pbu practice
TRANSCRIPT
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Pressure Buildup Test Interpretation
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Lecture Outline
• Brief overview of PBU • Test Procedure
• Interpretation • Equations
• Plots
• Ideal versus Actual Test• Near Wellbore Effects- Early time
• “True Reservoir Signal”- Middle time
• Outer boundary Effects – Late time
• Exercise Problems
• More Discussion on tp and Average Reservoir Pressure
• Good practices for plotting
• Common mistakes
• Lecture Summary
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Lecture Outcomes
• At the end of this class, a student should be able to:• Describe how a pressure build up test is conducted
• Synthesize the various data and information to interpret a pressure build up test
• Isolate the correct data for interpretation
• Draw conclusions from test results
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Pressure Build Up Test
Test Procedure
• producing a well at constant rate for some time
• then shutting the well in (usually at the surface), allowing the pressure to build up in the wellbore
• and recording the pressure (usually down hole) in the wellbore as a function of time
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Pressure Build Up Test
Information gathered/required
• Pressure versus time recording
• Flow rate prior to shut in (q)
• Fluid properties- B, µ
• Formation and well parameters –Ø, ct, h, rw
Test interpretation results
From these data, it is frequently possible to estimate
1. formation permeability (k)
2. current drainage-area pressure (pavg)
3. wellbore condition - damage or stimulation- skin (s)
4. Reservoir heterogeneities or boundaries (distance to a sealing fault/barrier)
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PBU: Mathematical Modeling
Assumptions
1. a well is producing from an infinite-acting reservoir (one in which no boundary effects are felt during the entire flow and later shut-in period).
2. The formation and fluids have uniform properties, so that the Ei function (and, thus, its logarithmic approximation) applies, and
3. That Horner's pseudo-producing time approximation is applicable.
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PBU: Mathematical Modeling
pws = pressure at the wellbore any time after shut in
pi = initial pressure
tp = producing time (or pseudo-producing time, or Horner approximation time) before shut in
Δt = elapsed time after shut in
this equation is the main mathematical model for the PBU
Equation of a straight line on semi-log paper, with slope
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PBU Interpretation: Equations
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skin
pressure drop due to skin
flow efficiency
radius of investigation
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PBU Interpretation: PlotsMain plot types
• Cartesian (not very useful)
• Semi log – Horner Plot (very useful)
• Log-log – Type curves (very useful)
The model equation suggest that plotting of shut in bottom hole pressure (Pws ) against {(tp+∆t)/∆t}, yields a straight Line with slope of
m= -162.6 qBµ/ kh
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PBU Interpretation: Semi-log (Horner) plot
• k can be obtained from the slope of the straight line
• The straight line can be extrapolated to {(tp+∆t)/∆t}=1, to get the value of original formation pressure (pi )
• when {(tp+∆t)/∆t}=1, represents infinite shut in time
• pressure at this point (pi) is also called p*, extrapolated pressure, or infinite shut in time pressure
• p* can be equal to average reservoir pressure (for new/less depleted reservoirs)
• plot on semi-logarithmic paper with values of {(tp+∆t)/∆t} decreasing from left to right.
• The slope (m) is found by simply subtracting the pressures at any two points on the straight line that are one cycle apart on the semi-log paper
• The absolute value of slope must be used in equations
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PBU Interpretation: Semi-log (Horner) plot
Locating the straight line is a challenge
1- an early-time region during which a pressure transient is moving through the formation nearest the wellbore;
2- a middle-time region during which the pressure transient has moved away from the wellbore and into the bulk formation
3- late-time region, in which the radius of investigation has reached the well's drainage boundaries.
• We are interested in the middle time region
• It corresponds to the “true reservoir signal”
• It shows the correct straight line
• Rest of the data are “distorted” by wellbore and boundary effects, cannot be used in semi-log analysis 11
PBU Interpretation: Example Semi-log (Horner) plot with Wellbore & Boundary Effects
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PBU Interpretation: Example log-log plot with Wellbore & Boundary Effects
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PBU Interpretation: Example log-log plot with Wellbore & Boundary Effects
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100
1,000
0.1 1 10 100
pw
s -
pw
f
DT or Dte
Unit slope line = wbs
Approx. 1 ½ cycle
End of WBS
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PBU: Estimating end of Wellbore Storage
relationships below to verify the time, tWbs , marking the
end of wellbore storage distortion.
twbs estimated from both techniques (from graph & from correlation) should be compared
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Average Drainage Area Pressure
• MBH method
• Modified Muskat Method
• Both are applicable for a well in a reservoir with significant depletion
• MBH Involves reading p* from Horner Plot, and modifying it to obtain the AVERAGE pressure in the drainage-area
Horner Time Ratio=1
p* p
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Average Drainage Area Pressure: MBH Method
• Calculate dimensionless time with respect to drainage area
• Select appropriate MBH chart ("shape")
• Read pMBHD at tAD from chart
• Calculate average pressure from:
Ac
ktt
t
AD
0002637.0
303.2* MBHDp
mpp
Average Drainage Area Pressure: MBH Method
Steps to use MBH method:
1- Read the value of p * from the extrapolation of Middle time straight line.
2-Estimate the drainage area shape.
3- Choose the proper curve (just like the one in below) for the drainage-area shape of the tested well.
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MBH example (Lee 2.2)
• Calculate dimensionless time with respect to drainage area
• Select appropriate MBH chart ("square")
• Read pMBHD at tAD from chart: 5.45
• Calculate average pressure from:
4.7)560,43160)(1017)(8.0)(039.0(
)630,13)(7.7(0002637.06
ADt
psia 411,4303.2
45.5)70(577,4 p
Distance to Fault
• Well in an "infinite acting" reservoir, located near to a no-flow boundary (fault)
L L
well image well
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Estimating distance to a fault from Horner plot
Log of Horner Time Ratio
pws
intersection
m
2m
t
tt p
Example: Distance to Fault
• Assume that h= 50 ft
• production time before a build-up test was 500 hr,
• production rate 250 stb/d,
• ( B )=1 (cp resb/stb)
• ( ct )= 1x10-6 (cp / psi)
• There are two straight lines on the Horner plot, one
with m=11 psi/cycle the other with 22 psi/cycle
• They intersect at Horner-time ratio 251
• Question: what is the distance to the fault?
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Solution: Distance to Fault
• Estimate permeability from the first straight line (m =11 psi/cycle)
• Estimate tx from the Value of Horner time ratio at intersection
• Estimate L from formula
mh
qBk
)(6.162
2/1
000148.0
t
x
c
tkL
More on tp
• If q is constant prior to shut in, tp is simply the producing time
• If q is not constant, tp = Cumulative production/last rate
• Be careful about units
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0
200
400
600
800
1000
1200
0 50 100 150 200 250
q, S
TB/D
t, hr
t ,hr rate (STB/D) Qp (STB)
10 1000 417
10 650 271
48 400 800
Total prod = 1488
tp = 89.25
0
50
100
150
200
250
300
350
400
450
0 50 100 150 200 250
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25
2500
3000
3500
4000
4500
1.0010.00
pw
s, p
sia
(tp + Dt)/Dt
Horner Plot for Semi-log Analysis of PBU
p1hr = 3100 psia
slope, m = 4460 - 3260 = 1200 psi/cycle
p* = pi = 4460
k = 19.12 mds = - 2.9
Common Mistakes• Incorrect Reading of plot
• p*, slope
• p1hr
• pwf
• tp
• Units
• log term calculation
• using skin in the equation (superposition problems)
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Lecture Summary
• Remember the axes of the plots- what goes along which axis
• for semi lof plot, pws along Y-axis (Cartesian), tp+Dt/DT along X-axis (log)
• for log-log plot, (pws-pwf) along Y-axis, DT or Dte along X-axis
• Semi log plot is most useful for interpretation of PBU
• Not all data will fall on the straight line
• MTR straight line is most important- but locating it is a challenge
• log-log plot is useful for identifying end of wbs
• plots must be nice, clean, and informative
• Be careful about the common mistakes
• practice, practice, practice
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