Environmental hydrogeology

Second Edition ENVIRONMENTAL HYDROGEOLOGY Second Edition ENVIRONMENTAL HYDROGEOLOGY Philip E LaMoreaux Mostafa M Soliman Bashir A Memon James W LaMoreaux Fakhry A Assaad Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2009 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed in the United States of America on acid-free paper 10 International Standard Book Number-13: 978-1-4200-5502-3 (Ebook-PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface .xi Acknowledgments xiii Chapter Introduction 1.1 Introduction 1.2 Suggestions and References References 11 Chapter Geological Aspects for Assessment, Clean-up, and Siting of Waste Disposal Sites 13 2.1 2.2 Introduction 13 Geological Aspects 15 2.2.1 Rock Types 15 2.2.2 Candidate Sites 19 2.2.3 Stratigraphy .20 2.2.4 Structural Geology 20 2.2.5 Physical Properties 20 2.2.6 Hydrogeologic Considerations 24 2.3 Data Acquisition of Rock and Formation Fluid Testings .24 2.3.1 Data Obtained Prior to Drilling Potential Disposal Sites 24 2.3.2 Well Logs 25 2.4 Summary Site Selection .26 References .26 Chapter Hydrogeology 29 3.1 Introduction 29 3.1.1 Historical Background 29 3.2 Hydrologic Cycle 30 3.3 Main Components of Hydrology 31 3.4 Watershed Hydrology 32 3.4.1 Climatic Factors 33 3.4.2 Physiographic Factors 33 3.4.3 Mechanism of Erosional Deposition 34 3.5 Hydrogeology .34 3.5.1 Distribution of Subsurface Water 35 3.5.2 Groundwater Flow Theories 35 3.5.3 Steady-State Groundwater Flow in Aquifers 38 3.5.4 Unsteady-State Groundwater Flow in Confined Aquifers 38 3.5.5 Effects of Partial Penetration of Well 49 3.5.6 Hydraulics of the Well and Its Design 51 3.5.7 Slug Tests 52 3.5.8 Groundwater Recharge 54 References 59 v vi Contents Chapter Environmental Impacts Related to Hydrogeological Systems 61 4.1 4.2 4.3 Natural and Manmade Disasters 61 Land Subsidence 63 Causes of Subsidence 65 4.3.1 Collapse into Voids: Mines and Underground Cavities 66 4.3.2 Sinkholes 67 4.3.3 Sediment Compaction 68 4.3.4 Underground Fluid Withdrawal 69 4.3.5 Natural Compaction 70 4.3.6 Hydrocompaction 71 4.3.7 Organic Soil 71 4.4 Damage Cost and Legal Aspects of Land Subsidence 72 References 74 Chapter Kinds of Waste and Physiography of Waste Disposal Sites 77 5.1 Kinds and Sources of Wastes 77 5.1.1 Solid Wastes 79 5.1.2 Liquid Wastes 81 5.2 Types of Waste .84 5.2.1 Urban Wastes 84 5.2.2 Municipal Wastes 84 5.2.3 Petroleum Waste .84 5.2.4 Mining Waste 85 5.2.5 Industrial Waste 86 5.3 Gaseous Wastes 86 5.3.1 Industrial Wastes 86 5.3.2 Radon Risk 87 5.3.3 Forest Growth Reduction by Air Pollution 88 5.3.4 Acid Rain 88 5.3.5 Mines 88 5.3.6 Hydrocarbons 90 5.4 Hazardous Wastes 90 5.4.1 Definition 90 5.4.2 Toxic Materials 91 5.4.3 Soil Hazardous Wastes 91 5.4.4 Radioactive Wastes 93 5.5 Physiography of Waste Sites 94 5.5.1 Permeable Formations (3,000–12,000 ft) Containing Connate Brine 95 5.5.2 Impermeable Formations 95 5.6 Environmental Concerns on Hydrogeological Systems .97 5.6.1 Man-Made Earthquakes 97 5.6.2 Transport of Polluted Waters by Subterranean Karst Flow Systems 97 References 98 Chapter Environmental Impacts on Water Resource Systems 101 6.1 6.2 6.3 Introduction 101 Climatic Changes and Their Effect on Water Resources 101 Surface-Water Pollution 102 Contents vii 6.4 Groundwater Pollution 104 6.4.1 Migration of Pollutants in Aquifers 104 6.4.2 Saltwater Intrusion 109 6.4.3 Landfill Leachate 115 6.5 Groundwater Monitoring 118 References 120 Chapter Waste Management for Groundwater Protection 125 7.1 7.2 7.3 Primary Concept 125 Alternative of Waste Disposal 126 Disposal and Control 128 7.3.1 Types of Disposal 128 7.3.2 Disposal of Hazardous Wastes 131 7.3.3 Salt Caverns for Disposal 132 7.4 Groundwater Protection 133 7.4.1 Damage Prevention to the Water Resource System 133 7.4.2 Remediation of Groundwater Aquifers 134 7.5 Risk and Legal Aspects of Waste Disposal Sites 137 7.5.1 Definition of Risk and Risk Assessment 138 7.5.2 Application of Risk Assessment in the Context of Waste Disposal 138 7.5.3 An Outline of the Risk Assessment Process 141 7.6 Components of the Risk Assessment Process 142 7.6.1 Risk or Hazard Identification 142 7.6.2 Risk Estimation 144 7.6.3 Exposure Assessment: Identification of Sources of Chemicals 147 7.6.4 Exposure Assessment: Chemical Releases/Environmental Fate and Transport 148 7.6.5 Exposure Assessment: Routes of Exposure 155 7.6.6 Dose–Response Estimation 157 7.7 Hydrogeological Systems and Monitoring 158 References 160 Chapter Hydrogeologic and Environmental Considerations for Design and Construction in Karst Terrain/Sinkhole-Prone Areas 165 8.1 8.2 8.3 8.4 Introduction 165 Investigation-Design Considerations 166 8.2.1 Desk Top Investigations 168 8.2.2 Field Investigations 168 8.2.3 Surface Geophysical Exploration 169 8.2.4 Borehole Geophysics 170 8.2.5 Risk Assessment 171 8.2.6 Site Characterization for Planning and Design 171 Design and Construction Considerations 172 8.3.1 Distribution of Solution Features at a Site 172 8.3.2 Site Preparation 173 8.3.3 Site Excavation and Sinkhole Activity 174 Remediation 175 8.4.1 Preventive Measures to Stop Raveling and Erosion at Soil–Rock Interface 175 8.4.2 Overburden Dome Collapse and Repair 176 8.4.3 Repair of Sinkhole 176 viii Contents 8.4.4 Partially Supported Structure on Sinkhole-Prone Ground Structure 177 8.4.5 Design Structure Resistant to Erosion-Dome Collapse 178 8.4.6 Emergency Actions 178 References 179 Chapter Groundwater Modelling 183 9.1 9.2 9.3 9.4 9.5 Introduction 183 Electric Simulation Model 183 Hele–Shaw Model 184 Resistance Network Model 184 Simulation Technique 187 9.5.1 Forward-Difference Simulation 188 9.5.2 Backward-Difference Simulation 189 9.6 Resistor Capacitor Network Model 192 9.7 Analog Computers 193 9.8 Digital Computer 194 9.8.1 Model Development 194 9.8.2 Groundwater Equation 195 9.8.3 Digital Computer Solution 196 9.9 Finite — Element Method 198 9.9.1 The General Quasi-Harmonic P.D.E 200 9.9.2 Finite Element Discretization 201 9.10 Groundwater Quality Models 202 9.10.1 Quality Mathematical Model 203 9.10.2 Basic Equations .203 9.11 Difficulties and Shortcomings 204 References .205 Chapter 10 Case Studies 207 10.1 The Nubian Sandstone Aquifer System in Egypt 207 10.1.1 Introduction 207 10.1.2 Geological and Hydrogeological Characteristics 207 10.1.3 Hydrogeology 213 10.1.4 Regional Flow Pattern 214 10.1.5 Groundwater Models 214 10.1.6 Environmental Problems 219 References 221 10.2 Siting a Secure Hazardous Waste Landfill in a Limestone Terrane 223 10.2.1 Introduction 223 10.2.2 Topographic and Geographic Setting 224 10.2.3 Geologic Setting 224 10.2.4 Structural Geology 229 10.2.5 Hydrogeology 229 10.2.6 Aquifer Test 234 10.2.7 Procedure 235 10.2.8 Conclusions 240 References 245 10.3 Catastrophic Subsidence: An Environmental Hazard, Shelby County, Alabama .246 10.3.1 Introduction 246 Contents ix 10.3.2 General Hydrogeologic Setting .246 10.3.3 Geology of the Dry Valley Area 246 10.3.4 Water Level Decline and Catastrophic Subsidence 248 10.3.5 Hydrology of Dry Valley 251 10.3.6 Use of Remote Sensing Methods 254 10.3.7 Test Drilling 257 10.3.8 Inventory and Monitoring of Subsidence 257 10.3.9 Prediction of Induced Sinkholes 257 10.3.10 Southern Natural Gas Pipeline: A Case History 258 References .260 10.4 Environmental Hydrogeology of Figeh Spring, Damascus, Syria 261 10.4.1 Introduction 261 10.4.2 Geomorphology 261 10.4.3 Geology: Stratigraphic Sequence 263 10.4.4 Hydrogeology of the Figeh Area: Geologic Structural Setting and Karst Development 270 10.4.5 Recharge, Storage, and Discharge of Groundwater 273 10.4.6 Discharge Groundwater to the Barada River 283 10.4.7 Environmental Constraints to Future Use of Figeh System 297 References 299 10.5 Collection and Disposal of Naturally Occurring Chloride-Contaminated Groundwater to Improve Water Quality in the Red River Basin .300 10.5.1 Introduction 300 10.5.2 Geologic Setting 303 10.5.3 Hydrogeologic Setting 305 10.5.4 Field Investigations .306 10.5.5 Induced Infiltration 311 10.5.6 Drawdown in Bedrock Aquifer System and Overburden/Alluvial Aquifer 317 10.5.7 Effects of Pumping on Jonah Creek 318 10.5.8 Effects of Pumping on Brine Emissions 321 10.5.9 Chloride Load 322 10.5.10 Collection and Disposal of Chloride Contaminated Groundwater 324 10.5.11 Conclusions 329 Bibliography 331 10.6 Groundwater Recharge and Its Environmental Impact with Case Studies 332 10.6.1 Introduction 332 10.6.2 Purpose 335 10.6.3 Positive Impacts of Artificial Groundwater Recharge 336 10.6.4 Environmental Impacts of an Artificial Recharge 337 10.6.5 Adverse Recharge in Arid Regions of Egypt 338 10.6.6 