Groundwater Hydrology Conceptual and Computational Models

Contents

Preface xiii
1 Introduction 1
1.1 Groundwater Investigations – a Detective Story 1
1.2 Conceptual Models 2
1.3 Computational Models 2
1.4 Case Studies 3
1.5 The Contents of this Book 3
1.6 Units, Notation, Journals 5
Part I: Basic Principles 7
2 Background to Groundwater Flow 9

2.1 Introduction 9
2.2 Basic Principles of Groundwater Flow 9
2.2.1 Groundwater head 10

2.2.2 Direction of flow of groundwater 10
2.2.3 Darcy’s Law, hydraulic conductivity and permeability 11
2.2.4 Definition of storage coefficients 13
2.2.5 Differential equation describing three-dimensional time-variant groundwater flow 14
2.3 One-dimensional Cartesian Flow 14
2.3.1 Equation for one-dimensional flow 15
2.3.2 Aquifer with constant saturated depth and uniform recharge 16
2.3.3 Definition of transmissivity 17
2.3.4 Aquifer with constant saturated depth and linear variation in recharge 18
2.3.5 Aquifer with constant saturated depth and linear decrease in recharge towards lake 19
2.3.6 Confined aquifer with varying thickness 20
2.3.7 Unconfined aquifer with saturated depth a function of the unknown groundwater head 20
2.3.8 Time-variant one-dimensional flow 22
2.4 Radial Flow 23

2.4.1 Radial flow in a confined aquifer 23
2.4.2 Radial flow in an unconfined aquifer with recharge 24
2.4.3 Radial flow in an unconfined aquifer with varying saturated depth 26
2.4.4 Radial flow in a leaky aquifer 27
2.4.5 Time-variant radial flow 28
2.4.6 Time-variant radial flow including vertical components 28
2.5 Two-dimensional Vertical Section (Profile Model) 28
2.5.1 Steady-state conditions, rectangular dam 28
2.5.2 Time-variant moving water table 31
2.6 Regional Groundwater Flow 32
2.6.1 Analysis of Connorton (1985) 32
2.6.2 Illustrative numerical examples of one-dimensional flow 34
2.6.3 When vertical flows must be included explicitly 35
2.7 Numerical Analysis 36

2.7.1 One-dimensional flow in x-direction 36
2.7.2 Example 37
2.7.3 Radial flow 38
2.7.4 Vertical section 38
2.8 Monitoring and Additional Indirect Evidence 39
2.8.1 Introduction 39
2.8.2 Monitoring groundwater heads 40
2.8.3 Surface water monitoring 43
2.8.4 Monitoring borehole discharge 46
2.8.5 Monitoring groundwater quality 46
2.8.6 Data handling and presentation 47
2.9 Introduction to Quality Issues 49
2.9.1 Introduction 49
2.9.2 Fresh and saline groundwater 49
2.9.3 Conditions at the coast 51
2.9.4 Upconing 53

2.9.5 Monitoring the movement of a saline interface 54
2.9.6 Hydrodynamic dispersion and contaminant transport 56
2.10 Concluding Remarks 58


3 Recharge due to Precipitation or Irrigation 60
3.1 Introduction 60
3.1.1 Representative field situations 60
3.1.2 Symbols used in this chapter 61
3.2 Brief Review of Alternative Methods of Estimating Recharge 61
3.2.1 Methods based on field measurements 62
3.2.2 Estimates using properties of unsaturated soil 62
3.3 Conceptual models for the Soil Moisture Balance Technique 64
3.3.1 Introduction 64
3.3.2 Representation of moisture conditions in the soil 64
3.3.3 Bare soil evaporation 67
3.3.4 Crop transpiration 68
3.3.5 Nature of the soil 70
3.3.6 Runoff 70

3.3.7 Occurrence of recharge 70
3.3.8 Combining crops and bare soil 71
3.3.9 Water storage near the soil surface 71
3.4 Quantified Conceptual and Computational Models for the Soil Moisture Balance Technique 74
3.4.1 Crops and crop coefficients 74
3.4.2 Reduced transpiration when crops are under water stress 75
3.4.3 Reduced evaporation due to limited soil water availability 76
3.4.4 Runoff 77
3.4.5 Combining the influence of crop transpiration and bare soil evaporation 78
3.4.6 Soil moisture balances 78
3.4.7 Soil moisture balances with near surface soil storage 81
3.4.8 Algorithms for soil moisture balance 82
3.4.9 Annual soil moisture balance for a temperate climate 83
3.4.10 Estimating recharge in a semi-arid region of Nigeria 84
3.4.11 Estimating recharge due to precipitation and irrigation in a semi-arid region of India 87


3.4.12 Bypass recharge 90
3.4.13 Estimating catchment-wide recharge distributions 90
3.5 Estimating Recharge when Drift is Present 90
3.5.1 Introduction 90
3.5.2 Recharge factors 91
3.5.3 Recharge through Drift estimated using Darcy’s Law 92
3.5.4 Delay in recharge reaching the water table 93
3.6 Delayed Runoff and Runoff Recharge 95
3.6.1 Delayed runoff from minor aquifers in the Drift 95
3.6.2 Runoff recharge 97
3.6.3 Incorporating several recharge processes 98
3.7 Concluding Remarks 98


4 Interaction between Surface Water and Groundwater 100
4.1 Introduction 100

4.2 Canals 101
4.2.1 Introduction 101
4.2.2 Classification of interaction of canals with groundwater 101
4.2.3 More detailed consideration of boundary conditions and canal dimensions 103
4.2.4 Effect of lining of canals 106
4.2.5 Perched canals 108
4.2.6 Estimation of losses from canals 111
4.2.7 Artificial recharge using spreading techniques 111
4.3 Springs, Rivers, Lakes and Wetlands 112
4.3.1 Introduction 112
4.3.2 Spring–aquifer interaction 113
4.3.3 River–aquifer interaction: basic theory and modelling 115
4.3.4 River–aquifer interaction in practice 116
4.3.5 Lakes and wetlands 121
4.3.6 Impact of groundwater abstraction on springs, rivers, lakes and wetlands 125
4.4 Drains 126
4.4.1 Introduction 126
4.4.2 Field evidence 126
4.4.3 Formulation of drainage problems 127
4.4.4 Approximate methods of analysis
for steady-state problems 129
4.4.5 Numerical solutions 131
4.4.6 Representative time-variant analysis 134
4.4.7 Interceptor drains 135
4.5 Irrigated Ricefields 138
4.5.1 Introduction 138
4.5.2 Formulation of flow processes in ricefields 139
4.5.3 Representative results 140
4.5.4 Ricefields with different geometry and water levels 141
4.6 Concluding Remarks 142


Part II: Radial Flow 145
5 Radial Flow to Pumped Boreholes – Fundamental Issues 147
5.1 Aquifer Response due to Pumping from a Borehole 147
5.1.1 Introduction 147
5.1.2 Details of field s
tudy 147

5.1.3 Measurements in pumped borehole and observation piezometers 148
5.1.4 Conceptual models of flows for different times 149
5.1.5 Recovery phase 151
5.1.6 Results for open borehole instead of individual piezometers 152
5.1.7 Analysis of pumping test results 153
5.1.8 Summary 154
5.2 Classification of Radial Flow Problems 154
5.3 Steady Radial Flow in Confined Aquifers 157
5.4 Analytical Solutions for Unsteady Radial Flow in Confined Aquifers 158
5.4.1 Analytical solutions 158
5.4.2 Theis method using log-log graphs 159
5.4.3 Cooper–Jacob technique 160
5.4.4 Transmissivity and storage coefficient varying with radius 161
5.5 Numerical Solution for Unsteady Radial Flow 162
5.5.1 Theoretical basis of the numerical model 162

5.5.2 Comparison of analytical and numerical solutions 163
5.5.3 Example of the use of the numerical model 163
5.5.4 Representation of well losses 164
5.6 Analysis of the Recovery Phase for Unsteady Radial Flow in Confined Aquifers 164
5.7 Comparison of Analytical and Numerical Techniques of Pumping Test Analysis 165
5.8 Analysis of Leaky Aquifers Without Storage in the Aquitard 167
5.9 Further Consideration of Single-Layer Aquifers 168
5.10 Aquifer with Restricted Dimensions (Boundary Effects) 169
5.11 Change in Transmissivity or Storage Coefficient with Radius 170
5.12 Changing Saturated Depth and Changing Permeabilities in Unconfined Aquifers 173
5.13 Varying Abstraction Rates 174
5.14 Overflowing Artesian Boreholes 174
5.15 Interfering Boreholes 176

5.15.1 Introduction to interference 176
5.15.2 Theoretical analysis of interfering boreholes 177
5.15.3 Practical example of the significance of interfering boreholes 178
5.16 Conditions Changing between Confined and Unconfined 180
5.17 Delayed Yield 183
5.17.1 Background 183
5.17.2 Inclusion of delayed yield in radial flow numerical model 184
5.17.3 Comparison of analytical and numerical solutions of a field example
with delayed yield 185
5.18 Concluding Remarks 185


6 Large Diameter Wells 187
6.1 Introduction 187
6.2 Description of Flow Processes for Large Diameter Wells 187
6.3 Analytical Solutions for Large Diameter Wells 189
6.3.1 Conventional analyses 189

6.3.2 Drawdown ratio method 189
6.3.3 Alternative methods including Kernel function techniques 191
6.4 Numerical Analysis of Large Diameter Well Tests using Observation Well Data 193
6.5 Analysis with Varying Abstraction Rates 194
6.6 Use of Large Diameter Wells for Agriculture 195
6.6.1 Representative problem 196
6.6.2 Agrowells in Sri Lanka 198
6.6.3 Case study of a Miliolite limestone aquifer 199
6.7 Concluding Remarks 200


7 Radial Flow where Vertical Components of Flow are Significant 201
7.1 Introduction 201
7.2 Radial-Vertical Time-variant Flow [r, z, t] 203
7.2.1 Mathematical formulation 203
7.2.2 Analytical solutions 204
7.2.3 Numerical methods 206

7.2.4 Examples of numerical solutions in [r, z, t] 206
7.3 Radial-Vertical Time-instant [r, z] 209
7.3.1 Principles of the approach 209
7.3.2 Case study: reduction of discharge due to partial penetration of borehole 209
7.3.3 Case study: effectiveness of water table control using tubewells 210
7.4 Two-zone Approximation [r, t, vZ] 213
7.4.1 Introduction 213
7.4.2 Examples of formulation using the two-zone model 213
7.4.3 Details of the two-zone model 214
7.4.4 Discrete space–discrete time equations for the two-zone model 216
7.4.5 Solution of simultaneous equations 218
7.4.6 Examples of the use of the two-zone model 218
7.5 Inclusion of Storage in Aquitards [r, t: z, t] 223
7.5.1 Introduction 223

7.5.2 Analytical solutions 223
7.5.3 Case study: influence of aquitard storage on an aquifer system; increase
and subsequent decrease in flows from the aquitard 224
7.5.4 Influence on aquitard storage of pumping from sandstone aquifers 226
7.6 Concluding Remarks 227


8 Practical Issues of Interpreting and Assessing Resources 228
8.1 Introduction 228
8.2 Step Drawdown Tests and Well Losses 228
8.2.1 Introduction 228
8.2.2 Confined, leaky or unconfined conditions 230
8.2.3 Estimating the coefficients B and C 230
8.2.4 Exploring well losses 231
8.2.5 Causes of well loss 231

8.2.6 Field examples of well losses 235
8.3 Packer Testing to Identify variations in Hydraulic Conductivity with Depth 236
8.3.1 Conducting packer tests 236
8.3.2 Interpretation of packer tests using analytical expressions 237
8.3.3 Do the analytical solutions provide a reasonable approximation to hydraulic
conductivity variations? 238
8.3.4 Effectiveness of fissures in collecting water from the aquifer 240
8.3.5 Comparison of properties of sandstone aquifers based on cores, packer
testing and pumping tests 241
8.3.6 Slug tests 241
8.4 Information about Groundwater Heads in the Vicinity of Production Boreholes 242
8.4.1 Background 242

8.4.2 Case Study: identifying the water table elevation 243
8.5 Realistic Yield from Aquifer Systems 245
8.5.1 Introduction 245

8.5.2 Weathered-fractured aquifers 246
8.5.3 Alluvial aquifers with an uppermost layer of low hydraulic conductivity 247
8.5.4 Response of an alluvium-sandstone aquifer system 252
8.6 Injection Wells and Well Clogging 254
8.6.1 Introduction 254
8.6.2 Alluvial aquifer in India 254
8.6.3 Initial pumping test 256
8.6.4 Artificial recharge results and interpretation 257
8.6.5 North London Artificial Recharge Scheme 258
8.7 Variable Hydraulic Conductivity with Depth in Chalk and Limestone 259
8.7.1 Introduction 259

8.7.2 Case study in Berkshire Downs, the UK 259
8.7.3 Consequences of variation in hydraulic conductivity 261
8.8 Horizontal Wells 262
8.8.1 Collector wells 262
8.8.2 Mathematical expressions for horizontal wells 263
8.8.3 Horizontal well in a shallow coastal aquifer 264
8.9 Concluding Remarks 267


Part III: Regional Groundwater Flow 269

9 Regional Groundwater Studies in which Transmissivity is Effectively Constant 271
9.1 Introduction 271
9.2 Nottinghamshire Sherwood Sandstone Aquifer 271
9.2.1 Identifying the conceptual model, focus on recharge components 271
9.2.2 Idealisations introduced in the regional groundwater model 274
9.2.3 Quantifying the parameters of the conceptual model 274
9.2.4 Numerical groundwater model 276
9.2.5 Adequacy of model 276

9.2.6 Flow balances 278
9.3 Northern Extension of Nottinghamshire Sherwood Sandstone Aquifer 279
9.3.1 Brief description of groundwater catchment 280
9.3.2 Conceptual models 281
9.3.3 Numerical groundwater model and flow balances 282
9.4 Lower Mersey Sandstone Aquifer 284
9.4.1 Conceptual model 284
9.4.2 Recharge through drift 286
9.4.3 Saline water 287
9.4.4 Numerical groundwater model 289
9.4.5 Flow balances and predictions 291
9.5 Barind Aquifer in Bangladesh 292
9.5.1 Background 293

9.5.2 Development of conceptual models 293
9.5.3 Can this rate of abstraction be maintained? 296
9.5.4 Possible provision of a regional groundwater model 297
9.6 Concluding Remarks 298


10 Regional Groundwater Flow in Multi-Aquifer Systems 299
10.1 Introduction 299
10.2 Mehsana Alluvial Aquifer, India 299
10.2.1 Introduction 300

10.2.2 Description of the aquifer system 301
10.2.3 Field records of groundwater head 301
10.2.4 Flow processes in aquifer system 304
10.2.5 Mathematical model of a vertical section 305
10.2.6 Origin of flows as determined from vertical section model 307
10.2.7 More detailed study of smaller area 308
10.2.8 Concluding discussion 310

10.3 Vanathavillu Aquifer System, Sri Lanka 311
10.3.1 Introduction 311
10.3.2 Aquifer parameters 312
10.3.3 Groundwater head variations and estimates of aquifer resources 313
10.4 San Luis Potosi Aquifer System, Mexico 315
10.4.1 Shallow aquifer system 316
10.4.2 Deeper aquifer system 316
10.4.3 Input of deep thermal water: 318
10.4.4 Further considerations 319
10.5 Bromsgrove Sandstone Aquifer, UK 319
10.5.1 Summary of field information 320
10.5.2 Conceptual model 322
10.5.3 Mathematical model 322
10.5.4 Presentation of model outputs 323
10.5.5 Management issues 325

10.6 Further examples where vertical components of flow are significant 326
10.6.1 Madras aquifer 326
10.6.2 Waterlogging in Riyadh, Saudi Arabia 327
10.6.3 SCARPS: Saline Control and Reclamation Projects in Pakistan 328
10.6.4 Fylde aquifer, UK 329
10.7 Concluding Remarks 331


11 Regional Groundwater Flow with Hydraulic Conductivity Varying with Saturated Thickness 332
11.1 Introduction 332
11.2 Chalk Aquifer of the Berkshire Downs 333
11.2.1 Changing estimates of yields of the Lambourn Valley catchment 334
11.2.2 Conceptual and mathematical modelling 335
11.3 Southern Lincolnshire Limestone 337

11.3.1 General description of Southern Lincolnshire Limestone catchment 337
11.3.2 Recharge including runoff-recharge 338
11.3.3 Surface water–groundwater interaction 341
11.3.4 Wild boreholes 343
11.3.5 Variable hydraulic conductivity with depth 343
11.3.6 Résumé of conceptual models 345
11.3.7 Brief description of the total catchment models 346
11.3.8 Selected results and insights from the numerical model 347
11.4 Miliolite Limestone Aquifer in Western India 350
11.5 Gipping Chalk Catchment, Eastern England 351
11.5.1 Conceptual model 351
11.5.2 Quantified conceptual model 353
11.6 Further Examples 354
11.6.1 South Humberside Chalk 354
11.6.2 Candover Augmentation Scheme 354
11.6.3 Hesbaye aquifer, Belgium 357
11.7 Concluding Remarks 358


12 Numerical Modelling Insights 360
12.1 Introduction 360
12.2 Representation of Rivers 360
12.2.1 Intermittent rivers 360
12.3 Representing Boreholes Pumping Water from Multi-layered Aquifers 364
12.4 Time-Instant Conditions 366
12.4.1 Introduction 366
12.4.2 Basis of time-instant approach 367
12.4.3 Examples of sandstone and limestone aquifers 367
12.4.4 Time-instant solutions 368
12.5 Initial Conditions 368
12.5.1 Specified heads or specified flows 368
12.5.2 Initial conditions for Sandstone and other high storage aquifers 369
12.5.3 Initial conditions for aquifers with seasonal changes in transmissivity 370
12.6 Dimensions and Detail of Numerical Models 372
12.6.1 Identification of the area to be represented by a numerical model 372
12.6.2 Identification of the duration of a numerical model simulation 374
12.6.3 External boundary conditions 376

12.6.4 Estimating parameter values for a numerical model 377
12.6.5 Refinement of numerical groundwater models 378
12.6.6 Sensitivity analysis 379
12.6.7 Preparing exploratory groundwater models with limited field information 379
12.7 Predictive Simulations 381
12.7.1 Issues to be considered 381
12.7.2 Representative example 382
12.8 Evaluation of Conceptual and Computational Models 384
12.8.1 Approach to groundwater modelling 384
12.8.2 Monitoring 384
12.8.3 Recharge 385
12.8.4 Model calibration and refinement 385
12.8.5 Sustainability, legislation and social implications 386
12.8.6 Climate change 387
12.8.7 Substantive issues requiring further investigation 387
Appendix: Computer Program for Two-zone Model 389
List of Symbols 397

References 399
Index 408

Download Link

Groundwater Hydrology Conceptual and Computational Models