path: root/Mass_Transfer_Operations_by_R_E_Treybal/9-Distillation.ipynb

{
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 {
		   "cell_type": "markdown",
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	   "source": [
       "# Chapter 9: Distillation"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.10: Optimum_Reflux_Ratio_McCabe_Thiele_Method.sce"
		   ]
		  },
  {
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"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.10\n",
"// Page: 412\n",
"\n",
"printf('Illustration 9.10 - Page: 412\n\n');\n",
"\n",
"// solution\n",
"\n",
"// a:methanol b:water\n",
"Ma = 32.04;// [kg/kmol]\n",
"Mb = 18.02;// [kg/kmol]\n",
"// Feed:\n",
"F1 = 5000;// [kg/h]\n",
"F = 216.8;// [kmol/h]\n",
"Tempo = 19.7;// [OC]\n",
"zF = 0.360;// [mole fraction methanol]\n",
"MavF = 23.1;// [kg/kmol]\n",
"Tempf = 58.3;// [OC]\n",
"// Distillate:\n",
"D1 = 2620;// [kg/h]\n",
"D = 84.4;// [kkmol/h]\n",
"xD = 0.915;// [mole fraction methanol]\n",
"// Residue:\n",
"R1 = 2380;// [kg/h]\n",
"R = 132.4;// [kmol/h]\n",
"xW = 0.00565;// [mole fraction methanol]\n",
"\n",
"// From Fig. 9.42 (Pg 413):\n",
"BtF = 76.0;// [Bubble point if the feed, OC]\n",
"DtF = 89.7;// [Dew point of the feed, OC]\n",
"// Latent heat of vaporisation at 76 OC\n",
"lambda_a = 1046.7;// [kJ/kg]\n",
"lambda_b = 2284;// [kJ/kg]\n",
"ha = 2.721;// [kJ/kg K]\n",
"hb = 4.187;// [kJ/kg K]\n",
"hF = 3.852;// [kJ/kg K]\n",
"// If heats of solution is ignaored:\n",
"// Enthalpy of the feed at the bubble point referred to the feed temp.\n",
"HF = hF*MavF*(BtF-Tempf);// [kJ/kmol]\n",
"// enthalpy of the saturated vapour at dew point referred to the liquid at feed temp.\n",
"HL = (zF*((ha*Ma*(DtF-Tempf))+(lambda_a*Ma)))+((1-zF)*((hb*Mb*(DtF-Tempf))+(lambda_b*Mb)));// [kJ/kmol]\n",
"q = HL/(HL-HF);\n",
"slope = q/(q-1);\n",
"// In fig. 9.42: xD,xW & zF are  located on the 45 degree diagonal & the q line is drawn with slope = 'slope' .\n",
"// The operating line for minimum reflux ratio in this case pass through the intersection of the q line and the equilibrium curve.\n",
"ordinate = 0.57;\n",
"deff('[y] = f62(Rm)','y = ordinate-(xD/(Rm+1))');\n",
"Rm = fsolve(0,f62);// [mole reflux/mole distillate]\n",
"// from fig. 9.42 (Pg 413):\n",
"// The minimum number of theoretical trays is determied using the 45 degree diagonal as operating line.\n",
"Np = 4.9;// [including the reboiler]\n",
"R = 1.5*Rm;// [mole reflux/mole distillate]\n",
"// From Eqn. 9.49:\n",
"L = R*D;// [kmol/h]\n",
"// From Eqn. 9.115:\n",
"G = D*(R+1);// [kmol/h]\n",
"// From Eqn. 9.126:\n",
"L_bar = (q*F)+L;// [kmol/h]\n",
"// From Eqn. 9.127:\n",
"G_bar = (F*(q-1))+G;// [kmol/h]\n",
"ordinateN = xD/(R+1);\n",
"// As in Fig. 9.43:\n",
"// The y-intercept = ordinateN and enriching and exhausting operating lines are plotted.\n",
"// Number of theoretical stages are determined.\n",
"NpN = 8.8;// [including the reboiler]\n",
"printf('Number of theoretical stages is %f\n',NpN-1);"
   ]
   }
,
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		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.11: Suitable_Reflux_Ratio.sce"
		   ]
		  },
  {
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"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.11\n",
"// Page: 423\n",
"\n",
"printf('Illustration 9.11 - Page: 423\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// a:ethanol b:water\n",
"zF = 0.3;\n",
"xa = 0.3;// [mole fraction of ethanol]\n",
"Temp = 78.2;// [OC]\n",
"Ao = 0.0462;// [Area of perforations,square m]\n",
"t = 0.450;// [m]\n",
"//******//\n",
"\n",
"Ma = 46.05;// [kg/kmol]\n",
"Mb = 18.02;// [kg/kmol]\n",
"xb = 1-xa;// [mole fraction of water]\n",
"ma = 0.3*Ma/((0.3*Ma)+(xb*Mb));// [mass fraction of ethanol]\n",
"mb = 1-ma;// [mass fraction of water]\n",
"\n",
"\n",
"// Feed:\n",
"F1 = 910;// [kg/h]\n",
"Xa = F1*ma/Ma;// [moles of ethanol]\n",
"Xb = F1*mb/Mb;// [moles of water]\n",
"F = Xa+Xb;// [Total moles]\n",
"// Distillate:\n",
"xD = 0.80;// [mole fraction of ethanol]\n",
"// If essentially all the ethanol is removed from the residue:\n",
"D = Xa/xD;// [kmol/h]\n",
"MavD = (xD*Ma)+((1-xD)*Mb);// [kg/kmol]\n",
"D1 = D*MavD;// [kg/h]\n",
"Density_G = (MavD/22.41)*(273/(273+Temp));// [kg/cubic meter]\n",
"Density_L = 744.9;// [kg/cubic meter]\n",
"sigma = 0.021;// [N/m]\n",
"\n",
"// From Table 6.2,Pg 169:\n",
"alpha = (0.0744*t)+0.01173;\n",
"beeta = (0.0304*t)+0.015;\n",
"At = %pi*(0.760^2)/4;// [Tower cross sectional Area, square m]\n",
"WByT = 530/760;// [Table 6.1, Pg 162]\n",
"Ad = 0.0808*At;// [Downspout area,square m]\n",
"Aa = At-(2*Ad);//  [Active area,square m]\n",
"// abcissa = (L/G)*(density_G/Density_L)^0.5\n",
"// Assume:\n",
"abcissa = 0.1;\n",
"// From Eqn.6.30:\n",
"Cf = (alpha*log10(1/abcissa)+beeta)*(sigma/0.020)^0.2;\n",
"// From Eqn. 6.29:\n",
"Vf = Cf*((Density_L-Density_G)/Density_G)^(1/2);// [m/s]\n",
"An = At-Ad;// [square m]\n",
"R = 3;// [Reflux Ratio]\n",
"G = D*(R+1);\n",
"G1 = (G*22.41/3600)*((273+Temp)/273);// [cubic meter/s]\n",
"V = G1/An;// [Vapour velocity,m/s]\n",
"percent = (V/Vf)*100;\n",
"// Vapour velocity is 58 percent of flooding velocity (amply safe)\n",
"L = R*D;// [kmol/h]\n",
"L1 = L*MavD;// [kg/h]\n",
"abcissa = (L1/(G1*3600*Density_G))*(Density_G/Density_L)^0.5;\n",
"// Since the value of abcissa is less than0.1, the calculaed value of Cf is correct.\n",
"// Since the feed is at the buubble point.\n",
"q = 1;\n",
"// From Eqn. 9.126:\n",
"L_bar = L+(q*F);// [kmol/h]\n",
"// From Eqn. 9.127:\n",
"G_bar = G+F*(q-1);// [kmol/h]\n",
"// The enthalpy of saturated steam,referred to 0 OC,69 kN/square m:\n",
"HGNpPlus1 = 2699;// [kN m/kg]\n",
"// This will be the enthalpy as it enters the tower if expanded adiabatically to the tower pressure\n",
"// The enthalpy of steam at 1 std. atm:\n",
"HGsat = 2676;// [kN m/kg]\n",
"lambda = 2257;// [kN m/kg]\n",
"// From Eqn. 9.140:\n",
"deff('[y] = f63(GNpPlus1_bar)','y = G_bar-(GNpPlus1_bar*(1+((HGNpPlus1-HGsat)*Mb/(lambda*Mb))))');\n",
"GNpPlus1_bar = fsolve(7,f63);\n",
"// From Eqn. 9.141:\n",
"LNp_bar = L_bar-(G_bar-GNpPlus1_bar);\n",
"\n",
"// Tray Efficiencies:\n",
"// Consider the situation:\n",
"x = 0.5;\n",
"y_star = 0.962;\n",
"Temp = 79.8;// [OC]\n",
"// This is in the enriching section.\n",
"Density_L = 791;// [kg/cubic meter]\n",
"Density_G = 1.253;// [kg/cubic meter]\n",
"// From equilibrium data:\n",
"m = 0.42;\n",
"A = L/(m*G);\n",
"// From chapter 2:\n",
"ScG = 0.930;\n",
"Dl = 2.065*10^(-9);// [square m/s]\n",
"// For L = 38.73 kmol/h\n",
"q = 4.36*10^(-4);// [cubic meter/s]\n",
"// For G = 51.64 kmol/h\n",
"Va = 1.046;// [m/s]\n",
"// From tray dimensions:\n",
"z = 0.647;// [m]\n",
"Z = 0.542;// [m]\n",
"hW = 0.06;// [m]\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. 6.38\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. 6.64:\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;\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",
"// Entrainment is neglible:\n",
"// Similarly for other x\n",
"// Value = [x Entrainment]\n",
"Value = [0 0.48;0.1 .543;0.3 0.74;0.5 EMG;0.7 0.72];\n",
"\n",
"// Tray Calculation:\n",
"op_intercept = xD/(R+1);\n",
"// From Fig. 9.48:\n",
"// The exhausting section operating line, on this scale plot, for all practical purposes passes through the origin.\n",
"// The broken curve is located so that, at each concentration, vertical distances corresponding to lines BC and AC are in the ratio of EMG.\n",
"// This curve is used instead of equilibrium trays to locate the ideal trays.\n",
"// The feed tray is thirteenth.\n",
"x14 = 0.0150;\n",
"alpha = 8.95;\n",
"EMG = 0.48;\n",
"A_bar = L_bar/(alpha*G_bar);\n",
"// From Eqn. 8.16:\n",
"Eo = log(1+(EMG*((1/A_bar)-1)))/log(1/A_bar);\n",
"// The 6 real trays corresponds to: \n",
"NRp = 6*Eo;\n",
"xW = 0.015/((exp(NRp*log(1/A_bar))-A_bar)/(1-A_bar));// [mole fraction ethanol]\n",
"// This corresponds to ethanol loss of 0.5 kg/day.\n",
"printf('The Reflux ratio of %d will cause the ethanol loss of 0.5 kg/day\n',R);\n",
"printf('Larger reflux ratios would reduce this, but the cost of additional steam will probaby make them not worthwile.\n');\n",
"printf('Smaller values of R, with corresponding reduced steam cost and larger ethanol loss, should be considered, but care must be taken to ensure vapour velocities above the weeping velocities.');"
   ]
   }
,
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		   "metadata": {},
		   "source": [
			"## Example 9.12: Dimension_of_Packed_Section.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.12\n",
"// Page: 429\n",
"\n",
"printf('Illustration 9.12 - Page: 429\n\n');\n",
"\n",
"// solution\n",
"\n",
"// a:methanol b:water\n",
"// Vapour and liquid quantities throughout the tower, as in Illustration 9.8, with the Eqn. 9.62, 9.64, 9.72, 9.74:\n",
"// Data = [x tL(OC) y tG(OC) Vapor(kmol/h) Vapor(kg/h) Liquid(kmol/h) Liquid(kg/h)]\n",
"Ma = 34.02;// [kg/kmol]\n",
"Mb = 18.02;// [kg/kmol]\n",
"Temp = 78.7;// [OC]\n",
"x = [0.915 0.600 0.370 0.370 0.200 0.100 0.02];\n",
"y = [0.915 0.762 0.656 0.656 0.360 0.178 0.032];\n",
"scf(17);\n",
"plot(x,y);\n",
"xgrid();\n",
"xlabel('mole fraction of methanol in liquid');\n",
"ylabel('mole fraction of methanol in vapour');\n",
"title('Operating Line curve');\n",
"//x = 0.370: the dividing point between stripping and enriching section\n",
"tL = [66 71 76 76 82 87 96.3];// [Bubble point, OC]\n",
"tG = [68.2 74.3 78.7 78.7 89.7 94.7 99.3];// [Dew Point, OC]\n",
"Vapor = [171.3 164.0 160.9 168.6 161.6 160.6 127.6];// [kmol/h]\n",
"Vapor1 = [5303 4684 4378 4585 3721 3296 2360];// [kg/h]\n",
"Liquid = [86.7 79.6 76.5 301 294 293 260];// [kmol/h]\n",
"Liquid1 = [2723 2104 1779 7000 6138 5690 4767];// [kg/h]\n",
"Data = zeros(7,8);\n",
"for j = 1:7\n",
"        Data(j,1) = x(j);\n",
"        Data(j,2) = tL(j);\n",
"        Data(j,3) = y(j);\n",
"        Data(j,4) = tG(j);\n",
"        Data(j,5) = Vapor(j); \n",
"        Data(j,6) = Vapor1(j);\n",
"        Data(j,7) = Liquid(j);\n",
"        Data(j,8) = Liquid1(j);\n",
"end\n",
"// The tower diameter will be set by the conditions at the top of the stripping section because of the large liquid flow at this point.\n",
"// From Illustration 9.8:\n",
"G = Data(4,6);\n",
"L = Data(4,8);\n",
"Density_G = (Data(4,6)/(22.41*Data(4,5)))*(273/(273+Temp));// [kg/cubic m]\n",
"Density_L = 905;// [kg/cubic m]\n",
"// abcissa = (L/G)*(Density_L/Density_G)^0.5\n",
"abcissa = (Data(4,8)/Data(4,6))*(Density_G/Density_L)^0.5;\n",
"// From Fig. 6.34, choose a gas pressure drop of 450 N/square m/m\n",
"ordinate = 0.0825;\n",
"// From Table 6.3 (Pg 196):\n",
"Cf = 95;\n",
"viscosity_L = 4.5*10^(-4);// [kg/m.s]\n",
"sigma = 0.029;// [N/m]\n",
"J = 1;\n",
"G_prime = (ordinate*Density_G*(Density_L-Density_G)/(Cf*viscosity_L^0.1))^0.5;// [kg/square m.s]\n",
"A = G/(3600*G_prime);// [Tower ,cross section area,square m]\n",
"L_prime = L/(A*3600);// [kg/square m.s]\n",
"// Mass transfer will be computed for the same location:\n",
"// From Table 6.4 (Pg 205):\n",
"m = 36.4;\n",
"n = (0.0498*L_prime)-0.1013;\n",
"p = 0.274;\n",
"aAW = m*((808*G_prime/Density_G^0.5)^n)*L_prime^p;// [square m/cubic m]\n",
"// From Table 6.5 (Pg 206):\n",
"dS = 0.0530;// [m]\n",
"beeta = 1.508*dS^0.376;\n",
"shi_LsW = 2.47*10^(-4)/dS^1.21;\n",
"shi_LtW = ((2.09*10^(-6))*(737.5*L_prime)^beeta)/dS^2;\n",
"shi_LOW = shi_LtW-shi_LsW; \n",
"shi_Ls = (0.0486*viscosity_L^0.02*sigma^0.99)/(dS^1.21*Density_L^0.37);\n",
"H = ((975.7*L_prime^0.57*viscosity_L^0.13)/(Density_L^0.84*((2.024*L_prime^0.430)-1)))*(sigma/0.073)^(0.1737-0.262*log10(L_prime));// [m]\n",
"shi_Lo = shi_LOW*H;\n",
"shi_Lt = shi_Lo+shi_Ls;\n",
"// From Eqn. 6.73:\n",
"aA = aAW*(shi_Lo/shi_LOW);// [square m/cubic m]\n",
"// From Table 6.3 (Pg 196):\n",
"e = 0.71;\n",
"// From Eqn. 6.71:\n",
"eLo = e-shi_Lt;\n",
"// From Chapter 2:\n",
"ScG = 1;\n",
"MavG = 0.656*Ma+(1-0.656)*Mb;// [kg/kmol]\n",
"G = G_prime/MavG;\n",
"viscosity_G = 2.96*10^(-5);// [kg/m.s]\n",
"// From Eqn. 6.70:\n",
"Fg = (1.195*G/ScG^(2/3))*((dS*G_prime/(viscosity_G*(1-eLo)))^(-0.36));// [kmol/square m s (mole fraction)]\n",
"kY_prime = Fg;// [kmol/square m s (mole fraction)]\n",
"DL = 4.80*10^(-9);// [square m/s]\n",
"ScL = viscosity_L/(Density_L*DL);\n",
"// From Eqn. 6.72:\n",
"kL = (25.1*DL/dS)*((dS*L_prime/viscosity_L)^0.45)*ScL^0.5;// [kmol/square m s (kmol/cubic m)]\n",
"// At 588.33 OC\n",
"Density_W = 53.82;// [kg/cubic m]\n",
"kx_prime = Density_W*kL;// [kmol/square m s (mole fraction)]\n",
"// Value1 = [x G a ky_prime*10^3 kx_prime]\n",
"Value1 = [0.915 0.0474 20.18 1.525 0.01055;0.6 0.0454 21.56 1.542 0.00865;0.370 0.0444 21.92 1.545 0.00776;0.370 0.0466 38 1.640 0.0143;0.2 0.0447 32.82 1.692 0.0149;0.1 0.0443 31.99 1.766 0.0146;0.02 0.0352 22.25 1.586 0.0150];\n",
"// From Fig: 9.50\n",
"// At x = 0.2:\n",
"y = 0.36;\n",
"slope = -(Value1(5,5)/(Value1(5,4)*10^(-3)));\n",
"// The operating line drawn from(x,y) with slope. The point where it cuts the eqb. line gives yi.\n",
"// K = ky_prime*a(yi-y)\n",
"// For the enriching section:\n",
"// En = [y yi 1/K Gy]\n",
"En = [0.915 0.960 634 0.0433;0.85 0.906 532.8 0.0394;0.8 0.862 481.1 0.0366;0.70 0.760 499.1 0.0314;0.656 0.702 786.9 0.0292];\n",
"// For the Stripping section:\n",
"// St = [y yi 1/K Gy]\n",
"St = [0.656 0.707 314.7 0.0306;0.50 0.639 124.6 0.0225;0.40 0.580 99.6 0.01787;0.3 0.5 89 0.0134;0.2 0.390 92.6 0.00888;0.10 0.232 154.5 0.00416;0.032 0.091 481 0.00124];\n",
"// Graphical Integration, according to Eqn.9.52::\n",
"scf(18);\n",
"plot(En(:,4),En(:,3));\n",
"xgrid();\n",
"xlabel('Gy');\n",
"ylabel('1 / (ky_prime*a*(yi-y))');\n",
"title('Graphical Integration for Enriching section');\n",
"// From Area under the curve:\n",
"Ze = 7.53;// [m]\n",
"// Graphical Integration:\n",
"scf(19);\n",
"plot(St(:,4),St(:,3));\n",
"xgrid();\n",
"xlabel('Gy');\n",
"ylabel('1 / (ky_prime*a*(yi-y))');\n",
"title('Graphical Integration for Stripping section');\n",
"// From Area under the curve:\n",
"Zs = 4.54;// [m]\n",
"// Since the equlibrium curve slope varies so greatly that the use of overall mass transfer coeffecient is not recommended:\n",
"printf('Height of Tower for enriching Section is %f m\n',Ze);\n",
"printf('Height of Tower for Stripping Section is %f m\n',Zs);"
   ]
   }
,
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		   "source": [
			"## Example 9.13: Multicomponent_Systems.sce"
		   ]
		  },
  {
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"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.13:\n",
"\n",
"printf('Illustration 9.13\n\n');\n",
"\n",
"//**************************Calculation Of Minimum Reflux ratio************************//\n",
"// Page: 436\n",
"printf('Page: 436\n\n');\n",
"\n",
"//***Data***//\n",
"// C1:CH4 C2:C2H6 C3:n-C3H8 C4:n-C4H10 C5:n-C5H12 C6:n-C6H14\n",
"// zF = [zF(C1) zF(C2) zF(C3) zF(C4) zF(C5) zF(C6)]\n",
"zF = [0.03 0.07 0.15 0.33 0.30 0.12];// [mole fraction]\n",
"LF_By_F = 0.667;\n",
"Temp = 82;// [OC]\n",
"ylk = 0.98;\n",
"yhk = 0.01;\n",
"//**********//\n",
"\n",
"// Data = [m HG HL(30 OC);m HG HL(60 OC);m HG HL(90 OC);m HG HL(120 OC);]\n",
"Data1 = [16.1 12790 9770;19.3 13910 11160;21.8 15000 12790;24.0 16240 14370];// [For C1]\n",
"Data2 = [3.45 22440 16280;4.90 24300 18140;6.25 26240 19890;8.15 28140 21630];// [For C2]\n",
"Data3 = [1.10 31170 16510;2.00 33000 20590;2.90 35800 25600;4.00 39000 30900];// [For C3]\n",
"Data4 = [0.35 41200 20350;0.70 43850 25120;1.16 46500 30000;1.78 50400 35400];// [For C4]\n",
"Data5 = [0.085 50500 24200;0.26 54000 32450;0.50 57800 35600;0.84 61200 41400];// [For C5]\n",
"Data6 = [0.0300 58800 27700;0.130 63500 34200;0.239 68150 40900;0.448 72700 48150];// [For C6]\n",
"\n",
"// T = [Temparature]\n",
"T = [30;60;90;120];\n",
"\n",
"// Flash vaporisation of the Feed:\n",
"// Basis: 1 kmol feed throughout\n",
"// After Several trials, assume:\n",
"F = 1;// [kmol]\n",
"GF_By_F = 0.333;\n",
"LF_By_GF = LF_By_F/GF_By_F;\n",
"m82 = zeros(6);\n",
"y = zeros(6);\n",
"m82(1) = interpln([T';Data1(:,1)'],Temp);// [For C1]\n",
"m82(2) = interpln([T';Data2(:,1)'],Temp);// [For C2]\n",
"m82(3) = interpln([T';Data3(:,1)'],Temp);// [For C3]\n",
"m82(4) = interpln([T';Data4(:,1)'],Temp);// [For C4]\n",
"m82(5) = interpln([T';Data5(:,1)'],Temp);// [For C5]\n",
"m82(6) = interpln([T';Data6(:,1)'],Temp);// [For C6]\n",
"for i = 1:6\n",
"    y(i) = zF(i)*(LF_By_GF+1)/(1+(2/m82(i)));\n",
"end\n",
"Sum = sum(y);\n",
"// Since Sum is sufficiently close to 1.0, therefore:\n",
"q = 0.67;// [LF_By_F]\n",
"// Assume:\n",
"// C3: light key\n",
"// C5: heavy key\n",
"zlkF = zF(3);// [mole fraction]\n",
"zhkF = zF(5);// [mole fraction]\n",
"ylkD = ylk*zF(3);// [kmol]\n",
"yhkD = yhk*zF(5);// [kmol]\n",
"\n",
"// Estimate average Temp to be 80 OC\n",
"m80 = zeros(6);\n",
"alpha80 = zeros(6);\n",
"m80(1) = interpln([T';Data1(:,1)'],80);// [For C1]\n",
"m80(2) = interpln([T';Data2(:,1)'],80);// [For C2]\n",
"m80(3) = interpln([T';Data3(:,1)'],80);// [For C3]\n",
"m80(4) = interpln([T';Data4(:,1)'],80);// [For C4]\n",
"m80(5) = interpln([T';Data5(:,1)'],80);// [For C5]\n",
"m80(6) = interpln([T';Data6(:,1)'],80);// [For C6]\n",
"for i = 1:6\n",
"    alpha80(i) = m80(i)/m80(5);\n",
"end\n",
"// By Eqn. 9.164:\n",
"yD_By_zF1 = (((alpha80(1)-1)/(alpha80(3)-1))*(ylkD/zF(3)))+(((alpha80(3)-alpha80(1))/(alpha80(3)-1))*(yhkD/zF(5)));// [For C1]\n",
"yD_By_zF2 = (((alpha80(2)-1)/(alpha80(3)-1))*(ylkD/zF(3)))+(((alpha80(3)-alpha80(2))/(alpha80(3)-1))*(yhkD/zF(5)));// [For C2]\n",
"yD_By_zF6 = (((alpha80(6)-1)/(alpha80(3)-1))*(ylkD/zF(3)))+(((alpha80(3)-alpha80(6))/(alpha80(3)-1))*(yhkD/zF(5)));// [For C6]\n",
"// The distillate contains:\n",
"yC1 = 0.03;// [kmol C1]\n",
"yC2 = 0.07;// [kmol C2]\n",
"yC6 = 0;// [kmol C6]\n",
"// By Eqn 9.165:\n",
"deff('[y] = g1(phi)','y = (((alpha80(1)*zF(1))/(alpha80(1)-phi))+((alpha80(2)*zF(2))/(alpha80(2)-phi))+((alpha80(3)*zF(3))/(alpha80(3)-phi))+((alpha80(4)*zF(4))/(alpha80(4)-phi))+((alpha80(5)*zF(5))/(alpha80(5)-phi))+((alpha80(6)*zF(6))/(alpha80(6)-phi)))-(F*(1-q))');\n",
"// Between alphaC3 & alphaC4:\n",
"phi1 = fsolve(3,g1);\n",
"// Between alphaC4 & alphaC5:\n",
"phi2 = fsolve(1.5,g1);\n",
"// From Eqn. 9.166:\n",
"// Val = D*(Rm+1)\n",
"// (alpha80(1)*yC1/(alpha80(1)-phi1))+(alpha80(2)*yC2/(alpha80(2)-phi1))+(alpha80(3)*ylkD/(alpha80(3)-phi1))+(alpha80(4)*yD/(alpha80(4)-phi1))+(alpha80(i)*yhkD/(alpha80(5)-phi1))+(alpha80(6)*yC6/(alpha80(6)-phi1)) = Val.....................(1)\n",
"// (alpha80(1)*yC1/(alpha80(1)-phi2))+(alpha80(2)*yC2/(alpha80(2)-phi2))+(alpha80(3)*ylkD/(alpha80(3)-phi2))+(alpha80(4)*yD/(alpha80(4)-phi2))+(alpha80(i)*yhkD/(alpha80(5)-phi2))+(alpha80(6)*yC6/(alpha80(6)-phi2)) = Val ....................(2)\n",
"// Solving simultaneously:\n",
"a = [-alpha80(4)/(alpha80(4)-phi1) 1;-alpha80(4)/(alpha80(4)-phi2) 1];\n",
"b = [(alpha80(1)*yC1/(alpha80(1)-phi1))+(alpha80(2)*yC2/(alpha80(2)-phi1))+(alpha80(3)*ylkD/(alpha80(3)-phi1))+(alpha80(i)*yhkD/(alpha80(5)-phi1))+(alpha80(6)*yC6/(alpha80(6)-phi1));(alpha80(1)*yC1/(alpha80(1)-phi2))+(alpha80(2)*yC2/(alpha80(2)-phi2))+(alpha80(3)*ylkD/(alpha80(3)-phi2))+(alpha80(i)*yhkD/(alpha80(5)-phi2))+(alpha80(6)*yC6/(alpha80(6)-phi2))];\n",
"soln = a\b;\n",
"yC4 = soln(1);// [kmol C4 in the distillate]\n",
"Val = soln(2);\n",
"// For the distillate, at a dew point of 46 OC\n",
"ydD = [yC1 yC2 ylkD yC4 yhkD yC6];\n",
"D = sum(ydD);\n",
"yD = zeros(6);\n",
"m46 = zeros(6);\n",
"alpha46 = zeros(6);\n",
"m46(1) = interpln([T';Data1(:,1)'],46);// [For C1]\n",
"m46(2) = interpln([T';Data2(:,1)'],46);// [For C2]\n",
"m46(3) = interpln([T';Data3(:,1)'],46);// [For C3]\n",
"m46(4) = interpln([T';Data4(:,1)'],46);// [For C4]\n",
"m46(5) = interpln([T';Data5(:,1)'],46);// [For C5]\n",
"m46(6) = interpln([T';Data6(:,1)'],46);// [For C6]\n",
"for i = 1:6\n",
"    alpha46(i) = m46(i)/m46(5);\n",
"    yD(i) = ydD(i)/D;\n",
"    // Ratio = yD/alpha46\n",
"    Ratio1(i) = yD(i)/alpha46(i);\n",
"end\n",
"// mhk = mC5 at 46.6 OC, the assumed 46 OC is satisfactory.\n",
"\n",
"// For the residue, at a dew point of 46 OC\n",
"xwW = [zF(1)-yC1 zF(2)-yC2 zF(3)-ylkD zF(4)-yC4 zF(5)-yhkD zF(6)-yC6];\n",
"W = sum(xwW);\n",
"xW = zeros(6);\n",
"m113 = zeros(6);\n",
"alpha113 = zeros(6);\n",
"m113(1) = interpln([T';Data1(:,1)'],113);// [For C1]\n",
"m113(2) = interpln([T';Data2(:,1)'],113);// [For C2]\n",
"m113(3) = interpln([T';Data3(:,1)'],113);// [For C3]\n",
"m113(4) = interpln([T';Data4(:,1)'],113);// [For C4]\n",
"m113(5) = interpln([T';Data5(:,1)'],113);// [For C5]\n",
"m113(6) = interpln([T';Data6(:,1)'],113);// [For C6]\n",
"for i = 1:6\n",
"    alpha113(i) = m113(i)/m113(5);\n",
"    xW(i) = xwW(i)/W;\n",
"    // Ratio = yD/alpha46\n",
"    Value(i) = alpha113(i)*xW(i);\n",
"end\n",
"// mhk = mC5 at 114 OC, the assumed 113 OC is satisfactory.\n",
"Temp_Avg = (114+46.6)/2;// [OC]\n",
"// Temp_avg is very close to the assumed 80 OC\n",
"Rm = (Val/D)-1;\n",
"printf('Minimum Reflux Ratio is %f mol reflux/mol distillate\n \n',Rm);\n",
"printf('*****************Distillate Composition*********************\n');\n",
"printf('C1\t \t \t \t: %f\n',yD(1));\n",
"printf('C2\t \t \t \t: %f\n',yD(2));\n",
"printf('C3\t \t \t \t: %f\n',yD(3));\n",
"printf('C4\t \t \t \t: %f\n',yD(4));\n",
"printf('C5\t \t \t \t: %f\n',yD(5));\n",
"printf('C6\t \t \t \t: %f\n',yD(6));\n",
"printf('\n');\n",
"printf('*****************Residue Composition*********************\n');\n",
"printf('C1\t \t \t \t: %f\n',xW(1));\n",
"printf('C2\t \t \t \t: %f\n',xW(2));\n",
"printf('C3\t \t \t \t: %f\n',xW(3));\n",
"printf('C4\t \t \t \t: %f\n',xW(4));\n",
"printf('C5\t \t \t \t: %f\n',xW(5));\n",
"printf('C6\t \t \t \t: %f\n',xW(6));\n",
"printf('\n');\n",
"\n",
"//**********************Number of Theoretical stage***********************//\n",
"// Page:440\n",
"printf('Page: 440\n\n');\n",
"\n",
"for i = 1:6\n",
"    alpha_av(i) = (alpha46(i)*alpha113(i))^0.5;\n",
"end\n",
"alphalk_av = alpha_av(3);\n",
"// By Eqn. 9.167:\n",
"xhkW = xwW(5);\n",
"xlkW = xwW(3);\n",
"Nm = log10((ylkD/yhkD)*(xhkW/xlkW))/log10(alphalk_av)-1;\n",
"// Ratio = yD/xW\n",
"for i = 1:6\n",
"    Ratio2(i) = (alpha_av(i)^(Nm+1))*yhkD/xhkW;\n",
"end\n",
"// For C1:\n",
"// yC1D-Ratio(1)*xC1W = 0\n",
"// yC1D+xC1W = zF(1)\n",
"// Similarly for others\n",
"for i = 1:6\n",
"    a = [1 -Ratio2(i);1 1];\n",
"    b = [0;zF(i)];\n",
"    soln = a\b;\n",
"    yD2(i) = soln(1);// [kmol]\n",
"    xW2(i) = soln(2);// [kmol]\n",
"end\n",
"D = sum(yD2);// [kmol]\n",
"W = sum(xW2);// [kmol]\n",
"// The distillate dew point computes to 46.6 OC and the residue bubble point computes to 113 OC, which is significantly close to the assumed.\n",
"printf('Minimum number of theoretical stage is: %f\n',Nm);\n",
"printf('\n');\n",
"\n",
"//***************Product composition at R = 0.8***********************//\n",
"// Page:441\n",
"printf('Page: 441\n\n');\n",
"\n",
"// Since C1 and C2 do not enter in the residue nor C6 in the distillate, appreciably at total reflux or minimum reflux ratio, it will be assumed that they will not enter R = 0.8. C3 and C5 distribution are fixed by specifications. Only that C4 remains to be estimated.\n",
"// R = [Infinte 0.8 0.58] [Reflux ratios For C4]\n",
"R = [%inf 0.8 0.58];\n",
"// Val = R/(R+1)\n",
"Val = R./R+1;\n",
"// ydD = [Inf 0.58] \n",
"y4D = [0.1255 0.1306];\n",
"yC4D = (((1-Val(2))/(1-Val(3)))*(y4D(2)-y4D(1)))+y4D(1);// Linear Interpolation\n",
"// For Distillate:\n",
"Sum1 = sum(Ratio1);\n",
"x0 = Ratio1./Sum1;\n",
"printf('For the reflux ratio of 0.8\n');\n",
"printf('*****************Distillate Composition*********************\n');\n",
"printf('\t\t\t Liquid reflux in equilibrium with the distillate vapour\n');\n",
"for i = 1:6\n",
"    printf('C%d\t \t \t \t: %f\n',i,x0(i));\n",
"end\n",
"// For boiler:\n",
"Sum2 = sum(Value);\n",
"yNpPlus1 = Value./Sum2;\n",
"printf('*****************Distillate Composition*********************\n');\n",
"printf('\t\t\t Reboiler vapour in equilibrium with the residue\n');\n",
"for i = 1:6\n",
"    printf('C%d\t \t \t \t: %f\n',i,yNpPlus1(i));\n",
"end\n",
"printf('\n');\n",
"\n",
"//**********Number Of Theoretical Trays***************//\n",
"// Page: 443\n",
"printf('Page: 443\n\n');\n",
"\n",
"R = 0.8;// [reflux ratio]\n",
"// From Eqn. 9.175\n",
"intersection = (zlkF-(ylkD/D)*(1-q)/(R+1))/(zhkF-(yhkD/D)*(1-q)/(R+1));\n",
"// Enriching Section:\n",
"y1 = zeros(5);\n",
"L = R*D;// [kmol]\n",
"G = L+D;// [kmol]\n",
"// Assume: Temp1 = 57 OC\n",
"// alpha57 = [C1 C2 C3 C4 C5]\n",
"alpha57 = [79.1 19.6 7.50 2.66 1];\n",
"// From Eqn. 9.177, n = 0:\n",
"for i = 1:5\n",
"    y1(i) = (L/G)*x0(i)+((D/G)*yD(i));\n",
"    Val57(i) = y1(i)/alpha57(i);\n",
"end\n",
"x1 = Val57/sum(Val57);\n",
"mC5 = sum(Val57);\n",
"Temp1 = 58.4; // [OC]\n",
"// Liquid x1's is in equilibrium with y1's.\n",
"xlk_By_xhk1 = x1(3)/x1(5);\n",
"// Tray 1 is not the feed tray.\n",
"// Assume: Temp2 = 63 OC\n",
"// alpha63 = [C1 C2 C3 C4 C5]\n",
"alpha63 = [68.9 17.85 6.95 2.53 1.00];\n",
"// From Eqn. 9.177, n = 1:\n",
"for i = 1:5\n",
"    y2(i) = (L/G)*x1(i)+((D/G)*yD(i));\n",
"    Val63(i) = y1(i)/alpha63(i);\n",
"end\n",
"mC5 = sum(Val63);\n",
"x2 = Val63/sum(Val63);\n",
"xlk_By_xhk2 = x2(3)/x2(5);\n",
"// The tray calculation are continued downward in this manner.\n",
"// Results for trays 5 & 6 are:\n",
"// Temp 75.4 [OC]\n",
"// x5 = [C1 C2 C3 C4 C5]\n",
"x5 = [0.00240 0.0195 0.1125 0.4800 0.3859];\n",
"xlk_By_xhk5 = x5(3)/x5(5);\n",
"// Temp6 = 79.2 OC\n",
"// x6 = [C1 C2 C3 C4 C5]\n",
"x6 = [0.00204 0.0187 0.1045 0.4247 0.4500];\n",
"xlk_By_xhk6 = x6(3)/x6(5);\n",
"// From Eqn. 9.176:\n",
"// Tray 6 is the feed tray\n",
"Np1 = 6;\n",
"\n",
"// Exhausting section:\n",
"// Assume Temp = 110 OC\n",
"L_bar = L+(q*F);// [kmol]\n",
"G_bar = L_bar-W;// [kmol]\n",
"// alpha57 = [C3 C4 C5 C6]\n",
"alpha110 = [5 2.2 1 0.501];\n",
"// From Eqn. 9.178:\n",
"xNp = zeros(4);\n",
"k = 1;\n",
"for i = 3:6\n",
"    xNp(k) = ((G_bar/L_bar)*yNpPlus1(i))+((W/L_bar)*xW(i));\n",
"    Val110(k) = alpha110(k)*xNp(k);\n",
"    k = k+1;\n",
"end\n",
"yNp = Val110/sum(Val110);\n",
"mC5 = 1/sum(Val110);\n",
"// yNp is in Eqb. with xNp:\n",
"xlk_By_xhkNp = xNp(1)/xNp(4);\n",
"// Results for Np-7 to Np-9 trays:\n",
"// For Np-7\n",
"// Temp =  95.7 OC\n",
"// xNpMinus7 = [C3 C4 C5 C6]\n",
"xNpMinus7 = [0.0790 0.3944 0.3850 0.1366];\n",
"xlk_By_xhkNpMinus7 = xNpMinus7(1)/xNpMinus7(3);\n",
"// For Np-8\n",
"// Temp =  94.1 OC\n",
"// xNpMinus8 = [C3 C4 C5 C6]\n",
