Dr Y zhou Lecture notes 2005 Groundwater Hydraulics W)X h h K L h2=h2-( L UNESCO-IHE institute for Water Education
Dr Y Zhou Lecture Notes 2005 Groundwater Hydraulics w 0 L x h h0 K hL x w)x x+)x x K w )x - K wL - L h - h h = h -( L 2 2 0 2 0 2 2
Table of Contents 1. Introduction l. 1 Hydrological Cycle…… 2 Aquifer systems 1. 2. 1 Aquifer, aquitard, and aquiclude 1.2.2 uifer type 1.3 Vertical distribution of groundwater 33346 1. 4 Groundwater flow systems 2. Fundamental Equations of groundwater Flow. 2.1 2.2 Generalization of Darcy's Law 2.3 Equation of continuity 2.4 Basic equations for steady incompressible flow 3578 2.5 Basic equations for non-steady compressible flow Steady groundwater Flow in Aquifers 3.1 Groundwater flow in a confined aquifer. 3.1 Conceptual hydrogeological model 3.1.2 Mathematical model 3.1.3 Analytical solution 3.1.4 3.2 Groundwater Flow in an Unconfined Aquifer. 3.2. 1 Conceptual hydrogeological model 3.2.2 Mathematical model 3.2.3 Analytical solution 3.2.4 Analysis of solution 3.3 Groundwater flow in a semi-confined aquifer. 3.3.1 Conceptual hydrogeological model 3.3.2 Mathematical model 778922234 3.3.3 Analytical solution 3.3.4 Analysis of result 4. Steady Groundwater Flow to Wells 4.1 Groundwater flow to a well in a confined aquifer. 4.1.1 Conceptual hydrogeological model.. 4.1.2 Mathematical model 4. 1.3 Analytical solution 4.1.4 Analysis of results 4.1.5 Application to pumping test 4.2 Groundwater flow to a well in an unconfined aquifer hydrogeological model 4.2.2 Mathematical model 4.2.3 4.2.4 Analysis of results 4.2.5 Application to pumping test 4.3 Groundwater flow to a well in a semi-confined aquifer. hydrogeological mo 4.3.2 Mathematical model
Table of Contents 1. Introduction...............................................................................................................................................1 1.1 Hydrological Cycle ...........................................................................................................................1 1.2 Aquifer systems................................................................................................................................3 1.2.1 Aquifer, aquitard, and aquiclude ................................................................................................3 1.2.2 Aquifer types..............................................................................................................................3 1.3 Vertical distribution of groundwater .............................................................................................4 1.4 Groundwater flow systems..............................................................................................................6 2. Fundamental Equations of Groundwater Flow.......................................................................................9 2.1 Darcy's Law......................................................................................................................................9 2.2 Generalization of Darcy's Law......................................................................................................13 2.3 Equation of continuity ...................................................................................................................15 2.4 Basic equations for steady incompressible flow...........................................................................17 2.5 Basic equations for non-steady compressible flow ......................................................................18 3. Steady Groundwater Flow in Aquifers...................................................................................................23 3.1 Groundwater flow in a confined aquifer......................................................................................23 3.1.1 Conceptual hydrogeological model..........................................................................................23 3.1.2 Mathematical model.................................................................................................................23 3.1.3 Analytical solution ...................................................................................................................24 3.1.4 Analysis of solution..................................................................................................................25 3.2 Groundwater Flow in an Unconfined Aquifer.............................................................................27 3.2.1 Conceptual hydrogeological model..........................................................................................27 3.2.2 Mathematical model.................................................................................................................27 3.2.3 Analytical solution ...................................................................................................................28 3.2.4 Analysis of solution..................................................................................................................29 3.3 Groundwater flow in a semi-confined aquifer.............................................................................32 3.3.1 Conceptual hydrogeological model..........................................................................................32 3.3.2 Mathematical model.................................................................................................................32 3.3.3 Analytical solution ..................................................................................................................33 3.3.4 Analysis of result......................................................................................................................34 4. Steady Groundwater Flow to Wells ........................................................................................................37 4.1 Groundwater flow to a well in a confined aquifer.......................................................................37 4.1.1 Conceptual hydrogeological model..........................................................................................37 4.1.2 Mathematical model.................................................................................................................37 4.1.3 Analytical solution ...................................................................................................................39 4.1.4 Analysis of results....................................................................................................................40 4.1.5 Application to pumping test .....................................................................................................41 4.2 Groundwater flow to a well in an unconfined aquifer ................................................................43 4.2.1 Conceptual hydrogeological model..........................................................................................43 4.2.2 Mathematical model.................................................................................................................43 4.2.3 Analytical solution ...................................................................................................................44 4.2.4 Analysis of results....................................................................................................................46 4.2.5 Application to pumping test .....................................................................................................46 4.3 Groundwater flow to a well in a semi-confined aquifer..............................................................48 4.3.1 Conceptual hydrogeological model..........................................................................................48 4.3.2 Mathematical model.................................................................................................................48 4.3.3 Analytical solution ...................................................................................................................49 1
4.4 Methods of superposition and images 4.4.1 Method of superposition 44.2 Method of images 4.5 Flow net…… 4.5.1 Potential function and equipotential lines 4.5.2 Stream function and stream lines 4.5.3 Flow net 5. Non-Steady Groundwater Flow in Aquifers 5.1 Basic equations for non-steady flow in aquifers. 5.1.1 Confined aquifer 5.2 Non-steady Groundwater Flow in a confined aquifer. 5.2.1 Conceptual hydrogeological model 5.2.2 Mathematical model 5.2.3 Analytical solution 76 5.2. 4 Analysis of the resul .3 Non-steady Groundwater Flow in an unconfined aquifer 5.3.1 Conceptual hydrogeological model 78 5.3.2 Mathematical model 78 5.3.3 Analytical solutions 5.3.4 Analysis of results 6. Non-steady Groundwater Flow to wells 6.1 Groundwater flow to a well in a confined aquifer 6.1.1 Conceptual hydrogeological model 6.1.2 Mathematical model 6.1.3 Analytical Solution: Theis formula(1935) 6. 1. 4 Analysis of the solution 86 6. 1. 5 Simplification of Theis formula: Jacob's formula 6.1.6 Applications 6.2 Non-steady groundwater to a well in an unconfined aquifer. 6.2.1 Conceptual hydrogeological model 6.2.2 Mathematical model 6.2.3 Analytical Solution 96 6.2.5 Application of the solution 3 Non-steady groundwater flow to a well in a semi-confined aquifer 6.3.1 Conceptual hydrogeological model 6.3.2 Mathematical model 6.3.3 Analytical solution 6.3.4 Analysis of the results 6.3.5 Application of the solution 7. Refe 8. Anneres T1 Well function of confined aquifers T2 Well function of semi-confined aquifers 12 T3 Function e Ko(x)…., T 4 Function Io(x),I, (x), Ko(x), K(x) 114 9. Exercise
4.4.4 Analysis of results ................................................................................................................... 52 4.4 Methods of superposition and images.......................................................................................... 55 4.4.1 Method of superposition.......................................................................................................... 55 4.4.2 Method of images.................................................................................................................... 61 4.5 Flow net .......................................................................................................................................... 65 4.5.1 Potential function and equipotential lines................................................................................ 65 4.5.2 Stream function and stream lines............................................................................................. 66 4.5.3 Flow net................................................................................................................................... 66 5. Non-steady Groundwater Flow in Aquifers........................................................................................... 71 5.1 Basic equations for non-steady flow in aquifers.......................................................................... 71 5.1.1 Confined aquifer...................................................................................................................... 71 5.1.2 Unconfined aquifer.................................................................................................................. 72 5.2 Non-steady Groundwater Flow in a confined aquifer ................................................................ 75 5.2.1 Conceptual hydrogeological model ......................................................................................... 75 5.2.2 Mathematical model ................................................................................................................ 75 5.2.3 Analytical solution................................................................................................................... 76 5.2.4 Analysis of the result ............................................................................................................... 77 5.3 Non-steady Groundwater Flow in an unconfined aquifer ......................................................... 78 5.3.1 Conceptual hydrogeological model ......................................................................................... 78 5.3.2 Mathematical model ................................................................................................................ 78 5.3.3 Analytical solutions................................................................................................................. 79 5.3.4 Analysis of results ................................................................................................................... 81 6. Non-steady Groundwater Flow to Wells................................................................................................ 83 6.1 Groundwater flow to a well in a confined aquifer ...................................................................... 83 6.1.1 Conceptual hydrogeological model ......................................................................................... 83 6.1.2 Mathematical model ................................................................................................................ 84 6.1.3 Analytical Solution: Theis formula (1935).............................................................................. 85 6.1.4 Analysis of the solution ........................................................................................................... 86 6.1.5 Simplification of Theis formula: Jacob's formula.................................................................... 87 6.1.6 Applications............................................................................................................................. 87 6.2 Non-steady groundwater to a well in an unconfined aquifer..................................................... 94 6.2.1 Conceptual hydrogeological model ......................................................................................... 94 6.2.2 Mathematical model ................................................................................................................ 94 6.2.3 Analytical Solution.................................................................................................................. 96 6.2.4 Analysis of results ................................................................................................................... 97 6.2.5 Application of the solution ...................................................................................................... 98 6.3 Non-steady groundwater flow to a well in a semi-confined aquifer .......................................... 99 6.3.1 Conceptual hydrogeological model ......................................................................................... 99 6.3.2 Mathematical model .............................................................................................................. 100 6.3.3 Analytical solution................................................................................................................. 101 6.3.4 Analysis of the results............................................................................................................ 102 6.3.5 Application of the solution .................................................................................................... 104 7. References............................................................................................................................................. 110 8. Annexes................................................................................................................................................. 111 T.1 Well function of confined aquifers............................................................................................. 111 T.2 Well function of semi-confined aquifers.................................................................................... 112 T.3 Function e K (x) 0 x ..................................................................................................................... 113 T.4 Function I (x), I (x) 0 1 , K (x), K (x) 0 1 ...................................................................................... 114 9. Exercises............................................................................................................................................... 116 2
9.1 Fundamental Equations of Groundwater Flow I16 9.2 Steady groundwater Flow in Aquifers 117 9.3 Steady groundwater Flow to wells 9.4 Non-steady groundwater Flow to Wells 127
9.1 Fundamental Equations of Groundwater Flow.........................................................................116 9.2 Steady Groundwater Flow in Aquifers ......................................................................................117 9.3 Steady Groundwater Flow to Wells............................................................................................120 9.4 Non-steady Groundwater Flow to Wells....................................................................................127 3