{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains course material from [CBE20255](https://jckantor.github.io/CBE20255)\n", "by Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE20255.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [General Mass Balance on a Single Tank](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/04.03-General-Mass-Balance-on-a-Single-Tank.ipynb) | [Contents](toc.ipynb) | [Reactors](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/05.00-Reactors.ipynb) >

\"Open" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Unsteady-State Material Balances" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "This [Jupyter notebook](http://jupyter.org/notebook.html) demonstrates the application of the general material balance equations to a variety of example problems." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unsteady-State Material Balances" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The general principle of material balances is stated in words as \n", "\n", "Accumulation = Inflow - Outflow + Generation - Consumption\n", "\n", "An equation like this can be written for any conserved quantity, whether it is chemical species that chemical or bio engineers work with, or moeny in the case of finance, or populations for social scientists. Whenever terms on the right-hand side of the equation do not yield a zero result we are left with an _unsteady-state_ balance, which are some of the most fascinating and challenging problems in engineering practice." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1: Population Growth" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first example concerns population growth. Looking birth and death rates in various countries around the globe, one comes across the following data maintained by the World Bank.\n", "\n", "For Afghanistan (the first country on the World Bank charts), the 2011 population was estimated to be 29,105,480 with a [birth rate of 37.0 births per year per 1,000 people](http://data.worldbank.org/indicator/SP.DYN.CBRT.IN), and a [death rate as 8.0 per year per 1,000](http://data.worldbank.org/indicator/SP.DYN.CDRT.IN). Assuming there is no in-migration or out-migration, can we predict the population in 2014?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Population Balance Equation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Writing out the balance equation, we get\n", "\n", "$\\underbrace{\\mbox{Accumulation}}_{\\frac{dP}{dt}} = \\underbrace{\\mbox{Inflow}}_{=0} - \\underbrace{\\mbox{Outflow}}_{=0} + \\underbrace{\\mbox{Generation}}_{births=\\frac{37}{1000}P} - \\underbrace{\\mbox{Consumption}}_{deaths=\\frac{8}{1000}P}$\n", "\n", "the algebraic combination of the two terms on the left leaves us an equation for the rate of change of population\n", "\n", "$\\frac{dP}{dt} = 0.029\\,P$\n", "\n", "with an initial condition $P(2011) = 29,105,480$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculus Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll use the shorthand notation $t_0 = 2011$ and $P(t_0) = 29,105,480$. Then separating the variables\n", "\n", "$\\int_{P(t_0)}^{P(t)}\\frac{1}{P}\\,dP = 0.029\\,\\int_{t_0}^t dt $\n", "\n", "Doing the integrals (if this is the first time you've seen this, be sure you do this by hand!) leads to\n", "\n", "$P(t) = P(t_0)\\,e^{0.029(t-t_0)}$\n", "\n", "This solution demonstrates the exponential growth of populations in circumstances where growth rate is constant and there are no other factors to consider." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.integrate import odeint\n", "\n", "P_0 = 29105480\n", "t_0 = 2011\n", "t_1 = 2014\n", "\n", "t = np.linspace(t_0,t_1)\n", "P = P_0*np.exp(0.029*(t-t_0))\n", "\n", "plt.plot(t,P)\n", "plt.xlabel('Year')\n", "plt.ylabel('Count')\n", "plt.title(\"Proj. Population in Afganistan {:4d} to {:4d}\".format(t_0,t_1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Numerical Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another way of generating solutons to unsteady-state problems is by direct, numerical solution of the differential equations. This requires us to set up a function to numerically evaluate the right hand-side of the differential equation. That function, along with initial conditions and a list of time values for which we want to the know the solution, are passed to a solver that does the hard work." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 1. Right a function to evaulate the RHS of the differential equation." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def Inflow(t) : return 0\n", "def Outflow(t): return 0\n", "def Births(P) : return (37.0/1000)*P\n", "def Deaths(P) : return (8.0/1000)*P\n", "\n", "def Accumulation(P,t) : return Inflow(t) - Outflow(t) + Births(P) - Deaths(P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 2. Establish the initial condition and time values for a desired solution." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "P_0 = 29105480\n", "t_0 = 2011\n", "t_1 = 2014\n", "t = np.linspace(t_0,t_1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 3. Pass this information to a solver to compute values of the solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `SciPy` package provides a number of tools for the numerical solution of differential equations. Of these, perhaps the easiest to use is `odeint` which is demonstrated here. `odeint` needs to be imported from `scipy.integrate`, and then given three pieces of information:\n", "\n", "1. A function that takes two arguments. The first argument is the value of quantity we're trying to integrate, and the second is time. The function must return the value of the right-hand side of the differential equations.\n", "2. The initial value of the quantity we're trying to integrate.\n", "3. A list of times at which we wish to evaluate the solution. The first value in the list must be the initial value of time." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "P = odeint(Accumulation,P_0,t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 4. Plot the result." ] }, { "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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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t,P)\n", "plt.xlabel('Year')\n", "plt.ylabel('Population')\n", "plt.title('Afghanistan')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2: Dilution of a Trace Contaminant" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have a tank partially filled with an initial volume V(t0) = 1000 liters of water that is contaminated by a toxic species X at an concentration CX(t0) = 100 ppm by volume. We wish to dilute this to 20 ppm by volume before sending it for further cleanup. We know adding 4000 liters of water would accomplish the goal, but for process monitoring purposes we'd like to compute concentration as a function of time assuming water enters at a steady rate of q(t) = 1 liter/second.\n", "\n", "The total amount of X in the tank is the product of concentration times volume, that is CXV. The material balance for X is \n", "\n", "For component X: $\\underbrace{\\mbox{Accumulation}_X}_{\\frac{d(C_XV)}{dt}} = \\underbrace{\\mbox{Inflow}_X}_{=0} - \\underbrace{\\mbox{Outflow}_X}_{=0} + \\underbrace{\\mbox{Generation}_X}_{=0} - \\underbrace{\\mbox{Consumption}_X}_{=0}$\n", "\n", "This is a two component system, so we need two material balances. We'll do the second balance on overall volume on the assumption that density is a constant this dilute solution. The overall balance is\n", "\n", "For total volume: $\\underbrace{\\mbox{Accumulation}}_{\\frac{dV}{dt}} = \\underbrace{\\mbox{Inflow}}_{=q} - \\underbrace{\\mbox{Outflow}}_{=0} + \\underbrace{\\mbox{Generation}}_{=0} - \\underbrace{\\mbox{Consumption}}_{=0}$\n", "\n", "This gives us a pair of differential equations\n", "\n", "$\\begin{align*}\n", "\\frac{d(C_XV)}{dt} & = 0 \\\\\n", "\\frac{dV}{dt} & = q\n", "\\end{align*}$\n", "\n", "What we're looking for is CX. But what we have are differential equations for product (CXV) and volume V. How can we get a differential equation for CX? \n", "\n", "Using the chain rule\n", "\n", "$\\frac{d(C_XV)}{dt} = C_X\\,\\underbrace{\\frac{dV}{dt}}_{=q} + V\\,\\frac{dC_X}{dt} = 0$\n", "\n", "Substituting in the second equation leaves us with a pair of differential equations\n", "\n", "$\\begin{align*}\n", "\\frac{dC_X}{dt} & = -\\frac{q}{V} C_X \\\\\n", "\\frac{dV}{dt} & = q\n", "\\end{align*}$\n", "\n", "(Be sure you go through the algebra and understand both how and why we did this.)\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# parameter values\n", "q = 1 # liters/second\n", "\n", "# initial conditions\n", "C_0 = 100 # ppm\n", "V_0 = 1000 # liters\n", "\n", "# time grid in seconds\n", "t = np.linspace(0,4000)\n", "\n", "# compute list of derivative values\n", "def deriv(X,t):\n", " C,V = X\n", " return [-q*C/V,q]\n", "\n", "# solve with odeint\n", "soln = odeint(deriv,[C_0,V_0],t)\n", "\n", "# display the result\n", "plt.plot(t,soln[:,0])\n", "plt.xlabel('Time [seconds]')\n", "plt.ylabel('[ppm/v]')\n", "plt.title('Concentration of X')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3: Hare and Lynx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](files/images/Lynx-Hare_cycle.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\begin{align*}\n", "\\frac{dH}{dt} & = r H \\left(1-\\frac{H}{k}\\right) - \\frac{a H L}{c + H}\\\\\n", "\\frac{dL}{dt} & = \\frac{b a H L}{c + H} - d L\n", "\\end{align*}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameter Values" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "a = 3.2\n", "b = 0.6\n", "c = 50\n", "d = 0.56\n", "k = 125\n", "r = 1.6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Derivatives" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def deriv(x,t):\n", " H,L = x\n", " dH = r*H*(1-H/k) - a*H*L/(c+H)\n", " dL = b*a*H*L/(c+H) - d*L\n", " return [dH,dL]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solve" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "t = np.linspace(0,150,500)\n", "ic = [20,30]\n", "soln = odeint(deriv,ic,t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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syQGy0VH/DzOst254c7b/i8DfCCGawJ3Aa1Dk80EhxOuAe4CXzXkNFg9D/MnV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QPYbv15C9CMqtg4CDwONM0BXa8Dfm79PKf0A9YB26zr+FOgcQ7q+NfAPmAX8M9AeLZ1BB5E5SwS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\n8QAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(t,soln)\n", "plt.xlabel('Time [yr]')\n", "plt.ylabel('Population');\n", "plt.title('Lynx-Hare Population Model')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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wFDaGJJGSX46NmREzB7kwe4grXvad23t49RBC8Gd4Gu/uvEhWcSX3DXblxYk+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "H = soln[:,0]\n", "L = soln[:,1]\n", "plt.plot(H,L)\n", "plt.xlabel('Hare Population')\n", "plt.ylabel('Lynx Population')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [General Mass Balance on a Single Tank](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/04.03-General-Mass-Balance-on-a-Single-Tank.ipynb) | [Contents](toc.ipynb) | [Reactors](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/05.00-Reactors.ipynb) >

\"Open" ] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }