INFLUENCES OF GAS PHASE MOVEMENT ON CONTAMINANT TRANSPORT DURING ELECTRICAL RESISTANCE HEATING

Transcription

1 INFLUENCES OF GAS PHASE MOVEMENT ON CONTAMINANT TRANSPORT DURING ELECTRICAL RESISTANCE HEATING by Dai Zhang A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Department of Civil Engineering University of Toronto Copyright by Dai Zhang 2014

2 Influences of Gas Phase Movement on Contaminant Distributions under Electrical Resistance Heating Abstract Dai Zhang Master of Applied Science Graduate Department of Civil Engineering University of Toronto 2014 This thesis examined the influence of relative permeability, constant concentration contaminant sources, multi-component gases, and latent heat effects on electrical resistance heating (ERH). An existing electro-thermal model coupled to a macroscopic invasion percolation model (ETM- MIP) was modified for the study. Simulations results showed that ERH may generate enough gas to significantly reduce aqueous phase relative permeability, thereby significantly reducing aqueous phase velocity and mass transport. When a constant concentration source zone is simulated, gas generation persists and gas bubbles travel much further with greater redistribution of contaminant. By including dissolved nitrogen and oxygen as background components, multicomponent partitioning increases, resulting in more gas bubble generation. Finally, by taking into account latent heat, the model is able to simulate energy associated with vaporization, and constant co-boiling temperature plateaus are predicted in contaminant source zones. ii

3 Acknowledgments I would like to thank my thesis supervisor Professor Brent Sleep for the patient guidance, advice, and encouragement throughout the course of this thesis. I feel lucky to have a supervisor who has been constantly supportive for my work. I would also like to thank Dr. Magdalena Krol and Dr. Kevin Mumford who helped and guided me throughout this research. I am also deeply thankful to my second thesis reader Professor Bryan Karney who inspired me to enter the world of environmental engineering. I am also so thankful to everyone in groundwater research group who provided priceless feedback for my thesis. Last but not least, it would not have been possible to write this thesis without the constant support from my family. I would like to give special thanks to my parents. iii

4 Table of Contents ABSTRACT... II ACKNOWLEDGEMENTS... III TABLE OF CONCENTS... IV LIST OF TABLES... VI LIST OF FIGURES... VII LIST OF APPENDICES... IX CHAPTER 1.0 INTRODUCTION Groundwater Contamination Evidence of Gas Bubble Formation Gas Bubble Expansion and Mobilization Modeling Gas Bubble Movement Research Objectives Thesis Overview... 4 CHAPTER 2.0 LITERATURE REVIEW AND THEORY Multiphase Flow Multi-component Partitioning Entrapped Gas Diffusion Nucleation Interphase Partitioning of Dissolved Gas Mass Transfer from NAPL Redistribution of Dissolved Compounds Macroscopic Invasion Percolation Percolation Theory Macroscopic Percolation Theory Fingering Flow of Immiscible Fluids Latent Heat Electrical Resistance Heating (ERH) iv

5 CHAPTER 3.0 MODEL DESCRIPTION ETM-MIP Model Electrical Resistance Heating (ERH) Module Water Flow Module Mass Transport Module Gas Movement Module Model Implementation Modification of the Existing ETM-MIP Relative Permeability Constant Concentration Source Zone Multi-Component Partitioning Latent Heat Effects CHAPTER 4.0 Results and Discussion Simulation 1: Base Simulation Simulation 2: Constant Contaminant Source Scenario Simulation 3: Relative Permeability Scenario Simulation 4: Effect of Multi-Component Gases Simulation 5: Latent Heat Simulation 6: Smaller Source Zone with Latent Heat Effects CHAPTER 5.0 Conclusion and Recommendations Conclusions Recommendations CHAPTER 6.0 Reference v

6 TABLE List of Tables 4.1 Summary of All Simulation Conditions vi

7 List of Figures FIGURE 2.1 Two-dimensional lattice Gas bubble movement a Initial contamination zone b Permeability distribution a Temperature distribution b Streamline distribution c Velocity vector d Water density e Concentration distribution f Gas bubble distribution a Temperature distribution with constant contaminant source b Streamline distribution with constant contaminant source c Velocity distribution (expanded view below the low permeability lens) with constant contaminant source d Concentration distribution with constant contaminant source e Gas bubble distribution with constant contaminant source f Superimposed gas bubble and streamline distribution with constant contaminant source a Temperature distribution with relative permeability b Concentration distribution with relative permeability c Gas bubble distribution with relative permeability d Superimposed gas bubble and streamline distribution with relative permeability e Velocity distribution (expanded view below the lower permeability lens) with relative permeability f NAPL distribution with relative permeability g Water phase velocity distribution with relative permeability a Gas bubble distribution at the first time step b Temperature distribution with multi-component gases vii

8 4.4c Concentration distribution with multi-component gases d Gas bubble distribution with multi-component gases e Velocity distribution with multi-component gases f Nitrogen concentration distribution with multi-component gases g Oxygen concentration distribution with multi-component gases a Average temperature plot without latent heat b Temperature distribution without latent heat c Average temperature plot with latent heat d Temperature distribution with latent heat e Gas bubble distribution with latent heat a Initial contamination location b Average temperature plot with latent heat (smaller source zone) c Temperature distribution with latent heat (smaller source zone) d Gas bubble distribution with latent heat (smaller source zone) viii

9 List of Appendices Appendix A Model Flow Charts Appendix B Initial Conditions and Important Parameters ix

10 1 Chapter 1: Introduction 1.1 Groundwater Contamination Common groundwater contaminants such as chlorinated solvents are widely used in industries and their products can also be found in households. Chlorinated solvents are also the most commonly identified organic compounds in groundwater (Squillace, Scott, Moran, Nolan, & Kolpin, 2002). Chlorinated solvents have both acute and chronic effects on human health such as liver damage, abortions, and cancer (Moran, Zogorski, & Squillace, 2007). Once released to the groundwater, the unique physical and chemical properties of solvent contaminants such as their high volatility and low viscosities compared to other volatile organic compounds cause them to spread further and thus to be harder to remediate. Non-aqueous phase liquids (NAPLs) are common sources of groundwater contamination. Light non-aqueous phase liquids (LNAPLs) such as petroleum compounds are less dense than water, and pool on the water table. In contrast, dense non-aqueous phase liquids (DNAPLs) such as chlorinated solvents are denser than water, and tend to move downward into the saturated zone due to gravitational forces. NAPLs are essentially immiscible with water. However, even at low dissolved aqueous concentration, the soluble concentration may substantially exceed drinking water standards. Transport of NAPL compounds in the aqueous phase will be reduced when adsorption to soil grain surfaces occurs. 1.2 Mechanisms of Gas Bubble Formation In the subsurface gas bubble formation could result from biogenic gas degradation or gas entrapment by water table oscillations (Amos & Ulrich Mayer, 2006). Biogenic gas formation is usually associated with methanogenesis (Reebwgh, 1985). NAPL volatilization can also lead to gas bubble formation (Revesz, Coplen, Baedecker, Glynn, & Hult, 1995). Furthermore, gas bubble formation can cause other non-reactive chemicals such as dissolved nitrogen to partition into the soil gas phase resulting in a decrease in the dissolved aqueous concentration (Reebwgh, 1985). Gas bubble formation will change the hydraulic properties of porous media. A field study in Strathroy (Reebwgh, 1985) showed that hydraulic conductivity was reduced by a factor of 35 in a bubble induced layer.

11 2 1.3 Gas Bubble Expansion and Mobilization Studies have shown that even a tiny trapped gas bubble above a NAPL pool could expand and flow vertically away from the NAPL pool, which may potentially change the NAPL mass transfer rate as well as NAPL distribution (Mumford, Smith, & Dickson, 2009). The gas bubble movement cannot be predicted by continuum transport models. Gas expansion depends on hydrostatic pressure, capillary pressure, and partial pressure associated with the dissolved gas concentration. Partitioning from the dissolved aqueous concentration to gas phase is governed by Henry s law. Contaminants such as chlorinated solvents typically have high volatility (Mumford, Smith, & Dickson, 2008) which can result in substantial gas generation and gas phase movement, often as a discontinuous gas phase consisting of gas bubbles or gas clusters. When gas expansion is initially triggered by the presence of NAPL due to its high volatility, the process can be sustained by additional partitioning from other dissolved gases such as oxygen and nitrogen. Continued growth of bubbles will eventually lead to gas bubble mobilization, fragmentation, and collapse. Evidence shows that gas bubbles can travel significant distances above NAPL pools. Mumford et al.(mumford, Smith, & Dickson, 2010) demonstrated that gas clusters traveled 44 cm above a NAPL pool characterized by groundwater velocities less than 0.01 m/day in laboratory experiments and would have travelled further if not limited by an upper barrier. 1.4 Modeling of Gas Movement Percolation theory has been used to model a number of porous media phenomena. Percolation was introduced for multiphase flow in porous media by Broadbent (Broadbent & Hammersley, 1957). In a classic percolation model, the complex microscale network of pore bodies and pore throats in a porous medium is represented by an ordered lattice of sites and bonds generated using suitable statistical distributions. In simulating a non-wetting fluid displacing a wetting fluid, the non-wetting fluid in a particular site is allowed to invade an adjacent site if the fluidfluid capillary pressure exceeds the entry pressure of the connecting bond. The drainage process is usually associated with bond percolation while the imbibition process associated with site percolation.

12 3 Macroscopic Invasion Percolation (MIP) is more often used in solving larger scale multiphase flow problems. In a typical MIP model, a matrix of cells will be superimposed on a heterogeneous porous medium. Each cell is treated as if it represents local porosity and permeability. An arbitrary capillary pressure saturation relationship may be assigned to each cell depending on the characteristics of the porous medium. The invasion percolation process can simulate drainage or imbibition depending on whether the invading fluid is wetting or non wetting (Kueper & McWhorter, 1992). 1.5 Research Objectives The present research is a further development of the existing ETM-MIP model developed by Magdalena Krol (Krol, Sleep, & Johnson, 2011a). The ETM-MIP model is able to simulate current flow associated with ERH, heat transport, gas movement, aqueous phase flow, and aqueous phase transport. However, the ETM-MIP model lacks the ability to represent many physical phenomena. The present model only considers gas phase movement and aqueous phase mass transport. The impact of changes in gas saturation on water flow, gas generation from NAPL pools modelling, multi-component partitioning, and considerations of latent heat are not included in the current model. The primary research objectives focus on modifying ETM-MIP model are to: 1: Account for the impact of the gas phase and changes in water saturation on water phase relative permeability, water phase velocity, and contaminant transport. 2: Model gas generation from NAPL pools. 3: Add the capability to model multi-component systems consisting of a volatile organic compound, nitrogen, and oxygen. 4: Allow for condensation and NAPL formation. NAPL will form when the maximum aqueous concentration exceeds solubility. 5: Include latent heat effects.

13 4 1.6 Thesis Overview Chapter 2 describes laboratory observations of gas bubble formation and macroscopic invasion percolation theory for modeling gas movement. Chapter 3 describes the existing ETM-MIP model. The ETM-MIP model consists of four modules, which are electrical, heat transport and water flow, mass transport, and gas movement. In addition, the four new modules for relative permeability calculations, gas generation from a constant source, multi-component partitioning, and latent heat effects are described in this section. Chapter 4 presents the results from various simulations. The results primarily focus on the influences of relative permeability, constant source, multi-component partitioning, and latent heat on water velocity, gas generation and movement, dissolved contaminant transport, and heat transport. Chapter 5 presents the overall conclusions and recommendations for future work.

14 5 Chapter 2: Literature Review and Theory 2.1 Multiphase Flow The process of gas phase formation and flow in initially water-saturated porous media requires the presence of volatile compounds that have combined vapor pressures that exceed the confining pressure. This situation can result in the formation of a gas phase, and further partitioning of volatile components to the gas phase. The gas phase may flow as a cluster, displacing water. Water and air are immiscible fluids. The drainage process involves water displacing air, and the imbibition process is the opposite. The original studies of multiphase flow (Brooks & Corey, 1964) can be found in petroleum and soil physics journals. Surface energy plays an important role in determining behavior of two immiscible fluids in a porous medium. Molecules with similar structures and chemical natures tend to attract each other with equal forces in all direction. However, the molecules at the interface between fluids have higher energy than molecules in the interior of either fluid. This causes the fluid to reshape into spherical shapes to minimize surface area and surface energy. As a result of the interfacial tension between two immiscible fluids, there will be a pressure drop across the interface, as related by equation 2-1 (Bloomsburg & Corey, 1964). is pressure difference, and is the interfacial energy constant. r 1 is and r 2 are radii of curvature of the interface, which are related to the pore geometry and the contact angle between the gas-water interfaces and the soil grains. In a partially saturated porous medium, there will be gas-liquid (air-water) interfaces and a pressure difference across the gas-liquid interface that is typically referred to as the capillary pressure. In water-wet media containing water and air, the air pressure will exceed the water pressure. If that happens, the difference between air pressure and water pressure is defined as capillary pressure. In addition to interfacial tension and capillary pressures, the physical properties of porous media are also important when considering two immiscible fluids. Brook and Corey (Brooks & Corey, 1964) characterizes porous media with two important parameters. The first parameter is bubble

15 6 pressure or air entry pressure, which is the minimum capillary pressure at which the air permeability is greater than zero. The second parameter is pore-size distribution index, which is the slope of the effective saturation versus capillary pressure curve. Brooks and Corey (Brooks & Corey, 1964) began with assuming Darcy s law governs each phase. The relative mobility of each phase is characterized by the contact angle and interfacial tension between the fluids. On a macroscopic level, these effects can be described with relative permeability and capillary pressure functions (Riaz & Tchelepi, 2006). Equation 2-2 is the Darcy s law for variably saturated flow where q is the Darcy velocity, is the intrinsic permeability of soil, is the viscosity of water, is relative permeability, is pressure gradient, is density, is acceleration constant, and is the elevation. Equation 2-3 is the final form of relative permeability derived by Brooks and Corey k rw is relative permeability for the water phase. S e is effective saturation, and λ is a parameter representing the pore-size distribution, which is an intrinsic property of the soil. Equation 2-4 shows the correlation between current water saturation and effective water saturation. S w is current water saturation. S wr is the irreducible water saturation and S m is the maximum water content. Maximum water content and irreducible water saturation are related to the properties of the soil and the fluids (air and water). When the effective saturation term in equation 2-3 is replaced with equation 2-4, the relative permeability becomes a function only dependent on water saturation. With the decrease in water content, water relative permeability decreases, which indicates the decrease in overall permeability of water flow.

16 7 2.2 Multi-component Partitioning Entrapped Gas Diffusion When water saturations due to water displacing gas, complete displacement of gas will not likely occur and some gas will be entrapped at residual saturations. Entrapped gas can be found in unconfined aquifer due to water table oscillation. A sudden decrease in pressure in an aquifer could also lead to gas bubble formation (Fry, Istok, Semprini, O'Reilly, & Buscheck, 1995). It was found entrapped gas could be removed by diffusion in a very slow and long process (Bloomsburg & Corey, 1964). When gas is in contact with liquid, a curved interface is formed between the liquid and gas, creating a slightly higher pressure in gas bubble than in the liquid phase (Fry et al., 1995). As a result, gas tends to diffuse into the liquid and eventually will diffuse to the water surface where concentration equilibrium is established between liquid and air at atmosphere Nucleation A simple nucleus model can be considered as a gas bubble presents in a bulk liquid (Crum, 1982). All liquid possesses surface tension relative to a gas bubble so that a gas bubble is not stable. As a result, interfacial tension tends to force the gas out of the bubble into the liquid. An expected lifetime of bubbles is correlated to bubble size. On the other hand, large bubbles tend to overcome Brownian motion through buoyancy and move to the surface (Epstein & Plesset, 19) Interphase Partitioning of Dissolved Gas Dissolved gases, like solutes, can be transported through porous media through advection and dispersion. Oxygen and nitrogen are commonly dissolved gases in groundwater. With the presence of a trapped gas bubble, dissolved gas transport could be changed due to mass transfer between gas phase and dissolved gas phase. For example, if a plume of gas dissolved in water flowed through a region containing a gas phase, dissolved gas transport would be slowed down due to mass transfer from the water phase to the gas phase to achieve concentration equilibrium between the dissolved gas in the water phase and the gas phase (Fry et al., 1995). However, if the concentration in the gas phase is higher than the corresponding equilibrium concentration of

17 8 dissolved gas in the water phase, mass transfer would be from the gas phase to the water phase. Local equilibrium between gas and aqueous phases for compounds that are sparingly soluble in water is governed by Henry s law(fry et al., 1995). H is the dimensionless Henry s constant. C w is the concentration of dissolved gas in aqueous phase, and C g concentration of dissolved gas in the gas phase. In Fry et al (Fry et al., 1995) one-dimensional tracer experiment, they demonstrated that small quantities of gas saturation can slow down dissolved gas transport due to mass transfer from the aqueous phase to the gas phase. A retardation factor was included in the advection-dispersion equation to account for this mass transfer. The conclusion of this work was based on the assumptions that the gas phase was immobile but the aqueous phase was mobile; mass transfer between aqueous phase to gas phase was instantaneous; partitioning process was governed by Henry s law. However, Cirpka (Cirpka & Kitanidis, 2001) points out that linear partitioning theory in a onedimensional column test may not be valid in multi-component mixtures in multi-phase flow. In Cirpka s experiment, instead of varying a single tracer, oxygen and nitrogen are added as well. Additional tracers will cause the initially injected concentration to decrease because the sum of the partial pressures is fixed, and the total gas pressure cannot exceed hydrostatic pressure of the gaseous phase. For instance, if a mobile tracer is injected following by an increase in concentration, a decrease in concentration in other components due to constant total pressure is predicted by linear partitioning model. Moreover, gas saturation may increase corresponding to the increase in tracer concentration. Retardation will be changed with the change of gas saturation. Cirpka proposed modified the linear partitioning equations. Gas saturation is a function of solute compositions. Even though each individual component partitioning is proportional to the concentration, the mass-transfer mixture may not be linear. Total mass C of each component is the sum of gas mass and aqueous mass where S g is gas saturation.

18 9 Combining with Henry s law, partial pressure P i can be expressed in terms of total concentration (Helfferich, 1981). Where R is ideal-gas constant, T is temperature, and H i is associated Henry s constant Mass Transfer from NAPL Roy and James (Roy & Smith, 2007) provide a good overview of volatile gas growth with presence of NAPL. For a three phase system, two main processes dominate gas to NAPL and water interaction, mass transfer between gas and liquid interface and bubble size adjustment according to pressure changes at the interface. Usually, these two processes happen simultaneously. To model a mass transfer Atchley and Prosperetti (1989) proposed an equilibrium equation at the gas-liquid interface. Where is partial pressure of dissolved gas i, and is vapor pressure. is liquid pressure and is capillary pressure. The gas will expand if gas pressure on the left side of the equation increases. In contrast, liquid pressure and capillary pressure tend to contract with gas expansion. Liquid pressure is usually treated as constant in the system, but capillary pressure is subject to change at the interface between gas bubbles and the liquid phase (Tsimpanogiannis & Yortsos, 2002). The Young Laplace equation shows capillary pressure for a spherical shape is a function of interfacial tension and radius. The interfacial tension is a constant between air and water for constant temperature and phase composition. If a gas bubble expands, capillary pressure would decrease. Further, if we assume

19 10 gas bubble expansion is valid under ideal gas law, we combine equation 2-8, 2-9, and ideal gas law to derive the following equation. where r is radius, R is universal gas law constant, T is temperature, is interfacial tension constant, is liquid pressure, and n is mole mass. After arranging equilibrium equation, equation 2-10 suggests an increase in mass transfer n will induce gas bubble expand and vice versa. Equilibrium equation 3-7 suggests that at a gas-napl interface, with mass transfer from NAPL to gas phase, increase in mass n will cause increase in r, indicating gas expansion. With the increase in radius, capillary pressure will decrease, which suggests total gas pressure on the left side of equation 3-7 decreases as well. As a result, this will slow down partitioning process of other components in the dissolved gas. In addition, research shows that mass transfer in gas- NAPL system is much greater than gas-dissolved gas system (Rathfelder, Lang, & Abriola, 2000). In Roy and Smith (2007) reporting results of a two dimensional flow cell experiment, a few important phenomena were observed. With the presence of a small gas bubble in the NAPL zone, gas expansion and mobilization were observed. If no gas was present in the NAPL zone, gas expansion and mobilization were not observed. In a natural groundwater condition, gas mobilization is controlled by capillary pressure and buoyancy force. is capillary pressure on the top of bubble cluster, and is bottom capillary pressure. is the density difference between water and gas. is acceleration constant for gravity and is the vertical height of bubble cluster. When capillary pressure P c exceeds the minimum displacement pressure P d, gas cluster can expand. Equation 2-11 suggests will increase if a bubble grows and h increases.

20 11 Gas cluster mobilization can be related to the Bond number (Tsimpanogiannis & Yortsos, 2004). is the density difference between liquid and gas, and is permeability. is the interfacial tension between liquid-gas phase, and is gravity constant. The gravity bond number is found to have inversely proportional to the size of gas cluster (I. N. Tsimpanogiannis & Yortsos, 2004). In addition to bubble growth, bubble fragmentation was also observed (Roy & Smith, 2007). Mass transfer between liquid-gas phases causes continuous bubble growth and mobilization. In the observation of the continuous bubble expansion process, tiny gas bubbles are found always in contact with NAPL pool, following by repeatedly mobilization and fragmentation Redistribution of Dissolved Compounds Spontaneous gas expansion below water table can significantly affect mass transfer from NAPL pool (K. G. Mumford et al., 2010). This may lead to re-distribution of contaminants as they move upwards in gas clusters and then dissolve into flowing water. As a result, conventional transport models will not be able to predict such concentration re-distribution. It is important to understand the mechanism of gas expansion, fragmentation, and mobilization. Even a small amount of aqueous concentration transported away from a NAPL pool may cause water contamination. For a system consisting of discontinuous gas phase and NAPL, gas expansion is expected to happen near the NAPL zone while dissolution is expected to occur far away from the NAPL pool. As discussed in above section, when a small gas bubble grows, its volume increases. Due to density difference between gas and liquid phase, buoyancy force drives the gas cluster to grow vertically, which produces a capillary pressure gradient within the gas cluster. Once the critical cluster length is reached (R. J. Glass & Yarrington, 2003), mobilization of the gas cluster occurs due to water imbibition starting at the bottom of gas cluster. In a relatively heterogeneous system, a gas cluster can be trapped again after initial mobilization due to various capillary forces generated by a range of pore sizes. When this happens, continued vertical growth or remobilization requires coalescence with other gas clusters (Mumford et al., 2010). In contrast to continued vertical bubble growth observed in Roy and Smith experiment (Roy & Smith, 2007),

21 12 the experiment conducted by Mumford et al. (Mumford et al., 2010) shows that repeated trapping and coalescence play an important role in aqueous concentration distribution. 2.3 Macroscopic Invasion Percolation Percolation Theory In nature, many processes happen in a random fashion such as a solute diffusion through solvent. Besides the randomness, external forces may be exerted on such random processes such as water percolating under gravity. In general, many physical phenomena involve a fluid spreading randomly through a medium (Broadbent & Hammersley, 1957). The simple example of random walk can illustrate the difference between diffusion and percolation process. A particle, a fluid, can move from an initial location either to the left or to the right with equal chance at a unit length. After n walks, this linear walk has a distribution with zero mean and variance n. Now, if a medium is treated as a random factor rather than the fluid, each point in the medium has equal opportunity of directing the fluid to the right or left. The motion of a fluid is entirely determined by the medium, not the fluid (Broadbent & Hammersley, 1957) Macroscopic Percolation Theory Capillary pressure saturation relationships can be applied at many different scales for the prediction of multiphase flow. For example, local scale may refer to the scale at which laboratory experiment is carried out. This scale is on the order of magnitude of the size of a few grains, and can be used to define smallest scale of many properties of porous media such as porosity (Kueper & McWhorter, 1992). If analysis at this scale is applied to a large heterogeneous soil matrix, every change of soil property has to be accurately accounted for. The application of local scale requires large expensive data collection, and a large amount of computational power and time to process data, particularly in multi-dimensional cases. The macroscopic scale is one level above local scale. This scale may be considered as an average of several local scales. The idea behind macroscopic scale is to predict the most important flow properties and capture the fundamentals of system characteristics using average properties. In

22 13 addition, using the macroscopic scale one can overcome the problem of limited knowledge about local scale variability (Mantoglou & Gelhar, 1987). In percolation models void spaces in porous media are considered as pores (sites), and non-void constrictions are treated as throats (bonds) in a three dimensional network. This can be illustrated in Figure 2.1 (Kueper & McWhorter, 1992). Figure 2.1 Two-dimensional lattices (Kueper 1992) Two-dimensional lattice consists of sites (pore) connected by bonds (throat). Information such as bond radii and statistical distribution is stored for the lattice. Each site is connected by four bonds. When a given capillary pressure exceeds the entry pressure of the bonds, the non-wetting fluid displaces the wetting fluid, and drainage occurs. The drainage process is usually associated with bond percolation, while the imbibition process (wetting fluid displacing non-wetting fluid) is associated with site percolation. Kueper and McWhorter (1992) proposed a percolation process at a macroscopic level. An array of cells is superimposed on a heterogeneous porous media. Each cell may represent multiple grains, and a local scale capillary pressure saturation relationship is defined. Both drainage and imbibition can occur depending on whether the invading fluid is wetting or non-wetting. Drainage usually starts with all cells completely wetting fluid saturated. If the displacement pressure is exceeded by the capillary pressure, an invasion process occurs. Once a node has been invaded, the non-wetting fluid is allowed to invade neighboring nodes if minimum displacement pressure is met.

23 Fingering Flow of Immiscible Fluids Fingering in a multiphase flow may occur due to density and viscosity differences between immiscible fluids such as water and air. In the context of contaminant transport, density instability has a greater more influence on such fingering patterns in both saturated and unsaturated flow than viscosity (Glass & Yarrington, 2003). The interaction between viscous and gravity forces in determining advancing front separating two immiscible fluids in absence of capillary pressure is modeled by Saffman and Taylor in equation 2-13 (Saffman & Taylor, 1958). Where k is the intrinsic permeability of media, g is gravitational constant, is the angle between the gravitational force and the direction of flow. is porosity, and is interfacial velocity.,,, and are upstream and downstream densities and viscosities respectively. Equation 3-12 suggests 4 possible combinations of gravitational and viscous effects on fluid fluid displacement (R. Glass & Nicholl, 1996). Both gravity and viscosity stabilized: unconditionally stable fluid accelerated upward and downward into a less/more dense, but less viscous fluid; Gravity destabilized/viscosity stabilized: conditionally unstable fluid accelerated downward/upward into a less/more dense, but less viscous fluid; Gravity stabilized/viscosity destabilized: conditionally unstable fluid accelerated upward/downward into a less/more dense, but more viscous fluid; Both gravity and viscosity destabilized: unconditionally unstable fluid accelerated into a less/more dense, but more viscous fluid.

24 15 If the inequality is satisfied in equation 2-13, a stability condition is established. Otherwise, any disturbance at the interface may dominate the displacement process. For example, in a water-air system where water is dense, more viscous than air by water, a water table rise is considered as a stable displacement with respect to viscosity and gravity. On the other hand, air injection below the water table indicates the situation where both gravity and viscosity are unstable (R. Glass & Nicholl, 1996). The gravity driven fingering of water movement into unsaturated porous media has been studied as well as DNAPL downward movement below the water table (Hill & Parlange, 1972). Glass and Yarrington (2003) conducted experiments and simulated multiphase flow by using macroscopic invasion percolation theory. The conclusion was that fingering, nonmonotonicity, and fragmentation phenomena are complex resulting from gravity, invasion and reinvasion at the interface between two fluids. However, fingering flow is also dependent on many other factors such as viscosity and local geometry. 2.4 Latent Heat The enthalpy of vaporization is an important quantity characterizing the energetics of vaporliquid phase changes. The enthalpy of vaporization can be obtained by both direct and indirect approaches. Direct approaches involve experimental measurement at various physical conditions. Indirect approaches usually involve the Clapeyron equation. The enthalpy of vaporization of a pure substance is defined as the difference between enthalpies of the vapor and liquid phase at a given temperature and saturated vapor pressure (Majer, Svoboda, & Kehiaian, 1985). is enthalpy difference between two phase. is the enthalphy of the gas phase and is the enthalpy in liquid phase. is amount of energy requires to break binding force of molecules in a liquid. Practically, this amount of energy is needed to convert a substance from liquid to gas phase at saturated vapor pressure. The Clapeyron equation may be used if vapor pressure-temperature data is known (Majer et al., 1985).

25 16 Where is the specific latent heat, is the specific volume change during a phase transition, and T is the temperature. This equation states that along the pressure-temperature saturation curve, if pressure and temperature are available and enthalpy of vaporization is known, the volume change can be calculated through the Clapeyron equation. Equation 2 15 is considered a good estimation only if pressure Psat < 0 kpa. Latent heat is a very important parameter in modeling electrical resistance heating (ERH) because vapor extraction is the primary means to recovery contaminants. In application of ERH a mixture of NAPL and water is heated up to the co-boiling point, and the resulting vapors are extracted through extraction wells. With water and NAPL the temperature in liquid cannot be higher than the co-boiling temperature of the NAPL-water system until all NAPL or water is removed. Additional energy will speed up the evaporation process rather than increase the temperature in the liquid. In addition to bubble generation, bubble collapse may also occur. The transport of gas clusters from hotter regions near gas cluster formation to colder regions where gas clusters collapse has been observed (Robin & Snyder, 1970). When a gas cluster collapses due to condensation of the vapors, the latent heat energy stored in the gas cluster will be released in condensation region. 2.5 Electrical Resistance Heating (ERH) Thermal treatment is a proven technology for removing volatile organic contaminants (VOCs) from soil. In conjunction with air stripping, by circulating the surface air through soil, aircontaminant vapor mixture is stripped away from the source zone to the extraction well. Thermal enhanced air stripping is a simple and inexpensive way to clean up VOCs. Before thermal treatment is applied for groundwater remediation, excavation of contaminant has been used extensively. But excavation method could be costly especially when contaminants are located at the great depth. In addition, excavation may present potential risks for spreading contaminant and is not always practical to implement, particularly under or around surface structure. Air stripping is first approximated from numerical modeling (Massmann, 1989). In addition, air stripping alone and pump-and treat methods were used extensively for unsaturated zone VOCs recovery for specific sites and contaminants. However, due to low solubility of NAPL and geographical constraints such as low gas permeability zone, neither pump-and-treat nor air

26 17 stripping is effective for removing VOCs. In contrast, when organic contaminant is heated, its vapor pressure increases; viscosity decreases; and its adsorption or adsorption decreases; which all favor to thermal enhanced air stripping method. Thermal treatment proves to be more effective for removal of VOCs (Davis, 1997). However, different thermal treatment technologies may work better for different geographical conditions such as the permeability of media, heterogeneity of soil, or solubility of contaminant. Electrical Resistance heating is more effective than other thermal treatment technologies in less permeable media with higher water content (Davis, 1997). Electrical heating has been used extensively in the oil field to reduce viscosity of bitumen to a point at which oil can be extracted. Electrical heating is usually achieved by heating up soil and contaminant. VOC s vapor pressure increases with temperature, which is favorable for air stripping. The concept of electrical heating is not new. Power dissipates heat in the soil when current flow through the soil. Electrical power can be supplied both from commercial used power-line (60 Hz) and radio-frequency at high frequency range. Chute and Vermeulen (1988) summarizes that preferable condition for using power-line is when desirable temperature in the formation is lower than the in-situ boiling point in the soil. In contrast, if desirable temperature in the formation is higher than in-situ boiling temperature, radio-frequency should be used. In addition, when the formation contains low moisture, radiofrequency method has advantage over power-line method. However, the capital cost of radiofrequency method is much higher than power-line method (Dev, Sresty, Bridges, & Downey, 1988). ERH usually consists of an array of electrodes placed in the soil in a hexagonal or triangular pattern. A three phase or six phase AC power source is supplied to the electrodes. Current flow through electrodes creates subsurface heating. Typical ERH requires to heat subsurface temperature to boiling temperature of NAPL-water mixture. Vapor extraction is primary mean to recovery contaminant. However, operating ERH at sub-boiling temperature sometimes is preferred due to costs of less energy and less infrastructure. In addition, co-boiling point is always lower than the boiling point of each individual compound.

27 18 Modeling of ERH is based on Ohm s law which relates the current density to electrical conductivity of media and electric potential. Ohm s law states (Hiebert, Vermeulen, & Chute, 1989): where J is the current density, V is the electrical potential, and is the electrical conductivity. Due to spatial variation of electrical conductivity, Equation 2-16 can be arranging as equation Where Q is sink sources of electrical charge. The power dissipation in the subsurface (U) is derived based on equation In the ERH, electrical current will primarily flow through the water phase, and water saturation has a significant effect on electrical conductivity. It is a challenge to determine electrical conductivity of a porous media partially filled with conductive fluids. However, an empirical law (Kozlov, Schneider, Montaron, Lagues, & Tabeling, 2012) can be related to the conductivity of porous media to several key physical parameters characterizing surface system. where is the electrical conductivity of the brine solution is, is the porosity, and is the brine volumetric fraction within the pores. Superscript n is the Archie s saturation exponent.

28 19 Chapter 3: Model Description 3.1 ETM-MIP Model The electrical-thermal and macroscopic invasion percolation (ETM-MIP) model, used in this research, was developed by Magdalena Krol (Krol, Sleep, & Johnson, 2011a). The model is based on finite difference method to discretize energy, flow, mass, and current, using a blockcentered grid. The model uses the implicit method to solve flow and energy and contaminant transport equations. Flow and heat equations are coupled through temperature dependent properties. An iterative method is used to calculate temperature and flow. Since temperature and temperature dependent properties cannot be solved simultaneously, an absolute convergence criterion is set to 1x10-6 for the iteration. The model first solved for temperature, then temperature dependent properties. With updated temperature dependent variables, temperature is re-calculated. If the difference between current temperature and the previous temperature is smaller than the convergence value, the iteration process ends. Otherwise, the iteration process continues until the convergence is reached. Both harmonic mean and arithmetical mean are used if parameters are changed spatially such as water density and hydraulic conductivity. The model contains four modules: electrical; flow; mass transport; gas movement. Each of these modules will be updated within each time step. In the ETM-MIP, temperature is calculated from the heat generated by ERH. Heat is solved in a non-linear fashion based on each individual electrode. If latent heat is considered, the energy consumption is also calculated prior to temperature. With known heat generated from ERH and latent heat, temperature can be solved by energy balance equation. The updated temperature will be used to calculate all the temperature dependent properties such as water density and Henry s coefficient. The temperature dependent variables are used to calculate the flow. Gas saturation is solved after the flow. Mass transport module only calculates aqueous concentration transport assuming no gas phase transport. Finally, MIP module accounts for gas movement. The detailed flow chart is attached in Appendix A.

29 Electrical Resistance Heating (ERH) Module The ERH module calculates current, voltage, power, and energy. The energy is used to calculate the temperature and velocity distributions. Temperature is calculated in energy transport equation. All the temperature dependent variables are also calculated. These include the Henry s coefficient, water vapor pressure, water density, viscosity, and hydraulic conductivity. In addition, new gas saturation is solved through equilibrium calculations Water Flow Module Darcy s velocity is calculated in this module. With updated Henry s constant, new gas saturation can be calculated through implicit non-linear pressure equilibrium equation. Gas saturation is strongly dependent on dissolved concentration and temperature. Whenever temperature or dissolved concentration changes, new gas saturation should be recalculated. Darcy s velocity can be obtained through pressure, density, and temperature. where is the Darcy s velocity, is the intrinsic permeability of the soil, is the viscosity, P is the pressure, z is the elevation, is density, and g is the acceleration due to gravity Mass Transport Module The mass transport module calculates aqueous phase solute transport according to the advectiondispersion equation. During solute transport, the gas phase mass is assumed to be immobile. The total mass in each cell is re-calculated at the end of the mass transport step to allow calculation of partitioning to the gas phase. Dispersion is the process of mechanical mixing that takes place in porous media as a result of the movement of fluids through pore space. Mechanical dispersion occurs in both longitudinal and transverse direction. But dispersivity in the direction of low is typically larger than the dispersivity in the directions perpendicular to the flow. Mechanical dispersion is the product of average linear velocity and dispersivity.

30 21 Diffusion is associated with molecular scale movement of molecules and results in molecules moving from areas of higher concentration to areas of lower concentration. Water and gas phase diffusion of contaminants in the subsurface is usually described by Fick s Laws, although more rigorous relationships such as the Dusty Gas Law have been used for gas phase diffusion. In a porous medium, diffusion can be represented by effective diffusion coefficient, which is the molecular diffusion coefficient multiplied by the tortuosity. The tortuosity is a function of the soil pore structure, and can be calculated from constitutive relationships such as the Millington- Quirk relationship (Millington & Quirk, 1961). For determining transport in porous media, the process of mechanical dispersion and diffusion cannot be easily separated. Hydrodynamic dispersion is defined as the simple sum of diffusion and mechanical dispersion. The retardation factor represents the effects of adsorption to soils, particularly adsorption of hydrophobic organic solutes to organic matter in the soil grains. However, retardation is not considered in the mass transport Gas Movement Module The spontaneous expansion of a discontinuous gas phase in the presence of dissolved volatile organic compounds results in mass transfer of these compounds to the gas phase. The mass transfer is driven by partitioning from the aqueous phase to gas phase (Roy & Smith, 2007). The mass transfer process may also cause other dissolved gases such as oxygen and nitrogen to participate partitioning process. In addition, it has been found the mass transfer from the aqueous phase to gas phase is much faster at higher temperature due to increased volatility. This may cause significantly re-distribution of NAPL (Krol, Sleep, & Johnson, 2011a). Gas bubble expansion, mobilization, and collapse are determined by a multiple-component partitioning mechanism in which the total gas pressure depends on the concentration of all dissolved gases, partitioning coefficients, and the gas phase pressure. Gas expansion or mobilization is assumed to be a discrete process, occurring as multiple gas clusters rather than continuous channels of gas bubbles. Discontinuous gas flow is the result of local competition between capillary and buoyancy forces (K. G. Mumford et al., 2009). When a gas cluster expands, buoyancy forces associated with the density difference between two fluids and the

31 22 cluster height increase. Vertical cluster growth also leads to increase in the difference in capillary pressure across the gas cluster due to the water pressure difference. The gas phase expansion pressure is given by: Equation 3-2 states gas phase pressure equals the sum of water pressure and capillary pressure. is gas pressure. In the model, is the sum of all the partial and vapor pressures from each dissolved component. is water pressure. is capillary pressure. A multi-component partitioning model is proposed based on local equilibrium conditions (Helfferich, 1981). where is the individual gas pressure, is total concentration of each component, is Henry s constant for each component, R is the universal gas constant, T is the temperature, and is the gas saturation. The total concentration of each component is defined as: where is aqueous concentration of component i, and is gas phase concentration of component i. The gas phase concentration is derived from the Universal Gas Law. Capillary pressure is equation 3-6 can be obtained from Brook-Corey expression. where is the displacement pressure, which can be assigned to each cell initially, is pore-size distribution index, is water saturation, and is irreducible water saturation. By combining from equation 3-1 to equation 3-5, gas saturation is the only unknown variable and can be solved by an iteration method.

32 23 To account for gas expansion or mobilization between grid blocks, each block is assigned an entry pressure P e and a terminal pressure P t, and a capillary-saturation parameters P d. Two thresholds T e, T t can be defined at each cell. where T t is the threshold for imbibitions, T e is the threshold for drainage. P w is the water pressure, is the water density, h is the water height. is the water pressure at height h 0. Local displacement pressure P d is assigned randomly following a normal distribution (Glass & Nicholl, 1996). Entry level pressure is assigned as P e = P c where gas saturation is defined as critical gas saturation capillary pressure calculation. Critical gas saturation is set to 0.3 in the model. is an empirical constant based on capillary pressure measurement(ioannidis, Chatzis, & Dullien, 1996). The gas phase expansion, mobilization, and fragmentation are simulated using macroscopic invasion percolation (MIP) approach. Gas saturation in each cell is solved independently. Once gas saturation reaches the critical gas saturation, the cell is labeled to allow connecting to adjacent cells. A gas cluster forms if the cell connects adjacent cells. A coordination number is usually used to represent the number of neighboring cells connected to the target cell. The coordination number is 4 in the current model. The cell with gas saturation greater than critical gas saturation is allowed to expand to adjacent cells following MIP rules. MIP will lead to identification of the maximum terminal pressure in a gas cluster, and gas will invade the adjacent minimum entry pressure. The newly invaded cell is assigned the critical gas saturation because the gas saturation a buble must exceed critical gas saturation in order to expand or mobilize. Gas pressure is re-calculated at the end of each MIP step. The MIP model assumes the no pressure variation in an individual gas cluster during MIP step. So the average pressure is assigned to gas clusters. Mobilization of a gas cluster is calculated in the same way as expansion except the gas phase mass is completely

33 24 moved from the original cell to the invaded cell. At the end of the MIP step, the aqueous concentration is calculated. In addition to concentration, the pressure in the invading cell is adjusted based on the law of mass conservation as well as the Ideal Gas Law: where P i, S i, and T i are the pressure, gas saturation, and temperature for the invading cell, P j, S critical and T i are the pressure, gas saturation, and temperature for the invaded cell. If the gas saturation is zero after calculation, then it suggests bubble collapse occurs. where M is the total mass, and is gas saturation. A more detailed description of MIP process can be found in Mumford s Paper (Mumford et al., 2010). The followings are the assumptions made to the MIP model Local equilibrium between aqueous phase and gas phase is achieved instantaneously at the end of each MIP step; Gas phase expansion occurs as a quasi-static displacement so no gas advection or diffusion occurs in mass transport step; Gas mobilization occurs faster than gas phase expansion; Thermal equilibrium exists between the water gas and the gas phase; The gas phase pressure does not vary with space through each gas cluster.

34 25 Figure 3.1 Gas bubble movements Figure 3.1 is the illustration of three gas bubble movements in MIP model. The purple cells are water saturated, and the white cells contain gas. Gas expansion occurs when the average gas pressure in a gas cluster is greater than the drainage threshold of the adjacent block. In this case, the gas cluster is allowed to invade adjacent cell. Gas mobilization occurs when the minimum drainage threshold of a cell adjacent to a gas cluster is less than the threshold for imbibition for another block in the cluster. In this case the gas cluster is allowed to invade the adjacent cell, while in the meantime, water is allowed to re-invade the cell with the low imbibition threshold. Gas fragmentation is the same as mobilization except that after water re-invasion, the initial gas cluster is split into two gas clusters.

35 Model Implementation The system dimension is 34 cm by 34 cm, and is divided into 86 by 86 cells. Each single cell in the matrix is 4 mm by 4 mm. Figure 3.2 is an illustration of the system. The blue rectangular box is the initial contamination zone. The contaminant is chosen to be 1, 1, 1 TCA, a common groundwater contaminant with boiling point of 73 o C and solubility of 13 mg/l. The initial concentration of TCA is set to 9 mol/m 3, slightly below its solubility limit. The six bulges on the side of the initial contamination zone are the locations of the electrodes. The electrodes are placed outside, but close to the initial contamination zone. Six electrodes are used in the simulation with one phase heating. The lens above initial contamination zone is a low permeability lens, which tends to prevent water and gas bubble entry due to the high displacement pressure. Figure 3.2b is the permeability distribution. The lowest permeability is the lens, which is roughly 100 times smaller than the highest permeability in the system. In the model, permeability of each cell is taken to be the average permeability of Ottawa sand, multiplied by a random number between 0 and 1 calculated from the normal distribution. Both flow and gas bubbles tend to move into the high permeability zone. A Darcy velocity of 5 x 10-8 m/s is specified at the left boundary. A constant head is specified at the right boundary so that the water always flows from inlet to outlet. Ottawa sand is used, and the detailed information of soil is attached in Appendix B. The maximum temperature is set to 80 o C. When the maximum temperature in each time step is set to 80 o C, electrodes will be automatically turned off in the next time step until the maximum temperature drops below 80 o C. At the beginning of the simulation, the subsurface is fully water saturated. Water is filled with dissolved oxygen and nitrogen only in the multi-component scenario. A uniform temperature of 20 o C is initialized in the system. The top and bottom boundary conditions of heat and mass transport are defined to zero flux, which means neither mass nor heat can cross top and bottom boundaries. All boundary of voltage is also zero, so no current can flow outside boundary. The water pressure at the top is at atmospheric pressure. Water pressure increases with an increase in depth.

36 nodes 27 The reference displacement pressure, pore size distribution index, residual water saturations, and permeability are the same as those used by Kueper (Kueper, Abbott, & Farquhar, 1989). The simulation runs for minutes. Each time step is 10 second except for latent heat scenario, for which the time step is changed from 10 second to 1 second at the point when temperature reaches the co-boiling point. All the initial values and important parameters are summarized in Appendix B Flow 3 mm nodes 3 mm Figure 3.2a Initial contamination zone

37 28 x Figure 3.2b Permeability distribution 3.3 Modification of the Existing ETM-MIP The goal of this research is to investigate the effects of several mechanisms not included in the ETM-MIP model of Krol, Sleep, and Johnson (2011). These mechanisms include relative permeability effects, volatilization from a constant source, multi-component partitioning, and latent heat considerations. The ETM-MIP model was modified and new functions to simulate these mechanisms were added to the ETM-MIP model Relative Permeability The soil effective permeability to water will change with the presence of a gas phase and reduced water saturation. The ETM-MIP model does not take into account of the influence of water saturation on permeability of the soil. With the presence of a gas phase, the permeability of the soil needs to be modified with the relative permeability. Relative permeability is a dimensionless number that ranges from 0 to 1. Equation 3-13 is the Darcy s law with relative permeability

38 29 where q is the Darcy s velocity, is the intrinsic permeability of soil, is the viscosity of water, is relative permeability, is pressure, is density, is acceleration constant, and is the elevation. Equation 3-13 shows the result of Darcy velocity is smaller than the Darcy s velocity without relative permeability. Relative permeability is based on the Brooks-Corey (Brooks & Corey, 1964) function: where S e is the effective saturation, λ is pore-size distribution parameter, S w is current water saturation, S wr is the irreducible water saturation, and S m is the maximum water content Constant Concentration Source Zone For the constant concentration source zone simulations the dissolved TCA concentration in the initial contamination zone is always kept constant. If the TCA concentration is lower than the initial concentration 9 mol/m 3 in initial contamination zone, the model would force the concentration in the source zone to increase to 9 mol/m 3. This is done in the mass transport module before the MIP module is called. In contrast, if the dissolved TCA concentration in any cell is above the TCA solubility, NAPL will be produced. A solubility check function is added into the ETM-MIP model. The solubility check is called before mass transport step. If the TCA concentration is above the solubility level, the current aqueous concentration will be set equal to the solubility, and the additional mass is saved as NAPL mass, which will be traced separately from dissolved concentration. Equation 3-16 is the mass balance equation. The right side of the equation is the total mass of TCA with aqueous concentration adjusted to solubility limit as opposed to left side of equation without adjustment of aqueous concentration. The gas saturation, temperature, and Henry s constant are assumed to be not affected by the change of aqueous concentration.

39 Equation 3-16 is the molar balance of TCA, where is old NAPL concentration, is dissolved concentration, is the gas saturation, is Henry s constant, is the gas law constant, is the temperature, is the new NAPL concentration, and is the concentration at solubility limit. In addition to NAPL phase formation, NAPL is allowed to dissolve back into aqueous phase if aqueous concentration is below solubility limit. In this situation, all the NAPL mass or a portion of NAPL mass can dissolve back into aqueous phase. Equation 3 17 is a rearrangement of equation If equation 3-17 holds true, that means only a portion of NAPL mass will redissolve into aqueous phase. Aqueous concentration will equal to solubility limit. The resulting NAPL mass can be calculated from equation If equation 3-17 does not hold with presence of NAPL, that means all the NAPL mass will redissolve into aqueous phase. The [resulting NAPL mass is zero. The resulting aqueous concentration can be calculated through equation The solubility check is done before and after mass transport. Whenever aqueous concentration changes, solubility check function is called to separate the NAPL phase from the aqueous concentration Multi-Component Partitioning The goal of simulating the multi-component scenario is to examine the effect of multiple aqueous components partitioning to the gas phase. Specifically, dissolved oxygen and nitrogen are modeled as background components. Equation 3-20 and equation 3-21 calculate initial dissolved nitrogen and oxygen respectively (Sander, 1999).

40 31 where and are nitrogen and oxygen concentration, 0.79 and 0.21 are the volume fractions of nitrogen and oxygen respectively in the atmosphere, is atmospheric pressure, T ref is reference temperature at 20 o C. Partial pressures of both oxygen and nitrogen are calculated from equation 3-3. The presence of nitrogen and oxygen will have major influence on gas bubble formation Latent Heat Effects The enthalpy of vaporization, also called the latent heat, is an important quantity characterizing the energetics of vapor-liquid equilibrium. In the ETM-MIP model of Krol et al (Krol, Sleep, & Johnson, 2011a), only sensible heat is considered in the energy balance, not latent heat. As a result, phase change from liquid to gas has no effect on energy balance. For example, without latent heat, the temperature in the ETM-MIP model can easily go over 100 o C, which will not happen physically with presence of water. Since many parameters are temperature dependent such as density, an unrealistically high temperature will also have effects associated with other temperature dependent variables. Latent heat is calculated by multiplying specific latent heat, which is an intrinsic property of a substance, by the amount of liquid mass being vaporized. In a multi-component scenario, the latent heat of water, TCA, nitrogen, and oxygen are calculated. Equation 3-21 is the result of latent heat calculation. Equation 3-22 calculates the amount of mass of each component being vaporized through ideal gas law.

41 32 where is latent heat energy, is specific latent heat constant, is mass, is pressure, is universal gas constant, is temperature, is gas saturation. The latent heat function is called before the MIP module. In order to calculate latent heat energy, gas saturation must be known. However, the gas saturation is only computed after all the temperature dependent variables are updated. It is difficult to combine temperature, latent heat, gas saturation into one equation. Thus, a time-lagging approach is used to calculate latent heat energy. That means the latent heat energy calculated in one time step can only be counted in the energy balance in the next time step. This approach may cause temperature fluctuations at the coboiling point.

42 33 Chapter 4: Results and Discussion The objective of this research is to determine the influences of relative permeability, constant concentration source, multi-component partitioning, and latent heat on velocity, temperature, aqueous concentration, NAPL concentration and gas bubble distribution associated with ERH. Four scenarios are investigated in sequences in a way that each new scenario is built on the previous scenario. Table 4.1 summarizes all simulation conditions. Yes in the table means the process is included in the simulation; No means if is not included. Table 4.1 Summary of All Simulation Conditions Constant-source Relative Multi- Latent heat Scenario Permeability component Simulation 1 No No No No Simulation 2 Yes No No No Simulation 3 Yes Yes No No Simulation 4 Yes Yes Yes No Simulation 5 Yes Yes Yes Yes Simulation 6 Yes Yes Yes Yes 4.1 Simulation 1: Base Simulation All the presented represents conditions at the end of the simulations (simulation of minutes of ERH). Results presented from Figure 4.1a to Figure 4.1f are for the initial version ETM-MIP model before adding any new modules.

43 34 Figure 4.1a shows the temperature distribution. Figure 4.1b shows streamlines of velocity at 80 o C without relative permeability effects, and Figure 4.1c shows the velocity vectors without relative permeability while Figure 4.1d is the water density distribution at 80 o C. The reference water density is set at room temperature, 20 o C. Once electrodes are turned on, the updated water density is re-calculated each time step. As the temperature increases, water density decreases inducing buoyant flow and convection. Two circular flows are induced around the electrodes where temperature is high. Velocity is a function of both viscosity and density, and can be characterized by the buoyancy ratio Ra/Pe, where Ra is Rayleigh number and Pe is thermal Peclet number. When the buoyancy ratio is greater 1, the buoyant flow dominates (Mealey & Merkin, 2009). The buoyancy ratios of all the simulations are greater than 1000, which implies buoyant flow dominates advective flow. The low permeability lens interferes with flow in the middle. At the two sides of the lens, flow passes around lens, but due to the large buoyant force, flow is able to penetrate the low permeability barrier in the middle, but at a low velocity due to the low permeability. Advective flow coming from inlet can barely be observed in Figure 4.2b. The highest temperature occurs in the center, and the temperature decreases away from the center. However, the highest temperature is not located at the electrodes, but is between the electrodes. As shown in the velocity streamline distribution in Figure 4.1b, two strong buoyant flows meet in the center, forming a convective cell. Due to the low permeability lens, a stagnation point is formed in the center where velocity is very low, which can be observed in the velocity vector distribution plot. As a result, there is very little inflow of cooler water from below, producing a peak temperature in the center of the ERH target zone. Figure 4.2e shows the concentration distribution while 4.2f shows the gas phase distribution. All the gas bubbles are observed within the initial contamination zone. The highest gas saturation is smaller than 0.5, and the majority of gas bubbles have gas saturations smaller than the critical gas saturation, so they are not mobile. The highest dissolved phase TCA concentration, present in the low permeability lens is around 7 mol/m 3, which is below the solubility limit. Since no gas bubbles are present inside the lens, the highest concentration is the result from mass transport (strong buoyant flow and diffusion).

44 Figure 4.1a Temperature distribution Figure 4.1b Streamline distribution

45 Figure 4.1c Velocity vector (rotated view)

46 Figure 4.1d Water density Figure 4.1e Concentration distribution

47 Figure 4.1f Gas bubble distribution

48 Simulation 2: Constant Contaminant Source Scenario The dissolved TCA concentration in the initial contamination zone is kept constant at 9 mol/m 3 under the constant source scenario, simulating the presence of a NAPL. At the laboratory scale, it was found that a small entrapped gas bubble could expand, mobilize, and collapse while a NAPL pool was present{{27 Mumford,Kevin G. 2010}}, causing redistribution of water, gas, and aqueous phase contaminant in the system. If the concentration in any cell is greater than the TCA solubility, it is assumed that a NAPL phase will form and the partitioning algorithm is adjusted to account for the presence of a NAPL. The concentration above TCA solubility is converted to a NAPL mass and is tracked separately from the aqueous concentration. NAPL movement is not considered in this simulation. In contrast, if the dissolved concentration in a particular cell is below the solubility limit, NAPL is allowed to dissolve back into aqueous phase. Figure 4.2a shows the temperature contours, Figure 4.2b shows the water flow streamlines, and Figure 4.3c shows the velocity vectors, all for a constant contaminant source. These can be contrasted with Figures 4.1a, 4.1b, and 4.1c, respectively for the case with a non-constant contaminant source. Figures 4.1a and 4.2a show a similar distribution where the highest temperatures are located in the center. In the Figure 4.1a, the temperature distribution is symmetric, while highest temperature in Figure 4.2a is not symmetric in the center due to the change in buoyant flow in the constant source scenario and different gas phase conditions. Figure 4.2d shows the dissolved concentration distribution with a constant source, while 4.2e and 4.2f show the gas phase distribution. In the constant source there is a continual high source of TCA to produce gas phase, resulting in much greater upward movement of gas clusters to the top of the domain. Gas bubbles tend to move from the hot zone (near the electrodes) to the cold zone (away from the electrodes). Once a gas bubble moves to the colder zone, it tends to collapse, and its gas mass dissolves into the aqueous phase. In the constant source simulation, the dissolved concentration is much higher than the concentration in non-constant source simulation. The aqueous phase TCA concentration almost reaches the solubility limit everywhere and in some locations exceeds the TCA aqueous solubility, forming a NAPL.

49 Figure 4.2g is the NAPL concentration distribution in the constant source scenario. NAPL phase formation is only observed under the constant source scenario. The total TCA concentration of each cell is the sum of aqueous concentration and gas phase concentration. If a gas bubble dissolves into the aqueous phase where the aqueous concentration previously at or near the solubility limit, the total mass in aqueous phase will now exceed the TCA solubility limit. The concentration above solubility limit is saved as NAPL concentration, which could be converted to a saturation using the TCA density. The highest NAPL concentration is above 135 kg/m 3, and this concentration is almost 100 times higher than the aqueous phase concentration, which suggests a significant amount of mass can be transferred from aqueous phase to gas phase at high temperature. NAPL formation in the initial contamination zone is caused by gas mobilization. When gas mobilization occurs within the initial contamination zone, gas phase TCA mass is completely transferred from one cell to another. This may potentially cause NAPL formation in a newly invaded cell if the cell previously contained TCA near the solubility limit in the water phase. This is not a physically realistic scenario as the model does not properly simulate the displacement of the water phase when gas invades a cell. This would require more direct coupling of the water and gas phases, which is difficult when the water phase is simulated using a continuum approach, while the gas phase movement is simulated using the MIP method.

50 Figure 4.2a Temperature distribution with constant contaminant source Figure 4.2b Streamline distribution with constant contamination source

51 Figure 4.2c Velocity distribution (expanded view below the low permeability lens) with constant contaminant source Figure 4.2d Concentration distribution with constant contaminant source

52 Figure 4.2e Gas bubble distribution with constant contaminant source nz = 361 Figure 4.2f Superimposed gas bubble and streamline distribution with constant contaminant source

53 Simulation 3: Relative Permeability Scenario Relative permeability has a direct influence on Darcy velocity. Relative permeability is a function of water saturation. With the presence of a gas phase, relative permeability reduces the flow through the unsaturated zone. For example, if a cell is 100% saturated with gas phase, the relative permeability in that cell is 0, which means no water flow can go through the cell. Figure 4.3a shows temperature contours with relative permeability considerations and can be compared to Figure 4.2a. The temperature distributions of the two figures are similar except in the center where the highest temperature contour is more spread out in the simulation without relative permeability than the simulation with relative permeability. The change of temperature is the result of the heat accumulation, and the heat distribution is strongly affected by the buoyant flow which is reduced when relative permeability is considered due to gas phase accumulation and decreases in water saturation. Figure 4.3b shows the concentration distribution, Figure 4.3c shows the gas phase distribution, Figure 4.3d shows the gas phase distribution superimposed on the streamlines, Figure 4.3e shows the water phase velocity vectors in an expanded view under the low permeability lens and Figure 4.3f shows the predicted NAPL distribution. There is little difference in the aqueous phase and NAPL concentrations and gas phase distributions between the simulations with and without relative permeability effects for the conditions simulated. There is a slight difference in the concentrations as in the simulation with relative permeability, NAPL concentration is more spread out within the initial contamination zone, which suggests more frequent gas mobilization within this zone. But the highest concentration is observed outside initial contamination zone in the simulation without relative permeability in both simulations. Figure 4.3e shows a magnified section below the low permeability lens, the magnitude of velocity is much lower in the simulation with relative permeability as expected, compared to the case in which relative permeability is not considered. However, the direction of flow is similar in both simulations. Figure 4.2f and Figure 4.3d are the superimposed gas bubble and streamline distributions without and with the relative permeability. In Figure 4.3d, buoyant flow is reduced through gas bubble zone. Without the influence of the relative permeability, buoyant flow in Figure 4.2f is stronger and results in higher heat convection, accounting for the higher temperature in Figure 4.2a.

54 Figure 4.3a Temperature distribution with relative permeability Figure 4.3b Concentration distribution with relative permeability

55 Figure 4.3c Gas bubble distribution with relative permeability nz = 344 Figure 4.3d Superimposed gas bubble and streamline distribution with relative permeability

56 Figure 4.3e Velocity distribution (expanded view below the lower permeability lens) with relative permeability Figure 4.3f NAPL distribution with relative permeability

57 Figure 4.3g Water phase velocity distribution with relative permeability (rotated view)

58 Simulation 4: Effect of Multi-Component Gases In this simulation, dissolved oxygen and nitrogen are modeled as background components, and the dissolved concentrations are assumed to be in equilibrium with the atmosphere initially. Incoming water is assumed to contain dissolved oxygen and nitrogen, but not TCA. Each component in the model is treated in the same way in that they are all transported in both the aqueous phase and gas phase. Mass transport in the aqueous phase of each component is modeled separately, assuming no interference or interaction between each component. Total partial pressure of gas phase is the sum of the partial pressures of each component. Figures 4.4a to Figure 4.4f show the various results for the simulation with oxygen and nitrogen present. At the first time step when electrodes are just turned on, the temperature inside the initial contamination zone is slightly above constant temperature, 20 o C. The temperature outside the initial contamination zone is at constant temperature. The boiling point of TCA is at 73 o C (Gälli & McCarty, 1989). The co-boiling point is lower than the boiling temperature of any component in the mixture. In a TCA-water mixture, the co-boiling point is calculated to be 67 o C, meaning that no gas bubble can be formed below the co-boiling point in a TCA-water system. However, in a multi-component system, bubbles appear almost everywhere (Figure 4.4a) in the top half of the system with multi-component scenario. All the bubbles have small gas saturations, so they are not mobile. Even the biggest gas saturation in Figure 4.5c is smaller than Bubbles within the TCA source have slightly higher gas saturation because temperature inside is slightly higher that the constant temperature, ranging from 20 o C to 25 o C. A gas phase is formed in the upper regions of the system where the water pressure is lower and the sum of oxygen and nitrogen partial pressures at 20 o C, calculated from Henry s Law, exceed the water pressure. At 20 o C, Henry s temperature dependent constants for both oxygen and nitrogen are higher than that for TCA. Thus, the gas phase is primarily composed of oxygen and nitrogen. The gas phase distribution at the end of the simulation (Figure 4.4d) below the low permeability lens for the multi-component simulation is similar to that for the simulation with only TCA and water (Figure 4.3c), while there is greater gas accumulation at the top of the system in the multicomponent case. The temperature and concentration in the center is more spread out in the simulation with the additional components (Figures4.4b and 4.4c). Temperature and contaminant

59 transport are strongly influenced by the influx of cool water and the model predicts greater buoyant flow in the simulation with multi-component around the center location. Stronger buoyant flow results in higher temperature in the middle region and causes greater spread of the dissolved TCA. Figure 4.5f and Figure 4.5g are the results of both nitrogen and oxygen concentration distribution with multi-component scenario. Both concentration distributions look identical, but opposite to TCA concentration distribution. Initially, both oxygen and nitrogen concentrations are the same in all cells. Without gas mass transport, the concentration gradient between nieghbouring cells is zero, so concentration distributions are uniform and would not be affected by flow. Whenever gas mobilization occurs, concentration gradients will be produced due to gas mass transport and stripping of nitrogen and oxygen from the water. For both simulations, the concentration is the highest at the top of the system due to gas bubble upward movement and collapse. The lowest concentration is observed in the TCA source zone where gas bubbles constantly mobilize within or outside the TCA source zone.

60 51 x Figure 4.4a Gas bubble distribution at the first time step Figure 4.4b Temperature distribution with multi-component gases

61 Figure 4.4c Concentration distribution with multi-component gases Figure 4.4d Gas bubble distribution with multi-component gases

62 Figure 4.4e Velocity vector with multi-component gases (rotated view)

63 Figure 4.4f Nitrogen concentration distribution with multi-component gases Figure 4.4g Oxygen concentration distribution with multi-component gases

64 Simulation 5: Latent Heat The enthalpy of vapourization, also called latent heat, is an important quantity characterizing the energetics of vapor-liquid mass transfer. Latent heat is a important parameter in modeling thermal remediation. In the majority of thermal remediation approaches, vapour extraction is usually the primary mean to recover highly volatile contaminants from groundwater. The coboiling point of water-contaminant mixture should be determined prior to remediation. The temperature in the water-contaminant mixture cannot be higher than the co-boiling point when both contaminant and water are present and the contaminant concentration is constant, as occurs with the presence of contaminant as a NAPL. Additional energy will speed up vapourization process rather than increase the temperature until either the contaminant concentration decreases or all the water is boiled away. Due to the time-lagging of latent heat calculations, experimentation with time step length for water flow, aqueous mass transport, and heat energy transport was required to balance the energy from ERH with the latent heat associated with gas generation in a time step. Ultimately, a time step of 10 seconds was used until the peak temperature reached 65 o C, a little bit below co-boiling temperature. At this point, just before the first gas was generated, the time step was reduced to 1 second. Average temperature plot, temperature distribution, and NAPL distribution in Figure 4.5a, and Figure 4.5b, show the results of the simulations without latent heat at 10 minutes using the reduced time step. Figure 4.5c is the plot of average temperature at 10 minutes with the inclusion of latent heat. To better demonstrate the influence of latent heat on temperature distribution, the maximum temperature was set to 100 o C. In Figure 4.5c, when temperature reached 68 o C over 5 minutes, it stabilized and fluctuated within 1 degree for the rest of the simulation. The small bump on the plot is due to sudden time step change from 10 to 1 second. In Figure 4.5a, without latent heat, the temperature shows a steady increase from 20 o C to 77 o C until the end of the simulation. The temperature shows no sign of stabilizing at a specific point, and increases to 77 o C by the end of simulation. The first gas bubble appears in a TCA-water mixture at 67 o C. With nitrogen and oxygen present, the co-boiling point is around 66 o C because of additional partial pressures from nitrogen and oxygen. In addition, gas saturation could range from to 0.93 in the model.

65 56 However, gas saturation increases rapidly with temperature. For example, gas saturation could increase from 0.01 to 0.5 with an increase of 4 o C such as from 67 o C to 71 o C. Figure 4.5b and Figure 4.5d show the temperature distributions without and with latent heat. Without latent heat, highest temperature is observed within the initial contamination zone. In contrast, with latent heat, the highest temperature is observed at electrodes outside initial contamination zone. Within contamination zone, the temperature is evenly distributed at 68 o C. The temperature distribution shows temperature is stabilized at 68 o C. Any additional energy will not lead to an increase in temperature. Figure 4.4d and Figure 4.5e are the gas bubble distributions for the simulation without and with latent heat. Due to high dissolved concentration and high temperature in both simulations, no significant influence of latent heat is observed within initial contamination zone. But more gas bubble formation is observed below the initial contamination zone in the simulation without latent heat due to higher temperature. The latent heat effect for the fifth simulation shows additional electrical energy cannot increase temperature beyond co-boiling point. Latent heat has significant influence on temperature distribution, but not on gas bubble or NAPL distributions, which implies operating above coboiling point in the model has little influence on the results except temperature if vaporization rate is not considered.

66 Average Temperature o C 57 Average Temperature within Initial Contamination Zone Time (minute) Temperature Figure 4.5a Average temperature plot without latent heat Figure 4.5b Temperature distribution without latent heat

67 Average Temperature o C 58 Average Temperature within Initial Contamination Zone Time (minute) Temperature Figure 4.5c Average temperature plot with latent heat Figure 4.5d Temperature distribution with latent heat

68 Figure 4.5e Gas bubble distribution with latent heat

69 Simulation 6: Smaller Source Zone with Latent Heat Effects The sixth simulation investigates the influence of temperature heterogeneity on gas bubble movement. In this simulation, only the top half of the initial contamination zone contains TCA. Figure 4.6a illustrates the new initial contamination zone. The maximum temperature for ERH is set to 95 o C. Figure 4.6b is the average temperature of the top half of the source zone. Similar to the previous case, the temperature reaches 68 o C over 5 minutes and fluctuates at this temperature for the rest of the simulation. Figure 4.6c shows the temperature spatial distribution. The highest temperature is observed within uncontaminated area and it exceeds the TCA-water co- boiling temperature. In the source zone, the temperature is uniformly distributed around 67 o C due to the effect of latent heat. Figure 4.6d is the gas bubble distribution. No gas bubbles are observed in the uncontaminated zone. Unlike the gas bubble distribution in Figure 4.5e, in the source zone, no gas bubble is formed in the middle region, which suggests the temperature in the middle region may be lower than co-boiling point. Temperature distribution in Figure 4.6c shows the temperature in middle region is between 60 o C and 65 o C.

70 Average Temperature o C Low Permeability Lens 60 TCA Figure 4.6a Initial contamination location Average Temperature within Initial Contamination Zone Time(min) Temperature Figure 4.6b Average temperature plot with latent heat (smaller source zone)

71 Figure 4.6c Temperature distribution with latent heat (smaller source zone) Figure 4.6d Gas bubble distribution with latent heat (smaller source zone)

72 63 Chapter 5: Conclusion and Recommendations 5.1 Conclusions The main objectives of this research were to extend an existing numerical model in order to examine the influences of relative permeability, multi-component gases, and latent heat on velocity, temperature, aqueous phase concentration, NAPL formation and gas movement. Results from the constant source scenario showed higher gas saturation was achieved, and gas bubbles have the potential to travel much further than in the non-constant source case. The dissolved concentration was much higher, particularly outside the source one. Due to more frequent gas expansion and mobilization, NAPL formation was observed within and outside the initial contamination zone. Results from the relative permeability scenario showed relative permeability significantly lowered the water phase velocity in the presence of a gas phase. The lower velocity in the gas zone allowed heat to accumulate, increasing the temperature and producing more gas generation. The lower velocity also caused the dissolved TCA to transport slowly. But overall, the influence of relative permeability on temperature, gas bubble, and concentration distributions was small. The influence of relative permeability on gas bubble distribution was insignificant because at high temperature, gas movement dominated gas phase mass transport while relative permeability only affects aqueous phase mass transport. Results from the multi-component scenario, showed that the presence of oxygen and nitrogen, had low impacts on gas bubble distributions as well as temperature distribution due to low dissolved concentration and low volatility at co-boiling temperature. However, at constant temperature, Henry s constants of oxygen and nitrogen were much higher than the Henry s constant of TCA. As a result, low gas saturations could be produced with slightly temperature increases.

73 64 Results from latent heat simulations showed that latent heat considerations produced temperature plateaus at the co-boiling temperature. However, the influence of latent heat on gas bubble distribution was insignificant for the conditions examined in this study. With heterogeneous source zones simulations indicated that significant heterogeneity in temperature distributions could result from the establishment of plateaus at the co-boiling temperature in NAPL source zones, and much higher temperatures outside the NAPL source zone.

74 Recommendations Results from six simulations showed significant improvements of the existing ETM-MIP model. When it comes to modeling complex hydro-geological systems, there is always room for improvement. The following are recommended for further research. Instead of randomly assigning permeability in each cell, if permeability is assigned by different layers with different soils, then greater influence of soil heterogeneity on temperature, gas bubble, and concentration distribution may be observed. Gas phase movement is discrete, and NAPL is assumed to be immobile. Specifically, the volume of gas phase and NAPL phase is not accurately accounted for. For example, the water being pushed out by an expanding gas phase is not considered, which causes incorrect NAPL formation and distribution. A multi-phase flow model is needed to simulate continuous gas phase movement as well as NAPL movement. In addition to components such as oxygen and nitrogen, other volatile compounds such as DCE, TCE could be simulated to observe the influence on gas bubble distribution as well as NAPL distribution of each component. Neither gas bubble generation in the ETM model nor gas movement in the MIP model is strictly associated with time. In contrast, the processes of electric heat generation, water flow, aqueous phase mass transport, and heat energy transport are simulated with timedependent equations. To accurately account for energy balance, it is necessary to include temporal considerations for bubble generation and transport. Solving the non-linear implicit equation in the gas solver is highly time consuming. Gas solver tries to solve gas saturation in each cell in a large matrix. Even the cell without real solution can return an imaginary root to the solver. If such cells can be determined prior to gas solver, then the running time for each simulation can be significantly reduced.

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80 71 Appendix A Model Flow Charts Set initial value Calculate Voltage Iterate between temperature and temperature dependent properties Update temperature dependent variables Solve gas saturation Calculate solute transport Check TCA Solubility Solve gas saturation after obtained new concentration from solute transport Compute Latent heat MIP Figure A.1: Electro-thermal model flowchart