MODELLING DESIGN OF CONTINUOUS ANAEROBIC DIGESTERS FOR MUNICIPAL SOLID WASTE IN BIOGAS PRODUCTION

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1 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember MODELLING DEIGN OF CONTINUOU ANAEROBIC DIGETER FOR MUNICIPAL OLID WATE IN BIOGA PRODUCTION Asinyetgha Hilkiah Igni* and Ibiye epirib Kingnana Harry Department f Agriultural & Envirnmental Engineering, Faulty f Engineering, Rivers tate University f iene and Tehnlgy, PMB, Prt Harurt, Nigeria ABTRACT: Mathematial mdels have been develped fr the design f anaerbi ntinuus digesters fr the prdutin f bigas frm muniipal slid waste (MW) in Prt Harurt metrplis, Nigeria. Field and labratry investigatins were nduted and used t determine the physial, hemial and bi-kineti prperties f the MW relevant t the digester design. The design mdels were simulated fr ttal slids (T) nentratin f -% and fratinal nversin f.-. using Mirsft Visual Basi Versin. prgram. The simulatin results were analyzed with Mirsft Chart Editr; and mathematial relatinships established between T nentratin and vlume f digester; residene time; vlume f bigas prdued; net heat required; and st f digester. It was fund that, at maximum fratinal nversin f., whereas the T nentratin varied diretly as the vlume f digester, it was inversely prprtinal t the time f digestin fr the same levels f perentage stabilizatin. This is indiative f an aelerated grwth rate f mirbes with inreasing T nentratin. KEYWORD: Cntinuus Anaerbi Digester; Bigas Prdutin; Muniipal lid Waste; Waste Management INTRODUCTION Muniipal lid Waste Management The lad f muniipal slid waste (MW) in Prt Harurt metrplis, Nigeria has been estimated at,,.kg with a prjeted ppulatin f,, persns; and despite this magnitude f waste the management has been grssly ineffetive and ineffiient (Igni, a). The urrent MW management pratie in Prt Harurt invlves lletin, transprtatin and dispsal f the waste at a dumpsite. Despite the inadequay f the MW management funtinal elements, the nes that are implemented are als imprperly dne, as the rate f generatin is always higher than the rate f lletin. The absene f a treatment press fr the waste befre dispsal exaerbates the already debilitating adverse nsequenes f its imprper lletin, transprtatin and dispsal. A treatment ptin that has beme very attrative is the anaerbi digestin f the waste t generate bigas (Igni, ). lid waste is a nn-fluid type f waste and this makes its handling and management relatively diffiult, mpared t the types f waste that an flw frm ne latin t anther, r even vaprize (Ogunbiyi, )., MW, arding t Bailie et al () mprises small and mderately sized slid waste items frm huses, businesses, and institutins. It is desribed as waste lleted by private and publi authrities frm dmesti, mmerial and sme industrial (nn-hazardus) sures is referred t as muniipal slid waste (Kiely, ). Fr Byrne () MW is generated frm urban areas, partiularly huses and shps. IN -(Print), IN -(Online)

2 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember Fllwing the apparent mismanagement f the MW in Prt Harurt and the nmitant adverse impats n the peple and envirnment, an alternative management predure that wuld nsider the redutin f the waste vlume and its pllutin lad wuld be required. Igni et al () investigated the ptential f generating bigas frm MW in Prt Harurt and fund that the waste has rih rgani ntent f abut %, whih predispses it as a veritable material fr the generatin f bigas in anaerbi digestin. Therefre, treating the waste using anaerbi digestin press will nt nly redue the waste vlume and pllutin lad, but als yield an energy sure that wuld mitigate the energy quest f the peple. Presses in Bigas Generatin Bigas is gas given ff when rgani materials dempse in an anaerbi envirnment. This dempsitin is either physial r hemial presses at high temperature and/r pressure, r bilgial presses using mirrganisms at lw temperature and atmspheri pressure. These methds impat n the envirnment differently, espeially in terms f their ability t redue waste lad. Gas is prdue in all the presses, but referred t as bigas when derived frm the bilgial system (Hbsn et al, ). Bigas is a lrless, relatively drless and inflammable gas, with the fllwing mpsitin (Madu and deinde, ), shwn in Table, that burns with a blue flame and has a heat value f kal/m when its methane ntent is in the range f %. It is als stable and nn-txi. Table. Cmpsitin f bigas Cnstituents % Cmpsitin Methane (CH) % Carbn dixide (CO) % Hydrgen ulphide (H) % Nitrgen (N) % Hydrgen (H) % Carbn Mnxide (CO) Traes Oxygen (O) Traes The basis f rgani waste dempsitin The design f anaerbi digesters is based n the inherent ability f rgani materials t dempse when ated upn by mirrganisms in the absene f xygen. The digester prvides the ntrlled nditins where the interatin between the waste and mirbes urs. The bi-kineti behavir f the MW influenes the pattern f dempsitin, and aid the determinatin f digester physial parameters. Anaerbi digestin (AD) had been widely used fr the treatment and stabilizatin f industrial, agriultural and muniipal waters and sludge (Hbsn et al, ), but Kiely () states that reently anaerbi digestin is als being applied t the treatment f MW, with bigas generated nly as a waste prdut Researh bjetive There are different types f anaerbi digesters fr the pressing f MW. T develp an apprpriate bi-digester fr MW in Prt Harurt wuld require the nsideratin f the prperties f the MW. Igni et al (, ) have reprted n the prperties f MW in Prt Harurt and relevant t digester designs. There are different types f appliable anaerbi IN -(Print), IN -(Online)

3 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember bireatrs fr MW pressing, inluding bath, plug-flw and ntinuusly stirred tank reatrs. The bjetive f this paper is t ease the design f ntinuusly stirred tank reatrs in anaerbi digestin f MW in Prt Harurt fr bigas prdutin, by prviding design mdels frmulated fr that purpse. THEORETICAL FORMULATION The presses f anaerbi digestin In anaerbi digestin, faultative anaerbes, desribed as bligate anaerbes during methangenesis dempse the rgani material in using it as a fd sure. Reynlds and Rihards () lassified them as (i) liquefatin f slids, (ii) digestin f sluble slids, and (iii) gas prdutin; and Kiely () identified fur different trphi mirbilgial baterial grups peratinal in AD, and that it is the umulative effet f all these grups that ensures press ntinuity and stability in the three pressing stages f i) hydrlysis, ii) aidgenesis and iii) methangenesis. Cmplex rgani substrates suh as arbhydrates, prteins, fats and lipids will be hydrlyzed int simpler sluble prduts, whih are further nverted int aeti aid, hydrgen and arbn dixide. Arding t Ekenfelder () the breakdwn f arbhydrates, nitrgenus mpunds and fats an be expressed using hemial frmula as fllws: C H O + H O C H O + CO + H () Frm the aeti aid and hydrgen prduts f the abve reatin, methane wuld be prdued thus: C H O CH + CO () H + CO CH + H O () When these expressins are mbined, the generalized equatin fr the anaerbi digestin press is btained as fllws: Organi matter () + Cmbined water Anaerbi mirbes New ells + Energy fr ells + CH + CO + Other end prduts Anaerbi digestin reatin mehanism Anaerbi digestin is mdelled as a first rder press, where the rate f inrease in bimass is prprtinal t the initial bimass nentratin and desribed by the rate equatin (). r x d X X () dt rx - grwth rate f bimass, mg/l/day X - initial nentratin f bimass, mg/l - speifi grwth rate f the mixed ppulatin (days - ) IN -(Print), IN -(Online)

4 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember = mass f ells prdued / mass f ells present per unit time t - time, days METHODOLOGY Labratry experimentatin The kineti behavir f the MW in anaerbi pressing was investigated using five bathwise anaerbi digesters, eah f liters vlume. Igni (b) has reprted the suessful adaptatin f bath experiment data fr the design f anaerbi ntinuus digesters, after the predure utlined by Bailey and Ollis (). The shemati diagram f the experimental design layut fr a single bath reatr set-up is shwn in Figure. The full view f the reatr experimentatin set-up is shwn in Figure. IN -(Print), IN -(Online)

5 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember The digesters were imprvised with large ans beause f the limitatin f the unavailability f mdel digesters, but deriving substantial impetus frm Hbsn et al. (), wh said with a bath digester a smaller experimental system may be suitable as the digester has nly t be laded ne and may nt even need t be stirred. One r tw liters uld be big enugh. The ntainers were prperly lagged with wl material f abut mm thikness, t minimize the interatin between the temperatures inside and utside f the digesters. Tw perfratins were made n the ver f the digester thrugh whih the gas hse and thermmeter were fitted. The hse extending frm the digester tp was nneted t the tail f a burette, whih in turn was then partly immersed in water in a graduated ylinder. The waste materials were pressed (shredded and mashed), and the digesters were then laded with kg f rgani MW, whih was diluted t a.% ttal slids (T) nentratin after metals, glass and ther nn-bidegradable materials had been remved. The prperties f MW relevant t its anaerbi bidegradatin was investigated and presented by Igni et al. (). The T nentratin was determined by adpting the predure fr the determinatin f T utlined in G f tandard Methds fr the Examinatin f Water and Waste Water (APHA, ); and the misture ntent was determined by the ven drying methd. The ph was measured frm a digital ph meter, and the substrate and bimass nentratins, were respetively determined in terms f the hemial xygen demand (COD), and the mixed liqur vlatile suspended slids (MLV) using the respetive predures in b.b and G f tandard Methds fr the Examinatin f Water and Waste Water. The arbn and nitrgen ntents were determined, frm where the arbn t nitrgen (C:N) rati was mputed. The arbn was determined by adapting the Walkley-Blak methd fr determining sil rgani matter (Walkley and Blak, ); and the nitrgen was determined with the usual mar-kjedahl methd. The thermmeter, was passed int the headspae f the digester, and measured the temperature f the headspae inside f the digester. The ambient temperature was measured frm maximum and minimum thermmeters at the same time. These temperature measurements were taken at hurs and hurs, and aimed at determining temperature variatin within and utside the digester, t ensure prper digester insulatin with respet t digester nstrutin materials. After these initial measurements frm the waste repliatins, the digesters were made airtight with glue and ther adhesives, and the set-up allwed running. Eah f the digesters was dismantled at intervals f days, whih gave the experimentatin a ttal lifespan f days. At eah dismantling, substrate (COD) and mirbial (MLV) nentratin measurements were repeated. Design Mdels Frmulatin The general frm f material balane expressin, whih has been variusly desribed [Andrews, ; Kiely, ; Reynlds and Rihards, ; Thbanglus et al, ] as in equatin (a), was used fr the frmulatin f mdels fr MW in the ntinuus digester. IN -(Print), IN -(Online)

6 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember Rate f aumulatin f material in Reatr (a) = Rate f material flw int Reatr ± Rate f appearane r disappearane f material due t Reatin Rate f material flw ut f Reatr A simplified frm is: Aumulatin = Inflw + Net grwth - Outflw (b) Fr the anaerbi digestin press, this expressin is symblially represented as: () d[ X ] V dt r Q[ X ] V r net Q[ X ] d [ X ] dt - rate f hange f mirrganism nentratin in the reatr measured in terms f mass (mixed liqur vlatile suspended slids), mass MLV/unit vlume. time Vr - vlume f reatr, m Q X X net - flw rate, vlume / time - nentratin f mirrganisms in influent, mass MLV/unit vlume - nentratin f mirrganism in reatr, mass MLV/unit vlume - net rate f mirrganisms grwth, mass MLV/unit vlume time Mnd () desribed the kinetis f substrate dempsitin by the fllwing empirial relatinship. max - maximum grwth rate, days - - nentratin f limiting substrate, mg/l max () K Ks - half saturatin nstant (i.e. nentratin f when μ = μ max ), mg/l [ ] and net = max [ X ] kd[ X ] () K [ ] s s IN -(Print), IN -(Online)

7 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember d[ X ] [ ] then, Vr Q[ X ] V r max [ X ] kd[ X ] Q[ X ] dt Ks [ ] (a) d[ X ] [ ] V [ ] [ ] r Q X X V [ X ] k [ X ] (b) r r max d dt Ks [ ] and k d = μ max Y This is the general mdel fr the anaerbi digestin press. () REULT/FINDING The results frm the bath experimentatin fr the anaerbi digestin f the MW and the dedued data fr the CTR are presented in Tables -. Table. Experimental bath digesters' data Digester n. Duratin f digestin, t (days) Initial MW nentratin, (mg/l) Effluent MW nentratin, e (mg/l) Initial mirbial nentratin, X (mg/l) Effluent mirbial nentratin, Xe (mg/l) Table. Redued data frm bath experimentatin fr the determinatin f press kineti parameters Digester n. Duratin f digestin, t (days) X t ln ( e e ) ln ( e X t ) e X t X = average ell mass nentratin during the bihemial reatin - that is X = ½(X + Xt), where X and Xt are the ell mass nentratins at the respetive times t = and t = t (Reynlds and Rihards, ) X IN -(Print), IN -(Online)

8 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember Table : Redued data frm bath experimentatin fr determinatin f CTR parameters Rate f MW utilizatin, ds /dt, mg/l/day peifi rate f MW utilizatin, U, day - /U Rate f grwth f mirbes, dx /dt, mg/l/day Mean ell residene time,, days / /e Appliatin f Material Balane t Cntinuus Reatr Presses This is dne in tw stages, fr the mirrganisms and substrate. Material Balane fr Mass f Mirrganism The mass balane fr the mass f mirrganisms in a mplete-mix reatr, will, therefre be: d X dt V Q X X X k X d V max () K d X Fr a steady state nditin, where, assuming X is negligible at the dt mmenement f the press, equatin () bemes: r (eliminating [X]) Q X But Q V is defined as the mean ell residene time (). X k X d V max (a) K Q V max kd (b) K Therefre (a) C max K k d IN -(Print), IN -(Online)

9 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember r (b) max kd ( K K ) Material balane fr ttal substrate utilizatin The mass balane fr substrate utilizatin in a CTR will be given as V d dt r V Q Q (a) d V dt rsv Q (b) rs - rate f substrate utilizatin, and defined mathematially as r s k X () K, substituting fr rs in equatin (b) frm equatin () and assuming steady state d nditin i. e. gives: dt r (b) X V k Q O (a) K [ ] [ ] V k Q K k X h () K h - hydrauli retentin time, whih is the same as the mean ell residene time () fr n ell reyle anaerbi system. This desribes the digestin time fr the CTR, suh that () Frm equatin (a) h ([ ] e )( K s [ e ] k[ ][ X ] K e max k C d X () IN -(Print), IN -(Online)

10 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember And frm equatin () () K [ ] [ e k[ X ] h ] Cmbining equatins () and () gives: [ ] h e k[ X ] max C k d (a) (b) r X r X k max h k X k d max (a) k d h k Y d h (b) Als, rearranging equatin () and substituting fr max frm equatin () k d Yk k K d () again frm equatin (b) (a) r kd X h Y kd X Y Y h (b) and frm mbining equatins () and (a), then k K s d () Cnsidering the fratinal nversin () f the substrate (), defined as: then Yk Yk (a) (b) IN -(Print), IN -(Online)

11 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember ubstituting fr [] in equatin () gives r (b) k h Ks k h K s X X K s k X (b) (a) h (a) h K h k K s X k X () Mdels fr the Cntinuus digester design The mdels fr the CTR is stritly based n the requirements f a high rate, lw slids pressing, where there is ntinuus mixing and ntinuus r intermittent sludge feeding and sludge withdrawal, and the ntents are in a hmgenus state (Reynlds and Rihards, ). The fixed ver variatin was nsidered fr the mdel develpment, beause highrate digesters usually have fixed vers (Reynlds and Rihards, ). Vlume Cntinuus digester vlume is desribed by the prdut f the flw rate f the medium and the hydrauli retentin time (Kiely, ; Reynlds and Rihards, ); Thbanglus et al, ) This is stated mathematially as: V = Qh (a) V - verall vlume f the ntinuus digester, m Q - influent sludge flw rate, m /day ubstituting fr h frm equatin () in equatin (a) gives: V K Q kx (b) IN -(Print), IN -(Online)

12 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember Dimensins and Cnfiguratin The nfiguratin f tanks fr ntinuus-flw anaerbi presses, arding t Kiely (), tends t be irular r square in shape and rarely retangular. Fr the develpment f the CTR dimensins in this wrk, a irular rss-setinal nfiguratin is adapted t guarantee effetive and effiient mixing as Thbanglus et al () state that the nditins will depend n the reatr gemetry and the pwer input. Diameter and Height The diameter and height f the tank is related t the tank vlume by the fllwing equatin; () V = A x H A - rss-setinal area f the tank H - height f the tank. Fr a irular rss-setin, the area f the rss-setin is: A D () ubstituting fr A in equatin () gives: V D H () Using the rati f : fr the relatinship between digester tank diameter and height s that D D = H r H =, then V () D r V D () ubstituting fr V frm equatin (b) gives: D X K Q () k and H Q K () kx IN -(Print), IN -(Online)

13 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember Gas diffusin Rates fr CTR Mixing taffrd et al () present the frmula fr the rate f gas diffusin as: Q = KV e D (a) (b) Q g = KV e { π Q [( α α ) (K s+[] k[x] )] } Qg - gas disharge rate (m /s) K - prprtinality nstant Ve - representative velity (m/s) They reprted a velity value f. m/s as apprpriate fr effetive mixing f digester ntent and preventin f sum frmatin; and that K values between and gave satisfatry mixing perfrmane fr nventinal-size digesters. Digester Heating Ambient temperature in Prt Harurt ranges between C and C. T maintain the digester at the design mesphilli temperature f C external heaters are used, where the sludge is pumped at high velity thrugh the tubes, while water irulates at high velity arund the utside f the tubes (Thbanglus et al, ). The irulatin f water prmtes high turbulene n bth sides f the heat transfer surfae and results in higher heat transfer effiients and better heat transfer. Reynlds and Rihards () say the use f an external heater, whih heats the pumped sludge utside the digester, ntrls the prblem f aking assiated with internally heated digesters, sine any sludge aking will ur in the pipes in the heat exhanger. It enhanes de-aking f the pipes, digester maintenane and high heat transfer effiieny. Heater Requirements (i) Required Quantity f Water fr Heating The speifi digester heat requirement is defined as: Mw - mass flw rate f ht water, kg.s - Cw - speifi heat f ht water, J.kg -. C q t w w d M C T T () q t M w () C w T d T (ii) Required urfae Area fr Heat Exhange The heat flw arss the walls f a tube is desribed as IN -(Print), IN -(Online)

14 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember QN - Net heat transfer int the digester. J.s - U - heat transfer effiient, J.m -.s. C QN = UAT () T - temperature differene between digester and inming sludge, C Fr the externally heated digester, A in the abve equatin is the surfae area with whih heat is exhanged with the inming sludge stream t the digester; and U = Uw. Therefre, () A = U QN T T d () A = πrl r - radius f heat exhanger pipe, m l - length f pipe in water bath, m Cst Estimatin The st f an anaerbi digester is estimated as a funtin f an existing digester with similar harateristis. t ahieve adequate estimatin is smewhat diffiult, as there are very few mmerial digesters in peratin. Peter and Timmerhaus () presented the pwer fatr equatin that gives a fairly aurate estimate. () Xd - st f prpsed digester, N X d C Y C. Y - urrent st f existing digester, N C - apaity f existing digester with knwn st C - apaity f prpsed digester This empirial frmulatin nsiders the prie index f the base year f manufature f the digester with knwn st; and the atual apital st f the prpsed digester determined relative t the prie index f the urrent year. The first step is t use the relative prie indies f the respetive years t determine what wuld have been the atual st f the digester with knwn st and apaity in the urrent year. Whitesides () said st indies must be used when basing the apprximated st n ther than urrent pries. He states that the knwn st f the digester must be multiplied by the rati f the st index f the urrent year t that f the base year. This translates mathematially thus: IN -(Print), IN -(Online)

15 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember () C - base st f existing digester, N I - urrent prie index I - base prie index Y C I I When this is related t the pwer fatr equatin, then, the estimated st f the prpsed digester will be: () X C I I C C... Mdels fr Methane and Bigas Prdutin The basi stihimetri equatin () presented by Buswell and Mueller () in Kiely () is used t determine the amunt f methane (CH). C n H a O b a b n a b n a b n H O CO CH () The vlume f bigas prdued is estimated by prediting the vlume f methane gas and applying the equatin (). Cnsidering an rgani matter represented as CHO, suh that n =, a = and b =, then the fllwing hemial relatinship an be established. () CHO + HO CO + CH Knwing that the mleular weights: CHO =, CO =, and CH =, then frm equatin () mle f CHO mles CH kg CHO g g/g/mle =. mles. mles CHO will yield (. x ) =. mles CH. Relying n Avgadr s pstulatin, then mle f CH. m. Therefre,. mles CH. x. IN -(Print), IN -(Online)

16 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember =. m. This shws that kg f the rgani matter wuld yield. m f CH, whih aunts fr the differene in nentratin f the MW as it is digested frm t e. Therefre, the unit f CH generated will be represented as: (a) kg/m f CH prdued =. ( e) Then with a nversin fatr (M =.) f COD t V the equatin bemes (b) Cm =.M ( - e) Cm - atual nentratin f disslved methane gas, kg.m - Vlume f Methane Prdued The weight f gas transferred frm a liquid t a gas regin urs arss a liquid gas interfae, with the interfaial area equal t the rss-setinal area f the digester. Therefre, the rate f diffusin in the gas-liquid ntat system is desribed by the diffusin equatin: (a) dc dt g K L A V L C st C m A integrating Cg K L C st Cm t (b) V dc dt -rate f diffusin, kg.m-.day KL - diffusin effiient, m.day - A - interfaial gas transfer area, m VL - vlume f liquid, m Cst - saturatin nentratin f gas in the liquid, kg.m - Cg - nentratin f methane gas in gas lletr, kg.m - L The saturatin nentratin f the gas is given as: Pm - partial pressure f the methane gas H - Henry s nstant P m Cst () H IN -(Print), IN -(Online)

17 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember Graef and Andrews () said that fr mesphilli digester, Henry s nstant has been fund as. x - ml/ (l/mmhg). Mass f methane gas prdued is () M m = C g xv g And the vlume is () V m M m m Mm - mass f methane gas, kg Vg - vlume f gas lletr, m m - density f methane gas, kg/m Vm - vlume f methane gas prdued, m Perry and Green () give the density f methane as.kg/m... Vlume f bigas prdued Cnsidering bigas mpsitin as % methane and % ther nstituents, then ttal vlume f bigas prdued wuld be: () V t V m Charateristis f Waste Effluent Cnentratin Effluent Vlatile lids Cnentratin This is defined as: () e = eb + R e - effluent V nentratin, mg/l eb -effluent bidegradable substrate nentratin mg/l R Refratry fratin = () Cnentratin f refratry V Cnentratin f influent V IN -(Print), IN -(Online)

18 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember Effluent bidegradable substrate nentratin This is btained as: () eb = ib ( α) where: ib - influent bidegradable substrate nentratin, mg/l - fratinal nversin Perentage tabilizatin The effiieny f the waste stabilizatin system fr bigas generatin has been presented by Viessman and Hammer () as: E where: E - effiieny f remval f bidegradable waste lad. e () IN -(Print), IN -(Online)

19 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember DICUION Validatin f design mdels The mdels develped were used t design the ntinuus digester fr MW in Prt Harurt and simulate its perfrmane ver a range f fratinal nversin f. t. and perentage ttal slids nentratin f t %, using Mirsft Visual Basi Versin.. The simulatin results are presented in Tables t. Digester vlume and ttal slids nentratin Figure shws the relatinship between vlume f digester and ttal slids nentratin. It is haraterized by a linear equatin () an indiatin that any inrease in ttal slids nentratin will result in a rrespnding inrease in vlume f digester. V d =.(T) +. () Vlume f digester, m y =.x +. R² = Thusands Ttal slids nentratin, Figure. Effet f ttal slids n vlume f digester Time f digestin and ttal slids nentratin The relatinship between ttal slids nentratin and time f digestin, Figure, is desribed by the plynmial equatin () f rder, with a rrelatin perentage f.. IN -(Print), IN -(Online)

20 Time f digestin, days Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember.. y = E-x - E-x +. R² =.... Thusands Ttal slids nentratin Figure. Effet f ttal slids nentratin n time f digestin t d = E (T) E T +. () The indiatin is that a gemetri inrease in T nentratin results in an arithmeti derease in the time f digestin. This may be nneted with the multiplied inrease in mirbial nentratin with inreasing T nentratin (Table ); s that MW dempsitin tk less and less time. This rrbrates the reprts f earlier investigatins reprted by Bailey and Ollis, ; and Levenspiel,. Ttal slids nentratin and vlume f gas prdued In Figure, the inrease in T nentratin results in an inrease f the vlumes f bigas and methane prdued. The relatinship is als desribed by a plynmial funtin as in equatins () and () V t = E (T).T +. () V m = E (T).T +. () The similarity in the urves in Figure and the ensuing equatins are indiative f the diret prprtinality relatinship between vlumes f bigas and methane fr the same T nentratin. IN -(Print), IN -(Online)

21 Vlume f gas Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember y = E-x -.x +. R² = Vl f bigas Vl f methane y = E-x -.x +. R² =..... Thusands Ttal slids nentratin, m Figure. Effet f T nentratin n vlumes f bigas and methane Digester vlume and net heat required Figure shws the effet f digester vlume n the net heat required by the digester, desribed by equatin (), whih is a perfet plynmial funtin f rder. Q n =.V +.V +. () It shws that suessive inreases in the net heat required fr inreasing digester vlume is a nstant. Net heat required, J.s - y = -.x +.x +. R² = Vlume f digester, m Figure. Effet f vlume f digester n the net heat required by digester IN -(Print), IN -(Online)

22 Cst f digester, N Millins Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember Digester vlume and st The urve f Figure desribes the variatin f st f digester with its vlume. A pwer funtin expressed by equatin () perfetly fits the relatinship. X d = E + V. () Equatin () shws that a ntinual inrease in the vlume f digester will result in inreasing sts, with delining marginal differene between suessive st amunts. When this is related t Figure, given the relatinship between vlume f digester and T nentratin, it wuld shw that the st f the digester wuld be ptimal fr the maximum T nentratin, usually % (Hbsn et al, ), desired fr lw-slids digesters f whih the CTR is suited. y = E+x. R² = Vlume f digester, m Figure. Variatin f digester st with its vlume Impliatins t Researh and Pratie The develpment f mdels fr the design f a CTR fr anaerbi digestin f MW will ease the nstrutin f different sales f bireatrs fr bth labratry and field peratins. The tedium assiated with the pressing f MW will be drastially redued, thus making MW management relatively easy. The prdutin f bigas will relieve energy demand, espeially fr a develping untry, like Nigeria, with dire energy nstraints. CONCLUION The rises f muniipal slid waste management f Prt Harurt, Nigeria have attained ritial dimensins, suh that a treatment mpnent must neessarily be inrprated int its hierarhy. The treatment methd that wuld ffer ptimal advantage wuld invlve redutin f pllutin lad and nversin f the waste t useful end prdut. The anaerbi ntinuus digester is ne suh faility that wuld press the waste and prdue bigas as an energy sure. The mdels develped in this wrk have shwn the pssibility f develping a CTR IN -(Print), IN -(Online)

23 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember fr varying amunts f ttal slids nentratin and desired fratinal nversin fr the MW type in Prt Harurt, Nigeria. The maximum T nentratin wuld be % fr ease f flw and ptimal digester st relative t vlume f bigas prdued. Future Researh This paper prvides a basis fr the investigatin f the effiay f using the CTR fr MW pressing, in relatin t ther types f reatrs. It wuld als further researh int -digestin f MW and ther rgani substrates, fr ptimum prdutin f bigas. REFERENCE Amerian Publi Health Assiatin (APHA). (). tandard methds fr the examinatin f water and wastewater, th Editin; Greenberg A. E. (Ed). Byrd pringfield, Washingtn D. C. pp Andrews, J. F. (): The develpment f a dynami mdel and ntrl strategies fr the anaerbi digestin press. In James, A (Ed.) Mathematial Mdels in Water Pllutin Cntrl; Jhn Wiley & ns, Chihester. p Bailey, J. E. and Ollis, D.F. (): Bihemial engineering fundamentals; MGraw-Hill Bk Publishers, New Yrk, p. Bailie, R. C., Everett, J. W., Liptak, B. G., Liu, D. H. F., Rugg, F. M. and witzenbaum, M.. (). lid waste, In Envirnmental Engineers Handbk. (Eds) Liu, D. H. F., Liptak, B. G. and Buis, P. A., Lewis Publishers, New Yrk.. Bushwell, A. M. and Mueller, H. F. (). Mehanis f methane fermentatin. Jurnal f Industrial Engineering Chemistry, (),. Byrne, K. (): Envirnmental siene, Thmas Nelsn & ns Ltd, UK. p Ekenfelder, W. W. Jr (). Industrial water pllutin ntrl. MGraw-Hill Higher Eduatin, Bstn Burr Ridge, pp-. Graef,. P. and Andrews, J. F. (). Mathematial mdelling and ntrl f anaerbi digestin, in C. F. Bennett (Ed), Water, Chemial Engineering Prgress ympsium eries, N., Vl., p. Hbsn, P. N., Busfield,. and ummers, R. (). Methane prdutin frm agriultural and dmesti wastes, Applied iene Publishers Ltd., Lndn. p Igni, A. H. (). Design f anaerbi bireatrs fr simulatin f bigas prdutin frm muniipal slid waste. PhD Thesis, Rivers tate University f iene and Tehnlgy, Nigeria. pp Igni, A. H. (a). Analyses f anaerbi bath digestin f muniipal slid waste in the prdutin f bigas using mathematial mdels; Energy and Envirnment Researh; Vl., N. ; pp-. URL: Igni, A. H. (b). Adaptatin f bath experiment data t the design f an anaerbi ntinuus digesters. Agriultural Engineering Internatinal, CIGR Jurnal ():-. Igni, A. H., Abwei, M. F. N., Aytamun, M. J. and Eze, C. L. (). Bi-kinetis f anaerbi digestin f muniipal slid waste. Newviews Engineering Analysis and Mdelling, Vl., N., -. Igni, A. H., Aytamun M. J., Ogaji,. T., & Prbert,. D. (). Muniipal slid waste in Prt Harurt, Nigeria. Applied Energy, (), - IN -(Print), IN -(Online)

24 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember Igni, A. H., Eze, C. L., Aytamun, M. J., and Abwei, M. F. N. (). Ptentials f bigas generatin frm muniipal slid waste in Prt Harurt metrplis. Preedings f the st Annual Cnferene f iene and Tehnlgy Frum, Uy, Nigeria. Vl., N., pp-. Kiely, G. (). Envirnmental engineering, Internatinal Editin, Irwin MGraw-Hill, Bstn. p Levenspiel, O. (). Chemial reatin engineering, ( rd Editin). Jhn Wiley and ns, In; New Yrk. p. Madu, C. and deinde, O. A. (). Relevane f bimass in the sustainable energy develpment in Nigeria. Preedings f the Natinal Engineering Cnferene and Annual General Meeting f the Nigerian iety f Engineers. Pp-. Mnd, J. (). The grwth f baterial ultures. Annual Review f Mirbilgy, Vl. Ogunbiyi, A. (). Lal tehnlgy in slid waste management in Nigeria. Preedings f the Natinal Engineering Cnferene and Annual General Meeting f the Nigerian iety f Engineers. Pp. -. Perry, H. R. and Green, W. D. (): Perry s Chemial Engineering Handbk. th Editin. MGraw-Hill Publishers, New Yrk. P. Peter, M.. and Timmerhaus, K. D. (). Plant design and enmis. MGraw-Hill Bk Cmpany, Tky. P. Reynlds, T. D. and Rihards, P. A. (): Units peratins and presses in envirnmental engineering, end Editin, PW Publishing Cmpany, Bstn. p taffrd, O. A., Hawks, O. L. and Hrtn, R. (). Methane prdutin frm Waste rgani matter, CRC Press In. Lndn. p Thbanglus, G., Burtn, F. L. and tensel, H. D (). Wastewater engineering: Treatment and Reuse. Tata MGraw-Hill Publishing Cmpany Limited, New Delhi. p Viessman, W. (Jr) and Hammer, M. J. (): Water supply and pllutin ntrl. Harper Cllins Cllege Publishers New Yrk, pp-. Walkley, A. and Blak, I. A. (). An examinatin f the Degtjareff methd fr determining sil rgani matter and a prpsed mdifiatin f the hrmi aid titratin methd. il iene. : - Whitesides, R. W. (): Press equipment st estimating by rati and prprtin a PDH nline Curse. p IN -(Print), IN -(Online)

25 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember APPENDIX imulatin results fr the ntinuus digester Table. ummary f CTR Parameters at % T (T =,., V =,.) e Xe t Vd E Vm Vt Vms Qn Xd ,,.,,.,,.,,.,,.,,.,,. Table. ummary f CTR Parameters at % T (T =,., V =,.) e Xe t Vd E Vm Vt Vms Qn Xd ,,.,,.,,.,,.,,.,,.,,. Table. ummary f CTR Parameters at % T (T =,., V =,.) e Xe t Vd E Vm Vt Vms Qn Xd ,.,,. IN -(Print), IN -(Online)

26 Internatinal Jurnal f Energy and Envirnmental Researh Vl., N., pp.-, Nvember ,,.,,.,,.,,.,,. Table. ummary f CTR Parameters at % T (T =,., V =,.) e Xe t Vd E Vm Vt Vms Qn Xd ,,.,,.,,.,,.,,.,,.,,. Table. CTR Results fr Varius Perentage Ttal lids (PT) Cnentratins PT T V Xe td Vd Vm Vt Qn Xd,., ,,.,., ,,.,., ,,.,., ,,. IN -(Print), IN -(Online)