DNAPL MIGRATION IN SINGLE FRACTURES:

Transcription

1 DNAPL MIGRATION IN SINGLE FRACTURES: ISSUES OF SCALE, APERTURE VARIABILITY & MATRIX DIFFUSION By Katherine I. Hill A thesis submitted to the, Faculty of Engineering, Computing and Mathematics, in conformity with the requirements for the degree of Doctor of Philosophy Perth, W.A. June 2007

2 Declaration This thesis is wholly my own composition, and where I have used other sources I have acknowledged their contribution. This thesis has not previously been accepted for any other degree in this or another institution and has been entirely accomplished during enrolment in the degree held at the. This thesis is largely composed of three papers which have been submitted, or are in preparation for submission, to refereed journals. The coauthors of these papers are aware and have given permission for these papers to be included in this thesis. Katherine I. Hill (Candidate) David A. Reynolds (Supervisor) i

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4 Abstract To date, many subsurface contaminant modelling studies have focused on increasing model complexity and measurement requirements to improve model accuracy and widen model application. However, due to the highly complex and heterogeneous nature of flow in the subsurface, the greater benefit in model development may lie in decreasing complexity by identifying key processes and parameters, simplifying the relationships that exist between them, and incorporating these relationships into simple models that recognise or quantify the inherent complexity and uncertainty. To address this need, this study aims to identify and isolate the key processes and parameters that control dense nonaqueous phase liquid (DNAPL) and aqueous phase migration through single, onedimensional fractures. This is a theoretical representation which allows the study of processes through conceptual and mathematical models. Fracture systems typically consist of multiple two-dimensional fractures in a three-dimensional network; however, these systems are computationally and conceptually demanding to investigate and were outside of the scope of this study. This work initially focuses on DNAPL migration in single, one-dimensional fractures. The similitude techniques of dimensional and inspectional analysis are performed to simplify the system and to develop breakthrough time scale factors. This approach relies heavily on the limitations of the equation used for the analysis and on the difficulty in representing variable aperture scenarios. The complexity of the conceptual model is then increased by embedding the fracture in a two-dimensional, porous matrix. The similitude technique of inspectional analysis is coupled with a more qualitative mass storage analysis which iii

5 formulates fracture (M f ) and matrix (M m ) mass storage capacities. The resulting mass storage ratio (M m :M f ) is found to accurately identify when matrix effects will significantly delay breakthrough times in parallel plate fractures if the condition M m :M f < 1 is satisfied, but becomes increasingly inaccurate as aperture variability and matrix effects are increased. The methods employed in these investigations go some way to explaining the magnitude of effects that different DNAPL, matrix and fracture properties have on breakthrough times in single fractures, and the outcomes demonstrate how useful predictive tools can still be generated from simple conceptual models. These tools can be readily applied by the field investigator or computer modeller to make order-of-magnitude estimates of breakthrough times, reduce or target measurement requirements, and lessen the need to employ numerical multiphase flow models. To determine the implications of the results found in the one-dimensional studies to applications at the field scale, the complexity of the conceptual model was increased to a single, two-dimensional, planar fracture embedded in a three-dimensional porous matrix. The focus of this study was not DNAPL breakthrough times but the relative importance and interaction of different mass transport processes and parameters on plume migration and evolution. Observations clearly show that estimates of the size, location and concentration of the plume is highly dependent on the geologic media, the temporal and spatial location and resolution of measurements, and on the history, mass and location of the DNAPL source. In addition, the processes controlling mass transport (especially matrix diffusion and back diffusion) act in combination at the field scale in ways not always expected from an analysis of processes acting individually at smaller spatial and iv

6 temporal scales. Serious concerns over the application of the common 1% Rule of Thumb to predict DNAPL presence and the use of remediation efforts that rely largely on natural attenuation are raised. These findings have major implications for the field worker and computer modeller, and any characterisation, monitoring or remediation program development needs to be sensitive to these findings. v

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8 Acknowledgements The author wishes to acknowledge the University Postgraduate Award, the Graduate Research School and the Council of Convocation, all from the University of Western Australia, and the Centre for Groundwater Studies Top-Up Scholarship, for financial support. Project support for this research has also been funded by the Australian Research Council and is greatly appreciated. Dr. David Reynolds is acknowledged for his guidance, sole supervision of the research and his model SUBCONS which was used extensively in this thesis. Dr. Bernard Kueper is acknowledged for his expertise and advice on DNAPL migration, and for hosting me at Queen s University on two occasions. Dr. Jason Gerhard is also acknowledged for granting permission to use DNAPL3D-MT and providing user support. Very special thanks to Mum, Megan, Sarah and Tom for their support and encouragement throughout the study, for everything we have shared up until now, and for all our adventures together in the future. vii

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10 Forward This thesis has been written in manuscript style. Chapter 1.0 presents an introduction to the goals and motivation of the research contained within the thesis, and Chapter 2.0 gives a review of the literature that is relevant to this work. Chapters 3.0 through 5.0 can be read as stand-alone chapters and consist of manuscripts which are in preparation to be submitted to refereed journals for publication. Conclusions and recommendations are given in Chapter 6.0 and auxiliary information gathered or developed in this study that is not included in the main body of the text is listed in the Appendices. At the time of submission of this thesis, Chapters 3.0 and 4.0 had been submitted to the Journal of Mathematical Geology, and Chapter 5.0 was in preparation to be submitted to Ground Water. The primary author of all three papers is K. I. Hill, who was the lead investigator and prepared all three papers for submission. This work was done under the supervision of D. A. Reynolds, with collaborations with B. H. Kueper and J. I. Gerhard, and they are listed as coauthors where appropriate. The models used in this thesis were used with permission from the developers (D. A. Reynolds SUBCONS; J. I. Gerhard DNAPL3D-MT). ix

11 TABLE OF CONTENTS 1.0 INTRODUCTION REFERENCES LITERATURE REVIEW INTRODUCTION NONAQUEOUS PHASE LIQUIDS FRACTURED MEDIA THE PHYSICS OF DNAPL MIGRATION IN FRACTURES MATRIX EFFECTS MODELLING MULTIPHASE FLOW ISSUES OF SCALE AND SIMILITUDE DIMENSIONS, UNITS AND SCALE THEORY OF SIMILARITY AND SIMILITUDE ANALYSIS DIMENSIONAL ANALYSIS INSPECTIONAL ANALYSIS STOCHASTIC METHODS AND THE MONTE CARLO APPROACH REFERENCES SIMILITUDE ANALYSIS OF DNAPL BREAKTHROUGH TIMES IN A SINGLE FRACTURE INTRODUCTION PROBLEM FORMULATION PARALLEL PLATE FRACTURES VARIABLE APERTURE FRACTURES DNAPL PROPERTIES METHODS OF ANALYSIS NUMERICAL MODELLING DIMENSIONAL ANALYSIS OF MULTIPHASE FRACTURE FLOW INSPECTIONAL ANALYSIS OF DARCY S MULTIPHASE EQUATION RESULTS PARALLEL PLATE FRACTURES DIMENSIONAL ANALYSIS INSPECTIONAL ANALYSIS VARIABLE APERTURE DISTRIBUTION DISCUSSION AND CONCLUSIONS REFERENCES IDENTIFYING THE IMPORTANCE OF MATRIX DIFFUSION ON DNAPL BREAKTHROUGH TIMES IN SINGLE FRACTURES INTRODUCTION PROBLEM FORMULATION PARALLEL PLATE FRACTURES VARIABLE APERTURE FRACTURES DNAPL AND MATRIX PROPERTIES METHODS OF ANALYSIS NUMERICAL MODELLING ANALYTICAL DIFFUSION APPROXIMATION INSPECTIONAL ANALYSIS MASS STORAGE ANALYSIS i

12 4.4. RESULTS PARALLEL PLATE FRACTURES VARIABLE APERTURE FRACTURES IMPLICATIONS CONCLUSIONS REFERENCES INVESTIGATING FIELD SCALE DNAPL MASS TRANSPORT PROCESSES IN FRACTURED POROUS MEDIA INTRODUCTION REVIEW OF CONTAMINANT MASS TRANSPORT PROCESSES PROBLEM FORMULATION FRACTURE, MATRIX AND DNAPL PROPERTIES SIMULATION PLAN NUMERICAL MODELLING RESULTS MASS FLUX ACROSS FRACTURE-MATRIX INTERFACE DOWNSTREAM WELL CONCENTRATIONS IMPLICATIONS CONCLUSIONS REFERENCES CONCLUSIONS AND RECOMMENDATIONS REFERENCES Appendix A - Summary of probability distributions and parameters used in the literature to describe fracture aperture variability...a A.1 REFERENCES... B Appendix B - The REV Debate... d B.1 REFERENCES... H Appendix C - Some representations of the Capillary and Bond numbers... i C.1 REFERENCES... J Appendix D Derivation of the Dimensional Analysis Breakthrough Time... k Appendix E - Inspectional analysis of macroscopic mass balance and Fick s Equations... m D.1 REFERENCES...P Appendix F Variable aperture study results with matrix diffusion... q ii

13 LIST OF TABLES Table 3.1 Fracture and DNAPL parameter value ranges for the parallel plate study Table 3.2 Fracture and DNAPL properties used in the variable aperture study Table 3.3 Summary of the variable aperture study results. The parallel plate study results (σ = 0 µm) are shown in italics for comparison Table 4.1 Fracture and DNAPL parameter value ranges for parallel plate study Table 4.2 Matrix parameter value ranges and constants used in parallel plate study Table 4.3 Summary of the variable aperture study results. The parallel plate study results (σ = 0 µm) are shown for comparison Table 5.1 Summary of the contaminant mass transport processes acting in the fractured porous media Table 5.2 Summary of the variable parameters used Table 5.3 DNAPL input parameter values for TCE and constant parameters Table 5.4 Simulation plan iii

14 LIST OF FIGURES Figure 2.1 Schematic of a contamination scenario arising from a spill of DNAPL (from Kueper & McWhorter, 1991) Figure 2.2 Typical capillary pressure (P C ) saturation (S W ) curve showing hysteresis (from McWhorter & Kueper, 1996), where S W is the wetting phase saturation, S NW is the nonwetting phase saturation, S Wr is the residual wetting phase, and S NWr is the residual nonwetting phase. The displacement pressure is analogous to P E in fractured media Figure 2.3 Typical threshold value curves indicating Ni = 1 for a typical fractured a) clay, b) sandstone and c) granite. If the point defined by the solubility of the DNAPL (Sw) and fracture aperture (e = 2b) lies above and to the left of the line corresponding to the fracture length (L) then Ni will be greater than unity and matrix diffusion may be significant (from Ross & Lu, 1999) Figure 3.1 Simulation domain and boundary conditions, where γ = fracture dip from horizontal, L = fracture length, e = fracture aperture, NW indicates the non-wetting DNAPL phase and W indicates the wetting water phase Figure 3.2 Comparison of dimensional analysis breakthrough time and numerically modelled breakthrough time for different fracture lengths for (a) base case (k rnw = 1) and (b) case where k rnw is equal to the value calculated at the fracture entrance. The dashed grey line indicates ± an order of magnitude from a 1:1 relationship (black line) Figure 3.3 Example of non-wetting phase saturation (S NW ) profile at breakthrough time generated from the numerical model for each fracture length. The dashed line indicates the constant S NW scenario calculated at the fracture entrance Figure 3.4 Comparison of inspectional analysis breakthrough time and numerically modelled breakthrough time for different fracture lengths. The dashed grey line indicates ± an order of magnitude from a 1:1 relationship (black line) Figure 3.5 Determining the effects of wetting phase viscosity on selected data points with different fracture lengths for (a) µ w = 1.00E-03 kgm -1 s -1 (base case) and (b) µ w = 1.00E-07 kgm -1 s -1 (reduced µ w case). The dashed grey line indicates ± an order of magnitude from a 1:1 relationship (black line) Figure 3.6 The cumulative mean of the numerically modelled breakthrough time and hydraulic aperture for the variable aperture study for the medium mobility scenario with a standard deviation from the mean mechanical aperture (50 µm) of (a) 10 µm, (b) 20 µm, and (c) 30 µm Figure 3.7 Comparison of inspectional analysis breakthrough time to numerically modelled breakthrough time (parallel plate) and cumulative mean breakthrough time (variable aperture). The dashed grey line indicates ± an order of magnitude from a 1:1 relationship (black line) Figure 4.1 Simulation domain and boundary conditions, where e = fracture aperture, L = fracture length, a = fracture spacing, NW indicates the non-wetting DNAPL phase and W indicates the wetting water phase Figure 4.2 The relative concentration of a solute along a fracture for the Analytical Solution and Numerical- Analytical Solution Figure 4.3 Comparison of inspectional analysis breakthrough time and numerically modelled breakthrough time for scenarios with and without matrix effects. The solid black line indicates a 1:1 relationship, and the dashed grey lines indicate ± an order of magnitude from a 1:1 relationship Figure 4.4 Comparison of breakthrough times generated by the numerical model for the case with (t = t m ) and without (t = t a ) matrix effects. Data points highlighted in grey indicate when the conditions a) (M m :M f ) MAX > 1 and b) M m :M f > 1 are satisfied. The solid black line indicates a 1:1 relationship and the dashed grey line indicates an order of magnitude greater than a 1:1 relationship Figure 4.5 Comparison of dimensionless ratio of breakthrough times with and without matrix diffusion (t m :t a ), to the dimensionless ratio of the mass storage (M m :M f ) Figure 4.6 Comparison of ratio of breakthrough times with and without matrix effects (t m :t a ), to the dimensionless ratio of the mass storage M m :M f and the Nitao number (Ni). M m :M f and Ni are calculated for scenarios including and ignoring S NW and k r Figure 4.7 Comparison of breakthrough times for no, low and fast matrix effects, compared to hydraulic aperture, for each random field number (realisation) for a standard deviation of 10 µm Figure 4.8 Comparison of inspectional analysis breakthrough time to numerically modelled breakthrough time (parallel plate = par ) and cumulative mean breakthrough time (variable aperture = var ) for the iv

15 scenarios involving no, low and high matrix effects. The black line indicates a 1:1 relationship and the dashed grey line indicates an order of magnitude less than a 1:1 relationship Figure 4.9 Calculated values of M m :M f for some commonly occurring DNAPLs in a vertical fracture for a range of a) fracture lengths (e = 10 µm) and b) fracture apertures (L = 10 m) Figure 5.1 Simulation domain for the case of interest (not to scale). Each multilevel well contains three monitoring intervals with screen length of 0.25 m with midpoints located at y = m (2 nd node), m (10 th node) and m (18 th node) from the top of the domain Figure 5.2 DNAPL mass dissolution curves for simulations of interest where t = 0 months corresponds to the time taken when the DNAPL spill first reaches residual Figure 5.3 Maximum penetration of aqueous phase contaminant into the matrix over 2 years from commencement of the DNAPL spill. The leading edge of the plume has a concentration in excess of 1 µg/l Figure 5.4 Summary of time to complete DNAPL disappearance, time to peak aqueous phase mass, and peak aqueous mass for the entire domain (fracture and matrix) after the source has ceased for simulations with a high DNAPL solubility (Sim 17 to 32). Complete DNAPL disappearance was only achieved in one low S simulation (Sim 13) after approximately 20 months Figure 5.5 Fraction of fracture face with active nodes contributing to mass flux a) from the fracture into the matrix (negative flux) and b) from the matrix into the fracture (positive flux) for selected simulations Figure 5.6 Total mass diffused into the fracture (from the matrix) and into the matrix (from the fracture) across the fracture-matrix interface for simulations of interest compared to the base case (Sim 17) summed for 1 month < t < 2 years since the spill is turned off. Net mass defined as difference between total mass into the fracture and matrix Figure 5.7. Net flux across the fracture face for a given timestep of interest for 100 sec to 24 months after the spill is released. The time period of 1 to 24 months (shown by box) is the time period plotted in detail in Figure Figure 5.8 Downstream observation well concentration curves for the inline, edge and offline observation nodes at a distance x of a) 15 m, b) 25 m, c) 35 m and d) 45 m Figure 5.9 The a) first arrival time, b) peak arrival time, and c) peak concentration of aqueous phase contaminant in the x = 15 and 25 m observation wells for the inline (2 nd node), edge (10 th node) and offline (18 th node) observation points. First arrival occurs when concentration exceeds 1 µg/l Figure 5.10 Inline concentration levels recorded in all observation wells 10 years after the occurrence of the DNAPL spill for simulations of interest v

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17 1.0 INTRODUCTION Many contaminated groundwater situations develop as a result of the subsurface presence of dense, nonaqueous phase liquids (DNAPLs) such as polychlorinated biphenyl (PCB) oils, chlorinated hydrocarbons, coal tar, and creosote. In many subsurface scenarios, three mobile phases will exist; gas, aqueous and nonaqueous, and each phase will be composed of a number of components (for example, water in the gas phase as vapour, and DNAPL dissolved in the aqueous phase). A release of DNAPL to the subsurface will distribute itself as both disconnected blobs and ganglia of organic liquid referred to as residual, and in continuous distributions referred to as pools. An aqueous phase plume may also develop down-gradient of the DNAPL over time. Residual DNAPL is formed at the trailing edge of a migrating DNAPL body due to pore-scale snap-off and trapping mechanisms (Kueper et al., 1993). DNAPL pools are formed when a migrating DNAPL body encounters an aquitard or capillary barrier and bulk downward migration ceases. In many cases, the aquitard comprises fractured bedrock or clay, and these fractures form preferential flow paths allowing DNAPL to penetrate greater distances in relatively short periods. Whether the DNAPL will enter fractures, the rate at which it will move upon entry, and the magnitude that dissolved contaminant in the aqueous phase will diffuse into the surrounding matrix are important aspects to consider in developing site conceptual models, characterisation programs, and remedial strategies. Entry of the DNAPL into the fractures and the rate at which the DNAPL travels will depend on a number of factors including the amount of matrix diffusion, fracture aperture characteristics, capillary properties, fracture orientation, DNAPL density, DNAPL viscosity, DNAPL-water interfacial tension and the driving head. DNAPL migration is also dependent on the 1

18 connectivity of fracture network; however, connectivity was considered outside of the scope of this study and only single one-dimensional fractures are simulated. To date, many DNAPL studies in the subsurface have focused on increasing the complexity and measurement requirements of models to improve their accuracy and widen their application. However, due to the highly complex and heterogeneous nature of fluid and contaminant flow in the subsurface, measurements are costly, timely, highly dependent on spatial and temporal scales, and limited in resolution. Therefore, the author believes that the greater benefit in model development lies in decreasing complexity by identifying key processes and parameters of the system, simplifying the relationships that exist between them, and incorporating these relationships into simple models that recognise or quantify the inherent complexity and uncertainty. To this end, the ultimate goal of this work was to identify and isolate the key processes and parameters that control DNAPL and plume migration through single fractures. In particular, the significance of aperture variability and matrix diffusion were investigated using conceptual models of increasing complexity and scale, allowing for a close quantitative and qualitative examination of the fundamental factors controlling migration in the system. The major implications of the research outcomes to the investigator in the field or the numerical modeller are emphasised wherever possible and recommendations on their application are made. This work initially focused on single, one-dimensional fractures, which can be conceptualised as a fracture trace on an outcrop. An understanding at this scale is a prerequisite to understanding and analysis at other scales, such as two-dimensional planar 2

19 fractures and three-dimensional fracture network systems. Although many studies have been conducted at the single fracture scale, few have looked specifically at DNAPL breakthrough times, and even less have deconstructed the problem and looked closely at how each DNAPL, fracture and matrix parameter influences breakthrough times. The first stage of this study ignored matrix diffusion effects in a one-dimensional fracture (Chapter 3.0) and this assumption is then relaxed in the second stage by embedding the single fracture in a porous matrix (Chapter 4.0). Breaking up the investigation this way allowed for a thorough investigation of the DNAPL, matrix and fracture parameters that characterise breakthrough times, isolating matrix effects. This meant that cases when matrix effects significantly increased breakthrough times in single one-dimensional fractures could be readily identified and also quantified. The final stage (Chapter 5.0) then increased the complexity further and investigated the mass transport processes that control DNAPL migration and plume evolution at large spatial and temporal scales in a single two-dimensional planar fracture embedded in a three-dimensional matrix. In the matrix studies, DNAPL flow was assumed to occur exclusively in the fracture which is the case for most geological systems (e.g. clays, dolostone). However, other geologies (e.g. sandstone) are characterized by larger pore throat diameters which can be invaded by DNAPL. Therefore, this study is not applicable to sandstones. In Chapter 3.0, the similitude techniques of dimensional and inspectional analysis are demonstrated for a scenario of DNAPL flow in a single, one-dimensional parallel plate and 3

20 variable aperture fracture with a focus on breakthrough time scale factors. The similitude analysis acts to transform or scale the important variables. The dimensional analysis uses the Buckingham Pi Theorem to express the complete physical system in terms of a set of an independent dimensionless term composed of the relevant physical parameters, and the inspectional analysis scales each parameter in the equations describing the system. The dimensional analysis in this study is coupled with an empirical approach and the inspectional analysis is performed on the Darcy equation for multiphase flow. Although other studies have examined DNAPL travel times through fractures (e.g., Kueper & McWhorter, 1991; Reynolds & Kueper, 2002), these have solely employed numerical models. The objective of this investigation was to utilise similitude analyses to estimate DNAPL travel times for a variety of fracture and DNAPL properties and compare the obtained time scale factors to the breakthrough times generated by the numerical model. This study, therefore, provides insight into the strengths and limitations of similitude techniques for estimating the time taken for the DNAPL to traverse a one-dimensional fracture trace. Advancements are also made in explaining the effects of different DNAPL and fracture properties on breakthrough times through fracture traces so that order-ofmagnitude estimates of breakthrough times can be calculated without the need to employ a numerical multiphase flow model. The complexity of the conceptual model is increased in Chapter 4.0, which embeds the fracture in a porous matrix and allows DNAPL dissolution and matrix diffusion. The primary aim of increasing the complexity in this way was to test the validity of the assumption made in the first study that matrix effects can be ignored at the breakthrough 4

21 time scale when the DNAPL source is infinite. These results were then compared to, in particular, Ross and Lu s (1999) work which derived a dimensionless Nitao number to predict under what conditions matrix diffusion influences DNAPL migration rates in fractured media for the case of an immobile water phase and no capillary overpressurisation. Inspectional analysis, which was used successfully to predict breakthrough times in Chapter 3.0, was explored again here in an attempt to quantify the effect of matrix diffusion on breakthrough times. A more qualitative mass storage analysis was also performed; directly observing the conceptual model and formulating fracture and matrix mass storage capacities based on parameters such as fracture aperture, matrix porosity, DNAPL density and DNAPL solubility. This study also resulted in the development and validation of a numerical-analytical diffusive flux model which describes the migration of a dissolving and diffusing DNAPL through a single one-dimensional fracture without explicitly representing the matrix using additional nodes. This new model allowed for an investigation into the effects of aperture variability on breakthrough times which would have otherwise been computationally time restrictive due to issues the numerical model experienced in converging, and the very small times steps required for stability during some of the simulations performed. To determine the implications of the results found in the one-dimensional studies to applications at the field scale, the complexity of the conceptual model was again increased to a single, two-dimensional, planar fracture embedded in a three-dimensional porous matrix at the field scale (Chapter 5.0). The complexity is increased compared to the onedimensional fracture studies, but this is still a simple representation for a field scale 5

22 fracture. The effect of different parameter values on contaminant transport processes in two-dimensional fractures at the field scale, and the implications this has on groundwater quality and management over large periods of time and space, has yet to be investigated. In this study, the focus was not on DNAPL breakthrough times but on the relative importance and interaction of different mass transport processes and parameters on DNAPL and plume migration and evolution. In particular, the role that matrix diffusion plays in attenuating or slowing plume migration was investigated for the planar twodimensional fracture, and the potential persistence of contaminant mass in the fracture due to matrix back diffusion was examined. The simulations in this study were chosen to closely resemble DNAPL spills and geologic media that are commonly encountered in reality (except sandstone), allowing for direct and relevant implications to be identified and conclusions to be drawn. As a final note, it is important to note that this thesis was written in manuscript style. As a result, there is some unavoidable repetition between chapters. Chapter 2.0 presents a review of the literature that is relevant to this work. Chapters 3.0 and 4.0 can be read as stand-alone chapters and describe the investigations conducted on one-dimensional fracture traces with and without consideration of a porous matrix and DNAPL dissolution, and at the time of publication of this thesis, manuscripts of the work described in these chapters had been submitted to the Journal Mathematical Geology. Chapter 5.0 summarises the work done on two-dimensional fracture at the field scale and is in preparation for submission to the journal Ground Water for publication. Conclusions and recommendations are outlined in Chapter 6.0 and auxiliary information gathered or 6

23 developed in this study that is not included in the main body of the text is listed in the Appendices References Kueper, B.H., McWhorter, D.B., The behaviour of dense, nonaqueous phase liquids in fractured clay and rock. Ground Water 29(5), Kueper, B.H., Redman, D., Starr, R., Reitsma, S., Mah, M., A field experiment to study the behaviour of Tetrachloroethylene below the water table: spatial distribution of residual and pooled DNAPL. Ground Water 31(5), Reynolds, D.A., Kueper, B.H., Numerical examination of the factors controlling DNAPL migration through a single fracture. Ground Water 40(4), Ross, B., Lu, N., Dynamics of DNAPL penetration into fractured porous media. Ground Water 37(1),

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25 2.0 LITERATURE REVIEW 2.1. Introduction This chapter contains a review of the literature that is relevant to this study. The review covers topics including a discussion on the unique contamination scenario of DNAPLs in fractures, mass storage and matrix effects, the history and development of modelling multiphase flow in fractured media, issues of scale and similitude in hydrogeology, stochastic methods and the Monte Carlo approach Nonaqueous Phase Liquids Nonaqueous phase liquids (NAPLs) are liquids that exist as a separate phase to water because they are not readily soluble in water. The term NAPL was first used in 1981 during the study of a hazardous waste landfill in Niagara Falls, New York (Pankow et al., 1996). The term was selected to differentiate the liquid found from other contaminated material, and from the groundwater. More specifically, NAPLs can be categorised as being lighter than water NAPLs (LNAPLs) or denser than water NAPLs (DNAPLs). Once in an aquifer, the importance of this classification becomes apparent, as LNAPLs will tend to not penetrate deeply below the water table, while DNAPLs will generally disregard the geometry of the water table in its downward migration (Pinder & Abriola, 1986) and will continue to move vertically downwards until it encounters a capillary barrier. This capillary barrier is typically represented as a low permeability layer. 9

26 Commonly occurring LNAPLs found in the subsurface include many hydrocarbon products such as crude oil, gasoline and diesel fuels. DNAPL contaminants of particular importance include polychlorinated biphenyl (PCB) oils, chlorinated hydrocarbons, coal tar, and creosote. Of the many different industrial organic chemicals found in groundwater, the common chlorinated hydrocarbons are the most ubiquitous (Pankow et al., 1996). Manufacture and use of chlorinated hydrocarbons, such as trichloroethene (TCE) and tetrachloroethylene (PCE), was wide spread in the U.S.A. and increased during the post-world War II manufacturing boom (Pankow et al., 1996). In Australia, similar use has led to groundwater impacts (e.g. Benker et al., 1996; 1997; 1998). These hydrocarbons are used extensively for processes such as dry cleaning and textile manufacturing, metal cleaning and degreasing, and paint removal and stripping. The wide spread use of large volumes of chlorinated hydrocarbons has led to many cases of subsurface contamination (e.g. Johnson et al., 1989; Mercer & Cohen, 1990; McKay et al., 1993; Clement et al., 2002) due mainly to accidental spillages, and poor storage and disposal procedures. Many chlorinated hydrocarbons are central nervous system depressants, and inhaling the vapour at high concentrations can cause dizziness, headache, nausea, unconsciousness, and death. Repeated or extended skin contact may dissolve fats from the skin, resulting in severe skin irritation. The health effects of sustained breathing in of air or drinking of water contaminated with low levels of chlorinated hydrocarbons are not known, but many are suspected carcinogens and evidence also suggests that excessive exposure may result in kidney and liver damage (Pankow et al., 1996). Because of these health concerns, 10

27 drinking water standards (e.g. maximum concentration limits (MCLs) in the U.S.A.) for chlorinated hydrocarbons are set very low by regulators. Although chlorinated hydrocarbons are not readily soluble in water, they dissolve into water at concentrations many orders of magnitude higher than their drinking water standard, resulting in largescale groundwater contamination plumes even from relatively small quantities in the subsurface. Therefore, the study of DNAPLs in the subsurface is an important problem from a public health and remediation perspective. The migration of DNAPLs is affected primarily by the properties of the DNAPL spill (including the volume of spill, area of infiltration, and length of release), the physical and chemical properties of the DNAPL and the properties of the subsurface media (Mercer & Cohen, 1990). Unlike dissolved solutes, DNAPL flow will tend to be influenced by geologic rather than readily measurable hydrodynamic parameters (Pinder & Abriola, 1986), and DNAPL migration is largely uncoupled from the hydraulic gradient that drives advective transport of solutes (Mackay et al., 1985). A release of DNAPL to the subsurface will distribute itself as both disconnected blobs and ganglia of organic liquid referred to as residual, and in continuous distributions referred to as pools (Figure 2.1). An aqueous phase plume may also develop down-gradient of the DNAPL over time. Residual DNAPL is formed at the trailing edge of a migrating DNAPL body due to pore-scale snapoff and trapping mechanisms (Kueper et al., 1993). DNAPL pools are formed when a migrating DNAPL body encounters an aquitard or capillary barrier and bulk downward migration ceases. In many cases, the aquitard comprises fractured bedrock or clay, and these fractures form preferential flow paths allowing DNAPL to penetrate greater distances 11

28 in relatively short periods. Whether the DNAPL will enter the fractures, the rate at which it will move upon entry, and the magnitude that the dissolved contaminant in the aqueous phase will diffuse into the surrounding matrix are important aspects to consider in developing site conceptual models, characterisation programs, and remedial strategies. Entry of the DNAPL into the fractures and the rate at which the DNAPL travels will depend on a number of factors including capillary properties, fracture orientation, fracture permeability, DNAPL density, DNAPL viscosity, and DNAPL-water interfacial tension. Figure 2.1 Schematic of a contamination scenario arising from a spill of DNAPL (from Kueper & McWhorter, 1991) 12

29 2.3. Fractured Media Fractured geological formations are found throughout the world and are of interest in a number of contexts, including reservoir exploration for water and petroleum supply, contamination from waste repositories, waste isolation, and as a conduit for water and contaminant movement. Within the field of fractured media research, there are many broad areas of interest that can be considered including saturated and unsaturated domains, porous and nonporous fractured media, parallel plate and variable aperture fractures, and single fractures and fracture network systems. Most studies have focused on fractures in crystalline rocks and hard sedimentary rocks, such as sandstones, limestones and chalk (Neuman, 2005), and a growing field of research is being developed around fractured clays. Fractures embedded in porous media usually represent a small fraction of the total bulk porosity but have a large permeability compared to the surrounding media. Therefore, fractures have a low contaminant storage capacity, but are conduits for fluid flow, carrying contaminants farther from the source in potentially much shorter periods of time. And unlike porous media, which provides interconnected and continuous flow paths in multiple directions, fractured media allows preferential flow in the direction of the fracture, and can halt or slow flow at fracture terminations and small aperture regions. The complexity of fracture network systems, and the possible interaction of fluid in the fracture with the surrounding porous matrix and vice versa, means unique challenges arise when predicting contaminant migration and planning remediation strategies. 13

30 Fractures are primarily characterised by their size, aperture (separation distance between fracture faces) and dip from the horizontal. Furthermore, fracture aperture can be represented as constant along the fracture length (parallel plate), or more realistically as rough and variable along the fracture length. Aperture is generally denoted with the symbol e or 2b, where b is half of the separation distance between fracture faces. In the literature it is well established that fractures are rough-walled conduits with a variable aperture, and that DNAPL behaviour within a single fracture can differ from what may be expected in a fracture conceptualised as parallel plates with an average aperture (Ge, 1997; Esposito & Thompson, 1999; Konzuk & Kueper, 2004). Fracture apertures have been measured non-destructively with a variety of techniques including computer aided tomography (CAT) x-ray scanning (Keller, 1998), computed tomography (CT) scanning (Bertels et al., 2001), and light transmission methods (Detwiler et al., 1999). The hydraulic aperture or cubic law aperture, a flow- or volume-averaged aperture which is derived from fluid flow rates using the cubic law (Tsang, 1992), can also be calculated using non-destructive techniques. However, the destructive measurement technique of fracture surface image analysis used by Konzuk and Kueper (2004) is more accurate, gives more detail and can measure surface profiles simultaneously with apertures. For any of these measurement methods, there is a limit to the upper size of the fracture that can be measured due to the difficulty in obtaining a large and undisturbed fracture sample, and the additional time required to measure larger samples. It is also important to note that all detailed and direct fracture aperture measurements reported in the literature have been conducted on fractured rock, such as sandstone, limestone and granite, or on replicas of 14

31 natural rock fractures, but no such detailed measurements have been reported for fractured clays. A summary of measured and adopted fracture aperture characteristics and the fitted probability distribution types reported in the literature is shown in Appendix A. Other features of interest found in measured fractures include considerably larger aperture regions at the edges of a fracture (side effects) (Bertels et al., 2001) and at fracture intersections (Keller, 1998). Infilling was reported by Wealthall et al. (2001), and debris in the form of rock fragments and secondary branching of the fracture was reported by Konzuk and Kueper (2004). A representation of fracture aperture variability has been implicitly incorporated into models using capillary pressure and permeability constitutive relationships, most commonly represented using the Brooks-Corey model (Brooks & Corey, 1966) shaped by a pore size distribution index (λ). A fracture characterised by a pore size distribution index implies that a distribution of aperture variability exists. A true one-dimensional parallel plate fracture would be characterised by a capillary pressure-saturation step function, and would exhibit plug flow rather than relative permeability effects. Fracture aperture variation can be explicitly described using a probability distribution, most commonly with a skewed probability function, such as log-normal or gamma (Konzuk, 2001). These probability distributions are commonly chosen because measured aperture distributions tend to be centered on the smaller apertures, with longer tails extending towards the larger apertures (Konzuk, 2001). It is important to note, however, that both of these distributions 15

32 are infinite and have a long tail, when in reality apertures are bounded by the maximumminimum altitude differences of the surfaces (Oron & Berkowitz, 1998). Also, in lognormal and gamma distributions an aperture of zero (that is, a closure point) cannot exist. Therefore, aperture distributions may often be truncated to eliminate unrealistically large apertures, and a truncated normal distribution has also been proposed (Konzuk, 2001) as it allows for zero apertures. The majority of studies suggest that fracture apertures decrease with depth due to an increase in confining stress, but some studies draw the opposite conclusions. A field experiment performed by McKay et al. (1993) in a weathered and fractured clay-rich till found that the most prominent fractures were vertical, and that the fracture density decreased with depth. However, with the exception of a few high aperture values in the upper region of the sample, apertures did not display a decreasing trend with depth. Oron and Berkowitz (1998) used a numerical fracture sample with a symmetric truncated Gaussian aperture distribution to show that as normal stress is increased, the fracture faces are pressed together and the aperture distribution becomes more and more skewed towards lower apertures, increasing the frequency of closure points. Normal stress tests conducted by Muralidharan et al. (2004) used x-ray CT scanning on a rock fracture to show that as the overburden pressure is increased (i.e. as depth into the subsurface is increased) the mean of the fracture aperture and its standard deviation decreases. The results also showed that the aperture distribution followed a lognormal distribution before and after the normal stress was applied for the stress conditions tested. Recent tests on rock fracture replicas conducted by Koyama et al. (2006) showed that shear stress affects fracture apertures quite 16

33 differently to normal stress. The study found that with increasing shear displacement, the shape of the frequency histogram of the aperture distribution changes from being sharp to flatter, increasing both the mean aperture and its standard deviation. This result was more pronounced in the direction perpendicular to the shear displacement, which could cause significant fluid flow channeling effects in this direction. When considering flow in three-dimensional fracture network systems consisting of multiple fractures, and the possibility of contaminant breakthrough, the connectivity of the system is of primary interest, as the fractures must be interconnected for breakthrough to occur. If fractures are assumed to be spatially infinite with different orientations then the fracture network will be perfectly interconnected and the system will behave essentially as a porous medium continuum. However, this assumption may not be very realistic, especially for sparsely fractured, very low permeability rock masses (Gelhar, 1993). Three-dimensional fracture characteristics are difficult to measure and cannot be completely detailed in situ, so there is a heavy reliance on extrapolation and subjectivity when making measurements. Consider, for example, that many fracture measurements are taken from fracture traces visible on two-dimensional exposed slices of a threedimensional network (e.g. a rock outcrop or excavation) and it can be expected that these traces will exhibit less interconnection than the three-dimensional network. In addition, accurate measurement of fracture aperture and variability cannot be made without destructive techniques, making experimental precision impossible once the fracture has been opened, and even for fracture systems that are highly characterised in the field it is difficult to reliably predict contaminant migration quantitatively. However, there are 17

34 standard methods for reconstructing three dimensional fracture networks from outcrop mapping and stochastic discrete fracture network model reconstruction (e.g. Ehlen, 1999). Three dimensional fracture network systems were not considered in this study primarily due to restrictions in computational capacity. The challenge in studying fractures and fracture network systems is to find methods that can use relatively limited local scale observations and extrapolate to larger-scale systems. In this search, numerical modelling has proven to be a useful tool in improving the understanding of flow processes in fractures The Physics of DNAPL Migration in Fractures For DNAPL penetration into a fracture to occur, the capillary pressure (P C ) of the DNAPLwater system needs to exceed the required entry pressure (P E ) of the fracture (Kueper & McWhorter, 1991). If the condition of P C > P E is satisfied, DNAPL invasion and migration through the fracture will occur preferentially through the largest aperture pathways. For a finite DNAPL source, residual DNAPL will be formed at the trailing edge of the migrating body, and may take the form of small, disconnected blobs or larger, interconnected fingers. The size, shape and surface area of this residual can greatly influence other processes such as DNAPL dissolution rates, the characteristics of the evolving plume and the magnitude and direction of the wetting phase flux. The entry pressure (P E ) of a fracture is defined in a parallel plate fracture as (Kueper & McWhorter, 1991): 18

35 P E 2σ cosθ = (2.1) e where σ is the DNAPL-water interfacial tension [MT -2 ], θ is the contact angle measured through the wetting phase, and e is the fracture aperture (separation distance between the fracture faces, sometimes represented as 2b) [L]. Capillary pressure (P C ) is defined as the difference between the nonwetting and wetting phase pressures (P NW P W ), and can be expressed as an equivalent height of DNAPL pooled above the fracture entrance which cannot always be readily measured in practice. However, the percentage of pore space occupied by a DNAPL in an otherwise water saturated porous medium (the DNAPL saturation, S NW ) can be measured in laboratory experiments and has been represented as a function of the capillary pressure at which the DNAPL and water exist (Kueper & McWhorter, 1991). A relationship was given by Brooks and Corey (1966) as: λ PC S e = (2.2) PD where P C is the capillary pressure of interest [MT -2 ], P D is the displacement pressure [MT - 2 ] of the porous medium giving rise to the initial entry of nonwetting fluid (analogous to P E in fractured medium), λ is a pore-size distribution index or fitting parameter reflecting grain sorting, and S e is an effective wetting saturation given by: S e S S S W Wr = (2.3) 1 Wr where S W is the wetting phase saturation (the fraction of the pore space occupied by the wetting phase), and S Wr is the residual wetting phase saturation. 19

36 Figure 2.2 Typical capillary pressure (P C ) saturation (S W ) curve showing hysteresis (from McWhorter & Kueper, 1996), where S W is the wetting phase saturation, S NW is the nonwetting phase saturation, S Wr is the residual wetting phase, and S NWr is the residual nonwetting phase. The displacement pressure is analogous to P E in fractured media. A typical curve illustrating the relationship between capillary pressure and wetting phase saturation is shown in Figure 2.2. Once capillary pressure exceeds displacement pressure DNAPL invasion can occur, increasing the capillary pressure and nonwetting phase saturation, and decreasing the wetting phase saturation (main drainage curve). The wetting phase is at residual (S Wr ) when no further increase in capillary pressure will reduce the wetting phase saturation. If the DNAPL source is exhausted, it will continue to migrate away from the source, the capillary pressure will decrease and areas once occupied by DNAPL will be replaced by water (main wetting curve). The maximum wetting phase 20

37 saturation after wetting is less than unity due to the formation of residual DNAPL blobs and ganglia which are cut off and disconnected from the continuous DNAPL body by the invading water. These residual blobs and ganglia have zero capillary pressure, are distributed over the contaminated area, are immobile and by definition do not move with the flowing groundwater. It is also important to note that the relationship between capillary pressure and saturation is hysteretic and can be largely different for drainage, wetting and scanning curves Matrix Effects For the case of DNAPL migration in fractured geologic media, DNAPL flow is generally assumed to occur exclusively in the fractures which provide the main avenue for DNAPL distribution (e.g. Sudicky & Frind, 1982; Mercer & Cohen, 1990; Parker et al., 1994; Ross & Lu, 1999; Reynolds & Kueper, 2002) but the matrix surrounding the fracture contains nearly all of the bulk porosity and potential storage. This is the case for most geological systems (e.g. clays, dolostone); however, other geologies (e.g. sandstone) are characterized by larger pore throat diameters which can be invaded by DNAPL. This study is not applicable to geological systems such as sandstones. The transfer of solutes from the fracture to the porous matrix, and vice versa, due to molecular diffusion is called matrix diffusion (Carrera et al., 1998). Matrix diffusion is driven by the presence of a concentration gradient between the fracture and the matrix, and can be described mathematically using Fick s First Law (Parker et al., 1996): 21