Optimization and Simulation of Secondary Settler Models

Transcription

1 Proceeding of the 6th WE Interntionl Conference on imultion Modelling nd Optimiztion Libon Portugl eptember Optimiztion nd imultion of econdry ettler Model I.. C. P. EPÍRITO NTO E. M. G. P. FERNNDE M. M. RÚO 2 E. C. FERREIR ytem nd Production Deprtment 2 Centre of Biologicl Engineering Minho Univerity Cmpu de Gultr Brg PORTUGL btrct: - Thi work focu on the ccomplihing of the bet model to econdry ettler to ue in minimum cot optimiztion procedure concerning the contruction nd opertion of wtewter tretment plnt (WWTP). Two trditionl model re teted well new model tht reult from the combintion of the other two. The obtined optiml deign re then imulted in order to evlute the model tht provide the bet performnce. Key-Word: - WWTP optiml deign econdry ettler modeling Cot function minimiztion imultion deign Introduction In the plnning nd deign of wtewter tretment plnt (WWTP) the role plyed by the econdry ettler i mot of the time underetimted. Due to the high cot ocited with the contruction nd opertion of WWTP it i convenient to conduct creful nlyi of the involved model in prticulr the econdry ettler model nd perform n optimiztion of the entire ytem. The mot commonly ued model in literture to decribe the econdry ettler re the TV [2] nd the double exponentil (DE) [9] model. The TV model i uully ued deign procedure to new WWTP. It i bed on empiricl eqution tht were obtined by experiment nd doe not contin ny olid blnce lthough it contemplte pek wet wether flow (PWWF) event. The DE model i the mot widely ued in imultion nd it produce reult very cloe to relity. However it doe not provide extr edimenttion re needed during PWWF event the reulting deign h to conider the ue of ecurity fctor mny time indequte. The optimiztion procedure found in the literture involving econdry ettler re bed on very imple model [] or on the TV model [ 3 5]. fr we know there hve been no optimiztion ttempt uing the DE model. We believe tht the combintion of the two model overcome the limittion of ech one nd thi combintion w ued for the firt time in [4]. In thi work optimiztion procedure were conducted in the ene tht minimum cot deign ought to be chieved with the two trditionl model (DE nd TV) eprtely nd with combintion of both model. It i the firt time tht the DE model i ued with n optimiztion gol nd compred with the other model. Beide bed on the obtined optiml deign GP- [] imultion were crried out to be ble to evlute the goodne of the olution. ome tre condition were impoed in order to e the mot robut olution. The deign tht relie on the combined model (TV+DE) to decribe the econdry ettler w the only one ble to overcome the tre condition. Thi pper i orgnized follow. In ection 2 brief decription of the mthemticl model relted with the ctivted ludge ytem of WWTP i preented. ection 3 decribe the cot function ued in our optimiztion procedure. ection 4 yntheize the obtined mthemticl progrmming model nd ection 5 report on the obtined optiml deign well on the crried imultion. Finlly ection 6 contin the concluion nd the ide for future work. 2 The ctivted ludge ytem Conidering the performnce nd ocited cot the mot importnt tretment in WWTP i the econdry tretment. The ctivted ludge ytem compoed by n ertion tnk nd econdry ettler i the mot commonly found econdry tretment. Thee two unitry procee re intimtely relted therefore one hould not be conidered without the other. To model the ertion tnk the M model [8] i ued. M blnce were done to ech one of the compound conidered by thi model for ech involved biologicl proce. For the econdry ettler we propoe combintion of the two trditionl model TV nd DE.

