# Groundwater pumping to remediate groundwater pollution - PowerPoint PPT Presentation

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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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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

• Units within a flow net are curvilinear figures…

• In certain cases, squares will be formed

### 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

a1

K1

K2

a2

### 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

### Unconfined Aquifer

• Well discharge under steady state can be determined using

### Unconfined Aquifer

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

### 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 D

### 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

### 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