Section9Slides_v1

Section9Slides_v1 - Groundwater Involves study of...

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Involves study of subsurface Fow in saturated soil media (pressure greater than atmospheric); Groundwater (GW) constitutes ~30% of global total freshwater, ~99% of global liquid freshwater Basic de±nitions: An “aquifer” is a geologic unit capable of storing/transmitting signi±cant amounts of water; ²low still governed by Darcy Law (P > 0) Uncon±ned 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 Fow in streams) Piezometric surface (h=P/ ρ g + z) corresponds to w.t. Con±ned aquifers : Saturated soil that is bounded above and below by low conductivity layers Boundary of aquifer does not change in time (analogous to pipe Fow) Major recharge occurs upstream or via leaky con±ning layers Water generally under high pressure; piezometric surface is above top of aquifer Groundwater
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(Unconfned aquiFer)
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(h) Unconfned vs. Confned AquiFers
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Unconfned aquiFers : storage changes correspond directly to change in water table level (w.t. increases = water going into storage and vice versa) storage parameter: “specifc yield” or storage coeFF. ( S y ) = volume oF GW released per unit decline in water table (per unit area) Confned 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: “specifc 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"= s S y S s = Vol. of water released from storage Vol. of aquifer 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 fow 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 ±or h(x,y,z,t) However, GW fow in aqui±ers largely consists o± horizontal fow (in the x-y plane) Dupuit approx .: We can simpli±y the equation ±or these cases by integrating the above equation with respect to z , assuming no vertical fow inside aqui±er ( q z = 0 ) and that the aqui±er has a horizontal lower boundary ( h = h(x,y,t) ) We can integrate ±rom z=0 to z=h’ , where h’= h (water table) ±or uncon²ned aqui±ers and h’=b (aqui±er thickness) ±or con²ned aqui±ers: This equation consists o± ±our terms (one on LHS; three on RHS). We will integrate them one-by-one. First (term #1): Derivation o± 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 = x
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Section9Slides_v1 - Groundwater Involves study of...

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