Hydrothermal Oxidation of Fecal Sludge: Experimental Investigations and Kinetic Modeling

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1 This is a ope access article published uder a Creative Commos Attributio (CC-BY) Licese, which permits urestricted use, distributio ad reproductio i ay medium, provided the author ad source are cited. pubs.acs.org/iecr Hydrothermal Oxidatio of Fecal Sludge: Experimetal Ivestigatios ad Kietic Modelig Tobias Hu ber,, Markus Roth, ad Fre deŕic Vogel*,, Fachhochschule Nordwestschweiz, Hochschule fu r Techik, Klosterzelgstrasse, 50 Widisch, Switzerlad Paul Scherrer Istitut, 53 Villige, Switzerlad ABSTRACT: Hydrothermal oxidatio (HTO) provides a efficiet techique to completely destroy wet orgaic wastes. I this study, HTO was applied to treat fecal sludge at well-defied experimetal coditios. Four differet kietic models were adjusted to the obtaied data. Amog others, a distributed activatio eergy model (DAEM) was applied. A total of 33 experimets were carried out i a ustirred batch reactor with pressurized air as the oxidat at temperatures of <470 C, oxyge-to-fuel equivalece ratios betwee 0 ad.9, feed cocetratios betwee 3.9 ad 9.8 mol TOC L (TOC = total orgaic carbo), ad reactio times betwee 86 ad 57 s. Decompositio of the fecal sludge was moitored by meas of the coversio of TOC to CO ad CO. I the presece of oxyge, igitio of the reactio was observed aroud 300 C, followed by further rapid decompositio of the orgaic material. The TOC was completely decomposed to CO withi 5 mi at 470 C ad a oxyge-to-fuel equivalece ratio of.. CO was formed as a itermediate product, ad o other combustible products were foud i the gas. At certai reactio coditios, the formatio of uwated coke ad tarlike products occurred. The reactio temperature ad oxyge-to-fuel equivalece ratio showed a sigificat ifluece o TOC coversio, while the iitial TOC cocetratio did ot. Coversio of TOC to CO could be well described with a first-order rate law ad a activatio eergy of 39 kj mol.. INTRODUCTION AccordigtoaestimateoftheWorldHealthOrgaizatio (WHO) for 05, approximately.4 billio people worldwide have o access to hygieically safe saitatio facilities. The lack of a safe saitatio ifrastructure is especially ecoutered i rural areas of low-icome coutries ad i iformal urba settlemets (slums). Problems that arise from the lack of saitatio are, for example, cotamiatio of drikig water, the promotio of diseases, ad high ifat mortalities. Decetral collectio ad treatmet of the fecal matter could provide a solutio for this problem. Because a supply of electric eergy might be scarce i the target regios, treatmet techologies that work off the grid are ecessary. Hydrothermal oxidatio (HTO) could provide a techology that allows safe i situ saitatio of fecal matter ad does ot require a exteral ifrastructure. HTO is a process by which orgaic material is subjected to temperatures betwee ca. 300 ad 700 C ad pressures betwee ca. 4 ad 44 MPa i the presece of a oxidat ad water. The material is rapidly decomposed to carbo dioxide (CO ), ammoia (NH 3 ), water (H O) ad its mieral compoets.,3 Pure gaseous oxyge (O ), air, ad hydroge peroxide (H O ) have bee mostly used as oxidats. 3 The term supercritical water oxidatio is used for HTO processes performed at thermodyamic coditios above the critical poit of water (374 C,. MPa).,4 The term wet air oxidatio is commoly used for processes performed i liquid water at lower temperatures ad pressures. 5 7 Fecal matter is a semisolid waste product of huma digestio cosistig of H O (63 86%), orgaic compouds (84 93% of total solids), ad iorgaic salts (7 6% of total solids). The orgaic fractio (volatile solids, VS) of fecal sludge cotais bacteria (5 54% of VS), carbohydrates (5 5% of VS), proteis ad itroge-cotaiig compouds ( 5% of VS), lipids (9 6% of VS) ad fiber (<5% of VS). 8,9 Durig HTO, biomass polymers, such as polysaccharides, proteis, ad fats, are hydrolyzed ito their oligomers ad moomers 0, which are subsequetly oxidized. 4 Price 5 ivestigated HTO of a mixture of fecal sludge ad urie i a cotiuous reactor system. O was used as the oxidat. Coversios of total orgaic carbo (TOC) raged from % at 4 mi of residece time ad C to87 93% at 3 5 mi of residece time ad C. Takahashi ad co-workers 6,7 ivestigated HTO of fecal matter usig a stirred cylidrical batch reactor. After h, total coversio of the chemical oxyge demad (COD) was achieved at supercritical coditios ( C), while 30%, 75%, ad 90% coversio were Received: August 5, 06 Revised: October 7, 06 Accepted: October 7, 06 Published: October 7, America Chemical Society 90

2 achieved at 50, 300, ad 350 C, respectively. Uder subcritical coditios, total removal of COD was oly possible whe a catalyst was applied (gold, palladium, platium, rhodium, or rutheium). The work of Jagow 8 cofirms these fidigs. He compared HTO of fecal waste i a cotiuously stirred tak reactor ad a packed-bed reactor at temperatures betwee 30 ad 340 C usig air as the oxidat. He showed that the TOC coversio could be raised from 70 90% to >98% by the applicatio of a catalyst at subcritical coditios. Takahashi et al. 6 also showed that amie-derived itroge cotaied i fecal matter is coverted maily to NH 3 at temperatures of <550 C. At temperatures of >600 C, the mai part of itroge is coverted to diitroge (N ) ad itrous oxide. Miller et al. 9 ivestigated supercritical water oxidatio of a model fecal sludge i a cotiuous reactor system. They examied differet process parameters such as the reactor ilet temperature ( C), solids cocetratio of the feed (5 8% by weight), reactor pressure, ad oxyge-to-fuel equivalece ratio (.3.5). They foud that the latter had the greatest ifluece o their process. I this study, the treatmet of fecal sludge by HTO was ivestigated at well-defied experimetal coditios. The aim was to obtai a kietic model that is able to accurately predict fecal sludge decompositio over the tested rage of experimetal coditios for the developmet of a prototype applicatio. Coversio of TOC to its gaseous oxidatio products CO ad carbo mooxide (CO) was measured uder varyig reactio coditios: reactio temperature, reactio time, oxygeto-fuel equivalece ratio, ad feces dilutio (or feed cocetratio). The data were used to adjust the kietic parameters for four differet reactio models. The obtaied best-fit parameters of those models were compared to each other ad to literature values of similar materials.. MATERIALS AND METHODS.. Compositio of the Fecal Sludge. The fecal sludge used i this study was obtaied from the Swiss Federal Istitute of Aquatic Sciece ad Techology, EAWAG, Du bedorf, Switzerlad, collected from a diversio toilet. Urie ad other material (e.g., toilet paper) were ot mixed with the sludge. After a 3-moth collectio period, the material was homogeized usig a kitche mixer ad deep-froze i freezer bags i portios of 50 g. Three radom samples were take from the thawed material ad aalyzed (Table ). Parts of the samples were dried to costat weight usig a LP6 thermogravimetric moisture aalyzer (Mettler Toledo, Greifesee, Switzerlad). The ash cotet was determied accordig to Sluiter et al. (008) by icieratig dried samples i a muffle furace at a maximum temperature of 575 C for 3 h 0 (two repetitios per sample). The higher heatig value (HHV) of the dried samples was determied usig a IKA C bomb calorimeter (Cole-Parmer, USA; three repetitios per sample). The carbo, hydroge, ad sulfur cotets of the wet fecal sludge were determied usig a Vario ElCube elemetal aalyzer (Elemetar, Germay; five repetitios per sample). The carbo, hydroge, ad itroge cotets of the dried material were measured by a TrueSpec Micro elemetal aalyzer. The oxyge cotet was measured by a RO-487 aalyzer ad the sulfur cotet by a CHNS-93 aalyzer (Leco, USA; two repetitios per sample). Most of the obtaied results are i good agreemet with the literature data of feces compositio. 8,9 The measured HHV is higher tha the average feces HHV reported i the literature (7. MJ kg ). 9 Feces used i this study origiate most likely Table. Chemical Compositio of the Fecal Sludge Used i This Study a dried at 05 C (total as received solids) water cotet % by weight 74.4 ± 0.8 total solids % by weight 5.6 ± ash % by weight 3.8 d 4.8 ± 0.3 HHV MJ kg 5.8 ± 0.0 b,d.7 ± 0.3 LHV MJ kg 3.6 b,c,d. b,c TOC % by weight.8 d,e 46. ± 0.8 C % by weight 3.0 ± ± 0.7 H % by weight 7. ± 0. N % by weight.38 ± ± 0. O % by weight 7.8 ± 0.5 S % by weight 0.7 ± ± 0.04 ξ mol O kg. ± 0.4 f,d 47. ± 0.7 f a Ucertaity expressed as stadard deviatios from repetitios. Calculatio basis: b HHV of the dried material. c Hydroge cotet of the dried material. d Water cotet of the wet material. e TOC cotet of the dried material. f Equatio. from a protei-rich utritio that especially affects their HHV ad itroge cotets. We ote that the compositio of feces ecoutered i developig coutries might be substatially differet, presumably exhibitig lower HHVs... Batch Reactor Setup ad Experimetal Procedure. For the experimets, a ustirred cylidrical batch reactor (legth, 5.5 mm; ier diameter, 3.5 mm; volume, 4.7 ml) made of 36 L stailess steel (HIP, USA) was used (Figure, left). The reactor was heated by immersio ito a preheated fluidized sad bath (Teche SBL-D). The sad was fluidized usig pressurized air to achieve rapid heatig of the reactor. A stailess steel capillary was attached to the reactor coectig a pressure sesor, a relief valve, ad a valve for chargig the reactor with pressurized sythetic air. The reactio temperature was measured by a thermocouple situated 4 mm above the reactor bottom (i.e., i the liquid or supercritical reactio phase), except for experimets labeled Miemp, i which the reactio temperature was measured i the middle of the reactor (i.e., i the gas phase or supercritical reactio phase). The upper measurig ad chargig sectio of the reactor remaied uheated throughout the experimet. The resultig uheated dead volume was 6.6 ml (ca. % of the total reactor volume). The ifluece of this dead volume o the reactio was assumed to be small because oxyge that stayed iside this regio was cosidered ot to be accessible for the reactio. This assumptio was verified by a test experimet i which a substoichiometric amout of oxyge was supplied (λ < ). After a reactio time sufficiet for complete oxidatio (30 mi, 470 C; i.e., all oxyge should have bee cosumed by the reactio), the product gas cotaied approximately the same amout of oxyge that was calculated to fit ito the dead volume, whereas the fecal sludge sample was ot fully oxidized. We presume that a liquid water droplet codeses iside the steel capillary durig reactor heatup, blockig mass trasport betwee the hot reactio chamber ad the dead volume. For each experimet, a defied amout (0.8.4 g) of wet fecal sludge was weighed ito the reactor. For dilutio of the iitial TOC cotet, additioal distilled water was added to the reactor. The reactor was charged with pressurized sythetic air (9.5 ± 0.08 mol % O i N ). The oxyge-to-fuel equivalece ratio (eq 3) was set by adjustig the ratio of supplied air pressure to the amout of dry fecal mass i the reactor. The reactor was 9

3 Figure. Experimetal setup used (left), adapted from Zoḧrer, ad exemplary temperature ad pressure evolutio (right). heated util the desired retetio time was reached. To stop the reactio, the reactor was queched i a water bath. A typical evolutio of the pressure ad temperature is show i Figure (right). The heat-up times, defied to reach 95% of the fial temperature, were i the rage of 6 8 mi. The decompositio of the sludge durig the heat-up time was accouted for i the kietic modelig (eq ). As reactio products, a suspesio of liquid ad solid particles ad a gas phase were obtaied. The gas was collected i a gas samplig bag. These bags were purged with N ad, subsequetly, evacuated. This procedure was repeated three times before reuse of each bag. The compositio of the product gas (CO, CO, CH 4,O,N, ad H ) was aalyzed usig a HP 6890 gas chromatograph ad a thermal coductivity detector (both Agilet, USA). Helium was used as the carrier gas. For the separatio of CO, a HP PLOT Q colum (30 m 0.53 mm; 0.40 μm film thickess) made of diviylbezee styree porous polymer was used. For the separatio of all other gases, a AT-Molecular Sieve colum (30 m 0.53 mm) was used. The total product gas volume was determied usig a 000 ml gastight syrige (Hamilto, USA). The liquid reactio product of each experimet was draied from the reactor, weighed, ad filtered through a syrige filter (0.45 μm pore size). The filtrate was diluted by a factor of 0 or 50. The dissolved orgaic carbo (DOC) ad dissolved iorgaic carbo (DIC) of the diluted filtrate were determied usig a Dimatoc 000 TOC aalyzer (DIMATEC, Germay). After the reactor was emptied, it was flushed with ca. 5 ml of methaol to remove residual water adherig to the reactor walls. The water cotet of this methaol phase was aalyzed by Karl Fischer titratio (37 KF coulometer by Metrohm, Switzerlad). Usig this method, the water mass balace was closed to approximately 80 90%..3. Experimetal Desig. The reproducibility of the experimets was tested at oe set of fixed experimetal coditios. The experimet was repeated three times at the stadard coditios: 5 mi (300 s) of reactio time, 470 C sad-bath temperature, a oxyge-to-fuel equivalece ratio of., ad 0.0 MPa iitial air pressure usig udiluted fecal sludge (c TOC,0 = 9.8 mol TOC L ). For the kietic experimets, the reactio times were varied betwee.5 ad 6 mi (86 57 s) at two differet sad-bath temperatures (360 ad 470 C), keepig the other stadard coditios costat. The reactio times were chose to yield reasoably distributed coversios over the rage of 0 99%. The TOC cocetratio of the feed ( mol TOC L ) ad the oxyge-to-fuel equivalece ratio (0.9) were varied ad the other parameters fixed to stadard reactio coditios..4. Oxyge-to-Fuel Equivalece Ratio. The overall equatio for the total oxidatio of orgaic matter, assumig itroge-bearig orgaic compouds to be coverted to NH 3,is β δ γ + α + 3 CHON α β γ δ 4 O β 3δ αco + HO+ δnh 3 Accordigly, the stoichiometric amout of oxyge eeded for complete oxidatio, ξ (mol O kg total solids ) is give by wc wh 3 wn ξ = + M 4 M 4 M C H N () w O MO 00% () where w C, w H, w N, ad w O (% by weight) are the mass fractios of biomass-boud carbo, hydroge, itroge, ad oxyge of the dried material (total solids), respectively. Their values were take from Table. M C, M H, M N, ad M O (kg mol ) are their respective molar masses. Durig HTO at temperatures of <550 C, biomass-boud itroge is trasformed to NH 3. 6, Because the maximum reactio temperatures i this study reached 480 C, we assume NH 3 to be the oxidatio ed product. If N is assumed as the oxidatio ed product, as is the case for reactio temperatures above 550 C, the stoichiometric amout of oxyge eeded for complete oxidatio is slightly higher tha the ξ value calculated by eq (ca. 5% higher for the itroge cotet of the fecal sludge used i this study). The ξ value, as defied by eq, is equal to the COD because, i the determiatio of the COD, NH 3 is also assumed as the fial product of itroge-bearig orgaic compouds. The oxyge-to-fuel equivalece ratio λ is calculated by O,0 λ = = ξm O,stoichiometric O,0 TS where m TS (kg) is the mass of total solids weighed ito the reactor ad O,0 (mol) is the amout of oxyge available for the reactio. O,0 was calculated from the iitial sythetic air pressure, the oxyge cotet of the sythetic air, ad the reactor volume available for the gas usig the va der Waals equatio of (3) 9

4 state for real gases: p 0 O,0 R T amb = * a O y V,0 b* y V O,0 r,eff y O,0 O,0 O,0 r,eff where p 0 (Pa) is the pressure i the reactor after sythetic air fillig at ambiet temperature T amb (K), R (J mol K ) is the uiversal gas costat, y O,0 is the oxyge molar fractio of the used sythetic air, ad the va der Waals coefficiets for air 3 are a* = Pa m 6 mol ad b* = m 3 mol. V r,eff (m 3 ) is the effective reactor volume cotaiig accessible air for the reactio: Vr,eff = Vr,total Vr,dead Vsample (5) where V r,total (m 3 ) is the total reactor volume, V r,dead (m 3 ) is the reactor dead volume, ad V sample (m 3 ) is the sample volume..5. TOC to CO ad CO Coversio. TOC is commoly used as a idicator for the reactio of orgaic compouds i the HTO process. I fecal sludge, orgaic carbo maily appears as solid orgaic carbo (SOC) ad DOC. SOC (e.g., cellulose, proteis) is first hydrolyzed ito DOC, 0, which is subsequetly oxidized to CO.,3 I our work, CO was detected as the itermediate product of DOC oxidatio: The evolutio of the gaseous reactio products of TOC oxidatio, i.e., CO ad CO, was used as a idicator for TOC coversio. The coversio of TOC was calculated as CO + CO XTOC = (7) where CO (mol) ad CO (mol) are moles of CO ad CO measured i the product phases, respectively. TOC,0 (mol) is the amout of orgaic carbo cotaied i the reactat, calculated by wtoc mts = 00% MC (8) where w TOC (% by weight) is the mass fractio of TOC i the total solids of the fecal sludge, m TS (kg) is the mass of total solids that was weighed ito the reactor prior to the experimet, ad M C (kg mol ) is the molar mass of carbo. The molar amout of carbo cotaied i the product gas i the form of CO ad CO was calculated by CO = + CO,gas CO,dissolved p V β ρ m amb gas DIC liq,prod liq,prod = y + CO RT M (9) amb = = y CO CO,gas CO C (4) p V amb gas RTamb (0) CO,gas (mol) ad CO,gas (mol) are the amouts of CO ad CO cotaied i the product gas, respectively, CO,dissolved (mol) is the amout of CO dissolved i the reactio liquid. The amout of CO dissolved i the liquid phase was eglected because of its much lower solubility compared to CO. y CO (mol CO mol gas ) ad y CO (mol CO mol gas ) are the molar fractios of CO ad CO cotaied i the product gas measured by gas chromatography, respectively. T amb (K) ad p amb (Pa) are the ambiet temperature ad pressure at the momet of the volume measuremet of the gas. T amb was assumed to be 93.5 K, ad p amb was assumed to be 0.03 MPa. V gas (m 3 ) is the total volume of the product gas. β DIC (kg m 3 ) represets the mass cocetratio of DIC measured i the product liquid, m liq,prod (kg) is the mass of the recovered liquid product phase (draied liquid + water detected i the methaol flushig phase), ρ liq,prod (kg m 3 ) is the liquid product desity (estimated as 0 3 kg m 3 ), ad M C (kg mol )is the molar mass of carbo. All DIC cotaied i the liquid product was assumed to be dissolved CO ad/or carboates origiatig from the orgaic fractio of the feces. This assumptio is supported by the fact that DIC was oly detected i the liquid product whe the CO cocetratio of the product gas was 4.5 mol %. Ay dissolved CO ad carboates already preset i the feces would add to the value of CO. Because the amout of iorgaic carbo i the feces is small (approx. 5 % of total C; compare Table ), this cotributio was eglected..6. Approximatio of the Reactio Temperature Curves. The mai part of the TOC was already decomposed to CO ad CO before the reactio temperature had reached steady state (i.e., T r = T sad ). The evolutio of the reactio temperature T r (K) with time t (s) of each experimet was approximated by bheatigt Tsteady + aheatige ; 0 < t t Tr() t = Tsteady + ccoolig( t t ); t < t < ted () where t (s) is the retetio time of the reactor i the sad bath, t ed (s) is the time whe the reactio was assumed to have completely stopped (T r 300 C after the reactio). t ed defies the overall reactio time (t r = t ed ). T steady (K), a heatig (K), b heatig (s ), ad c coolig (K s ) are costats that were determied by regressio of the temperature evolutio curves. All parameters were determied idividually for each experimet. 3. KINETIC MODELING APPROACHES FOR HYDROTHERMAL FECAL SLUDGE OXIDATION The experimetal data were used to parametrize the four differet kietic reactio models summarized i Table. Model I (eqs 5 ad 6) assumes that all TOC is directly decomposed to CO oly. Coversio of TOC to CO was ot icluded i this model. The ouiformity of the TOC decompositio rate (because of the idividual reactio rates of differet biomass compouds) was take ito accout by applyig a DAEM. A detailed descriptio of the DAEM (distributed activatio eergies model) applied to HTO reactios ca be foud i the work of Vogel et al. 4 The fecal sludge TOC was assumed to cosist of j idividual compouds that react i j parallel first-order reactios with rate costats k i to CO. The reactio order of oxyge was assumed to be zero. The Arrheius expressio was used for the calculatio of the reactio rate costats: ( k) = ( k ) e im, 0 im, ( E) im, / RT () with k 0 (s ) beig the preexpoetial factor, E (J mol ) the activatio eergy, R (J mol K ) the uiversal gas costat, ad T (K) the reactio temperature (eq ). i ad m are idices for the reactio ad model, respectively. 93

5 Table. Summary of the Kietic Models Used for Data Fittig model reactios cosidered rate law expressio eq adjustable parameters I j I I TOC + O CO II III IV The iitial molar amouts of each TOC compoet at t =0 [that were used to solve the ordiary differetial equatios (ODEs) (5) ad (6)] are give by = f ( E)dE i,0 TOC,0 0 (3) where i,0 (mol) is the molar amout of a sigle carbocotaiig reactat i i the raw material, TOC,0 (mol) is the molar amout of TOC i the raw material, f 0 (E) is the approximated probability desity fuctio (PDF), ad de is the ormalizig variable (equal to the class wih of the distributio). The distributio of activatio eergies of the fecal sludge TOC was approximated by a Gaussia PDF: f ( E) = j ( k,..., k ),, TOC =,I +,I + + j,i j = k,ii k,ii k3,ii TOC + O CO, TOC + O CO, CO + O CO β k,iii kco, III TOC + + O βco + ( β)co, O + O CO β ( k, IV,..., kj, IV) kco, IV TOC + + O βco + ( β)co, CO + O CO πσ ( σ e E E ) / 0 0 (4) E (J mol ) is the activatio eergy of a idividual compoud i, E 0 (J mol ) is the mea activatio eergy of the distributio, ad σ (J mol ) is the variace of the distributio. Model II (eqs 7 9) assumes that the fecal sludge TOC is decomposed to CO aocoproceedigastwoparallel first-order reactios with idividual rate costats k,ii ad k,ii, respectively. CO is oxidized to CO i a cosecutive first-order reactio (k 3,II ). The rate costats were calculated as show i eq. Theifluece of the oxyge-to-fuel equivalece ratio was eglected i all equatios. Two differet cases were tested: (a) All six adjustable kietic parameters (k 0,,II, k 0,,II, k 0,3,II, E,II, E,II, ad E 3,II ) were varied durig the parameter optimizatio. (b) Kietic parameters for the oxidatio of CO to CO (k 0,3,II ad E 3,II ) were fixed at values published by Hellig ad Tester, 5 CO TOC CO CO TOC CO CO TOC CO CO ( k k... k ) [ ki,ii] 5 k 0,I, E 0,I, σ I j = [ k ] i,i i = k k,ii TOC,II TOC 7 = k k,ii TOC 3,II CO 8 = k + k = k,ii TOC who measured the first-order rate costats for CO oxidatio i supercritical water. Oly four parameters were varied (k 0,,II, k 0,,II, E,II, ad E,II ). Model III (eqs 0 ) assumes that the fecal sludge TOC decomposes i a simple first-order reactio (rate costat k,iii )itoafractioβof CO ad a fractio β of CO. β is assumed to be idepedet of the reactio coditios (i.e., temperature, oxyge-to-fuel equivalece ratio. etc.). CO is coverted to CO i a cosecutive first-order reactio (k CO,III ). The rate costats were calculated as show i eq. The ifluece of the oxyge-to-fuel equivalece ratio was eglected i all equatios. Model IV (eqs 3 5) assumes that the fecal sludge TOC is decomposed i j parallel first-order reactios (accordig to the DAEM) ito a fractio β of CO ad a fractio β of CO (similar to model III). CO is coverted to CO i a cosecutive first-order reactio (k CO,IV ). The rate costats for TOC decompositio (k,iv, k,iv,...,k j,iv )werecalculated by eq. The iitial molar amouts of each TOC compoud were calculated by eq 3 assumig a Gaussia distributio of activatio eergies of the fecal sludge TOC (eq 4). Because of computatio performace limits, the total umber of TOC compouds was limited to 40 (j = 40). The iterval wih de was set equal to σ/5, ad the upper ad lower boudaries of the PDF of the activatio eergies were set to E 0 +4σad E 0 4σ, respectively. The ifluece of the oxyge-to-fuel equivalece ratio was eglected. Each of the preseted models was best fitted to the experimetally obtaied fractios of TOC coverted to CO CO ad CO ( CO ) by oliear least-squares regressio. ( ) TOC,0 3,II CO,III TOC 0 = ( β) k k 6 9,III TOC CO,III CO = βk + k,iii TOC j = [ k ] CO,III CO i,iv i 3 j = ( β) [ k ] k 94 j = β [ k ] + k i,iv i i,iv i CO,IV CO 4 CO,IV CO 5 k 0,,II, k 0,,II, k 0,3,II, E,II, E,II, E 3,II k 0,,III, k 0,CO,III, E,III, E CO,III, β k 0,IV, k 0,CO,IV, E 0,IV, σ IV, E CO,IV, β

6 The sum of squared errors (SSQ) of the CO ad CO values were added to form the SSQ value, which was miimized: CO SSQ = i,experimetal CO CO + i,experimetal CO TOC,0 i,calculated TOC,0 i,calculated (6) with i beig the idex of the experimetal data poit ad the total umber of experimetal data poits used for the fit. Equatio 6 was miimized by iterative variatio of the adjustable kietic parameters (see Table ) usig the Simplex algorithm (fuctio f misearch i MATLAB) or the Patter search algorithm (fuctio pattersearch i MATLAB). Differet sets of iitial parameter values were tested to icrease the certaity that the foud miimal SSQ represeted a global miimum. For a compariso of the models, the stadard error of the estimate (SEE) was calculated by SEE = SSQ p (7) where is the total umber of experimetal data poits used for the fit ad p the umber of adjustable parameters of the model. The ODE systems were solved aalytically by trasformatio ito liear fuctios. If a aalytical solutio was ot possible (models II, III, ad IV), the ODE systems were solved umerically usig the ode45 fuctio i MATLAB. 4. RESULTS AND DISCUSSION 4.. Experimetal Ivestigatio HTO of Fecal Sludge. Depedig o the degree of coversio, a trasparet brow-yellowish to colorless liquid reactio product was obtaied. A solid fractio was suspeded i the liquid reactio product cosistig of black or white particles that settled withi miutes. I several experimets (V4, V4, V43, Lambda 3, Dilute, ad Dilute 3; compare Table 3), a sticky coke or tarlike byproduct was obtaied. The gas phase cotaied residual O, N,CO, ad CO. Formatio of H ad CH 4 was ot observed i ay of the experimets. The results of all performed experimets are reported i Tables 3 ad 4. A rapid reactio start, similar to a igitio, idicated by a reproducible sharp peak i the measured temperature ad pressure curves was observed at aroud 300 C for experimets where the thermocouple for reactio temperature measuremet was situated i the gas phase (Miemp series; Figure ad Table 4). The maximum temperature reached up to 490 C. Peak temperatures icreased with icreasig oxyge-to-fuel ratio. Experimets where the temperature was measured i the liquid phase exhibited a similar peak i the pressure curve ad a small peak (or o peak at all) i the temperature curve at 300 C. The temperature ad pressure peaks are cosidered to be caused by a rapid gas-phase reactio. It is supposed that durig the heat-up of the reactor (below 300 C) volatile compouds are formed that igite i the presece of oxyge. Oly a margial carbo coversio was observed for experimets that were stopped before the igitio temperature was reached (Heiz 3; Table 4). Because o CO, H, ad CH 4 were detected at these coditios, we assume that some volatile orgaic compouds (e.g., lowmolecular-weight alcohols, aldehydes, carboxylic acids, ketoes, etc.) are formed 0 ad igite aroud 300 C. The reactio kietics are oly slightly iflueced by this (gas-phase) igitio because the temperature rise measured i the liquid phase, which cotaied the majority of the orgaic fractio, was very small. Geerally, icreasig both the reactio temperature ad reactio time icreased the coversio of TOC to CO. At both tested sad-bath temperatures (360 ad 470 C), aroud 8% of the TOC was first coverted to CO ad cosecutively oxidized to CO. The oxidatio rate of CO was cosiderably iflueced by the reactio temperature. At 470 C sad-bath temperature, all of the TOC ad CO was coverted to CO after ca. 5 mi (570 s). At 360 C sad-bath temperature, >99% of the TOC was decomposed, ad there was still 6% carbo foud as CO after 5 mi (Table 4). Table 3. Results of Batch Experimets: Prelimiary Experimets ad Variatio of the Oxyge-to-Fuel Equivalece Ratio λ ad Iitial TOC Cocetratio at Stadard Reactio Coditios CO ad CO yield (%) expt label iitial air pressure p air,0 (MPa) iitial TOC cocetratio c TOC,0 (mol L CO ) oxyge-to-fuel equivalece ratio λ 00% 00% Variatio of the Oxyge-to-Fuel Equivalece Ratio (T sad = 470 C, t r = 306 ± 5 s, ad T ed = 45 ± 4 C) Lambda b 9.8 ± ± 0.. ± 0.0 Lambda 3 a ± ± ± ± 0.5 Lambda ± ± ± ± 0.4 Lambda ± ± ± 6 5. ± 0.4 Lambda ± ± ± ± 0.4 Variatio of the Iitial TOC Cocetratio (T sad = 470 C, t r = 30 ± 3s, ad T ed = 49 ± 3 C) Dilute ± 0.3. ± ± ± 0.6 Dilute ± 0..3 ± ± ± 0.6 Dilute ± 0..4 ± ± ± 0.6 Dilute a ± 0..9 ± ± ± 0.7 Dilute 3 a ± 0..5 ± ± ± 0.3 Screeig Experimets (T sad = 550 C ad T ed = 400 C) V4 a ± ± V4 a ± ± V43 a ± ± a Formatio of coke ad tar observed. b Helium used istead of air. CO 95

7 Table 4. Results of Batch Experimets: Variatio of the Reactio Time [Iitial Air Pressure p air,0 = 0.0 MPa, Oxyge-to-Fuel Equivalece Ratio λ = (.5.3) ± 0.06, ad Iitial TOC Cocetratio c TOC,0 = 9.8 ± 0.3 mol L ] a CO ad CO yield (%) expt label sad-bath temperature T sad ( C) reactio time t r (s) ed temperature T b CO ed ( C) 00% 00% Heiz ± 0.0 b.d.l. Heiz ± 0.6 b.d.l. Heiz ± 0.8 b.d.l. Heiz ± ± 0.3 Heiz ± ± 0.6 Heiz ± 6 8. ± 0.7 Heiz ± ± 0.5 Heiz ± ± 0.4 Heiz ± ± 0.3 Heiz ± 7. ± 0. Heiz ± 7. ± 0.4 Heiz ± 6 b.d.l. Miemp ± Miemp ±.5 ± 0. Miemp ± 4 6. ± 0.4 Miemp ± ± 0.4 Miemp ± ± 0.5 Miemp ± ± 0.5 Miemp ± ± 0.4 Miemp ± ± 0.4 Reproducibility Test Rep ± 6 7. ± 0.4 Rep ± ± 0.4 Rep ± ± 0.5 Average 89 c ± 5 d 7 c ± d a The ucertaities of the calculated values were estimated by ucertaity propagatio from aalytical values. CO ad CO yields from TOC decompositio were calculated usig eqs 8 0. b.d.l. = below detectio limit. b Temperature that was reached whe the reactor was removed from the sad bath. c Average of Rep, Rep, ad Rep 3. d Stadard error of Rep, Rep, ad Rep 3. CO Figure. Temperature curves of the experimets where the temperature was measured i the gas phase durig heat-up idicatig a igitio at aroud 300 C. The reproducibility of TOC coversios was assessed from three reproduced experimets at stadard coditios (Rep 3 i Table 4) ad was aroud 5% for the TOC to CO coversio ad % for the TOC to CO coversio. Ucertaities of all coversio data were also estimated by Gaussia ucertaity propagatio from measuremet ucertaities. The estimated ucertaities at stadard coditios (6 7% for the TOC to CO coversio ad 0.5% for the TOC to CO coversio; Table 4) are i a rage similar to that of ucertaities measured from the reproducibility test. The iaccuracy of gas compositio measuremet ad ihomogeeity of the used feedstock were foud to have the greatest ifluece o the reproducibility. A icrease of the oxyge-to-fuel equivalece ratio λ icreased the coversio of TOC to CO (Lambda 5iTable 3). These fidigs are i accordace with the fidigs of Goto et al. 6 Formatio of CO was isigificatly iflueced by a icrease of λ. A icrease i the feces dilutio (or a decrease i the feed cocetratio) slightly decreased the coversio of TOC to CO ad slightly icreased the TOC to CO coversio i those experimets where o coke ad tar was formed (Dilute, 4, ad 5; Table 3 ad Figure 3). Whe coke ad tar were formed (Dilute ad 3), the coversio of TOC to CO was cosiderably lower. Several authors reported a first-order depedece of the rate of TOC disappearace o the reactat cocetratio (i.e., TOC coversio is idepedet of the iitial TOC cocetratio) for HTO of biomasses that are similar to fecal sludge, e.g., muicipal sewage sludge, 4 dog food waste, 7 or biological sludge. 8 We tested whether the observed icrease of coversio with the iitial TOC cocetratio of our results (Figure 3) was statistically sigificat. A F test 9 was performed icludig values Dilute, 3, ad 5 ad Rep 3 ( = 6). Values that were associated with coke ad tar formatio (Dilute ad 3) were ot cosidered for the test. The test was based o the ull hypothesis that there was o sigificat liear tred (p = ). At a level of 96

8 Figure 3. TOC to CO ( ) ad TOC to CO ( ) coversio for various fecal sludge dilutios measured at stadard coditios (T sad = 470 C, t r = 300 s, ad λ =.). cofidece of α = 5%, the ull hypothesis was ot rejected for both TOC to CO ad TOC to CO coversio. The icrease of coversio with icreasig TOC cocetratio is thus ot supposed to be sigificat. This result justifies the assumptio of a first-order depedece o the reactat cocetratio of the reactio rates for TOC disappearace i our work. Whe our data are compared to those of Price, 5 Goto et al., 4 ad Shaableh ad Gloya 30 for other biological sludges, we fid similar coversios of carbo at comparable reactio coditios. Price 5 observed mior formatio of CH 4 ad H, aside from CO ad CO i their product gas. Miller ad co-workers 9 foud that the solids cocetratio of the feed had a ifluece o the temperature icrease of the reactio. This could also provide a explaatio for the slightly lower coversios observed for the experimets with a lower iitial TOC cotet CO Formatio ad Subsequet Oxidatio to CO. Little is kow about the formatio of CO from biological sludges uder HTO coditios. Four mai routes are coceivable: (a) All orgaic carbo reacts first with oxyge to CO, which is the further oxidized to CO i a cosecutive reactio. CO would thus be the primary product ad CO the secodary oe. (b) CO is formed from the orgaic carbo i a idepedet reactio (with or without the ivolvemet of oxyge), parallel to the formatio of CO from the orgaic carbo (eq 6). Both CO ad CO would the be primary products. (c) CO is formed from CO ad solid carbo i a Boudouarype equilibrium reactio: CO +C CO. (d) CO is formed via the reverse water gas shift reactio: CO +H CO + H O. Our data support route b because the CO yield icreases later tha the CO yield (Table 4). For route a, the CO yield would icrease first, followed by a icrease of CO. Furthermore, i route a, a lack of oxyge (λ < ) would result i large amouts of CO i the product gas. The highest CO cocetratio of.3 vol % was obtaied i experimet V4 with λ = 0.6, alog with aco cocetratio of 7. vol %. This carbo distributio is ot compatible with that of route a for λ = 0.6, which would just be eough to covert all carbo to CO ad oly a small fractio further to CO ; i.e., the CO cocetratio should i that case be much higher tha the CO cocetratio. Route c is implausible because the high pressures i our experimets drive the equilibrium to the reactats, CO ad C. Because o solid carbo was foud i most of the experimets, this pathway seems ulikely to have cotributed sigificatly to the formatio of CO. Route d is also dropped because CO would oce more be a secodary product from CO ad thus exhibit a differet tred. Furthermore, sigificat amouts of hydroge would have to be formed first to drive this reactio toward CO ad water. Oly a little formatio of CO, i.e., 0.3 vol % or 0 times less tha that for λ = 0.6, was observed uder oxyge-free coditios (λ = 0). This suggests that oxyge is eeded for the formatio of CO from the orgaic carbo. The most probable explaatio for CO formatio is decarboylatio of orgaic itermediates, formed by the partial oxidatio of orgaic carbo. Acetaldehyde is kow to form CO uder hydrothermal coditios. 3 Aother likely cadidate is formic acid. It is formed as a itermediate durig HTO of sewage sludge. 6 It was further show 3 to decompose to CO ad H O ad to CO ad H. Because hydroge was ot detected i ay of our experimets, decompositio of formic acid to CO ad water would be aother plausible source for some of the measured CO Coke ad Tar Formatio. Coke ad tar were formed especially whe the p T trajectory of a experimet crossed the vapor pressure curve of water (Figure 4). This happeed, for Figure 4. Measured p T curves of exemplary experimets Dilute with itersectio (---) ad Dilute without itersectio ( ) of the vapor pressure curve of pure water. λ was. i both experimets. example, whe a low iitial air pressure was applied or whe the reactor loadig was icreased by the additio of water for dilutio (experimets Dilute ad 3). Tars are ill-defied high-molecular-weight compouds, adcokeisacarbo-richsolid.cokeaarsareformed by repolymerizatio of liquefied orgaic compouds durig thermal decompositio of biomass. Compared to other biomass compouds, both tar ad coke are slowly decomposed durig thermal treatmet. 33 They are formed as byproducts of hydrothermal gasificatio processes 34 ad of pyrolysis ad dry gasificatio, 33 where o oxyge or oly limited oxyge is available. I experimet Lambda 5 of this study, where o air was supplied (λ =0;compareTable 3), o tar ad coke formatio occurred. At a λ value slightly below, tars ad coke were formed (Lambda 3). These observatios do ot pait a clear picture of the reasos for coke ad tar formatio i our experimets. Oe explaatio for coke ad tar formatio is that whe the vapor pressure curve of water is itersected, all liquid water is vaporized, formig a dry biomass phase i the reactor. Because of the high reactor temperatures ad slow reactio of oxyge with solid biomass, the biomass would be pyrolyzed, formig tars ad coke. 97

9 Table 5. Summary of the Obtaied Best-Fit Model Parameters preexpoetial factor activatio eergy model k 0, (s ) k 0, (s ) k 0,3, k 0,CO (s ) E 0, E (kj mol ) E (kj mol ) E 3, E CO (kj mol ) σ (kj mol ) β SSQ SEE b I IIa IIb a a III IV a Fixed values published by Hellig ad Tester. 5 b Calculatio basis: model I, 3 data poits (CO oly); models II IV, 46 data poits (CO ad CO). The exact reasos for the formatio of coke ad tars were ot further ivestigated i this study. Their formatio ca be avoided by applyig a low ratio of water to air, i.e., a high iitial air pressure ad a small amout of water (water cotaied i the fecal sludge plus water added for dilutio). The data poits from experimets where tar ad coke formatio occurred were ot icluded i the kietic aalysis. 4.. Kietic Aalysis Kietic Modelig of Hydrothermal Fecal Sludge Oxidatio. The obtaied coversio results from Table 4 were used for kietic modelig. Data poits from Table 3 were ot icluded i the kietic study. Models I III (Table ) showed quick covergece whe the Simplex algorithm (fmisearch) was used. Model IV oly reached a global miimum whe the Patter search algorithm was used. Covergece was relatively slow because of a high umber of iteratio steps. Model I did ot coverge to a global miimum if oly data poits from experimets coducted at 470 C sad-bath temperature were used (Heiz series). Oly local miima were foud, resultig i implausible parameter values (e.g., activatio eergies of >00 kj mol ). Best-fit activatio eergies (models II ad III) ad mea activatio eergies (models I ad IV), respectively, for TOC to CO decompositio betwee 37 ad 43 kj mol were obtaied (Table 5). Best-fit activatio eergies for TOC to CO decompositio were slightly higher, betwee 46 ad 54 kj mol. Models I ad IV usig the DAEM gave best-fit σ values betwee. ad 3.8 kj mol. Models that icluded CO to CO oxidatio (II IV) yielded activatio eergies betwee 0 ad 0 kj mol for this reactio. Models III ad IV that assumed a fractioal TOC decompositio ito CO ad CO yielded a best-fit β value of The highest predictio accuracy was achieved by model III (SEE = 0.044; Table 5). The model curves smoothly fit the CO ad CO data poits over the whole reactio time (Figure 5, model III). TOC-to-CO coversio is slightly uderpredicted at 360 C sad-bath temperature (t r = s) ad slightly overpredicted at 470 C sad-bath temperature (t r = 0 50 s). Model IIa achieves almost the same predictio accuracy (SEE = 0.047) ad exhibits similar deviatios at the same retetio times as model III. The predictio of model IV is slightly less accurate (SEE = ) despite its use of the DAEM. Models I ad IIb showed the lowest predictio accuracy (higher SEE) compared to the other models, especially for TOC-to-CO coversios of >90%. The model predictio accuracy was slightly icreased by icreasig the model complexity (e.g., icrease of the cosidered reactio paths) ad the umber of adjustable parameters. However, the use of DAEM did ot icrease the model accuracy. All models exhibit similar activatio eergies for TOC decompositio to CO i the rage of kj mol, regardless of the model approach used, uderliig the plausibility of the obtaied values. The lack of accuracy of model I is assumed to be caused by the eglected formatio of CO. Because CO reacts relatively slowly, especially at lower reactio temperatures, the predictio becomes iaccurate after the mai part of the TOC is decomposed (Figure 5, model I). The activatio eergies for CO oxidatio to CO i models IIa ad III (0 ad 0 kj mol, respectively) are slightly lower tha the value reported by Hellig ad Tester 5 ( kj mol ). Vice versa, model IIb that uses this literature value exhibits a low predictio accuracy for loger retetio times ad higher coversios (Figure 5, model IIb). O the other had, model IV exhibits a activatio eergy for CO oxidatio (3 kj mol ) similar to the reported literature value of E CO. This idicates that the DAEM approach of model IV leads to a icrease i the robustess of the model because it results i parameter values similar to accurately determied kietic data for the sigle reactio of CO to CO. The β values obtaied for models III ad IV idicate that ca. 9% of TOC is coverted to CO ad 9% of TOC is coverted to CO i parallel reactio paths. The oxyge-to-fuel equivalece ratio λ had a small ifluece o the rate of TOC coversio i the rage of λ values studied, i.e.,..9, with higher λ leadig to a higher TOC coversio. We tried to iclude this ifluece i our kietic models, with usatisfactory results. The ifluece o TOC coversio was ot well captured ad extrapolatio to λ values of < led to a urealistic formatio of CO. Thus, we decided to exclude ay ifluece of λ o the rates of reactio i our models Compariso of the Observed Coversio Results with the Literature Data. TOC coversios observed i this work were plotted agaist the predictios made by model III (Figure 6). Additioally, model III was used to calculate coversios usig the experimetal coditios (t ad T) published by other authors 6,7,30 ad plotted agaist the coversios observed i those studies i the same figure. Model III fits the experimetal coversios of this work well except for experimets that are associated with coke ad tar formatio. This idicates that the model has poor validity if coke ad tar are formed durig the reactio because these products are ot accouted for i the kietic scheme. Model III shows a poor fit upo predictios of the coversios of muicipal sewage sludge 6 ad dog food. 7 TOC coversios of these substrates are geerally uderpredicted by the model. The predictio of model III for activated sludge 30 is accurate whe coversios at reactio temperatures of C are predicted. The fit for coversios at 300 ad 343 C is poor. The followig activatio eergies for global first-order reactio models for TOC or COD coversios were reported by the 98

10 Idustrial & Egieerig Chemistry Research Figure 5. Coversio of TOC to CO ad CO over reactio time: experimetal data (symbols) from Table 4 ad model predictios (lies) usig best-fit parameters from Table for the four models I IV. other authors: 76 kj mol (TOC) for supercritical water oxidatio of muicipal sewage sludge,4 67 kj mol (COD) for wet oxidatio of biological sludge5 (ot show i Figure 6), 54 kj mol (COD) for wet oxidatio of activated sludge,8 ad 97 kj mol (TOC) for supercritical water oxidatio of dog food.7 The activatio eergies for TOC decompositio obtaied i this study, betwee 37 ad 43 kj mol, are lower tha these literature values. This explais the poor predictio of model III for some of the experimetal poits for other substrates i Figure 6. The most obvious explaatio would be that all of these sludges exhibit a differet reactivity durig HTO. Differet ratios of the mai costituets, i.e., carbohydrates, proteis, lipids, etc., lead to differet overall reactivities. A further reaso for the deviatios could be that the sludges used i the other studies uderwet a pretreatmet (e.g., aerobic/aaerobic digestio). Easily degradable compouds would be elimiated by these pretreatmet steps, causig a chage of the overall activatio eergy i a global kietic model. However, Shaableh ad Imteaz35 showed that aaerobic sludge treatmet had almost o ifluece o the first-order HTO reactio kietics, i.e., activatio eergy. Aother reaso for the deviatios is the limited rage of λ values, i.e., aroud., used i our experimets, whereas values as high as were used i the other studies. The ifluece of the oxyge cocetratio o the reactio rates should thus be icorporated ito the rate expressios of the kietic model i future work. Furthermore, importat cotributios to the deviatios betwee our model predictios ad the data of other authors show i Figure 6 are the differet methods for calculatig coversio. While i our study coversio is calculated from the CO ad CO formed, 99

11 Figure 6. Compariso of the observed ad calculated TOC (or COD) coversios usig model III with best-fit parameters (Table 5) at give reactio coditios: this study [ ; X TOC =( CO + CO )/ TOC,0, T < 470 C, ad λ =0.9], muicipal sewage sludge 4 ( ; X TOC = TOC,ed / TOC,0, ustirred batch reactor, T = C, ad λ =.0), activated sludge 30 ( ; X COD = COD,ed / COD,0 ), ustirred batch reactor, T = C, ad λ =.), ad dog food waste 7 ( ; X TOC = TOC,ed / TOC,0, ustirred batch reactor, ad λ =.0). the ucoverted TOC or COD was used i other studies. Depedig o how the samples were draw ad worked up, small solid particles suspeded i the solutio would ot be icluded i the TOC or COD aalysis. We have compared some of our coversio data usig the method with CO ad CO versus the method with the ucoverted DOC ad foud a sigificat differece, o the same order of magitude as the differeces show i Figure 6. It is therefore importat to apply our model for predictig coversio data correspodig to CO ad CO yields ad ot to ucoverted carbo i the liquid phase. Vogel et al. 4 used the data of Goto et al. 4 (SCWO of muicipal sewage sludge) ad adjusted a DAEM usig a Gaussia PDF. A mea activatio eergy for TOC decompositio of 9 kj mol ad a σ value of 0.9 kj mol were obtaied. The two models usig the DAEM approach i this study (models I ad IV) exhibit a relatively small breah of the PDF with σ values of. ad 3.8 kj mol. A detailed aalysis of the reactio itermediates would be eeded to uderstad the relatively arrow rage of reactivities durig HTO of feces. Because of this arrow rage, the models with a sigle reactio approach for TOC decompositio (models II ad III) are able to predict the experimetal data with a accuracy similar to that of the models usig a DAEM Ifluece of the Rate of Oxyge Mass Trasfer o the Measured Reactio Rate. At coditios below the critical poit of water (T < 374 C ad p <. MPa), the majority of oxidatio reactios are supposed to occur i the liquid phase amog dissolved compouds. Because the reactor cotet was ot agitated, oxyge had to diffuse from the gas phase ito the liquid phase to be able to react with the orgaic material. Thus, the measured reactio rates might be limited by the oxyge masstrasfer rate. At supercritical coditios, the compoets are assumed to be completely mixed i a sigle-phase, homogeeous fluid because of the complete miscibility of orgaic compouds ad gases with supercritical water. 36 Therefore, oxyge trasport should ot play a role. To esure that the measured reactio rates were ot limited by the oxyge trasport at subcritical coditios, the oxyge mass-trasfer rate was estimated usig literature values ad compared to the observed rate of oxyge disappearace. The hypothesis of oxyge-trasport limitatio ca be rejected if the followig coditio is fulfilled: < O O measured trasport,max (8) ( O ) measured (mol O s ) is the rate of oxyge disappearace, cosumed for the reactio of TOC to CO, which was calculated usig kietic model I. ( O ) trasport,max (mol O s ) is the maximum oxyge mass-trasfer rate from the gas phase to the liquid phase. Accordig to the two-film theory, the oxyge mass-trasfer rate is calculated by O trasport = kat ( )( c * c ) V ( p, T) L O O HO (9) k L a [s ] is the volume-specific oxyge mass-trasfer coefficiet, c O * (mol m 3 ) is the oxyge cocetratio at the liquid gasphase boudary, c O (mol m 3 ) is the oxyge cocetratio i the reactig phase, ad V H O (m 3 ) is the volume of the reactig phase depedig o the reactor temperature ad pressure. For simplificatio, the reactig phase (fecal sludge) was cosidered to be pure water. The oxyge cocetratio at the liquid gas iterface, c O *, was take as the oxyge solubility i water calculated with Hery s law. 37 To determie the maximum oxyge mass-trasfer rate, a fast reactio i the liquid phase was assumed, leadig to c O =0. k L a was estimated usig a correlatio determied by Foussard: ± 0K(/ Tref / T) kat L ( ) = ( ka L ) T e (30) ref where (k L a) Tref (s ) is the k L a value at a referece temperature T ref (K; experimetal values of s ad 93 K from Foussard s work were used as referece values, respectively) ad T (K) is the temperature. Foussard 38 measured k L a values of oxyge i a cylidrical stirred batch reactor i a temperature rage betwee 0 ad 40 C at stirrer speeds betwee 00 ad 800 mi. For this study, eq 30 was extrapolated to 374 C ad to a rotatioal speed of 0 mi, i.e., o mixig. The obtaied k L a values were corrected by dividig k L a by the volume-specific surface area of the reactat [a (m ) = liquid gas iterface (m )/liquid volume (m 3 )] used i Foussard s work ad multiplyig it by the volume-specific surface area of the reactat used i this study. The highest oxyge reactio rates were observed i the experimets coducted at 470 C sad-bath temperature. Betwee the reactio start at aroud 300 C ad before the critical poit of water (374 C) is reached, fast oxidatio reactios occur i the two-phase system, idicated by the high TOC coversio rates. I this regio, the calculated oxyge mass-trasfer rate is higher tha the oxyge reactio rate (Figure 7). Below ca. 80 C, the oxyge mass-trasfer rate is smaller tha the measured rate of oxyge cosumptio. Because at these temperatures almost o coversio of TOC takes place, the ifluece of oxyge trasport o the kietic parameters is miimal. 5. CONCLUSION TOC cotaied i fecal sludge is decomposed to CO ad CO as withi miutes i supercritical water i the presece of stoichiometric amouts of oxyge at temperatures below 480 C. 90