EPA/600/R-97/054
                                          September  1997
  Theoretical  and  Experimental Modeling
   of Multi-Species  Transport in  Soils
           Under Electric  Fields
                      By

    Yalcin B.  Acar and Akram N.  Alshawabkeh
             Electrokinetics,  Inc.
             Baton Rouge,  LA 70809

                Randy A.  Parker
 National  Risk  Management  Research  Laboratory
     U.S.  Environmental Protection Agency
              Cincinnati, OH  45268
   Cooperative Agreement No.  CR-816828-01-1
                Project Officer:

                Randy A.  Parker
Land Remediation and Pollution Control Division
 National Risk  Management  Research  Laboratory
              Cincinnati, OH  45268
 National Risk  Management  Research  Laboratory
      Office  of Research and  Development
     U.S. Environmental Protection  Agency
              Cincinnati, OH 45268

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                                         TECHNICAL REPORT DATA
                                (Please read Instructions on tfie reverse before completing)
1. REPORT NO.
 EPA/600/R-97/054
                                  2.
                                                                     3. RECIPIENT'S ACCESSION NO.
                          PB97-193056
 : . TITLE AND SUBTITLE
                                                                     5. REPORT OTE    ,
                                                                               September 1997
 Theoretical and Experimental Modeling  of Multi-Species
 Transport  in Soils Under Electric  Fields
                5. PERFORMING ORGANIZATION COOE
 A7. AUTHOR(S)
                                                                     ). PERFORMING ORGANIZATION REPORT NO,
 Yalcin B. Acar1, Akram N. Alshawabkeh', and Randy A. Parker
  9. PERFORMING. ORGANIZATION NAME  AND  ADRESS
 Electrokinetics, Inc., 11552 Cedar Park Ave.
 Baton Rouge, LA 70809
 National Risk Management Research Laboratory, USEPA
 Cincinnati,  OH 45268
                                                                     10. PROGRAM ELEMENT NO.
                 11. CONTRACT/GRANT NO.
                          CR-816828-Ol-l
 12. SPONSORING AGENCY NAME ANO AOORESS
 National Risk Management Research Laboratory
 Office of Research and Development
 U.S.  Environmental  Protection  Agency
 Cincinnati. OH 45268	
                13. TYPE OF REPORT Aj
                   Project Report,
OVERED
                14. SPONSORING AGENCY CODE
                          EPA/600/14
    SUPPLEMENTARY NOTES
 Project Officer:  Randy A. Parker  (5 13) 569-7271
 16. ABSTRACT
Electrokinetics employs the use of electrodes implanted in soils-contaminated media. Electrodes are supplied
with direct current (dc) facilitating ionic transport and subsequent, removal.   This project investigates the
feasibility and  efficiency of electrokinetic transport of lead  in soils at bench and pilot-scale.  A  theoretical model
was developed using numerical algorithms based on differential and algebraic equations. The theoretical model
is presented and  compared with pilot-scale results.
17.
                                            KEY WOROS ANO DOCUMENT ANALYSIS
                      DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS c.  COSATI Field/Group
Emerging
Technology
Lead
Soils
    Electrokinetics
    Site Program
 8. DISTRIBUTION STATEMENT

 Release to Public
                                                      19. S
                                                                                     21. NO. OF PAGES
                                                     20. SECURITY CLASS (This page)
                                                         Unclassified
                                                                                     22. PRICE
EPA Form  2220-1 (Rev. 4-77    PREVIOUS EDITION   OBSOLETE

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                            DISCLAIMER


The U.S.  Environmental  Protection Agency through its Office  of
Research and  Development  partially funded and collaborated in  the
research described here  under  Cooperative Agreement No.  CR
816828-01-0 to Electrokinetics, Inc.   it has been subject to the
Agency's peer and  administrative  review,  and it has been approved
for publication as an EPA document.   Mention of trade names  or
commercial products  does  not  constitute endorsement or
recommendation for use.
                                11

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                              FOREWORD
      The  U.S.  Environmental Protection Agency  (EPA)  is  charged by
Congress  with  protecting  the Nation's land, air, and water
resources.   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.    To meet  this
mandate,   EPA's  research program is providing data  and  technical
support for  solving environmental  problems today and building  a
science knowledge base necessary  to manage our  ecological
resources wisely,  understand how pollutants affect our  health,
and prevent  or  reduce  environmental risks in the future.

      The  National Risk Management Research Laboratory  is  the
Agency's  center for investigation of  technological and management
approaches for  reducing risks  from threats to  human health and
the environment.   The  focus of the  Laboratory's research  program
is on methods  for the  prevention  and control of pollution to air,
land,  water,  and subsurface resources: protection  of water
quality in public water  systems;  remediation of  contaminated
sites and ground water:  and prevention of  indoor air pollution.
The goal  of  this research effort  is to catalyze  development  and
implementation  of innovative,  cost  effective environmental
technologies;  develop  scientific  and  engineering information
needed by EPA  to support  regulatory and policy  decisions;  and
provide technical  support  and information  transfer to  ensure
effective implementation  of environmental  regulations and
strategies.

      This publication  has  been produced as part of the
Laboratory's strategic long-term  research plan.  it  is  published
and made  available  by  EPA's office of Research  and Development to
assist the user community and to  link researchers  with  their
clients.
                     E.  Timothy Oppelt,  Director
                     National  Risk Management Research  Laboratory
                                111

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                           ACKNOWLEDGEMENTS
The pilot-scale studies reported herein are supported by the US Environmental protection Agency
(USEPA) National Risk Management Research Laboratory (NRMRL)  under the SITE-E03
program through the Cooperative Agreement CR81682801-1 with Electrokinetics  Inc. of Baton
Rouge, Louisiana. Don Sanning, Norma Lewis, Randy Parker and Guy Simes of the SITE
program of NRMRL are gratefully acknowledged for their collaboration and cooperation during the
course of this project

"Fundamental Aspects of Electrokinetic Remediation of Soils" is another project funded  with
Federal Funds as part of the program of the Gulf Coast Hazardous Substance Research Center
(GCHSRC) which is supported under cooperative agreement R815197 with the United States
Environmental  Protection Agency. Monsanto Corporation partnered with GCHSRC through the
Industrial Ties Program in partial support of some of the tasks in the pilot-scale testing and the
theoretical development effort. We thank Alan Ford of GCHSRC and Sa Ho of Monsanto for their
efficient input and  collaboration.

We appreciate the materials and the labor donated in manufacturing the liners used in the pilot-scale
boxes by the Gundle Corporation and Robert Johnson of this corporation.

The contents and opinions expressed in this report are those of the authors and do not necessarily
reflect the views and policies of the USEPA and other sponsors.
                                         IV

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                          TABLE OF CONTENTS



DISCLAIMER   , , ,		-	    »

FOREWORD	  iii

ACKNOWLEDGEMENTS			  iv

LIST OF TABLES  	•  IX

LIST OF  FIGURES	-.....-  »

LIST  OF PLATES  ,.-	   xvii

EXECUTIVE SUMMARY	   xvlli


Section 1
  INTRODUCTION	 . . .   1-1
      1.1    Objectives	   1-5
      1.1'  Scope  	   1-5
      1.3   Organization of the Manuscript	   1-8

Section 2
BACKGROUND  ....'..	.-.	•	;. .   2-1
      2.1    Introduction	 .'	   2-1
      2.2   Electrokinetic Phenomena in Soils	! ..	   2-1
      2.3   Heavy Metals, in Soils  	   2-6
      2.4   Soil Contamination With Lead	 .   2-7
      2.5   Principles of Hectrokinetic Soil Remediation   	   2-8
            2.5.1  Electrolysis   Reactions	   2-8
            2.5.2 Changes in Soil pH 	   2-9
            2.5.3  Sorotiqn Reactions	   2-12
            2.5.4    Precipitation/Dissolution	   2-15
            2.5.5  Contaminant Transport, Capture, and Removal	   2-15
            2.5.6    Enhancement/Conditioning	   2-16
      2.6   Applications of Electrokinetics in Environmental Geotechnics   	   2-18
            2.6.1  Eertrokmetic Flow Barriers.—  	   2-18
            2.6.2 Hydraulic Conductivity  Measurements	   2-20
            2.6.3  Concentration   and  Dewatering	   2-20
            2.6.4  Plume  Diversion  Schemes  	   2-20
            2.6.5  Hydrofracturing/Electrokinetics/Bioremediation	   2-20
      2.7   Feasibility Studies On Eectrokinetic Soil Remediation  	   2-21
      2.8   Theoretical Modeling of Electrokinetic Soil Processing  	   2-32

Section 3
THEORETICAL  DEVELOPMENT . -.	   3-1
      3.1   Introduction  	   3-1
      3.2   Assumptions 	   3-1

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       3.3    Transport Processes	     3-3
             3.3.1   FluidFlux  	     3-5
                    3.3.1.1 Darcy's Law of Advection   	    3-3
                    3.3.1.2 ElectroosmoticFluid Flux   	    3-6
                    3.3.1.3 Total Fluid Flux   	  3-10
             3.3.2   Mass Flux	   3-12
                    3.3.2.1 Pick's Law of Diffusion  	   3-12
                    3.3.2.2  Mass Fiux by Ion Migration	   3-18
                    3.3.2.3 Advective Mass Flux  	   3-19
                    3.32.4 Total Mass Flux	   3-19
             3.3.3  ChargeFlux  	   3-19
                    3.3.3.1  Migrational Charge Flux   	3-21
                    3.3.3.2 Transport Number  	: ..   3-23
                    3.3.3.3 Diffusiqnal Charge Flux	    3-25
                    3.3.3.4 Advective Charge Flux	  3-25
                    3.3.3.5  Total Charge Flux  	   3-26
       3.4    Conservation "of" Mass ~ and  Charge   	    3-26
             3.4.1  Soil Consolidation	   3-27
             3.4.2  Conservation of Mass	   3-27
             3.4.3  Conservation of Charge	    3-28
             3.4.4  Chemical Reactions  	    3-28
                    3.4.4.1  Sorption Reactions  	   3-29
                    3.4.4.2 Aqueous Phase Reactions	   3-30
                    3.4.4.3  Precipitation/Dissolution Reactions  	     3-31
       3.5    General System for Modeling Species Transport	   3-32
             3.5.1  Initial and Boundary Conditions 	    3-34
             3.5.2  Preservation of Electrical Neutrality   	    3-35
       3.6    Modeling Acid/Base  Distribution-	   3-37
             3.6.1  H+Transport   	   3-38
             3.6_.2  OH- Transport-	   3-39
             3.6.3  Pore Pressure  	   3-40
             3.6.4  Charge Transport Equation 	    3-40
             3.6.5  WaterAuto-ionizationReaction	  3-41
       3.7    Modeling Lead Transport	   3-42
             3.7.1  Pb+2  Transport	    3-43
             3.7.2  H+ Transport	3-43
             3.7.3  OH-Transport	   3-44
             3.7.4  NO-3  Transport  		   3-45
             3.7.5  Soil Consolidation Equation   	3-46
             3.7.6.  Charge Transport Equation  	3-46
             3.7.7   Chemical Reactions	   3-47

Section 4
NUMERICAL  SIMULATION  	   4-1
       4.1    Introduction		   4-1
       4.2    Solution  Scheme	   4-2
       4.3    Finite Element Solution  of PDE's	   4-4
             4.3.1  Variational Formulation  	  4-5
             4.3.2   Local   Matrices     	   4-12
              4.3.3   Gauss  Legendre  Quadrature    	   4-15
                                          VI

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            4.3.4 Global       ....................................   4-16
            4.3,5                     ,,,,,,.	   4-17
      4,4    Verification of the                   ......................   4-18
                                                           *    *
Section  5
                          ..'......................................   5-1
      5,1    JktrodudiQQ .	...................................   5-1
      5.2            and	   5-1
            5.2.1 Test          .-....................•............'.'    5-1
            5.2.2           .......................................   5-2
            5,2.3 Power Supply  ...........................	   5.2
          "  5,2.4	   5-5
      5.3    Dm Acquisition	   5-9
      5.4    SoiDescription	,..,...,	   5-10
      5,5    Chemical        . , ,	, , ,	   5.10
      5.6    PermeationFlui^	   5-10
      5.7                   ................................!.!!!"   5-14
      5.3    Pilot-Scale Tests	,	., , .    5,14
      5.9    Test	,	   5-17
      5.10   Ctamcai Analysis  .	  -5-21
      5.11   Soil Sampling	,,.,;.,,..,   5-21
      5.12                and	   5-24

        
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                 7.3.1.5       Hydraulic  Conductivity  	   7-10
                 7.3.1.6       Lead Sorption  	   7-12
                 7.3.1.7       Hydrogen Retardation   	   7-12
            7.3.2 Initial and Boundary Conditions	   7-13
      7.4    Results and Analysis	   7-17
            7.4.1  SoilpH	   7-17
            7.4.2 Electric Conductivity  	   7-19
            7.4.3 Total Pore Fluid Flow and Pressure	   7-27
            7.4.4 Lead Transport and Removal  	   7-34

Section  8
SUMMARY AND CONCLUSIONS 	  8-1
   .   8.1    summary  	  8-1
      8.2    Conclusions 	  	   8-3
      8.3    Considerations for In-situ Implementation   	  8-6
      8.4    Recommendations for Future Studies  	  8-9

REFERENCES   	  9-1

APPENDICES

Appendix-A
EK-REM PROGRAM  LISTING	   A-l

Appendix-B
INPUT 7 OUTUT FILES LISTING 	  B-l

Appendix-C
VERIFICATION  OF THE FINITE ELEMENT SOLUTION	      C-l

Appendix-D
EXPERIMENTAL DATA	,	     D-l

Appendix-E
CONVERSION FACTORS    	   E-l

Appendix-F
CALCULATION  OF DATA QUALITY INDICATORS  	   F-l
                                 VIM

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                                 LIST  OF TABLES
Table 2.1:


Table 2.2:

Table 2.3:


Table 2.4:

Table 3.1:

Table 3.2:


Table 3.3:
Standard Reduction Electrochemical Potentials in Aqueous Solution at 25* C
(Kotz and Purcell 1987)  ....,...,	

Selectivity of Different Soil Types for Divalent Metals (Alloway 1990)   . . ,

Synthesis of Laboratory Data Reported by Various Investigators on the
Removal  of Chemical Species  from  Soils 	
References  for Data Presented  in Table  2.3

Direct and Coupled Plow Phenomena   	
Representative Tortuosity Factors (Adapted from  Schackelford and Daniel,
 1991) 	

Absolute Values of Diffusion Coefficients and Ionic Mobilities for
Representative Cations at Infinite Dilution at 25* C (Adapted from Dean
 2-10

2-13


 2-33

2-37

 3-4


3-14



3-15
Table 3.4:
Table 3.5:
Table 3.6:
Table 5.1:
Table 5 2-
Table 5 3-
Table 6.1:
Table 6.2:
Table 6.3
Table 6.4
Table 6.5
Absolute Values of Diffusion Coefficients and Ionic Mobilities for
Representative Anions at Infinite Dilution at 25* C (Adapted from Dean,
1985) 	
Limiting Free-Solution Diffusion Coefficients for Representative Simple
Electrolytes at 25* C (Schackelford and Daniel, 1991) 	
Transport Numbers of Cations at Various Concentrations (Koryta and
Dvorak 1987)
Physicochemical Properties of Georgia Kaolinite Provided by Thiele Kaolin
Company 	
Characteristics of Georgia Kaolinite (Hamed 1990)
Chemical Concentrations of Kaolinite and Tap Water 	
Initial Conditions for Bench-Scale and Pilot-Scale Tests 	
Measurement Units Used for Variables Identified in EK-REM
Sample Precision Calculations for the Second Layer in PST2
Sample Accuracy (% Recovery) calculation for Lead Spiked Samples ....
Target and Measured Lead Concentrations in Bench-Scale and Pilot-Scale
Tests 	
3-16
3-17
3-24
5-11
5-12
5-13
6-2
6-58
6-64
6-64
fi-R4
                                         IX

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Table 7.1:     Measurement Units Used for variables Identified in EK-REM	, . .  .   7-7

Table 7.2:     Parameters and Relations Used in Modeling Lead Removal from Kaolinite
             by Electrokinetics	   7-8

Table 7.3:    Initial and Boundary Conditions Used in EK-KEM	    7-14

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                                LIST OF FIGURES
Figure 1.1:    Estimated Number of Contaminated Sites and Clean-up Costs in the US
              (Adapted from Morse 1989)	     1-2

Figure 1.2:    Most Frequently Identified Species in Soils in the 1217 Sites Listed on the
              National Priority List in 1989 (Adopted from EPA 1991)	    1-7

Figure 2.1:    Charge Distribution Adjacent to Clay Surface (Mitchell 1993)   	     2-2

Figure 2.2:    Electrokinetic Phenomena in Soils (Mitchell  1993)	      2-4

Figure 2.3:    Schematic Diagram of Advection by Electroosmosis, Depicting the Excess
              Cations  on the Clay Surface and  an Approximate Velocity Profile Across the
              Pore Capillary (Acaretal.l994b) 	      2-5

Figure 2.4:    Acid/Base Distribution across Specimen of Slurry Consolidated Georgia
              Kaolinite Processed under an Electric Current of 12.5 ^iA/on2 (Acar et al.
              1990)	      2-11

Figure 2.5:    A Schematic Representation of Protons Displacing Lead from the Soil
              Surface  and Transport of Both the Protons and Lead towards  the Cathode
              (Acar et al. 1993)    	       2-14

Figure 2.6:    Schematic of Electrodinetic Soil Processing Showing Migration of Ionic
              Species, Transport of Acid Front and/or Processing Fluid across the
              Process Medium (Acar and Alshawabkeh)  .       	    2-16

Figure 2.7:    (a) Electrokinetic Flow Barriers and (b) Plume Diversion Scheme	    2-19

Figure 2.8:    Hydrofractiiring/Ekctrokinetics/Biodegradationin Soil Remediation  (Ho
              1993)	       2-21

Figure 2.9:    Pb  Removal  by Electrodinetics (Hamed  1990) 	    2-24

Figure 2.10:    Post Treatment Distribution of Lead and Calcium across Specimens from a
              Site Processed with Acetic Acid Enhanced Electrokinetic Treatment  (500
              HA/cm* Current Density for 2,320 h with Average Gradient of 5.0 V/cm)
              (Acar   and   Alshawabkeh   1993)   	    2-25

Figure 2.11:   Post-Treatment Distribution of Uranyl Ion across the Specimen in
              Unenhanced  Electrokinetic Experiments (Acar et al.  1992c), (b) Post-
              Treatment Mass Balance in Acetic Acid Enhanced Electrokinetics
              Remediation  Experiments for Uranyl Ion Removal from Kaolinite
              Specimens     (Acar   et  al.  1993b)  	     2-27

Figure 2.12:   Phenol Removal by Electrokinetics (Acar et al. 1992)   	     2-28
                                           XI

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Figure 2.13:

Figure 2.14:

Figure 3.1:


Figure 3.2:


Figure 3.3:


Figure 3.4:
Figure 3.5:
Hexachlorobutadiene  Transport under Electric Gradients (Acar et al 1993)

A Schematic Diagram of the Field System  Reported by Lageman (19889) .  .

A Comparison of pH and Conductivity Profiles across a Specimen (Acar et
al.     1992b)    .............................................

ElectricalPotential Profile across a Specimen in Q3+ Removal Test
(Named,  1990)   ........................................

The Effect of pH and Ion Concentration Zeta potential of  Colloidal
(iep is the Isoelectric point) (Hunter, 198 1)
A Schematic Diagram of Concentration Profiles in Transport of
(a)Positively  Charged and (b) Negatively Charged Species
2-30

2-31


 3-8


 3-9


3-11


3-20
A Schematic Diagram of Possible Paths of an Electric Charge through a
Soil-Water Electrolyte Medium (i) All Possible Paths, (ii) Simplified Case
Accounting only for the DDL ana Pore Fluid, and (iii) Electric Circuit for
                                                                                      3-22
Figure 3.6:

Figure 4.1:
Figure 4.2:

Figure 4.3:
Figure 5.1:

Figure 5.2:
Figure 5.3:
Figure 5.4:
Figure 5.5:

Figure 5.6:
Figure 5.7:
Figure 5.8:
Figure 5.9:
Lead Sorption at Different pH Values (Experimental Data from Yong et al.,
1990) 	
Flow Chart Describing the Sequential Iteration Scheme Used 	
General Space Domain for Two-Dimensional Problem with the Boundary
Conditions 	
Eight Node Quadratic Isoparametric Quadrilateral Element 	
A Schematic Diagram of the Wooden Container and Lining Material Used
for Testing 	
Voltage Divider 	 -. . . .
A Schematic View of Suction Measurement Devices 	
Schematic View of the Bench-Scale Test Set-Up (Hamed, 1990)
Longitudinal Cross-Section of the Pilot-Scale Test Sample Depicting the . . .
System Used for the Hydraulic Flow
A Schematic Diagram of the Pilot-Scale Test Set-Up 	
A Schematic Diagram of the Data Aquisition System
Sampling Locations for Final Analysis in the Second Pilot-Scale Test ....
Distribution of Monitoring Probes and Locations of Sampling Points

3-49
4-3

4-6
4-9

5-3
5-6
. 5-7
5-15

5-19
5-22
5-23
5-25
5-26
                                             XII

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 Figure 6.1:    Catholyte and Anolyte pH Changes with Time in (a) BSTI and (b) BST2       6-5

 Figure 6.2:    Catholyte and Anolyte pH Changes with Time in (a) PST1 and (b) PST2 ....   6-6

 Figure 6.3:    Final pH Distributions across BercbScale Specimens at a Current Density
              of 127 uA/cm2  	    6-8

 Figure 6.4:    Final pH Distribution across the Middle Layer of PST1 (a) 3-D Contour
              Diagram and (b) Mean and Stadard Deviation	    6-9

 Figure 6.5:    Final pH Distributions  across Cell A in the Middle Layer(Layer 3) of PST2
              (a) 3-D Contour Diagram and (b) Mean and Standard Deviation    	    6-10

 Figure 6.6:    Final pH Distributions across Cell B in the Middle Layer (Layer 3) of PST2
              (a) 3-D Contour Diagram and (b) Meanand Standard Deviation	    6-11

 Figure 6.7:    Mean and Standard Deviation of Final pH Distribution across all Layers of
              PST2(a)CellAand(b)CelIB	   6-13

 Figure 6.8:    Prediction of Rate of Advance of the Acid Front (a) Time Changes in pH at
              Distance of 5,15, and 25 cm from the Anode, and (b) Rate Of Advance of
              The Acid Front  	     6-14

 Figure 6.9:    Changes in the Total Applied Voltage in (a) BSTI  and (b) BST2	    6-15

 Figure 6. 10:   Time Changes in the Total Applied Electric Voltage in PST1, PST2, and
              PST3  	:	    6-17

 Figure 6. II:   Apparent Electric'Conductivities of (a) Bench-Scale specimens and  (b)
              Pilot-Scale Specimens  	        6-19

 Figure 6.12:   Electric Potential Distribution Across (a) BSTI and (b) BST2 (Current
              Density, !<, - 127 nA/cm*)   	    6-21
 Figure 6.13 ;   Electric Potential Distribution Across the Soil Specimen (a) PST1 and (b)
              PST2CI,,- 133 jiA/cm2)   	    6-22

Figure  6.14: Pore Pressure Developed inTensiometer with Time	     6-25

 Figure 6.15:   Comparison  between Electric Potential Profile  and Pore Pressure Profile
              across PST2 after 300h and500  h	    6-27

 Figure 6.16:   Pore Fluid Flow in PSTI   	    6-28

 Figure 6.17:   Changes in Coefficients of Electroosmotic Permeability and Electroosmotic
              Water Transport Efficiency in PST1   	    6-31

 Figure 6.18:   Significance of Migration  with Respect to Electroosmosis	    6-33

 Figure 6.19:   Final Water Content Distribution in Bench-Scale Specimens  	    6-34
                                        XIII

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Figure 6.20:   Final Water Content Distribution in across Cell A in the Middle Layer
             (Layer 3) of PST2 (a) 3-D Figure and (b) Mean and Standard Deviation   .    6-35

Figure 6.21:   Final Water content Distribution in across Ceil B in the Middle Layer (Layer
             3) of PST2 (a) 3-D Figure and (b) Mean and Standard Deviation   .......    6-36

Figure 6.22:   Final Lead Concentration across Bench-Scale Soil Specimens   .........    6-39

Figure 6.23:   Mass Balance for Bench-Scale Tests (BST1=169 h, BST2=598 h, !» = 127
                       for  Both)  .......................................     6-40
Figure 6.24:   Final Lead Concentration acrossthe Middle Layer of PST1 (a) 3-D Contout
             Diagramand (b) Mean and Standand Deviation   ...................    6-41

Figure 6.25:   Final Lead Distribution across the Top Layer of PSTI   ..............    6-44

Figure 6.26:   Mass Balance for PSTI (Duration=1300 h, !„ = 127"(M/cm2)  .........    6-45

Figure 6.27:   Final Lead Concentration across Ceil A in the Middle Layer (Layer 3) of
             PST2 (a) 3-D Contour Diagram and (b) Mean Standard Deviation .......    6-46

Figure 6.28:   Final Lead Concentration across Cdl B in the Middle Layer (Layer 3) of
             PS T2 (a) 3-D  Contour Diagram and (b) Mean and Standard Deviation  ....    6-47

Figure 6.29:   Mass Balance for Ceils A and B'in PST2 (Duration=2950 h, Current
             Density, !<,=«  133 ^A/cmZ)  ................................    649
Figure 6.30:  Mean and Standard Deviation of Final Lead Concentration across all Layers
             in PST2 after 2950 h at a Current Density of I* * 133 ^lA/cm* (a) Ceil A
             and(b)Cell  B ........................................    6-50

Figure 6.31 :  Energy  Consumption  in  Bench-Scale  Tests  ......................    6-53

Figure 6.32:  Energy  Consumption  in  PSTI, PST2,  and PST3 ...................    6-54

Figure 6.33 :   Changes in the Electric Power in Bench-Scale Tests  .................    6-55

Figure 6.34:   Changes in the Electric Power in Pilot-Scale Tests  .................    6-56

Figure 6.35:  Final  Anion  Concentration in the Soil Pore Fluid in  PST2 ............    6-59

Figure 6.36:  (a) Final Cation Distribution across the Soil Specimen in PST2 (b) Final Al
             Distribution across the Soil Specimen in PST2  ...................    6-60

Figure 6.37:  Temperature Changes in PST2  ..............................   6-62

Figure 7. I:   Flow Chart for EK-REM  ..................................     7-2

Figure 7.2:   Flow   Chart  for  Subroutine  INPUT  ............................     7-3
                                           XIV

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Figure 7.3:    Flow  Chart  for  Subroutine  ELSTIF	     7-5

Figure 7.4:    Hydraulic Conductivity Measurement of the Horizontal Sample (Gokmen
               1994) 	    7-11

Figure 7.5:    Finite Element Mesh of 40 Elements  	    7-16

Figure 7.6:    Predicted Changes in SoilpH Across the Soil Specimen in Time	   7-18

Figure 7.7:    Comparison Between Predicted and Experiment pH Profiles After 8 days
              and 15 days of Processing   	   7-20

Figure 7.8:    Comparison Between Predicted and Experiment pH Profiles After 22 days
              of Processing  	,	, .  .    7-21

Figure 7.9:    Predicted Electric Conductivity Distribution Across the Pilot-Scale Test
              Specimen	    7-22


Figure 7.10:    Predicted and Experimental Electric Potential Distributions After 100 h and
              3 OOh of Processing PST3	,	,  . .  	         7.24

Figure 7.11:    Model and Experimental Results of the Electric Gradient Distributions After
              100 hand 300 h of Processing PST3	     7-25

Figure 7.12:   Comparison of Electric Potential Distribution After 1200 h of Processing
              PST3  	    7-26

Figure 7.13:   Comparison of the Electric Gradient Distributions inPST3  	;    7.28

Figure 7.14:   Predicted  Pore Fluid Flow Rates Across the Specimen   	    7_29

Figure 7.15:   Predicted and Measured Pore Water Pressure in Tensiometers Located at a
              Distance of 14 cm and42 cm from the Cathode             ,	    7.30

Figure 7.16:   Comparison Between Suction Generated in the Model and in the Experiment
              After 37  ad 40 days of Processing	    7.32

Figure 7.17:   Comparison Between Suction Generated in the Model and in the Experiment
              After  45   and   50  days   of Processing	    7.33

Figure 7.18:   Predicted Dissolved Lead Concentration in the Pore Fluid  	    7.35

Figure 7.19:   Predicted Adsorbed Lead Profile  	    7.36

Figure 7.20:   Predicted Precipitated Lead Hydroxide Profile  	    7.33

Figure 7.21:   Predicted Total Lead Profile	,	    7.39

Figure 7.22:   A Comparison of Pilot-Scale Test Results and Predicted Total Lead
              Concentration Afer 8 and 15 days   ,	      7-40

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Figure 7.23:   A Comparison of Pilot-Scale Test Results and Modeled Total Lead
             Concentration After 22 and 37 days	    7-41

Figure 7.24:   A Comparison of Pilot-Scale test Results and Modeled Total Lead
             Concentration  After 50  days	,	       7-42
                                          XVI

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                               LIST OF PLATES

Plate 5.1:     Graphite Electrodes Used in Pilot-Scale Tests	   5.4
Plate 5.2:     Various Probes Used in Large-Scale Experiments	    5-18
Plate 5.3:     The Wooden Box Used in Pilot-Scale Tests Showing the Two Cells (A, and
             B), the Anode and Two Cathodes	     5-20
Plate 6.1:     Surface of the Soil Specimen on PST1 Depicting Development of Cracks at
             Midsections  and Near  Cathode  	        6-42
                                         XVII

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                            EXECUTIVE  SUMMARY
The feasibility and efficiency of transporting lead under electric fields are investigated at pilot-scale
in three one ton Georgia kaolinite specimens spiked with lead nitrate solution and at an dectrode
spacing of 72 cm. In order to establish the relation between chemistry and mechanics, enhancement
methods such as cathode depolarization and/or catholyte neutralization techniques are not  employed
in processing. A constant direct current density of 133 jiA/can^is applied. Two of the tests are
conducted on specimens spiked with lead at concentrations of 856 mg/kg and 1,533 mg/kg. The
third test is conducted on a  I :  1  mixture of compacted kaolinite/sand spiked with lead at a
concentration of 5,322 mg/kg. pH distributions, electric potential distributions, lead transport,
pore pressures and temperatures developed across the soil mass are presented, evaluated and
discussed. The tests demonstrated that the lead was transported towards the cathode and
precipitated at its hydroxide solubility value within the basic zone in direct contact with the cathode
compartment. Subsequent to  2,950 h of processing and an energy expenditure of 700kWh/m3,55
% of the lead removed across the soil was found precipitated within the last 2 cm close to the
cathode, 15 % was left in the soil before reaching this zone, 20 % was found precipitated on the
fabric separating the soil from the cathode compartment and 10% was unaccounted. The results
demonstrate that heavy metals and species that are solubilized in the anodic acid front can be
efficiently transported by electromigration under an electrical field applied across electrodes placed
in soils. The results also disclose the rdation between chemistry and mechanics in pore fluid
transport and electroosmotic  consolidation. In direct response to the changes in electrochemistry,
 suction and electroosmotic consolidation prevail in the soil even when egress and ingress of pore
fluids into the soil are allowed  at the electrodes.

 A mathematical model also is presented for multi-component  species transport under coupled
 hydraulic, electric, and  chemical potential differences.  Mass balance of species and  pore fluid
together with charge balance  across the medium result in a set of differential equations. Sorption,
 aqueous phase and precipitation reactions are accounted by  a set of algebraic equations.
 Instantaneous chemical equilibrium conditions are assumed. Transport of H*, OH-, Pb2* the
 associated chemical reactions, electric potential and pore pressure distribution across the electrodes
 in electrokinetic remediation  are modeled. Model predictions of acid transport, lead transport, and
 pore pressure distribution display very good agreement with the pilot-scale test results  validating
                                           XVUl

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the formalisms offered for multi-component transport of reactive species under an electric field.
The model also bridges the gap between the electrochemistry and mechanics in electroosmotic
consolidation of soils.

This report was submitted in fullfillment of Cooperative Agreement CR81682801-1 between the
National Risk Management Research Laboratory of the U. S. Environmental Protection Agency
and Electrokinetics  Inc. The accomplishment presented by the report covers a period from August
1990 to August 1994 and the work is completed as of June 1994.
                                      XIX

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                                     Section 1


                                INTRODUCTION

       The impact of soil  contamination on groundwater resources is becoming increasingly
significant as the disclosed number of unengineered waste containment facilities and contaminated
sites grow and remediation costs increase.  The growing size of the problem has given way to a
comprehensive national program that endeavors to encourage waste reduction, advance treatment,
and disposal of hazardous wastes.  As a result, a Resource Conservation and Recovery Act
(RCRA) has been enacted in 1976 and  amended several times since its enactment, most importantly
by the Hazardous and Solid Waste Amendments of 1984 (HSWA). Over 500,000 companies
and/or individuals in the United States who generate over 172 million metric tons of hazardous
waste each year must comply with the  RCRA regulatory program (Arbuckle et al. 1989). In 1980,
Congress established the Comprehensive Environmental, Response, Compensation, and Liability
Act (CERCLA), usually referred to as the Superfund, which is subsequently reauthorized by
Superfund Amendments Reauthorization Act (SARA) of 1986.  Both CERCLA and RCRA seek to
provide  a veil coverage of the hazardous waste problem.  While RCRA is designed as a regulatory
program for present and new hazardous waste sites,  CERCLA establishes a comprehensive
response program for the past hazardous waste activities. According to CERCLA,

       ... Whenever there  is a release  or substantial threat of release into the environment of any
       hazardous substance or pollutant or contaminant under circumstances where the pollutant or
       contaminant may present an  imminent and substantial danger, EPA is authorized to
       undertake removal  and/or remedial action

Removal and remedy  differ in that removal is a short-time limited response  to a more
manageable problem while remedy is a longer-term more permanent and expensive  solution
for a complex problem.

       From among the over 40,000  sites reported to  United States Environmental Protection
Agency (USEPA or EPA) which might need remedial action, about 2,000 sites are  listed as
Superfund sites. While the  estimated remediation cost for the Superfund sites is 50 billion dollars,
the total  estimated cost for all the contaminated sites may run up to 350 billion dollars. Figure 1.1

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            I
            "3
                        SUPERFUND


                        RCEU FAOLITY


                        DOD FACILITY
Q   DOE FACILITY

S   STATE FACILITY
                      CLEANUP COST
                                                    SITES IN PROGRAM
Figure 1.1:    Estimated Number of Contaminated Sites and Clean-up Costs in the US (Adapted

             from Morse 1989).
                                        1-2

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presents an estimate of the number of contaminated sites and the associated cleanup cost reported
by different state agencies in the United Stares (Morse, 1989).

       In 1980, CERCLA has required EPA to develop and to provide criteria for determining
priorities among sites that require remedial action and to devdop and maintain a National  Priority
List (NPL). Under EPA regulations, these sites are eligible for remedial action. Although 149
sites have been cleaned and  removed from the NPL since Superfund's inception, the list continues
to grow.  Recently, EPA added 33 new sites bringing the NPL total to 1250 sites (Austin, 1993).

       A variety of options may exist to select a cleanup remedy at a site; however, the efficiency
and costs  of these options may vary widely. Accordingly, the decision of "how clean is clean?"
and "how expensive is expensive?" is taken independently for each site by the EPA  Although
conventional ground burial and land disposal are  often  economical, they do not provide the best
solutions,  and in some cases they are not necessarily the most effective solution. There exists an
everlasting need to introduce new, innovative, and preferably in-situ remediation technologies.
Several such  schemes  are  introduced  in the  last  decade including  incineration,
solidification/stabilization, bioremediation, dechlorination, flushing, vitrification, washing, thermal
desorption, vacuum extraction, and chemical treatment (EPA 199 1). Each technology exhibits
certain  advantages and limitations in  remediating a myriad of organic/inorganic  contaminants
encountered in different types of soil deposits.  As an example there is a growing use of vacuum
extraction technique for removing organic contaminants. This technology favors partially saturated
deposits having relatively high hydraulic conductivities (silt and sand). The technique is ineffective
in removing inorganic contaminants. There is not one specific technology that can be considered
as a panacea to  all types of contaminants and  soil deposits (Acar et al. 1992a).

       A major limitation of the most successful remediation technologies, such as vacuum
extraction and soil flushing, is that they are restricted to soils with high hydraulic conductivity and
hence, cannot be used for fine-grained deposits.  Furthermore, they are not specifically effective in
removing  contaminants adsorbed  on the soil particles (such as pump and treat).  Such adsorption
may pose threat for ground water and plant contamination.

        The challenging demand to develop new, innovative and cost effective in-situ  remediation
technologies  in waste management stimulated the vision to employ conduction phenomena under
electrical  currents as  a soil remediation technology  (Acar and Alshawabkeh 1993; Acar et al.
                                           1-3

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 1993a).  This technology uses low level  DC electrical potential differences (ii the order of few
volts per cm) or electrical currents (in the order of milliamps/cm2 of soil cross sectional area) across
a soil mass applied through inert electrodes placed in an open flow arrangement.  The application
of low level  DC across electrodes placed in holes filled with fluid in a soil mass causes
physicochemicai and hydrological changes in the soil-water-dectrolyte medium leading to
contaminant transport and removal. The applied electric current (or electric potential difference)
leads to electrolysis reactions at the electrodes generating an acidic medium at the anode and an
alkaline medium at the cathode.  The acid generated at the anode advances through the soil towards
the cathode by different  transport mechanisms including ion migration due to electrical gradients,
pore fluid advection due to prevailing dectroosmotic flow, pore fluid flow due to any externally
applied or internally generated hydraulic potential difference, and diffusion due to  generated
chemical gradients. The alkaline medium developed at the cathode will first advance towards the
anode by ionic migration and diffusion; however,  the mass transport of H+ will neutralize this base
front, preventing its transport towards the anode. Acidification of the soil causes desorption  of the
contaminants. Species present in the soil pore fluid, or desorped from the soil surface, are
transported towards the  electrodes depending on their dectric  charge. The driving mechanisms  for
species transport are the same as the acid-base transport mechanisms. As a  result, cations are
accumulated at the cathode and anions at the anode while there is a continuous transfer of hydrogen
and hydroxyi ions into'the medium, various bench scale, studies have shown that heavy metals
and other cationic species can be removed from the-soil either with the effluent or deposited-at or
dose to the cathode (Hamed  1990; Hamed et al. 1991; Eykholt 1992; Wittle and Pamukcu  1993;
Acar etal. 1993).

       The demonstrated feasibility of dectrokinetic soil remediation through bench-scale studies
necessitates a pilot scale study investigating the effect of up-scaling bench scale experiments on the
efficiency and performance of the process.  Furthermore, a comprehensive theoretical model which
accounts for the transport mechanisms and the physicochemicai  changes associated with the
process is required. The predictions of the theoretical model should be compared with the results
obtained in pilot-scale experimental model.  The developed theoretical model  is expected to provide
the basis for a comprehensive design/analysis tool for the  different boundary conditions, site
specific contamination and variable soil profiling encountered in full  scale implementation of the
process.  Such a theoretical model will also allow assessment of the principles of multi species
transport under electric fields.
                                           1-4

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 1.1  Objectives
        The objectives of this study are identified as:
        1.     to investigate  the feasibility and efficiency of field-scale electrokinetic  soil
              remediation by conducting pilot-scale laboratory tests with Pb(II)  loaded
              kaolinite and kaolinite/sand mixture. The size of the samples is chosen to simulate
              one-dimensional conditions and to represent  an intermediate Scale between
              bench-scale and full-scale  in-situ remediation,
        2.     to monitor and investigate the changes expected in electrical, chemical  and
              hydraulic potentials, and geophysicochemical properties  of the  soil-water-
              electrolyte medium during processing,
        3.     to provide a theoretical model, numerical solution algorithm and a computer code
              for coupled transient transport of fluid, charge, and chemically reactive species
              under hydraulic, electric, and chemical gradients,
        4.     to evaluate the necessary  soil properties and model parameters required  by the.
              theotical model in predicting the pilot-scale experimental  model resuits, and
        5.     to evaluate the theoretical model developed for electrokinetic soil processing
              through  comparisons of the  chemical, electrical,  and hydraulic  potentials
              obtained from theoretical model with measurements made in the experimental
              model.
 1.2   Scope

       The study is aimed to investigate, theoretically and experimentally, the complexity of
changes in chemical, electrical, and hydraulic  potentials, and physicochemical  properties of soil-
water-electrolyte medium associated with removing contaminants by application of a DC current.
Two bench-scale tests on Pb2+spiked kaoiinite, two pilot-scale laboratory tests on Pb2* loaded
kaolinite, and one pilot-scale test on Pb2* spiked kaolinite/and mixture are conducted. The size of
these samples is chosen to simulate one-dimensional conditions and to represent an intermediate
scale between bench-scale and full-scale in-situ remediation.  One-dimensional conditions  are
selected since two-dimensional conditions will result in spatial variability in electrical gradients
both due to the changing chemistry and also due to the electrode geometry unduly complicating
                                          1-5

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 evaluation of the results. The effect of spatial variability in the electrical gradients due to the
 electrode configuration and geometry is not included as a variable in this study.

       Tests are conducted for only removal of lead species from the specified soil samples.  Lead
 is chosen for this  study for the following reasons,
       it is the most identified species in hazardous waste sites listed in the NPL (Figure 1.2),
       bench-scale studies demonstrate that it can be removed successfully at relatively high
       concentrations (1,500 (ig/gfrom kaolinite, Hamed et al. 1991; and 9,000 jiG/gfrom fme
       argillaceous sand, Lageman 1989, 1993),
       it is highly retarded by clayey soils and it is hypothesized that lead removal by the process
       may implicate the feasibility of removing other less retarded ionic species.  However, the
       validity of this hypothesis depends upon the chemistry of the species in the concern and
       surface chemistry of the soils,
       lead poisoning can occur by digestion or inhaling which would minimize the health and
       safety hazard  in laboratory studies, specially pilot-scale tests, when comparing it  with
       radionuclides or other contaminants,  and
       current research work on electrokinetic soil remediation involves conducting field-scale
       remediation  of a lead contaminated site at Ethyl Corporation, Baton Rouge. This makes the
       study a perfect link between bench-scale tests and the first field application of electrokinetic
       soil remediation in the United States.

       Modeling  lead removal by electrokinetics is  chosen for this study in an attempt to evaluate
the current understanding of the technology and to check the validity of the theoretical model
presented. Though  variouscations and anions might be present in the soil pore fluid at different
concentrations, only four ions  are  included  in this model. These are Pb2* the contaminant of
concern,  N0"3, since lead nitrate salt is used for the experiment,  and H* and OH" because they are
necessary in describing the acid/base distribution that has a great influence on the  pore fluid
chemistry.  Dramatic changes in the concentration of these ions will result in different chemical
reactions.    Chemical reactions  included in this  model  are the  reactions  describing
precipitation/dissolution of lead hydroxide (Pb(OH)2)theWater auto ionization reaction, and
sorption reactions.  Two approaches have been developed and used in the literature to describe
chemical  reactions; instantaneous  equilibrium approach and kinetics approach.
                                           1-6

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   2
   3
   o
   3
140'



120



100



 80



 60



 40



 20
                      »


                        8
                        '
8-
                                                  o
                                                       o



                                                                    S

Figure 1.2:    Most Frequently Identified Species in Soils in the 1217 Sites Listed on the

              National Priority List in 1989 (Adopted from EPA 1991)
                                     1-7

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       For several species, chemical reactions, specially precipitation/dissolution and sorption
reactions, have been found to vary with time before reaching equilibrium. It may be more
appropriate to use kinetics approach to model these reactions; however, this will unduly complicate
the modeling effort and it will require an independent investigation of each reaction kinetics.
Furthermore, chemical reactions involved in this study are expected to reach equilibrium at a very
short time.   Sorption reactions in low activity soils and precipitation reactions of heavy metals in
solutions often take minutes to reach chemical equilibrium.   On the other hand, processes related to
the transport of these chemical species in fme grained deposits under electric, hydraulic and
chemical gradients are siow compared to the rate of sorption or precipitation reactions.
Consequently, the ratio of the rate of chemical reactions to the rate of transport of heavy metals in
low activity fine grained deposits is  expected to be high enough to meet the assumption of
instantaneous equilibrium for these chemical reactions.
1.3   Organization of the Manuscript

       The manuscript contains 8 (eight) Sections that covers the work conducted. A brief
summary of the contents of these Sections is presented in this section.

       Section 2 describes  various electrokinetic phenomena, in soils  and principles of
electrokinetic soil remediation The effects of application of an electric cument through a saturated
soil medium on  the physicochemicai properties of the medium are discussed. Electrolysis reactions
at the electrodes, changes in the soil pH and their effect on  sorption and precipitation/dissolution
reactions, and transport mechanisms are addressed.  Potential uses of electrokinetic phenomena in
different aspects of environmental geotechnics are presented. This Section also summarizes
available literature on electrokinetic soil remediation which is divided into two parts;  experimental
and theoretical.  The experimental part covers bench-scale studies conducted by various researchers
together with the feasibility and cost efficiency of the technique and limited pilot-scale studies
conducted in the field. The theoretical part summarizes and reviews  different  attempts of numerical
simulations of contaminant transport under electric fields.

       Section 3 presents the  theoretical development and  mathematical  formulation attained in
electrokinetic soil processing. This Section describes the coupled fluxes of fluid, mass, and charge
under hydraulic, electric, and chemical  concentration gradients. Principles  of conservation of
                                            1-8

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matter and energy are applied to these fluxes resulting in partial differential equations describing the
coupled transient hydraulic, electric, and chemical potentials distributions. Chemical reactions  in
the soil pore fluid, such as sorption and precipitation/dissolution, are.decriribed by algebraic
equations employing laws of mass action. The resulting differential/algebraic equations are
summarized for a system of reactive chemical  species in the soil pore fluid.  Finally,  this Section
describes the resulting system  of equations, initial and boundary conditions for modeling soil pH
and modeling lead transport and removal by electrokinetic soil processing

       Section 4 summarizes different numerical schemes that could be used to solve the
developed system of differential and algebraic equations and explains the iterative scheme utilized
for this study. This Section also describes the finite element approach and the variational
formulation used to solve the  system of differential equations. The isoparametric element used,
formulation of local and global matrices, and the technique utilized for matrix inversion are
summarized.

       Section 5  presents design of the bench-scale and pilot-scale experiments conducted in this
study.  Size and shape of the container and soil samples together with type and configuration of the
electrodes are described. The procedure used  for mixing and compacting kaolinite with lead  is
discussed. A description  of the probes and instruments used for measuring voltage distribution,
soil suction, temperature, and pH is provided. The implemented data acquisition system is
summarized and the procedures used for soil sampling and chemical analysis are presented.

       Section 6 presents the  results and analysis of the experimental work. Changes in soil,
catholyte, and anolyte pH, final water content, and voltage distribution of all bench-scale and pilot-
scale experiments are presented, analyzed, and  discussed. This Section discusses the effects of the
electrochemical changes  during processing bench-scaie and pilot-scale  specimens and their impact
on the electric and hydraulic potential distributions.  Significance of the different lead transport
mechanisms under the applied electric gradient are discussed. Final lead distributions across the
soil and removal efficiencies for these experiments are presented. Energy expenditure and-cost for
these experiments  are  evaluated.

       Section 7  describes the results of the numerical model and the results of the computer code
developed for lead transport and removal  under  electric fieids.  Comparisons between the results of
                                        1-9

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the model with the results of the pilot-scale experiment with initial lead concentration of 5322p,g/g
are presented.

       Section 8 summarizes the findings and conclusions of the study.  Recommendations for
future research are presented. Program listing, a list oft  diinput and output files, and data
generated in bench-scale and pilot-scale tests are presented in Appendices A through D.
                                           1-10

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                                        Section 2

                                   BACKGROUND
2.1  Introduction
       Multi-species transport unde r electric fields is an area that is gaining increasing attention
and interest.  Species transport mechanisms under electric  fields are envisioned to-be employed in
remediating  soils from inorganic and organic species (electrokinetic remediation), injection of
microorganisms and nutrients in bioremediation, injection  of grouts in soil stabilization and waste
containment, soil and pore fluid characterization and species extraction using penetrating probes,
diversion systems for contaminant plumes, and leak detection systems in containment barriers
(Acarand Gale 1986,  Acar etaL 1989).  Bench-scale  and limited pilot-scale studies in electrokinetic
remediation demonstrate that the technique has significant potential. It becomes necessary to gain a
better understanding of multi-species transport mechanisms both in an effort to critically evaluate
the fundamental basis of the processes and also to develop the necessary design/analysis tools in
engineering the implemented techniques.
2.2  Electrokinetic  Phenomena  in  Soils

       Generally,  discret e clay particles have a negative surface charge that influences and controls
the particle environment. This surface electric charge can be developed  in different ways, including
the presence of broken bonds and due to isomorphous substitution (Mitchell 1993). Thereupon,
the clay particle-water-electrolyte system is usually considered to consist of three different zones;
the clay particle with negatively charged surface, pore fluid with excess positive charge, and the
free pore fluid with zero net charge (Figure 2.1).  The net negative charge on the clay  particle
surfaces requires an excess positive charge (or exchangeable cations) distributed in the fluid zone
adjacent to the clay surface forming the diffuse double layer.  The quantity of these  exchangeable
cations required to balance  the charge deficiency of clay is termed the cation exchange capacity
(CEC), and expressed in milliequivalents per 100 grams of dry clay.

       Several theories have been proposed for modeling charge distribution adjacent  to clay
surface. The Gouy-Chapman diffuse double layer theory has been widely accepted and applied to

                                           2-1

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                     Distance From clay Surface
Figure 2.1: Charge Distribution Adjacent to Clay Surface (Mitchell 1993)
                             2-2

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 describe clay behavior. A detailed description of the diffuse  double layer theories for a single flat
 plate is found in Hunter (1981), Stumm (1992), Mitchell(1993), and Yeung  (1993).

       Electrokinetics is defined as the physicochemical transport of charge, action of charged
 particles, and effects of applied electric potentials on formation and fluid transport in  porous media.
 The presence of the diffuse double layer gives rise to several  electrokinetic phenomena in soils,
 which may result from either the movement of different phases with respect to each other including
 transport of charge, or the movement  of different phases relative to each other due  to the
 application of electric field. The electrokinetic phenomena include electroosmosis, electrophoresis,
 streaming potential, and sedimentation potential. Electroosmosis  is defined as fluid movement with
 respect to a solid wall as a result of an applied electric potential gradient. In other words,  if the soil
 is placed between two electrodes in a fluid, the fluid will move  from one side to the other when an
 electromotive force is applied. Electrophoresis  is the movement of solids  suspended in a liquid due
 to application of an electric potential gradient. Streaming potential is the reverse of electroosmosis.
 It difines the generation of an electric potential difference due to fluid flow in soils. Sedimentation
 (or migration) potential, known as Dorn effect (Kruyt 1952),  is an electric potential generated by
 the movement of particles suspended in a liquid. Figure 22 displays the electrokinetic phenomena
 identified  herein.

       Under certain conditions, electroosmosis  will have a-  significant role in electrokinetic soil
 remediation.  Several  theories  are  established  to describe  and evaluate water  flow by
 electroosmosis;  the most common being the Helmholtz-Smoluchowski theory, Schmid  theory,
 Spiegler friction model, and ion hydration theory. Descriptions of these theories  are given in
 Casagrande (1952) ,  Gray and  Mitchell  (1967), and Mitchell (1993). Helmholtz-Smoluchowski
 model is the most common theoretical description of electroosmosis  and is based on  the
 assumption of fluid transport in  the soil pores  due to transport of the excess positive charge in the
 diffuse double layer towards the cathode (Figure 2.3).
2.3 Heavy  Metals  in Soils

       The term "heavy metals" is adopted as a group name for metals and metalloid that are
associated with pollution and toxicity. The term also includes some elements which are essential
for living organisms at low concentrations (Alloway 1990). General classification of heavy metals
                                           i-J

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         BPC)
(a) Electric Gradient
Induces Water Flow
        E  (DC)
(c) Electrical Gradient
Induces Particle Movement
          H
                                                       Particle
                                                       vfovement,

        (b) Water Flow Induces
        Electric Potential E
     (d) Particle Movement
     Induces Electric Potential
         Figure 2.2: Electrokinetic Phenomena in Soils (Mitchell 1993)
                              2-4

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Figure 2,3:    Schematic Diagram of Advection by Electroosmosis, Depicting the Excess Cations
             on the Clay Surface and an Approximate Velocity Profile Across the Pore Capillary
             (Acaretal. 1994b)
                                          2-5

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is based on the atomic density of 6 g/on3 or greater.  Studies of heavy metals in ecosystems have
indicated that many areas near urban complexes, metalliferous mines or major road systems contain
anomalously high  concentrations of 1hese elements. In particular, soils in such regions have been
polluted from a wide range of sources with Pb, Cd, Hg, As, and other heavy metals. Some
recently have shown concerns that we may be experiencing a silent epidemic of environmental
metal poisoning from the ever increasing amounts of metals discharged into the biosphere (Brady
1984; Alloway 1990).

