{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "##### The latest version of this IPython notebook is available at [http://github.com/jckantor/CBE20255](http://github.com/jckantor/CBE20255) for noncommercial use under terms of the [Creative Commons Attribution Noncommericial ShareAlike License](http://creativecommons.org/licenses/by-nc-sa/4.0/).\n", "\n", "J.C. Kantor (Kantor.1@nd.edu)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Ammonia Synthesis Reactor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This [IPython notebook](http://ipython.org/notebook.html) demonstrates the solution to material balances for an ammonia synthesis reactor operating at chemical equilibrium." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Background\n", "\n", "
\n", "\"Ammoniak
\"Ammoniak Reaktor BASF\" by Drahkrub. Licensed under CC BY-SA 3.0 via Wikimedia Commons.\n", "
\n", "\n", "Ammonia is produced on an enormous scale, and crucial to global agriculture. The main pathway is by way of the Haber-Bosch process based on the reaction\n", "\n", "$$N_2 + 3\\,H_2 \\longleftrightarrow 2\\,NH_3$$\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For these calculations we will import `pylab` and the `fsolve` function from the `scipy` library." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "from pylab import *\n", "from scipy.optimize import fsolve" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f(x):\n", " Kq = (2.0*x)**2*(4000.0-2.0*x)**2/((1000.0-x)*(3000.0-3.0*x)**3*200.0**2)\n", " Ka = 0.001172\n", " return Kq - Ka" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-0.001172" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(0)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.481481481955498e+19" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(999.999)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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5/dp/xcxKzWyPmV3iX+XvNkRf7jazCm/aFjO7vF/7aO5Ljpn90cx2m9kuMzs7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\n/Bf6hI8FUM78BgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = linspace(500,800)\n", "plot(x,f(x))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "682.08889272012129" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fsolve(f,650)[0]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 682.08889272]\n" ] } ], "source": [ "x = fsolve(f,0.0)\n", "print x" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "24.622103766343365" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(972.16)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }