{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "ESE - Numerical Methods I: Loading an Plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the primary purposes of programming is automatization. Whenever you work on data, you should try to avoid any manual intervention such as copying and pasting from one file to another, for example into an excel spreadsheet. This introduces a source of error and severely limits the amount of data you can process. Further, whenever you change parts of your program, it is likely that the manual steps have to be repeated. For all your work on data, good practice is to work on the rawest form of files you get, i.e., the ones supplied by a contractor or produced by the measurement apparatus." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the most important data sources in subsurface geoscience are well logs. These are cylindrical logging tools of a length between one and several dozens of meters that are being run up and down wellbores along a wireline and measure, collect and transmit rock formation data such as electrical resistivity, radiation, temperature and more, as a function of depth. This allows for accurate chracterization of lithologic layers, rock properties, oil saturation and more, to a high resolution.\n", "\n", "\n", "" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "import os\n", "import numpy as np\n", "from scipy import integrate\n", "import matplotlib.pyplot as plt" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "A common well log file in the raw *LAS* format looks as follows (we print the first 55 lines and skip the rest of the data section):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fname = '1044944685.las'\n", "lines_to_display = 55\n", "with open(fname, 'r') as f:\n", " for i in range(lines_to_display):\n", " print f.readline().rstrip()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "~Version Information\n", "VERS. 2.0: CWLS Log ASCII Standard - VERSION 2.0\n", "WRAP. NO: One line per depth step\n", "~Well Information Block\n", "STRT.FT 245.0000: START DEPTH\n", "STOP.FT 2530.5000: STOP DEPTH\n", "STEP.FT 0.5000: STEP\n", "NULL. -999.2500: NULL VALUE\n", "COMP. Vess Oil Corporation: COMPANY\n", "WELL. Wilson A #448: WELL\n", "FLD. El Dorado: FIELD\n", "LOC. 330' FNL & 1550' FWL: LOCATION\n", "CNTY. Butler: COUNTY\n", "SRVC. : SERVICE COMPANY\n", "DATE. Wed Apr 17 07-22-29 2013: LOG DATE\n", "UWI. : UNIQUE WELL ID\n", "STAT. Kansas: STATE\n", "SECT. 9: SECTION\n", "TOWN. 25S: TOWNSHIP\n", "RANG. 5E: RANGE\n", "API. 15-015-23969-00-00: API#\n", "PDAT.FT Ground Level: PERMANENT DATUM\n", "LMF.FT Kelly Bushing: LOG MEASURED FROM\n", "DMF.FT Kelly Bushing: DRILLING MEASURED FROM\n", "EKB.FT 1371: KB\n", "EDF.FT : DF\n", "EGL.FT 1365: GL\n", "DATE1. 