path: root/Mass_Transfer_Operations_by_R_E_Treybal/8-Gas_Absorption.ipynb

{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 8: Gas Absorption"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.1: Ideal_Liquid_Solutio.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 8.1\n",
"// Page: 278\n",
"\n",
"printf('Illustration 8.1 -  Page: 278\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"P_star = 2*10^(5);// [N/square m]\n",
"X_methane = 0.6;\n",
"X_ethane = 0.2;\n",
"X_propane = 0.08;\n",
"X_nbutane = 0.06;\n",
"X_npentane = 0.06;\n",
"//******//\n",
"\n",
"MoleFraction = [0.6 0.2 0.08 0.06 0.06]\n",
"Heading = ['Component' 'Equilibrium Partial Pressure' 'Vapour Pressue    ' 'Mole Fraction'];\n",
"Component = ['Methane' 'Ethane   ' 'Propane' 'n-Butane' 'n-Pentane'];\n",
"VapPressure = [0 42.05 8.96 2.36 0.66];// [N/square m]\n",
"Sum = 0;\n",
"for i = 1:4\n",
"    printf('%s \t',Heading(i));\n",
"end\n",
"printf('\n');\n",
"for i = 1:5\n",
"    printf('%s \t ',Component(i));\n",
"    printf('%e \t \t \t',(MoleFraction(i)*P_star));\n",
"    printf('%e \t \t',(VapPressure(i)*10^(5)));\n",
"    if  (VapPressure(i) =  = 0)\n",
"        printf('\t \n');\n",
"        Sum = Sum+0;\n",
"    else\n",
"         printf('%f \n',(MoleFraction(i)*P_star)/(VapPressure(i)*10^(5)));\n",
"         Sum = Sum+(MoleFraction(i)*P_star)/(VapPressure(i)*10^(5));\n",
"\n",
"end\n",
"end\n",
"printf('Mole Fraction Of solvent Oil is %f',1-Sum);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.2: Minimum_Liquid_Gas_Ratio_for_absorbers.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 8.2\n",
"// Page: 286\n",
"\n",
"printf('Illustration 8.2 - Page: 286\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// Absorber:\n",
"G = 0.250;// [cubic m/s]\n",
"Temp1 = 273+26;// [K]\n",
"Pt = 1.07*10^(5);// [N/square m]\n",
"y1 = 0.02;\n",
"x2 = 0.005;\n",
"//******//\n",
"\n",
"G1 = G*(273/Temp1)*(Pt/(1.0133*10^(5)))*(1/22.41);// [kmol/s]\n",
"Y1 = y1/(1-y1);// [kmol benzene/kmol dry gas]\n",
"Gs = G1*(1-y1);// [kmol dry gas/s]\n",
"// For 95% removal of benzene:\n",
"Y2 = Y1*0.05;\n",
"X2 = x2/(1-x2);// [kmol benzene/kmol oil]\n",
"// Vapour pressure of benzene:\n",
"\n",
"P_star = 13330;// [N/square m]\n",
"X_star = zeros(20);\n",
"Y_star = zeros(20);\n",
"j = 0;\n",
"for i = 0.01:0.01:0.20\n",
"    j = j+1;\n",
"    x = i;\n",
"    X_star(j) = i;\n",
"    deff('[Y] = f27(y)','Y = (y/(1+y))-(P_star/Pt)*(x/(1+x))');\n",
"    Y_star(j) = fsolve(0,f27);\n",
"end\n",
"// For min flow rate:\n",
"X1 = 0.176;// [kmolbenzene/kmol oil]\n",
"DataMinFlow = [X2 Y2;X1 Y1];\n",
"scf(6);\n",
"plot(X_star,Y_star,DataMinFlow(:,1),DataMinFlow(:,2));\n",
"minLs = (Gs*(Y1-Y2)/(X1-X2));// [kmol/s]\n",
"// For 1.5 times the minimum:\n",
"Ls = 1.5*minLs;// [kmol/s]\n",
"X1_prime = (Gs*(Y1-Y2)/Ls)+X2;// [kmol benzene/kmol oil]\n",
"DataOperLine = [X2 Y2;X1_prime Y1];\n",
"plot(X_star,Y_star,DataMinFlow(:,1),DataMinFlow(:,2),DataOperLine(:,1),DataOperLine(:,2));\n",
"xgrid();\n",
"xlabel('moles of benzene / mole wash oil');\n",
"ylabel('moles benzene / mole dry gas');\n",
"legend('Equlibrium Line','Min Flow Rate Line','Operating Line');\n",
"title('Absorption')\n",
"printf('The Oil circulation rate is %e kmol/s\n',Ls);\n",
"\n",
"// Stripping\n",
"Temp2 = 122+273;// [K]\n",
"// Vapour pressure at 122 OC\n",
"P_star = 319.9;// [kN/square m]\n",
"Pt = 101.33;// [kN/square m]\n",
"X_star = zeros(7);\n",
"Y_star = zeros(7);\n",
"j = 0;\n",
"for i = 0:0.1:0.6\n",
"    j = j+1;\n",
"    x = i;\n",
"    X_star(j) = i;\n",
"    deff('[Y] = f28(y)','Y = (y/(1+y))-(P_star/Pt)*(x/(1+x))');\n",
"    Y_star(j) = fsolve(0,f28);\n",
"end\n",
"X1 = X2;// [kmol benzene/kmol oil]\n",
"X2 = X1_prime;// [kmol benzene/kmol oil]\n",
"Y1 = 0;// [kmol benzene/kmol steam]\n",
"// For min. steam rate:\n",
"Y2 = 0.45;\n",
"DataMinFlow = [X2 Y2;X1 Y1];\n",
"minGs = Ls*(X2-X1)/(Y2-Y1);// [kmol steam/s]\n",
"slopeOperat = 1.5*(Y2-Y1)/(X2-X1);\n",
"deff('[y] = f29(x)','y = slopeOperat*(x-X1)+Y1');\n",
"x = 0:0.01:0.14;\n",
"scf(7);\n",
"plot(Y_star,X_star,DataMinFlow(:,1),DataMinFlow(:,2),x,f29);\n",
"xgrid();\n",
"xlabel('moles of benzene / mole wash oil');\n",
"ylabel('moles benzene / mole dry gas');\n",
"legend('Equlibrium Line','Min Flow Rate Line','Operating Line');\n",
"title('Stripping');\n",
"printf('The Steam circulation rate is %e kmol/s\n',1.5*minGs);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.3: Countercurrent_Multistage_Operation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 8.3\n",
"// Page: 292\n",
"\n",
"printf('Illustration 8.3 - Page: 292\n\n');\n",
"\n",
"// solution\n",
"\n",
"// Since tower is a tray device:\n",
"// Following changes in notation is made:\n",
"// L1 to LNp\n",
"// L2 to L0\n",
"// X1 to XNp\n",
"// X2 to X0\n",
"// G1 to GNpPlus1\n",
"// G2 to G1\n",
"// Y1 to YNpPlus1\n",
"// Y2 to Y1\n",
"// x1 to xNp\n",
"// x2 to x0\n",
"// y1 to yNpPlus1\n",
"// y2 to y1\n",
"// From Illustration 8.2:\n",
"yNpPlus1 = 0.02;\n",
"Y1 = 0.00102;\n",
"y1 = Y1/(1+Y1);\n",
"GNpPlus1 = 0.01075;// [kmol/s]\n",
"x0 = 0.005;\n",
"m = 0.125;// [m = y_star/x]\n",
"Ls = 1.787*10^(-3);// [kmol/s]\n",
"Gs = 0.01051;// [kmol/s]\n",
"XNp = 0.1190;\n",
"LNp = Ls*(1+XNp);// [kmol/s]\n",
"ANp = LNp/(m*GNpPlus1);\n",
"X0 = x0/(1-x0);\n",
"L0 = Ls*(1+X0);// [kmol/s]\n",
"G1 = Gs*(1+Y1);// [kmol/s]\n",
"A1 = L0/(m*G1);\n",
"A = (ANp*A1)^0.5;\n",
"// From Eqn. 5.55:\n",
"Np = (log((yNpPlus1-(m*x0))/(y1-(m*x0))*(1-(1/A))+(1/A)))/log(A);\n",
"printf('Absorber\n');\n",
"printf('From Analytical Method, no. of theoretical trays required is %f \n',Np);\n",
"// From Fig. 8.13 (Pg292):\n",
"Np = 7.6;\n",
"printf('From Graphical Method, no. of theoretical trays required is %f \n',Np);\n",
"\n",
"// Stripper\n",
"SNp = 1/ANp;\n",
"S1 = 1/A1;\n",
"// Due to relative nonconstancy of the stripping factor,graphical method should be used.\n",
"printf('Stripper\n');\n",
"// From Fig. 8.11 (Pg 289):\n",
"Np = 6.7;\n",
"printf('From Graphical Method, no. of theoretical trays required is %f \n',Np);\n",
"// From Fig. 5.16 (Pg 129):\n",
"Np = 6.0;\n",
"printf('From Fig. 5.16, no. of theoretical trays required is %f \n',Np);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.4: Nonisothermal_Operation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 8.4\n",
"// Page: 295\n",
"\n",
"printf('Illustration 8.4 - Page: 295\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// a = CH4 b = C5H12\n",
"Tempg = 27;// [OC]\n",
"Tempo = 0;// [base temp,OC]\n",
"Templ = 35;// [OC]\n",
"xa = 0.75;// [mole fraction of CH4 in gas]\n",
"xb = 0.25;// [mole fraction of C5H12 in gas]\n",
"M_Paraffin = 200;// [kg/kmol]\n",
"hb = 1.884;// [kJ/kg K]\n",
"//********//\n",
"\n",
"Ha = 35.59;// [kJ/kmol K]\n",
"Hbv = 119.75;// [kJ/kmol K]\n",
"Hbl = 117.53;// [kJ/kmol K]\n",
"Lb = 27820;// [kJ/kmol]\n",
"// M = [Temp (OC) m]\n",
"M = [20 0.575;25 0.69;30 0.81;35 0.95;40 1.10;43 1.25];\n",
"// Basis: Unit time\n",
"GNpPlus1 = 1;// [kmol]\n",
"yNpPlus1 = 0.25;// [kmol]\n",
"HgNpPlus1 = ((1-yNpPlus1)*Ha*(Tempg-Tempo))+(yNpPlus1*(Hbv*(Tempg-Tempo)+Lb));// [kJ/kmol]\n",
"L0 = 2;// [kmol]\n",
"x0 = 0;// [kmol]\n",
"HL0 = ((1-x0)*hb*M_Paraffin*(Templ-Tempo))+(x0*hb*(Templ-Tempo));// [kJ/kmol]\n",
"C5H12_absorbed = 0.98*xb;// [kmol]\n",
"C5H12_remained = xb-C5H12_absorbed;\n",
"G1 = xa+C5H12_remained;// [kmol]\n",
"y1 = C5H12_remained/G1;// [kmol]\n",
"LNp = L0+C5H12_absorbed;// [kmol]\n",
"xNp = C5H12_absorbed/LNp;// [kmol]\n",
"// Assume:\n",
"Temp1 = 35.6;// [OC]\n",
"Hg1 = ((1-y1)*Ha*(Temp1-Tempo))+(y1*(Hbv*(Temp1-Tempo)+Lb));// [kJ/kmol]\n",
"\n",
"// Eqn. 8.11:\n",
"Qt = 0;\n",
"deff('[y] = f30(HlNp)','y = ((L0*HL0)+(GNpPlus1*HgNpPlus1))-((LNp*HlNp)+(G1*Hg1)+Qt)');\n",
"HlNp = fsolve(2,f30);\n",
"\n",
"deff('[y] = f31(TempNp)','y = HlNp-(((1-x0)*hb*M_Paraffin*(TempNp-Tempo))+(x0*hb*(TempNp-Tempo)))');\n",
"TempNp = fsolve(35.6,f31);\n",
"// At Temp = TempNp:\n",
"mNp = 1.21;\n",
"yNp = mNp*xNp;// [kmol]\n",
"GNp = G1/(1-yNp);// [kmol]\n",
"HgNp = ((1-yNp)*Ha*(TempNp-Tempo))+(yNp*(Hbv*(TempNp-Tempo)+Lb));// [kJ/kmol]\n",
"// Eqn. 8.13 with n = Np-1\n",
"deff('[y] = f32(LNpMinus1)','y = LNpMinus1+GNpPlus1-(LNp+GNp)');\n",
"LNpMinus1 = fsolve(2,f32);// [kmol]\n",
"\n",
"// Eqn. 8.14 with n = Np-1\n",
"deff('[y] = f33(xNpMinus1)','y = ((LNpMinus1*xNpMinus1)+(GNpPlus1*yNpPlus1))-((LNp*xNp)+(GNp*yNp))');\n",
"xNpMinus1 = fsolve(0,f33);// [kmol]\n",
"\n",
"// Eqn. 8.15 with n = Np-1\n",
"deff('[y] = f34(HlNpMinus1)','y = ((LNpMinus1*HlNpMinus1)+(GNpPlus1*HgNpPlus1))-((LNp*HlNp)+(GNp*HgNp))');\n",
"HlNpMinus1 = fsolve(0,f34);// [kJ/kmol]\n",
"deff('[y] = f35(TempNpMinus1)','y = HlNpMinus1-(((1-xNpMinus1)*hb*M_Paraffin*(TempNpMinus1-Tempo))+(xNpMinus1*hb*(TempNpMinus1-Tempo)))');\n",
"TempNpMinus1 = fsolve(42,f35);// [OC]\n",
"\n",
"// Thecomputation are continued upward through the tower in this manner until the gas composition falls atleast to 0.00662.\n",
"// Results = [Tray No.(n) Tn(OC) xn yn]\n",
"Results = [4.0 42.3 0.1091 0.1320;3 39.0 0.0521 0.0568;2 36.8 0.0184 0.01875;1 35.5 0.00463 0.00450];\n",
"scf(8);\n",
"plot(Results(:,1),Results(:,4));\n",
"xgrid();\n",
"xlabel('Tray Number');\n",
"ylabel('mole fraction of C5H12 in gas');\n",
"\n",
"scf(9);\n",
"plot(Results(:,1),Results(:,2));\n",
"xgrid();\n",
"xlabel('Tray Number');\n",
"ylabel('Temparature(OC)');\n",
"\n",
"// For the cquired y1\n",
"Np = 3.75;\n",
"printf('The No. of trays will be %f',Np);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.5: Real_Trays_and_Tray_Efficiency.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 8.5\n",
"// Page: 299\n",
"\n",
"printf('Illustration 8.5 - Page: 299\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// a = NH3 b = H2 c = N2 w = water\n",
"P = 2;// [bars]\n",
"Temp = 30;// [OC]\n",
"L = 6.38;// [kg/s]\n",
"W = 0.53;// [weir length,m]\n",
"pitch = 12.5/1000;// [m]\n",
"D = 0.75;// [Tower diameter,m]\n",
"hW = 0.060;// [weir height,m]\n",
"t = 0.5;// [tray spacing,m]\n",
"//*******//\n",
"\n",
"// From Geometry of Tray Arrangement:\n",
"At = 0.4418;// [Tower Cross section,square m]\n",
"Ad = 0.0403;// [Downspout Cross section,square m]\n",
"An = At-Ad;// [square m]\n",
"Ao = 0.0393;// [perforation area,square m]\n",
"Z = 0.5307;// [distance between downspouts,square m]\n",
"z = (D+W)/2;// [average flow width,m]\n",
"h1 = 0.04;// [weir crest,m]\n",
"// From Eqn. 6.34\n",
"Weff = W*(sqrt(((D/W)^2)-((((D/W)^2-1)^0.5)+((2*h1/D)*(D/W)))^2));// [m]\n",
"q = Weff*(1.839*h1^(3/2));//[cubic m/s]\n",
"// This is a recommended rate because it produces the liquid depth on the tray to 10 cm.\n",
"Density_L = 996;// [kg/s]\n",
"Mw = 18.02;// [kg/kmol]\n",
"L1 = 6.38/Mw;// [kmol/s]\n",
"Ma = 17.03;// [kg/kmol]\n",
"Mb = 28.02;// [kg/kmol]\n",
"Mc = 2.02;// [kg/kmol]\n",
"MavG = (0.03*Ma)+(0.97*(1/4)*Mb)+(0.97*(3/4)*Mc);// [kg/kmol]\n",
"Density_G = (MavG/22.41)*(P/0.986)*(273/(273+Temp));// [kg/cubic m]\n",
"G = 0.893;// [kg/s]\n",
"sigma = 68*10^(-3);// [N/m]\n",
"abcissa = (L/G)*(Density_G/Density_L)^0.5;\n",
"// From Table 6.2 (Pg169):\n",
"alpha = 0.04893;\n",
"beeta = 0.0302;\n",
"// From Eqn. 6.30\n",
"Cf = ((alpha*log10(1/abcissa))+beeta)*(sigma/0.02)^0.2;\n",
"// From Eqn. 6.29\n",
"Vf = Cf*((Density_L-Density_G)/Density_G)^(1/2);// [m/s]\n",
"// 80% of flooding value:\n",
"V = 0.8*Vf;// [m/s]\n",
"G = 0.8*G;// [kg/s]\n",
"G1 = G/MavG;// [kmol/s]\n",
"Vo = V*An/Ao;// [m/s]\n",
"l = 0.002;// [m]\n",
"Do = 0.00475;// [m]\n",
"// From Eqn. 6.37\n",
"Co = 1.09*(Do/l)^0.25;\n",
"viscosity_G = 1.13*10^(-5);// [kg/m.s]\n",
"Reo = Do*Vo*Density_G/viscosity_G;\n",
"// At Reynold's No. = Reo\n",
"fr = 0.0082;\n",
"g = 9.81;// [m/s^2]\n",
"// From Eqn. 6.36\n",
"deff('[y] = f36(hD)','y = (2*hD*g*Density_L/(Vo^2*Density_G))-(Co*(0.40*(1.25-(Ao/An))+(4*l*fr/Do)+(1-(Ao/An))^2))');\n",
"hD = fsolve(1,f36);\n",
"// From Eqn. 6.31;\n",
"Aa = (Ao/0.907)*(pitch/Do)^2;// [square m]\n",
"Va = V*An/Aa;// [m/s]\n",
"// From Eqn. 6.38\n",
"hL = 6.10*10^(-3)+(0.725*hW)-(0.238*hW*Va*(Density_G)^0.5)+(1.225*q/z);// [m]\n",
"// From Eqn. 6.42\n",
"hR = 6*sigma/(Density_L*Do*g);// m\n",
"// From Eqn. 6.35\n",
"hG = hD+hL+hR;// [m]\n",
"Al = 0.025*W;// [square m]\n",
"Ada = min(Al,Ad);\n",
"// From Eqn. 6.43\n",
"h2 = (3/(2*g))*(q/Ada)^2;// [m]\n",
"// From Eqn.6.44\n",
"h3 = hG+h2;\n",
"// since hW+h1+h3 is essentially equal to t/2, flooding will not occur\n",
"abcissa = (L/G)*(Density_G/Density_L)^0.5;\n",
"V_by_Vf = V/Vf;\n",
"// From Fig.6.17, V/Vf = 0.8 & abcissa = 0.239\n",
"E = 0.009;\n",
"\n",
"// At the prevailing conditions:\n",
"Dg = 2.296*10^(-5);// [square m/s]\n",
"viscosity_G = 1.122*10^(-5);// [kg/m.s]\n",
"ScG = viscosity_G/(Density_G*Dg)\n",
"Dl = 2.421*10^(-9);// [square m/s]\n",
"\n",
"// From Henry's Law:\n",
"m = 0.850;\n",
"A = L1/(m*G1);\n",
"\n",
"// From Eqn. 6.61:\n",
"NtG = (0.776+(4.57*hW)-(0.238*Va*Density_G^0.5)+(104.6*q/Z))/(ScG^0.5);\n",
"// From Eqn. 6.64:\n",
"thetha_L = hL*z*Z/q;// [s]\n",
"// From Eqn. 6.62:\n",
"NtL = 40000*(Dl^0.5)*((0.213*Va*Density_G^0.5)+0.15)*thetha_L;\n",
"// From Eqn. 6.52:\n",
"NtoG = 1/((1/NtG)+(1/(A*NtL)));\n",
"// From Eqn. 6.51:\n",
"EoG = 1-exp(-NtoG);\n",
"// From Eqn. 6.63:\n",
"DE = ((3.93*10^(-3))+(0.0171*Va)+(3.67*q/Z)+(0.1800*hW))^2;// [square m/s]\n",
"// From Eqn. 6.59:\n",
"Pe = Z^2/(DE*thetha_L);\n",
"// From Eqn. 6.58:\n",
"eta = (Pe/2)*((1+(4*m*G1*EoG/(L1*Pe)))^0.5-1);\n",
"// From Eqn. 6.57:\n",
"EMG = EoG*(((1-exp(-(eta+Pe)))/((eta+Pe)*(1+(eta+Pe)/eta)))+((exp(eta)-1)/(eta*(1+(eta/(eta+Pe))))));\n",
"// From Eqn. 6.60:\n",
"EMGE = EMG/((1+(EMG*(E/(1-E)))));\n",
"// From Eqn. 8.16:\n",
"EO = log(1+EMGE*((1/A)-1))/log(1/A);\n",
"Np = 14*EO;\n",
"yNpPlus1 = 0.03;\n",
"x0 = 0;\n",
"// From Eqn. 5.54(a):\n",
"deff('[y] = f37(y1)','y = ((yNpPlus1-y1)/(yNpPlus1-m*x0))-(((A^(Np+1))-A)/((A^(Np+1))-1))');\n",
"y1 = fsolve(0.03,f37);\n",
"printf('Mole Fraction Of NH3 in effluent is %e',y1);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.6: Continuous_Contact_Equipment.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 8.6\n",
"// Page: 304\n",
"\n",
"printf('Illustration 8.6 - Page: 304\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****// \n",
"// Gas:\n",
"// In:\n",
"y_prime1 = 0.02;\n",
"Y_prime1 = 0.0204;// [mol/mol dry gas]\n",
"// Out:\n",
"y_prime2 = 0.00102;\n",
"Y_prime2 = 0.00102;// [mol/mol dry gas]\n",
"// Non absorbed gas:\n",
"MavG = 11;// [kg/kmol]\n",
"G = 0.01051;// [kmol/s nonbenzene]\n",
"Gm = 0.01075;// [kmol/s]\n",
"T = 26;// [OC]\n",
"viscosity_G = 10^(-5);// [kg/m.s]\n",
"DaG = 1.30*10^(-5);// [square m/s]\n",
"\n",
"// Liquid:\n",
"// In:\n",
"x_prime2 = 0.005;\n",
"X_prime2 = 0.00503;// [mol benzene/mol oil]\n",
"// Out:\n",
"x_prime1 = 0.1063;\n",
"X_prime1 = 0.1190;// [mol benzene/mol oil]\n",
"// Benzene free oil:\n",
"MavL = 260;// [kg/kmol]\n",
"viscosity_L = 2*10^(-3);// [kg/kmol]\n",
"Density_L = 840;// [kg/cubic cm]\n",
"L = 1.787*10^(-3);// [kmol/s]\n",
"DaL = 4.77*10^(-10);// [square m/s]\n",
"sigma = 0.03;// [N/square m]\n",
"m = 0.1250;\n",
"//*******//\n",
"\n",
"A = 0.47^2*%pi/4;// [square m]\n",
"// At the bottom:\n",
"L_prime1 = ((L*MavL)+(X_prime1*L*78))/A;// [kg/square m.s]\n",
"// At the top\n",
"L_prime2 = ((L*MavL)+(X_prime2*L*78))/A;// [kg/square m.s]\n",
"L_primeav = (L_prime1+L_prime2)/2;// [kg/square m.s]\n",
"// At the bottom\n",
"G_prime1 = ((G*MavG)+(Y_prime1*G*78))/A;// [kg/square m.s]\n",
"// At the top\n",
"G_prime2 = ((G*MavG)+(Y_prime2*G*78))/A;// [kg/square m.s]\n",
"G_primeav = (G_prime1+G_prime2)/2;// [kg/square m.s]\n",
"\n",
"// From Illustration 6.6:\n",
"Fga = 0.0719;// [kmol/cubic cm.s]\n",
"Fla = 0.01377;// [kmol/cubic cm.s]\n",
"// Operating Line:\n",
"X_prime = [0.00503 0.02 0.04 0.06 0.08 0.10 0.1190];\n",
"x_prime = zeros(7);\n",
"Y_prime = zeros(7);\n",
"y_prime = zeros(7);\n",
"for i = 1:7\n",
"    x_prime(i) = X_prime(i)/(1+X_prime(i));\n",
"    deff('[y] = f38(Y_prime)','y = (G*(Y_prime1-Y_prime))-(L*(X_prime1-X_prime(i)))');\n",
"    Y_prime(i) = fsolve(Y_prime1,f38);\n",
"    y_prime(i) = Y_prime(i)/(1+Y_prime(i));\n",
"end\n",
"deff('[y] = f39(x)','y = m*x')\n",
"x = [0:0.01:0.14];\n",
"\n",
"// Interface compositions are determined graphically and according to Eqn. 8.21:\n",
"yi = [0.000784 0.00285 0.00562 0.00830 0.01090 0.01337 0.01580];\n",
"ylog = zeros(7);\n",
"y_by_yDiffyi = zeros(7);\n",
"for i = 1:7\n",
"    ylog(i) = log10(yi(i));\n",
"    y_by_yDiffyi(i) = y_prime(i)/(y_prime(i)-yi(i));\n",
"end\n",
"scf(10);\n",
"plot(x_prime,y_prime,x,f39,x_prime,yi);\n",
"legend('Operating Line','Equilibrium Line','Interface Composition');\n",
"xgrid();\n",
"xlabel('mole fraction of benzene in liquid');\n",
"ylabel('mole fraction of benzene in gas');\n",
"scf(11);\n",
"plot(ylog,y_by_yDiffyi);\n",
"xgrid();\n",
"xlabel('log y');\n",
"ylabel('y/(y-yi)');\n",
"title('Graphical Integration Curve');\n",
"// Area under the curve:\n",
"Ac = 6.556;\n",
"// Eqn. 8.28:\n",
"NtG = (2.303*Ac)+1.152*(log10((1-y_prime2)/(1-y_prime1)));\n",
"Gav = (Gm+(G/(1-Y_prime2)))/(2*A);// [kmol/square m.s]\n",
"HtG = Gav/Fga;// [m]\n",
"Z = HtG*NtG;// [m]\n",
"printf('The depth of packing recquired is %f m',Z);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.7: Overall_height_of_Transfer_Units.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 8.7\n",
"// Page: 312\n",
"\n",
"printf('Illustration 8.7 - Page: 312\n\n');\n",
"\n",
"// solution\n",
"\n",
"// Fom Illustration 8.6:\n",
"y1 = 0.02;\n",
"y2 = 0.00102;\n",
"m = 0.125;\n",
"x2 = 0.005;\n",
"x1 = 0.1063;\n",
"\n",
"// Number of transfer units:\n",
"// Method a:\n",
"y1_star = m*x1;\n",
"y2_star = m*x2;\n",
"yDiffy_star1 = y1-y1_star;\n",
"yDiffy_star2 = y2-y2_star;\n",
"yDiffy_starm = (yDiffy_star1-yDiffy_star2)/log(yDiffy_star1/yDiffy_star2);\n",
"// From Eqn. 8.48:\n",
"NtoG = (y1-y2)/yDiffy_starm;\n",
"printf('NtoG according to Eqn. 8.48: %f\n',NtoG);\n",
"\n",
"// Mehod b:\n",
"// From Illustration 8.3:\n",
"A = 1.424;\n",
"NtoG = (log((((y1-(m*x2))/(y2-(m*x2)))*(1-(1/A)))+(1/A)))/(1-(1/A));\n",
"printf('NtoG according to Eqn. 8.50: %f\n',NtoG);\n",
"\n",
"// Method c:\n",
"// Operating Line:\n",
"// From Illustration 8.3:\n",
"X_prime = [0.00503 0.02 0.04 0.06 0.08 0.10 0.1190];\n",
"x_prime = [0.00502 0.01961 0.0385 0.0566 0.0741 0.0909 0.1063]\n",
"Y_prime = [0.00102 0.00357 0.00697 0.01036 0.01376 0.01714 0.0204];\n",
"y_prime = [0.00102 0.00356 0.00692 0.01025 0.01356 0.01685 0.0200];\n",
"deff('[y] = f2(x)','y = m*x')\n",
"x = [0:0.01:0.14];\n",
"scf(12);\n",
"plot(x_prime,y_prime,x,f2);\n",
"legend('Operating Line','Equilibrium Line',);\n",
"xgrid();\n",
"xlabel('mole fraction of benzene in liquid');\n",
"ylabel('mole fraction of benzene in gas');\n",
"// From graph:\n",
"NtoG = 8.7;\n",
"printf('NtoG from graph: %f\n',NtoG);\n",
"\n",
"// Method d:\n",
"// from Fig 8.10:\n",
"Y_star = [0.000625 0.00245 0.00483 0.00712 0.00935 0.01149 0.01347];\n",
"ordinate = zeros(7);\n",
"for i = 1:7\n",
"    ordinate(i) = 1/(Y_prime(i)-Y_star(i));\n",
"end\n",
"scf(13);\n",
"plot(Y_prime,ordinate);\n",
"xgrid();\n",
"xlabel('Y');\n",
"ylabel('1/(Y-Y*)');\n",
"title('Graphical Integration');\n",
"// Area under the curve:\n",
"Ac = 8.63;\n",
"// From Eqn. 8.36:\n",
"NtoG = Ac+(1/2)*log((1+y2)/(1+y1));\n",
"printf('NtoG from graphical integration: %f\n',NtoG);\n",
"\n",
"// Height of transfer units:\n",
"NtoG = 9.16;\n",
"// From Illustration 6.6:\n",
"Fga = 0.0719;// [kmol/cubic m.s]\n",
"Fla = 0.01377;// [kmol/cubic m.s]\n",
"Gav = 0.0609;// [kmol/square m.s]\n",
"L = 1.787*10^(-3);// [kmol/s]\n",
"X1 = x1/(1-x1);\n",
"X2 = x2/(1-x2);\n",
"Area = 0.1746;// [square m]\n",
"Lav = L*((1+X1)+(1+X2))/(2*Area);\n",
"// From Eqn. 8.24:\n",
"Htg = Gav/Fga;// [m]\n",
"// From Eqn. 8.31:\n",
"Htl = Lav/Fla;// [m]\n",
"// since Solutions are dilute:\n",
"HtoG = Htg+Htl/A;// [m]\n",
"printf('HtoG: %f m\n',HtoG);\n",
"Z = HtoG*NtoG;// [m]\n",
"printf('The depth of packing recquired is %f m',Z);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.8: Adiabatic_Absorption_and_Stripping.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 8.8\n",
"// Page: 317\n",
"\n",
"printf('Illustration 8.8 - Page: 317\n\n');\n",
"\n",
"// Solution\n",
"\n",
"//***Data***\n",
"// a:NH3 b:air c:H2O\n",
"ya = 0.416;// [mole fraction]\n",
"yb = 0.584;// [mole fraction]\n",
"G1 = 0.0339;// [kmol/square m.s]\n",
"L1 = 0.271;// [kmol/square m.s]\n",
"TempG1 = 20;// [OC]\n",
"//********//\n",
"\n",
"// At 20 OC\n",
"Ca = 36390;// [J/kmol]\n",
"Cb = 29100;// [J/kmol]\n",
"Cc = 33960;// [J/kmol]\n",
"lambda_c = 44.24*10^6;// [J/kmol]\n",
"// Enthalpy base = NH3 gas, H2O liquid, air at 1 std atm.\n",
"Tempo = 20;// [OC]\n",
"lambda_Ao = 0;// [J/kmol]\n",
"lambda_Co = 44.24*10^6;// [J/kmol]\n",
"\n",
"// Gas in:\n",
"Gb = G1*yb;// [kmol air/square m.s]\n",
"Ya1 = ya/(1-ya);// [kmol NH3/kmol air]\n",
"yc1 = 0;// [mole fraction]\n",
"Yc1 = yc1/(1-yc1);// [kmol air/kmol NH]\n",
"// By Eqn 8.58:\n",
"Hg1 = (Cb*(TempG1-Tempo))+(Ya1*(Ca*(TempG1-Tempo))+lambda_Ao)+(Yc1*(Cc*(TempG1-Tempo)+lambda_Co));// [J/kmol air]\n",
"\n",
"// Liquid in:\n",
"xa1 = 0;// [mole fraction]\n",
"xc1 = 1;// [mole fraction]\n",
"Hl1 = 0;// [J/kmol air]\n",
"\n",
"//Gas out:\n",
"Ya2 = Ya1*(1-0.99);// [kmol NH3/kmol air]\n",
"// Assume:\n",
"TempG2 = 23.9;// [OC]\n",
"yc2 = 0.0293;\n",
"deff('[y] = f(Yc2)','y = yc2-(Yc2/(Yc2+Ya2+1))');\n",
"Yc2 = fsolve(0.002,f);// [kmol H2O/kmol air]\n",
"Hg2 = (Cb*(TempG2-Tempo))+(Ya2*(Ca*(TempG2-Tempo))+lambda_Ao)+(Yc2*(Cc*(TempG2-Tempo)+lambda_Co));// [J/kmol air]\n",
"\n",
"// Liquid out:\n",
"Lc = L1-(Yc1*Gb);// [kmol/square m.s]\n",
"La = Gb*(Ya1-Ya2);// [kmol/square m.s]\n",
"L2 = La+Lc;// [kmol/square m.s]\n",
"xa = La/L2;\n",
"xc = Lc/L2;\n",
"// At xa & tempo = 20 OC\n",
"delta_Hs = -1709.6*1000;// [J/kmol soln]\n",
"\n",
"// Condition at the bottom of the tower:\n",
"// Assume:\n",
"TempL = 41.3;// {OC}\n",
"// At(TempL+TempG1)/2:\n",
"Cl = 75481;// [J/kmol]\n",
"deff('[y] = f40(Cl)','y = Hl1+Hg1-((Gb*Hg2)+(L2*(Cl*(TempL-Tempo)+delta_Hs)))');\n",
"Cl = fsolve(7,f40);// [J/kmol.K]\n",
"\n",
"// For the Gas:\n",
"MavG = 24.02;// [kg/kmol]\n",
"Density_G = 0.999;// [kg/cubic m]\n",
"viscosity_G  =  1.517*10^(-5);// [kg/m.s]\n",
"kG  =  0.0261;// [W/m.K]\n",
"CpG  =  1336;// [J/kg.K]\n",
"Dab  =  2.297*10^(-5);// [square m/s]\n",
"Dac  =  3.084*10^(-5);// [square m/s]\n",
"Dcb  =  2.488*10^(-5);// [square m/s]\n",
"PrG  =  CpG*viscosity_G/kG;\n",
"\n",
"// For the liquid:\n",
"MavL  =  17.97;// [kg/kmol]\n",
"Density_L  =  953.1;// [kg/cubic m]\n",
"viscosity_L  =  6.408*10^(-4);// [kg/m.s]\n",
"Dal  =  3.317*10^(-9);// [square m/s]\n",
"kl = 0.4777;// [W/m.K]\n",
"ScL = viscosity_L/(Density_L*Dal);\n",
"PrL = 5.72;\n",
"sigma = 3*10^(-4);\n",
"G_prime = G1*MavG;// [kg/square m.s]\n",
"L_prime = L2*MavL;// [kg/square m.s]\n",
"// From data of Chapter 6:\n",
"Ds = 0.0472;// [m]\n",
"a = 57.57;// [square m/cubic m]\n",
"shiLt = 0.054;\n",
"e = 0.75;\n",
"// By Eqn. 6.71:\n",
"eLo = e-shiLt;\n",
"// By Eqn. 6.72:\n",
"kL = (25.1*Dal/Ds)*(Ds*L_prime/viscosity_L)^0.45*ScL^0.5;// [m/s]\n",
"c = Density_L/MavL;// [kmol/cubic m]\n",
"Fl = kL*c;// [kmol/cubic m]\n",
"// The heat mass transfer analogy of Eqn. 6.72:\n",
"hL = (25.1*kl/Ds)*(Ds*L_prime/viscosity_L)^0.45*PrL^0.5;// [m/s]\n",
"// The heat transfer analogy of Eqn. 6.69:\n",
"hG = (1.195*G_prime*CpG/PrG^(2/3))*(Ds*G_prime/(viscosity_G*(1-eLo)))^(-0.36);// [W/square m.K]\n",
"// To obtain the mass transfer coeffecients:\n",
"Ra = 1.4;\n",
"Rc = 1-Ra;\n",
"// From Eqn. 8.83:\n",
"Dam = (Ra-ya)/(Ra*((yb/Dab)+((ya+yc1)/Dac))-(ya/Dac));// [square m/s]\n",
"Dcm = (Rc-yc1)/(Rc*((yb/Dcb)+((ya+yc1)/Dac))-(yc1/Dac));// [square m/s]\n",
"ScGa = viscosity_G/(Density_G*Dam);\n",
"ScGc = viscosity_G/(Density_G*Dcm);\n",
"// By Eqn. 6.69:\n",
"FGa = (1.195*G1/ScGa^(2/3))*(Ds*G_prime/(viscosity_G*(1-eLo)))^(-0.36);// [kmol/square m.K]\n",
"FGc = (1.195*G1/ScGc^(2/3))*(Ds*G_prime/(viscosity_G*(1-eLo)))^(-0.36);// [kmol/square m.K]\n",
"Ra = Ra-0.1;\n",
"// From Eqn. 8.80:\n",
"scf(14);\n",
"for i = 1:3\n",
"    deff('[yai] = f41(xai)','yai = Ra-(Ra-ya)*((Ra-xa)/(Ra-xai))^(Fl/FGa)');\n",
"    xai = xa:0.01:0.10;\n",
"    plot(xai,f41)\n",
"    Ra = Ra+0.1;\n",
"end\n",
"xgrid();\n",
"xlabel('Mole fraction NH3 in the liquid, xa');\n",
"ylabel('Mole fraction NH3 in the gas ya');\n",
"title('Operating Line curves');\n",
"Rc = Rc-0.1;\n",
"// From Eqn. 8.81:\n",
"scf(15);\n",
"for i = 1:3\n",
"    deff('[yci] = f42(xci)','yci = Rc-(Rc-yc1)*((Rc-xc)/(Rc-xci))^(Fl/FGc)');\n",
"    xci = xc:-0.01:0.85;\n",
"    plot(xci,f42)\n",
"    Rc = Rc+0.1;\n",
"end\n",
"xgrid();\n",
"xlabel('Mole fraction H2O in the liquid, xc');\n",
"ylabel('Mole fraction H2O in the gas, yc');\n",
"title('Operating line Curves');\n",
"// Assume:\n",
"Tempi = 42.7;// [OC]\n",
"// The data of Fig. 8.2 (Pg 279) & Fig 8.4 (Pg 319) are used to draw the eqb curve of Fig 8.25 (Pg 320).\n",
"// By interpolation of operating line curves with eqb line and the condition: xai+xci = 1;\n",
"Ra = 1.38;\n",
"Rc = 1-Ra;\n",
"xai = 0.0786;\n",
"yai = f41(xai);\n",
"xci = 1-xai;\n",
"yci = f42(xci);\n",
"// From Eqn. 8.77:\n",
"dYa_By_dZ = -(Ra*FGa*a/Gb)*log((Ra-yai)/(Ra-ya));// [kmol H2O/kmol air]\n",
"// From Eqn. 8.78:\n",
"dYc_By_dZ = -(Rc*FGc*a/Gb)*log((Rc-yci)/(Rc-yc1));// [kmol H2O/kmol air]\n",
"// From Eqn. 8.82:\n",
"hGa_prime = -(Gb*((Ca*dYa_By_dZ)+(Cc*dYc_By_dZ)))/(1-exp(Gb*((Ca*dYa_By_dZ)+(Cc*dYc_By_dZ))/(hG*a)));// [W/cubic m.K]\n",
"// From Eqn. 8.79:\n",
"dtG_By_dZ = -(hGa_prime*(TempG1-Tempi))/(Gb*(Cb+(Ya1*Ca)+(Yc1*Cc)));// [K/m]\n",
"// When the curves of Fig. 8.2 (pg 279) & 8.24 (Pg 319) are interpolated for concentration xai and xci, the slopes are:\n",
"mar = 0.771;\n",
"mcr = 1.02;\n",
"lambda_c = 43.33*10^6;// [J/kmol]\n",
"// From Eqn. 8.3:\n",
"Hai = Ca*(Tempi-Tempo)+lambda_Ao-(mar*lambda_c);// [J/kmol]\n",
"Hci = Cc*(Tempi-Tempo)+lambda_Co-(mcr*lambda_c);// [J/kmol]\n",
"// From Eqn. 8.76\n",
"Tempi2 = TempL+(Gb/(hL*a))*(((Hai-Ca*(TempG1-Tempo)-lambda_Ao)*dYa_By_dZ)+((Hci-Cc*(TempG1-Tempo)-lambda_Co)*dYc_By_dZ)-((Cb+(Ya1*Ca)+(Yc1*Cc))*dtG_By_dZ));// [OC]\n",
"// The value of Tempi obtained is sufficiently close to the value assumed earlier.\n",
"\n",
"deltaYa=-0.05;\n",
"// An interval of deltaYa up the tower\n",
"deltaZ = deltaYa/(dYa_By_dZ);// [m]\n",
"deltaYc = (dYc_By_dZ*deltaZ);\n",
"// At this level:\n",
"Ya_next = Ya1+deltaYa;// [kmol/kmol air]\n",
"Yc_next = Yc1+deltaYc;// [kmol H2O/kmol air]\n",
"tG_next = TempG1+(dtG_By_dZ*deltaZ);// [OC]\n",
"L_next = L1+Gb*(deltaYa+deltaYc);// [kmol/square m.s]\n",
"xa_next = ((Gb*deltaYa)+(L1*xa))/L_next;// [mole fraction NH3]\n",
"Hg_next = (Cb*(tG_next-Tempo))+(Ya_next*(Ca*(tG_next-Tempo))+lambda_Ao)+(Yc_next*(Cc*(tG_next-Tempo)+lambda_Co));// [J/kmol air]\n",
"Hl_next = (L1*Hl1)+(Gb*(Hg_next-Hg2)/L_next);// [J/kmol]\n",
"// The calculation are continued where the specified gas outlet composition are reached.\n",
"// The packed depth is sum of all deltaZ\n",
"Z = 1.58;// [m]\n",
"printf('The packed depth is: %f m\n',Z);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.9: Multicomponent_Sysems.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 8.9\n",
"// Page: 327\n",
"\n",
"printf('Illustration 8.9 - Page: 327\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// C1=CH4 C2=C2H6 C3=n-C3H8 C4=C4H10\n",
"Abs=0.15;// [Total absorption,kmol]\n",
"T=25;// [OC]\n",
"y1=0.7;// [mol fraction]\n",
"y2=0.15;// [mol fraction]\n",
"y3=0.10;// [mol fraction]\n",
"y4=0.05;// [mol fraction]\n",
"x1=0.01;// [mol fraction]\n",
"x_involatile=0.99;// [mol fraction]\n",
"L_by_G=3.5;// [mol liquid/mol entering gas]\n",
"//******//\n",
"\n",
"LbyG_top=L_by_G/(1-y2);\n",
"LbyG_bottom=(L_by_G+y2)/1;\n",
"LbyG_av=(LbyG_top+LbyG_bottom)/2;\n",
"// The number of eqb. trays is fixed by C3 absorption:\n",
"// For C3 at 25 OC;\n",
"m=4.10;\n",
"A=LbyG_av/m;\n",
"Frabs=0.7;// [Fractional absorption]\n",
"X0=0;\n",
"// From Eqn. 8.109:\n",
"deff('[y]=f43(Np)','y=Frabs-((A^Np)-A)/((A^Np)-1)');\n",
"Np=fsolve(2,f43);\n",
"printf('Number of trays required is %f \n',Np);"
   ]
   }
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