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Section9Slides_v1

Section9Slides_v1 - Groundwater Involves study of...

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Involves study of subsurface flow in saturated soil media (pressure greater than atmospheric); Groundwater (GW) constitutes ~30% of global total freshwater, ~99% of global liquid freshwater Basic definitions: An “aquifer” is a geologic unit capable of storing/transmitting significant amounts of water; Flow still governed by Darcy Law (P > 0) Unconfined aquifers : Pores saturate by “pooling up” on top of an impervious or low conductivity layer Aquifer upper boundary is the water table (w.t.) [ p =0 at w.t.] Aquifer supplied by recharge from above Elevation of w.t. changes as storage in aquifer changes (analogous to flow in streams) Piezometric surface (h=P/ ρ g + z) corresponds to w.t. Confined aquifers : Saturated soil that is bounded above and below by low conductivity layers Boundary of aquifer does not change in time (analogous to pipe flow) Major recharge occurs upstream or via leaky confining layers Water generally under high pressure; piezometric surface is above top of aquifer Groundwater
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(Unconfined aquifer)
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(h) Unconfined vs. Confined Aquifers
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Unconfined aquifers : storage changes correspond directly to change in water table level (w.t. increases = water going into storage and vice versa) storage parameter: “specific yield” or storage coeff. ( S y ) = volume of GW released per unit decline in water table (per unit area) Confined aquifers : storage changes correspond mainly to compression of aquifer as weight of overlying material is transferred from liquid to solid grains (change in porosity) when water is removed (or vice versa) storage parameter: “specific storage” ( S s ) Also often use “storativity” (S): Water Storage in Aquifers S y typically 0.05 0.35; [ S y ] = [ ] Physically, 0 S y θ s "Specific retention"= θ s S y S s = Vol. of water released from storage Vol. of aquifer Δ h = change in porosity change in piez. head S s typically 5 × 10 5 5 × 10 3 m 1 ; [ S s ] = [ L 1 ] S = S s × b ; where b is the aquifer thickness; [ S ] = [ ]
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From mass balance considerations the 3D GW flow equation is given by: Provided the necessary boundary conditions (2 per spatial dimension) and an initial condition we could solve the above 2nd order PDE for h(x,y,z,t) However, GW flow in aquifers largely consists of horizontal flow (in the x-y plane) Dupuit approx .: We can simplify the equation for these cases by integrating the above equation with respect to z , assuming no vertical flow inside aquifer ( q z = 0 ) and that the aquifer has a horizontal lower boundary ( h = h(x,y,t) ) We can integrate from z=0 to z=h’ , where h’= h (water table) for unconfined aquifers and h’=b (aquifer thickness) for confined aquifers: This equation consists of four terms (one on LHS; three on RHS). We will integrate them one-by-one. First (term #1): Derivation of 2D GW Flow Equation S s h t = x K x h x + y K y h y + z K z h z S s h t 0 h dz =
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