pcb3013 hw#5 solution

8/13/2019 PCB3013 HW#5 Solution

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PCB3013-Well Test Analysis

HW# 5

Prof. Dr. Mustafa Onur, UTP, September 2013

SOLUTIONS

Given Date: October 29, 2013Due Data: November 07, 2013

Subject: Analysis of a buildup test with wellbore storage and skin effects by using type-curve

matching and semi-log techniques.

Table 1 gives reservoir/well/fluid data for a vertical well known to be producing at the center

of a closed reservoir. Table 2 presents the pressure data obtained from a buildup testconducted in that well.

(a) (10 pts)Estimate producing time using total production and rate prior to shut-in.

(b) (20 pts)Make a log-log diagnostic plot of delta shut-in pressure change and its derivative

versus elapsed time, and identify flow regimes exhibited by the buildup data and their timeintervals. Also calculate wellbore storage coefficient from unit-slope line if it exists and kh

from radial flow derivative (i.e., from zero-slope line) if it exists.

(c) (30 pts) Perform Horner Analysis to determine permeability, skin, and initial staticpressure. Note that to determine which time interval you will fit your radial flow straight lineon Horner graph, you should look at log-log diagnostic plots of delta pressure and its

derivative.

(d) (40 pts) Analyze the same data using type curve matching to estimate k, s, wellborestorage coefficient. Please tabulate your results for comparison.

Table 1. Reservoir/well/fluid property data.

Reservoir Thickness, h, 30 ft

Well radius, rw,, 0.3 ft

Viscosity, , 1.0 cp

Formation Volume Factor,Bo, 1.0 RB/STB

Porosity 0.1Total compressibility, ct 1x10

-51/psi

Flow rate before shut-in 300 STB/D

Total production prior to shut-in 150000 STB


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Table 2. Buildup Test Pressure Data

Shut-in Time

t, h.

Shut-in

Pressures

pws, psi

Delta Pressure

p=pwf,s-pws

psi

Delta

pressure-

derivative

(based on

Equivalent

time)psi

0.0 3961.98 0.0 -

0.01 3965.16 2.40 2.27

0.06 3977.23 15.25 15.84

0.14 3997.14 35.16 33.79

0.2 4011.03 49.05 48.55

0.32 4037.89 75.91 74.83

0.57 4091.54 129.56 113.62

1.01 4175.46 213.48 174.77

1.43 4244.22 282.24 222.47

2.01 4326.49 364.51 253.54

4.02 4515.62 553.64 271.05

6.37 4631.6 669.62 217.87

8.02 4678.39 716.41 182.83

10.1 4715.24 753.26 142.92

12.71 4743.4 781.42 105.56

16 4764.25 802.27 77.89

20.15 4780.28 818.3 58.99

25.37 4792 830.02 46.92

31.93 4801.62 839.64 39.37

35.83 4806.51 844.53 39.64

40.2 4810.72 848.74 36.25

50.61 4819.51 857.53 36.63

56.79 4823.23 861.25 35.65

71.49 4831.93 869.95 33.68

80.21 4835.39 873.41 34.1

127.13 4851.33 889.35 33.45

a-) The total production is given as 150000STB and the flow rate prior to shut in is

given as 300STB/D. From the above we can approximate the production time as:

Total Production 150000500 12000

300p p pt t Days t hrs

q= = = =

b-) The log-log plot is given below:


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It is clear from the points that fall on the unit slope line that a wellbore storage

dominated flow period exists. Using the point at t=0.14 hrs.

05.016.3524

14.01300

24=

=

=

p

tBqC osc bbl/psi

From the radial flow period we have:

70.6 70.6

ln

ln

sc o sc od p q B q Bkhd pd t kh

d t

= =

If we use the point at t=71.49 hrs. Then we have:

9.62868.33

10.13006.70

ln/

6.70=

=

=

tdpd

Bqkh osc

md-ft

c-) Since we have taken tpas 12000hrs, we can say tp>>t. The horner plot of the data

is given below:

0.01 0.1 1 10 100 1000t, hrs

1

10

100

1000

pwf,s

-pws,psi

Unit slope line

Flat line


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The equation for the semi-log straight line of the Horner plot is given as follows:

81.7log 5013.48pt t

pt

+ = +

Hence from the slope of the semilog straightline we can estimate the kh product:

1.5977.81

10.13006.162ln/

6.162 ==

=tdpd

Bqkh osc md-ft

From the semilog equation we can compute the pressure at t =1hr.

( )12000 1

( 1) 81.7log 5013.48 1 4680.21

p t p t psi+

= = + = =

We can solve for skin using the below equation

23.4

23.33.011011.0

9.19log

7.81

98.39612.4680151.1

23.3log151.1

25

2

,1

=

+

=

+

=

s

s

rc

k

m

pps

wt

swfhr

Estimate of initial static pressure can be found from extrapolation of the straight line

to Horner ratio of 1 aspi= 5013 psia.

1 10 100 1000 10000 100000 1000000 10000000

(tp+t)/t

3800

4000

4200

4400

4600

4800

5000

Shutin

pressure,psi

p=-81.7log((tp+t)/t)+5013.48


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d-) Data have been analyzed using type curve matching. The following values of kh,

C and S are obtained.

kh, md-ft 661

s 5.55

C, bbl/psi 0.0495

All values determined from all analysis methods are given below:

Unit Slope line

and log-log

derivative plot,

part-b

Horner part-c Type-Curve Matching

kh, md-ft 628.9 597.1 661

S 4.23 5.55

C, bbl/psi 0.05 0.0495

pi, psi 5013 -

pcb3013 hw#5 solution

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