1 Homework 6: Analysis and Interpretation of a Pump Test Sequence Given: READ THIS FIRST! This problem consists of a pressure drawdown/buildup test sequence performed on a pumping WATER well (our campus water well). There are no "tricks" involved this should be a straightforward analysis/interpretation sequence. Be sure to perform all analyses and crosscheck/double-check your work whenever possible. These attached data were taken from a pressure drawdown/buildup test sequence performed on our campus water well. The reservoir interval is a water sand at about 450 ft the well is not stimulated and should not be damaged. The reservoir should be assumed to be homogeneous and infinite-acting. Reservoir properties: φ=0.25 r w =0.36 ft c t =6.5x10-6 psia -1 h=23 ft Water properties: B w =1.0 RB/STB Production parameters: Event µ w =1.0 cp Duration of Event (hr) Pressure at Start of Event (psia) Water Flowrate (STB/D) 1. Drawdown Test 2.267 p i =147.29 60 2. Buildup Test 1.82 p wf ( t=0)=139.33 0 Summary Plots: (Drawdown/Buildup Test Sequences)
2 Required Results Pressure Drawdown Case Required: Drawdown Case (Analysis of Water Well Test Data (Texas A&M University)) You are to estimate the following: Log-log analysis: a. The wellbore storage coefficient, C s. b. The formation permeability, k. Cartesian analysis of "early" time (wellbore storage distorted) data: a. The pressure at the start of the test, p i. b. The wellbore storage coefficient, C s. Semilog analysis of "middle" time (radial flow) data: a. The formation permeability, k. b. The near well skin factor, s. c. The radius of investigation, r inv, at the end of radial flow. Results: Drawdown Case (Analysis of Water Well Test Data (Texas A&M University)) Log-log Analysis: Wellbore storage coefficient, C s = RB/psia Formation permeability, k = md Cartesian Analysis: Early Time Data Pressure at start of test, p i = psia Wellbore storage coefficient, C s = RB/psia Semilog Analysis: Formation permeability, k = md Near well skin factor, s = Radius of investigation, rinv (end of radial flow) = ft
3 Required Results Pressure Buildup Case Required: Buildup Case (Analysis of Water Well Test Data (Texas A&M University)) You are to estimate the following: Log-log analysis: a. The wellbore storage coefficient, C s. b. The formation permeability, k. Cartesian analysis of "early" time (wellbore storage distorted) data: a. The pressure at the start of the test, p wf ( t=0). b. The wellbore storage coefficient, C s. Semilog analysis of "middle" time (radial flow) data: a. The formation permeability, k. b. The near well skin factor, s. c. The radius of investigation, r inv, at the end of radial flow. d. The extrapolated pressure, p*. e. Average reservoir pressure, p (MBH technique if data are available) Cartesian analysis of "late" time (boundary-dominated) data: "Muskat Plot" a. Average reservoir pressure, p. Results: Buildup Case (Analysis of Water Well Test Data (Texas A&M University)) Log-log Analysis: Wellbore storage coefficient, C s = RB/psia Formation permeability, k = md Cartesian Analysis: Early Time Data Pressure at start of test, p wf ( t=0) = psia Wellbore storage coefficient, C s = RB/psia Semilog Analysis: (MDH and Horner analysis) Formation permeability, k = md Near well skin factor, s = Radius of investigation, r inv (end of radial flow) = ft Extrapolated pressure, p* (from Horner analysis) = psia Average reservoir pressure, p (MBH technique) = psia Cartesian Analysis: Late Time Data ("Muskat Plot") Average reservoir pressure, p = psia
4 Drawdown Test Data Data Functions: Pressure Drawdown Case Point t (hr) p wf (psia) p p' 1 0.005556 146.93 0.36 0.380 2 0.009722 146.68 0.61 0.597 3 0.012500 146.55 0.74 0.859 4 0.016667 146.28 1.01 0.967 5 0.021389 145.95 1.34 1.259 6 0.025000 145.79 1.50 1.378 7 0.033333 145.41 1.88 1.548 8 0.037500 145.16 2.13 1.552 9 0.041667 144.98 2.31 1.634 10 0.044722 144.84 2.45 1.606 11 0.052778 144.60 2.69 1.614 12 0.057500 144.44 2.85 1.740 13 0.062500 144.30 2.99 1.715 14 0.067500 144.17 3.12 1.717 15 0.074167 144.04 3.25 1.718 16 0.079167 143.86 3.43 1.762 17 0.083333 143.74 3.55 1.754 18 0.090556 143.72 3.57 1.779 19 0.095833 143.57 3.72 1.778 20 0.100000 143.48 3.81 1.856 21 0.104167 143.41 3.88 1.876 22 0.108333 143.34 3.95 1.877 23 0.112500 143.25 4.04 1.770 24 0.125000 143.07 4.22 1.877 25 0.133333 142.92 4.37 1.869 26 0.141667 142.82 4.47 2.066 27 0.158333 142.64 4.65 1.762 28 0.166667 142.47 4.82 1.745 29 0.175000 142.38 4.91 1.542 30 0.183333 142.40 4.89 1.743 31 0.191667 142.27 5.02 1.723 32 0.200000 142.18 5.11 1.709 33 0.208333 142.13 5.16 1.680 34 0.216667 141.95 5.34 1.633 35 0.225000 141.73 5.56 1.658 36 0.229167 141.95 5.34 1.615 37 0.237500 141.86 5.43 1.598 38 0.245833 141.84 5.45 1.565 39 0.266667 141.77 5.52 1.486 40 0.275000 141.66 5.63 1.447 41 0.283333 141.86 5.43 1.444 42 0.291667 141.59 5.70 1.544 43 0.300000 141.55 5.74 1.499 44 0.316667 141.46 5.83 1.423 45 0.333333 141.41 5.88 1.388 46 0.350000 141.34 5.95 1.238 47 0.366667 141.28 6.01 1.310 48 0.383333 141.21 6.08 1.252 49 0.400000 141.17 6.12 1.265 50 0.416667 141.12 6.17 1.278
5 Drawdown Test Data Data Functions: Pressure Drawdown Case (Continued) t p wf p p' Point (hr) (psia) 51 0.433333 141.05 6.24 1.319 52 0.450000 141.03 6.26 1.499 53 0.466667 140.96 6.33 1.161 54 0.483333 140.94 6.35 1.133 55 0.566667 140.76 6.53 1.108 56 0.650000 140.61 6.68 1.062 57 0.733333 140.45 6.84 1.013 58 0.816667 140.43 6.86 0.967 59 0.900000 140.29 7.00 0.933 60 0.983333 140.24 7.05 0.955 61 1.066667 140.13 7.16 0.909 62 1.150000 140.07 7.22 0.936 63 1.233333 140.02 7.27 0.881 64 1.316667 139.97 7.32 0.924 65 1.400000 139.91 7.38 0.875 66 1.500000 139.86 7.43 0.846 67 1.583333 139.78 7.51 0.909 68 1.666667 139.77 7.52 0.870 69 1.750000 139.71 7.58 0.850 70 1.827778 139.64 7.65 0.890 71 1.916667 139.57 7.72 0.913 72 2.000000 139.57 7.72 0.891 73 2.083333 139.53 7.76 0.891 74 2.166667 139.53 7.76 0.867 75 2.258333 139.53 7.76 0.823 76 2.266667 139.50 7.79 0.851
6 Pressure Buildup Test Data Data Functions: Pressure Buildup Case Point t (hr) t e (hr) Horner Time p ws (psia) p p'( t) p'( t e ) 1 0.004166 0.004158 545.17 139.57 0.24 0.260 0.263 2 0.008333 0.008302 273.05 139.82 0.49 0.538 0.541 3 0.012500 0.012431 182.36 140.07 0.74 0.753 0.759 4 0.017500 0.017366 130.54 140.36 1.03 1.074 1.084 5 0.021944 0.021734 104.31 140.58 1.25 1.202 1.216 6 0.029166 0.028795 78.73 141.03 1.70 1.522 1.544 7 0.033333 0.032850 69.01 141.23 1.90 1.590 1.617 8 0.038889 0.038233 59.29 141.44 2.11 1.810 1.845 9 0.045833 0.044925 50.46 141.79 2.46 1.912 1.955 10 0.050000 0.048921 46.34 141.97 2.64 1.934 1.981 11 0.054166 0.052902 42.85 142.09 2.76 2.024 2.077 12 0.058333 0.056869 39.86 142.26 2.93 2.039 2.097 13 0.062500 0.060823 37.27 142.42 3.09 2.086 2.169 14 0.066666 0.064761 35.01 142.56 3.23 2.101 2.166 15 0.070833 0.068687 33.00 142.67 3.34 2.101 2.160 16 0.075000 0.072598 31.23 142.82 3.49 2.103 2.175 17 0.079166 0.076494 29.64 142.89 3.56 2.061 2.137 18 0.083333 0.080378 28.20 143.05 3.72 2.025 2.101 19 0.087500 0.084248 26.91 143.18 3.85 2.092 2.192 20 0.091666 0.088103 25.73 143.27 3.94 2.081 2.188 21 0.095833 0.091946 24.66 143.36 4.03 2.072 2.157 22 0.100000 0.095775 23.67 143.41 4.08 2.043 2.146 23 0.104166 0.099589 22.76 143.52 4.19 2.029 2.119 24 0.108333 0.103391 21.93 143.59 4.26 2.017 2.115 25 0.112500 0.107180 21.15 143.66 4.33 2.027 2.090 26 0.117222 0.111458 20.34 143.74 4.41 1.994 2.156 27 0.125000 0.118467 19.14 143.90 4.57 1.971 2.066 28 0.129166 0.122202 18.55 143.92 4.59 1.992 2.086 29 0.137500 0.129636 17.49 144.02 4.69 1.961 2.082 30 0.141666 0.133333 17.00 144.10 4.77 1.898 2.066 31 0.145833 0.137018 16.55 144.17 4.84 1.906 1.994 32 0.150000 0.140690 16.11 144.24 4.91 1.881 1.983 33 0.154166 0.144348 15.70 144.28 4.95 1.856 1.992 34 0.162500 0.151629 14.95 144.37 5.04 1.882 1.993 35 0.166666 0.155251 14.60 144.42 5.09 1.862 1.947 36 0.170833 0.158860 14.27 144.46 5.13 1.849 1.928 37 0.179166 0.166041 13.65 144.55 5.22 1.772 1.933 38 0.183333 0.169614 13.37 144.60 5.27 1.785 1.921 39 0.187500 0.173175 13.09 144.62 5.29 1.777 1.931 40 0.191666 0.176723 12.83 144.71 5.38 1.761 1.907 41 0.204166 0.187296 12.10 144.80 5.47 1.688 1.865 42 0.208333 0.190797 11.88 144.82 5.49 1.727 1.816 43 0.213055 0.194749 11.64 144.84 5.51 1.706 1.883 44 0.216666 0.197762 11.46 144.91 5.58 1.678 1.838 45 0.220833 0.201228 11.27 144.96 5.63 1.694 1.766 46 0.225833 0.205371 11.04 144.98 5.65 1.690 1.744 47 0.229166 0.208124 10.89 145.03 5.70 1.644 1.817 48 0.233333 0.211555 10.72 145.05 5.72 1.569 1.686 49 0.238055 0.215430 10.52 145.07 5.74 1.532 1.657 50 0.245833 0.221780 10.22 145.11 5.78 1.565 1.608
7 Pressure Buildup Test Data Data Functions: Pressure Buildup Case (Continued) Point t (hr) t e (hr) Horner Time p ws (psia) p p'( t) p'( t e ) 51 0.250000 0.225166 10.07 145.13 5.80 1.446 1.722 52 0.254166 0.228539 9.92 145.16 5.83 1.424 1.697 53 0.258333 0.231903 9.78 145.20 5.87 1.424 1.692 54 0.263611 0.236147 9.60 145.20 5.87 1.506 1.684 55 0.266666 0.238596 9.50 145.27 5.94 1.525 1.690 56 0.270833 0.241926 9.37 145.29 5.96 1.510 1.688 57 0.279166 0.248554 9.12 145.27 5.94 1.478 1.483 58 0.283333 0.251852 9.00 145.31 5.98 1.469 1.478 59 0.287500 0.255139 8.89 145.32 5.99 1.478 1.457 60 0.300000 0.264935 8.56 145.41 6.08 1.282 1.491 61 0.308333 0.271413 8.35 145.45 6.12 1.188 1.549 62 0.316666 0.277849 8.16 145.50 6.17 1.144 1.551 63 0.325000 0.284244 7.98 145.52 6.19 1.227 1.511 64 0.333333 0.290598 7.80 145.56 6.23 1.308 1.445 65 0.342500 0.297541 7.62 145.59 6.26 1.307 1.484 66 0.350000 0.303185 7.48 145.61 6.28 1.253 1.482 67 0.358333 0.309418 7.33 145.67 6.34 1.258 1.490 68 0.366666 0.315611 7.18 145.67 6.34 1.164 1.420 69 0.383333 0.327882 6.91 145.67 6.34 1.170 1.337 70 0.391666 0.333960 6.79 145.74 6.41 1.178 1.300 71 0.416666 0.351966 6.44 145.70 6.37 1.119 1.325 72 0.420833 0.354935 6.39 145.81 6.48 1.102 1.325 73 0.425000 0.357895 6.33 145.85 6.52 1.041 1.327 74 0.433333 0.363786 6.23 145.86 6.53 1.024 1.304 75 0.443889 0.371196 6.11 145.88 6.55 1.073 1.269 76 0.450000 0.375460 6.04 145.90 6.57 1.041 1.294 77 0.458333 0.381243 5.95 145.94 6.61 1.086 1.224 78 0.466666 0.386991 5.86 145.95 6.62 1.068 1.268 79 0.475000 0.392705 5.77 145.95 6.62 1.055 1.267 80 0.508333 0.415215 5.46 145.85 6.52 0.936 1.245 81 0.516666 0.420758 5.39 145.94 6.61 0.950 1.201 82 0.525000 0.426269 5.32 146.01 6.68 0.949 1.203 83 0.533333 0.431746 5.25 146.05 6.72 0.982 1.183 84 0.541666 0.437190 5.19 146.06 6.73 0.982 1.176 85 0.550000 0.442604 5.12 146.08 6.75 0.961 1.152 86 0.558333 0.447984 5.06 146.12 6.79 0.954 1.148 87 0.575000 0.458651 4.94 146.15 6.82 0.892 1.145 88 0.583333 0.463937 4.89 146.12 6.79 0.904 1.124 89 0.591666 0.469193 4.83 146.12 6.79 0.899 1.120 90 0.666666 0.515151 4.40 146.26 6.93 0.957 1.090 91 0.723611 0.548506 4.13 146.28 6.95 0.788 1.096 92 0.752222 0.564789 4.01 146.35 7.02 0.764 1.079 93 0.836944 0.611247 3.71 146.42 7.09 0.785 0.993 94 0.850000 0.618182 3.67 146.48 7.15 0.758 0.997 95 0.866666 0.626950 3.62 146.50 7.17 0.751 1.020 96 0.883333 0.635626 3.57 146.50 7.17 0.734 1.013 97 0.902777 0.645632 3.51 146.51 7.18 0.721 1.003 98 0.977777 0.683105 3.32 146.55 7.22 0.732 1.015 99 1.066666 0.725333 3.13 146.60 7.27 0.651 0.941 100 1.150000 0.762927 2.97 146.64 7.31 0.686 0.977
8 Pressure Buildup Test Data Data Functions: Pressure Buildup Case (Continued) Point t (hr) t e (hr) Horner Time p ws (psia) p p'( t) p'( t e ) 101 1.233333 0.798730 2.84 146.69 7.36 0.637 0.973 102 1.316666 0.832868 2.72 146.73 7.40 0.629 0.932 103 1.400000 0.865455 2.62 146.77 7.44 0.584 0.933 104 1.477777 0.894560 2.53 146.82 7.49 0.607 0.993 105 1.566666 0.926377 2.45 146.84 7.51 0.600 0.938 106 1.662500 0.959067 2.36 146.86 7.53 0.583 0.923 107 1.733333 0.982222 2.31 146.88 7.55 0.579 0.876 108 1.816666 1.008435 2.25 146.91 7.58 0.582 0.888
Log-Log Plot (Pressure Drawdown Case) Log-Log Plot: Pressure Drawdown Case Pressure Drop and Pressure Drop Derivative Data 9
Early-Time Cartesian Plot: Pressure Drawdown Case Early-Time Cartesian Plot (Pressure Drawdown Case) 10
Semilog Plot: Pressure Drawdown Case Semilog Plot (Pressure Drawdown Case) 11
Log-Log Plot (Pressure Buildup Case t Format (No Rate History)) Log-Log Plot: Pressure Buildup Case Pressure Drop and Pressure Drop Derivative Data ( t Format (No Rate History)) 12
Log-Log Plot (Pressure Buildup Case t e Format (Includes Rate History)) Log-Log Plot: Pressure Buildup Case Pressure Drop and Pressure Drop Derivative Data ( t e Format (Includes Rate History) 13
Early-Time Cartesian Plot: Pressure Buildup Case Early-Time Cartesian Plot (Pressure Buildup Case) 14
Semilog Plot: Pressure Buildup Case t Format (No Rate History) Semilog Plot (Pressure Buildup Case t Format (No Rate History)) 15
Semilog Plot (Pressure Buildup Case Horner Time Format (Includes Rate History)) Pressure Buildup Case: Horner Time Format (Includes Rate History) 16
Late-Time Cartesian Plot ("Muskat Plot"): Pressure Buildup Case Late-Time Cartesian Plot ("Muskat Plot") (Pressure Buildup Case) 17