CalculationsSpreadsheet for the optimized design of a conventional activated sludge system for secondary treatmentCopyright 2007 - JGM van der Lubbe and Adrianus van HaandelSystem configuration consists of an aeration tank, final settler, sludge thickener and anaerobic digesterIt is assumed that nitrification does not developSection 1: Input data1. General data for the activated sludge systemY =0.45b =0.24k =0.46Sfd =2fcv =1.5fv =0.7vo =144Sfth =1.5f =0.2eta =1.2DSVI =120Hd =4fn =0.1Hth =3fp =0.0252. Influent compositionQi =12000Sti =650Nti =50T min =20P.E. =77515fns =0.1Pti =15T max =24fnp =0.08T dig =203. Financial dataCr =175i =0.06Cel =0.15p =3.0% of the investments costs per yearCd =300n =20Csd =200o =1.0% of the investments costs per yearCth =400Ch =0.35m =2.0% of the investments costs per yearCdi =350fac =1.6n =0.3% of the investments costs per yearCae =3500fi =1.35Section 2: System calculationsRs3COD removal is substantially complete at lower values of Rs: higher value is required to obtain a sludge that settles wellA - Optimisation of the System Consisting of the Aeration Tank and the Final Settler(a1) Calculate the sludge mass that will developmXa =0.64MXa =5020Xa1.21mXe =0.09MXe =723mXi =0.16MXi =1248mXv =0.90MXv =6991Xv1.68mXt =1.28MXt =9987fat0.50Cr =0.78(a2) Determine the optimal sludge concentration in the aeration tanktotal constructionconstruction costs in million dollarsXtVrVdcostsaeration tankfinal settlertotal1.09,9871,0562,064,5681.750.322.061.28,3231,1581,803,8061.460.351.801.47,1341,2691,629,2121.250.381.631.66,2421,3921,509,8591.090.421.511.85,5481,5261,428,7210.970.461.432.04,9941,6731,375,7350.870.501.382.24,5401,8341,344,6530.790.551.342.44,1612,0111,331,4720.730.601.332.63,8412,2051,333,5850.670.661.332.83,5672,4171,349,3030.620.731.353.03,3292,6501,377,5650.580.791.383.23,1212,9051,417,7610.550.871.423.42,9373,1851,469,6240.510.961.473.62,7743,4921,533,1500.491.051.533.82,6283,8291,608,5560.461.151.614.02,4974,1981,696,2460.441.261.704.22,3784,6021,796,7920.421.381.804.42,2705,0461,910,9240.401.511.914.62,1715,5322,039,5220.381.662.044.82,0816,0652,183,6160.361.822.185.01,9976,6492,344,3870.351.992.345.21,9217,2902,523,1750.342.192.525.41,8497,9932,721,4830.322.402.725.61,7838,7632,940,9900.312.632.945.81,7229,6073,183,5600.302.883.186.01,66510,5333,451,2610.293.163.456.21,61111,5483,746,3740.283.463.756.41,56012,6614,071,4190.273.804.076.61,51313,8814,429,1690.264.164.436.81,46915,2194,822,6780.264.574.827.01,42716,6855,255,3030.255.015.26Optimal (minimal costs) solution =1,331,472Xt =2.40!! Enter in the cell to the left the value of Xt for which the construction costs are mimimum !!Vr =4,161Vd =2,011Vx288Rhdmax =3.0for s = sckXt1.104Rdh =2.0for s = 1sc =0.35Xr4.8for s = 1B - Optimization of the System Consisting of Sludge Thickener and Anaerobic Digester(b1) Determine the optimum thickened sludge concentrationq =1387MEt =3329MEv =2330total constructionconstruction costs in million dollarsXthrXthlFlqthVthVdicoststhickenerdigestertotal12.09.182.4277.41826,9362,500,1160.072.432.5012.59.772.0266.32086,6582,413,6150.082.332.411310.262.5256.12406,4022,336,5600.102.242.3413.510.854.1246.62776,1652,268,4910.112.162.271411.346.6237.83215,9452,209,1440.132.082.2114.511.840.1229.63745,7402,158,4440.152.012.161512.434.3221.94365,5482,116,5100.171.942.1215.512.929.3214.85115,3692,083,6630.201.882.081613.425.0208.16005,2022,060,4440.241.822.0616.513.921.2201.87065,0442,047,6370.281.772.051714.418.0195.88324,8962,046,3060.331.712.0517.515.015.2190.29834,7562,057,8380.391.662.061815.512.9184.91,1644,6242,083,9990.471.622.0818.516.010.8179.91,3814,4992,127,0050.551.572.131916.59.1175.21,6414,3802,189,6080.661.532.1919.517.07.7170.71,9534,2682,275,2040.781.492.282017.56.4166.52,3294,1612,387,9650.931.462.3920.518.05.4162.42,7804,0602,533,0021.111.422.532118.54.5158.53,3243,9632,716,5631.331.392.7221.519.03.8154.83,9793,8712,946,2741.591.352.952219.63.1151.34,7683,7833,231,4411.911.323.23Optimal (minimal costs) solution =2,046,306Xthr =17!! Enter in the cell to the left the value of Xthr for which the construction costs are mimimum !!Vth =832Rhth =14.4qth =196Vdi =4896Rdi =25.0q - qth =1191C - Finalization of System Design(c1) Nutrient demand(c2) Oxygen demand(c3) Digester performanceMNl =233.0MSti =7800fav =0.72MNp =58.3MOc =3524MEv =2330Nl =19.4OUR =35.3Rdp =0.494Pl =4.85Pb,avg =122Rdn =0.138Nte =30.6Pb,max =184MSd =1376Pte =10.1Pdiss =29.4MSxve =2120MEve =1413MEte =2412Xte =12.3fve =0.59conversion effic.0.35Mch4 =344(c4) Mass balancesPch4 =70COD(-)kg CZV/dNitrogen(-)mg N/lPhosphorus(-)mg P/lmSte =0.10780Nti =1.0050.0Pti =15mSo =0.453524Nl =0.3919.4Pl =0.324.9mSd =0.181376Nle =0.2411.8Ple =0.202.9mSXve =0.272120Nld =0.157.6Pld =0.131.9Bo =1.007800Nte,max =0.7638.2Pte,max =0.8012.1Nte,min =0.6130.6Pte,min =0.6810.1Bn =1.0050.0Bp =1.0015.0D - Financial Analysisi =0.06a_i,n =11.5n =20anual =0.087Construction costsVolumeCostsFraction of total costsAeration Tank4,161730,0008%Final Settler2,011600,0007%Thickener832330,0004%Digester4,8961,710,00020%Aeration Equipment184640,0007%Total constr. Main Units11,9004,010,00046%Add. Constr Units1,400,00016%Total construction costs5,410,00062%Total investment costs3,250,0008,660,00038%Annualized treatment costsPer yerUS$ ct per m3US$ ct per P.E.FractionFinancing cost760,00017.49.846%Aeration costs160,0003.72.110%Costs of sludge disposal180,0004.12.311%Personnel costs260,0005.93.416%Operational costs90,0002.11.25%Maintenance costs170,0003.92.210%Insurance costs30,0000.70.42%Cost of digester heating00.00.00%Total operational costs890,00020.311.554%Total costs1,650,00037.721.3100%

Calculations

Total costsDigesterThickenerk = 0,46 l.g-1 TSSv0 = 144 m.d-1Xrth (kg TSS.m-3)Construction costs (million US$)

Symbol list

Total costsSettlerReactork = 0,46 l.g-1 TSSv0 = 144 m.d-1Xt (kg TSS.m-3)Construction costs (million US$)

Symbol listSymbolDescriptionUnit of measurea_i,n =annualization factor(-)b =decay rate1/dBn =mass balance recovery factor for nitrogen(-)Bo =mass balance recovery factor for COD(-)Bp =mass balance recovery factor for phosphorus(-)Cae =construction cost of aeration systemUS$/kWCd =construction cost of the final settlerUS$/m3Cdi =construction cost of the anaerobic digesterUS$/m3Cel =cost of electricityUS$/kWhCh =cost of heating (gas)US$/m3 natural gasconversion effic.efficiency of gas motor%Cr =construction cost of the aeration tankUS$/m3Cr =specific active sludge production per unit mass daily applied biodegradable CODmg VSS/(mg COD/d)Csd =cost of sludge disposalUS$/ton sludgeCth =construction cost of the thickenerUS$/m3DSVI =diluted sludge volume indexml/g TSSeta =oxygen transfer efficiencykg O2/kWhf =endogenous residuemg VSS/mg VSSfac =fraction of construction costs for additional units(-)fat =active sludge fractionmg VSS/mg TSSfav =active fraction of volatile sludgemg VSS/mg VSSfcv =proportionality constant between bacterial mass and mass of CODmg COD/mg VSSfi =additional investment costs (non construction)(-)Fl =limiting solids fluxkg TSS/(m2*d)fn =nitrogen fraction in biomassmg N/mg VSSfnp =non biodegradable, particulate influent COD fractionmg COD/mg CODfns =non biodegradable, soluble influent COD fractionmg COD/mg CODfp =phosphorus fraction in biomassmg P/mg VSSfv =ratio between volatile and total sludge concentrationmg VSS/mg TSSfve =volatile sludge fraction in stabilized sludgemg VSS/mg TSSHd =height of final settlermHth =height of sludge thickenermi =interest rate%I =investment costsUS$k =vesilind constantl/g TSSm =maintenance costs% of I per yearMch4 =daily production of methanekg CH4/dMEt =daily excess sludge productionkg TSS/m3MEte =daily production of stabilized sludgekg TSS/dMEv =daily volatile excess sludge productionkg VSS/m3MEve =daily production of stabilized volatile sludgekg VSS/dMNl =daily nitrogen demand for excess sludge productionkg N/dMNp =daily phosphorus demand for excess sludge productionkg P/dMOc =daily oxygen demandkg O2/dmSd =fraction of influent COD that is digested(-)MSd =daily amount of digested CODkg COD/dmSo =fraction of influent COD that is oxidized(-)mSte =fraction of influent COD leaving the system with the effluent(-)MSti =daily applied COD loadkg COD/dMSxve =daily amount of COD in the stabilized excess sludgekg COD/dmSXve =fraction of influent COD leaving the system with stabilized excess sludge(-)mXa =specific active sludge production per unit mass daily applied CODmg VSS/(mg COD/d)MXa =total active sludge mass in systemkg VSSmXe =specific endogenous sludge production per unit mass daily applied CODmg VSS/(mg COD/d)MXe =total endogenous sludge mass in systemkg VSSmXi =specific inert sludge production per unit mass daily applied CODmg VSS/(mg COD/d)MXi =total inert sludge mass in systemkg VSSmXt =specific total sludge production per unit mass daily applied CODmg TSS/(mg COD/d)MXt=total sludge mass in systemkg TSSmXv =specific volatile sludge production per unit mass daily applied CODmg VSS/(mg COD/d)MXv =total volatile sludge mass in systemkg VSSn =insurance costs% of I per yearn =economical lifetimeyearsNl =influent Kjeldahl nitrogen concentration removed with the excess sludgemg N/lNld =influent Kjeldahl nitrogen concentration in digested sludge (i.e. released to liquid phase)mg N/lNle =influent Kjeldahl nitrogen concentration removed with the stabilized excess sludgemg N/lNte =effluent total nitrogen concentrationmg N/lNte,max =maximum nitrogen effluent concentration (all released nitrogen recycled to aeration tank)mg N/lNte,min =mimimum nitrogen effluent concentration (no recyle of released nitrogen to aeration tank)mg N/lNti =influent Kjeldahl nitrogen concentrationmg N/lo =operational costs% of I per yearOUR =oxygen uptake ratemg O2/(l.h)p =personnel costs% of I per yearP.E. =people equivalents---Pb,avg =average blower capacitykWPb,max =maximum blower capacitykWPch4 =power recovered from sludge digestionkWPdiss =dissipated powerW/m3Pl =influent phosphorus concentration removed with the excess sludgemg P/lPl =influent phosphorus concentration removed with the excess sludgemg P/lPld =influent phosphorus concentration in digested sludge (i.e. released to liquid phase)mg P/lPle =influent phosphorus concentration removed with the stabilized excess sludgemg P/lPte =effluent total phosphorus concentrationmg P/lPte,max =maximum phosphorus effluent concentration (all released phosphorus recycled to aeration tank)mg P/lPte,min =mimimum phosphorus effluent concentration (no recyle of released phosphorus to aeration tank)mg P/lPti =influent phosphorus concentrationmg P/lq =excess sludge flowm3/dqth =thickened excess sludge flowm3/dRdi =hydraulic retention time in sludge digesterdaysRdn =degree of solids conversion inert and endogenous sludge(-)Rdp =degree of solids conversion active sludge(-)Rs =sludge agedaysRth =hydraulic retention time in sludge digesterhourssc =critical sludge recirculation factor(-)Sfd =safety factor in design final settler(-)Sfth =safety factor in design sludge thickener(-)Sti =influent COD concentrationmg COD/lT dig =temperature in the anaerobic digesterdeg CT max =maximum reactor temperaturedeg CT min =minimum reactor temperaturedeg CVd =volume of final settlerm3Vdi =digester volumem3vo =vesiling constantm/dVt =volume of aeration tankm3Vth =thickener volumem3Xa =active sludge concentration (in aeration tank)kg VSS/m3Xr =return sludge concentrationkg TSS/m3Xt =total sludge concentration (in aeration tank)kg TSS/m3Xte =stabilized total sludge concentrationkg TSS/m3Xthl =limiting thickening sludge concentrationkg TSS/m3Xthr =thickened sludge concentrationkg TSS/m3Xv =volatile sludge concentration (in aeration tank)kg VSS/m3Y =yieldmg VSS/mg COD