:
(PSDFR - 1)
(VIII-7)
Substituting Equation VIII-7 into Eqnttion YIII-6 tnd simplifying results
in the following equation:
3C.
D s
(PSDFE) (VIII-8)
Taking the partial derivative of the Frenndlich isothem equation with
respect to the liquid-phase concentration. C results ia thi« •qoa'tion:
l/n I C,
(1/n - 1 )
(VII1-9)
ac.
7he quantity, dq/dC . was determined from the Freondlich isotherm equation.
Pa r t i t i on i r. g is defined as the ratio of the concentration in the adsorbent
P |. R •. r t>. tlir concentration in the fluid phase. The average partitioning was
-------
taken over the entire concentration rang*. The lower limit of the
concentration was tero and the upper limit of the concentration was the
initial concentration, CQ. Thit reanlting equation ia:
•q / <»q/ec0) dc
*— (VIII-10)
•S / d(V
Snbatitntinj the quantit7, dq/»G, into Equation VIII-10 resulted im the
following equation:
dq / (1/n I C (1/n ~ 1} dC
^ (VIII-11)
Integrating and evaluating the equation at ita limits yields:
~cT~ i cov*
- (VIII-12)
dCp Co
Substituting Equation VIII-12 into Equation VIII-S results in the
following equation:
« DJI C
D'g - (PSDFR) (VIII-13)
Tp 'a * Co1 °
C. Correlation Based om th* Liquid Diffuaivity and th* Average
Driving Fore* of th* Adaorbat**
The correlation which was baaed on the liquid diffusivity and th*
average driving force of the adaorbates waa uaed to take th* average of that
which appeara ia Equation VIII-8. Th* lower limit of th* concentration waa
zero and the upper limit of the concentration waa the initial concentration.
The result waa:
69
-------
(VXII-14)
»q / dcp
Substituting the quantity, »q/dC , into Equation VIII-14 results U the
following equation:
~~ Jt CB(1/B - X) dC_
2 - » (VIII-15)
I&t«grtti&t and •Talntting th« •quation at its limits yields tk«
fol loving equation:
-X- c a - i/.)
dq (1/n) K (2 - 1/n)
Sabstitvti&g Equation VIII-16 into Equation VIII-8 xssultsd in tn«
following equation:
(PSDFR) (VIII-17)
p. (1/n) I (2 - 1/n)
D. Correlatio* Based
-------
k T f N0 1 l/S
1- (VIII-18)
2n ^ I Vb J
Equation VIII-18 was based on hydrodrnamieal theory. It take* •• it*
starting point the Stokas-Einstein equation. The ascnmptions of this equation
are: 1) there is no tendency for th« flnid to stick at the auxfaee of the
diffusing particle, and 2) the Molecule* are all alike and can be arranged lm
a cubic lattice with all Molecules touching.
Equation VIII-18 was substituted into Equation VIIJ-13 in place of Dj to
yield the final equation based on self-diffusion:
«_ DJJ^ C
(PSDFR) (VIII-1J)
*, P. K o
B. E* suit a and DiacuaaioB
The experimentally neasnred surface diffusiTities of various synthetic
organic compounds were obtained from the literature (Crittenden, 1978;
Pirbazari, 1981; Thacker. 1983; Tan Vliet eJL^ l_l^ 1981; Liu et. al.. 1981;
and Sab in. 1981). The important parameters, along with the calculated
contribution of the diffusion flux are presented in Tables VIII-2 through
VIII-4.
For the Suzuki method, measured surface dif fnsiTitiea of aliphatic,
N
halogenated hydrocarbons were plotted versus the ratio of the boiling point of
the adsorbate to the temperature of the experiment. The experimental surface
diffnaivities, along with the boiling points of the adtorbatea are displayed
in Table VIII-1. The data were fit using the International Mathematical and
Statictical Libraries (IMSL) nonlinear least squares method and was determined
by B In in i ring the sum of the differences between the experimental surface
d if f otiT it lei and the ratio of the boiling point of the adsorbate to the
71
-------
Im Ik. Chrrtl.tKm
laUUl t«ur
ilm Ktuli
Out**
telu T>j.
of Expir
f°T)
tolli* fotat
I«U
Dttfwirlty
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tvapersture of the batch rats study. The final form for the lituki equation
D. - 4.73 x ID"9 expl-11'665
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T*ki« vm-2.
el
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UtTI)
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11.0 L0« !.« 1.40 Tkit lotr
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-------
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P-TOLUF.NE SULFONAIE
F-400 <16X20>
PHENOL _
<16X20>
DODECVL BENZENS 5ULFOHATE
F-400 <18X20>
CIS-1.5! DICHLOROETHENE
F-400 <12X40>
3,5 DICHLOROPHENOL
/~- <18X20>
BRUMODinHLO COMETH ANE
F-400 <18X20>
F-400 <80X80> I
DIMETHYLPHENOL
"F-400 <16X20>
CHLOROFORM
F-400 <18X20>
DICHLOROETHANE
F-400 <18X20>
BENZENE
F-400 <18X20>
_CARSON TETRACHLOR1DE
F-400 <18X20>
f
TRICHLOROETHENE
F-400 <12X40>
TETRACHLOnOETHENE
F-400 <12X40>
TRICHLOROETHENE
WVQ <12X40>
TRICHLOROETHENE
WVQ <12X40>
WAUSAU WATER
TRICHLOROETHENE
— F-400 <12X40>
WAUSAU WATER
a io"n
• • • • ' ' it.l..i.l...iliml ilihlil 1 I I I I I Mlllli,liiiil...l i 1.1 ,1,1 I 1 I I I I I i,l,iiil.,,,li,.il iltlitil i , , , 1
10
10
10*
CALC. PORE DIFFUSION FLUX CONTRIBUTION, CM2/S
10
? VIII-l. Comparison Between the Measured Surface Di f fusivl I les and the Pore FHffnsion
Kuix•Contrlhution Using the Liquid niffuslviLy Correlation. Carbon Type a
Mesh Size is Indicated.
-------
poie flux rate was greater. This was the only occurrence of the pore flux
rate being greater in the literature. Coaaeqneatly. it was act used. beoaaee
it would affect the PSDFR determination. The p-bromopheaol and1 toluene
surface dif f us it it let were excluded, since these compounds l*ve « pore to
surface diffu*ion flux ratio that was each greater than the average pore to
surface diffusion flux ratio. The exclusion of these data allow the
correlation to nnd«re«ti»at« the surface diffusirities of SOM solutes.
The correlation which was baaed on the liquid diffusivity and on the
arerace driring force of the adsorbates was determined by plotting
experimental surface dif f us iy i t ie s versus the pore diffusion flux
contribution (PDFC) fro* the following equation:
PDFC - - - - (VIII-22)
(2 - I/a)
The experimental surface dif f usiv ities and the PDFC froat Table VIII-3
were fit using the IMfSL linear least squares. The best fit slope of the line
was 4.372 with 95% confidence limit* of 2.331 to 6'. 367. The correlation
coefficient for this method was O.S849. As show* ia Table 7III-J. only the
data for the aliphatic, halogenated. volatile organic compounds and the two
carbons of interest were used to determine the PSDFR.
The correlation which waa based oa the se 1 f-dif f uslv ity and the
partitioning evaluated at the initial concentration of the adsorbates waa
determined by plotting experimental surface dif f usivities versus the pore
diffusion flux contribution (PDFC) as shows i» the following equation:
• D». C
PDFC - - - - • - (VIII-2S)
T D K C 1/B
Tp pa *• *"o
The experimental surface dif f nsiv it ies from Table VIII-4 and the PDFC
-------
•UIU Vin-i. Onrarim •( U» CVlnUud wl Cb
••d <• U» *»»l»|» brt»U| Fore* cW
nrn* IwfM* DiffixtvttI**
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I
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P-400 (JJaJO)
1.21 , KU1M) 224. 0
F-4CO (.11x30)
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1. 10 lUlli-Q 106.0
•>*000 (13*40)
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F-WO (12*40)
1-23 MUli-Q 37.)
T-tOD (12x40)
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i.n mil HO icaa.f
F-400 C12r40)
4.0* Ullr-0 m.7
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P-400 <«0>«0}
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!/• ^»*^«^ ^&^$i
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unu
0.7430 2.0 1-X U TJMclm
umi
O.OOO 22.0 ]_4< JJ Kcbunri
UfC)
0.7S20 22.0 U5* n.0 Duckn
U>«1)
0.4470 20.0 2-»l !.» l*ta •
unu
O.C30 &.» 7J4 U bka •
UMI)
0.3(11 12-0 l.OH 37.0 TkU *M»f
O.Olf 21.0 4.n n.7 **^TIJL.*i»
a«tw
0.437* 11-0 0-33 LJ Tku (cvtr
0.457* Li-0 OJJ 0.4i 7XU tad?
p yr«; 13.0 3.0S 11.00 Tkij ladr •
.
0.41CI ]i n 1.71 4-30 Tki« *aAr
0.410 11.0 1.33 1.10 Iku iatfr
0.41(1 ii-O l.7f a.f tku (a«r
0.4071 rue i-w i_» iki» SMr
o.4on n.0 1.17 u iku tiadr
-------
from Equation VI11-23 were again fit naing the IMSL linear least squarei. The
best fit slops of the line was 4.349 with 95% confidence limits of 1.451 to
7.646. The correlation coefficient for this method was 0.7956. A. shown in
Table VIII-4. only the data for the aliphatic, halogen*ted, volatile organic
compounds and the two oarbont of interest were used.
The best correlation as determined from the correlation coefficient was
based on the liquid diffusivity and the partitioning evaluated at the initial
concentration of the adsorbates. Equation VIII-13. This equation is valid for
halogenated, one and two carbon molecules, and some aromatic substituted
organic compounds on F-400 and TV-G carbons. To make conservative estimates
.for fixed-bed design. Equation VIII-13 may be used to estimate the surface
diffusivity of a variety of adsorbates. With the exception of data from van
Vliet et. ajyu Equation VIII-13 either predicts the surface diffusivity with
reasonable precision or a lower surface diffusivity for some compounds. See
Table VIII-2 for a comparison between the measured and calculated surface
diffnsivity. Consequently, the calculated surface diffusivity can be used to
make a conservative estimate of the mass transfer xone lengths in a fixed-bed
(Band et. a_l.. 1984). This estimate would be conservative because, the
surface diffusivity would either be correct or underestimated such that there
would not be premature breakthrough of the solute in the fixed-bed.
79
-------
'..M. VUI
l-«^»— '
&>ulrn>
L^"""""
U^Llorv*
OJo.*-.
tti.«.o«
Ciiorcfpm
cir-1.: it-
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Tr u:M ?rm Lhn»
TV it .MOTTMthrtw
i r i^ Jtj OTX^I (ARBP
-4. r.«v«ri««K of \t» ,(Vlc«lil«< Ml | |i» Um.l Cmomr
cJl'J:! u, L7,'u """" "tk Uoa"r" r"~*u"
:<.*,IWM IU./.IO.V..U. T^!;^...,
3.7S MilIl-Q 1:4(1,0 O.J7»0
F--400 (ttiiO)
0.7« Kllli-Q J43.0 0.74SO
F--4OD (l»tiO)
I.n Mill.<3 E-4.0 O.«3t»
F-4OO (l*l»)
1.47 milt~Q 4J.J I.Tlio
3.10 MIIH-Q 1M.O O.W70
3.74 min-Q m.o o.^iio
BD--4000 (JQtlOO)
3.U Milli-O 357.0 O.M18
F-WO (Ui40)
9.01 Milli-O IfflM.i 0.4J79
P-400 («Ck80)
t.fi Miiii-u> J2il.? 0.4OTJ
rv c (iii4O)
10.0 Mllli-4 3^11. > 0.4T73
TV^-C (12t40)
Mirillx B..W m Ite kll-Ol(f«
-------
EC. CONQJJSIONS AND RECOMMENDATIONS
A. ConeInsions
1.) For single-solute differential column batch reactor studies on both
the 12x40 and 60x80 mesh carbons, the batch homogeneous surface diffusion
model and the batch pore and surface diffusion model were able to
simulate the concentration history profiles for the following volatile
organic compounds: cis-1,2 dichloroethene. tetrachloroethene, toluene.
and trichloroethene.
2.) The batch pore diffusion model was not able to predict the
differential column batch reactor experimental data for single-solutes on
the 12x40 .and 60x80 mesh carbons. Therefore, surface diffusion was the
controlling mechanism, because the pore diffusion mechanism alone did not
predict the data. In addition, the batch pore and surface diffusion
model, BPSDM, and the batch homogeneous surface diffusion model, BHSDM,
were compared and it was found that the surface diffusivity did not
change significantly from the BPSDM to the BHSDM. Therefore, the
contribution to the total intraparticle flux from pore diffusion was
negligible.
3.) The rates of uptake for trichloroethene in organic-free water and
trichloroethene in thawed Wan au water matrix were almost identical.
Since most of the VOCS were lost when the Wausau water was frozen, the
background total organic carbon present had no effect on the adsorption
rate or capacity of the carbon for the solute trichloroethene.
4.) It was not possible to conduct a multicomponent rate study on the raw
Wausau water matrix, since degradation and proper selection of the carbon
dosage were a problem. It was demonstrated that toluene degraded over &
period of eight days to 30% of it original concentration., while the
81
-------
aliphatic halogenated hydrocarbons (cis-1,2 dichloroethene.
trichloroetheue, and tetrachloroethene). showed little degradation.
Therefore, both degradation and adsorption were occurring in the
multicomponent rate study. It was not possible to select an appropiate
carbon dosage for a multicoaponent rate study. If a high carbon dosage
was chosen to observe the concentration history profile of the weakly
adsorbing solute, it would result in a film transfer limited case for the
strongly adsorbing solute. If a low carbon dosage was chosen to observe
the concentration history profile of the strongly adsorbing solute, the
concentration history for the weakly adsorbing solute would not be
significantly depressed enough, to see a profile and measurement of the
intraparticle surface diffusion coefficient for the weakly adsorbing
solute would not be possible.
5.) To properly design and evaluate DCBR data for the determination of
the surface diffusivity, the following three requirements, which are
based on the sensitivity analysis and other calculations, must be met:
(a) the Biot numbers should be greater than 30, such that the surface
diffusion is the rate-limiting mechanism, (b) the Stanton numbers
should be less than or equal to 0.017, sucli that the concentration
across the differential column is the same as the concentration in the
DCBR reservoir, (c) the Freundlich isotherm constants, K and 1/n. are
know to a high degree of accuracy.
6.) Four correlations were developed to determine the surface
diffusivities of aliphatic, halogenated volatile organic compounds from
the physical properties of the adsorbent and the chemical properties of
the adsorbates. The properties of the adsorbates that were investigated
for correlation were: (a) the boiling point of the adsorbates, (b) the
82
-------
liquid diffusivity of the adsotbates and the average driving force of the
adsorbates, (c) the self diffusivity of the adsorbates and the
partitioning evaluated at the initial concentration of the adsorbates.
and (d) the liquid diffusivity of the adsorbates and the partitioning of
the adsorbate between the bulk fluid and the adsorbent evaluated at the
initial concentration of the adsorbates. The correlation coefficients
for each of the above methods were 0.7016, 0.8849, 7699, and 0.9450,
respectively. Since the correlation which was based on the liquid
diffnsivity and the partitioning of the adsorbate between the bulk fluid
and the adsorbent evaluated at the initial concentration of the
adsorbates was the best fit, other compounds from the literature were
included in the correlation. The correlation is now applicable to
halogenated, one and two carbon molecules, and some aromatic substituted
organic compounds for the WV-G and F-400 carbons. The correlation
i
coefficient for this method was 0.8987.
7.) This correlation is useful to make conservative estimates for fixed-
bed design, because the correlation may be combined with the method
developed by Hand et, al.; 1984, to calculate the mass transfer zone
length in a fixed-bed.
Recomendations for Future work
Based on the results of this work, the following areas are
recommended for further study:
1.) More adsorbate-adsorbent systems need to be examined for the
correlation which is based on the liquid diffusivity and the partitioning
of the initial concentration of the adsorbate;. Also the effect of
particle size of the adsorbent and the initial concentration of the
83
-------
adsorbates should be examined to determine if a more general correlation
for the surface diffusivities can be developed.
2.) Finally, the correlation which was based on the liquid diffusivity
and the partitioning of the initial concentration, should be used to
calculate the surface diffusivities of the compounds of interest in the
Wausau water matrix. These surface diffusivities should be used in a
column pore and surface diffusion model to see if the breakthrough
profiles from a pilot column of the major components found in the Wansan
water matrix can be predicted.
84
-------
APPENDIX 1. REFERENCES
Bird, R.B., Stewart, W.E., and LIghtfoot, E.N., "Transport
Phenomena", John Wiley and Sons, New York, Hew York , 1960, pg.515.
Cheremlslnoff, P.N. and El lerbusch F., "Carbon Adsorption Handbook", Ann
Arbor Science Publisher Inc., Ann Arbor, Michigan, 1978, pp.3-6.
Crlttenden, J.C., "Mathematical Model Ing of Adsorber Dynamics-Single
Components and Multi-Components," thesis presented to the University of
Michigan, Ann Arbor, Michigan, In 1976, In partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
Crlttenden, J. C., and Weber, W. J., Jr., "A Predictive Model for Design
of Fixed-Bed Adsorbers: Single Component Model Verification," Journal o±
the Env 1 ronmenta I Eng I neer I ng D I v I s l.QQf Proceed 1 ngs of the Amer lean
Society of Civil Engineering, vol. 104, No. EE6, p.433, 1978.
Draper, N.R., and Smith, H., "Appl led Regression Analysis", John WI ley
and Sons. New York, New York, 1981, pp. 472, f34.
Fair, G.M., Geyer, J. C., and Okun, D.A., F laments of Water Supply and
Waste-water D1sposaj, John Wiley and Sons, Inc., New York, 1971, pp. 403-
7.
Fisher R.A., and Yates, F., Stat I stlcal Tab leg for Bio I og leal f
Agricultural, and. Medical Research, (6th ed!t:~n, 1963), p. 258.
Friedman, G., "Mathematical Model Ing of MuItlcomponent Adsorption In
Batch and Fixed-Beds," Thesis presented to Michigan Technological
University, at Houghton, Ml, In 1984, In partial fulfillment of the
requirements for a degree of Masters In Chemical Engineering.
Fritz, W., Merk, W., and Schl under, E.U., "Competitive Adsorption of Two
Dissolved Organlcs onto Activated carbon," Chemical FnglneerIng .Science,
vol. 36, 1980, p.743.
Furusawa, T., and Smith, J. M., "FI uId-Particle and Intra-Partlcl e Mass
Transport Rates In Slurries," Industrie I ajul Fnglneer tng .Chemistry
Journal, vol. 12, No. 2, p.197, 1973.
Hand, D.W., "User-Oriented Solutions to the Homogeneous Surface
Diffusion Model for Adsorption Process Design Calculations: Batch
Reactor Solutions", Thesis presented to Michigan Technological
University, at Houghton, Ml, In 1982, In partial fulfillment of the
requlrenents for a degree of Masters In Civil Engineering.
Hand, D.W., Crlttenden, J. C., M.ASCE, and Thacker, W. E., "User-Oriented
Solutions to the Homogeneous Surface Diffusion Model", Journal at
FnvIronmentaI Engineering, Vol.109, No.1, February, 1983, p.87.
Hand, D.W., Crlttenden, J. C., M.ASCE, and Thacker, W. E., "Simplified
Models for Design of Fixed-Bed Adsorption Systems", Journal oj.
Fnv I ronmenta I Eng I nc^r I ngr Vol.110, No.2, April, 1984 p. 440.
85
-------
Hayduk, W. and Laudle, H., "Prediction of Diffusion Coefficients for Non-
electrolytes In DIIute Aqueous Solutions," American Institute of Chemical
Eng1naerIng Journalf vol. 28, 1974, p.61l.
Johnson, A.S., "Transport of Ha Iogenated OrganIcs In Saturated Soil
Columns: Experimental and Theoretical ResuI ts," thesis presented to
Michigan Technological University, at Houghton, Ml, In 1994, In partial
fulfil Iment of the requirements for a degree of Masters ir. Chemical
Engineering.
Kato, S. and Crlttenden, J. C., Personal Communication, December 1984,
Department of Civ I I Engineering, Mich Igan Techno!oglea I University,
Houghton, Michigan.
Lae, M. C., "Humlc Substances Removal by Activated Carbon," thesis
presented to the University of Illinois, Urbana, Illinois, In 1979, In
partial fulfil Iment of the requirements for the degree of Doctor of
Philosophy.
Lee, M. T., Crlttenden, J. C., Snoeylnk, V. L., and Arl., M.,"Prel Imlnary
Design of Granular Carbon Beds for the Removal of Humlc Substances Using
the Homogeneous Surface Diffusion Model," Journal of the Environmental.
Fng \ hear I ng D 1 v I s lonf Proceed 1 ngs of the Amer lean Soc Ie-ty of C1 v 1.1
Engineering, vol. 109, No. 3, p.631, 1978.
Liu, K. T., and Weber, W. J., Jr., "Characterization of Mass TRansfer
Parameters fcr Fixed-Bed Model Ing and Design," Journa I sd. the Water
Pollutlon Control Federation, Vol. 53, *no. 10, 1981, p.151.
Luft, P.J., "Modeling of MuItlcomponent Adsorption onto Granular
Activated Carbon In Mixtures of Known and Unknown Composition", Thesis
presented to Michigan Technological University, at Houghton, Ml, In 1984,
In partial fulfillment of the requirements for a degree of Masters In
Chemical Engineering.
Mathews, A., and Weber, W. J., Jr., "Mathematical Modeling of
Mu I tlcomponent Adsorption Kinetics," presented at the November, 1875,
68th Annual Meeting, American Institute of Chemical Engineers, held at
Los Angeles, California.
MIeure, J.P. "A Rapid and Sensitive Method for Determining Volatile
OrganohalIdes In Water", Journal of American Water Works Association. 69
(1), 1977, pp. 60-2.
Neretnleks, 1., "Analysis of Some Adsorption Experiments With Activated
Carbon," Chemical Engineering gclence, vol. 31, 1976, p.1029.
Plrbazarl, M., "Prediction for Removal of Toxic and Carcinogenic
Compounds from Water Supplles by Adsorption", thesis presented to the
University of Michigan, Ann Arbor, Michigan, In 1981, In partial
fulfil Iment of the requirements for the degree of Doctor of Philosophy.
Radke, C.J., and J.M. Prausnltz, "Thermodynamics of MulTlsolute
Adsorption from Dilute Liquid Solutions", Journal cf the American
Institute of Chemical Engineer*^, vol. 18, 1972, p.761. -
-------
Sablh, B.R., "Competitive Interactions Between Humlc Substances and
Chloroform In Fixed-Bed Adsorbers", thesis presented to Michigan
Technological University, Houghton, Michigan, In 1981, In partial
fulfil Iment of the requirements for the degree of Master of Science.
Suzuki, M., and Kawazoe, K., "Batch Measurement of Adsorption Rates in a
Agitated Tank," JournaI of Chemtea I EngIpeering Japan, vol. 7, p.346,
1974.
Thacker, W.E. Snoeylnk, V. U, and Crlttenden, J. C., ""modeI Ing of
Activated Carbon and Coal Gasification Char Adsorbents In Single Solute
and BI=solute Systems," Research Report No. 161, Water Resources Center,
the University of 11 I I noIs at Urbana-Champalgn, July, 1981.a
van Ller, W.C., "On the Kinetics of Adsorption on Activated Carbon from
the Aqueous Phase," Act Ivated Carbon— £ Fasc t natIng Mater I a If 0.,
Nor It N.V., Edited by A. Capelle and F. de Vooys, Amersfoot, Netherlands,
1983, p. 129.
van VI let, B. M., Weber, W. J., Jr., and Hozuml, H., "Modeling and
Prediction of Specific Adsorbents," Water Research,. Vol. 14, 1981,
P.1719.
Wakao, N., and Funazkrl, T., "Effect of Fluid Dispersion Coefficients In
Dilute Sol u+lens," Chemical Engineering Science, vol. 33, 1978, p.1375.
Weber, T.W., and ChakravortI, R.K., "Pore and Solid Diffusion Models for
Fixed-Bed Adsorbers," JournaI of the American Instttute jif Chemlea I
Engineers,, vol. 20, no. 2, 1974, p.228.
Weber, W.J., and Morris, J.C. R.K., "Kinetics of Adsorption on Carbon
From Solution," JournaI of the San I tary Engineering PI vIslon.
Proceedings at the American £oe 1 ety of Civ I I Fnglneersr vol. 89, no. SA2,
1963.
-------
APPENDIX 2. NOMENCLATURE
Bic ^ Biot number based on surface and pore diffusivity
(dimensionless): R kf -(l-e)/[D. ^(Dg., . + Dg .) +
** n. ""1 * * * *» 1 P» *
D • DE • J E
Bic ; Biot number based on surface diffusivity (dimensionless);
* .
C^(t) reduced adsorbate concentration in bulk phase as a
function of dimensionless time (dimensionless);C.(t)/C •
C • initial bulk phase concentration (M/LJ)
C ^(r.t) reduced adsorbate concentration in adsorbent pores as a
function of dimensionless radial position and
dimensionless time (dimensionless); C .(r.t)/C
C .(r,t) adsorbate concentration in adsorbent pores as a
function of radial position and time (M/LJ)
D.. self-diffusivity of the adsorbent (M/L-t)
Dg . combined solute distribution (dimensionless);
s f i p t i
Dg . solute distribution parameter based on pore diffusivity
(dimensionless); e (l-e)/e
Dg . solute distribution parameter based on surface diffusivity
(dimensionless); P_<1- j(l-e)/eC •
a C t 1. v f l.
D, liquid diffusivity of the adsorbent (LVt)
D dosage of adsorbent (M/L1)
D . pore diffusivity based on pore void fraction (L2/t)
PI i
D . surface diffusivity (L*/t)
D' . effective surface diffusivity (L2/t)
surface diffnsivity of the fastest diffusing component
F distribution function (dimensionless)
T total mass flux based on surface and pore diffusion (M/L1)
tot
k Boltzmann constant; 1.38054 10~6 erg/°K
88
-------
K£ Freundlich isothenn capacity constant (M/M) (L»/M)1/n
kf>i film transfer coefficient (L/t)
M mass of adsorbent (M)
N£C Reynolds number; 2p& vs / p
Ngc ^ Schmidt number for component i; fi/p. D, •
N0 Avogadro's number; 6.023 10t23/mol
n number of data points
1/nj Freundlich isotherm intensity constant (dimensionlcss)
p number of parameters
qe j adsorbent phase concentration in equilibrium with initial
bulk phase concentration (M/M); K-C,, -1/ni
i Of 1
q^tr.t) adsorbent phase concentration as a function of radial
position and time (M/M)
q^(r,t) reduced adsorbent phase concentration as a function of
dimens ionl e ss radial position and dimens ionless time
(dimensionless); q^r, t)/qe> ^
Q volumetric flow rate through the differential carbon
column (LVt)
r radial coordinate (L)
r reduced radial coordinate (dimensionless); r/R
R adsorbent radius (L)
S(min) minimum relative error (dimensionless)
S(6) relative error for a given confidence contour
St= modified Stanton number; kf • (1 -e) T/ R (e)
i ^ f i
1 temperature (°K)
Tg boiling point of the adsorbent (°Z)
t reduced time based on surface and pore diffusion
P (dimensionless);
t reduced timr based on surface diffusion (dimensionless);
(D
_ V -volume of ^reactor (L*)
89
-------
molar volume of adsorbent (L'/M)
volume of the carbon bed; M/p.
superficial velocity (L/t)
total adsorbent phase concentration in equilibrium with
initial balk phase concentration (M/M)
total adsorbent phase concentration as a function of
radial position and time (M/M); q.= (r,t) + e_C_ .(r,t)/p.
x p p» i •
reduced total adsorbent phase concentration as a function
of dimensionless radial position and dimensionless time
(dimensionless); Y.(r.t)/Y. .
* e» i
ratio of intrapart icle phase mass fluz due to surface
diffusion to total intrapart ic 1 e phase mass fluz
(dimensionless); Dc ;Dg./(D -Dg = + D_ 4Dg_ •)
5*11 S»ll Pflprl
ratio of mass fluz in adsorbent pores due to difference
between pore and surface diffusion to total intrapart icle
phase mass fluz (dimensionless);
CHEEK SYMBOLS
a confidence contour (dimensionless)
•
E porosity of the differential column batch reactor
(dimensionless)
e fraction of volumetric space in adsorbent phase unoccupied
by adsorbent (dimensionless)
p adsorbent density which includes pore volume (M/L1 )
pb bulk density of the carbon (M/L1)
p density of graphite which ranges from 2.0 to 2.2 g/cm*
T hydraulic retention time (t)
T fluid residence time in the packed bed; Vg/Q
T tortuosity of adsorbent (dimensionless)
)i viscosity of water (M/L~t)
Ui viscosity of adsorbent (M/L-t)
90
-------
ABBREVIATIONS
BHSDM
BPSDM
CMBR
DCBR
DCE
EB
F-400
GAC
IAST
IWSL
PCE
PGAC
PDFC
PSDFR
SOCS
TCE
TOL
VOCS
WV-G
Batch Homogeneous Surface Diffusion Model
Batch Pore and Surface Diffusion Model
Completely Mixed Batch Reactor
Differential Column Batch Reactor
cis-1,2 Dichloroethene
Ethylbenzene
Calgon's Filtrasorb 400
Granular Activated Carbon
Ideal Adsorbed Solution Theory
International Mathematical and Statistical Libraries
Tetrachloroethene
Powdered Granular Activated Carbon
Pore Diffusion Flux Contribution
Pore to Suface Diffusion Flux Ratio
Synthetic Organic Compounds
Trichloroethene
Toluene
Volatile Organic Compounds
ffestvaco's Carbon
91
-------
APPENDIX 3. TRACE OKGAN1CS KESEAKCH EQUIPMENT CLEANING PROCEDURE
All of tho materials tLat cane into contact with either the activated
carbon or the volatile organic compounds vere cleaned by the trace organics
research equipment cleaning procedure. This procedure prevented leaching cf
volatile organic compounds from the glassware to the carbon.
A. Glassware
1. The glassware was cleaned with MICRO (International Products
Corporation, Trenton, N.J.) . a laboratory detergent.
The soap was a phosphate free laboratory cleaner.
2. All glassware which was used in experiments were
chromerged. Cbromerge is a trade name for a chromic acid
cleaning solution.
3. The cleaned glassware was soaked with the chromerge solution
for at least two hours.
4. The chromerge solution was removed and the glassware was
thoroughly rinsed with distilled water.
5. The glassware was allowed to air dry. A dilute solution of
sulfnric acid (10 parts distilled water : 1 part concentrated
sulfuric acid ) was used to rinse the glassware. The
glassware was soaked with the acid solution for one-half hour.
6, The sulfuric acid solution was removed and the
glassware was rinsed with distilled water.
7. The glassware was baked for one hour at 250 °C to remove
the water.
8. The glassware was silinized to remove any active sites on
the glassware where adsorption could occur. The mixture used
92
-------
was a 10% solution of dimethyldichlorosilane in toluene.
9. The glassware was soaked in the silane solution for 10
minutes. The glassware was baked at 250°C for one hour.
10. Steps 2 through 9 were conducted every four months on the
glassware used in the laboratory.
11. The glassware was rinsed with tap water.
12. The glassware was rinsed with distilled water and allowed
to air dry.
13. The glassware was rinsed with technical grade methanol. The
glassware was allowed to air dry to evaporate the aethanol.
14. The glassware was placed in an oven at 250°C for at least
one hour. This helped to drive off any organics that may have
been present upon the glassware.
15. The glassware was cooled and covered with aluminum
foil, shiny side up.
B. Teflon
1. The teflon was washed with the MICRO detergent.
2. The teflon was rinsed with tap water.
3. The teflon was rinsed with distilled water and allowed to
air dry.
4. The teflon was rinsed with technical grade methanol and
allowed to air dry.
5. The teflon was baked in a forced air oven at 105°C for one
hour.
6. The teflon circles were stored in a clean beaker and
covered with aluminum foil, shiny side up.
93
-------
C. Rubber septa
1. The robber septa were washed with the MICRO detergent.
2. The rubber septa were rinsed with tap water.
3. The rubber septa were rinsed with distilled water and
allowed to air dry.
4. The rubber septa were rinsed with technical grade methanol.
5. The rubber septa were placed in the forced air oven at 105°C
for ten minutes.
6. The rubber septa were stored in a clean beaker and covered
with aluminum foil, shiny side up.
D. Stainless steel
1. The stainless steel fittings were washed with the KICRO
detergent and rinsed with tap water.
2. The stainless steel fittings were rinsed with distilled
water end allowed to air dry.-
3. The stainless steel fittings were rinsed with technical
grade methanol and allowed to air dry.
4. The stainless steel fittings were baked in a forced air
oven at 105°C for one hour.
5. The stainless steel fittings were removed from the oven and
covered with aluminum foil, shiny side up.
-------
APPENDIX 4, CARBON PREPARATION AND CHARACTERIZATION
A. Procedure for Obtaining a Representative Sample of GAG
In this study, Calgon's Filtrasorb 400 (F-400), (lot number 52095), and
Westvaco's WV-
-------
Wisconsin.
B. Procedure for fashing the GAC
Before the carbon was used for experimentation, it was washed to remove
the fine carbon particulates. The presence of the fine carbon particles could
sanse the adsorption rate to be faster than it would be if only uniform
particles were used.
1. Approximately 500 ml of GAC was placed in a 1 liter beaker.
2. 300 ml of Milli-Q water was added into the beaker.
3. The contents were swirled with a glass stirring rod.
4. The contents were alloved to settle for five minutes.
5. The supernatant was decanted and more Mil 1 i-Q water was added
until the supernatant was clear.
6. The GAC was placed in an oven at 105°C for 16 hours.
7. The carbon was removed and allowed to cool in a dessicator.
8. The carbon was transferred into clean, brown, borosilicate
bottles with teflon circles in the caps and stored in a cool place.
C. Procedure to Determine the Particle Size Distribution
A good value of the mean particle size will enable the mathematical
models to better describe the data. A particle size distribution was conducted
for this purpose.
1. A 500 gm sample of the washed F-400 and WV-G carbons were
obtained. Since the carbon was 12x40 mesh, the following U.S.
standard mesh sieves were used: 10, 12, 18, 20. 25, 30, and 40.
2. The sieves were stacked in the following order: 10, 12, 18, 20,
25, 30, and 40. The smallest mesh was at the top of the stack and
96
-------
the largest mesh was at the bottom of the stack.
3. The sieves were placed on a Ro-tnp and the 500 gm sample was
added.
4. The GAC was agitated on the Ro-tap for 30 minutes.
5. The GAC on each sieve vas placed in a clean beaker and the
carbon weight was determined.
The raw data for the sieve analysis for both carbons are presented in
Table 4-1. Table 4-2 contains the sieve size and sieve openings along with the
amount of carbon which passed each sieve. The results are plotted in Figures
4-1 and 4-2 (Fair et. al.. 1971). The mean particle diameters for the WV-G and
F-400, 12x40 mesh carbons, were 0.1074 cm and 0.1026 cm, respectively. The
uniformity coefficients, CQ, for the WV-G and F-400, 12x40 mesh carbons were
1.9 and 1.7, respectively.
D. Procedure to Determine Grain Shape and Shape Variation of the GAC
1. A representative sample of both the WV-G and F-400, 12x40
carbons were obtained.
2. Both carbons were observed under « microscope and compared to
Figure 4-3 (Fair sJLt. filt.. 1971).
The results for the WV-G and F-400 carbons are shown in Figure 4-4. The
bed void fractions for the WV-G and F-400 carbons are 0.425 and 0.405,
respectively (Kato, 1984).
E. Procedure to Determine the Bulk Density of the GAC
1. A clean. 100 ml, graduated cylinder was obtained for this
experiment. A round, porous, glass plate fit tightly in the
graduated cylinder.
2. Various amounts of weighed, dry carbon were placed in clean
97
-------
Table 4-1. Results of the Sieve Analysis for the F-400 and WV-G
Carbons.
Standard
Sieve
Size
10 x 12
12 x 18
18 x 20
20 x 25
25 x 30
30 x 40
> 40
Table 4-2.
Standard
Sieve
Size
10
12
18
20
25
30
40
WV-G Percent F-400
Carbon We ight Carbon
We ight WV-G We ight
(gm) (%) (8m)
11.5
268.0
76.0
47.0
44.0
32.5
13.5
2.34 5.0
54.42 285.0
15.43 81.0
9.54 52.0
8.93 39.5
6.60 28.5
2.74 8.0
100%
Percent
We ight
F-400
(%)
1.00
57.11
16.23
10.42
7.92
5.71
1.61
100%
Sieve Size and Percent Carbon Passing a Given Sieve
for the F-400 and WV-G Carbons.
Sieve
Opening
(cm)
0.200
0.168
0.100
0.084
0.071
0.056
0.042
Percent Percent
Passed Passed
F-400 WV-G
(%) (%)
100.0 100.0
99.0 97.7
41.9 43.2
25.7 27.8
11.8 18.2
7.3 9.3
1.6 2.7
Log
Size
(cm)
-0.699
-0.775
-1.000
-1.076
-1.149
-1.125
-1.377
Note: The original weight basis was 500 gm for each carbon.
98
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ii-Eii- DET ERMlfviAiflONiS
=zfl,, -Y. n'' 'IT—rir-
. -ri-" I .-.{.^-. rrrr-ii;....f.-rrrrr:i.._... ~.
•1.5 -1.0 -0.5
Log of the Size of Separation, cm
Figure 4-1. Percent Carbon (by weight) Passing a Given Sieve
Size Versus the Log of the Size of Separation for
WV-G Carbon.
99
-------
;l U
iT
1
-U.
tiff
Ml
m
—
a
"o
•o
o
-U-l
^.ARTICLE-
= DETERMINATIONS
05
0.-
e
o
" J3
9 a
O
a —
c
o
U
k.
» e
TTu
T|T
1111111
ill
Illl
III!
Tiri
1 i i 11111111 iTT
TTTl
i in
tHI iiiiin'iilij'
m
fir
1.5 -1.0 -0.5
*
Log of the Size of Separation, cm
0.0
Figure 4-2. Percent Carbon (by weight) Passing a Given Sieve
Size Versus the Log of the Size of Separation for
F-400 Carbon.
100
-------
SPHERICAL
SHARP
ROUNDED
WORN
ANGULAR
CRUSHED
Figure 4-3. Shape Factors of Granular Materials and Typical Porosities Associated
with them (Fair jit. al., 1971).
-------
ca
WV-G
0°
o
Q
O
F-400
o
o
t
o
I
CO
Q)
JC
Q.
to
(U
T)
C
a
o
cc
C
o
TO
CO
03
5
T3
cu
CO
O
0.0
1.0
2.0
3.0 4.0
PARTICLE SHAPE
6.0
6.0
7.0
Figure 4-4. Relationship Between the Bed Void Fraction and the Particle Shape.
-------
4
beakers containing Hilli-Q water and allowed to set overnight.
3. A beaker containing the oarbon was ponred into the graduated
cylinder and the carbon was allowed to settle.
4. The round, porous, glass plate was placed on top of the carbon
and the volume was recorded.
The size of the graduated cylinder was important in the determination of
the bulk density. For the wall effects to be negligible, the diameter of the
graduated cylinder should be at least 20 particle diaaeters. In this case,
the graduated cylinder was 25 particle diameters. The data for the bulk
density experiment are shown in Table 4-3 (Cato. 1984). Figure 4-5 shows the
data plotted using the International Mathematical and Statistical Libraries
(IMSL) linear least squares method. The bulk densities for both 12x40 carbons
were determined by minimizing the sum of the squares of the percent error in
the weight measurements. The equation was of the form, T=A*I, and the line
was forced through zero. The bulk densities for the WV-G and F-400 carbons
were 0.433 g/cm3 and 0.478 g/cm , respectively.
F. Calculation of th* Apparent Density
The apparent density was calculated using the void fractions and bulk
densities from 4-D and 4-E. respectively:
(1 - s)
(4-1)
The apparent densities for the WV-G and F-400 carbons were 0.7530 g/cm
«
and 0.8034 g/cm , respectively.
103
-------
Table 4-3. Data Collected From" tho Bulk Density Expex'nent for
12 z 40 mesh F-400 and VV-G Carbons.
Weight of
F-400
Carbon
(gm)
3.76
6.75
9.89
15.61
16.09
19.06
-
Volume of
F-400
Carbon
(cm3)
8.2
14.5
19.9
27.1
33.6
39.7
M^_^_J
Weight of
WV-G
Carbon
(gm)
2.05
3.97
5.90
8.51
10.91
12.85
14.99
Volume of
WV-G
Carbon
(cm3)
4.8
8.8
13.6
19.5
26.0
29.6
34.2
Note: This experiment was conducted with a IOC ml graduated
cylinder (Sato, 1984).
104
-------
o
U»
q
d
q
to
D)
CD
0.0
o «
= WV-G Carbon
=» F-400 Carbon
10.0
BULK DENSITY
F-400: 0.478 g/cnV"3
WV-G: 0.433 g/cm»*3
20.0 30.0
VOLUME. cm**3
40.0
60,0
IIJ, Ulll
'Figure 4-5. Determination of the Bulk Density of F-400 and WV-G Carbons Using a Dry Weight of
Carbon Versus the Volume Occupied by Milli-Q Water (Kato, 198A).
-------
0. Calculation of the Intraparticle Void Fxactioa
The intrapartiele void fraction vac calculated using the apparent
densities from Appendix 4-F and the density of graphite, p$. which is 2.2
«p 1 - — (4-2)
PS
The intrapartiele void fractions for the W-G and F-400 carbons were
49 •
0.658 g/cm and 0.641 g/cm , respectively.
*. .
H. Preparation of Powdered and Ground Activated Carbon
The powdered activated carbon (200 x 400 MESH) was used in the bottle
point isotherm studies and the ground granular activated carbon (60 x 80 MESH)
was used in some of the differential column batch reactor (DCBR) and mini-
column studies.
There are two methods to produce either powdered or ground activated
carbon: the use of a ball mill or mortar and pestle. The mortar and pestle
was employed, since it was the most convenient and available method. The
yield from the mortar and pestle for both the powdered and ground carbon was
60*.
1. Procedure for Obtaining Powered and Ground Activated Carbon
a. The mortar and pestle were cleaned according to the procedure
presented in Appendix 3.
b. An initial neoimt of carbon (100 g) was crushed. This carbon
was separated using the following sieves: 30. 35. 40. 60, 80, 100,
and 200. This was done to observe the amount of carbon which would
pass the 60 mesh, but be retained on the 80 mesh.
106
-------
c. The carbon which was retained on the 80 mesh was set aside and
the carbon which did not pass the 60 mesh sieve was further
crushed.
d. Steps 2 through 3 were continued until all of the original 100
gm sample had passed the 60 mesh and the desired amount of ground
activated carbon was obtained.
e. For Powered Granular Activated carbon, the following sieves were
used: 40, 50, 60. 80, 100, 200, and 400. In this case, the carbon
must pass the 200 mesh, but be retained on the 400 mesh.
2. Procedure to Clean its. Ground and Powdered Activated Carbon
a. The carbon was placed in a centrifuge bottle (250 ml). The
bottle was filled about full.
b. Milli-Q water, purged with helium, was added to the centrifuge
bottle. The Milli-Q water was purged because trace amounts of
chloroform were detected in the Milli-Q system. Care was also
observed when the water was added to the dry carbon.' The powdered
or ground carbon will adsorb water and displace air, causing the
carbon to splatter.
c. The centrifuge bottles were placed into the centrifuge and
rotated at 2000 EPM for 15 minutes.
d. The bottles were removed and the supernatant was observed.
e. Steps 2 through 4 were continued until the supernat&.at was clear.
f. The carbon slurry which remained were placed into an oven at
105°C for 16 hours.
g. The carbon was transferred into clean, dark, borosilicate glass
bottles with teflon circles in the caps. The bottles were placed in
a dessicator for future use.
107
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APPENDIX 5. PROCEDURE FOR DIFFERENTIAL COLUMN BATCH REACTOR
The following procedure was used iA the evaluation of tL'. surface
diffnsivities of various volatile organic compounds (VOCS). Figure 5-1
displays the general design of the differential column batch reactor (DCBR).
Table 5-1 contains the equipment list for the DCBR. The unit was constructed
using glass, teflon, and stainless steel parts. These materials are chemically
inert and reduce the possibility of biased results due to system leaching.
The glassware, teflon, and stainless steel appurtances were cleaned according
to the Trace Organics Cleaning Procedure, Appendix 2.
A. General Operation of ths Differential Colun. Batch Reactor
1. A continuously mixed glass reaction vessel was
completely filled with a water matrix run at isothermal conditions.
2. A pH of 6.0 was controlled using a suitable buffer.
3. The suction line leaving the reactor was connected to a punp.
The discharge line can either pass the water through a bypass loop
or through a column packed with a differential height of granular
activated carbon (GAC). Figure 3-2 describes the suction and
discharge port for each reactor design, respectively.
B. Selecting the Proper Colurn
Various column diameters may be used in the study. The
column diameter was chosen, based on the mass of carbon used and on
the carbon particle size, to insure a minimum of channeling and wall
effects.
