pressure drawdown test

8/9/2019 pressure drawdown test

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Assignment No. 01: PCB 3013 Well Test AnalysisLast date for submission : 26Feb., 2015 Max. Marks-05

Q.No.1: What do you know about Linear Discontinuities

(Sealing Faults)? Discuss in detail Draw Down behavior

of a well in the vicinity of a fault.

Q.No.2: State and explain Buildup case and Effect of

Producing time on Pressure Response.

Q.No.3(a): What are the conditions at which fault may bedetected by conducting well test?

(b)Differentiate:

Multiple Fault Systems and Late Transient AnalysisInternal


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PRESSURE DRAWDOWN TEST

A drawdown test is run as follows:

1. The well is shut-in for a period of time longenough to allow the pressure to equalize

throughout the reservoir.2. The pressure measuring equipment is

lowered into the well.

3. The flow is begun at a constant rate and the

bottom-hole pressure is continuouslymeasured.

Internal


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The duration of DDT depending upon

objectives & Formation characteristics:

Few hours or several days

Extended DDT (Reservoir Limits) are

primarily run to estimate drainage volume of

Well.

Internal


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PRESSURE BEHAVOIR OF A SINGLE

WELL IN AN INFINITE RESERVOIR

The dimensionless pressure at the well

(r D=1) is given by Eq

),(2.141,1

D Di D

n

i

ii t r P Bqkh

t r P

80907.0)ln(21 D D t s P

Internal


5/33

s

r c

kt P P

Bq

kh

wt

wf i 280907.00002637.0

ln

2

1

2.141 2

s

r c

k

kh

Bq P P

wt iwf

8686.023.3log6.162

2

in oilfield units:

solving for Pwf ;

Internal


6/33

It indicates that a plot of bottom-hole pressure

(also known as the sand-face pressure) Pwf vs.

time, t , should yield a straight line with a slope m

kh

Bqm

6.162

The beginning time of the “semi-log straight line” may be estimated from:

khC st

SSL )000,12000,200(

Internal


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SKIN EFFECT

The damaged zone is called the “skin." The main factors responsible for this damage are:

Invasion by drilling fluids

Partial well penetration

Partial completion (productive interval not entirely perforated)

Plugging of perforations

Organic/Inorganic precipitation Improper perforation density or limited perforation

Bacterial growth

Dispersion of clays

Presence of a mud cake and of cement

Presence of a high gas saturation around the wellbore

Internal


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The additional pressure drop due to the skin

effect is:

sm skh

Bq P s )(87.0

2.141

or;

w

s

w

s

s

sr

r

kh

Bq

r

r

hk

Bq P ln

2.141ln

2.141

w

s

s

s

r

r

k k h

Bq P ln

112.141

w

s

r

r

sk sk k m s P ln)(87.0

Internal


9/33

Semilog plot of a pressure drawdown test indicating

pressure at 1 hr

1200

1300

1400

1500

1600

1700

1800

1900

2000

0.1 1 10 100

P1hr

k h

Bqm

6.1 6 2

Deviation from straight line is due to

wellbore storage and skin effects

P w

f ,

psi

Internal


10/33

If the radius, r s, and the permeability, ks, of the skin

zone are known, the skin factor may be estimated

from

sm skh

Bq P s )(87.02.141

w

s

r

r

sk

sk k

m s P ln)(87.0

w

s

s r

r

k

k s ln1

Internal


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Thus, if:

(1) ks < k, then s > 0; damaged well

(2) ks > k, then s < 0; stimulated well (fracturing or acidizing)

(3) ks = k, then s = 0; the well is neither damaged nor stimulated.

Hydraulically fractured wells often show values of S rangingfrom -3 to -5. It is not possible to obtain both rs and ks fromEq.

even if k, s, and rw are known. For this, we define an“effective (or apparent) wellbore radius”, rw’, suchthat:

w

s

s r

r

k

k s ln1

w

w

skinr

r

kh

Bq P

'ln

2.141

Internal


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Thus;

s r

r w

w

ln'

or;

r r ew w s'

where;

23.3log1513.1

2

1

wt

hr

r c

k

m

Pi P s

where;

Internal


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FLOW EFFICIENCY (OR PRODUCTIVITY

RATIO, OR COMPLETION FACTOR)

This parameter measures the degree of producing capability for an

undamaged well.

