Lorenz_coefficient_demo.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Demonstration of Lorenz Coefficient for Quantifying Spatial, Subsurface Heterogeneity\n",
    "\n",
    "#### Alan Scherman, Rice University, UT PGE 2020 SURI\n",
    "\n",
    "#### Supervised and Updated Plots by:\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, The University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1) | [GeostatsPy](https://github.com/GeostatsGuy/GeostatsPy)\n",
    "\n",
    "***\n",
    "#### Introduction\n",
    "\n",
    "This is a demonstration of how to calculate the Lorenz Coefficient of a subsurface sample from well log porosity and permeability measurements. The Lorenz Coefficient is an important heuristic imported form the sphere of macroeconomics used to quantify the spatial heterogeneity of a subsurface sample. The Lorenz Coefficient is obtained by doubling the area between the Lorenz Curve and the Homogeneous Line. It ranges from 0 to 1 where, by convention, a coefficient of less than 0.3 suggests low heterogeneity and a coefficient of more than 0.6 indicates high heterogeneity. In practical terms, a low spatial heterogeneity allows for simple displacement of subsurface fluids and a high recovery factor.\n",
    "***\n",
    "#### Objective\n",
    "\n",
    "To understand and apply the methodology to calculate the Lorenz Curve and Coefficient from porosity and permeability measurements through Python functionalities.\n",
    "\n",
    "***\n",
    "#### Calculation procedure\n",
    "\n",
    "The following list contains the necessary steps to determine the Lorenz Coefficient of a subsurface sample:\n",
    "\n",
    "**(1)** Sort porosity ($\\phi$) and permeability (**_k_**) in descending order of ratio **_k_**/$\\phi$;\n",
    "\n",
    "**(2)** Calculate storage (**_S.C._**) and flow capacity (**_F.C._**) of each layer (region between depth measurements) with:\n",
    "\n",
    "<br>\n",
    "\\begin{equation}\n",
    "S.C. = \\phi*h\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "F.C. = k*h\n",
    "\\end{equation}\n",
    "\n",
    "where **_h_** is the layer thickness;\n",
    "\n",
    "**(3)** Calculate the _cumulative_ storage (**_C.S.C._**) and flow capacities (**_C.F.C._**) of each layer with:\n",
    "\n",
    "<br>\n",
    "\\begin{equation}\n",
    "C.S.C. = \\sum^{current layer}_{i = 1} \\phi*h\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "C.F.C. = \\sum^{current layer}_{i = 1} k*h\n",
    "\\end{equation}\n",
    "\n",
    "**(4)** Normalize the cumulative storage and flow capacities by dividing them by the largest cumulative storage and flow capacities (i.e. the last cumulative capacities calculated), respectively;\n",
    "\n",
    "**(5)** _(Optional)_ Plot the normalized cumulative flow capacities against the normalized cumulative storage capacities (i.e. the Lorenz Curve);\n",
    "\n",
    "**(6)** Find a curve fit for the normalized capacities in the Cartesian plane (usually a 3rd degree polynomial is sufficient);\n",
    "\n",
    "**(7)** Integrate to find the area between the Lorenz Curve and the Homogenous Line;\n",
    "\n",
    "**(8)** Divide the result found in **(7)** by 0.5 to obtain the Lorenz Coefficient:\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "LorenzCoefficient = \\frac{\\int^{1}_{0} (LorenzCurve - HomogeneousLine)}{0.5}\n",
    "\\end{equation}\n",
    "***\n",
    "#### Load the required libraries\n",
    "\n",
    "The program below utilizes some standard Python packages. These should be previously installed if you have Anaconda or other similar software."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd                                                  # To import data from .xlsx or .csv file\n",
    "import numpy as np                                                   # For numerical array management\n",
    "from matplotlib import pyplot as plt                                 # For graphical display of Lorenz Curve\n",
    "from matplotlib.ticker import (MultipleLocator, AutoMinorLocator) # control of axes ticks\n",
    "plt.rc('axes', axisbelow=True)                            # set axes and grids in the background for all plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you get a package import error, you may have to first install some of these packages. This can usually be accomplished by opening up a command window on Windows and then typing 'python -m pip install [package-name]'. More assistance is available with the respective package docs. \n",
    "***\n",
    "#### Importing porosity and permeability data\n",
    "\n",
    "The data file for this demonstration is availbale at [here](https://github.com/GeostatsGuy/GeoDataSets/blob/master/WellPorPermSample_3.xlsx). \n",
    "\n",
    "The well log data will be imported from an Excel (.xlsx) file. There are similar Pandas methods which allow the importation of data from .csv and other common file types. First, the Excel data is stored as a Pandas data frame. Then, the depth, porosity, and permeability data are placed into separate data frames by means of their Excel column names. Make sure that the strings match every character of the column titles in the Excel file.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#df = pd.read_excel('WellPorPermSample_3.xlsx')                # Include file directory with os.chdir() method if necessary\n",
    "df = pd.read_csv('https://raw.githubusercontent.com/GeostatsGuy/GeoDataSets/master/WellPorPermSample_3.csv') # load from Dr. Pyrcz's GitHub respository\n",
    "depth = pd.DataFrame(df, columns = ['Depth (m)']); \n",
    "poros = pd.DataFrame(df, columns = ['Por (%)']); \n",
    "perme = pd.DataFrame(df, columns = ['Perm (mD)']); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To certify that the subsurface data have been imported appropriately:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Depth (m)</th>\n",
       "      <th>Por (%)</th>\n",
       "      <th>Perm (mD)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.25</td>\n",
       "      <td>13.0</td>\n",
       "      <td>265.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.50</td>\n",
       "      <td>13.6</td>\n",
       "      <td>116.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.75</td>\n",
       "      <td>9.0</td>\n",
       "      <td>136.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.00</td>\n",
       "      <td>17.6</td>\n",
       "      <td>216.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.25</td>\n",
       "      <td>9.4</td>\n",
       "      <td>131.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Depth (m)  Por (%)  Perm (mD)\n",
       "0       0.25     13.0      265.5\n",
       "1       0.50     13.6      116.9\n",
       "2       0.75      9.0      136.9\n",
       "3       1.00     17.6      216.7\n",
       "4       1.25      9.4      131.6"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "#### Convert data frames to NumPy arrays\n",
    "\n",
    "In order to facilitate data management and allow the use of helpful mathematical methods, we'll convert the Pandas data frames to NumPy arrays. Also, let's transpose the arrays to row format for conventionality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "depth = np.transpose(depth.to_numpy()[:,0])\n",
    "poros = np.transpose(poros.to_numpy()[:,0])\n",
    "perme = np.transpose(perme.to_numpy()[:,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's always a good idea to check after every step in our workflows! Let's preview the resulting arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "depth = [0.25 0.5  0.75 1.   1.25] \n",
      "poros = [13.  13.6  9.  17.6  9.4] \n",
      "perme = [265.5 116.9 136.9 216.7 131.6]\n"
     ]
    }
   ],
   "source": [
    "print('depth =', depth[:5], '\\nporos =', poros[:5], '\\nperme =', perme[:5])   # To visualize the first 5 elements of each array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "#### Determine thicknesses of layers\n",
    "\n",
    "The layer thickness is found by subtracting a shallower depth from a deeper depth. For most well logs, the layers will have a uniform thickness. However, irregular thicknesses are also possible and should be accounted for. Whichever is the case, the layer thicknesses array can be calculated in the following manner:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "layer_thick = depth - np.concatenate(([0],depth[:-1])) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the layer_thick array should have the same dimensions as the porosity and permeability arrays.\n",
    "***\n",
    "#### Step (1) - Sort data in decreasing order of k/$\\phi$ \n",
    "\n",
    "Recall that the first step to calculate the Lorenz Coefficient is to sort all layers in descending order of their ratio of permeability by porosity. Because both the porosity and permeability values are expressed as NumPy arrays, these ratios can be easily obtained by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ratio = perme/poros                                                           # Equivalent to np.multiply(perme,poros)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, it's possible to sort the layer thickness, porosity and permeability arrays in the desired pattern:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "layer_thick = np.flip(layer_thick[np.argsort(ratio)], axis = 0); \n",
    "poros = np.flip(poros[np.argsort(ratio)], axis = 0)\n",
    "perme = np.flip(perme[np.argsort(ratio)], axis = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "#### Step (2) - Calculate storage and flow capacities\n",
    "\n",
    "The storage and flow capacities are found by performing element-wise multiplication of the porosity and permeability arrays by the thickness array. Hence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "storage_cap = poros*layer_thick\n",
    "flow_cap = perme*layer_thick"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "#### Step (3) - Calculate the cumulative storage and flow capacities\n",
    "\n",
    "The next step is to compute the cumulative capacities for each layer. An easy solution to this assignment is provided by a for-loop. First, we pre-allocate the cumulative storage and flow capacities arrays. Then, we set the cumulative capacities of the first layer equal to its own capacities. Finally, we run a for-loop to compute the remaining cumlative capacities for the sequential layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "cumul_storage_cap = np.zeros(len(flow_cap)+1)\n",
    "cumul_flow_cap = np.zeros(len(flow_cap)+1)\n",
    "    \n",
    "cumul_storage_cap[1] = storage_cap[0]\n",
    "cumul_flow_cap[1] = flow_cap[0]\n",
    "        \n",
    "for i in range(2,len(flow_cap)+1):\n",
    "    cumul_storage_cap[i] = cumul_storage_cap[i-1] + storage_cap[i-1]\n",
    "    cumul_flow_cap[i] = cumul_flow_cap[i-1] + flow_cap[i-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the length of the cumulative capacities arrays are one index greater than the flow and storage capacity arrays. In fact, the first entry of both arrays is set to 0 (zero) in order to ensure convergence of the future Lorenz Curve to the origin.\n",
    "\n",
    "***\n",
    "#### Step (4) - Normalize the cumulative storage and flow capacities\n",
    "\n",
    "To normalize the cumulative storage and flow capacities (i.e. limiting the range to [0,1]), we'll perform element-wise division of the cumulative storage and flow capacities by the sum of the all layers' storage and flow capacities, respectively. Thus, the normalized (also known as fractional) storage and flow capacities are given by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "frac_storage_cap = cumul_storage_cap/cumul_storage_cap[-1]\n",
    "frac_flow_cap = cumul_flow_cap/cumul_flow_cap[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "#### Step (5) - Plot the Lorenz Curve\n",
    "\n",
    "Even though we say plot the Lorenz Curve, we'll indeed plot the fractional flow capacities against the fractional storage capacities (i.e. we'll plot some of the points on the Lorenz Curve).\n",
    "\n",
    "Let's instantiate a figure to hold our Lorenz Curve points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(111)\n",
    "plt.plot([0,1], [0,1], color = 'red', label = 'Homogeneous Line',linewidth=2)            # Homogeneous line\n",
    "plt.scatter(frac_storage_cap, frac_flow_cap, marker = 'o',s=20, \n",
    "         label = 'Lorenz Curve Points',color = 'darkorange',edgecolor = 'black',alpha=0.8)                # Sample points of Lorenz Curve\n",
    "plt.xlim([0,1]); plt.ylim([0,1])\n",
    "plt.grid(True, which='major',linewidth = 1.0); plt.grid(True, which='minor',linewidth = 0.2) # add y grids\n",
    "plt.tick_params(which='major',length=7); plt.tick_params(which='minor', length=4)\n",
    "plt.gca().xaxis.set_minor_locator(AutoMinorLocator()); plt.gca().yaxis.set_minor_locator(AutoMinorLocator()) # turn on minor ticks\n",
    "\n",
    "plt.title('Lorenz Curve')\n",
    "plt.xlabel('Cumulative Fraction of Storage Capacity ($m$)')\n",
    "plt.ylabel('Cumulative Fraction of Flow Capacity ($mD \\cdot m$)')\n",
    "plt.legend(loc = 'lower right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.1, wspace=0.2, hspace=0.3); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "#### Step (6) - Find a curve fit\n",
    "\n",
    "Now that we have some of the data points of the Lorenz Curve, we can apply a curve fit to predict the behavior of this entire subsurface sample. We'll use a 3rd degree polynomial to fit the Lorenz Curve. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "poly_fit =  [ 2.83252318e-01 -1.00166028e+00  1.71840790e+00  1.64140836e-07]\n"
     ]
    }
   ],
   "source": [
    "weights = np.ones(len(frac_storage_cap))                                     \n",
    "weights[0] = 1000; weights[-1] = 1000                                           # To ensure the fit converges to (0,0) and (1,1)\n",
    "    \n",
    "poly_fit = np.polyfit(frac_storage_cap, frac_flow_cap, deg=3, w=weights)\n",
    "print('poly_fit = ', poly_fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting array contains the coefficients of the polynomial fit. To better visualize this polynomial in standard equation form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        3         2\n",
      "0.2833 x - 1.002 x + 1.718 x + 1.641e-07\n"
     ]
    }
   ],
   "source": [
    "poly_fit = np.poly1d(poly_fit)\n",
    "print(poly_fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "#### Step (7) - Integrate to find the area between the Lorenz Curve and the Homogenenous LIne\n",
    "\n",
    "The advantage of having applied the _numpy.poly1d()_ method on Step (6) is that we now have a callable object for which we can evaluate it over any domain (here [0,1]). Then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         4          3          2\n",
      "0.07081 x - 0.3339 x + 0.8592 x + 1.641e-07 x\n"
     ]
    }
   ],
   "source": [
    "integral = np.polyint(poly_fit)\n",
    "print(integral)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result above can be easily validated since the fit has polynomial behavior. Now, we can evaluate the definite integral for the area under the Lorenz Curve and then subtract the area under the homogeneous line (i.e. area of isosceles triangle of side length 1 = 0.5):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.09613043353885176\n"
     ]
    }
   ],
   "source": [
    "lorenz_area = integral(1) - integral(0) - 0.5 \n",
    "print(lorenz_area)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that for practical purposes the integral(0) term could have been ignored since the integration constant is assumed to be 0.\n",
    "***\n",
    "#### Step (8) - Obtain the Lorenz Coefficient\n",
    "\n",
    "The final step of this procedure is to divide the _lorenz_area_ calculated on Step (7) by 0.5, which is the total area between the lines **y = 1** and **y = x** in the domain [0,1]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lorenz Coefficient = 0.192\n"
     ]
    }
   ],
   "source": [
    "lorenz_coefficient = lorenz_area/0.5\n",
    "print('Lorenz Coefficient = %.3f' %lorenz_coefficient)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the Lorenz Coefficient sits below the conventional threshold of 0.3, we can assume that the subsurface sample near the well exhibits simple displacement of fluids and a potentially high recovery factor.\n",
    "\n",
    "Let's replicate the plot from Step (5) with shaded areas to better illustrate this Lorenz Coefficient:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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    }
   ],
   "source": [
    "#plt.plot([0,1], [0,1], color = 'black', label = 'Homogeneous Line',linewidth=2)            # Homogeneous line\n",
    "plt.scatter(frac_storage_cap, frac_flow_cap, marker = 'o',s=20, \n",
    "         label = 'Lorenz Curve Points',color = 'darkorange',edgecolor = 'black',alpha=0.8,zorder=10)                # Sample points of Lorenz Curve\n",
    "plt.xlim([0,1]); plt.ylim([0,1])\n",
    "plt.grid(True, which='major',linewidth = 1.0); plt.grid(True, which='minor',linewidth = 0.2) # add y grids\n",
    "plt.tick_params(which='major',length=7); plt.tick_params(which='minor', length=4)\n",
    "plt.gca().xaxis.set_minor_locator(AutoMinorLocator()); plt.gca().yaxis.set_minor_locator(AutoMinorLocator()) # turn on minor ticks\n",
    "\n",
    "plt.plot(np.linspace(0,1,100), poly_fit(np.linspace(0,1,100)),\n",
    "         linewidth = 2, label = 'Polynomial Fit', color = 'black', zorder = 10)                            # Polynomial fit\n",
    "plt.fill_between(np.linspace(0,1,100), poly_fit(np.linspace(0,1,100)),\n",
    "                 np.linspace(0,1,100), alpha = 0.75,label = 'Heterogeneous Zone',facecolor='red')                                            # Blue area\n",
    "plt.fill_between(np.linspace(0,1,100), np.linspace(0,1,100),\n",
    "                 np.zeros(100), alpha = 0.5,hatch='XX',facecolor='gray')    \n",
    "    \n",
    "plt.title('Lorenz Curve, Emprical Points, Curve Fit and Coefficient')\n",
    "plt.xlabel('Cumulative Fraction of Storage Capacity ($m$)')\n",
    "plt.ylabel('Cumulative Fraction of Flow Capacity ($mD \\cdot m$)')\n",
    "plt.legend(loc = 'lower right',facecolor='white',framealpha = 1.0,edgecolor='black')\n",
    "plt.text(0.3, 0.8, 'Lorenz Coefficient = \\n %.3f' %lorenz_coefficient, size = 10, horizontalalignment = 'center', \\\n",
    "         bbox=dict(facecolor='white', edgecolor='black'))\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.1, wspace=0.2, hspace=0.3); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's now clear that, graphically, the Lorenz Coefficient is equivalent to the red area divided by the non-hatched area.\n",
    "***\n",
    "#### Conclusion\n",
    "\n",
    "This exercise detailed the procedure towards calculating the Lorenz Coefficient of a subsurface sample from its porosity and permeability measurements. We also covered some of the Python resources available to improve management of well data, perform the necessary mathematical transformations, and visualize the solution curve and the Lorenz Coefficient.\n",
    "\n",
    "If you use the GeostatsPy package, the calculation and display of the Lorenz Coefficient are available through the **lorenz_curve()** and **lorenz_display()** functions. Please check the documentation on those for more detail. \n",
    "\n",
    "\n",
    "***\n",
    "\n",
    "#### More on Michael Pyrcz and the Texas Center for Geostatistics:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n"
   ]
  }
 ],
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