Microorganisms fuel their lives by performing redox reaction that generate the energy and reducing power needed tomaintain and construct themselves.

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1 CHAPTER 3. Microbil Kinetics

2 3.Microbil Kinetics Microorgnisms fuel their lives by performing redox rection tht generte the energy nd reducing power needed tomintin nd construct themselves. Becuse redox rections re nerly lwys very slow unless ctlyzed, microorgnisms produce enzyme ctlysts tht increse the kinetics of their redox rections to exploit chemicl resources in their environment. Engineers wnt to tke dvntge of these microbilly ctlyzed rections becuse the chemicl resources of the microorgnisms usully re the pollutnts tht the engineers must control : Orgnics (BOD, e - donor), NH 4 + (e - donor, nutrient), NO (e cceptor, nutrient), PO 4 (nutrient), etc.

3 3.Microbil Kinetics Engineers who employ microorgnisms for pollution control must recognize two interrelted principles p (connections between the ctive biomss (the ctlyst) nd the primry substnces): First : Active microorgnisms ctlyze the pollutnt removing rections. o the rte of pollutnt t removl depends d on the concentrtion ti of the ctlyst, or the ctive biomss. econd : The ctive biomss is grown nd sustined through the utiliztion of its energy - nd electron (e - ) - generting primry substrtes. o the rte of biomss production is proportionl to the utiliztion rte of the primry substrtes.

4 3.1 Bsic Rte Expressions Mss blnce modeling is bsed on i) the ctive biomss nd ii) the primry substrte tht limits the growth rte of the biomss. In the vst mjority of cses, the rte limiting substrte is e - donor. o the term substrte now refers to the primry e - donor substrte. Jcques Monod : Nobel prize winner, director of Psteur Institute. Monod eqution : reltionship most frequently used to represent bcteril growth kinetics developed in the 194s. : His originl work relted the specific growth rte of fst growing bcteri to the concentrtion of rte limiting, e - donor substrte.

5 3.1 Monod eqution Monod eq : lrgely empiricl, but wide spred pplied for microbil systems μ syn 1 d dt μ K + syn [3.1] μ syn t specific growth rte due to synthesis(t -1 ) concentrtion of ctive biomss(m -3 x L ) Time (T) concentrtion of the rte-limiting substrte (M s L -3 ) μ μ mximum specific growth rte(t -1 ) K substrte concentrtion giving one-hlf the mximum rte (M -3 s L )

6 3.1 Monod eqution Compre eq. 3.1 with eq μ syn 1 d ( ) syn μ dt K + [3.1] v v v + [1.13] m Michelis-Menten eqution : K M - developed in theory of enzyme ction nd kinetics : Rection velocity KM : ubstrte concentrtion giving one-hlf of the mximum velocity Microorgnisms re bgs full of enzymes so tht it is not surprising tht the growth rte of microorgnisms (Monod eq.) is relted to the rections of the ctlysts tht medite mny rections (Michelis nd Menten eq.)

7 3.1 Bsic Rte Expressions Endogenous decy: 1) Environmentl engineers study more slowly growing g bcteri tht hs n energy demnd for mintennce. 2) Active biomss hs n energy demnd for mintennce of cell functions ( motility, repir nd re-synthesis synthesis, osmotic regultion, trnsport nd het loss). 3) Flow of energy nd electrons re required to meet mintennce needs. 4) The cell oxidize themselves to meet mintennce- energy needs. μ 1 d dt dec decy - b [3.2] b endogenous-decy coefficient(t -1 ) μ dec specific growth rte due to decy(t -1 )

8 3.1 Endogenous Decy μ 1 d dt dec decy -b [3.2] Oxidtion decy rte : Although most of the decyed biomss is oxidized, smll frction ccumultes s inert biomss μ 1 d dt resp decy f d - f d b [3.3] : frction of ctive biomss tht is biodegrdble The rte t which ctive biomss is converted to inert biomss μ μ -μ inert dec resp 1 di 1 d b ( fdb) (1 f dt dt inert : inert biomss concentrtion(m -3 x L ) i d ) b [3.4] - inert biomss formed from ctive biomss decy -inert biomss represents frction of only the orgnic portion of ctive biomss

9 3.1 Net specific growth rte The net specific growth rte of ctive biomss(μ) is the sum of new growth nd decy 1 d μ μsyn + μdec μ dt K + -b [3.5]

10 3.1 Net specific growth rte Mximum specific growth rte Figure3.1 schemtic of how the synthesis nd net specific growth rtes depend on the substrte concentrtion. At 2K, μsyn o.95 μ If o, then μ μ syn b + μ dec μ K + -b

11 3.1 Rte of substrte utiliztion The ultimte interest is to remove substrte r q K + ut [3.6] r ut rte of substrte utiliztion (M L -3 T -1 ) rte of substrte utiliztion (M s L T ) q mximum specific rte of substrte utiliztion (M s M -1 x T -1 ) ubstrte utiliztion nd biomss growth re connected by μ q Y [3.7 ]

12 3.1 Net rte of ctive-biomss growth μ q Y (T -1 ) (M s M x -1 T -1 ) (M x M s -1 ) (T -1 ) The net rte of cell growth : μ μ K + -b K + rnet μ μ - r net q Y K + -b b [3.7 ] [3.5] [3.8] r net the net rte of ctive-biomss growth (M x L -3 T -1 )

13 3.1 Bsic Rte Expressions is connected with. r net μ r net Y K μ q + - b ome prefer to think of cell mintennce s being shunting of substrte - derived electrons nd energy directly for mintennce. This is expressed by [3.1]. μ q Y ( K + - m) [3.9] [3.1] m mintennce-utiliztion rte of substrte (M s M x -1 T -1 ) When systems go to stedy stte, there is no difference in the two pproch, nd b Ym

14 3.1 Bsic Rte Expressions μ μ r net q Y K + q Y ( - m) K + d / dt Y ( m) ) d / dt b < m μ < Y - b [3.9] m mintennce-utiliztion rte of substrte (M s M -1 x T -1 ) b/y At strvtion stte, the substrte utiliztion rte is less thn m At stedy stte, the net specific growth rte of cell (μ), or the net yield (Y n )is zero., const. μ d / dt m b Y - Any growth of biomss (Ym) only supplements the decy of biomss (b). o pprently the concentrtion of biomss does not chnge. - The energy supplied through substrte utiliztion is just equl to m, the mintennce ene

15 3.2 PARAMETER VALUE

16 3.2 PARAMETER VALUE---Y Aerobic heterotrophs: Denitrifying heterotrophs: H 2 -Oxidizing sulfte reducers: Next slide

18 3.2 PARAMETER VALUE---Y Experimentl estimtion of Y - A smll Inoculum is grown to exponentil phse nd hrvested from btch growth. Mesure the chnges in biomss nd substrte conc. from inoculum until the time of hrvesting. - The true yield is estimted from Y -Δ / Δ - The btch technique is dequte for rpidly growing g cells, but cn crete errors when the cells grow slowly so tht biomss decy cn not be neglected.

19 3.2 PARAMETER VALUE -- q q is controlled lrgely by e - flow to the electron cceptor. For 2 o C, the mximum flow to the energy rection is bout 1 e - eq / gv d, where 1 g V represents 1g of biomss. - q e bout 1 e eq / V - d t 2 q q e / f / e C [3.11] For exmple (Tble 3.1), if f s.7, then f e.3. o q q e / f e 8g BOD L / V d /.3 27 g BOD L / gv d q is temperture q T q q function T q T R 2 (1.7) (1.7) ( T- T ( T -2) R ) [3.12] [3.13]

20 3.2 PARAMETER VALUE--q b is depends on species type nd temperture. b.1-.3 /d for erobic heterotrophs b <.5 /d for slower-growing species b T b T R (1.7) ( T -T R ) Biodegrdble frction (f d ) is quite reproducible nd hs vlue ner.8 for wide rnge of microorgnisms

21 3.2 PARAMETER VALUE---k q r net Y -b K + [3.8] K is the Monod hlf-mximum-rte concentrtion most vrible nd lest predictble prmeter Its vlue cn be ffected by the substrte`s ffinity for trnsport or metbolic enzymes mss-trnsport resistnces (pproching of substrte nd microorgnisms to ech other) ignored for suspended growth re lumped into the Monod kinetics by n increse in K

22 3.3 Bsic Mss Blnces Chemostt: completely mixed rector, uniform nd stedy concentrtions of ctive cell, substrte, inert biomss nd ny other constituents. Active biomss μ V Q. ubstrte V r ut + Q [ 3 14] ( ) [ 3. 15] Q constnt feed flow rte Q constnt feed flow rte o feed substrte concentrtion

23 3.3 Bsic Mss Blnces Active biomss μ V Q. [ 3 14] μ qˆ q Y V b V Q K + r net [ ] Y qˆ K + b [ 3.9] K V 1+ b Q V V Yqˆ q 1+ b Q Q [ 3. 18]

24 3.3 Bsic Mss Blnces ubstrte V r ut + Q ( ) [ 3. 15] r ut qˆ K + [ 3.6] qˆ q K + V + Q ( ) [ 3. 17] b V + Q Y qˆ K + V from [ 3.16 ] Y 1 V b Q ( ) [ 3. 19] 1+

25 3.3 HRT & RT HRT (Hydrulic detention time) hydrulic detention time ( T) θ V / Q [ 3.2] 1 dilution rte( (T ) D Q / V [ ] θ RT (olids retention time) MCRT (Men cell residence time) ludge ge ctive biomss in the system μ production rte of ctive biomss 11 [ 3.22] d μ μ 1 μsyn + μdec dt K + -b [3.5]

26 3.3 RT ( θ ) θ ctive biomss in the system μ production rte of ctive biomss 1 [ 3. 22] RT : Physiologicl sttus of the system : Informtion bout the specific growth rte of the microorgnisms

27 3.3 RT ( θ ) RT with quntittive prmeters V V θ θ Q Q 1 D [ 3.23 ] θ θ in chemostt t stedy stte V 1+ b Q K V V Yqˆ 1 b + Q Q [ 3. 18] 1+ bθ Yqˆ θ ( 1+ bθ ) V Q θ θ K [ 3. 24] 1 ( ) [ 3. 19] Y Y [ ] V 1+ b 1 b + θ Q

28 3.3 RT ( θ ) nd re controlled by RT( θ ) 1+ bθ K Yq ˆ qθθ + b Y 1 + b θ ( [ 3.24] 1+ b θ ) 1 [ 3. 25]

29 3.3 RT ( min θ ) 1) t very smll θ :, min θ wshout : vlue t which wshout begins θ min : θ < θ by letting in eq 3.24 nd solving for θ K Yqˆ θ 1+ bθ ( 1+ bθ ) [ 3. 24] θ min θ K + ( Yqˆ b ) bk θ V / Q, θ then Q ( V const.) [ 3.26]

30 3.3 RT ([ θ min ] ) lim min θ K + ( Yqˆ b ) bk [ 3.26] min θ decreses with incresing [ θ min ] lim lim min [ θ ] lim o lim s o s K / K + ( Yqˆ b ) + 1 ( Yqˆ b ) bk / bk 1 [3.27] Yqˆ b defines n bsolute minimum θ (or mximum ) boundry for hving stedy-stte stte biomss. It is fundmentl delimiter of biologicl process. μ

31 3.3 RT ( min θ ) min 2) For ll θ > θ, declines monotoniclly with incresing θ θ θ V / Q, θ then Q ( V const.)

32 3.3 RT ( min ) 3) For very lrge θ, pproches nother key limiting vlue, min. K Yqˆ θ 1+ b θ b [ 3.24] ( ) 1+ bθ min 1+ bθ lim K x Yqˆ θ 1 + θ lim θx b K Yq ˆ b ( 1+ b θ ) 1/ θ + b K Yqˆ 1/ θ b 1 θ θ V / Q, θ then Q ( V const.)

33 3.3 RT ( min ) min is the minimum concentrtion cpble of supporting stedy-stte stte biomss. - If < min, the cells net specific growth rte is negtive. μ - In eq 3.9,, then - b. μ r net Y q K + - b [3.9] - Biomss will not ccumulte or will grdully dispper. - Therefore, stedy-stte biomss cn be sustined only when > min.

34 3.3 RT ( vrition) θ min θ 4) When >, rises initilly, becuse Q( ) increses s θ becomes lrger. - However, reches mximum nd declines s decy becomes dominnt (Q( ) decreses) for lrge (smll Q) - If θ were to extend to infinity, would pproch zero (eq 3.25) θ Y 1 + bθ [ 3. 25]

35 3.3 Microbiologicl fety Fctor 5) We cn reduce from o to min min s we increse θ from θ to infinity. - The exct vlue of θ we pick depends on blncing of substrte removl ( ), biomss production ( Q ), rector volume (V) nd other fctors. - In prctice, engineers often specify microbiologicl sfety fctor, min defined by /. θ θ - Typicl sfety fctor 5 ~ 1.

36 3.4 Mss Blnces on Inert Biomss nd Voltile olids Becuse some frction of newly synthesized biomss is refrctory to self-oxidtion, endogenous respirtion leds to the ccumultion of inctive biomss ( 1 f b ). Rel influents often contin refrctory voltile suspended solids ( i ) tht we cnnot differentite esily from inctive biomss. ( ) V d tedy-stte mss blnce on inert biomss ( 1 fd ) b V + Q( i i ) [ 3. 29] Formtion rte of inert biomss from ctive biomss decy i i concentrtion of inert biomss input concentrtion of inert biomss θ V Q i i + ( 1 f ) bθ [ 3.3] d

37 3.4 Mss Blnces on inert Biomss nd Voltile olides i i + ( 1 f ) bθ [ 3.3] d Influent inert - inert biomss formed from ctive biomss decy -inert biomss represents frction of only the orgnic portion of ctive biomss i By introducing, we re relxing the originl requirement tht only substrte enters the influent. 1+ bθ From 3.25 nd θ θ, Y [ 3.25 ] i ( 1 f ) bθ d + Y ( ) i 1+ bθ

38 3.4 Mximum of inert biomss ( ) i i ( 1 f ) b θ ( ) ( f ) d i + Y 1+ bθ mx i + ( b + θ lim i + Y (1 fd ) 1 b θ θ Y b θ lim i (1 fd) θ ( ) min (1 fd ) from Fig 3.33 min lim mx i i + Y θ

39 3.4 Mss Blnces on inert Biomss nd Voltile olides mx i i + Y ( )(1 fd) min gret ccumultion of inert biomss - tom m i increses monotoniclly from i mximum mx i - Opertion t lrge θ results in greter ccumultion of inert biomss

40 3.4 v: voltile suspended solids concentrtion (V) v i + v : voltile suspended solids concentrtion(v) v i i + + Y ( + (1 (1 + (1 fd) bθ + fd ) b θ ) ) [1 + (1 fd) bθ ] i 1 + bθθ [3.31]

41 3.4 v: voltile suspended solids concentrtion (V) - v generlly follow the trend of, but it does not equl zero; (When goes to zero, v equls i ) - if θ min x < θ x, v i,

42 3.4 Yn: net yield or observed yield (Yobs) from [3.31] + + (1 f b v i d ) Y ( + ) [1 + (1 f θ ) bθ ] d i 1+ b θ i + Y n ( ) < by int uition > Net ccumultion of biomss from ynthesis nd decy. Y 1+ b θ [ 3. 25] Y n : net yield or observed yield (Y obs ) Y n Y 1 + (1 f d ) b 1 + b θ x θ x [3.32] [3.32] is prllel to the reltionship between f s nd f s : f s f 1 + (1 + f d ) b θ b θ x s 1 x [3.33] 33]

43 3.5 oluble Microbil Products MP(soluble microbil products) Much of the soluble orgnic mtter in the effluent from biologicl rector is of microbil origin. It is produced by the microorgnisms s they degrde the orgnic substrte in the influent to the rector. The mjor evidence for this phenomenon comes from experiments ; single soluble substrtes of known composition were fed to microbil cultures nd the resulting orgnic compounds in the effluent were exmined for the presence of the influent substrte. The bulk of the effluent orgnic mtter ws not the originl substrte nd ws of high moleculr weight, suggesting tht it ws of microbil origine. It is clled oluble Microbil Products (MP).

44 3.5 oluble Microbil Products MP: Biodegrdble, lthough some t very low rte : Moderte formul weights(1s to 1s) : The mjority of the effluent COD nd BOD : They cn complex metls, foul membrnes nd cuse color or foming : They re thought to rise from two processes: 1) growth ssocited (UAP), 2) non-growth ssocited (BAP) MP UAP + BAP UAP ( substrte-utiliztion-ssocited products ) growth ssocited they re generted from substrte utiliztion nd biomss growth they re not intermedites of ctbolic pthwys BAP (biomss-ssocited ssocited products ) non-growth ssocited relted to decy nd lysis of cell relese of soluble cellulr constituents through lysis nd solubiliztion of prticulte cellulr components

45 3.5 MP vs. EP - MP chool focuses on i) MP, ii) ctive biomss nd iii) inert biomss, but does not include EP. - EP chool focuses on i) EP (soluble nd bound) nd ii) ctive biomss, but does not include MP. - Compred to other spects of biochemicl opertions, little reserch hs been done on the production nd fte of soluble microbil products. o little is known bout the chrcteristics of UAP nd BAP.

46 3.5 UAP nd BAP formtion kinetics - UAP formtion kinetics : r UAP - k 1 r ut r rte of UAP-formtion (MpL -3 T -1 UAP ) k 1 UAP- formtion coefficient (MpM -1 s ) - BAP formtion kinetics : r BAP k 2 r BAP rte of BAP-formtion (MpL -3 T -1 ) 1 k 2 BAP- formtion coefficient (MpMx -1 )

47 3.5 oluble Microbil Products Exmple 3.3 Effluent BOD 5 The BOD exertion eqution : BOD BOD (1- exp{ - kt}) t BOD L L - BOD L exp{ - kt} BOD5 : BODL 1exp{ k 5d} [3.41] [3.42] k BOD 5 :BOD L rtio originl substrte.23/d.68 ctive biomss.1/d.4 MP.3/d.14

48 3.6 Nutrients nd Electron Acceptors Biotechnologicl i l Process must provide sufficient i nutrients ti t nd electron cceptors to support biomss growth nd energy genertion. Nutrients, being elements comprising the physicl structure of the cells, re needed in proportion to the net production of biomss. Active nd inert biomss contin nutrients, s long s they re produced microbiologiclly. e - cceptor is consumed in proportion to e - donor utiliztion multiplied by the sum of exogenous nd endogenous flows of e - to the terminl cceptor.

49 3.6 How to determine nutrient requirements - Nutrients re needed in proportion to the net production of biomss (r ut Y n ) - In chemostt model, rte of nutrients consumption (r n ) r n γ γ n n r r ut ut Yn Y 1 + (1 1 Y (M x M s -1 ) + f d ) bθ x bθ x [3.43 ] r n rte of nutrient consumption (M n L -3 T -1 ) (negtive vlue) γ -1 n the stochiometric rtio of nutrient mss to V for the biomss [M n M x ] γ N 14g N/113g cell V.124g N/g V < C 5 H 7 O 2 N > γ P 2*.2 γ N 25gP/gV (1 1 + f d ) b θ x b θ x [ Yn Y x ] [ ]

50 3.6 Nutrient requirements - Overll mss blnce QC n QC n + r n V [3.44 ] C n C n + rnθθ [3.45 ] C n : Influent concentrtion of nutrient ( M -3 n L ) C n : Effluent concentrtion of nutrient ( M n L -3 ) r n : rte of nutrient consumption (M n L -3 T -1 ) (negtive vlue) * The supply of nutrients must be supplemented if C n is negtive in eq 3.45.

51 3.6 Use rte of Electron Acceptors Use rte of electron cceptor [Δ / Δ t (M T -1 )] - mss blnce on electron equivlents expressed s oxygen demnd (OD) gcod OD inputs Q v Q [3.46] ee tble 2.1 gv gcod ODoutputs Q + Q( MP) v Q [3.47] gv - the cceptor consumption s O 2 equivlents, Δ / Δ t OD inputs OD outputs Δ Δtt γ Q [ MP ( )] [3.48] γ 1g O 2 /g COD for oxygen γ.35g NO 3- - N/g COD for NO 3- -N γ 3 3 O 2 (32g) + 4 e - 2 O -2 NO 3 - (14g) + 5 e - N v v 14g NO 3 N /5e - / 32g O 2 /4e -.35 g NO 3 N / g O 2

52 3.6 Amoumt of e - cceptors to be supplied - the cceptor cn be supplied in the influent flow or by other mens, such s ertion to provide oxygen ( ). Δ Δ t Q R [ ] + R [3.49 ] Acceptor consumption rte R: the required mss rte of cceptor supply (M T -1 ) : Influent concentrtion of e - cceptor ( M L -3 ) : effluent concentrtion of e - cceptor ( M L -3 )

53 3.7 Input Active Biomss - Three circumstnces for inputs of ctive biomss in degrdtion of the substrte : When processes re operted in series, the downstrem process often receives biomss from the upstrem process. Microorgnisms my be dischrged in wste strem or grown in the sewers. Biougmenttion is the deliberte ddition of microorgnisms to improve performnce. - When ctive biomss is input, the stedy-stte mss blnce for ctive biomss (3.16), must be modified. qˆ q Y V b V Q K + [ ] q ˆ Q Q + Y V b V K + [3.5 ]

54 3.7 Input Active Biomss Q Q q ˆ + Y K + b [3.5 ] Eq 3.5 cn be solved for when ctive biomss is input, + b θ K Y q ˆ θ + 1 x x V ( 1 b θ ) x V [ 3.51 ] The solution for s (eq 3.51) is exctly the sme s eq 3.24, K 1+ bθ Yqˆ θ ( 1+ bθ ) [ ] but the θ x is now redefined. - When the RT is redefined s the reciprocl of the net specific growth rte, θ x 1 V μ Q Q [3.52 ]

55 3.7 HOW does ffect nd wshout? -, wshout occurs for θ x of bout.6 d. - As Increses, complete wshout is eliminted, becuse the rector lwys contins some biomss. - Incresing, lso mkes lower, nd the effect is most drmtic ner wshout.

56 3.7 Input Active Biomss For biomss, Q For substrte, Q qˆ K + V q ˆ + Y K + + Q V b V ( ) [ 3. 17] For inert, ( 1 f ) b V + Q( ) [ 3. 29] d i i [3.5 ] v i + (1 + (1 fd) bθ ) Due to the chnge in definition of θx, solutions of the mss blnces differ. θ θ x Y ( ) b θ x [3.53 ] i i + (1 f d ) b θ [3.54] v i + i + (1 + (1 f d ) bθ ) [3.55] When, v i + (1 + (1 fd) bθ ) [3.31]

57 3.7 Input Active Biomss Due to the chnge in definition of θx, solutions of the mss blnces differ. θ x 1 Y ( ) [3.53 ] θ 1 + b θ x θx/θ rtio represents the build up of ctive biomss by the input. Rerrnging Eq. 3.52, θ θ x < : θ x > θ / - > : θ x is negtive. [3.56 ] The net biomss decy which mkes the stedy-stte μ negtive nd sustin < min. If θx is negtive, < min from eqs below 1 + bθ K Yq ˆθ ( 1 + bθ ) 1/ θ + b K Yqˆ 1/ θ b min lim θ x b K Yqˆ b 1/ θ + b K Yqq ˆ 1/ θ b /

58 3.8 Hydrolysis of Prticulte nd Polymeric ubstrtes Orgnic substrte of prticles (lrge polymers) - Orgnic substrtes t tht t originte i s prticles or lrge polymer tke importnt ppliction in environmentl biotechnology Effect of hydrolysis - Before the bcteri cn begin the oxidtion rection, the prticles or lrge polymers must be hydrolyzed to smller molecules - Extrcellulr enzymes ctlyze these hydrolysis rection - Hydrolysis kinetics is not settled, becuse the hydrolytic enzymes re not necessrily ssocited with or proportionl to the ctive biomss -level of hydrolytic enzymes is not estblished, nd mesurement is neither simple

59 3.8 Hydrolysis of Prticulte nd Polymeric ubstrtes Hydrolysis of kinetics - Relible pproch is first-order reltionship r k hyd hyd p [3.57] * r hyd : rte of ccumultion of prticulte substrte due to hydrolysis (M s L -3 T -1 ) * p : concentrtion of the prticulte (or lrge-polymer) substrte (M s L -3 ) * k :firstorder -1 hyd first-order hydrolysis rte coefficient (T ) - k hyd is proportionl to the concentrtion of hydrolytic enzymes s well s to the intrinsic hydrolysis kinetics of the enzymes - some reserchers include the ctive biomss concentrtion s prt of k hyd ' ' k hyd k ( k specific hydrolysis rte coefficient) i hyd hyd

60 3.8 Hydrolysis of Prticulte nd Polymeric ubstrtes - When Eqution 3.57 is used, the stedy-stte mss blnce on prticulte substrte V r ut + Q( ) [3.14] Q( p P p ) k hyd p V [3.58] p p 1 + k hyd θ [3.59] - θ represent the liquid detention time nd should not be substituted by θ x

61 3.8 Hydrolysis of Prticulte nd Polymeric ubstrtes The stedy-stte mss blnce on soluble substrte - The stedy-stte mss blnce on substrte q ˆ V + Q ( ) [3.17] K + - The stedy-stte mss blnce on soluble substrte ( ) q ˆ K + V / Q + k hyd p V / Q [3.6] * effectively is incresed by k V Q hyd p /

62 3.8 Hydrolysis of Prticulte nd Polymeric ubstrtes Other constituents of prticulte substrte lso re conserved during hydrolysis - Good exmples of prticulte substrte : the nutrient nitrogen, phosphte, r hydn γ k n hyd p [3.61] sulfur * r hydn : rte of ccumultion of soluble form of nutrient n by hydrolysis (M -3-1 n L T ) γ n M n M * : stoichiometric rtio of nutrient n in the prticulte substrte( ) s1

63 3.8 Hydrolysis of Prticulte nd Polymeric ubstrtes Exmple 3.6

64 3.8 Hydrolysis of Prticulte nd Polymeric ubstrtes Y of csein (pp. 17) ( 1 θ x Y ) 1+ bθ θ x [3.53] i i + (1 f d ) bθ [3.54] v i + [ 3.55] v i + + p [3.55]' 1 2 COD /weight the conversion fctor (pp. 129, 181) 3 The biodegrdble frction.8 (pp. 171)

CHEMICAL KINETICS

CHEMICAL KINETICS Long Answer Questions: 1. Explin the following terms with suitble exmples ) Averge rte of Rection b) Slow nd Fst Rections c) Order of Rection d) Moleculrity of Rection e) Activtion Energy