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CAPTURE ZONE OF A MULTI-WELL SYSTEM IN BOUNDED AQUIFERS

تعداد89 صفحه در فایل word

Ph.D. Thesis

In Hydrogeology

CAPTURE ZONE OF A MULTI-WELL SYSTEM IN BOUNDED AQUIFERS

ABSTRACT

The capture zone of a well is defined as a volume of an aquifer that supplies water to the well under steady state condition. In many hydrogeological projects such as sustainable development of groundwater resources, surface-subsurface water interaction, well head protection, remediation of contaminated groundwater (e.g. pump-and-treat, bioremediation, chemical oxidation), and water right adjudication the study of well capture zone is of great concern. In this thesis we derived several analytical equations to delineate the capture zone of a multi-well system in bounded aquifers of various configurations.

The thesis is organized in several chapters. In Chapter 1 the objectives of research is introduced and the theoretical background of the research is given through a comprehensive literature review.

In Chapter 2 we present the equation of capture zone of a multi-well system in wedge-shaped confined and unconfined aquifers. Three wedge boundary configurations: barrier-barrier wedge, barrier-constant head wedge and constant head-constant head wedge are considered. Method of image wells is used in the wedge-shaped domain and an appropriate complex function is formulated to find the capture zone. The stream function and velocity potential are derived from the imaginary part and real part of the complex function, respectively. Also, the drawdown equation for each boundary configuration is derived. Solutions are provided for the wedge domains with and without a uniform regional flow and can also be used for aquifers of infinite extent. The effect of well positions, well types, well numbers, regional flow rate and direction and wedge angle on the capture envelope is also studied. Finally the application of the solutions as tools for the containment and remediation of a contaminant plume and for the verification of numerical models is demonstrated.

In Chapter 3 we present the equation of capture zone for multi-well system in peninsula-shaped confined and unconfined aquifers. The aquifer is rectangular in plan view, bounded along three sides and extends to infinity at the fourth side. The bounding boundaries are either no-flow (impervious) or in-flow (constant head) so that aquifers with six possible boundary configurations are formed. The complex velocity potential equations for such a well-aquifer system are derived to delineate the capture envelope. Solutions are provided for the aquifers with and without a uniform regional flow of any directions. Solutions are presented in form of dimensionless capture type curves and their application in engineering project is demonstrated. Also, the drawdown equation for each boundary configuration is derived.

In Chapter 4 the capture zone equations of a multi-well system in bounded confined and unconfined rectangular-shaped aquifers are derived. The aquifer is rectangular in plan view and bounded along all four sides. The boundaries could be in-flow (constant head) or no-flow (impervious) and hence six possible boundary configurations are formed. Using the image well theory the flow field in bounded aquifers is first transformed to its equivalent in extensive aquifers and then the complex velocity potential theory is applied for the generation of stream function delineating the capture envelope. Also, the drawdown equations for each boundary configuration are derived.

In Chapter 5, the solution of for capture zone of a partially penetrating multi-well system in isotropic and anisotropic confined aquifers with infinite extend is derived. The method of image well theory is used to derive the drawdown, velocity potential and stream function equations. These equations are flexible in terms of screen length and location along the aquifer thickness. Two types of partial penetration are considered. Also the effect of Partial Penetration Factor (PPF), anisotropy and screen location is discussed.

In Chapter 6, the capture zone of a partially penetrating multi-well system in isotropic and anisotropic confined aquifer near one in-flow or no-flow boundary is derived for two partial penetration types that mentioned in chapter 5. In addition, in this chapter the capture zone of a partially penetrating well near one inflow boundary is also presented for two well -boundary distance of less than and greater than 1.5 times of aquifer thickness and (compared the capture envelopes with those of fully penetrating wells. .

In Chapter 7, we derive the capture zone of a partially penetrating multi-well system in isotropic and anisotropic confined aquifer between two parallel boundaries. The boundaries may be in-flow, no-flow or a combination of both. Therefore, three unique boundary configurations are formed for two partially penetrating well types that mentioned in chapter 5. In addition, in this chapter the capture zone of a partially penetrating well between two parallel boundaries is also presented for two well distances to the boundary (1) less than 1.5 times of aquifer thickness and (2) greater than 1.5 times of aquifer thickness and compared the capture envelope with the fully penetrating well with the same condition.

In Chapters 8 and 9 the solution of capture zone for the well-aquifer system of chapter 3 and 4 are respectively modified by considering the wells as being partially penetrating wells.

For all above solutions, the well system may be consisted of any number of production or injection wells or a combination of both with any flow rate. The presented equations are of general character and have removed the limitations of the previous equations in regards to well numbers, positions and types, extraction/injection rate, fully or partially penetrating wells, screen length and location and regional flow rate and direction. These solutions are presented in form of capture type curves which are useful tools in hands of practitioners to design in-situ groundwater remediation systems, to contain contaminant plumes, and to evaluate the surface-subsurface water interaction.

دسته: زبان خارجه, زبان خارجه برچسب: CAPTURE ZONE OF A MULTI-WELL SYSTEM IN BOUNDED AQUIFERS

توضیحات

Table of Contents

List of Tables. XI

List of Figures. XII

Chapter 1: Research objective, background and Theory. 2

1-1- Research objectives. 2

1-2- Literature review.. 3

1-3- Theory. 6

1-3-1- Capture zone. 6

1-3-2- Complex velocity potential 7

1-3-3- Some potential flow fields. 8

a) Uniform Flow.. 9
b) Flow to a source or sink. 10
c) Flow to a sink in a uniform flow.. 11
d) Flow for a source and a sink of equal strength. 11
e) Two sources of equal strength. 12
f) An infinite array of sinks. 14
g) A sink between two parallel streams. 14

1-4- Definitions. 16

1-4-1- Wedge shaped aquifers. 16

1-4-2- Peninsula-shaped aquifers. 17

1-4-3 Rectangular-shaped bounded aquifer 17

1-4-4- Well 18

1-4-5- Point sink. 18

1-4-6- Partially penetrated well 18

1-4-7- Three dimensional flow around a partially penetrated well 19

1-4-8- Image well theory. 19

Chapter 2: Capture zone of fully penetrating multi-well system in wedge-shaped aquifers 22

2-1- Capture zone of a Multi well system in wedge-shaped aquifers with image well theory 23

2-1-1- Conceptual model 23

2-1-2- Mathematical formulation. 25

2-1-3- Stagnation points. 29

2-1-4- Drawdown. 30

2-1-4- Results and discussions. 31

2-1-4-1- Capture zone of well(s) in a constant head-constant head wedge. 32

2-1-4-2- Capture zone of well(s) in a barrier-constant head wedge. 38

2-1-4-3- Capture zone of well(s) in a barrier-barrier wedge. 43

2-1-4-4- Effect of extraction rate on the capture envelope. 48

2-1-4-5- Capture zone of wells in unconfined wedge-shaped aquifers. 49

2-1-4-6- Complex velocity potential of a well in wedge-shaped aquifers without regional flow 53

2-1-5- Application. 54

2-2- Capture zone of a multi-well systems in wedge-shaped aquifers without image well theory 58

2-2-1- Mathematical formulation. 58

2-2-2- Results and discussion. 63

2-2-2-1- Flow in wedge-shaped aquifers without uniform flow.. 63

2-2-2-2 Flow in wedge-shaped aquifers with uniform flow.. 65

2-3 Conclusions. 68

Chapter 3: Capture zone of a fully penetrating multi-well system in peninsula-shaped aquifers 71

3-1- Conceptual model 71

3-2- Theoretical development. 74

3-3- Stagnation points. 78

3-4- Drawdown. 79

3-5- Results and discussions. 81

3-5-1 Groundwater remediation system and plume containment design. 82

3-5-2 Surface-subsurface water interaction. 84

3-5-3- Capture type curves. 87

3-6- Conclusion. 90

Chapter 4: Capture zone of a fully penetrating multi-well system in rectangular-shaped bounded aquifers 92

4-1- Conceptual model 92

4-2- Theoretical formulation and solution. 95

4-3- Stagnation point. 99

4-4- Drawdown of Multi-well system in rectangular bounded aquifers. 100

4-5- Results and discussions. 102

4-5-1- The effect of regional uniform flow direction on capture envelope. 102

4-5-2- Contaminant plume containment 104

4-5-3- Surface-subsurface interaction. 107

4-5-4- Capture zone without uniform flow.. 109

4-5-5- Unconfined aquifer 114

4-5-6- Conclusion. 116

Chapter 5: Capture zone of a partially penetrating multi-well system in isotropic and anisotropic aquifers 118

5-1- Conceptual model 119

5-2- Mathematical formulation. 121

5-2-1- Capture zone of type (a) partially penetrating multi-well system in isotropic aquifers. 122

5-2-2- Capture zone of type (a) partially penetrating multi-well system in anisotropic aquifers 123

5-2-3- Capture zone of type (b) partially penetrating multi-well system in isotropic aquifer 125

5-2-4- Capture zone of type (b) partially penetrating multi-well system in anisotropic aquifers 126

5-3- Results and discussions. 127

Chapter 6: Capture zone of a partially penetrating multi-well system in isotropic and anisotropic confined aquifers near a boundary. 137

6-1- Introduction. 137

6-2- Conceptual model 138

6-3- Mathematical formulation. 139

6-3-1- Capture zone of type (a) partially penetrating multi- well system… 139

6-3-2- Capture zone of type (b) partially penetrating multi -well system… 142

6-4- Results and discussions. 144

Chapter 7: Capture zone of a partially penetrating multi-well system in isotropic and anisotropic confined aquifer between two parallel boundaries 148

7-1- Introduction. 148

7-2- Conceptual model 149

7-3- Mathematical equations. 150

7-3-1- Capture zone of type (a) partially penetrating multi-well system… 151

7-3-2- Capture zone of type (b) partially penetrated multi-well system… 153

7-4- Results and discussions. 156

Chapter 8: Capture zone of a partially penetrated multi-well system in peninsula-shaped confined aquifer 159

8-1- Introduction. 159

8-2- Conceptual model 159

8-3- Mathematical equations. 160

8-3-1- Capture zone of type (a) partially penetrating multi-well system… 160

8-3-2- Capture zone of type (b) partially penetrating multi-well system… 163

8-4- Results and discussions. 164

Chapter 9: Capture zone of a partially penetrating multi-well system in rectangular bounded confined aquifers 168

9-1- Introduction. 168

9-2- Conceptual model 168

9-3- Mathematical equations. 171

9-3-1- Capture zone of the type (a) partially penetrating multi- well system… 171

9-3-2- Capture zone of the type (b) partially penetrating multi-well system… 173

9-4- Results and discussions. 186

Summery and conclusion. 189

References. 191

List of Tables

Table 1- Values of parameters J1 and J2 in Eq. (2-6) for various wedge boundary configurations. 27

Table 2- The value of J₁, J₂ and J₃ for eight boundary types. Boundary configuration type vii and viii are the mirror image of boundary configurations type v and vi, respectively. 76

Table 3. Values of parameters J₁to J₈ in Eq. (4-6). 98

Table 4. Values of parameters J1 and J2 in Eq. (7-1). 152

List of Figures

Fig. 1 (a) Illustration of drawdown contours (i.e. zone of influence) and the capture zone of a single pumping well in a uniform medium, (b) Equation for dividing stream lines (w) that separate the capture zone of the single well from the rest of an isotropic, confined aquifer with a uniform regional hydraulic gradient (Todd and Mays, 2007). 7

Fig. 2. A schematic diagram showing equipotentials and streamlines for a uniform flow making an angle a with the positive x axis (Goundwater Transport: Handbook of Mathematical Model, Javandel et al. 1984). 9

Fig. 3 Flow to a sink (Bear, 1972) 10

Fig. 4- A sink in a uniform flow (Todd and Mays, 2005). 11

Fig. 5- A well near a stream may be regarded as a flow field with a source and a sink. Flow lines illustrate the steam function and equipotential lines show the velocity function(Bear, 1972) 12

Fig. 6- Flow toward two sources of equal strength (Bear, 1972) 13

Fig. 7- An infinite array of sinks (Bear, 1972) 14

Fig. 8- Flow net and envelope of the capture zone between two parallel stream when a single stagnation point is located at the intercept of the x axis and stream 2. aD is normalized well location and QCD is corresponding normalized critical pumping rate. This case is without low-permeability streambeds (Intaraprasong and Zhan, 2007). 15

Fig. 9 Wedge-shaped and peninsula-shaped aquifer between Kor and Sivand rivers. Fars province, Iran (www.ngdir.com) 17

Fig. 10 Wedge-shaped and peninsula-shaped aquifer between Kor and Sivand rivers. Fars province, Iran (www.ngdir.com) 17

Fig. 11 Peninsula-shaped aquifer in Gheshm Island, Iran (www.ngdir.com) 17

Fig. 12 Rectangular-shaped aquifer in Atlantic Ocean(www.ngdir.com) 17

Fig. 13 Rectangular-shaped aquifer in Pacific Ocean (www.ngdir.com) 17

Fig. 14. Effect of partial penetration on the drawdown in partially penetrating wells in a confined aquifer (Todd and Mays, 2005) 19

Fig. 15- Schematic plan view of wedge-shaped aquifer boundary configurations a) constant head-constant head wedge, b) barrier-constant head wedge, c) barrier-barrier wedge and d) constant head-barrier wedge 24

Fig. 16- A schematic plan view of real and imaginary wells for 60° (figures on the left, with five imaginary wells) and 45° (figure on the right, with 7 imaginary wells) wedge for the three possible wedge boundary configurations. 25

Fig. 17 Velocity potential (a) and stream function (b) of a well in a confined constant head-constant head wedge- shaped aquifer. 34

Fig. 18 Velocity potential (a) and stream function (b) of two wells in a confined constant head-constant head wedge 35

Fig. 19 Velocity potential (a) and stream function (b) of three wells in a confined constant head-constant head wedge-shaped aquifer. 36

Fig. 20- Velocity potential (a) and stream function (b) for three wells in a confined constant head-constant head wedge-shaped aquif. 37

Fig. 21 Velocity potential (a) and stream function (b) of a well in a confined barrier-constant head wedge-shaped aquifer (stream along the RHS boundary: r,=0°), 39

Fig. 22 Velocity potential (a) and stream function (b) of two wells in a confined barrier-constant head wedge-shaped aquifer (stream along the RHS boundary: r, =0°). 40

Fig. 23 Velocity potential (a) and stream function (b) for three wells in a confined barrier-constant head wedge-shaped aquifer (stream along the RHS boundary: r, =0°). 41

Fig. 24 Velocity potential (a) and stream function (b) of three wells in a confined barrier-constant head wedge-shaped aquifer (stream along the RHS boundary: r, =0°). 42

Fig. 25- Velocity potential (a) and stream function (b) of a well in a confined barrier-barrier wedge-shaped aquifer 44

Fig. 26- Velocity potential (a) and stream function (b) of two wells in a confined barrier-barrier wedge-shaped aquifer 45

Fig. 27- Velocity potential (a) and stream function (b) of three wells in a confined barrier-barrier wedge-shaped aquifer 46

Fig. 28- Velocity potential (a) and stream function (b) of three wells in a confined barrier-barrier wedge-shaped aquifer 47

Fig. 29- A set of dimensionless capture envelopes of an extraction well for five different extraction rates in confined wedge-shaped aquifers. 49

Fig. 30- Velocity potential (a) and stream function (b) of a well in an unconfined constant head-constant head wedge-shaped aquifer. 51

Fig. 31- Velocity potential (a) and stream function (b) for two wells in an unconfined constant head- constant head wedge-shaped aquifer (the RHS boundary is a no-flow boundary: r, =0°), 52

Fig. 32 Velocity potential (a) and stream function (b) of a pumping well in wedge shaped-aquifers without regional uniform flow. Left figures: constant head-constant head wedge, figures in the middle: constant head-barrier wedge and figures in the right: barrier-barrier wedge. 54

Fig. 33 Comparison of capture envelopes generated by the numerical models (left figures) and their counterparts (right figures) developed by the proposed analytical model in Cartesian coordinates. 57

Figure 34- Schematic view of confined wedge-shape aquifer. 60

Fig. 35 Stream function and velocity potential contours for a confined 28 ° wedge-shaped aquifer without uniform flow (r₀ = 14.14, θ₀ = 15 °) (Q = 0.015 (m3 / s), K_h = 0.001 (m / s), b (aquifer thickness) = 10 meter) 64

Fig. 36 Stream function and velocity potential contours for a confined 57 ° wedge-shaped aquifer without uniform flow. 64

Fig. 37 Stream function and velocity potential contours for a confined wedge-shaped aquifer in wedge 97.2 ° without uniform flow. (r₀=14.14 (m), θ₀=67°) (Q=0.015 (m3/s), K_h=0.001 (m/s), b=10 meter) 65

Fig. 38 Stream function (b) and velocity potential (a) contours for a confined 60° wedge-shaped aquifer with uniform flow. (r₀=700 (m), θ₀=30°) (α=330°, Q=0.005 (m3/s), K_h=0.0001 (m/s), b=20 meter) 67

Fig. 39 Stream function (b) and velocity potential (a) contours for a 60° confined wedge-shaped aquifer with uniform flow. (r₀₁=800 (m), r₀₂=1100 (m), θ₀₁= θ₀₂=30°) (α=330°, Q₁=Q₂=0.005 (m3/s), K_h=0.0001 (m/s), b=20 meter). 67

Fig. 40 Schematic plan view of six possible peninsula-shaped aquifers formed by no-flow and in-flow boundaries. The aquifers may be under stress by any number of injection/extraction wells. 73

Fig. 41 Schematic plan view of image-well systems for the peninsula-shaped aquifer of Fig. 40 (ii) 73

Fig. 42 Velocity potential field (solid lines are potential and broken lines are steam lines) for three wells in a peninsular (type ii) confined aquifer. 83

Fig. 43- Velocity potential field for three wells in a peninsular (type ii) confined aquifer. 84

Fig. 44 Velocity potential and stream function for three wells in aquifer of Fig. 1 (iii) 86

Fig. 45 Velocity potential and stream function for three wells in the peninsular aquifer of Fig. 1 (iv) 87

Fig. 46- A set of dimensionless capture envelopes of an extraction well for five different extraction rates in confined aquifers of Fig. 1. 89

Fig. 47 Schematic plan view of six possible bounded aquifer formed by no-flow and in-flow boundaries. The aquifers may be under stress by any number of injection/extraction wells. 94

Fig. 48- Schematic plan view of image-well systems for the bounded aquifer of Fig. 47 (ii). 94

Fig. 49 Capture envelope for five uniform flow directions in type ii boundary configuration for the well in confined aquifer located at the center of aquifer. (UFD is uniform flow direction) 103

Fig. 50 Capture envelope for one recharge and two pumping wells First step in type iii boundary configuration in confined aquifer. 105

Fig. 51 Capture envelope for one recharge and two pumping wells Second step in type iii boundary configuration in confined aquifer. 106

Fig. 52 Capture envelope for one recharge and two pumping wells Third step in type iii boundary configuration in confined aquifer. 107

Fig. 53 Velocity potential and stream function for two wells in (type vi) confined aquifer illustrating the surface-subsurface water interaction. 108

Fig. 54 Velocity potential and stream function for one well in (type ii) confined aquifer without uniform flow 110

Fig. 55 Velocity potential and stream function for three wells in (type iii) confined aquifer without uniform flow 111

Fig. 56 Velocity potential and stream function for one well in (type iv) confined aquifer without uniform flow 112

Fig. 57 Velocity potential and stream function for one well in (type v) confined aquifer without uniform flow 113

Fig. 58 Velocity potential and stream function for two wells in (type vi) confined aquifer without uniform flow 114

Fig. 59 Velocity potential and stream function for three wells in (type iii) unconfined aquifer. 115

Fig. 60 Cone of depression around a partially penetrating well type (a. 129

Fig. 61 Velocity potential and capture envelope curve around a partially penetrating well type (a) in x-z plane 130

Fig. 62 Velocity potential and capture envelope curve around a partially penetrating well type (a) in x-y plane, 131

Fig. 63 Velocity potential and capture envelope curve found by Faybishenko et al. (1995), 132

Fig. 64 Comparison of capture envelope in x-z plane for well type (a) with constant anisotropy ratio (A=1), constant regional flow gradient (i=0.0025) and varying well penetration. 133

Fig. 65 Comparison of capture envelope in x-y plane for the well type (a) for different PPF and different anisotropy ratios 134

Fig. 66 Velocity potential and capture envelope in x-z plane for same screen length and five different screen place in the confined aquifer. 135

Fig. 67 Schematic view of one partially penetrated well near a stream with x and y-axes. 139

Fig. 68 Velocity potential and capture envelope of one well in confined aquifer with distance 60 meter from one in-flow boundary. (1) Fully penetrating well, (2) partially penetrating well type (a) with PPF %10. 145

Fig. 69 Velocity potential and capture envelope of one well in confined aquifer with distance 150 meter from one in-flow boundary. (1) fully penetrating well, (2) partially penetrating well type (a) with PPF %10. 146

Fig. 70 Schematic plan view of three possible boundary configurations for the confined aquifer limited between two parallel boundaries: (i) constant head-constant head aquifer, (ii) the impermeable-impenetrable aquifer and (iii) impermeable-constant head aquifer. 150

Fig. 71 Schematic plan view of a constant head-constant head (type i) aquifer and partially penetrating pumping well and the location of imaginary pumping and recharging wells that are located along the x-axis and extend to infinity in positive and negative directions. 150

Fig. 72 Velocity potential and capture envelope of one well in confined aquifer between two parallel in-flow boundaries 100 meters far (P=100 m). (1) Fully penetrating well, (2) partially penetrating well type (a) with PPF %10. 157

Fig. 73 Velocity potential and capture envelope of one well in confined aquifer between two parallel in-flow boundaries 300 meters far (P=300 m). (1) Fully penetrating well, (2) partially penetrating well type (a) with PPF %10. 157

Fig. 74 Schematic plan view of the image well system for peninsular-shape confined aquifer, as shown in Figure 40 (ii) 160

Fig. 75 Velocity potential and capture envelope of one well in peninsula-shape confined aquifer. (1) fully penetrating well, (2) partially penetrating well type (a) with PPF %10. 165

Fig. 76 Velocity potential and capture envelope of one well in peninsula-shape confined aquifer. (1) fully penetrating well, (2) partially penetrating well type (a) with PPF %10. 166

Fig. 77 Schematic view of the real and imaginary well systems for a bounded confined aquifer of Figure 47 (ii). 170

Fig. 78 Velocity potential and capture envelope of one well in a bounded confined aquifer. (1) Fully penetrating well, (2) partially penetrating well type (a) with PPF %10. 186

Fig. 79 Velocity potential and capture envelope of one well in a bounded confined aquifer. (1) fully penetrating well, (2) partially penetrating well type (a) with PPF %10. 187

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