## Modeling Groundwater Flow and PollutionGroundwater constitutes an important component of many water resource systems, supplying water for domestic use, for industry, and for agriculture. Management of a groundwater system, an aquifer, or a system of aquifers, means making such decisions as to the total quantity of water to be withdrawn annually, the location of wells for pumping and for artificial recharge and their rates, and control conditions at aquifer boundaries. Not less important are decisions related to groundwater qUality. In fact, the quantity and quality problems cannot be separated. In many parts of the world, with the increased withdrawal of ground water, often beyond permissible limits, the quality of groundwater has been continuously deteriorating, causing much concern to both suppliers and users. In recent years, in addition to general groundwater quality aspects, public attention has been focused on groundwater contamination by hazardous industrial wastes, by leachate from landfills, by oil spills, and by agricultural activities such as the use of fertilizers, pesticides, and herbicides, and by radioactive waste in repositories located in deep geological formations, to mention some of the most acute contamination sources. In all these cases, management means making decisions to achieve goals without violating specified constraints. In order to enable the planner, or the decision maker, to compare alternative modes of action and to ensure that the constraints are not violated, a tool is needed that will provide information about the response of the system (the aquifer) to various alternatives. |

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### Contents

Introduction | 1 |

12 Management of Groundwater | 7 |

13 Groundwater Modeling | 11 |

14 Continuum Approach to Porous Media | 17 |

15 Horizontal TwoDimensional Modeling of Aquifers | 21 |

16 Objectives and Scope | 23 |

Groundwater Motion | 27 |

22 Aquifer Transmissivity | 43 |

72 Modeling Seawater Intrusion in a Vertical Plane | 198 |

73 Modeling Regional Seawater Intrusion | 208 |

Introduction to Numerical Methods | 216 |

82 Survey of Numerical Methods | 217 |

83 Computer Programming | 223 |

The Finite Difference Method | 225 |

92 Unsteady Flow | 233 |

93 Accuracy and Stability | 239 |

23 Dupuit Assumption | 45 |

Modeling ThreeDimensional Flow | 53 |

32 Mass Storage | 56 |

33 Fundamental Mass Balance Equation | 60 |

34 Initial and Boundary Conditions | 65 |

35 Complete Statement of Mathematical Flow Model | 76 |

36 Modeling Soil Displacement | 78 |

Modeling TwoDimensional Flow in Aquifers | 85 |

42 Fundamental Continuity Equations | 88 |

43 Initial and Boundary Conditions | 102 |

44 Complete Statement of Aquifer Flow Model | 104 |

45 Regional Model for Land Subsidence | 105 |

46 Streamlines and Stream Function | 114 |

Modeling Flow in the Unsaturated Zone | 123 |

52 Motion Equations | 138 |

53 Balance Equations | 145 |

54 Initial and Boundary Conditions | 149 |

55 Complete Statement of Unsaturated Flow Model | 152 |

Modeling Groundwater Pollution | 153 |

61 Hydrodynamic Dispersion | 155 |

62 Advective Dispersive and Diffusive Fluxes | 159 |

63 Balance Equation for a Pollutant | 167 |

64 Initial and Boundary Conditions | 179 |

65 Complete Statement of Pollution Model | 184 |

66 Pollution Transport by Advection Only | 186 |

67 Macrodispersion | 190 |

Modeling Seawater Intrusion | 196 |

94 Generalizations | 242 |

The Finite Element Method | 247 |

102 Steady Flow in a Confined Aquifer | 257 |

103 Steady Flow with Infiltration and Leakage | 268 |

104 Steady Flow through a Dam | 272 |

105 Unsteady Flow in an Aquifer | 276 |

106 Generalizations | 281 |

Transport by Advection | 285 |

112 SemiAnalytic Solution | 286 |

113 System of Wells in an Infinite Field | 288 |

114 System of Wells in an Infinite Strip | 296 |

115 Numerical Solution in Terms of the Piezometric Head | 299 |

116 Numerical Solution in Terms of the Stream Function | 300 |

117 Tracing Particles Along a Stream Line | 311 |

Transport by Advection and Dispersion | 316 |

122 Numerical Dispersion | 323 |

123 A Finite Element Model for TwoDimensional Problems | 326 |

124 Random Walk Model | 336 |

Numerical Modeling of Seawater Intrusion | 344 |

132 Basic Equations for a Regional Model of Seawater Intrusion | 351 |

133 Finite Element Model for Regional Interface Problems | 355 |

Solution of Linear Equations | 364 |

381 | |

Problems | 386 |

409 | |

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### Common terms and phrases

advection approximation aquifer's aquitard assumed average basic boundary conditions capillary capillary fringe Chapter coefficients components computer program concentration confined aquifer considered constant curve Darcy's law dataset defined denotes derivative determined distribution Dupuit assumption expressed extensive quantity finite difference finite difference method finite element method flow domain fluid flux freshwater GOSUB groundwater flow homogeneous horizontal flow hydraulic conductivity infiltration initial integral interface isotropic linear mesh microscopic molecular diffusion nodes numerical models obtain partial differential equation particles permeability phase phreatic aquifer phreatic surface piezometric head pointer matrix pollutant pore porosity porous medium domain pressure PRINT problem pumping region saturated flow Section semipervious layer shown in Figure soil solid matrix solved specific discharge steady flow step storage storativity stream function streamlines Subsection system of equations thickness three-dimensional two-dimensional unsaturated zone values variables vector velocity Verruijt vertical void space water level water table zero

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Page iii - JACOB BEAR Albert and Anne Mansfield Chair in Water Resources Technion - Israel Institute of Technology Haifa 32000, Israel YEHUDA BACHMAT Hydrological Service, Jerusalem 91060, Israel.