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|
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 7 : Combustion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.1 Page 434"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a Net H2 in coal = 0.535 kg. b \n",
"Combined water in the coal = 20.304 kg. c \n",
"GCV by Dulongs formula = 17855.94 kJ/kg. d \n",
"NCV of the coal = 16057.95325 kJ/kg. e \n",
"Total Carbon by Calderwood eq = 43.5822593081 .\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables \n",
"# basis 100 kg as received coal\n",
"O2 = 18.04 #kg\n",
"nH2 = 2.79-(O2/8) #kg\n",
"print \"a Net H2 in coal = \",nH2,\" kg. b \"\n",
"cbW = 1.128*18 # kg \n",
"print \"Combined water in the coal = \",cbW,\" kg. c \"\n",
"\n",
"# Calculation \n",
"# Dulong's formula\n",
"GCV1 = 33950*(50.22/100) + 144200*nH2/100 + 9400*.37/100 # kJ/kg\n",
"\n",
"# Result\n",
"print \"GCV by Dulongs formula = \",GCV1,\" kJ/kg. d \"\n",
"tH2 = 1.395 # kmol\n",
"wp = tH2*18 + 7\n",
"Hv = 2442.5*wp/100 # kJ/kg fuel\n",
"GCV2 = 23392*(1-.21-.07) # as of received coal\n",
"NCV = GCV2-Hv\n",
"print \"NCV of the coal = \",NCV,\" kJ/kg. e \"\n",
"# Calderwood eq\n",
"# Total C = 5.88 + .00512(B-40.5S) +- .0053[80-100*(VM/FC)]**1.55\n",
"C = 5.88 + .00512*(7240.8-40.5*.37)+.0053*(80-56.52)**1.55\n",
"print \"Total Carbon by Calderwood eq = \",C,\".\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.2 Page 436"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"NCV = 42323.1875 kJ/kg.\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables \n",
"# basis 1 kg crude oil\n",
"H2 = .125 # kg burnt\n",
"\n",
"# Calculation \n",
"H2O = H2*18/2.\n",
"Lh = H2O*2442.5 #kJ\n",
"GCV = 45071\n",
"NCV = GCV-Lh #kJ/kg oil\n",
"\n",
"# Result\n",
"print \"NCV = \",NCV,\" kJ/kg.\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.3 Page 444"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"NHV = 2043.160519 kJ/mol.\n"
]
}
],
"source": [
"# solution \n",
"# Variables \n",
"\n",
"# basis 1 mol of gaseous propane\n",
"H2O = 4*18.0153 #g\n",
"\n",
"# Calculation \n",
"NHV = 2219.17-(H2O*2442.5/1000.)\n",
"\n",
"# Result\n",
"print \"NHV = \",NHV,\" kJ/mol.\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.4 Page 444"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" GCV = 52126.6269579 kJ/kg. NCV = 47260.2164681 kJ/kg.\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables \n",
"# basis 1 mol of natural gas\n",
"# using table 7.7\n",
"# Calculation \n",
"H2O = (2*.894+3*.05+.019+5*(.004+.006))*18 # g\n",
"Hv = H2O*2442.5/1000.\n",
"NCV1 = 945.16-Hv\n",
"GCV = 945.16*1000/18.132\n",
"NCV = NCV1*1000/18.132\n",
"\n",
"# Result\n",
"print \" GCV = \",GCV,\" kJ/kg. NCV = \",NCV,\" kJ/kg.\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.5 Page 451"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a Theoratical O2 requirement per unit mass of coal = 1.38592 kg. b Theoratical dry air requirement = 5.94790666667 kg/kg coal.\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables \n",
