Well Efficiency- Step Drawdown

Tests

Well EfficiencyWell Efficiency-- Step Drawdown TestsStep Drawdown Tests

The total drawdown at a pumping well is given by:The total drawdown at a pumping well is given by:

sstt = s + = s + ssww = = Q Q W(uW(u) + CQ) + CQ2 2 = BQ + CQ= BQ + CQ22

44ππTT

stst= Q(B+CQ)= Q(B+CQ)

St/Q= B+CQSt/Q= B+CQ

The specific capacity is given by: The specific capacity is given by: QQ = = 1 1 ..

sstt B + CQB + CQ

The ratio of the aquifer loss and total drawdown (The ratio of the aquifer loss and total drawdown (s/ss/stt) is known as the ) is known as the well efficiency.well efficiency.

ss = = B B ..

sstt B + CQB + CQ

MoggMogg (1968) defines well efficiency at a fixed time (t = 24 hrs). Th(1968) defines well efficiency at a fixed time (t = 24 hrs). Thus, us, writing writing W(uW(u) as the Cooper) as the Cooper--Jacob approximation gives:Jacob approximation gives:

it is clear that well efficiency reduces with pumping rate (Q) ait is clear that well efficiency reduces with pumping rate (Q) and nd increases with well radius (increases with well radius (rrww), where B is inversely related to well ), where B is inversely related to well radius.radius.

S= B Q +C Q n

S= B Q +C Q 2

StepStep--Drawdown TestDrawdown Test

StepStep--drawdown tests are tests at drawdown tests are tests at

different pumping rates (Q) designed to different pumping rates (Q) designed to

determine well efficiency.determine well efficiency.

Normally pumping at each successively Normally pumping at each successively

greater rate Qgreater rate Q1 1 < Q< Q22 < Q< Q33 < Q< Q44 < Q< Q55

takes place for 1takes place for 1--2 hours (2 hours (∆∆tt) and for 5 ) and for 5

to 8 steps. The entire test usually takes to 8 steps. The entire test usually takes

place in one day. place in one day.

Equal pumping times (Equal pumping times (∆∆tt) simplifies the ) simplifies the

analysis.analysis.

At the end of each step, the pumping At the end of each step, the pumping

rate (Q) and drawdown (s) is recorded.rate (Q) and drawdown (s) is recorded.

Time, t

Dra

wd

ow

n,

s

s1

s2

s3

s4

s5

StepStep--Drawdown Test AnalysisDrawdown Test Analysis

StepStep--drawdown tests are drawdown tests are

analysedanalysed by plotting the by plotting the

reciprocal of specific capacity reciprocal of specific capacity

(s/Q) against the pumping rate (s/Q) against the pumping rate

(Q).(Q).

Q (L/s)

s/Q

(m

/m3/d

)

The intercept of the graph at The intercept of the graph at

Q=0 is B = W(u)/4Q=0 is B = W(u)/4ππT and the T and the

slope is the well loss slope is the well loss

coefficient, C.coefficient, C.

B can also be obtained B can also be obtained

independently from a Theis or independently from a Theis or

CooperCooper--Jacob analysis of a Jacob analysis of a

pump test. pump test.

For Q = 2700 mFor Q = 2700 m33/d and s = 33.3 /d and s = 33.3

m the B = 0.012 m/mm the B = 0.012 m/m33/d/d

If C = 4 x 10If C = 4 x 10--55, then CQ, then CQ22 == 18.2 18.2

m m

The well efficiency is The well efficiency is

33.3/(33.3+18.2) = 65%33.3/(33.3+18.2) = 65%

B

C

Step Pumping

rate (Q)

m3/min

drawdown

(sw(m)

Specific

drawdown

(sw/q(min/

m2)

1 1.59 3.69 2.32

2 1.98 5.14 2.60

3 2.44 7.08 2.90

4 2.96 9.63 3.25

5 3.27 11.29 3.45

Example Step Pumpi

ng

rate

(Q)

m3/mi

n

drawd

own(s

w(m)

Specifi

c

drawd

own

(sw/q(

min/m

2)

Delta

Q

Delta

Sw

Delta S/Delta

Q

C(min2/

m5)

C(Sec2/

m5)

1 1.59 3.69 2.32

2 1.98 5.14 2.60 0.39 1.45 3.72

3 2.44 7.08 2.90 0.46 1.94 4.22 0.58758

2115.28

6

4 2.96 9.63 3.25 0.52 2.55 4.90

0.70046

4

2521.67

1

5 3.27 11.29 3.45 0.31 1.66 5.35

0.54336

5

1956.11

2

Average well

loss 2197.69

C= ((Delta S2/Delta Q2)-(Delta S1/Delta Q1))/(deltaQ1+delta Q2)

sec2/m5