"xNpMinus8 = [0.0915 0.3897 0.3826 0.1362];\n",
"xlk_By_xhkNpMinus8 = xNpMinus8(1)/xNpMinus8(3);\n",
"// For Np-9\n",
"// Temp =  93.6 OC\n",
"// xNpMinus9 = [C3 C4 C5 C6]\n",
"xNpMinus9 = [0.1032 0.3812 0.3801 0.1355];\n",
"xlk_By_xhkNpMinus9 = xNpMinus9(1)/xNpMinus9(3);\n",
"// From Eqn. 9.176:\n",
"// Np-8 is the feed tray.\n",
"deff('[y] = g2(Np)','y = Np-8-Np1');\n",
"Np = fsolve(7,g2);\n",
"printf('Number of theoretical Trays required for R = 0.8: %d\n',Np);\n",
"printf('\n');\n",
"\n",
"//**************Composition Correction*****************//\n",
"// Page: 446\n",
"printf('Page: 446\n\n');\n",
"\n",
"// New Bubble Point:\n",
"// Temp = 86.4 OC\n",
"x6_new = x6*(1-xNpMinus8(4));\n",
"x6_new(6) = xNpMinus8(4);\n",
"// alpha86 = [C1 C2 C3 C4 C5 C6]\n",
"alpha86 = [46.5 13.5 5.87 2.39 1.00 0.467];\n",
"// From Eqn. 9.181:\n",
"xhkn = x5(5);\n",
"xhknPlus1 = x6_new(5);\n",
"xC65 = alpha86(6)*x6_new(6)*xhkn/xhknPlus1;\n",
"x5_new = x5*(1-xC65);\n",
"x5_new(6) = 1-sum(x5_new);\n",
"// Tray 5 has a bubble point of 80 OC\n",
"// Similarly , the calculations are continued upward:\n",
"// x2_new = [C1 C2 C3 C4 C5 C6]\n",
"x2_new = [0.0021 0.0214 0.1418 0.6786 0.1553 0.00262];\n",
"// y2_new = [C1 C2 C3 C4 C5 C6]\n",
"y2_new = [0.0444 0.111 0.2885 0.5099 0.0458 0.00034];\n",
"// x1_new = [C1 C2 C3 C4 C5 C6]\n",
"x1_new = [0.00226 0.0241 0.1697 0.7100 0.0932 0.00079];\n",
"// y1_new = [C1 C2 C3 C4 C5 C6]\n",
"y1_new = [0.0451 0.1209 0.3259 0.4840 0.0239 0.000090];\n",
"// x0_new = [C1 C2 C3 C4 C5 C6]\n",
"x0_new = [0.00425 0.0425 0.2495 0.6611 0.0425 0.00015];\n",
"// yD_new = [C1 C2 C3 C4 C5 C6]\n",
"yD_new = [0.0789 0.1842 0.3870 0.3420 0.0079 0.00001];\n",
"// From Eqn. 9.184:\n",
"// For C1 & C2\n",
"alphalkm = alpha86(3);\n",
"xlkmPlus1 = xNpMinus7(1);\n",
"xlkm = x6_new(3);\n",
"xC17 = x6_new(1)*alpha86(3)*xlkmPlus1/(alpha86(1)*xlkm);\n",
"xC27 = x6_new(2)*alpha86(3)*xlkmPlus1/(alpha86(2)*xlkm);\n",
"// Since xC17 = 1-xC27\n",
"// The adjusted value above constitute x7's.\n",
"// The new bubbl point is 94 OC\n",
"// The calculations are continued down in the same fashion.\n",
"// The new tray 6 has:\n",
"// xC1 = 0.000023 & xC2 = 0.00236\n",
"// It is clear that the conc. of these components are reducing so rapidly that there is no need to go an further.\n",
"printf('******Corrected Composition***********\n');\n",
"printf('Component\t \tx2\t \t \t y2\t \t \t x1\t \t \t y1\t \t \tx0\t \t \tyD\n');\n",
"for i = 1:6\n",
"    printf('C%d\t \t \t%f\t \t %f\t \t %f\t \t %f\t \t%f\t \t%f\n',i,x2_new(i),y2_new(i),x1_new(i),y1_new(i),x0_new(i),yD_new(i));\n",
"end\n",
"printf('\n');\n",
"\n",
"//*************Heat Load of Condensor & Boiler & L/G ratio**********//\n",
"// Page 448\n",
"printf('Page: 448\n\n');\n",
"\n",
"// Values of x0, yD & y1 are taken from the corrected concentration.\n",
"// HD46 = [C1 C2 C3 C4 C5 C6]\n",
"HD46 = [13490 23380 32100 42330 52570 61480];// [kJ/kmol]\n",
"for i = 1:6\n",
"    yDHD(i) = yD_new(i)*HD46(i);\n",
"end\n",
"HD = sum(yDHD);// [kJ]\n",
"// HL46 = [C1 C2 C3 C4 C5 C6]\n",
"HL46 = [10470 17210 18610 22790 27100 31050];// [kJ/kmol]\n",
"for i = 1:6\n",
"    xHL(i) = x0_new(i)*HL46(i);\n",
"end\n",
"HL0 = sum(xHL);// [kJ]\n",
"// HG58 = [C1 C2 C3 C4 C5 C6]\n",
"HG58 = [13960 24190 37260 43500 53900 63500];// [kJ/kmol]\n",
"for i = 1:6\n",
"    yHG1(i) = y1_new(i)*HG58(i);\n",
"end\n",
"HG1 = sum(yHG1);// [kJ]\n",
"// From Eqn. 9.54:\n",
"Qc = D*((R+1)*HG1-(R*HL0)-HD);// [kJ/kmol feed]\n",
"// Similarly:\n",
"HW = 39220;// [kJ]\n",
"HF = 34260;// [kJ]\n",
"// From Eqn. 9.55:\n",
"Qb = (D*HD)+(W*HW)+Qc-(F*HF);// [kJ/kmol feed]\n",
"// For tray n = 1\n",
"G1 = D*(R+1);// [kmol]\n",
"// With x1 & y2 from corrected composition;\n",
"// HG66 = [C1 C2 C3 C4 C5 C6]\n",
"HG66 = [14070 24610 33800 44100 54780 64430];// [kJ/kmol feed]\n",
"for i = 1:6\n",
"    yHG2(i) = y2_new(i)*HG66(i);\n",
"end\n",
"HG2 = sum(yHG2);// [kJ]\n",
"// HL58 = [C1 C2 C3 C4 C5 C6]\n",
"HL58 = [11610 17910 20470 24900 29500 33840];// [kJ/kmol feed]\n",
"for i = 1:6\n",
"    xHL1(i) = x1_new(i)*HL58(i);\n",
"end\n",
"HL1 = sum(xHL1);// [kJ]\n",
"// From Eqn. 9.185:\n",
"G2 = (Qc+D*(HD-HL1))/(HG2-HL1);// [kmol]\n",
"L2 = G2-D;// [kmol]\n",
"L2_By_G2 = L2/G2;\n",
"// Similarly, the calculations are made for other trays in enriching section.\n",
"// For tray, Np = 14:\n",
"// C1 & C2 are absent.\n",
"// HG113 = [C3 C4 C5 C6]\n",
"HG113 = [38260 49310 60240 71640];// [kJ/kmol feed]\n",
"k = 3;\n",
"for i = 1:4\n",
"    yHG15(i) = yNpPlus1(k)*HG113(i);\n",
"    k = k+1;\n",
"end\n",
"HG15 = sum(yHG15);\n",
"// HL107 = [C3 C4 C5 C6]\n",
"HL107 = [29310 31870 37680 43500];// [kJ/kmol feed]\n",
"for i = 1:4\n",
"    xHL14(i) = xNp(i)*HL107(i);\n",
"end\n",
"HL14 = sum(xHL14);// [kJ]\n",
"// Similarly:\n",
"HL13 = 36790;// [kJ]\n",
"HG14 = 52610;// [kJ]\n",
"// From Eqn. 9.186:\n",
"G15_bar = (Qb+(W*(HL14-HW)))/(HG15-HL14);// [kmol]\n",
"L14_bar = W+G15_bar;// [kmol]\n",
"G14_bar = (Qb+(W*(HL13-HW)))/(HG14-HL13);// [kmol]\n",
"L14_By_G14 = L14_bar/G14_bar;\n",
"printf('Condensor eat Load %f kJ:\n',HL0);\n",
"printf('Reboiler eat Load %f kJ:\n',HG15);\n",
"// For other Exhausting Section Trays:\n",
"// Result = [Tray No. L_By_G Temp(OC)]\n",
"// Tray 0: Condensor\n",
"// Tray 15: Reboiler\n",
"Result = [0,0.80 46.6;1 0.432 58.4;2 0.437 66;3 0.369 70.4;4 0.305 74;5 0.310 80.3;6 1.53 86.4;7 4.05 94.1;8 3.25 96.3;9 2.88 97.7;10 2.58 99;11 2.48 100;12 2.47 102.9;13 2.42 104.6;14 2.18 107.9;15 1.73 113.5];\n",
"printf('**************L/G*************\n')\n",
"printf('Tray No. \t\t L/G\t\t\t\t Temp(OC)\n');\n",
"for i = 1:16\n",
"    printf('%d\t \t \t%f\t \t \t%2.2f\n',Result(i,1),Result(i,2),Result(i,3));\n",
"end\n",
"// These values are not final.\n",
"// They scatter eratically because they are based on the temp. and conc. computed with the assumption of constant L/G\n",
"printf('\n');\n",
"\n",
"//**************Thiele Geddes Method******************//\n",
"// Page:452\n",
"printf('Page: 452\n\n');\n",
"\n",
"// Use the tray Temperature to obtain m.\n",
"// For C4:\n",
"// m = [0(Condensor) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15(Reboiler)]\n",
"m = [0.50 0.66 0.75 0.81 0.86 0.95 1.07 1.22 1.27 1.29 1.30 1.32 1.40 1.45 1.51 1.65];\n",
"for i = 1:7\n",
"    A(i) = Result(i,2)/m(i);\n",
"end\n",
"for j = 1:9\n",
"    i = i+1;\n",
"    S(j) = 1/(Result(i,2)/m(i));\n",
"end\n",
"// f = Tray No. 6\n",
"f = 7;\n",
"// From Eqn. 9.196:\n",
"// Value1 = Gf*yf/(D*zD)\n",
"Sum = 0;\n",
"for i = 1:f-1\n",
"    Val = 1;\n",
"    for j = i:f-1\n",
"        Val = Val*A(j);\n",
"    end\n",
"    Sum = Sum+Val;\n",
"end\n",
"Value1 = 1+Sum;\n",
"// From Eqn. 9.206:\n",
"// Value2 = Lf_bar*xf/(W*xW);\n",
"Sum = 0;\n",
"for i = 9:-1:1\n",
"    Val = 1;\n",
"    for j = i:-1:1\n",
"        Val = Val*S(j);\n",
"    end\n",
"    Sum = Sum+Val;\n",
"end\n",
"Value2 = 1+Sum;\n",
"// From Eqn. 9.208:\n",
"// Value3 = W*xW/(D*zD)\n",
"Value3 = A(f)*Value1/Value2;\n",
"// From Eqn. 9.210:\n",
"DyD = F*zF(4)/(Value3+1);// [kmol,C4]\n",
"// From Eqn. 9.209:\n",
"WxW = (F*zF(4))-(DyD);// [kmol, C4]\n",
"// Similarly:\n",
"// For [C1; C2; C3; C4; C5; C6]\n",
"// Result2 = [Value1 Value2 Value3 DyD WxW]\n",
"Result2 = [1.0150 254*10^6 288*10^(-10) 0.03 0;1.0567 8750 298*10^(-5) 0.07 0;1.440 17.241 0.0376 0.1447 0.0053;1.5778 1.5306 1.475 0.1335 0.1965;15580 1.1595 45.7 0.00643 0.29357;1080 1.0687 7230 0.0000166 0.1198];\n",
"D = sum(Result2(:,4));// [kmol]\n",
"W = sum(Result2(:,5));// [kmol]\n",
"// In the Distillate:\n",
"DyD_C3 = Result2(3,4);// [kmol]\n",
"zFC3 = zF(3);// [kmol]\n",
"percentC3 = (DyD_C3/zFC3)*100;\n",
"DyD_C5 = Result2(5,4);// [kmol]\n",
"zFC5 = zF(5);// [kmol]\n",
"percentC5 = (DyD_C5/zFC5)*100;\n",
"// These do not quite meet the original speification.\n",
"// For Tray 2 & C4\n",
"// From Eqn. 9.195:\n",
"// Value4 = G2*y2/(D*zD)\n",
"n = 2;\n",
"Sum = 0;\n",
"for i = 1:n\n",
"    Val = 1;\n",
"    for j = i:n\n",
"        Val = Val*A(j);\n",
"    end\n",
"    Sum = Sum+Val;\n",
"end\n",
"Value4 = 1+Sum;\n",
"// From The enthalpy Balnce:\n",
"G2 = 0.675;\n",
"// From Eqn. 9.211:\n",
"y2 = Value4*DyD/G2;\n",
"// Similarly:\n",
"// Value4 = [C1 C2 C3 C4 C5 C6]\n",
"Value4 = [1.0235 1.1062 1.351 2.705 10.18 46.9];\n",
"for i = 1:6\n",
"    y2(i) = Result2(i,4)*Value4(i)/G2;\n",
"end\n",
"Y2 = sum(y2);\n",
"// Since Y2 is not equal to 1. THerefore the original temperature is incorrect. By adjusting y2 to unity.\n",
"// The dew point is 77 OC instead of 66 OC\n",
"// y2_adjusted = [C1 C2 C3 C4 C5 C6]\n",
"y2_adjusted = [0.0419 0.1059 0.2675 0.4939 0.0896 0.00106];\n",
"printf('*****************Composition By Thiele Geddes Method*****************\n');\n",
"printf('Component\t \t \t y2\n')\n",
"for i = 1:6\n",
"    printf('C%d\t \t \t \t%f\n',i,y2_adjusted(i));\n",
"end"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.1: Raoults_law.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.1\n",
"// Page: 349\n",
"\n",
"printf('Illustration 9.1 - Page: 349\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// a:n-heptane b:n-octane\n",
"Pt = 760; // [mm Hg]\n",
"//*****//\n",
"\n",
"Tempa = 98.4;// [boiling point of A,OC]\n",
"Tempb = 125.6;// [boiling point of B,OC]\n",
"x = zeros(6);\n",
"y_star = zeros(6);\n",
"alpha = zeros(6);\n",
"// Data =  [Temp Pa (mm Hg) Pb(mm Hg)]\n",
"Data = [98.4 760 333;105 940 417;110 1050 484;115 1200 561;120 1350 650;125.6 1540 760];\n",
"for i = 1:6\n",
"    x(i) = (Pt-Data(i,3))/(Data(i,2)-Data(i,3));// [mole fraction of heptane in liquid]\n",
"    y_star(i) = (Data(i,2)/Pt)*x(i);\n",
"    alpha(i) = Data(i,2)/Data(i,3);\n",
"end\n",
"printf('T(OC)\t\t\t Pa(mm Hg)\t\t\t Pb(mm Hg)\t\t\t x\t\t\t\t y*\t\t\t alpha\n');\n",
"for i = 1:6\n",
"    printf('%f\t \t %d\t \t \t \t %d\t \t \t \t %f\t \t \t %3f\t \t %f\t \t\n',Data(i,1),Data(i,2),Data(i,3),x(i),y_star(i),alpha(i));\n",
"end"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.2: Azeotropes.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.2\n",
"// Page: 354\n",
"\n",
"printf('Illustration 9.2 - Page: 354\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// a:water b:ethylaniline\n",
"Pt = 760; // [mm Hg]\n",
"ma1 = 50;// [g]\n",
"mb1 = 50;// [g]\n",
"//*******//\n",
"\n",
"// Data =  [Temp Pa(mm Hg) Pb(mm Hg)]\n",
"Data = [38.5 51.1 1;64.4 199.7 5;80.6 363.9 10;96.0 657.6 20;99.15 737.2 22.8;113.2 1225 40];\n",
"Ma = 18.02;// [kg/kmol]\n",
"Mb = 121.1;// [kg/kmol]\n",
"\n",
"for i = 1:6\n",
"    p = Data(i,2)+Data(i,3);\n",
"    if p =  = Pt\n",
"        pa = Data(5,2);// [mm Hg]\n",
"        pb = Data(i,3);// [mm Hg]\n",
"        T = Data(i,1);// [OC]\n",
"    end\n",
"end\n",
"ya_star = pa/Pt;\n",
"yb_star = pb/Pt;\n",
"ya1 = ma1/Ma;// [g mol water]\n",
"yb1 = mb1/Mb;// [g mol ethylalinine]\n",
"Y = ya1*(yb_star/ya_star);// [g mol ethylalinine]\n",
"printf('The original mixture contained %f g mol water and %f g mol ethylalinine\n',ya1,yb1);\n",
"printf('The mixture will continue to boil at %f OC, where the equilibrium vapour of the indicated composition,until all the water evaporated together with %f g mol ethylalinine\n',T,Y);\n",
"printf('The temparature will then rise to 204 OC, and the equilibrium vapour will be of pure ethylalinine');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.3: Multicomponent_Sysems.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.3\n",
"// Page: 362\n",
"\n",
"printf('Illustration 9.3 - Page: 362\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// a:n-C3H8 b:n-C4H10 c:n-C5H12 d:n-C6H14\n",
"// Bubble Point Calculation\n",
"xa = 0.05;\n",
"xb = 0.30;\n",
"xc = 0.40;\n",
"xd = 0.25;\n",
"P = 350;// [kN/square m]\n",
"//******//\n",
"\n",
"// Assume:\n",
"Temp = 60;// [OC]\n",
"x = [0.05 0.30 0.40 0.25];\n",
"m = [4.70 1.70 0.62 0.25];// [At 60 OC]\n",
"// Reference: C5H12\n",
"mref = m(3);\n",
"Sum = 0;\n",
"alpha = zeros(4)\n",
"alpha_x = zeros(4);\n",
"for i = 1:4\n",
"    alpha(i) = m(i)/m(3);\n",
"    alpha_x(i) = alpha(i)*x(i);\n",
"    Sum = Sum+alpha_x(i);\n",
"end\n",
"// From Eqn. 9.23:\n",
"SumF = Sum;\n",
"Sum = 0;\n",
"mref = 1/SumF;\n",
"// Corresponding Temparature from the nomograph:\n",
"Temp = 56.8;// [OC]\n",
"m = [4.60 1.60 0.588 0.235];// [At 56.8 OC]\n",
"for i = 1:4\n",
"    alpha(i) = m(i)/m(3);\n",
"    alpha_x(i) = alpha(i)*x(i);\n",
"    Sum = Sum+alpha_x(i);\n",
"end\n",
"SumF = Sum;\n",
"mref = 1/SumF;\n",
"//  Corresponding Temparature from the nomograph:\n",
"Temp = 56.7;// [OC]\n",
"Bt = 56.8;// [OC]\n",
"yi = zeros(4);\n",
"for i = 1:4\n",
"    yi(i) = alpha_x(i)/Sum;\n",
"end\n",
"printf('The Bubble Point is %f OC\n',Bt);\n",
"printf('Bubble point vapour composition \n');\n",
"printf('\t   yi\n');\n",
"printf('n-C3\t %f\n',yi(1));\n",
"printf('n-C4\t %f\n',yi(2));\n",
"printf('n-C5\t %f\n',yi(3));\n",
"printf('n-C6\t %f\n',yi(4));\n",
"\n",
"printf('\n \n \n');\n",
"\n",
"// Dew Point Calculation\n",
"// Asume:\n",
"ya = 0.05;\n",
"yb = 0.30;\n",
"yc = 0.40;\n",
"yd = 0.25;\n",
"Temp = 80;// [OC]\n",
"y = [0.05 0.30 0.40 0.25];\n",
"m = [6.30 2.50 0.96 0.43];// [At 60 OC]\n",
"// Reference: C5H12\n",
"mref = m(3);\n",
"Sum = 0;\n",
"alpha = zeros(4)\n",
"alpha_y = zeros(4);\n",
"for i = 1:4\n",
"    alpha(i) = m(i)/m(3);\n",
"    alpha_y(i) = y(i)/alpha(i);\n",
"    Sum = Sum+alpha_y(i);\n",
"end\n",
"\n",
"// From Eqn. 9.29:\n",
"SumF = Sum;\n",
"Sum = 0;\n",
"mref = SumF;\n",
"// Corresponding Temparature from the nomograph:\n",
"Temp = 83.7;// [OC]\n",
"m = [6.60 2.70 1.08 0.47];// [At 56.8 OC]\n",
"for i = 1:4\n",
"    alpha(i) = m(i)/m(3);\n",
"    alpha_y(i) = y(i)/alpha(i);\n",
"    Sum = Sum+alpha_y(i);\n",
"end\n",
"SumF = Sum;\n",
"mref = 1/SumF;\n",
"//  Corresponding Temparature from the nomograph:\n",
"Temp = 84;// [OC]\n",
"Dt = 84;// [OC]\n",
"xi = zeros(4);\n",
"for i = 1:4\n",
"    xi(i) = alpha_y(i)/Sum;\n",
"end\n",
"printf('The Dew Point is %f OC\n',Dt);\n",
"printf('Dew point liquid composition \n');\n",
"printf('\t   xi\n');\n",
"printf('n-C3\t %f\n',xi(1));\n",
"printf('n-C4\t %f\n',xi(2));\n",
"printf('n-C5\t %f\n',xi(3));\n",
"printf('n-C6\t %f\n',xi(4));"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.4: Partial_Condensation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.4\n",
"// Page: 365\n",
"\n",
"printf('Illustration 9.4 - Page: 365\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// Basis:\n",
"F = 100;// [mol feed]\n",
"zF = 0.5;\n",
"D = 60;// [mol]\n",
"W = 40;// [mol]\n",
"//*******//\n",
"\n",
"// From Illustration 9.1, Equilibrium data:\n",
"Data = [1 1;0.655 0.810;0.487 0.674;0.312 0.492;0.1571 0.279;0 0];\n",
"Feed = [0 0;1 1];\n",
"// The operating line is drawn with a slope -(W/D) to cut the equilibrium line.\n",
"deff('[y] = f44(x)','y = -((W/D)*(x-zF))+zF');\n",
"x = 0.2:0.1:0.6;\n",
"scf(16);\n",
"plot(Data(:,1),Data(:,2),Feed(:,1),Feed(:,2),x,f44);\n",
"xgrid();\n",
"xlabel('Mole fraction of heptane in liquid');\n",
"ylabel('Mole fraction of heptane in vapour');\n",
"legend('Equilibrium Line','Feed Line','Operating Line');\n",
"// The point at which the operating line cuts the equilibrium line has the following composition* temparature:\n",
"yd = 0.575;// [mole fraction heptane in vapour phase]\n",
"xW = 0.387;// [mole fraction heptane in liquid phase]\n",
"Temp = 113;// [OC]\n",
"printf('mole fraction of heptane in vapour phase %f \n',yd);\n",
"printf('mole fraction of heptane in liquid phase %f\n',xW);\n",
"printf('Temparature is %d OC\n',Temp);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.5: Multicomponent_Systems_Ideal_Solution.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.5\n",
"// Page: 366\n",
"\n",
"printf('Illustration 9.5 - Page: 366\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"Pt = 760;// [mm Hg]\n",
"zFa = 0.5;// [mol fraction benzene]\n",
"zFb = 0.25;// [mol fraction toulene]\n",
"zFc = 0.25;// [mol fraction o-xylene]\n",
"//********//\n",
"\n",
"// Basis:\n",
"F = 100;// [mol feed]\n",
"// For Summtion of Yd_star to be unity, W/D = 2.08 \n",
"// The Eqn.are \n",
"// (1): W+D = F \n",
"// (2): W-2.08D = 0\n",
"a = [1 1;1 -2.08];\n",
"b = [F;0];\n",
"soln = a\b;\n",
"W = soln(1);\n",
"D = soln(2);\n",
"Sub = ['A','B','C'];\n",
"p = [1370 550 200];// [mm Hg]\n",
"m = zeros(3);\n",
"zF = [zFa zFb zFc];// [Given]\n",
"yd_star = zeros(3);\n",
"xW = zeros(3);\n",
"for i = 1:3\n",
"    m(i) = p(i)/Pt;\n",
"    yd_star(i) = zF(i)*((W/D)+1)/(1+(W/(D*m(i))));\n",
"    xW(i) = yd_star(i)/m(i);\n",
"end\n",
"printf('\t \t \t \t \t \t \t \t  At W/D = 2.08\n\n\n');\n",
"printf('Substance \t \t p(mm Hg)\t \t m\t \t \t \t zF\t \t \t \t yd*\t\t\t\txW\n');\n",
"for i = 1:3\n",
"    printf('%c\t \t \t %d\t \t \t %f\t \t \t %f\t \t \t %f \t \t \t%f\n',Sub(i),p(i),m(i),zF(i),yd_star(i),xW(i));\n",
"end"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.6: Differential_Distillation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.6\n",
"// Page: 370\n",
"\n",
"printf('Illustration 9.6 - Page: 370\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// Basis:\n",
"F = 100;// [mol]\n",
"xF = 0.5;\n",
"D = 0.6*100;// [mol]\n",
"//******//\n",
"\n",
"W = F-D;// [mol]\n",
"// From Illustration 9.1:\n",
"alpha = 2.16;// [average value of alpha]\n",
"// From Eqn.9.46;\n",
"deff('[y] = f45(xW)','y = log(F*xF/(W*xW))-(alpha*log(F*(1-xF)/(W*(1-xW))))');\n",
"xW = fsolve(0.5,f45);// [mole fraction heptane]\n",
"deff('[y] = f46(yD)','y = F*xF-((D*yD)+(W*xW))');\n",
"yD = fsolve(100,f46);// [mole fraction heptane]\n",
"printf('Mole Fraction of heptane in the distillate is %f \n',yD);\n",
"printf('Mole Fraction of heptane in the residue is %f \n',xW);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.7: Multicomponent_Systems_Ideal_Solution.sce"
		   ]
		  },
  {
"cell_type": "code",
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"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.7\n",
"// Page: 371\n",
"\n",
"printf('Illustration 9.7 - Page: 371\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"// a:benzene b:toulene c:o-xylene\n",
"// Assume:\n",
"Bt = 100;//[OC]\n",
"pa = 1370;// [mm Hg]\n",
"pb = 550;// [mm Hg]\n",
"pc = 200;// [mm Hg]\n",
"xFa = 0.5;// [mole fraction]\n",
"xFb = 0.25;// [mole fraction]\n",
"xFc = 0.25;// [mole fraction]\n",
"// Basis:\n",
"F = 100;// [mol]\n",
"D = 32.5;// [mol]\n",
"//*******//\n",
"\n",
"ref = pb;\n",
"alpha_a = pa/ref;\n",
"alpha_b = pb/ref;\n",
"alpha_c = pc/ref;\n",
"W = F-D;// [mol]\n",
"xbW = 0.3;// [mol]\n",
"xaW = 0.4;// [mol]\n",
"xcW = 0.3;// [mol]\n",
"err = 1;\n",
"while(err>(10^(-1)))\n",
"    // From Eqn. 9.47:\n",
"    deff('[y] = f47(xaW)','y = log(F*xFa/(W*xaW))-(alpha_a*log(F*xFb/(W*xbW)))');\n",
"    xaW = fsolve(xbW,f47);\n",
"    deff('[y] = f48(xcW)','y = log(F*xFc/(W*xcW))-(alpha_c*log(F*xFb/(W*xbW)))');\n",
"    xcW = fsolve(xbW,f48);\n",
"    xbW_n = 1-(xaW+xcW);\n",
"    err = abs(xbW-xbW_n);\n",
"    xbw = xbW_n;\n",
"end\n",
"// Material balance:\n",
"// for A:\n",
"deff('[y] = f49(yaD)','y = F*xFa-((D*yaD)+(W*xaW))');\n",
"yaD = fsolve(100,f49);// [mole fraction benzene]\n",
"// For B:\n",
"deff('[y] = f50(ybD)','y = F*xFb-((D*ybD)+(W*xbW))');\n",
"ybD = fsolve(100,f50);// [mole fraction toulene]\n",
"// For C:\n",
"deff('[y] = f51(ycD)','y = F*xFc-((D*ycD)+(W*xcW))');\n",
"ycD = fsolve(100,f51);// [mole fraction o-xylene]\n",
"printf('The residual compositions are:\n');\n",
"printf('Benzene:%f\n',xaW);\n",
"printf('Toulene:%f\n',xbW);\n",
"printf('o-xylene:%f\n',xcW);\n",
"printf('The composited distillate compositions are:\n');\n",
"printf('Benzene:%f\n',yaD);\n",
"printf('Toulene:%f\n',ybD);\n",
"printf('o-xylene:%f\n',ycD);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.8: Optimum_Reflux_Ratio.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
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"source": [
"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.8\n",
"// Page: 388\n",
"\n",
"printf('Illustration 9.8 - Page: 388\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data*****//\n",
"// a:methanol b:water\n",
"Xa = 0.5;// [Wt fraction]\n",
"Temp1 = 26.7;// [OC]\n",
"Temp2 = 37.8;// [OC]\n",
"F1 = 5000;// [kg/hr]\n",
"//******//\n",
"\n",
"//(a)\n",
"Ma = 32.04;// [kg/kmol]\n",
"Mb = 18.02;// [kg/kmol]\n",
"Xa = 0.5;// [Wt fraction]\n",
"Xb = 1-Xa;// [Wt fraction]\n",
"Temp1 = 26.7;// [OC]\n",
"Temp2 = 37.8;// [OC]\n",
"F1 = 5000;// [kg/hr];\n",
"// Basis: 1hr\n",
"F = (F1*Xa/Ma)+(F1*Xb/Mb);// [kmol/hr]\n",
"// For feed:\n",
"zF = (F1*Xa/Ma)/F;// [mole fracton methanol]\n",
"MavF = F1/F;// [kg/kmol]\n",
"// For distillate:\n",
"xD = (95/Ma)/((95/Ma)+(5/Mb));// [mole fraction methanol]\n",
"MavD = 100/((95/Ma)+(5/Mb));// [kg/kmol]\n",
"// For residue:\n",
"xW = (1/Ma)/((1/Ma)+(99/Mb));// [mole fraction methanol]\n",
"MavR = 100/((1/Ma)+(99/Mb));// [kg/kmol]\n",
"// (1): D+W = F [Eqn.9.75]\n",
"// (2): D*xD+W*xW = F*zF [Eqn. 9.76]\n",
"// Solvving simultaneously:\n",
"a = [1 1;xD xW];\n",
"b = [F;F*zF];\n",
"soln = a\b;\n",
"D = soln(1);// [kmol/h]\n",
"W = soln(2);// [kmol/h]\n",
"printf('Quantity of Distillate is %f kg/hr\n',D*MavD);\n",
"printf('Quantity of Residue is %f kg/hr\n',W*MavR);\n",
"printf('\n');\n",
"\n",
"// (b)\n",
"// For the vapour-liquid equilibria:\n",
"Tempo = 19.69;// [Base Temp. according to 'International Critical Tables']\n",
"BtR = 99;// [Bubble point of the residue, OC]\n",
"hR = 4179;// [J/kg K]\n",
"hF = 3852;// [J/kg K]\n",
"deff('[y] = f52(tF)','y = (F1*hF*(tF-Temp1))-((W*MavR)*hR*(BtR-Temp2))');\n",
"tF = fsolve(Temp1,f52);// [OC]\n",
"BtF = 76;// [Bubble point of feed, OC]\n",
"// For the feed:\n",
"delta_Hs = -902.5;// [kJ/kmol]\n",
"Hf = ((hF/1000)*MavF*(tF-Tempo))+delta_Hs;// [kJ/kmol]\n",
"// From Fig 9.27:\n",
"HD = 6000;// [kJ/kmol]\n",
"HLo = 3640;// [kJ/kmol]\n",
"HW = 6000;// [kJ/kmol]\n",
"printf('The enthalpy of feed is %f kJ/kmol\n',Hf);\n",
"printf('The enthalpy of the residue is %f kJ/kmol\n',HW);\n",
"printf('\n');\n",
"\n",
"// (c)\n",
"// From Fig.9.27:\n",
"// The miium reflux ratio is established by the tie line (x = 0.37 y = 0.71), which extended pass through F,the feed.\n",
"// At Dm:\n",
"Qm = 62570;// [kJ/kmol]\n",
"Hg1 = 38610;// [kJ/kmol]\n",
"// From Eqn. 9.65:\n",
"Rm = (Qm-Hg1)/(Hg1-HLo);\n",
"printf('The minimum reflux ratio is %f\n',Rm);\n",
"printf('\n');\n",
"\n",
"// (d)\n",
"// From Fig. 9.28:\n",
"Np = 4.9;\n",
"// But it include the reboiler.\n",
"Nm = Np-1;\n",
"printf('The minimum number of theoretical trys required is %f \n',Nm);\n",
"printf('\n');\n",
"\n",
"// (e)\n",
"R = 1.5*Rm;\n",
"// Eqn. 9.65:\n",
"deff('[y] = f53(Q_prime)','y = R-((Q_prime-Hg1)/(Hg1-HLo))');\n",
"Q_prime = fsolve(2,f53);// [kJ/kmol]\n",
"deff('[y] = f54(Qc)','y = Q_prime-(HD+(Qc/D))');\n",
"Qc = fsolve(2,f54);// [kJ/hr]\n",
"Qc = Qc/3600;// [kW]\n",
"printf('The Condensor heat load is %f kW\n',Qc);\n",
"// From Eqn. 9.77:\n",
"deff('[y] = f55(Q_dprime)','y = (F*Hf)-((D*Q_prime)+(W*Q_dprime))');\n",
"Q_dprime = fsolve(2,f55);\n",
"deff('[y] = f56(Qb)','y = Q_dprime-(HW-(Qb/W))');\n",
"Qb = fsolve(2,f56);// [kJ/hr]\n",
"Qb = Qb/3600;// [kW]\n",
"printf('The Reboiler heat load is %f kW\n',Qb);\n",
"printf('\n');\n",
"\n",
"// (f)\n",
"// From Fig: 9.28\n",
"Np = 9;\n",
"// But it is including the reboiler\n",
"printf('No. of theoretical trays in tower is %d\n',Np-1);\n",
"G1 = D*(R+1);// [kmol/hr]\n",
"Lo = D*R;// [kmol/hr]\n",
"// From Fig. 9.28:\n",
"// At the feed tray:\n",
"x4 = 0.415;\n",
"y5 = 0.676;\n",
"x5 = 0.318;\n",
"y6 = 0.554;\n",
"// From Eqn. 9.64:\n",
"deff('[y] = f57(L4)','y = (L4/D)-((xD-y5)/(y5-x4))');\n",
"L4 = fsolve(2,f57);// [kmol/hr]\n",
"// From Eqn. 9.62:\n",
"deff('[y] = f58(G5)','y = (L4/G5)-((xD-y5)/(xD-x4))');\n",
"G5 = fsolve(2,f58);// [kmol/hr]\n",
"// From Eqn. 9.74:\n",
"deff('[y] = f59(L5_bar)','y = (L5_bar/W)-((y6-xW)/(y6-x5))');\n",
"L5_bar = fsolve(2,f59);// [kmol/hr]\n",
"// From Eqn. 9.72:\n",
"deff('[y] = f60(G6_bar)','y = (L5_bar/G6_bar)-((y6-xW)/(x5-xW))');\n",
"G6_bar = fsolve(2,f60);// [kmol/hr]\n",
"// At the bottom:\n",
"// Material Balance:\n",
"// Eqn. 9.66:\n",
"// (1): L8_bar-GW_bar = W;\n",
"// From Fig. 9.28:\n",
"yW = 0.035;\n",
"x8 = 0.02;\n",
"// From Eqn. 9.72:\n",
"L8ByGW_bar = (yW-xW)/(x8-xW);\n",
"// (2): L8_bar-(L8ByGW_bar*Gw_bar) = 0\n",
"a = [1 -1;1 -L8ByGW_bar];\n",
"b = [W;0];\n",
"soln = a\b;\n",
"L8_bar = soln(1);// [kmol/h]\n",
"GW_bar = soln(2);// [kmol/h]\n",
"printf('The Liquid quantity inside the tower is %f kmol/hr\n',L8_bar);\n",
"printf('The vapour quantity inside the tower is %f kmol/hr\n',GW_bar);\n",
"printf('\n');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.9: Use_of_Open_Steam.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
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"clear;\n",
"clc;\n",
"\n",
"// Illustration 9.9\n",
"// Page: 395\n",
"\n",
"printf('Illustration 9.9 - Page: 395\n\n');\n",
"\n",
"// solution\n",
"\n",
"//****Data****//\n",
"P = 695;// [kN/square m]\n",
"//********//\n",
"\n",
"// a:methanol b:water\n",
"// From Illustration 9.8:\n",
"Ma = 32.04;// [kg/kmol]\n",
"Mb = 18.02;// [kg/kmol]\n",
"F = 216.8;// [kmol/h]\n",
"Tempo = 19.7;// [OC]\n",
"zF = 0.360;// [mole fraction methanol]\n",
"HF = 2533;// [kJ/kmol]\n",
"D = 84.4;// [kkmol/h]\n",
"zD = 0.915;// [mole fraction methanol]\n",
"HD = 3640;// [kJ/kmol]\n",
"Qc = 5990000;// [kJ/h]\n",
"// Since the bottom will essentially be pure water:\n",
"HW = 6094;// [kJ/kmol]\n",
"// From Steam tables:\n",
"Hs = 2699;// [enthalpy of saturated steam, kJ/kg]\n",
"hW = 4.2*(Tempo-0);// [enthalpy of water, kJ/kg]\n",
"HgNpPlus1 = (Hs-hW)*Mb;// [kJ/kmol]\n",
"// (1): GNpPlus1-W = D-F [From Eqn. 9.86]\n",
"// (2): (GNpPlus1*HgNpPlus1)-(W*HW) = (D*HD)+Qc-(F*HF) [From Eqn. 9.88]\n",
"a = [1 -1;HgNpPlus1 -HW];\n",
"b = [D-F;(D*HD)+Qc-(F*HF)];\n",
"soln = a\b;\n",
"GNpPlus1 = soln(1);// [kmol/h]\n",
"W = soln(2);// [kmol/h]\n",
"// From Eqn. 9.87:\n",
"deff('[y] = f61(xW)','y = (F*zF)-((D*zD)+(W*xW))');\n",
"xW = fsolve(2,f61);\n",
"// The enthalpy of the solution at its bubble point is 6048 kJ/kmol, sufficiently closed to 6094 assumed earlier.\n",
"// For delta_w:\n",
"xdelta_w = W*xW/(W-GNpPlus1);\n",
"Q_dprime = ((W*HW)-(GNpPlus1*HgNpPlus1))/(W-GNpPlus1);// [kJ/kmol]\n",
"// From Fig 9.27 ad Fig. 9.28, and for the stripping section:\n",
"Np = 9.5;\n",
"printf('Steam Rate: %f kmol/h\n',GNpPlus1);\n",
"printf('Bottom Composition: xW: %f\n',xW);\n",
"printf('Number of theoretical stages: %f\n',Np);"
   ]
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