)0(

s J

J FE

ideal

actual

wf

actual P P

q J

skinwf

ideal P P P

q J

wf

skinwf

P P

P P P

FE

where;

Internal


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In presence of steady state or a new well .

If FE < 1 = damaged well

If FE > 1 = stimulated well

Internal


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DAMAGE RATIO AND DAMAGE FACTOR

Both damage ratio and damage factor reflect wellbore

conditions

The damage ratio is defined as the inverse of

flow efficiency and

The damage factor results by subtracting theflow efficiency from unity.

skinwf

wf

p p P

p P

FE DR

1

wf

skin

P P

P FE DF

1If DF > 0; damaged well

If DF < 0; improved or stimulated wellInternal


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WELLBORE STORAGE

Wellbore storage or afterflow is the continued

influx from a formation into the wellbore after

the well is shut-in.

During short-time production, dimensionlesspressure is directly proportional to

dimensionless time:

D

Dwf i

ct P P

Bqkh

2.141

C hr c

C wt

D 2

89359.0

Internal


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Parameter C in Eq. is the wellbore storage

coefficient given in bbl/psi, and may be

estimated from completion data.

a) For a completely fluid-filled wellbore (injectionwell), i.e. compressive wellbore storage, the

expected value of C is given by:

where c is the compressibility of the fluid in the

wellbore, and Vw is the total wellbore volume in

bbl.

wcV C

Internal


18/33

For a wellbore with a rising (pumping well)

or falling liquid level, i.e. non-compressive

wellbore storage:

Thus, wellbore storage and skin effect

determine the time required to reach thesemi-log straight line of a drawdown plot.

This time may be estimated from:

)/)(144/( c

u

g g V C

D D Cst )5.360( Internal


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Substituting Eq. for dimensionless time

22

89359.0)5.360(

0002637.0

wt wt hr hc s

r c

kt

kh

C st SSL

)5.360(66.3388

D

DSSL

C

t

kh

C t

66.3388or;

Internal


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After plugging the dimensionless parameters

tD and CD, it yields:

This equation is extremely useful in well testdesign. Thus, if one log cycle of straight line

is desired, the test should be run for a period

of time T:

C kh

st SSL

)12000200000(

SSLt T 10

Internal


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The drawdown stabilization time and the drainage

radius during the test can be determine by:

The maximum pressure response occurs at tmax

which is defined a

and for any producing time, tp, the radius of

investigation is given by:

k

Act t s

43560380

t

sd

c

t k r

029.0

k

r ct t

2

max

948

t

p

inv c

t k

r 0325.0Internal


22/33

The time at which the pseudosteady state period

takes place is given by:

For any producing time, tp, Eq. can be expressed as:

t

p

invc

t k r

0325.0

k

r ct et pss

2948

Eq is appropriate for square geometries.

Internal


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For circular systems, the appropriate relationship is

The wellbore storage coefficient may be estimatedfrom a plot of P vs. time on a log-log graph paper.

The slope of such a curve is one during the period

dominated by wellbore storage effect. Any point i on this straight line portion may be used to

find C, or:

k

r ct et pss

21190

i

i

p

t qBC

24Internal


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For a drawdown test, the time is simply theflowing time and P = Pi - Pwf, thus:

C calculated from Eqs. should be similar

If they are not, it could be an indicator ofwhether the liquid level is falling or rising.

Other reasons for this difference might beeither high gas-oil ratio at the wellbore orhighly stimulated well, among others.

wf i

P P

t qBC

24

Internal


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RESERVOIR LIMIT TEST

This is a drawdown test run long enough for

the purpose of estimating the drainage

volume of the well.

This test uses the pseudo-steady stateportion of the plot of Pwf vs. flowing time.

Internal


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k

r ct

et

0 0 0 2 6 3 7.0

2

k

r ct et

0 0 0 8 8.0

2

P

,

ps

i

wf

Time, hrs

Region I Region II Region III

Internal


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Region I in Fig. corresponds to the portion of

the test responsible to analysis by transient

methods.

Region II in the same plot is referred to latetransient method

Region III, semi-steady state behavior, is the

reservoir limit test itself which is governed by:

Aw

DA DC r

At P

2458.2ln

2

1ln

2

12

2

where the area, A, is given in ft2Internal


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Substituting

A

r t

C

kt t w D

A

DA

20002637.0

s P P kh

Bq P wf i D

2.141

s

C r

A

kh

Bq P t

Ahc

qB P

Aw

i

t

D 22458.2

lnln6.7023395.0

2

Internal


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This equation is of the general form y = mx + b.

Thus, during pseudo-steady state, a Cartesian plot of Pwf vs. t

should be a straight line.

The slope and intercept of such a straight line are:

0

500

1000

1500

2000

2500

0 20 40 60 80 100

Pint

Slope=m

t, hr

P w

f ,

psi

*

Internal


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The slope m* in Fig. may be used to calculate thevolume of the reservoir portion being drained by the

test well (drainage volume in ft3):

The Dietz shape factor, C A, may be estimated from:

Ahc

qBm

t

23395.0*

s

C r

A

kh

Bq P P

Aw

i 22458.2

lnln6.70

2int

*

23395.0

mc

qB Ah

t

m P P

A

hr

em

mC

int130 3.2

*456.5

Internal


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The shape factor is used to determine the reservoir

configuration (circle, rectangle, hexagon, etc.) as follows:

From table 1 find a value of CA which corresponds most

closely to the value calculated from Eq.

Calculate the dimensionless time at start of pseudo-steadystate period

Compare (tDA)pss obtained from following Eq. with the “Exact

for (tDA)pss > ” column of the table 1. If (tDA)pss the value

obtained from this column, then the shape corresponding to

the “most closely” value of C A is the most likely configuration

of the system. Mattews, Brons and Hazebroek first studied

shape factors for several drainage geometries.

Internal


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Table 1. Shape factors for various single-well drainage areas

C A

31.62

31.6

27.6

27.1

21.9

30.8828

12.9851

4.5132

3.3351

21.8369

10.8374

4.5141

2.0769

3.1573

0.1

0.1

0.2

0.2

0.4

0.1

0.7

0.6

0.7

0.3

0.4

1.5

1.7

0.4

0.06

0.06

0.07

0.07

0.12

0.05

0.25

0.30

0.25

0.15

0.15

0.50

0.5

0.15

Less than1 % error

for tDA >

0.1

0.1

0.09

0.09

0.08

0.09

0.03

0.025

0.01

0.025

0.025

0.06

0.02

0.005

Use infinite system solutions with less than

1 % error for tDA >

1

1

0.098 0.9 0.6 0.015

Exact for

for tDA >

60°

1

1/3

43

1

1

1

1

1

1

1

Bounded

reservoirs

Internal


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C A

0.5813

0.1109

5.379

2.6896

0.2318

2.3606

2.6541

2.0348

1.9986

1.662

1.3127

0.7887

19.1

25.0

2.0

3.0

0.8

0.8

4.0

1.0

0.175

0.175

0.175

0.175

0.175

0.175

--

--

0.6

0.6

0.3

0.3

2.0

0.4

0.08

0.09

0.09

0.09

0.09

0.09

--

--

Less than1 % error

for tDA >

0.02

0.005

0.01

0.01

0.03

0.025

Cannot use

Cannot use

Cannot use

Cannot use

Cannot use

Cannot use

--

--

Use infinite system solutions with less th

1 % error for tDA >

1

2

1

2

1

4

1

4

1

4

1

5

Vertical-Fractured

reservoirs

1

1

xf/xe=0.1

1

1

xf/xe=0.2

1

1

xf/xe=0.3

1

1

xf/xe=0.5

1

1

xf/xe=0.7

1

1

xf/xe=1.0

Water-Drive reservoirs

Unknown Drive mechanism

0.1155 4.0 2.0 0.011

4

Use (Xe/Xf) in place of A/rw

for fractured reservoirs

2 2

Exact for

for tDA >

Internal

pressure drawdown test

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