<%BANNER%>

A Quasi-Analytical Model to Predict Water Quality during the Operation of an Aquifer Storage and Recovery System


PAGE 1

A QUASI-ANALYTICAL MODEL TO PR EDICT WATER QUALITY DURING THE OPERATION OF AN AQUIFER STOR AGE AND RECOVERY SYSTEM By ALI SEDIGHI A REPORT PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2003

PAGE 2

Copyright 2003 by Ali Sedighi

PAGE 3

ACKNOWLEDGMENTS I would like to offer my utmost appreciation to Dr. Kirk Hatfield, chairperson of my supervisory committee, who was much more than an advisor to me. He played a key role in guiding me with unlimited patience and energy and gave me all the support I could ask for. His experience and guidance have enlightened my education, as well as my life. I would also like to thank my committee members, Dr. Louis H. Motz and Dr. Michael D. Annable, for all of their valuable encouragements, ideas, and compassion throughout my study at the University of Florida. I am also grateful to all my previous professors at Sharif University of Technology in Tehran, Iran. Behind the scenes was my loving girlfriend, Rachel Johnson, who rejoiced with me in good times and cheered me up in bad times. I thank her for her hard work in editing this paper and also her support and patience throughout the past year. I am grateful to my friend, Harald Klammler, for all of his help, support, and great contribution to my work. I also wish to thank all my friends, especially Ali-Reza Kazemi, who has added richness to my life. I am endlessly grateful to my parents, Parvin Bagherzadeh and Abdolvahab Sedighi, and my sister Vida for the emotional and financial support afforded me throughout my life. iii

PAGE 4

TABLE OF CONTENTS Page ACKNOWLEDGMENTS.................................................................................................iii LIST OF FIGURES.............................................................................................................v CHAPTER 1 INTRODUCTION........................................................................................................1 Applications and Benefits of ASR Technology............................................................4 Research Objective and Scope......................................................................................6 2 LITERATURE REVIEW.............................................................................................7 ASR Modeling..............................................................................................................7 Hydraulic Factors and Characteristics of ASR Systems...............................................9 Operation of the Aquifer Storage and Recovery Systems..........................................14 3 ASR MODEL.............................................................................................................17 Analytical Statement of Front Movement..................................................................17 Validation of the Quasi-analytical Model using Numerical Model....................27 Developing the Model for Multiple Layers.........................................................30 Modeling the Distribution of Hydraulic Conductivity in the Aquifer........................33 Theory..................................................................................................................33 Sensitivity Analysis and Comparison of the Results from Analytical Model with the Real ASR Performance Data.............................................................37 4 CONCLUSIONS AND RECOMMENDATIONS.....................................................39 LIST OF REFERENCES...................................................................................................41 BIOGRAPHICAL SKETCH.............................................................................................44 iv

PAGE 5

LIST OF FIGURES Figure page 1-1. Distribution of operational and under development ASR systems in North America......................................................................................................................2 1-2. Miami-dade County, Florida, recovers water stored in a 1000 to 1300 foot deep (300-400 m) brackish limestone aquifer....................................................................3 2-1. Captured water from rainfall is treaded and pumped into an aquifer through ASR wells.........................................................................................................................15 2-2. After storage period, transition zone is created and it separates freshwater from ambient water in the confined aquifer. Also injected freshwater has moved downgradient due to the natural groundwater velocity............................................16 3-1. Plan view of the injected water after time t and before movement.......................18 3-2. Plan view of the injected water after time t and after movement..........................19 3-3. Position of the injected water after time 2t and before movement........................20 3-4. Position of the injected water after time 2t and after movement...........................21 3-5. Position and shape of the interface after injection period (t=Ti)..............................22 3-6. Position and shape of the interface after storage period (t=Ti+Ts)..........................23 3-7. Position and shape of the interface at the beginning of the recovery phase.............24 3-8. Position of the interface at two different times during recovery..............................26 3-9. The front position at time=18.55 days.....................................................................29 3-10. Concentration of recovered water obtained from numerical and analytical models......................................................................................................................30 3-11. Probability Density Function for the Normal Distribution, N: (2, 2).......................35 3-12. Cumulative probability function, F(x 0 ), for N: (2, 2)...............................................36 v

PAGE 6

3-13. Sensitivity analysis for the analytical results from the FORTRAN code.................37 3-14. Comparison of the analytical model results with the real ASR performance data..38 vi

PAGE 7

Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering A QUASI-ANALYTICAL MODEL TO PREDICT WATER QUALITY DURING THE OPERATION OF AN AQUIFER STORAGE AND RECOVERY SYSTEM By Ali Sedighi August 2003 Chair: Kirk Hatfield Major Department: Civil and Coastal Engineering Aquifer Storage Recovery (ASR) is defined as the storage of freshwater in an aquifer by injecting water through the wells during wet periods for subsequent retrieval from these same wells during dry periods. The freshwater forms a bubble of injected water within the aquifer around the ASR well, and it can be retrieved when needed to meet seasonal, long-term, emergency or other demands. During the past ten years, ASR technology has evolved from merely a concept to a proven, cost-effective and environmentally desirable water management tool. The objective of this paper is to develop an analytical model to determine recovered water quality based on the position of the injected water, surrounded by the ambient water of the aquifer. Injected water and ambient water are characterized as two separate zones by the differing concentrations of specific dissolved species. When these two zones are introduced to each other, a transition zone is created across which the concentration varies. The transition between these two zones is modeled by creating a vii

PAGE 8

distribution of hydraulic conductivity across the depth of the aquifer. Thus, in a layer with a constant value of hydraulic conductivity, the transition zone is replaced by a sharp front, which, while moving, continuously separates the two zones with different concentrations. By keeping track of the front position during injection, storage, andrecovery, we can obtain the fraction of injected water contained in the pumped water from the angle of the injected water body surrounding the well; thus, the concentration of recovered water will be a number between the concentration of injected water and the concentration of ambient water. To validate this analytical model, the results are compared with numerical models, using MODFLOW-96 and MT3DMS packages. The running time for this analytical model is less than 10 percent of the running time in existing numerical models. Also, considering the simple way of introducing input data, it can be superior to the existing numerical models. viii

PAGE 9

CHAPTER 1 INTRODUCTION Population growth during the past few decades has accelerated the demand on both surface and groundwater supply. Aquifer Storage and Recovery (ASR) is an important component of groundwater management. ASR is defined as the storage of freshwater in an aquifer through the wells during periods when surface supplies are plentiful for subsequent retrieval from these same wells during dry periods. The injected water forms a bubble within the aquifer around the ASR well, and can be retrieved when needed to meet seasonal, long-term, emergency or other demands. The potential for seasonal storage and drought protection have made ASR one of the most promising storage methods for potable, surface and reclaimed water. The term "Aquifer Storage Recovery" was coined by David G. Pyne in 1983 when the first ASR system in Manatee County, Florida, began successful operation (Pyne, 2003). As of January 2003, fifty-six ASR systems are believed to be operational in the United States, 12 of which are located in Florida. This compares to the three ASR systems in 1983. Most systems are storing treated drinking water. At least 100 other ASRs are in various stages of development, ranging from planning to operational startup. Figure1-1 shows the location of ASR systems in the North America as of January 2002. Other systems are known to be operating in the United Kingdom, Canada, Australia and Israel. ASR development programs are underway in several other countries, including the Netherlands, New Zealand, Thailand, Taiwan, Saudi Arabia, and Kuwait (Pyne, 2002 and Lloyd, 2001). 1

PAGE 10

2 Figure 1-1. Distribution of operational and under development ASR systems in North America (Pyne, 2003). The Comprehensive Everglades restoration Plan (CERP) proposes to use as many as to 333 ASR wells to store as much as 1.6 billion gallons of freshwater per day to ensure the quantity of water available to the Everglades, improve water quality conditions in Lake Okeechobee, and prevent damaging releases of freshwater to coastal estuaries (Figure 1-2). Some of this water would also be available to support surrounding agriculture and to protect urban wells located near the coast from salt-water intrusion. Muniz and Ziegler (1994) detail the feasibility, construction, testing and initial operation of the Boynton Beach, Florida ASR well. This case study is of particular value to the CERP because it is within 20 miles of proposed ASR wells in CERP. The first step in hydrogeologic characterization of the site was the boring of pilot holes. Geologic logs

PAGE 11

3 from the pilot holes were used to assist in correlating formation samples to identify specific lithologic boundaries design. Cycle testing was successful in determining operational performance, evaluating potential recharge and recovery of treated drinking water, confirming that recovered water met drinking water standards, and estimating the hydraulic performance of the storage zone. Successful experience at most monitoring sites has confirmed that ASR is not only practical, but cost-effective for storing water deep underground. However, Nguyen and Mueller (1996) recommend that all ASR projects should be considered only on an experimental basis in the initial phase to allow collection of valuable data to assess the aquifer characteristics and the quality of the native water in the storage zone. Figure 1-2. Miami-dade County, Florida, recovers water stored in a 1000 to 1300 foot deep (300-400 m) brackish limestone aquifer (Pyne, 2003).

PAGE 12

4 Applications and Benefits of ASR Technology The primary driving force behind the current rapid global implementation of ASR technology is water supply economics. ASR provides a cost-effective solution to many of the worlds water management needs and can usually meet water management needs at less than half the capital cost of other water supply alternatives (Pyne, 2002). Large water volumes are stored deep underground, reducing or eliminating the need to construct large and expensive surface reservoirs. ASR is most commonly used in conjunction with the potable water treatment systems for purposes of storing excess treated water in the ground. Water treatment plants typically face their peak demand only during short periods each year. An ASR can replace the storage capacity that otherwise must be built into a plants surface facilities; hence, it can minimize capital and operating costs. Wells can be located where most needed and because wells require little land, the costs of large land acquisitions are avoided. ASR also results in less water lost. Some areas have seasonally abundant water resources (like Florida) but few good places to store the water. Evapotranspiration and seepage losses are high in surface reservoirs, whereas for underground storage these two problems are insignificant. ASR systems could potentially allow for multi-year storage, whereas evaporation during severe droughts limits the ability of reservoirs to provide similar long-term storage. Several benefits can be cited with respect to the adoption of ASR systems. First, most obviously these systems can be used to store water when the supply is abundant and the water quality is good for purposes of recovering it later during emergencies or times of water shortage, or when source water quality is poor. Second, during the recharge cycle, groundwater levels can then be restored where aquifers have experienced long

PAGE 13

5 term declines in water levels due to heavy pumping to meet increasing urban and agricultural water needs. Finally, ASR is generally viewed as an environmentally good alternative to surface water reservoirs because they reduce or eliminate the need for dam construction, and they provide for reliable water supplies through the diversion of flood flows instead of low flows. In addition to meeting increased water demands, ASR plays a role in solving the challenges of wet weather surface flows and groundwater and wastewater management. For example, as urban development continues, the area of impermeable ground cover continues to expand, raising the level of surface runoff and its attendant problem of erosion, silting, and pollution. Stormwater serves a better purpose when it can be captured and safely reintroduced to the aquifer. In addition, with saltwater intrusion threatening drinking water supplies in coastal areas, ASR injection wells can create water barriers that protect vulnerable aquifers. Finally, ASR can also be used to recycle treated wastewater (Missimer et al. 1992). ASR applications, particularly in Florida, are for seasonal water storage, but other applications include long term water storage or water banking from wet years to drought years, emergency water storage, restoring water levels in depleted aquifers, controlling subsidence, maintaining pressures and flows in water distribution systems, improving water quality, reducing the cost of water system expansions, maintaining minimum flows and levels, and many other applications. Increasingly, ASR is being considered for development of Strategic Water Reserves to provide water supply security from terrorism or warfare (Reese, 2002 and Pyne, 2002).

PAGE 14

6 Research Objective and Scope The objective of this research was to predict water quality changes during the operation of an ASR system. The efficiency of ASR operations is dependent on the volume of stored water recovered. The recovered volume depends on transient changes in water quality that result from ASR operations. Tools developed to better predict water quality changes during ASR operations could be used to optimize the management of ASR systems. To meet the above stated research objective, a quasi-analytical model has been developed. In this model, the recovered water quality is calculated based on the simulated position of the injected volume of water with respect to the ambient water of the aquifer, the quality of the injected water, and the quality of the ambient groundwater. To validate the quasi-analytical model, results are compared to the well-known numerical models, MODFLOW-96 (Harbaugh and McDonald, 1996a and 1996b) and MT3DMS (Zheng and Wang, 1999).

