{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Beispiel 19.4: Berechnung der Umsetzung eines kugelförmigen Partikels nach dem isothermen Modell des schrumpfenden Partikels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_(Dieses Beispiel finden Sie im Lehrbuch auf Seite 315)_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In diesem Berechnungsbeispiel sollen der Reaktionsfortschritt einer Gas-Feststoff-Reaktion bei einem kugelförmigen schrumpfenden Partikel bei isothermen Verhältnissen betrachtet werden. Die erforderlichen Gleichungen ergeben sich aus den Ausdrücken in Tabelle 19.7 (Seite 315) mit Gleichung 19.12 (Seite 297), sind aber auch noch einmal explizit auf Seite 315 angegeben."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Laden der benötigten Pakete"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Innerhalb dieses Beispiels werden die Pakete _numpy_ und _matplotlib.pyplot_ benötigt. Während _numpy_ wichtige Rechenoperationen und Funktionalitäten bereitstellt, werden mit Hilfe des Pakets _matplotlib.pyplot_ die Ergebnisse grafisch dargestellt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Festlegung von Parametern"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Geschwindigkeitskonstante der Reaktion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Geschwindigkeitskonstante der Chlorierungsreaktion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Cl<sub>2</sub> + Ni ⇌ NiCl<sub>2</sub>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "hat den Wert:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "k_s = 0.1 # m / s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Konzentration der gasförmigen Spezies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Chlorkonzentration $c_{1,\\mathrm{b}}$ im Kern der Gasphase beträgt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "c_1b = 5.0 # mol / m^3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Eigenschaften des Feststoffs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Dichte des Nickels und die charakteristische Abmessung $L=d_\\mathrm{p}/2$ des kugelförmigen Partikels betragen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "rho_2 = 151770 # mol / m^3\n",
    "L = 0.0025 # m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stoffübergang des Gases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Stoffübergangskoeffizient zu Beginn der Reaktion $k_{1,\\mathrm{G},0}$ und der Exponent für den Einfluss der Partikelabmessung $m$ haben folgende Werte:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "k_1G0 = 0.05 # m / s\n",
    "m = 0.5 # -"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Als Verhältnis von Stoffübergangskoeffizient zu Beginn der Reaktion $k_{1,\\mathrm{G},0}$ und Geschwindigkeitskonstante $k_\\mathrm{s}$ ergibt sich die dimensionslose Kenngröße $W_1$ schließlich zu:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "W_1 = 0.5 # -"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Berechnung der Reaktionszeiten"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mit den angegebenen Gleichungen können nun die Reaktionszeiten (in der Einheit Minuten) bei Limitierung des Vorgangs durch Reaktion $t_\\mathrm{R}$ bzw. durch Diffusion im Gasfilm $t_\\mathrm{G}$ sowie die Gesamtreaktionszeit $t=t_\\mathrm{R}+t_\\mathrm{G}$ und der relative Anteil der Reaktionszeit bei Filmdiffusionslimitierung $t=t_\\mathrm{G}/(t_\\mathrm{R}+t_\\mathrm{G})$ in Abhängigkeit vom Umsatzgrad des Nickels $U$ berechnet werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def t_R(U):\n",
    "    return (1-(1-U)**(1/3)) * L * rho_2 / (60*k_s*c_1b)\n",
    "\n",
    "def t_G(U):\n",
    "    return (1-(1-U)**((1+m)/3)) * L * rho_2 / (60*k_s*c_1b*W_1*(1+m))\n",
    "\n",
    "def t(U):\n",
    "    return (t_R(U)+t_G(U))\n",
    "\n",
    "def ratio(U):\n",
    "    return (t_G(U)/t(U))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Darstellung der Ergebnisse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Für die Darstellung der Ergebnisse muss der zu betrachtende Umsatzgradbereich $U_\\mathrm{range}$ angegeben werden. In diesem Fall ist dies der Bereich von 0 bis 1 in Schritten von 0.001."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "U_range = np.linspace(0.001, 1.0, 1001) # -"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Anschließend werden die Funktionen in Abhängigkeit vom Umsatzgrad mit Hilfe des Pakets _matplotlib.pyplot_ dargestellt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
    "\n",
    "ax1.plot(U_range, t_R(U_range), color='blue', label=\"$t_\\mathrm{R}$\")\n",
    "ax1.plot(U_range, t_G(U_range), color='red', label=\"$t_\\mathrm{G}$\")\n",
    "ax1.plot(U_range, t(U_range), color='black', label=\"$t$\")\n",
    "ax1.set_xlabel(\"U / 1\")\n",
    "ax1.set_ylabel(\"t / min\")\n",
    "ax1.set_xlim(0.0,1.0)\n",
    "ax1.set_ylim(0,30)\n",
    "ax1.legend(loc='best')\n",
    "\n",
    "ax2.plot(U_range, ratio(U_range), color='black')\n",
    "ax2.set_xlabel(\"U / 1\")\n",
    "ax2.set_ylabel(\"$t_\\mathrm{G}/(t_\\mathrm{R}+t_\\mathrm{G})$ / 1\")\n",
    "ax2.set_xlim(0.0,1.0)\n",
    "ax2.set_ylim(0.5,0.7)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Berechnungsergebnisse sind ebenfalls im Lehrbuch in Abbildung 19.9 auf Seite 316 dargestellt."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}