Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004

Homework 3: Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)This problem set considers the "classic" Bourdet example for a pressure buildup test analyzed using derivative type curve analysis — YOU ARE NOT TO PERFORM "TYPE CURVE ANALYSIS" IN THIS ASSIGNMENT . For completeness, the Bourdet, et al. paper is also attached — however, you must provide your own analysis — you are to only use the Bourdet analysis as a guide, there are considerable differences of opinion as to what the "correct" answers should be.Be sure to work the problem using BOTH shut-in time (t) and effective shut-in time (te). Recall that te is the time function for the equivalent pressure drawdown case. A Horner plot is provided, as well as the semilog t and effective shut-in time te plots — YOU ARE TO USE ALL OF THESE PLOTS.Finally, for some reason, Bourdet, et al. chose not to work in terms of pressure, pws, but instead to work in terms of the pressure drop, p. This is not a limitation, but it does require that you use p1hr rather than pws,1hr-pwf(t=0) in the semilog skin factor relation.

Given:These data are taken from the Bourdet, et al. reference and are to be considered sufficiently accurate for engineering analysis. You are to assume that wellbore storage and skin effects are present.Reservoir properties:

=0.25 rw=0.29 ft ct=4.2x10-6 psia-1 h=107 ftOil properties:

Bo=1.06 RB/STB o=2.5 cpProduction parameters:

pwf(t=0) = ? psia qo=174 STB/D (constant) tp=15.33 hr

References:1. Bourdet, D.P., Ayoub, J.A., and Pirard, Y.M.: "Use of Pressure Derivative in Well Test Interpretation,"

SPEFE (June 1989) 293-302.

Required:For this problem, you are to perform the following analyses: "Preliminary" log-log analysis. Cartesian analysis of "early" time (wellbore storage distorted) data. Semilog analysis of "middle" time (radial flow) data. Cartesian analysis of "late" time (boundary-dominated) data (i.e., the "Muskat Plot").You are to complete the table on the next page provided for you to tabulate your results.

Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Required Results

Required: Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)You are to estimate the following:

"Preliminary" log-log analysis:a. The wellbore storage coefficient, Cs.b. The dimensionless wellbore storage coefficient, CD.c. The formation permeability, k.

Cartesian analysis of "early" time (wellbore storage distorted) data:a. The pressure drop at the start of the test, pwi(t=0) — this should be ≈ 0 psi.b. The wellbore storage coefficient, Cs.c. The dimensionless wellbore storage coefficient, CD.

Semilog analysis of "middle" time (radial flow) data: (use both Horner and MDH methods)a. The formation permeability, k.b. The near well skin factor, s.c. The radius of investigation, rinv, at the end of radial flow or the end of the test data.

Cartesian analysis of "late" time (boundary-dominated) data: "Muskat Plot"a. Average pressure DIFFERENCE, (if applicable).

Results: Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)Log-log Analysis:

Wellbore storage coefficient, Cs = RB/psiDimensionless wellbore storage coefficient, CD = Formation permeability, k = md

Cartesian Analysis: Early Time DataPressure drop at the start of the test, pwi(t=0) = psiWellbore storage coefficient, Cs = RB/psiDimensionless wellbore storage coefficient, CD =

Semilog Analysis: Horner or te t (MDH)Formation permeability, k = md = mdNear well skin factor, s = = Radius of investigation, rinv (end of radial flow or end of test) = ft = ft

Cartesian Analysis: Late Time Data ("Muskat Plot" — if applicable)

Average pressure DIFFERENCE, = psia

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Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Well Test Data Functions

Well Test Data Functions:Point t, hr te, hr p, psi p'(t), psi p'(te), psi

1 8.330E-03 8.325E-03 3.81 6.75 6.762 1.250E-02 1.249E-02 6.55 9.87 9.883 1.667E-02 1.665E-02 10.03 13.98 13.994 2.083E-02 2.080E-02 13.27 17.29 17.325 2.500E-02 2.496E-02 16.77 20.08 20.126 2.917E-02 2.911E-02 20.01 23.33 23.377 3.333E-02 3.326E-02 23.25 21.12 21.178 3.750E-02 3.741E-02 26.49 23.48 23.539 4.583E-02 4.569E-02 29.48 30.80 30.9010 5.000E-02 4.984E-02 32.48 33.76 33.8911 5.833E-02 5.811E-02 38.96 43.84 44.0212 6.667E-02 6.638E-02 45.92 57.78 58.0613 7.500E-02 7.463E-02 51.17 66.91 67.2614 8.333E-02 8.288E-02 57.64 72.79 73.2215 9.583E-02 9.523E-02 71.95 77.66 81.6416 1.083E-01 1.076E-01 80.68 81.64 82.2217 1.208E-01 1.199E-01 88.39 80.55 89.0918 1.333E-01 1.322E-01 97.12 88.78 89.6019 1.488E-01 1.474E-01 104.24 100.16 101.2220 1.625E-01 1.608E-01 115.90 107.64 108.8421 1.792E-01 1.771E-01 126.68 117.25 118.6922 1.958E-01 1.934E-01 137.89 131.18 132.9123 2.125E-01 2.096E-01 148.37 136.13 138.1124 2.292E-01 2.258E-01 159.07 144.82 147.0625 2.500E-01 2.460E-01 171.79 152.26 154.8426 2.917E-01 2.862E-01 197.12 172.53 175.9227 3.333E-01 3.262E-01 220.15 155.13 158.4728 3.750E-01 3.660E-01 244.34 197.70 202.6629 4.167E-01 4.056E-01 266.27 208.73 214.6030 4.583E-01 4.450E-01 264.98 246.72 254.9431 5.000E-01 4.842E-01 304.44 229.26 237.0432 5.417E-01 5.232E-01 323.90 236.52 245.1433 5.833E-01 5.619E-01 343.83 283.48 293.9734 6.250E-01 6.005E-01 358.05 283.25 294.7835 6.667E-01 6.389E-01 376.25 255.69 267.0336 7.083E-01 6.770E-01 391.97 254.54 266.4737 7.500E-01 7.150E-01 403.69 253.64 266.4338 8.125E-01 7.716E-01 428.63 260.60 274.4639 8.750E-01 8.278E-01 447.34 261.24 276.3340 9.375E-01 8.835E-01 463.55 263.38 278.8741 1.000E+00 9.388E-01 481.75 262.50 279.7042 1.062E+00 9.936E-01 496.23 255.25 273.2243 1.125E+00 1.048E+00 512.95 255.65 272.9444 1.188E+00 1.102E+00 527.41 255.70 270.0545 1.250E+00 1.156E+00 541.15 250.50 270.7946 1.312E+00 1.209E+00 550.86 239.87 260.3447 1.375E+00 1.262E+00 562.85 237.73 259.3948 1.438E+00 1.314E+00 574.32 229.43 252.1649 1.500E+00 1.366E+00 583.81 224.24 246.4050 1.625E+00 1.469E+00 602.27 207.76 229.24

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Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Well Test Data Functions (continued)

Well Test Data Functions: (continued)Point t, hr te, hr p, psi p'(t), psi p'(te), psi

51 1.750E+00 1.571E+00 615.52 197.56 219.8152 1.875E+00 1.671E+00 629.25 182.27 202.8053 2.000E+00 1.769E+00 642.23 169.91 191.0654 2.250E+00 1.962E+00 659.71 151.22 169.0755 2.375E+00 2.056E+00 667.19 139.88 165.1456 2.500E+00 2.149E+00 673.44 134.31 153.4757 2.750E+00 2.332E+00 684.65 116.75 144.4858 3.000E+00 2.509E+00 695.11 114.03 137.6159 3.250E+00 2.682E+00 704.06 107.18 122.8760 3.500E+00 2.849E+00 709.80 96.38 112.8961 3.750E+00 3.013E+00 719.50 82.69 106.9462 4.000E+00 3.172E+00 725.97 78.06 100.5963 4.250E+00 3.328E+00 730.20 72.36 93.6664 4.500E+00 3.479E+00 731.95 69.85 87.7965 4.750E+00 3.626E+00 733.70 58.90 78.1566 5.000E+00 3.770E+00 736.45 48.95 73.9567 5.250E+00 3.911E+00 739.69 41.46 63.3268 5.500E+00 4.048E+00 742.64 39.18 55.6869 5.750E+00 4.182E+00 744.70 38.76 52.8970 6.000E+00 4.312E+00 747.19 41.04 50.4171 6.250E+00 4.440E+00 748.94 37.92 51.8472 6.750E+00 4.686E+00 748.02 32.48 49.5773 7.250E+00 4.922E+00 750.78 26.91 46.6174 7.750E+00 5.148E+00 753.01 23.84 40.4275 8.250E+00 5.364E+00 754.52 21.86 38.5476 8.750E+00 5.570E+00 756.27 26.74 35.8077 9.250E+00 5.769E+00 757.51 24.21 33.9478 9.750E+00 5.960E+00 758.52 23.62 39.4579 1.025E+01 6.143E+00 760.01 22.26 38.2980 1.075E+01 6.319E+00 760.75 21.34 36.7781 1.125E+01 6.488E+00 761.76 20.27 35.6382 1.175E+01 6.652E+00 762.50 19.60 35.3883 1.225E+01 6.809E+00 763.51 19.01 34.6084 1.275E+01 6.961E+00 764.25 18.93 34.1485 1.325E+01 7.107E+00 765.07 17.59 33.7586 1.375E+01 7.249E+00 765.50 17.89 33.3787 1.450E+01 7.452E+00 766.50 17.21 32.5288 1.525E+01 7.645E+00 767.25 16.33 32.8289 1.600E+01 7.829E+00 767.99 15.40 31.4390 1.675E+01 8.004E+00 768.74 15.19 31.9091 1.750E+01 8.172E+00 769.48 15.04 31.7692 1.825E+01 8.332E+00 769.99 14.50 31.4293 1.900E+01 8.484E+00 770.73 13.35 31.8994 1.975E+01 8.631E+00 770.99 13.31 30.7795 2.050E+01 8.771E+00 771.49 13.13 30.6696 2.125E+01 8.905E+00 772.24 12.41 31.1997 2.225E+01 9.076E+00 772.74 11.84 30.6698 2.325E+01 9.239E+00 773.22 11.72 30.9099 2.425E+01 9.392E+00 773.48 10.67 30.07

100 2.525E+01 9.539E+00 773.99 11.14 30.15101 2.625E+01 9.678E+00 774.49 11.10 30.34102 2.725E+01 9.811E+00 774.73 10.04 29.98103 2.850E+01 9.968E+00 775.23 10.06 29.97

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Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Cartesian Plot — Early-Time Pressure Data

Cartesian Plot: Early-Time Pressure Data

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Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Semilog Plot — "MDH" Plot — Pressure Data versus Shut-In Time

Semilog Plot: "MDH" Plot — Pressure Data versus Shut-In Time

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Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Semilog Plot — "Horner" Plot — Pressure Data versus Horner Time

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

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Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Semilog Plot — "Agarwal" Plot — Pressure Data versus Effective Shut-In Time

Semilog Plot: "Agarwal" Plot — Pressure Data versus Effective Shut-In Time

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Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Log-log Plot — Pressure Drop and Pressure Drop Derivative Data versus Shut-In Time (1 inch x 1 inch)

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

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Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Log-log Plot — Pressure Drop and Pressure Drop Derivative Data versus Effective Shut-In Time (1 inch x 1 inch)

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

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Petroleum Engineering 324 — Well PerformanceHomework No. 3 — Analysis of Pressure Buildup Data (Bourdet (Radial Flow) Example)

19 April 2004 — Due: Friday 23 April 2004Late-Time Cartesian Plot ("Muskat Plot") — Pressure Buildup Case

Late-Time Cartesian Plot ("Muskat Plot"): Pressure Buildup Case

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