module3_lesson1.ipynb

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      "name": "module3_lesson1.ipynb",
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      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
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      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
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        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/alexeynick/msu_oil_gas/blob/main/module3_lesson1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jGXuKWMmxKvB"
      },
      "source": [
        "## Задачи модуля №3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fxm6Rsyfhqv5"
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import plotly.graph_objects as go\n",
        "import matplotlib.pyplot as plt \n",
        "from plotly.subplots import make_subplots\n",
        "from scipy.optimize import curve_fit"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_P48Jqk5cx6t"
      },
      "source": [
        "anno_font = dict(\n",
        "        family=\"arial bold\",\n",
        "        size=18,\n",
        "        color=\"Black\"\n",
        "    )"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PbaJBf9XxQtu"
      },
      "source": [
        "## Задача 3.1 Расчет обводненности скважины через плотность жидкости"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5xuJCY2YyJj-"
      },
      "source": [
        "С помощью фактических замеров (плотномер) определена плотность жидкости $\\rho_{Ж} = 0,920\\;г/см^3$, плотность нефти в поверхностных условиях (отчеты по исследованиям глубинных проб) $\\rho_{Н} = 0,896\\;г/см^3$, плотность воды в поверхностных условиях (отчеты по исследованиям глубинных проб, важно понимать какая это вода) $\\rho_{В} = 1, 010\\;г/см^3$.\n",
        "\n",
        "Рассчитать:\n",
        "- обводненность скважины\n",
        "- обводненность скважины с замеренной плотностью жидкости -0,900 г/см3, и -0,910 г/см3"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zbMRNwPYzh0N"
      },
      "source": [
        "### Расчеты\n",
        "\n",
        "$\\rho_{Ж} = \\rho_{Н} \\cdot (1 - S_{В}) + \\rho_{В} \\cdot S_{В}$\n",
        "\n",
        "$S_{В} = \\cfrac{\\rho_{Ж} - \\rho_{Н}}{\\rho_{В} - \\rho_{Н}}$\n",
        "\n",
        "Обводненность (объемная) = $(1 - S_{В})$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Uy_kSJLuxQQV"
      },
      "source": [
        "rho_n_value = 0.896\n",
        "rho_v_value = 1.01"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xKCIw9vQxQYm",
        "outputId": "3de3317e-5fe2-44ee-8ee9-eee497642cd2"
      },
      "source": [
        "for rho_g_value in (0.92, 0.91, 0.90):\n",
        "  s_value = (rho_g_value - rho_n_value) / (rho_v_value - rho_n_value)\n",
        "  print('Обводненность скважины при плотности жидкости {0:,.3f} равна: {1:,.3f}'.format(rho_g_value, s_value))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Обводненность скважины при плотности жидкости 0.920 равна: 0.211\n",
            "Обводненность скважины при плотности жидкости 0.910 равна: 0.123\n",
            "Обводненность скважины при плотности жидкости 0.900 равна: 0.035\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "95XP5IgU15Iq"
      },
      "source": [
        "## Задача 3.2 Расчет забойного давления скважины через плотность жидкости\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H6FptRumGfVc"
      },
      "source": [
        "Дано:\n",
        "- глубина скважины по вертикали $H = 1000\\;м$ (из инклинометрии по скважине)\n",
        "- глубина уровня в скважине по вертикали $H_{СТ} = 107,63\\;м$ (расстояние от дневной поверхности)\n",
        "- устьевое давление $P_{У} = 5 \\;атм$\n",
        "- плотность жидкости в скважине $\\rho_{Ж} = 942\\;кг/м^3$\n",
        "\n",
        "Рассчитать:\n",
        "- забойное давление $P_{З}$ в МПа, атм"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N7_cGzJ86mXB"
      },
      "source": [
        "### Расчеты\n",
        "\n",
        "$P_{З} = P_{СТ} + P_{У}$\n",
        "\n",
        "где:\n",
        "- $P_{СТ}$ - давление столба жидкости в скважине\n",
        "\n",
        "$P_{З} = \\rho_{Ж} \\cdot g \\cdot h + P_{У}$\n",
        "\n",
        "$P_{З} = \\rho_{Ж} \\cdot g \\cdot (H - H_{СТ}) + P_{У}$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GlA7HrLhxQkF"
      },
      "source": [
        "ATM_TO_PA = 101325\n",
        "G_VALUE = 9.81\n",
        "SECONDS_IN_HOUR = 3600"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GMXVYIUMxRHy"
      },
      "source": [
        "rho_g_value = 942\n",
        "h_total = 1000\n",
        "h_st = 107.63\n",
        "p_ust = 5"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eMBYpe2UxRLf",
        "outputId": "154602d1-ef14-472e-a885-2164561a321f"
      },
      "source": [
        "p_zab = rho_g_value * G_VALUE * (h_total - h_st) + p_ust * ATM_TO_PA\n",
        "\n",
        "print('Забойное давление равно: {0:,.2f} МПа'.format(p_zab / 10**6))\n",
        "print('Забойное давление равно: {0:,.2f} атм'.format(p_zab / ATM_TO_PA))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Забойное давление равно: 8.75 МПа\n",
            "Забойное давление равно: 86.39 атм\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YGXF_bs58z3q"
      },
      "source": [
        "## Задача 3.3 Определение коэффициента продуктивности скважины при обработке индикаторной диаграммы (метод установившихся отборов) (нефтяная)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qFZU9amT8ghf"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
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          "height": 198
        },
        "id": "AZvdlKu4Ae0Q",
        "outputId": "d1903a1c-7e29-40e9-9955-baa9122f088d"
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      "source": [
        "data = {\n",
        "    'delta_p' : [10, 20, 30, 40, 50],\n",
        "    'Q': [11.5, 20, 27, 34.6, 39.7]\n",
        "}\n",
        "\n",
        "df_data = pd.DataFrame(\n",
        "    data, \n",
        "    columns = ['delta_p','Q']\n",
        "    )\n",
        "\n",
        "df_data['dpq'] = df_data['delta_p'] / df_data['Q']\n",
        "df_data['dpq'] = df_data['dpq'].fillna(0)\n",
        "df_data"
      ],
      "execution_count": null,
      "outputs": [
        {
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              "      <th>delta_p</th>\n",
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              "      <th>1</th>\n",
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              "   delta_p     Q       dpq\n",
              "0       10  11.5  0.869565\n",
              "1       20  20.0  1.000000\n",
              "2       30  27.0  1.111111\n",
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        "fig.add_trace(go.Scatter(x=df_data['delta_p'], y=df_data['Q'],\n",
        "                    mode='lines+markers',\n",
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        "\n",
        "fig.show()"
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      "execution_count": null,
      "outputs": [
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          "metadata": {
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    {
      "cell_type": "code",
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      },
      "source": [
        "#fig = go.Figure()\n",
        "\n",
        "#fig.add_trace(go.Scatter(x=df_data['dpq'], y=df_data['Q'],\n",
        "#                    mode='lines+markers',\n",
        "#                    name='non-linear'))\n",
        "\n",
        "#fig.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CJmGGzRuAe55"
      },
      "source": [
        "def line_func(x, a, b):\n",
        "    return a + b * x"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
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        },
        "id": "4a89L1UQCfmI",
        "outputId": "26a98f99-0906-4121-f259-e0e64c2789d2"
      },
      "source": [
        "popt, pcov = curve_fit(line_func, df_data['delta_p'], df_data['Q'])\n",
        "popt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5.25999998, 0.71      ])"
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          },
          "metadata": {
            "tags": []
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          "execution_count": 12
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        "id": "_ZttUj2ECfpF",
        "outputId": "4c375ce2-3674-4744-bbee-d7da0e475770"
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      "source": [
        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_data['delta_p'], y=df_data['Q'],\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_data['delta_p'], y=line_func(df_data['delta_p'], *popt),\n",
        "                    mode='lines+markers',\n",
        "                    name='linear appr'))\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
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      "source": [
        ""
      ],
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    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LcVAOnDdCf0D"
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      "source": [
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
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      "source": [
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      "outputs": []
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    {
      "cell_type": "markdown",
      "metadata": {
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      },
      "source": [
        "## Задача 3.6 Гидропрослушивание (Interference Testing)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iV_JMfNW1ZKk"
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      "source": [
        "Цель работы - определить свойства пласта (пьезопроводность, гидропроводность и проницаемость) в межскважинном пространстве по результатам гидропрослушивания.\n",
        "\n",
        "\n",
        "Дано:\n",
        "- расстояние между скважинами $R = 504\\;м$\n",
        "- глубина пласта $H = 786\\;м$\n",
        "- толщина пласта $h = 1\\;м$\n",
        "- вязкость нефти $\\mu = 7.4\\;сПз$\n",
        "- плотность нефти $\\rho = 833\\;кг/м^3$ \n",
        "- динамический уровень (начальный) $h_{ДИН} = 220\\;м$\n",
        "- дебит возмущающей скважины $Q_{ВС} = 78\\;м^3/сут$\n",
        "\n",
        "\n",
        "Отслеживайте изменение динамического уровня жидкости в реагирующей скважине. Исходной информацией для дальнейших расчётов является зависимость динамического уровня в реагирующей скважине от времени $h_{ДИН} = f(t)$\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CJzy7iLL4-oS"
      },
      "source": [
        "R_value = 504\n",
        "H_value = 786\n",
        "h_plast = 1\n",
        "mu_value = 7.4\n",
        "rho_value = 833\n",
        "h_dyn = 220\n",
        "Q_value = 78\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Yd8Fivjt1Gg3",
        "outputId": "2a79e0cd-7b38-4f76-ba7b-564979218867"
      },
      "source": [
        "data = {\n",
        "    'h' : [220, 220, 221, 223, 227, 229, 232, 233, 235, 237, 239, 241, 242, 243, 245, 246, 249, 251, 255, 258, 260, 263, 266, 269, 271, 277, 281, 284, 288, 290, 292],\n",
        "    't':  [  0,   3,   6,   9,  12,  14,  16,  17,  18,  19,  21,  22,  23,  24,  25,  26,  28,  30,  33,  35,  37,  40,  42,  45,  48,  53,  58,  62,  66,  69,  72]\n",
        "}\n",
        "\n",
        "df_data = pd.DataFrame(\n",
        "    data, \n",
        "    columns = ['h','t']\n",
        "    )\n",
        "\n",
        "p_zab0 = rho_value * G_VALUE * (H_value - h_dyn)\n",
        "\n",
        "df_data['t'] = df_data['t'] * SECONDS_IN_HOUR\n",
        "df_data['p_zab'] = rho_value * G_VALUE * (H_value - df_data['h'])\n",
        "df_data['delta_p'] = df_data['p_zab'] - p_zab0\n",
        "df_data['delta_p_1'] = df_data['delta_p'].shift(1) - df_data['delta_p']\n",
        "df_data['t_diff'] = df_data['t'].diff()\n",
        "df_data['delta_p_2'] = df_data['delta_p_1'] / df_data['t_diff']\n",
        "df_data['t_inv'] = (1 / df_data['t'] + 1 / df_data['t'].shift()) / 2\n",
        "df_data['t_inv_delta_p'] = df_data['t_inv'] * df_data['delta_p_1']\n",
        "df_data['phi'] = df_data['t_inv_delta_p'].cumsum()\n",
        "df_data['ln_phi'] = np.log(df_data['phi'])\n",
        "\n",
        "df_data = df_data.dropna()\n",
        "df_data"
      ],
      "execution_count": null,
      "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>h</th>\n",
              "      <th>t</th>\n",
              "      <th>p_zab</th>\n",
              "      <th>delta_p</th>\n",
              "      <th>delta_p_1</th>\n",
              "      <th>t_diff</th>\n",
              "      <th>delta_p_2</th>\n",
              "      <th>t_inv</th>\n",
              "      <th>t_inv_delta_p</th>\n",
              "      <th>phi</th>\n",
              "      <th>ln_phi</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>221</td>\n",
              "      <td>21600</td>\n",
              "      <td>4617027.45</td>\n",
              "      <td>-8171.73</td>\n",
              "      <td>8171.73</td>\n",
              "      <td>10800.0</td>\n",
              "      <td>0.756642</td>\n",
              "      <td>0.000069</td>\n",
              "      <td>0.567481</td>\n",
              "      <td>0.567481</td>\n",
              "      <td>-0.566548</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>223</td>\n",
              "      <td>32400</td>\n",
              "      <td>4600683.99</td>\n",
              "      <td>-24515.19</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>10800.0</td>\n",
              "      <td>1.513283</td>\n",
              "      <td>0.000039</td>\n",
              "      <td>0.630535</td>\n",
              "      <td>1.198016</td>\n",
              "      <td>0.180667</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>227</td>\n",
              "      <td>43200</td>\n",
              "      <td>4567997.07</td>\n",
              "      <td>-57202.11</td>\n",
              "      <td>32686.92</td>\n",
              "      <td>10800.0</td>\n",
              "      <td>3.026567</td>\n",
              "      <td>0.000027</td>\n",
              "      <td>0.882749</td>\n",
              "      <td>2.080765</td>\n",
              "      <td>0.732735</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>229</td>\n",
              "      <td>50400</td>\n",
              "      <td>4551653.61</td>\n",
              "      <td>-73545.57</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>7200.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000021</td>\n",
              "      <td>0.351298</td>\n",
              "      <td>2.432063</td>\n",
              "      <td>0.888740</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>232</td>\n",
              "      <td>57600</td>\n",
              "      <td>4527138.42</td>\n",
              "      <td>-98060.76</td>\n",
              "      <td>24515.19</td>\n",
              "      <td>7200.0</td>\n",
              "      <td>3.404888</td>\n",
              "      <td>0.000019</td>\n",
              "      <td>0.456012</td>\n",
              "      <td>2.888074</td>\n",
              "      <td>1.060590</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>233</td>\n",
              "      <td>61200</td>\n",
              "      <td>4518966.69</td>\n",
              "      <td>-106232.49</td>\n",
              "      <td>8171.73</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000017</td>\n",
              "      <td>0.137698</td>\n",
              "      <td>3.025772</td>\n",
              "      <td>1.107166</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>235</td>\n",
              "      <td>64800</td>\n",
              "      <td>4502623.23</td>\n",
              "      <td>-122575.95</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>4.539850</td>\n",
              "      <td>0.000016</td>\n",
              "      <td>0.259632</td>\n",
              "      <td>3.285404</td>\n",
              "      <td>1.189490</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>237</td>\n",
              "      <td>68400</td>\n",
              "      <td>4486279.77</td>\n",
              "      <td>-138919.41</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>4.539850</td>\n",
              "      <td>0.000015</td>\n",
              "      <td>0.245577</td>\n",
              "      <td>3.530981</td>\n",
              "      <td>1.261576</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>239</td>\n",
              "      <td>75600</td>\n",
              "      <td>4469936.31</td>\n",
              "      <td>-155262.87</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>7200.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000014</td>\n",
              "      <td>0.227561</td>\n",
              "      <td>3.758542</td>\n",
              "      <td>1.324031</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>241</td>\n",
              "      <td>79200</td>\n",
              "      <td>4453592.85</td>\n",
              "      <td>-171606.33</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>4.539850</td>\n",
              "      <td>0.000013</td>\n",
              "      <td>0.211270</td>\n",
              "      <td>3.969812</td>\n",
              "      <td>1.378719</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>242</td>\n",
              "      <td>82800</td>\n",
              "      <td>4445421.12</td>\n",
              "      <td>-179778.06</td>\n",
              "      <td>8171.73</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000012</td>\n",
              "      <td>0.100935</td>\n",
              "      <td>4.070747</td>\n",
              "      <td>1.403827</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>243</td>\n",
              "      <td>86400</td>\n",
              "      <td>4437249.39</td>\n",
              "      <td>-187949.79</td>\n",
              "      <td>8171.73</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000012</td>\n",
              "      <td>0.096636</td>\n",
              "      <td>4.167384</td>\n",
              "      <td>1.427288</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>245</td>\n",
              "      <td>90000</td>\n",
              "      <td>4420905.93</td>\n",
              "      <td>-204293.25</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>4.539850</td>\n",
              "      <td>0.000011</td>\n",
              "      <td>0.185377</td>\n",
              "      <td>4.352761</td>\n",
              "      <td>1.470810</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>246</td>\n",
              "      <td>93600</td>\n",
              "      <td>4412734.20</td>\n",
              "      <td>-212464.98</td>\n",
              "      <td>8171.73</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000011</td>\n",
              "      <td>0.089051</td>\n",
              "      <td>4.441812</td>\n",
              "      <td>1.491062</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>249</td>\n",
              "      <td>100800</td>\n",
              "      <td>4388219.01</td>\n",
              "      <td>-236980.17</td>\n",
              "      <td>24515.19</td>\n",
              "      <td>7200.0</td>\n",
              "      <td>3.404887</td>\n",
              "      <td>0.000010</td>\n",
              "      <td>0.252560</td>\n",
              "      <td>4.694372</td>\n",
              "      <td>1.546364</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>251</td>\n",
              "      <td>108000</td>\n",
              "      <td>4371875.55</td>\n",
              "      <td>-253323.63</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>7200.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000010</td>\n",
              "      <td>0.156733</td>\n",
              "      <td>4.851105</td>\n",
              "      <td>1.579207</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>255</td>\n",
              "      <td>118800</td>\n",
              "      <td>4339188.63</td>\n",
              "      <td>-286010.55</td>\n",
              "      <td>32686.92</td>\n",
              "      <td>10800.0</td>\n",
              "      <td>3.026567</td>\n",
              "      <td>0.000009</td>\n",
              "      <td>0.288900</td>\n",
              "      <td>5.140005</td>\n",
              "      <td>1.637054</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>258</td>\n",
              "      <td>126000</td>\n",
              "      <td>4314673.44</td>\n",
              "      <td>-310525.74</td>\n",
              "      <td>24515.19</td>\n",
              "      <td>7200.0</td>\n",
              "      <td>3.404887</td>\n",
              "      <td>0.000008</td>\n",
              "      <td>0.200461</td>\n",
              "      <td>5.340465</td>\n",
              "      <td>1.675313</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>260</td>\n",
              "      <td>133200</td>\n",
              "      <td>4298329.98</td>\n",
              "      <td>-326869.20</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>7200.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000008</td>\n",
              "      <td>0.126204</td>\n",
              "      <td>5.466670</td>\n",
              "      <td>1.698670</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>263</td>\n",
              "      <td>144000</td>\n",
              "      <td>4273814.79</td>\n",
              "      <td>-351384.39</td>\n",
              "      <td>24515.19</td>\n",
              "      <td>10800.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000007</td>\n",
              "      <td>0.177146</td>\n",
              "      <td>5.643816</td>\n",
              "      <td>1.730560</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>266</td>\n",
              "      <td>151200</td>\n",
              "      <td>4249299.60</td>\n",
              "      <td>-375899.58</td>\n",
              "      <td>24515.19</td>\n",
              "      <td>7200.0</td>\n",
              "      <td>3.404887</td>\n",
              "      <td>0.000007</td>\n",
              "      <td>0.166191</td>\n",
              "      <td>5.810007</td>\n",
              "      <td>1.759582</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>269</td>\n",
              "      <td>162000</td>\n",
              "      <td>4224784.41</td>\n",
              "      <td>-400414.77</td>\n",
              "      <td>24515.19</td>\n",
              "      <td>10800.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000006</td>\n",
              "      <td>0.156733</td>\n",
              "      <td>5.966740</td>\n",
              "      <td>1.786201</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>271</td>\n",
              "      <td>172800</td>\n",
              "      <td>4208440.95</td>\n",
              "      <td>-416758.23</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>10800.0</td>\n",
              "      <td>1.513283</td>\n",
              "      <td>0.000006</td>\n",
              "      <td>0.097733</td>\n",
              "      <td>6.064473</td>\n",
              "      <td>1.802448</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>277</td>\n",
              "      <td>190800</td>\n",
              "      <td>4159410.57</td>\n",
              "      <td>-465788.61</td>\n",
              "      <td>49030.38</td>\n",
              "      <td>18000.0</td>\n",
              "      <td>2.723910</td>\n",
              "      <td>0.000006</td>\n",
              "      <td>0.270357</td>\n",
              "      <td>6.334829</td>\n",
              "      <td>1.846063</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>281</td>\n",
              "      <td>208800</td>\n",
              "      <td>4126723.65</td>\n",
              "      <td>-498475.53</td>\n",
              "      <td>32686.92</td>\n",
              "      <td>18000.0</td>\n",
              "      <td>1.815940</td>\n",
              "      <td>0.000005</td>\n",
              "      <td>0.163931</td>\n",
              "      <td>6.498760</td>\n",
              "      <td>1.871611</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>284</td>\n",
              "      <td>223200</td>\n",
              "      <td>4102208.46</td>\n",
              "      <td>-522990.72</td>\n",
              "      <td>24515.19</td>\n",
              "      <td>14400.0</td>\n",
              "      <td>1.702444</td>\n",
              "      <td>0.000005</td>\n",
              "      <td>0.113622</td>\n",
              "      <td>6.612383</td>\n",
              "      <td>1.888944</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>288</td>\n",
              "      <td>237600</td>\n",
              "      <td>4069521.54</td>\n",
              "      <td>-555677.64</td>\n",
              "      <td>32686.92</td>\n",
              "      <td>14400.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000004</td>\n",
              "      <td>0.142009</td>\n",
              "      <td>6.754392</td>\n",
              "      <td>1.910193</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>290</td>\n",
              "      <td>248400</td>\n",
              "      <td>4053178.08</td>\n",
              "      <td>-572021.10</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>10800.0</td>\n",
              "      <td>1.513283</td>\n",
              "      <td>0.000004</td>\n",
              "      <td>0.067290</td>\n",
              "      <td>6.821682</td>\n",
              "      <td>1.920106</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>30</th>\n",
              "      <td>292</td>\n",
              "      <td>259200</td>\n",
              "      <td>4036834.62</td>\n",
              "      <td>-588364.56</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>10800.0</td>\n",
              "      <td>1.513283</td>\n",
              "      <td>0.000004</td>\n",
              "      <td>0.064424</td>\n",
              "      <td>6.886106</td>\n",
              "      <td>1.929506</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      h       t       p_zab  ...  t_inv_delta_p       phi    ln_phi\n",
              "2   221   21600  4617027.45  ...       0.567481  0.567481 -0.566548\n",
              "3   223   32400  4600683.99  ...       0.630535  1.198016  0.180667\n",
              "4   227   43200  4567997.07  ...       0.882749  2.080765  0.732735\n",
              "5   229   50400  4551653.61  ...       0.351298  2.432063  0.888740\n",
              "6   232   57600  4527138.42  ...       0.456012  2.888074  1.060590\n",
              "7   233   61200  4518966.69  ...       0.137698  3.025772  1.107166\n",
              "8   235   64800  4502623.23  ...       0.259632  3.285404  1.189490\n",
              "9   237   68400  4486279.77  ...       0.245577  3.530981  1.261576\n",
              "10  239   75600  4469936.31  ...       0.227561  3.758542  1.324031\n",
              "11  241   79200  4453592.85  ...       0.211270  3.969812  1.378719\n",
              "12  242   82800  4445421.12  ...       0.100935  4.070747  1.403827\n",
              "13  243   86400  4437249.39  ...       0.096636  4.167384  1.427288\n",
              "14  245   90000  4420905.93  ...       0.185377  4.352761  1.470810\n",
              "15  246   93600  4412734.20  ...       0.089051  4.441812  1.491062\n",
              "16  249  100800  4388219.01  ...       0.252560  4.694372  1.546364\n",
              "17  251  108000  4371875.55  ...       0.156733  4.851105  1.579207\n",
              "18  255  118800  4339188.63  ...       0.288900  5.140005  1.637054\n",
              "19  258  126000  4314673.44  ...       0.200461  5.340465  1.675313\n",
              "20  260  133200  4298329.98  ...       0.126204  5.466670  1.698670\n",
              "21  263  144000  4273814.79  ...       0.177146  5.643816  1.730560\n",
              "22  266  151200  4249299.60  ...       0.166191  5.810007  1.759582\n",
              "23  269  162000  4224784.41  ...       0.156733  5.966740  1.786201\n",
              "24  271  172800  4208440.95  ...       0.097733  6.064473  1.802448\n",
              "25  277  190800  4159410.57  ...       0.270357  6.334829  1.846063\n",
              "26  281  208800  4126723.65  ...       0.163931  6.498760  1.871611\n",
              "27  284  223200  4102208.46  ...       0.113622  6.612383  1.888944\n",
              "28  288  237600  4069521.54  ...       0.142009  6.754392  1.910193\n",
              "29  290  248400  4053178.08  ...       0.067290  6.821682  1.920106\n",
              "30  292  259200  4036834.62  ...       0.064424  6.886106  1.929506\n",
              "\n",
              "[29 rows x 11 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
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        "outputId": "9af68dc8-afce-4599-d9b9-153e0e8d5efc"
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        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_data['t'], y=df_data['delta_p_2'] / 101325,\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.update_layout( \n",
        "     xaxis=dict(\n",
        "        #range=[0, 150],\n",
        "        #title=\"Давление, МПа\",\n",
        "    ), \n",
        "     yaxis=dict(\n",
        "        #range=[-0.1, 0.25],\n",
        "        #title=\"Давление, МПа\",\n",
        "    ),   \n",
        "\n",
        "    autosize=False,\n",
        "    width=1000,\n",
        "    height=700\n",
        ")\n",
        "\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": null,
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      "execution_count": null,
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              "      <th>11</th>\n",
              "      <td>241</td>\n",
              "      <td>79200</td>\n",
              "      <td>4453592.85</td>\n",
              "      <td>-171606.33</td>\n",
              "      <td>16343.46</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>4.539850</td>\n",
              "      <td>0.000013</td>\n",
              "      <td>0.211270</td>\n",
              "      <td>3.969812</td>\n",
              "      <td>1.378719</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>242</td>\n",
              "      <td>82800</td>\n",
              "      <td>4445421.12</td>\n",
              "      <td>-179778.06</td>\n",
              "      <td>8171.73</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000012</td>\n",
              "      <td>0.100935</td>\n",
              "      <td>4.070747</td>\n",
              "      <td>1.403827</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>243</td>\n",
              "      <td>86400</td>\n",
              "      <td>4437249.39</td>\n",
              "      <td>-187949.79</td>\n",
              "      <td>8171.73</td>\n",
              "      <td>3600.0</td>\n",
              "      <td>2.269925</td>\n",
              "      <td>0.000012</td>\n",
              "      <td>0.096636</td>\n",
              "      <td>4.167384</td>\n",
              "      <td>1.427288</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      h      t       p_zab  ...  t_inv_delta_p       phi    ln_phi\n",
              "6   232  57600  4527138.42  ...       0.456012  2.888074  1.060590\n",
              "7   233  61200  4518966.69  ...       0.137698  3.025772  1.107166\n",
              "8   235  64800  4502623.23  ...       0.259632  3.285404  1.189490\n",
              "9   237  68400  4486279.77  ...       0.245577  3.530981  1.261576\n",
              "10  239  75600  4469936.31  ...       0.227561  3.758542  1.324031\n",
              "11  241  79200  4453592.85  ...       0.211270  3.969812  1.378719\n",
              "12  242  82800  4445421.12  ...       0.100935  4.070747  1.403827\n",
              "13  243  86400  4437249.39  ...       0.096636  4.167384  1.427288\n",
              "\n",
              "[8 rows x 11 columns]"
            ]
          },
          "metadata": {
            "tags": []
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          "execution_count": 17
        }
      ]
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        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x=1 / df_data_gr['t'], y=df_data_gr['ln_phi'],\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.update_layout( \n",
        "    autosize=False,\n",
        "    width=1000,\n",
        "    height=700\n",
        ")\n",
        "\n",
        "\n",
        "fig.show()"
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      "execution_count": null,
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    {
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        "id": "IAXeAO9hBTBQ",
        "outputId": "c969cc24-0884-4364-b161-6eb8aa7e242c"
      },
      "source": [
        "popt, pcov = curve_fit(line_func, 1 / df_data_gr['t'], df_data_gr['ln_phi'])\n",
        "popt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2.19582899e+00, -6.54606188e+04])"
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          "execution_count": 19
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    {
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        "id": "divN1tjsHn60",
        "outputId": "15b19a47-c648-4582-92b0-49f18ab31de9"
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      "source": [
        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x=1 / df_data_gr['t'], y=df_data_gr['ln_phi'],\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x=1 / df_data_gr['t'], y=line_func(1 / df_data_gr['t'], *popt),\n",
        "                    mode='lines+markers',\n",
        "                    name='linear appr'))\n",
        "\n",
        "fig.update_layout( \n",
        "    \n",
        "\n",
        "    autosize=False,\n",
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        "    height=700\n",
        ")\n",
        "\n",
        "\n",
        "fig.show()"
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      "execution_count": null,
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              "                        {\"responsive\": true}\n",
              "                    ).then(function(){\n",
              "                            \n",
              "var gd = document.getElementById('06f073ca-f10a-4170-ba45-30de69dac7cf');\n",
              "var x = new MutationObserver(function (mutations, observer) {{\n",
              "        var display = window.getComputedStyle(gd).display;\n",
              "        if (!display || display === 'none') {{\n",
              "            console.log([gd, 'removed!']);\n",
              "            Plotly.purge(gd);\n",
              "            observer.disconnect();\n",
              "        }}\n",
              "}});\n",
              "\n",
              "// Listen for the removal of the full notebook cells\n",
              "var notebookContainer = gd.closest('#notebook-container');\n",
              "if (notebookContainer) {{\n",
              "    x.observe(notebookContainer, {childList: true});\n",
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              "\n",
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              "var outputEl = gd.closest('.output');\n",
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              "    x.observe(outputEl, {childList: true});\n",
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              "\n",
              "                        })\n",
              "                };\n",
              "                \n",
              "            </script>\n",
              "        </div>\n",
              "</body>\n",
              "</html>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3IkGZO-2Ds1M",
        "outputId": "1d0c3439-7c6a-40ec-dfc1-f817c90a7a2a"
      },
      "source": [
        "print('Коэффициенты уравнения прямой Ax+B: \\nA: {0:,.2f} \\nB: {1:,.2f}'.format(popt[1], popt[0]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Коэффициенты уравнения прямой Ax+B: \n",
            "A: -65,460.62 \n",
            "B: 2.20\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OEc_HVNiI_ZZ",
        "outputId": "df92b63c-f7cc-49d1-f676-e4fb08304836"
      },
      "source": [
        "kappa = R_value ** 2 / (4 * np.abs(popt[1]))\n",
        "epsilon = (Q_value / (24 * SECONDS_IN_HOUR)) * kappa / (np.pi * R_value ** 2 * np.exp(popt[0]))\n",
        "k_value = epsilon * mu_value * 10 ** -3 / h_plast\n",
        "\n",
        "print('Коэффициент пьезопроводности пласта: {0:,.3f}'.format(kappa))\n",
        "print('Коэффициент гидропроводности пласта: {0:,.2e}'.format(epsilon))\n",
        "print('Коэффициент проницаемости пласта: {0:,.2e}'.format(k_value))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Коэффициент пьезопроводности пласта: 0.970\n",
            "Коэффициент гидропроводности пласта: 1.22e-10\n",
            "Коэффициент проницаемости пласта: 9.04e-13\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qjaOVwI9WMYc"
      },
      "source": [
        "## Задача 3.7 Измерение коэффициента абсолютной проницаемости (VirtualPetroLab, Lab2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X0AxPoWaZK2V"
      },
      "source": [
        "Лабораторная работа №2. Цель - измерение коэффициента абсолютной проницаемости горной породы. Для выполнения необходим образец керна, подготовленный в ходе лабораторной работы №1.\n",
        "\n",
        "Рассчитать:\n",
        "- построить график зависимости коэффициента проницаемости по газу $K_{Г}$ от $1/P_{СР}$, найти по графику коэффициент абсолютной проницаемости."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DddPi_rvZjqj",
        "outputId": "4534cd50-6666-4084-f206-7aad121e0bbf"
      },
      "source": [
        "data = {\n",
        "    'p_inv' : [0.3, 0.32, 0.35, 0.38, 0.42, 0.48, 0.55],\n",
        "    'k':  [0.64, 0.65, 0.66, 0.68, 0.69, 0.71, 0.73]\n",
        "}\n",
        "\n",
        "df_data = pd.DataFrame(\n",
        "    data, \n",
        "    columns = ['p_inv','k']\n",
        "    )\n",
        "\n",
        "df_data"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "    .dataframe tbody tr th {\n",
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              "    }\n",
              "\n",
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>p_inv</th>\n",
              "      <th>k</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.30</td>\n",
              "      <td>0.64</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.32</td>\n",
              "      <td>0.65</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.35</td>\n",
              "      <td>0.66</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.38</td>\n",
              "      <td>0.68</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.42</td>\n",
              "      <td>0.69</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>0.48</td>\n",
              "      <td>0.71</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>0.55</td>\n",
              "      <td>0.73</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   p_inv     k\n",
              "0   0.30  0.64\n",
              "1   0.32  0.65\n",
              "2   0.35  0.66\n",
              "3   0.38  0.68\n",
              "4   0.42  0.69\n",
              "5   0.48  0.71\n",
              "6   0.55  0.73"
            ]
          },
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          },
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        }
      ]
    },
    {
      "cell_type": "code",
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        "id": "4PjxhYRjbD_H",
        "outputId": "c75fc22c-3142-4a75-b2c3-932a2b0bbf01"
      },
      "source": [
        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_data['p_inv'], y=df_data['k'],\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.update_layout( \n",
        "    autosize=False,\n",
        "    width=1000,\n",
        "    height=700\n",
        ")\n",
        "\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
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          "metadata": {
            "tags": []
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      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G5BWBGDsbhOo",
        "outputId": "e6cee433-25b9-495d-d74f-663a16c4689b"
      },
      "source": [
        "popt, pcov = curve_fit(line_func, df_data['p_inv'], df_data['k'])\n",
        "popt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.53596708, 0.3600823 ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GfiuJp_ibhSU",
        "outputId": "52235eba-7f94-4fcc-cf66-23914673c8e6"
      },
      "source": [
        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_data['p_inv'], y=df_data['k'],\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_data['p_inv'], y=line_func(df_data['p_inv'], *popt),\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.add_annotation(x=0.4, y=0.72, text=\"y = {0:.3f}x + {1:.3f}\".format(popt[1], popt[0]), showarrow=False, yshift=10, font=anno_font)\n",
        "\n",
        "fig.update_layout( \n",
        "    autosize=False,\n",
        "    width=1000,\n",
        "    height=700\n",
        ")\n",
        "\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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              "                        {\"responsive\": true}\n",
              "                    ).then(function(){\n",
              "                            \n",
              "var gd = document.getElementById('a532691d-2665-4dfa-9aa9-4a8f4887a9cb');\n",
              "var x = new MutationObserver(function (mutations, observer) {{\n",
              "        var display = window.getComputedStyle(gd).display;\n",
              "        if (!display || display === 'none') {{\n",
              "            console.log([gd, 'removed!']);\n",
              "            Plotly.purge(gd);\n",
              "            observer.disconnect();\n",
              "        }}\n",
              "}});\n",
              "\n",
              "// Listen for the removal of the full notebook cells\n",
              "var notebookContainer = gd.closest('#notebook-container');\n",
              "if (notebookContainer) {{\n",
              "    x.observe(notebookContainer, {childList: true});\n",
              "}}\n",
              "\n",
              "// Listen for the clearing of the current output cell\n",
              "var outputEl = gd.closest('.output');\n",
              "if (outputEl) {{\n",
              "    x.observe(outputEl, {childList: true});\n",
              "}}\n",
              "\n",
              "                        })\n",
              "                };\n",
              "                \n",
              "            </script>\n",
              "        </div>\n",
              "</body>\n",
              "</html>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EBEOqTvberqY",
        "outputId": "88c0d4b4-3dc7-4f64-854e-b2619a8abc78"
      },
      "source": [
        "print('Коэффициент абсолютной проницаемости: {0:,.3f}'.format(popt[0]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Коэффициент абсолютной проницаемости: 0.536\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rQhf_AtdfJNc"
      },
      "source": [
        "## Задача 3.8 Измерение динамической вязкости с помощью ротационного вискозиметра (Virtual Viscometer)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CmJBfQXofM0o"
      },
      "source": [
        "Ротационные вискозиметры используют для измерения вязкости нефтей и нефтепродуктов, смазочных материалов, лаков и красок, пищевых продуктов и \n",
        "других жидкостей. Принцип работы ротационного вискозиметра основан на вращении \n",
        "измерительного цилиндра («шпинделя», англ. – «spindle») в исследуемой жидкости с помощью электродвигателя прибора. \n",
        "\n",
        "Процесс измерения вязкости заключается в следующем: с помощью вискозиметра задают угловую скорость вращения шпинделя 𝑅𝑃𝑀 (rate per minute – обороты в минуту) и определяют соответствующее ему значение относительного момента 𝑀отн"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hw6eZZMKvcKV"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WApA7Vo5lFLX",
        "outputId": "ba49ed58-782b-47a1-f1e0-bc107417c29f"
      },
      "source": [
        "#data = {\n",
        "#    'rpm' : [0.3, 0.6, 1.5, 3, 6, 12],\n",
        "#    'M':    [1.1, 3.1, 7.9, 15.5, 31.2, 63],\n",
        "#    'M':    [2, 4, 9.5, 19, 38, 75.5],\n",
        "#    'M':    [0.7, 1.5, 4, 7, 14, 29.5, 73],\n",
        "#    'factor' : [200, 100, 40, 20, 10, 5],\n",
        "#}\n",
        "\n",
        "data = {\n",
        "    'rpm' : [0.3, 0.6, 1.5, 3, 6, 12, 30],\n",
        "    'M':    [0.7, 1.5, 4, 7, 14, 29.5, 73],\n",
        "    'factor' : [200, 100, 40, 20, 10, 5, 2],\n",
        "}\n",
        "\n",
        "df_data = pd.DataFrame(\n",
        "    data, \n",
        "    columns = ['rpm','M', 'factor']\n",
        "    )\n",
        "\n",
        "df_data['shpnd'] = 3\n",
        "df_data['mu'] = df_data['M'] * df_data['factor']\n",
        "df_data['speed'] = df_data['rpm'] * 0.22\n",
        "df_data['tau'] = df_data['speed'] * df_data['mu']\n",
        "\n",
        "df_data"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "    .dataframe tbody tr th:only-of-type {\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>rpm</th>\n",
              "      <th>M</th>\n",
              "      <th>factor</th>\n",
              "      <th>shpnd</th>\n",
              "      <th>mu</th>\n",
              "      <th>speed</th>\n",
              "      <th>tau</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.3</td>\n",
              "      <td>0.7</td>\n",
              "      <td>200</td>\n",
              "      <td>3</td>\n",
              "      <td>140.0</td>\n",
              "      <td>0.066</td>\n",
              "      <td>9.24</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.6</td>\n",
              "      <td>1.5</td>\n",
              "      <td>100</td>\n",
              "      <td>3</td>\n",
              "      <td>150.0</td>\n",
              "      <td>0.132</td>\n",
              "      <td>19.80</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1.5</td>\n",
              "      <td>4.0</td>\n",
              "      <td>40</td>\n",
              "      <td>3</td>\n",
              "      <td>160.0</td>\n",
              "      <td>0.330</td>\n",
              "      <td>52.80</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3.0</td>\n",
              "      <td>7.0</td>\n",
              "      <td>20</td>\n",
              "      <td>3</td>\n",
              "      <td>140.0</td>\n",
              "      <td>0.660</td>\n",
              "      <td>92.40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>6.0</td>\n",
              "      <td>14.0</td>\n",
              "      <td>10</td>\n",
              "      <td>3</td>\n",
              "      <td>140.0</td>\n",
              "      <td>1.320</td>\n",
              "      <td>184.80</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>12.0</td>\n",
              "      <td>29.5</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>147.5</td>\n",
              "      <td>2.640</td>\n",
              "      <td>389.40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>30.0</td>\n",
              "      <td>73.0</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>146.0</td>\n",
              "      <td>6.600</td>\n",
              "      <td>963.60</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    rpm     M  factor  shpnd     mu  speed     tau\n",
              "0   0.3   0.7     200      3  140.0  0.066    9.24\n",
              "1   0.6   1.5     100      3  150.0  0.132   19.80\n",
              "2   1.5   4.0      40      3  160.0  0.330   52.80\n",
              "3   3.0   7.0      20      3  140.0  0.660   92.40\n",
              "4   6.0  14.0      10      3  140.0  1.320  184.80\n",
              "5  12.0  29.5       5      3  147.5  2.640  389.40\n",
              "6  30.0  73.0       2      3  146.0  6.600  963.60"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "q4L5J1Syno-C",
        "outputId": "97b08e1f-1da0-4be3-de4b-58f677d006b8"
      },
      "source": [
        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_data['speed'], y=df_data['tau'],\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.update_layout( \n",
        "    autosize=False,\n",
        "    width=700,\n",
        "    height=700\n",
        ")\n",
        "\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
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    {
      "cell_type": "code",
      "metadata": {
        "id": "e3ZvU5nwnpGC"
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      "source": [
        "def pow_func(x, a, b):\n",
        "    return a + x ** b"
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      "execution_count": null,
      "outputs": []
    },
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      "metadata": {
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        "popt"
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      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "array([118.11210933,   3.57455684])"
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      "metadata": {
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        "outputId": "02133917-b395-4cc6-806a-28076f620441"
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        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_data['speed'], y=df_data['tau'],\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_data['speed'], y=pow_func(df_data['speed'], *popt),\n",
        "                    mode='lines+markers',\n",
        "                    name='linear'))\n",
        "\n",
        "fig.update_layout( \n",
        "    autosize=False,\n",
        "    width=1000,\n",
        "    height=700\n",
        ")\n",
        "\n",
        "\n",
        "fig.show()"
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      "execution_count": null,
      "outputs": [
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "74MYQsiMGDvw"
      },
      "source": [
        "## Задача 3.9 Взаимная проницаемость, функция обводненности"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hLnh9B3vHRtX"
      },
      "source": [
        "Дано:\n",
        "\n",
        "Зависимость коэффициентов проницаемости воды и нефти в зависимости от обводненности S. \n",
        "\n",
        "Рассчитать:\n",
        "- построить график зависимости коэффициентов проницаемости воды и нефти в зависимости от обводненности.\n",
        "- построить график функции обводненности"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 498
        },
        "id": "xyw3yHIWGYPU",
        "outputId": "fa27756f-378c-423c-88cd-ed3706df4d1d"
      },
      "source": [
        "s_arr = []\n",
        "\n",
        "for i in range(20, 81, 5):\n",
        "  s_arr.append(i/100)\n",
        "\n",
        "for i in range(90, 101, 10):\n",
        "  s_arr.append(i/100)\n",
        "\n",
        "\n",
        "data = {\n",
        "    'S' : s_arr,\n",
        "}\n",
        "\n",
        "df_data = pd.DataFrame(\n",
        "    data, \n",
        "    columns = ['S']\n",
        "    )\n",
        "\n",
        "df_data['k_v'] = df_data.apply(lambda row: 0 if row['S'] <= 0.2 else ((row['S'] - 0.2) / 0.75) ** 2, axis = 1)\n",
        "df_data['k_n'] = df_data.apply(lambda row: None if row['S'] < 0.2 else (0 if row['S'] >= 0.75 else (1 - row['S'] / 0.75) ** 2), axis = 1)\n",
        "\n",
        "mu_water = 1\n",
        "for mu in [2, 4, 40, 140]:\n",
        "  df_data['fs_{0}'.format(mu)] = (df_data['k_v'] / mu_water) / (df_data['k_v'] / mu_water + df_data['k_n'] / mu)\n",
        "\n",
        "df_data"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "    }\n",
              "\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>S</th>\n",
              "      <th>k_v</th>\n",
              "      <th>k_n</th>\n",
              "      <th>fs_2</th>\n",
              "      <th>fs_4</th>\n",
              "      <th>fs_40</th>\n",
              "      <th>fs_140</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.20</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.537778</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.25</td>\n",
              "      <td>0.004444</td>\n",
              "      <td>0.444444</td>\n",
              "      <td>0.019608</td>\n",
              "      <td>0.038462</td>\n",
              "      <td>0.285714</td>\n",
              "      <td>0.583333</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.30</td>\n",
              "      <td>0.017778</td>\n",
              "      <td>0.360000</td>\n",
              "      <td>0.089888</td>\n",
              "      <td>0.164948</td>\n",
              "      <td>0.663900</td>\n",
              "      <td>0.873635</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.35</td>\n",
              "      <td>0.040000</td>\n",
              "      <td>0.284444</td>\n",
              "      <td>0.219512</td>\n",
              "      <td>0.360000</td>\n",
              "      <td>0.849057</td>\n",
              "      <td>0.951662</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.40</td>\n",
              "      <td>0.071111</td>\n",
              "      <td>0.217778</td>\n",
              "      <td>0.395062</td>\n",
              "      <td>0.566372</td>\n",
              "      <td>0.928882</td>\n",
              "      <td>0.978593</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>0.45</td>\n",
              "      <td>0.111111</td>\n",
              "      <td>0.160000</td>\n",
              "      <td>0.581395</td>\n",
              "      <td>0.735294</td>\n",
              "      <td>0.965251</td>\n",
              "      <td>0.989819</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.160000</td>\n",
              "      <td>0.111111</td>\n",
              "      <td>0.742268</td>\n",
              "      <td>0.852071</td>\n",
              "      <td>0.982935</td>\n",
              "      <td>0.995064</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>0.55</td>\n",
              "      <td>0.217778</td>\n",
              "      <td>0.071111</td>\n",
              "      <td>0.859649</td>\n",
              "      <td>0.924528</td>\n",
              "      <td>0.991903</td>\n",
              "      <td>0.997673</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>0.60</td>\n",
              "      <td>0.284444</td>\n",
              "      <td>0.040000</td>\n",
              "      <td>0.934307</td>\n",
              "      <td>0.966038</td>\n",
              "      <td>0.996497</td>\n",
              "      <td>0.998997</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>0.65</td>\n",
              "      <td>0.360000</td>\n",
              "      <td>0.017778</td>\n",
              "      <td>0.975904</td>\n",
              "      <td>0.987805</td>\n",
              "      <td>0.998767</td>\n",
              "      <td>0.999647</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>0.70</td>\n",
              "      <td>0.444444</td>\n",
              "      <td>0.004444</td>\n",
              "      <td>0.995025</td>\n",
              "      <td>0.997506</td>\n",
              "      <td>0.999750</td>\n",
              "      <td>0.999929</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>0.75</td>\n",
              "      <td>0.537778</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>0.80</td>\n",
              "      <td>0.640000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>0.90</td>\n",
              "      <td>0.871111</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>1.00</td>\n",
              "      <td>1.137778</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       S       k_v       k_n      fs_2      fs_4     fs_40    fs_140\n",
              "0   0.20  0.000000  0.537778  0.000000  0.000000  0.000000  0.000000\n",
              "1   0.25  0.004444  0.444444  0.019608  0.038462  0.285714  0.583333\n",
              "2   0.30  0.017778  0.360000  0.089888  0.164948  0.663900  0.873635\n",
              "3   0.35  0.040000  0.284444  0.219512  0.360000  0.849057  0.951662\n",
              "4   0.40  0.071111  0.217778  0.395062  0.566372  0.928882  0.978593\n",
              "5   0.45  0.111111  0.160000  0.581395  0.735294  0.965251  0.989819\n",
              "6   0.50  0.160000  0.111111  0.742268  0.852071  0.982935  0.995064\n",
              "7   0.55  0.217778  0.071111  0.859649  0.924528  0.991903  0.997673\n",
              "8   0.60  0.284444  0.040000  0.934307  0.966038  0.996497  0.998997\n",
              "9   0.65  0.360000  0.017778  0.975904  0.987805  0.998767  0.999647\n",
              "10  0.70  0.444444  0.004444  0.995025  0.997506  0.999750  0.999929\n",
              "11  0.75  0.537778  0.000000  1.000000  1.000000  1.000000  1.000000\n",
              "12  0.80  0.640000  0.000000  1.000000  1.000000  1.000000  1.000000\n",
              "13  0.90  0.871111  0.000000  1.000000  1.000000  1.000000  1.000000\n",
              "14  1.00  1.137778  0.000000  1.000000  1.000000  1.000000  1.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
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          "height": 717
        },
        "id": "OhptMa37TTYA",
        "outputId": "a9b3a45e-c370-4700-cab7-e7dcbcf762e4"
      },
      "source": [
        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x= df_data['S'], y=df_data['k_v'],\n",
        "                    mode='lines+markers',\n",
        "                    name='К воды'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x= df_data['S'], y=df_data['k_n'],\n",
        "                    mode='lines+markers',\n",
        "                    name='K нефти'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x= df_data['S'], y=df_data['fs_2'],\n",
        "                    mode='lines',\n",
        "                    name='Функция обводненности (вязкость нефти = 2)'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x= df_data['S'], y=df_data['fs_4'],\n",
        "                    mode='lines',\n",
        "                    name='Функция обводненности (вязкость нефти = 4)'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x= df_data['S'], y=df_data['fs_40'],\n",
        "                    mode='lines',\n",
        "                    name='Функция обводненности (вязкость нефти = 40)'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x= df_data['S'], y=df_data['fs_140'],\n",
        "                    mode='lines',\n",
        "                    name='Функция обводненности (вязкость нефти = 140)'))\n",
        "\n",
        "fig.update_layout( \n",
        "    yaxis=dict(\n",
        "        range=[-0.1, 1.1],\n",
        "        #title=\"Давление, МПа\",\n",
        "    ), \n",
        "\n",
        "    autosize=False,\n",
        "    width=1200,\n",
        "    height=700\n",
        ")\n",
        "\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
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              "\n",
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              "                        })\n",
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              "        </div>\n",
              "</body>\n",
              "</html>"
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          },
          "metadata": {
            "tags": []
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        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eKxCnJ1V0IK_"
      },
      "source": [
        "## Задача 3.5"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6O1r3rRZ0IgY"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 198
        },
        "id": "gxJcLFaX09h5",
        "outputId": "f945a51a-977e-4843-f15b-398c3f84b6e4"
      },
      "source": [
        "df_graph = pd.read_csv('https://raw.githubusercontent.com/alexeynick/msu_oil_gas/main/datasets/task_35_data.csv')\n",
        "df_graph.columns=['vnk', 'oil']\n",
        "df_graph.head(5)"
      ],
      "execution_count": null,
      "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>vnk</th>\n",
              "      <th>oil</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.133980</td>\n",
              "      <td>23210.93</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.140033</td>\n",
              "      <td>23356.61</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.205795</td>\n",
              "      <td>23458.07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.244604</td>\n",
              "      <td>23499.77</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.253296</td>\n",
              "      <td>23563.49</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        vnk       oil\n",
              "0  0.133980  23210.93\n",
              "1  0.140033  23356.61\n",
              "2  0.205795  23458.07\n",
              "3  0.244604  23499.77\n",
              "4  0.253296  23563.49"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2ttto6yI1Cvm",
        "outputId": "fa7d6322-fd3d-45e7-d9bf-8d26ebc1aaff"
      },
      "source": [
        "popt, pcov = curve_fit(line_func, df_graph['oil'], df_graph['vnk'])\n",
        "popt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-3.68889448e+00,  1.63653285e-04])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qXTfeI8X1u_i",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "54700fa7-7d57-4db4-deee-e5b33df1ce3a"
      },
      "source": [
        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_graph['oil'], y=df_graph['vnk'],\n",
        "                    mode='markers',\n",
        "                    name='src'))\n",
        "\n",
        "fig.add_trace(go.Scatter(x=df_graph['oil'], y=line_func(df_graph['oil'], *popt),\n",
        "                    mode='lines+markers',\n",
        "                    name='linear appr'))\n",
        "\n",
        "fig.update_layout( \n",
        "    xaxis=dict(\n",
        "        range=[0, 50000],\n",
        "        #tickmode = 'array',\n",
        "        #tickvals = df_object2['year'],\n",
        "        tickangle=-45,\n",
        "        title='Год',\n",
        "    ),\n",
        "\n",
        "    yaxis=dict(\n",
        "        range=[0, 21],\n",
        "        title=\"Число скажин (шт)\",\n",
        "        titlefont=dict(\n",
        "            color=\"green\"\n",
        "        ),\n",
        "        tickfont=dict(\n",
        "            color=\"green\"\n",
        "        )\n",
        "    ),\n",
        ")\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
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