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Pressure Drawdown Draw down Test Test
Lecture Outline
Brief overview of PDD
Test Procedure
Test Types
Information obtained
Mathematical Model
Interpretation
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Semi-log analysis
Cartesian and log-log analysis
Ideal versus Actual Test
ETR, MTR & LTR
Practice Problems
Common mistak m istakes es
Summary
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Lecture Outcomes 3
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
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
q , e t a R
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drawdown
P , e r u s s e r P
Time, t
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Types of Flow Tests 5
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)
q6
q2
, e t a R q
qn
q4 q1
qn-1
q3 q5 t1
t2
t3
t4
t5
time
Test Outcomes
tn-1
6
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 7
The basis for flow-test analysis techniques is the line source solution to the diffusivity equation:
P i P wf
P wf P i
70.6qB
1,688 ct r w2 ln kt
kh
70.6qB kh
1,688 ct r w2 ln 2 s kt
If natural logarithm is changed to base-10 logarithm and rearranged
P wf P i
162.6qB kh
3 . 23 0 . 869 s 2 ct r w
logt log
k
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Mathematical Model P wf P i
k 162.6 qB 3.23 0.869 s log t log 2 kh ct r w
this equation is the main mathematical model for the PBU 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 This equation is similar to
Y B m log X
and suggest a semi-log plot of P wf vs log t
with a slope of
162.6
should be a straight line
qB kh
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Semi-log Plot 9
One log cycle
Pwf Pwf1 Pwf2 Slope = Pwf2 – Pwf1
100
101
102
103
104
105
t
Analysis Method (Estimate k, s) 10
Draw the best fit straight line through the MTR data points Obtain the slope of the straight line slope m 162.6
qB kh
The absolute value of the slope is used to estimate the effective permeability to the fluid flowing in the drainage area of the well k 162.6
qB mh
And the skin factor is (absolute value of m must be used here as well)
P i P 1hr
s 1.151
m
k log 3 . 23 2 ct r w
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Analysis Method (Estimate Pore Volume) Here we use a Cartesian Plot- Pseudo-Steady State MUST be reached For a well centered in a cylindrical drainage area the pore volume of the drainage area can be estimated by: V p
0.234qB dP wf ct dt
where
dP wf dt
is the slope of the straight line of the Cartesian plot of Pwf versus t
slope=dPwf /d t i s p , f
w
P
t, hours 11
Actual Drawdown Data 12 Because 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.
Pwf
Early Time Region (ETR)
100
Middle Time Region (MTR)
101
Late Time Region (LTR)
102
103 t
104
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PBU versus PDD
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PBU
PDD
Pressure-Time data when the well is producing
Pressure-Time data when the well is shut in
Involves 1 rate only (ideal)
Difficult to maintain constant flow rate
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
No revenue loss due to shut in
PBU versus PDD
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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: PDD- semi-log analysis pwf vs t no transformation of t wellbore & boundary effects may be present to distort data
P
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
Pw f1 Pw
wf
f2
10 0
10 1
10 2
10
t
3
10 4
10 5
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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 Pi h r w B ct
= 90 STB/D = 2140 psia = 5 ft = 21.7 % = 0.49 ft = 1.091 RB/STB = 7.8 x 10-6 psi-1 = 2.44 cp
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PDD Test Example Drawdown Test Data: Time (minutes)
Pressure (psi)
Time (minutes)
Pressure (psi)
15 30 45 60 75 90 105 120 135 150 165 180
538.8 499.2 479.1 465.4 455.0 446.6 439.6 433.5 428.1 423.4 419.1 415.2
195 210 225 240 255 270 285 300 315 330 345 360
411.6 408.3 405.2 402.4 399.7 397.1 394.7 392.4 390.3 388.2 386.2 384.3
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PDD Test Example Time must be in hours.
Time (minutes)
Time (hours)
Pressure (psi)
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0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00
538.8 499.2 479.1 465.4 455.0 446.6 439.6 433.5 428.1 423.4 419.1 415.2
30 45 60 75 90 105 120 135 150 165 180
Time (minutes)
195 210 225 240 255 270 285 300 315 330 345 360
Time (hours)
Pressure (psi)
3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00
411.6 408.3 405.2 402.4 399.7 397.1 394.7 392.4 390.3 388.2 386.2 384.3
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PDD Test Example- Semi-log Plot 530
500
462
m 362 462 100 psi / cycle
450
Pwf, psi
P 1hr 462
400
362 350 10-1
100
101
t
102
103
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PDD Test Example Formation permeability:
k 162.6
qB mh
from the semi-log plot, we got
m 362 462 100 psi / cycle
putting in the equation
k 162.6
901.0912.44 5100
k 77.9md
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PDD Test Example Skin factor: s
P P 1hr k 1.151 i log 3 . 23 c r 2 m t w
from the semi-log plot, we got
s
P 1hr 462
2140 462 77.9 3 . 23 1.151 log 2 6 0 . 217 2 . 44 7 . 8 10 0 . 49 100 x
s 13.94
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PDD Test Example V p
550.0 530.0 510.0
x1 =
5y1 = 394
490.0
x2 =
6 y2 = 382
470.0
m=
0.234qB dP wf ct dt
-12
450.0 430.0 410.0
dP wf dt
390.0 370.0 350.0 0.00
1.00
= -12
2.00
3.00
4.00
5.00
6.00
7.00
Vp = 0.234 X 90 X 1.091/(7.8X10-6X12) = 245,475 cu.ft.
Common Mistakes
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Incorrect Reading of plot
slope
p1hr
dP wf dt
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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Lecture Summary
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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
Lecture Outline
Discussions on WBS
Estimating WBS & twbs
Application of various plots
Lecture Outcomes: Students should be able to
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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
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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 :
Awb = cross sectional area of wellbore, ft 2
ρ = density of the fluid in wellbore, lb/ft3
bbl/psi
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 Plots
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q = 2500 STB/D pi = 6009 psi ρ = 55 lb/ft3 Bo =1.21 RB/STB µ = 0.92 CP ct = 8.72E-06 /psi rw = 0.401 ft Ø = 0.21 h = 23 ft
6500 6000 5500 5000 4500 4000 3500 3000 2500 0.01
0.1
1
10
100
10000
From log-log & Semi-log plots end of wbs ≈ 2.5 hrs From Semi-log plot m = 250 psi/cycle
1000
k = 78.7 mD s = +6.7 100 0.01
0.1
1
10
100
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Estimating Cs, twbs & Vp 6050
y = -8238x + 6006.8 R² = 0.9988
6000 5950 5900 5850 5800 5750 5700 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
From Early Time Cartesian Plot: mwbs = 8238 psi/hr Cs = 0.0153 RB/psi kh/µ = 1967.46 (previous results) twbs = 2.2 hrs (close to log-log & semi-log estimates)
3500
if we use Cs from formula: Awb = 0.5054 ft2 Cs = 0.2446 RB/psi twbs = 34.8 hrs (NOT close!)
3400 3300 3200 3100 3000 2900 0
5
10
15
20
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From Late-Time Cartesian Plot dp/dt = -6 psi/hr Vp = 1.35E+07 ft3 = 2.41E+06 Bbl
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