Modelling of Electrokinetic Phenomena in Soils

Transcription

1 University of Southern Queensland Faculty of Engineering & Surveying Modelling of Electrokinetic Phenomena in Soils By Abdurrahman Feturi S. Huweg B.Sc.Eng., M.Sc.Eng. In fulfilment of the requirements for the degree of Doctor of Philosophy September 2013

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3 Copyright by Abdurrahman Feturi S. Huweg 2013

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5 Abstract The aim of this work was to develop theoretical methods for the prediction of remediation time and the electrical energy requirements for the remediation of soil contaminated with sodium chloride. Laboratory scale experiments were specially designed and performed on sand and clay samples at field capacity moisture content to identify the key features of electrokinetic processes in soil. The experiments confirmed the existence of a prominent ionic concentration or conductivity front travelling away from the cathode. The dissertation offers a novel theoretical explanation that links this front to the electronegative charge bound onto soil particles. A mathematical model of electromigration in soil is developed based on that theory. The model is essentially a set of partial differential equations (PDEs) with some coefficients behaving non-linearly. An algorithm for numerical solution of the PDEs is developed using a finite difference time domain approach. Reasonable agreement was found between laboratory test results and prediction of the corresponding numerical models. In addition, approximate analytical solutions to the PDEs allow remediation time and remediation energy requirements to be evaluated. The results of this work may be generalised to soils with ionic contamination other than sodium chloride. i

6 Dedicated to My very unique mother, My dear father, and siblings, My wife and children (Shaima, Sharafalden, Sufyan and Abdelmalek) ii

7 Certification of Dissertation I certify that the ideas, experimental work, results, analysis, software and conclusion reported in this dissertation are entirely my own effort expect where otherwise acknowledged. I also certify that the work is original and has not been previously submitted for any other award, except where otherwise acknowledge. Abdurrahman Feturi S. Huweg Signature of Candidate Date ENDORSEMENT Dr. Tony Ahfock Date Professor Steven Raine Date iii

8 Acknowledgments First and foremost, I am thankful to Almighty ALLAH for all his bounties and blessings, for giving me the ability to complete this research. Without him, none of this work would have been possible. I would sincerely like to express my thanks and appreciation to my principal supervisor, Dr. Tony Ahfock, for his unrivalled support, constructive criticism, scientific support, insightful comments, guidance and suggestions, without which this thesis could not have been produced in its present form. I would like to express my sincere gratitude to my co-supervisor Professor Steven Raine for his constant support, availability and constructive suggestions, which were helpful for the accomplishment of work presented in this thesis. Special thanks to Dr Fouad Kamel, the first to teach me what electrokinetic treatment was and who, at the beginning of this work, always had encouraging words and was always ready to help me. I would also like to express my gratitude to the Libyan government, its Higher Education Ministry and Almergheb University for providing me the scholarship to pursue my higher education. To the University of Southern Queensland and School of Electrical and Mechanical Engineering, I would like to express my sincere gratitude for providing excellent support, ranging from technical service to pastoral care which have helped in the development of this research work. iv

9 I am also indebted to my family and friends who provided essential moral support during my PhD study. Finally, I wish to express my thanks to Manar whose love and companionship makes every day more enjoyable. Lastly I wish to thank many other people whose names are not mentioned here but this does not mean that I have forgotten their help. v

10 Table of contents Contents Abstract...i Acknowledgments...iv List of Figures... x List of Tables... xiv List of symbols and abbreviations... xv 1 Chapter 1: Introduction Project justification First order estimation Aim and objectives Organisation of the thesis Summary of outcomes Chapter 2: Literature Review Introduction Transport processes Principle of electrokinetic soil remediation Electroosmosis Electroosmosis theory Electroosmosis permeability coefficient vi

11 Table of contents Hydraulic gradient and matric suction development during electroosmosis Electromigration Electromigration theory Electrophoresis Diffusion Electrochemical reaction Factors affecting electrokinetic processes Electrode type Applied voltage Electrical conductivity of soils Coupling phenomena Summary Chapter 3: One-Dimensional Laboratory Tests Introduction General explanation of tests performed Electrokinetic cell setup Soil preparation Soil analysis methods Tests results Key findings from experimental work vii

12 Table of contents 3.5 Explanation for formation of concentration fronts during electrokinetic treatment Cation exchange capacity of soils Proposed theory Limitations of the proposed theory Summary Chapter 4: Model Development and validation The electrical equation and its solution The set of electromigration equations Determination of mobilities and initial ionic concentrations Initial and boundary conditions Discretisation of the electromigration equations Validation of the proposed theory Summary Chapter 5: 2-D and 3-D Modelling of Electromigration D and 3-D modelling Two-dimensional validation test Influence of the anode Generalised analytical expression for remediation time and remediation energy requirements Chapter 6 Conclusions and Further work Conclusions viii

13 Table of contents 6.2 Further work References Appendix ix

14 List of Figures List of Figures Figure 1.1: Simplified decontamination process... 5 Figure 1.2: Salt accumulation around root zone drip irrigated plants... 7 Figure 1.3: Targeted remediation area... 7 Figure 2.1: Distributions of cations and anions adjacent to clay surface (Mitchell, 1993) Figure 2.2: Principle of electroosmosis through soil (Probstein, 1989) Figure 2.3: Variation of electroosmosis permeability with ph value Figure 2.4: Variation of pore water pressures for one-dimensional electroosmosis with given boundary conditions Figure 2.5: Electromigration of ions (adapted from (Acar et al., 1994)) Figure 2.6: Electrophoresis phenomenon in soils Figure 2.7: Na concentration profiles during electrokinetic treatment Figure 3.1: Electrokinetic set-up (a) sketch of electrokinetic experiment set-up (b) soil column sections and (c) anode and cathode segments Figure 3.2(a): Voltage variations across different soil sections during electrokinetic treatment Figure 3.2(b): Current variations during electrokinetic process Figure 3.2(c): Sodium ion distribution in soil-water sampled at suction points during electrokinetic treatment Figure 3.2(d): Sodium ion distribution in soil column before and after electrokinetic treatment Figure 3.2(e): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment x

15 List of Figures Figure 3.2(f): Variation of ph in soil columns before and after electrokinetic treatment Figure 3.2(g): Variation of soil moisture content before and after electrokinetic treatment Figure 3.3(a): Voltage distribution across different soil sections during electrokinetic treatment Figure 3.3(b): Voltage and current waveforms during electrokinetic treatment Figure 3.3(c): Sodium ion distribution in soil-water sampled at suction points during electrokinetic treatment Figure 3.3(d): Sodium ion distribution in soil column before and after electrokinetic treatment Figure 3.3(e): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment Figure 3.3(f): Variation of ph in soil columns before and after electrokinetic treatment Figure 3.3(g): Variation of soil moisture content before and after electrokinetic treatment Figure 3.4(a): Voltage distribution across different soil sections during electrokinetic treatment Figure 3.4(b): Total voltage variation with time during electrokinetic treatment Figure 3.4(c): Sodium ion distribution in soil column before and after electrokinetic treatment Figure 3.4(d): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment xi

16 List of Figures Figure 3.4(e): Variation of ph in soil columns before and after electrokinetic treatment Figure 3.4(f): Variation of soil moisture content before and after electrokinetic treatment Figure 3.5(a): Voltage distribution across different soil sections during electrokinetic treatment Figure 3.5(b): Voltage and current waveforms during electrokinetic treatment Figure 3.5(c): Sodium ion distribution in soil column before and after electrokinetic treatment Figure 3.5(d): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment Figure 3.5(e): Variation of ph in soil columns before and after electrokinetic treatment Figure 3.5(f): Chlorine ion distribution in soil column before and after electrokinetic treatment Figure 3.5(g): Variation of soil moisture content before and after electrokinetic treatment Figure 3.6: Electrokinetic setup with cathode chamber design Figure 3.7(a): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment Figure 3.7(b): Variation of ph in soil columns before and after electrokinetic treatment Figure 3.8: Conductivity or ionic concentration regions Figure 3.9: Idealised voltage (V_xy) across middle segment of soil column Figure 3.10: Conductivity at point x xii

17 List of Figures Figure 3.11: Sodium concentration profile Figure 3.12: The depletion surface Figure 4.1: One-dimensional model Figure 4.2: One-dimensional representation of equation Figure 4.3: One-dimensional representation of equation Figure 4.4: Effective mobilities Figure 4.5: Anionic and cationic currents Figure 4.6: Flow chart for numerical solution of electromigration equations Figure 4.7: Comparison between measured and calculated voltage profiles Figure 4.8: Effect of the choice of anionic to cationic current ratio for = (0.2 and 0.8) Figure 5.1: Resistance branches between nodes in 2-D geometry (conductances due to cations and anions combined into a single branch) Figure 5.2: Resistance branches between nodes in 3-D geometry (conductances due to cations and anions combined into a single branch) Figure 5.3: flow chart for numerical solution of the one, two or three-dimensional discretized electromigration equation Figure 5.4: Two-dimensional validation test (a) Photograph of the setup (b) Positions of the voltage probes Figure 5.5: Voltage profiles used to identify the position of the concentration front Figure 5.6: Comparison of concentration front movement Figure 5.7: Effect of Anode size on the speed and shape of the concentration front xiii

18 List of Tables List of Tables Table 2.1: Coefficients of electroosmosis permeability Table 2.2: Electrode materials and voltage transfer Table 3.1: Key finding from experiments Table 4.1: Effect of choice of anionic to cationic current on remediation energy Table 5.1: Theoretical resistance of basic earthing electrodes xiv

19 List of symbols List of symbols and abbreviations Cross-sectional area of soil tube (m 2 ) Concentration of ions in (mol/l) or (C/m 3 ) CEC Cation exchange capacity Concentration of species i (moles/m 3 ) Pre-treatment ionic concentration (C/m 3 ) Dielectric constant of the pore fluid (F/m) Diffusion coefficient (m 2 /s) Effective diffusion coefficient in soil (m 2 /s) Incremental distance normal to depletion surface (m) Incremental time (s) Electric field gradient (V/m) Electrical conductivity (S/m) Faraday constant (C/ mol) Soil conductance due to negative ionic species (S) Soil conductance due to positive ionic species (S) + Hydrogen ion Hydraulic head gradient xv

20 List of symbols Current through soil column (A) Anionic current in the depletion region (A) Anionic current in high conductivity region (A) Cationic current in the depletion region (A) Cationic current in the high conductivity region (A) Current density (A/m 2 ) Ion flux due to diffusion (mol /m 2. s) Total Flow rate of specific ion (mol /m 2.s) Migration flux of salt ions (mol /m 2.s) Anionic contribution to current density (A/m 2 ) Cationic contribution to current density (A/m 2 ) Electrode injected current (A) Anionic to cationic current ratio within the high conductivity region Coefficient of electroosmosis permeability (m 2 /V.s) Hydraulic conductivity (m/s) Average anionic mobility (m 2 /V.s) Average cationic mobility (m 2 /V.s) xvi

21 List of symbols Pressure permeability coefficient (m 2 /Pa.s) Length of soil tube (m) Anode to cathode distance (m) Hydroxyl ion PDEs Partial differential equations Electroosmosis flow rate (m 3 /s) Universal gas constant (J /K mol) Branch resistance representing electrical current carried by negative ions (Ω) Branch resistance representing electrical current carried by positive ions (Ω) Radius of depletion surface (m) Total anode to cathode resistance (Ohm) Speed of the depletion surface (m/s) Absolute temperature (K) Total applied voltage (V) Anode potential (V) Cathode potential (V) Remediation energy (Watt) Seepage velocity due to hydraulic gradient (m/s) Charge number xvii

22 List of symbols Length of depleted region (m) Soil electrical permittivity (C 2 /N.m 2 ) Zeta potential (V) Viscosity of the pore fluid (N.s/m 2 ) Mobility of ions in the electrolyte solution (m 2 /V.s) Effective mobility of ion in soil (m 2 /V.s) Electrical resistivity (Ω m) Soil electrical conductivity (S/m) Soil conductivity in depletion region (S/m) Per-treatment soil conductivity (S/m) Partial conductivity of soil at node i due to anion electromigration (S/m) Partial conductivity of soil at node i due to cation electromigration (S/m) Minimum soil conductivity (S/m) The soil tortuosity Soil porosity Pressure gradient (Pa/m) t Time interval (s) Electrical potential (V) xviii

23 Chapter 1: Introduction 1 Chapter 1: Introduction 1.1 Project justification The existence of soluble salts in soil, groundwater and surface water bodies is a major land degradation problem worldwide. Salinity could result in several economic and environmental costs. These include a reduction in agricultural productivity, a decline in the quality of water supplies for drinking, irrigation and industrial use, damage to urban infrastructure and the loss of biodiversity in both terrestrial and aquatic ecosystems (Williams, 2001). Like many land degradation processes, including wind and water erosion, salinity is a natural process. However land use practices, such as land clearing, and the agricultural practices of irrigation and chemical application have significantly increased the extent of the problem. The United States Department of Agriculture estimates that, worldwide, 10 million hectares of arable land is lost to irrigation caused salinity every year. In Australia alone approximately 2.4 million hectares of land is affected by salinity and 5.7 million hectares of productive land are at risk. It has been estimated that the area of salt-affected land in Australia could increase six-fold in the next few decades (Williams, 2001). Irrigators in Australia are increasingly faced with declining water availability due to climate change, increased incidences of drought and increased competition for water resources from urban and industrial uses. Hence, there is increasing focus on the potential to use more marginal quality water for agriculture. Current irrigation 1

24 Chapter 1: Introduction techniques like precision irrigation systems deliver water to only part of the soil surface or root zone. This means that water will move both vertically and laterally from the point of application (Raine et al., 2007). However, plant roots remove water from the soil, concentrating salts in the root zone. Hence, in these systems, there is a non-uniform distribution of salt which is inversely related to the soil water movement and results in the accumulation of salts around the periphery of the wetted zone (Raine et al., 2005). The word salinity refers to the total concentration of all soluble salts in the soil, which include chlorides, carbonates or sulphates of calcium, sodium and magnesium with sodium chloride (NaCl) being the most common salt. Soil sodicity is identified as a significant form of land degradation and the greatest environmental threat in many parts of the world, in particular in the arid and semiarid regions. It affects almost a third of all soils in Australia (including a third of all agricultural soils), causing poor water infiltration, low water storage, toxicity, surface crusting, erosion and water logging (Miller, 2008). The sodicity represents the amount of exchangeable sodium ions (Na + ) in the soil compared to other exchangeable cations mostly being calcium (Ca +2 ), potassium (K + ), hydrogen (H + ), magnesium (Mg +2 ) and aluminium (Al +3 ). On the other hand, soil salinity is a major determinant of agricultural productivity in many regions of Australia. The cost of increases in root zone salinisation due to inappropriate irrigation management in the Murray and Murrumbidgee irrigation areas was estimated at AUD245 million dollars (in 2000/01) or 13.5% of the revenue from these cropping systems (Raine et al., 2005). 2

25 Chapter 1: Introduction The mobility of salts from surface to subsurface can be quite rapid and can impact significant volumes of soils and groundwater and therefore represents great environmental threat. The increased usage of marginal water in agriculture, fertilizer to achieve improvements in crop yield and inadequate irrigation practise is responded to increase salinity problems. A current technique commonly used to deal with sodicity in soil is soil reclamation by adding gypsum or chemical materials. However, the current technology to solve salinity problems is by collecting or pumping the saline water, concentrating it and extracting the salt by evaporation. The excavation of contaminated soil and disposal either on site or off site is also reported in some regions. Reddy and Shirani (1997) reported that due to the low hydraulic conductivity of fine-grained soils, the remediation of some contaminated soils by conventional methods such as in-situ bioremediation and in-situ chemical treatment is costly and mostly ineffective. Electrical treatment of soil is the treatment of soil by using an applied electrical current or voltage and it is one of the developing techniques that have significant potential for in-situ remediation of fine-grained soils. The capability of an electric field to transport water, free ions and charged particles through fine grained soils has been well established since the discovery of the electrokinetic phenomena by Reuss in the early part of the 19th century (Casgrande, 1949). The water content has effect on the physical characteristic of fine grained soil; consequently it largely impacts the soil strength. Therefore, controlling water in this fine grained material is of great importance. Reuss observed that when a direct current (DC) was passed through a clay-water mixture, the water was induced to move under the electric field effect. Once the electric field was removed, the flow of water immediately stopped. 3

26 Chapter 1: Introduction The electrokinetics phenomenon includes, but is not limited to electroosmosis, electromigration and electrochemical reduction (oxidation). Electroosmosis is the uniform movement of water from the anode toward the cathode as a result of an applied electric potential gradient. Cations move toward the cathode, transporting the pore water, causing a net pore water flow towards the cathode. This process can efficiently dewater a section of soil as well as carry contamination into an extraction area for decontamination processes. The migration of charged ions towards oppositely charged electrodes under the effect of an electrical field is known as electromigration. In this process the positively charged cations move towards the negative electrode (cathode) and the negatively charged anions move toward the positive electrode (anode). These ionic movements are essential when treating soils contaminated with metals, nitrates, chlorides, sulphates and other salts. Electrochemical reduction is the chemical reaction in which atoms can have their oxidation number or oxidation state changed. This reaction changes the chemical make-up of the compounds (salts and contaminants) at the molecular level, readying them for electromigration and movement. The use of electrokinetic methods for agricultural land remediation has not been adequately investigated. There is an urgent need for research in this area. 1.2 First order estimation When selecting a soil remediation technique several factors need to be taken into account. These factors include the effectiveness of the method, the time needed for remediation, practicality and the availability of the technique. However, the treatment cost is a key factor in evaluating the feasibility of any method. 4

27 Chapter 1: Introduction Consider a typical situation with a contamination of 1.5 kg/m 3 of sodium chloride. This translates to an ionic or cationic concentration of 2.5*10 6 C/m 3. Figure 1.1: Simplified decontamination process 5

28 Chapter 1: Introduction Assume: (a) As shown in figure 1.1(a), a contaminated soil sample of cross-sectional area 1 m 2 and length 1 m. (b) Electrodes of area A are located at each end of the soil sample. (c) As shown in figure 1.1(b), during treatment the soil sample conductivity drops from an initial value of σ 0 to a final value of 0.1σ 0. (d) An average ionic mobility of 10-8 m 2 /V.s. (e) An injected current of 5 A. Based on the above: Initial soil conductivity = σ 0 = S/m Remediation time =.. = 4.5*10 5 s/m 3 = 125 h/m 3 Approximate remediation energy =. = 9*10 8 J/m 3 = 250 kwh/m 3 The results of the above analysis could be applied to practical situations. An example is the root-zone drip irrigated vineyard shown in figure 1.2. The combined effects of salt transport by the water away from the root-zone and uptake of water by the plant 6

29 Chapter 1: Introduction result in salt accumulation in a region around each plant at a radial distance of 0.2 m to 0.4 m from the base of the plant. This region is shown in figure 1.3. The accumulated salt per plant for one growing season is estimated to be kg. This estimation is based on the assumption that the water used for irrigation has a salinity level of 4 ds/m. With appropriately designed and placed electrodes and with a current of 5A the estimated remediation time would be about 53.6 hours per plant. An estimate of the energy consumption would be 250 kwh per plant. Figure 1.2: Salt accumulation around root zone drip irrigated plants 600 mm 400 mm Figure 1.3: Targeted remediation area 7

30 Chapter 1: Introduction The above analysis has a number of weaknesses that this research project will address. Firstly the conductivity profile of figure 1.1(b) has no theoretical basis. In other words, during remediation conductivity may not drop uniformly throughout the space between the electrodes. A very non-uniform drop may give rise to much higher remediation energy requirements. Secondly the three-dimensional nature of the problem has been completely ignored. For example, in practice electrodes are of finite sizes giving rise to a three-dimensional distribution of current in the soil. There is also a need to consider how the ionic components of the salt are extracted from the soil once they arrive at the electrodes. 1.3 Aim and objectives The aim of this work is to develop a method to estimate the cost and effectiveness of using electric fields for land remediation. The specific objectives are to: 1. Identify the critical factors affecting ionic transport in soil during electrokinetic remediation. 2. Develop a three-dimensional model to simulate electromigration in soils. 3. Validate the theoretical model by comparison of theoretical predictions with laboratory test measurements. 4. Demonstrate the use of the developed model to predict remediation time and remediation energy requirements. 8

31 Chapter 1: Introduction 1.4 Organisation of the thesis Chapter 2 is a review of the literature on electrokinetic remediation. It includes the basic principles of electromigration and electroosmosis. It is shown that at field capacity moisture content the dominant ionic transport mechanism during the electrokinetic process is electromigration. It is found that understanding of electromigration in soil needs to be improved to allow a useful mathematical model of the process to be developed. The literature review pointed to the existence of concentration or conductivity fronts traveling away from the cathode during the electrokinetic process. Chapter 3 reports on laboratory tests that were performed to verify existence of those fronts. A physical interpretation for the fronts is offered. That physical interpretation forms the basis of a novel theory of electromigration in soils. Chapter 4 presents the development of a mathematical model that is based on the proposed theory. The model is in the form of partial differential equations (PDEs). A simple test performed on a sample of the soil of interest is suggested to determine the parameters required to solve the PDEs. Chapter 5 presents algorithms for one, two and three-dimensional numerical solutions of the proposed mathematical model. It also provides approximate analytical solutions which allow quick estimation of remediation time and remediation energy requirements. Chapter 6 presents a summary and conclusions of the research. Recommendations are made for future work. 9

32 Chapter 1: Introduction 1.5 Summary of outcomes 1. It has been demonstrated that, at field capacity as defined on page (23), and with an injected current density of the order of 5 A/m 2, electromigration is the dominant ionic transport mechanism in soil. 2. It has been demonstrated that if the cathode is effectively washed then the applied electric field causes a concentration front to travel away from the cathode at a speed that is proportional to the current density. The front forms a closed surface which separates two regions: (a) a treated low conductivity region around the cathode and enclosed by the surface and (b) an external untreated high conductivity region. 3. A novel theory has been proposed that explains the existence of the conductivity front. 4. Based on the above theory, a mathematical model has been developed to analyse electromigration in soils. 5. It has been shown that all parameters (such as effective ionic mobilities) that are required to solve the model equations can be obtained by carrying out a simple test on a sample of the soil under investigation. 6. An approximate analytical solution to the electromigration model equations has been derived which allows quick estimation of the remediation time and remediation energy requirements. 7. Reasonably good correlation has been obtained between numerical solutions of the electromigration model equations and laboratory test results. 10

33 Chapter 2: Literature Review 2 Chapter 2: Literature Review 2.1 Introduction In the twentieth century, the practice of irrigation was greatly increased to provide food for the world s growing population. It is estimated that 69 percent of worldwide water use is for irrigated agriculture with 15-35% of irrigation withdrawals being unsustainable. The increasing of requirement for food production will lead to increased usage of more marginal water for irrigation. This may adversely affect the land resulting, for example, in increased salinity of arable land. There is a need to identify and/or develop irrigation methods that can incorporate a range of features such as minimisation water losses, minimisation of energy consumption, careful management of fertiliser usage, salinity control as well as externalities such as environmental impacts. The focus of this research project is to evaluate the potential to use electrokinetic methods for salt management and to develop a theoretical model to understand the electrokinetic process and predict power consumption and soil remediation time. The ability of the electric field to transport water, charged particles and free ions through fine grained soils has been well established since electrokinetic effects were discovered by Reuss in the early part of the 18 th century (Mitchell, 1993). In 1809 Reuss became the first researcher to demonstrate water flow in soils due to electrical application (Mitchell, 1993). In an experiment, water was observed to move through capillary pores towards the cathode when a direct current (DC) potential difference was applied to a clay water mixture. When the electric potential was removed, the flow of water immediately stopped. 11

34 Chapter 2: Literature Review The application of an electric field to a soil environment engages several complex physical and chemical effects. The most important electrokinetic phenomena which will be considered in this research are electroosmosis (Casgrande, 1949, Bjerrum et al., 1967, Shapiro and Probstein, 1993, Segall and Bruell, 1992), electromigration (Cho et al., 2010, Lima et al., 2012, Jia et al., 2005, Kim et al., 2009, Cairo et al., 1996, Athmer et al., 2012) and electrolysis (Acar et al., 1990). Electrokinetics is a powerful tool for transporting ions and charged species into or out of porous materials and it has been used in a wide range of disciplines including civil engineering, environmental engineering, geotechnical engineering and membrane and separation science. Electrokinetic transport processes are utilized in civil engineering for repair and maintenance purposes and in environmental engineering for contaminant removal. The two most well-known methods are desalination of concrete and soil remediation. However, there are also other possible applications such as re-impregnation of wood, desalination of brick masonry, upgrading of fly ash for use in concrete, remediation of harbour sediment and wastewater sludge. Several studies have been performed to assess electrokinetic remediation processes to extract heavy metal ions (Mahmoud and Beaugrand, 2010, Ryu et al., 2009, Reddy and Al-Hamdan, 2008, Li et al., 1996, Pazos et al., 2006), radionuclide (Kim et al., 2003, Korolev, 2009) and mixed inorganic and organic species from soils (Maturi et al., 2009, Reddy and Al-Hamdan, 2008, Szpyrkowicz et al., 2007, Banerjee and Law, 1997). In civil engineering electrokinetic treatment is widely used to improve the shear strength of clays, stabilize slopes (Hamir et al., 2001, Alshawabkeh et al., 2004, 12

35 Chapter 2: Literature Review Chew et al., 2004),, de-water construction sites (Chen and Mujumdar, 2002, Iwata, 2007), desalinate masonry materials (Ottosen et al., 2007), bricks and structures and reduce port construction settlements to tolerable levels (Kamran et al., 2012). Extensive research has been carried out on clay and construction materials (Lefebvre and Burnotte, 2002, Shang and Lo, 1997, Chew et al., 2004, Reddy et al., 2006, Iwata et al., 2007, Zhuang and Wang, 2007, Hu et al., 2010). The use of the electrokinetic process in agricultural application has to some extent been investigated with a focus on improving the salt removal efficiency of subsurface drains, nitrate movement and retention in root zones and improvement of plant growth (Scopa et al., 2009, Wang and Wang, 2004, Cho et al., 2009, Jia et al., 2005, Jia et al., 2006, Ha et al., 2009, Cho et al., 2010, Eid et al., 2000, Ryu et al., 2009). The technique of removing contaminates from soils and waste sites by means of electric fields has attracted considerable attention from industry, academia and government due to its high potential to achieve safe and cost effective in situ remediation. This process is known by several names with the most common currently used being electroremediation, electro-restoration, electro-decontamination and electro-reclamation. This technology relies mainly on the electrokinetic phenomena of electroosmosis and electromigration to collect the contaminants at predefined discharge points. The most important processes involved in the electrokinetic treatment are described in this chapter. 2.2 Transport processes Clay particles are small in size but have a very large surface area. Generally, the surface of clay particles is negatively charged because of the complex arrangement of elements that make up the clay structure. Charge neutrality of clay is due to the 13

36 Chapter 2: Literature Review positive ions present in the soil matrix or the exchangeable cations which are electrostatically attracted to the negative clay surface. The quantity of these exchangeable cations required to balance the surface charge is named the cation exchange capacity (CEC). Consequently, the clay-water-electrolyte system is usually considered to consist of three different regions; i) region of the clay particle with negative charge surface, ii) region of pore fluid with excess positive charge and iii) region of the free pore fluid with zero net charge figure 2.1. Figure 2.1: Distributions of cations and anions adjacent to clay surface (Mitchell, 1993) Flow of fluids, chemicals and energy in various forms can result in soil deformation and instability. The focus of this thesis is to evaluate a particular type of coupled flow involving the flow of water and salts under an applied electrical field. During electrokinetic treatment an electric field is applied across a soil volume, which provides a driving force that may induce a mass movement of particles, similar to the effect of other driving forces, such as pressure gradient, concentration gradient and thermal gradient. Mitchell (1993) indicated that the flow of fluids, electricity, chemicals and heat through soils are created by certain driving forces and some are 14

37 Chapter 2: Literature Review more apparent than others. Provided the flow process does not change the state of the soil, the flow rate J i, is linearly related to its corresponding driving force X i according to J = L X (2.1) where L ii is the conductivity coefficient for flow (Mitchell, 1993) In addition to the above mentioned flow types, there are other flow phenomena induced by an electrical field. Application of the electric field causes three main transport phenomena in soils. These are known as electroosmosis, electromigration and electrophoresis (Probstein and Hicks, 1993, Acar et al., 1995, Alshawabkeh et al., 1999b, Jia et al., 2005). Beside these transport phenomena the migration of the salt ions towards the electrodes regions establish a concentration gradient within the medium and thereby can induce ionic diffusion. 2.3 Principle of electrokinetic soil remediation The electrokinetic soil remediation technology involves the use of a relatively low electrical current density, of the order of several amperes per m 2 of soil crosssectional area, to transport and remove the contaminant species from soils. The application of a low level electrical current will cause the soil water-electrolyte system to undergo physicochemical and hydrological changes leading to contaminant transport and removal. The applied electrical current to soil leads to a number of complex transport processes and electrolytic reactions at the electrodes. From the point view of soil remediation, the processes induced by electrical current can be categorised as electrokinetic and electrochemical. The main transport 15

38 Chapter 2: Literature Review processes caused by an electric current flowing in saturated porous media are described in the following sections. 2.4 Electroosmosis Electroosmosis is the main mechanism of water flow through fine-grained porous media under the influence of an electric field. When an electric potential is applied to soil, water particles are mostly forced to move from the anode towards the cathode because of the electrical potential difference between the negatively charged soil surface and the soil solution (Casgrande, 1952, Acar et al., 1995). A simplified diagrammatic representation of the water movement in a soil by electroosmosis is shown in figure 2.2. Because the electroosmosis driven flow is relatively insensitive to pore sizes, electroosmosis permits a more uniform flow distribution and a high degree of control of the direction of flow (Tallarek et al., 2002). Usually, the electroosmotic flow exists only in fine-grain soils like silts and clays. The flow rate, which is proportional to the electric field strength and the soil features, is typically around 0.1 m/day (Wong et al., 1997) 16

39 Chapter 2: Literature Review Figure 2.2: Principle of electroosmosis through soil (Probstein, 1989) Electroosmosis has been used for soil contaminated treatment and ground improvement since the 1950s. The electroosmosis effect has been extensively used in a variety of civil engineering applications such as acceleration of the consolidation process and the dewatering process of sludge (Bjerrum et al., 1967, Yukawa, 1976, Mohamedelhassan and Shang, 2001). Electroosmosis has also been effectively used for de-watering biomass, wastewater sludges, coal washings and mine tailings which have high water content (Lockhart, 1983a, Banerjee and Law, 1997, Al-Asheh et al., 2004). Dewatering by electroosmosis is a technology that removes water by placing the material that needs dewatering between two electrodes. The water is commonly driven towards the perforated cathodes so that water is collected and can easily flow 17

40 Chapter 2: Literature Review out of the system. Early publications on the principles and applications of electroosmosis dewatering include (Casgrande, 1949, Casgrande, 1952, Bjerrum et al., 1967, Yukawa, 1976, Lockhart, 1983a, Raats et al., 2002). Zhou et al. (2001) investigated the dewatering of activated sludge by the application of a horizontal electric field. The results showed that 60% of the water was removed under an electric field of 1200 V/m and 35% removal was achieved at 400 V/m. For comparison 20% was removed under gravity alone. Shang and Lo (1997) tested the variation of applied voltage on the electroosmosis dewatering of phosphate clay and showed that increasing the applied voltage resulted in an increase in the volume of water removed. Reddy et al. (2006) investigated de-watering of sediment and found that gravity alone produced less than 5% moisture content reductions; while the application of an electric potential of 100 V/m resulted in a moisture content reduction of 35% near the bottom of the sediment sample and 51% at the top of the sediment sample. Al-Asheh et al. (2004) conducted an experiment to concentrate tomato paste suspension using a direct current electroosmotic dewatering technique. The results showed that, 38% of water was removed with an applied voltage of 500 V/m and 19% was removed at an applied voltage of 250 V/m. They reported that the process saved 70% of the energy compared with that necessary to vaporize the same amount of water. Shapiro and Probstein (1993) investigated the feasibility of using electroosmosis for purging contaminations from saturated clay. The results showed that the electroosmotic process is very effective in achieving at least 94% removal of 18

41 Chapter 2: Literature Review contaminants from the clay with measured energy costs about $2/ton of effluent removed Electroosmosis theory Among several theories explaining electroosmosis, the Helmholtz and Smoluchowski theory, which was originally proposed by Helmholtz in 1879 and later refined by Smoluchowski in 1914, is the most commonly accepted (Mitchell, 1993). The theory states that in water-filled capillaries of a wet fine-grained soil there exist two layers, the first layer is negatively charged and rigidly bound to the capillary wall and the second layer is made up of cations loosely held to the first. When two electrodes are positioned in soil mass and an electrical current is passed between them the positively charges ions (cations) are attracted to the cathode and it is accompanied by water movement in the same direction. Electroosmosis-induced water flow rate caused by the application of a voltage gradient for practical purposes is described by an equation analogous to Darcy s law (Casgrande, 1949, Bjerrum et al., 1967, Alshawabkeh et al., 1999a), = (2.2) Where indicates the electroosmosis-induced water flow rate (m 3 /s), is the coefficient of electroosmosis permeability of soil (m 2 /V.s), E is the electric field gradient (V/m) and is the cross-section of the treated volume (m 2 ) Electroosmosis permeability coefficient The rate of the electroosmosis-induced water flow is mainly controlled by the very important parameter named electroosmosis permeability coefficient of the soil 19

42 Chapter 2: Literature Review (, m / V. s) which is directly proportional to the Zeta potential of the soil-pore fluid interface ζ (V), the dielectric constant of the pore fluid D (dimensionless), the soil tortuosity (dimensionless), the soil electrical permittivity (C 2 /N.m 2 ) and soil porosity (dimensionless), while it is on the other hand inversely proportional to the viscosity of the pore fluid (N.s/m 2 ) (Banerjee and Law, 1997, Arnold, 1973): =.. (2.3) The electroosmosis permeability coefficient depends on the soil type and ranges between 1*10-8 m 2 /V.s and 1*10-9 m 2 /V.s for fine-grained soils (Mitchell, 1993). However, Casgrande (1949) suggested that, for practical purposes the could be assumed as a constant with value of 5*10-9 m 2 /V.s for most soils. Acar et al. (1994) referenced values for from 1*10-8 to 1*10-10 m 2 /V.s, the higher values being in fine-grained soils. However, Acar et al. (1994) in their experiments found the value of the varied in the range of 1*10-9 to 1*10-11 m 2 /V.s for Georgia Kaolinite. Table 2.1 shows some typical values of the coefficients of electroosmotic permeability ( ) of some different soils (Mitchell, 1993, Alshawabkeh et al., 2004). 20

43 Chapter 2: Literature Review Table 2.1: Coefficients of electroosmosis permeability (Mitchell, 1993) No Soil Type K e (m 2 / V. s) 1 London Clay 5.8* Boston Blue Clay 5.1* Kaolin 5.7* Clayey silt 5.0* Rock Flour 4.5* Na-Montmorillonite 2.0* Mica powder 6.9* Fine Sand 4.1* Quartz powder 4.3* As quick clay * Bootlegger Cove clay * Silty clay, West Branch Dam * Clayey silt, Little Pic River, Ontario 1.5*10-9 Beddiar et al. (2005) experimentally found that the electroosmosis permeability coefficient is ph dependent and derived the following empirical relation: = (2.4) where: α= ± m 2 /V.s β = ± m 2 /V.s γ =8.9±2.8 21

44 Chapter 2: Literature Review Figure 2.3 presents the variation of electroosmosis permeability coefficient when ph changes in a range from 4 to 10 units according to the equation 2.4. The plot illustrate that the electroosmosis permeability coefficient varies in a narrow range. Since the electroosmosis is of importance to this research project and the electroosmotic flow is governed by the electroosmotic permeability coefficient of the soil, a pilot-scale experiment was performed in the laboratory to measure this important parameter. Figure 2.3: Variation of electroosmosis permeability with ph value Hydraulic gradient and matric suction development during electroosmosis Water flows due to the applied electric potential gradient and the existing hydraulic gradient. Darcy s law governing the flow of liquid through a porous medium due to a hydraulic gradient (Lewis and Humpheson, 1973) is given by: 22

45 Chapter 2: Literature Review =. H (2.5) where denotes the seepage velocity due to hydraulic gradient (m/s), is the hydraulic conductivity tensor usually of the order of 1*10-9 (m/s) and H is the hydraulic head gradient. On the other hand, the electroosmotic flow of the liquid through a porous medium due to a voltage gradient is governed by the following equation (Casgrande, 1949, Lewis and Humpheson, 1973): =. (2.6) where denotes the electroosmotic velocity (m/s), is the electroosmosis permeability coefficient (m 2 /V.s) and E is the electrical potential gradient (V/m). Superimposing electroosmotic and hydrodynamic flows we get: = + (2.7) Substituting equations (2.5) and (2.6) into equation (2.7): = + (2.8) where denotes the total flow due to voltage gradient and hydraulic gradient. In fine-grained soils, the flow of water under the effect of electroosmosis is highly significant when compared to the flow of water due to a hydraulic gradient. An example will elucidate the relative importance of electroosmosis flow compared to the flow caused by a typical hydraulic gradient. Consider the hydraulic conductivity data collected from experimental work performed on thirteen different clays which showed that the value of is about 1.3*10-10 m/s at field capacity which defined as the amount of soil moisture remaining in the soil after free excess 23

46 Chapter 2: Literature Review water has drained away (Benson and Trast, 1995). The electroosmosis permeability of clay is assumed to be 5*10-9 m 2 /V.s. For equal flow rates: = If an electric potential gradient of 50 V/m is applied then: = = Therefore, the electroosmotic flow produced by an electrical potential gradient of 50 V/m can oppose the flow of water caused by hydraulic gradient of Since this value is orders of magnitude greater than what the hydraulic gradient would normally be, it is concluded that at or near field capacity moisture content with an electric potential gradient of 50V/m hydraulic flow is negligible compared to electroosmotic flow. The development of excess pore water pressure or suction is the result of either different flow boundary conditions or non-uniform driving force between the electrodes (Eykholt, 1997, Esrig, 1968, Alshawabkeh et al., 2004). Esrig (1968) stated in his electroosmosis consolidation model that under ideal conditions no excess pore water pressure will be generated in the case of open boundaries. The four basic drainage boundary conditions and the corresponding final steady state pore pressure for a linear potential gradient are illustrated in figure 2.4 (Butterfield and Johnston, 1980, Esrig, 1968). In figure 2.4(a) water excess at the cathode with a closed anode, the electroosmosis induced water to flow away from the anode which causes a corresponding reduction in pore pressure from the anode producing a negative excess pore pressure. This, in 24

47 Chapter 2: Literature Review turn, would create a hydraulic gradient, working in the opposite direction to electroosmosis flow. Ultimately, this induced hydraulic gradient becomes large enough to cause pore water flow to stop and equilibrium is achieved. In figure 2.4(b), both the anode and the cathode are open and the water moving by electroosmosis to the cathode region is replaced at the anode, so that there is no change in pore pressure. Figure 2.4(c) presents the condition where the cathode is closed and water is provided at the anode. In this case the soil will be over saturated developing a positive pore pressure at the cathode which will produce a hydraulic gradient that eventually prevents further water flow. Figure 2.4(d) illustrates the boundary condition where both anode and cathode are closed, so that the electroosmosis produces a redistribution of pore water with a drying anode region and saturation in the cathode region. In soil remediation applications open fluid flow boundaries are usually implemented. In this project the open boundary and field capacity moisture content will be adapted to eliminate the effect of pore pressure and hydraulic conductivity. As illustrated in the example above, the hydraulic gradient is relatively small compared to electrical gradient and may be neglected. The author assumed that the hydraulic gradient is non-significant because the soil moisture content has to be close to field capacity. In other words at that level of moisture the hydraulic gradient is practically zero. 25

48 Chapter 2: Literature Review conditions (Butterfield and Johnston, 1980) Figure 2.4: Variation of pore water pressures for one-dimensional electroosmosis with given boundary conditions 26

49 Chapter 2: Literature Review 2.5 Electromigration Electromigration is another transport mechanism generated by applied potential difference across an electrolytic solution. Electromigration is defined as movement induced by the electric field of dissolved salt ions in the pore solution. The charged ions will migrate toward opposite electrodes. The positive ions (cations) will migrate towards the cathode while negative ions (anions) are transported towards the anode as shown in figure 2.5. Electromigration is the major transport process for ions and the degree of the electromigration depends on the mobility of the ionic species involved. Kim et al. (2005a) reported that the electromigration of different ions toward the opposite electrodes is proportional to the ion concentration in the pore water solution and the intensity of the electric field. Figure 2.5: Electromigration of ions (adapted from (Acar et al., 1994)) Cho et al. (2009) conducted a laboratory-scale experiment to investigate the movement and removal of salts in greenhouse soil under an electric field. The water 27

50 Chapter 2: Literature Review content of the soil sample was approximately 30% w/w. The results showed salt removal efficiency depends on salt type with the highest percentage removed deing 82% nitrates (due to their high solubility) and the lowest percentage was 50%, achieved for chloride and sulphate ions. Cairo et al. (1996) conducted an electromigration experiment to concentrate and remove nitrates from contaminated soil. The results obtained showed that nitrate concentration in saturated soil tended to increase from anode to cathode after the application of electrical field. Likewise, Eid et al. (2000) conducted a laboratory soil column experiment to investigate nitrate migration in sandy soil using a constant current of 3 ma. Electromigration was found to be an effective means for concentration and retaining nitrates close to the anode. Lindgren et al. (1994) evaluated in situ remediation by measuring the migration of anionic food dye ions through unsaturated sand under constant current conditions at gravimetric moisture contents ranging from 4 to 27 %. The results showed a highest migration rate at moisture content between 14 and 18%. Mattson and Lindgren (1995) designed an electrode system to remove water soluble chromium from unsaturated soils. The results showed that by applying a 10 ma constant current for a period of eight days, 88% of the chromate was removed from the unsaturated soil near the anode Electromigration theory The ionic mobility is defined as the average velocity of a charged species when a force of one N/mol is applied and its unit therefore is mol/kg. The values of ionic mobility in dilute solution, that is the velocity of the ions under the influence of 28

51 Chapter 2: Literature Review electric field are in the range of 3*10-8 to 1*10-7 m 2 /V.s except for H + or OH, which have mobilities one order of magnitude greater (Page and Page, 2002). However, (Wise, 2000) stated that the effective ionic mobility of heavy metals is usually in the range of 10-9 to 10-8 m 2 /V.s, which causes a migration rate of a few centimetres per day under a voltage gradient of 100 V/m. The major influences on electromigration during electrokinetics treatment are the local electric field strength, the mobility of the species and the charge concentration of ionic species present. Generally, electromigration is the predominant transport mechanism in soils under an electrical gradient (Alshawabkeh et al., 1999a). The ionic mobility is greater than the electroosmosis permeability, in other words the velocity of electromigration of the ions is typically higher than electroosmosis flow rate and is not directly affected by variation in zeta potential of the soil. Therefore during electrokinetic treatment the anions can migrate toward the anode despite being transported in the opposite direction by the electroosmosis flow (Denisov et al., 1996). The ratio of electromigration flux to electroosmosis flux is approximately (Sullivan, 2008). As part of this current research, some initial experiments were performed to compare the ionic mobility and the electroosmotic permeability of the soil type being investigated. Details of these experiments and their results are presented in the appendix. It was found that the ionic mobility rate was typically two orders of magnitude higher than the electroosmotic permeability resulting from the same electric field gradients. On the other hand, the ionic mobility of salt ions is at least one order of magnitude higher than the diffusion coefficient of the same ion. 29

52 Chapter 2: Literature Review The flux of salt ions through a bulk solution during the electromigration process is governed by following relationship (Kamran et al., 2012): = (2.9) where: = the migration flux of salt ions (mol /m 2.s) = the mobility of ions in the electrolyte solution (m 2 /V.s) C = the ionic concentration in electrolyte solution (mol/ l) V = the total applied voltage (V) In contrast the ion migration in soils is restricted by the effective ionic mobility which accounts for the soil porosity, soil tortuosity and longer paths in the soil (Jia and Buffalo, 2006). Hence, the electromigration for a soil medium can be described by: = (2.10) where is the effective mobility of the particular ion in soil (m 2 /V.s) However, the effective ionic mobility can be theoretically estimated by using the Nernst-Townsend-Einstein relation. Consequently, the effective ionic mobility of a specific ion is a function of its molecular diffusion coefficient, soil porosity, soil tortuosity factor and charge as follows (Probstein and Hicks, 1993): 30

53 Chapter 2: Literature Review =.. =... (2.11) where: = the diffusion coefficient (m 2 /s) Z = the charge number F = the Faraday s constant = (C/ mol) R = the universal gas constant= (J /K mol) T = the absolute temperature (K) 2.6 Electrophoresis The electrophoresis phenomenon is a combination of the movement of charged particles and colloids under the influence of an electric field (see figure 2.6). Similar to electromigration when a DC electric field is applied across a colloidal suspension, positively charged particles and colloids tend to move toward the cathode and negatively charged particles and colloids are induced to move toward the anode. As the colloids and the charged particles are of a distinct size, electrophoresis can take place only if pore sizes are large enough. Li et al. (1996) stated that the electrophoresis should be of limited importance since the solid phase is restrained from movement. Therefore, electrophoresis is less important than electroosmosis and electromigration in terms of mass flux. Although in some cases, electrophoresis may play a role in decontamination if the migrating colloids have the contaminants adsorbed on them. 31

54 Chapter 2: Literature Review In the research reported in this dissertation, the assumption is made that none of the pore water constituents tend to form a colloidal electrolyse, therefore electrophoresis plays no role in the electrokinetic transport process and is not included. Figure 2.6: Electrophoresis phenomenon in soils 2.7 Diffusion Diffusion is defined as the transport of ions under the effect of a concentration gradient. Fick s first law of diffusion was originally formulated by Adolf Fick in It can be used to describe the flux of dissolved ions in free solution: = (2.12) where = the flux of ions resulting from diffusion (mol /m 2. s) = the diffusion coefficient (m 2 /s) 32

55 Chapter 2: Literature Review In porous materials like soil the salt ions do not diffuse freely and their diffusion rates are constrained by the porosity and tortuosity of the soil. In addition, the electrical or chemical interaction of the material with the pore solution could also affect the diffusion rates. For non-reactive porous materials the diffusion can be described by: = (2.13) where represents the effective diffusion coefficient for a given porous material (m 2 /s). This effective diffusion coefficient is given by: = (2.14) The diffusion coefficient of the major cations and anions in water are in the range of 10-9 to m 2 /s. Diffusion has been considered by some researchers in their work on electrokinetic processes in soil whereas others have ignored it. As part of this work some initial experiments were performed specifically to investigate the importance of diffusion. Details of these experiments and their results are presented in the appendix. It was found that diffusion rates due to very high imposed concentration gradients were at least an order of magnitude lower than ionic flow rates due to electromigration resulting from an electric field of 100 V/m. 2.8 Electrochemical reaction The application of an electrical field during electrokinetic treatment produces ionic species and changes the soil ph due to electrochemical reactions at the electrode boundaries. In the case of inert electrodes oxidation of water occurs at the anode which generates hydrogen ions (H + ). In contrast, reduction of water occurs at the 33

56 Chapter 2: Literature Review cathode which generates hydroxyls ions (OH ) (Acar and Alshawabkeh, 1993). This generation process is necessary to maintain the charge neutrality in the system. At the anode (oxidation), 2H O 4e 4H + O (2.15) and, at the cathode (reduction), 4H O + 4e 4OH + 2H (2.16) Equations 2.15 and 2.16 indicate that H + and OH ions are generated at an identical rate at the anode and cathode although the amount of water reduced at the cathode is twice that oxidized at the anode. Generally, the generation of H + ions will develop an acidic region at the anode that will advance through the soil towards the cathode by different transport mechanisms including pore fluid flow due to electroosmosis, diffusion due to concentration and migration due to electric gradients. In contrast, the base environment generated at the cathode region due to production of OH will move towards the anode by migration and diffusion. The advance of the acid front is faster than the advance of the base front unless the H + transport is not obstructed by the soil buffering capacity. The advance is due to the counteracting electroosmotic flow and also because the ionic mobility of H + is about 1.76 times that of OH. It can be concluded that the migration of the acid and base is strongly affected by the initial soil ph as well as the buffering capacity of the soil, which means neutralisation of H + ions. 34

57 Chapter 2: Literature Review In a soil containing NaCl as the electrolyte solution an oxidant agent such as chlorine (Cl 2 ), hypochloric acid (HClO) and hypochlorite ions (ClO - ) will be generated as a result of NaCl electrolysis (Szpyrkowicz et al., 2007): (2.17) (2.18) + (2.19) The formation of the active chloride species (Cl 2, HClO and ClO ) causes an increase in redox potential of the solution and may enhance the treatment process (Szpyrkowicz et al., 2007). In soil treatment, the generated oxidant agents (OH, Cl 2, HClO and ClO ) near the electrodes will diffuse within the soil profile. The mobility of these oxidant agents is known to be limited in fine grain soils due to the low permeability of the soil and the short lives of these chemical species (ITRC, 2005, Szpyrkowicz et al., 2007). 2.9 Factors affecting electrokinetic processes Electrode type Electrodes are made of electrically conducting material and used to pass or transmit electric current to a predetermined location. The electrodes are made in various forms such as wires, plates or rods and they may be fabricated of metals such as lead, copper or zinc. However the electrodes may also be constructed of a non-metallic substance such as carbon. Generally in electrokinetic applications the most favoured 35

58 Chapter 2: Literature Review electrode materials are those having low resistance and minimum voltage drop at the soil-electrode interface while resisting corrosion. Historically, steel/alloy metal plates, tubes and wires have been used to pass current into the ground to act as the electrodes. Recently, the interest has shifted towards the implementation of other types of conductor materials such as copper, stainless steel, zinc, graphite and titanium coated with a mixed metal oxide due to their high electrical conductivity and easy installation (Chen et al., 2002, Lockhart, 1983b). Materials used for electrodes must be as conductive as possible to minimize the electrical resistance and energy consumption. A copper electrode is one of the most commonly used electrodes due to its high electrical conductivity and low cost. Nettleton et al. (1998) also recommended the use of copper as it restrains the generation of oxygen gas at the anode by forming copper oxide which is also a good conductor. However, the tendency of copper to corrode may cause it to break during the treatment process consequently reducing efficiency. The high electrical conductivity of graphite materials and its good chemical stability are attractive features for its use as electrodes (Ermolenko, 1990). The ability of different electrode materials to transfer electrical charge efficiently to the soil has been studied by Mohamedelhassan and Shang (2001) (see Table 2.2). These results support the use of metallic electrodes in laboratory investigations. However, usage of metallic electrodes during electrokinetic soil treatment results in corrosion problems due to electrochemical reactions (Bjerrum et al., 1967). Consequently, the effectiveness of the process may decrease and there may be an associated loss of contact between the electrode and adjacent soil. Bjerrum et al. 36

59 Chapter 2: Literature Review (1967) reported that corrosion led to significant voltage drops between 25-50% of the applied voltage at the electrodes. Table 2.2: Electrode materials and voltage transfer (Mohamedelhassan and Shang, 2001) Cathode Carbon Steel Copper Anode Carbon Steel Carbon Steel Carbon Copper Applied Voltage (V) Voltage drop at anode-soil interface (V) Voltage drop at cathode-soil interface (V) Effective voltage (V) carbon or graphite cathodes are commonly preferred because they exhibit oxygen reduction, hydrogen evolution and low catalytic tendencies (Meinero and Zerbinati, 2006). In this work, stainless steel electrodes were examined in preliminary tests described in section A.3.2 of the appendix, but there was significant corrosion during the initial tests. Thereafter, inert carbon electrodes were chosen as operating electrodes in order to overcome corrosion problems, for ease of fabrication and to avoid the introduction of any secondary products due to the electrolytic reaction. 37

60 Chapter 2: Literature Review Applied voltage Appropriate design and application of the systems to efficiently induce the electrokinetic processes has been the interest of several researchers. Laboratory investigations commonly use low voltage at the beginning gradually increasing to a maximum over a period of time, while the current is kept constant or nearly constant. In contrast, a pre-calculated voltage can be applied right from the start and maintained constant throughout the duration of the treatment process. Shang and Dunlap (1996) used a voltage gradient ranging between 39 and 107 V/m and they achieved slightly better performance with increasing voltage gradient. Voltage gradients of 15 V/m and 30 V/m were used by Lo et al. (1991) to illustrate that electrokinetic soil consolidation was very similar to that of typical conventional consolidation under mechanical loading. The voltage gradient applied to the soil should not exceed about 50 V/m to avoid energy losses and the heating of the soil (Casgrande, 1949). Nevertheless, Shang and Dunlap (1996) and other researchers have applied voltage gradients as high as 200 V/m before noticing extreme heating of the soil. Shang and Dunlap (1996) reported that physical and electro-chemical effects due to very high voltage gradients were not beneficial to the electrokinetic process. This reduction in the efficiency of the treatment process is demonstrated in the decrease in current and electroosmotic permeability with the application of high voltage gradients. Lockhart (1983c) showed that the higher the voltage the faster the dewatering. In comparing with the condition of constant electric current, Yoshida (1980) reported that a constant voltage condition produced a higher water removal for the same amount of energy consumption. 38

61 Chapter 2: Literature Review Chew et al. (2004) observed during the field trial that there should be sufficient voltage gradient to initiate the electrokinetic process. At the beginning of the field trial the predesigned voltage gradient was just 25 V/m with a single generator and the monitored current was found to be too small and no electrokinetic was initiated. Thereafter, the number of generators was increased to four to increase the applied voltage gradient to 100 V/m. The monitored current was then found to be much higher and signs of electrokinetic became apparent. Hence, the application of adequate voltage gradient is a significant aspect of the design of the electrokinetic systems. Safety is also an important consideration. Thus, there is necessity for risk assessment when designing and operating electrokinetic systems. During the electrokinetic operation, faults may occur creating hazardous situations. Hence, any earthing system the significance of step and touch potentials need to be considered Electrical conductivity of soils The resistivity of the soils is based on several factors, among which are the properties of the soil, initial moisture content and the type and concentration of ions existing in the soil. Soil conductivity is commonly expressed in unites of Siemens per meter (S/m). Typical values of soil conductivity are about 10 to 500 ms/m for uncontaminated clays and 0.1 to 5 ms/m for sand and gravels (Samouëlian et al., 2005). During the electrokinetic treatment process the specific conductivity of the soil changes with the change of water content, cation exchange capacity, the free electrolyte content of the soil and the prevailing chemistry (Acar and Hamed, 1991 & Gray and Mitchell, 1967). Generally, when constant voltage mode is adopted the resulting current flow will decrease with time because of the formation of a high 39

62 Chapter 2: Literature Review electric resistivity zone near the cathode, due to the ions extraction by electromigration. For soil-water systems the electrical conductivity is a function of the pore fluid composition, porosity, degree of saturation, surface conductance of the particles, the shape and orientation of the particles, temperature, and pressure (Sadek 1993). In electrokinetic processes the variation in electrical conductivity of the soil can be explained as a result of ion migration and moisture content variation. A mathematical model relating electrical conductivity and electrolyte concentrations of a fluid is presented in Yeung et al. (2011): = ɀ (2.20) where is electrical conductivity of the liquid (S/m), C i is concentration of species i (moles/m 3 ), µ is ionic mobility of species i (m 2 /V.s), F is Faraday's constant and ɀ represents the charge per ion of species i. Thus, the bulk electrical conductivity of contaminated soil could be calculated by = + (2.21) where σ o is represents the initial conductivity of the uncontaminated soil-water mixture which can be obtained experimentally Coupling phenomena Several researchers have conducted electrokinetic tests on soil samples and have proposed theoretical transport models for ions or soil water. Some have focused on 40

63 Chapter 2: Literature Review the electroosmotic phenomenon in consolidation applications while others have explicitly considered electromigration, diffusion and electroosmosis in applications such as remediation or decontamination. Initial electrokinetic models were developed for analysing enhancement of soil stability in the civil engineering field, focussing on electroosmotic water movement and ignoring electromigration. Esrig (1968) developed an electroosmotic model for clay soils. This model was developed for the analysis of consolidation and dewatering of soil which directly affects the soil electrical resistivity thus affecting the electrical potential gradient. The work presented by Esrig assumed that the electrical potential gradient did not change with time during the operation. That assumption is in contradiction with the fact that conductivity does change with time and with position from the electrodes. However this conductivity change may not affect Esrig s findings on the overall amount of pore water removal by electroosmosis. Lewis and Garner (1972) developed a two-dimensional model for studying aquifer de-watering applications. They simulated the water flow by coupling electroosmosis and advection hydraulic flow but ignored other interaction phenomenon including electromigration and chemical reactions during the process. Again their assumption of constant electric potential gradient is in contradiction with what happens in practice. A general model of contaminate removal by electroosmosis has been developed by Shapiro and Probstein (1993). This model includes equations representing electroosmotic convection, diffusion and chemical equilibrium. Chemical reactions are also included to characterise the transient behaviour of concentration fields for a 41

64 Chapter 2: Literature Review group of chemical species in solution that are transported by the combined effects of electroosmotic convection, ion migration and diffusion in an electric field. Predictions based on the model were compared with experimental data for the case of constant applied voltage. Good agreement was observed only in the case of acetic acid removal from Kaolinite soil. In this case, both the model and the experiment showed the development of a sharp concentration fronts during the process. Other experimental data for the case of phenol contamination did not show good agreement with model results. It appears that this model does not explicitly enforce electric charge neutrality. Alshawabkeh and Acar (1996) developed a comprehensive model which incorporates changes in pore water pressure and suction that develop during electrokinetic metal precipitation. The model also accounts for changing electric potential gradient but does not account for the changes in soil ph and pore fluid chemistry. Soil parameters, proportionality constants and coefficients needed for the model were either obtained from test data nor available literature. Electric potential gradient predicted by the model did not show good agreement with experimental results suggesting some of the assumptions may be questionable. However, they demonstrated acid and base fronts advancing toward each other across the electrokinetic cell. The rate of acid fronts advanced toward the cathode was faster than the transport rate of the base front toward the anode which allowed the acid front to neutralize the alkaline medium developed at the cathode. Mahmoud and Beaugrand (2010) presented a two dimensional mathematical model for simulation of removal of heavy metals from contaminated soils using an electrical field. The model describes the coupling transport of mass and charge. This 42

65 Chapter 2: Literature Review model considered electroosmosis, pressure driven convection, electromigration and diffusion. The model presents the total flux of an individual species as: = + + (2.22) where: = total flux of species (mol/m 2.s) = effective ionic mobility of the species in soil (m 2 /V.s) = permeability coefficient (m 2 /Pa.s) = pressure gradient (Pa/m) The computer model was based on COMSOL multiphysics. Difficulties were experienced in finding the solution. The authors explained that the cause of the problem was the interaction between the transport of mass and charge and the development of thin boundary layers of high localized electrical potential gradient which results in numerical stability problems. The authors introduced an artificial diffusivity factor of 1000 which was added to the diffusion coefficient used. This helped to stabilize the model. No experimental verification was carried out. It would appear that the requirement of the artificial diffusivity factor would make their model unrealistic. Kamran et al. (2012) developed a one-dimensional model to simulate the desalinisation of building materials by the electrokinetic method. The model presents the total mass flux of ions through a porous material under the combined effect of electromigration, advection and diffusion as: 43

66 Chapter 2: Literature Review = + + (2.23) where: = the effective mobility of a particular ion (m 2 / V.s) = the effective diffusion coefficient of a particular ion (m 2 /s) = the volumetric flux caused by a hydraulic gradient (m/s) = the molar concentration of ions (mol/l) They concluded that the salt ions removal rate is proportional to the applied electrical field across the porous material. An interesting observation, as shown in figure 2.7, is the existence of ionic concentration fronts travelling from the electrodes. Although this was reported, they did not offer a physical interpretation for it. The other limitation of their work is that they considered a treatment time of only three and a half hours. Figure 2.7: Na concentration profiles during electrokinetic treatment 44

67 Chapter 2: Literature Review Denisov et al. (1996) provide an analytical solution to the one-dimensional multispecies electrokinetic transport problem in soils. The purpose of this model was to draw a conceptual picture for the whole electrokinetic process. It took into consideration the change in electric potential gradient and electrical charge neutrality was imposed. In order to obtain the analytical solution many assumptions were made. The porous specimen is assumed to have a planar geometry and to be practically uncharged and chemically inert. Therefore the influence of both electroosmosis though the pores and adsorption of species at the pore wall are neglected. The model was further simplified to consider electromigration only, which they stated to be the most important driving force for influencing transport of charged contamination species. Their analytical expressions predicted variations in the soil conductivity that were consistent with their experimental results. Given that they mention an acidic front travelling from the anode and a basic front travelling from the cathode, it would appear that their model is limited to a closed system. Jacobs and Probstein (1996) developed a multi-dimensional electrokinetic model to predict ionic migration in a saturation porous medium. Their two-dimensional model accounts for electroosmosis, electromigration, hydraulic advection and diffusion value as well as chemical reactions. However they had to use an artificial diffusivity to stabilise their model and achieve convergence during simulation of phenol removal from homogeneous clay. In this case, they obtained reasonable agreement between predictions and measurements from physical tests. However, there is no evidence or mention of concentration fronts and the introduction of an artificial diffusion factor to reach a solution raises doubt regarding the validity of the theoretical predictions. 45

68 Chapter 2: Literature Review Mattson et al. (2002) developed an electromigration transport model for ion transport in unsaturated soil. They assumed constant electric potential gradient and constant moisture content with respect to operation time. They also simplified the model by neglecting the effect of electroosmosis and hydraulic transport. The numerical model was tested against laboratory experiments. It did not accurately predict acetate ion transport in soil samples Summary This literature review has revealed the following: (a) There has been a substantial amount of research work done on electrokinetic induced mass and ionic transport in soil. The work that has been done is mostly focused on specific applications such as soil consolidation and soil decontamination. (b) Most of the published works involve experimental observations without any theoretical framework in the form of mathematical models that would be suitable for the objectives of this research project. (c) The few attempts that have been made to mathematically model electrokinetic processes in soils have a number of limitations. Some are strictly one-dimensional and will not be appropriate for this project due to the wide variation of the parameters that have been used. There are others that are three-dimensional but there is doubt about their validity because they required an artificial diffusion factor to converge and they do not seem to predict the movement of concentration fronts that have been observed in practice and that are characteristic of electrokinetic processes in soil. 46

69 Chapter 2: Literature Review (d) There is evidence and agreement among a number of researchers that at high enough moisture content and at high enough applied electric potential gradient electromigration is the dominant form of ionic transport in soil. (e) Although concentration fronts during the electrokinetic process have been observed by a number of researchers, there has been no explanation or physical interpretation of them. Based on the above findings the following have been addressed in this thesis: (a) A set of one-dimensional experiments specifically designed to find a physical interpretation for the existence of concentration fronts during electrokinetic processes in soil (Chapter 3). (b) Development and validation of a mathematical model for electromigration in soil based on the physical interpretation of the existence of concentration fronts (Chapter 4). (c) Prediction of performance of practical soil remediation systems that are based on electromigration (chapter 5) 47

70 Chapter 3: One Dimensional Laboratory Tests 3 Chapter 3: One-Dimensional Laboratory Tests Three dimensional analysis is essential to address the objectives of this work. However, 3-D model needs to be based of adequate understanding of the electrokinetic phenomena. The 1-D tests presented in this chapter helped achieve this understanding. In addition, as will be demonstrated the 1-D test allows determination of parameters needed for 3-D modelling. 3.1 Introduction The aim of this work was to carry out laboratory tests that would help develop a onedimensional model of electromigration. The objectives of the tests included confirming the existence of sharp concentration fronts and identifying the conditions under which electromigration becomes the dominant ionic transport mechanism. General information about the tests is provided in section 3.2. Test results are reported in section 3.3. The main findings and a discussion of those results are presented in section 3.4. A theoretical explanation for the existence of the sharp concentration fronts is proposed in section 3.5. The development of a mathematical model in the next chapter is based on the key outcomes of this chapter. 3.2 General explanation of tests performed Electrokinetic cell setup Figure 3.1(a) shows the schematic of the electrokinetic test setup used for all the tests performed in the laboratory. The setup consisted of a PVC cylinder of length 500 mm and diameter 65 mm. For easy soil sampling the cylinder is divided into five equal sections attached to each other by PVC tape to prevent any leakage of water 48

71 Chapter 3: One Dimensional Laboratory Tests (figure 3.1(b)). The two ends of the cylinder were closed with a removable cap. Two inert perforated electrodes fabricated from carbon sheet material were used for both anode and cathode to prevent participation of the electrodes in chemical reactions that would complicate the electrokinetic process. On the cathode side, as shown in figure 3.1(a), a small water collection chamber exists between the removable cap and the perforated electrode. Water accumulated due to electroosmosis can be drained through a rubber tube attached to the bottom of the chamber. The programmable DC power supply (Sorensen XHR DC 1020W) used for all the tests was capable of delivering up to 1.7 A at a voltage of up to 600 V. It could be used either in the constant current mode or in constant voltage mode. A data acquisition system (Agilent Data Acquisition systems) was used for continuous monitoring of the electrical potential distribution across each soil section and the current through the soil mass. Figure 3.1: Electrokinetic set-up (a) sketch of electrokinetic experiment set-up (b) soil column sections and (c) anode and cathode segments 49

72 Chapter 3: One Dimensional Laboratory Tests Soil preparation Two soil types were used. A fine washed sand was obtained from a commercial landscape provider and mm surface of a Red Ferrosol from the university of Southern Queensland Agriculture field station, Toowoomba. Prior to testing each soil sample was crushed to pass through 2 mm sieve and dried in an oven at 105ºC for 24 hours. The required amount of sodium chloride (NaCl) that would yield the desired concentration of salt in the soil was weighed and dissolved in distilled water. This saline solution was then sprayed on the soil and mixed thoroughly by hand in a high density polyethylene (HDPE) container. HDPE is the most chemically inert plastic that is readily available. The mixture was then allowed to equilibrate for at least twenty four hours to achieve improved uniformity of contaminant concentration. The initial soil conductivity and ph were measured and recorded. All the tests were performed with initial moisture content at field capacity Soil analysis methods After the electrokinetic application, the soil was removed from the experimental setup and sliced into five equal sections. The soil sections were oven dried for 24 hours at 105ºC and the water content determined gravimetrically. As shown in figure 3.1(c) the sections nearest to the electrodes were further sliced into 4 equal segments of 25 mm. Measurements were carried out on samples from the eight end segments and the three middle sections to determine final electrical conductivity (EC), ph, and sodium ion concentration at different distances from the anode. Chemical analysis of the treated soil was performed on samples taken after drying and homogeneously mixing the entire soil volume collected from each soil column section or segment. The soil EC and ph were measured using the 1:5 soil water suspension method and 50

73 Chapter 3: One Dimensional Laboratory Tests a combined conductivity and ph meter (LabCHEM-CP-Cond/pH probe version 1.01 TPS Pty Ltd, Brisbane). Triplicate samples of eight grams of soil were carefully weighed and suspended in 40 ml of distilled water, shaken well for one hour by an electrical shaker and allowed to settle for 20 to 30 minutes. The suspension was separated by centrifugation at 3000 rpm for 10 minutes. The supernatants were introduced into an atomic absorption spectrometer (AAS) analyser (Shimadzu AA- 7000) and ion chromatography system (IC) analyser (DIONEX ICS-2000) for the determination of residual Na + and Cl concentration in the soil. In addition to the above measurements, tests were also performed on water samples collected by micro suction approximately every twenty-four hours during the treatment. The suction points are shown in figure 3.1(a). This allowed the sodium ion concentration profile to be tracked during the electro-kinetic treatment. 3.3 Tests results The results of a series of 1-D tests are presented in this section. In general each test was designed to satisfy a specific aim which was part of the overall project methodology. However, initially, only limited interpretation of the results was possible because of the multiplicity of interacting factors. As more tests were performed and their results analysed, the processes resulting from current flow in the soil became better understood. The test results guided the development of a novel theoretical representation of electromigration in soil. Detailed explanations of the logical relationship between the test results and the proposed theory will be presented in the next section. 51

74 Chapter 3: One Dimensional Laboratory Tests The purpose of this section is to present the test results of a number of experiments and to provide a brief statement on the initial motivation for carrying out each experiment. Test 1 Sandy soil treatment with constant voltage of 50V The main intention of this test was to verify the existence of conductivity and concentration fronts travelling away from the cathode. The main test conditions were: Sandy soil with initial moisture content equal to 10% w/w Constant applied voltage equal to 50 V Amount of added sodium chloride equal to 0.5 kg/m 3 of soil Figures 3.2(a) and 3.2(c) respectively confirm the existence of conductivity and concentration fronts travelling away from the cathode. Comparing the voltage waveforms of figure 3.2(a) together with the current waveform of figure 3.2(b), it was found that the sections next to the cathode are the first ones to suffer from very significant reduction of salt content. This occurs from the beginning of the test and continues for approximately one hundred and ten hours. During that time conductivity of the middle and anode sections remain high. There is clear evidence of a direct relationship between the onset of reduction in salt content and distance from the cathode. From figure 3.2(a) it is clear that the front passes through the middle region between time of 110 hours and 180 hours. Figure 3.2(d) shows a comparison between initial and final sodium ion concentration. There is a significant reduction of sodium content throughout the soil column except at the cathode. Not surprisingly, since there was no washing of any 52

75 Chapter 3: One Dimensional Laboratory Tests of the electrodes, the final sodium concentration in the first cathode section was found to be much higher than the initial concentration. The measured electrical conductivity shown in figure 3.2(e) correlates qualitatively with final concentration curve of figure 3.2(d). The reduction in salt concentration figure (3.2(d)) in the middle three sections is consistent with the reduction of conductivity of those three sections (figure 3.2(e)). Near the electrodes conductivity goes above the initial level because, in the absence of electrode washing there is an accumulation of ions. Figure 3.2(f) shows a comparison of initial ph and final ph. The rise in ph within the cathode sections is due to the formation of sodium hydroxide at the cathode whereas the fall in ph at the anode is due to the accumulation of hydrogen ions. Figure 3.2(g) provides evidence of electroosmosis. Water moves towards the cathode making the moisture content higher in the neighbourhood of the cathode sections and lower in the neighbourhood of the anode. 53

76 Chapter 3: One Dimensional Laboratory Tests Voltage across first Cathode section Voltage across second Cathode section Voltage across middle section (Vxy) Voltage across second Anode section Voltage across first Anode section Voltage (V) Elapsed time (h) Figure 3.2(a): Voltage variations across different soil sections during electrokinetic treatment 5 4 Current (ma) 3 2 Current (ma) Elapsed time (h) Figure 3.2(b): Current variations during electrokinetic process 54

77 Chapter 3: One Dimensional Laboratory Tests Na concentration at second Anode section Na concentration at middle section (Vxy) Na concentration at second Cathode section No data for Anode and Cathode sections Na salt concentration (ppm) Elapsed time (h) Figure 3.2(c): Sodium ion distribution in soil-water sampled at suction points during electrokinetic treatment Final Na concentration Initial Na concentration Na salt concentration (ppm) Nominal distance from anode (cm) Figure 3.2(d): Sodium ion distribution in soil column before and after electrokinetic treatment 55

78 Chapter 3: One Dimensional Laboratory Tests Final EC 1:5 Initial EC 1:5 EC 1:5 (µscm -1 ) Nominal distance from Anode (cm) Figure 3.2(e): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment Final ph 1:5 Initial ph 1:5 8 ph Units Nominal distance from Anode (cm) Figure 3.2(f): Variation of ph in soil columns before and after electrokinetic treatment 56

79 Chapter 3: One Dimensional Laboratory Tests Final Moisture content (%) Initial Moisture content (%) Moisture cintent (%) Nominal distance from Anode (cm) Figure 3.2(g): Variation of soil moisture content before and after electrokinetic treatment Test 2: Sandy soil treatment with constant current of 5mA The main motivation for this test, carried out at constant current, was for comparison with tests one which was done at constant voltage. Given the hypothesis that electrokinetic effects are directly related to operating current, it was thought that compared to constant voltage operation, constant current operation will make it easier to interpret test results. The main features of the constant current test results (figures 3.3(a) to 3.3(g)) are the same as those of the constant voltage test results (figures 3.2(a) to 3.2(g)). As expected the ambient temperature related twenty-four hour ripple effect is more prominent in the voltage waveforms of figures 3.3(a) and 3.3(b) compared with those of figures 3.2(a) and 3.2(b). With a constant current source voltage is automatically adjusted to compensate for changes in soil column resistance due to variation in ambient temperature In figure 3.2(a), the voltage across the first cathode section after rising for forty hours, falls at a relatively fast rate. This could be due to sodium ions that previously electromigrated to the cathode diffusing back into the soil column. The hypothesis 57

80 Chapter 3: One Dimensional Laboratory Tests was that adequate washing of the cathode would solve this problem and further tests involving washing of the cathode were undertaken in test Voltage across Cathode accumulation section Voltage across Cathode depletion section Voltage across middle depletion section (Vxy) Voltage across Anode depletion section Voltage across Anode accumulation section Voltage (V) Elapsed time (h) Figure 3.3(a): Voltage distribution across different soil sections during electrokinetic treatment Voltage (V) Current (ma) 3 50 Total voltage (V) 2 0 Current (ma) Elapsed time (h) Figure 3.3(b): Voltage and current waveforms during electrokinetic treatment 58

81 Chapter 3: One Dimensional Laboratory Tests Na salt concentration (ppm) Na at first Cathode section Na at second Cathode section Na at Midlle section (Vxy) Na at second Anode section Na at first Anode section Elapsed time (h) Figure 3.3(c): Sodium ion distribution in soil-water sampled at suction points during electrokinetic treatment Final Na concentration Initial Na concentration Na salt concentration (ppm) Nominal distance from anode (cm) Figure 3.3(d): Sodium ion distribution in soil column before and after electrokinetic treatment 59

82 Chapter 3: One Dimensional Laboratory Tests 600 Final EC 1:5 Initial EC 1:5 450 EC 1:5 (µscm -1 ) Nominal distance from Anode (cm) 12 Figure 3.3(e): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment 9 ph Units Final ph 1:5 Initial ph 1: Nominal distance from Anode (cm) Figure 3.3(f): Variation of ph in soil columns before and after electrokinetic treatment 60

83 Chapter 3: One Dimensional Laboratory Tests Final Moisture content (%) Initial Moisture content (%) Moisture content (%) Nominal distance from anode (cm) Figure 3.3(g): Variation of soil moisture content before and after electrokinetic treatment Test 3: Clay soil treatment with constant current of 5 ma The sandy soil chosen for test 1 and 2 is not as complex as other soils due to their low cation exchange capacity. This allowed easier interpretation of the test results because of low effect of cation exchange. However, from an agricultural point of view, clay soils are generally of higher importance. It was therefore necessary to extend the testing programme to include a more typical agricultural soil. Red clay soil was chosen for this reason. The main test conditions were: Red clay soil with initial moisture content equal to 30% w/w Constant current density equal to 0.45 ma/cm 2 Amount of added sodium chloride sample equal to 0.8 kg/m 3 of soil In comparing the results of figures 3.3(a) to 3.3(g) with those of figures 3.4(a) to 3.4(f), four main differences were identified. These were: 61

84 Chapter 3: One Dimensional Laboratory Tests The significantly lower operating voltage in the case of the red clay soil. At 5 ma, the maximum voltage across the first cathode section was only about 5 V (figure 3.4(a)) compared to about 50 V in the case of the sandy soil (figure 3.3(a)). This is due to the cation exchange capacity and the availability of ion that act as current carriers which includes sodium ions originally present in the clay. The significantly lower reduction of the salt content in the case of the red clay soil. Comparison of figures 3.3(d) and 3.3(e) with figures 3.4(c) and 3.4(d) illustrates this point. The ability of the red clay soil to buffer ph changes along most of the soil column. As shown in figure 3.4(e) there is no significant change in ph except for thin soil layers close to the electrodes. This is a natural feature of red soil called buffering ability which involves neutralization of H + ions or OH ions. 8 6 Voltage across first Cathode section Voltage across second Cathode section Voltage across middle section (Vxy) Voltage across second Anode section Voltage (V) Elapsed time (h) Figure 3.4(a): Voltage distribution across different soil sections during electrokinetic treatment 62

85 Chapter 3: One Dimensional Laboratory Tests Total Voltage Current (ma) 7 6 Voltage (V) Current (ma) Elapsed time (h) Figure 3.4(b): Total voltage variation with time during electrokinetic treatment Final Na concentration Initial Na concentration Na Concentration ppm Nominal distance from Anode (cm) Figure 3.4(c): Sodium ion distribution in soil column before and after electrokinetic treatment 63

86 Chapter 3: One Dimensional Laboratory Tests Final EC 1:5 Initial EC 1:5 EC 1:5 (µscm -1 ) Nominal distance from Anode (cm) Figure 3.4(d): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment 10 8 Final ph 1:5 Initial ph 1:5 ph Units Nominal distance from Anode (cm) Figure 3.4(e): Variation of ph in soil columns before and after electrokinetic treatment 64

87 Chapter 3: One Dimensional Laboratory Tests Final Moisture content (%) Initial Moisture content (%) Moisture cintent (%) Nominal distance from Anode (cm) Figure 3.4(f): Variation of soil moisture content before and after electrokinetic treatment Test 4: Clay soil treatment with constant current (15mA) Given the relatively small change observed with red clay soil at 5 ma (test 3), it was decided to preform another test on the same soil type using 15 ma. The results are shown in figures 3.5(a) to 3.5(g). The presence of conductivity fronts travelling away from the cathode is clear from the voltage and current waveforms of figures 3.5(a) and 3.5(b). Figures 3.5(c) and 3.5(d) provide convincing evidence of the significant effect of electrokinetic treatment with 15 ma of current. After about six days of treatment more than 80% of the sodium chloride contaminant had been removed from the over 90% of the soil column away from the electrodes. As expected, with the cathode not being washed, sodium ions accumulate in the soil segment next to the cathode. Strictly speaking the results of figure 3.5(f) were not 65