108
-------
BYPASS
LOOP
GAC
GLASS
COLUMN
Figure 5-
SYRINGES
tJ^^^^AAj^l ILl£^^44^LJ
I
X
STIRBAR
D.P.
SU.P.
I.P. S.P.
PUMP
D.P. - DISCHARGE PORT SU.P. - SUCTION PORT
I.P. - INJECTION PORT S.P. - SAMPLING PORT
% - WIITEY REGULATING VALVE
Busic Design for tlie Differential Column Dutch Reactor,
GLASS
REACTION
/ESSEL
MAGNETIC
STIRRER
-------
Table 5-1. Equipment List for the Differential Column Batch Reactor
1-F.M.I. Pomp, Model HP, 1/4 Inch Piston
1-12L Glass Carboy Reactor
1-Fisher Scientific Stirplate
3-3/8 Inch Whitey Regulating Valves, (SS)
3-3/8 Inch Swagelot Union Tee, (SS)
5-3/8 Inch Swage lot Union Elbows, (SS)
2-3/8 Inch to 1/4 Inch Swagelot Reducing Union, (SS)
2-3/8 Inch to 3/8 NPT Swag el ok Hale Connector, (SS)
2-Hamilton 4-Port Valve
1-5 ml Hamilton Syringe With Luer-Loc
1-30 ml Hamilton Syringe With Luer-Loc
1-50 ml Hamilton Syringe With Lner-Loc
1-1 Inch Teflon Stirbar
1-#12 Rubber Stopper
2-TefIon End Plugs, #15
lOOgm, 3mm Diameter Glass Beads
Silanized Glass Wool
Glass Columns:
6,11,15,25mm
Tubing:
3/8 Inch Teflon For Main Lines
1/8 Inch Teflon for sampling and Injection Lines
110
-------
SYRINGES
SAMPLING PORT
SUCTION
PORT
INJECTION PORT
DISCHARGE
PORT
«
I II
! II
I II
I II
I II
I I I
I I I
I I I
RUBBER
STOPPER, #12
tnt
TEFLON TUBING
1/8 INCH TEFLON TUBING
Figure 5-2, Schematic of the Ports for the Differential Column
Batch Reactor,
111
-------
C. Selecting the Proper Carbon Dosage
To the extent possible, the mass of carbon used in a rate study should
reduce the concentration of a VOC by at least 50% of the initial concentration
to obtain good rate data Hand et. al.. 1983).
To calculate the carbon dosage, DO> an overall mass balance for component
i in the DCBR may be written in word fora as:
Mass of Component i Mass of Component i Mass of Component i
in the DCBR •* in the Liquid Phase + in the solid phase
Initially at Equilibrium at Equilibrium
In mathematical terms this is expressed as:
Ce.i
Substituting the Freundlich isotherm equation into equation 5—1 yields:
M
D . _ - 2li ^ (5-2)
V K , Ce U*l
» *• Cf X
in which. H is the mass of adsorbent, gm. V is the volume of the DCBR, cm3.
C_ • is the initial concentration of component i, umol/L, C , is the
-0*1 » • *
equilibrium concentration of component i, umol/L. K is the Freundlich
isotherm constant, umol/g (L/umol) 'ni, and 1/n^ is the Freundlich isotherm
constant, (dimensionless).
D. Packing the Differential Carbon Colwm
Figure 5-3 displays the packed column. Teflon end caps were packed with
silianized glass wool to contain the 3.0 mm glass beads. The carbon was
packed between a bed of silanized glass wool.
112
-------
OUTLET
SWAGELOK
UNION
TEFLON
PLUG
SILANIZED
GLASS WOOL
GLASS BEADS
SILANIZED
GLASS WOOL
0-RING
GLASS
COLUMN
CARBON
INLET
Figure 5-3. Schematic of the Packed Differential Carbon Column.
113
-------
B. Measuring the flow rate of the DCBH
The flow rate to the DCBR was an important consideration in the
determination of the surface diffusivity. See Section V-A for further
discussion. A high flow rate was required to obtain a good estimate of the
snrface diffusivity. The hydraulic retention time is the ratio of the the
reactor volume vo the flow rate (See Equation V-l). This indicated the
frequency at which samples could be taken. The flow rate was measured by
packing the column with 3.0 mm glass beads and collecting the water over an
elapsed time period.
F. Spiking the Reactor with a VOC
1. When the batch reactor system showed no sign of leakage, the
water matrix was spiked with a VOC.
2. A concentrated stock solution of the desired organic chemical
was prepared in methaool.
3. The stock solution was injected into the reactor and Milli-Q
water was displaced. This allowed for no headspace in the system.
4. The system was run with the bypass loop open until a steady-
state concentration was realized.
5. Elapsed time for the batch test started when the bypass loop was
closed and the water began to flow through the column.
6. Sampling from the Differential Colon Batch Reactor
Samples were analyzed using either the liquid-liquid extraction or the
purge and trap technique. See Section II-B for further discussion. The
techniques used to remove a sample for analysis are presented below.
114
-------
Ij. Samoling for the Liquid-Liquid Extraction Technique
a.) The 25 ml »ample bottles with teflcn circles, rubber septa, and
tear-off aluminum seals (Wheaton Scientific, Hillville. N.J.) were
tared.
b.) The extraction ratio was calculated (Johnson. 1984) and the
appropriate volume of isooctane was added to the 25 ml bottle.
c.) The bottle was weighed again to determine the amount of
isooctane added.
d.) Samples were taken with a 5 ml syringe by displacement with a 30
ml syringe filled with an nnspiked water matrix.
e.) To insure a representative sample was taken at an elapsed time.
a 1 ml sample was removed, since there was dead volume in the sample
line. Figure 5-4 describes the design of the sampling and injection
ports for the DCBEL
f.) The water sample was injected below the isooctane phase so
volatilization would be minimized.
g.) Tl j bottle was re-weighed and the mass recorded. The volume of
the isooctane and water were calculated by using the densities. An
extraction ratio was also calculated.
h.) Collection of the samples were continued until the organic
saturated the GAC.
2j. Sampling for tbo Puree and Jus. Technique
a.) A 25 ml extraction bottle with a teflon circle, rubber septa.
and aluminum seal were used.
b.) Samples were taken with a 30 ml syringe by displacement with a
50 ml syringe filled with an unspiked water matrix.
i
c.) To insure a representative sample at a given elapsed time, a 1
115
-------
SYRINGE
1/6 INCH
TEFLON TU3IN3
FEMALE
LUER-LOC
HAMILTON
3-PORT VALVE
SAMPLING PORT (S.P.) 8. INJECTION PORT (I.P)
Figure 5-4. Design of the Sampling and Injection Ports for the
Differential Column Batch Reactor.
116
-------
4
=
ml sample was removed, since there vat dead volume in the sampling
line.
d.) The aqueous sample was added to the the 25 ml bottle allowing
fox no headspace.
e.) Collection of samples axe continued until the oxganic saturated
the GAC.
117
-------
APPENDIX 6. DIFFERENTIAL COLUMN BATCH REACTOR DAIA
Table 6-1. Batch Kinetic Data for Trichloroethese and (12x40) F-400
Carbon Using Thawed fansan Vater.
PARAMETERS:
Volume of Reactor: 4975 ca*
Initial Concentration: 1441.6 pg/L
Particle Radius: 0.05129 cm
Particle Density: 0.8034 g/cm3
Column Diameter: 1.10 cm
Freundlich Intensity Constant: 0.4165
Freundlich Capacity Constant: 196.6 um/gdVum)1'11
Weight of Carbon Used: 0.30185 g
Best Fit Surface Diffusion
Coefficient Using BHSDM: 2.60 10~10 cm2/s
Calculated Film Transfer Coefficient
Using Fiied Bed Correlation: 1.50 10~2 cn/s
Best Fit Film Transfer Coefficient
Using BHSDM: 1.50 10~2 cm/s
95% Confidence Interval For
Surface Diffusion Coefficient: 2.35-2.95 10~10 cn2/s
Solute Distribution Factor: 2.9474
Biot Number: 75.82
Stanton Number: 0.0085
Reactor Porosity: 0.99992
Temperature of Reactor: 11.0 °C
Superficial Velocity: 14.46 cm/s
Hydraulic Retention Time: 6.03 min
pH of Water Matrix: 6.93
118
-------
Table 6-1 (Continued).
Initial Concentration: 1441.7 |ig/L
Carbon Type: F-400 (12x40) M3SH
Water Matrix: Thawed Wausao Water
Elapsed Time
(minute a)
150.0
210.0
270.0
330.0
395.0
450.0
525.0
1185.0
1260.0
1355.0
1425.0
1520.0
1600.0
1815.0
1920.0
2495.0
2610.0
2790.0
2970.0
3165.0
3330.0
3645.0
4055.0
4245.0
4410.0
4600.0
5505.0
5745.0
6040.0
6150.0
6905.0
6990.0
7110.0
7290.0
7530.0
7650.0
7770.0
8370.0
8490.0
Experimental Concentration
(ug/L)
1032.3
952.8
886.3
849.1
814.4
772.0
732.0
610.0
543.1
521.4
500.0
488.5
471.3
450.0
439.0
405.6
386.5
360.2
343.1
350.5
333.6
327.8
314.5
306.3
296.8
286.0
293.9
272.0
250.2
254.6
264.7
249.9
244.1
242.8
241.3
239.7
236.5
241.1
237.8
119
-------
Table 6-2. Batch Kinetic Data for Trichloroetneno and (12x40)
Carbon Using Thawed Wavsan Yater.
PARAMETERS:
Volume of Reactor: 4920 cm-
Initial Concentration: 1241.6 ug/L
Particle Radius: 0.05370 cm
Particle Density: 0.7530 g/cm3
Column Diameter: 1.10 cm
Freundlich Intensity Constant: 0.4073
Freundlich Capacity Constant: 181.0
Weight of Carbon Used: 0.30304 g
Best Fit Surface Diffusion
Coefficient Using BHSDM:
2.8 10~10 c»2/s
Calculated Film Transfer Coefficient
Using Fixed Bed Correlation:
Best Fit Film Transfer Coefficient
Using BHSDM:
1.54 10~2 cm/s
1.54 10~2 cm/s
95% Confidence Interval For
Surface Diffusion Coefficient:
Solute Distribution Factor:
Biot Number:
Stanton Number:
Reactor Porosity:
Temperature of Reactor:
Superficial Velocity:
Hydraulic Retention Time:
pH of Water Matrix:
2.4-3.25 10~10 cm2/s
2.9450
82.03
0.0077
0.99992
11.0 °C
15.38 cm/s
5.67. min
6.93
120
-------
Table 6-2 (Continued).
Initial Concentration: 1241.6 jig/L
Carbon Typo: WV-G (12x40) MESH
Water Matrix: Thawed Wausan Water
Elapsed Time
(minutes)
75.0
135.0
195.0
255.0
315.0
375.0
760.0
840.0
930.0
1050.0
1110.0
1260.0
1320.0
1395.0
1445.0
1560.0
1635.0
2370.0
2470.0
2535.0
2630.0
2710.0
2925.0
3030.0
3605.0
3720.0
3900.0
4080.0
4275.0
4440.0
4755.0
5165.0
5355.0
5520.0
5710.0
5910.0
6855.0
6965.0
7150.0
7260.0
7365.0
Experiment si Concentration
(|ig/L)
1073.6
992.5
786.0
773.3
743.1
700.6
663.0
579.6
533.3
508.6
471.7
432.8
419.9
411.6
400.6
367.0
382.6
366.3
348.8
317.8
323.1
313.8
336.7
324.2
369.6
319.5
306.3
282.4
297.8
274.6
289.6
302.0
285.7
264.1
260.9
254.6
235.0
210.6
215.0
215.4
208.4
121
-------
Table 6-3. Batch Kinetic Data for Trichloroethene and (12x40) F-400
Carbon Using Milli-Q Water.
PARAMETERS:
Volume of Reactor:
Initial Concentration:
Particle Radius:
Particle Density:
Column Diameter:
Freundlich Intensity Constant:
Frenndlich Capacity Constant:
Weight of Carbon Used:
Best Fit Surface Diffusion
Coefficient Using BHSDM:
4970 cm3
1322.7 ng/L
0.05129 cm
0.8034 g/cm3
1.10 cm
0.4165
196.6 nm/g(L/jim)1/n
0.27587 g
3.1 10~10 cm2/s
Calculated Film Transfer Coefficient
Using Fixed Bed Correlation: 2.5 10~3 cm/s
Best Fit Film Transfer Coefficient
Using BHSDM:
95% Confidence Interval For
Surface Diffusion Coefficient:
95% Confidence Interval For
Film Transfer Coefficient:
Solute Distribution Factor:
Biot Number:
Stanton Number:
Reactor Porosity:
Temperature of Reactor:
Superficial Velocity:
Hydraulic Retention Time:
pH of Water Matrix Using
10~3 M Phosphate Buffer:
4.51 10~3 cm/s
2.55-3.8 10~10 cm2/s
2.75-10.0 10~3 cm/s
2.8359
18.14
0.0316
0.99993
11.0 °C
1.01 cm/s
85.7 min
6.0
122
-------
Table 6-3 (Continued).
Initial Concentration: 1322.7 ug/L
Carbon Type: F-400 (12x40) >ESH
Water Matrix: Killi-Q
Elapsed Tine
(minutes)
30.0
120.0
210.0
240.0
300.0
360.0
420.0
1110.0
123.0.0
1350.0
1470.0
1590.0
1710.0
1950.0
2520.0
2670.0
2880.0
3150.0
3270.0
4050.0
4110.0
4230.0
4380.0
4440.0
4710.0
5490.0
5670.0
5790.0
6045.0
6165.0
6990.0
7275.0
7665.0
Experimental Concentration
(ug/L)
1319.3
1141.6
1170.0
1047.4
1097.6
1048.0
913.8
700.0
668.7
628.1
661.0
571.1
541.8
433.0
442.1
460.1
402.1
377.6
351.6
352.1
319.5
293.9
299.3
287.3
283.5
275.3
247.1
225.9
213.4
212.2
220.0
206.5
224.6
123
-------
Table 6-4. Batch Kinetic Data for Tetrachloroethene and (12x40)
F-400Carbon Using Milli-Q Water.
PARAMETERS:
Volume of Reactor:
Initial Concentration:
Particle Radius:
Particle Density:
Column Diameter:
Freundlich Intensity Constant:
Frenndlich Capacity Constant:
Weight of Carbon Used:
Best Fit Surface Diffusion
Coefficient Dsing BHSDH:
4735 cm3
1438.4 ug/L
0.05129 en
0.8034 g/cm3
0.6 en
0.4579
650.6
0.10072 g
4.8 10"11 CB2/
Calculated Film Transfer Coefficient
Dsing Fixed Bed Correlation: 6.03 10~3 cm/s
Best Fit Film Transfer Coefficient
Using BHSDM:
95% Confidence Interval For
Surface Diffusion Coefficient:
95% Confidence Interval For
Film Transfer Coefficient:
Solute Distribution Factor:
Biot 'Number:
Stanton Number:
Reactor Porosity:
Temperature of Reactor:
Superficial Velocity:
Hydraulic Retention Time:.
pH of Water Matrix Using '
10~3 H Phosphate Buffer:
7.10 10~3 cm/s
3.5-6.5 10"11 cm2/s
4.25-100.0 10~3 cm/s
4.2896
46.81
0.0202
0.99997
11.0 °C
3.44 cm/s
81.19 min
6.0
124
-------
Table 6-4 (Continued).
Initial Concentration: 1438.4 ug/L
Carbon Type: F-400 (12x40) MESH
later Matrix: Hilli-Q
Elapsed Time
(ninutes)
60.0
170.0
290.0
410.0
510.0
600.0
690.0
1275.0
1380.0
1625.0
1740.0
1845.0
2055.0
2100.0
2720.0
2880.0
3000.0
3060.0
3190.0
3375.0
3450.0
4125.0
4245.0
4365.0
4510.0
4650.0
4860.0
4920.0
5010.0
5840.0
6135.0
7320.0
7650.0
8805.0
9040.0
10080.0
11895.0
Experimental Concentration
(|ig/L)
1421.0
1386.9
1336.9
1298.1
1299.3
1193.1
1208.1
935.6
883.0
868.6
824.3
823.7
775.0
745.5
684.3
691.9
706.9
657.1
673.5
677.8
520.9
561.7
579.5
567.9
608.4
597.4
550.0
548.7
555.8
460.0
458.0
416.6
392.5
430.0
420.0
376.4
338.2
125
-------
Table 6-5. Batch Kinetic Data for Trichlorootheno and (60x80) F-400
Carbon Using Xilli-Q Vater.
PARAMETERS:
Volume of Reactor:
Initial Concentration:
Partible Radius:
Particle Density:
Column Diameter:
Freundlich Intensity Constant:
Freundlich Capacity Constant:
- Weight of Carbon Used:
Best Fit Surface Diffusion
Coefficient Using BHSDM:
4975 en3
1329.8 ug/L
0.01050 cm
0.8034 g/CB3
1.10 cm
0.4165
196.6
0.2220 g
4.3 10~10 cm2/
Calculated Film Transfer Coefficient
Using Fixed Bed Correlation: 2.89 10~2 cm/s
Best Fit Film Transfer Coefficient
Using BHSDM:
95% Confidence Interval For
Surface Diffusion Coefficient:
95% Confidence Interval For
Film Transfer Coefficient:
Solute Distribution Factor:
Biot Number:
Stanton Number:
Reactor Porosity:
Temperature of Reactor:
Superficial Velocity:
Hydraulic Retention Time:
pB of Water Matrix Using
10~3 M Phosphate Buffer:
1.4 10~2 cn/s
3.0-8.5 10~10 cm2/s
0.9-3.5 10 3 cm/s
2.2719
8.37
0.029
0.99994
11.0 °C
14.46 cm/s
6.03 min
6.2
126
-------
Table 6-5 (Continued).
Initial Concentration: 1329.8 pg/L
Carbon Type: F-400 (60x80) MESH
Water Matrix: Milli-Q
Elapsed Time
(minutes)
5.0
10.0
30.0
60.0
90.0
.110.0
130.0
150.0
170.0
190.0
225.0
300.0
325.0
350.0
380.0
405.0
455.0
475.0
500.0
525.0
550.0
600.0
700.0
7*0.0
800.0
850.0
900.0
1005.0
1100.0
Experimental Concentration
(|ig/L)
1273.3
1005.9
1076.6
830.0
636.1
684.8
480.9
429.2
378.4
394.3
455.0
279.0
252.7
236.5
222.2
255.6
204.6
200.0
182.9
174.7
171.5
172.1
182.9
195.5
168.7
161.6
167.3
153.9
163.1
127
-------
Table 6-6. Batch Kinetic Data for Tetrachloroettene and (60x80) F-400
Cazbon Using Milli-d Vater.
PARAMETERS:
Volume of Reactor:
Initial Concentration:
Particle Radius:
Particle Density:
Column Diameter:
Freundlich Intensity Constant:
Freundlich Capacity Constant:
Weight of Carbon Used:
Best Fit Surface Diffusion
Coefficient Using BBSDM:
13240 cm3
1504.0 jig/L
0.01050 ca
0.8034 g/cm3
1.10 cm
0.4579
650.6 nm/g(L/nm)1/n
0.1720 g
1.5 10~10 cm2/s
Calculated Film Transfer Coefficient
Using Fixed Bed Correlation: 2.08 10~2 cm/s
4.3 10~2 cm/s
Best Fit Film Transfer Coefficient
Using BHSDM:
95% Confidence Interval For
Surface Diffusion Coefficient: 1.25-1.8 10~10 cia2/s
95% Confidence Interval For
Film Transfer Coefficient:
Solute Distribution Factor:
Biot Number:
Stanton Number:
Reactor Porosity:
Temperature of Reactor:
Superficial Velocity:
Hydraulic Retention Time:
pH of Water Matrix Using
10~3 M Phosphate Buffer:
3.25-9.0 10 2 cm/s
2.5573
19.07
0.038
0.99998
11.0 °C
9.61 cm/s
24.12 min
5.95
.128
-------
Table 6-6 (Continued).
Initial Concentration: 1504.0 pg/L
Carbon Type: F-400 (60x80) MESH
Tater Matrix: Milli-Q
Elapsed Time
(minutes)
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
100.0
110.0
120.0
140.0
160.0
200.0
240.0
270.0
300.0
330.0
420.0
480.0
540.0
600.0
720.0
840.0
960.0
1080.0
1200.0
1320.0
1440.0
Experimental Concentration
(|ig/L)
1457.6
1318.9
1144.4
1136.7
1034.2
931.7
927.3
978.7
826.5
802.0
754.5
738.6 -.
699.6
591.8 J
533.5
516.7
467.3
465.1
378.9
351.9
380.4
300.0
287.0
242.0
233.0
221.6
210.7
214.1
221.2
-------
Table 6-7. Batch Kinetic Data fox Txiohloxoetlieae and (12x40) WV-O
Carbon Using Milli-Q Water.
PARAMETERS:
Volute of Reactor:
Initial Concentration:
Particle Radius:
Particle Density:
Column Diameter:
Freundlich Intensity Constant:
Freundliob, Capacity Constant:
Weight of Carbon Used:
Best Fit Surface Diffusion
Coefficient Using BHSDM:
4970 cm3
1318.6 ug/L
0.05370 ca
0.8034 9/cm3
1.10 ca
0.4073
181.0
0.27840 g
3.3 10~10 ca2/s
Calculated Film Transfer Coefficient
Using Fixed Bed Correlation: 3.10 10~3 co/s
Best Fit Film Transfer Coefficient
Using BHSDM:
95% Confidence Interval For
Surface Diffusion Coefficient:
Solute Distribution Factor:
Biot Number:
Stanton Number:
Reactor Porosity:
Temperature of Reactor:
Superficial Velocity:
Hydraulic Retention Time:
pH of Water Matrix Using
10~3 H Phosphate Buffer:
3.10 10~3 ca/*
2.5-4.7 10~10 cm2/s
2.5828
14.515
0.02050
0.99993
11.0 °C
1.03 ca/s
85.7 min
6.0
130
-------
Table 6-7 (Continued).
Initial Concentration: 1318.6 ug/L
Carbon Type: YV-G (12x40) MESH
Water Matrix: Milli-Q
Elapsed Time Experimental Concentration
(minutes)
30.0
90.0
120.0
180.0
240.0
300.0
360.0
420.0
510.0
1320.0
1440.0
1560.0
1860.0
1950.0
2820.0
3240.0
4320.0
4620.0
5670.0
6120.0 .
7260.0
7680.0
8490.0
f.000.0
10410.0
11610.0
13410.0
14430.0
16140.0
17460.0
1271.8
1265.8
1175.6
1110.7
1054.7
932.4
909.3
857.6
802.9
642.3
555.8
484.2
461.3
444.8
394.6
346.9
346.6
324.2
323.1
284.7
274.6
255.1
235.4
227.5
215.5
217.2
234.3
207.5
198.5
190.7
131 '
-------
Table 6-8. Batch Kinetie Data for ois-1.2 dichloroethene and
(12x40) F-400 Carbon Using Milli-Q Tatar.
PARAMETERS:
Volume of Reactor:
Initial Concentration:
Particle Radius:
Particle Density:
Column Diameter:
Freundlich Intensity Constant:
Preundlich Capacity Constant:
Weight of Carbon Used:
Best Fit Surface Diffusion
Coefficient Using BHSDM:
13050 cm3
507.0 »ig/L
0.05129 ca
0.8034 9/cm3
1.10 cm
0.5616
51.0 ttWg(L/um)1/n
0.4537 g
2.7 10~9 cm2/s
Calculated Film Transfer Coefficient
Using Fixed Bed Correlation:
1.53 10~2 cm/s
Best Fit Film Transfer Coefficient
Using BHSDM:
95% Confidence Interval For
Surface Diffusion Coefficient:
95% Confidence Interval For
Film Transfer Coefficient:
Solute Distribution Factor:
Biot Number:
Stanton Number:
Reactor Porosity:
Temperature of Reactor:
Superficial Velocity:
Hydraulic Retention Time:
pH of Water Matrix:
3.00 10~2 cm/s
1.7-5.1 10~9 CQ2/s
.85-100 10~2 cm/s
0.85881
28.72
0.02660
0.99996
12.0 °C
12.1 cm/s
19.0 min
6.3
132
-------
T«blo 6-8 (Continued).
Initial Concentration: 507.0 ng/L
Carbon Type: F-400 (12r40) MESH
Water Matrix: Hilli-Q
Elapsed Time Experimental Concentration
(minutes) (jig/L)
30.0 460.7
90.0 430.6
120.0 442.9
180.0 433.4
240.0 391.9
300.0 387.2
360.0 343.6
660.0 272.8
720.0 297.7
1335.0 312.9
1675.0 263.1
2040.0 257.7
2910.0 268.8
3180.0 278.2
4410.0 228.5
4870.0 226.0
6095.0 225.0
133
-------
Tabl» 6-9. Bate* Kiaotio Data for Toluene and (12x40) F-400 Carbon
Dsia» Hilli-a later.
PARAMETERS:
Volume of Reactor: 13160 cm3
Initial Concentration: 373.4 ug/L
Particle Radius: 0.05129 cm
Particle Density: 0.8034 9/cm3
Column Diameter: 1.10 cm
Frenndlica Intensity Constant: 0.3282
Frenndlicn Capacity Constant: 475.0 um/g(L/um)1/n
Weight of Carbon Used: 0.1000 g
Best Fit Surface Diffusion
Coefficient 0sing BHSDM: 1.8 10~9 cm2/i
Calculated Film Transfer Coefficient
Using Fixed Bed Correlation: 1.48 10 cn/s
Best Fit Filn Transfer Coefficient
Using BHSDM: 0.7 10"1 cm/i
95% Confidence Interval For
Surface Diffusion Coefficient: 1.50-2.25 10~9cm2/*
Solute Distribution Factor: 1.4111
Biot Number: 133.5
Stanton N'umber: 0.0134
Reactor Porosity: 0.99999
Temperature of Reactor: 13.0 °C
Superficial Velocity: 14.02 cm/s
Hydraulic Retention Time: 16.45 min
pH of Water Matrix: 6.3
134
-------
Tablo 6-9 (Continued).
Initial Concentration: 372.4 |ig/L
Carbon Type: F-400 (12x40) MESH
Water Matrix: Milli-Q
Elapsed Time Experimental Concentration
(minutes) (|ig/L)
60.0 365.0
90.0 316.4
122.0 309.8
180.0 224.4
240.0 214.0
300.0 209.0
360.0 191.9
485.0 174.6
570.0 162.8
690.0 159.0
820.0 156.4
1275.0 160.2
1545.0 " 154.3
1995.0 132.2
2225.0 98.3
3140.0 85.6
4260.0 76.5
4700.0 65.0
5820.0 64.0
135
-------
APPENDIX 7. MDLTICOMPONENT DIFFERENTIAL COLUMN BATCH REACTOR
DATA AND RESULTS
Seven components which were found in the original fresh Wausau Water were
trichloroethene, tetrachloroethene, cis-1,2 d ich 1oroethene, toluene,
ethyIbenzene, m-xylene, and o-xylene. A seven component equilibrium
calculation us in,} ideal adsorbed solution theory (IAST) was compared to a five
component equilibrium calculation for trichloroethene, tetrachloroethene, cis-
1,2 dichloroethene, toluene, ethyIbenzene. Luft; 1984, developed the
algorithm that was used in the IAST calculations. The initial concentrations
for the m-xylene and o-xylene were 5.0 (ig/L and 5.6 ug/L, respectively. At
these low concentrations, the seven component and five component equilibrium
concentrations were nearly identical. Therefore, a five component batch pore
and surface diffusion calculation was conducted for the prediction of the
multicomponent Wansau water matrix because difficulties arose when the seven
component model WL.'* attempted.
136
-------
Table 7-1. Batch Kinetic Data for the Multicomponent Run and
(12x40) F-400 Carbon Using Fresh tfansau Water.
Carbon Type: F-400 (12X40) MESH
Water Matrix: Fresh Wansau Water
Date: 1/10/85
Elapsed Tine
(minutes)
DCE
0.0
410.0
1910.0
3465.0
4587.0
5727.0
74.6
64.0
58.0
46.0
22.0
18.0
TCE
42.4
38.0
28.0
22.0
19.0
12.0
Experimental Concentrations
(ug/L)
PCE TOL EB
32.8
28.0
18.0
14.0
12.0
8.0
13.5 5.0
11.0 5.0
5.0 4.0
2.0 ND
ND ND
ND ND
ND were not detected using the Hewlett-Packard 5840A with Purge and Trap
137
-------
Tkkl. 7-1 OoqxBMt nd S^CUB Ptrwun for U» IUti«ipu»t Fmk touts
fcUr Km UiiBf U2c4d HOO Cuba
ODtFOOOS: OZ HZ PCE TO.
EB
OCMQOff PHMBB&
Initial Cane tat rat ion; iWL 0.7699 03227 01971 O146J OJX71
Vrradliek Intauity ConstancO/a) 05562 O4328 O3S50 OJ2S2 OO353
Fmnlliek C»p«jtrCai»UiiU 46.9 192.0 435.0 475.0 714J
Q^lnUttd Sorfic* Diffuioa
Cwfficieot Uim« Bprntioi V
10 a «Vt
duff iciot Ciiaj Fixed Bed
Comlatuu 10* ca/i
Biot Uvtm Q»t*d on pon
aod nzfae* dnffuion) ;
1.75
27.44
O.S32
1.64
29.24
0.2315
LJ3
0.1547 O.C374
LJ1 1.42
30.33 30^5 33. U
Stantn Hsber;
0.00915 0.00295 0.002756 0.002720 0.002558
Pan I
Coefficient;
10* a'/t
7.79
6.S5
6.03
5.50
SISDa PtfMQDS:
Beaetor Porosity: OJ9999
Tofxnm. of Boctot: °C 11.0
Sopufkul Velocity; ca/i 15.0
Bydaalie Ictatia tarn; mn 15.4
ifl of bur Jfcuix; <•«
Tol:w of Bctctoc c^ 1313OO
Particle BuiiiuE <• O05129
Putielf D«»itr. 1/tJ OJOM
Cblan Di—«tr; c* 1.1
fct of Ckibca Dud; f 0.1303
138
-------
Table 7-3. Comparison of the Mnlticbmponent Fresh Wausau Water Data
and the Predicted BPSDH Calculations.
MODEL PREDICTION vs. DATA
RESULTS FOR CIS-1.2 DICHLOROETHENE
TIME(dim)
CONC(data) CONC(pred) RESIDUAL
410.000
1910.000
3465.000
4587.000
5727.000
FHIN BASED
.8579
.7775
.6166
.2948
.2413
ON 5 DATA
.9738
.9488
.9338
.9259 *
.9194
POINTS: FMIN =
13.51244
22.02802
51.44782
***••••*
•***•**•
178.94372
RESULTS FOR TRICHLOROETHENE
TIME(dim)
410.000
1910.000
3465.000
4587.000
5727.000
FHIN BASED
CONC(data)
.8962
.6604
.5187
.3551
.2829
ON 5 DATA
CONC(pred)
.9098
.8222
.7562
.7179
.6837
POINTS: FMIN =
RESIDUAL
1.51885
24.51027
45.77514
•«»**»*»
**••****
91.09805
/RESULTS FOR TETRACSLOROETHENE
XI ME (dim)
410.000
1910.000
3465,000
4587.000
5727.000
CONC(data)
.8534
.5485
.4267
.3660
.2437
CONC(pred)
.7478
.5373
.4018
.3388
.2903
RESIDUAL
********
-2.05477
-5.82380
-7.43914
19.12429
FMIN BASED ON 5 DATA POINTS: FMIN = 12.37352
139
-------
Table 7-3 (Continued). Comparison of the Multiconponent Fresh Wausau Water
Data and the Predicted BPSDM Calculations.
RESULTS FOR TOLUENE
TIHE(dim) CONC(data) CONC(pred) RESIDUAL
410.000 .8150 .6359 ••*••***
1910.000 .3706 .3674 -.88960
3465.000 .1481 .2277 53.72225
4587.000 .0000 .1758 ********
5727.000 .0000 .1403 •••••**•
FMIN BASED ON 5 DATA POINTS: FMIN = *********
RESULTS FOR ETHYLBENZENE
TIME(dim) CONC(data) CONC(pred) RESIDUAL
410.000 1.0000 .6434 ********
IS" 10.000 .8004 .0549 ********
3465.000 .0000 .0496 ********
4587.000 .0000 .0351 ••*•**•*
5727.000 .0000 .0265 ********
FMIN BASED ON 5 DATA POINTS: FMIN = *********
140
-------
APPENDIX 8. S/WLE INPUT AND OUTPUT FILES FOR USE WITH THE BHSDM AND THE BPSDM
The purpose of this appendix is to acquaint the potential user with the
BHSDM and the BPSDM. The samp I e run used here is presented in figure V 1-1.
This appendix is broken into two parts: the BHSDM and the BPSDM sample runs.
The procedure is ser up in the following manner:
1. MAPPING ROUTINE
2. INPUT DATA FILE
3. PROGRAM RUNSTREAM
4. OUTPUT FILE
A. The BHSDM Sample Run
1. The computer code for the BHSDM3 (three component batch homogeneous
surface diffusion model) along with code for the program GEAR were presented
by Friedman (1984). The fol lowing mapping routine was used to create the
absolute and relocatable elements for the BHSDM3 program.
€FTN,G BATCH'S.BHSDM3
,@MAP,E ,BATCH*S.BHSDM3
IN BATCH*S.BHSDM3
IN BATCH*S.GEAR12
LIB MTU*FTN.
END
2. This was the input data for the BHSDM3 program:
SDATA,
OS = 3. IE-10,
KF - 4.5E-3,
CBO = 10.06,
XK = 196.6,
XN = .4163,
RAD = 0.05129, RHOP = 0.8034, VOL = 4970.0, WT = 0.27587,
EPS = 1.0E-4, DHO = 1.0E-5, NCOL = 2,
DTO = 0.0, DSTEP = 0.5, DTOL = 8000.0,
DOUT = 0.5, NM = 3,
TIE=50.0,500.0,1000.0,
TINC= 10.0,25.0,100.0,
NDATA=34,NCOf'P=1,
&END
30.0 10.04
120.0 8.69
210.0 8.91
240.0 7.97
141
-------
2. Input Data Continued
300.0 8.35
360.0 7.98
420.0 6.95
1110.0 5.33
1230.0 5.09
1350.0 4.78
1470.0 5.03
1590.0 4.35
1710.0 4.12
1950.0 3.30
2520.0 3.36
2670.0 3.50
2880.0 3.06
3150.0 2.87
3270.0 2.68
4050.0 2.68
4110.0 2.43
4230.0 2.24
4380.0 2.28
4440.0 2.18
4710.0 2.16
5490.0 2.10
5670,0 1.88
5790.0 1.72
6925.0 1.63
6045.0 1.62
6165.0 1.61
6990.0 1.67
7275.0 1.57
7665.0 1.71
3. The runstream was set up in the following manner:
gSUSPEND
6ASG,A BATOH*S.
@ASG,T 4.
gASG.T 8.
§ASG,T 7.
gDATA, IL 4.
gADD.PD BATCH*S.IF400/TCE
SEND
gDATA, I 8.
gADD,PD BATCH*S.10COL
gEND
gXQT BATCH*S.8HSDM3
gCOPY, I 7.,BATCH*S.OUT
gPRT.L BATCH*S.OUT
gRESUME,E
LOG FM1N
EX I
§ED,U BATCH*S. IF400/TCE
2
The collocation constants (10COL) were determined by Friedman (1984),
142
-------
4. The abbreviated output file for the BHSDM3 is'shown belcw:
NUMBER OF COLLOCATION POINTS, NC = 10
TOTAL NO. OF DIFFERENTIAL EQUATIONS, NEQ = 1]
MASS OF ADSORBENT, WT (GRAMS) = .27587+000
VOLUME OF REACTOR, VOL (CM**3) = .49700+004
VOID FRACTI ON OF REACTOR, ECf-BR (DIM.) = . 99993+000
RADIUS OF ADSORBENT PARTICLE, RAD (CM) = .51290-001
APPARENT PARTICLE DENSITY, RHOP (GM/CM**3).. = .80340+000
ERROR CRITERIA FOR INTEGRATION, EPS (DIM.).. = .10000-003
INITIAL INTEGRATION STEP, DHO (MIN) = .10000-004
INITIAL OUTPUT TIME, DOUT (MIN) = .50000+000
TOTAL RUN TIME* DTOL (MIN) = .80000+004
PARAMETERS FOR COMPONENT 1
INITIAL BULK CONCENTRATION, CBO (MMOL/L) = .10060+002
FREUNDLICH ISO. CAP., XK (MMOL/GM)/(L/MMOL)**XN = .19660+003
FREUNDLICH ISOTHERM EXPONENT, XN (DIM.) - .41630+000
SOLUTE DISTRIBUTION PARAMETER, DGS (DIM.) = .26359+001
SURFACE DIFFUSION COEFFICIENT, DS (CM**2/SEC).. = .31000-009
FILM TRANSFER COEFFICIENT, KF (CM/SEC) = .45000-002
HOMOGENEOUS BIOT NUf-BER, BIS (DIM.) = -18138+002
MODEL PREDICTION
ITP
1
2
3
4
5
6
7
8
9
TIME(min)
.50
.00
.50
.00
1,
1,
2.
2.50
.00
.50
3.
3.
4.00
4.50
CU)/CO(1)
.999455
.998910
.998365
.997821
.997277
.996734
.996191
.995650
.995108
230
231
232
233
234
235
236
7400.50
7500.50
7600.50
7700.50
7800.50
7900.50
8000.00
,149490
,147937
,146424
,144951
,143516
,142114
,140754
143
-------
4. Output File. Continued
MODEL PREDICTION vs. DATA
RESULTS FOR CONPONENT 1
TIME(dlm) CONC(data) CONC(pred) RESIDUAL
30.000
120.000
210.000
240.000
300.000
360.000
420.000
1110.000
1230.000
1350.000
1470.000
1590.000
1710.000
1950.000
2520.000
2670.000
2880.000
3150.000
3270.000
4050.000
4110.000
4230.000
4380.000
4440.000
4710.000
5490.000
5670.000
5790.000
6925.000
6045.000
6165.OOC
6990.000
7275.000
7665.000
.9980
.8638
.8857
.7922
.8300
.7932
.6909
.5298
.5060
.4751
.5000
.4324
.4095
.3280
.3340
.3479
.3042
.2853
.2664
.2664
.2416
.2227
.2266
.2167
.2147
.2087
.1869
.1710
.1620
.1610
.1600
.1660
.1561
.1700
.9686
.8893
.8268
.8087
.7755
.7458
.7188
.5184
.4952
.4739
.4544
.4364
.4199
.3902
.3337
.3213
.3055
.2872
.2798
.2393
.2366
.2316
.2255
.2231
.2132
.1892
.1844
.1814
- 1575
.1753
.1726
.1563
.1515
.1455
-.02947
.02949
-.06647
.02074
-.06568
-.05984
.04052
-.02165
-.02136
-.00255
-.09114
.00932
.02517
. 1 8950
-.00101
-.07636
.00434
.00684
.05023
-.10177
-.02033
.03991
-.00512
.02976
-.00696
-.09388
-.01323
.06085
-.02814
.08362
.07848
-.05836
-.02922
-.14417
FMIN BASED ON 34 DATA POINTS: FMIN = 6.42623
144
-------
B. The BPSDH Sample Ron
1. The computer code for the BPSDM3 (three component batch pore and
surface diffusion mode!) along with code for the program GEAR were presented
by-Friedman (1984). The following mapping routine was used to create the
absolute and relocatable elements for the BPSDM3 program.
gFTN,G BATCH*PS.BPSDM3
gMAP.E ,BATCH*PS.BPSDM3
IN BATCH*PS.BPSDM3
IN BATCH*PS.GEAR40
LIB MTU*FTN.
END
2. This was the input data for the BPSDM3 program:
SDATA,
DS = 3.1E-10,
KF = 4.5E-3,
CBO = 10.06,
DP=6.43E-6,EPOR=0.641,
XK = 196.6,
XN = .4163,
RAD = 0.05129, RHOP = 0.8034,VOL = 4970.0, WT = 0.27587,
EPS = 1.0E-4, DHO = 1.0E-5, NCOL = 2,
DTO = 0.0, DSTEP = 0.5, OTOL = 8000.0,
DOUT = 0.5, NM = 3,
TIE=50.0,500.0,1000.0,
TINC= 10.0,25.0,100.0,
NDATA=34,NCOMP=1,
&END
30.0 10.04
.Data Same.
.as BHSDM .
7665.0 1.71
3. The runsTream was set up in the following manner:
gSUSPEND
6ASG,A BATCH*PS.
6ASG,T 4.
gASG.T 7.
@ASG,T 8.
CDATA, IL 4.
gADD,PD BATCH*PS.IF400/TCE
gEND
gDATA. I 8.
gADD.PD BATCH*S.10COL
gEND
gXQT BATCH*PS.BPSDM3
145
-------
3. Runstream Continued
gCOPY, ! 7..BATCH*PS.OUT
6PRT,L BATCH*PS.OUT
PRESUME,E
LOG FMIN
EXI
§ED,U BATCH*PS.IF400/TCE
4. The abbreviated output file for the BPSDM3 is shown below:
NUM3ER OF COLLOCATION POINTS, NC = 10
TOTAL NO. OF DIFFERENTIAL EQUATIONS, NEQ = 11
MASS OF ADSORBENT, WT (GRAMS) = .27587+000
VOLUME OF REACTOR, VOL (CM**3) = .49700+004
VOID FRACTION OF REACTOR, ECKBR (DIM.) = .99993+000
VOID FRACTION OF ADSORBENT, EPOR (DIM.) = .64100+000
RADIUS OF ADSORBENT PARTICLE, RAD (CM) = .51290-001
APPARENT PARTICLE DENSITY, RHOP (GM/CM*»3).. = .80340+000
ERROR CRITERIA FOR INTEGRATION, EPS (DIM.).. = .10000-003
INITIAL INTEGRATION STEP, DHO (MIN) = .10000-004
INITIAL OUTPUT TIME, DOUT (MIN) = .50000+000
TOTAL RUNTIME, DTOL (MIN) = .60000+004
PARAMETERS FOR COMPONENT 1
INITIAL BULK CONCENTRATION, CBO (MMOL/L) = .10060+002
FREUNDLICH ISO. CAP., XK (MMOL/GM)/(L/MMOL)**XN. = .19660+003
FREUNDLICH ISOTHERM EXPONENT, XN (DIM.) = .41630+000
FILM TRANSFER COEFFICIENT, KF (CM/SEC) - .45000-002
SURFACE DIFFUSION COEFFICIENT, DS (CM**2/SEC)... = .24500-009
SURFACE SOLUTE DIST. PARAMETER, DGS (DIM.) = .26359+001
PORE DIFFUSION COEFFICIENT, DP (CM**2/SEC) = .64300-005
PORE SOLUTE DIST. PARAMETER, DGP (DIM.) = .44284-004
SURFACE 4 PORE BASED BlOT NUNBER, BIC (DIM.) = .16278+002
ITP
1
2
3
4
5
6
7
8
9
TIKEunin)
.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
MODEL PREDICTION
CU)/CO(1)
.999455
.998910
.998365
.997821
.997277
.996734
.996192
.995650
.995103
230 7400.50
231 7500.50
232 7600.50
233 7700.50
.152406
.150682
.149398
.147950
146
-------
4. Output File Continued.
MODEL PREDICTION vs. DATA
RESULTS FOR COMPONENT 1
TIME(dim) CONC(data) CONC(pred) RESIDUAL
30.000
120.000
210.000
240.000
300.000
360.000
420.000
1110.000
1230.000
1350.000
1470.000
1590.000
1710.000
1950.000
2520.000
2670.000
2880.000
3150.000
3270.000
4050.000
4110.000
4230.000
4380.000
4440.000
4710.000
5490.000
5670.000
5790.000
6925.000
6045.000
6165.000
6990.000
7275.000
7665.000
.9980
.8638
.8857
.7922
.8300
.7932
.6909
.5298
.5060
.4751
.5000
.4324
.4095
.3280
.3340
.3479
.3042
.2853
.2664
.2664
.2416
.2227
.2266
.2167
.2147
.2087
.1869
.1710
.1620
.1610
.1600
.1660
.1561
.1700
.9638
.8903
.8281
.8100
.7768
.7468
.7197
.5167
.4934
.4720
.4525
.4344
.4179
.3883
.3324
.3203
.3047
.2868
.2795
.2400
.2374
.2324
.2265
.2242
.2146
.1911
.1865
.1836
. 1602
.1776
.1750
.1591
.1544
.1465
-.02931
.03063
-.06501
.02240
-.06417
-.05849
.04170
-.02474
-.02493
-.006^8
-.09509
.00471
.02034
.18387
-.00478
-.07945
.00170
.00527
.04913
-.09927
-.01729
.04381
-.00059
.03478
-.00066
-.08434
-.00192
.07366
-.01112
.10317
.09354
-.04160
-.01079
-.12658
FMIN BASED ON 34 DATA POINTS: FMIN = 6.33310
147
-------
Page Intentionally Blank
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