{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tube Diameter effect on Plug Flow Reactors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Author: Franz Navarro ([CAChemE.org](http://CAChemE.org)) \n", "##### Copyright: Text and images CC-BY / Code MIT - Original source [LearnChemE](http://demonstrations.wolfram.com/EffectOfTubeDiameterOnPlugFlowReactor/)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This IPython notebook shows the effect of tube diameter on conversion, temperature, and pressure drop for a plug flow reactor (PFR). The original example came from [this LearnChemE.com simulation](http://demonstrations.wolfram.com/EffectOfTubeDiameterOnPlugFlowReactor/). Specifically, a first-order exothermic reaction takes place in a PFR accounting for the pressure drop and heat transfer through the walls. The user can vary the reactor diameter keeping total feed flow rate constant (by changing the number of parallel reactors, named as \"# equivalent reactors\"). Thus, the total reactor cross section remains constant so its (total) molar feed flow rate does as well.\n", "\n", "![Tube Diameter effect on Plug Flow Reactors](diameter-effect-plug-flow-reactor.gif)\n", "\n", "Notice that, for smaller-diameter reactors, the pressure drop is higher since the volumetric flow rate increases and the residence time is reduced (lowering the conversion). Besides, heat transfer is more efficient for smaller-diameter reactors because the surface area per volume is larger which allow better reaction control. In this simple case, the temperature increases less in the reactor, and this also lowers conversion. The physics being modeled here are the fundamentals of [Microreactors](http://en.wikipedia.org/wiki/Microreactor).\n", "\n", "
[IPython](http://ipython.org/) provides a rich architecture for interactive computing as Mathematica or MATLAB do, but Python is open-source and completely free (instead of propietary and expensive software). If you want to run this notebook in your computer we recommend [Anaconda with Python 3](http://continuum.io/downloads#py34).
\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Loading our favorite python libraries\n", "\n", "%matplotlib inline\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint\n", "\n", "plt.style.use('bmh')\n", "\n", "# The following code will only work in Python 3 since we will be using unicode characteres" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAR4AAAH8CAYAAAAHRcBfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXl8VdXVv5+VmcwDCWGKBJAZGVScUEEc24r2rVq1TkVr\n", "Cx1otYN27q+tWlva2vrWt63Waiu2FuuAEyJSKmqxCsFAmIJAwpAZMpJ5/f44J+ESMt0kN/fsy34+\n", "n0Pu2Wfvc773cO+6e6+9z1qiqlgsFstgEhZsARaL5eTDGh6LxTLoWMNjsVgGHWt4LBbLoGMNj8Vi\n", "GXSs4bFYLIOONTwnKSIyRkRaReTcYGuxnHxYwxMgRCRVRO4Xka0iUisiFSKySUR+IiKjgq3P67hG\n", 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"number_reactors = A_cross_0 / A_cross # equivalent reactors to keep same area and flow rate\n", "\n", "# Operating conditions\n", "FA_0 = 100 # [mol m^{-3}] inlet molar flow rate \n", "FA_0_n = 100/number_reactors # [mol m^{-3}] inlet molar flow rate within one reactor\n", "\n", "P_0 = 6.08e5 # [Pa] Pressure inlet\n", "T_0 = 300 # [K] Temperature inlet\n", "\n", "\n", "def diffEqs(y, z, FA_0_n, T_0, P_0, A_cross):\n", " ''' y is a vector with the concentration\n", " z is the indpendt variable (time)\n", " '''\n", " \n", " FA_z = y[0] # [mol] molar flow (dependent variable)\n", " T_z = y[1] # [K] temperature (dependent variable)\n", " P_z = y[2] # [Pa] pressure (dependent variable)\n", " \n", " # Constants\n", " # ---------\n", " R_const = 8.314 # [m^{3} Pa K^{−1} mol^{−1}]\n", " \n", " ρ = 230 # [kg m^{-3}] fluid density (average)\n", " μ = 2.3e-5 # [kg m^{-1} s^{-1}] dynamics viscosity (average)\n", " \n", " ϵ = 45e-6 # [m] wall roughness\n", "\n", " ΔH = -25000 # [J mol^{-1}] heat of reaction\n", " Cp = 550 # [J mol^{-1} K^{-1}] heat capacity of reactants (average)\n", " Ua = 500 # [J m^{-3} s^{-1} K^{-1}] heat transfer coefficient times area/volume\n", " T_cool = 300 # [K] Cooling temperature inlet\n", " \n", " # Lenght dependent parameters\n", " # ---------------------------\n", " \n", " vol_flow_0 = (FA_0_n * R_const * T_0) / P_0 # [m^3/s] inlet gas velocity\n", " vol_flow = vol_flow_0 * FA_z/FA_0_n * P_0/P_z* T_z/T_0 # [m^3/s] volumetric flow\n", "\n", " \n", " # Mass balance\n", " # ------------\n", " Afactor = 0.0715 # [s^{-1}] pre-exponential factor\n", " Ea = 17000 # activation energy\n", "\n", " T_m = 300 # [K] Temperature \n", " \n", " k = Afactor * np.exp(-Ea/R_const * (1/T_z - 1/T_m)) # [s^{-1}]reaction rate\n", " CA_z = FA_z/vol_flow # [mol/s] molar flow rate\n", " \n", " dFdz = -k * CA_z * A_cross # first-order exothermic reaction\n", " \n", " # Energy Balance\n", " # --------------\n", " dTdz = (Ua*(T_cool-T_z) - k*CA_z*A_cross*ΔH) / (FA_z * Cp)\n", " \n", " # Pressure drop\n", " # --------------\n", " NRe = (ρ * vol_flow/A_cross * diameter) / μ # [-] Reynolds number\n", "\n", " if NRe <= 2300:\n", " f_factor = 64/NRe\n", " elif NRe > 2300:\n", " f_factor = 0.25 * np.log10(ϵ/(3.7*diameter) + 5.74/NRe**0.9)**-2\n", " \n", " dPdz = -ρ * f_factor/diameter * ((vol_flow/A_cross)**2/2)\n", "\n", "\n", " return [dFdz, dTdz, dPdz]\n", "\n", "\n", "z = np.linspace(0., length, 1000)\n", "\n", "y0 = [FA_0_n, T_0, P_0] # [molar flow, temperature, pressure]\n", "\n", "# We call the ode in order to intregate\n", "Y = odeint(diffEqs, y0, z, args=(FA_0_n, T_0, P_0, A_cross))\n", "\n", "# Taking back the solutions\n", "F_A = Y[:, 0] # mol*L-1\n", "T = Y[:, 1] # mol*L-1\n", "P = Y[:, 2] # mol*L-1\n", "\n", "F_A_total = F_A * number_reactors\n", "T_Celsius= T - 273.15 # [K]->[ºC] Conversion of temperature\n", "P_bar = P/1e5 # [Pa]->[bar] conversion of pressure\n", "\n", "conversion = (1 - F_A[-1]/F_A[0]) * 100 # for the B component\n", "\n", "# Plotting results\n", "# -------------------\n", "fig, (ax1, ax2, ax3) = plt.subplots(nrows=3, ncols=1,\n", " figsize=(4,8))\n", "# Molar flow alongside the reactor\n", "ax1.plot(z, F_A_total)\n", "# ax1.set_xlabel(\"reactor length (m)\")\n", "ax1.set_ylabel(\"$F_{A}$ (mol/s)\")\n", "ax1.set_title(\"Gas-phase PFR: A > B\")\n", "\n", "ax1.set_xlim([0,50])\n", "ax1.set_ylim([0,100])\n", "\n", "# Temperature alongside the reactor\n", "ax2.plot(z, T_Celsius)\n", "# ax2.set_xlabel(\"reactor length (m)\")\n", "ax2.set_ylabel(\"$T$ (°C)\")\n", "# ax2.set_title(\"Evolution of the temperature within the PFR\")\n", "ax2.set_xlim([0,50])\n", "ax2.set_ylim([0,150])\n", "\n", "# Pressure alongside the reactor\n", "ax3.plot(z, P_bar)\n", "ax3.set_xlabel(\"reactor length (m)\")\n", "ax3.set_ylabel(\"$P$ (bar)\")\n", "# ax3.set_title(\"Evolution of the pressure within the PFR\")\n", "ax3.set_xlim([0,50])\n", "ax3.set_ylim([0,7])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code works like a charm! You can check that the results variate if we hand change the value of the diameter. But we want to add some interactivity as the orginal. So first let's wrap the code from above within a function:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def gasPFR(diameter=0.3):\n", " \"\"\" Plug flow reactor model\n", " For a simple gas-phase A --> B\n", "\n", " input arguments:\n", " diameter [m] Diameter of the tube\n", "\n", " returns a plot with the mass, heat and moment Diff. eqs. solved\n", " \"\"\"\n", " # Reactor parameters\n", " diameter_0 = 0.3 # [m] Diameter of the initial tube reactor being studied\n", " length = 50 # [m] Length of the tube reactor\n", "\n", " A_cross = np.pi/4*diameter**2 # [m^2] Cross sectional aera of the tube reactor\n", " A_cross_0 = np.pi/4*diameter_0**2 # [m^2] Cross sectional aera of the tube reactor\n", "\n", " number_reactors = A_cross_0 / A_cross # equivalent reactors to keep same area and flow rate\n", "\n", " # Operating conditions\n", " FA_0 = 100 # [mol m^{-3}] inlet molar flow rate \n", " FA_0_n = 100/number_reactors # [mol m^{-3}] inlet molar flow rate within one reactor\n", "\n", " P_0 = 6.08e5 # [Pa] Pressure inlet\n", " T_0 = 300 # [K] Temperature inlet\n", "\n", "\n", " def diffEqs(y, z, FA_0_n, T_0, P_0, A_cross):\n", " ''' y is a vector with the concentration\n", " z is the indpendt variable (time)\n", " '''\n", "\n", " FA_z = y[0] # [mol] molar flow (dependent variable)\n", " T_z = y[1] # [K] temperature (dependent variable)\n", " P_z = y[2] # [Pa] pressure (dependent variable)\n", "\n", " # Constants\n", " # ---------\n", " R_const = 8.314 # [m^{3} Pa K^{−1} mol^{−1}]\n", "\n", " ρ = 230 # [kg m^{-3}] fluid density (average)\n", " μ = 2.3e-5 # [kg m^{-1} s^{-1}] dynamics viscosity (average)\n", "\n", " ϵ = 45e-6 # [m] wall roughness\n", "\n", " ΔH = -25000 # [J mol^{-1}] heat of reaction\n", " Cp = 550 # [J mol^{-1} K^{-1}] heat capacity of reactants (average)\n", " Ua = 500 # [J m^{-3} s^{-1} K^{-1}] heat transfer coefficient times area/volume\n", " T_cool = 300 # [K] Cooling temperature inlet\n", "\n", " # Lenght dependent parameters\n", " # ---------------------------\n", "\n", " vol_flow_0 = (FA_0_n * R_const * T_0) / P_0 # [m^3/s] inlet gas velocity\n", " vol_flow = vol_flow_0 * FA_z/FA_0_n * P_0/P_z* T_z/T_0 # [m^3/s] volumetric flow\n", "\n", "\n", " # Mass balance\n", " # ------------\n", " Afactor = 0.0715 # [s^{-1}] pre-exponential factor\n", " Ea = 17000 # activation energy\n", "\n", " T_m = 300 # [K] Temperature \n", "\n", " k = Afactor * np.exp(-Ea/R_const * (1/T_z - 1/T_m)) # [s^{-1}]reaction rate\n", " CA_z = FA_z/vol_flow # [mol/s] molar flow rate\n", "\n", " dFdz = -k * CA_z * A_cross # first-order exothermic reaction\n", "\n", " # Energy Balance\n", " # --------------\n", " dTdz = (Ua*(T_cool-T_z) - k*CA_z*A_cross*ΔH) / (FA_z * Cp)\n", "\n", " # Pressure drop\n", " # --------------\n", " NRe = (ρ * vol_flow/A_cross * diameter) / μ # [-] Reynolds number\n", "\n", " if NRe <= 2300:\n", " f_factor = 64/NRe\n", " elif NRe > 2300:\n", " f_factor = 0.25 * np.log10(ϵ/(3.7*diameter) + 5.74/NRe**0.9)**-2\n", "\n", " dPdz = -ρ * f_factor/diameter * ((vol_flow/A_cross)**2/2)\n", "\n", "\n", " return [dFdz, dTdz, dPdz]\n", "\n", "\n", " z = np.linspace(0., length, 1000)\n", "\n", " y0 = [FA_0_n, T_0, P_0] # [molar flow, temperature, pressure]\n", "\n", " # We call the ode in order to intregate\n", " Y = odeint(diffEqs, y0, z, args=(FA_0_n, T_0, P_0, A_cross))\n", "\n", " # Taking back the solutions\n", " F_A = Y[:, 0] # mol*L-1\n", " T = Y[:, 1] # mol*L-1\n", " P = Y[:, 2] # mol*L-1\n", "\n", " F_A_total = F_A * number_reactors\n", " T_Celsius= T - 273.15 # [K]->[ºC] Conversion of temperature\n", " P_bar = P/1e5 # [Pa]->[bar] conversion of pressure\n", "\n", " conversion = (1 - F_A[-1]/F_A[0]) * 100 # for the B component\n", "\n", " # Plotting results\n", " # -------------------\n", " fig, (ax1, ax2, ax3) = plt.subplots(nrows=3, ncols=1,\n", " figsize=(4,8))\n", " # Molar flow alongside the reactor\n", " ax1.plot(z, F_A_total)\n", " # ax1.set_xlabel(\"reactor length (m)\")\n", " ax1.set_ylabel(\"$F_{A}$ (mol/s)\")\n", " ax1.set_title(\"Gas-phase PFR: A > B\")\n", "\n", " ax1.set_xlim([0,50])\n", " ax1.set_ylim([0,100])\n", "\n", " # Temperature alongside the reactor\n", " ax2.plot(z, T_Celsius)\n", " # ax2.set_xlabel(\"reactor length (m)\")\n", " ax2.set_ylabel(\"$T$ (°C)\")\n", " # ax2.set_title(\"Evolution of the temperature within the PFR\")\n", " ax2.set_xlim([0,50])\n", " ax2.set_ylim([0,150])\n", "\n", " # Pressure alongside the reactor\n", " ax3.plot(z, P_bar)\n", " ax3.set_xlabel(\"reactor length (m)\")\n", " ax3.set_ylabel(\"$P$ (bar)\")\n", " # ax3.set_title(\"Evolution of the pressure within the PFR\")\n", " ax3.set_xlim([0,50])\n", " ax3.set_ylim([0,7])\n", "\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Done! Let's test the function with different arguments:\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAR4AAAH8CAYAAAAHRcBfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXl8VdXVv5+VmcwDCWGKBJAZGVScUEEc24r2rVq1TkVr\n", "Cx1otYN27q+tWlva2vrWt63Waiu2FuuAEyJSKmqxCsFAmIJAwpAZMpJ5/f44J+ESMt0kN/fsy34+\n", "n0Pu2Wfvc773cO+6e6+9z1qiqlgsFstgEhZsARaL5eTDGh6LxTLoWMNjsVgGHWt4LBbLoGMNj8Vi\n", "GXSs4bFYLIOONTwnKSIyRkRaReTcYGuxnHxYwxMgRCRVRO4Xka0iUisiFSKySUR+IiKjgq3P67hG\n", "sW2rEZEcEVnkc/y2DnXatt+5x+d1KD8iIv8VkRv6oSnG/X88KiIpA/E+e3HNju+zTkS2ichdg3H9\n", "QGENTwAQkdHAJuAa4D7gLGAG8FUgDfh68NQZxReBTGAm8ArwqIh8yud4i3vcd/tmh3PMcsvPBv4D\n", "/FVEzuujnuuAZqAAuLU3DUTklD5eyxff9zkZ+BXwgIjcNADnDg6qarcB3oCVwAEgvhd1LwH+BZQD\n", "R9zXZ3aocwewDTjq1lsHjOzmnGOAVuAzwBqgDtgNfLqTOtcCLwG1bp1bO5xrKY4RrQYOAU8DmT7H\n", "I4FfAoVAPXAQeLrDOa4Hclz9e4BlQGwP96UVuLFD2Q7gKff1bUBTN+3nuecY4VOW4Jbd1cf/1/XA\n", 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{}, "source": [ "Look at that! The results reproduce the phyisics under study. In our last example we have a tiny reactor with a diameter of just 1.5 cm. As you can see, now the pressure loss is significant but the temperature remains almost constant. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Making an interactive plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Time for the magic of IPython Notebook! We will rearrange some code and use the interactivy of IPython, but this is just for showing off don't be scared if this is your first time reading Python code. The vary basic idea is to use the function we just wrote above and call the awesome widgets of IPython." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from IPython.html.widgets import interact_manual\n", "from matplotlib.patches import Ellipse, Rectangle, Arrow" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def diameter_PFR(diameter=0.3):\n", " \"\"\" Plug flow reactor model\n", " For a simple gas-phase A --> B\n", "\n", " input arguments:\n", " diameter [m] Diameter of the tube\n", "\n", " returns a plot with the mass, heat and moment Diff. eqs. solved\n", " \"\"\"\n", " # Reactor parameters\n", " diameter_0 = 0.3 # [m] Diameter of the initial tube reactor being studied\n", " length = 50 # [m] Length of the tube reactor\n", "\n", " A_cross = np.pi/4*diameter**2 # [m^2] Cross sectional aera of the tube reactor\n", " A_cross_0 = np.pi/4*diameter_0**2 # [m^2] Cross sectional aera of the tube reactor\n", "\n", " number_reactors = A_cross_0 / A_cross # equivalent reactors to keep same area and flow rate\n", "\n", " # Operating conditions\n", " FA_0 = 100 # [mol m^{-3}] inlet molar flow rate \n", " FA_0_n = 100/number_reactors # [mol m^{-3}] inlet molar flow rate within one reactor\n", "\n", " P_0 = 6.08e5 # [Pa] Pressure inlet\n", " T_0 = 300 # [K] Temperature inlet\n", "\n", "\n", " def diffEqs(y, z, FA_0_n, T_0, P_0, A_cross):\n", " ''' y is a vector with the concentration\n", " z is the indpendt variable (time)\n", " '''\n", "\n", " FA_z = y[0] # [mol] molar flow (dependent variable)\n", " T_z = y[1] # [K] temperature (dependent variable)\n", " P_z = y[2] # [Pa] pressure (dependent variable)\n", "\n", " # Constants\n", " # ---------\n", " R_const = 8.314 # [m^{3} Pa K^{−1} mol^{−1}]\n", "\n", " ρ = 230 # [kg m^{-3}] fluid density (average)\n", " μ = 2.3e-5 # [kg m^{-1} s^{-1}] dynamics viscosity (average)\n", "\n", " ϵ = 45e-6 # [m] wall roughness\n", "\n", " ΔH = -25000 # [J mol^{-1}] heat of reaction\n", " Cp = 550 # [J mol^{-1} K^{-1}] heat capacity of reactants (average)\n", " Ua = 500 # [J m^{-3} s^{-1} K^{-1}] heat transfer coefficient times area/volume\n", " T_cool = 300 # [K] Cooling temperature inlet\n", "\n", " # Lenght dependent parameters\n", " # ---------------------------\n", "\n", " vol_flow_0 = (FA_0_n * R_const * T_0) / P_0 # [m^3/s] inlet gas velocity\n", " vol_flow = vol_flow_0 * FA_z/FA_0_n * P_0/P_z* T_z/T_0 # [m^3/s] volumetric flow\n", "\n", "\n", " # Mass balance\n", " # ------------\n", " Afactor = 0.0715 # [s^{-1}] pre-exponential factor\n", " Ea = 17000 # activation energy\n", "\n", " T_m = 300 # [K] Temperature \n", "\n", " k = Afactor * np.exp(-Ea/R_const * (1/T_z - 1/T_m)) # [s^{-1}]reaction rate\n", " CA_z = FA_z/vol_flow # [mol/s] molar flow rate\n", "\n", " dFdz = -k * CA_z * A_cross # first-order exothermic reaction\n", "\n", " # Energy Balance\n", " # --------------\n", " dTdz = (Ua*(T_cool-T_z) - k*CA_z*A_cross*ΔH) / (FA_z * Cp)\n", "\n", " # Pressure drop\n", " # --------------\n", " NRe = (ρ * vol_flow/A_cross * diameter) / μ # [-] Reynolds number\n", "\n", " if NRe <= 2300:\n", " f_factor = 64/NRe\n", " elif NRe > 2300:\n", " f_factor = 0.25 * np.log10(ϵ/(3.7*diameter) + 5.74/NRe**0.9)**-2\n", "\n", " dPdz = -ρ * f_factor/diameter * ((vol_flow/A_cross)**2/2)\n", "\n", "\n", " return [dFdz, dTdz, dPdz]\n", "\n", "\n", " z = np.linspace(0., length, 1000)\n", "\n", " y0 = [FA_0_n, T_0, P_0] # [molar flow, temperature, pressure]\n", "\n", " # We call the ode in order to intregate\n", " Y = odeint(diffEqs, y0, z, args=(FA_0_n, T_0, P_0, A_cross))\n", "\n", " # Taking back the solutions\n", " F_A = Y[:, 0] # mol*L-1\n", " T = Y[:, 1] # mol*L-1\n", " P = Y[:, 2] # mol*L-1\n", "\n", " F_A_total = F_A * number_reactors\n", " T_Celsius= T - 273.15 # [K]->[ºC] Conversion of temperature\n", " P_bar = P/1e5 # [Pa]->[bar] conversion of pressure\n", "\n", " conversion = (1 - F_A[-1]/F_A[0]) * 100 # for the B component\n", "\n", " # Plotting results\n", " # -------------------\n", " fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2,\n", " figsize=(11,11))\n", " # Molar flow alongside the reactor\n", " ax1.plot(z, F_A_total)\n", " ax1.set_xlabel(\"reactor length (m)\")\n", " ax1.set_ylabel(\"$F_{A}$ (mol/s)\")\n", " ax1.set_title(\"Gas-phase PFR: A > B\")\n", "\n", " ax1.set_xlim([0,50])\n", " ax1.set_ylim([0,100])\n", " \n", " # Original code taken from:\n", " # https://gist.github.com/franktoffel/843e58486fea9d795400#file-plot_pfr-py\n", "\n", "\n", " reactor_length = 10 # [for graphing porposes]\n", " reactor_diameter = diameter*10 # [for graphing porposes] \n", "\n", " arrow_lenght = 3 # [units]\n", "\n", " # Let's begin with the arrow representing the outlet\n", " arrow_outlet = Arrow(reactor_length, reactor_diameter/2, # x, y (coordinates)\n", " arrow_lenght, 0, width=0.2, # dx, dy\n", " facecolor=\"black\") # color options\n", " ax2.add_patch(arrow_outlet) # adds the path to the plot\n", "\n", " # Now we create and plot elliplse representing the end of the cillinder\n", " ellipse_outlet = Ellipse((reactor_length,reactor_diameter/2), # x, y (coordinates)\n", " reactor_diameter/2, reactor_diameter, # width, height\n", " facecolor=\"grey\", edgecolor=\"black\") # color options\n", " ax2.add_patch(ellipse_outlet) # adds the patch to the plot\n", "\n", " # Create and plot the tube as rectangle \n", " rectangle = Rectangle((0, 0), # x, y (coordinates)\n", " reactor_length, reactor_diameter, # width, height \n", " facecolor=\"grey\", edgecolor=\"none\") # color options \n", " ax2.add_patch(rectangle) # adds the patch to the plot\n", "\n", " # Again we create an ellipse but this time at the inlet\n", " ellipse_inlet = Ellipse((0,reactor_diameter/2), # x, y (coordinates)\n", " reactor_diameter/2, reactor_diameter, # width, height\n", " facecolor=\"grey\", edgecolor=\"black\") # color options\n", " ax2.add_patch(ellipse_inlet) # adds the patch to the plot\n", "\n", " # And finally the inlet arrow\n", " arrow_inlet = Arrow(-arrow_lenght, reactor_diameter/2, # x, y (coordinates)\n", " arrow_lenght, 0, width=0.2, # dx, dy \n", " facecolor=\"black\") # color options\n", " ax2.add_patch(arrow_inlet) # adds the patch to the plot\n", "\n", " ax2.set_xlim([-5,15]) # fixes the x axes\n", " ax2.set_ylim([-1,4]) # fixes the y axes\n", " \n", " ax2.set_xticklabels([]) # removes grid an y ticks\n", " ax2.set_yticklabels([]) # removes grid an x ticks\n", " ax2.grid(False)\n", " \n", " ax2.set_title(\"PFR diameter size: \" +\n", " str(diameter) +\" m\")\n", " \n", " ax2.text( 0, -0.5, \"Conversion of B: \" +\n", " str(round(conversion,2)) +\n", " \" %\")\n", " ax2.text( -3.2, -0.75, \"Number of equivalent reactors in parallel: \"+\n", " str(round(number_reactors)))\n", " \n", " ax2.text( -1, 3.75, \"Reactor length (constant): \"+\n", " str(round(length)) + \" m\")\n", " \n", "\n", " # Temperature alongside the reactor\n", " ax3.plot(z, T_Celsius, color=\"red\")\n", " ax3.set_xlabel(\"reactor length (m)\")\n", " ax3.set_ylabel(\"$T$ (°C)\")\n", " ax3.set_title(\"Evolution of the temperature\")\n", " ax3.set_xlim([0,50])\n", " ax3.set_ylim([0,150])\n", "\n", " # Pressure alongside the reactor\n", " ax4.plot(z, P_bar, color=\"purple\")\n", " ax4.set_xlabel(\"reactor length (m)\")\n", " ax4.set_ylabel(\"$P$ (bar)\")\n", " ax4.set_title(\"Evolution of the pressure\")\n", " ax4.set_xlim([0,50])\n", " ax4.set_ylim([0,7])\n", "\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAqUAAAKkCAYAAAA5hEaXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl4VOX5//H3nYSwJJCwJaxhkR2RRVGECMgmVgStaNUq\n", "ilrq0tpaW7f+tNpN1Nr6rVat+4q2VsUNVAQEgwIiICj7vhMIhIQlLMnz++NMYgghGxkm5+Tzuq65\n", 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