Biological sulphate reduction with primary sewage sludge in an upflow anaerobic sludge bed reactor Part 5: Steady-state model

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1 Biological ulphate reduction with primary ewage ludge in an upflow anaerobic ludge bed reactor Part 5: Steadytate model J Poinapen and GA Ekama 1 Water Reearch Group, Department of Civil Engineering, Univerity of Cape Town, Rondeboch 7701, South Africa Abtract Thi paper decribe the development of a teadytate anaerobic digetion model for biological ulphate reduction uing primary ewage ludge (PSS a ubtrate. The model comprie: a chemical oxygen demand (COD baed hydrolyi kinetic part in which the PSS biodegradable COD and ulphate removal are calculated for given hydraulic and ludge retention time; a C, H, O, N, P, S, COD and charge ma balance toichiometry part in which the alkalinity generated (from both the H and HS i determined from the COD and ulphate removal; and an inorganic carbon (C and ulphide mixed weak acid/bae chemitry part in which the digeter ph i calculated from the H and HS pecie formed. From the toichiometry, it wa found that the PSS i carbon limited in that it doe not generate ufficient H alkalinity for the ulphate reduction, i.e., it COD/C ratio i too high which account for the oberved zero ga (C generation. The H 2 S/HS ytem provide the alkalinity hortfall and etablihe the ytem ph. Once developed and calibrated, the model reult were compared with experimental data from 2 laboratorycale upflow anaerobic ludge bed reactor (operated at 35 o C and 20 C repectively fed PSS and ulphate. The predicted COD and ulphate removal, alkalinity and digeter ph correpond very well to the meaured data. The model ait in identifying deign and operation parameter enitive to the ytem and provide a bai for developing an integrated biological, chemical and phyical proce dynamic model. Keyword: biological ulphate reduction, primary ewage ludge, upflow anaerobic ludge bed reactor, teady tate model, kinetic, toichiometry, mixed weak acid/bae chemitry Nomenclature a molar nitrogen compoition of organic in anaerobic digetion Alk H 2 S alkalinity with repect to the H 2 S reference pecie excluding the water pecie AMD acid mine drainage b molar phophoru compoition of organic in b endogenou repiration rate of acidogen BPO biodegradable particulate organic BRT bed retention time BSO biodegradable oluble organic BSR biological ulphate reduction COD chemical oxygen demand E flux of acidogen and endogenou ma wated per day a a fraction of the flux of hydrolyable biodegradable organic utilied per day EDC electron donating capacity f proportion H 2 in phophate (H 2 + H weak acid bae pecie f unbiodegradable fraction of acidogen bioma FBR fluidied bed reactor f c ma carbon to ma (VSS ratio f cv ma COD to ma (VSS ratio ma hydrogen to ma (VSS ratio f h 1 To whom all correpondence hould be addreed ; fax: ; George.Ekama@uct.ac.za Received 10 Augut 2009; accepted 15 February f n ma OrgN to ma VSS ratio f o ma oxygen to ma (VSS ratio f p ma OrgP to ma VSS ratio f PS up unbiodegradable fraction of PSS with repect to total COD (S ti FRBCOD fermentable readily biodegradable (oluble COD FRBO fermentable readily biodegradable (oluble organic FSA free and aline ammonia H 2 * alk Alkalinity with repect to the H 2 reference pecie including the water pecie HAc acetic acid HRT hydraulic retention time ISS inorganic upended olid k molar carbon compoition of acidogen bioma in C k K I ulphide inhibition kinetic contant K M Monod maximum pecific hydrolyi rate for aturation kinetic K MT Monod maximum pecific hydrolyi rate for aturation kinetic at T C K M20 Monod maximum pecific hydrolyi rate for aturation kinetic at 20 C K S Monod half aturation coefficient for hydrolyi for aturation kinetic K ST Monod half aturation coefficient for hydrolyi for aturation kinetic at T C K S20 Monod half aturation coefficient for hydrolyi for aturation kinetic at 20 C l molar hydrogen compoition of acidogen bioma in C k m molar oxygen compoition of acidogen bioma in C k ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April

2 M experimentally meaured M B molar ma of acidogen bioma M S molar ma of biodegradable organic n molar nitrogen compoition of acidogen bioma in C k OLR organic loading rate OP orthophophate P theoretically predicted p molar phophoru compoition of acidogen bioma in C k PBR packed bed reactor pk S1 1 t diociation contant for the ulphide weak acid bae ytem corrected for ionic trength effect PSS primary ewage ludge Q e effluent flow Q i influent flow Q r recycle flow Q w wate flow R1 UASB Reactor 1 R2 UASB Reactor 2 RBCOD readily biodegradable COD (S bi r h volumetric hydrolyi rate gcod/(l.d R h hydraulic retention time R ludge age S bp biodegradable particulate COD concentration S bpi biodegradable particulate COD concentration in influent S bi biodegradable oluble COD concentration in influent S bai VFA (all aumed acetic acid COD concentration in influent S bfi fermentable biodegradable oluble COD concentration in influent SBR equencing batch reactor SLR ludge loading rate SRB ulphate reducing bacteria SRT olid retention time SS teady tate SSD ample tandard deviation S T total ulphide pecie concentration S ti total COD concentration in influent S up unbiodegradable particulate COD concentration S upi unbiodegradable particulate COD concentration in influent S ui unbiodegradable oluble COD concentration in influent S bpi biodegradable particulate COD concentration in influent T temperature in o C TKN total Kjeldahl nitrogen TOC total organic carbon Total alk um of weak acid/bae ubytem alkalinitie TSS total upended olid (VSS+ISS UASB upflow anaerobic ludge bed reactor UCTM1 Univerity of Cape Town Anaerobic Digeter Model No. 1 UCTM1BSR Univerity of Cape Town Anaerobic Digeter Model No. 1 including biological ulphate reduction UPO unbiodegradable particulate organic USCOD unbiodegradable oluble COD USO unbiodegradable oluble organic V d volume of digeter (equivalent to bed volume, V b VFA VSS V up WS WWTP x y Y z Z B Z E γ B γ S θ Introduction volatile fatty acid volatile upended olid hydraulic upflow velocity in UASB reactor wate ludge watewater treatment plant molar carbon compoition of organic in molar hydrogen compoition of organic in pecific yield coefficient of acidogen molar oxygen compoition of organic in acidogen bioma concentration mgcod/l acidogen endogenou ma concentration mgcod/l electron donating capacity of acidogen bioma electron donating capacity of biodegradable organic Arheniu temperature enitivity coefficient for K M Biological ulphate reduction (BSR i an attractive treatment proce in the remediation of ulphaterich water uch a acid mine drainage (AMD. Conventionally, organic ubtrate uch a molae, ethanol, acetate or lactate have been ued a electron donor and organic carbon ource for BSR. However, thee organic are relatively expenive, making AMD remediation via BSR cotly. Since the economic of BSR are governed by the cot of the carbon ource, the BioSURE technology wa developed, in which BSR i achieved uing primary ewage ludge (PSS a carbon ource and electron donor (Roe et al., The core unit proce in the BioSURE ytem i BSR with PSS. To ait in, and optimie, the deign, operation of, and reearch into thi unit proce, mathematical model (both teadytate and dynamic repreent very ueful proce evaluation tool. Mathematical model provide quantitative decription of the treatment ytem of interet that allow prediction of the ytem repone and performance to be made. Baed on the prediction, deign and operation criteria can be identified to optimie the ytem performance. The model prediction can be evaluated and a uch make it poible to tet hypothee of the ytem behaviour, uch a biological procee and their repone to ytem contraint, in a conitent and integrated fahion. In thi paper, a teadytate (SS anaerobic digetion model for BSR uing PSS a energy ource i developed and calibrated. The SS BSR model reult are compared with experimental data from the 2 laboratorycale UASB reactor, R1 at 35 C (when fed and mgso 4 /l and R2 at 20 C (fed mgso 4 /l (Poinapen et al., Importance of teadytate model Steadytate model are comparatively imple kinetic and toichiometric model baed on contant flow and load a input to determine the ytem deign parameter. They are baed on the lowet proce kinetic rate governing the overall behaviour of the ytem and relate thi proce to the ytem deign and operating parameter. Thee deign and operating parameter, uch a reactor volume, recycle ratio and retention time, can be etimated in a relatively imple and quick way with explicit equation from the ytem performance criteria, for intance, effluent quality. Uually, teadytate model contitute the 194 ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April 2010

3 initial tep to etimate the deign and operating parameter of a ytem. Thee parameter then erve a input to the more complex kinetic dynamic imulation model to explore the timevarying behaviour of the ytem and refine the deign and operating parameter. A dynamic model for BSR in a UASB reactor fed PSS i developed in the lat paper of thi 6part erie (Poinapen and Ekama, Characteriation of PSS In conformity with ma balance and continuity principle, the effluent parameter (COD (all contituent, TKN, FSA, VFA, H 2 * alk, Alk H 2 S, H 2 S/HS and ph are defined by the influent PSS and SO 4 contituent tranformed in the ytem. Thu, in the development of the teadytate (SS model for BSR, the PSS i fully characteried baed on the COD (total and unbiodegradable particulate fraction, f PS up, hort chain (volatile fatty acid (VFA COD, TKnd FSA and the PSS CHON compoition of the particulate olid, i.e. x, y, z and a in. Thi approach i imilar to that ued by Sötemann et al. (2005a and characterie the PSS in term of the meaurable parameter ued in calculating the COD, C, H, O, N, S and charge ma balance. Anaerobic digetion teadytate model for methanogenei Sötemann et al. (2005a developed a SS model for anaerobic digetion ( of PSS under methanogenic condition. Thi model conit of 3 equential part, namely: A CODbaed kinetic part in which the influent COD concentration hydrolyed, VFA COD utilied, methane ga COD generated, bioma COD produced and COD concentration of the effluent are determined for a given ludge age A C, H, O, N, charge and COD ma balance baed toichiometry part in which the ga compoition (or partial preure of C, ammonia releaed and alkalinity generated are calculated from the VFA and PSS COD concentration hydrolyed (and utilied and it x, y, z and a compoition in of the biodegradable organic An inorganic carbon ytem weak/acidbae chemitry part in which the ph of the digeter i obtained from the partial preure of C and H (or H 2 * alkalinity generated H 2 S, HS, H, C, NH 4 + and bioma. Thu, the SS BSR model include the ame 3 part a the methanogenei SS model of Sötemann et al. (2005a, namely: CODbaed kinetic of the hydrolyi/acidogenei proce (a for Sötemann et al. (2005a becaue Ritow et al. (2005 found that thi alo applie to BSR C,H,O,N,P,S, charge and COD ma balance baed toichiometric converion of the reactant from the 1 t part and utiliation of VFA to BSR endproduct Effect of the endproduct on the digeter ph by applying mixed weak acid/bae chemitry of the inorganic carbon (C and ulphide ytem. For PSS, the orthophophate and, under normal operating condition, the VFA (acetic acid weak acidbae ytem are low enough to have a negligible effect on digeter ph. Steadytate model for BSR With the modified UASB configuration operated in thi reearch, the ludge recycle line from the top to the bottom of the reactor bed enured that the bioma wa fairly evenly ditributed along the bed axi. Thi bioma recycle line offered 2 advantage it initiated BSR at the bottom of the bed thu maximiing the ytem performance, and it allowed the UASB reactor bed to be modelled a a completely mixed digeter. Thi avoid the neceity of evaluating uncertain and complex granular ludge dynamic, along the reactor bed height in UASB reactor, caued by diperion, edimentation and convection. Hydrolyi of primary ewage ludge Conider a UASB reactor of bed volume V b (l and influent flow rate Q i (l/d. The UASB reactor configuration ha the benefit of uncoupling the olid and liquid (hydraulic retention time compared with a flowthrough digeter. For thi reaon, the fundamental deign parameter, ludge age, (R in day i conidered in thi cae (Fig. 1. Baed on the above, a teadytate model for BSR of ulphaterich water uing a generic biodegradable organic a carbon ource wa developed. Thi SS BSR model will be ueful to: Etimate product generation from influent organic C, H, O, nd P compoition and etablih whether or not a particular organic type i Cdeficient, i.e. generate inufficient inorganic C to upply the alkalinity (H required for the SO 4 reduction Etimate reactor volume and retention time for a required ubtrate COD loading and ulphate removal rate Etimate product concentration (uch a hydrogen ulphide and their enitivity to ytem performance Provide a bai for crochecking BSR kinetic dynamic imulation model reult In the development of the SS model uing PSS a organic, it i aumed that the lowet biological proce, i.e. hydrolyi/acidogenei, generate directly the BSR endproduct, which are Figure 1 Schematic diagram of the UASB reactor ued in thi reearch ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April

4 Total COD, S ti Unbiodegradable COD Unbiodegradable particulate COD, S upi Particulate Biodegradable COD Biodegradable particulate COD, S bpi Unbiodegradable oluble COD, S ui Soluble Biodegradable oluble COD, S bi VFA, S bai Fermentable RBCOD, S bfi Figure 2 Influent primary ewage ludge COD fractionation for the teadytate anaerobic digetion model for biological ulphate reduction Undiociated CH 3 COOH VFA i fractionated uing the influent ph Diociated CH 3 COOH The influent PSS COD i characteried in term of meaurable parameter (Fig. 2. The influent parameter are a follow: Total influent PSS COD, S ti (mgcod/l Total oluble COD (membrane filtered, S bi + S ui (mgcod/l Volatile fatty acid (VFA, S bai (mghac/l, then converted to mgcod/l, with the 5 point titration method of Moobrugger et al. (1992 With a known (or aumed value of the unbiodegradable particulate fraction (f PS up of the influent total PSS COD (S ti, the biodegradable particulate COD (S bpi concentration in the influent i defined. The unbiodegradable oluble COD (S ui concentration form part of the total oluble COD. Since the S ui concentration i very low in relation to the S bi, it can be given an approximate value baed on previou reearch. Uually S ui i about 50 to 75 mgcod/l in PSS. With the above, the influent PSS COD can be fully characteried (Fig. 2. Knowing S ui and S bai, the fermentable readily biodegradable oluble COD (FRBCOD, S bfi concentration can be quantified. The S bfi alo undergoe the ame hydrolyi/acidogenei procee a the S bpi and both are converted to VFA and H 2 which then get utilied in BSR to generate hydrogen ulphide (H 2 S/HS, bicarbonate (H, NH 4 + and bioma. In contrat, the influent VFA (S bai i not included in the hydrolyi proce but it doe generate H 2 S/HS and H with negligible (aumed zero bioma production. So, S bai i included in the toichiometry part of the teadytate model. The zero ludge production for the utiliation of influent VFA i accepted in the SS model becaue the yield of acetoclatic ulphidogen i very low compared with that of the acidogen. Ritow et al. (2005 concluded that the rate of PSS hydrolyi i the ame under both methanogenic and ulphidogenic condition. Since BSR doe not affect the rate of PSS hydrolyi, the ame hydrolyi kinetic (rate formulation and rate contant for methanogenic can be applied to ulphidogenic condition. A outlined by Sötemann et al. (2005a, the acidogen have the highet yield coefficient (Y = gcod bioma/gcod organic hydrolyed and contitute more than 77% of the total bioma formed in the of hydrolyable organic. By increaing the Y value from to 0.113, the bioma formation of the other organim group i taken into account. Thi adjutment in the Y value reulted in imilar percentage COD removal prediction and o wa alo accepted for BSR. The SS model for BSR derived here alo ue the COD to quantify the organic and bioma concentration and the aturation equation for the hydrolyi/acidogenei rate. The teadytate anaerobic digeter equation for the hydrolyi part of the SS BSR model applied to the UASB ytem (Fig. 1 were derived and are lited below. Hydrolyi rate equation aturation (Contoi kinetic: K MT S bp Z B r h [gcod/(l.d] Z B (1 [K (S / Z ] Reidual biodegradable organic concentration in reactor and wate flow: S bp (gcod/ 1 S YK MT1 R b 1 br 1 Y1 f Y K 1 R b bpi ST R Acidogen bioma concentration in reactor and wate flow: Z B Y (gcod/ 1 b ST Unbiodegradable organic concentration in reactor and wate flow, S R S up = S upi R /R h (4 h bpi R R R (1 Y bp h B S bp (1 f (2 (3 196 ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April 2010

5 The acidogen endogenou reidue concentration: Z E where K MT = the aturation maximum pecific hydrolyi rate contant at T C = 5.27 gcod organic/(gcod bioma d at 35 o C K ST = the half aturation coefficient at T C = 7.98 gcod organic/gcod bioma at 35 o C Y = peudo acidogen yield coefficient = gcod bioma/gcod organic hydrolyed S bpi, S bp = (gcod/ f Influent and wate flow (bed COD concentration to and from digeter (gcod/l b = acidogen endogenou repiration rate = (/d R = bed olid retention time or ludge age (d R h = hydraulic retention time in the bed volume (d f = endogenou reidue of acidogen (aumed zero Equation (2 to (4 are the ame a for flowthrough ytem except that the influent particulate COD concentration (S upi and S bpi are multiplied by R /R h to take account of the bed olid retention effect. From the hydrolyi kinetic, the COD concentration of the biodegradable particulate organic utilied in the BSR (S bpi R /R h S bp i known. Following the hydrolyi proce, the toichiometry of BSR need to be etablihed taking into account the utiliation of the influent volatile fatty acid (VFA, undiociated and diociated, and aumed to be all acetate which alo affect alkalinity generation and hence digeter ph. Stoichiometry of BSR b R Z By following the generalied procedure of McCarty (1975, the general toichiometry of BSR with a biodegradable organic compound of compoition and generating ludge ma of compoition C k and C ga (i.e. C ufficiency i given by: B (5 tate (note the unbiodegradable ludge ma i not included becaue it doe not originate from the influent biodegradable organic, i.e. from the CODbaed kinetic model: E = V d (Z B + Z E /[R (Q i S bpi Q w S bp ] = Y (1+f b R /[1+ b R (1 Y {1f }] (8 (ludge COD produced/cod utilied where Z B, Z E = COD concentration of the anaerobic bioma and endogenou reidue repectively (gcod/l. V d = volume of the digeter (l = UASB Sludge bed volume (l Q i = influent flow to digeter (l/d Q w = bed wate flow from the digeter (l/d From γ S and γ B, the COD of the biodegradable organic and ludge ma (accepting the live bioma and endogenou reidue have the ame compoition i 8γ S and 8γ B gcod/mol repectively. Alo, from Ekama (2009, with known value of the COD/VSS (f cv, TOC/VSS (f c, OrgN/VSS (f n and OrgP/ VSS (f p ratio, the elemental compoition of the biodegradable organic (x, y, z, a and b can be calculated from Eq. (9, which alo applie to the bioma (k, l, m, n and p. Accepting y = 7, then: y = 7 (9a z = y/2[(1f cv /88f c /117f n /1426f p /31/ (1+f cv 44f c /12+10f n /1471f p /31] (9b x = f c /12[(y+16z/(1f c f n f p ] (9c a = f n /14[(y+16z/(1f c f n f p ] (9d b = f p /31[(y+16z/(1f c f n f p ] (9e f c = 12x/M S ; f h =1y/M S ; f o =16z/M S ; f n =14a/M S ; f p =31b/M S ; f cv = 8 γ S /M S (9e where f c, f h, f o, f n, f p and f cv are the ma fraction of C, H, O, N, P and COD of the organic repectively (9 (6 where γ S = 4x + y 2z 3a +5b = EDC per mole biodegradable organic (7a γ B = 4k + l 2m 3n+5p = EDC per mole bioma C k (7b EDC = electron donating capacity M S = molar ma of organic 12x+y+16z+14a+31b g/mol (7c M B = molar ma of bioma 12k+l+16m+14n+31p g/mol (7d f = fraction H 2 of the Oecie formed (OP= H 2 + H E = the ma of COD exiting the digeter a active (Z B and endogenou (Z E ludge ma per day a a fraction of the ma of biodegradable organic (COD utilied in the digeter per day at teady Alternatively, if the compoition of the biodegradable influent organic (x, y, z, a, b and bioma (k, l, m, n, p are known, the COD/VSS (f cv, TOC/VSS (f c, OrgN/VSS (f n and OrgP/VSS (f p ratio of the influent organic and bioma can be calculated from Eq. (10. f cv = 8[4x+y2z3a+5b]/[12x+y+16z+14a+31b]; f c = [12x]/[12x+y+16z+14a+31b]; f n = f p = [14a]/[12x+y+16z+14a+31b]; [31b]/[12x+y+16z+14a+31b]; f o = 16/18(11/8f cv 8/12f c 17/14f n 26/31f p ; f h = 2/18(1+f cv 44/12f c +10/14f n 71/31f p ; f cv = 8(4/12f c +1/1f h 2/16f o 3/14f n +5/31f p ; z = y/16 f o /f h (10 The influent VFA i aumed to be acetate. The plit between the undiociated and diociated acetate (HAc and Ac repectively pecie i governed by the influent ph and, ince the ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April

6 influent ph wa alway greater than 5.9, almot all the influent VFA wa in the diociated (Ac form. Equation (6 hold alo for acetate, both aociated (HAc and undiociated (Ac provided the correct compoition x(=2, y(=4 for HAc, =3 Ac, z(=2 and charge (=0 for HAc, =1 for Ac are inerted. Becaue the yield of ulphidogen i very low, E = 0 when applying Eq. (6 to acetate, which yield: CH 3 COOH + SO 4 H 2 S + 2H (no bioma but H alkalinity generation (11a CH 3 COO + SO 4 HS + 2H (no bioma but H and HS alkalinity generation (11b From Eq (11a and (11b it can be een that the influent VFA (both undiociated and diociated concentration i important for etablihing the digeter ph becaue it utiliation make a ignificant contribution to the alkalinity generated. Equation (6 i valid for organic that generate ufficient C for the required alkalinity increae. Thi will be the cae if the C term in Eq. (6 i poitive, i.e. xa +2b(f Eγ S /γ B [kn+p(f] 2(1E γ S /8 > 0 Accepting zero bioma production (E=0 and negligible organic P content (b=0, ubtituting 4x+y2z3a+5b for γ S yield 2z>y+a. So organic with a compoition that conform to 2z>y+a are carbon ufficient. Mot organic do not conform to thi, e.g. the amino acid, alcohol, all of the fatty acid except formic and acetic acid, and PSS. The mono, di and polyaccharide and acetic acid conform exactly, i.e. 2z=y for a=0, but with bioma growth (E>0 they alo become carbon deficient. The COD/C ratio of thee organic i 2.67, o organic with a COD/C ratio>2.67 are C deficient for BSR in the ene that they can donate more electron for BSR than upply C for the alkalinity increae. So for mot organic, the gaeou C term in Eq. (6 i negative. In thi event the ulphide ytem produce the alkalinity hortfall in the form of HS. Rearranging Eq. (6 for C deficiency (HS and zero gaeou C production yield: (12 The PSS (which contained negligible P, f p <0.015 gp/gvss with it determined compoition from thi invetigation (ee below of C 3.35 O 1.45 N 0.45 i C deficient, o Eq. (12 intead of Eq. (6 applie in thi SS BSR model development. Mixed weak acid/bae chemitry Once the BSR product are known from the toichiometry above, the digeter ph i predicted uing the mixed weak acid/bae chemitry. For C deficient ytem and low P content PSS, in effect the H 2 S/HS ytem with a pk S1 value near 7 etablihe the reactor ph becaue a gaeou C phae i abent, namely: [H + ] = K 1 [H 2 S]/[HS ] (13a ph = log(k 1 [H 2 S]/[HS ] = pk 1 + log[hs ] log[h 2 S] (13b where K 1 = firt diociation contant (H 2 S/HS of the ulphide ytem (13c pk 1 = log(k S1 = 7.05 at 25 C (Lide, 2001 pk 1 = pk 1 adjuted for ionic trength (TDS~4000 mg/l and temperature = at 35 C and at 20 C. The validity of Eq. (13b to approximate the reactor ph can be hown from the principle of mixed weak acidbae ytem (Loewenthal et al., 1989; For a mixed weak acid/ bae ytem compriing the inorganic carbon, acetic acid, ammonia, phophate and ulphide ytem in water, the total alkalinity with repect to the mot protonated pecie i defined a: Total alk = Alk H 2 * + Alk HAc + Alk H 2 S + Alk NH Alk H 3 + Alk H 2 O = [H ] +2[ ] +[Ac ] +[HS ] +[NH 3 ] +[H 2 ] +[H ] +[ 3 ] +[OH ] [H + ] (14a In Eq. (14a, the nomenclature of Loewenthal et al.(1989 i adopted, i.e. Alk a a prefix refer to the alkalinity with repect to the named reference pecie without the water (+[OH ] [H + ] term, i.e. the alkalinity of only the named weak acidbae ytem by itelf. Alk a a uffix refer to the alkalinity with repect to the named reference pecie including the water term. For example, H 2 * alk = Alk H 2 * + [OH ] [H + ]. Auming the acetic acid i completely utilied o it concentration i too low to affect ph and noting that in the ph range 6.5 to 8, [ ], [NH 3 ], [ 3 ], [OH ] and [H + ] are negligible compared with [H ], [HS ], [H 2 ] and [H ], the Total alkalinity reduce to: Total alk = [H ] + [HS ] + [H 2 ] + 2[H ] (14b With 6 weak acidbae ytem (inorganic carbon, acetic acid, ammonia, phophate, ulphide and water, 6 parameter need to be known to define all the ytem pecie including the ph. From the toichiometry (Eq. (12, thee 6 known are the [H ], the Total alk (Eq. (14b, the total ulphide and Oecie concentration (S T = [HS ] + [H 2 S], P T =[H 2 ] + [H ], the acetic acid concentration (aumed zero and the ammonia concentration (not required in Eq. (14b completely protonated between ph 6.5 and 8. Accepting that for PSS the organic P content i very low (b 0, o that the alkalinity generated by the phophate ytem i very low in relation to the inorganic carbon alkalinity, the Total alk reduce to: Total alk = [H ] + [HS ] (14c For the ulphide ytem, from equilibrium chemitry it can be hown that: S T = [H 2 S] + [HS ] = [HS ] (1+10 pk 1pH (15 Hence Total alk = [H ] + [HS ] = [H ] + ([H 2 S]+[HS ] /(1+10 pk 1pH from which Eq. (13b can be obtained. For the experimental ytem fed carbon deficient organic, the 6 parameter which are required to be known are the ame 6 parameter a mentioned above, except that the [H ] concentration i exchanged for the ph. The reactor in itu ph, total ulphide (S T, OP (P T and ammonia (N T concentration are direct meaurement; the ulphide i meaured with the 198 ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April 2010

7 COD tet (Poinapen et al., 2009b. The H 2 * Alk and VFA concentration are meaured with the 5point titration method of Moobrugger et al. (1992 uing the 4 direct meaurement a input. Interetingly, the Total alk generated i governed only by the compoition of the biodegradable organic utilied and the type of bioproce, e.g. methanogenei or ulphidogenei. With methanogenei, the Total alk generated i a conequence of the difference between the proton taken up or releaed in the breakdown of the biodegradable organic and the production of bioma. When organic N i preent in the biodegradable organic in ignificant concentration, effectively in the nonionied NH 3 form, the releaed NH 3 take up a proton from the aqueou phae to form NH 4+. The H + i upplied by the diolved C (H 2 * to form H, viz. H 2 *+NH 3 NH H. The Total alk increae becaue the releaed NH 3 i not reference pecie for the ammonia ytem. The C produced by the breakdown of the biodegradable organic that cannot be held in the digeter in thi way ecape a ga with the methane (which i governed by the COD of the biodegradable organic and et the partial preure of the ga phae. Similarly, when diociated acetic acid (Ac i utilied, a H + i taken up, viz. H 2 *+Ac HAc + H. So the N content of the biodegradable organic and the influent acetic acid concentration and ph, fix the Total alkalinity ( [H ] generated in the digeter and partial preure of the ga phae and hence the ph in the digeter. When organic P i preent in the biodegradable organic in ignificant concentration, effectively in the nonionied H 3 form, the releaed H 3 releae proton to the aqueou phae to form H 2 and H. The releaed proton (H + react with H to form diolved C and water, viz. H + H + H 2 * H 2 O + C. Thi decreae the diolved C that can be held in the digeter with the reult that more C ecape a ga. Thi decreae the Alk H 2 * (H and increae the C partial preure of the ga phae, but the Total alk (= [H ] + [H 2 ] + 2[H ] remain contant. The reaon the Total alk remain contant i becaue the phophate pecie releaed by the organic are reference pecie (H 3 for the phophate ytem. Although the Total alk remain contant, the pecie making up the Total alk are not the ame and now include phophate ytem pecie, o the ph in the digeter i now governed by both the inorganic carbon and phophate ytem. The above alo applie to ulphidogenic ytem but, additionally, proton are taken up by the ulphate reduction, i.e. in effect H 2 SO 4 i utilied. Thi increae the Total alkalinity by o much that not even all of the C produced by the breakdown of the biodegradable (carbon deficient organic and held in the aqueou phae, i ufficient to upply it. The alkalinity deficit therefore ha to be upplied by the other weak acid/bae ytem to meet the Total alkalinity required. The phophate ytem in effect make more of the C available to form H and the difference between the Total alkalinity required and the um of the Alk H 2 * (= [H ] and Alk H 3 (=[H 2 ] + 2[H ] produced ha to be upplied by the ulphide ytem a Alk H 2 S (= [HS ] from H 2 S H + + HS. So the Total alkalinity generated i governed only by the compoition of the biodegradable organic utilied and the type of bioproce. Steadytate BSR model validation Figure 3 illutrate the characteriation of the different component of the influent (PSS and bed wate ludge (WS and the determination of their repective elemental compoition from the ma fraction ratio (f cv, f n ; f p wa accepted a zero. The circled note 1 to 4 marked in Fig. 3 are decribed below. Characteriation of primary ewage ludge (PSS (Unbiodegradable particulate COD fraction (Fig. 3; Note 1: In thi tudy, the unbiodegradable particulate fraction ( f PS up of the PSS wa et at Ritow et al. (2005 and Sötemann et al. (2005a conducted tudie on methanogenic and ulphidogenic anaerobic digetion of PSS at different retention time (ludge age between 5 and 60 d and o were able to determine the f PS up value of PSS. They found that the f PS up of different batche of PSS collected from the ame watewater treatment plant (WWTP, Athlone, Cape, Figure 3 Characteriation of primary ewage ludge (influent and wate ludge in the development of the teady tate model (Note 1 to 4 are decribed in the text ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April

8 South Africa varied from 0.34 to The PSS ued in thi tudy wa obtained from the ame WWTP. Becaue running UASB ytem at different ludge age to determine the f PS up wa beyond the cope of thi invetigation, the f PS up value from previou tudie wa accepted. Accordingly, an f PS up value of 0.36 wa ued in the teadytate (SS BSR model developed in thi tudy. Diolved organic compound (USO, FRBO, VFA (Fig. 3; Note 2: The concentration of the unbiodegradable oluble organic (USO of the PSS wa aumed to be 75 mgcod/l, which i very low with repect to the total PSS COD (~ mgcod/l. The volatile fatty acid (VFA (and H 2 * Alk concentration wa meaured uing the 5pH point titration method (Moobrugger et al., 1992 and the unit mghac/l converted to mgcod/l by multiplying by 64/60. The concentration of the total oluble organic compriing the USO, VFA and fermentable readilybiodegradable organic (FRBO wa meaured in the COD tet. Thu, by difference the FRBO concentration wa calculated. The compoition of the USO and FRBO were determined uing f cv ratio of 1.42, 0.487, and 1.42, 0.470, 0.022, repectively, taken from Brink and Ekama (2008, who obtained thee f c from watewater characteriation tet uing an aumed f cv = 1.42 for both the USO and FRBO fraction. The actual VFA compoition (C 2 H 4 for HAc and C 2 H 3 for Ac wa ued. Biodegradable particulate organic (BPO compoition (Fig. 3; Note 3: To determine the compoition of the biodegradable particulate organic of the PSS, 4 meaurement are required, COD, TKN, VSS and total organic carbon (TOC, becaue there are 4 unknown, namely x, y, z and a. The COD, TKN and VSS (and TSS of the PSS particulate organic (compriing both unbiodegradable (UPO and biodegradable (BPO particulate organic were determined with the COD, TKnd VSS/TSS tet, wherea the TOC wa obtained from elemental analyi of dried PSS (TSS. The TOC of the influent PSS wa found to be ~43% of the total upended (dried olid (TSS. From thi, the TOC/VSS ratio (f c of the PSS particulate organic (PO=BPO+UPO wa calculated. With the accepted f PS up = 0.36, the UPO concentration wa calculated and it compoition, i.e. x, y, z and a in, wa determined from f cv value of 1.480, and , repectively, taken from Wentzel et al. (2006, which conform to the compoition of thee organic ued in Activated Sludge Model No.1 (ASM1, Henze et al., A compoition of C N 0.42 wa obtained for UPO. By fractionating the particulate COD concentration of the PSS uing the UPO f cv value of 1.480, and , repectively, the biodegradable particulate organic (BPO of the PSS wa found by ma difference between the PO (UPO + BPO and unbiodegradable (UPO and f cv value of 1.682, 0.524, 0.083, repectively, were obtained for the BPO. Accordingly, from thee value, the compoition of the BPO calculated from Eq. (9 wa found to be C 3.35 O 1.45 N Characteriation of wate ludge (WS WS concentration and compoition (Fig. 3; Note 4 To characterie the wate ludge (WS, the ame principle a above wa applied except that the WS compried: S upi (or UPO with known concentration (Eq. (4 and the ame compoition a the influent UPO; reidual biodegradable organic (BPO or S bp with concentration calculated from the hydrolyi kinetic model (Eq. (2 and with the ame compoition a the influent BPO (S bpi ; and bioma with concentration alo calculated from the hydrolyi kinetic model (Eq. (3 but with an unknown compoition (endogenou reidue concentration wa aumed zero, f = 0. The kinetic model aturation rate value were taken from Sötemann et al. (2005a with K M (the maximum pecific hydrolyi rate contant = 5.27 gcod organic/(gcod bioma.d and K S (the half aturation coefficient = 7.98 gcod organic/gcod bioma, both at T = 35 o C. The FRBO and VFA concentration combined were very low (< 0.8% with repect to that of the total WS and were thu conidered to have all been utilied and therefore zero in the wate ludge. To determine the bioma compoition, 4 meaurement are again required (COD, TKN, VSS and TOC. However, in uing the TOC value determined from elemental analyi of the WS, it wa found that the bioma compoition wa far out of the normal range obtained from previou tudie, in that the oxygen compoition (m in the bioma formulation of C k wa < 1.2. Thi value wa conidered too low and o the reult from the elemental analyi of the wate ludge were not ued to determine the bioma compoition. Intead, the compoition of the bioma wa obtained from the meaured WS COD/VSS and TKN/VSS ratio and an aumed value for m = 2 in the bioma compoition. Thi aumption make a mall difference to the overall WS compoition becaue the bioma i only a mall proportion (<8% of the total. Adding the concentration of all the three above wate ludge contituent (reidual S bp, S upi and bioma give the total particulate COD concentration of the wate ludge (and reactor ludge bed. The calculated wate total particulate COD concentration wa found to be very cloe to the meaured value; thi wa expected becaue the bioma concentration i a very mall part (<10% and indicate the elected hydrolyi kinetic contant and unbiodegradable particulate COD fraction apply to the UASB ytem. Knowing the COD concentration of the S upi and reidual S bp in the WS, their VSS concentration were calculated from their f cv value of 1.48 and 1.682, repectively, (a determined for the influent. The only f cv ratio till miing and required to obtain the overall (combined f cv of the total particulate organic in the WS i that of the bioma. For intance, in the cae of R1 at mgso 4 /l, the meaured wate total particulate COD/VSS (f cv and TKN/VSS (f n ratio were and repectively. To match thee meaured value, the f cv of the bioma wa found by iteration o that the combined f cv equalled to the 1.52 and meaured. Thi yielded a bioma f cv of Now, from thi f cv of 1.599, the k and n value for l=7 and m=2 in the C k bioma compoition were alo determined by iteration and were found to be 5 and 0.55, repectively, giving a bioma compoition of C 5 N 0.55, identical to the C 5 N 1 accepted by Sötemann et al. (2005b in the UCTM1 model, except for the N content. Thi bioma compoition give a TKN/VSS (f n ratio of mgn/ mgvss, compared with mgn/mgvss for C 5 N 1. A different bioma N content i expected becaue Sötemann et al. (2005b aumed the C 5 N 1 compoition from the commonly accepted value for activated ludge. From the reidual S bp, S upi and bioma individual COD concentration in the WS, and their repective f n ratio, the combined f n ratio of the WS wa calculated and found to be mgn/mgvss, very cloe to the meaured value of mgn/mgvss a expected and therefore the C 5 N 0.55 wa accepted here. The ame principle wa applied for UASB R1 fed mgso 4 /l and 200 ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April 2010

9 UASB R2 (20 o C fed mgso 4 /l. It wa found that uing the bioma compoition of C 5 N 0.55 and bioma f cv ratio of 1.599, the calculated wate ludge f cv cloely matched the meaured wate ludge f cv value of both ytem. A tated above, the aturation (Contoi hydrolyi rate equation and it aociated kinetic contant were ued in the hydrolyi kinetic part of the teadytate BSR model (and in the dynamic imulation model, UCTM1BSR, Poinapen and Ekama, At 35 o C, the aturation maximum pecific hydrolyi rate K M = 5.27 gcod organic/(gcod bioma d and the half aturation coefficient K S = 7.98 gcod organic/ gcod bioma. For UASB reactor R2 operated at 20 o C, both K M and K S were adjuted for temperature dependency in the teadytate model application. The temperature function K 2 T 2 T wa ued where K 1 and K 2 are here the maximum 1 θ K 1 pecific hydrolyi rate contant at T 1 = 35 C and T 2 = 20 C, repectively, and θ = K M20 wa found to be gcod organic/(gcod bioma d and K S = gcod organic/gcod bioma. SS BSR model application Once developed and calibrated, the SS BSR model wa validated by applying it to the UASB ytem operated in thi tudy. Table 1 compare the SS BSR predicted reult with the experimental data from the 2 laboratorycale UASB reactor. Overall the SS model prediction correpond well with the meaured data for all 3 ytem. The COD removal i lower for the meaured data becaue the UASB effluent contain ome particulate COD (ince the effluent i not 100% oluble COD while in the teadytate model thi i aumed to be zero. The predicted digeter ph value for R1 (1 800 mgso 4 /l and R2 correpond very well to the meaured value, while for R1 (at mgso 4 /l it i 0.1 ph unit lower. Though not ignificant, thi ph difference may be acribed to either minor experimental error in ph meaurement or to the compoition of the primary ludge. The compoition of the influent biodegradable particulate organic (BPO i calculated from the influent PSS characteriation uing the toichiometric equation and i found to be C 3.35 O 1.45 N 0.45 which differ lightly from that found by Sötemann et al. (2005a for the primary and humu ludge mixture of Izzett and Ekama (1992, i.e. C 3.5 N and their own tet on pure PSS, i.e. C 3.65 O 1.97 N In fact, with Cdeficient ubtrate for BSR, a PSS i, it i poible to calculate the C releaed from the utilied biodegradable organic from the C content of the H concentration, which i known from the H 2 * alkalinity, becaue no C ga i generated by the ytem (Eq. (12 and the C in the bioma generated i mall. For R1 (1 500 mgso 4 /l, R1 (1 800 mgso 4 /l and R2, the C releaed in the utiliation Table 1 Comparion of experimentally meaured (M value with SS BSR model prediction (P Parameter R1 (35 o C R1 (35 o C R2 (20 o C 4 (1 500 mgso 4 /l (1 800 mgso 4 /l (1 500 mgso 4 /l Influent total COD (mgcod/l Influent unbiodegradable particulate COD 1 (f PS up = 0.36 (mgcod/l Influent VFA (mgcod/l Influent fermentable readily biodegradable COD (mgcod/l Influent lowly biodegradable COD (mgcod/l Influent unbiodegradable oluble (mgcod/l Influent TKN/FSA (mgn/l 82/6 109/10 113/11 Reactor bed/liquid volume ratio 6.7/ / /7.8 Influent flow rate, Q i (l/d Sludge age, R (d, HRT (d 18, , , 0.85 E (ludge COD produced/cod utilied M P M P M P COD removal (mgcod/l Sulphate removal (mg SO 4 /l Effluent alkalinity (H 2 * alk + Alk H 2 S (mg/l a Ca Effluent H 2 * alk (mg/l a Ca Effluent H 2 S (mgs/l Effluent HS (mgs/l Effluent TKN (mgn/l FSA Ma balance (% COD S N C Effluent p : f cv, f n of unbiodegradable particulate organic (UPO in the influent PSS and wate ludge = 1.480, 0.515, , repectively. 2: Effluent H 2 S/HS determined via filtered COD tet before and after ZnS precipitation. 3. Lo of H 2 S in analytical procedure particularly during vacuum filtration. Speciation of HS /H 2 S i baed on p.6 and total ulphide 310 mgs/l after vacuum filtration. Procedure wa corrected by vacuum filtering at ph 10 which fixed the Sbalance to approximately 100%. 4. K M and K S were adjuted for temperature. K M20 =0.808 and K S20 =1.223 with Ө= ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April

10 of BPO, VFA and FRBO wa 283, 349 and 300 mgc/l, repectively, and the C in the H 2 Alk meaured wa 279, 326 and 275 mgc/l repectively. Thi validate the C content of the biodegradable organic and etablihed the C balance over the 3 ytem, i.e. 98.5%, 94.0% and 91.6%. In addition, the good correlation between the meaured and teadytate reult ugget that the aumption of a completely mixed digeter for the UASB reactor bed i valid and reaonable. Thi wa made poible becaue of the introduction of the ludge recycle line from the top to the bottom of the reactor. Concluion A teadytate model for BSR uing PSS a carbon ource and electron donor ha been developed. The model comprie 3 equential part: a CODbaed hydrolyi kinetic part, a C,H,O,N,P,S, COD and charge ma balanced toichiometry part and a mixed weak acid/bae chemitry part. The hydrolyi kinetic of PSS were taken from Ritow et al. (2005 and Sötemann et al. (2005a ince they concluded that thi i the ame for both ulphidogenic and methanogenic ytem. From the toichiometry, it wa found that the PSS i carbon limited in that it doe not generate ufficient H alkalinity for the ulphate reduction, i.e. it COD/C ratio i too high (>2.67, which account for the oberved zero ga (C generation. A a reult, the H 2 S/HS ytem provide the alkalinity hortfall, etablihe the ytem ph and allow the C releaed in the utiliation of the biodegradable organic to be accounted for in the C of the H 2 * alkalinity (H generated. Once developed and calibrated, the model reult were compared with experimental data from 2 laboratorycale UASB reactor (operated at 35 C and 20 C, repectively fed PSS and ulphate. The modelpredicted reult, including ph, correlate very well with the experimental reult. Thi provide upport for: The PSS hydrolyi rate determined by Ritow et al. (2005 and Sötemann et al. (2005a The developed BSR toichiometry which give coniderable inight into the interrelationhip between the biological procee and weak acid/bae chemitry ytem The method of characteriing the organic via the f cv, f n and f p ratio for ulphidogenic and methanogenic ytem. The SS BSR model alo provide a bai for crochecking the reult of an integrated phae (aqueouga mixed weak acid/bae chemitry and biological procee imulation model for BSR which i preented in the lat paper of thi erie (Poinapen and Ekama, Acknowledgement Thi reearch wa upported financially by the Water Reearch Commiion, National Reearch Foundation and Univerity of Cape Town and i publihed with their permiion. Reference BRINK IC and EKAMA GA (2008 Meaurement of compoition of organic contituent of municipal watewater for plant wide modelling. Reearch Report No. W131, Department of Civil Engineering, Univerity of Cape Town. EKAMA GA (2009 Uing bioproce toichiometry to build a plant wide ma balanced baed teady tate WWTP model. 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Water Tech. 7 ( MOOSBRUGGER RE, WENTZEL MC, EKAMA GA and MARAIS GvR (1992 Simple Titration Procedure to Determine H 2 * Alkalinity and Short Chain Fatty Acid Concentration in Aqueou Solution Containing Known Concentration of Ammonium, Phophate and Sulphide Weak Acid/Bae. WRC Report No. TT 57/92. Water Reearch Commiion, Pretoria, South Africa. POINAPEN J, EKAMA GA and WENTZEL MC (2009 Biological ulphate reduction with primary ewage ludge in an upflow anaerobic ludge bed reactor Part 3: Performance at 20 o C and 35 o C. Water SA 35 ( POINAPEN J and EKAMA GA (2010 Biological ulphate reduction with primary ewage ludge in an upflow anaerobic ludge bed reactor Part 6: Dynamic Model. Water SA 36 ( RISTOW NE, SÖTEMANN SW, LOEWENTHAL RE, WENTZEL MC and EKAMA GA (2005 Hydrolyi of Primary Sewage Sludge under Methanogenic, Acidogenic and Sulphate Reducing Condition. WRC Report No. 1216/1/05. Water Reearch Commiion, Pretoria, South Africa. ROSE PD, CORBETT CJ, WHITTINGTONJONES K and HART OO (2002 The Rhode BioSURE Proce Part 1: Biodealination of Mine Drainage Watewater, WRC Report No. TT 195/02. Water Reearch Commiion, Pretoria, South Africa.. SÖTEMANN SW, RISTOW NE, WENTZEL MC and EKAMA GA (2005a A teady tate model for anaerobic digetion of ewage ludge. Water SA 31 ( SÖTEMANN SW, VAN RENSBURG P, RISTOW NE, WENTZEL MC, LOEWENTHAL RE and EKAMA GA (2005b Integrated chemical, phyical and biological procee modelling Part 2: anaerobic digetion of ewage ludge. Water SA 31 ( WENTZEL MC, EKAMA GA and SÖTEMANN SW (2006 Ma balancebaed plantwide watewater treatment plant model Part 1: Biodegradability of watewater organic under anaerobic condition. Water SA 32 ( ISSN (Print = Water SA Vol. 36 No. 3 April 2010 ISSN (Online = Water SA Vol. 36 No. 3 April 2010