PAGE 15

CHAPTER 2 LITERATURE REVIEW ASR Modeling Numerical models such as MODFLOW-96 (Harbaugh and McDonald, 1996a and 1996b) and MT3DMS (Zheng and Wang, 1999) and SEAWAT (Guo and Langevin, 2002) are available to simulate the movement of injected water through an ASR well and to predict the transient quality of recovered water. To perform these simulations, the spatial and temporal scales of numerical discretization must be sufficiently small to minimize numerical dispersion and preserve mass balances on simulated water quality parameters. The high level of discretization and the associated increased computational demands required may all but preclude direct application of numerical codes except over small and unstratified aquifer domains. Analytical models potentially offer computation efficiencies for simulating transport through homogeneous aquifers not easily afforded through numerical transport models. Analytical models were developed to study movement of injected water in the aquifer. Muskat (1937) considered the steady flow pattern produced by a single pumping well near an equipotential boundary, while Bear (1979) studied the shape of the advancing front separating the indigenous water of a confined aquifer from a body of water injected into it through a well at the origin. However, Muskat and Bear did not seek to predict water quality during all operational phases of an ASR system. Their models do provide insight into the groundwater velocity field that ultimate plays a significant role in the transport of dissolved constituents. 7

PAGE 16

8 Nelson (1978) developed a semi analytical approach that provides location/arrival time distributions and location/outflow quantity distributions at critical outflow boundaries of the system. This model assumes that the concentration distribution at the beginning of the simulation is known. Javandel and others (1984) developed a particle-tracking model to show how spatial distribution in concentration versus time data for a single injection well reaches any desired outflow boundary. This model calculates the time it takes for a particle to flow to a pumping well given all pumping and injection rates. It is required to construct flow patterns and then use them to identify the locations of any contaminant fronts for various values of time. Javandel and Tsang (1986) developed the previous model to determine the capture zone of multiple wells. The new model can assist in the determination of the optimum number of pumping wells, their rates of discharge and locations, such that further degradation of the aquifer is avoided. Ahlfeld (1999) used particle tracking techniques to develop an optimization formulation for designing groundwater plume control systems. The limitation of these models is the inability to account for dispersion. The particle-tracking model developed by Javandel and others (1984) can be applied to predict water quality in an ASR system. However, the quasi-analytical model developed herein is simpler since there is no need to construct flow patterns in the aquifer. The quasi-analytical model does not simulate the transport of dissolved solutes but determines the transient fraction of ambient groundwater recovered during the ASR extraction phase. Because convective/dispersive transport process are not explicitly simulated, the quasi

PAGE 17

9 analytical model is limited to simulating water quality changes at the ASR well and during the recovery phase; however, these simulations can be achieved at significant computational efficiencies over traditional numerical transport models. To emulate the effects of hydrodynamic dispersion, these simulations are performed as if the aquifer were stratified and the horizontal hydraulic conductivity varied vertically in a statistically defined manner. Hydraulic Factors and Characteristics of ASR Systems For most ASR systems, storage volumes range from as small as 13 million gallons (MG) in individual ASR wells to as much as 2.5 billion gallons (BG) or more in large ASR well fields. The shallowest depth to the top of a storage zone is about 200 feet while the greatest depth to the base of an ASR storage zone is 2600 feet. The thinnest storage zone is about 50 feet while the thickest is about 1300 feet. Natural water quality in storage zones ranges from freshwater that is suitable for drinking without treatment to brackish water with total dissolved solids concentrations up to about 5000 mg/l. Most sites have one or more natural water quality constituents that are unsuitable for direct potable use except following treatment. Such constituents may include iron, manganese, fluoride, hydrogen sulfide, sulfate, chloride, radium, gross alpha radioactivity, and other elements that are typically displaced by the stored water as the bubble is formed underground. Arthur et al (2001) studied the geochemical aspects of the Florida Aquifer Storage and Recovery system. Results of this study indicate that chemical variability (including isotropy) exists within groundwater and carbonate of the Floridan aquifer system which may result site-specific geochemical processes affecting ASR well performance and water quality. Also, as oxygen-rich surface waters are injected into Floridan aquifer

PAGE 18

10 system, trace metals such as arsenic (As), iron (Fe), manganese (Mn) and uranium (U) are mobilized (chemically leached) from the carbonate rocks and withdrawn during recovery. Therefore, some of the periods of higher metals concentrations in the recovered water are short-lived, depending on the duration of the injection, storage, and recovery cycles. Their results confirm that understanding water-rock geochemical interactions are important to the continued success of ASR in Florida. Merritt (1985) studied the relationship of recovery efficiency to the hydrogeologic conditions that could prevail in brackish artesian aquifers. The principal tool of investigation used in his study was the INTRA model which has a variety of potential applications to variable-density solute-transport problems. He found that a loss of recovery efficiency was caused by (1) processes causing mixing of injected freshwater with native saline water (hydrodynamic dispersion), (2) process causing the more or less irreversible displacement of the injected freshwater with respect to the well (background hydraulic gradient, interlayer dispersion, buoyancy stratification), or (3) processes causing injection and withdrawal flow patterns to be dissimilar (directionally biased well-bore plugging, dissimilar injection and withdrawal schedules in multiple well systems). Success or failure of an ASR system is controlled by a wide variety of factors that are related to hydrogeologic conditions, well design, and operational management. Some of these factors are (Bear, 1979, Missimer et al, 2002, and Reese, 2002): Natural gradient Aquifer porosity Hydrodynamic dispersion (which includes the effects of molecular diffusion and mechanical dispersion)

PAGE 19

11 Confinement of the aquifer Aquifer permeability and its distribution Aquifer transmissivity Aquifer thickness Ambient water quality and density Injected water quality Desired extraction water quality Injection and recovery flow rates Duration of different periods (injection, storage, and recovery) Frequency of cycles and storage period at the end of each cycle Recovery efficiency is significantly affected by the downgradient movement of injected water due to the background hydraulic gradient. The average velocity of ambient flow is a function of the hydraulic conductivity and porosity as well as the natural gradient. The degree of mixing between the injected water and native water and the width of transition zone is controlled by hydrodynamic dispersion, which in turn is a reflection of the degree of spatial variability in aquifer conductivity. Some sites show minimal mixing on the initial cycle, and, if the natural hydraulic gradient in the aquifer is small, after two or three cycles the same volume stored the quality of recovered water is quite stable. On the other hand, some sites show substantial mixing, suggesting that even with a small hydraulic gradient a very large water quality transition zone would be encountered to achieve 100% recovery.

PAGE 20

12 If the storage zone is not well confined, injected water may move upward or downward out of the storage zone, or ambient water may move vertically into the storage zone during recovery. Most sites use confined or semi confined aquifers for storage; however, at several sites the aquifer is unconfined. Sometimes a subsurface zone must have barriers to contain stored water. Permeable sediments or rock must be present to allow flow of water through the aquifer. The hydraulic conductivity or permeability distribution in the storage zone greatly influences the recovery efficiency. Mechanical dispersion is related to the distribution of permeability within the storage zone. Higher permeability can cause higher dispersive mixing, and hence lower recovery efficiency. As a result, a sandy aquifer with relatively uniform permeability could have better recovery efficiency since the primary component of dispersion results from flow through intergranular pore space alone. However, suitable storage zones include a wide variety of geologic settings such as sand, sandstone, gravel, limestone, dolomite, glacial drift aquifers, and basalt. The transmissivity of an aquifer has an effect on the ability to recover injected freshwater. The transmissivity of the selected aquifer must be high enough to allow water to be injected and recovered at sufficient rates to allow the system to economically achieve the design goals. However, the transmissivity must be low enough to allow the injected water to be recovered without losing it in the aquifer as a result of migration under natural gradient condition. Therefore, the transmissivity must lie within a range of values depending on the desired pumping rates and the recoverability percentage (Missimer et al, 2002).

PAGE 21

13 Recovery efficiency is greater in a thin aquifer than in a thick aquifer because of the lower vertical extent of the transition zone along which mixing occurs. However, this effect can be partially offset by increasing the volume of water recharged during a cycle. Minimizing the thickness of the storage zone within a thick aquifer can also be beneficial depending on the aquifers distribution of vertical hydraulic conductivity (Reese, 2002). The ambient concentration in the aquifer is of primary importance in controlling recovery efficiency. This will be addressed later when the model is being developed. Buoyancy can play a significant role in the success or failure of an ASR system. In some places, like South Florida, ASR is mostly used to store water in an aquifer that contains brackish water. Therefore, the density difference between freshwater and ambient water is substantial and the greater the differential in density, the faster freshwater will move upward in an aquifer. When the density differential is relatively small, the issue of density-driven water movement is not significant because the lower vertical hydraulic conductivity compared to horizontal hydraulic conductivity tends to reduce the effect (Missimer et al, 2002). Increasing the injection and recovery flow rates would dominate the effect of freshwater displacement during injection and recovery. There is a portion of injected freshwater which has moved downgradient and can never be recovered. By increasing the recovery flow rate, we can reduce this volume of unrecoverable water. However, injection and recovery rates are site-specific parameters; therefore they must be confirmed at each well cluster location (Bouwer, 1996). Martin and Dean (2001) detail the presence of known fractures in the Floridan aquifer system of north-central Florida determined via dye trace studies and cave diving

PAGE 22

14 explorations. They also detail how this extensive fracture system, and the resulting simultaneous conduit and matrix groundwater flow, create the requirement for dual-porosity groundwater modeling. The ASCE Standard Guidelines for Artificial Recharge of Groundwater (2001) explains that determination of the critical injection pressure is the key factor to prevent hydrofracturing and it suggests a range of 0.2-0.6h depending on site specific conditions, where h is the head necessary to raise the potentiometric surface at the recharge well to the ground surface. Increasing the duration of different phases during the operation of an ASR system would decrease the recovery efficiency. The longer the duration of each phase, the more the displacement of injected freshwater. Also, dispersion and mixing would appear more during the long periods of injection, storage and recovery. Recovery efficiency would improve with repeated cycles because some of the recharged water from a previous cycle is left in the aquifer (especially when natural hydraulic gradient is low), and during the next cycle, recharged water mixes with water of a lower concentration. There are still some uncertainties about ASR systems, and an additional step in the path forward would be a better understanding of the processes by which changes in water quality occur during ASR operation. This will help determine the feasibility of using ASR on a much larger scale as proposed in Comprehensive Everglades Restoration Plan (CERP). Operation of the Aquifer Storage and Recovery Systems ASR wells are evaluated and operated through a cyclical process. Each cycle includes periods of injection (recharge), storage, and then recovery with each period lasting days or months. During the injection period, a portion of the excess available surface water supply is treated and injected via the ASR well into a deep and mostly

PAGE 23

15 confined aquifer, creating a large reservoir of stored water that slowly displaces the ambient groundwater. Figure 2-1 shows the position of injected water in the aquifer after the recharge cycle. Due to the natural hydraulic gradient in the aquifer, injected water moves down gradient throughout the phases of injection, storage and recovery. When the recharge water that is characterized by concentrations of multiple dissolved solutes is introduced into an aquifer with indigenous water comprised of different solutes and concentrations, a transition zone is created across which solute concentrations vary (Bear, 1979). The transition zone separates ambient water from the injected freshwater bubble. Figure 2-1. Captured water from rainfall is treaded and pumped into an aquifer through ASR wells (Pyne, 2003). Figure 2-2 shows the position of fresh water and transition zone at the end of the storage phase. As shown in Figure 2-2, the freshwater reservoir is asymmetrically distributed around the ASR well to indicate that it has migrated under natural gradient conditions. The degree of mixing between the injected and ambient water and the width

PAGE 24

16 of the transition zone increases with the length of flow of the advancing front and is controlled by hydrodynamic dispersion. Often, it is the case that the transition zone can be neglected, because it is narrow relative to the length dimension of the areas (or volume) occupied by the injected water (Bear, 1979). A SR WELL Figure 2-2. After storage period, transition zone is created and it separates freshwater from ambient water in the confined aquifer. Also injected freshwater has moved downgradient due to the natural groundwater velocity. FRESH WATER FRESH WATER CASING CASING CONFINING UNIT AQUIFER TRANSITION ZONE TRANSITION ZONE AMBIENT WATER AMBIENT WATER FLOW DIRECTI O N CONFINING UNIT

PAGE 25

CHAPTER 3 ASR MODEL This chapter focuses on two objectives. The first is to develop a quasi-analytical model to predict the quality of water recovered during the operation of an ASR system. The second objective is to validate the model by comparing simulation results of test cases against a numerical simulation generated using MODFLOW-96 (Harbaugh and McDonald, 1996a and 1996b) and MT3DMS (Zheng and Wang, 1999) packages. Analytical Statement of Front Movement The assumed conceptual model of an ASR system operating in homogeneous confined aquifer is that of a fully screened well, uniformly recharging or extracting water over the entire thickness of the aquifer, L. During extraction and recharge, stored water is continuously under the influence of regional hydraulic gradient. It is conceptually assumed that the regional aquifer flow is uniform and of a steady specific discharge q that is proportional to the regional hydraulic gradient in an aquifer that is both homogeneous and of constant thickness. Thus, dsdKq (3-1) in which K is the aquifer hydraulic conductivity [L/T]; is the hydraulic head [L], and s is the primary direction of groundwater flow [L]. This natural gradient flow is considered here to describe the horizontal displacement of water injected at the ASR well. 17

PAGE 26

18 To model the geometry of the advancing front separating the indigenous water of a confined aquifer from a body of injected water during the operation of an ASR system, the total injection time is discritized into n subintervals of t. nitT1 (3-2) where T i is the duration of the injection cycle [T]. The radius of the cylindrical volume of injected water after time t is C such that: 211LtQCrii (3-3) of which Q i is the injection flow rate [L3/T]; and is the effective porosity of the aquifer. Of the water stored in the aquifer, it may be assumed from equation (3-3) that a plan view of the injected bubble may be represented as follows: Figure 3-1. Plan view of the injected water after time t and before movement. P ri1=C i1 ASR Well Differences in density and viscosity between injected and ambient waters are neglected, such that the front separating injected from ambient waters of the aquifer is composed of all particles leaving the ASR well at t = 0. Clearly, it is necessary to monitor the migration of multiple fluid particles such that their positions may be used to reconstruct the geometry of the front. Thus, moving multiple fluid particles and tracking

PAGE 27

19 their positions over successive time intervals leads to an assessment of the position of the front at any time. In this development, the position of point P is followed where this point is situated on the boundary between the injected water and the ambient groundwater. After time t and under natural gradient conditions, it is assumed that the cylindrical volume of the stored water is displaced down gradient a distance B i from the ASR well. The position of the injected bubble at this time is shown in Figure 3-2. ( -i1 ) i2 1 Bi ri1' i 1 ri1=C P Direction of Regional Groundwater Flow Figure 3-2. Plan view of the injected water after time t and after movement. The displacement distance B i is estimated from equation (3-4): tqBi (3-4) The relation between parameters of Figure 3-2 can be written as: )cos(2'112211iBriBririii (3-5) or: 112211cos2'iBriBririii (3-6) where i 1 is specified and ri 1 is obtained from equation (3-3). In addition, there is: ')sin(sin111riiBi (3-7)

PAGE 28

20 111sin'siniriBi (3-8) )sin'sin(111iriBArci (3-9) )sin'sin(111112iriBArciiii (3-10) As freshwater injection continues at the constant rate of Q i for another time interval of t (total time=2t), the injected fresh water displaces the stored bubble in a manner as depicted in Figure 3-3. The total area is twice the area at t = t; thus, the shaded area in Figure 3-3 is equal to C 2 Direction of Regional Groundwater Flow P P' New boundary between the injected water and the ambient ri1' i2 M' M r ri2 ASR Well Figure 3-3. Position of the injected water after time 2t and before movement. From Figure 3-3, ri 2 equals the new distance of point P from the center of injection well: rriri'12

PAGE 29

21 For a small value of it can be assumed that arcs PP' and MM' define circles; thus: 360360)'(22122 Criri (3-11) 2122'riCri (3-12) Figure 3-4 shows the shape of the advancing front after time=2t. Again, under natural gradient conditions, the volume of the fresh water is displaced down gradient a distance B i from the ASR well from its location in Figure 3-3. Thus, i2 ri2' 2 i3 Bi ri2 ASR Well P Direction of Regional Groundwater Flow Figure 3-4. Position of the injected water after time 2t and after movement. Similar to what was needed to obtain the value of ri 1 and i 2 in equations (3-6) and (3-10), the distance of point P from the injection well is equal to r 2 where: 222222cos2'iBriBririii (3-13) )sin'sin(222223iriBArciiii (3-14)

PAGE 30

22 All the parameters on the right hand side of these equations are known. Therefore the polar coordinates with respect to the ASR well or (ri 2 ', i 3 ) can be determined for point P located on the injected/ambient water interface. Assuming the injection process continues for successive time intervals of t until, the displacement of point P along with a sufficient number of fluid particles (points) on a front (different values for i iTt n in Figure 3-1) maybe traced or followed such that the position of the front can be ascertained. By considering the displacement of multiple particles during small time intervals of t, the coordinates are known for several points like P that define the front at the end of injection time (T i ). Due to symmetry of the injected volume, values of i between 0 and also represent the values of i between 0 and (-i). rin' rin' i i ASR Well P Direction of Regional Groundwater Flow Figure 3-5. Position and shape of the interface after injection period (t=Ti). Figure 3-5 illustrates a typical position and shape of the interface after injection period (t=T i ), where:

PAGE 31

23 P = Point on the front separating the injected water from the ambient water (ri n ', i) = Polar coordinate of point P at the end of injection phase At the end of recharge period (t=T i ), comprised of n discrete time steps, the coordinate of point P will be (ri n ', i). Often, following the injection phase, there is a storage period. After a known time of storage, T s and under natural gradient condition, it is assumed that the volume of stored water is displaced down gradient a distance B s from the center of the ASR well. ssqTB (3-15) rs rin' i ASR Well P Direction of Regional Groundwater Flow s Bs Figure 3-6. Position and shape of the interface after storage period (t=Ti+Ts). At the end of the storage period, extraction takes place in the same ASR well. Figure 3-6 shows the starting of extraction phase (end of storage). In Figure 3-6, rs is the distance of point P from the well at the end of storage. The concentrations of water quality parameters such as chloride in the recovered water vary between that of ambient

PAGE 32

24 water of the aquifer and the recharge water. Similar to the injection period, the movement of fresh water is analyzed in small time increments of t. Assuming that Q r is the extraction flow rate of the ASR well, the radial extent of the water recovered is given by equation (3-16): 21LtQAr (3-16) Where A is the radial extent of the cylinder of water recovered from the ASR well, [L]; t is the duration of the time interval, [T]; and Q r is the extraction flow rate during the recovery phase [L 3 /T]. After pumping this volume, the plan view of freshwater may be depicted as in Figure 3-7, where the shaded area in this figure represents the area of recovered water, A 2 rs r M' M P' rr1 ASR Well P Direction of Regional Groundwater Flow New boundary between the injected water and the ambient Figure 3-7. Position and shape of the interface at the beginning of the recovery phase. In Figure 3-7, rr 1 equals to the new distance of point P from the center of injection well:

PAGE 33

25 rrsrr1 For a small value of it can be assumed that arcs PP' and MM' define circles. Thus: 360360)(2212 Arrrs (3-17) 221Arsrr (3-18) During the recovery time, t, the volume of stored water is displaced down gradient a distance B r from the center of the ASR well. tqBr (3-19) Similar to equations (3-6) and (3-10), the distance of point P from the injection well is equal to rr 1 where: sBrrBrrrrrrcos2'12211 (3-20) )sin'sin(1srrBArcsrnew (3-21) According to Figure 3-7, all the recovered water is injected freshwater; hence the concentration is the same as the concentration of injected water. But if recovery continues, some particles on the circumference of the freshwater body will reach the extraction well. From this moment, the concentration of dissolved solutes (i.e. chloride) in the recovered water is no longer at concentrations of the injected water. The first particle on the injected/ambient water interface that reaches the well is always located at =. After that, the target solute concentrations in the recovered water depend on the relative fractions of injected water and ambient water surrounding the well.

PAGE 34

26 Figure 3-8 shows the front positions at two different times during recovery. At every time increment an angle can be determined where the value of rr n =0. The fraction of ambient groundwater in the water recovered from ASR well is then calculated as: 360 F (3-22) where: )(2 (3-23) The concentration of recovered water is then calculated from equation (3-24): IARCFFCC)1( (3-24) In equation (3-24), C A is concentration of ambient water [M/L 3 ] and C I is concentration of injected water [M/L 3 ]. Direction of Regional Groundwater Flow ASR Well Figure 3-8. Position of the interface at two different times during recovery. Usually there is a storage time at the end of each cycle and then a new cycle of injection, storage, and recovery begins. The coordinate system of each point at the end of first cycle will be the initial coordinate for the second cycle. This process continues for the other cycles during operation of the ASR system.

PAGE 35

27 Based on the equations (3-1) to (3-24), a FORTRAN program was developed to simulate the concentration of recovered water during the recovery phase of an ASR system. The program requires one input file containing data on the number of cycles, the target solute concentration of injected water (C I ), the target solute concentration of ambient water (C A ), the aquifer hydraulic conductivity (K), the thickness of the aquifer (L), the effective porosity of the aquifer (), and the hydraulic gradient in the aquifer ( dsd ). In addition, for each individual cycle, the model input file requires: the injection time (T i ), the storage time (T s ), the total recovery time (T r ), the storage time at the end of each cycle (T d ), the number of time subintervals for each phase (n), the injection flow rate (Q i ), and the recovery flow rate (Q r ). Validation of the Quasi-analytical Model using Numerical Model A one-layer groundwater flow model was constructed using MODFLOW-96 (Harbaugh and McDonald, 1996) and MT3DMS (Zheng and Wang, 1998) to simulate the movement of the injected bubble in the aquifer and to compare the concentration of recovered water from this model with the values obtained from the quasi-analytical model. The input data for both models are from the engineering report for the Boynton Beach monitoring ASR site in Florida, prepared by CH2M HILL Southeast, Inc. in 1993. Aquifer properties are taken from USGS Water-Resources Investigations Report No. 02-4036 (Reese, 2002). Table 3-1 shows the duration and flow rates for different phases of operation at this site. Data are available for three cycles of injection, storage, and recovery. Transmissivity was estimated from the analysis of the recovery of water level after a period of constant rate pumping during a packer test, and it was reported to be 9400

PAGE 36

28 ft 2 /day. The thickness of the aquifer in the storage zone is 105 ft. Thus, the average horizontal hydraulic conductivity is equal to 89.52 ft/day. Ambient water quality data were collected from storage and monitoring wells. The chloride concentration of ambient water at this site was about 1950 mg/L and for the injected water it was reported to be 50 mg/L. Aquifer porosity is reported to be 0.3 for this site. Table 3-1. Duration and flow rates for three cycles of ASR operation in Boynton Beach, Florida. Cycle 1 Cycle 2 Cycle 3 Injection Time (day) 12.690 41.376 41.547 Storage Time (day) 0.130 0.010 8.768 Recovery Time (day) 6.981 15.979 21.750 Delay Time (day) 1.000 18.543 --------Injection Flow Rate (ft 3 /day) 131140.6 181875.7 179629.6 Injection Flow Rate (ft 3 /day) 183408.6 144955.7 195192.3 The numerical model consists of 101 columns and 101 rows and one confined layer with the thickness of 105 ft. A regular grid spacing of 10 ft is used for each row and column. The horizontal hydraulic conductivity of this layer is 89.52 ft/day and storativity is set to 0.0005. The effective porosity is 0.3. The flow field was first calculated with MODFLOW. The 3rd-order TVD scheme (Ultimate) with Courant number 0.75 was used in the simulation for the advection term and the GCG solver is used to solve the system equations. No dispersion is considered in the model. To obtain the desired hydraulic gradient, the cells in the first and last columns of the model are specified as fixed-head boundaries. Water of a constant concentration, C I is injected into the well at the cell [51, 51, 1]. The initial concentration, C B is set to 1950 mg/L. Eleven stress periods are

PAGE 37

29 simulated for three cycles of ASR operation and a transient flow is performed for the length of 168.774 days (Total operation time). The total simulation time for the numerical model was about ten minutes while it takes less than one minute to run the FORTRAN code for a one-layer model. Figure 3-9 shows the position of the front and contour map of the concentration field with the natural gradient of 0.01 at time=18.55 days, which is close to the end of recovery phase in the first cycle. This figure may be compared to Figure 3-8 of the analytical model. Figure 3-9. The front position at time=18.55 days. Figure 3-10 shows the concentration breakthrough curves at the injection/extraction well for three different background gradients of 0.1, 0.2, and 0.3 from numerical and quasi-analytical simulations. The results match showing that quasi-analytical model performed well. Considering the relatively short execution times required by the quasi-analytical model, one may be surmised it could serve as a good alternative model to MODFLOW/MT3DMS for simulating the performance of ASR systems.

PAGE 38

30 0200400600800100012001400160018002000020406080100120140160180Time(day)CL Concentration(mg/l) Modeled w/Fortran Gr=0.01 Modeled w/Fortran Gr=0.02 Modeled w/Fortran Gr=0.03 Modeled w/MT3DMS Gr=0.01 Modeled w/MT3DMS Gr=0.02 Modeled w/MT3DMS Gr=0.03 Figure 3-10. Concentration of recovered water obtained from numerical and analytical models. Developing the Model for Multiple Layers Several assumptions were made to expand the utility of the one layer model such that applications of ASR systems installed in stratified aquifers could be examined. These assumptions included: the absence of water movement between layers; a constant horizontal head gradient( dsd ) in all layers; and, layer specific injection and extraction flow rates which are proportional to transmissivity of each layer. Given unit thickness for each layer, the average of hydraulic conductivity of the aquifer is: NLKKNLiave1 (3-25) K i = Hydraulic conductivity of the i th layer in the aquifer [L/T]; and NL= Number of layers in the aquifer

PAGE 39

31 The transmissivity of i th layer is defined product the i th layer hydraulic conductivity [L/T] and layer thickness. Therefore, the transmissivity of the i th layer is equal to iiiLKT (3-26) where L i is layer thickness, [L]. The total transmissivity of the aquifer, T total then equals: LKTavetotal (3-27) in which L is the thickness of the aquifer [L]; hence, nitotalTT1 (3-28) The injection and recovery rates for the i th layer are calculated from equations (3-29) and (3-30): ItotaliIiQTTQ (3-29) RtotaliRiQTTQ (3-30) By defining totaliiTT (3-31) and LLii (3-32) then equations (3-29) and (3-30) reduce to: IiIiQQ (3-33) RiRiQQ (3-34)

PAGE 40

32 From equations (3-3) and (3-16), it was seen in a single layer that the two-dimensional horizontal geometry of injected water varied as a function of natural gradient and the injection/recovery flow rates. Therefore, the radial extent of the cylindrical volume of injected water for the i th layer is C i and is equal to: 2121iIiiIiiLtQLtQC (3-35) And in using the definition of i will have: 21LtQCiIii (3-36) Similarly, equation (3-16) converts to: 21LtQAiRii (3-37) The horizontal displacement B during time t for each layer is a function of constant hydraulic gradient and layer specific hydraulic conductivity; thus, tdsdKBii (3-38) Therefore, C Ri the concentration of the target solute in water recovered from each layer can be estimated. The total concentration of target solute is the summation of flow-weighted concentrations from all layers: NLRiRiRRtotalQCQC1 (3-39) From equation (3-29) and (3-30) and (3-39) the following is obtained:

PAGE 41

33 NLRiiRtotalCC1 (3-40) Modeling the Distribution of Hydraulic Conductivity in the Aquifer The geometry of the subsurface plume of injected freshwater is influenced by the aquifer properties and variation in hydraulic conductivity within the aquifer. In addition, dispersion and mixing between the injected water and native water are also related to the distribution of permeability within the storage zone The dispersivity in a stratified aquifer was discussed by Gelhar (1993) and Dagan (1994). A very simple description of mixing process in a heterogeneous aquifer can be developed if we assume that the aquifer exhibits perfect stratification, in the sense that horizontal hydraulic conductivity varies vertically through the depth of the aquifer (Gelhar, 1993). The values of hydraulic conductivity can be modeled as a random space function to account for their spatial variability and usually their logarithm tends to be normally distributed (Dagan, 1994). Theory A lognormal variant such as hydraulic conductivity will have a mean value of m and standard deviation and is expressed in brief form as L: (m, ). Similarly a normal variant (such as log transformed conductivities) will have a mean m' and standard deviation which is expressed by N: (m', '). The lognormal variant is related to the normal variant by the following equation: )),(:exp(),(: mNmL (3-41) The relationship between means and standard deviations of normal and lognormal distributions is as follow (David, 1977): )1)(exp(222m (3-42)

PAGE 42

34 and )2exp(2mm (3-43) In these equations, both m and are known (m is the average hydraulic conductivity and is manifestation of the apparent aquifer dispersivity). Previously it was stated that the total transmissivity of the aquifer was defined as the average hydraulic conductivity [L/T] times the thickness of the aquifer [L]: LKTavetotal (3-44) From equation (3-44) an appropriate mean value for the average hydraulic conductivity may be determined assuming the thickness of the aquifer and total transmissivity are known. If in addition a suitable value for variance of lognormal distribution can be estimated from the apparent aquifer dispersivity, then, equations (3-42) and (3-43) may be used to derive values of the mean (m') and the standard deviation (') for normal deviate of log transform hydraulic conductivity. The probability density function (PDF) curve representing this normal distribution is a function of m' and '. 221exp21)(mxxf (3-45) This curve is symmetrical about the mean value (m'). Figure 3-11 shows a sample curve of normal distribution with mean and standard deviation values of 2.

PAGE 43

35 00.20.4-3-2-101234567xf(x) Figure 3-11. Probability Density Function for the Normal Distribution, N: (2, 2) For each value of the normal deviate x, there is an associated density of probability f(x) and the probability of one value lying between x and x+dx will be f(x) dx. Consequently, the probability of x lying between a and b will be equal to: badxxfbxaprob)( (3-46) And this integral, if extended from to + is also equal to: 1)(dxxfxprob (3-47) The probability of x being smaller than or equal to a given value of x 0 is called the cumulative probability, F(x 0 ), and is equal to: 0)()(00xdxxfxxprobxF (3-48) By the definition, cumulative probability can be written as: F (-) =0 and F (+) =1 (3-49) The integral for a normally distributed deviate is not easily solved. Below is an approximation and was used herein to generate a normal distribution of log0)(xdxxf

PAGE 44

36 transformed hydraulic conductivities that were then used to simulate water quality changes in recovered water from an ASR well located in stratified aquifer: 212002exp115.0)(mxxF (3-50) 00.51-3-2-101234567xF(x) Figure 3-12. Cumulative probability function, F(x 0 ), for N: (2, 2). Figure 3-12 shows the cumulative probability function, F(x 0 ), for N: (2, 2). To generate a suite of hydraulic conductivities that are then used to characterize a uniformly layered aquifer, it is necessary that the conductivity assigned to each layer reflect a fraction of aquifer thickness that honors the assumed underlying log-normal conductivity distribution; hence, equation (3-50) is first rearranged to give x 0 : 2001)(215.0xFLnmx (3-51) Next, F(x 0 ) is incrementally increased by F(x 0 ) from 0 and 1, where the value of F(x 0 ) is equal to fraction of total aquifer thickness represented by a single layer. From each value F(x 0 ) a unique conductivity value of x o is estimated from equation (3-51). The resultant hypothetical aquifer will then have a lognormal distribution of conductivities with the mean conductivity of m and standard deviation of

PAGE 45

37 Sensitivity Analysis and Comparison of the Results from Analytical Model with the Real ASR Performance Data Figure 3-13 shows the results from the FORTRAN code based on the ASR data from a site in Boynton Beach, Florida. It is assumed that aquifer is made of 100 layers, with different hydraulic conductivities which are lognormally distributed through the depth of the aquifer. Mean value of hydraulic conductivity (m) is equal to transmissivity of the aquifer divided by thickness. The value of the standard deviation () is adjusted to simulate the apparent dispersion in the aquifer, based on ASR results. Higher values of the standard deviation will result in greater apparent dispersion at the ASR well during the recovery phase. As a result, target solutes concentrations will appear to increase sooner during the recovery phase than with a smaller value of (). Altering the value of natural gradient can also bring about a change in the solute breakthrough that is similar to changes effected by adjusting (). In general, an increase in the hydraulic gradient produces premature solute breakthrough. 020040060080010001200140016001800200005101520253035Time(day)Concentration(mg/l) Sigma=300 Gr=0.05 T=9406 (ft^2/day) Sigma=300 Gr=0.06 T=9406 (ft^2/day) Sigma=500 Gr=0.05 T=9422 (ft^2/day) Sigma=500 Gr=0.06 T=9422 (ft^2/day) Sigma=700 Gr=0.05 T=9404 (ft^2/day) Sigma=700 Gr=0.06 T=9404 (ft^2/day) Data from Boynton Beach, FL ASR well Figure 3-13. Sensitivity analysis for the analytical results from the FORTRAN code Figure 3-14 shows the results from the model with the real ASR performance data during two cycles of ASR operation. By calibrating the model to the first cycle data we

PAGE 46

38 can get an estimation of our variable parameters in the aquifer and then use them for other cycles. The best fitting line takes place when natural gradient is 0.06 and standard deviation is equal to 500. Figure 3-14 indicates that analytical model performs well in predicting extracted water quality during subsequent extraction cycles. 010020030040050060070080001020304050607080Time(day)Concentration(mg/l) Modeled with FORTRAN Gr=0.06 and Sigma=500 Data from Boynton Beach, FL ASR well Figure 3-14. Comparison of the analytical model results with the real ASR performance data.

PAGE 47

CHAPTER 4 CONCLUSIONS AND RECOMMENDATIONS Simulation results from the quasi-analytical model reproduced water quality simulations obtained using well known numerical models. Considering the relatively short execution times required by the quasi-analytical model and the quality of model validation results, it is concluded that the model developed herein is a good alternative to MODFLOW/MT3DMS for simulating the performance of ASR systems. In addition, given the minimal input data required, the quasi-analytical model is easier to apply than many existing numerical models. The groundwater flow modeling showed that the natural hydraulic gradient in the aquifer is of great importance in the operation of an ASR system and must be considered to achieve the desired extraction water quality. Maximum100% recovery efficiency is not viable unless the hydraulic gradient does not exist or is close to zero. To emulate the effects of hydrodynamic dispersion, simulations were performed as if the aquifer were stratified and the horizontal hydraulic conductivity varied vertically in a statistically defined manner. By calibrating the model to the water quality data from pilot tests performed at Boynton Beach, Florida, estimations of model parameters were obtained. The model parameters calibrated included the natural hydraulic gradient and the variance of hydraulic conductivity. Following calibration, the quasi-analytical model performed well in predicting the extracted water quality during subsequent extraction cycles of the pilot ASR system. 39

PAGE 48

40 This model could be used to optimize the operation of ASR systems. For instance, increasing recovery flow rate could increase recovery efficiency. Anisotropy within an aquifer will cause the geometry of freshwater stored in the subsurface to be irregular. This can greatly affect the extracted water quality. The current model does not address this anisotropy. Thus, it has a limitation in predicting water quality and cannot be applied in the presence of this irregularity. Future research could include developing the quasi-analytical model for a system of multiple ASR wells. Design of ASR systems, like other engineering design processes, is a sequence of decisions between alternatives under conditions of uncertainty. Short-term injection tests in pilot projects, coupled with regional studies and modeling tools, are crucial to assess the feasibility of using ASR in a much larger scale as proposed in CERP.

PAGE 49

LIST OF REFERENCES Ahlfeld D. P., 1999, Advective Control of Groundwater Contaminant Plumes: Model Development and Comparison to Hydraulic Control. Water Resources Research 35, no. 8, pp 2285-2293. American Society of Civil Engineers, 2001. Standard Guidelines for Artificial Recharge, EWRI/ASCE 34-01. Arthur J. D., Cowart J. B., Dabous A., 2001, Florida Aquifer Storage and Recovery Geochemical Study: Year Three Progress Report. Florida Geological Survey, Open File Report No. 83, p. 46. Bear J, 1979, Hydraulics of Groundwater. McGraw-Hill, New York, pp 276-299. Bouwer H., 1996, Issues in Artificial Recharge. Water Science and Technology 33, no. 10-11. Bouwer H., 2002, Artificial Recharge of Groundwater: Hydrology and Engineering. Journal of Hydrology 10, pp 121-142. CH2M Hill Southeast, Inc, June 1993, Engineering Report for the Boynton Beach Aquifer Storage and Recovery System. Report SEF26410.Q1. Dagan, G., 1994, An Exact Nonlinear Correction to Transverse Macrodispersivity for Transport in Heterogeneous Formations. Water Resources Research 30, no. 10, pp 2699-2705. David M, 1977, Geostatistical Ore Reserve Estimation. Elsevier Scientific Publishing Company, Amsterdam, pp 7-18. Evans M, Hastings N, Peacock B, 2000, Statistical Distributions. John Wiley and Sons, Inc, New York, pp 129-133, 145-150. Gelhar, L. W., 1993, Stochastic Subsurface Hydrology. Prentice-Hall, Englewood Cliffs, N.J, pp 204-207. Guo W., Langevin C. D., 2002, Users Guide to SEAWAT: A Computer Program for Simulation of Three-Dimensional Variable-Density Ground-Water Flow. USGS, Techniques of Water-Resources Investigations 6-A7, Tallahassee, Florida, pp 75. 41

PAGE 50

42 Harbaugh A. W., McDonald M. G., 1996a, Users Documentation for MODFLOW-96, an Update to the U.S. Geological Survey Modular Finite-Difference Ground-Water Flow Model. USGS Open-File Report 96-485. Harbaugh A. W., McDonald M. G., 1996b, Programmers Documentation for MODFLOW-96, an Update to the U.S. Geological Survey Modular Finite-Difference Ground-Water Flow Model. USGS Open-File Report 96-486. Javandel, I., Doughty, C., and Tsang, C., 1984, Groundwater Transport: Handbook of Mathematical Models. American Geophysical Union, Washington, D.C., pp 35-67. Javandel, I., Tsang, C., 1986, Capture-Zone Type Curves: A Tool for Aquifer Cleanup. Ground Water 24, no. 5, pp 616-625. Lloyd J. W., June 2001, Groundwater Vulnerability and the Reuse of Water, With Reference to Saudi Arabia. International Journal of Water Resources Development 17 (2), pp 179-184. Martin J. B., Dean R. W. September 2001. Exchange of Water between Conduits and Matrix in the Floridian Aquifer. Chemical Geology 179, pp 145-165. McDonald M. G., Harbaugh A. W., 1988, MODFLOW, a Modular Three-Dimensional Finite Difference Ground-Water Flow Model. USGS Open-File Report 83-875, Chapter A1. Merritt M. L., 1985, Subsurface Storage of Freshwater in South Florida: A Digital Model Analysis of Recoverability. U. S. Geological Survey Water-Supply Paper 2261, p 44. Missimer T. M., Walker CW, Bloetscher F, September 1992, Use of Aquifer Storage and Recovery Technology to Improve Membrane Water-Treatment Plant-Efficiency, Collier County, Florida. Desalination. Elsevier Science BV, Amsterdam, pp 269-280. Missimer T. M., Guo W, Walker CW, Maliva RG, February 2002, Hydraulic and Density Considerations in the Design of Aquifer Storage and Recovery Systems. Florida Water Resources Journal, pp 30-35. Muniz A. and Ziegler W. B., July 1994, Aquifer Storage and Recovery in Southeast Florida. Artificial Recharge of Groundwater, II: Proceeding of the Second International Symposium on Artificial Recharge of Groundwater, Published by the ASCE, New York 10017-2398, pp 311-323. Muskat M, 1937, The Flow of Homogeneous Fluids Through Porous Media. McGraw-Hill, New York, 763 pp.

PAGE 51

43 Nelson, R. W., 1978, Evaluating the Environmental Consequences of Groundwater contamination. 2, Obtaining Location/Arrival Time and Location/Outflow Quality Distribution for Steady Flow Systems. Water Resources Research 14, no. 3, pp 416-428. Nguyen P. D. and Mueller T. K., December 1996, A Cautious Look at Aquifer Storage Recovery in South Florida from a Public Health Viewpoint. Florida Water Resources Journal, pp 24-27. Available: www.fwrj.com/articles/9612.pdf Pyne D. G., July 1994, Seasonal Storage of Reclaimed Water and Surface Water in Brackish Aquifers Using Aquifer Storage Recovery (ASR) Wells. Artificial Recharge of Groundwater, II: Proceedings of the Second International Symposium on Artificial Recharge of Ground Water, Published by the ASCE, New York 10017-2398, pp 282-298. Pyne, D. G., February 2002, Aquifer Storage Recovery Wells: The Path Ahead. Florida Water Resources Journal, pp 19-22, 27. Pyne, D. G., ASR Systems, 2003, http://www.asrforum.com July 26, 2003. Reese R, 2002, Inventory and Review of Aquifer Storage and Recovery in Southern Florida. U.S. Geological Survey, Water-Resources Investigations Report 02-4036, 55 pp. Zheng C, Wang P. P., 1999, MT3DMS: A Modular Three-Dimensional Multispecies Model for Simulation of Advection, Dispersion and Chemical Reactions of Contaminants In Groundwater Systems; Documentation and Users Guide, Contract Report SERDP-99-1, U.S. Army Engineer Research and Development Center, Vicksburg, MS, University of Alabama, 168 pp.

PAGE 52

44 BIOGRAPHICAL SKETCH Ali Sedighi was born in 1975 in Tehran, Iran. He received a mathematics and physics diploma from Sadegh High School in 1993. In February, 1998, Ali graduated from Sharif University of Technology with a Ba chelor of Science in civil engineering. He enrolled in the graduate school at the Univer sity of Florida in fall of 2001. He joined the Master of Engineering program in the Depa rtment of Civil and Coastal Engineering under the guidance of his major pr ofessor, Dr. Kirk Hatfield.


Permanent Link: http://ufdc.ufl.edu/UFE0001247/00001

Material Information

Title: A Quasi-Analytical Model to Predict Water Quality during the Operation of an Aquifer Storage and Recovery System
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0001247:00001

Permanent Link: http://ufdc.ufl.edu/UFE0001247/00001

Material Information

Title: A Quasi-Analytical Model to Predict Water Quality during the Operation of an Aquifer Storage and Recovery System
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0001247:00001


This item has the following downloads:


Full Text












A QUASI-ANALYTICAL MODEL TO PREDICT WATER QUALITY DURING THE
OPERATION OF AN AQUIFER STORAGE AND RECOVERY SYSTEM















By

ALI SEDIGHI


A REPORT PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA


2003

































Copyright 2003

by

Ali Sedighi















ACKNOWLEDGMENTS

I would like to offer my utmost appreciation to Dr. Kirk Hatfield, chairperson of

my supervisory committee, who was much more than an advisor to me. He played a key

role in guiding me with unlimited patience and energy and gave me all the support I

could ask for. His experience and guidance have enlightened my education, as well as my

life. I would also like to thank my committee members, Dr. Louis H. Motz and Dr.

Michael D. Annable, for all of their valuable encouragements, ideas, and compassion

throughout my study at the University of Florida. I am also grateful to all my previous

professors at Sharif University of Technology in Tehran, Iran.

Behind the scenes was my loving girlfriend, Rachel Johnson, who rejoiced with me

in good times and cheered me up in bad times. I thank her for her hard work in editing

this paper and also her support and patience throughout the past year.

I am grateful to my friend, Harald Klammler, for all of his help, support, and great

contribution to my work. I also wish to thank all my friends, especially Ali-Reza Kazemi,

who has added richness to my life.

I am endlessly grateful to my parents, Parvin Bagherzadeh and Abdolvahab

Sedighi, and my sister Vida for the emotional and financial support afforded me

throughout my life.
















TABLE OF CONTENTS
Page

A C K N O W L E D G M E N T S ......... .................................................................................... iii

LIST OF FIGURES ................................... ...... ... ................. .v

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

Applications and Benefits of ASR Technology.........................................................4
R research O objective and Scope........................................................... ............... 6

2 LITER A TU RE REV IEW .................................................. ............................... 7

A SR M modeling ................................... ........................... 7
Hydraulic Factors and Characteristics of ASR Systems.............................................9
Operation of the Aquifer Storage and Recovery Systems............... ..................14

3 A SR M O D E L ....................................................... ................. 17

Analytical Statement of Front M movement ............................................................... 17
Validation of the Quasi-analytical Model using Numerical Model ..................27
Developing the M odel for M multiple Layers.......................................................30
Modeling the Distribution of Hydraulic Conductivity in the Aquifer........................33
T h eory .................................... ..................... ... ........................... ... .. 3 3
Sensitivity Analysis and Comparison of the Results from Analytical Model
with the Real ASR Performance Data .................................. ............... 37

4 CONCLUSIONS AND RECOMMENDATIONS ............................................. 39

L IST O F R E F E R E N C E S ........................................................................ .....................4 1

B IO G R A PH IC A L SK E TCH ..................................................................... ..................44










iv
















LIST OF FIGURES


Figure p

1-1. Distribution of operational and under development ASR systems in North
Am erica. ................................... .................................... .......... 2

1-2. Miami-dade County, Florida, recovers water stored in a 1000 to 1300 foot deep
(300-400 m) brackish limestone aquifer. ....................................... ............... 3

2-1. Captured water from rainfall is traded and pumped into an aquifer through ASR
w ells. ................................................................................15

2-2. After storage period, transition zone is created and it separates freshwater from
ambient water in the confined aquifer. Also injected freshwater has moved
downgradient due to the natural groundwater velocity.................... ...............16

3-1. Plan view of the injected water after time At and before movement. ....................18

3-2. Plan view of the injected water after time At and after movement..........................19

3-3. Position of the injected water after time 2At and before movement.....................20

3-4. Position of the injected water after time 2At and after movement...........................21

3-5. Position and shape of the interface after injection period (t=Ti)..............................22

3-6. Position and shape of the interface after storage period (t=Ti+Ts)..........................23

3-7. Position and shape of the interface at the beginning of the recovery phase.............24

3-8. Position of the interface at two different times during recovery..............................26

3-9. The front position at time=18.55 days. ............ ............................. ...... ............... 29

3-10. Concentration of recovered water obtained from numerical and analytical
m o d els. ........................................................... ................ 3 0

3-11. Probability Density Function for the Normal Distribution, N: (2, 2).....................35

3-12. Cumulative probability function, F(xo), for N: (2, 2).............................................36









3-13. Sensitivity analysis for the analytical results from the FORTRAN code.................37

3-14. Comparison of the analytical model results with the real ASR performance data. .38














Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering

A QUASI-ANALYTICAL MODEL TO PREDICT WATER QUALITY DURING THE
OPERATION OF AN AQUIFER STORAGE AND RECOVERY SYSTEM

By

Ali Sedighi

August 2003

Chair: Kirk Hatfield
Major Department: Civil and Coastal Engineering

Aquifer Storage Recovery (ASR) is defined as the storage of freshwater in an

aquifer by injecting water through the wells during wet periods for subsequent retrieval

from these same wells during dry periods. The freshwater forms a bubble of injected

water within the aquifer around the ASR well, and it can be retrieved when needed to

meet seasonal, long-term, emergency or other demands. During the past ten years, ASR

technology has evolved from merely a concept to a proven, cost-effective and

environmentally desirable water management tool.

The objective of this paper is to develop an analytical model to determine

recovered water quality based on the position of the injected water, surrounded by the

ambient water of the aquifer. Injected water and ambient water are characterized as two

separate zones by the differing concentrations of specific dissolved species. When these

two zones are introduced to each other, a transition zone is created across which the

concentration varies. The transition between these two zones is modeled by creating a









distribution of hydraulic conductivity across the depth of the aquifer. Thus, in a layer

with a constant value of hydraulic conductivity, the transition zone is replaced by a sharp

front, which, while moving, continuously separates the two zones with different

concentrations. By keeping track of the front position during injection, storage,

andrecovery, we can obtain the fraction of injected water contained in the pumped water

from the angle of the injected water body surrounding the well; thus, the concentration of

recovered water will be a number between the concentration of injected water and the

concentration of ambient water.

To validate this analytical model, the results are compared with numerical models,

using MODFLOW-96 and MT3DMS packages. The running time for this analytical

model is less than 10 percent of the running time in existing numerical models. Also,

considering the simple way of introducing input data, it can be superior to the existing

numerical models.














CHAPTER 1
INTRODUCTION

Population growth during the past few decades has accelerated the demand on both

surface and groundwater supply. Aquifer Storage and Recovery (ASR) is an important

component of groundwater management. ASR is defined as the storage of freshwater in

an aquifer through the wells during periods when surface supplies are plentiful for

subsequent retrieval from these same wells during dry periods. The injected water forms

a bubble within the aquifer around the ASR well, and can be retrieved when needed to

meet seasonal, long-term, emergency or other demands. The potential for seasonal

storage and drought protection have made ASR one of the most promising storage

methods for potable, surface and reclaimed water.

The term "Aquifer Storage Recovery" was coined by David G. Pyne in 1983 when

the first ASR system in Manatee County, Florida, began successful operation (Pyne,

2003). As of January 2003, fifty-six ASR systems are believed to be operational in the

United States, 12 of which are located in Florida. This compares to the three ASR

systems in 1983. Most systems are storing treated drinking water. At least 100 other

ASRs are in various stages of development, ranging from planning to operational startup.

Figure 1-1 shows the location of ASR systems in the North America as of January 2002.

Other systems are known to be operating in the United Kingdom, Canada, Australia and

Israel. ASR development programs are underway in several other countries, including the

Netherlands, New Zealand, Thailand, Taiwan, Saudi Arabia, and Kuwait (Pyne, 2002 and

Lloyd, 2001).









ASR wells have been storing water in the

United States since 1969
Over 54 Operating ASR $9Sit



NJ .iR





a Owwlat-fhi lw _\ r | ^^Jtf^^- FILAS



ASR wals are operalng or unddr
devlopmeAt tn many at ur coontrde



Figure 1-1. Distribution of operational and under development ASR systems in North
America (Pyne, 2003).

The Comprehensive Everglades restoration Plan (CERP) proposes to use as many

as to 333 ASR wells to store as much as 1.6 billion gallons of freshwater per day to

ensure the quantity of water available to the Everglades, improve water quality conditions

in Lake Okeechobee, and prevent damaging releases of freshwater to coastal estuaries

(Figure 1-2). Some of this water would also be available to support surrounding

agriculture and to protect urban wells located near the coast from salt-water intrusion.

Muniz and Ziegler (1994) detail the feasibility, construction, testing and initial

operation of the Boynton Beach, Florida ASR well. This case study is of particular value

to the CERP because it is within 20 miles of proposed ASR wells in CERP. The first step

in hydrogeologic characterization of the site was the boring of pilot holes. Geologic logs









from the pilot holes were used to assist in correlating formation samples to identify

specific lithologic boundaries design. Cycle testing was successful in determining

operational performance, evaluating potential recharge and recovery of treated drinking

water, confirming that recovered water met drinking water standards, and estimating the

hydraulic performance of the storage zone.

Successful experience at most monitoring sites has confirmed that ASR is not only

practical, but cost-effective for storing water deep underground. However, Nguyen and

Mueller (1996) recommend that all ASR projects should be considered only on an

experimental basis in the initial phase to allow collection of valuable data to assess the

aquifer characteristics and the quality of the native water in the storage zone.


S.. m ...77 C

Figure 1-2. Miami-dade County, Florida, recovers water stored in a 1000 to 1300 foot
deep (300-400 m) brackish limestone aquifer (Pyne, 2003).









Applications and Benefits of ASR Technology

The primary driving force behind the current rapid global implementation of ASR

technology is water supply economics. ASR provides a cost-effective solution to many of

the world's water management needs and can usually meet water management needs at

less than half the capital cost of other water supply alternatives (Pyne, 2002). Large water

volumes are stored deep underground, reducing or eliminating the need to construct large

and expensive surface reservoirs. ASR is most commonly used in conjunction with the

potable water treatment systems for purposes of storing excess treated water in the

ground. Water treatment plants typically face their peak demand only during short

periods each year. An ASR can replace the storage capacity that otherwise must be built

into a plant's surface facilities; hence, it can minimize capital and operating costs. Wells

can be located where most needed and because wells require little land, the costs of large

land acquisitions are avoided.

ASR also results in less water lost. Some areas have seasonally abundant water

resources (like Florida) but few good places to store the water. Evapotranspiration and

seepage losses are high in surface reservoirs, whereas for underground storage these two

problems are insignificant. ASR systems could potentially allow for multi-year storage,

whereas evaporation during severe droughts limits the ability of reservoirs to provide

similar long-term storage.

Several benefits can be cited with respect to the adoption of ASR systems. First,

most obviously these systems can be used to store water when the supply is abundant and

the water quality is good for purposes of recovering it later during emergencies or times

of water shortage, or when source water quality is poor. Second, during the recharge

cycle, groundwater levels can then be restored where aquifers have experienced long









term declines in water levels due to heavy pumping to meet increasing urban and

agricultural water needs. Finally, ASR is generally viewed as an environmentally good

alternative to surface water reservoirs because they reduce or eliminate the need for dam

construction, and they provide for reliable water supplies through the diversion of flood

flows instead of low flows.

In addition to meeting increased water demands, ASR plays a role in solving the

challenges of wet weather surface flows and groundwater and wastewater management.

For example, as urban development continues, the area of impermeable ground cover

continues to expand, raising the level of surface runoff and its attendant problem of

erosion, silting, and pollution. Stormwater serves a better purpose when it can be

captured and safely reintroduced to the aquifer. In addition, with saltwater intrusion

threatening drinking water supplies in coastal areas, ASR injection wells can create water

barriers that protect vulnerable aquifers. Finally, ASR can also be used to recycle treated

wastewater (Missimer et al. 1992).

ASR applications, particularly in Florida, are for seasonal water storage, but other

applications include long term water storage or water banking from wet years to drought

years, emergency water storage, restoring water levels in depleted aquifers, controlling

subsidence, maintaining pressures and flows in water distribution systems, improving

water quality, reducing the cost of water system expansions, maintaining minimum flows

and levels, and many other applications. Increasingly, ASR is being considered for

development of Strategic Water Reserves to provide water supply security from terrorism

or warfare (Reese, 2002 and Pyne, 2002).









Research Objective and Scope

The objective of this research was to predict water quality changes during the

operation of an ASR system. The efficiency of ASR operations is dependent on the

volume of stored water recovered. The recovered volume depends on transient changes in

water quality that result from ASR operations. Tools developed to better predict water

quality changes during ASR operations could be used to optimize the management of

ASR systems. To meet the above stated research objective, a quasi-analytical model has

been developed. In this model, the recovered water quality is calculated based on the

simulated position of the injected volume of water with respect to the ambient water of

the aquifer, the quality of the injected water, and the quality of the ambient groundwater.

To validate the quasi-analytical model, results are compared to the well-known numerical

models, MODFLOW-96 (Harbaugh and McDonald, 1996a and 1996b) and MT3DMS

(Zheng and Wang, 1999).














CHAPTER 2
LITERATURE REVIEW

ASR Modeling

Numerical models such as MODFLOW-96 (Harbaugh and McDonald, 1996a and

1996b) and MT3DMS (Zheng and Wang, 1999) and SEAWAT (Guo and Langevin,

2002) are available to simulate the movement of injected water through an ASR well and

to predict the transient quality of recovered water. To perform these simulations, the

spatial and temporal scales of numerical discretization must be sufficiently small to

minimize numerical dispersion and preserve mass balances on simulated water quality

parameters. The high level of discretization and the associated increased computational

demands required may all but preclude direct application of numerical codes except over

small and unstratified aquifer domains. Analytical models potentially offer computation

efficiencies for simulating transport through homogeneous aquifers not easily afforded

through numerical transport models.

Analytical models were developed to study movement of injected water in the

aquifer. Muskat (1937) considered the steady flow pattern produced by a single pumping

well near an equipotential boundary, while Bear (1979) studied the shape of the

advancing front separating the indigenous water of a confined aquifer from a body of

water injected into it through a well at the origin. However, Muskat and Bear did not seek

to predict water quality during all operational phases of an ASR system. Their models do

provide insight into the groundwater velocity field that ultimate plays a significant role in

the transport of dissolved constituents.









Nelson (1978) developed a semi analytical approach that provides location/arrival

time distributions and location/outflow quantity distributions at critical outflow

boundaries of the system. This model assumes that the concentration distribution at the

beginning of the simulation is known.

Javandel and others (1984) developed a particle-tracking model to show how

spatial distribution in concentration versus time data for a single injection well reaches

any desired outflow boundary. This model calculates the time it takes for a particle to

flow to a pumping well given all pumping and injection rates. It is required to construct

flow patterns and then use them to identify the locations of any contaminant fronts for

various values of time.

Javandel and Tsang (1986) developed the previous model to determine the capture

zone of multiple wells. The new model can assist in the determination of the optimum

number of pumping wells, their rates of discharge and locations, such that further

degradation of the aquifer is avoided.

Ahlfeld (1999) used particle tracking techniques to develop an optimization

formulation for designing groundwater plume control systems.

The limitation of these models is the inability to account for dispersion. The

particle-tracking model developed by Javandel and others (1984) can be applied to

predict water quality in an ASR system. However, the quasi-analytical model developed

herein is simpler since there is no need to construct flow patterns in the aquifer. The

quasi-analytical model does not simulate the transport of dissolved solutes but determines

the transient fraction of ambient groundwater recovered during the ASR extraction phase.

Because convective/dispersive transport process are not explicitly simulated, the quasi-









analytical model is limited to simulating water quality changes at the ASR well and

during the recovery phase; however, these simulations can be achieved at significant

computational efficiencies over traditional numerical transport models. To emulate the

effects of hydrodynamic dispersion, these simulations are performed as if the aquifer

were stratified and the horizontal hydraulic conductivity varied vertically in a statistically

defined manner.

Hydraulic Factors and Characteristics of ASR Systems

For most ASR systems, storage volumes range from as small as 13 million gallons

(MG) in individual ASR wells to as much as 2.5 billion gallons (BG) or more in large

ASR well fields. The shallowest depth to the top of a storage zone is about 200 feet while

the greatest depth to the base of an ASR storage zone is 2600 feet. The thinnest storage

zone is about 50 feet while the thickest is about 1300 feet. Natural water quality in

storage zones ranges from freshwater that is suitable for drinking without treatment to

brackish water with total dissolved solids concentrations up to about 5000 mg/1. Most

sites have one or more natural water quality constituents that are unsuitable for direct

potable use except following treatment. Such constituents may include iron, manganese,

fluoride, hydrogen sulfide, sulfate, chloride, radium, gross alpha radioactivity, and other

elements that are typically displaced by the stored water as the bubble is formed

underground.

Arthur et al (2001) studied the geochemical aspects of the Florida Aquifer Storage

and Recovery system. Results of this study indicate that chemical variability (including

isotropy) exists within groundwater and carbonate of the Floridan aquifer system which

may result site-specific geochemical processes affecting ASR well performance and

water quality. Also, as oxygen-rich surface waters are injected into Floridan aquifer









system, trace metals such as arsenic (As), iron (Fe), manganese (Mn) and uranium (U)

are mobilized (chemically leached) from the carbonate rocks and withdrawn during

recovery. Therefore, some of the periods of higher metals concentrations in the recovered

water are short-lived, depending on the duration of the injection, storage, and recovery

cycles. Their results confirm that understanding water-rock geochemical interactions are

important to the continued success of ASR in Florida.

Merritt (1985) studied the relationship of recovery efficiency to the hydrogeologic

conditions that could prevail in brackish artesian aquifers. The principal tool of

investigation used in his study was the INTRA model which has a variety of potential

applications to variable-density solute-transport problems. He found that a loss of

recovery efficiency was caused by (1) processes causing mixing of injected freshwater

with native saline water hydrodynamicc dispersion), (2) process causing the more or less

irreversible displacement of the injected freshwater with respect to the well (background

hydraulic gradient, interlayer dispersion, buoyancy stratification), or (3) processes

causing injection and withdrawal flow patterns to be dissimilar directionallyy biased well-

bore plugging, dissimilar injection and withdrawal schedules in multiple well systems).

Success or failure of an ASR system is controlled by a wide variety of factors that

are related to hydrogeologic conditions, well design, and operational management. Some

of these factors are (Bear, 1979, Missimer et al, 2002, and Reese, 2002):

* Natural gradient

* Aquifer porosity

* Hydrodynamic dispersion (which includes the effects of molecular diffusion and

mechanical dispersion)









* Confinement of the aquifer

* Aquifer permeability and its distribution

* Aquifer transmissivity

* Aquifer thickness

* Ambient water quality and density

* Injected water quality

* Desired extraction water quality

* Injection and recovery flow rates

* Duration of different periods (injection, storage, and recovery)

* Frequency of cycles and storage period at the end of each cycle

Recovery efficiency is significantly affected by the downgradient movement of

injected water due to the background hydraulic gradient. The average velocity of ambient

flow is a function of the hydraulic conductivity and porosity as well as the natural

gradient.

The degree of mixing between the injected water and native water and the width of

transition zone is controlled by hydrodynamic dispersion, which in turn is a reflection of

the degree of spatial variability in aquifer conductivity. Some sites show minimal mixing

on the initial cycle, and, if the natural hydraulic gradient in the aquifer is small, after two

or three cycles the same volume stored the quality of recovered water is quite stable. On

the other hand, some sites show substantial mixing, suggesting that even with a small

hydraulic gradient a very large water quality transition zone would be encountered to

achieve 100% recovery.









If the storage zone is not well confined, injected water may move upward or

downward out of the storage zone, or ambient water may move vertically into the storage

zone during recovery. Most sites use confined or semi confined aquifers for storage;

however, at several sites the aquifer is unconfined. Sometimes a subsurface zone must

have barriers to contain stored water.

Permeable sediments or rock must be present to allow flow of water through the

aquifer. The hydraulic conductivity or permeability distribution in the storage zone

greatly influences the recovery efficiency. Mechanical dispersion is related to the

distribution of permeability within the storage zone. Higher permeability can cause

higher dispersive mixing, and hence lower recovery efficiency. As a result, a sandy

aquifer with relatively uniform permeability could have better recovery efficiency since

the primary component of dispersion results from flow through intergranular pore space

alone. However, suitable storage zones include a wide variety of geologic settings such as

sand, sandstone, gravel, limestone, dolomite, glacial drift aquifers, and basalt.

The transmissivity of an aquifer has an effect on the ability to recover injected

freshwater. The transmissivity of the selected aquifer must be high enough to allow water

to be injected and recovered at sufficient rates to allow the system to economically

achieve the design goals. However, the transmissivity must be low enough to allow the

injected water to be recovered without losing it in the aquifer as a result of migration

under natural gradient condition. Therefore, the transmissivity must lie within a range of

values depending on the desired pumping rates and the recoverability percentage

(Missimer et al, 2002).









Recovery efficiency is greater in a thin aquifer than in a thick aquifer because of

the lower vertical extent of the transition zone along which mixing occurs. However, this

effect can be partially offset by increasing the volume of water recharged during a cycle.

Minimizing the thickness of the storage zone within a thick aquifer can also be beneficial

depending on the aquifer's distribution of vertical hydraulic conductivity (Reese, 2002).

The ambient concentration in the aquifer is of primary importance in controlling

recovery efficiency. This will be addressed later when the model is being developed.

Buoyancy can play a significant role in the success or failure of an ASR system. In some

places, like South Florida, ASR is mostly used to store water in an aquifer that contains

brackish water. Therefore, the density difference between freshwater and ambient water

is substantial and the greater the differential in density, the faster freshwater will move

upward in an aquifer. When the density differential is relatively small, the issue of

density-driven water movement is not significant because the lower vertical hydraulic

conductivity compared to horizontal hydraulic conductivity tends to reduce the effect

(Missimer et al, 2002).

Increasing the injection and recovery flow rates would dominate the effect of

freshwater displacement during injection and recovery. There is a portion of injected

freshwater which has moved downgradient and can never be recovered. By increasing the

recovery flow rate, we can reduce this volume of unrecoverable water. However,

injection and recovery rates are site-specific parameters; therefore they must be

confirmed at each well cluster location (Bouwer, 1996).

Martin and Dean (2001) detail the presence of known fractures in the Floridan

aquifer system of north-central Florida determined via dye trace studies and cave diving









explorations. They also detail how this extensive fracture system, and the resulting

simultaneous conduit and matrix groundwater flow, create the requirement for dual-

porosity groundwater modeling. The ASCE Standard Guidelines for Artificial Recharge

of Groundwater (2001) explains that determination of the critical injection pressure is the

key factor to prevent hydrofracturing and it suggests a range of 0.2-0.6h depending on

site specific conditions, where h is the head necessary to raise the potentiometric surface

at the recharge well to the ground surface.

Increasing the duration of different phases during the operation of an ASR system

would decrease the recovery efficiency. The longer the duration of each phase, the more

the displacement of injected freshwater. Also, dispersion and mixing would appear more

during the long periods of injection, storage and recovery. Recovery efficiency would

improve with repeated cycles because some of the recharged water from a previous cycle

is left in the aquifer (especially when natural hydraulic gradient is low), and during the

next cycle, recharged water mixes with water of a lower concentration.

There are still some uncertainties about ASR systems, and an additional step in the

path forward would be a better understanding of the processes by which changes in water

quality occur during ASR operation. This will help determine the feasibility of using

ASR on a much larger scale as proposed in Comprehensive Everglades Restoration Plan

(CERP).

Operation of the Aquifer Storage and Recovery Systems

ASR wells are evaluated and operated through a cyclical process. Each cycle

includes periods of injection (recharge), storage, and then recovery with each period

lasting days or months. During the injection period, a portion of the excess available

surface water supply is treated and injected via the ASR well into a deep and mostly









confined aquifer, creating a large reservoir of stored water that slowly displaces the

ambient groundwater. Figure 2-1 shows the position of injected water in the aquifer after

the recharge cycle.

Due to the natural hydraulic gradient in the aquifer, injected water moves down

gradient throughout the phases of injection, storage and recovery. When the recharge

water that is characterized by concentrations of multiple dissolved solutes is introduced

into an aquifer with indigenous water comprised of different solutes and concentrations, a

transition zone is created across which solute concentrations vary (Bear, 1979). The

transition zone separates ambient water from the injected freshwater bubble.





















Figure 2-1. Captured water from rainfall is traded and pumped into an aquifer through
ASR wells (Pyne, 2003).

Figure 2-2 shows the position of fresh water and transition zone at the end of the

storage phase. As shown in Figure 2-2, the freshwater reservoir is asymmetrically

distributed around the ASR well to indicate that it has migrated under natural gradient

conditions. The degree of mixing between the injected and ambient water and the width










of the transition zone increases with the length of flow of the advancing front and is

controlled by hydrodynamic dispersion. Often, it is the case that the transition zone can

be neglected, because it is narrow relative to the length dimension of the areas (or

volume) occupied by the injected water (Bear, 1979).


ASR WELL


FRESH
\\ WATER


~ .i.F. ER
f,3,UI==ER
~xA


FRESH
\\ WATER


Figure 2-2. After storage period, transition zone is created and it separates freshwater
from ambient water in the confined aquifer. Also injected freshwater has
moved downgradient due to the natural groundwater velocity.


-K* f; ^ ?fC J

^y^^













CHAPTER 3
ASR MODEL

This chapter focuses on two objectives. The first is to develop a quasi-analytical

model to predict the quality of water recovered during the operation of an ASR system.

The second objective is to validate the model by comparing simulation results of test

cases against a numerical simulation generated using MODFLOW-96 (Harbaugh and

McDonald, 1996a and 1996b) and MT3DMS (Zheng and Wang, 1999) packages.

Analytical Statement of Front Movement

The assumed conceptual model of an ASR system operating in homogeneous

confined aquifer is that of a fully screened well, uniformly recharging or extracting water

over the entire thickness of the aquifer, L. During extraction and recharge, stored water is

continuously under the influence of regional hydraulic gradient. It is conceptually

assumed that the regional aquifer flow is uniform and of a steady specific discharge q

that is proportional to the regional hydraulic gradient in an aquifer that is both

homogeneous and of constant thickness. Thus,


q= -Kd (3-1)
ds

in which K is the aquifer hydraulic conductivity [L/T]; (p is the hydraulic head [L], and s

is the primary direction of groundwater flow [L]. This natural gradient flow is considered

here to describe the horizontal displacement of water injected at the ASR well.









To model the geometry of the advancing front separating the indigenous water of a

confined aquifer from a body of injected water during the operation of an ASR system,

the total injection time is discritized into n subintervals of At.


T =-At (3-2)


where Ti is the duration of the injection cycle [T]. The radius of the cylindrical volume of

injected water after time At is C such that:


ri =C = QAt 2 (3-3)


of which Qi is the injection flow rate [L3/T]; and 11 is the effective porosity of the aquifer.

Of the water stored in the aquifer, it may be assumed from equation (3-3) that a plan view

of the injected bubble may be represented as follows:



rii= C



ASR Well



Figure 3-1. Plan view of the injected water after time At and before movement.

Differences in density and viscosity between injected and ambient waters are

neglected, such that the front separating injected from ambient waters of the aquifer is

composed of all particles leaving the ASR well at t = 0. Clearly, it is necessary to monitor

the migration of multiple fluid particles such that their positions may be used to

reconstruct the geometry of the front. Thus, moving multiple fluid particles and tracking









their positions over successive time intervals leads to an assessment of the position of the

front at any time. In this development, the position of point P is followed where this point

is situated on the boundary between the injected water and the ambient groundwater.

After time At and under natural gradient conditions, it is assumed that the

cylindrical volume of the stored water is displaced down gradient a distance Bi from the

ASR well. The position of the injected bubble at this time is shown in Figure 3-2.




Direction of Regional B P
Groundwater Flow
ri= ri"'- __-(-0ii)

Oi. .i2






Figure 3-2. Plan view of the injected water after time At and after movement.

The displacement distance Bi is estimated from equation (3-4):

B = qAt (3-4)


The relation between parameters of Figure 3-2 can be written as:

ri,'= ri2 + B2 2rilB, cos(r 0/) (3-5)

or:

ri1'= ri + B2 + 2riB cos 01 (3-6)

where Oil is specified and ril is obtained from equation (3-3). In addition, there is:

sin0, sin(- 0i,)
(3-7)
B, ri'









B
sin 0, =- sin 6, (3-8)
ri,'

B
01 = Arcsin(-',sin 1 ) (3-9)
ril

B
02 = 0/1 01 = 61, Arc sin( sin 0,) (3-10)
ril

As freshwater injection continues at the constant rate of Qi for another time interval

of At (total time=2At), the injected fresh water displaces the stored bubble in a manner as

depicted in Figure 3-3. The total area is twice the area at t = At; thus, the shaded area in

Figure 3-3 is equal to 7CC2.




Direction of Regional
Groundwater Flow I
"i n AO M



ASR Well




New boundary
between the injected
water and the ambient


Figure 3-3. Position of the injected water after time 2At and before movement.

From Figure 3-3, ri2 equals the new distance of point P from the center of injection

well:


ri2 = ril '+Ar









For a small value of A it can be assumed that arcs PP' and MM' define circles;

thus:

r(ri ri, 2) = 7C2 (3-11)
2 360 360

ri2 = C2 r2 (3-12)

Figure 3-4 shows the shape of the advancing front after time=2At. Again, under

natural gradient conditions, the volume of the fresh water is displaced down gradient a

distance Bi from the ASR well from its location in Figure 3-3. Thus,



Bi P
Direction of Regional
Groundwater Flow ri2'

i2 ) i3

ASR Well








Figure 3-4. Position of the injected water after time 2At and after movement.

Similar to what was needed to obtain the value of ril' and 0i2 in equations (3-6) and

(3-10), the distance of point P from the injection well is equal to r2' where:

ri 2'= jri2 +B2 + 2ri2B, cos 2 (3-13)


0i, = 6i2 -0 = 62 Arcsin( 'sinOi2) (3-14)
ri2'









All the parameters on the right hand side of these equations are known. Therefore

the polar coordinates with respect to the ASR well or (ri2', Oi3) can be determined for

point P located on the injected/ambient water interface.

Assuming the injection process continues for successive time intervals of At

until At = T, the displacement of point P along with a sufficient number of fluid

particles (points) on a front (different values for O6i in Figure 3-1) maybe traced or

followed such that the position of the front can be ascertained. By considering the

displacement of multiple particles during small time intervals of At, the coordinates are

known for several points like P that define the front at the end of injection time (Ti). Due

to symmetry of the injected volume, values of Oi between 0 and 7n also represent the

values of Oi between 0 and -7t (-Oi).




Direction of Regional
Groundwater Flow/ rin'




ASR Well

rin'







Figure 3-5. Position and shape of the interface after injection period (t=Ti).

Figure 3-5 illustrates a typical position and shape of the interface after injection

period (t=Ti), where:









P = Point on the front separating the injected water from the ambient water

(rin', Oi) = Polar coordinate of point P at the end of injection phase

At the end of recharge period (t=Ti), comprised of n discrete time steps, the

coordinate of point P will be (rin', Oi). Often, following the injection phase, there is a

storage period. After a known time of storage, Ts, and under natural gradient condition, it

is assumed that the volume of stored water is displaced down gradient a distance Bs from

the center of the ASR well.


B =q (3-15)





Direction of Regional Bs p
Groundwater Flow rin'
rs


ASR Well









Figure 3-6. Position and shape of the interface after storage period (t=Ti+Ts).

At the end of the storage period, extraction takes place in the same ASR well.

Figure 3-6 shows the starting of extraction phase (end of storage). In Figure 3-6, rs is the

distance of point P from the well at the end of storage. The concentrations of water

quality parameters such as chloride in the recovered water vary between that of ambient









water of the aquifer and the recharge water. Similar to the injection period, the movement

of fresh water is analyzed in small time increments of At.

Assuming that Qr is the extraction flow rate of the ASR well, the radial extent of

the water recovered is given by equation (3-16):


A = (QAt (3-16)


Where A is the radial extent of the cylinder of water recovered from the ASR well,

[L]; At is the duration of the time interval, [T]; and Qr is the extraction flow rate during

the recovery phase [L3/T].

After pumping this volume, the plan view of freshwater may be depicted as in

Figure 3-7, where the shaded area in this figure represents the area of recovered water,

xtA2




Direction of Regional i M
Groundwater Flow .. -
Pi-i- PNi



i|ASR Well



New boundary
between the injected
water and the ambient


Figure 3-7. Position and shape of the interface at the beginning of the recovery phase.

In Figure 3-7, rr1 equals to the new distance of point P from the center of injection


well:









rr, = rs- Ar

For a small value of A it can be assumed that arcs PP' and MM' define circles.

Thus:


2r(rs2 -rr) AO 2= A (3-17)
360 360

rr, = Jrs A (3-18)

During the recovery time, At, the volume of stored water is displaced down

gradient a distance Br from the center of the ASR well.


B qAt (3-19)
77

Similar to equations (3-6) and (3-10), the distance of point P from the injection

well is equal to rri' where:

r, '= rr2 +B2, + 2rrB, cosOs (3-20)


On = Os-Arc sin( sin 8s) (3-21)
rr'

According to Figure 3-7, all the recovered water is injected freshwater; hence the

concentration is the same as the concentration of injected water. But if recovery

continues, some particles on the circumference of the freshwater body will reach the

extraction well. From this moment, the concentration of dissolved solutes (i.e. chloride)

in the recovered water is no longer at concentrations of the injected water.

The first particle on the injected/ambient water interface that reaches the well is

always located at 6=7r. After that, the target solute concentrations in the recovered water

depend on the relative fractions of injected water and ambient water surrounding the well.









Figure 3-8 shows the front positions at two different times during recovery. At

every time increment an angle 0 can be determined where the value of rr.=0. The

fraction of ambient groundwater in the water recovered from ASR well is then calculated

as:


F = (3-22)
360

where:

/ = 2( 0) (3-23)

The concentration of recovered water is then calculated from equation (3-24):

CR= FCA + (1- F)CJ (3-24)

In equation (3-24), CA is concentration of ambient water [M/L3] and CI is

concentration of injected water [M/L3].





Direction of Regional /
Groundwater Flow L

ASR Well







Figure 3-8. Position of the interface at two different times during recovery.

Usually there is a storage time at the end of each cycle and then a new cycle of

injection, storage, and recovery begins. The coordinate system of each point at the end of

first cycle will be the initial coordinate for the second cycle. This process continues for

the other cycles during operation of the ASR system.









Based on the equations (3-1) to (3-24), a FORTRAN program was developed to

simulate the concentration of recovered water during the recovery phase of an ASR

system. The program requires one input file containing data on the number of cycles, the

target solute concentration of injected water (CI), the target solute concentration of

ambient water (CA), the aquifer hydraulic conductivity (K), the thickness of the aquifer

(L), the effective porosity of the aquifer (q), and the hydraulic gradient in the aquifer

(d). In addition, for each individual cycle, the model input file requires: the injection
ds

time (Ti), the storage time (Ts), the total recovery time (Tr), the storage time at the end of

each cycle (Td), the number of time subintervals for each phase (n), the injection flow

rate (Qi), and the recovery flow rate (Qr).

Validation of the Quasi-analytical Model using Numerical Model

A one-layer groundwater flow model was constructed using MODFLOW-96

(Harbaugh and McDonald, 1996) and MT3DMS (Zheng and Wang, 1998) to simulate the

movement of the injected bubble in the aquifer and to compare the concentration of

recovered water from this model with the values obtained from the quasi-analytical

model. The input data for both models are from the engineering report for the Boynton

Beach monitoring ASR site in Florida, prepared by CH2M HILL Southeast, Inc. in 1993.

Aquifer properties are taken from USGS Water-Resources Investigations Report No. 02-

4036 (Reese, 2002).

Table 3-1 shows the duration and flow rates for different phases of operation at this

site. Data are available for three cycles of injection, storage, and recovery.

Transmissivity was estimated from the analysis of the recovery of water level after

a period of constant rate pumping during a packer test, and it was reported to be 9400









ft2/day. The thickness of the aquifer in the storage zone is 105 ft. Thus, the average

horizontal hydraulic conductivity is equal to 89.52 ft/day. Ambient water quality data

were collected from storage and monitoring wells. The chloride concentration of ambient

water at this site was about 1950 mg/L and for the injected water it was reported to be 50

mg/L. Aquifer porosity is reported to be 0.3 for this site.

Table 3-1. Duration and flow rates for three cycles of ASR operation in Boynton Beach,
Florida.
Cycle 1 Cycle 2 Cycle 3

Injection Time (day) 12.690 41.376 41.547

Storage Time (day) 0.130 0.010 8.768

Recovery Time (day) 6.981 15.979 21.750

Delay Time (day) 1.000 18.543 ---

Injection Flow Rate (ft3/day) 131140.6 181875.7 179629.6

Injection Flow Rate (ft3/day) 183408.6 144955.7 195192.3



The numerical model consists of 101 columns and 101 rows and one confined layer

with the thickness of 105 ft. A regular grid spacing of 10 ft is used for each row and

column. The horizontal hydraulic conductivity of this layer is 89.52 ft/day and storativity

is set to 0.0005. The effective porosity is 0.3. The flow field was first calculated with

MODFLOW. The 3rd-order TVD scheme (Ultimate) with Courant number 0.75 was used

in the simulation for the advection term and the GCG solver is used to solve the system

equations. No dispersion is considered in the model. To obtain the desired hydraulic

gradient, the cells in the first and last columns of the model are specified as fixed-head

boundaries. Water of a constant concentration, CI, is injected into the well at the cell [51,

51, 1]. The initial concentration, CB, is set to 1950 mg/L. Eleven stress periods are








simulated for three cycles of ASR operation and a transient flow is performed for the

length of 168.774 days (Total operation time). The total simulation time for the numerical

model was about ten minutes while it takes less than one minute to run the FORTRAN

code for a one-layer model.

Figure 3-9 shows the position of the front and contour map of the concentration

field with the natural gradient of 0.01 at time=18.55 days, which is close to the end of

recovery phase in the first cycle. This figure may be compared to Figure 3-8 of the

analytical model.



1mmmmmm -_-_-:



mmmm --mmmmmm




mm m m m mm m -_----..m m m mm m m m m


Figure 3-9. The front position at time=18.55 days.
Figure 3-10 shows the concentration breakthrough curves at the injection/extraction

well for three different background gradients of 0.1, 0.2, and 0.3 from numerical and

quasi-analytical simulations. The results match showing that quasi-analytical model

performed well. Considering the relatively short execution times required by the quasi-

analytical model, one may be surmised it could serve as a good alternative model to

MODFLOW/MT3DMS for simulating the performance of ASR systems.















A1600 A Modeled w/M 13UMa ur=U.U1 -
IM Modeled w/MT3DMS Gr=0.02
1400 Modeled w/MT3DMS Gr=0.03

1000-"A
S800
0 600 A
0 400 ----
200 -

0 20 40 60 80 100 120 140 160 180
Time(day)
Figure 3-10. Concentration of recovered water obtained from numerical and analytical
models.

Developing the Model for Multiple Layers

Several assumptions were made to expand the utility of the one layer model such

that applications of ASR systems installed in stratified aquifers could be examined.

These assumptions included:

the absence of water movement between layers;


a constant horizontal head gradient( ) in all layers; and,
ds

layer specific injection and extraction flow rates which are proportional to

transmissivity of each layer.

Given unit thickness for each layer, the average of hydraulic conductivity of the

aquifer is:

NL
2K,
Kave L (3-25)


Ki= Hydraulic conductivity of the ith layer in the aquifer [L/T]; and

NL= Number of layers in the aquifer









The transmissivity of ith layer is defined product the ith layer hydraulic conductivity

[L/T] and layer thickness. Therefore, the transmissivity of the ith layer is equal to

T,= K, L, (3-26)

where Li is layer thickness, [L]. The total transmissivity of the aquifer, Ttotai, then equals:

Tota = Kave *L (3-27)

in which L is the thickness of the aquifer [L]; hence,

n
Tto0a1 = (3-28)


The injection and recovery rates for the ith layer are calculated from equations (3-

29) and (3-30):


0, = T, i (3-29)
total


QR, T, QR (3-30)
total

By defining


A,= T (3-31)
'total

and


Y, = (3-32)
L

then equations (3-29) and (3-30) reduce to:

Qi, = AQ (3-33)

QR, =A, QR (3-34)









From equations (3-3) and (3-16), it was seen in a single layer that the two-

dimensional horizontal geometry of injected water varied as a function of natural gradient

and the injection/recovery flow rates. Therefore, the radial extent of the cylindrical

volume of injected water for the ith layer is Ci and is equal to:

1 1
C, 4 ~Q11At 2 AQ, At 2 (3-35)
Li -)- (3-35)


And in using the definition ofyi, will have:

1

C, 2 (3-36)


Similarly, equation (3-16) converts to:

i

A, =-- (3-37)


The horizontal displacement B during time At for each layer is a function of

constant hydraulic gradient and layer specific hydraulic conductivity; thus,

K d(o At
B, ds (3-38)


Therefore, Cm, the concentration of the target solute in water recovered from each

layer can be estimated. The total concentration of target solute is the summation of flow-

weighted concentrations from all layers:

NL
CRtotalQR CR, QR (3-39)
1


From equation (3-29) and (3-30) and (3-39) the following is obtained:









NL
CRtotal = CR, (3-40)


Modeling the Distribution of Hydraulic Conductivity in the Aquifer

The geometry of the subsurface plume of injected freshwater is influenced by the

aquifer properties and variation in hydraulic conductivity within the aquifer. In addition,

dispersion and mixing between the injected water and native water are also related to the

distribution of permeability within the storage zone

The dispersivity in a stratified aquifer was discussed by Gelhar (1993) and Dagan

(1994). A very simple description of mixing process in a heterogeneous aquifer can be

developed if we assume that the aquifer exhibits perfect stratification, in the sense that

horizontal hydraulic conductivity varies vertically through the depth of the aquifer

(Gelhar, 1993). The values of hydraulic conductivity can be modeled as a random space

function to account for their spatial variability and usually their logarithm tends to be

normally distributed (Dagan, 1994).

Theory

A lognormal variant such as hydraulic conductivity will have a mean value of m

and standard deviation o and is expressed in brief form as L: (m, a). Similarly a normal

variant (such as log transformed conductivities) will have a mean m' and standard

deviation o' which is expressed by N: (m', '). The lognormal variant is related to the

normal variant by the following equation:

L: (m, )= exp(N : (m',a')) (3-41)

The relationship between means and standard deviations of normal and lognormal

distributions is as follow (David, 1977):

a2 =m2(exp(c'2) 1) (3-42)









and


m = exp(m' + -) (3-43)
2

In these equations, both m and o are known (m is the average hydraulic

conductivity and o is manifestation of the apparent aquifer dispersivity).

Previously it was stated that the total transmissivity of the aquifer was defined as

the average hydraulic conductivity [L/T] times the thickness of the aquifer [L]:

total = Kave L (3-44)

From equation (3-44) an appropriate mean value for the average hydraulic

conductivity may be determined assuming the thickness of the aquifer and total

transmissivity are known. If in addition a suitable value for variance of lognormal

distribution can be estimated from the apparent aquifer dispersivity, then, equations (3-

42) and (3-43) may be used to derive values of the mean (m') and the standard deviation

(a') for normal deviate of log transform hydraulic conductivity.

The probability density function (PDF) curve representing this normal distribution

is a function of m' and o'.

1 I x-m'
f (x)-p exp (3-45)


This curve is symmetrical about the mean value (m'). Figure 3-11 shows a sample

curve of normal distribution with mean and standard deviation values of 2.










0.4



0.2




-3 -2 -1 0 1 2 3 4 5 6 7


Figure 3-11. Probability Density Function for the Normal Distribution, N: (2, 2)

For each value of the normal deviate x, there is an associated density of probability

f(x) and the probability of one value lying between x and x+dx will bef(x) dx.

Consequently, the probability ofx lying between a and b will be equal to:

proba < x < b}= f(x)dx (3-46)
ra

And this integral, if extended from -oo to +oo is also equal to:

prob{- o < x < +c}= +c f (x)dx = 1 (3-47)

The probability ofx being smaller than or equal to a given value ofxo is called the

cumulative probability, F(xo), and is equal to:

F(xo) = prob{x < x, }= f (x)dx (3-48)

By the definition, cumulative probability can be written as:

F (-o) 0 and F (+o) =1 (3-49)

The integral ff f(x)dx for a normally distributed deviate is not easily solved.

Below is an approximation and was used herein to generate a normal distribution of log-









transformed hydraulic conductivities that were then used to simulate water quality

changes in recovered water from an ASR well located in stratified aquifer:


F(x) 0.5 1+ 1- exp 2xom 2j_ (3-50)






Lo.



Fn, X


-3 -2 -1 0 1 2 3 4 5 6 7


Figure 3-12. Cumulative probability function, F(xo), for N: (2, 2).

Figure 3-12 shows the cumulative probability function, F(xo), for N: (2, 2). To

generate a suite of hydraulic conductivities that are then used to characterize a uniformly

layered aquifer, it is necessary that the conductivity assigned to each layer reflect a

fraction of aquifer thickness that honors the assumed underlying log-normal conductivity

distribution; hence, equation (3-50) is first rearranged to give xo:

x0 =m' +cr'-0.57zLn( -(2F(xo)-1)2) (3-51)

Next, F(xo) is incrementally increased by AF(xo) from 0 and 1, where the value of

AF(xo) is equal to fraction of total aquifer thickness represented by a single layer. From

each value F(xo) a unique conductivity value ofx, is estimated from equation (3-51). The

resultant hypothetical aquifer will then have a lognormal distribution of conductivities

with the mean conductivity of m and standard deviation of -.










Sensitivity Analysis and Comparison of the Results from Analytical Model with the
Real ASR Performance Data

Figure 3-13 shows the results from the FORTRAN code based on the ASR data

from a site in Boynton Beach, Florida. It is assumed that aquifer is made of 100 layers,

with different hydraulic conductivities which are lognormally distributed through the

depth of the aquifer. Mean value of hydraulic conductivity (m) is equal to transmissivity

of the aquifer divided by thickness. The value of the standard deviation (o) is adjusted to

simulate the apparent dispersion in the aquifer, based on ASR results. Higher values of

the standard deviation will result in greater apparent dispersion at the ASR well during

the recovery phase. As a result, target solutes concentrations will appear to increase

sooner during the recovery phase than with a smaller value of (o).

Altering the value of natural gradient can also bring about a change in the solute

breakthrough that is similar to changes effected by adjusting (o). In general, an increase

in the hydraulic gradient produces premature solute breakthrough.


2000 Sigma=300 Gr=0.05 T=9406 (ft^
1800 x Sigma=300 Gr=0.06 T=9406 (ft'
0 Sigma=500 Gr=0.05 T=9422 (ftA
S1600 x Sigma=500 Gr=0.06 T=9422 (ft'
S1400 + Sigma=700 Gr=0.05T=9404(ftA
1200 Sigma=700 Gr=0.06 T=9404 (ft^
- 1200 Data from Boynton Beach, FL
5 1000
S800
u 600
400
200
n


0 5 10 15 20 25 30 35
Time(day)

Figure 3-13. Sensitivity analysis for the analytical results from the FORTRAN code

Figure 3-14 shows the results from the model with the real ASR performance data

during two cycles of ASR operation. By calibrating the model to the first cycle data we


2/day)
2/day)
2/day)
2/day)
2/day)
2/day)
ASR well


w












can get an estimation of our variable parameters in the aquifer and then use them for


other cycles. The best fitting line takes place when natural gradient is 0.06 and standard


deviation is equal to 500. Figure 3-14 indicates that analytical model performs well in


predicting extracted water quality during subsequent extraction cycles.



800

700 Modeled with FORTRAN Gr=0.06 and Sigma=600
+ Data from Boynton Beach, FL ASR well
S600

500
C *
0
S400

8300

S 200
S= _
100-


0 10 20 30 40 50 60 70 80
Time(day)

Figure 3-14. Comparison of the analytical model results with the real ASR performance
data.














CHAPTER 4
CONCLUSIONS AND RECOMMENDATIONS

Simulation results from the quasi-analytical model reproduced water quality

simulations obtained using well known numerical models. Considering the relatively

short execution times required by the quasi-analytical model and the quality of model

validation results, it is concluded that the model developed herein is a good alternative to

MODFLOW/MT3DMS for simulating the performance of ASR systems. In addition,

given the minimal input data required, the quasi-analytical model is easier to apply than

many existing numerical models.

The groundwater flow modeling showed that the natural hydraulic gradient in the

aquifer is of great importance in the operation of an ASR system and must be considered

to achieve the desired extraction water quality. Maximuml00% recovery efficiency is not

viable unless the hydraulic gradient does not exist or is close to zero.

To emulate the effects of hydrodynamic dispersion, simulations were performed as

if the aquifer were stratified and the horizontal hydraulic conductivity varied vertically in

a statistically defined manner. By calibrating the model to the water quality data from

pilot tests performed at Boynton Beach, Florida, estimations of model parameters were

obtained. The model parameters calibrated included the natural hydraulic gradient and the

variance of hydraulic conductivity. Following calibration, the quasi-analytical model

performed well in predicting the extracted water quality during subsequent extraction

cycles of the pilot ASR system.









This model could be used to optimize the operation of ASR systems. For instance,

increasing recovery flow rate could increase recovery efficiency.

Anisotropy within an aquifer will cause the geometry of freshwater stored in the

subsurface to be irregular. This can greatly affect the extracted water quality. The current

model does not address this anisotropy. Thus, it has a limitation in predicting water

quality and cannot be applied in the presence of this irregularity.

Future research could include developing the quasi-analytical model for a system of

multiple ASR wells. Design of ASR systems, like other engineering design processes, is a

sequence of decisions between alternatives under conditions of uncertainty. Short-term

injection tests in pilot projects, coupled with regional studies and modeling tools, are

crucial to assess the feasibility of using ASR in a much larger scale as proposed in CERP.
















LIST OF REFERENCES

Ahlfeld D. P., 1999, Advective Control of Groundwater Contaminant Plumes: Model
Development and Comparison to Hydraulic Control. Water Resources Research 35,
no. 8, pp 2285-2293.

American Society of Civil Engineers, 2001. Standard Guidelines for Artificial Recharge,
EWRI/ASCE 34-01.

Arthur J. D., Cowart J. B., Dabous A., 2001, Florida Aquifer Storage and Recovery
Geochemical Study: Year Three Progress Report. Florida Geological Survey, Open
File Report No. 83, p. 46.

Bear J, 1979, Hydraulics of Groundwater. McGraw-Hill, New York, pp 276-299.

Bouwer H., 1996, Issues in Artificial Recharge. Water Science and Technology 33, no.
10-11.

Bouwer H., 2002, Artificial Recharge of Groundwater: Hydrology and Engineering.
Journal of Hydrology 10, pp 121-142.

CH2M Hill Southeast, Inc, June 1993, Engineering Report for the Boynton Beach
Aquifer Storage and Recovery System. Report SEF26410.Q1.

Dagan, G., 1994, An Exact Nonlinear Correction to Transverse Macrodispersivity for
Transport in Heterogeneous Formations. Water Resources Research 30, no. 10, pp
2699-2705.

David M, 1977, Geostatistical Ore Reserve Estimation. Elsevier Scientific Publishing
Company, Amsterdam, pp 7-18.

Evans M, Hastings N, Peacock B, 2000, Statistical Distributions. John Wiley and Sons,
Inc, New York, pp 129-133, 145-150.

Gelhar, L. W., 1993, Stochastic Subsurface Hydrology. Prentice-Hall, Englewood Cliffs,
N.J, pp 204-207.

Guo W., Langevin C. D., 2002, User's Guide to SEAWAT: A Computer Program for
Simulation of Three-Dimensional Variable-Density Ground-Water Flow. USGS,
Techniques of Water-Resources Investigations 6-A7, Tallahassee, Florida, pp 75.









Harbaugh A. W., McDonald M. G., 1996a, User's Documentation for MODFLOW-96,
an Update to the U.S. Geological Survey Modular Finite-Difference Ground-Water
Flow Model. USGS Open-File Report 96-485.

Harbaugh A. W., McDonald M. G., 1996b, Programmer's Documentation for
MODFLOW-96, an Update to the U.S. Geological Survey Modular Finite-
Difference Ground-Water Flow Model. USGS Open-File Report 96-486.

Javandel, I., Doughty, C., and Tsang, C., 1984, Groundwater Transport: Handbook of
Mathematical Models. American Geophysical Union, Washington, D.C., pp 35-67.

Javandel, I., Tsang, C., 1986, Capture-Zone Type Curves: A Tool for Aquifer Cleanup.
Ground Water 24, no. 5, pp 616-625.

Lloyd J. W., June 2001, Groundwater Vulnerability and the Reuse of Water, With
Reference to Saudi Arabia. International Journal of Water Resources Development
17 (2), pp 179-184.

Martin J. B., Dean R. W. September 2001. Exchange of Water between Conduits and
Matrix in the Floridian Aquifer. Chemical Geology 179, pp 145-165.

McDonald M. G., Harbaugh A. W., 1988, MODFLOW, a Modular Three-Dimensional
Finite Difference Ground-Water Flow Model. USGS Open-File Report 83-875,
Chapter Al.

Merritt M. L., 1985, Subsurface Storage of Freshwater in South Florida: A Digital Model
Analysis of Recoverability. U. S. Geological Survey Water-Supply Paper 2261, p
44.

Missimer T. M., Walker CW, Bloetscher F, September 1992, Use of Aquifer Storage and
Recovery Technology to Improve Membrane Water-Treatment Plant-Efficiency,
Collier County, Florida. Desalination. Elsevier Science BV, Amsterdam, pp 269-
280.

Missimer T. M., Guo W, Walker CW, Maliva RG, February 2002, Hydraulic and Density
Considerations in the Design of Aquifer Storage and Recovery Systems. Florida
Water Resources Journal, pp 30-35.

Muniz A. and Ziegler W. B., July 1994, Aquifer Storage and Recovery in Southeast
Florida. Artificial Recharge of Groundwater, II: Proceeding of the Second
International Symposium on Artificial Recharge of Groundwater, Published by the
ASCE, New York 10017-2398, pp 311-323.

Muskat M, 1937, The Flow of Homogeneous Fluids Through Porous Media. McGraw-
Hill, New York, 763 pp.









Nelson, R. W., 1978, Evaluating the Environmental Consequences of Groundwater
contamination. 2, Obtaining Location/Arrival Time and Location/Outflow Quality
Distribution for Steady Flow Systems. Water Resources Research 14, no. 3, pp
416-428.

Nguyen P. D. and Mueller T. K., December 1996, A Cautious Look at Aquifer Storage
Recovery in South Florida from a Public Health Viewpoint. Florida Water
Resources Journal, pp 24-27. Available: www.fwrj.com/articles/9612.pdf

Pyne D. G., July 1994, Seasonal Storage of Reclaimed Water and Surface Water in
Brackish Aquifers Using Aquifer Storage Recovery (ASR) Wells. Artificial
Recharge of Groundwater, II: Proceedings of the Second International Symposium
on Artificial Recharge of Ground Water, Published by the ASCE, New York
10017-2398, pp 282-298.

Pyne, D. G., February 2002, Aquifer Storage Recovery Wells: The Path Ahead. Florida
Water Resources Journal, pp 19-22, 27.

Pyne, D. G., ASR Systems, 2003, http://www.asrforum.com, July 26, 2003.

Reese R, 2002, Inventory and Review of Aquifer Storage and Recovery in Southern
Florida. U.S. Geological Survey, Water-Resources Investigations Report 02-4036,
55 pp.

Zheng C, Wang P. P., 1999, MT3DMS: A Modular Three-Dimensional Multispecies
Model for Simulation of Advection, Dispersion and Chemical Reactions of
Contaminants In Groundwater Systems; Documentation and User's Guide,
Contract Report SERDP-99-1, U.S. Army Engineer Research and Development
Center, Vicksburg, MS, University of Alabama, 168 pp.















BIOGRAPHICAL SKETCH

Ali Sedighi was born in 1975 in Tehran, Iran. He received a mathematics and

physics diploma from Sadegh High School in 1993. In February, 1998, Ali graduated

from Sharif University of Technology with a Bachelor of Science in civil engineering. He

enrolled in the graduate school at the University of Florida in fall of 2001. He joined the

Master of Engineering program in the Department of Civil and Coastal Engineering

under the guidance of his major professor, Dr. Kirk Hatfield.