{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exothermic Continuous Stirred Tank Reactor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Description\n", "\n", "This example is intended as an introduction to the nonlinear dynamics of an exothermic continuous stirred-tank reactor. The example has been studied by countless researchers and students since the pioneering work of Amundson and Aris in the 1950's. The particular formulation and parameter values described below are taken from example 2.5 from Seborg, Edgar, Mellichamp and Doyle (SEMD).\n", "\n", "![Exothermic Reactor](https://upload.wikimedia.org/wikipedia/commons/thumb/b/be/Agitated_vessel.svg/500px-Agitated_vessel.svg.png)\n", "\n", "(Diagram By [Daniele Pugliesi](https://commons.wikimedia.org/wiki/User:Daniele_Pugliesi) - Own work, [CC BY-SA 3.0](http://creativecommons.org/licenses/by-sa/3.0), [Link](https://commons.wikimedia.org/w/index.php?curid=6915706))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reaction Kinetics\n", "\n", "We assume the kinetics are dominated by a single first order reaction\n", "\n", "$$A \\xrightarrow{kc_A}{} \\text{Products}$$\n", "\n", "The reaction rate per unit volume is modeled as the product $kc_A$ where $c_A$ is the concentration of $A$. The rate constant $k(T)$ is a increases with temperature following the Arrehenius law\n", "\n", "$$k(t) = k_0 e^{-\\frac{E_a}{RT}}$$\n", "\n", "$E_a$ is the activation energy, $R$ is the gas constant, $T$ is absolute temperature, and $k_0$ is the pre-exponential factor. \n", "\n", "We can see the strong temperature dependence by plotting $k(T)$ versus temperature over typical operating conditions." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# Arrehnius parameters\n", "Ea = 72750 # activation energy J/gmol\n", "R = 8.314 # gas constant J/gmol/K\n", "k0 = 7.2e10 # Arrhenius rate constant 1/min\n", "\n", "# Arrhenius rate expression\n", "def k(T):\n", " return k0*np.exp(-Ea/(R*T))\n", "\n", "# semilog plot of the rate constant\n", "T = np.linspace(290,400)\n", "plt.semilogy(T, k(T))\n", "plt.xlabel('Absolute Temperature [K]')\n", "plt.ylabel('Rate Constant [1/min]')\n", "plt.title('Arrenhius Rate Constant')\n", "plt.grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This graph shows the reaction rate changes by three orders of magnitude over the range of possible operating temperatures. Because an exothermic reaction releases heat faster at higher temperatures, there is a positive feedback that can potentially result in unstable process behavior." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Equations and Parameter Values\n", "\n", "The model consists of mole and energy balances on the contents of the well-mixed reactor.\n", "\n", "\\begin{align*}\n", "V\\frac{dc_A}{dt} & = q(c_{Ai}-c_A)-Vkc_A \\\\\n", "V\\rho C_p\\frac{dT}{dt} & = wC_p(T_i-T) + (-\\Delta H_R)Vkc_A + UA(T_c-T)\n", "\\end{align*}\n", "\n", "Normalizing the equations to isolate the time rates of change of $c_A$ and $T$ give\n", "\n", "\\begin{align*}\n", "\\frac{dc_A}{dt} & = \\frac{q}{V}(c_{Ai} - c_A)- kc_A \\\\\n", "\\frac{dT}{dt} & = \\frac{q}{V}(T_i - T) + \\frac{-\\Delta H_R}{\\rho C_p}kc_A + \\frac{UA}{V\\rho C_p}(T_c - T)\n", "\\end{align*}\n", "\n", "which are the equations that will be integrated below.\n", "\n", "| Quantity | Symbol | Value | Units | Comments |\n", "| :------- | :----: | :---: | :---- | |\n", "| Activation Energy | $E_a$ | 72,750 | J/gmol | |\n", "| Arrehnius pre-exponential | $k_0$ | 7.2 x 1010 | 1/min | |\n", "| Gas Constant | $R$ | 8.314 | J/gmol/K | |\n", "| Reactor Volume | $V$ | 100 | liters | |\n", "| Density | $\\rho$ | 1000 | g/liter | |\n", "| Heat Capacity | $C_p$ | 0.239 | J/g/K | |\n", "| Enthalpy of Reaction | $\\Delta H_r$ | -50,000 | J/gmol | |\n", "| Heat Transfer Coefficient | $UA$ | 50,000 | J/min/K | |\n", "| Feed flowrate | $q$ | 100 | liters/min | |\n", "| Feed concentration | $c_{A,f}$ | 1.0 | gmol/liter | |\n", "| Feed temperature | $T_f$ | 350 | K | |\n", "| Initial concentration | $c_{A,0}$ | 0.5 | gmol/liter | |\n", "| Initial temperature | $T_0$ | 350 | K | |\n", "| Coolant temperature | $T_c$ | 300 | K | Primary Manipulated Variable |\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Transient Behavior\n", "\n", "The first simulation assumes a cooling water temperature of 300 K. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "from scipy.integrate import solve_ivp\n", "\n", "Ea = 72750 # activation energy J/gmol\n", "R = 8.314 # gas constant J/gmol/K\n", "k0 = 7.2e10 # Arrhenius rate constant 1/min\n", "V = 100.0 # Volume [L]\n", "rho = 1000.0 # Density [g/L]\n", "Cp = 0.239 # Heat capacity [J/g/K]\n", "dHr = -5.0e4 # Enthalpy of reaction [J/mol]\n", "UA = 5.0e4 # Heat transfer [J/min/K]\n", "q = 100.0 # Flowrate [L/min]\n", "cAi = 1.0 # Inlet feed concentration [mol/L]\n", "Ti = 350.0 # Inlet feed temperature [K]\n", "cA0 = 0.5; # Initial concentration [mol/L]\n", "T0 = 350.0; # Initial temperature [K]\n", "Tc = 300.0 # Coolant temperature [K]\n", "\n", "def deriv(t, y):\n", " cA,T = y\n", " dcAdt = (q/V)*(cAi - cA) - k(T)*cA\n", " dTdt = (q/V)*(Ti - T) + (-dHr/rho/Cp)*k(T)*cA + (UA/V/rho/Cp)*(Tc-T)\n", " return [dcAdt, dTdt]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first define a visualization function that will be reused in later simulations." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# simulation\n", "IC = [cA0, T0]\n", "t_initial = 0.0\n", "t_final = 10.0\n", "t = np.linspace(t_initial, t_final, 2000)\n", "soln = solve_ivp(deriv, [t_initial, t_final], IC, t_eval=t)\n", "\n", "# visualization plots concentration and temperature on given axes\n", "def plot_reactor(ax, t, y):\n", " ax[0].plot(t, y[0], label=str(Tc))\n", " ax[0].set_xlabel('Time [min]')\n", " ax[0].set_ylabel('Concentration [gmol/liter]')\n", " ax[0].set_title('Concentration')\n", " ax[0].set_ylim(0, 1)\n", " ax[0].legend()\n", "\n", " ax[1].plot(t, y[1], label=str(Tc))\n", " ax[1].set_xlabel('Time [min]')\n", " ax[1].set_ylabel('Temperature [K]');\n", " ax[1].set_title('Temperature')\n", " ax[1].set_ylim(300, 450)\n", " ax[1].legend()\n", " \n", "fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n", "plot_reactor(ax, soln.t, soln.y);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Effect of Cooling Temperature\n", "\n", "The primary means of controlling the reactoris through temperature of the cooling water jacket. The next calculations explore the effect of plus or minus change of 5 K in cooling water temperature on reactor behavior. These simulations reproduce the behavior shown in Example 2.5 SEMD." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n", "for Tc in [295, 300, 305]:\n", " soln = solve_ivp(deriv, [t_initial, t_final], IC, t_eval=t)\n", " plot_reactor(ax, soln.t, soln.y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interactive Simulation\n", "\n", "Executing the following cell provides an interactive tool for exploring the relationship of cooling temperature with reactor behavior. Use it to observe a thermal runaway, sustained osciallations, and low and high conversion steady states." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "3f00b2b8607c4d4187d0875977a5b962", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=300.0, description='Tcooling', max=310.0, min=290.0), Output()), _dom_…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ipywidgets import interact\n", "from IPython.display import display\n", "\n", "# create an initial plot object, and close so it doesn't appear\n", "Tc = 300.0\n", "fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n", "soln = solve_ivp(deriv, [t_initial, t_final], IC, t_eval=t)\n", "plot_reactor(ax, soln.t, soln.y)\n", "plt.close()\n", "\n", "# function to update and display the plot object\n", "def sim(Tcooling):\n", " global Tc\n", " Tc = Tcooling\n", " soln = solve_ivp(deriv, [t_initial, t_final], IC, t_eval=t)\n", " ax[0].lines[0].set_ydata(soln.y[0])\n", " ax[0].legend().get_texts()[0].set_text(str(Tc))\n", " ax[1].lines[0].set_ydata(soln.y[1])\n", " ax[1].legend().get_texts()[0].set_text(str(Tc))\n", " display(fig)\n", "\n", "# interactive widget\n", "interact(sim, Tcooling = (290.0, 310.0), continuous_update=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Nullclines\n", "\n", "The nullclines of two first-order differential equations are points in the phase plane for which one or the other of the two derivatives are zero.\n", "\n", "\\begin{align*}\n", "V\\frac{dc_A}{dt} & = 0 = q(c_{Ai}-c_A)-Vkc_A \\\\\n", "V\\rho C_p\\frac{dT}{dt} & = 0 = wC_p(T_i-T) + (-\\Delta H_R)Vkc_A + UA(T_c-T)\n", "\\end{align*}\n", "\n", "The intersection of the nullclines correspond to steady states. The relative positions of the nullclines provide valuable insight into the dynamics of a nonlinear system." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot nullclines\n", "\n", "def plot_nullclines(ax):\n", " T = np.linspace(300.0,460.0,1000)\n", " ax.plot((q/V)*cAi/((q/V) + k(T)), T, 'b:')\n", " ax.plot(((q/V)*(Ti-T) + (UA/V/rho/Cp)*(Tc-T))/((dHr/rho/Cp)*k(T)), T, 'r:')\n", " ax.set_xlim(0,1)\n", " ax.set_ylim(300,460)\n", " ax.grid()\n", " ax.legend(['dC/dt = 0','dT/dt = 0'])\n", " ax.set_xlabel('Concentration')\n", " ax.set_ylabel('Temperature')\n", " \n", "fix, ax = plt.subplots(1, 1, figsize=(8,6))\n", "plot_nullclines(ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Phase Plane Analysis\n", "\n", "The final analysis is display the simulation in both time and phase plane coordinates. The following cell produces a " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "fc96639dec6f4ae08c8aa0795911f7a3", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.5, description='cinitial', max=1.0, step=0.01), IntSlider(value=350,…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def plot_phase(ax, t, y):\n", " ax.plot(y[0][0], y[1][0], 'r.', ms=20)\n", " ax.plot(y[0], y[1], 'g', lw=2)\n", "\n", "def phase(cinitial=0.5, Tinitial=350):\n", " global Tc\n", " soln = solve_ivp(deriv, [t_initial, t_final], [cinitial,Tinitial], t_eval=t)\n", " \n", " ax[0,0].lines[2].set_xdata(soln.y[0][0])\n", " ax[0,0].lines[2].set_ydata(soln.y[1][0])\n", " ax[0,0].lines[3].set_xdata(soln.y[0])\n", " ax[0,0].lines[3].set_ydata(soln.y[1])\n", " ax[1,0].lines[0].set_ydata(soln.y[0])\n", " ax[1,1].lines[0].set_ydata(soln.y[1])\n", " display(fig)\n", " \n", "Tc = 300.0\n", "cinitial = 0.5\n", "Tinitial = 350.0\n", "fig, ax = plt.subplots(2, 2, figsize=(12, 9))\n", "soln = solve_ivp(deriv, [t_initial, t_final], [cinitial, Tinitial], t_eval=t)\n", "plot_nullclines(ax[0,0])\n", "plot_phase(ax[0,0], soln.t, soln.y)\n", "plot_reactor(ax[1,:], soln.t, soln.y)\n", "plt.close()\n", "\n", "interact(phase, cinitial=(0,1,.01), Tinitial=(300,400,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Suggested Exercises" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "exercise" ] }, "source": [ "**1.** Using the interactive simulation, adjust the cooling temperature over the range of values from 290K to 310K, identify the cooling water temperatures at which you observe a qualitative difference in system behavior. Try to identify the following behaviors:\n", "\n", "* Stable steady state\n", "* Oscillatory steady state\n", "* The onset of a thermal runaway condition\n" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "exercise" ] }, "source": [ "**2.** Repeat the exercise using the phase plane simulation. Describe the underlying behaviors in light of the nullclines.\n" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "exercise" ] }, "source": [ "\n", "**3.** Assume the reactor is start up with a tank of reactant feed with a concentration $c_A = 1$. What is the maximum initial temperature that would avoid thermal runaway during reactor startup?" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }