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diff --git a/Mass_Transfer_Operations_by_R_E_Treybal/4-Diffusion_In_Solids.ipynb b/Mass_Transfer_Operations_by_R_E_Treybal/4-Diffusion_In_Solids.ipynb new file mode 100644 index 0000000..cf99f83 --- /dev/null +++ b/Mass_Transfer_Operations_by_R_E_Treybal/4-Diffusion_In_Solids.ipynb @@ -0,0 +1,387 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4: Diffusion In Solids" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.1: Ficks_Law_Diffusio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"\n", +"// Illustration 4.1\n", +"// Page: 89\n", +"\n", +"printf('Illustration 4.1 - Page: 89\n\n');\n", +" \n", +"// solution\n", +"\n", +"//***Data****//\n", +"P = 2;// [atm]\n", +"a1 = 0.025;// [m]\n", +"a2 = 0.050;// [m]\n", +"solub = 0.053*P;// [cubic m H2 (STP)/(cubic m rubber)]\n", +"Ca1 = solub/22.41;// inner surface of the pipe\n", +"Ca2 = 0;// resistance to difusion of H2 away from the surface is negligible.\n", +"Da = 1.8*10^(-10);// [square m/s]\n", +"l = 1;// [m]\n", +"//********//\n", +"\n", +"z = (a2-a1)/2;// [m]\n", +"// Using Eqn. 4.4\n", +"Sav = (2*(%pi)*l*(a2-a1))/(2*log(a2/a1));// [square m]\n", +"// Using Eqn. 4.3\n", +"w = (Da*Sav*(Ca1-Ca2))/z;// [kmol H2/s for 1m length]\n", +"w = w*2.02*10^3*3600;// [g H2/m.h]\n", +"printf('The rate of loss of H2 by diffusion per m of pipe length: %e g H2/m.h',w);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.2: Unsteady_State_Diffusion.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"\n", +"// Illustration 4.2\n", +"// Page: 92\n", +"\n", +"printf('Illustration 4.2 - Page: 92\n\n');\n", +"printf('Illustration 4.2 (a)\n\n');\n", +"\n", +"// solution (a)\n", +"\n", +"// Given\n", +"a = 3/2;// [cm]\n", +"thetha = 68*3600;// [s]\n", +"// Ca can e calculated in terms of g/100 cubic cm\n", +"Cao = 5;// [g/100 cubic cm]\n", +"Ca_thetha = 3;// [g/100 cubic cm]\n", +"Ca_Inf = 0;// [g/100 cubic cm]\n", +"//**********//\n", +"\n", +"E = (Ca_thetha-Ca_Inf)/(Cao-Ca_Inf);\n", +"// E = 0.6;\n", +"// From Fig. 4.2 (Pg 91): For diffusion from only one exposed surface D*thetha/(4*a^2) = 0.128\n", +"D = 0.128*4*(a^2)/thetha;// [square cm/s]\n", +"D = D*10^(-4);// [square m/s]\n", +"printf('Diffusivity of urea in gel from only one exposed durface: %e square m/s\n\n',D);\n", +"\n", +"printf('Illustration 4.2 (b)\n\n');\n", +"\n", +"// Solution (b)\n", +"\n", +"//****Data****//\n", +"// Ca can e calculated in terms of g/100 cubic cm\n", +"Cao = 5;// [g/100 cubic cm]\n", +"Ca_thetha = 1;// [g/100 cubic cm]\n", +"Ca_Inf = 0;// [g/100 cubic cm]\n", +"//*********//\n", +"\n", +"E = (Ca_thetha-Ca_Inf)/(Cao-Ca_Inf);\n", +"// E = 0.2;\n", +"// From Fig. 4.2 (Pg 91): For diffusion from only one exposed surface D*thetha/(4*a^2) = 0.568\n", +"D = 4.70*10^(-6);// From Illusration 4.2(a) [square cm/s]\n", +"thetha = 0.568*4*a^2/D;// [s]\n", +"thetha = thetha/3600;// [h]\n", +"printf('The time taken for the avg. conc. to fall to 1g/100 cubic cm is:%f h\n\n',thetha);\n", +"\n", +"printf('Illustration 4.2 (c)\n\n');\n", +"\n", +"// solution (c)\n", +"\n", +"//****Data*****//\n", +"Cao = 5;// [g/100 cubic cm]\n", +"Ca_thetha = 1;// [g/100 cubic cm]\n", +"Ca_Inf = 0;// [g/100 cubic cm]\n", +"//*******//\n", +"\n", +"E = (Ca_thetha-Ca_Inf)/(Cao-Ca_Inf);\n", +"// E = 0.2;\n", +"// From Fig. 4.2: For diffusion from two opposite exposed surface D*thetha/(a^2) = 0.568\n", +"D = 4.70*10^(-6);// From Illusration 4.2(a) [square cm/s]\n", +"thetha = 0.568*(a^2)/D;// [s]\n", +"thetha = thetha/3600;// [h]\n", +"printf('The time taken for the avg. conc. to fall to 1g/100 cubic cm is:%f h',thetha);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.3: Diffusion_through_Polymers.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"\n", +"// Illustration 4.3\n", +"// Page: 94\n", +"\n", +"printf('Illustration 4.3 - Page: 94\n\n');\n", +"\n", +"// solution \n", +"\n", +"//****Data****//\n", +"z = 0.1;// [cm]\n", +"pa1 = 1;// [cmHg]\n", +"pa2 = 0;// [cmHg]\n", +"Da = 1.1*10^(-10)*10^4;// [square cm/s]\n", +"//***********//\n", +"\n", +"// Solubility coeffecient in terms of Hg\n", +"Sa = 0.90/76;// [cubic cm gas (STP)/cubic cm.cmHg]\n", +"// Using Eqn. 4.15\n", +"Va = (Da*Sa*(pa1-pa2))/z;// [cubic cm(STP)/square cm.s]\n", +"// Using Eqn. 4.16\n", +"P = Da*Sa;// [cubic cm gas (STP)/square cm.s.(cmHg/cm)]\n", +"printf('The rate of diffusion of CO is:%e cubic cm(STP)/square cm.s\n',Va);\n", +"printf('The permeability of the membrane is %e cubic cm gas (STP)/square cm.s.(cmHg/cm)',P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.4: Diffusion_in_Porous_Solids.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"\n", +"// Illustration 4.4\n", +"// Page: 96\n", +"\n", +"printf('Illustration 4.4 - Page: 96\n\n');\n", +"\n", +"// solution\n", +"\n", +"//****Data****//\n", +"a = 0.005;// [m]\n", +"// For the KCl diffusion\n", +"Dab1 = 1.84*10^(-9);// [square m/s]\n", +"thetha = 4.75*3600;// [s]\n", +"Ca_Inf = 0;\n", +"// For K2CrO4 diffusion\n", +"Cao = 0.28;// [g/cubic cm]\n", +"Ca_Inf = 0.002;// [g/cubic cm]\n", +"Dab2 = 1.14*10^(-9);// [square m/s]\n", +"//*******//\n", +"\n", +"E = 0.1;// For 90% removal of KCl\n", +"// From Fig. 4.2 (Pg 91): Deff*thetha/a^2 = 0.18\n", +"Deff = 0.18*a^2/thetha;// [square m/s]\n", +"Dab_by_Deff = Dab1/Deff;\n", +"Ca_thetha = 0.1*0.28;// [g/cubic cm]\n", +"Es = (Ca_thetha-Ca_Inf)/(Cao-Ca_Inf);\n", +"// From Fig. 4.2 (Pg 91): Deff*thetha/a^2 = 0.30\n", +"Deff = Dab2/Dab_by_Deff;// [square m/s]\n", +"thetha = 0.3*a^2/Deff;// [s]\n", +"thetha = thetha/3600;// [h]\n", +"printf('The time reqd. is:%f h',thetha);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.5: Diffusion_in_Porous_Solids.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"\n", +"// Illustration 4.5\n", +"// Page: 98\n", +"printf('Illustration 4.5 - Page: 98\n\n');\n", +"printf('Illustration 4.5 (a)\n\n');\n", +"\n", +"// solution (a)\n", +"\n", +"//****Data****//\n", +"// a = H2 b = N2\n", +"Dab_eff = 5.3*10^(-6);// [square m/s]\n", +"Dkb_eff = 1.17*10^(-5);// [square m/s]\n", +"Dab = 7.63*10^(-5);// [square m/s]\n", +"//*******//\n", +"\n", +"R = 8314;//[Nm/kmol]\n", +"Mb = 2.02;// [kg/kmol]\n", +"T = 293;// [K]\n", +"Dtrue_by_Deff = Dab/Dab_eff;\n", +"// Since the ratio is strictly a matter of the geometry of the solid.\n", +"Dkb = Dkb_eff*Dtrue_by_Deff;// [square m/s]\n", +"// From Eqn. 4.20\n", +"d = 3*Dkb*((%pi*Mb)/(8*R*T))^0.5;// [m]\n", +"printf('The equivalent pore diameter is: %e m\n\n',d);\n", +"\n", +"printf('Illustration 4.5 (b)\n\n');\n", +"\n", +"// Solution (b)\n", +"\n", +"//****Data*****//\n", +"// a = O2 b = N2 c = H2\n", +"Ya1 = 0.8;\n", +"Ya2 = 0.2;\n", +"Pt = 10133;// [N/square m]\n", +"z = 0.002;// [m]\n", +"T = 293;// [K]\n", +"//*******//\n", +"\n", +"// From Table 2.1 (Pg 31):\n", +"Dab = 1.81*10^(-5);// [square m/s] at STP\n", +"Dkc = 1.684*10^(-4);// [square m/s] From Illustration 4.5(a)\n", +"Mc = 2.02;// [kg/kmol]\n", +"Ma = 32;// [kg/kmol]\n", +"Mb = 28.02;// [kg/kmol]\n", +"Dab = Dab*(1/0.1)*((293/273)^1.5);// [square m/s] at 0.1 atm & 20 C\n", +"DabEff = Dab/14.4;// [square m/s] From Illustration 4.5(a)\n", +"Dka = Dkc*((Mc/Ma)^0.5);// [square m/s]\n", +"DkaEff = Dka/14.4;// [square m/s]\n", +"Nb_by_Na = -(Ma/Mb)^0.5;\n", +"// Na/(Na+Nb) = 1/(1+(Nb/Na))\n", +"Na_by_NaSumNb = 1/(1+(Nb_by_Na));\n", +"DabEff_by_DkaEff = DabEff/DkaEff;\n", +"// By Eqn. 4.23\n", +"Na = (Na_by_NaSumNb)*(DabEff*Pt/(R*T*z))*log((((Na_by_NaSumNb)*(1+DabEff_by_DkaEff))-Ya2)/(((Na_by_NaSumNb)*(1+DabEff_by_DkaEff))-Ya1));// [kmol/square m.s]\n", +"Nb = Na*(Nb_by_Na);// [kmol/square m.s]\n", +"printf('Diffusion flux of O2 is %e kmol/square m.s\n',Na);\n", +"printf('Diffusion flux of N2 is %e kmol/square m.s\n',Nb);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.6: Hydrodynamic_flow_of_gases.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"\n", +"// Illustration 4.6\n", +"// Page: 100\n", +"\n", +"printf('Illustration 4.6 - Page: 100\n\n');\n", +"\n", +"// solution\n", +"\n", +"//***Data***//\n", +"// a = N2\n", +"// For N2 at 300K\n", +"viscosity1 = 1.8*10^(-5);// [kg/m.s]\n", +"Pt1 = 10133;// [N/square m.sec]\n", +"T = 300;// [K]\n", +"z = 0.0254;// [m]\n", +"T2 = 393;// [K]\n", +"//***********//\n", +"\n", +"Ma = 28.02;// [kg/kmol]\n", +"R = 8314;// [J/K.kgmol]\n", +"//From Eqn 4.22\n", +"lambda = (3.2*viscosity1/Pt1)*(R*T/(2*(%pi)*Ma))^0.5;\n", +"d = 10^(-4);// [m]\n", +"d_by_lambda = d/lambda;\n", +"// Kundsen flow will not occur\n", +"// N2 flow corresponding to 9 cubic ft/square ft.min at 300K & 1 std atm = 0.0457 cubic m/square m.min\n", +"Na1 = 0.0457*(273/T)*(1/22.41);// [kmol/square m.s]\n", +"Pt1_diff_Pt2 = 2*3386/13.6;// [N/square m]\n", +"Ptav = Pt1+(Pt1_diff_Pt2/2);// [N/square m]\n", +"// From Eqn. 4.26\n", +"k1 = Na1*R*T*z/(Ptav*(Pt1_diff_Pt2));// [m^4/N.s]\n", +"\n", +"//For N2 at 393K\n", +"viscosity2 = 2.2*10^(-5);// [kg/m.s]\n", +"k2 = (k1*viscosity1)/(viscosity2);// [m^4/N.s]\n", +"// From Eqn 4.26\n", +"Na = (k2*Ptav*Pt1_diff_Pt2)/(R*T2*z);// [kmol/square m.s]\n", +"printf('Flow rate to be expected is %e kmol/square m.s',Na);" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |