Post on 05-Jan-2016
Groundwater pumping to remediate groundwater
pollution
Groundwater pumping to remediate groundwater
pollution
March 5, 2002
TOCTOC
1) Squares
2) FieldTrip: McClellan
3) Finite Element Modeling
First: SquaresFirst: Squares
Oxford Dictionary says “a geometric figure with four equal sites and four
right angles”
SquaresSquares
Units within a flow net are curvilinear figures…
In certain cases, squares will be formedConstant head boundary…
FlownetFlownet
FlownetFlownet
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)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)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
K1
K22
1
tan
tan
2
1
K
K1
2
Second: McClellan AirbaseSecond: McClellan Airbase
Piping systemPiping system
Groundwater extraction wellsGroundwater extraction wells
Waste water treatment plantWaste water treatment plant
How to determine the spacing of wells?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 AquiferConfined Aquifer
Well discharge under steady state can be determined using
)ln(
2
1
2
12
rr
hhbKQ
Unconfined AquiferUnconfined Aquifer
Well discharge under steady state can be determined using
)ln(
1
2
21
22
rr
hhKQ
Unconfined AquiferUnconfined Aquifer
Well discharge under steady state WITH surface recharge can be determined using
21
22
)ln(
w
o
rr
wo hhKQ
What is optimal well design ?What is optimal well design ?
In homogeneous soil:
In heterogeneous situation:In heterogeneous situation:
Wells have flow rate between 1 and 100 gpm Some wells are in clay, others in sand
Finite Difference methodFinite Difference method
Change the derivative into a finite difference
Approach to numerical solutionsApproach 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 solutionsApproach to numerical solutions
2) Write the flow equation in algebraic form (using finite difference or finite elements) for each node or block
x
hK
xx
hK
x xx
Approach to numerical solutionsApproach 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 example1-D example
Boundaries: h left = 10, h right = 3 Initial conditions h = 0 K is homogeneous = 3 Delta x = 2