pcb3013 hw#6 solutions

8/13/2019 PCB3013 HW#6 Solutions

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PCB3013-Well Test Analysis

HW# 6

Prof. Dr. Mustafa Onur, UTP, September 2013

SOLUTIONS

Given Date: November 14, 2013Due Data: November 21, 2013

Subject: Analysis of a buildup test with wellbore storage and skin and boundary effects byusing log-log, Horner and MBH Analyses.

The data provided in Tables 1 and 2 are pertinent to a buildup test conducted in an oil

well producing at the center of a closed square reservoir. The length and width of the

reservoir is 500x500 ft.

(a) (30 marks)Make a log-log plot of buildup pressure change p and its derivativevs. shut-in time. Then identify the flow regimes exhibited by the data and theirtime intervals on the log-log diagnostic plot.

(b)(30 marks) Perform Horner analysis of buildup pressure data and determinepermeability and skin. You should state how you chose the time intervals to draw

your Horner semilog straight line.

(c) (40 marks)Compute the average reservoir pressure combining Horner analysisby MBH analysis (MBH Chart for the well/reservoir configuration is given in

Appendix I).

Table 1. Reservoir, Well and Fluid Data for the buildup test.

Reservoir thickness, h, 25 ft

Well radius, rw, 0.35 ft

viscosity, , 1.0 cp

Formation volume factor,Bo, 1.1 RB/STBFlow rate prior to buildup, q, 2000 STB/D

Total compressibility, ct, 1.0x10-4

1/psi

Porosity, , 0.25

Flowing pressure at the instant of shut-in, pwf,s............................2765 psi

Initial pressure, pi......................................................................5000 psiWell/Reservoir geometry: Well producing at the center of a closed square

reservoir.


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Table 2.

Shut-in time

t, hours.

0.0

0.4

0.8

1.5

2.0

3.60

4.30

6.10

8.1

11.4

17.2

21.125.4

30.0

Buildup pressure and derivative data.

orner Time

ratio RH

Buildup

pressure,

pws, psi

Delta pressure

change, p=pws-

pwf,spsi

Press

deriv

ps

2765.0 0.0 -

76.0 4185.2 1402.2 446

38.5 4470.3 1705.3 349

21.0 4611.4 1864.4 147

16.0 4655.3 1890.3 110

9.33 4730.8 1965.8 125

7.98 4751.0 1986.0 120

5.92 4788.1 2023.1 119

4.7 4815.0 2050.0 116

3.63 4844.8 2079.8 109

2.75 4873.4 2108.4 94.

2.42 4885.0 2120.0 82.2.18 4893.7 2128.7 71.

2.00 4899.3 2134.3 81.

APPENDIX I MBH CHART

ure-

tive

i

.3

.1

.0

.3

.2

.1

.9

.1

.4

5

70

3


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(a) Log-Log is shown in Fig. 1 with the flow regimes labeled on it.

Figure 1.a. Log-log diagnostic plot.

There is no unit slope line, but we have wellbore storage and skin effects in the time

interval from 0.4 to 2 hr. In the time interval from 3 to 10 hr we infinite-acting radial

flow. After 10 hr, we see the effect of no-flow (closed) boundaries on the buildup

response.

(b)Figure 1b shows the Horner graph. Horner straight line should be drawn in the time

interval from 3 to 10 hours in terms of shut-in time (or 3.6. to 9.33 in terms of Horner

time ratio) as determined from log-log diagnostic plot shown in Fig. 1.a. From the

slope of the Horner semi-log straight line, we can estimate khor kas

162.6_ sc

q Bm slope

kh

= (Sb.1)

162.6

_

scq B

khm slope

= (Sb.2)

162.6 2000 1.1 1.01219

127.4 2.303kh md ft

= =

(Sb.3)

121949

25

khk md

h= = (Sb.4)

0.1 1 10 100Shut-in time, hour

10

100

1000

10000

Buildup

pressure

change

and

derivative,ps

i

Buildup pressure change

Derivative

Wellbore storage and positive skineffects, but no data on unit slope line

Radial flow period(Horner analysis can be applied)

Boundary

(no-flow)effects


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Skin factor S is determined from (Note that p1hr= -127.4*ln(31)+5012.6 =

4575 psi)

1 ,

2

4 2

1.151 log 3.23_

4575. 2765 12191.151 log 3.23293 0.25 1 10 25 0.35 1

2.5

hr wf s

t w

p p khS

m slope c h r

= +

= +

=

1 10 100Horner Time Ratio

4100

4200

4300

4400

4500

4600

4700

4800

4900

5000

5100

Buildup

pressure

and

derivative,psi

Fit Results

Fit 1: LogEquation Y = -127.4210585 * ln(X) + 5012.593001Number of data points used = 6Coef of determination, R-squared = 0.997807

Figure 1.b Horner plot.

(c) We can perform MBH analysis based on MBH charts in combination with Horner

analysis to estimate the average pressure in the reservoir. To use MBH charts, we

first need to compute the dimensionless producing time based on the drainage area

given as follows:


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4 4

4

2.637 10 2.637 10 49 300.06

0.25 1 10 1 500 500

p

pDA

t

ktt

c A

= = =

(Sc.1)

Because it is known that the well is producing at the center of closed square, then

using the appropriate MBH curve for this geometry and using the dimensionless

producing time, we can determine the value of the dimensionless MBH pressure, asshown in Fig. 1.c.Note that pDMBH =0.8. Using this value and the value of Horner

false pressure determined from Horner plot, p* = 5012.6 psi, we can compute the

value of average pressure as follows:

70.6 70.6 2000 1.1 1 0.8* 5012.6 4911

1219

o DMBH qB p

p p psikh

= =

pcb3013 hw#6 solutions

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