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Pressure Drawdown Test

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Lecture Outline

Brief overview of PDD

Test Procedure

Test Types

Information obtained

Mathematical Model

Interpretation

Semi-log analysis

Cartesian and log-log analysis

Ideal versus Actual Test

ETR, MTR & LTR

Practice Problems

Common mistakes

Summary

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Lecture Outcomes

At the end of this class, a student should be able to do the following:

Describe how a pressure drawdown test is conducted

Synthesize the various data and information to interpret a pressure draw down test

Make qualitative judgment on the data and choose appropriate interpretation method

Isolate the correct data for interpretation

Draw conclusions from results

Make suggestions on the improvement of the test

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Test Procedure

A well that is static, stable, and shut in, is opened to flow. Ideally, the flow rate should be constant. Flow rate is usually measured as surface rate

recording the pressure (usually down hole) in the wellbore as a function of time

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Ra

te,

qP

ress

ure

, P

Time, t

drawdown

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Types of Flow Tests

PDD is also known as Flow Test. Actually, Flow Test is a more generalized term.

There may me several types of Flow Tests, as follows:

Single or Constant Rate Test (q = constant)

variable Rate Test [q = f(t)]

Rate changing smoothly

Rate changing abruptly (Multi-Rate Tests)

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Ra

te,

q

time

q1

q2

q3

q4

q5

q6

qn-1

qn

t1 t2 t3 t4 t5 tn-1

Test Outcomes

Information gathered/required

Pressure versus time recording (pwf – vs – t)

Flow rate (q)

Fluid properties- B, µ

Formation and well parameters –Ø, ct, h, rw

Test interpretation results Formation permeability (k)

Initial pressure (pi)

Wellbore condition - damage or stimulation- skin (s)

Reservoir heterogeneities or boundaries

Hydrocarbon Volume

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Mathematical Model

The basis for flow-test analysis techniques is the line source solution to the diffusivity equation:

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kt

rc

kh

qBPP wt

wfi

2688,1ln

6.70

If natural logarithm is changed to base-10 logarithm and

rearranged

s

rc

kt

kh

qBPP

wt

iwf 869.023.3loglog6.162

2

s

kt

rc

kh

qBPP wt

iwf 2688,1

ln6.70 2

8Mathematical Model

This equation is similar to XmBY log

and suggest a semi-log plot of vs wfP tlog

s

rc

kt

kh

qBPP

wt

iwf 869.023.3loglog6.162

2

should be a straight line

pwf = pressure at the wellbore any time during flow

pi = initial pressure

t = elapsed time after production begins

Ø = pororsity

µ = viscosity

ct = total compressibility; s = skin factor

with a slope of kh

qB6.162

this equation is the main mathematical model for the PBU

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Pwf

t

100 101 102 103 104 105

Pwf1

Pwf2

One log cycle

Slope = Pwf2 – Pwf1

Semi-log Plot9

Analysis Method (Estimate k, s)

Draw the best fit straight line through the MTR data points

Obtain the slope of the straight line

kh

qBmslope

6.162

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The absolute value of the slope is used to estimate the effective

permeability to the fluid flowing in the drainage area of the well

mh

qBk

6.162

23.3log151.1

2

1

wt

hri

rc

k

m

PPs

And the skin factor is (absolute value of m must be used here as well)

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Analysis Method (Estimate Pore Volume)

dt

dPc

qBV

wf

t

p

234.0

dt

dPwf

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For a well centered in a cylindrical drainage area the pore volume

of the drainage area can be estimated by:

where

is the slope

of the

straight line

of the

Cartesian

plot of Pwf

versus t

Pw

f, p

si

t, hours

slope=dPwf/d

t

Here we use a Cartesian Plot- Pseudo-Steady State MUST be reached

Actual Drawdown DataBecause many of the assumptions made during the derivation and solution of the diffusivity equation, in actual life instead of obtaining a straight line for all times, we obtain a curve which can be divided into three region:

1. An early time region in which well bore unloading effects are dominant,

2. A middle time region during which the transient flow regime is applicable and the diffusivity equation is purely valid, and

3. A late time region in which the radius of investigation has reached the well’s drainage boundaries.

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Pwf

100 101 102 103104

Late Time

Region

(LTR)

Early Time

Region

(ETR) Middle

Time

Region

(MTR)

t

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PBU versus PDD

PDD

Pressure-Time data when the well is producing

Involves 1 rate only (ideal)

Difficult to maintain constant flow rate

No revenue loss due to shut in

PBU

Pressure-Time data when the well is shut in

Involves at least 2 rates, the last rate MUST be zero

Constant flow rate is easily obtained (shut in period)

Difficult to obtain constant rate prior to shut in

Revenue loss

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PBU versus PDD

PDD- semi-log analysis

pwf vs t

no transformation of t

wellbore & boundary effects may be present to distort data

PBU- semi-log analysis

pws vs Horner Time Ratio

time is transformed as (tp + Δt)/ Δt

wellbore & boundary effects may be present to distort data

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Cartesian (useful- Early time and Late time)Log-log – Type curves (very useful)Semi log –Plot (very useful- if MTR straight line can be located)Semi-log plot may vary depending on the test type, as illustrated below:

Pwf

t100

101

102

103

104

105

Pw

f1Pw

f2

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PDD Test Example

Estimate formation permeability, skin factor and the reservoir pore

volume in the drainage area from the drawdown test data given

the following formation and fluid properties:

q = 90 STB/D

Pi = 2140 psia

h = 5 ft

= 21.7 %

rw = 0.49 ft

B = 1.091 RB/STB

ct = 7.8 x 10-6 psi-1

= 2.44 cp

PDD Test Example

Drawdown Test Data:

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Time

(minutes)

Pressure

(psi)

Time

(minutes)

Pressure

(psi)

15 538.8 195 411.6

30 499.2 210 408.3

45 479.1 225 405.2

60 465.4 240 402.4

75 455.0 255 399.7

90 446.6 270 397.1

105 439.6 285 394.7

120 433.5 300 392.4

135 428.1 315 390.3

150 423.4 330 388.2

165 419.1 345 386.2

180 415.2 360 384.3

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PDD Test Example

Time must be in hours.

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Time (minutes) Time

(hours)

Pressure

(psi)

Time (minutes) Time

(hours)

Pressure

(psi)

15 0.25 538.8 195 3.25 411.630 0.50 499.2 210 3.50 408.345 0.75 479.1 225 3.75 405.260 1.00 465.4 240 4.00 402.475 1.25 455.0 255 4.25 399.790 1.50 446.6 270 4.50 397.1

105 1.75 439.6 285 4.75 394.7120 2.00 433.5 300 5.00 392.4135 2.25 428.1 315 5.25 390.3150 2.50 423.4 330 5.50 388.2165 2.75 419.1 345 5.75 386.2180 3.00 415.2 360 6.00 384.3

350

400

450

500

530

10-1 100 101 102 103

t

Pwf,

psi

PDD Test Example- Semi-log Plot

cyclepsim /100462362

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462

362

4621 hrP

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PDD Test Example

mh

qBk

6.162

19

1005

44.2091.1906.162k

mdk 9.77

Formation permeability:

cyclepsim /100462362

from the semi-log plot, we got

putting in the equation

PDD Test Example

23.3

49.0108.744.2217.0

9.77log

100

4622140151.1

26xs

20

23.3log151.1

2

1

wt

hri

rc

k

m

PPs

4621 hrP

94.13s

Skin factor:

from the semi-log plot, we got

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PDD Test Example21

350.0

370.0

390.0

410.0

430.0

450.0

470.0

490.0

510.0

530.0

550.0

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

= - 12

x1 = 5y1 = 394

x2 = 6y2 = 382

m = -12

dt

dPwf

dt

dPc

qBV

wf

t

p

234.0

Vp = 0.234 X 90 X 1.091/(7.8X10-6X12) = 245,475 cu.ft.

Common Mistakes Incorrect Reading of plot

slope

p1hr

pi, pwf

Units

log term calculation

Scaling of the plot- choose scale such that paper usage is maximum, and covers the entire data range

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dt

dPwf

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Lecture Summary Remember the axes of the plots- what goes along which axis

for semi log plot, we have pwf along Y-axis (Cartesian), and t along X-axis (log)

Semi log plot is most useful for interpretation of PDD

Cartesian plot is also used for PDD, to obtain Reservoir Pore Volume. Only late time data is used for this purpose, assuming Pseudo-Steady Stae is reached

Not all data will fall on the straight line

MTR straight line is most important- but locating it is a challenge

plots must be nice, clean, and informative

Be careful about the common mistakes

practice, practice, practice

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Lecture Outline Discussions on WBS

Estimating WBS & twbs

Application of various plots

Lecture Outcomes: Students should be able to

Apply graphical techniques and equations in a comprehensive manner for PDD test interpretation:

locate the correct data set appropriate for analysis

estimate Cs & twbs

evaluate k, s, Vp

Comment and discuss on the relative merits/applicability of the techniques

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Estimating Wellbore Storage

During a pressure transient test (such as PBU, PDD etc) the early data usually gets distorted by Near Wellbore Effects

Skin, Wellbore Storage, Fractures

Quantifying skin from test data was covered before

Need to address Wellbore Storage

Define the term Cs = Wellbore storage coefficient

Cs is defined as : bbl/psi

Awb = cross sectional area of wellbore, ft2

ρ = density of the fluid in wellbore, lb/ft3

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Estimating Wellbore Storage

Once s and Cs are estimated, the end of WBS can be estimated from the equation:

Thus, the 2 contributors to the early time data distortion are quantified

Graphical Technique for Cs

early time data is plotted on CARTESIAN graph paper

slope is obtained in terms of psi/hr

using the formula:

twbs can be estimated from the equation, using this value of Cs

Finally- twbs is verified from the log-log & semi-log plots

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PDD Analysis- Application of Different Plots27

2500

3000

3500

4000

4500

5000

5500

6000

6500

0.01 0.1 1 10 100

100

1000

10000

0.01 0.1 1 10 100

q = 2500 STB/Dpi = 6009 psiρ = 55 lb/ft3Bo =1.21 RB/STBµ = 0.92 CPct = 8.72E-06 /psirw = 0.401 ftØ = 0.21h = 23 ft

From log-log & Semi-log plotsend of wbs ≈ 2.5 hrs

From Semi-log plotm = 250 psi/cycle

k = 78.7 mDs = +6.7

Estimating Cs, twbs & Vp28

y = -8238x + 6006.8

R² = 0.9988

5700

5750

5800

5850

5900

5950

6000

6050

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

2900

3000

3100

3200

3300

3400

3500

0 5 10 15 20 25

From Early Time Cartesian Plot:mwbs = 8238 psi/hrCs = 0.0153 RB/psikh/µ = 1967.46 (previous results)twbs = 2.2 hrs (close to log-log & semi-log estimates)

if we use Cs from formula:Awb = 0.5054 ft2

Cs = 0.2446 RB/psitwbs = 34.8 hrs (NOT close!)

From Late-Time Cartesian Plotdp/dt = -6 psi/hrVp = 1.35E+07 ft3 = 2.41E+06 Bbl