88 Chapter 3: One Dimensional Laboratory Tests essential for this project. They obtained because the test equipment for measuring chloride ion concentration became available for a short time during the duration of this project. The results confirmed that chloride ions are transported toward the anode. Comparison of figure 3.3(f) and figure 3.5(e) reveals a clear difference in ph levels after electrokinetic treatment. The clay soil displays an ability to buffer its ph near its pre-treatment level. Figure 3.3(g) and 3.5(g) respectively show the effect of electroosmosis in sand and clay. The increased effect of electroosmosis may have caused localised dry-up which in turn has caused the anode to cathode voltage to increase by a factor of more than three compared to test 3. A factor of 3 would normally be expected because current in test 4 was three times higher than current in test 3. Water flow towards the cathode is significant in the case of clay. This suggests that electroosmosis may be sufficient to wash the cathode Voltage (V) Voltage across first Cathode section Voltage across second Cathode section 0 Voltage across middle section (Vxy) Voltage across second Anode section Elapsed time (h) Figure 3.5(a): Voltage distribution across different soil sections during electrokinetic treatment 66

89 Chapter 3: One Dimensional Laboratory Tests Total Voltage (V) Current (ma) Voltage (V) Current (ma) Elapsed time (h) Figure 3.5(b): Voltage and current waveforms during electrokinetic treatment Final Na concentration Initial Na concentration Na Concentration ppm Nominal distance from Anode (cm) Figure 3.5(c): Sodium ion distribution in soil column before and after electrokinetic treatment 67

90 Chapter 3: One Dimensional Laboratory Tests Final EC 1:5 Initial EC 1:5 EC 1:5 (µscm -1 ) Nominal distance from Anode (cm) Figure 3.5(d): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment 10 8 ph Units Final ph 1:5 Initial ph 1: Nominal distance from Anode (cm) Figure 3.5(e): Variation of ph in soil columns before and after electrokinetic treatment 68

91 Chapter 3: One Dimensional Laboratory Tests Final Cl concentration Initial Cl concentration Cl Concentration ppm Nominal distance from Anode (cm) Figure 3.5(f): Chlorine ion distribution in soil column before and after electrokinetic treatment Moisture content (%) Final Moisture content (%) Initial Moisture content (%) Nominal distance from Anode (cm) Figure 3.5(g): Variation of soil moisture content before and after electrokinetic treatment 69

92 Chapter 3: One Dimensional Laboratory Tests Test 5 Clay soil with continuous current 5 ma and electroosmosis washing at the cathode This test was done to determine whether the electroosmotic effect is sufficient to wash the cathode in the clay soil. The configuration of the cathode to allow drainage is shown in figure 3.6 Figure 3.6: Electrokinetic setup with cathode chamber design 70

93 Chapter 3: One Dimensional Laboratory Tests Figures 3.7(a) and 3.7(b) confirmed that the electroosmotic water flow is sufficient to wash the accumulated ions (NaOH) at the cathode Final EC 1:5 Initial EC 1:5 800 EC μs/cm Nominal distance from Anode (cm) Figure 3.7(a): Variation of electrical conductivity (EC) in soil column before and after electrokinetic treatment 10 8 Final ph 1:5 Initial ph 1:5 ph Units Nominal distance from Anode (cm) Figure 3.7(b): Variation of ph in soil columns before and after electrokinetic treatment 71

94 Chapter 3: One Dimensional Laboratory Tests 3.4 Key findings from experimental work At the start of electrokinetic treatment conductivity is relatively high throughout the soil column and salt concentration is uniform. As shown in figure 3.5(a) during treatment, from the point of view of electrical conductivity or ionic conductivity, the soil column can be divided into four regions. Right next to the anode is a thin layer labelled in figure 3.8 as the anode accumulation region. In this region conductivity is higher than the pre-treatment conductivity due to an accumulation of anions. In the anode accumulation region electrical neutrality is maintained by hydrogen (H + ). Evidence of the presence of the H + ions is the low ph near the anode was observed in all the experiments. The hydrogen ions are generated at the anode by the following chemical reaction: Figure 3.8: Conductivity or ionic concentration regions 72

95 Chapter 3: One Dimensional Laboratory Tests In addition to the above, there may be other chemical reactions taking place at the anode. For example Cl ions may combine to form chlorine releasing electrons in accordance with: Right next to the cathode is a thin layer labelled in figure 3.8 as the cathode accumulation region. This region exists only in the absence of effective washing of the cathode. The region has high conductivity because of the accumulation of cations. In the cathode accumulation region electrical neutrality is maintained by hydroxyl (OH ) ions. Evidence of the presence of OH ions is the high ph observed in all experiments. The hydroxyl ions are generated at the cathode by the following chemical reaction: Effective washing of the cathode eliminates the cathode accumulation region and the depletion region extends right to the cathode. Without effective washing the accumulation cations together with the OH ions will eventually diffuse into the depletion region which would be counterproductive if the aim is to remove the cations from the soil. The depletion region is so named because it is a region of low conductivity. While the region is not completely depleted of mobile charge carriers, a relatively low conductivity has been consistently observed during the experiments. The conductivity front represented by the broken line in figure 3.8 separates the depletion region from the high conductivity region. 73

96 Chapter 3: One Dimensional Laboratory Tests As electrokinetic treatment progresses the conductivity front moves towards the anode causing the depletion region to expand with the high conductivity region contracting. The graphical results of the experiments that were performed (figures 3.2(a) to 3.5(a)) present a rather softened image of the conductivity or concentration front. For example as shown in figure 3.9 the idealised waveforms for voltage in figures 3.2(a) and 3.5(a) have three intervals. The first one is a low voltage interval corresponding to the time when both points x and y are in the high conductivity region. The high voltage section correspond to the time when both points x and y are in the depletion region. The ramp section corresponds to the time when point x is in the depletion region, point y is in the high conductivity region with the front travelling towards the anode. In contrast to the measured voltage waveforms of figure 3.5(a) or the idealised waveforms of figure 3.9 the theoretical conductivity profile of figure 3.10 better highlights the sharpness of the conductivity front. However it is impractical to obtain the profile of figure 3.10 by direct measurement. Figure 3.9: Idealised voltage (V_xy) across middle segment of soil column 74

97 Chapter 3: One Dimensional Laboratory Tests Figure 3.10: Conductivity at point x It is also not possible for the sodium ion concentration measurements in figures 3.2 to 3.5 to capture the real sharpness of the concentration front. The reason for this, as illustrated in figure 3.11, is the finite distance between suction points. More suction points would result in better location and representation of the concentration front. However practical problems arise if the number of suction points is too great. Figure 3.11: Sodium concentration profile 75

98 Chapter 3: One Dimensional Laboratory Tests It can be concluded that the strongest evidence for the existence of the conductivity front under constant current condition is the linear rise of voltage between two points along the soil column from a minimum value to a maximum value. The voltage waveforms in figures 3.2(a) to 3.5(a) do display this characteristic. Table 3.1 below summarises the main findings from the experiments that have been performed in terms of the soil column regions defined in figure 3.8. A prominent observation, especially in the case of the clay soil experiments, has been the significant flow of water as a result of electroosmosis. Moisture content in the neighbourhood of the anode can drop to a point where the soil resistivity becomes so high that electrokinetic treatment becomes impractical. On the other end moisture content near the cathode rises during treatment. Table 3.1: Key finding from experiments Region Main features Relatively thin highly conductive region due to accumulation of cations from the bulk of the soil column Cathode Accumulation Region and from OH formed as water molecules reacts with electrons injected from the cathode. Region does not exist if cathode is washed and cations efficiently removed. Electroosmosis causes moisture content to rise, specially in the case of clay soil. Depletion Region Low conductivity region typically less than 1/5 of pretreatment conductivity. 76

99 Chapter 3: One Dimensional Laboratory Tests Conductivity low because cations electromigrates to the cathode and anions electromigrates into the high conductivity region. Grows toward anode as electrokinetic treatment progresses. Electroosmosis causes moisture content to rise, specially in the case of clay soil. Conductivity remains high relative to the pre-treatment level because anions lost to the anode accumulation region are replaced by anions from the depletion region. Also cations loss to the depletion region are replaced by High Conductivity Region cations from the anode accumulation region. Shrinks towards the anode as electrokinetic treatment progresses. Electroosmosis can cause moisture content to drop to such an extent that conductivity becomes too low for electrokinetic treatment to continue. Region of high ph due to H + generation at the anode. H + generated at the anode migrates to or through the Anode Accumulation Region anode accumulation region to effectively replace cations electromigrating toward the cathode. Some generated H + ions remain in the anode accumulation region to maintain charge neutrality as anions accumulates. Electroosmosis can cause moisture content to drop to such 77

100 Chapter 3: One Dimensional Laboratory Tests an extent that conductivity become too low for electrokinetic treatment to continue. Boundary between depletion and high conductivity The sharp (high gradient) boundary between the depletion region and high conductivity region moves towards anode at a rate proportional to current. region 3.5 Explanation for formation of concentration fronts during electrokinetic treatment A definite outcome of the experiments described in section 3.3 is the confirmation of the concentration of electrical conductivity front moving away from the cathode. As mentioned before, while the existence of such fronts has been reported on a few occasions in the literature, to the author s knowledge no explanation has yet been suggested for the phenomenon. It was thought that to be able to construct the mathematical model required for this project a satisfactory explanation for the front was crucial. The basis of the theory being proposed is the well-known concept of soil cation exchange capacity Cation exchange capacity of soils Most soils are made up of particles that are negatively charged. These are electrically neutralised by exchangeable ions such as potassium (K + ), sodium (Na + ), magnesium (Mg +2 ), calcium (Ca +2 ), aluminium (Al +3 ) and hydrogen (H + ). Exchangeable means that addition to the soil solution of a particular cation, for example calcium, can result in the calcium ions taking the place of another exchangeable cation on the soil 78

101 Chapter 3: One Dimensional Laboratory Tests surcharge surface. Exchangeability is predictable and is generally in accordance with the following series (Havlin et al., 2011): Al +3 > H + > Ca +2 > Mg +2 > K + = NH 4 + > Na + A solution containing cations appearing on the list is able to displace an exchangeable ion appearing on its right. A soil may be considered to contain soluble ions and exchangeable ions. However, the soil is electrically neutral at all points. This means there are four possible electrical carriers in the soil: soluble cations, soluble anions, exchangeable cations and negatively charged colloids. It is assumed that the negatively charged colloids are not mobile enough to make significant contributions to the electrical current. The proposed theory presented in the next section is based on contributions made to the electrical current by soluble ions and exchangeable cations in the different soil regions defined in figure Proposed theory The nature of electrical conduction in the regions defined in figure 3.8 was considered in table 3.1. In addition the following simplifying assumptions are made: a) The cathode is effectively washed. This means that the cathode accumulation region is non-existent. b) All anions reaching the anode exit the soil column, for example, as chlorine gas in the case of Cl ions. This means that the anode accumulation region is non-existent. 79

102 Chapter 3: One Dimensional Laboratory Tests c) There is no soluble anion in the depletion region. The charges present are immobile negatively charged soil particles and exchangeable cations. d) The cation concentration and electrical conductivity throughout the depletion region remain uniform and constant with time. e) A cation leaving the depletion region with the cathode effluent is replaced by a cation entering the region at its boundary with the high conductivity region. f) A cation leaving the high conductivity region and entering the depletion region is replaced by an H + ion generated and entering the soil column at the anode. g) The cation concentration, anion concentration and electrical conductivity throughout the high conductivity region remain uniform and constant with time. h) Chemical reactions occur only at the electrode surfaces. Assumptions (a) to (h) above lead to the following equations: = (3.1) = 0 (3.2) + = (3.3) = = (3.4) where: = cationic current in the depletion region. 80

103 Chapter 3: One Dimensional Laboratory Tests = anionic current in the depletion region. = cationic current in the high conductivity region. = anionic current in high conductivity region. I = current through soil column. K = ratio of anionic to cationic conductivity in the high conductivity region. The voltage across the depletion and high conductivity region are respectively given by: = (3.5) = ( ) (3.6) where: L = length of soil tube = soil conductivity in depletion region figure 3.8 A = cross-sectional area of soil tube. Z b = length of depleted region. σ h = soil conductivity in high conductivity region. Figure 3.12 shows three thin soil slices in the soil column. The anionic and cationic concentration will be considered for each one of the slices. Generally current flow in 81

104 Chapter 3: One Dimensional Laboratory Tests an ionic environment is due to a combination of anionic and cationic contributions. This is indeed the situation for the high conductivity region as illustrated in figure 3.12(b). In the case of the high conductivity region, the cationic charge entering any soil slice from the anode side in a given time interval ( t) is equal to the cationic charge leaving the slice on the opposite side during that time. A similar statement can be made about anionic charge entering and leaving the slice. It can therefore be concluded that current flow does not alter the volumetric concentration of anionic charge and cationic charge in the high conductivity region. As illustrated in figure 3.12(d) the situation is similar in the depletion region, except that the totality of the soil column current is due to cationic flow. The conclusion that current flow does not alter volumetric concentration of anionic and cationic charge still applies. The situation is significantly different for a thin soil slice containing the boundary between high conductivity and the depletion region. As illustrated in figure 3.12(c), equal but opposite spatial discontinuities exist in the cationic and anionic current flow. These discontinuities result in the boundary between the high conductivity region and the depletion region shifting towards the anode at a speed in meters per second, given by: = (3.7) where = anionic charge concentration (C/m 3 ) 82

105 Chapter 3: One Dimensional Laboratory Tests Figure 3.12: The depletion surface Clearly, the explanation being offered for the existence of the ionic charge concentration front is based on the idea that a change in ionic concentration only happens where there is a spatial discontinuity in ionic current. In the soil column that 83

106 Chapter 3: One Dimensional Laboratory Tests happens only at the boundary between the depletion region and high conductivity region. For this reason that boundary has been termed, the depletion surface. Equation 3.7 can be used to estimate remediation time for one-dimensional cases or it can be used to estimate from measurement of the shifting speed of the depletion surface. The theory that has been presented allows remediation time and energy consumption to be evaluated if values for,, are known. These can be determined by one-dimensional testing on a representative soil sample. Once the results are known, as will be shown in chapter 5, they can be used in three-dimensional modelling Limitations of the proposed theory The focus of the theory that is being developed is on electromigration. A number of other effects are being neglected. Electrophoresis is neglected on the basis that soil colloidal particles are large making their mobility so small that their contribution to the overall soil current is negligible. Hydraulic effects are assumed to be insignificant because the soil moisture content has to be close to field capacity moisture content to ensure that electromigration is effective. At that level of moisture content hydraulic pressure is negligible. The results reported in the appendix support that the effects of diffusion can be neglected. While equation 3.5 and 3.6 were arrived at without considering the effect of electroosmosis, they can be used to estimate of flow rate of water. Thus, respectively, electroosmotic pressure in the high conductivity and depletion region are given by: 84

107 Chapter 3: One Dimensional Laboratory Tests = (3.8) = (3.9) where = electroosmosis permeability coefficient The argument based on figure 3.12(b), (c) and (d) was in terms of ionic charge and this led to the conclusion of the existence of an ionic charge concentration front termed the depletion surface. In developing the theory, the effect of co-existence of difference ionic species was not explicitly taken into consideration. For example, in the high conductivity region there would be at least two different cations H + and Na +. Generation of the H + ions would have at least two effects. Firstly, generation of the H + ions at the anode end of the high conductivity region will cause migration of other cations towards the cathode. The proposed theory accounts for this by the cationic contribution in the high conductivity region. This is shown as (1-k)I in figures 3.12(b) and 3.12(c). Another effect of generating H + at the anode would be a gradual change in average conductivity of the region. The proposed theory is based on a single cationic conductivity for the entire high conductivity region and for the whole treatment period. This was not considered to be a significant when determining the energy consumption as this is not strongly related to conductivity in the high conductivity region. Similarly, to determine remediation time, which according to equation 3.7 is a function of the anionic to cationic conductivity ration (K) in the high conductivity region, the proposed theory assumes that K is independent of time. Generation H + at the anode can cause K to change. If H + becomes the major cation in the high conductivity region, then K would fall because of the higher mobility of the H + ion. However it has been found that H + tends to be 85

108 Chapter 3: One Dimensional Laboratory Tests neutralised in the case of clay soil samples. This is due to the buffering capacity of clay soil. However, even if K is strictly not constant, an average value can be determined for a particular soil type. 3.6 Summary One of the key effects of electrokinetic treatment of soils that has been reported in the literature is the formation of a conductivity or concentration front that originates at the cathode and travels toward the anode. The existence of this front has been confirmed by a number of laboratory tests. It has been found that typically the conductivity on the anode side of the front can be more than five times that of the conductivity on the cathode side. The anode side of the conductivity front has been termed the high conductivity region while the cathode side has been termed the depletion region. The depletion region has been so named because this region is practically free of anions. The boundary between the high conductivity region and the depletion region is the location where the sharp conductivity or concentration gradient exists. That boundary has been termed the depletion surface. To the author s knowledge, to date there has been no report of a theoretical explanation for the depletion surface that exists during electrokinetic treatment. The theoretical explanation offered in this chapter is based on the concept of cation exchange capacity (CEC) of soils. The CEC makes it possible for discontinuities to exist in the anionic and cationic current. This discontinuity exists at the depletion surface. On the depletion region side of the surface only cationic current exists which is equal to the total soil current (I). Only cationic current exists because the region is 86

109 Chapter 3: One Dimensional Laboratory Tests depleted of its original anions which have migrated towards the anode. On the other hand both anionic and cationic currents exist in the high conductivity region. These two currents have to add up to I, which means that if the anionic current is KI then the cationic current will be (1-K)I. From the previous statements it can be deduced that the discontinuity in anionic and cationic currents at the boundary between the high conductivity and depletion region is equal to KI. This means that a conductivity or ionic concentration front exists and it shifts towards the cathode at a speed proportional to KI. The mathematical models developed in the next two chapters are based on the above proposed theory. A one-dimensional model is developed in chapter four. Multidimensional models are developed in chapter five. The main purposes of the models are to determine remediation time and energy requirements for remediation. The theory proposed in this chapter assumes that the effects of hydraulic pressure, diffusion and electrophoresis are insignificant. Justifications for the assumptions have been provided. Electroosmosis is ignored in the development of the proposed theory and the mathematical model that are based on it. However the potential gradients that are deduced from the models allow electroosmosis flow through the soil to be estimated. Electroosmosis is an important effect for this project because it is being relied upon for effective washing of the cathode. 87

110 Chapter 4: 1-D Model Development and Validation 4 Chapter 4: Model Development and validation A mathematical model is developed based on the theory presented in section The model is based on a set of partial differential equations. Simple tests are suggested which yield all the parameters needed to solve the equations. The model is discretized for one-dimensional numerical solution of the electromigration equations. A computer program is written which provides solutions in the form of concentration and voltage profiles. Predictions from the model are compared with experimental results. 4.1 The electrical equation and its solution Electrically, for a soil tube, the following equations have to be satisfied = (4.1) and = 0 (4.2) Combining equations 4.1 and 4.2 we have = 0 (4.3) where = current density = electrical conductivity = electrical potential 88

111 Chapter 4: 1-D Model Development and Validation Equations 4.2 or 4.3 represent the point form of Kirchhoff s Current Law (KCL). Equation 4.3 will be discretised with the help of figure 4.1. The figure represents the soil column divided in n segments of equal length z. An electrical node is assumed to exist at the centre of each segment. The segments are numbered consecutively from the anode towards the cathode. Figure 4.1: One-dimensional model Resistances and are associated with the i th segment. Thus conductance is given by: 89

112 Chapter 4: 1-D Model Development and Validation = 1 = (4.4) where: = partial conductance of soil at node i due to anion electromigration. A = cross-sectional area of soil column. is similarly defined. That is: = (4.5) where: = partial conductance of soil at node i due to cation electromigration. As shown is figure 4.1, the soil column is being represented by a network of resistances. Two branch resistances exist between each node pair, one representing electrical current carried by negative ions ( ) and one representing electrical current carried by positive ions ( ). Based on figure 4.1 we can write: = 0 (4.6) where: = the ɋ ɋ conductance matrix (S). V = the ɋ 1 node voltage vector. The equation corresponding to the i th row of matrix equation 4.6 is obtained by the application of KCL at node i. 90

113 Chapter 4: 1-D Model Development and Validation Thus except for (1, 1) and (ɋ, ɋ) all diagonal elements of are given by: (, ) = 2 ( + ) + 2 ( + ) + 2 ( + ) + 2 ( + ) (4.7) There is no need to find expressions for (1, 1) and (ɋ, ɋ) because the electrical potential at nodes and ɋ are known. Also, except for row 1 and row ɋ, the off diagonal elements of are given by: (, ) = (, ) = (4.8) where: ј = i + 1 or ј = i 1 For cases where: ј i +1 or ј i 1, ( i, j) = 0. Again there is no need to find expressions for (1, j) or (ɋ, j) because the electrical potential at node 1 and ɋ are known. At any point in time if and are known, the voltage profile along the soil column can be determined by solving equation 4.6. A convenient way to solve equation 4.6 is to make use of a slightly modified version of the equation which exploits the fact that the electrical potential at nodes 1 and ɋ are known. The modified version of the equation is given below. = (4.9) 91

114 Chapter 4: 1-D Model Development and Validation where: = modified conductance matrix. = vector of imposed boundary conditions. All elements of are the same as those of except for rows 1 and ɋ. Apart from (1, 1) and (ɋ, ɋ), all elements of the first row and ɋ th row of are set to zero. (1, 1) and (ɋ, ɋ) are equal to 1. Therefore, the first and last rows of matrix equation 4.9 give respectively: (1) = applied anode to cathode voltage. (1) = 0 (ɋ is the reference node). (ɋ) is equal to zero signifying that the cathode represents the electrical reference node. (1) is set to a value equal to the voltage imposed across the soil column. All other values are set to zero, consistent with application of Kirchhoff s Current Law (KCL) at each node. From equation 4.9 we obtain the solution to the electrical equation for the soil column. That is: = (4.10) where: = voltage vector describing the voltage profile along the soil column. = inverse of matrix. The solution given by equation 4.10 is strictly for constant voltage applied across the soil column. However the electrical equation 4.3 is a linear equation because 92

115 Chapter 4: 1-D Model Development and Validation conductivities are independent of voltage or current. Therefore the solution to 4.9 can be easily scaled to give the solution for the constant current case. The scaling factor ( ) is given by: = (1) = (4.11) where: = total anode to cathode resistance (1) = anode voltage used in equation 4.11 = actual injected current = anode (or cathode) current with anode voltage equal to (1) 4.2 The set of electromigration equations If only electromigration is considered then equation 2.22 reduces to: = (4.12) = (4.13) where = cationic contribution to current density (A/m 2 ) = anionic contribution to current density (A/m 2 ) = = ionic charge concentration (C/m 3 ) = average cationic mobility (m 2 /V.s) = average anionic mobility (m 2 /V.s) 93

116 Chapter 4: 1-D Model Development and Validation The following should be noted: (a) Most authors, possibly due to their chemistry background, have a slightly different form for equations 4.12 and A comparison of equation 2.9 and 4.12 illustrates this point. In equation 2.9 ionic flux is in mol/m 2.s whereas in equation 4.12 it is in A/m 2 or C/m 2 s. Similar on the right hand side ionic charge concentration is given in mol/m 3 in equation 2.9 and in C/m 3 in equation Fundamentally, however equations 2.9 and 2.12 are identical. (b) Strictly speaking if there are cations contributing to the current flow then there should be equations like equation In fact equation 4.12 may be regarded as an aggregate of those equations. Similarly if there are anions contributing to the current flow then there should be equations like equation 4.13 which may be regarded as an aggregate of those equations. In general for a particular ionic species the continuity equation is given by: =. (4.14) where: = charge concentration (C/m 2 ) = ionic flux (A/m 2 ) In particular, respectively for positive ions and for negative ions we can write: = (4.15) 94

117 Chapter 4: 1-D Model Development and Validation = (4.16) Physical interpretation of equations 4.15 and 4.16 may assist with understanding of the sign difference on the right hand side of the equations. Figure 4.2: One-dimensional representation of equation 4.15 Refer to figure 4.2 which is one-dimensional representation of equation If ( + 2) is greater than ( 2), then it means that is positive. Also it is clear from the diagram that if that was to be the case then more cations leave the elemental volume (defined by ) on the right hand side than what enter it on the left hand side. Hence a positive divergence leads to a reduction in. Refer to figure 4.3 which a one-dimensional representation of equation Figure 4.3: One-dimensional representation of equation

118 Chapter 4: 1-D Model Development and Validation Note that the existence of charge neutrality at all points in the soil sample requires that: = (4.17) If ( + 2) is greater than ( 2), then it means that is positive. Also it is clear from the diagram that if that was to be the case then more anions enter the elemental volume on the right hand side than what leave it on the left hand side. Hence a positive divergence leads to an increase in. Combination of equation 4.12 and 4.15 leads to: = (4.18) Combination of equations 4.13 and 4.16 leads to: = (4.19) Subtraction of equation 4.19 from 4.18 gives: + = 0 (4.20) Equation 4.20 is in fact equation 4.3 with conductivities explicitly expressed in terms of ionic charge concentration and mobilities. In equation 4.18 to 4.20, and are normally regarded as unknowns and mobilities and are normally assumed to be knowns. However, charge neutrality requires that is equal to. Therefore since we intend to use electrical 96

119 Chapter 4: 1-D Model Development and Validation equation 4.20, we have to consider one of equations 4.18 and 4.19 as redundant. The electromigration problem can therefore be mathematically defined as a search for the solution for simultaneous equations 4.18 (or 4.19) and 4.20 for given,, initial value of (or ) and imposed boundary condition for. The next section is about how to obtain and and the initial value of (or ) before a solution to the electromigration problem is attempted. 4.3 Determination of mobilities and initial ionic concentrations Concentrations may be obtained by direct measurment and mobilities may be estimated from fundamental constants as shown in equation The disadvantage of measuring ionic concentration by direct measurement is that it is time consuming since all ions contributing to current flow must be accounted for. Estimation of individual mobilites for all ionic species in soil sample is also tedious. The method proposed overcome those difficulties by using single effective values, one for cationic mobility ( ) and one for anionic mobility ( ). The effective values are determined empirically by simply tests similar to those described in chapter 3. When determining values for and it is important to take into consideration the theory in chapter 3 (section 3.4 and 3.5 respectively). In terms of and those key findings may be represented by the two graphs in figure 4.4. In the case of anions, as shown in figure 4.4(a), the following relationship is assumed to hold: = ( ) (4.21) where: = = 97

120 Chapter 4: 1-D Model Development and Validation = ionic concentration below which all negative ions are effectively bound to the soil particles. In the case of cations, there are no bound charge, therefore as shown in figure 4.4(b) the following relationship is assumed to hold: = ( ) + (4.22) where: = minimum soil conductivity (depletion region in figure 3.8) = post-treatment soil conductivity Combination of equations 4.21 and 4.22 gives ( + ) = ( + )( ) + (4.23) Note that after complete electrokinetic treatment becomes equal to and become equal to zero which gives: = (4.24) Also before electrokintic treatment: + = = ( + )( ) + (4.25) where: = per-treatment soil conductivity = pre-treatment ionic concentration 98

121 Chapter 4: 1-D Model Development and Validation Figure 4.4: Effective mobilities In addition, if a test similar to those described in chapter 3 is done with a current density set to then the following equation applies: ( ) = (4.26) where: = speed of the depletion surface = anionic to cationic current ratio within the high conductivity region 99

122 Chapter 4: 1-D Model Development and Validation Note that equation 4.26 is the same as equation 3.7 which is repeated as 4.26 for convenience. Equations 4.25 and 4.26 contain the parameters whose values are needed for the numerical solution of the electromigration problem defined by equations 4.18 (or 4.19) and 4.20 the parameters are,,, and. In equations 4.25 and 4.26,, and may be considered to be known. As mentioned before, they can be obtained by a simple test such as the ones described in chapter 3. On the other hand,,, and are unknown. The obvious problem is that we have three more unknowns than equations. It will be shown in the next section that is not explicitly required. In fact in equations 4.25 and 4.26 ( ) may be regarded as a single unknown. In addition with the help of figure 4.5 the follwing equation can be deduced: = ( ) = + ( ) + That is = (4.27) Figure 4.5: Anionic and cationic currents 100

123 Chapter 4: 1-D Model Development and Validation If is known, then, and ( ) can be deduced from equations 4.25, 4.26 and Since is the ratio of anionic to cationic current, it lies somewhere between zero and one. In practice will vary with time as the depletion surface expands towards the anode. This variation is due to concentrations of ionic species changing with time and position. Strictly there is no single value for. However it will be demonstrated in the next section that the mathematical solution to the electromigration problem, defined by equation 4.19 and 4.20, is only weakly dependent on. While it is important to have the right value for ( )/, only a reasonable estimate of is needed. In practice will lie somewhere between 0.2 and 0.8. It will be shown that over that range concentration profiles during the remediation process are practically independent of. The follwing steps represent a summary of the procedure determine to, and the initial ionic concentration required to solve equations 4.19 and Carry out a one-dimensional constant current test, using a soil tube similar to the ones used in chapter 3, and record voltage and current profiles. They would be similar to figures 3.5(a) and 3.5(b). 2. From the voltage and current profiles determine, and. Also determine from the injected current and the tube cross-sectional area. 3. Using equations 4.25, 4.26 and 4.27 together with a reasonable estimate for, calculate ( ), and. 101

124 Chapter 4: 1-D Model Development and Validation 4.4 Initial and boundary conditions Mathematically, as mentioned before, the electromigration problem is defined by equations 4.18 to However one of the equations, either 4.18 or 4.19 is redundant because the imposed condition of charge neutrality makes equal to. Since equations 4.18 to 4.20 are partial differential equations in general the following are required for their solution: (a) Initial condition for as a function spatial co-ordinate. (b) Boundary conditions for and. (c) Values of and as a function of and. In practice the initial (pre-treatment) ionic charge concentration may vary spatially. There are three boundaries to consider. There are the soil domain boundary, the anode boundary and the cathode boundary. In this chapter discussions will be restricted to the one-dimensional soil tube domain. Boundary conditions in this case are relatively simple. For the cylindrical soil tube electric current does not flow through the curved surface since the tube is made of an insulating material. That is: = 0 (4.28) where is distance along the normal to the curved surface of the cylindrical soil tube. The anode, which covers one of the soil tube flat surfaces, is an equipotential surface. The cathode is also assumed to be a perfect conductor. Therefore: 102

125 Chapter 4: 1-D Model Development and Validation At the anode, = (1) = (1) (4.29) Argument (1) in the above equation corresponds to node (1) in figure 4.1. The boundary condition for ionic concentration must also be specified. The assumption is that anionic and cationic currents are continuous through the anode. That is: (1) = 0 (4.30) Equation 4.30 implies that positive ions flowing away from the ions are replaced by other positive ions. Typically cations such as Na + flow away from the anode and are replaced by hydrogen ions (H + ) coming from the reaction: 2H O 4H + O + 4 Equation 4.30 also implies that negative ions reaching the anode do not accumulate. The assumption is that anions such as Cl flow towards the anode and when they reach there they are converted to Cl 2 (gas). That is: The cathode, which covers one of the soil tube flat surfaces, is an equipotential surface. It is also assumed to be a perfect conductor and it is chosen to represent the reference for electrical potential. Therefore: 103

126 Chapter 4: 1-D Model Development and Validation (ɋ) = 0 (4.31) Argument (ɋ) in the above equation corresponds to node (ɋ) in figure 4.1. The boundary condition for ionic concentration must also be specified. The assumption is that no anions enters or are generated at the cathode. Since charge neutrality has to be met, this means that: (ɋ) = 0 = (4.32 ) (ɋ) = = > (4.32 ) where n is distance along the normal to the cathode surface. Equations 4.32(a,b) imply that after conductivity drops to at the cathode cations electromigrating to the cathode are extracted by washing so that there is no accumulation of ionic charge there. The associated chemical reaction is water splitting. That is: 2H O + 2e H +2OH The cations reaching the cathode (say Na + ) is washed out as an alkaline solution of sodium hydroxide. When conductivity at the cathode reaches, there is no mobile anion leaving the region right next to the cathode. As conductivity at the cathode drops toward, there are mobile anions leaving region right next to the cathode. To maintain charge neutrality the cation concentration in that region has to also drop. This is implied by equation 4.32b. In other words, while conductivity at the cathode 104

127 Chapter 4: 1-D Model Development and Validation is above, there is a net depletion of cation concentration there. Again cations leave the cathode as a result of washing and they leave as an hydroxide solution. 4.5 Discretisation of the electromigration equations Numerical solution of the electromigration problem requires discretisation of equations 4.18 to 4.20 and the equations defining the boundary conditions. The time discretised approximations to equations 4.18 and 4.19 are: = (4.33) = ( ) (4.34) From figures 4.1 and 4.2, 2( ) ( + ) 2( ) ( + ) (4.35) 2( ) ( + ) 2( ) ( + ) (4.36) where: = cross-sectional area of soil tube. Substitution 4.35 and 4.36 into 4.33 and 4.34 respectively gives: = 2( ) ( + ) 2( ) (4.37) ( + ) 2( ) = ( + ) 2( ) (4.38) ( + ) From equation 4.30: 105

128 Chapter 4: 1-D Model Development and Validation (1) = 0 (4.39) From equation 4.32: = 0 = (4.40 ) = 2 ɋ ɋ + ɋ > (4.40 ) The flow chart in figure 4.6 represents the algorithm used to solve the electromigration equations. Equations 4.41 and 4.42 are for updating of the conductivities at each node. ( + ) = ( ) + (4.41) ( + ) = ( ) + (4.42) Note: ( = 0) = ( ) + (4.43) ( = 0) = ( ) (4.44) 106

129 Chapter 4: 1-D Model Development and Validation Start Obtain the following values which are assumed to be independent of time,,,, ( ) Set t =0 Use equations 4.4 and 4.5 to calculate branch conductances Use equations 4.7 and 4.8 to form conductance matrix Use equations 4.10 and 4.11 to solve for all node voltage Use equations 4.37, 4.38, 4.39 and 4.40 to calculate for each node Use equations 4.41and 4.42 to update the conductivities Increment time by t Yes < (t=final time) No Stop Figure 4.6: Flow chart for numerical solution of electromigration equations 107

130 Chapter 4: 1-D Model Development and Validation 4.6 Validation of the proposed theory The results of test 4 of chapter 3 will be used to validate the proposed theory. The measured voltage waveforms are repeated in figure 4.7(a) for convenience. From the voltage waveforms and the injected current of 15mA, and have been estimated to be S/m and S/m respectively. These estimation are based on Ohm s low. The speed of the depletion surface has been estimated to be 7.87*10-7 m/s. Using those values and equations 4.25, 4.26 and 4.27 we have: ( ) = / = /. = /. The above values together with an anionic to cationic current ratio of 0.5 were used to solve electromigration equations 4.19 and The algorithm described in section 4.5 was used to do this. Comparison between figures 4.7(a) and 4.7(b) shows reasonable agreement between the measured and calculated voltage profiles. Figure 4.8 shows the effect of different chosen values of the ratio of anionic to cationic current ( ). The simulation results provide confirmation, at least for this case, that there is flexibility in the choice of a value for. In particular figure 4.8 and table 4.1 show respectivly that predicted remediation time and remediation energy are practically independent of. Table 4.1 shows that remediation energy is also practically independent of. 108

131 Chapter 4: 1-D Model Development and Validation Table 4.1: Effect of choice of anionic to cationic current on remediation energy K Energy(kWh/m 3 ) (a) 20 Voltage (V) Voltage across first Cathode section Voltage across second Cathode section Voltage across middle section (Vxy) Voltage across second Anode section Voltage across first Anode section Elapsed time (h) (b) Figure 4.7: Comparison between measured and calculated voltage profiles 109

132 Chapter 4: 1-D Model Development and Validation K=0.8 K=0.2 Figure 4.8: Effect of the choice of anionic to cationic current ratio for = (0.2 and 0.8) 4.7 Summary The mathematical model developed in this chapter is based on the theory presented in section Following normal practice (Mattson et al., 2002, Kim et al., 2005b, Mahmoud and Beaugrand, 2010) the electromigration problem is defined as a set of partial differential equations (4.18 to 4.20). However unlike normal practice ionic mobilities are empirically determined based on the theory presented in section 4.3. Initial total ionic concentration is also determined empirically by a simple test on a soil sample. The test is identical to test 4 in chapter 3 except electrodes are assumed to be washed. Only voltage profiles and injected current need to be recorded. Once mobilities, initial ionic concentrations, pre-treatment conductivity and posttreatment conductivity are known, it is possible to solve the electromigration 110

133 Chapter 4: 1-D Model Development and Validation problem. Boundary conditions are based on the assumption that the electrodes are washed. However, reasonably accurate results are obtained even if the anode is not washed because generally voltage drop near the anode region is small for most of the treatment time. The algorithm based of the mathematical model developed in this chapter has been validated for the one-dimensional electromigration problem. Extension of the model to two-dimensional and three-dimensional problems is explored in the next chapter. 111

134 Chapter 5: 2-D and 3-D Modelling of Electromigration 5 Chapter 5: 2-D and 3-D Modelling of Electromigration A mathematical model of the electromigration problem was presented in chapter 4. The model, which is in the form of partial differential equations in terms of electric potential ( ) and ionic charge concentration ( ), is based on imposition of electrical current continuity and charge neutrality at all points in the soil domain. While the adopted formulation of the electromigration problem is strictly not new, a novel method has been suggested for obtaining the required parameters, that is the electrical mobilities and the pre-treatment ionic concentration. The other novel aspect of the proposed formulation is the imposition of the non-linear relationship between anionic conductivity and ionic charge concentration. This non-linearity is fundamentally due to the electronegativity of most soils. In other words below a cationic concentration threshold, the neutralising negative charge exists in colloidal form and has a relatively very low mobility. Chapter 4 also presented a one-dimensional numerical solution to the electromigration equations. The technique used could be described as a special case of the finite difference time domain (FDTD) method. In the next section the technique is extended to two-dimensional and three-dimensional numerical modelling D and 3-D modelling As shown in figure 5.1 to 5.3, two-dimensional and three-dimensional numerical modelling is based on exactly the same concepts as the ones presented in chapter 4. In general the diagonal elements of the conductance matrix are given by: 112

135 Chapter 5: 2-D and 3-D Modelling of Electromigration (, ) = 2 ( + ) + 2 ( + ) + 2 ( + ) + 2 ( + ) + 2 ɋ + ɋ + 2 ɋ + ɋ + 2 ɋ + ɋ + 2 ɋ + ɋ + 2 ɋ + ɋ + 2 ɋ + ɋ + 2 ɋ + ɋ + 2 ɋ + ɋ (5.1) where: = node number of node of interest (1 ɋ ) ɋ= number of nodes in direction (see figure 5.1 and 5.2) = number of nodes in direction (see figure 5.1 and 5.2) = number of nodes in direction (see figure 5.1 and 5.2) In the one-dimensional case (considered in chapter 4), and are effectively equal to 1 and is always smaller than or equal to ɋ. In the two-dimensional case (figure 5.1) is always smaller than or equal to ɋ. In the three-dimensional case is always smaller than or equal to ɋ. In equation 5.1, all terms containing ɋ are equal to zero in the case of one-dimensional analysis and all conductance terms containing are equal to zero in the case of two-dimensional analysis. Also, as was stated in chapter 4, (, ) does not need to be calculated if node lies either on the anode or on the cathode. 113

136 Chapter 5: 2-D and 3-D Modelling of Electromigration Figure 5.1: Resistance branches between nodes in 2-D geometry (conductances due to cations and anions combined into a single branch) Figure 5.2: Resistance branches between nodes in 3-D geometry (conductances due to cations and anions combined into a single branch) 114

137 Chapter 5: 2-D and 3-D Modelling of Electromigration The off diagonal elements of matrix is given by (, ) = (, ) = (5.2) where: = + 1 or = 1 or = + ɋ or = ɋ For 1-D For 2-D For 3-D or = + ɋ or = ɋ For all other cases where none of the above relationships between and is satisfied, (, ) = 0. There is also no need to calculate values for (, ) if either node or node falls on one of the electrodes. Insulating soil domain boundaries are assumed. For 2-D modelling, this implies that: (a) = = 0 if = ɋ where = 1, 2, 3., ; (b) = = 0 if = ɋ + 1 where = 0,1, 2,., ( 1); (c) ɋ = ɋ = 0 if ɋ ; (d) ɋ = ɋ = 0 if + ɋ > ɋ Referring to figure 5.1, conditions (a) to (d) above correspond respectively to the right, left, bottom and top boundaries. 115

138 Chapter 5: 2-D and 3-D Modelling of Electromigration For 3-D modelling, soil domain insulating boundaries imply that: (a) = = 0 if = ɋ + ɋ where = 1, 2, and = 0, 1,2.. ( 1); (b) = = 0 if = ɋ + ɋ + 1 where = 0,1, 2,.. and = 0, 1,2 ; (c) ɋ = ɋ = 0 if < ɋ ; (d) ɋ = ɋ = 0 if (e) ɋ = ɋ = 0 if + ɋ > ɋ; ɋ < ɋ + ɋ where = 0, 1,2 ( 1); (f) ɋ = ɋ = 0 if ɋ ɋ < ɋ where = 1,2 ; Referring to figure 5.2, conditions (a) to (f) above correspond respectively to the boundary surface on the right, left, bottom, top, front and back of the rectangular prismatic domain. Having constructed the conductance matrix using equations 5.1 and 5.2, the electrical equation for the system shown in either figure 5.1 or 5.2 would be of exactly the same form as equation 4.9 and its solutions can be obtained by using equations 4.10 and Electromigration equations 4.18 to 4.20 still apply. However, in chapter 4 equations 4.6 to 4.8 represented a one-dimensional discretised version of equation On the other hand equations 5.1 and 5.2 are more general and can represent one, two or three-dimensional systems. Figure 5.3 is a flow chart representing the algorithm that was adopted for solving 1-D, 2-D, or 3-D discretised versions of equation 4.18 to If time increment is set as t (one hour in this case), space dicretisation must be 116

139 Chapter 5: 2-D and 3-D Modelling of Electromigration significantly smaller (say factor of 5) less than the distance the concentration front travels in time t. If time increment is set as t (one hour in this case), space dicretisation must be significantly smaller (say factor of 5) less than the distance the concentration front travels in time t. 117

140 Chapter 5: 2-D and 3-D Modelling of Electromigration Start Obtain the following values which are assumed to be independent of time,,,, ( ) Set time t=0 Calculate conductances using 4.4 and 4.5 (Assume discretisation is the same in all direction that is x = y = z that is area A= z 2 Use equations 5.1 and 5.2 to construct the conductance matrix Use equations 4.10 and 4.11 to solve for all node voltage Use equations 4.37, 4.38, 4.39 and 4.40 to calculate for each node Use equations 4.41and 4.42 to update the conductivities Increment time by t Yes < ( = final time) No Stop Figure 5.3: flow chart for numerical solution of the one, two or three-dimensional discretized electromigration equation 118

141 Chapter 5: 2-D and 3-D Modelling of Electromigration 5.2 Two-dimensional validation test A laboratory experiment was performed to validate the model in 2-D geometry. This test was conducted in a closed small acrylic plastic container with a plastic cover that avoids the evaporation of water. The container having dimensions of 420 mm 150 mm 90 mm was filled with a clay soil of the same type used for test 5 in chapter 3. Two carbon electrodes were assembled vertically at the ends of the plastic container and separated by 230 mm. Voltage probes were installed in between the electrodes and connected to the data logger to record the voltages during the test. Figure 5.4(b) illustrates the positions of the voltage probes. The test was operated at a constant current intensity of 15 ma provided by a DC power supply. A photograph of the setup is shown in figure 5.4(a). The measured voltage profiles were used to identify the position of the conductivity or concentration front. In a two-dimensional domain, as shown in figure 5.6 the concentration front appears as a contour. The measured voltages were used to obtain the points on the contour. This is done by using the fact that before the concentration front passes a probe its voltage relative to cathode will be rising. Once the concentration front has passed it, there is no significant rise in its voltage relative to the cathode. For example as shown in figure 5.5, at time 100h the concentration front is between R 1 and probe R 2 (shown in figure 5.4(b)). By using voltage profile of three groups of electrode namely (R 1, R 2, R 3, R 4, R 5 ), (M 1, M 2, M 3, M 4, M 5 ) and (L 1, L 2, L 3, L 4, L 5 ) progression of the concentration front with time could be tracked and plotted. This has been done and as shown in figure 5.6, the concentration front obtained by test compare well with those obtained by numerical modelling. 119

142 Chapter 5: 2-D and 3-D Modelling of Electromigration (a) (b) Figure 5.4: Two-dimensional validation test (a) Photograph of the setup (b) Positions of the voltage probes 120

143 Chapter 5: 2-D and 3-D Modelling of Electromigration Cathode and Probe R1 Probe R2 and Probe R3 Probe R4 and Probe R5 Probe R1 and Probe R2 Probe R3 and Probe R4 Probe R5 and anode Voltage (V) Time (h) Figure 5.5: Voltage profiles used to identify the position of the concentration front 121

144 Chapter 5: 2-D and 3-D Modelling of Electromigration Numerical model results Laboratory results An Cat An Cat ode hod ode hod T = 48h T = 100h T = 150h T =175h T = 205h 150 Y dire ctio n (m T = 238h 0 X direction (mm) 240 Figure 5.6: Comparison of concentration front movement 122

145 Chapter 5: 2-D and 3-D Modelling of Electromigration 5.3 Influence of the anode From the theoretical and experimental results that have been obtained so far, it can be deduced that from an electrical point of view the anode has less influence over the remediation process compared to the cathode. The reason for this is the fact that the anode lies in soil of relatively high conductivity. Figure 5.7 illustrates this point. While the cathode has to be placed within the region where remediation is to take place, there is flexibility in the choice of location of the anode. As shown in figure 5.7, there is also flexibility in the choice of its size. 150 Figure 5.7: Effect of Anode size on the speed and shape of the concentration front 123

146 Chapter 5: 2-D and 3-D Modelling of Electromigration 5.4 Generalised analytical expression for remediation time and remediation energy requirements The theory that has been developed so far allows analytical expressions to be derived for remediation time and remediation energy requirements for simplified but still practically useful scenarios. It is assumed that the simple test described in section 3.2 has been performed and values for,, ( ) and are known for the soil type of interest. Let be the distance, measured along the soil surface, between the electrode and the furthest point to be treated. For 3-D cases, it is assumed that is large compared to the size of the cathode. It is also assumed that the anode to cathode distance is greater than. For the one-dimensional case, remediation time is given by: = Remediation time = = = = ( ) (5.1) where: = constant remediation current 124

147 Chapter 5: 2-D and 3-D Modelling of Electromigration The remediation time per unit volume is given by ( ). For the three-dimensional case assuming a small enough cathode compared to the depletion surface is approximately a hemispherical surface that balloons out from the cathode. The following equation can be written: = = 4 ( ) 2 (5.2) where: = incremental time = radius of depletion surface = incremental distance normal to depletion surface From equation 5.2 we have: = 2 ( ) 3 (5.3) The remediation time per unit volume is given by ( ) which is identical to the one-dimensional case. For the one-dimensional case: = ( ) + ( + ) (5.4) where: = anode to cathode resistance 125

148 Chapter 5: 2-D and 3-D Modelling of Electromigration = anode potential = cathode potential Since remediation current is constant with time, changes linearly from to ( ) where is the anode to cathode distance. Therefore: = ( + ) + (2 + ( ) ) 2 (5.5) For the three-dimensional case equation 5.4 still applies. The anode to cathode resistance may be regarded as the sum of the anode electrode resistance ( ) and the cathode electrode resistance ( ). If is sufficiently smaller than then: = ( + ) + ( + ) (5.6) Values for and may be obtain from simulation software, by using analytical expressions such as those in table 5.1 or by physical measurement. Energy requirements per unit volume for the one-dimensional and three-dimensional geometries are respectively given by = ( + )( ) = ( + )( ) + (2 + ( ) )( ) 2 + ( + )( ) (5.7) (5.8) 126

149 Chapter 5: 2-D and 3-D Modelling of Electromigration Table 5.1: Theoretical resistance of basic earthing electrodes (Baggini, 2008) Electrode type hemispherical Circular flat plate rod Dimension(s) (m) r r L= length d= diameter Electrode resistance (Ω) 2 4 /2 ln ( 8 ) 1 In summary while remediation time and energy requirements can be worked out by a computer program based on the algorithm shown in figure 3.5, much quicker estimates are possible using equations 5.3 and

150 Chapter 6: Conclusion and Further work 6 Chapter 6 Conclusions and Further work 6.1 Conclusions The four objectives of this work are listed in section 1.3. The first objective centred on the identification of critical factors affecting ionic transport in soils during electrokinetic remediation. The literature review and analysis of the results of electrokinetic laboratory tests reported in appendix A and chapter 3 pointed to: (a) Electromigration as the dominant ionic transport mechanism (under field capacity conditions) compared to electrophoresis, diffusion, hydraulic potential or electroosmosis. (b) The possibility of relying entirely on electroosmosis for washing of a perforated cathode and extraction of cationic contaminants. (c) The prominence of an ionic concentration or electrical conductivity front travelling away from the cathode. The second and third objectives of this research project involved development of a mathematical model for electromigration in soil and the validation of the model. Such a model has been developed. It is based on a set of partial differential equations (PDEs) in terms of ionic charge concentration (C) in the soil and electric potential (ϕ). The coefficients within the PDEs are the cationic mobility ( ) and the anionic mobility ( ). In practice there would be multiple anions and cations in the soil each with their own mobility. The proposed theory is based on single values for and which are effectively average cationic and anionic mobilities. 128

151 Chapter 6: Conclusion and Further work In order to solve the set of PDEs there is a need to know the relationships between the soil conductivity and also the initial distribution of ionic concentration in the soil. It has been shown that a simple test carried out on a representative sample of the soil of interest can provide values for, and the initial ionic conductivity. Given those values, the PDEs can be solved numerically. Reasonable agreement has been obtained on comparison between examples of predictions of the numerical model and their corresponding physical test measurements. The three dimensional numerical model that has been suggested can be used to analyse the remediation process for different types of soils, untreated soil ionic conductivity levels, electrode shape, electrode size, and anode-cathode separation. However an analytical solution to the electromigration equation has also been proposed. The solution is applicable to three-dimensional systems. It allows quick estimates of remediation times and remediation energy requirements. Remediation time per meter cube of soil is proportional to the difference between pre-treatment and post-treatment ionic concentration ( ) and inversely proportional to the current injected at the cathode. The injected current is limited by cathode region heating and by the need to keep voltage below safely limits. Increasing electrode size increases the maximum allowable current. Electrical resistance would typically range from about 1Ω in the case of deep electrodes to about 10 Ω for wide electrodes at or near the soil s surface. These electrodes could be rods at depth of approximately one meter into soil or mats near the soil surface. Assuming a total voltage limit of 100 V per electrode, the allowable maximum current would be 100 A in the case of a 1 Ω electrode and 10 A in the case of a 10 Ω electrode. For a soil salinity level of a 1.5 kg/m 3, based on equation 5.3 this current 129

152 Chapter 6: Conclusion and Further work range would typically correspond to a remediation time range of 12 h/m 3 and 124 h/m 3 respectively. With 100 V per electrode, remediation energy would be approximately about 250 kwh/m 3 irrespective of the current. 6.2 Further work An important outcome of this work has been the formulation and validation of a method that would allow prediction of performance of candidate electrode configurations for the treatment of particular soils including soils within pot plants. Applications of electrokinetic soil treatment range from removing salt from agricultural land to decontamination of industrial sites. The techniques proposed in this work would allow reasonable estimates of decontamination cost. Better cost estimates are possible if details of electrode design are available. There is a need for more research in electrode design and for a more complete validation of the 3-D electromigration model. There are a number of electrode design features that need investigation. They would include: (a) Development of cost effective electrodes with low corrosion rate, long life and adequate mechanical strength. (b) Comparison of performance for above ground electrodes and in ground electrodes. (c) Comparison between remote and close proximity anode configurations. (d) Development of extraction systems for anolytes and catholytes. (e) Extension of the proposed mathematical model for quantitative confirmation or otherwise of adequate electroosmotic flow for cathode washing. 130

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159 Appendix 8 Appendix Preliminary Investigations The tests described in this appendix served two purposes. The first one was to obtain some first-hand experience with electrokinetic processes in soils as well as some first-hand evidence of its effects. Secondly the tests are used to justify or support simplifying assumptions made at the beginning of this research project. Justification of certain assumptions, such as the dominance of electromigration as a mode of transport of ions compared to other modes of transport, could be based on previously published work. However the first hand evidence from the tests provides additional assurance. A.1 Large scale laboratory investigation A.1.1 Laboratory experimental setup The experiment was conducted in an electrokinetic tank of dimensions of 820 mm long, 230 mm wide and 610 mm high. Transparent acrylic plastic sheet of 10mm thickness was used for the construction of a rectangular shaped tank. Acrylic plastic isolated material was chosen for its electric insulation characteristics to prevent short-circuiting and for ease of cutting and fabricating into any desired size and shape. The inside corners of this electrokinetic tank were fully sealed with silicone sealant to avoid any possible leakages during installation and throughout the tests. The bottom of the soil container was pre-drilled with 10 mm diameter holes in order to enable water to flow into the lower part of the container and keep the soil at the bottom of the container near saturated conditions. 137

160 Appendix The preliminary trials involve the use of sandy soils with high porosity and low cations exchange capacity. The properties of the sand have been measured in the laboratory. The ph and EC of the sand was determined on a 1:5 soil:deionised water suspension in accordance to (Rayment, 1992). The physical and chemical properties of the selected soil are shown in table A.1. Table A.l: Chemical properties of the selected soil Property Values ph 1:5 7.5~8.5 Electrical conductivity EC 1:5 50~75 µs/m A direct current (DC) power supply (Model Sorensen XHR DC Power Supply 1020 W was used in all the test series. The power supply was capable of supplying a maximum voltage of 600V DC and a maximum current of 1.7 Amperes. PVC insulated copper cables were used to connect the metallic electrodes and the DC power supply. A.1.2 Experimental set-up Using vertical electrodes The electrokinetic test was conducted in a plexiglass isolated tank, 820mm long, 610mm height and 230 mm in width, Two 450 mm x 200 mm stainless steel plates were installed vertically at each end of the box to serve as electrodes. The distance between the two electrodes was 720 mm. The box was filled to a depth of 500 mm with sand (total volume ~ 84 L). The box was then placed onto a larger plastic tray 138

161 Appendix which was subsequently filled to a depth of 100 mm with rain water and the water was allowed to flow into the cell through the pre-drilled holes. The sand was left for a period of three days to reach equilibrium with the free water surface. Three hanging column tensiometers were installed at a depth of 350 mm from the surface at different distances between electrodes, one close to each electrode and the third in the middle between the electrodes. Six soil-water suction cups were also installed between the electrodes at two depths (210 and 450 mm from the soil surface). The schematic view of the test setup and instrumentation installation is shown in figure A.1. Figure A.2 shows a top view of the test cell with the instrumentation position. Figure A.1: Front view of the electrokinetic test cell 139

162 Appendix Figure A.2: Top view of electrokinetic test cell A constant electrical voltage 72 V was applied across the sand for 168 hours using a V and 0 to 1.7A DC power supply. A data acquisition system was used to record both the electric current and soil temperature during the experiment. Tensiometer measurements were taken at intervals ranging from 2 to 48 hours throughout the period of electrical field application. Soil-water samples were extracted using the suction cups by applying a suction of approximately 60 kpa for a period of 24 hours prior to applying the electrical field. The suction was then reapplied and soil-water samples were extracted at 48 and 168 hours after the electrical field was initiated. Soil core samples of 20 mm diameter were collected from five depths (0-100, , , and mm) at three locations (cathode region, middle region and anode region) on four occasions (prior to field initiation, 24, 48 and 168 hours after initiation). The collected sand samples were used to measure the ph and electrical conductivity (EC) of the suspension using a LabCHEM-Conductivity/pH probe (TPS Pty Ltd, Brisbane). 140

163 Appendix A.1.3 Electrokinetic process Observations The electrokinetic processing involves many coupled physical and chemical phenomena. The electroosmotic flow of pore fluid, the resulting change of soil-water potential, ionic migration and soil-water chemistry together, contribute to the electrokinetic treatment process. A.1.4 Results Electrical current and soil temperature Figure A.3 shows the current flow through the sand and the temperature near the electrodes with the applied voltage. The temperature of the soil within the electrokinetic cell was not affected by the electric current but rather varied diurnally in response to outside air temperature. There was no difference between the temperature observed near the anode or cathode. The electric current passing through the cell generally decreased with increasing period of electrical field application. The current was initially 1.8 ma but decreased rapidly during the first 16 hours to plateau at approximately 1.35 ma for a period of 8 hours before progressively declining to approximately 0.8 ma after 168 hours. Slight diurnal fluctuations in current were observed with the current increasing with higher temperatures and decreasing as soil temperature decreased. 141

164 Appendix Ampere Current Anode Temp Cathode Temp Time (h) Temperature (C o ) Figure A.3: Electric current through and sand temperatures within the electrokinetic cell Changes in soil-water potential The change in SWP during the electrokinetic process is shown in figure A.4. The hanging column water level for each tensiometer was the same as the water level in the tray prior to the application of the electrical field. Application of the voltage across the electrokinetic cell produced changes in SWP with the largest effect observed mid-distance between the electrodes. The SWP at the mid-point steadily increased with time of application reaching a potential of approximately 46 mm after 70 hours and remaining at that level for a further 59 hours before decreasing to 29mm at the end of the experiment. The SWP near the electrodes fluctuated throughout the period of electrical field application. The SWP initially increased by approximately 5 mm near both electrodes peaking after 7 hours at the cathode and 21 hours at the anode. The SWP at the cathode then decreased to -7 mm at 18 hours before increasing again to plateau 142

165 Appendix at 29 mm after 45 hours, remaining at that level for 59 hours and then decreasing to 9mm at the end of the experiment. In contrast, the SWP near the anode progressively declined from the 5mm peak to 5 mm after 80 hours and remained near this level until the end of the experiment. Change in soil-water potential (mm) Cathode Mid Anode Time (h) Figure A.4: Effect of applied electrical field on soil water potential in the sand sample Electrical conductivity The changes in the electrical conductivity of the soil-water (EC s ) extracted using the suction cups are shown in figure A.5. At depth of 210 mm (figure A.5a), the EC s increased from 353 to 657 µs/m near the anode, decreased slightly from 421 to 406 µs/m before increasing again to 460 µs/m in the middle region and decreased from 322 to 77 µs/m near the cathode. At a depth of 450 mm (figure A.5c), the EC s increased from 200 to 250 µs/m near the anode and decreased from 175 to 93 µs/m at the mid-point between the electrodes. In contrast, the EC s near the cathode at a depth of 450 mm decreased during the first 70 hours from 161 to 65 µs/m and then rose to reach almost the same starting level of 155 µs/m at the end of the experiment. 143

166 Appendix ph variation The ph of the soil-water (ph s ) extracted from a depth of 210 mm (figure A.5b) initially decreased from 7.3 to 6.9 near the anode then increased to 7.9 during the electrical field application. At the mid-point and a depth of 210 mm, ph s decreased from 7.4 to 6.9 before increasing to 7.3. Near the cathode, ph s progressively increased from 7.1 to 7.4 by the end of the experiment. At a depth of 450 mm, ph s decreased slightly from 7.4 to 7.3 near the anode and from 7.2 to 6.6 at the midpoint. However, ph s near the cathode changed little during the first 72 hours of field application but then increased from 7.4 to 10.3 over the last 96 hours (figure A.5d) Cathode 210 mm Mid 210 mm Anode 210 mm Cathode 210 mm Mid 210 mm Anode 210 mm EC s (μs/m) ph s a b EC s (μs/m) c Cathode 450 mm 11 Mid 450 mm 10 Anode 450 mm Time (h) ph s d Cathode 450 mm Mid 450 mm Anode 450 mm Time (h) Figure A.5: Changes of soil electric conductivity and ph during electrokinetic experiment measured by water suction at depths 210mm and 450mm 144

167 Appendix A.1.5 Discussion In the above series of electrokinetic tests, the electrical current was found to generally decrease during the process while there were slight diurnal changes due to temperature fluctuations. As it is well known that the soil resistivity is a function of soil moisture and the concentrations of ionic soluble salts. However the general decline in electrical current with period of electrical application indicates that the bulk soil electrical resistance was increasing during this period presumably due to changes in either soil moisture and/or salt concentration. The application of the electrical field produced changes in SWP. These changes which varied from anode to cathode suggest that the application of electrical field generally moved water from the anode towards the cathode. However, the results indicate that the magnitude of change in SWP will be a function of current. These responses are consistent with general electroosmosis theory and the findings of others e.g. (Eykholt and Daniel, 1994). On the other hand, the chemical measurements show that the electrokinetic process results in changes of soil chemical properties. In particular the soil ph has increased near the cathode and reduced closer to the anode. From the literature it has been shown that the H + ions are produced at the anode and OH ions are produced at the cathode therefore the variation of soil ph is most likely attributed to the migration of H + ions away from anode and OH ions away from the cathode (Probstein and Hicks, 1993, Yuan et al., 2009). The electrical conductivity varied from anode to cathode during the electrokinetic process which indicates that the electrical field affected the ionic distribution within the soil. 145

168 Appendix A.2 Small scale laboratory investigation A.2.1 MATERIALS AND METHOD Materials Sand was used to carry out the experimental investigation on sodium chloride movement/migration under electrical field effects. In order to prepare the sample used in this laboratory experiments, sand was passed through a sieve with 600 µm diameter holes, dried in an oven at 105 Cº for 24 hours and mixed with saline solution. Sodium chloride solution concentration of 1 ds/m and 4 ds/m were used. The electric conductivity was chosen based on the classification of water quality standards(ayers and Westcot, 1985). Soil with water content of 10%, 20% and 25% by weight were prepared and were allowed to settle for at least 24 hours to stabilize. Experimental apparatus and procedure In order to conduct the experimental investigation, a one-dimensional experimental setup for bench scale testing was developed and several laboratory tests were performed. The electrokinetic cell consisted of a soil column within a PVC cylinder of length 500 mm and of diameter 65 mm. Two circular steel plates of 64 mm diameter were installed at each end of the column to be used as electrodes. As shown in figure A.6 five bare copper probes were used for voltage measurement. They were made from standard commercial electrical conductors by stripping the insulation thus providing good electrical contact with soil. The sand was compacted between the electrodes to avoid leaving cavities in column and to achieve typical bulk density of sand. The sand samples were subjected to a direct current (DC) with a constant 146

169 Appendix voltage of 50 V between the electrodes for a period of 72 hours using a V and 0 to 1.7 A DC power supply. A data acquisition system was used for continuous current and sand temperature monitoring during the experiment. The voltage variation at various locations in between the anode and the cathode was measured and recorded by data acquisition system. A schematic of the electrokinetic set-up is shown in figure A.6. Figure A.6: Electrokinetic cell set-up A list of the tests performed during the experimental investigation is given in table A.2. During each experiment, a sand sample was placed in the electrokinetic cell and a constant electric potential was applied across it for a fixed period of time. At the end of each test, the sand specimen was removed from the test setup and sliced into five equal segments of 100 mm. Each segment was analysed for soil moisture content, electrical conductivity (EC) and ph in order to assess the electrokinetic effects at various distances from the electrodes. All the tests were performed at room temperature and no intentional hydraulic gradient was applied. 147

170 Appendix Three tests (test 1, 2 and 3) were performed on sand with salt concentration of 1 ds/m and moisture content of 10 ± 1 %, 20 ± 1 %, and 25 ± 2 % respectively. Another three tests (test 4, 5, and 6) were performed on sand with salt concentration of 4 ds/m and moisture content of 10 ± 1 %, 20 ± 1 %, and 25 ± 2 % respectively. Table A.2: List of the laboratory tests performed Test characteristic Moisture content by weight Salt concentration Status 10-1E 10 ± 1 % 1 ds/m NaCl EO 10-1C 10 ± 1 % 1 ds/m NaCl Control 20-1E 20 ± 1 % 1 ds/m NaCl EO 20-1C 20 ± 1 % 1 ds/m NaCl Control 25-1E 25 ± 1 % 1 ds/m NaCl EO 25-1C 25 ± 2 % 1 ds/m NaCl Control 10-4E 10 ± 2 % 4 ds/m NaCl EO 10-4C 10 ± 1 % 4 ds/m NaCl Control 20-4E 20 ±1 % 4 ds/m NaCl EO 20-4C 20 ± 1 % 4 ds/m NaCl Control 25-4E 25 ± 2 % 4 ds/m NaCl EO 25-4C 25 ± 2 % 4 ds/m NaCl Control Analysis The EC and ph were analysed using the 1:5 soil water suspension method. Triplicate samples of 8 grams of sand were carefully weighed and suspended in 40 ml of distilled water, shaken well for 1 hour by an electrical shaker and allowed to settle for 20 to 30 minutes. The suspension was centrifuged at 3000 rpm for 10 min and used to determine the concentrations of salt and ph changes. All the tests of treated sand were performed on specimens taken after drying and homogeneously mixing the entire soil volume collected from each of the five 100 mm section of the soil column. 148

171 Appendix A.2.2 RESULTS AND DISCUSSION Electric current densities and soil resistance This section focuses on the presentation of and discussion on measured current electrical conductivity and ph. The measured electric current for all the tests are plotted against elapsed time in figures A.7a and A.7b. In all tests the results showed that the electric current started to decrease rapidly after application of the voltage gradient and almost reached the steady state value after 48 hours. In the experiments preformed with 1 ds/m (tests 10-1E, 20-1E and 25-1E) the initial values of the electric current ranged from 2.1 ma to 8.7 ma, while at the steady state the current was between 1.3 ma and 2.64 ma. With 4 ds/m (tests 10-4E, 20-4E and 25-4E) the values of electric current were higher than those measured with 1 ds/m, the initial values ranged from 4.14 ma to 18.9 ma with steady state values about 2.25 to 5.07 ma. This difference in the initial measured current is due to the soil moisture content and to the soil electric conductivity. The applied voltage of 50 V was kept constant throughout the tests. The electrical resistance of the treated sand is computed by division of applied voltage between the electrodes by the measured current passed through the system. The computed electrical resistance of the soil plotted in figures A.8a and A.8b. The soil electrical resistance found to increasing from 23.6 kω to the maximum of 38.4 kω. The electrical resistance is affected by both water content and salt concentration. Slight diurnal fluctuations in current and soil resistance were observed with the current increasing and resistance decreasing with higher temperatures and vice versa. The 149

172 Appendix temperature of the soil within the test cell was not affected by the current but rather varied diurnally in response to outside air temperature. There was no difference between the temperature observed near the anode and cathode. Measured current (ma) (a) 10-1E 20-1E 25-1E Measured current (ma) (b) 10-4E 20-4E 25-4E Time (h) Time (h) Figure A.7: Measured current (a) test series 10-1E, 20-1E and 25-1E (b) test series 10-4E, 20-4E and 25-4E Eelectric resistance KΩ E 20-1E 25-1E (a) Eelectric resistance KΩ (b) 10-4E 20-4E 25-4E Time (h) Time (h) Figure A.8: Calculated resistance (a) test series 10-1E, 20-1E and 25-1E (b) test series 10-4E, 20-4E and 25-4E Variation of system electric conductivity 150

173 Appendix With the soil subjected to electrokinetic treatment there were several changes of the chemical, physical and electrical properties of the soil. The variation of electrical conductivity of the soil (EC 1:5 ) at different location across the sand column is plotted in figures A.9(a) and A.9(b). For tests 10-1E, 20-1E and 25-1E when compared with the controlled columns (10-1C, 20-1C and 25-1C) it is observed that the EC 1:5 of the soil is increased in the anode region. In the case of the cathode region the change in EC 1:5 is smaller. In middle of the column there is significant decrease in EC 1:5. The percentage increase of EC 1:5 near the anode depends on the soil water content and the initial salt concentration level. Figure A.9(c) shows the distribution of the EC 1:5 against time for tests using 4 ds/m salt concentration. It can be observed that the EC 1:5 near the anode has increased depending on the amount of moisture content. However, the EC 1:5 near the cathode has remained practically constant except in the case of 10% moisture content where there is a decrease of 40% compared to the control. Variation of system ph Previous publications have reported that applying an electrical potential across the soil will cause electrolytic reactions and generation of H + ions at the anode and OH ions at the cathode respectively. This causes a high ph at the cathode and a low ph at the anode. During the test, the acidic solution created at the anode gradually moves through the soil towards the cathode by electromigration and electroosmotic flow, and this lowers the ph of the soil (Acar et al. 1995). 151

174 Appendix (a) 10-1C 20-1C 25-1C (b) 10-1E 20-1E 25-1E E C 1:5 (µs/m) (c) 10-4C 20-4C 25-4C (d) 10-4E 20-4E 25-4E E C 1:5 (µs/m) Nominal distance from anode (mm) Nominal distance from anode (mm) Figure A.9: Variation of EC 1:5 across the sample (a) test series 10-1C, 20-1C and 25-1C (b) test series 10-1E, 20-1E and 25-1E (c) test series 10-4C, 20-4C and 25-4C (d) test series 10-4E, 20-4E and 25-4E The ph response of the tests series 10-1E, 20-1E and 25-1E are presented in figures A.10(a) and A.10(b). The ph values next to the anode changed very little with any moisture content level during the electrical treatment. Conversely, there were no changes of ph near the cathode during EO treatment for test 10-1E while for the test 20-1E the ph increased by 11.4% compared to control test (20-1C). The significant changes in ph occurred near the cathode in test 25-1E and the increase was 21.8% compared to control column (25-1C). 152

175 Appendix The measured ph variation in the tests with 4 ds/m is compared in figures A.10(c) and A.10(d). For the test 10-4E there was a slight increase of the ph value near the anode compared to control column 10-4C. However, for tests 20-4E and 25-4E the ph values were increased by about 40%. The ph of tests 10-4E and 20-4E decreased by 13% near the anode region. In contrast, the significant reduction of ph value was 47.3% observed near the anode region during test 25-4E. The ph in both control tests was almost constant through the soil column. 11 (a) 11 (b) 9 9 ph C 20-1C 25-1C E 20-1E 25-1E (c) 11 (d) 9 9 ph Nominal distance from anode (mm) C 20-4C 25-4C Nominal distance from anode (mm) 10-4E 20-4E 25-4E Figure A.10: Variation of ph across the sand sample (a) test series 10-1C, 20-1C and 25-1C (b) test series 10-1E, 20-1E and 25-1E (c) test series 10-4C, 20-4C and 25-4C (d) test series 10-4E, 20-4E and 25-4E 153

176 Appendix Electrode material selection Generally in electrokinetic applications the most favoured electrode materials are those having low resistance and minimum voltage drops at the soil-electrode interface while resisting corrosion. Metallic steel plate electrodes have been used in this laboratory tests. The metallic electrodes may dissolve as a result of electrolysis and introduce corrosive products into the soil mass. After each test the electrodes have been checked for any sign of corrosion. The corrosion takes place at the anode and introduces corrosive products into the soil samples as shown in figure A.11. The corrosive electrode plate is shown in figure A.12. Based on this results it has been decided to use carbon electrodes with all laboratory work of this research. Before electrokinetic treatment After electrokinetic treatment Figure A.11: Corrosive products on soil sample after electrokinetic treatment 154

177 Appendix Figure A.12: Corroded electrode plate A.3 Investigation of ionic diffusion The main mechanism affecting species transport in nature is diffusion due to concentration gradients where ions tend to diffuse from high concentration region to low concentration region. Ionic transport by diffusion in a saturated soil medium under effect of chemical concentration gradient can be expressed by Fick s first law: = (. 1) Because the value of the diffusion coefficient is span over a wide range for different saturated soils, experiments are often necessary to determine its value for a specific soil condition. The next section describes a laboratory bench scale experiment performed to estimate the diffusion coefficient. 155

178 Appendix A.3.1 Diffusion measurement experimentally Although each individual ion species has its own diffusion coefficient, each species does not diffuse at its own individual rate, as this would lead to significant charge separation (Jungnickel et al., 2004). The transport of ions in solution is influenced by electric fields that tend to force the ions back together so as to ensure local and overall electro-neutrality of the solution at all times. The electrical forces tend to slow down the faster ion and speed up the slower ion, and the ion pair moves at some weighted average speed of the individual ions. Nevertheless, the ion with the larger diffusion coefficient tends (on average) to lead and the slower ion tends (on average) to trail in the ion pair, thereby creating ion-pair dipoles in the solution (Jungnickel et al., 2004). In estimating ion diffusion coefficients some sort of average value is arrived at because a diffusing ion must either accompany an ion of opposite charge or exchange for one of like charge (Nye, 1966). A Experimental Apparatus and Procedure In order to estimate the diffusion coefficient value of Na +, Cl -, H + and OH with different concentration within the sandy specimen two bench scale laboratory tests were designed. The details of the test setup and procedure are given below. Sample preparation The washed sandy soil used in this laboratory experiments was passed through sieve with 600 µm diameter holes and dried in an oven at 105 C o. The tests were performed with two different saline solutions having a concentration of 4 ds/m. In 156

179 Appendix the first experiment the sandy soil was mixed with sodium chloride solution to get water content of 10% and 18% by the weight. The second test was the same as the first except sodium hydroxide was used instead of sodium chloride. The mixtures were allowed to settle for at least 24 hours to stabilize and ensure the homogeneity. Method of measurement The approach used to measure the effective diffusion coefficients is adapted from (Nye, 1966). The technique is to saturate two cells of soil at the same moisture content, one with saline solution and the other with distilled water. Then, place the two cells together and allow diffusion to occur. After sufficient diffusion time the apparatus is disassembled from the cells and the sandy soil is sectioned to determine the resulting concentration profile within the soil. The experimental concept is illustrated in figure A.13. Contaminated sample Uncontaminated sample Figure A.13: Method of Measuring Effective Diffusion Coefficients Experimental Procedure The test cells were fabricated from a PVC pipe having a diameter of 40 mm. The labelled sandy soil was placed in the 40 mm cell and the unlabelled sample was placed in the 100 mm cell. Four tests were performed with NaCl in a period of 196 hours and three tests performed with NaOH in a period of 120 hours. Table A.3 shows the details of the tests. 157

180 Appendix After allowing a period of time for diffusive transport to occur, the test is ended and the sample is disassembled from the test cells and sectioned to determine the resulting concentration profile within the soil using 1:5 soil water suspension analysis method. Table A.3: List of the laboratory tests performed Test characteristic Moisture content Salt concentration time 24-NaCl 10% & 18% 4 ds/m NaCl NaCl 10% & 18% 4 ds/m NaCl NaCl 10% & 18% 4 ds/m NaCl NaCl 10% & 18% 4 ds/m NaCl NaOH 10% & 18% 4 ds/m NaOH NaOH 10% & 18% 4 ds/m NaOH NaOH 10% & 18% 4 ds/m NaOH 120 A Results The experimental results for the case of sodium chloride are given in figures A.14(a) and A.14(b). For the case of sodium hydroxide the results are given in figures A.15(a) and A.15(b). From the figures it is clear that the diffusion is very slow compared to the electromigration. 158

181 Appendix 20 24H 48H H 192H Na concentration 12 8 initial Distance (mm) Figure A.14(a): Diffusion NaCl with moisture content of 10% 40 24H 48H H 192H Na concentration initial Distance (mm) Figuer A.14(b): Diffusion NaCl with moisture content of 18% 159

182 Appendix Na concentration H 48H 120H initial Distance (mm) Figuer A.15(a): Diffusion of NaOH with moisture content of 10% 12 24H 48H Na concentration ppm H initial Distance (mm) Figuer A.15(b): Diffusion of NaOH with moisture content of 18% 160

183 Appendix Table A.4: Measured diffusion coefficient Ion Average diffusion coefficient (m 2 /s) Na * Cl * A.4 Estimation of electroosmotic permeability coefficient and ionic mobility Electroosmotic permeability is an important factor that is needed to predict water flow induced by electroosmosis. It has been measured in many earlier works. Casgrande 1949 indicates that it could be taken as a constant value of 5*10-9 m 2 /V.s while others state that it varies in a range of 1*10-8 to 1*10-11 m 2 /V.s (Acar et al., 1994). Since it is an important parameter and the literature reports its value within a range of at least three orders of magnitude, an experiment was designed to measure its value specifically for the soil type being investigated in this research. In addition, data extracted from the test is used to estimate effective ionic mobility. Experimental Apparatus and Procedure In order to conduct the experiment to determine the coefficient of electroosmotic permeability a simple one-dimensional electrokinetic setup for bench scale testing was designed. The set-up consisted of a soil column inside a fabricated PVC pipe with diameter of 65 mm and 500 mm length. Two carbon electrodes were installed at each end of the soil column. As shown in figure A.16 at each end of the pipe an elbow was attached to be used as an electrode compartment. The column was filled with red clay soil and 161

184 Appendix the soil was compacted between the electrodes to avoid leaving cavities in the specimen and to achieve a typical bulk density that would be found in the field. Two drainage holes were positioned in the electrodes compartments at the same level with the soil in the pipe. These two drainage holes would keep the water level in the pipe and thereby maintain zero hydraulic gradient across the soil sample. Two plastic containers with screw cap were attached to each elbow to collect water. As the water will flow from the anode to the cathode compartment, a bottle of water was used to compensate for any reduction of water at the anode compartment. The water compensator system is arranged so that it does not constitute a hydraulic head at the anode. Figure A.16: coefficient of electroosmosis permeability measuring apparatus The coefficient of electroosmotic permeability is estimated using = (. 2) 162