       As, Ag, Cd, Cu, Hg, Pb, Sh, and Zn are naturally encountered in  the top (surface)
horizons  of the soil rather than the lower horizons due to the effect of cycling through vegetation,
atmospheric deposition, and adsorption by the soil organic matter. Though natural concentrations
of heavy  metals in soils are not high, polluted or contaminated soils exist due to one or more of the
following reasons  (Alloway 1990),

       *     the use of leaded petrol for motor vehicles has been responsible for atmospheric
             pollution and consequently deposition in soils,

       *      the disposal of urban and industrial wastes can lead to soil contamination  from the
             deposition of aerosol particles  emitted by incineration of materials containing
             metals. The unauthorized dumping or disposal of items containing metals, ranging
             from miniature dry-cell batteries (Ni, Cd+ and Hg) to abandoned cars and car
             components, such as Pb-acid batteries, can give rise to small areas of very high
             metal concentrations in soils. The disposal of some domestic waste by burning on
             garden bonfires  or burial  in the garden can  also result in localized  high
             concentrations of metals, such as Pb, in soils used for growing vegetables,

             organic manures which include  poultry  manures that may contain high
             concentrations of Cu or As fed to improve food conversion efficiency. Sewage
             sludge usually contain relatively high concentrations of several metals, especially
             those from industrial  catchments,

             contribution of metallurgical industries  due to  emissions of fumes and dusts
             containing metals which are transported in the air and eventually deposited onto
             soils and vegetations, effluent which may pollute soils when watercourses flood,
                                             2-6

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              and creation of waste dumps from which metals may be leached and thus pollute
              underlying or nearby soils,

              the mining and smelting of non-ferrous metals have caused soil pollution which
              dates back to Roman times and earlier in some places, although most has occurred
              since the Industrial Revolution. Metals are dispersed in dusts, effluent and seepage
              water. Tailings discharged into watercourses have polluted alluvial soils downriver
              from mines during flooding  especially when the dams in lagoons fail,

              the combustion of fossil fuels which results in the dispersion of many elements in
              the air over a large area. The disposal of ash is a further source of heavy metals,
              and

              agricultural fertilizers and pesticides which usually  contain various  combination of
              heavy metals, either as impurities or active constituents.
2.4 Soil  Contamination  With  Lead

       Soil contamination with lead has beendocumented to result from the use of different
chemical forms of lead in petrol, paints, batteries, and pesticides, due to smelting of metals and
mining, and due to disposal of lead-acid storage batteries (Harrison and Laxen 1981). Figure 1.2
displays that lead is the most frequently identified species in soils among the 1217 sites listed on
the NPL in 1989. Soil contamination with lead at high concentrations such as 100,000 ng/g (10%
by weight) is not uncommon.

       Compared with most other contaminants, lead has a tendency  of long residence time in
soils.  Together with its compounds, as lead accumulates in soils and deposits it remains accessible
to the food chain and human metabolism far into the future. Detrimental effects associated with lead
have been recognized for a long time. Lead is poisonous, and there are fears that body burdens
below those at which clinical symptoms of lead toxicity  appear may cause mental impairment in
young children (Harrison and Laxen 1981). Clinical symptoms associated with lead poisoning
include anemia, various  digestive disorders, and central nervous system  effects. Currently, no
widely accepted  remediation or treatment technology exists for lead-contaminated hazardous waste
                                           2-7

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 sites. The most common treatment methods for lead contamination are containment or landfill
 disposal.


 2.5 Principles  of Electrokinetic Soil Remediation

       Electrokinetic soil remediation technology uses a low level direct current, in the order of
 milliamps per cm2 of soil cross-sectionail area, to transport and remove species from soils. Upon
 application  of a low level direct current  the soil water-electrolyte  system  undergoes
 physicochemical and hydrological changes leading to contaminant transport and removal.  The
 applied electric current (or electric potential  difference) leads to electrolysis reactions at the
 electrodes, acid-base distribution drive by chemical, electrical, and hydraulic potential differences,
 adsorption/desorption  and precipitation/dissolution reactions, transport of the pore fluid and ions,
 and electrodeposition. These on-going physico-chemical processes are reviewed in the following
 subsections.


 2.5.1  Electrolysis  Reactions

       Application of direct electric current through electrodes immersed in water induces
electrolysis reactions in  the immediate vicinity of Electrodes. Oxidation of water at the anode
 generates an acid front while reduction at the cathode produces a base front  by the following
 electrolysis reactions,

               4*-      •  02 1+4H+    E°=-1.229           (anode)                (2 1}
               2e- >H2T -H20H-           E°= -0.8277         (cathode)               (2-2)

 Secondary reactions may exist depending upon the concentration of available species, e.g.,
              2e-  -HjT                   E°=0.0             (reference)              (2.3)
       Me*0 + ner  • Me(s)                                                            (2 4)

 where E° is the standard reduction electrochemical potential, which is a measure of the tendency of

                                           2-8

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the reactants in their standard states to proceed to products in their standard states, and Me refers to
metals. Table 2.1 presents standard reduction electrochemical potentials for different electrolysis
reactions in aqueous solution at 25°  C. The prevailing of electrolysis reactions at the electrodes
depends on the availability of chemical species and the eletrochemical potentials of these reactions.
Although some secondary reactions might be favored at the cathode because of-their lower
electrochemical potential, the water reduction half reaction (HjO/Hy is dominant at early  stages of
the process (the first two to three weeks of processing bench-scale tests). At later stages, the acid
front advances towards the cathode carrying H+ and the cationic contaminants and half cell
secondary reactions (ETVHj) or (Me+tVMe(s))  arc expected to dominate. Within the first 100 hours
of processing, electrolysis reactions will drop the pH at the anode to below 2 and increase it at the
cathode to above 12, depending upon the total current applied (Acar et al. 1990,1993).
2.5.2 Changes in Soil pH

       The acid generated at the anode will advance through the soil towards the cathode. This
advance is governed by  different transport mechanisms  including ionic migration due to electrical
gradients,  pore fluid advection due to the prevailing electroosmotic flow, pore fluid advection due
to any externally applied or internally generated hydraulic potential  differences, and-diffusion due
to concentration gradients. These transport mechanisms are discussed in more detail hereinafter.
The alkaline medium developed at the cathode due to production of OH- will initially advance
towards the anode by diffusion and ionic migration; however, the counterflow due to
electroosmosis  will retard this back-diffusion and migration: The advance of this front-towards the
anode will be much slower than the advance of the acid front towards the cathode because of the
counteracting electroosmotic flow and also because  the ionic mobility of H* is about 1.76 times
that of OH-.  As a consequence, the acid front dominates the chemistry across the specimen (Acar et
al. 1990;  Alshawabkeh and Acar 1992; Acar and Alshawabkeh 1994). Figure 2.4 displays
development of the acid/base profile across a  10 cm length cylindrical Georgia kaolinite specimen
processed under one-dimensional conditions at a current density of 12.5 |iA/cm2 (Acar et al.
 1990).

       The decrease in pH value in the soil depends on the amount of acid generated at the anode
(Acar et al. 1990,1993a)  and the buffering  capacity of the clay.  Yong et al. (1990) investigated
                                         2-9

-------
Table 2.1:     Standard Reduction Electrochemical Potentials in Aqueous Solution at 25° C(Kotz
             and Purcell 1987).
            Reduction Hall Reaction
                  2e~
                                   4-  2e~
                     2e~
                     + e'
                      + f
                  + It"
                  + 2e~
 +  2e
 +  2e
 +  2e

 4-  2e
+ 2e~
 +  3e'
  + 2<
 +  e~
                              4-  4e~
                                                 5n(4)
                                                 fffo) 4- 20ff'(aq)
+2J7
+1.77
+1.50
+0.855
+0.80
+0.771
+0.40
+Q.337
+O.IS
0.00
-0.14
-0.25
-0.40
-0.4T .
-O.T63
-0.3277
-1.66
-2J7
-2.T14"
-3.045
                                          2-10

-------
    •a

    .85
           14
           12  -
           4  -
                  Speciinea DCtioettn 5 cm
                             Length: "i« cm
                  k.s i.3 to 0.05 jj/A*h
                 k a3  to OJ  X10-5on-/s.V
                 water contents 0.75-0.90
?roc«*sing
TTm«
                       0.2        0.4        0.6        O.S        1

                 NORMALIZED  DISTANCE FROM ANODE
Figure 2.4:    Acid/Base Distribution across Specimen of Slurry Consolidated Georgia Kaolinite

            Processed under an Electric Current of 12.5 ^A/cm2 (Acar et al.  1990).
                                    2-11

-------
 the buffering capacity ofvarious types of clays and demonstrated that the cation exchange capacity
 and the organic content highly influence the soil PH. Furthermore, the study showed that kaolinite
 has low buffering capacity compared with different types of dayey soils.
 2.5.3  Sorption Reactions

       Heavy metals and other positively charged species are highly attracted and adsorbed on the
 negatively charged clay surfaces. Metals have different sorption characteristics and mechanisms
 that are also dependent upon the adsorbents. Sorption mechanisms include surface complexation
 (adsorption) and ion exchange. The adsorbents show differences in selectivity  sequences for
 different metals. Table 2.2 demonstrates that lead, compared to other metals, is highly  attracted and
 adsorbed by various clay types.

       Desorption of heavy metals from the clay is essential for the remedy to  be efficient in
 contaminated fine-grained deposits. The adsorption/desorption  mechanism depends upon the
 surface charge density of the clay mineral or CEC, characteristics and concentration of the cationic
 species, and existence of  organic matter and carbonates in the  soil. Furthermore,  the
 adsorption/desorption  mechanism is pH dependent. An increase in H+ concentration associated
with a decrease in pH results in desorption of cations by an amount controlled by the soil  type
 (Maguire  et al. 198 Barter 1983;and Yongetal. 1990). Therefore, acidification of the soil by  the
 electrolysis reaction at the anode is a fundamental mechanism that assists in desorption of these
 species (Figure 2.5).
 2.5.4 Precipitation/Dissolution

       Dramatic changes in the soil electrochemistry throughout electrokinetic soil processing
results in different chemical reactions including precipitation/dissolution of salts and soil minerals.
Species transport in soil pore fluid is highly influenced by formation and dissolution of these
precipitates.

       The base front generated by electrolysis at the cathode will cause precipitation of most
heavy metals and actinides. The amount of precipitate differs  from one species to another and it is
                                          2-12

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Table 2.2: Selectivity of Different Soil Types for Divalent Metals (Alloway 1990).
 Adsorbent
Selectivety Order
 Montmorillonite( Na)
  Kaolinite( Na)
 Smectitie, Vermiculite, and Kaolinite
 Albite, Labradorite
 Mineral soil  on marine clay,
 Peat.
Ca>Pb>Cu>Mg>Cd>Zn>Ni
Pb>Cu>Zn>Ca>Cd>Mg
Pb>Ca>Cu >Mg>Zn >Cd
Zn > Mn.> Cd  > Kg
Zn>Cd>Mn>Kg
Pb>Cu>Zn>Cd>Ca
Pb>Cu>Cd=Zn>Ca
                               2-13

-------
            S
            m
            Q
                  »
 BOO UK?
                          (1


                           *
^
 yej
                            o
ee'   •
I    •
• e   e   e

 e%ee
                                             e
                                             e
                                         e
Figure 2.5:  A Schematic Representation of Protons Displacing Lead from the Soil Surface and


         Transport of Both the Protons and Lead towards the Cathode (Acar et al.  1993)
                             2-14

-------
 highly dependent on soil and-pore fluid pH. Though the advance of the acid front generated at the
 anode will cause dissolution  of most precipitates  encountered, each precipitation or dissolution.
 reaction is treated independently  depending upon the solubility product constant. Acar et al. (1993)
 and Acar and Alshawabkeh (1993) recommend the use of different enhancement techniques in
 order to remove these precipitates from the cathode tine. The  advance of the acid front generated at
 the anode is also expected to cause dissolution of day minerals. Kaolinite dissolution, which is pH
 dependant, generates different chemical forms of aluminum and silica. The impact of mineral
 dissolution on the  efficiency of electrokinetic soil remediation has not yet been  investigated.
 However, Ugaz et al.  (1994)  investigated the effect of using  acid washed soil sections near the
 cathode  on the efficiency of the process for removal of radionuclides from kaolinite. The study did
 not  show any significant influence  of acid washing soil  sections near the  cathode prior to
 processing on species transport.
2.5.5 Contaminant Transport, Capture, and Removal

       Free chemical species present in the pore fluid and/or desorped from the soil surface will be
transported towards the electrodes depending upon their charge. The primary driving mechanisms
of species transport are the same as the acid or base transport mechanisms.  I0n migration,
advection, together with diffusion will  contribute to the movement  of species through the soil
mass.  At zones of high pH, both precipitation and sorption will retard species transport

       As a result of transport of chemical species in the soil pore fluid, cations will collect at the
cathode and anions at the anode. Heavy metals and other cationic species will be removed from the
soil either with the effluent or they will be deposited at the cathode. Treatment of the effluent (such
as ion exchange or resin columns) could be  used for removal of the excess ions.   Figure 2.6
presents a schematic diagram of in-situ electrokinetic soil remediation.
2.5.6. Enhancement/Coditioning

       Acar et al. (1993 a) recommend the use of different enhancement techniques in order to
remove and/or avoid precipitation in the cathode compartment "envisioned enhancement schemes
are expected to have the following characteristics; (a) the precipitate should be solubilized and/or
                                          2-15

-------
                                        Process Controi System
                     Extraction/
                     Exchange
                                                     Extraction/
                                                     Exchange
                                                                             AC/DC
                                                                             Converter
                                                                       -CATHQDCC
                                                                      -•"•PROCESS
                                                                       "FUUIO
AODFtQNT
•od/or ANODIC
PROCESS FLUID
                                            Processed
                                              Media
Figure 2.6     Schematic of Electrokinetic Soil Processing Showing Migration of Ionic Species,

              Transport of Acid Front  and/or Processing Fluid across the Processes Medium

              (Acar and Alshawabkeh)
                                         2-16

-------
 precipitation should be avoided (b) preferably, ionic conductivity across the specimen should not
increase excessively in a short period of time both to avoid a premature decrease in electroosmotic .
transport and to allow transference of species of interest, (c) the cathode reaction should possibly
be depolarized to  avoid generation of the hydroxide and its transport into the specimen,  (d) such
depolarization will also assist in decreasing the electrical potential difference across the electrodes
leading to lower energy consumption,  (e) if any chemical is used, the precipitate of the metal with
this new chemical should be perfectly soluble within the pH ranges attained, and (f) any special
chemicals introduced should not result in any increase in toxic residue in the soil mass" (Acar et al.
 1993a).

       Acar et al. (1993a) have investigated the depolarization of the cathode reaction by using an
acid which forms a soluble salt with species in transport "Low concentrations of hydrochloric acid
or acetic acid is introduced at the cathode to depolarize the cathode reaction. One concern with the
introduction of hydrochloric acid is its possible electrolysis and formation of chlorine gas when it
reaches the anode compartment.  Acetic acid is environmentally safe, it does not fully dissociate and
most acetate salts are  soluble and therefore it is preferred." (Acar et al. 1993a).

       Migration of  the acid generated at the anode  would generally  aid in desorptio  n of the
species.  However, when this process  is  considered in conjunction with migration of a species of
interest, the substantial increase in hydrogen ion concentration and the complementing increase in
the hydrogen ion transference number may hinder transport  of other species (Acar and
Alshawabkeh 1993). If hydrogen ion generation and supply at the anode  is not controlled, most of
the energy may be consumed by generation and migration of the proton across  the cell rather than
the transport of species of interest.  Therefore, if it is desired to promote the transport of species in
the pore fluid, it may  be necessary to depolarize the anode reaction and/or control acid production
and introduction into the soil mass (Acar and Alshawabkeh  1993). As discussed previously,
desorption and dissolution reactions will dominate the advance of the acid front in the specimen. In
an attempt to fully exploit the different conduction phenomena and transport  processes in field
implementation of electrokinetic remediation technique and to improve the efficiency under site
conditions,  it will be necessary to implement process  optimization schemes (Acar and
Alshawabkeh 1993).
                                            2-17

-------
 2.6    Applications of Electrokinetics in Enviromental  Geotechnics

        Electrokinetic soil processing is an emerging technology in waste remediation and
 separation. It is envisioned that various electrokinetic phenomena in soils, described in previous
 sections, will give a chance for additional applications in the area of environmental geotechnics
 other than the extraction chemical species from soils.
 2.6.1  Electrokinetic Flow Barriers

        Electrokinetic barriers could be used in clay liners to oppose contaminant transport due to
 hydraulic and chemical gradients. Though compacted clay liners are designed to retard or minimize
 contaminant transport to the underlying  soil and groundwater, sustained hydraulic and chemical
 gradient in landfills may result in transport and release of contaminant through liners. Figure 2.7a
 shows  that application of electrical gradient through day liners could be used to generate
 electroosmotic flow opposing contaminant transport. Yeung (1990) and Yeung and Mitchell
 (1991) have demonstrated that electrokinetic flow barriers may be effective in retarding transport of
 cationic species but accelerate transport of  anionic species. The feasibility of the proposed
 electrokinetic barrier requires study of the effect of electrochemical changes on the fabric and
 engineering characteristics (specifically hydraulic conductivity) of day liners (Alshawabkeh and
 Acar 1993).
2.6.2 Hydraulic  Conductivity  Measurements

       Application of direct or alternating current in fine-rained soil mass generates electroosmotic
flow from the anode to the cathode.  If an impermeable anode is used (no flow at the anode) a
negative pore water pressure  (suction) will generate to compensate the electroosmotic flow at the
anode. The amount of suction generated is dependent on the applied electric field,  hydraulic
conductivity, and coefficient  of electroosmotic permeability of the  soil mass. Using known values
of the coefficient of electroosmotic permeability and electric potential gradients, measurements of
the suction generated could be used to back calculate the hydraulic conductivity of the soil (Finno et
al. 1994).
                                          2-18

-------
           FLOW BARRIERS IN CLAY LINERS
              TRANSPORT OF CONTAMINANTS
     BY HYDRAULIC AND CHEMICAL POTENT! AL GRADIENTS
                                      I      I       I
                        Y BARRIER
t      t       t       t       t       t      t       t
         QPPGSINC'FLUXES BY ELECTRICAL GRADIENTS
              PLUME  DIVERSION SCHEMES
                                            DIVERSION
                                    MIGRATION DIRECTION
   Figure 2.7: (a) Electrokinetic Flow Barriers and (b) Plume Diversion Scheme.
                         2-19

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2.6.3 Concentration  and  Dewatering

       Waste sludge and degraded spoil material are usually stored in ponds which continually
threaten the environment. Electrophoresis could be first used for concentration of the solid
particles, followed by electroosmotic  consolidation and ion migration to separate and extract
contaminants (Mitchell 1986). The feasibility of using electrokinetics for dewatering waste sludge
and coal/washery slimes has been demonstrated by limited bench-scale studies  (Krizek 1976;
Lockhart 1981; Lockhart and Stickland 1984).
2.6.4  Plume  Diversion  Schemes

       Contaminant transport in subsurface soil may threaten the groundwater contamination. This
might require short-term immediate solutions by either retarding or changing flow directions.
Migrational mass flux and electroosmotic water flow could be generated towards any required
direction by application of direct current (or electric gradient) to the soil mass as shown in Figure
2.7b (Acar and Gale 1986; Acar et al. 1989; Acar and Hamed  1991). Though the feasibility of this
technique has not been investigated yet, bench-scale results of electrokinetic soil processing
demonstrate the significance of the applied electrical gradients on the amount and the direction of
water and contaminant fluxes.
2.6.5 Hydrofracturing/EIectrokinetics/Bioremediation

       Electrokinetics could be used in  combination with hydrofracturing and bioremediation for
removal of organic contaminants from soils (Ho et all993). Hydrofracturing Could be applied in
contaminated fine-grained deposits to introduce layers Of sand and carbon as shown in Figure 2.8.
Electric potentials  could be applied through the sand/carbon layers to cause electroosmotic water
flow in fine-grained deposits to transport contaminants to the cathode, where they can be adsorbed
by the carbon. Microorganisms might also be introduced for biodegradation of the captured
organic contaminants. Problems with soil hydrofracturing include generation of vertical cracks in
regions close to the surface (when the over consolidation ratio, OCR i 4 (By 1992)).
                                           2-20

-------
                                   .Borehole
      If OCR<4
  T,t
I
    I
  .11:
  I
      \
Hectroosmotic
     How
                                               Ground Surface
                                                  Granular Electrode
                                             Degradation Zone
                                                wiSSfr

                                                Contaminated
                                                     Soil   '
                                                       Degradation Zone
                                                      Granular Electrode
                  (a) Hydrofracairing/Biodegradation/Hectroosmosis
                   Degradation         .           Degradation
                      Zone     Contaminated        °Zonc
                                    Soil

                       (ij) Biodegradation/EIectitx3sraosis
Figure 2.8: Hydrofracturing/Electrokinetics/Biodegradationin Soil Remediation (Ho 1993)
                                     2-21

-------
       Other uses of eletrokinetics in environmental geotechnics include injection of grouts,
cleanup chemicals or nutrients for growth  of microorganisms essential to biodcgradation of specific
wastes,contaminant detection, monitoring the physicochemical  soil profiling (Acar and Gale 1986;
Mitchell 1986; Acar et al. 1989; Acar and Hamed 199 1), and the use of electrophoresis for sealing
impoundment leaks (Yeung eta.  1994).
2.7   Feasibility  Studies  On Eletrokinetic Soil  Remediation

       The uses  of direct electric  currents for electroosmotic consolidation and stabilization of fine-
grained deposits-have been investigated by geotechnical engineers since the late 1930's. Effective
applications of the processes have been demonstrated for slope stabilization, chemical alteration of
day soils, concentration, separation, and stabilization of polluted dredging, soil consolidation and
dewatering, reduction of negative skin friction of piles, and increasing the  capacity of friction piles
(Casagrande  1952a, 1983; Casagrande et al. 1961; Gladwell  1965; Mise  1961; Esrig 1968; Wan
and Mitchell  1976; Gray and Somogyi 1977; Johnston and Butterfield 1977; Banerjee and Mitchell
 1980a, 1980b). Most of this research has shown feasibility in  geotechnical  engineering
applications; however, the effects of the application of electric gradients and electroosmosis on
electrochemical changes of the soil medium have entertained limited attention.  Gray and Schlocker
1969) investigated the effect ofpHin controlling  changes in soil composition and the feasibility of
pH buffering during electrochemical treatment Their results demonstrated that composition and
physical properties of clayey soils are altered when aluminum is introduced in the anolyte.
Lockhart (1983) demonstrated that  when the pore fluid of the soil has  high electrolyte
concentrations,  strong electrolyte polarization  occurs resulting in limited electroosmotic flow.
However, Lockhart (1983) concluded that reasonable concentrations of electrolytes are not
necessarily detrimental to electroosmotic dewatering (the meaning of reasonable concentrations is
not defined). Putnam (1988) and Acar et al. (1989) discussed the effect of electrolysis reactions at
the electrodes on soil pH.  Acar et al. (1989) showed that the acid generated at the anode sweeps
across the soil specimen ultimately decreasing the soil pH  at the cathode.

       Feasibility and cost effectiveness of electrokinetics for the extraction of heavy metals such
as  copper, zinc,  and cadmium from  soils have been  demonstrated through bench-scale laboratory
studies (Runnels and Larson 1986; Hamed 1990; Pamukcu et al. 1990; Acar et al. 1992 and 1993).
A comprehensive treatise on the removal  of Pb2"*" from soils is reported by Hamed (1990), and
                                           2-22

-------
Named et 3l. (1991). Kaolinite samples are loaded with Pb2* at various concentrations below and
above the cation exchange capacity of the clay. As presented in Figure 2.9, the process removed
75% to 95% of Pb2"1" at concentrations up to 1,500 fig/g across the test specimens at an energy
expenditure of 29 to 60 kWb/m3 of soil processed.  Most  of the removed lead is found
eletrodeposited at the cathode. This study clearly  demonstrated that the removal is due to the
transport of the acid front  generated at the anode  by the primary electrolysis reaction The study is
the first to demonstrate the development of a nonlinear electric potential across the soil mass.
Hamed (1990) also investigated the effect of the initial concentration and current density on the
efficiency  of removal. Higher current densities result in removal efficiencies similar to lower
current densities, however, the energy requirement and cost of processing increases exponentially.
Acaret al. (1994) demonstrated 90%  to 95% removal of Cd24" from bench-scale kaolinite
specimens  with initial  concentration of 99-114 (ig/g. Acar and Alshawabkeh (1993) and Acar et al.
(1994) showed higher removal rates of charged species can be achieved by electric migration rather
than electroosmotic flow.

       Figure 2.10 presents the results of enhanced electrokinetic remediation  tests conducted on
soil from a contaminated  site (Acar et al.  1993). "Calcium and lead are mostly removed from the
leading sections of the specimen first by dissolution then by the transport processes described.
Close to 60% of the total lead (42 g) is  precipitated in the middle sections (123 g of dry soil)
clogging the soil pores and preventing further transport of the species. In such soils, it may be
necessary  to further enhance the processes by complementing the anodic acid with another
introduced in the processing fluid" (Acar and Alshawabkeh 1993).

       Runnels and Wahli (1993) emphasized the use of ion migration combined with soil
washing for removal of Cu2* and S042* from fine sands. Pamukcu and Wittle (1992) and Wittle
and Pamukcu (1993) demonstrated removal of Cd2*, Go2"*", Mi24", and Sr2* from different soil
types at variable efficiencies. The results showed that kaolinite, among different  types of soils, had
the highest removal efficiency followed by sand  with 10% Na-montmorillonite, while Na-
montmorillonite showed  the lowest removal efficiency. Furthermore, their results demonstrated
that lower  initial concentrations of cadmium result in higher electroosmotic efficiency;  however,
removal efficiencies are higher for samples with higher initial concentrations.   Other  laboratory
studies reported by Lageman (1989), Banerjee et al. (1990), Eykholt (1992), and Acar et al.
                                          2-23

-------
12
     1.4
     1.9

•3*2
•2J4S
•1.413
      4

      3
          [meal
          ?.?.?.6.
             NORMALIZED DISTANCE FROM A.NODE
Figure 2.9: Pb  Removal by Electrokinetics (Named 1990)
                      2-24

-------
          50
   0,
          30
         • 20
          10
                                                      51 _2 gm  of Umct
                                                      96.0 gm  of Calcium
                                                      In 737 frn of sfry soil
^ inttlaily  t*ch  s«ction
  contains  20%  of total
H
z
Ul
a
«•!
u.


IU
c
c
z
<




-------
(1993) further substantiate the applicability of the technique to a wide range of heavy metals in
soils.

       The process can potentially remove radionuclides from clayey soil samples (Ugaz et al
1994, Acar et al. 1992c). Bench-scale tests displayed that uranium at 1,000 pCi/g of activity is
efficiently removed from kaolinite. Figure 2.11 shows the change in uranium activity after different
processing periods. Removal decreased from the anode towards the cathode due to the increase in
pH values. A yellow  uranium hydroxide precipitate was encountend in sections close to cathode.
Enhanced electrokinetic  processing showed that 0.05M acetic acid  is just enough to depolarize the
cathode reaction and overcome uranium precipitation close to the cathode compartment (Figure
2.12). Most uranyl ion was found precipitated at the cathode while more was in the catholyte in the
acetic acid enhanced experiments (Acar et al.  1993b). The  efficiency  and feasibility of using this
and other enhancement techniques are currently under investigation (Acar et al 1993b; Acar and
Alshawabkeh 1993).

       Other radionuclides, such as thorium and radium, have shown limited removal (Acar et al.
1992c). In the case of thorium, it is postulated that precipitation of these radionuclides at their
hydroxide solubility limits at the cathode region formed a gel that prevented their transport and
extraction. Limited removal of radium is believed to be either due to precipitation of radium sulfate
or because radium strongly binds to the soil minerals causing its  immobilization (Acar et al.
1992c).

       Kaolinite specimens prepared with organic molding fluids demonstrated successful
application of the process in transport of the BTEX (benzene, toluene, ethylene and m-xyiene)
compounds in gasoline and trichloroethylene loaded on kaolinite specimens at concentrations
below the solubility limit of these compounds (Bruell et al. 1992; Segal et al. 1992). High degrees
of removal of phenol and acetic acid (up to 94%) also were achieved by the process (Shapiro et al.
1989; Shapiro and Probstein 1993). Acar et al. (1992) reported removal of phenol from saturated
kaolinite by the technique. Figure 2.12 demonstrates two pore volumes were sufficient  to remove
85% to 95% of phenol at an energy expenditure of 19 to 39 kWh/m3. Wittle and Pamukcu (1993)
investigated the feasibility of removal  of organics from  different synthetic soil types. Tests were
conducted on kaolinite, Na-montmorillonite,  and sand samples mixed with different organics.
Their results  showed the transport and migration of acetic acid and acetone towards the cathode.
Samples  mixed with  hexachlorobenzene and phenol are reported to show accumulation at the center
                                          2-26

-------
                               9.1      t,4      •.«
                            NORMALIZES OtSTAKCE

                                       («) tlacatanctd
t.t       1
AJfGQE
                              sa
                              o
                          •o
                                  2  f   2   S   2  2
                                        (*»
§   5
£   o
5   *
9   2
                                                                «
Figure 2.11:   Post-Treatment Distribution of Uranyl Ion across the Specimen in Unenhanced
              Electrokinetic Experiments (Acar et al.  1992c). (b) Post-Treatment Mass Balance in
              Acetic Acid Enhanced Electrokinetics Remediation Experiments for Uranyl Ion
              Removal from Kaolinite Specimens (Acar et al.  1993b)
                                           2-27

-------
           0
                   PORE VOLUMES OF FLOW
Figure 2.12: Phenol Removal by Electrokinetics (Acaretal. 1992)
                         2-28

-------
of each samples. The results of some of these experiments were inconclusive,  either because
contaminant concentrations were below detection limits or because the samples were processed for
only 24 hrs which might not be sufficient to demonstrate any feasibility in electrokinetic soil
remediation.

       Although removal of free phase non-polar organics is questionable, Mitchell (1990) stated
that this could be possible if they would be present as small bubbles (emulsions) that could be
swept along with the Water moving by electroosmosis. Acar et al. (1993) stated that unenhanced
electrokinetic remediation of kaolinite samples loaded up to 1,000 ug/g hexachlorobutadiene has
been unsuccessful. Acar et al. (1993) also reported that hexachlorobutadiene transport was
encountered only when surfactants are used. Figure 2.13 shows hexachlorobutadiene transport
through compacted kaolinite using sodium dodecyl sulfate (SDS) in the anode compartment.  The
surfactants form charged micelles which migrate across the soil  mass under an electric field.
Studies are ongoing at Louisiana State University on the use of this technique in  removing TNT
from soils.

       Field studies  of soil decontamination by electrokinetics  are  limited. Lageman (1989) and
(1993) reported the results of field studies conducted in the Netherlands. Figure 2.14 presents a
schematic diagram of the reported field Process.  These studies demonstrated 73% removal of Pb at
a concentration of 9000 jig/g from  fine argillaceous sand, 90% removal of As at 300  ng/g from
day and varying removal rates ranging between 50% to 91%  of Cr, Ni, Pb, Hg, Cu, and Zn from
fine argillaceous sand. Cd,  Cu, Pb, Ni, Zn, Cr,  Hg, and As at  concentrations of 10 to  173 ng/g
also were removed from a  river sludge at efficiencies  of 50  to 71%.  The energy expenditures
ranged between 60 to 220  kWh/m3 of soil processed. Afield study reported by  Banerjee et al.
(1990) investigated the feasibility to use electrokinetics in conjunction with pumping to
decontaminate a site from chromium. Although the effluent  chromium concentrations increased
slightly, the results of this study are inconclusive as the  investigators monitored only the effluent
concentrations and did not scrutinize removal across the electrodes.

       The laboratory studies reported by Runnels and  Larson (1986), Lageman (1989), Acar et
al. (1989), Shapiro et al. (1989), Pamukcu et al.  (1990), Earned (1990), Bruell et al. (1990), Acar
et al. (1990), Hamed et al. (199 I), Eykholt( 1992), Ugaz  et al.  (1994), Runnels and Wahil (1993),
Acar et al. (1993), and Acar et al. (1994) together with the pilot-scale study conducted by Lageman
(1989) display the feasibility of the process in removing inorganic species and low level organic
                                          2-29

-------
       2500
ts»
l-»
•-«

                             ,  ,
                             •   »
                            ;   /m
 O -SDS at 8 mM- Test 01


-•— SDS at 20 mM- Test 02


    -SDS at 20 mM-Test 03
             laKUi CMCMtraikM
                                       •*—:r
                       /;
              * ,»
               o-
                     03        0.4        0.6        0.8         1


                   NORMALIZED DISTANCE FROM ANODE
Figure 2.13: Hexachlorobutadiene Transport under Electric Gradients ( Acar et al. 1993)
                               2-30

-------
                                                                     GENERATOR
                                                                      OR MAIN
                                                           AC/DC
                                                         CONVERTER
                       •Sfsfs^$8&S£f ./.. >*tea;
Figure 2.14: A Schematic Diagram of the Field System Reported by Lageman  (1989)
                                2-31

-------
 contaminants from soils. Table 2.3 summarizes the laboratory data reported for removal of
 chemical species from soils by electrokinetics and the references used are listed in Table 2.4.
 2.8   Theoretical Modeling of Electrokinetic Soil Processing

       Modeling coupled transport of fluid, charge, and chemically reactive species is based on
 generally accepted set of transient (time-dependent) coupled partial differential equations that
 maintain conservation of matter and energy and the principles of continuum. A set of nonlinear
 algebraic equations accompanies  these partial differential equations to describe the chemical
 reactions among the constituent species.

       For electro-osmotic consolidation of soft clay deposits,  models which assume constant
 electrical potential gradient across the soil mass are proposed and analytical/numerical  solutions are
 presented  (Esrig 1968, Wan et al.  1976, Lewis et al.  1973, 1975, Bruch 1976, Banerjee et al.,
 1980a, 1980b). These models do not involve the chemistry associated with the process.

       Theoretical treatise and pertinent solutions to multidimensional contaminant transport
equations and hydrochemical transport equations in groundwater due to chemical and hydraulic
 gradients have shown significant  progress in the last decade.  Mangold and Tsang  (1991) have
 presented a summary of the geochemical, contaminant transport, hydrochemical models, their
 solutions and limitations. Yeh and Tripathi (1991) have developed and demonstrated a detailed
 two-dimensional finite element hydrogeochemical transport model for reactive multispecies solute
 transport.  The described model  can  be  applied  to  heterogeneous,  anisotropic, and
 saturated/unsaturated media, and can simultaneously account for chemical processes of
 complexation,  dissolution/precipitation, adsorption/desorption, ion exchange, redox, and acid/base
 reactions.

       Contaminant transport models which incorporate electrical  gradients are limited.  Acar et al.
 (1988) and Acar et al. (1989) presented a one dimensional pioneering model used to  estimate the
 pH distribution during electrokinetic soil processing. The model provides reasonably good
 qualitative agreement with experimental evaluation of H* transport and distribution. This model
 considers the electrochemistry  of the process. However, it neglects the time dependent changes in
 electrical and hydraulic gradients, disregards the coupling of electrical gradients with hydraulic
                                           2-32

-------
    Table A 2.3: Synthesis of Laboratory Data Reported by Various Investigators on the Removal of Chemical Species from Soils
Ref

1


2,3





2,4






5



Soil
Type
Silty


Kaotiuitc





Kaoliuitc






Silty
Clay


Pore
Fluid
NA


DIW





DIW






GW



Species

Cu


Pb





Cd
Cr





Cr



Initial
Cone,
617


100-1064
mg/kg




100-140
wg/kg





150-1500
ing/kg


Current
Density
.01-.05
BttA/ena^

0.012-
0.123
mAJcafl



0.037
wA/eni2


.


NA



Voltage

0,165
V/cm
•
2,5
V/cra




2-2.5
Went





0,1-10
V/cra


Duralioa
(lirs)
24-72


100-
1285




480.
1600




,
24-168



Energy
kWh/m
NA
*

29-60





50-120






,NA



Removal
<%)
50


75-95





92-100
65-70


#


NA



Remarks

Cylindrical Specimens
(D^O^Sift, L*"6 io,). Pitttl
concentration 290-543 mg/kg.
Bench-scale tests conducted on
kaolinite samples loaded with Pb
at concentrations below and
above (he CEC. Demonstrates
the effect of pH changes on the
process.
Bench-scale tests demonstrate
the fcasibilty of fhc proccs* The
study demonstrates the
development of nonlinear
electric potential distribution dm
to the electrochemical changes
across the sample.
Field specimens are used (D-5 1
cm, L"2,5cw to 6.7 cm).
Hydraulic and electric potentials
are used simultaneously
DIW: Deiontzed Water, DW: Distilled Water, QW: Ground Water, US: HumicSolution, TW: Tap Water, NA; Not Available.
                                                            2-33

-------
Table A 2.3: Synthesis of Laboratory Data Reported by Various Investigators on the Removal of Chemical Species from Soils (cont'd)
Ref.

6







7,19













Soil
Type
Kaolinite







Kaolinite


Kaolinite


Kaolinite


Na-
Montm.
Sand +
10% Na-
Montm.
Pore
Fluid
DIW







D W


HS.


GW


DW

DW


Species

Cu
C«(NO,)j
«ol.





Cd. co,
Ni, Sr

Cd. Co,
Ni, Sr

Cd, Co,
Ni. Sr

Cd, Co,
Ni, Sr
Cd, Co,
Ni, Sr'

Initial
cone.
1.3
mcq/kg






400-700
mg/kg

600-750
mg/kg

550-1100
mg/kg

4500-860
rngkg
400-I500
mg/kg

Current
Density
0.3-2.0
mA






NA


NA


NA


0 NA

NA


Voltage

0.25
V/cm






30 v
4 V/cm

30v
4 V/cm

30 v
4 V/cm

30 v
4 V/cm
30 v
4 V/cm

Duration
(hrs)
1648







2430


2430


24-50


24-50

24-50'


DIW: Deionized Waler, DW: Distilled Water, GW: Ground Waler, HS: Humic Solution, TW: 1
Energy

4.5-7.4







NA


NA


NA


NA

NA


Removal
(%)
NA



,



85-95


85-95


85-95


85-95

85-95


Remarks

Demonstrates that buffering
theanoderesultsinhigher
electroosmotic flow than
buffereing the cathode.
Citrate treatment was not
efficthein removing
precipitated copper from the
cathode zone.
Conducted bench-scale tests
on fhe feasibility of the
process. The results display
that removal efficiencies (or
%removal) is higher for high
initial concentrations. The
results show that kaoMnite has
the highest removal followed
by clayey sand while Na-
monimorillonite shows the
lowest removal efficiency



«p waler, NA: Not A v a i'f a b 1 e .
                                                          2-34

-------
Table A 2.3: Synthesis of Laboratory Data Reported by Various  Investigators on the Removal of Chemical Species from Soils (cont'd)
Ref
8
9
10
II
12, 13
Soil
Type
Kaolinite
Kaolinilc
Unsal.
Sand
Unsal.
Sand
Sand
Allamonl
Caly
(Illilc)
Pore
Fluid
Deion,
Water
Deion.
Water
0.005M
CaS04
NA
DW
NaCl
Sol.
Species
Uranium
Thorium
Chrom-
ale
Cu
(CuSO4
sol.)
CuSO4
NaCl
Initial
Cone.
1000
pCi/g
41-313
pCi/g
100
mg/kg
6l7mg/l
OOOIM
CuSO4
( 65 mg/l
CuSol)
0.02N
NaCl
Current
Density
0.127
mA/cm^
0.127
mA/cm2
0.35
raA/cm*
NA
NA
NA
Voltage
0.5-12
V/cm
0.5-12
V/cm
89-150
V
4-7
V/cm
2V
0.13
V/cm
2.5V
0.2
V/cm
10 V
O.I
V/cm
Duration
(his)
85-550
144-785
22
3, 5, 7,
and 9
days
7-48
500
day
Energy
kWh/m
3
50-300
kWh/ra3
100-300
kWh/m3
NA
NA
NA
NA
Removal
(%)
85-95
20-75
NA
NA
NA
NA
Remarks
The results demonstrate the
feasibility of removing
radionuct ides from bench-scale
kaolinlte sampler. Thorium and
radium removal were
incomplete due to formation of
(horuim hydroxide and radium
sulphate.
DemonsUules the efficiency of
using the process for partially
saturated samples. Rale of ion-
migration Is 20 times the rate of
electroosmosis.
Fully saturated samples showed
higher removal efficiencies
than unsaluralcd samples.
Demonslartes the efficiency of
using ion-migration for
preconcentration of tons that
are difficult to remove by
pump-and-treal
Investigates the feasibility of
using electrokinelic clay
barriers.
 DIW: Deionized water, DW: Distilled Water. GW Ground Waler, HS: Humic Solution TW:  Tap Waler, NA: Not Available.
                                                             2-35

-------
Table A 2.3: Synthesis of Laboratory Data Reported by Various Investigators on the Removal of Chemical Species from Soils (cont'd)
Ref.

14. 15.
16


17

18






19




Soil
Type
Kaolinilc

Kaolinile

Kaolinite

Kaolinile






Kaolinite
Na-Monl
Sand


Poro
Fluid
NA



DIW

TW






DW
GW
HS


Species

acetic
acid
Phenol

Phenol

BTX«
Comp.





Aceton
£ae
remarks)


loiiial
Cone.
0.5 M,
0.1 M
450 ppm
45 ppm
500
mgfog

1-150
nig/kg





100-6800
ppm



Current
Density
NA

NA

0.037
mA/cm^

NA






NA




D1W: Dcionizcd Water :])\\: Distilled Water, GW: Ground Water, HS:
Voltage

2s v

0.62
V/cm
0.4-2.4
V/cm

0.4
'V/cm





30 v
4 V/cm



Duration
(hrs)
20-100
days
up10
60 days
78-144

NA'






24-50




Energy
kWh/m
3
3.7
Kwh/t
5.3-260
kwh/t
18-39

NA






NA




Removal
(%)
95
45
9s
75
85-95

see
remarks





Varies
5.8-100



NumicSolulion. TW: Tap Water, NA NotAvai
Remarks

0. IM NaCI purging solution was
used to optimize the process.


Most of the phenol removed
from the sample was collected
with the effluent.
Different organics 
-------
Table 2.4: References for Data Fteentedin Table 2.3
    1    Runnels and Larson  (1986)
    2    Hauled (1990)
    3    Hamed, Acar, and Gale  (1991)
    4    Acar, Hamed, Alshawabkeh, and Gale (1994)
    5    Banerjee, Horng, Ferguson,  and Nelson (1990)
    6    Eykholt (1992)
    7    Pamukcu and Wittle ( 1992)
    8    Ugaz, Puppala, Gale,  and Acar  (1994)
    9    Lindgren, Mattson, and Kozak (1992)
    10   Dabab, Kelly, and Godaya (1992)
    11   Runnels and Wahli (1993)
    12   Yeung (1990)
    13   Mitchell and Yeung (1991)
    14   Shapiro, Renauld, and Probstein (1989)
    15   Shapiro and Probstein (1993)
    16   Probstein and Hicks (1993)
    17   Acar, Li, and Gale (1992b)
    18   Bruell, Segal, and  Walsh (1992)
    1 9  Wittle and Pamukcu  (1993)
                     2-37

-------
gradients and does not incorporate the complicated chemistry and reactions associated with the
process.

       Yeung (1990) and Mitchell and Yeung (199 I) have proposed another model in a study of
the feasibility of using electrical gradients to retard or stop migration of contaminants across
earthen barriers.  Principles of irrversible thermodynamics were employed by these authors and a
one dimensional model is developed for transport of contaminants across the liner. The integral
finite difference  method was used to solve the problem and the model reasonably predicted the
transport of sodium and chloride ions across the liner. The limitations of this model are similar to
those of Acar et al. (1989). Furthermore, the complicated chemistry of the electrode reactions
(acid/base distributions) were not included and nonlinear changes in electrical and  hydraulic
potentials are neglected.

       Shapiro et al. (1989) and Shapiro and Probstein (1993) incorporated the electrochemistry
of the process and developed a model for transport of chemical species under electrical  gradients.
The model  couples the transport equations  of chemical species together with the charge flux
equation and accounts for the chemical reactions in the soil pore fluid. A steady state electroosmotic
flux was assumed and calculated by averaging the  electrical gradient and zeta potential across the
soil sample.  Shapiro and Probstein  (1993) reported that the numerical solution is achieved using
finite element method in the spatial domain and Adams-Bashforth integration in time. The results
were compared with the experiments for the case of constant voltage at the boundaries (the current
changes with time depending upon the electrical conductivity of the soil sample). Comparisons
displayed a good agreement in one  case of acetic acid removal from a kaolinite specimen of 40 cm
length. Other experiments did not show good agreement with the model results. The model
integrates the charge flux equation to evaluate the electric potential distribution and did not solve the
equation describing preservation of the electric charge. The model assumes incompressible soil
medium, disregards  the changes in the hydraulic potential distribution, and also does not account
for any sorption  reactions.

       Eykholt (1992) attempted to model the pH distribution during the process using a mass
conservation equation accompanied by empirical relations to account for the nonlinearity in the
process. One transport differential equation is formed by  subtracting the equation describing OH-
transport from the equation describing H+ transport and assuming that hydrogen and hydroxyl ions
have the same diffusion coefficients and ionic mobilities. The approach of using a dummy

                                          2-38

-------
concentration of the difference between H* and OH- concentrations has been widely used in
 modeling contaminant trasport in ground-water to eliminate the rate of chemical reactions, actions, such as
 the water autoionization reaction, from the differential equations (Miller and Benson 1983).
 However, it is confusing to use this approach in the case of species transport under electric
 gradients, even when the equal ionic mobility assumption is made for these species; in an electric
 field, OH- migrates in a direction  opposite to that of H+ migration because of their opposite electric
 charge. This study showed that a  negative pore water pressure may develop in soil  due to changes
 in zeta potential. The  development of negative pore water pressure is modeled based on zeta
 potential measurements made by Lorenz (1969) for kaolinite at different pH values. The modified
 Smoluchowski equation (developed by Anderson and Idol 1986) was used together with the
 proposed empirical relations to predict changes in the electric potential distribution.

        Corapcioglu (1991) has presented a  formulation of the system of equations  governing the
 coupled transport of mass, charge, and fluid under electrical,  chemical and hydraulic gradients
 assuming  a nonreactive mass transport. Alshawabkeh and Acar (1992) have described a system of
 differential/algebraic  equations  for the process  accounting for the chemical reactions of
 adsorption/desorption,  precipitation/dissolution, and acid/base reactions. Acar and Alshawabkeh
 (1994) have modeled the changes in soil and effluent pH during electrokinetic soil processing.
 Two transient transport equations  for hydrogen and hydroxyl ions are used together with the water
 autoionization equation. This attempt also assumes linear electric and hydraulic gradients
 throughout the process  and disregards the coupling  of these components.  Furthermore,  in these
 models no special treatise is provided for the effect of conservation of electrical neutrality on
 transport of the chemical species present.

        A  comprehensive theoretical model  is required for electrokinetic soil processing. This
 model should account for coupled multicomponent species transport under  electric, hydraulic and
 chemical  gradients.   Chemical reactions in  the  soil  pore fluid,  such  as  sorption,
 precipitation/dissolution, aqueous phase, water autoionization, and electrolysis reactions, also
 should be included.  This model is expected to provide  the.  basis for  a comprehensive
 design/analysis tool for the different boundary conditions, site-specific contamination and variable
 soil profiling encountered in full scale implementation of the process. Such a theoretical model also
 would allow assessment of the principles of multispecies transport under electric fields.
                                           2-39

-------
                                       Section 3

                       THEORETICAL  DEVELOPMENT
3.1   Introduction

       Electrokinetic soil remediation encompasses a sundry of physico-chemical  processes that
cause species transport and removal.  Theoretical understanding and simulation of the technology
demand a grasp of the mathematical formulation of these processes. These processes  are
controlled by such variables as electrolysis reactions at the electrodes, pH and soil-surface
chemistry, equilibrium chemistry of the aqueous system, electrochemistry of the contaminants, and
geotechnical/hydrological characteristics of the porous medium. The complexity of the processes
involved necessitates simplifying assumptions which would allow numerical simulation  within the
proposed time frame.
3.2 Assumptions

       The following assumptions are employed in the theoretical development presented in this
study

              I      The soil medium is isotropic and saturated.

              2.     The soil medium consists of clay particles with negatively charged surface,
                    the fluid region with the excess cations, and the pore free fluid with N
                    number of chemically reactive species.

              3.     All fluxes are linear homogeneous functions of all  driving forces (or
                    potential gradients).

              4.     Isothermal conditions prevail (coupled heat transfer is neglected).

              5.     All the applied voltage is effective in fluid and charge transport.

                                          3-1

-------
              6.     Electrophoresis  is not present
              7.     Hydraulic conductivity, coefficient of eletroosmotic permeability, and
                     coefficient of volume compressibility are constant in time and space.

              8.     The chemicoosmotic coupling is negligible.

              9.     The chemical reactions (precipitation/dissolution, aqueous phase reactions,
                     and sorption) are at instantaneous equilibrium (rate kinetics are ignored).

              10.    Soil particles are treated as electrically nonconductive (insulators).

              11.    Surface conductance and  streaming potential  are negligible.

       Most of the stated assumptions are reasonable and they are made in an attempt to
accomplish the identified objectives within the scope and time frame  available for  this study.  Other
assumptions were also necessary since a limited understanding of the mathematical formulation of
the physical or chemical specific processes exists. Justification of some of these  assumptions is
presented below while further discussion is presented throughout the manuscript.

       Specific  amount of the applied electric  energy might be consumed in generation of heat,
which might generate thermal gradients.  The effect of the generated thermal  gradient on the
transport processes and performance and efficiency of electrokinetic processing  is not  included
herein and is yet to be  investigated. Therefore, an isothermal system is assumed where  all the
applied electrical energy is available for transport.

       Electrophoresis  is a significant transport mechanism for clay suspensions. In the case of
compacted or even soft clay deposits, electrophoresis will have a minor contribution in charge
transport under electric  currents.  The assumption of no  electrophoresis  is, therefore, assumed to
be valid in this study.

       Generation and  dissipation of pore water pressure in soils result in consolidation,  and
changes in soil porosity. Coefficients of hydraulic conductivity, electroosmotic  permeability, and
soil compressibility are expected to change in time and space as a  result of soil  consolidation. In
                                            3-2

-------
some cases, such as consolidation of shinies, consolidation greatly affects porosity, hydraulic
conductivity, and soil compressibility; however, in compacted clays, changes in hydraulic
conductivity are not expected to be significant. The effects of these changes are not accounted for
in this study because the uncertainty in evaluating these parameters would be more than the
changes expected in their values.

       The assumption of no chemicoosmosis is justified by the fact that this component becomes
significant only in the presence of large chain molecules and  in very  active clay deposits (Mitchell
et al.  1973).
3.3  Transport Processes

       Application of hydraulic, electric, chemical, and/or thermal gradients to a homogeneous
medium of soil-water-electrolyte results in transport of matter and energy.  The resulting fluxes of
fluid, charge, mass, and/or heat through the  soil medium, their changes with time, and their effects
on  the properties and  composition of  the soil  medium  are significant  in  various
geotechnical/geoenvironmental problems.

       The fluxes  of matter and/or energy through soil-water-electrolyte media could be
categorized into two types; uncoupled fluxes and coupled fluxes. Direct spontaneous uncoupled
fluxes  result from application of a potential gradient of the same type of the matter transported
(conjugated driving forces). Examples of direct fluxes are fluid transport due to a -hydraulic
gradient (Darcy's law), charge transport due to an electric gradient (Ohm's law), mass transport
due to a chemical gradient (Pick's raw), and heat transport due to a thermal gradient (Fourier's
law).  Coupled fluxes result from transport of matter and/or energy due to a potential gradient of
different type than the matter and/or energy transported (non-conjugated driving forces).   The
nature  of the soil-water-electrolyte system with  the presence  of the diffuse double layer gives arise
to spontaneous coupled transport fluxes. Examples of coupled fluxes in soil-water-electrolyte
system are water transport due to an electric gradient (electroosmosis),  heat transport due to a
chemical gradient (Dufour effect), and charge transport due to a thermal gradient (Soret effect).
Table 3.1 summarizes various coupled and uncoupled direct fluxes identified as a result of
                                          3-3

-------
Table 3.1: Direct and Coupled Flow Phenomena
Flux
J
Fluid
Flux
Mass
Flux
Charge
Flux
Heat
Flux
Hydraulic
Gradient
Hydraulic
Conduction
Filtration
Streaming
current
Thermo-
Filtration
Chemical
Gradient
Chemico-
. Osmosis
Diffusion
Diffusional
current
Thermo-
Diffusion
Electrical
Gradient
Electro-
Osmosis
Migration
Mass Flux
vligrational
current
Thermo-
Migration
Thermal
Gradient
Thermo-
Osmosis
Thermo-
Diffusion
Thermo-
current
Thermal
Flux
                  3-4

-------
 application of hydraulic, electric, chemical,  and thermal  gradients to a system of soil-water-
 electrolyte.

        Assuming that all fluxes are linear homogeneous  functions of all their applied and/or
 generated driving forces (or potential gradients), the following equation  is used to define a system
 Of m fluxes, J(m), due to m conjugate driving forces, F(m),
                      J(m)=L.F(m)                                               (3 ^

 where L is (m x  m) matrix of coefficients Lij relating the flux J^ to a force Fj.  jhe coefficients L-
 LJJ,..., in the main diagonal of the matrix are named straight (diagonal or uncoupled) coefficients,
 since they relate the fluxes to their conjugated forces. The other coefficients are called coupling (or
 cross) coefficients, as they  relate  the fluxes  to the non-conjugated forces. The flux J-t is, therefore,
-described by m

               J. * T" L.F.           j= 1,. . . . M                                     /"> o\
                   iftBV !•  I          J   ~                                           I ~S  / I
 3.3.1  Fluid  Flux

        Fluid flux results from application of a hydraulic gradient (Darcy's law), an electric
 gradient (electroosmosis) and/or a chemical gradient (chemicoosmosis). Chemicoosmosis is not
 included because, as stated in the assumptions, it is significant only in the presence of large chain
 molecules and in very active clay deposits.
3.3.1.1  Darcy's Law of Advection

       Fluid flux due to a hydraulic gradient, J* (LT1) is given by Darcy's law as,

                                                                                    (3.3)

where k^ is the coefficient of hydraulic conductivity (LT*1), h (L) is the hydraulic head (h= u /


                                           3-5

-------
u is the hydraulic potential (F/L*2), and y, in the unit weight of the pore fluid (F-L"3). Numerous
methods exist for evaluating the hydraulic conductivity of fine-grained soils. Daniel (1989) and
(1993) summarize various laboratory and field methods and equipment that can be used for
measurement of the hydraulic conductivity of different soil types.

       Extensive research has been carried out on the hydraulic conductivity of fine-grained soils
with a relatively good understanding of the fundamental factors affecting its value (Lambe 1954,
 1958; Mitchell  et al. 1965; Olson and Daniel 1981; Boynton and Daniel 1985; Acar and Olivieri
 1989).  These studies indicate that microstructure and fabric are among the factors that highly
influence fluid transport in fine-grained deposits.  Dispersed micro-structure generally results in
lower hydraulic conductivity than flocculated micro-structure. Acar and Olivieri (1989), in a study
on the effect  of pore fluid chemistry on fabric and hydraulic conductivity of compacted clays, show
that a change in the hydraulic conductivity occurs when organic fluids are permeated through them
in response to  changes in the diffise double layer,  particle interactions and consequently soil
fabric. Other factors that affect kh, include soil porosity and pore size distribution. The presence
of uniformly distributed fine  size pores results in lower hydraulic conductivity, while the presence
of macro pores results in higher hydraulic conductivity, even if soil porosity is the same in both
Cases.

        Electrokinetic soil remediation induces changes in the pore fluid chemistry, diffuse double
layer, soil fabric and consequently the hydraulic conductivity. Furthermore, electroosmotic
consolidation is expected to take place and influence  the hydraulic conductivity value. In
attempting to model electrokinetic soil remediation in this study, hydraulic conductivity is assumed
to be constant in time and space because of the following reasons; (a) there is no clear mathematical
formalism that  can  describe the effect of pore fluid chemistry on soil fabric and consequently the
hydraulic conductivity, and (b)  the uncertainties in evaluating the hydraulic conductivities are more
significant than the  changes expected in their values.
3.3.1.2      Electroosmotic  Fluid Flux

       The Helmholtz-Smoluchowski theory for electroosmosis is the most commonly adopted
theoretical description of fluid transport through soils due to electrical gradients. Similar to the
hydraulic conductivity, this theory introduces the coefficient of electroosmotic permeability, ke

                                            3-6

-------
       !"1), as the volume rate of fluid flowing through a unit cross sectional area due to a unit
 electrical gradient. Hence, the electroosmotic flow rateJ^OLT'1), is expressed by an empirical
 relation similar to Darcy's relation,
               j; =*.n-E)  =  *,i                                               (34)
 where E is the electric potential  (V), I is the electric current density (CL'2T*), and kt (L3C~l)
 is the electroosmotic coefficient Of fluid transport given by,

              *• •                                                                 (3.5)
              1) is the effective electrical conductivity of the soil medium.
       Although Equation 3.4 can provide an estimate of the flow rate for known value of the
coefficient  of electroosmotic permeability and electric conductivity under constant current
conditions, it assumes constant electrical gradient across the electrodes. Applying an electric
current through the soil medium will generate a zone of high electrical conductivity at the  anode  and
a zone of low electrical conductivity at the cathode (Hamed  1990; Acar et al.  1993).  Figure  3.1
presents a comparison of the pH and conductivity profiles across a soil specimen upon a complete
sweep of the acid front generated at the anode compartment. Figure 3.2 presents a typical profile
of electrical potential difference across the soil specimen in a test conducted for Cr3* removal.  AS
depicted in Figure 3.2,  the electrical potential drop is mostly realized in the cathode region,
resulting in  higher electroosmotic flow in that region rather than the anode region.

       The value of kg, is widely accepted to be a function of zeta potential, viscosity of the pore
fluid, porosity and electrical permittivity of the soil medium. When the soil pores are treated as
capillary tubes, the  coefficient of electroosmotic permeability is given by,
                           es.C
                     r-       9 *
                     kt =  -  n
                            T\

where s is the permittivity of the medium (Farad/L"'), £ is the zeta potential (v), n is the porosity
(L3L~3), and rj is the viscosity (FTL"2). While hydraulic conductivity, k^, is significantly
                                            3-7

-------
                        •      ta       «--»      «.*
                           ffORMALCEEII OlSTANCE FEOM AHODE
Figure 3.1:  A Comparison of pH and Conductivity Profiles across a Specimen (Acar et al. 1992b)
                                         3-8

-------
                              0.2
0.4
0.6
0.8
                        NORMALIZED  DISTANCE  FROM  ANODE
Figure 3.2: Electrical Potential Profile across a Specimen in Cr3* Removal Test (Hamed,
                                      3-9

-------
influenced by the pore size and distribution in the medium (Acar and Olivieri 1989), the
electroosmotic coefficient of permeability, ke according to the Heimhoitz-Smoluchowski theory is
dependent mainly on porosity and zeta potential. The valueof ke has been assumed to be constant
during the electrokinetic process as long as there is no change in the concentration of ions or pH of
the pore fluid. This was not a good assumption in the studies reported by Gray and Mitchell
(1967), Lorenz (1969), and Hunter (1981).

       Extensive research has been carried out on the zeta potential of the glass-water interface.
There is a good qualitative agreement in the results of different studies. Hunter (1981) in an
extensive summary of theoretical and experimental treatise of the zeta potential in colloid  science,
displays the effect of pH and ion concentration in the pore fluid on zeta potential.  Figure 3.3
shows that the zeta potential decreases linearly with the decrease of logarithm of electrolyte
concentration (Kruyt  1952; Hunter 1981) and/or the pH of the soil medium. The effect of
electrolyte chemistry on zeta potential could therefore represented by (Kruyt .1952),            (3.7)
                     Z-A-BlogC.

where, A and B are two constants that are evaluated experimentally, and  C0 (M/L3) is the total
electrolyte concentration

       It is hypothesized that the drop in pH of the soil due to electrokinetic processing will cause
a decrease in the  coefficient of electroosmotic permeability  associated with the drop in zeta
potential; hence, the electroosmotic flow will start to decrease and eventually stop at later stages of
the process.   The  results  of Acar et  al. (1989), Hamed et al. (1991), and Acar et al. (1993)
demonstrate the decrease and cessation of electroosmosis upon  continued testing.   Consequently,
the kg, value determined in one-dimensional tests is time-dependent and controlled by the chemistry
generated at the electrodes.
3.3.1.3 Total Fluid  Flux

       Adding Equation 3.3 and Equation 3.4, the total fluid flux, Jw, is given by,         (3.8)
              Jw = k^(-K)+k,  v(-E)
                                          3-10

-------
               J
               <
               p
               2
               —
               N
4U

20


-20

-40
-60
o/~v
'

&
A A %
A


.
e.
'~^
j .... i .... i . . i • • i
• 10 •* M KNO , •
3
O 10 4M KNOj -
A 10 *2 M KNO,
3
oA :
_Q A
V "A. ^

\°.*° o ^
If , ,* f ••
                                         6    7     8    9     10     11
Figure 3.3:    The Effect of pH and Ion Concentration on Zeta potential of Colloidal TiOj (iep is

              the isoelectric point) (Hunter, 1981)
                                             3-11

-------
 The total one-dimensional fluid flux is,
                         dh        3E
               -  = "** "a7  " *• "aT                                            (3.9)
3.3.2  Mass  Flus

       Mass flux of different chemical species relative to pore fluid is a consequence of different
coupled potential gradients. Hydrodynamic dispersion is mass transport due to a chemical
concentration gradient. Migrational mass flux is mass transport of charged species due to an
electric potential gradient. Filtration or ion sieving is mass (or species) transport due to a hydraulic
gradient (Groeneveit and Bolt 1969). Filtration is neglected in this study because it occurs only in
soils with very fine pores where the resistance against passage of water molecules is much smaller
than that for dissolved larger molecules. Total mass flux of dissolved species also includes the
advective component due to species transport by the flowing  fluid.
3.3.2.1  Pick's Law of Diffusion

       Hydrodynamic dispersion, the phenomenon of mass transport of chemical species due to a
concentration  gradient, is a result of two basic phenomena; mechanical dispersion and molecular
diffusion. While mechanical dispersion occurs as a result of velocity variation within the porous
medium, molecular diffusion is mass transport due to the difference in thermal kinetic energy of the
molecules. Perkins and Johnston (1963), Bear (1972), and Rowe (1987) indicate that mechanical
dispersion is a significant mechanism in contaminant transport in ground water because of the
relatively high hydraulic conductivity and advective  hydraulic flow in such deposits (higher than
1.0 * 10-7 cm/sec). On the other hand, molecular diffusion is the primary process that controls
hydrodynamic dispersion in clay deposits due to the low advective hydraulic flow in these
deposits.

       The diffusive mass transport of chemical species in  a saturated soil medium under chemical
concentration gradients is described by Pick's first law,
                    J,  = A *(-c,)                                                 (3.10)
where J1.(ML*2T1) is the diffusive mass flux of the ith chemical species per unit cross sectional

                                          3-12

-------
area of the porous medium, c^OViL") is the molar concentration of the ith chemical species, and

D, (I-2!"1) is the effective diffusion coefficient of the ith chemical species. The effective diffusion
                                    *
coefficient in the porous medium, Df , is related to the respective diffusion coefficient in free
solution, I}, by (Bear,  1972; Gillham  and Dherry,  1982; Shackelford and Daniel, 1991),

                     A" = A™                                                   (3.11)

where t (L2/L2) is an empirical coefficient accounting for the tortuosity of the medium. Values of
t span over a wide range for different saturated and unsaturated soils. Experiments are often
necessary to determine its value for a specific soil type.   Shackelford and Daniel (1991  a) have
summarized various values oft for different soil types reported by various authors (Table 3.2).
These values are as low as 0.01 and as high as 0.84, mostly ranging between 0.2 to 0.5.

       Diffusion  coefficients for different ions at infinite dilution have been evaluated and reported
by various authors. Tables 3.3 and  3.4 present absolute values of diffusion coefficients for
representative cations and anions attained under ideal conditions. Many factors might affect the
molecular diffusion coefficient  such as the electroneutrality requirement  concentration, and
electrolyte strength (Shackeiford,  1991). Irreversible thermodynamics could be used to evaluate
molecular diffusion coefficient for a single ion with respect to a counter ion in a single  electrolyte.
Utilizing preservation of electrical neutrality, nolecular-diffusion for a single electrolyte, D0 , is
evaluated as,
                *      Z.D.-ZD.

where D+. and D. are the diffusion coefficients of the particular cation and anion, respectively, and
Z+. and z. are the charges of the cation and anion, respectively.  Table 3.5  shows representative
diffusion coefficients for single electrolytes.  Limited research is encountered for multicomponent
diffusion coefficient of a solution of more than one electrolyte. Multicomponent
describes ion diffusion due to coupled concentration gradients of other ions present in the solution.
                                           3-13

-------
Table 3.2: Representative Tortuosity  Factors (Adapted from   Schackelford and Daniel, 1991).
Soil
50% Sand:Bentonite Mixture
Bentonite :Sand Mixture
Bentonite:Sand Mixture
Silt Loam
Sand
Loam
Clay
Clayey Till
SUtyClay
Silty clay
Sandy Loam
Silty Clay Loam; Sandy Loam
Kaolinite .
Smectite Clay
Clay
Silty Clay Loam; Sandy Loam
Kaolinite
Smectite Clay
Sandy Loam
Bentonite: Sand Mixtures
Bentonite: Sand Mixtures
Tracer
XCI
*Cl
*Cl
"Cl
MCl
*Cl
*Cl
cl-
Cl-
Cl-
Cl-
^f^ m
. Cl-
Cl-
Cl-
crksol-
Br-
Br~
Br-
Br-
3H
*H
Saturation
Saturated
Saturated
Saturated
Unsaturated
Saturated
Saturated
Saturated
Saturated
Saturated
Saturated
Unsaturated
Saturated
Saturated
Saturated
Saturated
Saturated
Saturated
Saturated
Saturated.
Saturated
Saturated
r
0.08-0.12
0.04-0.49
0.59-084
0.05-0.55
0.28
0.36
0.31
0.15
0.13-0.3
0.1
0.21-0.35
0.08-0.22
0.12-0.5
0.07-0.24
0.55
0.19-0.3
0.15-0.42
0.08
0.25-0.35
0.01-0.22
0.33-0.7
                                       3-14

-------
Table 3.3:     Absolute Values of Diffusion Coefficients and Ionic Mobilities for Representative
              Cations as Infinite Dilution at 25° C (Adapted from Dean,  1985).
Cation
A**
AL3*
Ba?+
^J,^3^K
^j C
Ca?+
C_/ &f ff \&^r
^j wl -i • ft J i A
C^en)!*
Cr3*
C3*
Cu2*
D+ (IPC)
Dy3*
Er3*
Eu3*
Ft1*
Ft3*
Gf*
H+
py ?A
XZ (j
Ho3*
D;xlQP
Cm / sec
16.47
5.41
8.50
5.99
7.93
7.19.
6.21
4.70
8.87
6.63
5.94
20.84
7.32
55.57
5.83
5.86
6.03
7.19
6.04
5.98
93.13
7.05
5.88
an2/V/3cc
64.1
63.2
66.2
46.6
61.7
56.0
72.5
54.9
103.6
77.4
69.4
80.1
57.0
221.5
68.1
68.4
70.4
56.0
70.5
69.8
362.5
54.9
68.7
Cation
K*
La3*
Li+
Mg
Mn2*
NH*
NiH*
Na*
N
-------
Table 3.4:     Absolute Values of Diffusion Coefficients and Ionic Mobilities for Representative
              Anions at Infinite Dilution at 25° C (Adaptel from Dean, 1985).
Anion
Au( CN}i
Au( CNK
B(CtH*)4
B,r-
Brj
BrOZ
ci-
C/Of
CIO$
ClO^
CN-
COl"
Co(C.Ar)f~
CrOtT
F-
Fe(C#)a~
Fe(C#)f~
HiAsOf
HCO;
HF;
HPO%~
H*PO;
H*PO;
Djx106
emulate
13.31
9.58
5.60
20.78
11.46
'14.85
20.32
13.85
17.19
18.09
20.76
9.58
8.78
11.32
14.49
7.39
8.97
5.04
11.84
19.96
7.59
8.79
12.25
u ,-xlQ*
51.81
37.3!
21.8i
80.9
44.6
57.8
79.1
53.9
66.9.
7
-------
Table  3.5:     Limiting Free-Solution Diffusion Coefficients for Representative Simple
             Electrolytes at 25° C(Scnackelford and Daniel, 1991).
Electrolyte
HC1
HBr
Lid
LiBr
NaCl
NaBr
Nal
KC1
KBr
KI
CsCl
CoCl,
B«Cl>
X
33.36
34.0
13.66
13.77
16.10
16.25
16.14
19.93
20.16
19.99
20.44
13.35
13.85
                                         3-17

-------
       Shackelford and Daniel (1991b) investigated the effective diffusion coefficients, D*, of
 different inorganic chemicals in compacted clay. Their results demonstrate that molding water
 content and compaction methods have little effect, if any, on the effective diffusion coefficients.
 Generally, changing molding water content in compaction tests results in significant changes in the
 compacted soil microstructure (Mitchell 1993): According to the results by Shackelford and Daniel
 (1991b)  the change in compacted clay microstructure due to different molding water contents will
 have little effect on the effective diffusion coefficient of different chemicals.
 3.3.2.2  Mass Flux by Ion  Migration

        The migrational mass flux of the free ionic species in the soil pore fluid due to the applied
 electric field is given by,
                     j' = M*c,v(-E)                                              (313)

 where J,(ML  T"1) is the migrational mass flux of the ith species, and ui (I^T'V1) is the

 effective ionic mobility of the ith species. The effective ionic mobility, u t , defines the velocity of
 the ion in soil pores under unit electric field. There is no method yet devised to directly measure
                                                 *
 the single ionic mobilities (Koryta 1982); however, ut , can be estimated theoretically by assuming
 that the Nernst-Townsend-Einstein relation between E>j , the molecular diffusion coefficient, and Uj
 holds for ions in the pore fluid of soils (Holmes, 1962);
u  = mu  =  —   -                                           (3
                       t
where U{ is the ionic mobility of species I at infinite dilution, Zj is the charge of the ith species, F is
Faraday's constant (96,485 C/mol electrons), R is the universal gas constant (8.3144 J/Kmol),
and T is the absolute temperature. Note that each of Uj in this case has a value and a sign that
                                                                                        *
reflects  the charge of species i (i.e. the ionic mobilities and effective ionic mobilities, u. and zi ,  ,

will have negative values for anions and positive values for cations),  j^e Smns are included in  the
ionic  mobilities, of cations and anions to simplify the mathematical equations. Tables 3.3 and
present absolute values of ionic mobilities for representative ions at infinite dilution.
                                           3-18

-------
 3.3.2.3 Advective Mass Flux



        The other important mechanism of species flux is advection by the soil pore fluid. The

 advective mass flux of species i relative to the soil particles is,
                       w
                      J<  =C'J-                                                     (3.15)

 where q, is the molar concentration of water (- 1).
 3.3.2.4  Total Mass  Flux

        Adding Equations 3.10, 3.13, and 3.15, the total flux is given by;

               J, = A *(-<:,) +  C,(H;"+  fc,) *(-£) + ct kk v(-h)


 For one-dinensional applications, the total mass flux of species i is given by,

:      j, = -4-£- -  ',  <»;  + *.)Jf  •, c,*.
 This equation demonstrates that the electrical gradient has two transport components, ion migration

 and electroosmotic advection. It also explains that for cations both components will act in the same
                             *
 direction since the values of «, and ktf have the same algebraic sign; however, for anions these

                                                *
 components will act in opposite directions since u (. , is negative for anions while k . is positive.

 Figure 3.4 conceptualizes the transport mechanisms of positively charged and negatively charged

 species, from a soil mass with q, initial concentration, due to the different potential gradients given

 in Equation 3.16.




3.3.3 Charge Flux


       Applying a DC potential across a soil-water-electrolyte  medium generates an electric field

causing charge transport. Figure 3.5 shows a schematic diagram of the mechanisms by which

charge is transported through a soil-water-electrolyte medium. Seven paths are identified in Figure



                                           3-19

-------
           Cone.
                                        (a)
                        itial  Concentration


           cone.
                                          (b)

                      (1) Hydraulic Advection
                      (3) Eletroosmosis
(2) Diffusion

(4) Ion Migration
Figure 3.4:    A Schematic Diagram of Concentration Profiles in Transport of (a) Positively
              Charged and (b) Negatively Charged Species
                                          3-20

-------
3.5 for charged transport through saturated clay; these are (a) through soil solids, (b) soil
solids/diffuse double layer, (c)diffuse double layer, (d) diffuse  double layer/free pore fluid, (e)
pore fluid, (f) pore fluid/soil solids, and (g) soil solids/pore fluid/diffuse double layer. These
charge transport mechanisms are based on the assumption that the soil pores are interconnected
and, at the same time, the-soil solids are interconnected, with at least several continuous paths that
connect the medium pores from one side to the other and several continuous paths that connect the
soil solids from one side to the other. This assumption is made to make it possible for the electric
charge to move from one side of the medium to the other, either through the pore fluid and/or
through the soil solids. Furthermore, charge transport through the soil pore fluid is divided into
two components, one due to the migration of the counter ions and co-ions of the diffuse double
layer and the second is due the migration of the free ions present in the free pore fluid.

       The  contribution of each path on charge transport vary widely for different types of soil-
water-electrolyte media. With the assumption that soil solids are non conductors, a simplified
model that accounts for only charge transport through the diffuse double layer and pore fluid (paths
£and 4 respectively) is shown in Figure 3.5 (ii).  Figure 3.5 (iii) represents these components by
an electric  circuit. Only when the soil pore fluid  has a relatively high ionic strength, the
contribution of the free pore fluid dominates the other charge transport mechanisms.   To simplify
the calculations below, the contributions of the soil solids and the diffuse double layer ions on
charge transport are neglected.
3.3.3.1 Migrational  Charge  Flux

       The simplest form of electrical conductance of the soil is governed by Ohm's  law
describeng the current density (charge transport) in the pore fluid due to electrical gradients,
                            I =  
-------
»
b
c
d
e
f
g

£
£


ircVi'i&y. .^"^^-Jlr^^^-
£^3*^ '" v>~&3&^^%ii£z&^*
£"^™* ^s*\JSs x" ''mpSv *%*v/ t r t f * t
tffjftfffftjjfffftt
8K05wSM:v-*>::::::*::*?S''!:**!::*>J'v'»'v'v'v'
Saturated Clay Medium


'N'X'X'X'%'X'X'Xx%'X'%'-


1
1
1


/
1

X
•a
•o
• e
a
t> / • \
•s d)
•3
' 8
Ll
mm
ee

~l *
U tfa
J
w
"S (§)
>
•o
r J
Ls




mm
Double layer

|j soil solids
^ Pore fluid


                   —WWW—i
                   I—AA/WW—'
Figure 3.5:   A Schematic Diagram of Possible Paths of an Electric Charge through a Soil-Water
             Electrolyte Medium (i) All Possible Paths, (ii) Simplified Case Accounting only for
             the DDL and Pore Fluid, and (iii) Electric Circuit for Case (ii)
                                          3-22

-------
Substituting Equation 3.13 into Equation 3.19, the migrational charge flux is given by,
                                  tr
                             •          •


Comparing Equation  3.20 with Equation 3.18, and assuming that the migrational charge flux is
equal to the total charge flux, the effective electrical conductivity of the soil bulk due to migrational
charge flux is evaluated by,
                                  -N
                            
-------
Table 3.6: Transport Numbers of Cations at Various Concentrations (Koryta and Dvorak, 1987).
            Electrolyte
C.
                                 0.01
       0.05  0.1  0.2
            SCI
            CH3COONa
            CHiCOOK
            KNOs
            NH4Cl
            KCl
            KI
            KBr
            AgNOz
            Nad
            LiCI
              '2504
             \LaCh
                                    3-24

-------
transport numbers for cations in a single electrolyte solution It should  be noted that the summation
of transport numbers of all ions in the soil pore fluid is equal to one,
                            I/, -  1                                                (3-26)

       The transport number of a  specific species will increase as the ionic concentration of that
species increases. Thrisimplies that when a concentration of a species decreases relative to the total
electrolyte concentration in the pore fluid, its transport number and removal under electric currents
will be less efficient. Therefore,  it is reasonable to assume that the efficiency of removal of a
specific species will decrease in time as its concentration in the pore fluid decreases.
3.3.3.3  Diffusional  Charge Flux

       Similar to the migrational charge flux, the diffusional charge flux due to the diffusional
mass flux of charged: species is evaluated using Faraday's law of the equivalence of mass flux and
charge flux,
                     l'=-X*X                                                  (3.27)

Substituting Equation 3.10 in Equation 3.27, ,

                          l'  =  Ir/Z>>(-c,)                                    (3.28)
3.3.3.4   Advective  Charge Flux
       Applying Faraday's Law to advective mass flux will result in the advective charge flux,
                            r=    '-J*                                       (
Employing the preservation of electrical neutrality,
                             H
                             £c.ry  =0                                              (3.30)
                            y»i
                                           3-25

-------
 Accordingly there is no contribution of the advective  fluid transport in charge transport (I* =0).


 3.3.3.5       Total Charge Flux

        The resulting total, migrational  and diffusional, charge flux is,

                     I = F £ Zjfyv(-Cj) + a"v(-£)                             (3.31)
For one-dimensional applications, the total charge flux is given by,

                                                                                 (332)
3.4   Conservation  of Mass and Charge

       There are two approaches in describing the position variable in a system; the Lagrangian
approach and the Eulerian approach. In the Lagrangian approach the coordinates of a moving
particle are represented as a function of time (this approach describes the history of individual
particles, material coordinates). On the other hand, the Eulerian approach describes the flux
changes by referring to specific points that are fixed in space (spatial  coordinates).  The Eulerian
approach, used in this formulation, requires a definite fixed volume in space that has an arbitrary
shape, termed as the control volume (Bear 1972). The boundaries of the control volume always
form a closed surface in space. Though the flux of matter in a control  volume may change with
time, the shape and position of the control volume must remain fixed.

       Consider a finite control  volume of dimensions AX, A y, A z, around a point 0(x,y,z) in
the porous medium.  The change in amount of matter or energy transported through a control
volume could be described by,
                           -*.J + *                                            (3.33)

where R is a source/sink term. Principles of conservation of matter or energy require that the
Term 3.33 equals the amount which matter or energy are stored in the  control volume during At
                                          3-26

-------
time.  Consequently, time dependent equations for consevation of mass, charge, and energy are
used to develop the partial differential equations for transient changes in hydraulic head, electric
potential, and concentration of the chemical species presented in the pore fluid.
3.4.1  Soil   Consolidation

       Applying the  Conservation  equation to fluid flux in a saturated soil medium (Terzaghi's
consolidation theory),
where ev is the volumetric strain of the soil mass.   In consolidation of fine-grained soils the
volumetric strain is equivalent to the change in void ratio per unit volume,
                           "if ~  l+e dt                                      (:
where e is the void ratio.  The change in void ratio, d e, due to the increase in effective stress is,
                           de =  -a,d& = avdu                                (3.36)

where a, is the coefficient of compressibility, u is the pore water pressure, and a1 is the
effective stress. Substituting Equation 3.36 in Equation 3.35,
                           3sv      a,   du        du
                            dt  = 777 77  = m-77                           (3.37)

where, mv  is the  coefficient of volume compressibility. Substituting  (u = Ayw), the
consolidation Equation  is given by
                                  j[A
                           (OT»Yj gt  = ~7- J»                                 (3.38)


3.4.2 Conservation  of Mass

       The partial differential equation describing transient mass transport of species i is developed
by applying the law of mass conservation of species i,
                                         3-2?

-------
                           a-7. J, +nR,                                         (3.39)

where, Rj (ML"3T"') is the production rate of the ith aqueous chemical species per unit fluid
volume due to chemical reactions such as sorption, precipitation-dissolution, oxidation/reduction,
and aqueous phase reactions.

3.4.3 Conservation of Charge

       Applying conservation   Of Charge to the charge flux  equation,
                           — =  -v.I                                         (3.40)

where Te is the volumetric charge density of the soil medium (CL*3). The electric potential is
related to the volumetric charge density by,


where Cp has the units of the electrical capacitance per unit volume (farad L*3) and measures the
ability of soils to hold electric charge. Substituting into Equation 3.40,
 3.4.4  Chemical  Reactions

        Equation 3.39 may be simplified by  expanding the production term, Rj, to account
 for sorption reactions (surface complexation and ion exchange), aqueous phase reactions and
 precipitation/dissolution reactions,
                            R,  = R' + ST+R!!                                      (3-43)
 where Ri is a term for sorption, similarly Rt  is a term for aqueous phase reactions and Rf, for

                                           3-28

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precipitation/dissolution reactions. Two approaches have been developed and used in the literature
to describe chemical reactions; instantaneous equilibrium approach and kinetics approach. In
instantaneous equilibrium reactions, be it sorption, precipitation/dissolution, or aqueous phase
reactions, species concentrations are assumed to reach equilibrium instantaneously whereby in
kinetic reactions approach concentrations in solution are assumed to be time dependent and change
before they roach chemical aquilibrium.

       For several species,  chemical reactions, specially precipitation/dissolution and sorption
reactions, have been found to vary with time before reaching equilibrium.  It may be more
appropriate to use kinetics approach to model these reactions; however, this will unduly complicate
the modeling effort and it will require an independent investigation of each kinetics.  Furthermore,
chemical reactions involved in this study are expected to reach equilibrium at a very short time.
Sorption reactions in low activity soils and precipitation/dissolution reactions of heavy metals in
solutions often take minutes to reach chemical equilibrium. On the other hand, transport processes
of these chemical species  in  fine-grained deposits under electric, hydraulic and chemical  gradients
are slow compared to the rate of sorption  or precipitation reactions.  Consequently, the ratio of the
rate of chemical reactions to the rate of transport of heavy metals in low activity fine-grained
deposits is expected to be high enough to satisfy the assumption of instantaneous equilibrium for
these chemical reactions.
3.4.4.1        Sorption  Reactions

       The following general term has been widely considered for evaluation of sorption of
species on thi soil particles,

                                                             N                    (3.44
where p is the bulk dry density of the soil, 3^ is the adsorbed concentration of the component i per
unit mass of the soil solids (mole/M)  The reversible term (d S, /d t)  is often used to describe the
sorption rate. The equilibrium partitioning between the adsorbed phase and the aqueous phase of
the chemical components are commonly measured under controlled temperature  and applied
pressure, and the resulting correlations of Sj versus Cj  are callled adsorption isotherms. Several
equilibrium models (linear, Freundlich, and Langmuir models) have been used to describe sorption
                                            3-29

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 of heavy metals on soils. Assuming instantaneous equilibrium in sorption reactions and linear
 isotherms, the change in concentration of the sorped phase of species i is linearly related to the
 change in concentration of the aqueous phase,
                            ds,
 where K^ is called the distribution coefficient K^ of species i. A retardation factor, R^j, have
 been introduced and used in modeling species transport accounting for linear sorption as,
                                       pKM
                            Mt -  I + -£-                                     (3.46)

 The retardation factors of species i, Rd$, define the relative rate of transport of a nonsorped species
 to that of a sorped species.  For a nonsorped species , Rd = 1.

       Recently other methods have been used to account for Rt'm. contaminant transport equations
 because the previous method ignores the effect of pH, ionic strength, redox reactions, competitive
 adsorption, and  the mechanism of adsorption.  These  methods include isotherm  equations, mass
 action models, and surface complexation models proposed by Langmuir (1987), Kirkner and
 Reeves (1988);  Yeh and Tripathi (19891, Mangold and Tsang (1991), and selim (1992), among
 others.
3.4.4.2     Aqueous  Phase Reactions

       In the following formulation, it is assumed that the N number of chemically reactive
aqueous species is divided into Nc number of components and Nv number of complexes. In
aqueous phase reactions, any complex j is the product of i's reactants components, i.e.:
                      f    _     	
                    £tf'C'"r>        J=I'	'Nx                            (3-47)

where  c, is the chemical formula for component i, x/r is the  chemical formula for the complex j,
ij is the stoichiometric coefficient in complex j for component i. The law of mass action implies
that
                                          3-30

-------
                              N
                              iml                    X

where Kj   is the equilibrium constant for aqueous reaction]. From Equation 3.47, the rate

accumulation of component I due to aqueous reactioERj, , is:

                     R'J,  = -OjRj                                               (3.49)
where Rj, is the rate of accumulation  of complex j due to the chemical reaction]. The total rate of
accumulation of component i due to all aqueous reactions, R, , is:
                            N,          N,
                     R? = 1*7  =  -IV,                                   (3-5°)
                         •  y-i        /.i

Consequently, evaluation of Rf  requires evaluation of N, number of R-O361,  . .  . . N,.)   and
                                                                  J             ™
therefore, Nx number of equations is required. These equations are obtained from Equation 3.50
for j = 1,...,NX  . Note that Equation 3.48 requires known values of the equilibrium constant
                Nx.
3.4.4.3 Precipitation/Dissolution  Reactions

       Bench-scale studies conducted at Louisiana State University involving removal of Pb2> ,
Cr-^  Cd2"1" and uranium by electrokinetics have shown that these metal ions precipitate close to
the cathode at pH values corresponding to their hydroxide solubility. It is necessary to account for
the precipitation/dissolution reactions in the formulation of mass transport equations.   In
precipitation reactions, the chemical components are assumed to be composed of products,
                     Ht
              ~Pi  "  L bft~t             j = 1, ...., N                            (3.51)
                    !»/                              P

where p} is the chemical formula for precipitate],  b^ is the stoichiometric coefficient in precipitate
j for component i, and Np is the number of precipitates for component i. The production of the
                                          3-31

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precipitate will not occur until the solution is saturated.  Therefore,  the law of mass action is
written as,
                     «-l                              r

Where  K.J  is the solubility product  equilibrium  constant for precipitate j.  By the same

rationalization of previous formulations, the total rate of production of component i due to

precipitation/dissolution reactions/?,, is,
                     ff          ef

                    jm\  '*     jml  *

         P                                                                         t
 where Rjf is the rate of accumulation of component i due to precipitation reaction j  and Rf is the

rate of production of precipitate j.

       Similar to the case of the aqueous phase reactions, evaluation of Rp requires evaluation of

N  number of Rf.  N  equations for this case are obtained from Equation 3.52 for j = 1,..,N  .

Solubility product equilibrium constants Kj are available for any jth precipitation/dissolution

reaction.
 3.5 General  System  for  Modeling  Species  Transport

       The theoretical formalism presented in this Section results in a mathematical system of
 equations describing the transient reactive coupled muiticomponent  species transport under
 hydraulic, electric, and chemical gradients. The resulting system consists  of differential equations
 for transport processes and algebraic equations for chemical reactions. The objectives of this study
 involve one-dimensional application of electrokinetic soil processing therefore, the formulations
 are summarized in this section only for the one-dimensional transport of matter and energy.
                                            3-32

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        The differential equations describing transport of N number of chemical species are
 obtained by substituting the total mass flux, Equation 3.17, in Equation 3.39, which describes
 conservation of mass. The resulting one-dimensional equation is,
                                             .   3*
                                                            »                       (3.54)

                     for I  = 1,2 ,,., N .
       Note that for the case of nonreactive solute transport (Rj = 0), steady state fluid flux
(dh/dx = const.) and no electrical gradient, Equation 3.54 becomes,
              3*c,     ^    5_zc^ dc,    8/r
               a/       ' a*2    /q"'   * •a'"
                                                                                  (3.55)
Usually, the advective fluid flux under hydraulic gradients is referred to by the advective velocity,
v, i.  e.,:
                                  i.  dh
                           v ~ ~k»~dx'                                          (3-56)
 Substituting the advective velocity in Equation 3.55,
                     dnct      .    32c.   dct
                             "    "  ' V17                                     (3-57)
which is the diffusive advective solute transport equation widely used to describe nonreactive
solute transport

       Changes in the electric potential distribution across the soil as a result of changes in the
chemistry of the soil pore fluid is formulated by substituting the charge flux equation in the charge
conservation equation (Equation 3.32 in Equation 3.42),
                                           3-33

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       The resulting partial differential equations describing the coupled transport of matter and
energy are initial-boundary value equations. Initial condition and two boundary conditions are
necessary for every transient transport differential equation present. Initial conditions for every
dependent variable (or potential) are evaluated according to the initial state of potential  and/or
potential gradient distribution different types of boundary conditions can be specified for solution
of the transport differential equations; these are  Dirichlet boundary conditions, homogeneous
boundary conditions, mixed boundary conditions, and Neumann boundary conditions (Zwillinger
1989). The type of boundary conditions used differ from one case to another.
3.5.2 Preservation of Electrical  Neutrality

      . According to Faraday's law for the equivalence of mass and charge, the rate of change in
the electric charge for a unit volume of the soil medium equals to the total rate of change of
chemical species concentrations, times their charge, times Faraday's constant,
                            y     dnc,
                            I'^-aT                                           (3-63)

Preservation of electrical neutrality requires that the rate of change of the electric charge per unit
volume must equal zero. Substituting Equation 3.39 in Equation 3.63,
                     *      dnc.,        "              y
                     I *f-rf «  -  I *i^-JJ  + » I */*i                    (3-64)
                    i-i      Vi        j-j             j«i  .

  The total rate of chang of all chemical species under chemical reactions times their charge is
zero,
                     y
                     l*tR>=0                                                   (3.65)
                    j-i
In other words, for any chemical reaction,
                    A»mB~l + ID-m                                             (3.66)

one mole of A will produce m moles of B  ** and I  moles of D"m. The total change in B +l
concentration times its  charge is (m moles of B ** x (+1)) = ml.   The total change in D'm
concentration times its charge is (I moles of D-*11 x (-m)) = -ml. Therefore, the total change in
electric  charge   is  ml-ml=0.

                                          3-35

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       For one dimensional applications,   substituting Equation 3.17 for mass flux of species
i and Equation 3.65 in Equation 3.64,
                      y        a2/.     N      r         a2r     321.1
                        *™ *    +    **'       *+ *>]
                                                                               (3-67)
However, Equation 3.61, already describes the right hand side of Equation 3.71 to be equal to
zero. Substituting £ z}c-} = 0,

                                             M
                                   .
                            >  fZ-.U-.
                                 J  '
Note  that,
                                  y
                           T? + ° 1?  * ^7^                       <3

However, Equation 3.61 already describes the right hand side of Equation 3.71 to be equal to zero.
Therefore,
                    y    dnc,
                    lFrj-r7i=0                                            (3.72)
                   j>i    w»

       In other words, the change in chemical concentration of species present in the soil pore
fluid due to different transport mechanisms will occur in a way to preserve the electrical neutrality.
                                        3-36

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Theoretically, preservation of electrical neutrality results from redistribution of the electrical
potential across the sample. The electrical potential undergoes a change in its distribution to account
for the electrical potential  component that results from the concentration gradients of the charged
chemical species. This implies that the electrical  gradient is not described by Ohm's law any more,
but includes a diffusional component that is a result of concentration gradients within the soil pore
fluid .    Failure to account for diflusional charge flux in charge transport equation results in failure to
preserve the electrical neutrality.
       Modeling Acid/Base Distribution

       The effect of soil acidity or alkalinity, represented by the soil pH, is significant in heavy
metal-soil interactions and sorption. Changes in soil pH influence sorption reactions in various
ways. Literature reviewed in soil science and colloid chemistry demonstrates that surface charge,
and therefore cation exchange capacity, increases with increasing soil pH resulting in different
sorption characteristics. (Pratt 1961; Lorenz 1969; Hunter 1981; Maguire et al. 1981; Stumm
1992).  Different sorption characteristics might be attributed to changes in the soil cation exchange
capacity. Furthermore, sorption by ion exchange is dependent on the availability of various cations
competing to balance the surface charge on clay particles. At low pH values; tf+ ions, behaving
like polyvalent ions, will replace  adsorbed metals by ion exchange.  The rates of ion exchange
reactions are dependent on ion concentration, pH, and the selectivity coefficient of each ion.

       As described elsewhere, application of direct electric current through a soil mass  oxidizes
the water at the anode, generating a local acidic medium, and reduces the water at the cathode,
generating an alkaline medium. Accordingly, soil pH decreases at the anode and increases at the
cathode. Furthermore,  the acid front at the anode will advance towards the cathode with time by
the different transport mechanisms discussed, The changes in the soil pH will greatly influence the
soil-water-electrolyte  interactions and consequently contaminant transport and removal. It is
therefore essential to model the changes in soil pH in modeling  contaminant transport and removal.

       Utilizing the theoretical  development described earlier for species transport and interactions,
a system of partial differential equations and algebraic equations is developed for modeling soil
pH. The differential equations are for transport of H+ ion, OH- ion, pore fluid, and charge. The
algebraic equations  account  for the water electrolysis reaction. All  equations  are

                                            3-37

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nondimensionalized in distance by the following transform,
                     Y    —    ax     J_
                     A =  L   •  dx  *  L
                                                                                   (3.73)
        where L is the spacing between the anode and cathode.  The anode is at X = 0 and
 the cathode  is atX  =1.
 3.6.1 H+  Transport

       Ion migration, advection, and diffusion are the processes considered in modeling transport
 in this study. The differental  equation describing one-dimensional transport of the hydrogen ion is
 therefore described by,
       Pd
          *  dt
                                                                                  (3.74)
       Boundary conditions for the hydrogen ion transport equation are developed from
electrolysis reactions at the anode. The flux of H + at the anode has two components, the first is
due to the advective flow and the second is due to the electric current.
                                             X
                                             F
                                                                                 (3.75)
where c^ is the concentration of H * at the anode compartment. The electroosmotic advective flux
at the anode will carry H + ions generated at the anode into the soil. The first term on the right
hand side of Equation 3.75 describes the advective mass flux of hydrogen ion which is equal to the
advective fluid flux times the concentration of hydrogen ion at the anode. in the second term, it is
assumed that all applied current at the anode will be efficient in generation of H * by the following
water electrolysis reaction,
                     2H20 -4e~  -02+4ir                                     (3.76)
Consequently, the boundary condition for H+ at the anode (X=O) is developed by applying
Faraday's law for equivalence of mass and charge to the rate of production of H+,
                                        3-38

-------
                _Dir
ac,
                 L2 ax  +    L
             'H*
                 X»0
FL
                         (3.77)
where,
                                             .
                                            L  ax
                                                          (3.78)
The boundary condition for H4" at the cathode (Xml\ is
                            ax
                                                                               (3.79)
3.6.2  OH-Transport
       Similar to H4", one dimensional transport of OH- is expressed by,
anCoH (V'w} a2°oH ^ „
at

+
" I L2 J ax2
5COH
ax
[("S.+ M
il L2 ]
T •*<
dE
ax
                                                              a2h,
                                                            2 ax*
                                                                               (3.80)
 Boundary conditions for the OH- ion transport are developed from electrolysis reactions at
 the cathode. The flux of OH- at the  cathode (X- 1) also has two  components,  due to
 advective flow and due to the electric current,

                                                                                (3.81)
 Note in this case that the advective component of mass flux of OH- at the cathode is an outflow
 (negative), i.e. transporting from the soil to the cathode compartment. The difference between this
 condition and the condition at the anode is that the fluid flux at the cathode is multiplied by the
 concentration of OH- in the soil mass while at the anode it is multiplied by the concentration of H+
 of the anode compartment. However, it is assumed that the boundary condition at the cathode will
 be equal to that in the soil mass.  In the second part of Equation 3.81, it is assumed that all applied
                                      3-39

-------
current at the cathode will be efficient in generation of OH- by the-following water electrolysis

reactor,
             4H,0 + 4e~  •  2H2 +  4 OH"                                        (3.82)

Again applying Faraday's law to the rate of production of  OHf at the cathode(X* 1) will result in,

                      D'ra,   3 C,™    V ,
                                       OH
                      L2    ax  T   L

where,
                                nil   *t«
                                         Cf
                                          OH
                                                               _
                                                             FL
(3.83)
                                                                                ,._.,
                                          ax          ax                      (3'84)
and the following boundary condition is used for OH- at the anode (X=0),
                      D«COH
                                               x_0
3.6.3 Pore  Pressure

       One dimensional eletroosmotic soil  consolidation is described by
                    8h   _fv_ HL  +    k.   .  1  a2E
                    at   -L2 ax2     m     L2  ax1
                                                                                 >   }
       Hydraulic head difference between the cathode and the anode is controlled and kept at zero
in the experiment conducted in this study. Boundary conditions for this equation are, therefore,
constant hydraulic   head at both the cathode and the anode,
                             Wx.i s  0                                          (3-87)
3.6.4  Charge Transport Equation

       Assuming that the soil medium has zero electrical  capacitance, the one dimensional electric


                                         3-40

-------
potential distribution in time is given by,


              0 = F  I {&-} |4
                    j. i \ L  )  O A
 l   da'
T7 TV"
 L   0X
                                                                       BE
                                                                      T~-
                                                                      OX
(3.88)
once again, the soil effective electric conductivity, o*f and its gradient are evaluated by,
                              =F7z
                                                                                     (3.89)
                           (3.90)
          Boundary conditions for charge conservation equation are developed from the current value

    at the boundary. The constant current  applied throughout the  experiment would result in the

    following boundary conditions,

                              *    Df  dC:     a"   3E
                                                         x»o
                                                                                     (3.91)
                                                                                     (3.92)
    3.6.5 Water Auto-ionization Reaction


          In aqueous solution water autoionization is an important reaction for H+ and OH- ions,

                               H,0 - H* + OH'                                     (3-93)

    Therefore it is essential to incorporate this autoionization to model the soil pH, This reaction will

    generate equal number of moles of H+ and OH-,

                               AcH = Ac,                                          (3.94)


    or,
                                 R»q _
                                 H ~
    Also, law of mass action for water ionization requires
                                      =K= 10
                                                 -14
                           (3.95)



                           (3.96)
                                              3-41

-------
Six unknowns are defined for modeling soil jiL these are h, E, Cjj, CQH, RE"**, an(^
Equations required for the  solution are 4 transport partial differential equations (Equations 3.74,
3.80, 3.86, and 3.88)  and two algebraic equations (Equations 3.95 and.3.96).
3.7  Modeling Lead  Transport

       Lead removal by electrokinetics is modeled in this study in an attempt to assess the
principles  of the technology and to check the validity of the theoretical model presented.  Though
various cations and anions might be present in the soil pore fluid at different concentrations, only
four ions are included in this model. These arc Pb2"1" because it is the species of concern, NO"3,
since lead nitrate salt is used for the experiment, and H+ and OH- because they are necessary in
describing the acid/base distribution that has a great influence on the pore fluid chemistry. Four
one dimensional partial differential equations are formulated in describing the transport of these
ions. Dramatic changes in the concentration of these ions will result in different chemical
reactions. Chemical reactions  included  in this  model  are the  reactions  describing
precipitation/dissolution of lead hydroxide (Pb(OH)2), the water auto ionization reaction, and
sorption  reactions.

       Other  dependent variables included in the model are the changes in distributions of the
electrical potential and the hydraulic head. The change in electrical conductivity across the soil as a
result of continuous change of ionic strength of the pore fluid will lead to changes in the electrical
potential distribution. The charge transport equation is used to  model the changes in the electrical
potential.  Changes in electrical gradient distribution will develop nonlinear pore water pressures,
resulting in suction in this case, across the soil between the  electrodes. Development of pore water
pressure is modeled using the fluid transport equation, which  is the electroosmotic  consolidation
equation based on Terzaghi's consolidation theory.

       Following the  theoretical development presented earlier, a  system of differential/algebraic
equations is developed to model transport and removal of lead from kaolinite by electrokinetics.
Boundary conditions for these equations are developed based  on the changes in hydro-electro-
chemical characteristics  of the anode and the cathode.  The anode  is taken to be at X = 0 and the
cathode at X=l.
                                       3-42

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3.7.1 Pb+2  Transport
      The following  equation is used to describe pb 2* transport under hydraulic, electric, and

concentration gradients,
             dnc
                 pb
         L2
                                        pb
                                                       8X2  +  L2  3X2
                     •Pb
                   ax
i)  aE
    ax
                                  ah
                                  ax
                                                                               (3.97)
      Boundary conditions for the given partial differential equation are evaluated assuming that

lead is not involved in electrolysis reactions at the cathode and the anode.  Therefore, the mass

fluxes of lead at the cathode and at the anode are equal its component in the advective mass flux,
p;h  a
 L   ax
                             P b   Pb
                                    x-o
                                            Pb
                                                                               (3.98)
     a   cpb   _
where,
                                           :Pb  w
           ,  + k.| _a_E
            L      ax  " l  L J ax
                                                                                (3.99)
                                                                               (3.100)
3.7.2 H+ Transport
       The differential equation describing H+ transport is  given by,
             Rd
   anc}

 H~aT
                   ax
                                 ax2
«i + k.) a2E
L2 J ax2 H
ah'
ax
.«.
- RH
kk a2h
h L2 ax2]


                                                                               (3.101)
                                        3-43

-------
       The electrolysis reactions at the electrode are assumed to be the same as those defined in
 Section 3.5.  Hence, the boundary condition given for H+ and OH- transport are the same as those
 denned for modeling soil pH in the previous section.  For H+ at the anode (X=O),
                                IT
                L2
where,
      ax  +
                        V
                   "IT
                                      X'O
                    dE
                    ax
=   L
 It  ah
  L   ax
 i
FL
(3.102)
                                                                                (3.103)
 and the boundary condition for H+ at the cathode (X = I),
DH*    aC>
T" "ax"
                                      X.L
                                                                                (3.104)
       The transport of H+ through the  soil towards the cathode will affect the sorption
characteristics of lead on the day surface.  H+ is expected to replace the adsorbed lead by ion
exchange and at the same time attack the clay surface and result in surface complexation that
changes the electrical charge of the soil particle.  Consequently, the transport of H+will be retarded
due to sorption  reactions (ion exchange and surface  complexation). The rate of H+ sorption or
retardation has  not  been thoroughly investigated, however, a retardation  factor, RdH, can be
incorporated in the model to account for these sorption reactions. Evaluation of tbis retardation
factor is presented in Section 7.3.1.
3.7.3 OH-  Transport
       The transport equation for OH- ion is given by,
                                         a2E
                                                                      a2h
                                                         ax2     L2  ax2
                                                                               (3.105)
                  ax
                                          kOH
                                        3-44

-------
with the boundary conditions, at the cathode (x = 1),
        ^OH

         L2
                      ac
                         OH
and at the anode (X=O),
                DOH
                       *OH
                L2   3X
                               'OH
                               'OH
                                             COH',
                                                         _
                                                       FL
                                      1X-0
                             c«L
                               L
                                                                             (3.106)
                                                                      (3.107)
 3.7.4 NO~3, Transport
      It is necessary to account for N0"3, because it is present at high concentrations since lead

nitrate salt is used in spiking the soil. The need to account for N0"3 also arises to achieve electrical

 neutrality in the system.  Like other charged species   N0~3 transport is given by,
       ->  ».    f T\' \  -i2_»T      I f it*  -i- Ir \  a2c     1r    a^U
3_ncN
 at
:D;\ a2cN
 L2J  ax2
                             4- C
'N .
                                              ax2
            acN  [fu;>k.)  aE     >„
       •   +"ax" [["T7"] "ax  *  L2
                                         ah_
                                         axT OH
                                                         .  a2h
                                                       L2  ax2
                                                                              (3.108)
with the boundary conditions,

             " U "ax" H

                DJ,  acN
                L2  a x
                                  ax    CN
                                              L   ax
                                                                              (3.109)
                                                                               (3.110)
                                                                               (3.111)
        Note that since the global electrical neutrality is necessary (as shown in Section 3.42)
 concentration of one of the species could be calculated from the equation requiring preservation of
                                          3-45

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 electrical neutrality. For example, since NO~3, is the least reactive species among the species


 present, its concentration can be evaluated by,

                       j
 where i = 1, 2, and 3 refer toPb2*, H+, and OH-.  Significant computation time can be saved when

 this equation is used.
 3.7.5  Soil  Consolidation  Equation



        Once again, the soil consolidation equation describing the hydraulic potential distribution is

 given by,


              !                    k.     1  d*E
With the boundary conditions,


              klx-o =  hlx-i = °                                                 (3.114)
3.7.6 Charge  Transport Equation




       As described before, the electric potential distribution in time is given by,
with the boundary conditions,
                Fr    5L1S.    £111
                  A  j L2   ax  - L'  ax
                                              x,
                           Elx.i = 0
(3.117)
                                         3-46

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3.7.7  Chemical  Reactions

       Solution of lead transport and removal requires evaluation of the chemical reactions that
might occur as a result of changes in the soil chemistry. As presented before, these chemical
reactions are described by a set of nonlinear algebraic equations under the assumption of local
equilibrium. Reactions included in this study are lead hydroxide precipitation/dissolution reaction;
water auto-ionization reaction, and lead-sorption.

       I.      Lead Hydroxide Precipitation/Dissolution
                    Pb(OH), ** Pb2* +  20H-                                  (3.118)

Law of mass action for this reaction requires
                    <4 cpb <; K^OH   = 2.8 MO'16                             (3.119)
       II.     Water Auto-lonization Reaction
                    H2O *•* H* + OH'                                         (3.120)
Law of mass action for water ionization requires
                    CHCOH =  KW  =IQ-1"                                        (3.121)

       111.    Mass conservation

       Dissolution of 1 mole of lead hydroxide will generate 1 mole of Pb*1" and 2 moles  of
OH-. This means  that the change in OH- molar concentration due to lead  hydroxide
dissolution/precipitation reaction is twice the change of Pb2+ molar concentration. At the same
time the change in molar concentration of OH- due to water autoionization equals the change in
molar concentration of H+.  Consequently, the total change in OH- concentration due to both
reactions is given by
                    A(cOH) =  A(cH) + 2A(cpb)                                    (3.122)
or,
                    ROH  = R£ +  2Rpb                                          (3.123)
                                       3-47

-------
        IV.     Lead Sorption Reaction

        Dissolved lead in the soil pore fluid is assumed to have, the form of Pb2* which is highly
retarded and adsorbed by  different types of clay, compared to  other heavy metas, as presented in
Table 2.2. Lead sorption characteristics  are controlled by a number of variables, most  importantly
soil pH and lead concentration Yong et al. (1990) describe lead adsorption isotherms at different
pH values and concentrations for differnt types of clay.  The results for lead sorption on kaolinite
are used for this study to describe lead sorption at different pH and concentration. The following
empirical relation is assumed to describe lead sorption on kaolinite,
        s?b =0.27c^(pH-  !)(—) (207.2 •  1000)1.04.7                                  (3.126)
where cfyb is the total adsorbed and solute concentration in mole/L (= Sp^ + Cp^), CEC is the cation
exchange capacity, which should be substituted in equivalent/gm (for kaolinite used CEC = 1 .06
milliequiv/100 gm, = 1.06* 10-5 equiv/gm), and 207.2 is the atomic weight of lead.  Note that
Equation 3.126 and. Equation 3.128 are  multiplied by 1000 and  106 respectively to evaluate the
sorped lead in mg/kg. Figure 3.6 presents a comparison between the  empirical relation assumed for
lead sorption at different pH values and the experimental results of Yong et al. (1990).
        10 unknowns are defined for this study, these are h, E, Cp^, CH, COH, CN,
and ROH- Six transport partial differential equations are used, these equations are 3.97 for Pb2*
transport, 3.101  for H* transport, 3.105 for OH" transport, 3.108 for NO'3, transport, 3.113  for
soil consolidation, 3. 1 15 for charge transport. The other four equations required for the solution
are the algebraic equations 3.119 for lead hydroxide precipitation/dissolution, 3.121  for water
autoionization, 3.122 for charge conservation of the chemical reactions, and one of 3.124-3.126
for lead  sorption (depending upon the soil pH).
                                           i-48

-------
                 1.2
             2     1
           CJ
             i
           B   0.8
           -O
           a.
           '
                0.2


                  0
                                  Total Pb» 0.05 onolH/kgsotl (0.05 meq/lOOg)
                                  Total pWXSauolH/kg soil  (0,5 meq/IOOg)
                                  Total Pb*5.0onolTkgsoil (5.0 meq/IOOg)
                                  Modd-
                                        2.
                                           Soil pH
Figure 3.6: Lead Sorption at Different pH Values (Experimental Data from Yong et al., 1990)
                                           3-49

-------
                                       Section 4

                          NUMERICAL  SIMULATION
4.1  Introduction

       Numerical simulations are of great importance in engineering and science. They are of
major interest in providing solutions  to the theoretical and mathematical formalism  of a particular
physical system, specially when analytical forms of solution are not possible,
              they are used to bridge the  gap between theoretical developments and experimental
              results,
              they can be used to evaluate the importance of a specific physical effect on the
              physical system by turning this effect on or off, changing its strength, or changing
              its functional form,
              they may be used to test the validity of the theoretical fornalism, and quantitatively
              test existing theories,
              once a numerical model is tested and verified, it can be used as  a design and
              analysis tool for full practical  application, and
              they can  be used to quantitatively evaluate new ideas.

       Theoretical models and numerical solutions for multidimensional transient coupled species
transport in groundwater under hydraulic and chemical gradients have shown significant progress
in recent years.  In most of these models, a coupled system of partial differential and nonlinear
algebraic equations is developed and solved by different numerical approaches. Three of these
numerical approaches are identified and used successfully by various authors,
       1.      providing a solution to the  mixed differential and algebraic equations in which the
              transport equations and chemical equilibrium reactions are solved simultaneously as
              a system (Miller and Benson  1983; Lichtner  1985),
       2.      direct substitution of the algebraic chemical equilibrium equations into the
              differential transport equations to form a highly nonlinear system of partial
              differential  equations (Vallocchi et al.  1981; Jennings et al. 1982;  Rubin 1983;
              Lewis et al. 1987), and
                                         4-1

-------
       3.      iterating between the sequentially solved differential  and algebraic equations
               (Kirkner et aL 1984,1985; Yeh and Tripathi 1991).

Detailed reviews of these methods have been presented by  Yeh  et al. (1989) and Kirkner et al.
(1988).

       The third approach, sequential iteration between partial differential transport equations and
chemical equilibrium algebraic  equations, is used in this study because,
               the above described first and second approaches require intensive computer work
               and CPU time, specially for two or three  dimensional applications (Yeh and
               Tripathi 1991),
               the algebraic equations do not include spatial  derivatives, hence they are applicable
               to a batch system  only (point equations) and  sequential solution of these equations
               at every time  step  is more realistic and a reasonable choice,
               since the transport equations for different  species are identical in form, it is
               convenient to solve them one by one independent  of each other and then iterating
               with the chemical  equilibrium  equations.
4.2  Solution  Scheme

       The theoretical formalism presented in previous Sections produces a coupled system of
partial differential equations, describing transport of fluid, charge, species, and nonlinear algebraic
equations describing species chemical reactions. The numerical solution scheme utilized for this
system, using the sequential iteration approach, is summarized in Figure 4.1. The procedure is
explained in detail in Section 7.

       Boundary and initial conditions arc specified at time (T{ = 0). The solution starts by solving
the differential equations  describing species transport to evaluate species concentrations at time
(T=*Ti + At).  Initial values of E and h  and their gradients  atT^Tj are first used in these equations.
The new concentrations of the chemical species are used in the algebraic equations for the chemical
reactions to evaluate the rates of production of species  due to chemical reactions.  The new
concentrations are then used to evaluate the electric conductivity distribution and the first and
second derivatives of concentrations. These values are used to solve the charge transport equations
                                        4-2

-------
                Initial Concentrations, Electric Potential,
             and Hydraulic Head at TH>(Cji (j-1,4), Ei, hi)
                                i
                            T-Ti + DT
                                i
               Solve Transport PDEs using E*Ei and iHu
                Evaluate C(H), C(OH), C(Pb), C(N03)
                                1
                Solve the Algebraic Equations Describing
           Chemical Reactions to Evaluate New Concentrations
             Evaluate First and Second Derivatives of Species
          Concentrations, Electric Conductivity and Its Derivative
                 Solve Charge Conservation Equation
                      to Evaluate E at T-Ti+DT
                Evaluate the First and Second Derivative
                     of the Electric Potential (E)
                  Solve Soil Consolidation Equation
                      to Evaluate h at T-Tr+DT
                                I
                 Evaluate First and Second Derivatives
                      of the Hydraulic Head (h)
                                T
NO


Check E with Ei


YES
T-Ti
Figure 4.1: Flow Chart Describing the Sequential Iteration Scheme Used
                             4-3

-------
to evaluate the electric potential distribution E at time T"T,+At The second derivative of the
electric potential is then evaluated across the specimen and used to solve the soil consolidation
equation to evaluate the new hybraulic potential distribution at T^T^AL  The new electric potential
distribution is then  compared with the distribution used to used to solve species transport
equations.  If the two distributions  do not compare within a specific tolerance, then the new
distribution of E is used in the species transport equations and these equation are resolved. If the
two distributions agree then the solution proceeds to the next time step.

       The computer program developed is discussed in more detail together  with its subroutines
in Section  7. Appendix A presents a listing of the computer program, while a sample data file
pertaining to the pilot-scale study is presented in Appendix.B. The numerical methods used for the
solution are described in the following sections.

       Extensive literature exists on numerical approximation of different transport partial
differential  equations with various boundary and initial conditions.  Finite-difference methods and
finite-element methods are the most widely used numerical approximations for solving transport
partial differential equations. Though finite-difference method can provide an adequate and accurate
solution for one dimensional transport equations, the finite element method is adopted in this
study. The finite element method is more appropriate in treating the flux boundary conditions, has
the ability to discretely describe complex boundaries, and it is easier to use this procedure in
calculating  the cross-derivative terms.

       The Galerkin weighted-residual method is used as the variational (or  weak) method of
approximation. In an attempt to prepare a two-dimensional transport model, two dimensional
elements are chosen for the finite element discretization in spite of the one dimensional application
in this study. The Choleski decomposition method is used for matrix inversion and the bisection
method is used for solving the chemical equilibrium algebraic equations.
4.3 Finite Element  Solution  of  PDE's

       The general form of the partial differential equation governing two-dimensional advective
diffusive species transport with zero and first order production rates is given by,
                                       4-4

-------
              _  8 c  -/- _ d c       dc        dc             n dc
              D,  —-r    D —T  - v_ -T	vr -5—  -t- jju: + y = R -=-
where DX, D.y are the diffusion coefficients in x and y directions respectively, vx and vy are the
flow velocities in x and y respectively, (I is the first order production rate, and y is the zero order
production rate. Boundary conditions can be defined as,
                                        c:-co                                    (4.2)

on the boundary Bl, and,
                        j. ir  v _ n
                                     3x
                          v, )c - D,-ff -  Dy      *q                         (4.3)
 on the boundary B2, where q is the mass flux of species at the boundary.  Figure 4.2 presents a
 schematic diagram of a two-dimensinal domain for this case with the given boundary conditions.
4.3.1 Variational Formulation

       Variational formulation is a weak  formulation that describes the differential equation as a
recast of an equivalent integral  form. A large number of variational formulations have been
introduced for deriving approximate solutions. For most linear problems the weak (or variational)
formulation is equivalent to the minimization of a quadratic functional I(c), known as the total
potential energy, that describes the physical system (Reddy 1985).

       The quadratic functional corresponding to Equation 4. 1 is described by,
                           /(c) = J  (L(c) + \ic + Y) dx dy                         (44)
                                  D

where I(c) (or I) is the variational  of c, D is the plane region with the boundaries Bl and B2
(Figure 4.2) and the operator L is defined by,
              L=  D,-      +  Dy- - vx- - vy- - R-                   (4.5)
                      8x        r dy       dx     7 8x       at
                                          4-5

-------
                                                                        X
                                                                       •*»•
Figure 4.2: General Space Domain for Two-Dimensional Problem with the Boundary Conditions
                                         4-6

-------
The first variation of this integral equation is

                     8,/=5.
Since the energy must be minimized, the first variation must equal zeros
                                                                                   (4.6)
                                                                                   (4.7)
Equation 6 can be further simplified by utilizing integration by parts.  The diffusion terms in x and
y directions are expressed as,
                                                                                   (4.8)
                                                                                   (4,9)
where the first term on the right side represents the boundary  conditions on the perimeter (B). The
boundary conditions are introduced as
                                               *   "-1"*

                                                                                   (4.11J
The value on B1 is equal to zero since the variation
boundary condition. From Equation 4.3,
                    _  <3c    «  <3c
                                                      is zero for the constant concentration
                                                                                  (4.12)

-------
              J [ D«!f + D*  17
                                         .IB

Substituting Equations 4.8-4.11, and 13 in Equation 4.6,
                                                 3c
J 5e
                     e[(vx -(-vy)c-q]ds                                        (4.14)
                 B2
 f .  f    3c      3c
J 5«  -v«aT  .  v^ a
                                                    3c
Two-dimensional 8-nodal (quadratic)  isoparametric  elements are  specified for domain
discretization. 8-node elements are selected in order to achieve reasonable evaluation of the first
and second order derivatives of the dependent variables.  Figure 4.3 shows the elements together
with the shape functions. Isoparametric element is used becaseboth the dependent variables and
the local coordinates can be interpolated from nodal values. Shape functions Ni for this sub-
domain are given as (Burnett 1987),


                    N,  - -(l-
                                                                               (4.15)
                                         4-8

-------
                                = 1/2
8
5
' 4
3
1 ™^^™
t
j
r
L
M^
                            Element
         4-9

-------
                   Ns=   (l-S2
and,
             [Nf » [N, N2 N3 N4 N5 N6 N7]                                    (4.16)

The coordinates and the functions are described by:
                   x= [N]T{xJ -EN.x,
y =  INlT{y»} =
                                                                             (417)
where xj and yt are the global values of the nodal coordinates and Cj is the nodal concentrations in
the specific element Consequently, the function spatial derivatives are
                   3c    f 81|1T
                   ax=  [ a^  tCi^
                   gc    r.xnr                                             (4.18)
                   5y =
Since the shape functions are dependent on the local coordinates 4 and T\
                                       4-10

-------
                                t  ax
                                                                                 (4.19)
                          "

                                ax  a
                                                         a
                                                        ay
                                                                                   (4.20)
       where [J] is the Jacobian matrix. Hence, the x and y derivatives are evaluated by

                                              d  1
                             ax
                                   . u

                                              (4.21)
J.
'Ul
                                                                                   (4.22)
The determinant | J] (or the Jacobian) is given by:
                                                                                   (4.23)
                                       4-11

-------
The determinant of the Jacobian matrix/j/can be regarded as ratio between an infinitesimal area in
the parent element to the corresponding infinitesimal area in the real elenent that it is mapped into,
                                                                                  (424)
The Jacobian matrix is evaluated using Equation 4.22.
4.3.2.       Local  Matrices
       Equation 4.14 can be formed at the local element k as:
                                                             dxdy
                 J 8 ck[(vk + vJV - qj ds
                 B2
                                                                   dxdy
(4.25)
        The dependent values for the local element k in Equation 4.25 are
                            c" =  [N]T{ck}
                            Sck  = [5ck]T{N}

                            5ck  =  [5ck]T{N}
                                                   J
(4.26)

(4.27)

(4.28)

(4.29)
  The local element (k) matrices can be formed by substituting Equations 4.26-4.29 into Equation
  4.25,
                                           4-12

-------
     4-
                       ffn48Nl
                     - J      a

              \C2

                                                                   ,
                                                             dy |c)
                                [N]T (c}k - [N] q] ds
                    * [N]  [N]T (c}k * y* [N] - Rk[N]  [N]T |4
                                                              ot
                                                                             (4.30)
The time derivative is evaluated using a forward finite difference approach described by,

                          dc     |c}^ +  (c}t
                         a  t  =
                                      At.
The resulting formulation of the local stiffness matrix can be represented by
5,
        At
                 [SKF]k  +  [VL]k - [AK]k - [VB]k
                              IF)
                                                                            (4.3 1)
                                                                            (4.32)
                                                                            (4.33)
                    k-.vk)  [N]  [Nfds
               c2
                                                                            (4.34)
                                       4-13

-------
 {F} =  -   J [N] qds                                                    (4.35)
          c2
»  J -»; [N]  f£f -  v;  (N]  l    dx d
                                                  dy                    (4.36)
(QQ}k = Jyk[N] dxdy                                                (4.37)
          D

[E]K=  /Rk[N]  [N]Tdxdy                                           (4.38)
        D

[AK]k =  JV [N!  [N]Tdx.dy                                           (4.39)
          D

where,
              [SKF]  represents diffusion terms,
              [VL] represents velocity terms,
              [E]    represents retardation term,
              [AK]   represents first order production term,
              [VL]   represents the velocity term at the boundaries,
              {QQ}  represents zero order production term, and
              |F}    represents the flux term.

Applying the Transform 4.21, these matrices are equal to,
          1    1
          f   ff    k  -   , fdN]T
       =  J   J I -vk  [N]  —I  -  vk [N]  !-^| |  Ui d^dti           (4.41)
         -1-1                J
                                  4-14

-------
                  1   1
              =  J  /Yk  [N] UldgdTi                                         (4.42)
                 -1 -1
               1   1
       [Ef =  J
                  IJI dq dri                                      (4.43)
-1 -1
                 I   1

       [AKjk =  J  JV[N]  [N]T!J|d$dTi                                    (4.44)
                 -1  -1
4.3.3  Gauss  Legendre  Quadrature

       The area integrals in Equations (4.40-4.44) are evaluated numerically using Gauss
quadrature. Gaussian product rules (multidimensional Gauss rules) are generated by successive
application of one  dimensional Gauss rules as  follows,
                     1   1

             Int. = J   J c(£,, n) d£ dri                                         (4.45)
                    -1 -1
                     1

                    _,l.          J       ,  j    '   J   "  J
where, Wl and WJ are the weight factors for the selected sampling points Q and th. Nine sampling

points are selected for Q and ^,±0.7745966692 and ± 0.0000000000. Weight factors for these
points are 0.5555555556 and 0.8888888889, respectively.
                                         4-15

-------
4.3,4 Global  Matrix
      The connectivity of each element is used to generate the global stiffness matrix.
      {Scf
      in
        At
 [SKF]S +  [VL]8'- [AK]8 - [VB]S

{c}?  - {QQ}' +  {F
                                                          [E]' }
                                                           At
                                                                            (4 ,,4 6)
Since the formulated global matrix accounts for all elements of'the inesh, then the first variation of
the integral equation Sjlg must equal zero to minimize the energy input to the system. Furthermore,
the variations 8C are arbitrary which renders Equation 4,46 to,
                                             ten,.,.
;SKF]g + [VL]8 -  [AK]B -  [VB]8

         •U-  {QQ)S +  IF} =o
                                             At
         .Ml
          At
                                                                            (4,4?)
or,
       [SKF]S +  [VL]8 - [AK]B - [VB]8 4-
                                     III
                                      At
          si
           At
                10Q}g -  IF}
                                                                            (4,48)
      The above formulation of the finite element solution of the partial differential equation will
result in the following matrix form
                         A * c - b                                           (4,49)
where A is the global matrix developed, c is the column vector describing unknown concentrations
at time (t+At), and b is the column vector developed for initial and boundary conditions and zero
order production rate.
                                       4-16

-------
4.3.5        Choleski  Decomposition
       For any nonsingular square matrix A» the rows can be reordered so that the resulting matrix
has an L-U factorization .
                             L -  U  = A                                             (4.50)
where L is the lower triangular and U is the upper triangular. For the case of a 4 x 4 matrix, as an
example, Equation 4.50 will be
@n o o o
**2t 22 O O
Qt*. tti< Ctii 0
~*3I 32 33
„/•),_-_-
tt41 @42 tt43 a44.




011 012 013 014
0 022 023 024
0 0 033 034
0 0 0 |344




ail a!2 a13 a!4
^1 ^2 ^3 ^4
a31 ^52 ^3 ^4
.*»' a«2 a*3 ***
                                                                                 (4.51)
 Instead of using an arbitrary lower and upper triangular factors L and U, Choleski decomposition
constructs a lower triangle matrix L whose transpose LT can itself serve as the upper triangular
part (Bathe and Wilson 1976; Krcyszig 1988). In other words,
                           L •  LT - A                                           (4.52)
The components of LT are, of course, related to those of L by
Solving for components of L will result in
U - U::
                                 i-l   xJ.
                              -  E tl V
                                 k.l.  }
                                                                                  (4.53)
(4.54)


                    LJi=  T-au-  I L^
                          *-u V      k.i
(4.55)
                                      4-17

-------
4.4    Verification of the  Finite Element  Solution

       It is necessary to verify the computer program to assure that the mathematical formalism
and the computer  code are correct. Program verification requires  comparison of the program results
with  verified analytical or numerical  solutions  to  known  problems.

       Various attempts are made to compare  the numerical  solution with existing analytical
solutions of specific problems.  Preliminary comparisons are made with ordinary differential
equations describing either boundary value problems or initial value problems and the finite
element solution showed good comparison with analytical solutions to these cases. Verifications
of the numerical model and computer code are accomplished through comparisons with various
analytical solutions for initial-boundary value problems, similar to those present in Van Genuchten
and Alven (1982). These comparisons are provided in Appendix C for certain practical problems
with constant and/or flux type boundary conditions.
                                           4-18

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                                       Section 5

                            EXPERIMENTAL  MODEL
 5.1     Introduction

        A laboratory testing program has been developed to investigate the effect of up-scaling
 bench-scale tests and to demonstrate the feasibility and cost efficiency of electrokinetic soil
 remediation at dimensions representative of field conditions.   Second, it was essential to compare
 the results of the experimental model with the results of the theoretical formalism developed.
 Accordingly, a pilot -scale test setup was designed. The following criteria were used in the design,

        *      one-dimensional conditions and an intermediate case between bench-scale and
              full-scale in-situ remediation w a s represented,
        *      introduction of any boundary effects  was minimized.
        •      constant hydraulic head difference between the anode and the cathode was main-
              tained throughout testing.
        »      constant electric current or electric potential difference could be applied across the
              soil mass,
              space  and time changes in electric potential, pressure head, and temperature, across
              the soil mass could be measured, and
        *      soil samples should be available for  chemical analysis during testing.
5.2  Equipment  and  Instrumentation

       There are  no  standards  available for conducting pilot-scale  laboratory tests and
consequently no standard equipment or instrumentation are available. Standard procedures are
used wherever and whenever available.
                                       5-1

-------
5.2.1  Test Container

       Figure 5.1 provides a schematic diagram of the container used for the pilot-scale
experimental study. The container was made of plywood so that it did not conduct electricity but
resists the lateral compaction pressure. Container dimensions were chosen to be 91.4 cm width x
91.4 cm height x  182.9 cm length (36.0 in x 36.0 in x 72.0 in). These dimensions were selected
in an attempt  to minimize boundary effects, establish one-dimensional flow conditions, and
presented a reasonable electrode spacing between bench-scale experiments and full scale field
implementation. The effect of electrode spacing to the efficiency of the process was not well
established. A  wooden base was used to separate the container from the ground and to detect any
leakage.

       The inside of the container was sealed with silicon sealant and then wax painted.  In order
to avoid any fluid leakage  from the container, 80-mil High Density Poly Ethylene (HOPE) Gundle
liner was fitted inside the plywood  container. HDPE/Bentonite composite (Gundseal) also was
placed inside the wooden container as a second liner along the walls  across the electrodes.
5.2.2  Electrodes

       Several types of electrodes can be used in electrokinetic soil remediation. Inert graphite
electrodes were used for both the anode and the cathode to prevent introduction of corrosion
products that might complicate the electrochemistry due to electrode  electrolysis reaction.
Electrodes are purchased in rods each 6.35 cm (2.5 in) diameter and 76.2 cm (30 in) length. Each
cathode and anode series consisted of a row of five equally spaced electrodes at a center to center
spacing of 18.3 cm (Figure 5.1). Electrodes were held by polyacrylite frames that fit inside the
anode and cathode compartments (Plate 5.1).
5.2.3  Power  Supply

       Sorensen (DCS  600-1.7) power supply was used that can provide 0-600 V DC and 0-1.7
Amps. The DCS 600-1  .7 had two operating modes; constant current and constant voltage. In the
constant voltage mode, the output voltage was  regulated at the selected value while the output
                                           5-2

-------
       Wall
          032 on
          HDPE/Bentonite
          Composite


          cm % 76,2 cm
      Sectrodes
                 Tubes
        (7
                                          ; '•' ±-'.
                             •'Soil         V-'r"?

                                                  !
——.
    12,7cm  (Geotextile-Gundnei
—JL
                                                    72,4cm

                                                ~T
                                                ~T
    12.7 on

Figure 5.1: A Schematic Kaynn of the W<»d«i Coniaiiier and Liaiag Mamai U^ for Testing
                                    5-3

-------
Plate 5.1:  Graphite Electrodes  Used  in Pilot-Scale  Tests
                           5-4

-------
current varied with the load requirements.  In the constant current mode, the output current was
regulated at the selected value while output voltage varies with the load requirements.  The constant
current mode was selected to generate the required electric field in order to control the electrolysis
reactions at the electrodes such that a constant rate of production of electrolysis products occurred.
The current displayed by the power supply was determined to be accurate to 0.1% as specified by
the manufacturer and any other current measurement was not found to be necessary.
5.2.4 Instrumentation

       Various probes and devices were used to monitor physicochemical changes in the soil
while processing. Voltage  probes were used to monitor the voltage distribution across the soil;
thermocouples to monitor  temperature changes, tensiometers and transducers to monitor suction,
and pH meters to monitor cathode and anode pH values.

       Tungsten wires were inserted at different locations  and used as voltage probes to measure
the electrical potential distribution across the soil mass. It was estimated that a 200 to 300 volt
difference  will be developed between the electrodes (2-4 V/cm) at 130jiA/cm.  A voltage divider
was designed and built to attenuate 0-300 V range to a 0-10 V range. A schematic diagram of the
voltage divider is shown in Figure 5.2.  T'he formula used for dropping  the voltage  proportionally
is given by
                                   Rl + R2
                     Attenuation  =———                                       (5. |)

An important factor in deciding the values of resistors  used was  that the resistors  RI and R2 are
going to dissipate all the power in the divider.  The higher the value of the resistance (Rl + R2) the
less power was dissipated by the divider circuit. The values of  Rl and R2 used were 10 M ohm
and 360 k ohm, respectively.

       Suction in the soil  across the electrodes was measured using tensiometers connected to
transducers linked  to a  demodulator. Figure  5.3 shows the  suction  measurement setup.
Tensiometers consisted of a  porous ceramic cup connected through an airtight tube filled with
water to a transducer (or manometer). When the porous  cup was placed in the soil, the bulk fluid
(water) inside came into contact with the soil pore fluid.  Generation of suction in the soil pore
fluid is then transmitted to the fluid inside the cup and consequently to the transducer. The

                                           5-5

-------
•
Signal Input


'<
i
<
<
<
Vk
<
<
•<
' _
1
>
i"
i
VI
.
, '
> m
>
.
1
Signal Output
V2 * To A/D Board
Vout
'
Vin _ R1+ R2
V out R2
Figure 5.2: Vol1ag£ Divider
            5-6

-------
                   Pressure Tnosdoccr
      :v:
i\\   %%%->.!*.***%%
 tt   ft Qjtii Ma««' ' f
k > \   s % \ jou aass \ \ \
                           (a)
                                           To MuKplexer
             Gapl
     CML
                                          ML2
                                             ftessarePoa
Figure 5.3: A Schematic View of Suction Measurement Devices
                           5-7

-------
 measured  pore water pressure or suction will have a gravitational component that varies with the
 reference  level. As shown in Figure 5.3, the gravitational component  Of the tensiometer pore fluid,
 z, was determined from the elevation of the porous cup relative to the reference level.   The porous
 ceramic cups, purchased from Soilmoisture Equipment Corporation, were 2.86 cm (9/8 in) length,
 0.64 cm (1/4 in) outer diameter and with 100 kPa air entry value.  Plate 5.2 shows the porous cup
 together "with other probes used in large-scale experiments.

       Pressure transducers, DP215 purchased from Validyne Engineering Corporation, were
 used to evaluate the suction generated in thetensiometers. Figure 5.3 presents a schematic diagram
 of the pressure transducer.   The transducer block consists of a diaphragm sensitive to pressure
 changes placed between two coils. When suction is developed in the tube coming from a
 tensiometer it will cause the  diaphragm to deflect towards the cavity.  As a re suit the magnetic field
 between the inductance coil emplaced in each block is disturbed and an electric potential is
 generated across the coil.   The magnitude of this potential represents the amount of diaphragm
 deflection.

       Pressure transducers require an AC excitation and return an AC signal. A carrier
 demodulator, therefore, is needed to provide the AC excitation and  convert the  AC sensor signal
 into a high level DC output. CD280 four channel carrier demodulator with ±10 V DC analog
 output is purchased from Valibyne Engineering Corporation and used for this purpose,  it is noted
 that tensiometers provide the matric suction and they measure suction up to 90-100 kPa.

       Measurements of anolyte and catholyte pH values were conducted using a ColeParmer
 Model 5656-00 pH controller and Model 5593-70  pH electrodes. pH electrodes were first
 immersed in the anolyte and catholyte.  Unfortunately, the electric field in the cathode and anode
 compartments affected the pH readings of the anolyte  and catholyte.  it Was therefore necessary to
 measure the anolyte and catholyte pH without the interference of this electric field. Water in each
 compartment was  cycled into a separate container using a Cole-Parmet Masterflex L/S pump.
 Water level in each container was kept at the same level with the electrode compartments. Water
was pumped from these containers to the anode (or cathode) compartment  using  the pump,  ]ffhe
water  level increased at the electrode compartments, it was drained back to the container to keep the
 same  head level (the hydraulic system used is described in details in Section 5.9). However, if
water level  increased in both of the electrode compartments and the  containers due to
 electroosmotic or  hydraulic flow,  then it would be drained from the container, collected in a
                                          5-8

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separate bucket, and the volume of the collected fluid was measured in time. pH meters were then
connected to the MUX32 multiplexer to monitor the pH readings by the computer.  At the same
time, samples of the cathode and anode fluid were taken continuously for pH measurements for
cross checking purposes.

       Thermocouples were used for temperature measurements during testing. Teflon coated
copper-constantan thermocouples, 30.5  cm (12.0 in) length and 0.32 cm (1/8  in)  outer diameter,
were purchased from OMEGA for this purpose.  Thermocouples were formed of two dissimilar
metals that were joined together at one end. When this end was heated a  thermoelectric (or
Seebeck) voltage was generated due to difference in thermoelectric properties of the two metals.
Thermocouples were connected to a multiplexer which provides a cold junction compensation and
amplifies  low level signals.
5.3  Data Acquisition  System

       The hardware utilized in the data acquisition process was a Zenith PC microcomputer with
CIO-DAS16 A/D (Analog/Digital) board and CIO-MIX32 multiplexer.  The software package
used was Labtech-Notebook Version 7.0.

       The DAS 16 board, purchased from CyberResearch  Inc.,  supplied 16 single-ended or 8
difffercntial input channds (256 differential with multiplexer). The input ranges were 0-1 0 for
unipolar inputs, or ± 5 for bipolar inputs. The MUX32 panel multiplexes every 16 channels into
one input channel on the DAS 16 board, allowing  up to 256 differential inputs to one DAS 16
board.  The multiplexer also supplies a coldj unction compensation for thermocouple measurement,
has selectable 7 Hz input filtering, and can amplify the input readings by a selectable gain. The
MUX32 panel was connected to the DAS 16 board through a 37-pin  shielded round cable.

       Labtech Notebook,  an integrated software package for data acquisition, process control,
monitoring, and data analysis was used. The software can support up to 500 single channels.
                                          5-9

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5.4  Soil  Description

       Air floated Georgia kaolinite from Thiele Kaolin Company, Georgia,  was used for this
study.  This mineral was selected because of its low activity (activity is defined  as the ratio of the
plasticity index to the clay size fraction of the soil) and high electroosmotic water transport
efficiency relative to other clay minerals. Table 5.1 presents the physicochemical  properties of the
soil provided by Thiele Kaolin Company for the soil used in this project. The  compositional and
engineering properties of Georgia kaolinite, determined by previous research work at Louisiana
State University (Putnam 1988; Hamed 1990), are summarized in Table 5.2.  These properties
were rechecked for this project and they were not found to be  significantly different.  Chemical
analysis of the kaolinite used in this project is presented in Table 5.3.
5.5  Chemical  Species
       Lead nitrate [PXNOj)^ Salt was used as the source of lead because it has high solubility in
water and can provide the necessary ionic forms of lead and nitrate. Lead nitrate solution was
prepared by mixing a pre-evaluated weight of lead nitrate salt (depending upon the required
concentration) with the required volume of tap water. For example, in PST1, 0.0094 M lead
nitrate solution is prepared using 31  g of lead nitrate and 10 L of tap water.  20 ml of nitric acid
was added to prevent hydroxide precipitation from the hydrolysis of lead ion.
5.6 Permeation  Fluid

       Tap water was used for the cathode and anode compartments.  Tap water was supplied at
the anode from a source tank and collected at the cathodes, as described in Section 5.9. Chemical
analysis was conducted  on some tap water samples and Table 5.3  presents  the  average
concentrations of the cations and anions present in the tap water used in this project.
                                       5-10

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Table 5.1: Physicochemical Properties of Georgia Kaolinite Provided by Thiele Kaolin Company
Hygroscopic Moisture Content (%)
Specific Surface Area (m2/j)
pH (20% Solids)
Silica (SiO2)%
Alumina (AIjO^ %
Iron Oxide (Fe^) %
Titanium Dioxide (TiO2) %
0.5 - 1.5
20-26
3.6
43.5-44.5 .
38.0 - 40.5
0.9 - 1.3
1.4 - 3.5
                                        5-11

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     Table 5.2: Charactaistics of Georgia Kaolinite (Hamed, 1990)
 Mineralogical Composition (% by Weight)
        Kaolinite
        Illite

 Index Properties (ASTM D 4318)a
        Liquid Limit (%)
        Plastic Limit (%)

 Specific Gravity (ASTM D 845)b

 % Finer than 2 pm Size

 Activity

 Cation  Exchange Capacity
 (milliequivalents/100 gm of dry soil)

 Proctor Compaction Parameters
        Maximum Dry Density (tms/rn3)
        Optimum Water Content (%)

 Initial  pH of SoUc

 Compression Index (Ce)

 Recompression Index (Cr)

 Permeability  of Specimens Compacted at the
 Wet of Standard Proctor Optimum (x 10"° cm/sec)
  98
  2
  64
  34
 2.65
  90
 0.32
 1.06
 1.37
 31.0
4.7-5.0
 0.25
 0.035
 6-8
a ASTM Method for Liquid Limit, plastic Limit, and Plasticity Index
of Soils (D 4318)
k ASTM Method for Specific Gravity of Soils (D 854-58)
* pH Measured at 50% Water Content
* Flexible Wall Permeability at Full  Saturation
                            5-12

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Table 5.3: Chemical Concentrations of Kaolinite and Tap Water
Cation

PP+
FJ+
Ca?+
Mi?*
Si"
AP+
Na+
Kaolinite + DI
PS/9
0.70
0.04
66.78
25.74
128.80
3.45
1323.80
Kaolinite + HNO*
W/9
2.75
109.20
183.20
125.32
639.60
615.00
1555.00
Tap Water
mg/l
0.05
0.00
1.48
0.06
10.90
0.03
98.99
Anion

Cl-
NOs-
S0:42+
Kaollinite + DI' '
Mia
502.0
126.0
114.0
'ap Wata
mg/l
22.8
8.2
9.0
            DI  :  Deionized Water
                       5-13

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5.7 Bench  Scale  Tests

       The procedure used in bench-scale tests was the same as that used by Hamed (1990).  Two
bench-scale tests were conducted at a concentration of about 1,500 ug/g.  For both tests, 0.0165 M
lead nitrate solution was prepared using 7.23 g of lead nitrate salt, 1.320 L of tap water and 2.0 ml
of nitric acid.  3.0 kg sample of dry kaolinite was mixed with 1.320 L of the solution to bring the
soil to 44% water content.   The soil sample was cured for 24 hours.  The specimen was then
divided into two parts and each one was compacted in polyacrylite sleeves of 10.2 cm (4 in) in
length and  10 cm (3.94 in) inside diameter. The sleeves were weighed before and after compaction
all then directly, inserted in the electroosmotic cell in  one-dimensional test.

       Electroosmotic  test specimens were then assembled as shown in Figure 5.4 (Hamed 1990).
Inert graphite discs of 0.13 cm (0.125 in) thickness and  10cm (3.94 in) diameter were selected as
electrodes.  Two sheets of 8 ^un filter papers were placed at both ends of the specimen.  Uniform
flow conditions through  the electrodes were  ensured by drilling fifty holes of 0.3 cm (0.12 in)
diameter into the electrodes. The electrodes were held in place by polyacrylite end caps connected
with threaded rods. A liquid reservoir of 1100  ml capacity was available  at each end. Holes were
drilled into the top of each cap above the reservoir to allow venting  of  gaseous electrolysis
products.
5.8  Pilot-Scale  Tests

       Two pilot-scale tests were conducted on kaolinite spiked with lead at concentrations of
about 850 mj/g and 1,500 jig/g. A third pilot-scale test was conducted on a Kaolinite/sand mixture
spiked with lead at a concentration of 5,000  ng/g. In these tests, kaolinite  samples were mixed
with lead nitrate solution in several batches before compaction. In each batch in the first test,
0.0094 M lead nitrate solution was prepared using 31.00 g of lead nitrate salt, 10 L of tap water
and 20 ml of 1.6M nitric acid. One bag of kaolinite (22.7 kg (50.0 Ib) of dry weight) was placed
on the Gundle liner on the laboratory floor.  The solution was then added to the  dry kaolinite using
a sprinkler with continuous mixing using a large shovel. The sample was placed  in the concrete
mixer and the mixer is turned on for about 10 minutes. Large clods (about 25 cm in diameter) of
spiked kaolinite were formed in the mixer.  These clods were then cut into smaller pieces (of about
                                           5-14

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    DATA ACQUISITION
    ERMINAL BOARD
                         POWER SUPPLY
                         CARBON
                      	ELECTRODES—
GLASS
BURETTE
FILTERPAPER
                       CliA'FSHECIMEN:
                           END CAP'
   TRANSDUCER
                          TRANSDUCER
                           POWERSUPPLY
 Figure 5.4: Schematic View of the Bench-Scale Test Set-Up (Hamed, 1990)
                          5-15

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5 cm in diameter)  and placed on the liner inside the box. For every layer, 8 bags were mixed each
day and cured for 24 hours.  Aplastie wrap wasusedto ooverlhe day while curingtominimize
evaporation.

        Compaction was  achieved  with a hammer manufactured fcrthe purpose. The hammer was
a steel rod, 91.44 on (36.0 in) in length, welded to a steel plate with a contact area of 15.24 cm x
 15.24  cm (6.0 in x 6.0 in). The gross weight of the hammer was 4.54 kg (10.0 Ib).  Each layer
was compacted by dropping the hammer a 1000 times on the top of the soil from a height of about
91.44 cm (36.0 in). The  compaction energy applied by this procedure was less than the standard
proctor compaction  energy; however it was enough to bring the soil to 1.2 t/m3 at the wet of
optimum water content dry density at a relatively high degree of saturtion (approximatdy 90%).

       Three small wooden boxes  were then placed on top of the first layer inside the container.
These boxes were placed at middle and at both sides of the container to form the electrode
compartments. The outer  dimensions  of these boxes were 13.5 cm x 89.0 cm x 91.4 cm (5.3 in x
35.0 in x 36.0 in). Gundle composite fabric  and geotextile grid were used to separate the wooden
boxes  from the compacted soil, as shown in Figure 5.1. The three boxes placed in the container
were removed using a fork-lift after compaction of all soil layers.

       A large fork was  used to scarify the  surface of the first layer before compacting the second
layer in an attempt to ensure  full integrity between  the first and second clay layers.  The remaining
layers  were then compacted using the same  procedure.

       The same mixing  procedure was employed  in the second test with only one difference.  The
 lead nitrate solution used  in each batch (22.7 kg of dry kaolinite) in the second test was 0.0166 M,
 prepared using 55.00 g of lead nitrate salt, 10 L of tap water and 20 ml of concentrated nitric acid
 (16MHN03).

       For the third pilot-scale test, kaolinite/sand mixture was spiked with lead nitrate solution at
 a concentration of 5,500 fig/g.  0.1213 M lead nitrate solution was prepared by mixing 400 g of
 lead nitrate salt with 10 L of tap water.  One bag of kaolinite (50.0 Ib dry.weight) was  mixed with
 a half bag of fine sand (50.0 Ib of dry weight) to form 1:1 kaolinite/sand mixture. The solution
 was then mixed with this soil to bring the required lead concentration to a water content of 22%.
 Compaction was then achieved by using a similar procedure to that above.
                                       5-16

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5.9  Test  Setup

       As demonstrated in previous sections,  three  rows  of electrodes  were  placed in
compartments in the soil, as shown in Figure 5.1. A  polyacrylite frame is placed in  each
compartment to hold the electrodes (plate 5.1). Each row was formed of five graphite electrodes.
The compartments were then filled with tap water up to a level of 4.0 cm below the clay surface
level (the total water volume in each cathode or anode compartment is 70.2 L). The central row of
electrodes was selected to be the anode while the two cathode rows are at the ends at a distance of
2.5 ft from the anode row.

       Since the electroosmotic flow was expected to occur from the anode towards  both
cathodes, a water tank was connected to the anode reservoir to supply  the rquired amount of
flowing fluid. Water was collected from both cathode compartments in separate containers. In
order to avoid introduction of advection due to any external hydraulic potential difference, the
hydraulic head was kept constant and equal at both  cathodes and anode compartments during the
experiment with zero head difference (Figure 5.5). This  provision permitted evaluation ofthe effect
only of the electrical potential gradients on water flow within  the system.

       Ttepilot-scale sample in each test was composed of two identical halfs or cells (plate  5.3).
An electric current of 1.7 A was supplied to the sample at the anode.  This current was divided to
supply the two halves with 0.85 A each. The cross sectional area ofthe soil treated was 6,398 cm2
(91.4 cm width x 70.0 cm height) and  the applied current density was 0.13  mA/cm.

       Voltage probes, tensiometers, and thgermocouples were used to monitor changes in voltage
distribution, suction, and  temperature across one cell (Figure 5.6), while the second cell was used
for sampling, to assess the concentration changes with time. Instruments were calibrated before
and after each test. Voltage probes were calibrated using a voltmeter. A power supply was used to
feed the data acquisition  system with a known voltage  (measured with  a voltmeter)  and  the
computer reading was adjusted to give the right value. The process was repeated three times with
different voltage values and then a check was made on the readings with another two voltage
readings.  The voltage values used for calibration covered the voltage range expected during
testing. Thermocouples were calibrated using ERTCO No.  65514 NBS traceable thermometer.
Two different temperature readings were used for calibration,  one is for a cold water sample and
                                          5-17

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Plate 5.2:  Various  Probes Used in Large-Scale Experiments
                       5-18

-------
CONSTANT HEAl
WATER SUPPLY
&
9
v

WATE1
T

If
T

L
^
J
->

E^M|
±
WATER SUPPLY
* DRAINAGE




I
V

r "*".»'""

. ' ' ' ' FLOW '
DIRECTION
. CONTAMINATED .
. . . SOIL . . .
<


\

........
Ftoir ."."."."."."
DIRECTION
	 - -


\




                        12.7 om
                        »-	H
12.7   am
H-	H

182.9  cm
12.7  om
Figure 5.5 Longitudinal Cross-Section of the Pilot-Scale Test Sample Depicting the System Used for the Hydraulic Flow
                                                     5-19

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Plate 5.3      The Wooden Box Used in Pilot-Scale Tests Showing the Two Cells (A and B), the
             Anode and Two Cathodes.
                                        5-20

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 another for a heated  water sample.  A third reading was taken for a normal water at the ambient
 room tenperature to check the thermoccouple calibration Tensiometers were calibrated using water
 columns with different heights to give different pressure heads. The water columns were used to
 give both positive and negative pressure values for calibration. A check was also made for
 tensiometer readings at different water levels. After calibration the probes were inserted in the soil
 as shown in Figure 5.6.

        The devices used for measuring voltage distribution, anode and cathode pH, pore water
 pressure, and temperature were then connected to the MUX32 multiplexer (Figure 5.7). The data
 generated were then transmitted to the DAS 16 A/D board in the 386 Zenith PC, and Labtech
 Notebook  software was used for data acquisition and monitoring
 5.10 Chemical Analysis

        Chemical analyses of soil and fluid samples were made using inductively coupled plasma
 (ICP), at the Wetland Biogeochemical Institute of Louisiana State University.  Soil samples were
. oven dried for 24 hours at a 110 C. Then, 2 g samples of the oven dried soil were placed in 50
 ml centrifuge tubes and mixed with 40 ml portions of 1.6 M nitric acid. The mixtures were treated
 for 48 hours with continuous shaking to allow dissolution of the salts present and desorption of the
 adsorbed species.  This procedure is a non-standard, simplified version of the standard U.S. EPA
 procedure for total lead analysis  (EPA 1992; SW-846). It was found that the lead concentrations
 obtained using this  method were within 2-4% of those obtained with the  EPA method.   The
 mixtures were filtered and the solutions were sent for ICP chemical analysis.
 5.11 Soil Sampling

       Pilot-scale test specimens were sampled during and after terminating the electrokinetic
 process.  Final analyses of the water content, pH, and chemical concentration were conducted by
 dividing each bench-scale and pilot-scale soil specimen into samples and subsamples. For
 bench-scale experiments, the soil specimens were divided into 10 cylindrical sections, each 1.0 cm
 length and 10.0 cm diameter. pH readings were taken for each section; before oven drying them
 for chemical analysis and water content evaluation.
                                           5-21

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    OUMDUNI + GUNDaCU
    OUNPU
 ft CUWON IUCTMODIS (».S"DIA.iSO-t)
   MIUBUU TRAMBPUCIR
•  TOLTiOl mO»8
Q  THMUOCOUPUa
                                                      ruti rimr
                        Figurp 5.6: A Schematic Diagram of the Pilot-Scale Test Setup
                                                    5-22

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    Anode ConiuaiuiieuE i
Gatfaode Compartment
    fenaometers I   I  Thcmococpiey I   I "Voltage Probes
?CD280 Demodulator
                                      :Vbltage Divider
                          MUX32 Multiplexer
                         LabTech Notebook V7.0
                       •-•• T. .ft'	   •' —•  •.  • •• ':.-..'  :.
                         OOXIW?
                                                  386 Zenith PC
       Figure 5.7: A Schematic Diagram Of the Data Acquisition System
                                5-23

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       For the first pilot-scale test, the soil was divided into 3 horizontal layers, top layer (layer
 1), middle layer (layer 2), and bottom layer (layer 3). Each layer was divided into 10 longitudinal
 sections each of 7.0 cm length and 6 lateral sections of equal  size. As a result, 180 soil  samples
 were taken from the first pilot-scale test; each sample represented a soil volume of (7.0 cm x 15.2
 cm x 25.4 cm).  The same procedure was used for the second pilot-scale test but with a change in
 azeof sections.  Each cell of this test was divided into five horizontal layers with the  top layer
 being layer 1 and the bottom layer being layer 5. Each layer was divided into 10 longitudinal
 sections and 4 lateral sections of equal size.  Figure 5.8 displays a schematic diagram of these
 sections in the  second pilot-scale test  .  Consequently,  each cell in the second pilot-scale test was
 divided into 200 samples of equal volume (7.0 cm x 22.8 cm  x 15.2 cm). A total of 400 samples
 were collected for the second pilot-scale test. Each cell  of the third pilot-scale test was divided into
 three horizontal layers with the top layer being layer I and the bottom layer being layer 3. Each
 layer was divided into 10  longitudinal sections and 2 lateral sections of equal size. Consequently,
 each cell in the third pilot-scale test was divided into 60 samples of equal volume (7.0 cm x 45.6
 cm x 25.4 cm).  A total of 80 samples were collected at the end of processing the third pilot-scale
 test

       Soil sampling for chemical  analyses during processing of the pilot-scale-tests were
 accomplished using sampling probes of 2.54 cm (1.0 in) diameter and 6 1.0 cm (24.0 in) length.
 These probes were used to  take core sample at three different  elevations in the soil, each sample
 representing one third the depth. Each sample was oven dried and mixed thoroughly. Chemical
 analyses were then made for these  specimens  as described before. Locations for sampling points
 are shown in Figure 5.9.

 5.12 Standard Methods  and  Procedures

       As mentioned in Section  5.2, there are no standards available for conducting pilot-scale
 laboratory tests. Standard procedures  were used whenever and  wherever possible. Measurements
 conducted in this study include:  water content, pH, suction, and cation and anion  analysis. The
 electric current was set constant in all tests. The following methods were used:

water content: The standard method used  for water content calculation is ASTM D2216
"Laboratory Determination  of Water (Moisture) Content of Soil and Rock". Measurements were
 conducted immediately after sampling without any holding time.
                                           5-24

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              CATHODE
                                                                Cell  A
                     36in

A1-D7




D



A2-C7



C




A3-B7


B






A5-A7
A

x
/
s
/
/
/


                                            ~6in
                                                   13 in
         Sample (A3-B7) a Sample in Cdl A, Layer 3, Secrion B7
Figure 5.8: Sampling Locations for Final Analysis in the Second Pilot-Scale Test
                             5-25

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(-OC1THODI
ANOOK(
                                                         R CATHODE
        sio  it•  to . to
          o  o   o  o.o  o  o
          O  O   Q  O  9  O  O-
          o'o'o'o.'o'o  'o
'. O.O.O.O.O.O
                                               .«  .5.  4.  3.  2 7P«
        I  .   -IB.
        1BZS4  THBK3
                                                     	.  t
                                                     THXKl;
                                                  TP« . TDf?  IBfl.
                                                    A.   -A  -  1_
              14.4   14^
                                                                 14.5
                                                                            M
                                                                            O
                                                                            01
       • Voltage probes

       • Thermocouples
A Tensiometers     (all  dimentions are in cm)

0 Sample locations
Figure 5.9: Distribution of Monitoring Probes and Locations of Sampling Points
                                   5-26

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pH: Two methods were used in pH measurement. The first is following the procedure described
by Hamed et al. (1991) and the second is ASTM D4972 "Stardard Test Method for pH of Soils".
In the first method, all calibration and standardization procedure were conducted similar to ASTM
D4972. The difference between the two methods is that in the first procedure the pH electrodes
were inserted in the soil at processing  conditions. In the second test, the electrodes are inserted in a
soil/liquid suspension. Acar et al. (1989) and Hamed  (1990) discuss the differences between the
two procedures.  All pH measurements were conducted immediately without any holding time.

Pore Water presure: Pore water measurements were  taken during processing in accordance with
ASTMD3404 "Measuring Matric Potential in the Vadose Zone Using Tensiometers".

Metal fad) avfysis;  EPA  SW846  Method 6010A "Inductively Coupled Plasma-Atomic  Emission
Spectroscopy" was used for metal analysis in the extract Holding times were less than one month
for all metal analysis.

Anion analysis: EPA SW846 Method 9056 was used for anion analysis. Holding times for anion
analysis were within one week of sampling.

General procedures and methods for sample preparation, mixing,  compaction, testing, and
sampling are described in Section 5 (Experimental Model; see 5.8 and 5.9). A summary of these
procedures  is  presented:

Sample Preparation and mixing: No standard methods are available for spiking about 1 ton of   soil.
Based on each test requirements (mainly, water content and lead concentration requirements), pre-
calculations were made for Soil mass, water volume, and lead nitrate mass required for mixing.
Accordingly, a specific volume of lead nitrate solution was mixed with a specific weight of the
soil. This procedure was the most feasible for the study. Water content and lead concentrations in
the soil were evaluated after mixing and compaction.

Soil Compacting: Compaction procedure is described in 5.8 (Pilot-Scale Tests). Compaction was
conducted in a way similar to the Proctor Standard Compaction Test (ASTM D698). Compaction
effort was applied in a systematic way to minimize variations between the layers. The compaction
was achieved in layers  of similar thickness. Same compaction energy was applied to each layer.
Same personnel  were utilized in compaction. Compaction energy was calculated based on dry
                                          5-27

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density and water content requirements.

Sampling: Soil sampling is conducted in three stages (1) Initial Sampling (2) Sampling during
testing, and (3) Final sampling. Sampling was conducted in a systematic manner in all stages. Soil
sampling is described in Section 5.11.
                                          5-28

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                                       Section  6

                          EXPERIMENTAL  RESULTS
6.1  Introduction

       The primary objective of the pilot-scale testing was to demonstrate at 80% removal of the
lead content in the soil samples. Two bench-scale tests (BST) and three pilot-scale tests (PST)
were conducted. Experiment related parameters in these tests are summarized in Table 6.1.  Initial
conditions, such as dry densities, porosities, degree of saturation, and soil pH were similar in
almost all tests. Initial lead concentrations were similar in the bench-scale tests and the second
pilot-scale test PST2; both being above the cation exchange capacity of Georgia kaolinite.  The
current densities were  0.127 rnA/cm2 in bench-scale tests and 0.133  mA£rrf in pilot scale-tests.
All kaolinite specimens were prepared at a water content of 44% while the sand/kaolinite specimen
(PST3) was prepared at a water content of 24%. These water content levels were chosen to bring
the soil above the optimum-water content, which was 31% for kaolinite (Table 5.2) and 20% for
1: 1 sand/kaolinite mixture (Nyeretse 1985).

       Bench-scale tests (BST1 and BST2) were conducted using kaolinite samples at an initial
pH of 4.6 and loaded with lead at a concentration of 1,439 ms/g. The two tests differed in
processing periods; the first was disassembled after one week of processing (169 h), while the
second, after three and a half weeks  of processing (598 h).

       The first pilot-scale test (PSTI) was conducted using kaolinite spiked with lead at an initial
concentration of 856 ng/g and an initial pH of 4.7. The electrode support used in PSTI was
different than that for the other pilot-scale tests (PST2 and PST3). A trench was not used in PSTI
for the electrodes. Electrodes were placed in auger holes and they were separated from each other.
The decision to use a trench  and plexiglas support in PST2 and PST3 was taken to allow
homogeneous pore fluid chemistry in the catholyte and anolyte. Unfortunately, the liner in one of
the two cells in PSTI was punctured while compacting the clay leading to a leakage of the liquid in
one of the cathode compartments. It was decided to shut down that cell and continue processing
with the other half of the box by applying half the electric current. Soil samples were not taken for
                                        6-1

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Table 6.1: Initial Conditions for Bench-Scale and Pilot-Scale Tests
Parameter
current (mA)
Dimensions
Width (cm)
Depth (cm)
Length (cm)
Diameter (cm)
Duration (hr)
Current, Density (pA/cm3)
Initial Soil pH
Initial Concentration (pg/g]
Initial Water Content (%)
Initial Dry Density (g/an3}
Initial Saturation (%)
BST1
10.0

—
10.0
10.0
169
127.3
4.6
1,439
44.0
1.23
91
BST2
10.0

—
10.0
10.0
598
127.3
4.6
1,439
44.0
1.23
91
PST1
850.0

91.4
70.0
70.0
1,300
132.8
4.7
856
44.1
1.22
91
PST2
1,700.0

91.4
70.0
70.0
2,950
132.8
4.5
1,533
44.3
1.22
91
PST3
1,700.0

91.4
70.0
70.0
2,500
132.8
4.2
5,322
24.6
1.80
90
                               6-2

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