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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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