PETE 324

Lecture 21

Rosalind Archer

21.2 Analysis of Drawdown Tests

• Infinite-acting radial flow in a homogenous reservoir is governed by:

• This is of the form:

s8686.022.3

rc

ktlog

kh

qB6.162pp

2wt

iwf

)tlog(mpp hr1wf

21.3 Analysis of Drawdown Tests

• This implies the pressure data should form a straight line on a semilog plot.

s8686.022.3rc

klogmpp

kh

qB6.162m

:where

2wt

ihr1

21.4 Analysis of Drawdown Tests

• Analysis procedure– Plot all data!– Fit a straight line to the data, remembering this

solution does not account for radial flow which may distort the early time data. If the pressure derivative is also plotted it should be at a constant level during infinite-acting radial flow (m=2.303p’)

– Use the slope of the semilog straight line (m) to determine permeability (k)

– Use the value of p(1hr) [read from the semilog straight line] to determine skin (s).

21.5 Analysis of Drawdown Tests• If the data departs from the semilog straight line in late

time in indicates the presence of boundaries:

21.6 Analysis of Drawdown Tests

• Time can be related to radial distance in a well test via the concept of the radius of investigation:

• This can be used to estimate the distance to the reservoir boundary based on the time at which the pressure data departs from the semilog straight line.

t

2inv c

kt10434.2r

21.7 Analysis of Buildup Tests

• Pressure buildup tests involve recording pressure data while a well is shut in after a period of flow.

21.8 Analysis of Buildup Tests

• The pressure response for a buildup can be constructed by using superposition and the drawdown solution.– An fake injection well (located at the same

location as the production well) is turned on at t = tp. It’s rate is -q.

s8686.022.3rc

klog

ttlog)tlog(

kh

qB6.162)0t(pp

2wt

ppwfws

t

21.9 Analysis of Buildup Tests

• This implies a plot of pws versus (tp+t)/t should be a straight line. (Horner plot)

21.10 Analysis of Buildup Tests

• Analysis procedure– Plot all data (p versus (tp+t)/t)– Fit straight line to middle time region (early

time is distorted by wellbore storage).– Find slope (m) and extrapolation of straight line

to pws(1hr)k

22.3rc

klog

1t

tlog

m

)0t(p)hr1(p151.1s

mh

qB6.162k

2wtp

pwfws

21.11 Analysis of Buildup Tests

• Average reservoir pressure is estimated using p* (extrapolated from the straight line on the Horner plot) using the Matthew-Brons-Hazebrok (MBH) technique (not covered).

• Remember t =t-tp i.e. time since the well was shut-in.

21.12 Analysis of Buildup Tests

• In practice the production time (tp) may be unknown. Rather than assuming a value for tp it is ignored. This is strictly valid if the reservoir has been produced to pseudosteady state conditions.

• Miller-Dyes-Hutchinson (MDH) analyzed this situation.

21.13 Analysis of Buildup Tests

s8686.022.3rc

klog

tlogkh

qB6.162)0t(pp

2wt

wfws

21.14 Analysis of Buildup Tests

22.3rc

klog

m

)0t(p)hr1(p151.1s

mh

qB6.162k

2wt

wfws

21.15 Variable-Rate Tests

• The pressure response of a test with a sequence of variable flow rates can also be constructed using superposition.

s8686.022.3rc

klog

kh

Bq6.162

)ttlog()qq(kh

6.162pp

2wt

n

n

1j1j1jjwfi

21.16 Variable-Rate Tests

• It is convenient to normalise both sides of this equation by the current flowrate:

s8686.022.3rc

klog

kh

B6.162

)ttlog(q

)qq(

kh6.162

q

pp

2wt

n

1j1j

n

1jj

n

wfi

21.17 Variable-Rate Tests

• This equation is a straight line (Odeh-Jones plot):

s8686.022.3rc

klogmb

kh

B6.162m

q

)pp(y

)ttlog(q

)qq(x

:where

bmxy

2wt

n

wfi

j

n

1j n

1jj

21.18 Wellbore Storage

• Definition of wellbore storage coefficient:– Fluid filled wellbore

– Rising or falling liquid level

wbwbs VcC

)g/g(

A

615.5

144C

c

wbs

21.19 Wellbore Storage

• During wellbore storage dominated flow the following pressure-time relationships hold:

– Drawdown

– Buildup

tC24

qBpp

siwf

tC24

qB)0t(pp

swfws

21.20 Wellbore Storage

• Dimensionless wellbore storage coefficient

2wt

D hrc2

C615.5C

21.21 Type Curve: Pressure

21.22 Type Curve: Press. Derivative

21.23 Last Words

• Be consistent!– whatever is characterized as wellbore storage,

radial flow etc on one plot e.g. Cartesian must be consistent with the presentation of the data on all other plots e.g. semilog/Horner.