Modeling and imulation of Biological Anaerobic Treatment of ludge Reulted from Watewater Treatment AUREL PREURĂ, LĂCRĂMIOARA DIANA ROBECU 2, ILEANA IRINA PANAITECU 3.C. RAJA Contanța.A. 22-24 Călărași tr., 900590 Contanța ROMANIA aurel_preura@yahoo.com, http://www.rajac.ro/ 2 Department of Hydraulic, Hydraulical Machinery and Environmental Engineering UniverityPOLITEHNICA of Bucharet 33 plaiul Independentei tr., 060042 Bucharet ROMANIA diana.robecu@upb.ro http://www.hydrop.pub.ro 3 Department of Engineering cience in the Mechanical Field Contanta Maritime Univerity 04 Mircea cel Bătrân tr., 900663 Contanța ROMANIA ileana_irina@yahoo.com http://www.cmu-edu.eu Abtract: The paper preent a kinetic model of anaerobic digetion baed on ma balance of ubtrate, microorganim and methane production. The model i imulated uing a cutomized imulink model and the value of maximum pecific growth rate of microorganim i calibrated to fit the theoretical reult with experimental one regarding methane production. The experimental data were obtained during a three month meaurement campaign in 200 at Watewater Treatment Plant Contanța outh, Romania. Key-Word: - watewater treatment, anaerobic digetion, modeling, imulation Introduction Anaerobic fermentation i widely ued a ludge handling technology in watewater treatment plant. In bioreactor the organic ubtrate i mineralized to methane and carbon dioxide a the reult of biochemical reaction performed by ditinctive group of microorganim growing in the ame medium, [7]. The firt group conit of optional anaerobic bacteria which, by mean of extracellular enzyme, convert macro-cellular product into impler compound uch a alcohol, fatty acid, amino-acid, aldehyde, a well a into important amount of carbon dioxide and maller volume of other gae; thi i the acid tage. The acid tage of digetion i fat and le enitive to environment condition. The econd group of microorganim - the methane bacteria - i completely anaerobic and convert the product of the acid tage to methane and carbon dioxide by the action of intracellular enzyme. Thi i the gaification tage and it i the limited tage of the proce becaue of longer period of growth of methane bacteria. The main benefit of the proce i the bioga production that can be ued to decreae the operational cot of watewater treatment plant. Modeling anaerobic digetion i very complicated becaue of the unteady tate behavior and the interaction of different parameter phyical, chemical, biochemical and hydraulical. The kinetic of the digetion proce depend on everal factor: a) temperature; b) ph level; c) of organic matter expreed in D, ludge ; d) preence of inhibitor; e) mixing and external circulation; f) detention time; g) organic/mineral ratio; IBN: 978-960-474-343-8 55
organic/nutrient ratio, epecially nitrogen and phophoru. A large number of model are available: ma balance model, black-box model or heuritic model, [], [2], [3], [5], [6], [9], [0]. Thi paper preent a kinetic model of anaerobic digetion baed on ma balance of ubtrate, microorganim and methane production. The model i imulated uing a cutomized imulink model and the value of maximum pecific growth rate of microorganim i calibrated to fit the theoretical reult with experimental one regarding methane production. 2 Mathematical model A ingle tage model it i developed in thi paper to decribe anaerobic kinetic. Uually, the anaerobic digetion involve everal tage, every tage conducted by pecific microorganim. Only ome of them limit the proce, becaue of their low growth. In order to invetigate the kinetic of bioga production the proce of anaerobic digetion ha to conidered the growth of microorganim, the ubtrate degradation and the formation of final product, mainly bioga, C For modeling purpoe, the biological reactor can be conidered a a cloed tank with the following hypothei taken into account: a) biochemical reaction occur only in the bioreactor; b) complete mixing for ludge and microorganim and alo for temperature in order to maintain 36 0 C in the bioreactor, c) teady-tate regime It i conidered a chematic repreentation of a bioreactor with volume V (fig.): the inlet of ludge: Q ni of the ludge, i of the ubtrate at the entrance, X i of the anaerobic microorganim at the entrance the oultlet of digeted ludge: Q ne of the digeted ludge; e of the ubtrate at the outlet; Xe - of the anaerobic microorganim at the outlet bioga collection: Q g bioga ; Z methane in bioga. The mathematical model for the microorganim growth, the ubtrate decompoition and bioga formation i baed on the ma conervation law. In non-teady-tate condition, taking into account complete mixing in bioreactor and neglecting endogenou decay of the microorganim, the equation for the ma balance of the microorganim, of the ubtrate and repectively of the methane formation in control volume, can be written a: d V = Qni i Qne e rnv () dx V = Qni X i QneX e + rv c rdv (2) dz V = Q Z Q Z KV (3) ni i ne e + where: r n ubtrate degradation rate; r c growth rate of anaerobic microorganim; r d decay rate of anaerobic microorganim; K coefficient that take into account the tranformation of volatile organic compound in methane. Fig.. chematic repreentation of the anaerobic bioreactor The following aumption are made: Qni Zni = 0, Qne Zne = 0 Qni = Qne = Q D=Q/V dilution rate and the equation (), (2) and (3) become: dx = D ( X i X e) + rc rd (4) d = D ( i e) rn (5) dz = K (6) The equation for the ma balance of the microorganim can be written: dx = D ( X i X e) + µ X Kd X (7) where µ - pecific growth rate of microorganim and K d decay rate of microorganim. For the pecific growth rate of microorganim the Andrew relation i ued, that take into account ubtrate inhibition, [8]: µ = µ max (8) K + + Ki The ubtrate degradation ha to take into account the need of the microorganim, [3]: IBN: 978-960-474-343-8 56
new cell formation: dx µ X rnx = = (9) Yx Yx Y x yield coefficient energy upply for the growth and maintain of microorganim: rnp = Kx X µ + Kmx X (0) K + K x ubtrate degradation rate to upply energy for microorganim growth, K mx - ubtrate degradation rate to upply energy for microorganim maintain product formation, for example methane: dz rnc = () Y Y methane production coefficient. Ma balance equation (5) for ubtrate become: d µ X = D ( i e ) K x X µ Yx (2) dp K mx X K + Y Converting organic compound in methane depend on the microorganim growth, o that for the K coefficient can be ued the relation: K = Yp µ X (3) Y p coefficient that take into account converion of organic compound in methane. The equation (6) for methane production can be written: dz = Yp µ X (4) 3 imulation reult The equation (7), (2) and (4) are ued for theoretical imulation of microorganim, ubtrate and methane in time. A cutomized model wa developped in Matlab-imulink, fig.2, uing tandard block from the imulink library, [8]. The imulation input data were obtain during 3 month meaurement campaign in 200 at Watewater Treatment Plant Contanța outh, Romania. From the 4 digeter of the plant only 3 of them were in operation. Bioga wa meaured for 2 of them and for the third the wa calculated uing extrapolation. For the modeling purpoe it i conidered only digeter with the volume triple a the volume of one digeter: V= 3 x 4000 = 2 000 m 3. The inlet ludge for the 3 month are 350 m 3 /d, 298 m 3 /d and 32 m 3 /d. Thu, the dilution rate are 0.0292 d -, 0.02843 d - and 0.026 d -. Retention time i conidered 30 day. f(u) Fcn 0.35 umax u u*x 0.82 Yx 0.983 Kx 0.4 Kmx u /Yx f(u) /(K+) 4.35 Yp * * *4 0.02 Kd 6 0 3 X0 0.0292 D 0.27 Y dp/ D(0-) D(X0-X) *3 u /Y 0 G *5 *2 d/ dx/ Clock X CH4 t To Workpace Fig. 2. imulink model for imulation of anaerobic kinetic According to romanian tandard NP8-06, [], only 60-75% of the inlet ludge repreent organic compound.thu, conidering an average value of 8.38 g/l COD in influent ludge, a it wa meaured, only 5 g/l i organic matter, and thi value i taken into account for inlet ubtrate. Initial condition for ubtrate i 0 = 6 g/l and for microorganim X 0 = 3 g/l. For kinetic coefficient it i ued the value from the literature, [3], 4], [9], [0]: µ m = 0.2.2 d - ; K = 7. 360 mg/l COD; K d = 0.02 0.04 d - ; K ' i =0.5,.0, 0.0, 00.0; Y x = 0.3 0.82; Y = 0.04 0.27; Y p = 4.35; K mx = 0.4; K x = 0.983. The imulation data repreent variation in time of methane and meaurement data repreent bioga. In order to compare the reult it i conidered that 60% in bioga i methane and uing methane denity, ρ CH4 = 0.77 kg/m 3, it i calculated methane : 3 QCH [ kg / d] = Q [ m / d] 0,6 0,77 4 bioga (5) Ma of methane produced in the imulation time i: M CH [ kg] = QCH [ kg / d] 30d (6) 4 4 The of methane will be: 3 Z [ g / l] = M CH [ kg]/ V[ m ] (7) 4 The imulation were done for dilution rate D = 0,0292 d -, D = 0,02483 d - and D = 0,026 d -, according with experimental meaurement. For every dilution rate there wa realized imulation for three value of the pecific growth rate of microorganim: µ m = 0.35 [d - ], µ m = 0.38 [d - ] and µ m = 0.4 [d - ]. ome of the reult of the imulation for May, June and July 200 are preented in fig. 3 2. X Biomaa ubtrat CH4 Metan, X, X, CH4 IBN: 978-960-474-343-8 57
Fig.3. Variation in time of ubtrate and microorganim for µ m = 0.35 [d - ] and D= 0.0292 [d - ] Fig.7. Variation in time of ubtrate and microorganim for µ m = 0.35 [d - ] and D= 0.02483 [d - ] Fig.4. Variation in time of methane for µ m = 0.35 [d - ] and D= 0.0292 [d - ] Fig.8. Variation in time of methane for µ m = 0.35 [d - ] and D= 0.02483 [d - ] Fig.5. Variation in time of ubtrate and microorganim for µ m = 0.4 [d - ] and D= 0.0292 [d - ] Fig.9. Variation in time of ubtrate and microorganim for µ m = 0.4 [d - ] and D= 0.02483 [d - ] Fig.6. Variation in time of methane for µ m = 0.4 [d - ] and D= 0.0292 [d - ] Fig.0. Variation in time of methane for µ m = 0.4 [d - ] and D= 0.02483 [d - ] IBN: 978-960-474-343-8 58
According to the reult preented in the Table the pecific maximum growth rate of microorganim wa calibrated at the value µ m = 0.35 [d - ]. For thi value imulation data bet fit the experimental one. Fig.. Variation in time of ubtrate and microorganim for µ m = 0.35 [d - ] and D= 0.026 [d - ] Fig.2. Variation in time of methane for µ m = 0.35 [d - ] and D= 0.026 [d - ] Fig.3. Variation in time of ubtrate and microorganim for µ m = 0.4 [d - ] and D= 0.026 [d - ] Fig.4. Variation in time of methane for µ m = 0.4 [d - ] and D= 0.026 [d - ] Table May June July Experimental data Inlet ludge 350 298 32 Q ni [m 3 /d] Bioga 920 2246 557 Q bioga [m 3 /d] Dilution rate 0.0292 0.02483 0.026 D [d - ] ma 826 966.23 669.82 day, M CH4 [kg] 2.065 2.4.6746 imulation data µ m = 0.35 [d - ] ma 920.037 223.52 552.77 Q CH4 [kg/d] ma 826 960 668 day, M CH4 [kg] 2.065 2.4.67 µ m = 0.38 [d - ] ma 83. 766.62 766.62 Q CH4 [kg/d] ma 780 760 760 day, M CH4 [kg].95.9.9 µ m = 0.4 [d - ] ma 859.6 794.5 83. Q CH4 [kg/d] ma 800 772 780 day, M CH4 [kg] 2.93.95 IBN: 978-960-474-343-8 59
4 Concluion Modeling anaerobic digetion i very complicated becaue of the unteady tate behavior and the interaction of different nature of the parameter involved. The paper preent a imple ingle tage mathematical model for anaerobic digetion kinetic baed on the ma balance equation. imulation tudie were conducted uing input data obtained during a three month meaurement campaign in 200 in Watewater Treatment Plant Contanta outh, Romania. imulated reult obtained uing a cutomized imulink model are ued to calibrate the maximum growth rate of microorganim o that the imulation reult bet fit the experimental one. watewater procee (in Romanian), Technical Publihing Houe, Bucharet, 2004. [9] Tomei M.C., Braguglia C.M., Cento G., Mininni G. Modeling of Anaerobic Digetion of ludge, Critical Review. Environmental cience and Technology, 2009, pp. 003-05. [0] Wiemann U., u Choi I., Dombrowki E.M., Fundamental of biological watewater treatment, Wiley-VCH, 2007. [] ***. Regulatory deign of building and intallation for municipal watewater treatment 5 th part: ludge Handling (in Romanian -Normativ pentru proiectarea contrucțiilor și intalațiilor de epurare a apelor uzate orășenști Partea a V-a: Prelucrarea nămolurilor), NP8-06. Reference: [] Battone D.J., Keller J., Angelidaki I., Kalyuzhnyi.V., Pavlotathi.G., Rozzi A., ander W.T.M. *, iegrit H., Vavilin V.A.. The IWA Anaerobic Digetion Model No (ADM), Water cience & Technology, Vol. 45, No. 0, 2002, pp 65 73. [2] Dimitrova N., Kratanov M. Nonlinear adaptive tabilizing control of an anaerobic digetion model with unknown kinetic, International Journal of Robut and Nonlinear Control Publihed online in Wiley Online Library (wileyonlinelibrary.com), 20. [3] Gerber M., pan R. An Analyi of Available Mathematical Model for Anaerobic Digetion of Organic ubtance for Production of Bioga, International Ga Reearch Conference, Pari, 2008. [4] Metcalf & Eddy Inc., Watewater Engineering. Treatment and Reue. Fourth edition, 2003 [5] iegrit H., Vogt D., Garcia Hera J.L., Gujer W. Mathematical Model for Meo- and Thermophilic Anaerobic ewage ludge Digetion, Environmental cience and Technology, 2002, 36, pp. 3-23. [6] imeonov I., Diop. tability Analyi оf ome Nonlinear Anaerobic Digetion Model, International Journal of Bioautomation, 200, 4(), 37-48. [7] Robecu D., Lanyi., Robecu Diana, Contantinecu I., Veretoy A., Watewater Treatment Technologie, Intallation and Equipment (in Romanian), Technical Publihing Houe, Bucharet, 200. [8] Robecu Diana, Lanyi., Veretoy A., Robecu D., Modeling and imulation of IBN: 978-960-474-343-8 60