unconve/homework 4/homework4_unconve_geomech.ipynb

{
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  "metadata": {
    "colab": {
      "name": "homework4-unconve-geomech.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyP2zyAf1C0ozbiNHGfYTJ3c",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/yohanesnuwara/reservoir-geomechanics/blob/master/unconve/homework%204/homework4_unconve_geomech.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U-2rB_ynaH4S",
        "colab_type": "text"
      },
      "source": [
        "# **Homework 3. Flow Mechanism and Permeability**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GI3Qqx5QWIOE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5CMQ8c5TaTv1",
        "colab_type": "code",
        "outputId": "82158d80-bd5e-4698-b325-a9448f1a8868",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        }
      },
      "source": [
        "!git clone https://github.com/yohanesnuwara/reservoir-geomechanics"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Cloning into 'reservoir-geomechanics'...\n",
            "remote: Enumerating objects: 108, done.\u001b[K\n",
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            "Receiving objects:  85% (329/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  86% (333/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  87% (337/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  88% (341/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  89% (345/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  90% (349/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  91% (353/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  92% (357/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  93% (360/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  94% (364/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  95% (368/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  96% (372/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  97% (376/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  98% (380/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects:  99% (384/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects: 100% (387/387), 18.71 MiB | 37.42 MiB/s   \rReceiving objects: 100% (387/387), 24.90 MiB | 37.67 MiB/s, done.\n",
            "Resolving deltas:   0% (0/179)   \rResolving deltas:  36% (66/179)   \rResolving deltas:  45% (82/179)   \rResolving deltas:  46% (83/179)   \rResolving deltas:  51% (92/179)   \rResolving deltas:  52% (94/179)   \rResolving deltas:  53% (95/179)   \rResolving deltas:  56% (101/179)   \rResolving deltas:  59% (106/179)   \rResolving deltas:  60% (109/179)   \rResolving deltas:  62% (112/179)   \rResolving deltas:  63% (113/179)   \rResolving deltas:  64% (116/179)   \rResolving deltas:  65% (118/179)   \rResolving deltas:  70% (126/179)   \rResolving deltas:  83% (150/179)   \rResolving deltas:  86% (155/179)   \rResolving deltas:  89% (161/179)   \rResolving deltas:  91% (163/179)   \rResolving deltas:  92% (166/179)   \rResolving deltas:  93% (168/179)   \rResolving deltas:  94% (170/179)   \rResolving deltas:  95% (171/179)   \rResolving deltas:  96% (173/179)   \rResolving deltas:  99% (178/179)   \rResolving deltas: 100% (179/179)   \rResolving deltas: 100% (179/179), done.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "td3I2_gRnY85",
        "colab_type": "text"
      },
      "source": [
        "## Part 1. Pressure-dependent Permeability\n",
        "\n",
        "High pressure curve (1000-4000 psi)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b9YJLSR3ACEv",
        "colab_type": "text"
      },
      "source": [
        "Calculate:\n",
        "* Change of log k to change of Pp (pore pressure) at constant Pc (confining pressure)\n",
        "\n",
        "$$(\\frac{\\partial log(k)}{\\partial Pp})_{4000<Pc<6000}$$\n",
        "\n",
        "* Change of log k to change of Pc at constant Pp\n",
        "\n",
        "$$(\\frac{\\partial log(k)}{\\partial Pc})_{1000<Pp<4000}$$\n",
        "\n",
        "* Effective stress coefficient\n",
        "\n",
        "$$\\chi = -(\\frac{|\\partial log(k)/\\partial Pp|_{Pc}}{|\\partial log(k)/\\partial Pc|_{Pp}})$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YdlSQ-a3anWd",
        "colab_type": "code",
        "outputId": "84573032-7b7c-4f63-ee16-8a46825a9786",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "# Permeability data for pore pressure range 250 to 750 psi\n",
        "perm1 = np.loadtxt('/content/reservoir-geomechanics/unconve/homework 4/Permeability data Pp 250-750 psi.txt', skiprows=1)\n",
        "\n",
        "# Permeability data for pore pressure range 1000 to 4000 psi\n",
        "perm2 = np.loadtxt('/content/reservoir-geomechanics/unconve/homework 4/Permeability data Pp 1000-4000 psi.txt', skiprows=1)\n",
        "\n",
        "# take logarithmic of k\n",
        "log_k1 = np.log10(perm1[:,2])\n",
        "log_k2 = np.log10(perm2[:,2])\n",
        "\n",
        "perm1 = pd.DataFrame({'Pp': perm1[:,0], 'Pc': perm1[:,1], 'k': perm1[:,2], 'log_k': log_k1})\n",
        "perm2 = pd.DataFrame({'Pp': perm2[:,0], 'Pc': perm2[:,1], 'k': perm2[:,2], 'log_k': log_k2})\n",
        "perm2"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Pp</th>\n",
              "      <th>Pc</th>\n",
              "      <th>k</th>\n",
              "      <th>log_k</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>40.234177</td>\n",
              "      <td>1.604595</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>3000.0</td>\n",
              "      <td>23.280851</td>\n",
              "      <td>1.366999</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>4000.0</td>\n",
              "      <td>11.917827</td>\n",
              "      <td>1.076197</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5.479152</td>\n",
              "      <td>0.738713</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>3000.0</td>\n",
              "      <td>28.033594</td>\n",
              "      <td>1.447679</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>4000.0</td>\n",
              "      <td>16.847878</td>\n",
              "      <td>1.226545</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>10.143126</td>\n",
              "      <td>1.006172</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>6000.0</td>\n",
              "      <td>5.035496</td>\n",
              "      <td>0.702042</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>3000.0</td>\n",
              "      <td>4000.0</td>\n",
              "      <td>22.044199</td>\n",
              "      <td>1.343294</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>3000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>10.015574</td>\n",
              "      <td>1.000676</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>3000.0</td>\n",
              "      <td>6000.0</td>\n",