4/17/2013: DATE1\n", "ENGI1. D. Schmidt: RECORDED BY\n", "WITN1. Roger Martin: WITNESSED BY\n", "~Curve Information Block\n", "DEPT.FT 0 000 00 00: Depth\n", "BVTX. :\n", "AVTX. :\n", "DCAL.GAPI CDL Caliper:\n", "RHOB. CDL Bulk Density:\n", "RHOC. CDL Density Correction:\n", "DPOR. CDL Density Porosity:\n", "CNLS. CN Limestone Porosity:\n", "GR. Gamma Ray:\n", "CILD. DIL Deep Conductivity:\n", "RILD. DIL Deep Resistivity:\n", "RILM. DIL Medium Resistivity:\n", "RLL3. DIL Shallow Resistivity:\n", "RxoRt. Rxo / Rt:\n", "SP.MV DIL Spontaneous Potential:\n", "DGA. Apparent Grain Density:\n", "~Parameter Information Block\n", "~A Depth BVTX AVTX DCAL RHOB RHOC DPOR CNLS GR\n", " 245.0000 0.0000 0.0000 1.7734 1.8916 0.2025 47.8581 29.3674 52.3655\n", " 245.5000 0.0000 0.0000 1.7738 1.9023 0.2070 47.2337 29.6285 49.6518\n", " 246.0000 0.0000 0.0000 1.7741 1.9094 0.2103 46.8160 30.6172 47.9509\n", " 246.5000 0.0000 0.0000 1.7740 1.9142 0.2122 46.5372 32.2842 50.2727\n", " 247.0000 0.0000 0.0000 1.7745 1.9168 0.2133 46.3889 33.6512 52.2234\n", " 247.5000 0.0000 0.0000 1.7739 1.9171 0.2146 46.3682 33.4263 50.6780\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll try to keep things simpel here. Say we *know* that the data array always starts at line 49, then we can load the entire dataset by using loadtxt, telling the method to skip everything before that line/row." ] }, { "cell_type": "code", "collapsed": false, "input": [ "las_data = np.loadtxt(fname, skiprows=49)\n", "print 'readings/rows, logs/columns:'\n", "print las_data.shape\n", "print 'values:'\n", "print las_data" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "readings/rows, logs/columns:\n", "(4544L, 9L)\n", "values:\n", "[[ 2.45000000e+02 0.00000000e+00 0.00000000e+00 ..., 4.78581000e+01\n", " 2.93674000e+01 5.23655000e+01]\n", " [ 2.45500000e+02 0.00000000e+00 0.00000000e+00 ..., 4.72337000e+01\n", " 2.96285000e+01 4.96518000e+01]\n", " [ 2.46000000e+02 0.00000000e+00 0.00000000e+00 ..., 4.68160000e+01\n", " 3.06172000e+01 4.79509000e+01]\n", " ..., \n", " [ 2.51550000e+03 0.00000000e+00 0.00000000e+00 ..., 7.16980000e+00\n", " 2.88235000e+01 9.78750000e+00]\n", " [ 2.51600000e+03 0.00000000e+00 0.00000000e+00 ..., 7.43490000e+00\n", " 2.97673000e+01 1.15010000e+00]\n", " [ 2.51650000e+03 0.00000000e+00 0.00000000e+00 ..., 7.61220000e+00\n", " 3.22248000e+01 6.37000000e-02]]\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Which creates a two-dimensional array containing all logs (columns) and their readings (rows). If we further know that `Depth` is in column `0`, and our log of interest `RHOB` is in column `4`, we can extract the corresponding data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "las_depth = las_data[:,0] # all readings of log 0\n", "las_rhob = las_data[:,4] # all readings of log 4\n", "print las_depth\n", "print las_rhob" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 245. 245.5 246. ..., 2515.5 2516. 2516.5]\n", "[ 1.8916 1.9023 1.9094 ..., 2.5874 2.5829 2.5798]\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have now extracted our arrays of interest, and can plot the measured rock density as a function of depth:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(las_rhob, las_depth)\n", "# so that depth, albeit positive, increases downward\n", "plt.gca().invert_yaxis()\n", "# cosmetics\n", "plt.xlim(0.,3.)\n", "plt.xlabel('Specific Bulk Density [-]')\n", "plt.ylabel('Depth [ft]')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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RtG2rGRtS38r/YR0dHV2r49T7UBY/Pz9s2rQJBQUF2LRpkzoQ+Pr6Yvfu3bh27RoSEhJg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\nJMnZ2Vm9PiYmRvrwww8rHL9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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will operate on the extracted data now, and plot the result. The simple operation is\n", "\n", "$\\sigma(z) = g \\int \\rho dz$\n", "\n", "to compute the overburden stress resulting from the lithostatic (rock) weight. We will therefore first convert the density from specific to [kg m-3] and the depth from [ft] to [m]" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rhob = las_rhob*1.0E3\n", "depth = las_depth*0.3048" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "and then use a `scipy` function to perform the integration" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# sigma(z) = g int rho dz\n", "overburden_stress_pa = 9.81 * integrate.cumtrapz(rhob, depth, initial=0)\n", "overburden_stress_mpa = overburden_stress_pa/1.0E6" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(overburden_stress_mpa, depth)\n", "# so that depth, albeit positive, increases downward\n", "plt.gca().invert_yaxis()\n", "# cosmetics\n", "plt.xlabel('$\\sigma_v$ [MPa]')\n", "plt.ylabel('Depth [m]')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Problems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. The log `DCAL` measures the diamater of the wellbore in [in]. Plot its readings vs depth, and integrate the cross-sectional area (use `np.pi` as $\\pi$) to plot the cumulative borehole volume in [m3] vs [m]. (Download the notebook and las file here)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "las_dcal = las_data[:,3] # all readings of log 3" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(las_dcal, las_depth)\n", "# so that depth, albeit positive, increases downward\n", "plt.gca().invert_yaxis()\n", "# cosmetics\n", "plt.xlabel('Wellbor Diameter [in]')\n", "plt.ylabel('Depth [ft]')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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HJu5Oo6dEqrDr12H5cjh2DFavhhdegIgI6N/f6sjEXSlpiHgAw4D4eJgyBWrV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\nmWf49ttvATh+/DhxcXGEhIT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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "dcal = las_dcal*0.0254 # from [in] to [m]\n", "xarea = np.pi * dcal**2/4. # cross-sectional area [m2], dcal=diameter" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "# V(z) = int area dz\n", "volume_m3 = integrate.cumtrapz(xarea, depth, initial=0)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(volume_m3, depth)\n", "# so that depth, albeit positive, increases downward\n", "plt.gca().invert_yaxis()\n", "# cosmetics\n", "plt.xlabel('Wellbore Volume [m3]')\n", "plt.ylabel('Depth [m]')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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EBNi2zeqo5FxaOvPgR48eZdu2bUybNo1BgwbxwAMP8O6779arU8Rms9V4LjMz\n03E/Pj6e+Pj4BohWRBpLjx6wdq259EZ0NGRkwLhx0KqV1ZE1HwUFBRQUFFzw550+WikoKIiKigoA\nFi9ezBtvvMHx48eZOHEi4eHhrF+/nsmTJ/P++++zcOFC8vPzycrKAiAsLIzVq1fj4+Pzc8AarSTS\nrOzcCQ88APv3w6uvmpsLScNzudFK/v7+FBcXc/r0aT766CMGDRpEZGQkeXl5VFVVkZeXR1RUFAAR\nEREsXbqU3bt3U1BQgIeHR7XEICLNz7XXwtKl8Pjj5uimp56CqiqroxKnVw7btm3j7rvv5ujRowwa\nNIhnn32W06dPM2rUKMrLy+nduzfz5s3D29sbgKysLHJycvD09GT27NnExMRUD1iVg0iz9e23kJ5u\nLsXxj3+AWowbTn1/OzUJTkRczoIF5npNN98MU6dCu3ZWR9T0uVyzkohIfQ0dak6ea9HC7Lz+8EOr\nI3I/qhxExKWtXAl/+IO5ydDLL8MVV1gdUdOkykFEmpW4OHNr0m7doGdPmD/f6ojcgyoHEWkyiopg\nzBjo18+cI6GF/M6fKgcRabb694cNG6BjRwgNhY8+sjqi5kuVg4g0SStWQEqKuQTHjBnmyq9SO1UO\nIuIWBg6ETZvMEU09e8Ly5VZH1LyochCRJm/JErjvPrjtNnjhBWjb1uqIXI8qBxFxO4mJsHkzHDxo\nLge+Zo3VETV9qhxEpFn58ENIS4PRo+Evf4HWra2OyDWochARt5acbPZFfPkl9OkD69ZZHVHTpOQg\nIs3O5ZfDe+/BxIlw660wYQIcPWp1VE2LkoOINEs2G4wcac6L2LbNHNF0EXvfuB31OYiIWziz0uvg\nwTBtGrRvb3VEjUt9DiIi5zB0KGzZYnZQh4TAu++C/s6snSoHEXE7a9eaK73+5jcwcyZcc43VETmf\nKgcRkTpER0N5OUREmHtW5+TAqVNWR+VaVDmIiFv7/HO4/344ccLcmrRHD6sjcg5VDiIi9RAYaI5i\nuucec72miRM17BWcnBz+/e9/Ex4e7rj5+vqSnZ3N4cOHSUpKwm63k5yczOHDhx2fyc7Oxt/fn+Dg\nYAoLC50ZnogIAB4e8MAD5qZCFRXmrnMrV1odlbUarVnp9OnTXH311ZSUlPDWW2+xZ88epk+fzrhx\n4/Dz8yMjI4N9+/YRGxvLsmXL2LlzJ2PHjqWsrKx6wGpWEhEn+/BDePRRuOUWmDoVfH2tjujiuWyz\nUn5+Pt2ED9QWAAAPEUlEQVS7d+eaa66hpKSE1NRUvLy8SElJobi4GIDi4mISExOx2+3ExcVhGAaV\nlZWNFaKICGAuwfHZZ+ZQ1x493HNToUZLDm+//TYjR44EoLS0lMDAQAACAwMpKSkBzOQQFBTk+ExA\nQIDjNRGRxuTrC6+8AnPmmFXE3XfDgQNWR9V4WjbGSY4fP87ChQuZMmUKQL1KG5vNVuO5zMxMx/34\n+Hji4+MvNkQRkXNKSDCXA58wwdyaNDsbfvc7q6OqW0FBAQUXs16I0Qg+/PBDY/DgwY7Hw4YNM8rK\nygzDMIx169YZw4cPNwzDMBYsWGCkp6c73terVy/j0KFD1Y7VSCGLiNSwZo1hBAQYxvDhhvHNN1ZH\nUz/1/e1slGalt956y9GkBBAZGUleXh5VVVXk5eURFRUFQEREBEuXLmX37t0UFBTg4eGBj49PY4Qo\nIlKn6GhzIb/rrjNHNM2d23yX4HD6aKUff/yRrl27snPnTscPfWVlJaNGjaK8vJzevXszb948vL29\nAcjKyiInJwdPT09mz55NTExM9YA1WklEXEBZGdx7L1x9Ncye7fpLcNT3t1MzpEVELtDx4zBlitkP\n8dxz5npNHi46tVjJQUSkkW3ZAikp0LatuQRHt25WR1STy85zEBFprkJCzJVeb70VIiNhxoymv5Cf\nKgcRkQa0fTvcd5/Z5JSXB2dN3bKUKgcREQv5+8OKFeakudhYeP55c8XXpkaVg4iIk/znP+aCfvv2\nmVVEWJh1sahyEBFxEV27wuLFkJ4ON91kLgd+7JjVUZ0fJQcRESey2cy9IjZuNEc19e4NP6016tLU\nrCQi0kgMA957Dx57DO68E/76V7jkksY5t5qVRERclM0GI0aYC/nt3Qs9e5q70LkiVQ4iIhZZuBDS\n0mDIEHOm9aWXOu9cqhxERJqIIUPMTYVOnjSXA1+yxOqIfqbKQUTEBeTnm2szxcaaM6wvu6xhj6/K\nQUSkCRo0yOyL8PU1+yIWL7Y2HlUOIiIuZsUKc/jrtGlmB3ZD0KqsIiLNwMGD0KpVww11VXIQEZEa\n1OcgIiIXTclBRERqcGpy+Mc//kF0dDR9+vTh8ccfB8z9o5OSkrDb7SQnJ3P48GHH+7Ozs/H39yc4\nOJjCwkJnhiYiIr/Cacnh+++/5/nnn+eTTz6htLSUbdu2sXTpUnJzc7Hb7Wzfvp0uXbowa9YsAPbt\n28fMmTNZvnw5ubm5pKenOyu0ZqPAVefdW0DX4me6Fj/TtbhwTksObdq0wTAMDh48SFVVFUeOHKFd\nu3aUlJSQmpqKl5cXKSkpFP+0PGFxcTGJiYnY7Xbi4uIwDIPKykpnhdcs6Iv/M12Ln+la/EzX4sI5\nNTnk5ubi5+dH586dGTBgAJGRkZSWlhIYGAhAYGAgJSUlgJkcgs7aTy8gIMDxmoiINC6nJYf9+/eT\nlpbG1q1b2bVrF0VFRSxatKh+42xtNmeFJyIiv8ZwkkWLFhm333674/HMmTONP/7xj8awYcOMsrIy\nwzAMY926dcbw4cMNwzCMBQsWGOnp6Y739+rVyzh06FCN43br1s0AdNNNN910q8etW7du9foNb4mT\nxMTE8Nhjj/H999/Ttm1bFi9ezGOPPUaHDh3Iy8tj6tSp5OXlERUVBUBERARPPvkku3fv5ssvv8TD\nwwMfH58ax/3iiy+cFbKIiPzEacnh0ksvZeLEidx2220cOXKExMREBg4cSEREBKNGjSIgIIDevXsz\nZcoUADp16kRaWhoJCQl4enoye/ZsZ4UmIiJ1aHLLZ4iIiPM1qRnSq1atIigoCH9/f3JycqwOx1J+\nfn707NmT8PBwIiIirA6nUaWkpNCpUydCQ0Mdz/3a5Mrm7FzXIjMzky5duhAeHk54eDhLXGkHGSfZ\ns2cPAwcOJCQkhPj4eN58803APb8XtV2Len8v6t/VbJ2wsDBj5cqVxq5du4yAgABj//79VodkGT8/\nP+PAgQNWh2GJVatWGWVlZUaPHj0cz02ZMsV45JFHjKNHjxoPP/ywMW3aNAsjbDznuhaZmZnG3//+\ndwujanzffPONUV5ebhiGYezfv9+49tprjUOHDrnl96K2a1Hf70WTqRwOHjwIQGxsLF27duWmm25y\nTKBzV4abtgjGxMTQvn37as/VNrmyuTvXtQD3+2507tyZsLAwADp27EhISAilpaVu+b2o7VpA/b4X\nTSY5nD15DiA4OJhPP/3UwoisZbPZSEhIIDk5mQULFlgdjuVqm1zprnJycoiKimLKlClut9LAF198\nwZYtW4iIiHD778WZaxEZGQnU73vRZJKDVLdmzRo2btzI5MmTeeKJJ9i7d6/VIVnK3f5S/jVpaWns\n3LmTpUuXsmPHDrca+VdZWcntt9/OjBkz8Pb2duvvxdnXom3btvX+XjSZ5NCvXz8+//xzx+MtW7Y4\n5ki4oyuvvBKAoKAghg4dysKFCy2OyFr9+vWjoqICgIqKCvr162dxRNa54oorsNls+Pr68vDDD/Ov\nf/3L6pAaxYkTJxg+fDijR48mKSkJcN/vxbmuRX2/F00mOfj6+gLmiKVdu3bxySefOEold3PkyBFH\nSbh//36WLl1KYmKixVFZKzIykry8PKqqqqpNrnRH33zzDQAnT57kzTff5JZbbrE4IuczDIPU1FR6\n9Ojh2B4A3PN7Udu1qPf3osG7yp2ooKDACAwMNLp162ZkZWVZHY5lvvzyS6NXr15Gr169jISEBOPV\nV1+1OqRGdccddxhXXnml4enpaXTp0sXIy8szDh06ZAwdOtS45pprjKSkJKOystLqMBvFmWvRqlUr\no0uXLsarr75qjB492ggNDTX69OljjB071i1Gta1evdqw2WxGr169jLCwMCMsLMxYvHixW34vznUt\nPv7443p/LzQJTkREamgyzUoiItJ4lBxERKQGJQcREalByUFERGpQchARkRqUHEREpAYlBxERqUHJ\nQRrd2LFjycrKcjwePHgwf/jDHxyPx40bx4wZM2r9/D333MP8+fMBiI+Pp6ysDABvb28nRWxauXIl\n0dHR1Z47efIknTp1qnVtq9dff51HH33UqXH98nyXX345999/f70+98wzz9CrVy/CwsIYPXo0Bw4c\nAGD16tUEBwdX2y9C3IOSgzS666+/nrVr1wJw+vRpDhw4wNatWx2vFxUVMWDAgFo/b7PZsNlsjvtn\nP3+hTp06Ved7YmJi+Oqrr9i9e7fjufz8fEJDQ+ncuXOtsTYmm83GyJEjeeWVV+r1uT/+8Y9s3LiR\nDRs24O/v70jeMTExLF682BmhiotTcpBG179/f4qKigBzAcUePXrg4+PDDz/8wLFjx6ioqKB37978\n+9//Ji0tjcjISB5++GHHX7O/ZsKECQQGBvL444/zww8/ALB9+3ZSUlIICwtj0qRJjnWp4uPjmTBh\nAn379iU7O7vO83l4eDBixAjefvttx3Nvv/02I0eO5NChQzzzzDOEhYWRmprKjh07asR2dsUDP1c6\nBQUF3HDDDQwfPpzu3bvzwgsv8K9//Yu+ffty880389VXXwHw3//+l2effZYBAwbw+9//ng0bNpzz\nGpy96MHrr7/O7bffzk033cR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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }