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{
"metadata": {
"name": "",
"signature": "sha256:fc87d6d9b6be61c481eaede8b73c8cf240680807ed293ac553e78b065098e01d"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8: Evaporation"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4-1, Page number 498"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Heat Transfer Area in a Single-Effect Evaporator\n",
"\n",
"#Variable declaration\n",
"F = 9072. #Feed rate to the evaporator, kg/hr\n",
"xF = 1. #weight percent of salt, kg/kg\n",
"TF = 311.0 #Temperature of feed, K\n",
"xL = 1.5 #Weight percentage of concentrated product, kg/kg \n",
"P = 101.325 #Pressure of vapor space, kPa\n",
"Ps = 143.3 #Pressure of saturated steam used for heating, kPa\n",
"U = 1704. #Overall heat transfer coefficient, W/m2K\n",
"cpF = 4.140 #Specific heat of Feed to the evaporator, kJ/(kg.K)\n",
"Hv373 = 2257. #Latent heat of evaporation of water at 373.2 K\n",
"Hv143 = 2230. #Latent heat of evaporation of saturated water at 143.3 kPa\n",
"Ts = 383.2 #Temperature of Saturated steam at 143.3 kPa\n",
"TL = 373.2 #Temperature of concentrated Liquid enthalpy calculation, K\n",
"Tref = 373.2 #Reference temperature for enthalpy calculation, K\n",
"\n",
"#Calculation \n",
"L = F*xF/xL\n",
"V = F-L\n",
" #Energy Balance\n",
"hF = F*cpF*(TF-Tref)\n",
"hL = L*cpF*(TL-Tref)\n",
"hV = Hv373*V\n",
"#hF + q = hL + hV\n",
"q = (hL+hV-hF)\n",
"S = q/(Hv143)\n",
"qsi = q*1000/3600\n",
"A = qsi/(U*(Ts-TL))\n",
"\n",
"#Result\n",
"print 'Concetrated liquid Rate: %5.1f kg/h'%L\n",
"print 'Vapor rate from evaporator: %5.1f kg/h'%V\n",
"print 'Heat Transfer area required: %4.1f m2'%(A)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Concetrated liquid Rate: 6048.0 kg/h\n",
"Vapor rate from evaporator: 3024.0 kg/h\n",
"Heat Transfer area required: 149.3 m2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4-2, Page Number 499"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Use of Duhring Chart for Boiling point rise\n",
"\n",
"#Variable declaration\n",
"P = 25.6 #Pressure in the evaporator, kPa\n",
"C = 30 #Weight % of NaOH in solution, K\n",
"Tb256 = 65.6 #Boiling point of water at 25.6 kPa, \u00b0C or 150 \u00b0C\n",
"\n",
"#Calculation\n",
"#From Fig. 8.4-2 for 30% wt of NaoOH and boiling point of water 150 \u00b0F\n",
"Ts = 175 #Boiling point of solution \u00b0F\n",
"TsC = 79.5 #Boiling point of solution \u00b0C\n",
"BPR = TsC-Tb256\n",
"#Result\n",
"\n",
"print \"Boiling point rise: \",BPR,\"\u00b0C\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Boiling point rise: 13.9 \u00b0C\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4-3, Page number 501"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Evaporation of NaOH Solution\n",
"\n",
"# Variable declaration\n",
"F = 4536. #Feed rate to the evaporator, kg/hr\n",
"xF = 0.2 #weight percent of NaOH, kg/kg\n",
"TF = 60.0 #Temperature of feed, \u00b0C\n",
"xL = 0.5 #Weight percentage of concentrated product, kg/kg \n",
"P = 11.7 #Pressure of vapor space, kPa\n",
"Ps = 172.4 #Pressure of saturated steam used for heating, kPa\n",
"U = 1560. #Overall heat transfer coefficient, W/m2K\n",
"cpS = 1.884 #Specific heat of steam 11.7 kPa , kJ/(kg.K)\n",
"Hv895 = 2667. #Enthalpy of steam at 11.7 kPa and 89.5\u00b0C\n",
"Hv489 = 2590. #Enthalp of steam at 11.7 kPa and 49.5\u00b0C\n",
"LambdaV1724 = 2214 #Latent heat of evaporation of water at 172.4 kPa and at 115.6\u00b0C\n",
"Ts = 115.6 #Saturation temperature of 172.4kPa in \u00b0C\n",
"\n",
"# Calculation\n",
"L = F*xF/xL\n",
"V = F - L\n",
"BPw117 = 48.9 #BP of Water From steam table, \u00b0C\n",
"BPs117 = 89.5 #BP of Soln From Duhring Chart Fig 8.4-2, \u00b0C\n",
"BPR = BPs117-BPw117\n",
"hF = 214. #Enthalpy of 20% feed at 60\u00b0C, KJ/Kg from fig 8.4-3 \n",
"hL = 505. #Enthalpy of 50% feed at 89.5\u00b0C, KJ/Kg\n",
"HV = Hv489 + cpS*BPR\n",
"S = (L*hL+V*HV-F*hF)/LambdaV1724\n",
"Q = S*LambdaV1724/3600 #Heat addition rate in kW\n",
"#Newtons law of cooling \n",
"\n",
"A = Q*1000/(U*(Ts-BPs117))\n",
"SteamEco = V/S\n",
"#Result\n",
"print \"The steam used\",round(S,1),\"kg steam/h\"\n",
"print \"The calculated steam economy is \",round(SteamEco,3)\n",
"print \"The heating surface area is \", round(A,1),\"m2\"\n",
"print 'Difference in answers is due to machin precision'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The steam used 3253.2 kg steam/h\n",
"The calculated steam economy is 0.837\n",
"The heating surface area is 49.1 m2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.5-1, Page number 505"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Evaporation of Sugar Solution in a Triple-Effect Evaporator\n",
"import numpy as np\n",
"from scipy.interpolate import interp1d\n",
"\n",
"# Variable declaration\n",
"xF = 0.1 #wt fraction of sugar in Feed\n",
"xP = 0.5 #wt fraction of sugar in Product\n",
"Ts1 = 121.1 #Saturation temperature of the steam at 205.5kPa in \u00b0C\n",
"F = 22680. #Feed Rate kg/hr\n",
"TF = 26.7 #Temperature of the feed, \u00b0C\n",
"U1 = 3123. #Overall heat transfer coefficient for evaporator 1, W/(m2K) \n",
"U2 = 1987. #Overall heat transfer coefficient for evaporator 2, W/(m2K)\n",
"U3 = 1136. #Overall heat transfer coefficient for evaporator 3, W/(m2K)\n",
"T = np.array([50.,60.,70.,80.,90.,100.,110.,120,126.])\n",
"H = np.array([2592.2,2609.7,2626.9,2643.8,2660.1,2676.0,2691.3,2706.0,2714.4])\n",
"h = np.array([209.3,251.1,293.0,334.9,376.9,419.1,461.3,503.7,529.2])\n",
"lamb = np.array([2382.9,2358.6,2334.0,2308.8,2283.2,2256.9,2230.0,2202.2,2185.2])\n",
"cp = np.array([])\n",
"\n",
"# Calculation\n",
"def BPRDegC(xw):\n",
" return 1.78*xw+6.22*xw*xw\n",
"\n",
"def SpecHeat(xw):\n",
" return 4.19-2.35*xw\n",
"\n",
"fH = interp1d(T,H)\n",
"fh = interp1d(T,h)\n",
"flamb = interp1d(T,lamb)\n",
"\n",
"#Step 1\n",
"BPR3 = BPRDegC(xP)\n",
"Tvs3 = 51.67 #Saturation temperature of steam at 13.4 kPa for 3rd evaporator\n",
"T3 = Tvs3 + BPR3\n",
"\n",
"#Step 2\n",
"L3 = F*xF/xP #Concentrated product rate, kg/hr\n",
"V = F - L3 #Total water vaporised from three evaporators (V = V1 + v2 +v3 ), kg/hr\n",
"V1 = V/3 #Assuming V1 = V2 = V3\n",
"V2 = V1\n",
"V3 = V1\n",
"#Making liquid balance on each evaporator \n",
"L1 = F - V1 #Concentrated liquid rate from evaporator 1, kg/hr\n",
"L2 = L1 - V2 #Concentrated liquid rate from evaporator 2, kg/hr\n",
"L3 = L2 - V3\n",
"#Making Solid balance on each evaporator \n",
"x1 = F*xF/L1\n",
"x2 = L1*x1/L2\n",
"x3 = xP\n",
"\n",
"#Step 3\n",
"BPR1 = BPRDegC(x1)\n",
"BPR2 = BPRDegC(x2)\n",
"BPR3 = BPRDegC(x3)\n",
"SDelT = Ts1 - Tvs3 - (BPR1+BPR2+BPR3)\n",
"ISU13 = 1/U1+1/U2+1/U3\n",
"DelT1 = SDelT*(1/U1)/ISU13\n",
"DelT2 = SDelT*(1/U2)/ISU13\n",
"DelT3 = SDelT*(1/U3)/ISU13\n",
"T1 = Ts1 - DelT1\n",
"T2 = T1 - BPR1 - DelT2\n",
"Ts2 = T1 - BPR1\n",
"T3 = T2 -BPR2 - DelT3\n",
"Ts3 = T2 - BPR2\n",
"Ts4 = T3 - BPR3\n",
"\n",
"#Step4: \n",
"CpF = SpecHeat(xF) #Calculate Heat Capacities\n",
"Cp1 = SpecHeat(x1)\n",
"Cp2 = SpecHeat(x2)\n",
"Cp3 = SpecHeat(x3)\n",
"\n",
"H1 = fH(Ts2) + 1.884*BPR1 #for effect 1\n",
"lambdas1 = fH(Ts1)-fh(Ts1) \n",
"H2 = fH(Ts3) + 1.884*BPR2 #for effect 2\n",
"lambdas2 = fH(Ts2)-fh(Ts2) \n",
"H3 = fH(Ts4) + 1.884*BPR3 #for effect 3\n",
"lambdas3 = fH(Ts3)-fh(Ts3) \n",
"\n",
"a11 = Cp1*T1 - lambdas2 - H2\n",
"a12 = -(Cp2*T2 - H2)\n",
"b1 = -F*lambdas2\n",
"a21 = lambdas3\n",
"a22 = Cp2*T2 - lambdas3 - H3\n",
"b2 = L3*Cp3*T2 - L3*H3\n",
"\n",
"\n",
"a = np.array([[a11,a12], [a21,a22]])\n",
"b = np.array([b1,b2])\n",
"L1,L2 = np.linalg.solve(a, b)\n",
"V1 = F - L1\n",
"V2 = L1 - L2\n",
"V3 = L2 - L3\n",
"S = (L1*Cp1*T1 + V1*H1 - F*CpF*TF)/lambdas1\n",
"\n",
"#Step5:\n",
"q1 = S*lambdas1*1000/3600\n",
"q2 = V1*lambdas2*1000/3600\n",
"q3 = V2*lambdas3*1000/3600\n",
"\n",
"A1 = q1/(U1*DelT1)\n",
"A2 = q2/(U2*DelT2)\n",
"A3 = q3/(U3*DelT3)\n",
"\n",
"Am = Am1 = (A1+A2+A3)/3\n",
"\n",
"#Step6:\n",
"x1 = F*xF/L1\n",
"x2 = L1*x1/L2\n",
"x3 = L2*x2/L3\n",
"\n",
"#Step7:\n",
"BPR1 = BPRDegC(x1)\n",
"BPR2 = BPRDegC(x2)\n",
"BPR3 = BPRDegC(x3)\n",
"SDelT = Ts1 - Tvs3 - (BPR1+BPR2+BPR3)\n",
"\n",
"DelT1 = DelT1*A1/Am\n",
"DelT2 = DelT2*A2/Am\n",
"DelT3 = DelT3*A3/Am\n",
"\n",
"T1 = Ts1 - DelT1\n",
"T2 = T1 - BPR1 - DelT2\n",
"Ts2 = T1 - BPR1\n",
"T3 = T2 -BPR2 - DelT3\n",
"Ts3 = T2 - BPR2\n",
"Ts4 = T3 - BPR3\n",
"\n",
"\n",
"#Step8: \n",
"CpF = SpecHeat(xF) #Calculate Heat Capacities\n",
"Cp1 = SpecHeat(x1)\n",
"Cp2 = SpecHeat(x2)\n",
"Cp3 = SpecHeat(x3)\n",
"\n",
"H1 = fH(Ts2) + 1.884*BPR1 #for effect 1\n",
"lambdas1 = fH(Ts1)-fh(Ts1) \n",
"H2 = fH(Ts3) + 1.884*BPR2 #for effect 2\n",
"lambdas2 = fH(Ts2)-fh(Ts2) \n",
"H3 = fH(Ts4) + 1.884*BPR3 #for effect 3\n",
"lambdas3 = fH(Ts3)-fh(Ts3) \n",
"\n",
"a11 = Cp1*T1 - lambdas2 - H2\n",
"a12 = -(Cp2*T2 - H2)\n",
"b1 = -F*lambdas2\n",
"a21 = lambdas3\n",
"a22 = Cp2*T2 - lambdas3 - H3\n",
"b2 = L3*Cp3*T2 - L3*H3\n",
"\n",
"a = np.array([[a11,a12], [a21,a22]])\n",
"b = np.array([b1,b2])\n",
"L1,L2 = np.linalg.solve(a, b)\n",
"V1 = F - L1\n",
"V2 = L1 - L2\n",
"V3 = L2 - L3\n",
"S = (L1*Cp1*T1 + V1*H1 - F*CpF*TF)/lambdas1\n",
"\n",
"q1 = S*lambdas1*1000/3600\n",
"q2 = V1*lambdas2*1000/3600\n",
"q3 = V2*lambdas3*1000/3600\n",
"\n",
"A1 = q1/(U1*DelT1)\n",
"A2 = q2/(U2*DelT2)\n",
"A3 = q3/(U3*DelT3)\n",
"Am = (A1+A2+A3)/3\n",
"SEconomy = (V1+V2+V3)/S\n",
"\n",
"#Results\n",
"print 'Area A1 A2 and A3 for 1st 2nd and 3rd effect are %4.3f, %4.3f,and %4.3f'%(A1,A2,A3) \n",
"print \"The Average area of each effect\",round(Am,2),\"as compared to average area\",round(Am1,2),\"in first trial\" \n",
"print \"Steam Economy for tripple effect evaporator:\", round(SEconomy,3) \n",
"print 'Difference in answers is due to machin precision'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Area A1 A2 and A3 for 1st 2nd and 3rd effect are 111.421, 113.714,and 111.640\n",
"The Average area of each effect 112.26 as compared to average area 112.08 in first trial\n",
"Steam Economy for tripple effect evaporator: 1.999\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}
|
