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diff --git a/Fluidization_Engineering_by_K_Daizo_And_O_Levenspiel/ch14.ipynb b/Fluidization_Engineering_by_K_Daizo_And_O_Levenspiel/ch14.ipynb new file mode 100755 index 00000000..24a0ffbb --- /dev/null +++ b/Fluidization_Engineering_by_K_Daizo_And_O_Levenspiel/ch14.ipynb @@ -0,0 +1,416 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:a7839feeb371e4231dbf99a0d3738674ff633956f5fb373aea54d56b513c13f8" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 14 : The RTD and Size Distribution of Solids in Fluidized Beds" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 1, Page 343" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from scipy.optimize import fsolve \n", + "import math \n", + "\n", + "#INPUT\n", + "Fo=2.7; #Feed rate in kg/min\n", + "Fof=0.9; #Feed rate of fines in feed in kg/min\n", + "Foc=1.8; #Feed rate of coarse in feed in kg/min\n", + "W=17.; #Bed weight in kg\n", + "kf=0.8; #Elutriation of fines in min**-1\n", + "kc=0.0125; #Elutriation of coarse in min**-1\n", + "\n", + "#CALCULATION\n", + "F1guess=1; #Guess value of F1\n", + "def solver_func(F1): #Function defined for solving the system\n", + " return F1-(Fof/(1.+(W/F1)*kf))-(Foc/(1.+(W/F1)*kc));#Eqn.(17)\n", + "\n", + "F1=fsolve(solver_func,F1guess)\n", + "F1f=Fof/(1.+(W/F1)*kf); #Flow rate of fines in entrained streams from Eqn.(16)\n", + "F1c=Foc/(1.+(W/F1)*kc); #Flow rate of coarse in entrained streams from Eqn.(16)\n", + "F2f=Fof-F1f; #Flow rate of fines in overflow streams from Eqn.(9)\n", + "F2c=Foc-F1c; #Flow rate of coarse in overflow streams from Eqn.(9)\n", + "tbarf=1./((F1/W)+kf); #Mean residence time of fines from Eqn.(12)\n", + "tbarc=1./((F1/W)+kc); #Mean residence time of coarse from Eqn.(12)\n", + "\n", + "#OUTPUT\n", + "print 'Flow rate in entrained stream:\\tFines:%fkg/min\\tCoarse:%fkg/min'%(F1f,F1c);\n", + "print 'Flow rate in overflow stream:\\tFines:%fkg/min\\tCoarse:%fkg/min'%(F2f,F2c);\n", + "print 'Mean residence time:\\tFines:%fmins\\tCoarse:%fmins'%(tbarf,tbarc);\n", + "\n", + "#====================================END OF PROGRAM ======================================================" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Flow rate in entrained stream:\tFines:0.100000kg/min\tCoarse:1.600000kg/min\n", + "Flow rate in overflow stream:\tFines:0.800000kg/min\tCoarse:0.200000kg/min\n", + "Mean residence time:\tFines:1.111111mins\tCoarse:8.888889mins\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 2, Page 344\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "\n", + "import math\n", + "from numpy import linspace,array,zeros\n", + "from scipy.optimize import fsolve\n", + "from matplotlib.pyplot import *\n", + "%matplotlib inline\n", + "#Variable declaration\n", + "dt=4.; #Diameter of reactor in m\n", + "ephsilonm=0.4; #Void fraction of static bed\n", + "rhos=2500.; #Density of solid in the bed in kg/m**3\n", + "Lm=1.2; #Height of static bed in m\n", + "Fo=3000; #Feed rate in kg/hr\n", + "beta1=1.2; #Increase in density of solids\n", + "dp=array([3,4,5,6,7,8,9,10,11,12,3,14,16,18,20,22,24,26,28,30])*10**-2;#Size of particles in mm\n", + "po=[0,0.3,0.8,1.3,1.9,2.6,3.5,4.4,5.7,6.7,7.5,7.8,7.5,6.3,5.0,3.6,2.4,1.3,0.5,0];#Size distribution of solids in mm**-1\n", + "k=array([0,10,9.75,9.5,8.75,7.5,6.0,4.38,2.62,1.20,0.325,0,0,0,0,0,0,0,0,0])*10**-4;#Elutriation constant in s**-1\n", + "pi=3.14;\n", + "\n", + "#CALCULATION\n", + "W=(pi/4*dt**2)*Lm*(1-ephsilonm)*rhos;#Weight of solids in bed\n", + "n=len(dp);\n", + "i=0;\n", + "F1guess=1000.;#Guess value for F1\n", + "F1c=linspace(2510,2700,10);\n", + "F1 = zeros(n)\n", + "x = zeros(n)\n", + "c = zeros(n)\n", + "a = zeros(n)\n", + "while i<n:\n", + " if k[i]==0:\n", + " x[i]=0\n", + " #break \n", + " else:\n", + " x[i]=0#(float(po[i])/(W*k[i]/float(F1)))*math.log(1.+(W*k[i]/F1)); \n", + " def solver_func(Fo):\n", + " return F1/(Lm*Fo)-x[i];\n", + "\n", + " F1[i] = fsolve(solver_func,F1guess);#Using inbuilt function fsolve for solving Eqn.(20) for F1\n", + " #c[i]=F1c[i]/(Lm*Fo);\n", + " if F1[i]==0:\n", + " a[i]=0;\n", + " else:\n", + " a[i]=(po[i]/(W*k[i]/F1[i]))*math.log(1+(W*k[i]/F1[i]));\n", + "\n", + " i=i+1;\n", + "\n", + "#plot(F1,c);\n", + "\n", + "#xtitle('F1 vs a,c','F1','a,c');\n", + "F1n=2500.;#The point were both the curves meet\n", + "F2=beta1*Fo-F1n;#Flow rate of the second leaving stream\n", + "j=0;\n", + "m=len(dp);\n", + "p1 = zeros(m)\n", + "p2 = zeros(m)\n", + "tbar = zeros(m)\n", + "while j<m:\n", + " p1[j]=(1./F1n)*((Fo*po[j])/(1.+(W/F1n)*k[j]));#Size distribution of stream 1 in mm**-1 from Eqn.(16)\n", + " p2[j]=k[j]*W*p1[j]/F2;#Size distribution of stream 2 in mm**-1 from Eqn.(7)\n", + " if p1[j]==0 and p2[j]==0:\n", + " tbar[j]=0;\n", + " elif p1[j]==0:\n", + " tbar[j]=(W*p1[j])/(F2*p2[j]);\n", + " elif p2[j]==0:\n", + " tbar[j]=(W*p1[j])/(F1n*p1[j]);\n", + " else:\n", + " tbar[j]=(W*p1[j])/(F1n*p1[j]+F2*p2[j]);#Average time in hr from Eqn.(11)\n", + " j=j+1;\n", + "\n", + "#OUTPUT\n", + "print 'Flow rate of stream 1:%fkg/hr'%F1n\n", + "print 'Flow rate of stream 2:%fkg/hr'%F2\n", + "j=0;\n", + "print 'tbar(hr)'\n", + "while j<m:\n", + " print '%f'%tbar[j]\n", + " j=j+1;\n", + "\n", + "#DISCLAIMER: The value obtained for tbar is deviating highly\n", + "#form the one given in textbook. However, the value obtained by manual calculation is close to #\n", + "#the ones obtained from the program." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n", + "Flow rate of stream 1:2500.000000kg/hr" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Flow rate of stream 2:1100.000000kg/hr\n", + "tbar(hr)\n", + "0.000000\n", + "8.962153\n", + "8.964162\n", + "8.966171\n", + "8.972205\n", + "8.982279\n", + "8.994397\n", + "9.007522\n", + "9.021824\n", + "9.033397\n", + "9.040543\n", + "9.043200\n", + "9.043200\n", + "9.043200\n", + "9.043200\n", + "9.043200\n", + "9.043200\n", + "9.043200\n", + "9.043200\n", + "0.000000\n" + ] + }, + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "WARNING: pylab import has clobbered these variables: ['draw_if_interactive', 'pi']\n", + "`%pylab --no-import-all` prevents importing * from pylab and numpy\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 3, Page 351\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "dp=1; #Particle size in mm\n", + "Fo=10; #Feed rate in kg/min\n", + "k=0.1; #Particle shrinkage rate in mm/min\n", + "\n", + "#CALCULATION\n", + "R=k/2; #Particle shrinkage rate in terms of radius\n", + "W=(Fo*dp/2)/(4*R); #Bed weight from Eqn.(42)\n", + "\n", + "#OUTPUT\n", + "print 'Weight of bed:%d kg' %W\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Weight of bed:25 kg\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4, Page 352\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "dpi=[1.05,0.95,0.85,0.75,0.65,0.55,0.45,0.35,0.25,0.15,0.05]; #Mean size in mm\n", + "Fo=[0,0.5,3.5,8.8,13.5,17.0,18.2,17.0,13.5,7.3,0]#*10**-2 #Feed rate in kg/s\n", + "for i in range(len(Fo)):\n", + " Fo[i] = Fo[i] * 10**-2\n", + "k=[0,0,0,0,0,0,0,0,2.0,12.5,62.5]#*10**-5;#Elutriation constant in s**-1\n", + "for i in range(len(k)):\n", + " k[i] = k[i] * 10**-5\n", + "\n", + "R=-1.58*10**-5;#Rate of particle shrinkage in mm/s\n", + "deldpi=0.1;#Size intervals in mm\n", + "\n", + "#CALCULATION\n", + "n=len(dpi);\n", + "m=1;#Starting with the largest value size interval that contains solids\n", + "W = [0]\n", + "while m<n-1:\n", + " W.append((Fo[m]-R*W[m-1]/deldpi)/(k[m]-R/deldpi-3*R/dpi[m]));#From Eqn.(33)\n", + " m=m+1;\n", + "\n", + "Wt=sum(W);#Total sum\n", + "\n", + "#OUTPUT\n", + "print '\\nTotal mass in the bed:%fkg'%Wt\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Total mass in the bed:7168.981263kg\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5, Page 353\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "dpi=[0.17,0.15,0.13,0.11,0.09,0.07,0.05,0.03,0.01];#Mean size of particles in mm\n", + "a=[0,0.95,2.45,5.2,10.1,23.2,35.65,20.0,2.45]#*10**-2;#Feed composition Fo(dpi)/Fo\n", + "for i in range(len(a)):\n", + " a[i] = a[i] * 10**-2\n", + "\n", + "y=[0,0,0,0,0,0,0.625,10.225,159.25]#*10**-6;#Elutriation and cyclone efficiency k(dpi)(1-eta(dpi))\n", + "for i in range(len(y)):\n", + " y[i] = y[i] * 10**-6\n", + "\n", + "\n", + "F=0.01; #Rate at which solids are withdrawn in kg/s\n", + "W=40000; #Weight of bed in kg\n", + "dp1=0.11 #Initial size in mm\n", + "dp2=0.085; #Size after shrinking in mm\n", + "dpmin=0.01; #Minimum size in mm\n", + "deldpi=2*10**-2; #Size inerval in mm\n", + "t=20.8; #Time in days\n", + "si=1;\n", + "\n", + "#CALCULATION\n", + "kdash=math.log((dp1-dpmin)/(dp2-dpmin))/(t*24*3600);#Rate of particle shrinkage from Eqn.(24)\n", + "n=len(dpi);\n", + "m=1;\n", + "Fo=0.05;#Initial value of Fo\n", + "F1 = [0];\n", + "s=0;\n", + "c=0;\n", + "t=1E-6;\n", + "R = [0]\n", + "x = [0]\n", + "F1 = [0]\n", + "while m<n:\n", + " R.append(-kdash*(dpi[m]-dpmin));#Rate of size change\n", + " x.append((a[m]*Fo-W*R[m-1]*F1[m-1]/deldpi)/(F+(W*y[m])-(W*R[m]/deldpi)-3*W*R[m]/dpi[m]));#Eqn.(34)\n", + " F1.append(x[m]*F);\n", + " c=c+x[m];\n", + " m=m+1;\n", + " if abs(c-1)<t:\n", + " break\n", + " Fo=Fo+0.0001;#Incrementing Fo\n", + "\n", + "#OUTPUT\n", + "print 'Feed rate with deldpi=%fmm is %fg/hr'%(deldpi,Fo);\n", + "i=0;\n", + "print 'Bed composition'\n", + "for i in x:\n", + " print '%f'%(i*100)\n", + " i=i+1;\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Feed rate with deldpi=0.020000mm is 0.050800g/hr\n", + "Bed composition\n", + "0.000000\n", + "0.652911\n", + "1.859952\n", + "4.400781\n", + "9.668999\n", + "25.654298\n", + "28.575890\n", + "2.317749\n", + "0.019493\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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