              "      <td>6.061490</td>\n",
              "      <td>0.782579</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>3000.0</td>\n",
              "      <td>7000.0</td>\n",
              "      <td>4.148184</td>\n",
              "      <td>0.617858</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>4000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>13.215482</td>\n",
              "      <td>1.121083</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>4000.0</td>\n",
              "      <td>6000.0</td>\n",
              "      <td>6.200170</td>\n",
              "      <td>0.792404</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>4000.0</td>\n",
              "      <td>7000.0</td>\n",
              "      <td>4.242423</td>\n",
              "      <td>0.627614</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>4000.0</td>\n",
              "      <td>8000.0</td>\n",
              "      <td>3.216545</td>\n",
              "      <td>0.507390</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        Pp      Pc          k     log_k\n",
              "0   1000.0  2000.0  40.234177  1.604595\n",
              "1   1000.0  3000.0  23.280851  1.366999\n",
              "2   1000.0  4000.0  11.917827  1.076197\n",
              "3   1000.0  5000.0   5.479152  0.738713\n",
              "4   2000.0  3000.0  28.033594  1.447679\n",
              "5   2000.0  4000.0  16.847878  1.226545\n",
              "6   2000.0  5000.0  10.143126  1.006172\n",
              "7   2000.0  6000.0   5.035496  0.702042\n",
              "8   3000.0  4000.0  22.044199  1.343294\n",
              "9   3000.0  5000.0  10.015574  1.000676\n",
              "10  3000.0  6000.0   6.061490  0.782579\n",
              "11  3000.0  7000.0   4.148184  0.617858\n",
              "12  4000.0  5000.0  13.215482  1.121083\n",
              "13  4000.0  6000.0   6.200170  0.792404\n",
              "14  4000.0  7000.0   4.242423  0.627614\n",
              "15  4000.0  8000.0   3.216545  0.507390"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Wd_x20IxXH6C",
        "colab_type": "code",
        "outputId": "0c827801-921e-4e0c-f182-722a1262ad48",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 193
        }
      },
      "source": [
        "# calculate partial log k / partial Pp for Pc=4000, 5000, 6000\n",
        "\n",
        "Pc4000 = perm2.loc[perm2['Pc'] == 4000]\n",
        "logk_Pc4000 = np.array(Pc4000['log_k']); Pp_Pc4000 = np.array(Pc4000['Pp'])\n",
        "div_Pc4000 = np.array([j-i for i, j in zip(logk_Pc4000[:-1], logk_Pc4000[1:])]) / np.array([j-i for i, j in zip(Pp_Pc4000[:-1], Pp_Pc4000[1:])])\n",
        "print('div_Pc4000:', div_Pc4000)\n",
        "\n",
        "Pc5000 = perm2.loc[perm2['Pc'] == 5000]\n",
        "logk_Pc5000 = np.array(Pc5000['log_k']); Pp_Pc5000 = np.array(Pc5000['Pp'])\n",
        "div_Pc5000 = np.array([j-i for i, j in zip(logk_Pc5000[:-1], logk_Pc5000[1:])]) / np.array([j-i for i, j in zip(Pp_Pc5000[:-1], Pp_Pc5000[1:])])\n",
        "print('div_Pc5000:', div_Pc5000)\n",
        "\n",
        "Pc6000 = perm2.loc[perm2['Pc'] == 6000]\n",
        "logk_Pc6000 = np.array(Pc6000['log_k']); Pp_Pc6000 = np.array(Pc6000['Pp'])\n",
        "div_Pc6000 = np.array([j-i for i, j in zip(logk_Pc6000[:-1], logk_Pc6000[1:])]) / np.array([j-i for i, j in zip(Pp_Pc6000[:-1], Pp_Pc6000[1:])])\n",
        "print('div_Pc6000:', div_Pc6000)\n",
        "\n",
        "# calculate partial log k / partial Pc for Pp=1000, 2000, 3000, 4000\n",
        "\n",
        "Pp1000 = perm2.loc[perm2['Pp'] == 1000]\n",
        "logk_Pp1000 = np.array(Pp1000['log_k']); Pc_Pp1000 = np.array(Pp1000['Pc'])\n",
        "div_Pp1000 = np.array([j-i for i, j in zip(logk_Pp1000[:-1], logk_Pp1000[1:])]) / np.array([j-i for i, j in zip(Pc_Pp1000[:-1], Pc_Pp1000[1:])])\n",
        "print('div_Pp1000:', div_Pp1000)\n",
        "\n",
        "Pp2000 = perm2.loc[perm2['Pp'] == 2000]\n",
        "logk_Pp2000 = np.array(Pp2000['log_k']); Pc_Pp2000 = np.array(Pp2000['Pc'])\n",
        "div_Pp2000 = np.array([j-i for i, j in zip(logk_Pp2000[:-1], logk_Pp2000[1:])]) / np.array([j-i for i, j in zip(Pc_Pp2000[:-1], Pc_Pp2000[1:])])\n",
        "print('div_Pp2000:', div_Pp2000)\n",
        "\n",
        "Pp3000 = perm2.loc[perm2['Pp'] == 3000]\n",
        "logk_Pp3000 = np.array(Pp3000['log_k']); Pc_Pp3000 = np.array(Pp3000['Pc'])\n",
        "div_Pp3000 = np.array([j-i for i, j in zip(logk_Pp3000[:-1], logk_Pp3000[1:])]) / np.array([j-i for i, j in zip(Pc_Pp3000[:-1], Pc_Pp3000[1:])])\n",
        "print('div_Pp3000:', div_Pp3000)\n",
        "\n",
        "Pp4000 = perm2.loc[perm2['Pp'] == 4000]\n",
        "logk_Pp4000 = np.array(Pp4000['log_k']); Pc_Pp4000 = np.array(Pp4000['Pc'])\n",
        "div_Pp4000 = np.array([j-i for i, j in zip(logk_Pp4000[:-1], logk_Pp4000[1:])]) / np.array([j-i for i, j in zip(Pc_Pp4000[:-1], Pc_Pp4000[1:])])\n",
        "print('div_Pp4000:', div_Pp4000)\n",
        "\n",
        "average_div_Pc = np.average(np.concatenate([div_Pc4000, div_Pc5000, div_Pc6000]))\n",
        "print('Average of do(k)/do(Pp) at constant Pc:', average_div_Pc)\n",
        "average_div_Pp = np.average(np.concatenate([div_Pp1000, div_Pp2000, div_Pp3000, div_Pp4000]))\n",
        "print('Average of do(k)/do(Pc) at constant Pp:', average_div_Pp)\n",
        "\n",
        "X = -average_div_Pc / average_div_Pp\n",
        "print('Effective stress constant chi:', X)"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "div_Pc4000: [0.00015035 0.00011675]\n",
            "div_Pc5000: [ 2.67458472e-04 -5.49597633e-06  1.20407163e-04]\n",
            "div_Pc6000: [8.05371090e-05 9.82426807e-06]\n",
            "div_Pp1000: [-0.0002376  -0.0002908  -0.00033748]\n",
            "div_Pp2000: [-0.00022113 -0.00022037 -0.00030413]\n",
            "div_Pp3000: [-0.00034262 -0.0002181  -0.00016472]\n",
            "div_Pp4000: [-0.00032868 -0.00016479 -0.00012022]\n",
            "Average of do(k)/do(Pp) at constant Pc: 0.00010568975457593109\n",
            "Average of do(k)/do(Pc) at constant Pp: -0.0002458873305322805\n",
            "Effective stress constant chi: 0.4298300133932926\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1DIFp4eNywi5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "285b8e57-1a57-403e-b698-64d05ef3082f"
      },
      "source": [
        "plt.plot(Pp_Pc5000, logk_Pc5000, '.-')"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1b38043240>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hUyH090GcPrt",
        "colab_type": "code",
        "outputId": "ef7ac200-1f2e-4ca9-b327-f9230364eb56",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        }
      },
      "source": [
        "# X = 0.4\n",
        "\n",
        "Pc_min_Pp1000 = np.array(Pp1000['Pc'] - (X * Pp1000['Pp']))\n",
        "Pc_min_Pp2000 = np.array(Pp2000['Pc'] - (X * Pp2000['Pp']))\n",
        "Pc_min_Pp3000 = np.array(Pp3000['Pc'] - (X * Pp3000['Pp']))\n",
        "Pc_min_Pp4000 = np.array(Pp4000['Pc'] - (X * Pp4000['Pp']))\n",
        "\n",
        "p1 = plt.plot(Pc_min_Pp1000, np.array(Pp1000['k']), '.-')\n",
        "p2 = plt.plot(Pc_min_Pp2000, np.array(Pp2000['k']), '.-')\n",
        "p3 = plt.plot(Pc_min_Pp3000, np.array(Pp3000['k']), '.-')\n",
        "p4 = plt.plot(Pc_min_Pp4000, np.array(Pp4000['k']), '.-')\n",
        "plt.legend([p1[0], p2[0], p3[0], p4[0]], ['Pp = 1000 psi', 'Pp = 2000 psi', 'Pp = 3000 psi', 'Pp = 4000 psi'])\n",
        "plt.title('Permeability vs Effective Stress (X = 0.4)')\n",
        "plt.xlabel('$Pc-X \\cdot Pp$')\n",
        "plt.ylabel('Permeability (nD)')\n",
        "plt.show()"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OtaNev0knfdq",
        "colab_type": "text"
      },
      "source": [
        "## Part 2. The Klinkenberg Effect\n",
        "\n",
        "Low pressure curve (250-750 psi)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JODhkgEDne_v",
        "colab_type": "code",
        "outputId": "dfc71353-0701-48d1-f0d2-bb26f52c825c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 897
        }
      },
      "source": [
        "Pp250 = perm1.loc[perm1['Pp'] == 250]\n",
        "k_Pp250 = np.array(Pp250['k'])\n",
        "Pc_min_Pp250 = np.array(Pp250['Pc'] - (X * Pp250['Pp']))\n",
        "\n",
        "Pp500 = perm1.loc[perm1['Pp'] == 500]\n",
        "k_Pp500 = np.array(Pp500['k'])\n",
        "Pc_min_Pp500 = np.array(Pp500['Pc'] - (X * Pp500['Pp']))\n",
        "\n",
        "Pp750 = perm1.loc[perm1['Pp'] == 750]\n",
        "k_Pp750 = np.array(Pp750['k'])\n",
        "Pc_min_Pp750 = np.array(Pp750['Pc'] - (X * Pp750['Pp']))\n",
        "\n",
        "plt.figure(figsize=(15,15))\n",
        "\n",
        "p1 = plt.plot(Pc_min_Pp250, k_Pp250, '.-')\n",
        "p2 = plt.plot(Pc_min_Pp500, k_Pp500, '.-')\n",
        "p3 = plt.plot(Pc_min_Pp750, k_Pp750, '.-')\n",
        "\n",
        "p4 = plt.plot(Pc_min_Pp1000, np.array(Pp1000['k']), '--', color='red')\n",
        "p5 = plt.plot(Pc_min_Pp2000, np.array(Pp2000['k']), '--', color='black')\n",
        "p6 = plt.plot(Pc_min_Pp3000, np.array(Pp3000['k']), '--', color='blue')\n",
        "p7 = plt.plot(Pc_min_Pp4000, np.array(Pp4000['k']), '--', color='green')\n",
        "\n",
        "plt.legend([p1[0], p2[0], p3[0], p4[0], p5[0], p6[0], p7[0]], ['Pp = 250 psi', 'Pp = 500 psi', 'Pp = 750 psi', \n",
        "                                                               'Pp = 1000 psi', 'Pp = 2000 psi', 'Pp = 3000 psi', 'Pp = 4000 psi'])\n",
        "plt.title('Permeability vs Effective Stress (X = 0.4)')\n",
        "plt.xlabel('$Pc-X \\cdot Pp$')\n",
        "plt.ylabel('Permeability (nD)')\n",
        "plt.ylim(0, 90)\n",
        "\n",
        "# grid spacing\n",
        "grid_space_y = np.linspace(0, 90, 91)\n",
        "plt.yticks(grid_space_y)\n",
        "\n",
        "plt.grid('True')\n",
        "plt.show()"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x1080 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-Jv7OuXKWCqM",
        "colab_type": "text"
      },
      "source": [
        "### A. Plot the permeability data at each eﬀective stress as a function of inverse pore pressure"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dGl6rwh9DWys",
        "colab_type": "code",
        "outputId": "6f501b6b-358a-4f88-f1d5-523c601d61e8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        }
      },
      "source": [
        "# determine k at each Pp (250, 500, 750) and each effective stress (2000, 3000, 4000)\n",
        "\n",
        "# inverse of Pp\n",
        "Pp_inv_1 = 1 / 250; Pp_inv_2 = 1 / 500; Pp_inv_3 = 1 / 750\n",
        "Pp_inv = np.array([Pp_inv_1, Pp_inv_2, Pp_inv_3])\n",
        "\n",
        "# eff 2000 (0.4: 68.5, 44.5, 38)\n",
        "k_eff2000_Pp250 = 68; k_eff2000_Pp500 = 44; k_eff2000_Pp750 = 37.6\n",
        "k_eff2000 = np.array([k_eff2000_Pp250, k_eff2000_Pp500, k_eff2000_Pp750])\n",
        "# eff 3000 (0.4: 48, 28.7, 24.3)\n",
        "k_eff3000_Pp250 = 48; k_eff3000_Pp500 = 28.4; k_eff3000_Pp750 = 24\n",
        "k_eff3000 = np.array([k_eff3000_Pp250, k_eff3000_Pp500, k_eff3000_Pp750])\n",
        "# eff 4000 (0.4: 32.3, 17.5, 13.5)\n",
        "k_eff4000_Pp250 = 32; k_eff4000_Pp500 = 17.5; k_eff4000_Pp750 = 13.5\n",
        "k_eff4000 = np.array([k_eff4000_Pp250, k_eff4000_Pp500, k_eff4000_Pp750])\n",
        "\n",
        "# plot k vs inverse Pp\n",
        "p1 = plt.plot(Pp_inv, k_eff2000, '.-')\n",
        "p2 = plt.plot(Pp_inv, k_eff3000, '.-')\n",
        "p3 = plt.plot(Pp_inv, k_eff4000, '.-')\n",
        "plt.title('Permeability vs Inverse Pore Pressure')\n",
        "plt.legend([p1[0], p2[0], p3[0]], ['Eff. Stress = 2000 psi', 'Eff. Stress = 3000 psi', 'Eff. Stress = 4000 psi'])\n",
        "plt.xlabel('$Pp^{-1} (psi^{-1})$')\n",
        "plt.ylabel('Permeability (nD)')\n",
        "plt.grid('True')\n",
        "plt.show()"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3bx4/+9nPsFgs1NTUdCinRuNIRIRv88+RkZXHhpx8KuqaCB8ykAdmxrM4LYLIgJY892kjh1IZ62W3wR9cRAF0hYq6Jqxm1AurGNudKYCuMHDgwE4H9q7i7u7O+++/zzfffMOHH37Igw8+SHZ2Nk888US7xzcPtNu2bWPfvn1MnToVgIaGBqZMmYK/vz/e3t7ccccdLFy4kIULFwIwdepUVqxYwdKlS7nhhhu+U6+fnx9ffPHFRbuBPv3003h4eLB8+fKLOu9SWLRoEQMHDmTgwIHMmDGD7du3c9lll3H77bfT2NjI9ddf30YpazTOQElVPW/vzGdddh4HzlYywMON+UnDWJIeyZSYQNzcHOOc4BIK4EIzdTBX1V/ZRmOTFU8PN15YlmpXzXqxKKWYOHEiEydOZM6cOdx2220dKoBmP3YRYc6cObz55pvfOWb79u18+OGHrFu3jhdffJGPPvqIl156ia+//ppNmzaRlpZGdnY2gYGBtnMu5Q7gtddeY+PGjXz44Yc2D5vw8HByc3Ntx+Tl5REeHg7QbnlgYCDl5eU0NTXh4eHR5vj2rtP529OmTePTTz9l06ZNrFixgoceeohbbrml3fM1mt6iyWLlk0NFZGTlsXV/AU1WYXzkEJ66Polrxw/Hf2D3JqA9gUsogK6QNnIo/7hzMtuOlTA5JtCpBv/Tp09z9uxZJkyYAEBOTg4jR44EjFl5ZWVlu+dNnjyZ++67jyNHjhAXF0d1dTX5+fkMHz6cmpoaFixYwNSpU4mJiQHg6NGjTJo0iUmTJvHee++Rm5vbRgFc7B3A+++/z29/+1s++eQTBg1quXW97rrruPnmm3nooYc4ffo0hw8fZuLEiYgIhw8f5vjx44SHh7NmzRreeOMNlFLMmDGDdevWsWzZMlavXs2iRYvabXPDhg089thjVFdXk5mZybPPPsvJkyeJiIjgrrvuor6+nh07dmgFoHEYR4uqyMjK460deRRV1hPo48WKy6NYkh7J6GHO9ZBlv1EAYCiBnhz4z18DuPrqq9u4Np7P6dOnufPOO3n33XfblDc2NvLwww9z+vRpvL29CQ4O5qWXXgJgxYoV3HvvvQwcOJCvvvqqzXnBwcG89tpr3HTTTdTX1wPw1FNP4efnx6JFi6irq0NE+P3vfw8YbpuHDx9GRJg1axbjx4/vVv9/9KMfUV9fz5w5cwBDIb300kuMHTuWpUuXkpiYiIeHB3/84x9tD1+9+OKLzJs3D4vFwu23387Yscbd23PPPceyZcv4+c9/TmpqKnfccUe7bSYnJzNjxgyKi4t5/PHHGT58OKtXr+Z3v/sdnp6e+Pr68vrrr3erXxrNxVJZ18im3WfIyM4j+2QZ7m6KGaNDWJIewcyEEDzdndPfpk/kBE5PT5esrKw2Zfv372fMmDG9Kocrh0loxpn7+MQTT+Dr62vzarpUdu7cSWpqag9J5ZxkZmYyffp0R4thVxzdRxHh6+OlrM3K5b1vz1LbaCE22Iel6ZF8b0I4IX7e3W6ju31USnUaDrpf3QFoNBpNdzldXstb2Xms25HHyZIafAd4cH3qcJakR5IaOaRPPW2uFYCmz9DRorhGY2/qGi18sK+AjOw8PjtchAhMiQnkx7PimZ8UxkCvvhlfSisAjUajaQcRYe/pCtZm5bIh5zTnahsZ7u/N/TPiWJwWyYjAQReuxMnRCkCj0WhaUVrdwPqd+WRk57H/TAVeHm7MGzuMpekRXB4bhLuDfPbtgVYAGo2m39NksfLZ4WIysnP5YF8BjRYhOcKfXy8ay3Xjw/Ef5HiffXugFYBGo+m3HCuqIiM7j3/tyKOgop4AHy9+MDmKJekRjAkb7Gjx7I5zOqf2Efp7OOjHH3+c5ORkUlJSmDt3rk1OEeGBBx4gLi6O5ORkduzYYTtn9erVxMfHEx8fz+rVq23l2dnZjBs3jri4OB544AF6wj358ssv73YdGtejqr6Jtd/ksuSlL5n535/w50+OMna4Py/9xwS2PTaLX1yb2C8Gf0CHg74YdDjotpw7d872+YUXXpB77rlHREQ2bdokV199tVitVvnqq69k4sSJIiJSUlIi0dHRUlJSIqWlpRIdHS2lpUaY28suu0y++uorsVqtcvXVV8u7777bg71qiw4H7RpcTB+tVqt8faxEHl6bI2Mef09GrtwoM57/WP708RE5e67WfkJ2k+5+j1wgHHT/MgHlbocTn0HUlRA50S5NNIeD3rx5M++99x6VlZW2cNCPPfaYLZBba9oLB+3r69smHHTzk8Bjxozhxhtv5IMPPuDRRx8lICCAX/7yl9TX1xMbG8urr76Kr68vq1at4p133sHDw4O5c+fy/PPPk5GRwZNPPom7uzv+/v58+umn3err4MEts6Tq6mqb//OGDRu45ZZbUEoxefJkysvLOXPmDJmZmcyZM4eAgAAA5syZw/vvv8/06dOpqKiwRRC95ZZbWL9+PfPnz2/T3ooVK/D29iYrK4uKigp+//vfs3DhQvbu3cttt91GQ0MDVquVt956i/j4eHx9fW3hsTX9k7Pn6nhrRx4ZWbmcKKnBx8uda5OHs/SyCCaMGNqnfPbtgWsogPdWwdlvOz+mvgIK9oBYQblBaBIM6OQ2b9g4mN9xWAfQ4aABfvazn/H666/j7+/Pxx9/DBjhoM8P+5yfn99peURExHfK2+PEiRNs376do0ePMmPGDI4cOcJLL73Ej3/8Y5YvX05DQwMWi6XDa61xfeqbLGzdV0hGdi6fHirCKjAxOoAfzYxnwbhhDPJyjWGvJ+g/V6LunDH4g/Fed65zBdAFdDhoIxT0008/zTPPPMOLL77Ik08+eZG9vziWLl2Km5sb8fHxxMTEcODAAaZMmcLTTz9NXl4eN9xwA/Hx8XaVQeOc7D1txNlfn5NPeU0jYf7e/HB6HIvTIogK8nG0eE6JayiAC8zUAcP8s/o6sDSAuxd8/xW7mYEuhb4aDrqZ5cuXs2DBAp588skOw0GHh4eTmZnZpnz69OmEh4fbsom1Pr6j63T+9s0338ykSZPYtGkTCxYs4M9//jMzZ87sUFaN61BW3cCGHMNnf+/pCrzc3ZgzNpSl6ZFcEedaPvv2wDUUQFeInAi3vmP3NYBLoa+Ggz58+LBttr1hwwYSEhIAIxz0iy++yLJly/j666/x9/cnLCyMefPm8dOf/pSyMiMl55YtW3jmmWcICAhg8ODBbNu2jUmTJvH6669z//33t9tmRkYGt956K8ePH+fYsWOMHj2aY8eOERMTwwMPPMCpU6fYvXu3VgAujMUqfHa4iD/l1JHzwYc0WKwkhQ/myevGsihlOEMGeTlaxD5D/1EAYAz6PTjw9/dw0KtWreLgwYO4ubkxcuRIm8wLFizg3XffJS4ujkGDBvHqq68CEBAQwOOPP85ll10GwC9+8QvbgvCf/vQnVqxYQW1tLfPnz//OAnAzI0aMYOLEiVRUVPDSSy/h7e3N2rVr+fvf/46npyfDhg3jpz/9abf6pXFOThRXk5Gdy7925HPmXB2+nnDzJMNnf+xwf0eL1yfR4aAvAmcOldxTOHMfV6xY0WZx/VLR4aD7DtX1Tbz7rRFnf/vxUtwUTBsVzNL0SDyLDjBn5gxHi2hXdDhojUbTrxARsk+WkZGVx8bdp6lusBAd5MMj80bz/QkRDPM34uxnZh50sKR9H60ANH2G1157zdEiaOxIQYXhs78uK49jxdUM8nLnmnFhLL0skvSR2mffHthVASilhgCvAEmAALcDB4F/AlHACWCpiJTZUw6NRuOcNDRZ+XC/EWc/82AhVoHLooZy7/RYrhkXhs8APUe1J/a+ui8A74vIYqWUFzAI+CnwoYg8q5RaBawCVtpZDo1G40TsP1Nh89kvrW4gdPAA7r0qlsVpEcQE+zpavH6D3RSAUsofmAasABCRBqBBKbUImG4ethrIRCsAjcblOVfTyIZd+WRk5fFt/jk83RVzEkNZkh7JtPhg7bPvAOzmBaSUSgH+AuwDxgPZwI+BfBEZYh6jgLLm7fPOvxu4GyA0NDRtzZo1bfb7+/sTFxdnF9k7wmKx4O7eN1O/dZX+0MfDhw9TUVHhaDHsSlVVlS22lCOxirCvxMJneU1kF1poskKknxvTwj2YPNwDP69LH/SdpY/2pLt9nDFjRqdeQHaL4AmkA03AJHP7BeDXQPl5x5VdqC5njQbq5uYm48ePt72eeeYZERH59NNPJTExUcaPHy81NTXy8MMPS2Jiojz88MMd1v3Xv/5VkpKSZNy4cTJ27FhZv369iIi8+uqrkp+fb79OncfFRANt5vnnnxdAioqKRMSIvHj//fdLbGysjBs3TrKzs23HvvbaaxIXFydxcXHy2muv2cqzsrIkKSlJYmNj5f777xer1drtvkyZMqXdch0N1P6cLK6W/958QKb8ZquMXLlRkp/YLL9Y/618m1feY204uo+9gb2jgdpTAQwDTrTavhLYhLEIHGaWhQEHL1SXsyqA/h4OWkTk1KlTMnfuXBkxYoRNAehw0I7HEYNjdX2jrMvKlRv//KWMXLlRolZtlB/89Wv59658qW3o+d+qVgAX5kIKwG4JYUTkLJCrlBptFs3CMAe9A9xqlt0KbLCXDOeTU5jDK9++Qk5h9wO4dURzOOjHH3+c5cuXc91119nCQf/zn/9s95z2wkFHR0e3CQfdnFwmKiqKlStXMmHCBDIyMtiyZQtTpkxhwoQJLFmyxBb+eNWqVSQmJpKcnMzDDz8MGGEUkpKSGD9+PNOmTeuR/j744IP89re/beOi11E46M2bN9vCQQ8dOtQWDvrMmTO2cNBKKVs46PNpfio6PT2dUaNGsXHjRgD27t3LxIkTSUlJITk5mcOHD9uuo8a+iOmz/9i/djPx6Q/5ScYuzpyr4+G5o/hi5Uxev30iC5OH4+3p2mbFvoq9vYDuB/5hegAdA27DyEK2Vil1B3ASWNrdRp7b/hwHSg90ekxVQxUHyw4iCArF6KGj8fXqeIBICEhg5cTO16b7ezjoDRs2EB4e/p2QEjoctOtTWFnH2zvyWZuVy9GiagZ6urNgXBhL0yOYGB2gffb7CHZVACKSg7EWcD6z7Nlue1Q2ViIYC96CUNlY2akC6Ar9ORx0TU0Nv/nNb9iyZcsl9vrS0OGgHUdDk5WPDhSyLjuXjw8WYbEKaSOH8tz3Y7gmeTi+2me/z+ES39iFZupgmH/u2nIXjdZGPN08efbKZ0kJSbngeb1FXwsHffToUY4fP26b/efl5TFhwgS2b9+uw0G7GAfPVpKRlcvbO/MpqW4g2G8Ad10Zw5L0CGK1z36fxiUUQFdICUnh5bkvk1WQRXpoulMN/n0xHPS4ceMoLCy0bUdFRZGVlUVQUJAOB+0CnKtt5N+7TpORlcuuPMNnf1ZCKEsvi2BafDAe7nZbPtT0Iv1GAYChBHpy4O/v4aA7QoeD7ptYrcKXR0vIyM7l/T1nqW+ykjDMj8cXJnJ9ynACfQc4WkRND6PDQV8Ezhwquadw5j7qcNBd52LCCOeW1rAuO4912Xnkl9cy2NuDRSnhLE2PJCl8sNMu6LpKyOvO0OGgNRpNj1PbYGHz3rOszcrly6MlKAVXxAWxcn4CcxNDtdtmP0ErAE2fQYeD7h4iQk5uORnZefw75zSV9U1EBgzkoTmj+H5aBOFDBjpaRE0voxWARuPiFFXW8/bOPDKy8jhcWIW3pxsLksJYkh7JpOgA3HQQtn5Ln1YAIuK09kmNc9IX1rx6giar8MG+AtZm5fLxgUKarELqiCE8c8M4rkkOY7C3p6NF1DgBfVYBeHt7U1JSQmBgoFYCmi4hIpSUlLj0k8KHCyrJyM5jzbYaKhqyCPIdwB1XRLMkPYK4EOdc3Nc4jj6rACIiIsjLy6OoqKjX2qyrq8Pb27vX2nMErt5Hb29vqqurHS1Gj1JR1+yzn0dObjkeborkIHd+eHUqV40OxlP77Gs6oM8qAE9PT6Kjo3u1zczMzH7hPujqfTx58qSjReg2Vquw7VgJGdl5vLfnDHWNVkaF+vLza8ZwfWo4e7K+YnpiqKPF1Dg5fVYBaDT9kbyyGt7KzicjO5e8slr8vD34/oQIlqZHkhzhr82hmotCKwCNxsmpa8F+tgAAACAASURBVDR89jOy8vjiaDEiMDUukEfmjWbe2GHaZ19zyWgFoNE4ISLC7rxzZGTnsiHnNJV1TYQPGciPZ8Xz/QkRRAYMcrSIGhdAKwCNxokoqarn7Z1G4vSDBZUM8HBjftIwlqZHMjkmUPvsa3oUrQA0GgfTZLGSebCIjOxcPtxv+OyPjxzC099LYmHycPwHap99jX3QCkCjcRBHCqvIyM7lXzvyKaqsJ9DHi9umRrEkPZJRodpnX2N/tALQaHqRyrpGNu4+Q0ZWLjtOlePuppgxOoSl6RHMSAjRPvuaXkUrAI3GzlitwtfHS8nIzuXdbw2f/bgQX366IIHrU8MJ8XPdB+80zo1WABqNncgvr+UtM87+qdIafAd48L3UCJamR5ASOUT77GscjlYAGk0PUtdoYcu+AjKycvn8iOGzPyUmkAfnxHP12DAGemmffY3zoBWARtNNRIQ9+RVkZOeyfmc+FabP/v0z41mSpn32Nc6LVgAazSVSUlXP+hwjcfqBs5V4ebhx9VjDZ//yWO2zr3F+LqgAlFIhwFRgOFAL7AGyRMRqZ9k0GqejyWLl08NFZGTlsXV/AY0WITnCn19fn8R1ycPxH6R99jV9hw4VgFJqBrAKCAB2AoWAN3A9EKuUWgf8t4hU9IagGo0jOVZURUZ2Hm9l51FYWU+Ajxe3TIliSXoECcMGO1o8jeaS6OwOYAFwl4icOn+HUsoDWAjMAd6yk2wajUOpqm9i024jzn7WyTLcFMwYHcKS9EhmJoTg5aF99jV9mw4VgIg80sm+JmC9XSTSaByIiLD9eCkZ2Xls2n2G2kYLMcE+rJqfwA2p4YQM1j77Gteh0zUApdRo4G4gwSzaD7wsIge7UrlS6gRQCViAJhFJV0oFAP8EooATwFIRKbsU4TWanuLMuVr+tSOfjKxcTpTU4OPlzqKU4SxJj2TCCO2zr3FNOlsDmAL8C/gz8BdAAanAx0qpG0RkWxfbmCEixa22VwEfisizSqlV5vbKS5Jeo+kG9U0WPthXQEZWHp8dLsIqMCk6gPtnxjN/3DAGeWknOY1r09kv/BfATSKS2apsvVLqI+CXwPxLbHMRMN38vBrIRCsATS9yssLCE+/sZX1OPuU1jYT5e3PfjDgWp0UwMtDH0eJpNL1GZwog9rzBHwAR+UQp9Zcu1i/AFqWUAH8Wkb8AoSJyxtx/FtCJSzV2p6y6gQ05+azNymPfmTq83E8xd2woS9MjmRoXhLv22df0Q5SItL9DqWwRSetg3w4RmXDBypUKF5F881mCD4D7gXdEZEirY8pEZGg7596Nsf5AaGho2po1a7rUIXtSVVWFr6+vo8WwK67UR6sIe4otfJbfxM4CC00CIwe7MTHIwlVRPvh6ue6g70rfY0foPl6YGTNmZItIekf7O7sDiFRK/b92yhUQ3pXGRSTffC9USr0NTAQKlFJhInJGKRWG8XxBe+f+BWPtgfT0dJk+fXpXmrQrmZmZOIMc9sQV+ni8uJp12bm8lZ3P2Yp6hg7y5AeXR7IkLZLE4YNdoo8XQvfRNbB3HztTAB26gQJZF6pYKeUDuIlIpfl5LvAr4B3gVuBZ831D18XVaNqnur6Jd789Q0ZWHttPlOKm4KpRwfzy2kRmjglhgIcOwqbRnE9nzwGs7mbdocDbpvucB/CGiLyvlPoGWKuUugM4CSztZjuafoqIkHWyjIysXDbuPkNNg4XoIB8evXo0N6RGMMxf++xrNJ3RlVhAo4CHMfz2bceLyMzOzhORY8D4dspLgFkXK6hG00xBRR1v7cgjIyuP48XVDPJyZ2FyGEvSI0kfOVT77Gs0XaQrjs4ZwEvAKxgPdGk0vU5Dk5UP9xewNiuXTw4ZPvsTowL44fRYFowLw2eA9tnXuBi52xlxch3kDoLIiXZpoiv/NU0i8r92aV2juQD7TrfE2S+raSR08AD+c3osi9MiiQ7SPvsaF8RqhZ3/B5seJNraBKsz4NZ/20UJdEUB/Fsp9UPgbaC+uVBESntcGo0GKK9p4J1dp1mblcue/Aq83N2YkxjK4vQIpsUHa599jevR1AAnPoMDm+Dgu1BpPCqlACyNxj4HKYBbzffWXkECxPS4NJp+i8UqfHGkmLVZuWzZW0CDxUpi2GCeuDaRRSnhDPXxcrSIGk3PUlcBRz4wBv3DH0B9BXj6QNwsCB4DX76AtakBN3cviLrSLiJcUAGISLRdWtZogJMl1awzE6efOVeH/0BPbp40gsVpESSF+ztaPI2mZ6k4Y8zwD2yC45+CtRF8gmHs9TD6Goi5CjwHGsfGz+bER68TM/OW3l8DUEpdISKfd7J/MDBCRPbYRTKNy1LT0MS7354lIyuXr4+XohRMiw/m59ckMjtR++xrXAgRKD4EBzYag35+tlEeEAOT74WEhRBxGbi185uPnMipkTXE2Gnwh87vAL6vlPot8D6QDRRhZASLA2YAI4Gf2E0yjUshIuw4VUZGVh4bd5+hqr6JkYGDeGTeaG6YEE6Y/0BHi6jR9AxWK+R9Ywz6B9+FkiNGeXgazHzcGPSDR4MTuCt39iDYg2bs/u8DS4AwjJzA+zECu3V4d6DRNFNYUce/duazNiuXY0XVDPR055rkMJamR3JZlPbZ17gIjXVw/BNzEfc9qC4EN0+IvhIm/yeMXgCDhztayu/Q6RqA6enzsvnSaLpEQ5OVjw4YcfYzDxVhsQrpI4dy7/djWZAchq/22de4ArVlcGgLHNwEh7dCYzV4+UH8HEi4xnj3du51LP2fqOkxDpytICMrj7d35lNa3UCI3wDunhbD4rQIYoNdO2qjpp9wLg8OvGuYd05+AdYm8B0G4280Bv2oK8FjgKOl7DJaAWi6xbmaRt7ZfZqMrFx2553D010xe4wRZ//K+CA83HXidE0fRgQK9xmmnQMb4cwuozxoNFz+gGHPH54Kbn3zd64VgOaisVqFL44Wk5GVx/t7z9LQZCVhmB+/WJjI9anhBGiffU1fxtIEuV+3DPrlJwFluGLO+ZXhrhkU52gpe4SuBIPLBv6GEc1TJ2/vx+SW1pCRncdb2Xnkl9cy2NuDZZdFsjQ9krHDB+sFXU3fpaEGjn3csohbWwruAyBmOlz5EIyaD36ul7ywK3cANwK3Ad8opbKAV4Et0lEqMY1LUdtg4b09Rpz9r46VoBRcERfEqvkJzEkMxdtT++xr+ijVJXDofWPQP/oRNNUai7ajrja8duJmwQA/R0tpV7ryJPAR4GdKqceBhRh3Axal1KvACzomkOuQfbKMjUcb8IsqRbkpw2d/12kq65sYETCIn8wZxQ1pEYQP0T77mj5K6fGWJ3FPfQVihcERMOEHxiLuyKng7uloKXuNLq0BKKWSMe4CFgBvAf8ArgA+AlLsJp2m18g+WcbNL2+jvsnKW4e/QgBvTzcWjAtjSVokk6IDcNNB2DR9DRFj4fbAJuNVuNcoDxkLVz5sDPph453ioSxH0NU1gHLgr8AqEWmOCPq1UmqqPYXT2BcRYd+ZCrbuK+SN7Sepb7Ia5cC8saE8v2Q8ft79ZzakcREsjYaL5oFNhstmRR4oNxgxBeb9xjDvBOgQZ9C1O4AlZnYvG0qpaBE5LiI32EkujZ1oaLKy7VgJW/cXsHVfAafP1aEUxIf4UlLVgMUqDPB04+5psXrw1/Qd6qvgyFYzsuZmqDsHHgMhdibM+Klh1/cJdLSUTkdXFMA6YEI7ZWk9L47GHpTXNJB5sIgP9hfwycEiquqb8PZ048r4YP5r9ihmJIQQ7DeA7JNlvLn1G26afRlpI4c6WmyNplM8G8oh+zVjln8sEyz1MDDA8M1PuAZiZoDXIEeL6dR0Fg00ARgL+CulWs/0B2MEhdM4MSdLqvlgXwFb9xfwzYkyLFYhyHcAC5PDmJMYytS4oO948KSNHEplrJce/DXOS/ERI/TCgU1cnrsdEBgyEi67ExIWQORkcNePN3WVzq7UaAyvnyHAta3KK4G77CmU5uKxWoWdueU2087hwioARof6ce9VMcweE8r4iCF6IVfTt7Ba4fSOlkXc4oNGedh4TkTdRPT8H0FIYr9dxO0unUUD3QBsUEpNEZGvelEmTRepbbDw+ZFitu4r4MMDBRRXNeDuppgUHcBNE0cwe0woIwL1LbCmj9HUACc+bVnErToLyh2irjBm+qPnw5BITmZmEh061tHS9mk6MwE9KiK/BW5WSt10/n4RecCukmnapbCyjo/2F7J1fwGfHS6mvsmK3wAPpieEMHtMCNNHheA/SC/eavoYdeeMtIjN6REbKo30iPGzjdALo+bCQG2a7Gk6MwHtN9+zekMQTfuICIcKqti6v4AP9hWQk1sOQPiQgbZZ/sToALw8+mYwKk0/puJ0q/SIn7WkR0y6wVjEjb4KPPVyoz3pzAT0b/N9de+JowFotFj55kQpW/cZM/1TpTUAjI/w5ydzRjE7MZSEYX469o6mbyECRQdb0iOe3mGUB8QaSVMSFkJEevvpETV2oTMT0L8xnglqFxG5zi4S9VMq6hr55GARW/cX8PGBQirqmvDycOOKuCDuvSqWWWNCCB2sZ0OaPobV0pIe8cC7UHrUKA9Pg1m/MAb9oFF6EddBdGYCer7XpOin5JXVsHVfAVv3F7LtWAlNViHAx4u5Y4cxe0woV8YH4aOzZ2n6Go11hl/+web0iEVmesRpMOU+Mz1imKOl1NC5CeiT3hSkP2C1CntOn2PrvgI+2F/I/jMVAMQG+3DHldHMGRNK6oihuGtXTU1fo6YUDm8xTDtHPjTSIw4Y3JIeMW6206dH7I90ZgJaKyJLlVLf0tYUpAARkeSuNKCUcsdYSM4XkYVKqWhgDRAIZAM/EJGGS+6Bk1PXaOGroyV8sL+AD/cXUFBRj5uC9KgAfrZgDLPGhBCj0yVq+iLlueYi7kY48QWIBfzCYPyyVukRdXIgZ6Yz+8KPzfeF3WzjxxgeRYPN7eeAP4jIGqXUS8AdwP92sw2noqSqno8OtLhq1jRYGOTlzlWjgpk9JpSZCSEM1VmzNH0NESjY25Ip6+xuozw4Aa74L8Ndsw+nR+yPdGYCOmO+n1RKDQMmYtwJfCMiZ7tSuVIqArgGeBp4SBluKzOBm81DVgNP4AIK4GhRlWHa2VdA9qkyRGDYYG9umBDO7DGhTI4J1MlTNH0PSxPkbmuVHvEURnrESTDn18ZMPzDW0VJqLhF1ocReSqk7gV9gxP5XwFXAr0TkbxesXKl1wDOAH/AwsALYJiJx5v5I4D0RSWrn3LuBuwFCQ0PT1qxZ0/Ve2Ymqqip8fQ1zjcUqHCm3srPQQk5hE2drjOs4crAbKcHupIa4M3KwW59z1WzdR1dF97Fz3Cz1BJTuJKj4awJLvsGzqRKr8qQ0IIWSwIkUB02k0WtID0t88ejv8cLMmDEjW0TSO9rfFReTR4BUESkBUEoFAl9iZAbrEKXUQqBQRLKVUtO7LrKBiPwF+AtAenq6TJ9+0VX0OO9t/ZjawNF8YLpqltU04umumBIbxH1jQpg5JrTPZ8vKzMzEGa61PdF9bIfq4lbpET820yMOgcQFkHANbrGzCBrgSxBGkDBnQH+P3acrCqAEIwBcM5Vm2YWYClynlFqAET10MPACMEQp5SEiTUAEkH9xIvcuZ8/VGQHW9hfw+aEammQH/gM9mZkQwuwxoUwbFaTj5mv6JqXHzSTo77akR/SPhAm3mOkRL+9X6RH7I515AT1kfjyCkf1rA8YawCJg94UqFpHHgMfMuqYDD4vIcqVUBrAYwxPoVmBDdzrQ07TOkrV1fwHf5p8DYGTgIGaN9OC2uemkjxyKh7te6NL0MUTgTE5LkLXm9IihSTDtEWPQH5asH8rqR3R2B+Bnvh81X810d8BeCaxRSj0F7MRINelQOsqSNWHEUFZencCcxBBig3355JNPmByjswpp+hCWRjjxuemu2To94uUw7xkjhv7QKEdLqXEQnXkBPdlTjYhIJpBpfj6G4VHkUC6UJWvmmBCCfAc4WkyN5uKpryS48At46x9t0yPGzYKZP4P4eTo9ogboWlL4YOBRjOxgtmA0IjLTjnLZhfayZAX7DeDa8WHMHtN+liyNpk9QWQCH3jPMO8cyGWtpMNMjXmumR5yu0yNqvkNXFoH/AfwT44GwezHs9kX2FKqnyDpRyts786lpsLAn/5wtS1bCMD/+86pYZieGkhzur7NkafomxUdaImvmfQOIYc6ZeDc7a4eTeu09Oj2iplO68usIFJG/KqV+bMYH+kQp9Y29Besu2SfLWPrnr7CajzmMCx/ML69NZPaYUCID9ExI0wexpUc0B/3iQ0Z5WArM+Kkx0zfTI57LzNSDv+aCdOUX0mi+n1FKXQOcBgLsJ1LPsO1YCc3PuLkruDopjNumRjtWKI3mYmmqN5KlHNhoRNasOgtuHmZ6xLts6RE1mkuhKwrgKaWUP/AT4P/D8Od/0K5S9QCTYwIZ4OlGY5MVTw837b2j6TvY0iNuhMNbjfSIXr7GIm7CQiPCpk6PqOkBLqgARGSj+fEcMMO+4vQcaSOH8o87J7PtWAmTYwJJG6n/YTROzLn8lvSIJz430yOGmOkRFxqx9HV6RE0P0xUvoFEYwdpCRSRJKZUMXCciT9ldum6SNnKoHvg1zokIFB1oyZTVnB4xMA6m/NAY9MPTdWRNjV3pignoZYx4QH8GEJHdSqk3AKdXABqNU2G1QO52057/LpQeM8rD02HWL41BP3iUY2XU9Cu6ogAGicj286JaNtlJHo3GtWisNdIjHjDTI9YUg7uXYdK5/H4YNV+nR9Q4jK4ogGKlVCxmVjCl1GLgjF2l0mj6Mrb0iBvN9Ig1ZnrEua3SIw6+cD0ajZ3pigK4DyMsc4JSKh84DvyHXaXSaPoa5acMW/6BjXDySzM94nBIudmMrHmFTo+ocTq64gV0DJitlPIB3ESk8kLnaDQujwgU7GmVHvFbozx4DFzxoBFkLUynR9Q4N13xAhoC3AJEAR7NawEi8oBdJdNonA1LkxE3/8Am43XOTI84YjLMfQpGL9DpETV9iq6YgN4FtgHfAlb7iqPROBkN1XD0I2PAP/Q+1JaB+wCInQlXPWIs4voGO1pKjeaS6IoC8BaRhy58mEbjIlQXGx47BzbBsY+hqc5IjzjqasOeHzsTBrh2LlpN/6ArCuDvSqm7gI1AfXOhiJTaTSqNprcpPdaSKSt3m5kecQSkrTAG/RFTdHpEjcvRFQXQAPwO+BmmK6j5HmMvoTQauyMCp3e2hF8o3GeUh46DaY+a6RHH6fSIGpemKwrgJ0CciBTbWxiNxq40NcDJz4k/9DLs+CFU5BvpEUdOhaufNRZxh450tJQaTa/RFQVwBKixtyAajV2or4QjW81F3C1Qf45hbl4wai7MfBxGzYNBTh/dXKOxC11RANVAjlLqY9quAWg3UI1zUlnQYto5/glYGmBQICReCwkL+SLPjWmz5jlaSo3G4XRFAaw3XxqN81J8uFV6xCxap0ck4RqInARuRr5n65lMR0qq0TgNnSoApZQ7sEJE+kweAE0/wWqF/OyWQb/ksFE+PBVm/MxMjzhGL+Jq+iw5hTlsObeFIYVDSAlJsUsbnSoAEbEopaxKKX8ROWcXCTSartJUD8c/bZUescBMj3glTLrHSI/oH+FoKTWablFcW8z6w+t5MedFLGJhy5YtvDL3Fbsoga6YgKqAb5VSH2CsBwB6DUDTS9SWG+kRD24y3huqzPSIs1ulRxziaCk1mkvCKlaOlR9jZ9FOcgpzyCnM4VTlqTbHNFoaySrIcpgC+Jf50mh6hzbpET8Da5ORHnHc4pb0iB4DHC2lRnPR1DbVsqd4DzmFOews3Mmuol1UNFQAEOAdQEpwCktGLcHH04fnvnmORksjXu5epIem20WerkQDXa2UGgiMEJGDdpFC078RgcL9xiz/wCbjAS2AwHiY8iMzPWKajqyp6XMU1xazs3AnOwuNGf7+kv00iZFPK8Y/hjkj55ASkkJqSCoj/EbQOvFW/NB41n61lqVTljpmDQBAKXUt8DzgBUQrpVKAX4nIdXaRSNM/aJ0e8cAmKDtulEdcBrOfgNHX6PSImj6FVawcLT9qG+x3Fu4kryoPgAHuAxgbOJZbx95Kakgq44PHM8S7c9NlSkgK5f7ldhv8oWsmoCeAiUAmgIjkKKUuGAZCKeUNfAoMMNtZJyK/VEpFA2uAQCAb+IGINFyS9Jq+hS094kY4+H6r9IhXwdQfG4u4fsMcLaVG0yWazTnNM/xdRbuobDDSpQR4B5AaksqyhGWkhKSQGJCIpxPGkuqKAmgUkXPn5QTuSljoemCmiFQppTyBz5VS7wEPAX8QkTVKqZeAO4D/vVjBNX2EmlI4tNkY9I9+ZKZH9DeexG1OjzjAz9FSajQXpKimqI0550DpAZs5J9Y/lrkj55IakkpqSCqRfpGoPuCC3BUFsFcpdTPgrpSKBx4AvrzQSSIiGB5EAJ7mS4CZwM1m+WqMOwytAFyJspMti7ht0iMuN9MjTtXpETVOjVWsHCk/YjPl7CzcSX5VPmCYc5KCkliRtMJmzvEf4O9giS8NZYzTnRyg1CCMSKBzzaLNwFMiUnfByo0HybKBOOCPGFFFt4lInLk/EnhPRJLaOfdu4G6A0NDQtDVr1nS1T3ajqqoKX1/XjgN/SX0UwbfqOEHFXxNU/DW+1YY9v8pnJMVBkygJnEilX5zTPJSlv0fXoCf7WG+t52TDSY7VHeNY/TFO1J+gVmoB8HPzI8Y7hpgBxivCKwIP1ZW5c/fpbh9nzJiRLSIduhB12AvThn8vxuD9LTBFxLzf6SIiYgFSzLSSbwMJF3HuXzCS0ZOeni7Tp0+/mKbtQmZmJs4ghz3pch8tTXDqy5YY+rb0iFNg6h0wegG+gbH4YuQSdSb09+gadKePhTWFbRZrD5QewCIWAOKGxHHNiGsMc05wKhF+EQ4z59j7e+xMja0GGoHPgPnAGOC/LqURESk3g8lNAYYopTxMZRIB5F9KnRoH0FANRz40Bv3Dm430iB7eZnrER42MWTo9osbJsFgtLeYc84GrZnOOt7s3SUFJ3J50OykhKX3anHMpdKYAEkVkHIBS6q/A9oupWCkVjLGAXG4+RzAHeA74GFiM4Ql0K7DhUgTX9BJVRXDoPWOW35weceDQtukRvXwcLaVGY6OmsYZvi7+1zfB3Fe2iqtFYjgwaGERqSCo3J9xMakgqCYEJeLo5n3dOb9GZAmhs/iAiTZdwCxQGrDbXAdyAtSKyUSm1D1ijlHoK2An89WIr1tiJ3O2MOLkO9pTCuTxjIffUNkDM9Ii3tUqP2Ds2UI3mQhRUF9hm9jsLd3Kw9CAWsaBQxA6JZX70fFJDUkkJSSHC13HmHGeks//i8UqpCvOzAgaa2wrDyWdwZxWLyG4gtZ3yYxjPFWicAREjH+7uDPjsd0Rbm+D43419w8bB9FXGoB+a5DSLuJr+i8Vq4XD5YXYW7mRz0WZ+s+43nKk+AxjmnHHB47g96XbDOydkPIO9Oh2m+j0dKgARce9NQTS9RGWBEUb59A7jPX8H1JXbdqvmv5ffD3N/7SgpNRrAMOfsKtplm93vLt5NdaMRk9Lf3Z9JEZO4JfEWUkNSGRUwql+bcy4FfR/vytRVwJkcc6DPhvydUGE8mo5yh5BESFxkxNlx94KND2JtqsfNYwCMudaxsmv6JWerz7Z52Opg2UGsYkWhiB8az8KYhbbYOYe+OcSM6TpVSXfQCsBVaKqHgj3GjD7fnN0XH8J49g4YGg0jJkP4BGPAH5YMXoPa1hEYy4mPXidm5i0Qqa10GvtisVo4VHaoxR2zaCdnq88CMNBjIMlBydw17i5SQ1JJDk7Gz6vtE+OH1WFHiO1SaAXQF7FaoeRIy8z+9A44+62R+xbAJ9gY5McthuETjEG/K4nPIydyamQNMXrw19iB6sbqtuacot3UNNUAEDIohNSQVFaMXUFKSAqjh47Gw00PT/ZGX2FnRwQqTre125/OgXpzfd7L10iDOOleY9APTzOyYukFW42DOVN1psWcU5TDobJDNnPOqKGjuDb2WlvsnDCfMO2d4wC0AnA2asuMePjNNvv8bKgybotx8zC8ccYtaTHlBI2yJTvXaBxFk7WprTmncCcFNQWAac4JTubu5LtJDTbMOb5erh2moq+gFYAjaaw1TDfNNvv8bCg92rI/MB5irmqZ2Ycmgae34+TVaEyqGqrYXbSbnUXGDP/bom9t5pzQQaE2v/vUkFRGDR2lzTlOiv5WegurBYoOtrXbF+w10h0C+IUZg3zqcsNuPzxV57rVOAUiwpnqM228cw6XH8YqVtyUG6OGjuK62OtazDm+YY4WWdNFtAKwByJQfqqtr/3pHDD9lxngD8NT4PIHzNn9BBg83LEyazQmTdYmDpYdbBMKubCmEIBBHoNIDk7mnuR7SAlJITlIm3P6MloB9ATVJW0H+/xsI9sVGP71w5Ih9T9a7PYBsTq/rcZpqGyoNMw55ux+d/FuapuMUMjDfIaRFpJmM+fED43X5hwXQn+TF0tDNZzZ3erhqmwoP2nuVBCcAKPmtQz2IWN18hON0yAi5Fflt/G9P1J2BEFwU26MHjqa6+Out5lzhvnoFJ2ujFYAnWFphML9Npt9+sFP4ZNTIGZGTP9IY6BPv90Y7Ien6PSGGqei0drIwdKDLXlrC3dRWGuYc3w8fRgfPJ45I+eQEpxCcnAyPp46smt/QiuAZkSg7Hhbj5wzu8G8FWbgUBq8oyBtaYvd3jfEoSJrNOdT0VDBrsJdbCzbyOubX2dP8R6bOWe4z3DSh6XbZvdxQ+Jw1y7E/Zr+qwCqCtva7E/vMHzwwUhyEpYC6be1DPZDo9n9yScun2VJ03cQEfKq8tos1h4tP2qYc3AjwTOBG+JvICUkhZTgFG3O0XwH11YAudvhxGcwPM14WMrmgrkTzuUaQD/VsAAAEDlJREFUxyg3IyjamGtNM84ECBkD7jqqoMa5aLQ2cqDkgO3J2p2FOymuNZwNfD19GR88nnlR80gNSaV8fznzZs5zsMQaZ8d1FUDudnh1fouffTNDoyDispbQCWHJOqOVxik5V3+uTeycPcV7qLPUARDuG86ksEmkBhsPXJ1vzsk8mOkgqTV9CddVACc+Mx6+AkDB+Jtg7lPgE+hQsTSa9hAR8irzbE/W5hTmcKT8CADuyp2EgAQWj1psc8cMGaTXnzTdx3UVQNSVhi3f0mD44qffpgd/jdPQaGlkf+n+NrFzSupKAPDz9CM5JJmro64mNSSVpKAkBnkOukCNGs3F47oKIHIi3PqOcScQdaWOb69xKM3mnObF2j3Fe6i31AOGOWfK8Cm2+DlxQ+JwU/pBQY39cV0FAMagrwd+TS8jIuRW5raJnXP0nBHkz0N5kBCQwJJRS2zumMGDgh0ssaa/4toKQKPpBRotjewr3dfGHbO0rhQAPy8/xgePZ0HMAps5Z6DHQAdLrNEYaAWg0Vwk5+rPtRns95bstZlzInwjmDp8qm2xNnZIrDbnaJwWrQA0mk4QEU5VnmqzWHvs3DHAMOeMCRzD0tFLbeacoIFBDpZYo+k6WgFoNK1osDSwr6TFnJNTlNPGnJMSnMLCmIWkhKRoc46mz6MVgKZfU1ZXZouKuatwF3uK99BgbQAg0i+SK8KvMMw5wanEDInR5hyNS6EVgKbfICKcqDjBV1Vf8dEXH7GzcCcnKk4A4OHmQWJAIssSltncMbU5R+PqaAWgcVkaLA3sLdnbJhRyWb0R8M+/yp+U4BQWxS0iJdgw53h76HzLmv6F3RSAUioSeB0IBQT4i4i8oJQKAP4JRAEngKUiUmYvOTT/f3v3HhzVed5x/PtIoBU3XQ1CBiwJR7DcBZaZpsl4jOOhmLpx/yCQ2ONcTOJO3U7atJ0GxzOtk5lM3XTaZvpH47GTJk5jh5CESTPJTCeuY0jaZDDYEQYsiYswiTEgkBAXg4SEnv5xjpZdIYEWaXelPb/PzI52z+U978MR77P7nNV7oqOzu5Om9qZE/f5AxwF6+3sBqCmp4Z6597By1kp6j/Wy8f6NKudI5GXyE0Af8Nfu/oaZzQBeN7OXgU8Cr7j7M2a2BdgCfD6D/ZA85O4cPX/02sXa9qaUcs6SyiU8suiRxFTIlVOuTQOy490dGvxFyGACcPcTwInw+QUzawbmAA8B94abvQDsQAlAbqLnag8HzhxIDPZNp5vo6ukCoCxWRsPMhsStDJfctoRYYSzHPRYZ/7JyDcDMaoGVwC6gKkwOACcJSkQiKTq7O1O+e/9Wx1uJck5tSS33zrs3cbG2rqQOM8txj0UmHnP3zB7AbDqwE/iyu283sy53L0taf9bdy4fY73HgcYCqqqq7tm7dmtF+jsTFixeZPn16rruRUbmI0d051XeKtu422nqCx+m+0wBMYhLzYvOYH5vP/Nh86mJ1zCgc3X2XdR7zg2K8uTVr1rzu7o3Drc/oJwAzmwz8EHjR3beHi0+ZWbW7nzCzaqB9qH3d/TngOYDGxkYfD7di3LFjR97fEjIbMXb3dSe+nTNQzjnXcw4IyznVDYm/rF1cuXjMyzk6j/lBMY5eJr8FZMA3gGZ3/5ekVT8GPgE8E/78r0z1QcaHM5fPsLc9nAr5dFDO6Qvv1FZbUst98+5LlHNqS2pVzhHJkkx+AvgA8Ciwz8yawmVfIBj4t5nZZuAYsDGDfZAs6/d+jp47mjIV8m8v/BaAooIilty2hEcXP5q4lWF58XXVPxHJkkx+C+h/geHeyn0oU8eV7Oru62bfmX2JUk5TexPnr5wHoDxWTsOsBjYs2JAo5xQVFuW4xyIyQH8JLGk5c/lMyrv75o5m+jwo59SV1nF/zf00zAxq+DUlNSrniIxjSgAyrH7v50jXkZSvY75z8R0gKOcsvW0pH1/y8aB+P7OBsuKym7QoIuOJEoAk7Hp3Fy91vMTOX+/k5Hsn2Xt6LxeuXACgoriChpkNbFq4iYZZDSrniOQBJYCI6uzupKWjhebOZlo6W2hqb+LkpZPByoMwZ9oc1tasTdzZ6o4Zd6icI5JnlADynLtz/OJxWjqvDfYtHS20X7725xe3T7udqZOnYhiOU2AFbFi4gU8v+3QOey4imaYEkEd6+3tp62qj9WwrzR3BYN/a2cqF3qCMU2iF1JXWsbp6NfGKOIsqFrGwYiGlsVKa2pv4zM8+w5WrVygqKKKxatg/HhSRPKEEMEFd6r3EwbMHg3f04bv7w2cPJ+5mVVxYzILyBTxQ9wDxymCwf1/Z+4ad875hVgPPr32ebb/exsb3b6RhVkM2wxGRHFACmAA6uzsTA/1A3f7Y+WM4wTxOpbFS4hVxHl70cOKdfU1JDYUFhWkdp2FWA12lXRr8RSJCCWAcGajXt3a2Jur1zZ3NtF+6Vq+vnlZNvCLO+rr1wWBfuYiqqVW6QCsiaVMCyJG+/j7azrWlDPYtnS2Jr10WWAF1JXXcPftuFlUsIl4RJ14RpzRWmuOei0i+UALIgoF6ffJgf+jsoUS9PlYYY0H5AtbVrkuUcOrL63WPWhHJKCWAMXa2+yzNnc0pg/2x88fo934ASopKWFSxiI/FP5a4OFtTUsOkAp0KEckujTq3yN159713aelooeXstYuzpy6dSmwze9ps4hXxlHf2s6fNVr1eRMYFJYAR6Ovv4+i5o+y+uJvdu3cn6vUDs14WWAG1JbXcVXVXUK+vjBMvj2tuHBEZ15QABrncdzm1Xt/RwqGuQ/Rc7QEg1hWjvqyetbVrExdn68vrmTJpSo57LiKSnkgngK7uruvq9W+ffzulXh+viLNp4SbiFXEuHrnIR+7/iOr1IpIX8noka2pvYs+pPTRWNTJr6qzrBvuT751MbDt72mzi5XHW1q5N1Ourp1Wn1Ot3/G6HBn8RyRt5O5o1tTfxqf/+VOJmJQMG6vUrZ61M+X69bk0oIlGTtwlgz6k9KYP/mrlr2Lx8M/Vl9UydPDWHPRMRGR/yNgE0VjVSXFhMb38vkwsm89iyx1gxc0WuuyUiMm7kbQIYmN1y4BqAJjgTEUmVtwkAgiSggV9EZGgFue6AiIjkhhKAiEhEKQGIiESUEoCISEQpAYiIRJQSgIhIRJm757oPN2Vmp4Fjue4HcBtwJtedyDDFmB8UY34YbYw17j5zuJUTIgGMF2a2x90bc92PTFKM+UEx5odMx6gSkIhIRCkBiIhElBJAep7LdQeyQDHmB8WYHzIao64BiIhElD4BiIhElBKAiEhERSoBmNk6M2s1s8NmtmWI9TEz+164fpeZ1SatezJc3mpmf5C0/D/MrN3M9g9q62kzO25mTeFjfSZjSzrumMZoZvPM7FUze8vMDpjZXyRtX2FmL5vZofBnVu6rmeUYc3Iew2OPdZzFZvaame0N4/xi0vZ1YRuHwzaL8jDGb5nZ0aRzmZW54jMx7oTrCs3sN2b2k6Rl6Z1Hd4/EAygEjgDzgSJgL7B40DZPAM+Gzz8KfC98vjjcPgbUhe0UhuvuAVYB+we19TTwNxM9RqAaWBVuMwM4ONAm8BVgS/h8C/CPeRhj1s9jBuM0YHq4zWRgF/B74ettwEfD588Cf5qHMX4L2DDRz2PSfn8FvAT8JGlZWucxSp8AVgOH3b3N3a8AW4GHBm3zEPBC+PwHwIfMzMLlW929x92PAofD9nD3XwCd2QhgBMY8Rnc/4e5vALj7BaAZmDNEWy8Af5yhuJJlO8ZcyUSc7u4Xw+0nhw8P97kvbAMm9rkcMsZMB3IDGRl3zGwu8IfA1wcauZXzGKUEMAf4XdLrd7j+P3liG3fvA84BlSPcdyh/bmZvWlAmykZ5JKMxhh9NVxK8qwKocvcT4fOTQNVoAxiBbMcI2T+PkKE4w7JBE9AOvOzuu8J9usI2hjtWJmQzxgFfDs/lv5pZbCyDGUamfl+/Cvwt0J+0Pu3zGKUEkG1fA+4EGoATwD/ntjujY2bTgR8Cf+nu5wev9+Az54T+TvEwMebVeXT3q+7eAMwFVpvZ0lz3aazdIMYngThwN1ABfD5HXRwVM3sQaHf310fbVpQSwHFgXtLrueGyIbcxs0lAKdAxwn1TuPup8BexH3ie8KNbhmUkRjObTDAwvuju25O2OWVm1eE21QTvuDItqzHm6Dxyo74OtU26v6/u3gW8CqwL9ykL2xjuWJmQzRgJS33u7j3AN5m4/yc/AHzYzN4mKCndZ2bf4VbOYzYviOTyAUwC2ggupgxcjFkyaJs/I/VizLbw+RJSL8a0kXoxppbrLwJXJz3/HEEtb8LFSHBR7dvAV4c43j+RehH4K3kYY9bPYwbjnAmUhdtMAX4JPBi+/j6pFw+fyMMYq8OfRlBCeWYixjho33tJvQic1nnM+C/yeHoA6wm+4XEEeCpc9iXgw+Hz4vAf8DDwGjA/ad+nwv1agQeSln+XoDTQS1Bz2xwu/09gH/Am8OPkgWQixQh8kKC08ybQFD7Wh+sqgVeAQ8D/ABV5GGNOzmOG4lwO/CaMZT/wd0nbzw/bOBy2GcvDGH8ensv9wHcIvy000WIc1Pa9pCaAtM6jpoIQEYmoKF0DEBGRJEoAIiIRpQQgIhJRSgAiIhGlBCAiElFKACIiEaUEIDIEM5tvZt8wsx/cfOuJf1yJJiUAyTtm9idmdjKc873NzD6ZbhsezN64eYi2p5jZTjMrvIV+/b6ZfSnd45pZkZn9IulP/EXGhH6hJB8tA55292fNbBXwMsFc8Ncxs2XAPwxa/Ji7Dzev0WPAdne/mm6n3P1XwK/SPa67XzGzV4BNwIvpHldkOEoAko+Wc21O9HcI5ojBzL5L8Km3jmDq6ifc/afAg2m0/Qjw8MCL4do0s08AnyWYj/68u3/QzL4P/Ju7/9Ld96V53B8RJAwlABkzKgFJPloGNIc3yPgsMHDLvBVAm7uvJhjI/364Bsys0syeBVaa2ZPhsiKCeVreTtr0ujbNbAbBVMPvd/flXBvolxLMUTOsoY4b2k8wjbHImNFcQJJXzGwewayJBwgm6HsN+ALQQ3BzjXnu3m1mFcAud69Po+3bgZ+7ezx8XTxUmwRJ4QBB4nnB3feE2x5w9ztHEdtxIO7BXctERk0lIMk3y4BX3H1d8kIzawQOuXt3uGgVwVS76bhMMHPjgKVDtenul8KbkPwR8JyZfZ0gMbyV5vEGiwHdN91KZISUACTfLGfogX0FcEf4TrwQ+CLBLfVGzN3PhrcbLA4H/SHbNLN6dz8EbDWzxQRJYxk3Kf/ciJlVAmfcvfdW2xAZTNcAJN8MN9CuALYTvBPfDXzN3f/vFtr/GcH9A27U5lNm1mpmbxBcHP73G/RrpNYAPx3F/iLX0TUAiQQz2wk87u6to2xnFfA5d390rNoc4XG3E9x97WCmjyXRoU8AEhV3Ety5bFTc/Q3g1fAPwcakzZsJv330Iw3+Mtb0CUBEJKL0CUBEJKKUAEREIkoJQEQkopQAREQiSglARCSilABERCJKCUBEJKKUAEREIkoJQEQkov4fdSZ03xdnSVEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WILxImfBWOmA",
        "colab_type": "text"
      },
      "source": [
        "### B. Find the value of the permeability at inﬁnite pore pressure $(k_{\\infty})$ and Klinkenberg correction factor $(K_b)$\n",
        "\n",
        "$$k_a=k_{\\infty}[1+(Kb \\cdot Pp^{-1})]$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kHs0f8dyEgzi",
        "colab_type": "code",
        "outputId": "771c7f84-cccf-4403-da8b-0f263e2bb1de",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        }
      },
      "source": [
        "# function to fit\n",
        "def klinkenberg(Pp_inv, k_inf, Kb):\n",
        "  ka = k_inf * (1 + (Kb * Pp_inv))\n",
        "  return(ka)\n",
        "\n",
        "# fitting to line eff stress 2000 psi\n",
        "from scipy.optimize import curve_fit\n",
        "\n",
        "popt, pcov = curve_fit(klinkenberg, Pp_inv, k_eff2000)\n",
        "print('Permeability at infinite pore pressure (k_infinite) at 2000 psi effective stress:', popt[0], 'nD, and Klinkenberg correction factor (Kb):', popt[1],'psi')\n",
        "\n",
        "# fitting to line eff stress 3000 psi\n",
        "popt1, pcov1 = curve_fit(klinkenberg, Pp_inv, k_eff3000)\n",
        "print('Permeability at infinite pore pressure (k_infinite) at 3000 psi effective stress:', popt1[0], 'nD, and Klinkenberg correction factor (Kb):', popt1[1],'psi')\n",
        "\n",
        "# fitting to line eff stress 4000 psi\n",
        "popt2, pcov2 = curve_fit(klinkenberg, Pp_inv, k_eff4000)\n",
        "print('Permeability at infinite pore pressure (k_infinite) at 4000 psi effective stress:', popt2[0], 'nD, and Klinkenberg correction factor (Kb):', popt2[1],'psi \\n')\n",
        "\n",
        "plt.figure(figsize=(10,6))\n",
        "\n",
        "p1 = plt.plot(Pp_inv, k_eff2000, '.-', color='blue')\n",
        "p2 = plt.plot(Pp_inv, k_eff3000, '.-', color='orange')\n",
        "p3 = plt.plot(Pp_inv, k_eff4000, '.-', color='green')\n",
        "\n",
        "# plot the fitted Klinkenberg\n",
        "Pp_inv = np.concatenate([[0], Pp_inv], axis=0) # add 0 to get the y-intercept later in the plot\n",
        "ka_fit_2000 = popt[0] * (1 + (popt[1] * Pp_inv))\n",
        "pfit1 = plt.plot(Pp_inv, ka_fit_2000, '--', color='blue')\n",
        "\n",
        "Pp_inv = np.concatenate([[0], Pp_inv], axis=0) # add 0 to get the y-intercept later in the plot\n",
        "ka_fit_3000 = popt1[0] * (1 + (popt1[1] * Pp_inv))\n",
        "pfit2 = plt.plot(Pp_inv, ka_fit_3000, '--', color='orange')\n",
        "\n",
        "Pp_inv = np.concatenate([[0], Pp_inv], axis=0) # add 0 to get the y-intercept later in the plot\n",
        "ka_fit_4000 = popt2[0] * (1 + (popt2[1] * Pp_inv))\n",
        "pfit3 = plt.plot(Pp_inv, ka_fit_4000, '--', color='green')\n",
        "\n",
        "plt.title('Permeability vs Inverse Pore Pressure')\n",
        "plt.legend([p1[0], p2[0], p3[0], pfit1[0], pfit2[0], pfit3[0]], ['Eff. Stress = 2000 psi', 'Eff. Stress = 3000 psi', 'Eff. Stress = 4000 psi', \n",
        "                                                                 'Line ka={}[1+({}/Pp)]'.format(np.round(popt[0], 2), np.round(popt[1], 2)), \n",
        "                                                                 'Line ka={}[1+({}/Pp)]'.format(np.round(popt1[0], 2), np.round(popt1[1], 2)), \n",
        "                                                                 'Line ka={}[1+({}/Pp)]'.format(np.round(popt2[0], 2), np.round(popt2[1], 2))])\n",
        "plt.xlabel('$Pp^{-1} (psi^{-1})$')\n",
        "plt.ylabel('Permeability (nD)')\n",
        "plt.xlim(xmin=0)\n",
        "plt.grid('True')\n",
        "plt.show()"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Permeability at infinite pore pressure (k_infinite) at 2000 psi effective stress: 21.66153848342078 nD, and Klinkenberg correction factor (Kb): 532.6704537514858 psi\n",
            "Permeability at infinite pore pressure (k_infinite) at 3000 psi effective stress: 11.015384631244682 nD, and Klinkenberg correction factor (Kb): 833.7988810508397 psi\n",
            "Permeability at infinite pore pressure (k_infinite) at 4000 psi effective stress: 3.865384613309115 nD, and Klinkenberg correction factor (Kb): 1813.4328370142694 psi \n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vs-znJ-ig6TP",
        "colab_type": "text"
      },
      "source": [
        "## Part 3. Effective Pore Size"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uqAPuwDFlJ_t",
        "colab_type": "text"
      },
      "source": [
        "### A. Compute viscosity of Helium at given P, T"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pF2pZkFGi0EB",
        "colab_type": "code",
        "outputId": "78ef3735-1f88-407c-cf8a-59873b25423b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 105
        }
      },
      "source": [
        "# library for fluid property calculation\n",
        "!pip install CoolProp"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting CoolProp\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/03/d8/6cbeeb68464c7811a9d48f800618746d3415bf84d545add04eb4290f83c5/CoolProp-6.3.0-cp36-cp36m-manylinux1_x86_64.whl (4.0MB)\n",
            "\u001b[K     |████████████████████████████████| 4.0MB 2.8MB/s \n",
            "\u001b[?25hInstalling collected packages: CoolProp\n",
            "Successfully installed CoolProp-6.3.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5br2m0lCi3Ql",
        "colab_type": "code",
        "outputId": "bbb4bc1d-3b5d-4b7b-e560-18263e99af37",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "from CoolProp.CoolProp import PropsSI\n",
        "\n",
        "# known Helium properties\n",
        "temp = 40 + 273 # celsius to kelvin\n",
        "pressure = 500 * 6894.76 # psi to Pa\n",
        "c = 1 # geometric factor, dimensionless\n",
        "M = 4 * 0.001 # molar mass, g/mol to kg/mol\n",
        "R = 8.3145 # gas constant, J/mol*K\n",
        "\n",
        "# Kb = popt[1] * 6894.76 # psi to Pa\n",
        "Kb = 4068488\n",
        "\n",
        "# compute Helium viscosity at P, T\n",
        "visco = PropsSI('V', 'T', temp, 'P', pressure, 'helium') # result in unit (Pa*s)\n",
        "print('Viscosity of Helium at pressure 500 psi and temperature 40C:', visco * 1000, 'cP')"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Viscosity of Helium at pressure 500 psi and temperature 40C: 0.020626720217357453 cP\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Pn1Y2jfRlcLt",
        "colab_type": "text"
      },
      "source": [
        "### B. Plot the eﬀective slit pore width, w, as a function of eﬀective stress\n",
        "\n",
        "The equation shown in handout is INCORRECT, the correct one as follows:\n",
        "\n",
        "$$w=\\frac{16 c \\mu}{K_b} (\\frac{2RT}{\\pi M})^{\\frac{1}{2}}$$\n",
        "\n",
        "$c$ is dimensionless, $\\mu$ in $(Pa \\cdot s)$, $R$ in $(J \\cdot mol^{-1} K^{-1})$, $T$ in $K$, and $M$ in $kg \\cdot mol^{-1}$\n",
        "\n",
        "$K_b$ at the effective stress of 2000 psi is 535.52 psi"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-LoowZS_15sh",
        "colab_type": "code",
        "outputId": "3ccb3396-1fcc-479b-eed2-c022700a9003",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "w = ((16 * 1 * visco) / Kb) * np.sqrt((2 * R * temp) / (np.pi * M))\n",
        "print('Effective pore size at effective stress of 2000 psi:', w * 1E+09, 'nm')"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Effective pore size at effective stress of 2000 psi: 52.20564003228682 nm\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DMZ6JHEgtRL_",
        "colab_type": "text"
      },
      "source": [
        "## Part 4. Flow mechanisms"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5NBetAkUfUtS",
        "colab_type": "text"
      },
      "source": [
        "### A. Calculate the ratio of diﬀusive to viscous ﬂux at 2000 psi eﬀective stress (the ratio of the Klinkenberg corrected permeability to $k_∞$) as a function of pore pressure.\n",
        "\n",
        "$$ratio=\\frac{k_a}{k_\\infty}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ktA52zb9fRzc",
        "colab_type": "code",
        "outputId": "10b3a9d3-07fc-4d16-ac22-04f7f3a9a4aa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "# for all eff stress 2000, 3000, 4000 psi\n",
        "\n",
        "pp_line = np.array([250, 500, 750])\n",
        "dif_to_visc2000 = k_eff2000 / popt[0]\n",
        "dif_to_visc3000 = k_eff3000 / popt1[0]\n",
        "dif_to_visc4000 = k_eff4000 / popt2[0]\n",
        "\n",
        "p1 = plt.plot(pp_line, dif_to_visc2000, '.-', color='blue')\n",
        "p2 = plt.plot(pp_line, dif_to_visc3000, '.-', color='orange')\n",
        "p3 = plt.plot(pp_line, dif_to_visc4000, '.-', color='green')\n",
        "plt.title('Diffusive-to-Viscous Flux Ratio vs. Pore Pressure')\n",
        "plt.legend([p1[0], p2[0], p3[0]], ['Eff. Stress = 2000 psi', 'Eff. Stress = 3000 psi', 'Eff. Stress = 4000 psi'])\n",
        "plt.xlabel('Pore pressure (psi)'); plt.ylabel('Diffusive flux / Viscous flux')\n",
        "plt.show()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ANgjiqaa8xWt",
        "colab_type": "text"
      },
      "source": [
        "### B. Calculate mean free path (MFP) and Knudsen number\n",
        "\n",
        "**B.1. Calculate MFP**\n",
        "\n",
        "There is a typo in the equation in the handout. The correct one as follows:\n",
        "\n",
        "$$\\lambda=\\frac{K_B T}{\\sqrt{2} \\cdot \\pi d^2_m P_p}$$\n",
        "<br>\n",
        "$K_B$ Boltzmann constant in $(kg m^2 s^{-2} K^{-1})$, $T$ temperature in $K$, $d_m$ molecular diameter in $m$, $P_p$ pore pressure in $Pa$, so $\\lambda$ the mean free path (MFP) is in $m$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8G2iNiCx8wne",
        "colab_type": "code",
        "outputId": "952dad29-c8de-4a77-8a8d-13875eeb13c9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 386
        }
      },
      "source": [
        "# knowns\n",
        "K_B = 1.3806E-23 # unit consistent with above\n",
        "temp = 40 + 273 # Celsius to K\n",
        "d_m = 2.6E-10 # unit consistent with above\n",
        "pressure_range = np.arange(10, 1010, 10) \n",
        "pressure_range_conv = pressure_range * 6894.76 # psi to Pa\n",
        "\n",
        "pressure250 = 250 * 6894.76 # psi to Pa\n",
        "\n",
        "# calculate MFP\n",
        "mfp = (K_B * temp) / (np.sqrt(2) * np.pi * (d_m**2) * pressure_range_conv)\n",
        "mfp250 = (K_B * temp) / (np.sqrt(2) * np.pi * (d_m**2) * pressure250)\n",
        "print('Mean free path at pore pressure 250 psi:', mfp250 * 1E+09, 'nm \\n')\n",
        "\n",
        "# plot MFP vs pore pressure\n",
        "plt.figure(figsize=(10,5))\n",
        "plt.plot(pressure_range, mfp * 1E+09, '.-')\n",
        "plt.title('Mean Free Path vs Pore Pressure')\n",
        "plt.xlabel('Pore pressure (psi)'); plt.ylabel('Mean Free Path (nm)')\n",
        "plt.xlim(xmin=0); plt.ylim(ymin=0)\n",
        "plt.show()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean free path at pore pressure 250 psi: 8.347212659951989 nm \n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ihKgq110_LaA",
        "colab_type": "text"
      },
      "source": [
        "**B.2. Calculate Knudsen Number and Determine the Flow Regime**\n",
        "\n",
        "$$K_N=\\frac{\\lambda}{d_P}$$\n",
        "\n",
        "$\\lambda$ in unit $m$ is the mean free path (calculated previously), and $d_P$ in unit $m$ is the effective pore size (also calculated previously). $K_N$ is dimensionless. \n",
        "\n",
        "Criteria for $K_N$ for flow regime:\n",
        "\n",
        "|Flow regime|Knudsen number|Driving force|\n",
        "|:---:|:---:|:---:|\n",
        "|Knudsen/free<br> molecule flow|Kn>10|Total concentration<br> gradient and<br> molecular weight|\n",
        "|Transition flow|0.1<Kn<10|Mostly Knudsen<br> flow with some<br> Darcy flow|\n",
        "|Slip flow|0.01<Kn<0.1|Mostly Darcy flow<br> with some<br> Knudsen flow|\n",
        "|Continuum/Darcy/<br> Poiseuille flow|0.01>Kn|Total pressure<br> gradient|\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1m37EgMRCqzC",
        "colab_type": "code",
        "outputId": "1907b445-a09a-490b-c255-a7f15d34aa2d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "knudsen = mfp250 / w\n",
        "\n",
        "print('Knudsen number at effective pore size', np.round(w * 1E+09, 3), 'nm and gas mean free path', np.round(mfp250 * 1E+09, 3), 'nm at pressure', 250, 'psi is:', np.round(knudsen, 3))\n",
        "\n",
        "# determine what flow regime\n",
        "if knudsen > 10:\n",
        "  print('Flow regime is: Knudsen flow')\n",
        "if 0.1 < knudsen < 10:\n",
        "  print('Flow regime is: Transition flow')\n",
        "if 0.01 < knudsen < 0.1:\n",
        "  print('Flow regime is: Slip flow')\n",
        "if knudsen < 0.01:\n",
        "  print('Flow regime is: Darcy flow')"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Knudsen number at effective pore size 52.206 nm and gas mean free path 8.347 nm at pressure 250 psi is: 0.16\n",
            "Flow regime is: Transition flow\n"
          ],
          "name": "stdout"
        }
      ]
    },
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      "metadata": {
        "id": "bepBj438CYYs",
        "colab_type": "code",
        "outputId": "f8484b84-dd58-4969-ed05-352655a07115",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        }
      },
      "source": [
        "import plotly.graph_objects as go\n",
        "\n",
        "fig = go.Figure()\n",
        "fig.add_trace(go.Scatter(x=Pc_min_Pp250, y=k_Pp250,\n",
        "                    mode='lines+markers',\n",
        "                    name='lines+markers'))\n",
        "fig.show()"
      ],
      "execution_count": 16,
      "outputs": [
        {
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