08_Bullard_Plot.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bullard Plot  \n",
    "The Bullard plot method is used for calculating the specific heat flow in an area based on temperature data and the concept of *thermal resistance*.  \n",
    "Thermal resistance (R in [m² K W$^{-1}$) is the integrated reciprocal of thermal conductivities over a depth range z, i.e. how effectively a layered sequence of rocks retards the flow of heat.  \n",
    "\n",
    "$$ R = \\int \\frac{1}{\\lambda} dz $$  \n",
    "\n",
    "From Fouriers Law, we know:  \n",
    "$$q = \\lambda \\bigg(\\frac{\\partial T}{\\partial z}\\bigg) $$\n",
    "\n",
    "rearragning the equation yields:\n",
    "$$q = \\partial T \\bigg(\\frac{\\lambda}{\\partial z}\\bigg) $$\n",
    "\n",
    "this fraction is equal to 1/R:\n",
    "$$q = \\partial T \\bigg(\\frac{1}{\\partial R}\\bigg) $$\n",
    "\n",
    "which then yields to:\n",
    "$$q = \\bigg(\\frac{\\partial T}{\\partial R}\\bigg) $$  \n",
    "\n",
    "That means, the change in temperature with respect to the thermal resistance is equal to the specific heat flow.  \n",
    "Now let's assume we have a layercake model with discrete layers of rocks. The thermal resistance can then be rewritten as:  \n",
    "\n",
    "$$ R = \\sum_i \\bigg(\\frac{\\Delta z_i}{\\lambda_i}\\bigg) $$  \n",
    "\n",
    "where $i$ is the number of layers in the sequence and $\\Delta z$ the according layer-thickness.  \n",
    "\n",
    "The idea of the Bullard-Plot is to plot the cumulative thermal resistances vs measured temperatures. They exhibit a linear relation. Using a linear regression, the obtained slope is equal to the specific heat flow."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Small exercise / demonstration \n",
    "<img src='imgs/bullard_layer.png' style=\"float: right; width: 27%; margin-right: 3%; margin-bottom: 0.5em;\">\n",
    "Assume we have a borehole with a depth of 2.2 km. It penetrates multiple layers. The average surface temperature is 11 °C. At each layer boundary, temperatures were measured, as well as at the maximum depth of the borehole.  \n",
    "So in total, we have 4 temperature measurements:  \n",
    "* 22 °C @ 1 km depth  \n",
    "* 30 °C @ 1.4 km depth  \n",
    "* 41 °C @ 2 km depth  \n",
    "* 47 °C @ 2.2 km depth  \n",
    "\n",
    "In the following, we will calculate the cumulative thermal resistances and create a Bullard Plot.  \n",
    "Cumulative thermal resistances mean for example, that at the bottom of the yellow layer, the actual thermal resistance is equal to the sum of the *yellow thermal resistance* and *orange thermal resistance*.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from __future__ import division, print_function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# set up arrays\n",
    "z = np.array([1000, 400, 600, 200])\n",
    "tc = np.array([3.2, 2.3, 1.6, 4.2])\n",
    "\n",
    "T = np.array([10, 22, 30, 46, 49]) # here we also include the surface temperature\n",
    "\n",
    "\n",
    "# cumulative thermal resistances\n",
    "# We write out the resistances here manually to be better understandable, you could also do that in a loop!\n",
    "r0 = 0                 # thermal resistance at the surface\n",
    "r1 = z[0]/tc[0]\n",
    "r2 = r1 + (z[1]/tc[1])\n",
    "r3 = r2 + (z[2]/tc[2])\n",
    "r4 = r3 + (z[3]/tc[3])\n",
    "\n",
    "R = np.array([r0, r1, r2, r3, r4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The specific heat flow is about 0.0429 W/m²\n"
     ]
    }
   ],
   "source": [
    "# get the linear regression using polyfit\n",
    "m, b = np.polyfit(R,T,1)\n",
    "# set up resistance vector \n",
    "R_reg = np.linspace(0,1200,1200)\n",
    "# calculating temperature of resistance vector\n",
    "T_reg = m * R_reg + b\n",
    "\n",
    "print(\"The specific heat flow is about {} W/m²\".format(round(m,4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x93a6110>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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xMTEALF26lJycnGYfX0xMDLt27WLVqlWtel7Wrl3Ljz/+yG9/+1snQYfa2vVb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\nEAxcQYH7ruSTdIIPNXIOTCB6gdr5D0cyMbM3A+8FPpKyejn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      "text/plain": [
       "<matplotlib.figure.Figure at 0x8ff8950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the results\n",
    "fig = plt.figure(figsize=(12,5))\n",
    "dots, = plt.plot(R,T,'o', color='#660033', alpha=0.8)\n",
    "line, = plt.plot(R_reg,T_reg, '-', linewidth=2, color='#33ADAD')\n",
    "plt.xlabel('cumulative thermal resistance [m$^2$ K W$^{-1}$]', fontsize=16)\n",
    "plt.ylabel('Temperature [$^\\circ$C]', fontsize=16)\n",
    "plt.tick_params(axis='both', which='major', labelsize=13)\n",
    "plt.legend([dots,line], [\"Measured temperatures\", \"linear regression model\"], loc=2, fontsize=18)"
   ]
  }
 ],
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   "language": "python",
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  "latex_envs": {
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   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
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   "labels_anchors": false,
   "latex_user_defs": false,
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  "toc": {
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    "height": "48px",
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   "number_sections": false,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": "block",
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  "varInspector": {
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     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}