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Groundwater pumping to remediate groundwater pollution. March 5, 2002. TOC. 1) Squares 2) FieldTrip: McClellan 3) Finite Element Modeling. First: Squares. Oxford Dictionary says “a geometric figure with four equal sites and four right angles”. Squares. - PowerPoint PPT Presentation
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Groundwater pumping to remediate groundwater
pollutionMarch 5, 2002
TOC 1) Squares
2) FieldTrip: McClellan
3) Finite Element Modeling
First: Squares Oxford Dictionary says “a geometric figure with four equal sites and four
right angles”
Squares Units within a flow net are curvilinear figures…
In certain cases, squares will be formedConstant head boundary…
Flownet
Flownet No flow crosses the boundary of a flowline !
If interval between equipotential lines and interval between flowlines is constant, then volume of water within each curvilinear unit is the same…
Flow nets (rules) Flowlines are perpendicular to equipotential lines One way to assume that Q’s are equal is to
construct the flownet with curvilinear squares Streamlines are perpendicular to constant head
boundaries Equipotential lines are perpendicular to no-flow
boundaries
Flow nets (rules 2) In heterogeneous soil, the tangent law is
satisfied at the boundary
If flow net is drawn such that squares exist in one part of the formation, squares also exist in areas with the same K
K1K2
2
1
tantan
21
KK1
2
Second: McClellan Airbase
Piping system
Groundwater extraction wells
Waste water treatment plant
How to determine the spacing of wells? Determine feasible flow rates Determine range of influence Determine required decrease of water table Calculate well spacings
Confined Aquifer Well discharge under steady state can be
determined using
)ln(
2
1
2
12
rr
hhbKQ
Unconfined Aquifer Well discharge under steady state can be
determined using
)ln(
1
2
21
22
rr
hhKQ
Unconfined Aquifer Well discharge under steady state WITH surface
recharge can be determined using
21
22
)ln(
w
orr
wo hhKQ
What is optimal well design ? In homogeneous soil:
In heterogeneous situation: Wells have flow rate between 1 and 100 gpm Some wells are in clay, others in sand
Finite Difference method Change the derivative into a finite difference
Approach to numerical solutions 1) Subdivide the flow region into finite blocks or
subregions (discretization) such that different K values can be assigned to each block and the differentials can be converted to finite differences
Approach to numerical solutions 2) Write the flow equation in algebraic form
(using finite difference or finite elements) for each node or block
xhK
xxhK
x xx
Approach to numerical solutions 3) Use “numerical methods” to solve the
resulting ‘n’ equations in ‘n’ unknowns for h subject to boundary and initial conditions
1-D example Boundaries: h left = 10, h right = 3 Initial conditions h = 0 K is homogeneous = 3 Delta x = 2