Handbook of of Petroleum Exploration and Production
Well Test Analysis:
The Use of Advanced Interpolation Models
|
Field Examples Data and Analysis
EXAMPLE 1: Figures 2.1, 2.8, 2.13 and 2.15
Reference: "A new set of type curves simplifies well test analysis", Bourdet, D. P., Whittle, T. M., Douglas, A. A. and Pirard, Y. M., World Oil (May, 1983), 95-106. Gulf Publishing Co., Houston.
Production time tp = 15.33 hr
Flow rate q = 174 Bbl/D
Formation volume factor B = 1.06
Fluid viscosity mu = 2.5 cp
Porosity phi = 0.25
Formation thickness h = 107 ft
Total compressibility ct = 4.2 E-6 1/psi
Wellbore radius rw = 0.29 ft
|
|
|
| Time t | | Pressure p |
|---|
| (hr) | | (psi) |
|---|
|
| 15.33000 | | 3086.330 |
| 15.33417 | | 3090.570 |
| 15.33833 | | 3093.810 |
| 15.34250 | | 3096.550 |
| 15.34667 | | 3100.030 |
| 15.35083 | | 3103.270 |
| 15.35500 | | 3106.770 |
| 15.35917 | | 3110.010 |
| 15.36333 | | 3113.250 |
| 15.36750 | | 3116.490 |
| 15.37583 | | 3119.480 |
| 15.38000 | | 3122.480 |
| 15.38833 | | 3128.960 |
| 15.39667 | | 3135.920 |
| 15.40500 | | 3141.170 |
| 15.41333 | | 3147.640 |
| 15.42583 | | 3161.950 |
| 15.43833 | | 3170.680 |
| 15.45083 | | 3178.390 |
| 15.46333 | | 3187.120 |
| 15.47583 | | 3194.240 |
| 15.49250 | | 3205.960 |
| 15.50917 | | 3216.680 |
| 15.52583 | | 3227.890 |
| 15.54250 | | 3238.370 |
| 15.55917 | | 3249.070 |
| 15.58000 | | 3261.790 |
| 15.62167 | | 3287.210 |
| 15.66333 | | 3310.150 |
| 15.70500 | | 3334.340 |
| 15.74667 | | 3356.270 |
| 15.78833 | | 3374.980 |
| 15.83000 | | 3394.440 |
| 15.87167 | | 3413.900 |
| 15.91333 | | 3433.830 |
| 15.95500 | | 3448.050 |
| 15.99667 | | 3466.260 |
| 16.03833 | | 3481.970 |
| 16.08000 | | 3493.690 |
| 16.14250 | | 3518.630 |
| 16.20500 | | 3537.340 |
| 16.26750 | | 3553.550 |
| 16.33000 | | 3571.750 |
| 16.39250 | | 3586.230 |
| 16.45500 | | 3602.950 |
| 16.51750 | | 3617.410 |
| 16.58000 | | 3631.150 |
| 16.64250 | | 3640.860 |
| 16.70500 | | 3652.850 |
| 16.76750 | | 3664.320 |
| 16.83000 | | 3673.810 |
| 16.95500 | | 3692.270 |
| 17.08000 | | 3705.520 |
| 17.20500 | | 3719.260 |
| 17.33000 | | 3732.230 |
| 17.58000 | | 3749.710 |
| 17.70500 | | 3757.190 |
| 17.83000 | | 3763.440 |
| 18.08000 | | 3774.650 |
| 18.33000 | | 3785.110 |
| 18.58000 | | 3794.060 |
| 18.83000 | | 3799.800 |
| 19.08000 | | 3809.500 |
| 19.33000 | | 3815.970 |
| 19.58000 | | 3820.200 |
| 19.83000 | | 3821.950 |
| 20.08000 | | 3823.700 |
| 20.33000 | | 3826.450 |
| 20.58000 | | 3829.690 |
| 20.83000 | | 3832.640 |
| 21.08000 | | 3834.700 |
| 21.33000 | | 3837.190 |
| 21.58000 | | 3838.940 |
| 22.08000 | | 3838.020 |
| 22.58000 | | 3840.780 |
| 23.08000 | | 3843.010 |
| 23.58000 | | 3844.520 |
| 24.08000 | | 3846.270 |
| 24.58000 | | 3847.510 |
| 25.08000 | | 3848.520 |
| 25.58000 | | 3850.010 |
| 26.08000 | | 3850.750 |
| 26.58000 | | 3851.760 |
| 27.08000 | | 3852.500 |
| 27.58000 | | 3853.510 |
| 28.08000 | | 3854.250 |
| 28.58000 | | 3855.070 |
| 29.08000 | | 3855.500 |
| 29.83000 | | 3856.500 |
| 30.58000 | | 3857.250 |
| 31.33000 | | 3857.990 |
| 32.08000 | | 3858.740 |
| 32.83000 | | 3859.480 |
| 33.58000 | | 3859.990 |
| 34.33000 | | 3860.730 |
| 35.08000 | | 3860.990 |
| 35.83000 | | 3861.490 |
| 36.58000 | | 3862.240 |
| 37.58000 | | 3862.740 |
| 38.58000 | | 3863.220 |
| 39.58000 | | 3863.480 |
| 40.58000 | | 3863.990 |
| 41.58000 | | 3864.490 |
| 42.58000 | | 3864.730 |
| 43.83000 | | 3865.230 |
| 45.33000 | | 3865.740 |
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EXAMPLE 2: Figures 4.38 and 4.39
Reference: "Interpreting Well Test in Fractured Reservoirs", Bourdet, D., Ayoub, J. A., Whittle, T. M., Pirard, Y. M. and Kniazeff V., World Oil (Oct., 1983), 77-87. Gulf Publishing Co., Houston.
|
| Time t | | Rate q |
|---|
| (hr) | | (Bbl/D) |
|---|
|
| 0.00000 | | 800.000 |
| 3.80000 | | 2500.000 |
| 7.10000 | | 830.000 |
| 23.55000 | | 0.000 |
| 41.55000 | | end of test |
|
Formation volume factor B = 1.5
Fluid viscosity mu = 0.3 cp
Porosity phi = 0.05
Formation thickness h = 7 ft
Total compressibility ct = 2.0 E-5 1/psi
Wellbore radius rw = 0.29 ft
|
|
|
| Time t | | Pressure p |
|---|
| (hr) | | (psi) |
|---|
|
| 23.55000 | | 3816.990 |
| 23.55056 | | 3817.960 |
| 23.55111 | | 3819.730 |
| 23.55194 | | 3821.640 |
| 23.55250 | | 3823.400 |
| 23.55305 | | 3824.920 |
| 23.55361 | | 3826.960 |
| 23.55445 | | 3828.280 |
| 23.55500 | | 3829.520 |
| 23.55556 | | 3830.670 |
| 23.55611 | | 3831.710 |
| 23.55694 | | 3832.610 |
| 23.55750 | | 3833.390 |
| 23.55806 | | 3834.310 |
| 23.55861 | | 3835.180 |
| 23.55944 | | 3835.920 |
| 23.56000 | | 3836.810 |
| 23.56056 | | 3837.580 |
| 23.56111 | | 3838.360 |
| 23.56167 | | 3839.110 |
| 23.56250 | | 3839.940 |
| 23.56306 | | 3840.680 |
| 23.56361 | | 3841.530 |
| 23.56417 | | 3842.070 |
| 23.56500 | | 3842.790 |
| 23.56556 | | 3843.410 |
| 23.56611 | | 3843.970 |
| 23.56667 | | 3844.560 |
| 23.56750 | | 3845.110 |
| 23.56806 | | 3845.720 |
| 23.56861 | | 3846.350 |
| 23.56917 | | 3846.780 |
| 23.57000 | | 3847.490 |
| 23.57111 | | 3848.400 |
| 23.57167 | | 3848.910 |
| 23.57222 | | 3849.320 |
| 23.57306 | | 3849.990 |
| 23.57417 | | 3850.730 |
| 23.57556 | | 3851.610 |
| 23.57667 | | 3852.360 |
| 23.57806 | | 3853.160 |
| 23.57917 | | 3853.980 |
| 23.58055 | | 3854.570 |
| 23.58167 | | 3855.390 |
| 23.58306 | | 3855.960 |
| 23.58417 | | 3856.670 |
| 23.58528 | | 3857.140 |
| 23.58667 | | 3857.870 |
| 23.58778 | | 3858.420 |
| 23.58917 | | 3858.890 |
| 23.59028 | | 3859.480 |
| 23.59167 | | 3859.990 |
| 23.59361 | | 3860.740 |
| 23.59528 | | 3861.480 |
| 23.59722 | | 3862.030 |
| 23.59917 | | 3862.870 |
| 23.60083 | | 3863.310 |
| 23.60333 | | 3864.300 |
| 23.60583 | | 3864.990 |
| 23.60889 | | 3865.960 |
| 23.61139 | | 3866.470 |
| 23.61389 | | 3867.100 |
| 23.61639 | | 3867.740 |
| 23.61944 | | 3868.410 |
| 23.62278 | | 3869.120 |
| 23.62583 | | 3869.910 |
| 23.62889 | | 3870.320 |
| 23.63194 | | 3871.000 |
| 23.63500 | | 3871.520 |
| 23.63889 | | 3872.070 |
| 23.64139 | | 3872.480 |
| 23.64444 | | 3873.000 |
| 23.64750 | | 3873.540 |
| 23.65055 | | 3873.840 |
| 23.65361 | | 3874.330 |
| 23.65694 | | 3874.730 |
| 23.66167 | | 3875.470 |
| 23.66611 | | 3875.880 |
| 23.67083 | | 3876.510 |
| 23.67556 | | 3876.830 |
| 23.68056 | | 3877.440 |
| 23.68472 | | 3877.890 |
| 23.68972 | | 3878.250 |
| 23.69417 | | 3878.640 |
| 23.70333 | | 3879.370 |
| 23.71278 | | 3880.070 |
| 23.72333 | | 3880.860 |
| 23.73139 | | 3881.450 |
| 23.74055 | | 3881.920 |
| 23.75000 | | 3882.350 |
| 23.75945 | | 3882.770 |
| 23.76861 | | 3883.190 |
| 23.77806 | | 3883.630 |
| 23.78722 | | 3884.030 |
| 23.79667 | | 3884.390 |
| 23.80583 | | 3884.700 |
| 23.81528 | | 3884.990 |
| 23.82444 | | 3885.340 |
| 23.84306 | | 3885.900 |
| 23.86167 | | 3886.120 |
| 23.88056 | | 3886.690 |
| 23.89917 | | 3887.090 |
| 23.90833 | | 3887.390 |
| 23.91778 | | 3887.520 |
| 23.93639 | | 3887.940 |
| 23.95500 | | 3888.340 |
| 23.97361 | | 3888.580 |
| 23.99222 | | 3888.930 |
| 24.01083 | | 3889.200 |
| 24.02944 | | 3889.410 |
| 24.04806 | | 3889.310 |
| 24.06667 | | 3889.460 |
| 24.08528 | | 3889.720 |
| 24.10417 | | 3889.910 |
| 24.12278 | | 3890.200 |
| 24.16000 | | 3890.690 |
| 24.19722 | | 3891.140 |
| 24.23444 | | 3890.800 |
| 24.27167 | | 3891.380 |
| 24.30889 | | 3891.750 |
| 24.34639 | | 3892.040 |
| 24.38361 | | 3892.310 |
| 24.42083 | | 3892.100 |
| 24.45806 | | 3892.430 |
| 24.49528 | | 3892.600 |
| 24.53250 | | 3892.910 |
| 24.57000 | | 3892.970 |
| 24.60722 | | 3892.770 |
| 24.66306 | | 3893.210 |
| 24.71889 | | 3893.570 |
| 24.77500 | | 3893.800 |
| 24.83083 | | 3893.640 |
| 24.88667 | | 3893.970 |
| 24.94250 | | 3894.150 |
| 25.03583 | | 3894.240 |
| 25.12889 | | 3894.640 |
| 25.22222 | | 3894.760 |
| 25.31528 | | 3895.130 |
| 25.40833 | | 3895.200 |
| 25.50167 | | 3895.380 |
| 25.68806 | | 3895.650 |
| 25.87417 | | 3895.920 |
| 26.06056 | | 3896.220 |
| 26.24694 | | 3896.540 |
| 26.43333 | | 3896.620 |
| 26.61972 | | 3896.810 |
| 26.89917 | | 3897.180 |
| 27.17861 | | 3897.360 |
| 27.45806 | | 3897.360 |
| 27.73778 | | 3897.780 |
| 28.01722 | | 3898.080 |
| 28.29667 | | 3898.220 |
| 28.57611 | | 3898.450 |
| 28.85583 | | 3898.790 |
| 29.13528 | | 3898.800 |
| 29.41472 | | 3899.110 |
| 29.69417 | | 3899.230 |
| 29.97361 | | 3899.480 |
| 30.25333 | | 3899.620 |
| 30.53278 | | 3899.810 |
| 30.81222 | | 3900.030 |
| 31.09167 | | 3900.160 |
| 31.46445 | | 3900.370 |
| 31.83722 | | 3900.690 |
| 32.20972 | | 3900.690 |
| 32.58250 | | 3900.860 |
| 32.95528 | | 3901.080 |
| 33.32778 | | 3901.380 |
| 33.70055 | | 3901.430 |
| 34.07333 | | 3901.750 |
| 34.44584 | | 3901.790 |
| 35.00500 | | 3902.170 |
| 35.56389 | | 3902.310 |
| 36.12305 | | 3902.580 |
| 36.68195 | | 3902.770 |
| 37.24111 | | 3903.090 |
| 37.80000 | | 3903.190 |
| 38.35889 | | 3903.450 |
| 38.91806 | | 3903.450 |
| 39.47722 | | 3903.710 |
| 40.03611 | | 3903.780 |
| 40.59500 | | 3904.160 |
| 41.15583 | | 3904.220 |
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EXAMPLE 3: Figure 4.40
Reference: "New Type Curves Aid Analysis of Fissured Zone Well Tests", Bourdet, D., Alagoa A., Ayoub J. A. and, Pirard, Y. M., World Oil (April, 1984), 111-124. Gulf Publishing Co., Houston.
|
| Time t | | Rate q |
|---|
| (hr) | | (Bbl/D) |
|---|
|
| 0.00000 | | 2952.000 |
| 1.33000 | | 0.000 |
| 1.64000 | | 2952.000 |
| 6.69000 | | 0.000 |
| 7.08000 | | 960.0000 |
| 38.21000 | | 0.000 |
| 41.57000 | | end of test |
|
Formation volume factor B = 1.28
Fluid viscosity mu = 1.0 cp
Porosity phi = 0.07
Formation thickness h = 36 ft
Total compressibility ct = 1.0 E-5 1/psi
Wellbore radius rw = 0.29 ft
|
|
|
| Time t | | Pressure p |
|---|
| (hr) | | (psi) |
|---|
|
| 38.21000 | | 3245.000 |
| 38.21361 | | 3256.095 |
| 38.21917 | | 3265.693 |
| 38.22472 | | 3270.400 |
| 38.23028 | | 3273.105 |
| 38.23583 | | 3274.978 |
| 38.24139 | | 3276.407 |
| 38.24694 | | 3277.499 |
| 38.25250 | | 3278.386 |
| 38.25806 | | 3279.096 |
| 38.26917 | | 3280.288 |
| 38.28028 | | 3281.213 |
| 38.29139 | | 3281.985 |
| 38.30250 | | 3282.718 |
| 38.31361 | | 3283.330 |
| 38.33583 | | 3284.415 |
| 38.35806 | | 3285.385 |
| 38.38028 | | 3286.211 |
| 38.40250 | | 3286.975 |
| 38.42472 | | 3287.640 |
| 38.44695 | | 3288.281 |
| 38.46917 | | 3288.969 |
| 38.49139 | | 3289.542 |
| 38.51361 | | 3290.085 |
| 38.53583 | | 3290.658 |
| 38.59139 | | 3291.804 |
| 38.64695 | | 3292.836 |
| 38.70250 | | 3293.791 |
| 38.75778 | | 3294.700 |
| 38.81361 | | 3295.541 |
| 38.87472 | | 3296.305 |
| 38.92472 | | 3296.939 |
| 38.98028 | | 3297.589 |
| 39.03583 | | 3298.208 |
| 39.09139 | | 3298.796 |
| 39.14695 | | 3299.400 |
| 39.20250 | | 3299.874 |
| 39.25778 | | 3300.447 |
| 39.31361 | | 3300.875 |
| 39.42472 | | 3301.845 |
| 39.53583 | | 3302.686 |
| 39.64667 | | 3303.343 |
| 39.75778 | | 3304.054 |
| 39.86889 | | 3304.726 |
| 39.98028 | | 3305.354 |
| 40.09139 | | 3305.949 |
| 40.20250 | | 3306.476 |
| 40.31361 | | 3306.995 |
| 40.42472 | | 3307.477 |
| 40.64667 | | 3308.393 |
| 40.90250 | | 3309.303 |
| 41.12472 | | 3309.983 |
| 41.34667 | | 3310.686 |
| 41.56889 | | 3311.229 |
|
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EXAMPLE 4: Figure 4.50
Reference: "Pressure Behavior of Layered Reservoirs with Crossflow", Bourdet, D., S.P.E. paper 13628 (1985), California Regional Meeting, Bakersfield, Ca.
Production time tp = 720 hr
Flow rate q = 3000 Bbl/D
Formation volume factor B = 1.2
Fluid viscosity mu = 1.5 cp
Porosity phi = 0.10
Formation thickness h = 60 ft
Total compressibility ct = 5.0 E-6 1/psi
Wellbore radius rw = 0.29 ft
|
|
|
| Time t | | Pressure p |
|---|
| (hr) | | (psi) |
|---|
|
| 720.0000 | | 4592.300 |
| 720.0059 | | 4731.950 |
| 720.0070 | | 4756.890 |
| 720.0086 | | 4789.470 |
| 720.0117 | | 4852.540 |
| 720.0150 | | 4913.380 |
| 720.0186 | | 4993.290 |
| 720.0206 | | 5007.160 |
| 720.0225 | | 5061.810 |
| 720.0250 | | 5094.810 |
| 720.0275 | | 5139.330 |
| 720.0308 | | 5193.970 |
| 720.0342 | | 5245.600 |
| 720.0383 | | 5305.770 |
| 720.0425 | | 5362.890 |
| 720.0475 | | 5424.360 |
| 720.0517 | | 5473.000 |
| 720.0558 | | 5519.450 |
| 720.0600 | | 5570.900 |
| 720.0641 | | 5604.400 |
| 720.0684 | | 5642.800 |
| 720.0725 | | 5681.700 |
| 720.0767 | | 5715.000 |
| 720.0808 | | 5746.300 |
| 720.0850 | | 5776.000 |
| 720.0892 | | 5805.900 |
| 720.0933 | | 5830.400 |
| 720.0975 | | 5857.600 |
| 720.1017 | | 5881.300 |
| 720.1058 | | 5903.700 |
| 720.1100 | | 5914.900 |
| 720.1142 | | 5945.100 |
| 720.1183 | | 5964.500 |
| 720.1225 | | 5984.400 |
| 720.1266 | | 6001.900 |
| 720.1342 | | 6031.500 |
| 720.1406 | | 6056.300 |
| 720.1447 | | 6069.200 |
| 720.1486 | | 6084.300 |
| 720.1528 | | 6097.300 |
| 720.1614 | | 6121.900 |
| 720.1694 | | 6145.400 |
| 720.1780 | | 6166.400 |
| 720.1864 | | 6186.900 |
| 720.1945 | | 6205.200 |
| 720.2031 | | 6223.500 |
| 720.2111 | | 6240.400 |
| 720.2197 | | 6255.700 |
| 720.2278 | | 6270.900 |
| 720.2364 | | 6284.600 |
| 720.2444 | | 6297.700 |
| 720.2531 | | 6310.600 |
| 720.2611 | | 6322.300 |
| 720.2697 | | 6334.200 |
| 720.2778 | | 6344.900 |
| 720.2903 | | 6360.900 |
| 720.3025 | | 6375.200 |
| 720.3150 | | 6388.000 |
| 720.3281 | | 6400.700 |
| 720.3400 | | 6412.700 |
| 720.3525 | | 6423.800 |
| 720.3650 | | 6434.600 |
| 720.3775 | | 6445.200 |
| 720.3900 | | 6455.000 |
| 720.4025 | | 6464.600 |
| 720.4192 | | 6476.700 |
| 720.4359 | | 6488.100 |
| 720.4525 | | 6498.800 |
| 720.4692 | | 6510.000 |
| 720.4858 | | 6522.500 |
| 720.5025 | | 6530.100 |
| 720.5192 | | 6539.400 |
| 720.5591 | | 6561.800 |
| 720.5842 | | 6574.800 |
| 720.6092 | | 6587.400 |
| 720.6342 | | 6600.100 |
| 720.6592 | | 6611.700 |
| 720.6839 | | 6621.600 |
| 720.7125 | | 6632.500 |
| 720.7500 | | 6646.200 |
| 720.8250 | | 6675.000 |
| 720.9044 | | 6701.300 |
| 721.0036 | | 6734.400 |
| 721.1039 | | 6765.400 |
| 721.2045 | | 6793.800 |
| 721.3036 | | 6820.100 |
| 721.4039 | | 6845.000 |
| 721.5045 | | 6868.700 |
| 721.6036 | | 6891.900 |
| 721.7039 | | 6914.200 |
| 721.8044 | | 6935.700 |
| 721.9036 | | 6956.700 |
| 722.0042 | | 6977.100 |
| 722.1044 | | 6995.900 |
| 722.2036 | | 7014.800 |
| 722.3039 | | 7033.400 |
| 722.4044 | | 7051.400 |
| 722.5036 | | 7068.900 |
| 722.6039 | | 7085.900 |
| 722.7045 | | 7102.800 |
| 722.8036 | | 7118.800 |
| 722.9039 | | 7134.500 |
| 723.0045 | | 7149.200 |
| 723.0539 | | 7156.700 |
| 723.1036 | | 7164.400 |
| 723.2294 | | 7182.400 |
| 723.3795 | | 7203.700 |
| 723.5294 | | 7224.400 |
| 723.6794 | | 7244.500 |
| 723.8295 | | 7263.900 |
| 723.9794 | | 7282.900 |
| 724.1295 | | 7301.600 |
| 724.2794 | | 7319.200 |
| 724.4294 | | 7336.400 |
| 724.5795 | | 7353.500 |
| 724.7280 | | 7370.100 |
| 724.8781 | | 7386.200 |
| 725.0281 | | 7401.900 |
| 725.1780 | | 7417.000 |
| 725.3536 | | 7434.300 |
| 725.5289 | | 7451.300 |
| 725.7031 | | 7467.500 |
| 725.8786 | | 7483.600 |
| 726.1680 | | 7509.100 |
| 726.3989 | | 7528.700 |
| 726.4125 | | 7529.700 |
| 727.6575 | | 7624.500 |
| 727.8000 | | 7634.200 |
| 728.0536 | | 7651.500 |
| 728.1780 | | 7659.900 |
| 728.4286 | | 7676.100 |
| 728.6789 | | 7691.800 |
| 728.9280 | | 7707.000 |
| 729.3030 | | 7729.200 |
| 729.5536 | | 7743.700 |
| 729.8039 | | 7764.200 |
| 730.1789 | | 7777.500 |
| 730.5539 | | 7796.600 |
| 730.8030 | | 7809.100 |
| 731.0539 | | 7821.200 |
| 731.3039 | | 7833.000 |
| 731.5530 | | 7844.400 |
| 731.8039 | | 7855.500 |
| 732.0539 | | 7866.400 |
| 732.3030 | | 7877.000 |
| 732.5539 | | 7887.600 |
| 732.8039 | | 7898.000 |
| 733.0530 | | 7908.000 |
| 733.1789 | | 7912.900 |
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