{ "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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 7.12 Page 478" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "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" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }