Optimal Trajectory Finding and re-optimization of SBR for Nitrogen Removal

Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007, pp. 73-80 i m i n s o l n n y j m n i Çly *, Çmm 790-784 e q 31 * pn / l 446-701 npe } 1 (2006 10o 9p r, 2006 2007 1o 4p }ˆ) Optimal Trajectory Finding and re-optimization of BR for Nitrogen Removal Young-Whang Kim, ChangKyoo Yoo*,, and In-Beum Lee Dept. of Chemical Engineering, POTECH, an 31, Hyoja-dong, Nam-gu, Pohang 790-784, Korea *Dept. of Environmental cience and Engineering/Center for Environmental tudies, College of Environmental and Applied Chemistry, Kyung Hee University, 1 eocheon-dong, Giheung-gu, Yongin, Gyeonggi, 446-701, Korea (Received 9 October 2006; accepted 4 January 2007) k l r } rp l e p (sequencing batch reactor, BR)l v r r o m r (activated sludge model, AM No.1, AM1) r (iterative dynamic programming, IDP)p pn l BRp } tp s r nr s p ˆ p rp m. l e p p r o l v m e p v } p p r rp pn l p n performance index rk m. e l vl rl r r t(weight)p tp f e l v r el m. BRl IDP pn r nr r ns p r r~ e r~ l v nl el m p p k pl r nre sp nr p o v r el r~ np 20Í v tp pl. k rp p er rp l l p q p nl IDP pn l e qr ppp m. h Abstract This article aims to optimize the nitrogen removal of a sequencing batch reactor (BR) through the use of the activated sludge model and iterative dynamic programming (IDP). Using a minimum batch time and a maximum nitrogen removal for minimum energy consumption, a performance index is developed on the basis of minimum area criteria for BR optimization. Choosing area as the performance index makes the optimization problem simpler and a proper weighting in the performance index makes it possible to solve minimum time and energy problem of BR simultaneously. The optimized results show that the optimal set-point of dissolved oxygen affects both the total batch time and total energy cost. For two different influent loadings, IDP-based BR optimizations suggest each supervisory control of batch scheduling and set-point trajectory of dissolved oxygen (DO) concentration, and can save 20% of the total energy cost, while meeting the treatment requirements of COD and nitrogen. Moreover, it shows that the re-optimization of IDP within a batch can solve the modelling error problem due to the influent loading changes, or the process faults. Key words: Activated sludge model (AM), Dissolved Oxygen (DO) Control, Iterative Dynamic Programming (IDP), Model-based Optimization, Nitrogen Removal, equencing Batch ReactorG(BR), Wastewater Treatment Process 1. p o, v, p p mk m l } p mk e erp. p v p p rp r tp l p To whom correspondence should be addressed. E-mail: ckyoo@khu.ac.kr (sequencing batch reactor, BR)p. BRp o p v m pp rp el r p rl t p k m. BRp 1 p sl psm rvp p l p kp r, v, d v rp ps l } ep. pp ep p lv o p rp opp o l ps p n p BRp l l nr p. 1t op, p, r, } 73

74 m Ëo} Ëpp d v 5 p lv. p BR ed Šp fill-and-draw ep l d v rp l v 1980 l 2 } o p n l m. p p rp p k mp q rl o p q p r rp np v p p [1]. l p } ql p 2 } o l BR rp, e nr p. r e rp BRp n, p k, e, k p, ee rp l n, p n p p p l kr slp qt p p p l 1~2 r p p oe p. p l BR rp ee r l e l o nrqp l ps rp v p [1-3]. l p p l p p seˆ np r eˆ o } edšl rl r nrp n p rr tn v p. BRp rl o v r p rk lr m. ~ w ep n s, ph p m p pn rl r ep [4-6], w ep d v (Activated ludge Models)p pn rl r r ep [7-14]. Offlinel qt n r k rl p rn p l v rl r p m p pn ~ rp p k r p. q v r } rl q q k v p AM1, AM2, AM2dm p d v (activated sludge model family, AMs)p [8, 11]. AM p IWA(international water association)l 1980 re p } p l m rp qp nrp o r p re m. AM p } r l pl pl r p p rp p ep ˆp l l nr l p re t, q e rp v k } rl l l r. p AM p pn r } rl v m p r l r nr s p } n l m. v er q p } ql r l l k AMp p } q r l n l m AMp p p l er } qp nr r l vr rn p v k p. p BR rl p np rl l o p o v t n lp p l m p r m l v p k r m. r } qp r p n p m l p sn } q r l l l p n BRp rl r p r tp n. v v BR rp n p l rl r (batch control policy)p } e (minimum batch time) l l lr m. q v } kl BRp r rp } l v v k p. l o o45 o1 2007 2k v } p r nrp d v (activated sludge model, [8-14]) r (iterative dynamic programming, [19-22])l BR rp r r(optimal batch trajectory) p } rp l m. BRp l ns p r nr r e p }, r m e l v p el performance index r k, BRp t l op r p p p lp n qr (re-optimization)l l m. v r o BRp r rl e pn BRp l rl p m t n q performance index v l v r p n performance index rk m. pm r p p p n r rp } kp re m. 2. i m i s o m n Fig. 1p BRp l pl op, p, kp r, v, d v ˆ. BRp p p l p r p pn l rp } ep. BRp p nr l op, r nr s p e l r pp p v. BRl o v rp } o r rl r p }p n p. rp BR l rl r p p rp r pl p r m s e l p v. r pp m rl BRp } p, } n, r r p v. k nr e p w } t, r tp s v p nr e p } s p s v nr np v. m l, lv Fig. 1. Basic operation of a sequencing batch reactor [2].

o l v v [1, 2]. l r } rl v r l rp l v m. p rp l p v r v p, ˆv p v. BRp n v pp (aerobic phase), (anoxic phase)p v p n. v l l p mk k k kv mp eˆ. pl kv m p v mp eˆ. BR p l l ˆ r m v p, l ˆv pp pl. l v r l rp pp p. ~ q mk p ˆ qp p. q mk p k km ns pm dm kv mp eˆ. w s mk p qp s mk p v m o t ˆ p pn l pm dm v d. r r pn } qp r nr s p re o d v rl kk n p. v v p d v ep lp, IWAl 1982 p q v Task groupp d v rl r ep r l d v No. 1, 2, 2d, 3 m [18]. d v p o, v, p r p l r p r } rl v m p r l r nr s (optimal batch trajectory)p } n l m. l AM1p ˆp r p pn } qp nr r l np. BRl r p o tn nr m edš p rp l v m. p rp e p p r l r = op - o + - p el p p p rep p p ˆ p [18]. d ------ i dt q ----- in ( iin, i ) = + r i V l V, q in op, i ˆ m v p v, i,in op, rp p p. v r l rp AM1p 13 t Table 1 p ˆ m v r o 6 5 pp ˆ l l l e p l r v r o r r } m qr 75 (1) v m. rp l k AM1l r v p n m pr ˆl mr p re p p p ˆ p [18, 22]. d ------ i = r dt i l l BRp v m ˆ r l l 6 p rep ˆ l. l p o, k k, v m, ns, q mk, s mk p pp ˆ, v, ˆv pp. p Table 1 p k p l p p. 3. n (Iterative Dynamic Programming) 3-1. n r (IDP)p BR rp ˆ e (2)m p rep edšp r p p [19]. IDP s r p rrp qr p (mismatching grid point problem), p qrp p o r(high dimensionality), e p e p p r p e rl r rl r p } on p. r p l rl r q }p p qrp p [20-22]. p rp rp n p p r edšp p. dx ----- = fxut (,, ) dt x(0) tlr x ˆ, u α i u i β i (i = 1, 2,, m) rl ˆ. p edšl performance index(pi) s e l d tlv. PI[ x( 0), t f ] = Ψ( xt ( f )) + φ( xut,, ) dt f 0 l Ψ s ˆ p p, φ( )p rl p ˆ p ˆ l v [23]. (2) (3) (4) Table 1. Kinetics for carbon and nitrogen removal[18] Components Process Kinetics COD Dissolved Ammonium Nitrate Heterotroph Autotroph oxygen biomass biomass 1 Y Aerobic heterotrophic growth ------ H 1 -------------- i XB 1 µˆ H ---------------- O --------------------- X + + H 1 1 Anoxic heterotrophic growth ------ i XB ----------------- 1 µˆ 2.86 ---------------- H + Y Aerobic autotrophic growth A 4.57 --------------------- i 1 1 XB ------ ------ 1 µˆ NH H ----------------------- O -------------------- X + + H Y A K K OH O O --------------------- X+ NO ----------------------- ηg X K K OH + O K NO + H NO K NH NH K OA O Decay of heterotrophs 1 f P i XB f P i XB -1 b HX H Decay of heterotrophs 1 f P i XB f P i XB -1 b AX A Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

76 m Ëo} Ëpp Fig. 2. Basic scheme of iterative dynamic programming (IDP). 3-2. n m g r r p pn r rl r 0 t t f p l performance index ( )eˆ rl r u(t) } p [22]. Fig. 2l r l rp p ˆ l. Fig. 2p o r p k vp p p ~. 1) [0, t f ] P l e Lp. L=t f /P. 2) n rlp (M)m qr (N) r. rl u(0), r, pq γ p r. 3) rl r p r rep t=0l t f v l xp qrp eˆ. 4) v Pl eq l t f -Ll t f v p qrl l vp n rl l rep performance index eˆ rl p rq. 5) pr p P-1l v t f -2Ll t f -L v p qrl l v n rl p pn rep. v p r q n qrp } e t f -Ll t f v pr, v P l qrl rq rl p pn performance index eˆ rl p } rq eˆ. 6) p rp P-2, P-3,, 1 v e. 1 v mp performance index eˆ rl p rq eˆ. 7) p p p tl p r v eˆ. r j ( + 1) γr = j ( ) l j p. 8) 6 q sp rl r p rl r p n e 3 k 3-7 [19, 22]. 4. s o l BRm n oh BRp v r l trp m p pn v r m l v el p r~ e p tp o r nr kp m. } r p er q rnl np r o tn l ns r l, r v }, l v l nr e p tp o r p pn l BRp r nr s p }k k. o45 o1 2007 2k (5) Fig. 3. Relationships between used energy and batch completion time [23]. Fig. 4. Area of the ammonium and the oxygen concentration under constant aeration rate [23]. 4-1. BRm i ni m r rl p l q k v p p rp e r bang-bang rl p [21]. er } rl ns p r p r l nr e p nr e p tp pp p. p p l v r j p r l p. e p n nr n t l v n nl np, l vl p np v l v np er rl l p m p t p l r kk. BRp l p p o l n l vm m e p Fig. 3l ˆ l. l ns p r r e p tn p e, v } p ˆ l. l p n l vm m e p p vp k pl. e l v kp performance indexl

l e p l r v r o r r } m qr 77 lk p k p [23]. Fig. 4 pr kp mp n AM l p l p e l ns m k k p ˆ p. l p pr eˆ k kp l l t r(a NH )p o p v nr e rm p ppp k p. ns l l t r(a O )p n p l. p p vrrp n l v k l p. p rp p performance index l r nr s p }p p. l r ns } p rp r ns } o A O eˆ p lp p. k A O ƒ v p tpe k l n l v k v. A O qkv ns n p tl l pn l v k [23]. 4-2. k Performance Index og BRl v r l n l v np tp nr e p Performance index rk m. p o krl v r p d v p l e l k k( NH )p rl p r(a NH )p nr e o p vl p k p. n rl q r ns l v r eˆ p n m [23]. e l r ns l r (A O )p p tp. v, rp p t pe k l v p n. p p p ep e p. Q= at+ be Q, R= ce C + dc O l Q, Rp PIp s p o weight ep, T time cost, E Q effluent quality, E C l v, C O p, a, b, c, d Q, R e l weightp. op r(a O )p l v l vrr p k k r r(a NH )p nr e, o p vl p k l e r s eˆ p l tp l n performance index rk m [23]. J = N k = 0 ( Q NH ( k)l+ R U Do ( k)l) l Q e, o p vl tp Rp l v o tp Lp e p. nr e p t p o Q R p f r l r, l v r Q Rp p f r nr r p r p. 5. 5-1. i m m kn o l p l e p fill-and-draw ep 12.5 L (6) (7) Table 2. Initial conditions and systems of BR optimization Operational conditions Values Reactor volume 12.5 l Total batch reaction time 12 h Aerobic reaction time 8 h Anoxic reaction time 4 h Initial conditions COD concentration 150 mg/l Ammonium concentration 40 mg N/l Nitrate concentration 0 Dissolved oxygen concentration 3 mg/l Heterotrophic microorganism concentration 400 mg/l Autotrophic microorganism concentration 40 mg/l Fig. 5. Typical concentration profiles associated with the cyclic operation of the BR at steady state. p v (8e ) (4e )p t rp nr. op ep m p 150 mg/lp r + n (COD)p v 40 mg/lp ammonium(nh 4 -N)p o p [20]. Fixed time control(ftc) nr s nr r p 12e p e p v BRp nr ˆm ˆ Table 2l ˆ l. n p l, k AM 1 p l n m. Fig. 5 r ˆ nr mp n p l BRp l e l o, k k, ns, v pmp r rp lt. 5-2. Performance indexi i s m il k r p pn BRp e, l ns p r r p r nr s p }k k. r nr s p ˆ rl r performance indexl l v p lp l l vl n IDP m. p n BRp r rl r e rl. v, R=0p nl r m. e p s l P = 16, u (0) = 1.5, r (0) =2 qr 3p r m rk s p 0.5 u Do 3(mg/l) r m. r r (initial control policy)p u (0) = 1.5, r =2 r m 20 pr (0) m. Q 0.5, Rp 0.2 r m. Fig. 6 p r n s p 3 mg/l pr ov p k p. 5-3. BRi n n y kp l ˆp BR r l ns Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

78 m Ëo} Ëpp Fig. 6. When the performance index doesn t include the energy term. Fig. 8. Optimal control result of BR using IDP (scenario 2: Q:R = 0.2:0.5); (a) optimal trajectory of DO at aerobic phase, (b) nutrient concentration profiles [23]. Fig. 7. Optimal control result of BR using IDP (scenario 1: Q:R = 0.5:0.2); (a) optimal trajectory of DO at aerobic phase, (b) nutrient concentration profiles [23]. p r sp v r m l v l m p p k pl. pl k l l A NO p p r ns rl r l IDP e m. e rm ns l t(r)p Q mp 2 v e m k. l v n v r np l (1) Q:R = 0.5:0.2 (2) Q:R = 0.2:0.5 2 v np e m p l r m. rk s p kl m v 0.5 u Do 3(mg/l) r m [23]. k l l p Q nr n o vp np Rp tp, l v nl np. Initial control policy u (0) = 1.5, r =2p (0) o45 o1 2007 2k ˆ m 20 pr m. P 24 r l e p p mp r~rp 5 r p e p e p. Fig. 7p e m 1l r p pn BRp n s p r r o, v p r rp ˆ. p m e (t 1 )p 5.6(hr)p A O = 0.6728, J = 2.4446p m. r ˆ p A O = 0.725, J = 2.7692, p m e p 5.6(hr)p. v r nr s p n sp nr s l l v np 7.2Í r tp pl. r~ np sl l 11.7Í m. e m 2 l v p n s n J = 1.0717, A O = 0.4258 ˆ. r~ np 61.3Í m e p m e (t 1 )p 7.2(h) sl k 1e 20 v mpp k p [23]. Fig. 8p e m 2l r p pn BRp ns p r r r o, v p r rp ˆ. 5-4. o m l o k m n (re-optimization) } qp p op p sp r p p p er p n qt. er } ql BR rp r p p p er r ˆ lp r p l p m p r m m p r k eˆ. p l r r l m p l er nrq o r nr p. q r } rl qt pl p p r } o BRp t l r p p p lp n r p pn l nr t l e r nr s p t rp }p pvl BR qr (re-optimization)l l m.

l v r p r } l lr pp d v t v r m p v p q (µ H ) r p p nr s p r er n BR qr l l l m. v, p p op p p e r q p p n v k qr m. 2 p l m e m 3p l µ H p 1p r l p er p 0.75p np, e m 4 µ H p er p 0.5p np. v n p v 1e w r (in-situ respirometry) r µ H p p pv m r m. l rk s p 0.5 u Do 3(mg/l) r m. v s kr Fig. 9. The optimal dissolved oxygen and trajectories of scenario 3. l e p l r v r o r r } m qr 79 v Initial control policy u (0) = 1.5, r =2p ˆ m (0) 20 pr m. Q 0.5, Rp 0.2 r m. P 16 r l e p p mp r~ r e p 2 r n l. e m 3l qr Fig. 9m p p e p 8e p Cost p 1.5192 m. Fig. 9m 10l r e p l qr r nr s r e p l } o v p p. Fig. 9m 10p qr v p q p µ H l l sp r nr s p mr v r mr v r o l r ns 3mg/l v v lk p e v lk p k pl. e m 4 P = 28, r p e m 3 p m. Fig. 10 e m 4l lt p e p 12e p Cost p 2.7791p. e m 3 µ H p l r ns ov lk p k pl. rp e rp e q r e r k p k pl. 6. q v BR rll p t nr e p tp o l p lml. pl l IDP pn lbr l r rp } r p p q p p er m lp l q-r p l l m. l v nl ep l v np rl l m p k. l ns rl n mp r v } m l v e p m. r(a O )p l v, r ns l vrrp k k r r(a NH )p e, effluent qualityl p k l r performance index n m. v e ml r nr s p }p BRp ns p r v r k l v l m p p k pl r op t v rp r p nr s p re ppp m. k r p p er rp l l p q p nl IDP pn l e qr ppp m. l re p r } rp r o on n ppp k pl. p AM p r k p e rp dv k p e p n rp p. l tn e p r r p p l p. q edš l el r m r r p el l l l p. Fig. 10. The optimal dissolved oxygen and trajectories of scenario 4. l BK21 2 ll p vo k ld. Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

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