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
      focfec3l Information Service

-------
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

-------
                                                            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

-------
                                  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

-------
                                   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

-------
                                   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

-------
                              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

-------
     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

-------
     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

-------
          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

-------
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

-------
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

71       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

-------
                               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:
          
-------
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

-------
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

-------
                          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

-------
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 adsorbateadsorbent  systems (Crittenden,  1978; Lee,




1980; Thacker,  1983;  and Pirbazari,  1981).  The  important kinetic parameters




in  the  HSDM  are  the  liquidphase  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

-------
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 singlesolute 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

-------
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.

-------
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

-------
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 105C 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 105C 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.

-------
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

-------
(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  liquidliquid




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, -ptoluene 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  singlesolute 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
                                '
                                                      rdr
(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  liquidphase  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 III1.




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 batchwise  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 iqnidphase.  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
                   Ds.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  Cef/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 stronglyadsorbing  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

VI1 through VI6   contain  the experimental data for  trichloroethene,

tetrachloroethene. cii-1.2 dichlorottheno,  and toluene  along with the  BHSDM

-------
Tibl. 71-1. Sm(it Fit
Snf< Matrix Equilibration Fmullick
Carba Tim. Dayi C
7jp pB Oft CIJ
eii-LI dicLloxo- .
E^lb^
TctTirMoxoethr-t
Tttnchl ozoethoc
Tolacoc
Trichlonxticnt
TricUaroethesc
Trichloroethn*
K-Xjlcnc
0-Ijltn.
JI7-(Z Killi-0
(200x400)
J042-^i mil HJ
F-400
(200x400)
jm-7D5 MillrO
F-400
000x400)
Jfil-li.7 Hilli-Q
F-400
(200x400)
.DS6-37.S Mil 1 j-Q
F-*00
(200x400)
F-400
(200x400)
JD4-4J3 KillHJ
W-C
(200x400)
J14-23^ MUii-Q
F-400
(200x400)
.365-35.7 MillHi
F-400
(200x400)
J63-3J.7 KillHJ
r-00
(200x400)
J3J 45.9
28 (46J -<]>
7J-8.0
13J 710
21 (6E10-746X)
7^-10
9.0-1X0 65O6
6J)
13J 435J)
35 (426IM-WXI)
7^-U)
13J 475J)
7.5-84
9.0-110 19i6
6J (124^4-310.6)
9.0-11.0 181.0
to
13J 1910
31 (187.0-157.0)
7J-M
13J 1044J)
7J-8J)
134 8954
26 (ESLO-938.0)
7.5-84
Best Fit lt
-------
I.U
..

O
>. n o
0 '8
z
o
1
< 06
DC U'
H
Z
UJ
O
2
O -4
O
D
UJ
O
g o.
UJ
cc
n n
{ 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 Ti*ll 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
(5CI.)
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^BAifiBZ* )
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 fimrratlfiti t* tta Fa*!
Cbacrrcd GKMvtxmim tad Tiati for tb* Diflcxvu-ul QaJva LttA Jaartag Stadias
Cteooiiwi I&itlAl VciiW lbd>l aul^rt4B 7

f TriddortUn> 1141.3 1 DIM. TJJ 1C.4S 20B.4 TV-S CUi40) TriMnntiK^ 132S.V ftillr-4) 141.4 1.W 13.9 UblO) P-400 U2l40) Tritilortti 1S12. Kllli-Q 104.7 21.74 1M.7 (1^40) Ft&il Cb*rvd 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 VI4.  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; Co1322.7 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  11C. 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 11C.




     (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/n0.4163
                        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 Uine 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 Thv*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 dichlorothn  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 clculationi  for varioosBiot cu=brt. 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 prt  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/n0.4679
           	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  contnt (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            / 
-------
                                                             (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&tgrtti&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     tur
                      ilm  Ktuli
                           Out**
                    telu   T>j.
                                        of Expir

                                           fT)
                                                          tolli* fotat
                                                                                                IU
                                                     Dttfwirlty

                                                      i 1C10  (>/.>
hund icUerff-
Cutxx
UcncJ
Qilorcl
                  S.7

                  0.7(

                4(0.0

                  1.21
                           illr-Q
1,2
tkra
Hl
cl~1.2 itcklort-   5.23

                  1.07

                  L25

               4MC.O

                  J.07
                  4.04

                 10.3

                 10.0

                 10. f
Tolo
  Kill HI
F-400 Ufa20)
  mil HI
F-400 U2x40)
  Kill HI
P-40D CUUO)
  KUIH)
                  3.10     MUlr-Q
                         >-90DO (12x40)
                  3.74     KUlt-41
                                (50000)
                           MU1H)
                           Kill HI
                           400 (5O
                           Kttl>-0.
                           KU1H1
                         P-400 (Ui20)
                           Killt->a
  Kilir-O
r-tan uz>40)
  U1H)
P-* (1240)
  HillHS
                          F-400
                  10.0       KU1H)
                          TV-C  O240>
aw.u

2W.13

2*5.15

2W.15



2n.ll

2T7.15

2M.15

JW.15

2W.15

2K.13

2M.15



26.15

2*.15

214.19

n4.u

2*4.1$

2*4.15
153.15

MO. 15

59.15

150.15

334.15

134.15

134.15

133.15

445.15



455.15

3*4.15

3H.13

153.15

MO. 15

KKX.15

MO. 15

MO. 15

MO. 15
 13.0

  3J

tM.O



 n.o



  2-2

 27.0

oao

 17.7

153.0

  1-5

  0-5

 U.O

  4J

  1J



  2.1
                                                                      PlAuui  
                                                                         unu
                                                                                                  (im)
                                                                                                Crlttnri*
                                                                                                  UfTI)
                                                                                                 U5V1)
                                                                                                 
-------
tvapersture of the batch  rats  study.  The final form for the lituki equation





          D.       -  4.73 x ID"9 expl-11'665 
-------
     T*ki vm-2.
                            el
                                   CklnUu* 
                                                                                     U.
                                                                                      iut
               LUlui     >ur
                    tux  Micrti
            1C* i  felur
                                    I-T i TuxMM   0>
                                                         l/
                                                                                         Fun  M
                                                                            li/tuiTiij   MffvMB Flat
                                                                                 ICB na-n
                                                                                 .tn*o
                                                                                                         (rant)
                   5.7*
                            Killl-Q
                          f-VD
                                           11*0.0
                                                          o.mo
                                                                                   2.0
                                                                                             u.e
                                                                                                          *.n
                                                                                                                     UMU
                MOO.O       Killi-Q
                                                 H100
                                                                      ruo
                                                                                  17.40      IX. 0
                                                                                                                     tlfTf)
                 4*0.0       HU11-Q
                          T-tO) UfelOl
                                                *000
                                                                      21.0
                                                                                  J.74      900.0
                                                                                         SJ-42      U.tU. AU'
                                                                                                     UK1)
                   0.7*      H.U.IHQ          142.W
                          F-WC
                   1_T1      Kllll-Q          ZM.O
                          F-40C UAOO)
                                                                      n.o
                                                          O.OOO      ZLO
                                                                                  1.0
                                                                                              1J
                                                                                              JJ
                                                                                                                    UNI)
                                                                                                         1J1
                                                                                                                   UKL)
QJorcrfo
                            Kill HQ
                          F-OC UAcTO)
                                             43-J
                                                          0.75M
                                                                                  7.
                                                                                             C.G
                                                                                                                    UNU
QUorcrfo
                  1.10      KU1I--Q
                         CHODD U2>40)
                                            1.C
                                                          o.too      in.c
                                                                                  t.o
                                                                                                                    ami
Qdocviota
                  1.74      IU.Ur-0
                         B>~40DO IXklOO)
                                            ISt. 6
                                                          O.CM      34.0
                                                          0.31511
                                                                      12.0
                                                                                              U
                                                                                   X44       2JJ>
                                                                                                         11.1*      IVto larfy
L2 Ditklwrr-
   1.3      Billr-0
          P-400 (12l40)
                                             T.f
                                                          O.CU
                                                                      Z1.0
                                                                                             n.i
                                                                                                                     (1MU
I.S
J.J
DnUrrl
                lOnO.0      Kiilt-Q
                ucc.0
2MO.O       Kill 1-0
          F-*00
                                                *UtX>
                                                2300
                                                *noo
                                                                      7^ a
                                                                                  29 JO
                                                                                             K.I
                                                                                             44J
                                                                                                          1.12
                                                                                                          1J3
                                                                                                          S.CR
                                                                                                                     UN1J
                                                                                                                     tint)

-------
VH3-J  (Ccntincwl).
                             at U OJnlnud K) Cfcumrf Vrftrj DlflwrUi*i rnn<  tki
                                      rt O fM Ititmiaj Erxla.u4 t
                                of tkt
     liUtUl     Inter      Fmodlifk Iiatbttm fuimun  Tp>ntan   CUnUurf   F |ii  111

                                        1  00nnclM)              Dtta|      ftiffutrlry  Dlffuia Flat
                                        ir                         Iqntioi tin-B
                                        r*t rinmur                DjJP16       DjlC10
Tn

IW^
rw.!
TtncUorv-
S"~
TolMW
rial
Solfamu
LT;r:
IricXtoirv-
Tiuc^lm-
Tru-kJorrr-
 Ckn.
VxtkJoro-
TruUerv-
3C* i IkiltT (nr i Fii-xl Nrf CDmnuimJ
S30.0 MiUr-Q *Zt40
F-OO (4QK.50)
4600.0 Kill 1-4 *XOO
F-400 UAiJC)
1.07 Ulllt-S 10BW.I 0.457*
F-400 (MiM)
t.r7 KUIHO ioin.1 0.437*
P-400 (12i40)
4.04 KU1I-0 tl_7 O.HC
P-4OO U2i0)
loo.o KUI-<> noo
F-tCO UAUO)
r.O MU1H1 JOW
P-4O) (4(k50)
10.1 will i-o sn.7 0.410
P-400 (k*0)
1C.O Klllr-Q Xm.7 O.*l3
F-ao 112>40)
1C.* T>- ) fnun tM.? 0.4U3
P-400 (Ul01
'"** JvT*tl^4W n*1"' ^"^
1C.O HUlt-Q nil.* 0.4O71
l.) ft) l-r1/.) I1/.)
23.0 13 JO ]1.4 0,*4 T Tliat . .1.
unu 
Z2.0 n.09 JS1.0 11.4 ' CritMriM
UJ7I)
U.O OJf L4 1.77 Ikl* Ia4r
11.0 CLU CL* l-Tt IkU todr
13.0 OJM U.O 4J Du texir 
n.c xx.00 in.o  is Ciitt^u*
UtTI)
21.0 . DJ 0.79 TM nut tt. 1.
um; 
11.0 1.00 4J 4JO DUJ fcT
11.0 LOO 1.1 1.10 IkU fcaty
11.0 L0 !. 1.40 Tkit lotr
U.: l-TT I_H 1.40 Dkl* tadr
11.0 1-21 IJ 1.70 Tku fcMr

-------
o
U-
Q
UJ
O
<
LU-
CE 'o
ID *"
CO
LU
>
I
O2

E'S
U.
UJ
Q
UJ
CC
              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
                KuixContrlhution 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 nndretiat 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| brtU| Fore* cW
nrn* IwfM* DiffixtvttI**

tmlm,

rt-H^Manr.
_U
OLrtO.
MU^klar,*.
Olorafca

C-lcrofm

00cn(a

w-LJ 4*kl,w,
tta_
L: Dieklonr-
tUn.
I.tncklor-
tm.
TitTW^Um.-
.Un,
lolHM

7>ieklant*M

Tru^!su_a>

IricUnroLkcM

TtlcWoro.0 .

IriAklonMtlm

liii*l fftT FrviMdliAk ltjhi
fni inntK fctru
CUtat
I
5.7i Hllli-Q 1140.0
P-400 UJoJO)
0.7< Wlli-0. 14J.O
P-400 (JJaJO)
1.21 , KU1M) 224. 0
F-4CO (.11x30)
l.7 Hilli-Q 4I.J
F-40D Ufat20)
1. 10 lUlli-Q 106.0
>*000 (13*40)
1.74 KU1WJ 15>.0
B>-40aO CKklOO)
- S. tillMl 337.0
F-WO (12*40)
1-23 MUli-Q 37.)
T-tOD (12x40)
1.07 Killi-0 1(FS.I
P-WD (k*0)
i.n mil HO icaa.f
F-400 C12r40)
4.0* Ullr-0 m.7
P-400 U2r40)
10.1 MUli-Q WW.7
P-400 <0>0}
1C.C aOli- S3.7
F-4OO U240)
lO.f TJuml IMM J3W.7
P-OD (11.40)
*.4 7>nW foM JH1.
V-C U2i40)
10.0 Hillr-Q SX3.J
*-C tUr40)
_rwwitn Tfiaii Oll4U< iuil (
MF1M0* &^^^ A^^
furt wi4i^
OW| Pi/ftM 1* It/
!/ ^*^^ ^&^$i
^^V^ J ^^^* ^ ^ I ^^^* / A )
OJMO 21.0 4.12 U.O MlWkcri 
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 *Mf

O.Olf 21.0 4.n n.7 **^TIJL.*i
atw
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 (ar

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-
;'J^ri"'"
T~*
7(- 1 orn*
Tr uJxl TTCV then*
TT uc hi erne Una
Tr u:M ?rm Lhn
TV it .MOTTMthrtw
i r i^ Jtj OTX^I (ARBP
-4. r.vriK of \t ,(Vlclil< 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.J70
F--400 (ttiiO)
0.7 Kllli-Q J43.0 0.74SO
F--4OD (ltiO)
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)

 NC                 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   Sll   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 250C 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 250C 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 105C 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 105C




     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 105C 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 105C  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

-------


                            ii-Eii- DET ERMlfviAiflONiS
                                      =zfl,, -Y. n''  'ITrir-

                             . -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




     105C 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

-------
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 51 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 c2/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

-------
Tblo 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 IUtiiput 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 CpjtrCaiUiiU      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 Qt*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  Ditr.  1/tJ             OJOM

 Cblan Ditr; 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

-------