PCB3013 HW#7 Solutions

8/13/2019 PCB3013 HW#7 Solutions

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Tablo 2. RLT Pressure and Pressure-Derivative Data

Time, hour Delta pressure,

p, psi

Pressure-Derivative,

p, psi

1.00E-03 8.74E+00 7.71E+00

1.58E-03 1.29E+01 9.95E+00

2.00E-03 1.53E+01 1.15E+01

2.51E-03 1.82E+01 1.29E+01

3.16E-03 2.12E+01 1.43E+01

3.98E-03 2.48E+01 1.52E+01

5.01E-03 2.82E+01 1.56E+01

6.31E-03 3.20E+01 1.48E+01

7.94E-03 3.50E+01 1.43E+01

1.00E-02 3.86E+01 1.41E+01

1.26E-02 4.15E+01 1.29E+01

1.58E-02 4.45E+01 1.18E+01

2.00E-02 4.69E+01 9.26E+00

2.51E-02 4.88E+01 9.39E+00

3.16E-02 5.12E+01 5.22E+00

3.98E-02 5.12E+01 6.31E+00

5.01E-02 5.41E+01 8.69E+00

6.31E-02 5.52E+01 4.78E+00

7.94E-02 5.63E+01 5.64E+00

1.00E-01 5.78E+01 6.50E+00

1.26E-01 5.93E+01 5.00E+00

1.58E-01 6.01E+01 3.67E+00

2.00E-01 6.10E+01 7.25E+00

3.16E-01 6.36E+01 4.77E+00

3.98E-01 6.56E+01 5.42E+00

5.01E-01 6.61E+01 3.69E+00

6.31E-01 6.73E+01 3.25E+00

7.94E-01 6.76E+01 4.33E+00

1.00E+00 6.93E+01 7.58E+00

1.58E+00 7.28E+01 2.79E+00

2.51E+00 7.32E+01 5.44E+00

3.16E+00 7.48E+01 4.13E+00

3.98E+00 7.51E+01 7.17E+00

5.01E+00 7.81E+01 5.88E+00

6.31E+00 7.78E+01 6.11E+00

7.94E+00 8.09E+01 1.45E+01

1.00E+01 8.45E+01 1.39E+01

1.26E+01 8.73E+01 1.25E+01

1.58E+01 9.02E+01 1.84E+01

2.00E+01 9.59E+01 2.78E+01

2.51E+01 1.03E+02 3.30E+01

3.16E+01 1.11E+02 3.69E+01

3.98E+01 1.20E+02 4.56E+01

5.01E+01 1.32E+02 6.07E+01

6.31E+01 1.48E+02 7.60E+01

7.94E+01 1.67E+02 1.04E+02


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APPENDIX I

In Table C.1, CA represents the Dietz shape factor, the column with `Exact for tDA`

represents tDA,pss, and the last column `Use infinite system` represents tDA,esl. The

equations for tDA,pss and tDA,esl are given by

esl

t

eslDA thAc

kht

4

,

10637.2 = (I-1)

pss

t

pssDA thAc

kht

4

,

10637.2

= (I-2)


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SOLUTIONS

(a)Figure S.1 shows the log-log plot of the drawdown pressure change and its Bourdet

derivative data. As can be see from derivative data, there is a short period of unit-slope

indicating wellbore storage effect. We observe a hump in derivative data in the time

interval from 0.003 to 0.03 hr, possibly due to a positive skin factor. The wellbore

storage effect ends at about 0.003 hr. Although the derivative data are scattered due tonoise, an infinite acting-radial flow period can be identified as a zero-slope line in the

time interval from 0.03 to 6.0 hr. After about 6.5 hr, we observe a unit-slope line which

is indicative of the pseudo-steady state flow regime, when the no-flow boundaries of

the reservoir influence the well respons.

Figure S.1 Log-Log plot of pressure change and derivative

(b)Figure S.2 showns the semi-log plot based on p not pressure. The slope m is

calculated as:

( ) ( ) ( ) ( )./06.12

1.0log1log

48.5754.69

1log2log

12hrpsi

yy

yym =

=

= (1)

From this slope value, the permeability k is calculated as:

.9.8906.12*30

8.0*25.1*2006.1626.162 md

hm

qBk ===

(2)

1E-3 1E-2 1E-1 1E+0 1E+1 1E+2

Zaman, saat

1E+0

1E+1

1E+2

1E+3

De

lta-pveDelta-p'ninlogaritmikt

revi,psi

Delta-p

Delta-p'nin Trevi Birim Egimli Dogru(Kuyuici Depolanma Etkileri)

evrel Akis(Radyal Akis)

Birim Egimli Dogru(Dis Sinir Etkileri)

Unit-slope line (WBS)

Unit-slope line (PSS Flow)

IARF

Time, h


5/7

The skin is computed from the following equation:

52.023.3328.0*8.0*55.1*2.0

9.89

log06.12

54.69

151.1

23.3log151.1

2

2

1

=

+

=

+

=

e

rc

k

m

pS

wt

hr

(3)

As shown in Fig. S.2, the pressure change (p) data deviate from the semi-log line at about

6 hr so so tesl= 6 hr. Note that p1hr is equal to 4930.46 psi.

Figure S.2: Semi-log plot for IARF analysis.

(c)Figure S.3 shows a Cartesian plot of flowing bottom-hole pressure vs. time. As can be

seen, a well defined straight line with a slope equal to m*=1.202 psi/hr and a intercept

at t = 0 as p0hr= 4972.82 psi was fitted through the data after tpss= 6.5 hr. From the

slope, the pore volume is determined as:

3

5*6.3244014

202.1*105.1*24

25.1*200*615.5

24

615.5ft

mc

qBV

t

p =

==

(4)

The drainage area of the well can be computed as:

1E-3 1E-2 1E-1 1E+0 1E+1 1E+2

Zaman, saat

0.0

40.0

80.0

120.0

160.0

200.0

Delta-p,psi

Yapilan FitY=B*Ln(X)+AY = 5.24586 * Ln(X) + 69.5406

tesl=6 hr

Time, h


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2

5*4.540765

202.1*30*105.1*2.0

25.1*200*234.0234.0ft

hmc

qBA

t

=

==

(5)

(d)Using the equation given for the average pressure and evaluating it at the last test time

of t=79.4 hr

psie

tcV

qBt

Ahc

qBpp

tpt

i 456.954.7955.1*6.3244014

25.1*200*234.0234.0234.0=

===

(6)

psip 5.4904= olarak bulunur.

(e)The Dietz shape factor CAis computed as:

( )

( ) 07.3382.497246.493006.12303.2

exp202.1

06.12

456.5

303.2exp456.5 01*

=

=

=

hrhr

r

r

A pp

mm

mC

(7)

Figure S.3 Cartesian plot of pwf vs. time.

The values of tDA,eslve tDA,pss are computed from

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Zaman, saat

4800.0

4840.0

4880.0

4920.0

4960.0

5000.0

Kuyudibiakisba

sinci,psi

Linear, Y=B*X+ADenklem:Y = -1.20219 * X + 4927.82

pwf

Time, h


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1096.068.0*4.540765*30*105.1*2.0

30*9.89*10637.210637.25

44

, =

=

=

esl

t

eslDA thAc

kht

(8)

1187.05.68.0*4.540765*30*105.1*2.0

30*9.89*10637.210637.25

44

, =

=

=

pss

t

pssDA thAc

kht

(9)

Using these time values together with the value of CA=33.06, I determined a square or

hexagonal type reservoir with the well at the center could be plausible models for the test

data.

PCB3013 HW#7 Solutions

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