Darcy’s Law

1. Vol. = K.I.A.T2. Q= K.I.A3. V=K.I4. Q = T.I.W

Assumption: Steady state flow condition

Theis, 1935, New MexicoDeveloped the transient GW flow equation

GW Flow Equation in radial form

t

h

T

S

r

h

r

h

r

2

2

.1

r = distance from a wellh= hydraulic head at distance rS = storage coefficient of aquiferT = Transmissivityt = elapsed time

Groundwater Flow

1.Steady State

2.Non-Steady (Transient flow)

GW Flow Toward a WellIn Radial Coordinates

t

h

T

S

z

h

y

h

x

h

2

2

2

2

2

2

GW flow equation in Cartesian Coordinated

X, y and z are distance from origin

Theis (1935) used the concept ofHeat sink/source to solve theRadial form of GW flow equation

duu

e

T

Qs

u

u

4

s = drawdownQ =pumping rateT = transmissivity

tT

Sru

.4

2

duu

euW

u

u

)(

W(u) =[-0.5772-lnu+u-u2/(2.2!)+u3/(3.3!)-u4/(4.4!)+u5/(5.5!)-…]

Normally five elements within the bracketIs sufficient.

You can also use table 4.1, p29

Theis assumptions:1. No external recharge or discharge2. The aquifer is homogeneous, Isotropic andHas uniform thickness3. Aquifer is confined4.The well penetrates the entire aquifer and Is screened all the way through aquifer5. The flow lines are horizontal6.The well diameter is infinitely small7.The head in the aquifer responds instantly8. The aquifer is infinite

Why do we need Theis eq.

What is the first thing we need to doIf we want to drill a well?

1.Preliminary investigation using existing data2. Get a permit for a test holeNeed to advertise the intent.You get sued for infringement

If infringement is proven,What are possible remedies?

1. Rejection of permit2. Financial compensation for the impact3. Night versus day pumping4. Gun?

Cooper-Jacob eq.

01.04

]ln5772.0[42

Tt

Sru

uT

Qs

01.04

]ln56.0[ln42

Tt

Sru

uT

Qs

01.04

]4

ln56.0[ln42

2

Tt

Sru

Tt

Sr

T

Qs

01.04

])4(56.0

[ln42

2

Tt

Sru

Sr

Tt

T

Qs

]25.2

[ln4 2Sr

Tt

T

Qs

If s, drawdown = 0

2.25Tt/r2S =1

2

2

2

25.2

183.0

)(log

25.2log

183.0log

183.0

25.2log

183.0

r

TtS

s

QT

sa

btasSr

Tt

T

Qt

T

Qs

Sr

Tt

T

Qs

2

3.0

264

r

TtS

s

QT

In U.S. conventional unitst, is dayT is gpd/ftr is in ft