Naturally Fractured Reservoirs (DaPrat, et al Fractured Reservoirs (DaPrat, et al, paper SPE 13054) Orientation: DaPrat, et al, paper SPE 13054 Discussion: This homework concerns the

Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)

Orientation: DaPrat, et al, paper SPE 13054

Discussion:

This homework concerns the analysis of pressure drawdown and buildup test data for a well in western Venezuela (Well Mach 3X — 2 tests total, see attached paper by DaPrat, et al). The associated plots (Cartesian, semilog, and log-log data plots) are attached, as well as the appropriate type curves for dual porosity systems. As noted in the paper, these well tests are NOT contemporary — i.e., do not "tie" the pressure drawdown and pressure buildup tests to each other, use the production history as specified for the pressure buildup test. In short — ANALYZE THESE DATA SEPARATELY!

References:

1. DaPrat, G., Mannucci, J., Prado, L., and Millan, E.: "Use of Pressure Transient Testing to Evaluate Fractured Reservoirs in Western Venezuela," paper SPE 13054 presented at the 1984 SPE Annual Conference and Technical Exhibition, Houston, TX, 16-19 September, 1984.

Type Curve Analysis Relations:

Naturally Fractured Reservoir: (pwD' vs. tDλ/(1-ω) format, "Onur, et al " type curves)

Formation Permeability:

]or [

]or [ 2141MP

MP'wDwD'p'p

pph

qB.kΔΔ

=μ

Dimensionless Fracture Storativity:

ω is taken from the type curve match

Dimensionless Interporosity Flow Parameter:

)]1/([

][ 00026370)1/(

12 MPD

MP

wt tt

rc

k.ωλφμωλ −

=−

Note: The Cartesian and semilog data analysis techniques are used in exactly the same manner for natural-ly fractured (i.e., dual porosity) reservoirs as for homogeneous reservoir systems. There are other interpretation techniques for the semilog analysis of pressure data from naturally fractured reser-voirs (e.g., those techniques discussed in the second edition of the Lee, et al text), but for the purpose of this homework, you should only use "conventional" semilog (and Cartesian) data analy-sis methods.

Required:

1. You are to analyze the well test data in the paper by DaPrat, et al. in as complete detail as possible. The required data, plots, and instructions are attached.

Notes:

a. Various type curves are provided in a 1 inch-by-1 inch format in this handout — these type curves should be sufficient for your analysis.

b. You are to provide a comprehensive HAND ANALYSIS of these test data — type curves are provided for hand analysis..

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) "Cinco-Samaniego" Type Curve

"Cinco-Samaniego" Type Curve: pwD and pwD' vs. tDxf — Various CfD Values (NO WELLBORE STORAGE EFFECTS) (1"x1" format)

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) "Cinco-Samaniego" Skin Factor Correlation

"Cinco-Samaniego" Skin Factor Correlation: (used to relate the fractured well case to the Pseudoradial flow skin factor)

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) Bourdet-Gringarten Type Curve (Unfractured Well)

Bourdet-Gringarten Type Curve: pwD and pwD' vs. tD/CD — Various CD Values (Radial Flow Case — Includes Wellbore Storage and Skin Effects) (1"x1" format)

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) "Economides" Type Curve (CfD =1, CDf =various)

"Economides" Type Curve: pwD and pwD' vs. tDxf/CDf — CfD =1 (Fractured Well Case — Includes Wellbore Storage Effects) (1"x1" format)

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) "Economides" Type Curve (CfD =1x10-3, CDf =various)

"Economides" Type Curve: pwD and pwD' vs. tDxf/CDf — CfD =1x10-3 (Fractured Well Case — Includes Wellbore Storage Effects) (1"x1" format)

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) Ansah Type Curve — Pressure Buildup in a Bounded (Closed) Reservoir System

Ansah Type Curve: Pressure Buildup in a Bounded (Closed) Reservoir System (1"x1" format)

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) Stewart Type Curve — Well in an Infinite-Acting Reservoir System with a Single or Multiple Sealing Faults

Stewart Type Curve: Well in an Infinite-Acting Reservoir System with a Single or Multiple Sealing Faults. (1"x1" format)

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)

Type Curves for Naturally Fractured Reservoir Systems (1"x1" Format) (No Wellbore Storage or Skin Effects)

"Stewart and Ascharsobbi" Type Curve: pwD' vs. tDλ/4 — Various λ and ω Values

"Onur, Satman, and Reynolds" Type Curve: pwD' vs. tDλ/4 — Various λ and ω Values

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) Angel Type Curve — Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects

Angel Type Curve: Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects (1"x1" format) (αD=λCD=1x10-1, ω=1x10-1).

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) Well Mach-3X (SPE 13054)

Field Case: Well Mach-3X (SPE 13054)

These data were obtained from a field in Western Venezuela and in this case the analysts claim that the well performance indicates pseudosteady-state interporosity flow character. You are to verify (or disprove) this conjecture using both the drawdown and buildup test data. As noted earlier, these drawdown and buildup tests were not performed at the same relative time in the life of the well.

Reservoir properties:

φ=0.048 rw=0.2917 ft h=65 ft

Oil properties: (initial reservoir pressure unknown)

Bo=1.8235 RB/STB μo=0.362 cp ct=24.5x10-6 psia-1

Production parameters:

Drawdown Test Sequence Buildup Test Sequence qo=2700 STB/D (constant) qo=3224 STB/D (constant) pwf(t=0) =11,348.0 psia pwf (Δt=0) = 9911.0 psia tp=56 hr

Required:

Using the attached plots, you are to perform "type curve" analysis on these data and provide estimates of the following parameters (as appropriate):

a. The formation permeability, k. c. The dimensionless wellbore storage coefficient, CD. e. The near-well skin factor (compare to semilog analysis), s. f. The dimensionless fracture storativity ratio, ω.* g. The dimensionless interporosity flow coefficient, λ.*

* Assuming that naturally fractured reservoir behavior is exhibited.

Note:

You are also to verify/calculate properties using the specialized plots that are provided (pressure versus shut-in time and pressure versus logarithm of shut-in time, effective shut-in time, and Horner time—as well as the Muskat-Arps plot (pressure versus pressure derivative) for the analysis of late-time pressure buildup data). Be sure to perform all Cartesian and semilog analyses (which are relevant) and provide all results and calculations.

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence

Field Case: Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence

Well Test Data Functions:

Point t, hr pwf, psia Δp, psi Δp'(t), psi 0 0.0 11348.0 0.0 0.001 0.25 10989.0 359.0 517.932 0.50 10630.0 718.0 430.073 0.75 10486.0 862.0 369.694 1.00 10392.8 955.2 313.505 1.25 10318.5 1029.5 292.206 1.50 10268.3 1079.7 273.467 1.75 10229.5 1118.5 252.318 2.00 10195.4 1152.6 237.769 2.50 10141.0 1207.0 205.01

10 3.00 10106.9 1241.1 184.4511 3.50 10083.2 1264.8 168.7212 4.00 10063.2 1284.8 154.0413 4.50 10046.8 1301.2 145.8714 5.00 10034.3 1313.7 133.3715 5.50 10022.7 1325.3 132.0816 6.00 10012.6 1335.4 125.0717 7.00 9995.6 1352.4 122.7118 8.00 9981.9 1366.2 120.0819 9.00 9967.8 1380.2 120.5920 10.00 9956.1 1391.9 122.2921 12.00 9933.5 1414.5 128.7522 14.00 9913.1 1434.9 136.5923 16.00 9896.7 1451.3 145.0124 18.00 9879.6 1468.4 159.3025 20.00 9864.8 1483.2 168.0526 24.00 9834.1 1513.9 200.4227 28.00 9806.2 1541.8 228.7528 32.00 9780.8 1567.2 254.2529 36.00 9747.0 1601.0 283.9130 40.00 9723.1 1624.8 313.2431 45.00 9683.4 1664.6 348.8232 50.00 9642.7 1705.3 372.6933 55.00 9608.0 1740.0 395.8434 66.00 9531.0 1817.0 429.1135 67.00 9522.8 1825.2 431.8536 69.00 9508.3 1839.7 436.7437 71.00 9494.2 1853.8 440.9838 74.00 9473.1 1874.9 448.0039 77.00 9452.7 1895.3 452.8740 80.00 9430.5 1917.5 467.5141 84.00 9406.2 1941.8 473.8742 88.00 9377.3 1970.7 478.5943 92.00 9355.0 1993.0 486.9544 96.00 9333.2 2014.8 489.2245 100.00 9311.1 2036.9 496.1746 104.00 9290.4 2057.7 498.0147 108.00 9269.4 2078.6 500.1848 112.00 9251.4 2096.6 507.9149 116.00 9237.1 2110.9 505.9350 120.00 9223.0 2125.0 504.41

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Field Case: Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence (Continued)


Point t, hr pwf, psia Δp, psi Δp'(t), psi 51 131.00 9181.8 2166.2 503.9252 132.00 9177.8 2170.2 511.8653 134.00 9169.7 2178.3 511.8054 136.00 9161.9 2186.1 512.0055 138.00 9154.3 2193.7 512.5156 143.00 9135.4 2212.6 513.3557 148.00 9117.3 2230.7 513.7658 153.00 9099.2 2248.8 514.5059 158.00 9082.5 2265.5 514.6460 163.00 9064.6 2283.3 514.1761 168.00 9047.5 2300.5 515.9162 173.00 9031.1 2316.9 516.6963 178.00 9015.0 2333.0 514.26

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Cartesian Plot: "Wellbore Storage" Plot

Semilog Plot: Pressure versus Time Data

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Log-log Plot: Pressure Drop and Pressure Drop Derivative versus Time Data (1 inch x 1 inch)

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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054) Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence

Field Case: Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence


Point

Δt, hr

Δte, hr

(tp+Δt)/Δt

pws, psia

Δp, psi

Δp'(Δt), psi

Δp'(Δte), psi

0 0.00 0.00 ∞ 9911.0 0.0 0.0 0.0 1 0.25 0.25 2.2500E02 10095.0 184.0 220.30 265.20 2 0.50 0.50 1.1300E02 10255.0 344.0 298.85 338.76 3 0.75 0.74 7.5667E01 10451.0 540.0 365.64 354.43 4 1.00 0.98 5.7000E01 10564.0 653.0 378.13 343.78 5 1.25 1.22 4.5800E01 10631.0 720.0 343.81 340.45 6 1.50 1.46 3.8333E01 10703.0 792.0 335.86 302.70 7 1.75 1.70 3.3000E01 10743.0 832.0 291.83 300.09 8 2.00 1.93 2.9000E01 10806.0 895.0 267.04 265.53 9 2.25 2.16 2.5889E01 10814.0 903.0 236.67 243.20

10 2.50 2.39 2.3400E01 10830.0 919.0 205.22 219.14 11 3.00 2.85 1.9667E01 10854.0 943.0 158.34 175.86 12 3.50 3.29 1.7000E01 10878.0 967.0 125.30 141.91 13 4.00 3.73 1.5000E01 10878.0 967.0 102.86 116.87 14 5.00 4.59 1.2200E01 10902.0 991.0 74.52 87.79 15 6.00 5.42 1.0333E01 10902.0 991.0 59.44 73.16 16 7.00 6.22 9.0000E00 10917.0 1006.0 50.78 62.15 17 8.00 7.00 8.0000E00 10925.0 1014.0 46.09 55.65 18 9.00 7.75 7.2222E00 10933.0 1022.0 44.51 53.08 19 10.00 8.48 6.6000E00 10941.0 1030.0 41.84 56.31 20 12.00 9.88 5.6667E00 10941.0 1030.0 41.41 62.57 21 14.00 11.20 5.0000E00 10950.0 1039.0 44.58 83.61 22 16.00 12.44 4.5000E00 10959.0 1048.0 51.14 100.20 23 18.00 13.62 4.1111E00 10958.0 1047.0 60.74 128.69 24 20.00 14.74 3.8000E00 10973.0 1062.0 72.42 141.78 25 24.00 16.80 3.3333E00 10982.0 1071.0 93.77 167.70 26 28.00 18.67 3.0000E00 10939.0 1028.0 99.76 189.52 27 32.00 20.36 2.7500E00 10989.0 1078.0 116.79 237.36 28 36.00 21.91 2.5556E00 10989.0 1078.0 130.64 266.22 29 40.00 23.33 2.4000E00 11045.0 1134.0 135.97 273.14 30 45.00 24.95 2.2444E00 11109.0 1198.0 139.23 285.59 31 50.00 26.42 2.1200E00 11109.0 1198.0 146.94 300.55 32 55.00 27.75 2.0182E00 11109.0 1198.0 141.97 312.85 33 70.00 31.11 1.8000E00 11141.0 1230.0 158.57 332.95 34 72.00 31.50 1.7778E00 11149.0 1238.0 168.79 333.23 35 75.00 32.06 1.7467E00 11149.0 1238.0 178.69 335.10 36 79.00 32.77 1.7089E00 11156.0 1245.0 184.26 337.34 37 83.00 33.44 1.6747E00 11165.0 1254.0 185.18 339.55 38 87.00 34.07 1.6437E00 11165.0 1254.0 187.37 350.50 39 92.00 34.81 1.6087E00 11181.0 1270.0 181.19 352.44 40 97.00 35.50 1.5773E00 11181.0 1270.0 180.84 354.12 41 102.00 36.15 1.5490E00 11189.0 1278.0 173.67 355.42 42 107.00 36.76 1.5234E00 11197.0 1286.0 173.52 356.47 43 112.00 37.33 1.5000E00 11200.0 1289.0 166.55 365.64 44 117.00 37.87 1.4786E00 11200.0 1289.0 167.23 366.67 45 122.00 38.38 1.4590E00 11200.0 1289.0 167.96 367.76 46 127.00 38.86 1.4409E00 11200.0 1289.0 169.15 369.45 47 138.00 39.84 1.4058E00 11229.0 1318.0 174.65 377.30 48 140.00 40.00 1.4000E00 11229.0 1318.0 171.59 382.10 49 142.00 40.16 1.3944E00 11252.0 1341.0 175.64 385.93 50 145.00 40.40 1.3862E00 11252.0 1341.0 180.98 390.25

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Field Case: Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence (Continued)


Point

Δt, hr

Δte, hr

(tp+Δt)/Δt

pws, psia

Δp, psi

Δp'(Δt), psi

Δp'(Δte), psi

51 148.00 40.63 1.3784E00 11268.0 1357.0 185.83 395.20 52 153.00 41.00 1.3660E00 11284.0 1373.0 192.79 412.73 53 157.00 41.28 1.3567E00 11292.0 1381.0 195.98 417.38 54 160.00 41.48 1.3500E00 11300.0 1389.0 199.63 420.16 55 164.00 41.75 1.3415E00 11300.0 1389.0 201.20 423.25 56 169.00 42.06 1.3314E00 11308.0 1397.0 204.01 425.78 57 174.00 42.37 1.3218E00 11316.0 1405.0 206.54 427.72 58 178.00 42.60 1.3146E00 11316.0 1405.0 206.32 429.14 59 183.00 42.88 1.3060E00 11316.0 1405.0 206.17 430.96

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Cartesian Plot: "Wellbore Storage" Plot

Cartesian Plot: "Muskat" Plot — Pressure versus Pressure Derivative Data

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Semilog Plot: "MDH" Plot — Pressure versus Time Data

Semilog Plot: "Horner" Plot — Pressure versus Horner Time Data

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Log-log Plot: Pressure Drop and Pressure Drop Derivative versus Time Data (1 inch x 1 inch)

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Log-log Plot: Pressure Drop and Pressure Drop Derivative versus Effective Time Data (1 inch x 1 inch)

Documents

Naturally Fractured Reservoirs (DaPrat, et al Fractured Reservoirs (DaPrat, et al, paper SPE 13054) Orientation: DaPrat, et al, paper SPE 13054 Discussion: This homework concerns the