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