"# basis 100 kg fuel\n",
"O2req = 4.331*32 # kg\n",
"\n",
"# Calculation \n",
"rO2req = O2req/100\n",
"N2in = (79/21.)*4.331 # kmol\n",
"AIRreq = O2req+N2in*28 #kg\n",
"rAIRreq = AIRreq/100.\n",
"R = AIRreq/100.\n",
"AIRspld = R*2 # kg/kg coal\n",
"O2spld = 4.331*2 # kmol\n",
"N2spld = N2in*2\n",
"N2coal = 2.05/28 # kmol\n",
"tN2 = N2spld+N2coal\n",
"moist = 1.395+(7/18.) # kmol\n",
"\n",
"# Result\n",
"print \"a Theoratical O2 requirement per unit mass of coal = \",rO2req,\\\n",
"\" kg. b Theoratical dry air requirement = \",rAIRreq,\" kg/kg coal.\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.6 Page 452"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a Theoretical air required = 13.514 kg/kg fuel. \n",
"b Actual dry air supplied = 0.5825 kg/kg fuel. \n",
"c Concentration of SO2 = 2490.75695661 mg/kg. \n",
"d Concentration of SO2 = 1135.99480688 ppm vol/vol.\n",
"e Concentration of SO2 if gases are discharged at 523.15K and100.7kPa = 1683.25355648 mg/m**3. \n",
"f Dew Point of flue gas = 424.4 K.\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables \n",
"# basis 100 kg of RFO\n",
"O2req = 9.786 #kmol\n",
"N2req = (79/21.)*O2req #kmol\n",
"AIRreq = O2req+N2req #kmol\n",
"rAIRreq = AIRreq*29/100\n",
"AIRspld = AIRreq*1.25\n",
"rAIRspld = AIRspld/100\n",
"\n",
"\n",
"# Calculation \n",
"# using table 7.11 and 7.12\n",
"xSO2 = .07/(55.925+5.695) # kmol SO2/kmol wet gas\n",
"vSO2 = xSO2*10**6 # ppm\n",
"mSO2 = 4.48*10**6/(1696.14+102.51)\n",
"\n",
"# at 523.15 K and 100.7 kPa\n",
"V = ((55.925+5.695)*8.314*523.15)/100.7 # m**3\n",
"cSO2 = (4.48*10**6)/V # mg/m**3\n",
"#from fig 7.3\n",
"dp = 424.4 #K\n",
"\n",
"# Result\n",
"print \"a Theoretical air required = \",rAIRreq,\" kg/kg fuel. \"\n",
"print \"b Actual dry air supplied = \",rAIRspld,\" kg/kg fuel. \"\n",
"print \"c Concentration of SO2 = \",mSO2,\" mg/kg. \"\n",
"print \"d Concentration of SO2 = \",vSO2,\" ppm vol/vol.\"\n",
"print \"e Concentration of SO2 if gases are discharged at 523.15K and100.7kPa = \",cSO2,\" mg/m**3. \"\n",
"print \"f Dew Point of flue gas = \",dp,\" K.\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.7 Page 454"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a Percent excess air = 23.0320699708 . b In fuel C:H = 5.00333333333 .\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables \n",
"# basis 100 kmol of dry flue gas\n",
"O2acntd = 11.4+4.2 # kmol\n",
"O2avlbl = (21./79)*84.4 # kmol\n",
"O2excs = 4.2 #kmol\n",
"\n",
"# Calculation \n",
"O2unactd = O2avlbl-O2acntd\n",
"H2brnt = O2unactd*2\n",
"O2req = 11.4+O2unactd\n",
"pexcsAIR = O2excs*100/O2req\n",
"mH2brnt = H2brnt*2 # kg\n",
"mCbrnt = 11.4*12\n",
"r = mCbrnt/mH2brnt\n",
"\n",
"# Result\n",
"print \"a Percent excess air = \",pexcsAIR,\". b In fuel C:H = \",r,\".\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.8 Page 459"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a Theoretical air required = 2.3432 kg dry air/kg fuel. \n",
" b Percent excess air = 30.2652456295 . \n",
" c Dew Point of flue gas = 339.85 K. \n",
" d Thermal efficiency of the boiler = 0.728802718447 .\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables \n",
"# basis 100 kg of bagasse fired in th boiler\n",
"#(a)\n",
"O2req = 2.02 # kmol\n",
"N2in = (79/21)*O2req # kmol\n",
"AIRreq = (O2req+N2in)*29 # kg\n",
"rAIR = AIRreq/100\n",
"print \"a Theoretical air required = \",rAIR,\" kg dry air/kg fuel. \\n b \",\n",
"\n",
"# Calculation \n",
"# (b)\n",
"tflugas = 1.95/.1565 #/kmol\n",
"xcsO2N2 = tflugas - 1.95\n",
"x = (xcsO2N2-7.6)/4.76 # kmol\n",
"pxcsAIR = x*100/O2req\n",
"\n",
"# Result\n",
"print \"Percent excess air = \",pxcsAIR,\". \\n c \",\n",
"#(c)\n",
"pW = 100*.2677 # kPa partial p of water vap\n",
"# from fig 6.13\n",
"dp = 339.85 #K\n",
"print \"Dew Point of flue gas = \",dp,\"K. \\n d \",\n",
"# (d)\n",
"# from appendix IV\n",
"hfw = 292.97 #kJ/kg enthalpy of feed water at 343.15 K\n",
"Hss = 3180.15 # kJ/kg enthalpy of super heated steam at 2.15 bar and 643.15K\n",
"Hgain = Hss - hfw\n",
"H6 = Hgain*2.6*100 # kJ heat gained by water\n",
"H1 = 100*1030000. # kJ\n",
"GCV = H6*100/H1\n",
"print \"Thermal efficiency of the boiler = \",GCV,\".\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.9 Page 465"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overall efficiency rate = 0.0230701331531 percent.\n"
]
}
],
"source": [
"# solution \n",
"\n",
"\n",
"# Variables \n",
"# using mean heat capacity data Table 7.21\n",
"# basis 100 kmol of dry flue gas\n",
"\n",
"# Calculation \n",
"H7 = 1.0875*100*30.31*(423.15-298.15)\n",
"H71 = 3633.654*(423.15-298.15)\n",
"fi7 = H71*3900*.7671/162.2 # kJ/h\n",
"fi1 = 3.9*1000*26170 # kJ/h\n",
"# performing heat balance\n",
"Hsteamgen = 23546.07 \n",
"eff = Hsteamgen*100/fi1 # overall efficiency rate\n",
"\n",
"# Result\n",
"print \"Overall efficiency rate = \",eff,\" percent.\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.10 Page 468"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a NCV = 41561.332 kJ/kg. \n",
" b Theoretical air required = 12.8699733333 kg/kg fuel. \n",
" c When fluid is burnt with theoretical air AFT = 2612.71 K. d \n",
"When 30 percent excess air is supplied AFT = 2178.66 K. d Dew Point = 429.0 K. e For incomplete combustion AFT = 2561.42 K.\n"
]
}
],
"source": [
"# solution \n",
"\n",
"\n",
"# Variables \n",
"# basis 100 kg of fuel oil\n",
"O2req = 9.364 # kmol\n",
"N2in = (79/21.)*O2req\n",
"tN2 = N2in+.036\n",
"AIRreq = O2req*32 + tN2*28 \n",
"rAIR = AIRreq/100. # kg/kg\n",
"wp = 4.5 # kmol\n",
"Hloss = 2442.8*wp*18/100 # kJ/kg fuel\n",
"NCV = 43540-Hloss\n",
"print \"a NCV = \",NCV,\" kJ/kg. \\n b Theoretical air required = \",rAIR,\" kg/kg fuel. \\n c \",\n",
"H1 = 100*41561.33 # kJ\n",
"\n",
"# Calculation \n",
"# from table 5.1\n",
"H71 = 1349.726*(1500-298.15)+252.924*10**-3 * ((1500**2-298.15**2)/2)+ \\\n",
"257.436*10**-6*((1500**3-298.15**3)/3)-137.532*10**-9*((1500**4-298.15**4)/4) # upto 1500 K\n",
"H711 = H1-H71 # above 1500K\n",
"# F(T) = {1500 to T} integr[1477.301+375.2710*10**-3T-91.2760*10**-6T**2+8.146*10**-9T**3]dT-2147118 (i)\n",
"# solving it for T = 2000\n",
"AFT = 2612.71 # K\n",
"\n",
"# Result\n",
"print \"When fluid is burnt with theoretical air AFT = \",AFT,\" K. d \"\n",
"# with 30% excess air\n",
"O2spld = 9.364*1.3\n",
"xcsO2 = O2spld-O2req\n",
"N2in1 = (79/21.)*O2spld\n",
"tN21 = N2in1+.036\n",
"# now, using table 7.26, table 7.27 and eq(i) we get\n",
"AFT1 = 2178.66 # K\n",
"# from fig 7.3\n",
"dp = 429. # K\n",
"# similarly for incomplete combustion we find\n",
"AFT2 = 2561.42 #K\n",
"print \"When 30 percent excess air is supplied AFT = \",AFT1,\\\n",
"\" K. d Dew Point = \",dp,\" K. e For incomplete combustion AFT = \",AFT2,\" K.\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.11 Page 473"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" After performing material and thermal balance operations we get Overall thermal efficiency of the boiler based on GCV of the fuel = 67.4403345362 percent. Overall efficiency of the boiler based on NCV of the fuel = 71.464013185 percent. Steam to fuel ratio = 10.9125 at 16 bar. Equivalent boiler capacity = 5051.22697062 kg/h.\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables\n",
"# basis 100 kg of fuel\n",
"# material balance of carbon\n",
"CO2 = 7.092+.047 #kmol in flue gases\n",
"N2 = 11.94*7.139/7.01\n",
"O2 = 11.94*7.139/7.01\n",
"flue = CO2+N2+O2\n",
"\n",
"# Calculation \n",
"# material balance of O2\n",
"O2air = 21*N2/79.\n",
"airin = N2+O2air\n",
"tO2in = O2air+.078 # O2 in burner\n",
"O2xcs = tO2in-9.864\n",
"# material balance of water vapour\n",
"moistfrmd = 5.45 # kmol from combustion of H2\n",
"H = .0331 # kmol/kmol of dry air humidity at 100.7 kPa\n",
"moistair = H*104.482 #kmol\n",
"tmoist = moistfrmd+moistair\n",
"pxcsair = O2xcs*100/9.786\n",
"# now using table 7.32\n",
"H7 = 3391.203*(563.15-298.15) #kJ\n",
"Ff = 400. # kg/h fuel firing rate\n",
"tH = 2791.7-179.99 # kJ/kg total heat supplied in boiler\n",
"fi5 = tH*4365 # kJ/h\n",
"fi8 = 5.45*18*Ff*2403.5/100 # kJ/h\n",
"GCVf = 42260. #kJ/kg\n",
"fi1 = Ff*GCVf\n",
"Fdryair = 104.482*29*Ff/100\n",
"Cha = 1.006+1.84*.0205 # kJ/kg dry air K\n",
"fi3 = Fdryair*Cha*(308.15-298.15)\n",
"fi2 = Ff*1.758*(353.15-298.15)\n",
"BOILEReff1 = fi5*100/fi1\n",
"NCVf = GCVf-(18.0153/2.016)*.109*2442.8 # kJ/kg\n",
"BOILEReff2 = fi5*100/(Ff*NCVf)\n",
"r = 4365/Ff # steam:fuel\n",
"BOILERcapacity = fi5/2256.9\n",
"\n",
"# Result\n",
"print \" After performing material and thermal balance\\\n",
" operations we get Overall thermal efficiency of the boiler based on GCV\\\n",
" of the fuel = \",BOILEReff1,\" percent. Overall efficiency of the boiler based\\\n",
" on NCV of the fuel = \",BOILEReff2,\" percent. Steam to fuel ratio = \",r,\" \\\n",