Artificial Recharge in Arid Regions of Egypt 338 10.6.7 Future Role of Artificial Recharge in Egypt’s Water Management 341 References 342 Appendix A: Glossary 343 Appendix B: Conversion Tables 357 Appendix C: Math Modeling and Useful Programs 359 Appendix A: Glossary 353 and into pits where the cuttings are removed and the mud is picked up by pumps and forced back down the pipe Runoff  That part of precipitation that flows over the surface of the land as sheet wash and streamflow Salinization  The excessive build-up of soluble salts in soils or in water This often is a serious problem in the crop irrigation system Saltation  A form of wind erosion where small particles are picked up by wind and fall back to the surface in a “leap and bound” fashion The impact of the particles loosens other soil particles, rendering them prone to further erosion Sanitary landfill  A land site where solid waste is dumped, compacted, and covered with soil to minimize environmental degradation Sea level  An imaginary average level of the ocean as it exists over a long period of time It is also used to establish a common reference for standard atmospheric pressure at this level Secondary porosity  The porosity developed in a rock formation subsequent to its deposition or emplacement, either through natural processes of dissolution or stress distortion, or artificially through acidization or the mechanical injection of coarse sand Secondary wave  (S) A body earthquake that travels more slowly than a primary wave (P) The wave energy moves earth materials at a right angle to the direction of wave travel This type of shear wave cannot pass through liquids Sedimentation  The process of removal of solids from water by gravitational settling Seismic activity  Earth vibrations or disturbances produced by earthquakes Seismic survey  The gathering of seismic data from an area; the initial phase of seismic prospecting Seismograph  A device that measures and records the magnitude of earthquakes and other shock waves such as underground nuclear explosions Seismology  The science that is concerned with earthquake phenomena Seismometer  An instrument, often portable, designed to detect earthquakes and other types of shock waves Semiarid regions  Transition zones with very unreliable precipitation that are located between true deserts and subhumid climates The vegetation consists usually of scattered short grasses and drought-resistant shrubs Septic-tank system  An onsite disposal system consisting of an underground tank and a soil absorption field Untreated sewage enters the tank, where solids undergo decomposition Liquid effluent moves from the tank to the absorption field via perforated pipe Shear  The movement of one part of a mass relative to another, leading to lateral deformation without resulting in a change in volume Shear strength  The internal resistance of a mass to lateral deformation (see shear) Shear strength is mostly determined by internal friction and the cohesive forces between particles Sinkhole  A topographic depression developed by the solution of limestone, rock salt, or gypsum bedrock Sludge  (a) Mud obtained from a drill hole in boring; mud from drill cuttings The term has also been used for the cuttings produced by drilling (b) A semifluid, slushy, and murky mass or sediment of solid matter resulting from treatment of water, sewage, or industrial and mining wastes, and often appearing as local bottom deposits in polluted bodies of water Slurry  A very wet, highly mobile, semiviscous mixture or suspension of finely divided, insoluble matter Soil failure  Slippage or shearing within a soil mass because of some stress force that exceeds the shear strength of the soil 354 Environmental Hydrogeology, Second Edition Soil liquefaction  The liquefying of clayey soils that lose their cohesion when they become saturated with water and are subjected to stress or vibrations Soil salinization  The process of accumulation of soluble salts (mostly chlorides and sulfates) in soils caused by the rise of mineralized groundwater or the lack of adequate drainage when irrigation is practiced Soil structure  The arrangement of soil particles into aggregates that can be classified according to their shapes and sizes Soil texture  The relative proportions of various particle sizes (clay, silt, sand) in soils Solution  A process of chemical weathering by which rock material passes into calcium carbonate in limestone or chalk by carbonic acid derived from rainwater containing carbon dioxide acquired during its passage through the atmosphere Sorting  A dynamic gradational process that segregates sedimentary particles by size or shape Well-sorted material has a limited size range whereas poorly sorted material has a large size range Specific conductance  The electrical conductivity of a water sample at 25°C (77°F), expressed in micro-ohms per centimeter Specific gravity  The ratio of the mass of a body to the mass of an equal volume of water Spontaneous combustion  Type of fire started by the accumulation of the heat of oxidation until the kindling temperature of the material is reached Stage  Refers to the height of a water surface above an established datum plane Standing wave  An oscillating type of wave on the surface of an enclosed body of water The wave acts similarly to water sloshing back and forth in an open dish Stock  An irregularly shaped discordant pluton that is less than 100 km2 in surface exposure Storage coefficient  In an aquifer, the volume of water released from storage in a vertical column of ft2 when the water table or other potentiometric surface declines ft In an unconfined aquifer, it is approximately equal to the specific yield Stratification  The structure produced by a series of sedimentary layers or beds (strata) Stratigraphy  The study of rock strata, including their age relations, geographic distribution, composition, and history Stratosphere  The part of the upper atmosphere that shows little change in temperature with altitude Its base begins at about mi (11 km) and its upper limits reach to about 22 mi (35 km) Stream terraces  Elevated remainders of previous floodplains; they generally parallel the stream channel Stress  Compressional, tensional, or torsional forces that act to change the geometry of a body Structure-contour map  A map that portrays subsurface configuration by means of structure contour lines; contour map; tectonic map Syn: structural map, structure map Summit aridity  Dry conditions that may develop on convex hills as a result of excessive drainage and thin soil layers Surface casing  The first string of a well casing to be installed in the well The length will vary according to the surface conditions and the type of well Surficial deposit  Unconsolidated transported or residual materials such as soil, alluvial, or glacial deposits Surge  A momentary increase in flow in an open conduit or pressure in a closed conduit that passes longitudinally along the conduit, usually due to sudden changes in velocity Swab  A piston-like device equipped with an upward-opening check valve and provided with flexible rubber suction caps, lowered into a borehole or casing by means of a wire line for the purpose of cleaning out drilling mud or lifting oil Talus debris  Unconsolidated rock fragments that form a slope at the base of a steep surface Tectonic  Said of or pertaining to the forces involved in, or the resulting structures or features of, tectonics Syn: geotectonic Appendix A: Glossary 355 Till  Unstratified and unsorted sediments deposited by glacial ice Topsoil  The surface layer of a soil that is rich in organic materials Tornado  A highly destructive and violently rotating vortex storm that frequently forms from cumulonimbus clouds It is also referred to as a twister Total porosity  The measure of all void space of a rock, soil, or other substance Total porosity is usually expressed as a percentage of the bulk volume of material occupied by the void space Toxin  A colloidal, proteinaceous, poisonous substance that is a specific product of the metabolic activities of a living organism and is usually very unstable, notably toxic when introduced into the tissues, and typically capable of inducing antibody formation Transmissivity  In an aquifer, the rate at which water of the prevailing kinematic viscosity is transmitted through a unit width under a unit hydraulic gradient Though spoken of as a property of the aquifer, it embodies also the saturated thickness and the properties of the contained liquid Transpiration  The process by which water absorbed by plants is evaporated into the atmosphere from the plant surface Triangulation  A survey technique used to determine the location of the third point of a triangle by measuring the angles from the known end points of a base line to the third point Tsunami  A Japanese term that refers to a seismic sea wave that can be generated by severe submarine fault slippages or volcanic eruptions The tsunami reaches great heights when it enters shallow waters, but it is unnoticeable on the high seas Turbulence (meteorol.)  Any irregular or disturbed wind motion in the air Twister  An American term used for a tornado Unconfined aquifer  A groundwater body that is under water table conditions Unconsolidated material  A sediment that is loosely arranged, or whose particles are not cemented together, occurring either at the surface or at depth Urbanization  The transformation of rural areas into urban areas Also referred to as urban sprawl Vapor pressure  That part of the total atmospheric pressure that is contributed by water vapor It is usually expressed in inches of mercury or in millibars Vesicular  A textural term indicating the presence of many small cavities in a rock Viscosity  The property of a substance to offer internal resistance to flow; its internal friction The ratio of the rate of shear stress to the rate of shear strain is known as the coefficient of viscosity Vorticity (meteorol.)  Any rotary flow of air such as in tornadoes, mid-latitude cyclones, and hurricanes Wastewater  Spent water According to the source, it may be a combination of the liquid and water-carried wastes from residence, commercial buildings, industrial plants, and institutions, together with any groundwater, surface water, and storm water that may be present In recent years, the term wastewater has taken precedence over the term sewage Water quality  The chemical, physical, and biological characteristics of water with respect to its suitability for a particular purpose Water table  The surface marking the boundary between the zone of saturation and the zone of aeration It approximates the surface topography Weather  The physical state of the atmosphere (wind, precipitation, temperature, pressure, cloudiness, etc.) at a given time and location Well log  A log obtained from a well, showing such information as resistivity, radioactivity, spontaneous potential, and acoustic velocity as a function of depth; especially a lithologic record of the rocks penetrated Well monitoring  The measurement, by on-site instruments or laboratory methods, of the water quality of a water well Monitoring may be periodic or continuous 356 Environmental Hydrogeology, Second Edition Well plug  A watertight and gas-tight seal installed in a borehole or well to prevent movement of fluids The plug can be a block cemented inside the casing Well record  A concise statement of the available data regarding a well, such as a scout ticket; a full history or day-by-day account of a well, from the day the well was surveyed to the day production ceased Well stimulation  Term used to describe several processes used to clean the well bore, enlarge channels, and increase pore space in the interval to be injected, thus making it possible for wastewater to move more readily into the formation Well stimulation techniques include surging, jetting, blasting, acidizing, and hydraulic fracturing Windbreak  Natural or planted groups or rows of trees that slow down the wind velocity and protect against soil erosion Zone of aeration  The zone in which the pore spaces in permeable materials are not filled (except temporarily) with water Also referred to as unsaturated zone or vadose zone Zone of saturation  The zone in which pore spaces are filled with water Also referred to as phreatic zone Fluid flux Volume Area Length UK gal/min US gal/min cubic ft/s oil barrel US bushel UK gal = 0.987 · 10–12 m2 = 9.290 · 10–2 m2 = 1.438 · 10–7 m2/s = 9.290 · 10–2 m2/s = 4.720 · 10–7 m/s = 0.3048 m/s = 9.412 · 1010 darcy darcy ft2 US gal/day ft ft2/s US gal/day ft2 ft/s = 1.055 · 103 J = 4.185 J = 1.356 J = 7.576 · 10–2 liter/s Intrinsic permeability Transmissivity Hydraulic conductivity BTU calorie ft lbf = 0.1 MPa = 105 Pa = 1.013 · 105 Pa = 6.895 · 103 Pa = 47.88 Pa = (9/5) × °C + 32 = 4.448 N = 7.576 · 10–5 m3/s = 6.309 · 10–2 liter/s = 6.309 · 10–5 m3/s = 28.32 liter/s = 2.832 · 10–2 m3/s = 156 liter = 0.156 m3 = 35.24 liter = 3.524 · 10–2 m3 = 4.546 liter = 4.546 · 10–3 m3 = 3.785 liter = 3.785 · 10–3 m3 bar = 28.32 liter US gal atm = 2.832 · 10–2 m3 ft3 psi lbf/foot2 = 29.54 cm3 US ft oz Work or energy Stress and pressure = 0.4047 · 104 cm2 = 2.590 km2 × °F Temperature = 0.4047 mi2 lbf Force = 0.0929 m2 acre = 16.02 kg/m3 = 1016 kg lbm/ft3 = 907 kg l ton = 0.4536 kg = 28.35 g s ton lbm oz ft2 = 1.609 km mi Mass = 6.4516 cm2 = 0.3048 m ft English-SI Conversion Table inch2 = 2.54 cm inch pjwstk|402064|1435432640 Appendix B: Conversion Tables 357 358 Environmental Hydrogeology, Second Edition Prefixes for Multiplying and Dividing of SI Units 10–1 tenth deci d 101 ten deca da 10–2 hundredth centi c (%) 102 hundred hecto h 10–3 thousandth milli m (‰) 103 thousand kilo k 10–6 millionth micro μ (ppm) 106 million mega M 10–9 billionth nano n 109 billion giga G 10 trillionth pico p (ppb) 1012 trillion tera T –12 Note: ppm (parts per million)—particles per million particles; ppb (parts per billion)—particles per billion particles Chemical Symbols Mass Number Ion charge SYMBOL pjwstk|402064|1435432642 Number of protons Number of atoms Examples 12 C,Ca 2+ ,O2 Appendix C: Math Modeling and Useful Programs Groundwater governing 2-D equation: δ2 h δ2 h S δh + = T δr δx δy (9.1) a Finite difference method (backward-difference simulation), see Figure 9.1 h (i − 1, J ), n + h (i + 1, J ), n + h (i, J − 1), n + h (i, J + 1), n − h (i, j ), n a2 S h (i, J ), n − h (i, J ), ( n − 1) = T ∆t (9.2) where a = ∆x = ∆y b Finite element method Equation 9.1 may take the following form, including recharging (+) or discharging (–) well Q, Figure C.1  Finite difference notation 359 360 Environmental Hydrogeology, Second Edition ∇⋅ [T( x ,y )∇h ] ± Q( x ,y ,t ) = S( x ,y ) δh δt (9.3) Using variational methods, Equation 9.3 may take the following form: U=  δh   δh δh /2  Tx + Ty +S ∓ Q  h  dxdy  δx   δy δt   ∫∫ (9.3a) Minimizing Equation 9.3, δU = δhi s ∫ s  δh  δ δh   + T δh  δ δh  + e  Tx  y   δx  δhi δx  δy  δhi δy   δh δh   ds ±Q δt δhi  (9.4) hn − h(n − 1) δh Considering for simplicity to be as given in the finite difference notation, ∆t δt and differentiating Equation 9.3 with respect to hJ,hk, also, noting that (see Figure 9.2) hp = a1 + a2x + a3y where Figure C.2  Finite element (for a triangular element) (9.5) 361 Appendix C: Math Modeling and Useful Programs a  a1   i   b  a2  =   2∆  i  ci  a3     aj bJ cJ ak  bk  c k    h pi    h   pJ  h   pk  (9.6) ai,J,k, bi,J,k, and ci,J,k can be given by substitution in Equation 9.5 in terms of xi,J,k and yi,J,k 2Δ = area of the triangle = determinate of the triangle Equation 9.5 then becomes hp = ( ak + bk x + c k y ) h pk ] [( + bi x + ci y ) h pi + ( aJ + bJ x + c J y ) h pJ + 2∆ (9.7) having Ni = (ai + bix + ciy)/2Δ NJ = (a J + bJx + cJy)/2Δ NK = (aK + bKx + chy)/2Δ Equation 9.7 then becomes hp = [ N i N J N k ]  h pi  = [ N ]( h ) h   pJ  h   pk  (9.8) After assembling the whole set of minimizing equations for the whole region, [N][H] + [F] = (9.9) Equation 9.9 describes the steady-state condition, and for the unsteady state conditions, Δt can be set for reasonable time length, and the finite difference approximation for hn – hn–1/ Δt can be included in Equation 9.9 For the solute transport equation: δc δc δc δ  δc  δ  δc  +u +w - DL + DT +kc′=0 δt δx δy δx  δx  δy  δy  (9.10) Equation 9.4 is identical with Equation 7.7 and can be simulated the same way as the groundwater Equation 9.3 when the finite element method is used The difference between the two equations is that Equation 9.9 contains symmetrical matrices, whereas solute transport finite element equations not have this symmetry For this reason, for any numerical model of a solute transport problem, a memory of at least MB in the computer is required for more than 500 elements model Appendix D: Software Manual of Drawdown Around Multiple Wells This program can be used to calculate the drawdown of the water table around multiple well systems for dewatering purposes or for any other environmental problem The modified Theis equation is used to develop the drawdown contours around the well system for both confined and unconfined aquifers The aquifers are considered isotropic for simplicity, having uniform saturated thickness In this respect, the two-dimensional solution is adopted The three-dimensional solution is tried for solute transport problems that will be demonstrated in another book by the author The executable files are written in TPASCAL designed by Dr A A Hassan and modified by the author to suit some environmental problems The name of this file is MULTIP4.EXE The data file name can be any name the user can select For the example given here, the data file name is MULTIP4.DAT This file should include all the boundary conditions, aquifer characteristics, well positions, complete network of the area, etc The following steps can be followed to create your data file Step 1: Assign the name of your data file and write the data needed for each of the following step on a separate line Step (line 1): Specify the kind of aquifer: for confined, and for unconfined This should be stated on the first line of your data file Step (line 2): Assign the maximum and minimum coordinates of the problem boundaries with their scales as given in the following line: xm1  xm2  ym1  ym2  delta(x)  delta(y) Step (line 3): Try to adjust the groundwater flow direction parallel to one of the axes and then type the values of transmissivity, T, storativity, S, water-table slope, gi, and saturated thickness, M, as T  S  gi  M Step (line 4): Write the number of the pumping wells, n Step 6: Type the x, y coordinates of the pumping well and discharge (Q) of each well For example, if we have three wells, those values should be arranged as (line 5)  X1  Y1  Q1 (line 6)  X2  Y2  Q2 (line 7)  X3  Y3  Q3 Step (line 8): On the next line, type the number of times (NT) selected: NT Step (line 9): Type the value of the selected times (it) for the drawdown values to be calculated Note: keep in mind the time units to be the same in the problem; this means that if T is m2/d, the time unit is a day Thus, line contains t1  t2 tr 363 364 Environmental Hydrogeology, Second Edition Step (line 10): Type the number of points in the domain (np), the number of rows (nrows), and the number of vertical lines (nl) as follows: np  nrows  nl Step 10 (line 11): For irregular boundary problem, assign an integer 0, or integer for regular boundary (regular boundaries are either square or rectangular in shape) 0  or  Step 11 (line 12): On line 12, type the number of points on x-axis (nx) and the number of points on y-axis (ny) as: nx  ny Step 12 (line 13): For drawing the drawdown contours, assign the element dimensions delta x1 and delta y1 as delta x1  delta y1 Step 13 (line 14): Write the number of the corners: nc Step 14 (line 15): Write the corner numbers nc(i) of the boundary problem as i  ii  iii  iv  (supposing we have corners) Step 15 (line 16): Write the number of contours (nhl) you want to draw as nhl Step 16 (line 17): Write the contour values, hl(i) (note that you must have the exact number of contour values as specified in step 15): hl(1)   hl(2) hl(i) Step 17 (line 18): In the last line of the data file, write the contour information, considering a = contour interval, b = the lowest value of the contours, and c = the highest contour needed for demonstration; then line 18 should include contour intervals = a (from b to c) Step 18: After preparing the data file, you can start the program using MULTIP4.EXE Write the data file name upon request, then press (enter ←) The first figure appears on the screen showing the well locations Press (enter ←) to give the drawdown contours as specified after the first period Press (enter ←) again to show the drawdown contours for the second period, and so on until you execute the number of time periods required in the problem As an example, the following problem is given: For an unconfined aquifer with a saturated thickness of 50 m, three wells were drilled to discharge 100 m3/h/well Find the drawdown contours around the well group after three successive time periods 0.5, 1, and 1.5 d, respectively, if you are given the following data: Appendix D: Software Manual of Drawdown Around Multiple Wells 365 T = 750 m2/d, S = 0.01,  ig = 0.0001 if the aquifer occupies an area of 20 × 10 km, and the well coordinates are (3500,4500), (3250,4250), and (3750, 4000) m, respectively Notice that the data file for this problem is given in MULTIP4.DAT, which follows Steps to 17