Understanding Steady Flow to Wells in Unconfined Aquifers
Explore the concept of steady flow to a well in an unconfined aquifer with helpful visuals and in-depth descriptions. Learn about groundwater hydraulics, governing equations, and more in this comprehensive study.
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Flow to Wells 2 Steady flow to a well in an unconfined aquifer Groundwater Hydraulics Daene C. McKinney 1
Summary Notation Steady flow to a well in an unconfined aquifer Steady flow to a well in an unconfined aquifer with recharge 2
Flow to a Well in an Unconfined Aquifer 3
Groundwater Notation Unconfined aquifer ? ?? ?? ? ? ?? ?? ? ? ?? General equation, rectangular coordinates ? ? ? = + = ?? ?? ?? ? 2 ?? ? ??= 1 2 ? 2 ?? ? 2 ?? ?? 2 ? ? ? ?? ?? 2 ? ?? ? ?? 2? 2= + = ?? Steady flow, homogeneous, isotropic aquifer ?2 2 ??2 +?2 2 ??2 ?2 2= = 0 4
Groundwater Notation Unconfined aquifer ?? 2?? 2 ?? 2?? 2 ? ? 2? 2=1 ? ?? +1 ? ? ?? General equation, radial coordinates = ?? ?2 ? ?? ?? ?? ? ???? 2 ?2 2= Steady flow, homogeneous, isotropic aquifer = 0 ?? 5
Steady Flow to a Well in an unconfined Aquifer Q Ground surface Pre-pumping Water level Pumping well Water Table Observation wells h0 r1 hw h2 h1 Q Unconfined aquifer r2 Bedrock rw ? ???? 2 ?2 2 ??2 =2?? ?2 2=1 +1 ? ?? Governing equation in radial coordinates ?2 ? ?? ? ? ???? 2 Assumptions: Steady state flow, radial symmetry (isotropic medium), = 0 ?? 6
Steady Flow to a Well in an Unconfined Aquifer ? ???? 2 = 0 ?? Q Ground surface Pre-pumping Water level ?? 2 = ?1 Pumping well ?? Water Table Observation wells Darcy s law ? = ?? = 2?? ?? ??= ???? 2 h0 r1 hw ?? h2 h1 ?? 2 ? ??= ?1 Q Unconfined aquifer r2 = ?? Bedrock ? ?? ?? ? rw ? 2= ? ???? ? + ?2 2= 7
Steady Flow to a Well in an Unconfined Aquifer Q ? ???? ? + ?2 2= Ground surface Pre-pumping Water level Pumping well Water Table Boundary condition: = 1 @ ? = ?1 Observation wells ? ???? ?1 + ?2 ? ???? ?1 2= 1 h0 r1 hw h2 h1 Q Unconfined aquifer 2 r2 ?2= 1 Bedrock ? ???? ? + 1 ? ???? ?1 rw 2 2= ? ???? ? ?1 2+ 2= 1 8
Example Steady Flow to a Well in an Unconfined Aquifer Given: Q = 300 m3/hr Two observation wells, 1. h1 = 40 m @ r1 = 50 m 2. h2 = 43 m @ r2 = 100 m Find: K Q Ground surface Prepumping Water level Pumping well Water Table Observation wells h0 r1 hw h 2 h1 ? ???? ? ?1 2+ 2= 1 Q Unconfined aquifer r2 Bedrock ? ???? ?2 ?1 rw 2= 1 2+ 2 =300m3/hr/3600s/hr p (43m)2-(40m)2 [ ln100m 50m Q 2-h1 lnr2 = 7.3x10-5m/sec K = ( ) ] 2 r1 p h2 9
Steady flow to a Well in an Unconfined Aquifer with Recharge ? 2?? 2 1 ? ? ?? + ? = 0 ?? ? ???? 2 +2? ? = 0 ?? ? ?? 2 +? ??2= ?1 ?? ? 2 ?? =?1 ? ? ?? radius of influence 10
Steady flow to a Well in an Unconfined Aquifer with Recharge ? 2 ?? =?1 ? ? ?? Boundary condition 1: No flow across radius of influence ? 2 ?? ? = ? ? ??= ? = 0; 2 ? 2 ?? =?1 ? ??0= 0 ?0 ?=?0 radius of influence ?1=? 2 ??0 11
Steady flow to a Well in an Unconfined Aquifer with Recharge ? 2 ?? =?1 ? ? ?? ?1=? 2 ??0 Boundary condition 2: Recharge within radius of influence is captured by the well 2? ? = ?? = ??0 ? 2= ?0 ?? ? ?? radius of influence ?1= ? 2 ?? ? ?? 1 ? ? = ?? 12
Steady flow to a Well in an Unconfined Aquifer with Recharge ? 2 ?? ? ?? 1 ? ? = ?? ? ?? ?? ? ? ? 2= ???? ? ??ln ? ? 2= 2??2+ ?2 Boundary condition 3: Recharge within radius of influence is captured by the well radius of influence = 0 @ ? = ?0 ? ??ln ?0 ? ? ???? ? ?0 ? 2? 2+ 2 2= 0 ?2 ?0 2= 2+ ?2 0 2??0 13
Example - Steady flow to a Well in an Unconfined Aquifer with Recharge 50 m 25 cm diameter well to maintain lowered water table K = 1x10-5 m/s (0.864 m/d) Bottom of aquifer is horizontal at 20 m bgs Water table is 1 m bgs Unconfined aquifer is recharged at W = 0.06 m/d Water table must be lowered 3 m over site r Drawdown at corners must be at least 3 m r=35.35 m 2+?? ? ?0 ? 2? 2 2= 0 ?2 ?0 ???? 2 162= 192+0.06 ??0 35.35 ?0 0.06 2 35.352 ?0 ?? ?? 2(0.864) Solve by iteration: r0 = 70 m 2? = ? 7020.06 = 923.6 ?3/? ??= ??0 14
Summary Notation Steady flow to a well in an unconfined aquifer Steady flow to a well in an unconfined aquifer with recharge 15
