Groundwater pumping to remediate groundwater pollution
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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.

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TOC

  • 1) Squares

  • 2) FieldTrip: McClellan

  • 3) Finite Element Modeling


First squares
First: Squares

  • Oxford Dictionary says

  • “a geometric figure with four equal sites and four right angles”


Squares
Squares

  • Units within a flow net are curvilinear figures…

  • In certain cases, squares will be formed

    • Constant head boundary…



Flownet1
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
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

a1

K1

K2

a2






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 aquifer
Confined Aquifer

  • Well discharge under steady state can be determined using


Unconfined aquifer
Unconfined Aquifer

  • Well discharge under steady state can be determined using


Unconfined aquifer1
Unconfined Aquifer

  • Well discharge under steady state WITH surface recharge can be determined using


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 method
Finite Difference method

  • Change the derivative into a finite difference D


Approach to numerical solutions
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 solutions1
Approach to numerical solutions

  • 2) Write the flow equation in algebraic form (using finite difference or finite elements) for each node or block


Approach to numerical solutions2
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
1-D example

  • Boundaries: h left = 10, h right = 3

  • Initial conditions h = 0

  • K is homogeneous = 3

  • Delta x = 2


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