group 3 pbu in fractured reservoir

7/31/2019 Group 3 PBU in Fractured Reservoir

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PEER TEACHING (GROUP 3)

Outcome: Calculate the fracture and matrix properties (in BU test) using models and type curve

Problem 1

Analysis of a Buildup Test in a Naturally Fractured Reservoir with Pseudosteady-state Matrix FlowDetermine permeability, Skin factor, storativity ratio and interporosity flow coefficient,.

Given:

rw=0.3ft h=286ft A=43.0 acres

=0.0533 Sg=1.0 Bg=6.48012RB/Mscf

g=0.01118cp Ct=0.002658psia-1

pa wf(t=0)=36.67psia

tp = 19,836 hours

t

(hours)

te

(hours)

Horner

Time

Ratio

Pws

(psia)

Pa,ws

(psia)

pa

(psi)

te(dpa/dte),

psi

0.016998 0.007856 2525013 174.06 37.661 0.994 2.3237

0.034 0.015844 1251957 177.77 39.291 2.6241 3.2321

0.050999 0.023987 826947.9 181.26 40.854 4.1872 4.626

0.068001 0.032278 614536.2 184.62 42.382 5.7155 5.9853

0.084999 0.04071 487251.3 187.83 43.879 7.2125 7.2615

0.102 0.049278 402532.6 190.9 45.327 8.6606 8.3864

0.136 0.066799 296950.6 196.81 48.19 11.524 10.408

0.153 0.075745 261878.7 199.53 49.53 12.864 11.301

0.17 0.084804 233904.1 202.15 50.489 14.182 12.13

0.187 0.093973 211081.9 204.67 52.124 15.457 12.8260.204 0.10325 192116.2 207.09 53.371 16.704 13.545

0.221 0.11262 176132.1 209.41 54.575 17.908 14.266

0.238 0.12209 162470.3 211.64 55.749 19.082 14.888

0.255 0.13166 150660.8 213.77 56.882 20.215 15.402

0.272 0.14131 140372.2 215.83 57.986 21.319 15.834

0.289 0.15105 131320.8 217.79 59.052 22.385 16.132

0.323 0.17077 116156.2 221.69 61.19 24.523 16.678

0.34 0.18074 109748.8 223.41 62.147 25.48 16.875

0.357 0.19079 103967.7 225.06 63.064 26.397 17.031

0.374 0.20091 98730.77 226.63 63.953 27.286 17.104

0.391 0.21109 93.969.4 228.12 64.805 28.138 17.025

0.408 0.22134 89617.78 229.56 65.619 28.952 16.979

0.425 0.23164 85632.88 230.91 66.402 29.736 16.913

0.442 0.24199 81970.33 232.21 67.157 30.49 16.589

0.459 0.2524 78589.54 233.45 67.874 31.207 16.54

0.476 0.26286 75462.22 234.63 68.561 31.895 16.464

0.51 0.28393 69862.29 236.93 69.919 33.252 15.98

0.578 0.32657 60740.42 240.65 72.14 35.473 14.905

0.663 0.38063 52113.6 244.32 74.361 37.694 13.259

0.748 0.43536 45562.29 247.11 76.079 39.412 11.427


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0.85 0.50169 39538.36 249.52 77.573 40.906 9.5998

0.969 0.5797 34217.7 251.46 78.788 42.122 7.7489

1.088 0.65818 30137.65 252.76 79.609 42.942 6.2778

1.224 0.74826 26509.5 253.81 80.274 43.607 5.0686

1.377 0.84995 23337.84 254.62 80.787 44.121 4.1069

1.547 0.96323 20593.21 255.28 81.206 44.539 3.4501

1.751 1.0995 18040.93 255.89 81.599 44.932 2.9531

1.972 1.2474 15901.88 256.41 81.933 45.267 2.648

2.227 1.4184 13984.77 256.9 82.249 45.582 2.4722

2.499 1.601 12389.76 257.33 82.529 45.862 2.3507

2.805 1.8068 10978.53 257.74 82.793 46.126 2.2986

3.162 2.0473 9688.858 258.19 83.078 46.412 2.2832

3.553 2.3111 8582.926 258.61 83.347 46.681 2.327

3.995 2.6097 7600.874 259.04 83.63 46.963 2.4173

4.488 2.9433 6739.374 256.49 83.915 47.249 2.50825.049 3.3235 5968.407 259.97 84.228 47.561 2.6358

5.678 3.7505 5288.895 260.47 84.557 47.89 2.7666

6.375 4.2245 4695.467 260.99 84.895 48.228 2.9263

7.157 4.7572 4169.68 261.53 85.248 48.582 3.0626

8.041 5.3606 3700.332 262.06 85.619 48.953 3.2268

9.027 6.0349 3286.881 262.69 86.015 49.348 3.4188

10.047 6.7338 2945.736 263.26 86.386 49.719 3.6172

11.305 7.5976 2610.824 263.94 86.831 50.164 3.8846

12.699 8.5569 2318.129 264.66 87.304 50.637 4.1605

14.28 9.6476 2056.055 265.43 87.814 51.148 4.5003

16.031 10.859 1826.688 266.26 88.369 51.702 4.8366

18.003 12.226 1622.444 267.14 88.959 52.293 5.2031

20.213 13.764 1441.151 268.09 89.598 52.932 5.6083

22.695 15.496 1280.072 269.11 90.276 53.61 6.0201

25.466 17.436 1137.646 270.19 91.005 54.338 6.4496

28.594 19.633 1010.34 271.36 91.779 55.132 6.895

32.113 22.114 896.9883 272.61 92.65 55.984 7.3834

36.04 24.894 796.8185 273.92 93.547 56.88 7.8526

40.46 28.036 707.5189 275.32 94.505 57.839 8.328845.424 31.579 628.139 276.8 95.534 58.867 8.8366

51.022 35.592 557.3163 278.35 96.61 59.944 9.3601

57.33 40.136 494.2197 280.01 97.758 61.091 9.8884

64.385 45.241 438.4518 281.73 98.98 62.314 10.434

72.353 51.036 388.6668 283.56 100.27 63.604 10.985

81.234 57.526 344.818 285.45 101.61 64.948 11.598

91.194 64.843 305.9081 287.44 103.04 66.375 12.199

102.34 73.075 271.4471 289.48 104.51 67.844 12.836

114.96 82.44 240.6114 291.67 106.11 69.439 13.525

128.99 92.909 213.4992 293.92 107.76 71.091 14.186

144.78 104.76 189.3471 296.29 109.5 72.838 14.816


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162.46 118.1 167.9594 298.76 111.34 74.676 15.299

182.3 133.15 148.9748 301.3 113.25 76.582 15.667

204.57 150.14 132.1167 303.84 115.18 78.511 15.963

229.55 169.28 117.1786 306.38 117.11 80.448 16.093

257.63 190.9 103.9078 308.88 119.04 82.374 16.353

289.11 215.24 92.15759 311.4 121 84.332 16.691

324.47 242.67 81.74064 313.87 122.93 86.266 17.018

364.25 273.63 72.49205 316.53 125.03 88.361 17.314

408.77 308.38 64.32324 319.25 127.19 90.524 17.638

458.68 347.45 57.09023 321.93 129.35 92.683 17.72

507.42 385.68 51.43124 324.22 131.19 94.528 17.966

Dual porosity behavior can be identified from matching both adjusted pressure change andpressure derivative data with Bourdet et al. type curve for pseudosteady state interporosity

flow.

te> 100 hours can be aligned with the (tD/CD)PD = 0.5 line whereas earlier derivative data(0.3 < te < 100 hours) fall below this line, characteristic of a dual porosity system.


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Adjusted pressure change, pa vs equivalent time, te on semilog paper

i. Qualitative Type Curve Analysis1. From Horner semilog plot, get the slope of straight line,

2. Calculate permeability-thickness product (From the second (later-time) semilog straight line)

The average fracture permeability is

m = 40.0

k (mD) = 0.154kh (mD) = 43.97

skin = -3.5

Pa* = 198.90

P* 399.67

Horner Time Ratio


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ii. Quantitative Type Curve AnalysisPurpose:-To confirm the results from the semilog analysis

1. From the qualitative analysis, The average fracture permeability is From the semilog analysis, calculate the pressure match point using an arbitrary value of

PD = 10;

2. The match also forces the time derivative data to overlay and (interpolating to a better fit). The early time data are fit to the curve for ,

while our best estimate of the matching parameter for the transition data is

.

Finally we choose a time match point: and 3. Calculate the storativity ratio


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4. Compute the dimensionless wellbore-storage coefficient,

5. Calculate skin factor

which agrees with the estimation of from semilog analysis6. Calculate the interporosity flow coefficient,

Use from type curve match and from previous step, The estimates of

and

are not close to the values obtained by semi-log analysis. This is

because of wrong estimate of the early-time test to overlay at 0.5 line of the derivative typecurve and which is incorrect. Hence the initial straight line identified in the semilog analysis is not

correct and so do the and values.


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Problem 2

Analysis Of Pressure BU Test In Naturally Fractured Reservoir With Transient Matrix Flow

A Pressure BU test was simulated for an oil well in a naturally fractured reservoir with transient matrix

flow behavior. Well and reservoir data are as follow:

qg =333 STB/D h =33 ft o =1.3cp Pwf(t=0) =2692.05 psi

tp =2000 hrs =0.0633 Sw =0.33So =0.67 Bo =1.3 RB/STB cmt =4X10

-6 psi-1

rw =0.33 ft Ct =2.52X10-5 psi-1 Pi= =2876 psi

Pressure Build-Up Test Data:

Solution:

1. Construct data plots. Plot pressure change and pressure derivatives versus equivalent time on log-logpaper, and pressure versus Horner time ratio on semilog paper. The data for plotting is in Table 3 and

Table 4 below.

2. Initial qualitative type curve analysis is to determine whether Flow regime 1,2 and 3 can be identified. Match pressure change and pressure derivative data with Bourdet type curve. Dual porosity behavior is evident from the match of test data with type curve for transient flow in

the matrix.

The trend of earlier derivative data for 4te15 hours is flat & matches the (tD/CD)pD=0.25 line.


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The trend for derivative data for te150 hrs in horizontal & can be aligned on (tD/CD)pD=0.5 line. These behaviors are the characteristic for dual porosity system. With the earliest data trending towards a unit-slope line, we can establish a reasonable

horizontal match. The derivative type curve match suggest that Flow regimes 2 & 3 are present.

Table 3: Plotting Function For Horner Semilog

Analysis

Table 4: Plotting Function For Type Curve

Analysis


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i) Semilog Analysis

1. Intersection of two semi-log lines

Beginning of flow regime 2 is assume to be

2. Determine khftkavhfrom slope of semilog straight linekhftkavh=

= = 4899.3md.ft

Or for h=33ft, kav= 4399.3/33=133.3m

2680.00

2700.00

2720.00

2740.00

2760.00

2780.00

2800.00

2820.00

2840.00

2860.00

2880.00

1.00 10.00 100.00 1000.00 10000.00 100000.00 1000000.00 10000000.00

Pws,

psia

Horner Time Ratio

Horner Plot

Flow regime 3Slope, m-=20.8 psi/cycle

Horner time ration at intersection

of flow regime 2 and 3 = 59.8

Flow regime 2

Slope, m-=10.4 psi/cycle


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3. Calculate km/

4. Estimate

5. Estimate from .

* +

6. Estimate

.


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7. Calculate skin factor, s

ii) Quantitative type-curve analysis

Purpose: confirm the result form semi-log analysis

1. Using the log-log plot in figure 7.14, find the match points and matching parameters. In this case t tt h from semi log analysis, so we need to pre-calculate a pressure match

point. We arbitrarily choose pD =1.


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The match also forces the late time derivative data to overlay (tD/cD)pD = 0.5 and the early

derivative data to overlay (tD/cD)pD = 0.25. The type-curve correlating parameters were

(CDe2s)f=10

4 (early data), while parameter (CDe2s)f+m =10

2 (late time data). is estimated to be

1010. A time match point is te = 0.32 hours and tD/cD = 100.

2. Calculate (CD)f+m from the time match point.

3. Compute the skin factor

which agrees with S 0 from the semi log analysis

4. Calculate with equation 7.40

5. Calculate t qutn 7.41t gr ry ll t = 0.0108 r lg nly.

group 3 pbu in fractured reservoir

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