" at 16 bar. Equivalent boiler capacity = \",BOILERcapacity,\" kg/h.\"\n"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.12 Page 478"
]
},
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"execution_count": 12,
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"name": "stdout",
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"text": [
" a Moistproducer gas obtained = 3.9053717744 Nm**3/kg coal. \n",
" b Air supplied = 3.15945684695 kg/kg coal gassified. \n",
" c Steam supplied = 0.289649027717 kg/kg coal.\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables\n",
"# basis 100 kmol of dry producer gas\n",
"C = 33*12. # kg\n",
"O2 = 18.5*32 #kg\n",
"H2 = 20*2. # kg\n",
"O2air = 21*51/79. # kmol\n",
"COALgassified = 396/.672 # kg\n",
"\n",
"# Calculation \n",
"O2coal = COALgassified*.061/32 # kmol\n",
"tO2 = O2coal + O2air\n",
"O2steam = 18.5-tO2 # kmol\n",
"H2steam = 2*O2steam # kmol\n",
"H2fuel = 20-H2steam\n",
"dryproducergas = 100*22.41/COALgassified # Nm**3/kg coal\n",
"Pw = 2.642 # kPa\n",
"Ha = Pw/(100.7-Pw) # kmol/kmol dry gas\n",
"water = Ha*100.\n",
"moistproducergas = (100+water)*22.41/COALgassified # Nm**3/kg coal\n",
"dryair = (51*28+O2air*32)/COALgassified # kg/kg coal\n",
"tsteamsupplied = H2steam+water-(COALgassified*.026/18) # kmol\n",
"steam = tsteamsupplied*18/COALgassified\n",
"\n",
"# Result\n",
"print \" a Moistproducer gas obtained = \",moistproducergas,\" Nm**3/kg coal. \\n \\\n",
" b Air supplied = \",dryair,\" kg/kg coal gassified. \\n c Steam supplied = \",steam,\" kg/kg coal.\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 7.13 Page 479"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Heat Balance of Waste Heat Boiler kJ/h \n",
"Heat Output Steam rising Economiser 2864424.0 \n",
"Steam generator 14971273.0 \n",
"Super heater 1856650.0 \n",
"Heat loss in flue gases 11409604.8615 \n",
"Unaccounted heat loss 4715492.33477\n"
]
}
],
"source": [
"# solution \n",
"\n",
"# Variables\n",
"# solving by alternate method on page 483\n",
"# basis 100 kmol of dry producer gas\n",
"# using tables 7.38 and 7.39\n",
"fi7 = 6469.67*(833.15-298.15)*(27650/2672.) # kJ/h\n",
"\n",
"# Calculation \n",
"# heat output basis 1 kg of steam\n",
"# referring Appendix IV\n",
"H4 = 675.47-272.03 # kJ/kg\n",
"Ts = 463. # K\n",
"h = 806.69 # kJ/kg\n",
"lambdav = 1977.4 # kJ/kg\n",
"Hss = 2784.1 # kJ/kg at Ts\n",
"i = 3045.6 # kJ/kg\n",
"H6 = i-Hss\n",
"fi4 = H4*7100 # kJ/h\n",
"fi5 = (Hss-675.47)*7100 # kJ/h\n",
"fi6 = H6*7100 # kJ/h\n",
"recovery = fi4+fi5+fi6\n",
"BOILERcapacity = recovery*3600/2256.9 # kg/h\n",
"fi8 = 6125.47*(478.15-298.15)*(27650/2672.) # kJ/h\n",
"hloss = fi7-fi4-fi5-fi6-fi8 #/ kJ/h\n",
"\n",
"# Result\n",
"print \"Heat Balance of Waste Heat Boiler kJ/h \\nHeat Output Steam rising Economiser\",fi4,\\\n",
"\" \\nSteam generator \",fi5,\" \\nSuper heater \",fi6,\\\n",
"\" \\nHeat loss in flue gases \",fi8,\" \\nUnaccounted heat loss \",hloss\n"
]
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