2 Proceeding of the 6th WE Interntionl Conference on imultion Modelling nd Optimiztion Libon Portugl eptember Beide the blnce to ech unit ome blnce were done round the entire ytem. 2. ertion tnk The ertion tnk i where the biologicl rection tke plce. To decribe it the ctivted ludge model n. decribed by Henze et l. [8] i ued nd conider both the elimintion of the crbonceou mtter nd the removl of the nitrogen compound. The tnk i conidered completely tirred tnk rector (CTR) in tedy tte. The blnce round thi unit define ome of the contrint of our mthemticl model. The generic eqution for m blnce round certin ytem conidering CTR i Q V dξ ( ξ in ξ ) + r ξ () dt where Q i the flow tht enter the tnk V i the ertion tnk volume ξ e ξ in re the concentrtion of the component round which the m blnce re being mde inide the rector nd on entry repectively. In CTR the concentrtion of compound i the me t ny point inide the rector nd t the effluent of tht rector. The rection term for the compound in quetion r ξ i obtined by the um of the product of the toichiometric coefficient ξ with the expreion of the proce rection rte ρ of the M Peteron mtrix [8]: r ξ ξ ρ. In tedy tte the ccumultion term given by d ξ / dt in () i zero becue the concentrtion i contnt in time. WWTP in lbor for ufficiently long period of time without ignificnt vrition cn be conidered t tedy tte. our purpoe i to mke cot prediction in long term bi it i reonble to do o. The M model involve 8 procee incorporting 3 different component uch the ubtrte the bcteri diolved oxygen mong other. We refer to [5] for detil. 2.2 econdry ettler Trditionlly the econdry ettler i underetimted when compred with the ertion tnk. However it ply crucil role in the ctivted ludge ytem. When the wtewter leve the ertion tnk where the biologicl tretment took plce the treted wter hould be eprted from the biologicl ludge otherwie the chemicl oxygen demnd would be higher thn it i t the entry of the ytem. The mot common wy of chieving thi purpoe i by edimenttion in tnk. The optimiztion of the edimenttion re nd depth mut rely on the ludge chrcteritic which in turn re relted with the performnce of the ertion tnk. o the opertion of the biologicl rector influence directly the performnce of the ettling tnk nd for tht reon one hould never be conidered without the other. The TV deign procedure (Fig. ) contemplte the pek wet wether flow event during which there i reduction in the ludge concentrtion. To turn round thi problem certin depth i llocted to upport the fluctution of olid during thee event h 3 V DVI 48 (2) Thi wy reduction in the edimenttion re i llowed. compction zone h 4 DVI p (3) Fig. : Typicl olid concentrtion-depth profile dopted by the TV model (dpted from [2]) where the ludge i thickened in order to chieve the convenient concentrtion to return to the biologicl rector lo h to be contemplted nd depend only on the chrcteritic of the ludge. DVI i the diluted volumetric ludge index i the vrition of the ludge concentrtion inide the ertion tnk in PWWF event nd p i the ludge concentrtion during PWWF event. cler wter zone ( h ) nd eprtion zone ( h 2 ) hould lo be conidered nd re et empiriclly ( h + h2 y). The depth of the ettling tnk h i the um of h h 2 h 3 in (2) nd h 4 in (3). The edimenttion re i till relted to the pek flow Q p by the expreion Q p ( p DVI ).

3 Proceeding of the 6th WE Interntionl Conference on imultion Modelling nd Optimiztion Libon Portugl eptember The double exponentil model ume one dimenionl ettler in which the tnk i divided into ten lyer of equl thickne (Fig. 2). ome implifiction re conidered. No biologicl rection tke plce in thi tnk mening tht the diolved mtter concentrtion i mintined cro ll the lyer. Only verticl flux i conidered nd the olid re uniformly ditributed cro the entire cro-ectionl re of the feed lyer (7 in our ce). Thi model i bed on trditionl olid flux nlyi but the flux in prticulr lyer i limited by wht cn be hndled by the dcent lyer. The ettling function decribed by Tkác et l. in [9] i given by rh ( T fnt ) rp ( T fnt ) mx min ' e e ( ( ( ) where i the ettling velocity in lyer (m/dy) T i the totl upended olid concentrtion in ech of the ten conidered lyer of the ettler nd ' r h r p nd f n re the ettling prmeter. Note tht T 7 T. The olid flux due to the bulk movement of liquid my be up or down up nd dn repectively depending on it poition reltive to the feed lyer thu Qef up nd Q r + Qw dn. to the ubcript r concern the recycled ludge w the wted ludge nd ef the treted effluent. The edimenttion flux for the lyer under the feed lyer (7 ) i given by T nd bove the feed lyer ( 6) the clrifiction flux clr i given by T if T + Tt clr min( T + T + ) otherwie where T t i the threhold concentrtion of the ludge. The reulting olid blnce round ech lyer conidering tedy tte re the following: - for the top lyer () up ( T + T ) clr h / - for the intermedite lyer bove the feed lyer (2 6) up ( T + T ) + clr clr h / - for the feed lyer (7) Q T + clr ( up + dn ) T min( + ) h / lyer bove the feed lyer up2 up3 up7 feed lyer ( Q + Qu) e lyer below the feed lyer top lyer bottom lyer dn7 dn8 dn u 7 u 8 u 9 Bulk Movement u Grvity ettling clr clr2 clr6 ( 2 2 ) min v v ou v e 2 t ( ) min v v ou v22 e 3 t ( ) min v v ou v66 e 7 t ( ) min v v ( ) min v v ( ) min v v Fig. 2: olid blnce round the ettler lyer ccording to the double exponentil model (dpted from [9]) - for the intermedite lyer under the feed lyer (89) dn ( T T ) + min( ) min( + ) h / - nd for the bottom lyer () dn ( T T ) + min ( ). h / 2.3 Generl blnce The ytem behviour in term of concentrtion nd flow my be predicted by blnce. In order to chieve conitent ytem thee blnce mut be done round the entire ytem nd not only round ech unitry proce. They were done to the upended mtter diolved mtter nd flow. The eqution for prticulte compound genericlly repreented by? (orgnic nd inorgnic) hve the following form: V ( +r ) Qinf? entqinf?inf + ( +r) Qinf? (? r-? ef )-Qinf? ef RT where repreent the prticulte COD. For the oluble (? ) we hve: + r Q Q r Q ( ) inf? ent inf? inf + inf?? r

4 Proceeding of the 6th WE Interntionl Conference on imultion Modelling nd Optimiztion Libon Portugl eptember where r i the recycle rte RT i the ludge retention time nd Q? repreent the volumetric flow. to the ubcript inf concern the influent wtewter ent the entry of the ertion tnk r the recycled ludge nd ef the treted effluent. For the flow the reulting blnce re: Q Q inf + Q r nd Q Qef + Qr + Q. w 2.4 Other importnt definition The other importnt group of contrint in the mthemticl model i et of liner equlitie tht define compoite vrible. In rel ytem ome tte vrible re mot of the time not vilble for evlution. Thu redily meured compoite vrible re ued inted. They re the chemicl oxygen demnd (COD) voltile upended olid (V) totl upended olid (T) biochemicl oxygen demnd (BOD) totl nitrogen of Keldhl (TKN) nd totl nitrogen (N). It i lo necery to dd ome ytem vrible definition in order to define the ytem correctly. In thi group we include the ludge retention time (RT) the recycle rte (r) hydrulic retention time (HRT) recycle rte in PWWF event (r p ) recycle flow rte in PWWF event ( Q r p ) nd mximum overflow rte (Q p / ). ll the vrible in the model re conidered nonnegtive lthough more retricted bound re impoed to ome of them due to opertionl conitencie. For exmple the diolved oxygen h to be lwy greter or equl to 2 mg/l. Thee condition define et of imple bound on the vrible. Finlly the qulity of the effluent h to be impoed. The qulity contrint re uully derived from lw retriction. The mot ued re relted with limit in the COD N nd T t the effluent. In mthemticl term thee contrint re defined by portuguee lw COD ef 25 N ef 5 nd T 35. ef 3 The Cot Function The cot function i ued to decribe the intlltion nd opertion cot of WWTP in wy tht reflect the behviour of ech unitry proce. In the preent tudy only the ertion tnk nd the econdry ettler re conidered. The bic tructure of the cot function bed on b the work done by Tytec [] i C Z where C repreent the cot nd Z the vrible tht mot influence the deign of the unitry proce under tudy. The prmeter nd b re etimted ccording to the cot ocited with the unit under tudy nd depend on the locl condition where the WWTP i being built. lthough the model i nonliner it cn be eily linerized yielding ln C ln + b ln Z. The prmeter nd b were etimted by let qure technique conidering rel dt collected from portuguee WWTP building compny. t the preent the collected dt come from et of WWTP in deign therefore no opertion dt re vilble. However from the experience of the compny it i known tht the mintennce expene for the civil contruction re round % during the firt yer nd round 2% in the next. To the electromechnicl component the mintennce expene re negligible but ll the mteril i uully replced fter yer. The energy cot i directly relted with the ir flow. The power cot (P c ) in Portugl i.8 /KW.h. For the ke of implicity no pump were conidered which men tht ll the flow in the ytem move by the effect of grvity. lo ll the fixed cot re neglected they do not influence the optimiztion procedure. The opertion cot i uully in nul bi o it h to be updted to preent vlue with the prmeter Γ : n n ( + i) Γ ( + i) i with i the dicount rte nd n the life pn of the WWTP. We ued i.5 nd n2 yer. For ech unit the totl cot i given by the um of the invetment (IC) nd opertion cot (OC): TC IC + OC. (4) For the ertion tnk the influent vrible re the tnk volume (V ) nd the ir flow (G ). The invetment cot i given by.7.62 IC 48.6V G (5) nd the opertion cot by.7 (.Γ +.2Γ( + i) )( 48.7V ).62 ( + i) 7737G + 5.ΓP G. OC + c (6) In the econdry ettler the edimenttion re ( ) nd the depth (h) re the influent vrible. For the invetment nd opertion cot we obtined nd.97 IC (7) (..2 ( ) ) 48.6( ) ( ).7 OC Γ+ Γ + i h (8)

5 Proceeding of the 6th WE Interntionl Conference on imultion Modelling nd Optimiztion Libon Portugl eptember repectively. ccording to (4) the obective function i then the um of the cot term (5) (8). 4 The Optimiztion Problem mthemticl progrmming problem reult from the et of contrint tht were decribed in ection 2 with the obective function preented in ection 3. The mthemticl model tht relie on the TV model to decribe the ettling tnk h 57 prmeter 82 vrible nd 64 contrint where 28 re nonliner equlitie 35 re liner equlitie nd there i only one nonliner inequlity. 7 vrible re bounded below nd re bounded below nd bove. We refer to [3] for detil. When the DE model i ued to decribe the ettling tnk the mthemticl model h 64 prmeter 3 vrible nd 97 contrint from which 62 re nonliner equlitie 34 re liner equlitie nd one i nonliner inequlity. 2 vrible re bounded below nd re bounded below nd bove. The mthemticl model tht combine both TV nd DE eqution (ee [4]) h 64 prmeter 5 vrible nd 5 contrint where 67 re nonliner equlitie 37 re liner equlitie nd there i only one nonliner inequlity. 4 vrible re bounded below nd re bounded below nd bove. The choen vlue for the toichiometric kinetic nd opertionl prmeter tht pper in the mthemticl formultion of the problem re the defult vlue preented in the GP- imultor nd they re uully found in rel ctivted ludge bed plnt for dometic effluent. The three problem hve been coded in the MPL mthemticl progrmming lnguge [6] nd were olved with the oftwre pckge NOPT [7] vilble in the NEO erver ( 5 Comprtive Reult The min purpoe of the pper i to crry out comprtive nlyi of the reulting deign nd ue the GP- imultor to e their robutne under tre condition. Firt ll the problem were olved with identicl condition in the influent to the ytem. Tble report the optiml vlue of the ertion tnk volume edimenttion re depth of the econdry ettler ertion ir flow nd the deign totl cot (TC) in million of euro for the three model. The mot immedite reult i tht the TV model i the mot expenive. Thi i expected the model only ue empiricl eqution tht contemplte lrge ecurity fctor to ccount for PWWF event. Tble : Reult for the three mthemticl model model V h G TC TV DE TV+DE The DE model turn out to be the chepet one nd thi i due to the fct tht the PWWF event re not tken into ccount. Only verge condition bed on blnce re contemplted nd the extr ettler depth (h 3 nd h 4 ) re not incorported in the model. The mot equilibrted olution i obtined when combintion of the two model i conidered. The totl cot of thi deign i between the other two. The reulting model i prepred to turn round the PWWF event without over dimenioning becue it lo incorporte blnce. We point out tht with thi model the chieved qulity of the effluent in term of COD nd T i under the demnded by lw in contrt with the other two model where the limit vlue were ttined. Then the three obtined deign were introduced in the GP- imultor nd ome tre condition were impoed for period of 3 dy in order to e the goodne of ech olution. t firt n verge flow t the entry of the ytem w pplied. t dy 6 tre flow vlue w impoed nd the reulting impct on the oluble COD (drk line) nd on the T (light line) w regitered hown in Fig. 3 to 5. Only the combined TV+DE model i ble to upport thee condition. When the deign relie on the TV model the ytem give poitive repone for 8 imultion dy. From tht point on the ytem no longer give n pproprite nwer nd i not ble to upport uch n increing flow (Fig. 3). Thi i the ce where the demnded ir flow i greter (Tble ) mening tht the ludge concentrtion within the rector i bigger. In itution of PWWF the ytem cnnot mintin the correct concentrtion inide the tnk nd n exce of olid i releed with the treted effluent compromiing it qulity. The DE model i the mot enitive to flow vrition. From the moment tht the flow rie the T ty very cloe to it limit (35) nd from certin point it trt to grow progreively until the 22 nd dy where there i turtion nd the ytem cnnot give correct nwer (Fig. 4). When the combined TV+DE model i ued the mot robut deign i chieved nd the model cn upport the dvere condition for t let the period of 3 imultion dy (Fig. 5).

6 Proceeding of the 6th WE Interntionl Conference on imultion Modelling nd Optimiztion Libon Portugl eptember whole tretment plnt with the incorportion of the ludge digetion nd the finl dipol procee. Fig. 3: imultion uing the TV model Fig. 4: imultion uing the DE model Fig. 5: imultion uing the combined TV+DE model 6 Concluion The min concluion from thi comprtive tudy concerning the optimiztion procedure i tht the mot uitble model to decribe the proce inide the econdry ettler i the one tht combine the TV deign procedure with the double exponentil model. The limittion of the TV nd DE model when conidered eprtely re overlpped by ech other in the combined model nd the dvntge re powered. The reult i more equilibrted model in term of cot nd performnce. The conidered imultion procedure lo how tht the combined model i the mot robut even under dvere condition on the influent. The confirmed ucce in the econdry ettler modeling i giving u ome confidence to conider in the ner future the optimiztion of the Reference: [] P. N. C. M. fono. Modelção Mtemátic de Rectore Biológico no Trtmento Terciário de Efluente. PhD Thei Univeridde do Porto Portugl 2. [2] G.. Ekm. L. Brnrd F. W Günthert P. Kreb.. McCorquodle D.. Prker nd E. Whlberg. econdry ettling Tnk: Theory Modeling Deign nd Opertion Technicl Report 6. IWQ - Interntionl ocition on Wter Qulity 978. [3] I.. C. P. Epírito nto E. M. G. P. Fernnde M. M. rúo nd E. C. Ferreir. NEO erver Uge in Wtewter Tretment Plnt. Lecture Note in Computer cience pringer-verlg No pp [4] I.. C. P. Epírito nto E. M. G. P. Fernnde M. M. rúo nd E. C. Ferreir. Biologicl Proce Optiml Deign in Wtewter Tretment Plnt WCMO6 IBN (CD-Rom) Rio de neiro 25. [5] I.. C. P. Epírito nto E. M. G. P. Fernnde M. M. rúo nd E. C. Ferreir. How Wtewter Procee cn be Optimized Uing LOQO. Lecture Note in Economic nd Mthemticl ytem. eeger (ed.) pringer- Verlg No pp [6] R. Fourer D. M. Gy nd B. Kernighn. modeling lnguge for mthemticl progrmming Mngement cience Vol. 36 No pp [7] P. E. Gill W. Murry nd M. under. NOPT: n QP lgorithm for Lrge-cle Contrined Optimiztion IM ournl on Optimiztion Vol pp [8] M. Henze C. P. L. Grdy r G. V. R. Mri nd T. Mtuo. ctivted ludge model no Technicl Report IWPRC Tk Group on Mthemticl Modelling for Deign nd Opertion of Biologicl Wtewter Tretment 986. [9] I. Tkác G. G. Ptry nd D. Nolco. Dynmic Model of the Clrifiction-Thickening Proce Wter Reerch Vol. 25 No. 99 pp [] D. Tytec Y. meer nd E.. Nyn. Mthemticl Modeling nd Economic Optimiztion of Wtewter Tretment Plnt CRC Criticl Review in Environmentl Control Vol. 8 No. 977 pp []