The effect of incomplete mixing upon the performance of a membrane-coupled anaerobic fermentor

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University of Wollongong Reserch Online Fculty of Informtics - Ppers (Archive) Fculty of Engineering nd Informtion Sciences 0 The effect of incomplete mixing upon the performnce of membrne-coupled

, Nelson, M. I. & Kvngh, J. M. (0). The effect of incomplete mixing upon the performnce of membrne-coupled nerobic fermentor. HEMEA 0: Proceedings of the Austrlsin hemicl Engineering onference (pp.

1 University of Wollongong Reserch Online Fculty of Informtics - Ppers (Archive) Fculty of Engineering nd Informtion Sciences 0 The effect of incomplete mixing upon the performnce of membrne-coupled nerobic fermentor Ahmed Hussein Msmli University of Wollongong, msmli@uow.edu.u Mrk I. Nelson University of Wollongong, mnelson@uow.edu.u John M. Kvngh University of Sydney, jkvngh@usyd.edu.u Publiction Detils Msmli, A., Nelson, M. I. & Kvngh, J. M. (0). The effect of incomplete mixing upon the performnce of membrne-coupled nerobic fermentor. HEMEA 0: Proceedings of the Austrlsin hemicl Engineering onference (pp. -). (on USB drive): Engineers Austrli. Reserch Online is the open ccess institutionl repository for the University of Wollongong. For further informtion contct the UOW Librry: reserch-pubs@uow.edu.u

2 The effect of incomplete mixing upon the performnce of membrnecoupled nerobic fermentor Abstrct We consider model to describe the performnce of membrne-coupled nerobic fermentor which ws developed nd clibrted using experimentl by Kim nd hung (00). The model consists of six differentil equtions, modelling the concentrtion of five biochemicl species nd the rte of gsifiction. In the originl work it ws ssumed tht rector is well-mixed. We use two prmeter mixing model to investigte the effect of incomplete mixing upon the performnce of this process. The prmeters in the mixing mode re the size of the stgnnt region nd prmeter controlling the degree of mixing between the regions. Perfect mixing corresponds to the limit in which delt pproches infinity. There re six differentil equtions in ech region. We investigte how the concentrtion of voltile ftty cids in the gitted region depends upon the degree of mixing in the rector nd the size of the stgnnt region. Keywords nerobic, coupled, membrne, fermentor, performnce, effect, upon, mixing, incomplete Disciplines Physicl Sciences nd Mthemtics Publiction Detils Msmli, A., Nelson, M. I. & Kvngh, J. M. (0). The effect of incomplete mixing upon the performnce of membrne-coupled nerobic fermentor. HEMEA 0: Proceedings of the Austrlsin hemicl Engineering onference (pp. -). (on USB drive): Engineers Austrli. This conference pper is vilble t Reserch Online:

3 THE EFFET OF INOMPLETE MIXING UPON THE PERFORMANE OF A MEMBRANE-OUPLED ANAEROBI FERMENTOR Ahmed Hussein Msmli*, Mrk I Nelson, nd John Kvngh. School of Mthemtics nd Sttistics, University of Wollongong, Wollongong, NSW 5 Austrli *Emil: hom8@uowmil.edu.u ABSTRAT. School of hemicl nd Biomoleculr Engineering The University of Sydney, NSW 006. We consider model to describe the performnce of membrne-coupled nerobic fermentor which ws developed nd clibrted using experimentl by Kim nd hung (00). The model consists of six differentil equtions, modelling the concentrtion of five biochemicl species nd the rte of gsifiction. In the originl work it ws ssumed tht rector is well-mixed. We use two prmeter mixing model to investigte the effect of incomplete mixing upon the performnce of this process. The prmeters in the mixing mode re the size of the stgnnt region (ε ) nd prmeter controlling the degree of mixing between the regions (δ ). Perfect mixing corresponds to the limit in which delt pproches infinity. There re six differentil equtions in ech region. We investigte how the concentrtion of voltile ftty cids in the gitted region depends upon the degree of mixing in the rector nd the size of the stgnnt region. INTRODUTION Anerobic fermenttion is routinely used for the tretment of both industril nd municipl wstewter, converting orgnic mtter into methne rich biogs nd smll mount of sludge (Fleming, 00, p.). Although the overll process contins multiple steps in series nd prllel, involving diverse groups of microorgnisms, three stges re recognized s being importnt. In the first stge orgnic prticultes re hydrolysed. In the second stge, the hydrolysis products re converted into voltile ftty cids. In the finl stge the voltile ftty cids re converted into methne nd crbon dioxide (Dinopoulou et l., 988, p. 3). All three process re included in this model. We use mthemticl model for the performnce of microfiltrtion membrnecoupled nerobic fermentor due to Kim nd hung (00). The biochemicl model is described in section (.). Figure shows schemtic digrm of the rector. We extend the model of Kim nd hung to include incomplete mixing. In lb-scle experiments the use of smll rectors ensures tht mixing cn be ssumed to be perfect. However, s the size of the rector increses it becomes incresingly unlikely tht perfect mixing is chieved. In fct it is known to be difficult to mintin complete mixing in industril-scle fermenttion rectors (Fogler, 999; Shuler & Krgi, 00). Incomplete mixing is therefore the rule in such processes. In deed the ssumption of perfect mixing hs been shown to hinder ccurte performnce prediction nd thus hinder the widespred deployment of the process (Fleming 00, p. 4).

The gitted region nd the stgnnt region re both modelled s seprte STRs with mss trnsfer between the two regions. This mixing process is illustrted schemticlly in figure.

4 A. Msmli, M. Nelson, J. Kvngh Figure. Schemtic digrm for the membrne-coupled nerobic fermentor ssuming perfect mixing (Kim nd hung 00). We employ two-prmeter mixing model in which the membrne biorector is split into two comprtments: one representing highly gitted region nd one representing stgnnt region. The gitted region nd the stgnnt region re both modelled s seprte STRs with mss trnsfer between the two regions. This mixing process is illustrted schemticlly in figure. The gittion is the pump nd the production of gs. Figure. Schemtic digrm for the membrne-coupled nerobic fermentor ssuming imperfect mixing. The mixing model prmeters re the vlues for δ nd ε. MODEL EQUATIONS In this section we detil the biochemicl rections, nd provide the model equtions for the cses of perfect mixing nd imperfect mixing. Biochemicl model The biochemicl model consists of four biochemicl rections nd the deth of the bcteri (Kim nd hung, 00). These processes re: Hydrolysis of biodegrdble orgnic solids k α + + Y M + α γ Y ) G. () r ( onversion of soluble orgnic to ftty cids k β + Y M + β Y ) G. () 3 ( onversion of voltile ftty cids to methne k 3 3 EG. (3)

5 A. Msmli, M. Nelson, J. Kvngh Deth of cid-forming bcteri kd M YM + γ mr. (4) The model contins five stte vribles,,,, nd M ). ( 3 r Perfect mixing equtions The model equtions for the cse when the rection is crried out in well-stirred biorector re given below. In ddition to the five stte vribles there is sixth eqution for the rte of gsifiction. Biodegrdble orgnic solids d V Q0 ( Q Q ) FQ Vk + VYM k d M. (5) Dissolved orgnic mterils d V Q( 0 ) + Vα k Vk. (6) Voltile ftty cids d3 V Q( 30 3 ) + Vβ k VEk33. (7) Refrctory orgnic mterils dr V Qr 0 ( Q Q ) r FQ r + Vγ k + Vγ mkd M. (8) Acid-forming bcteri dm V QM 0 ( Q Q ) M + Vβ k VEk33. (9) Gsifiction rte dg V V ( α Y γ ) k + V ( β Y ) k + VEk33. (0) The permete flow Q Q. () Residence-time V. () Q The totl crbon content in the feed is given by (3). T r 0 In the system of equtions (5-0) refers to degrdble solids or polymer orgnic mterils (mg /l), refers to dissolved orgnic mterils (mg /l), 3 refers to voltile ftty cids (VFA) (mg /l), r refers to refrctory orgnic concentrtion (mg /l), E refers to VFAs consumption rtio by ertion, F refers to membrne pssge rtio of, F refers to membrne pssge rtio of r, G refers to gsifiction nd minerliztion rtio (%), M refers to hydrolysis by cid-forming bcteri (mg /l), Q refers to input dischrge (l/h), Q refers to permete flow rte (l/h), V refers to 3

6 A. Msmli, M. Nelson, J. Kvngh biorector volume ( l ), Y yield coefficient from, Y yield coefficient from, Y M yield coefficients from ( M to ), membrne filtrtion rtio, k refers to hydrolysis rte coefficient (/h), k refers to cid-forming rte coefficient (/h), k 3 refers to VFAs consumption rte coefficient (/h), k d refers to self-degrion rte coefficient for cid-forming bcteri (/h), α yield coefficients from ( to from ( to 3 ), γ yield coefficients from ( to ( M to r ). Imperfect mixing equtions ), β yield coefficients r ), nd γ m yield coefficients from The model equtions for n isotherml biochemicl process with perfect mixing cn be written in the generic mnner. dx X0 X + f ( X). (4) n In these equtions X 0 R is the concentrtion of the n biochemicl species in the n rector feed, X R is the concentrtion of the n biochemicl species tht tke prt in the process nd is the residence time. The function f (X ) models the biochemicl rections. A two-prmeter mixing model for this system is given by Fogler (999: hpter 4) In these equtions dx dx X nd b ( 0 X X ) + f ( X ( ε) f ( X b δ( X Xb) ). ( ε) δ( X Xb) ) +. ( ε) (5) (6) X b re the concentrtions of the n biochemicl species in the erted region nd the stgnnt region of the biorector respectively, δ is the mixing prmeter nd ε is the size of the stgnnt region. Prmeter vlues The prmeter vlues used re given in Tble. Tble : Vlues of kinetic nd stoichiometric prmeters (Kim & hung, 00). Prmeter Vlue Unit Prmeter Vlue Unit mg /l Y M mg /l mg /l α mg /l β r0 E γ F γ m F k 0.0 /h M k 0.96 /h 4

7 A. Msmli, M. Nelson, J. Kvngh Y k /h Y k d /h RESULTS hrcterising the performnce of the rector Figure 3 shows the stedy-stte concentrtion of the voltile ftty cids (VFA) s function of the residence time for both n idel nd non-idel rector. The feture of interest in this figure is tht there is vlue of the residence time,, t which the concentrtion of voltile ftty cids is imised,. For the idel (nonidel) rector these vlues re , 4., ( 7 ) nd 8., 3, ( 3, ). We refer to the vlue of s the `imum residence time. In wht follows we sometimes chrcterize the performnce of the rector through the imum crbon rtio ( R ). R is the rtio of the imum crbon content in the voltile ftty cids to the totl inlet crbon ( R 3, / T 0 ). Figure 4 shows how the imum residence time ( ) nd the imum crbon rtio ( R ) depend upon the vlue of the membrne filtrtion rtio () for n idel nd nonidel rector. Figure 3. Stedy-stte digrm showing the concentrtion of voltile ftty cids s function of the residence time. Prmeter vlues: 0., δ ε 0 (idel); δ 0., ε 0. 3(non-idel). Figure 4. shows tht the imum residence time is n incresing function of the membrne filtrtion rtio (). The vlue is lower for the rector with perfect mixing. The difference between the rectors decreses s increses: when we hve 8.9 (perfect mixing) nd 9.9 (imperfect mixing). Figure 4.b shows tht the imum crbon rtio ( R ) increses s the membrne filtrtion rtio ( ) increses. The vlue for the idel rector is slightly higher. However, t its imum extent (when 0 ) the difference is only

A. Msmli, M. Nelson, J. Kvngh Figure 4. [] The imum residence time (h) nd [b] the imum crbon rtio s function of the membrne filtrtion rtio. Prmeter vlues: δ ε 0 (idel); δ 0., ε 0. 3(non-idel).

8 A. Msmli, M. Nelson, J. Kvngh Figure 4. [] The imum residence time (h) nd [b] the imum crbon rtio s function of the membrne filtrtion rtio. Prmeter vlues: δ ε 0 (idel); δ 0., ε 0. 3(non-idel). The limiting cse of ded-volume model Figure 5 shows the stedy-stte digrm for the concentrtion of VFA in the limiting cse of the mixing model in which δ 0. In this cse the mixing model reduces to `ded-volume model (Fogler, 999: hpter 4). The stedy-stte digrm for the perfect mixing rector is lso shown. The importnt feture of this digrm is tht the imum VFA concentrtion is independent of the size of the ded-volume ( ). The vlue of the imum residence time does depend upon the 3, size of the ded volume. The imum residence times re: ( ε 0.0) 304.; ( ε 0.3) ( ε 0.) 337.9; ( ε 0.) 380.5; nd. It follows from eqution (.5), in the cse when δ 0, tht: ( ε 0.0) ε 0.0). ( ε ) ( Figure 5. Stedy-stte digrm showing the concentrtion of voltile ftty cids (mg /l) s function of the residence time (h) for four vlues of stgnnt region. Prmeter vlues: 0.5, δ, ε 0 (idel); 0.5, δ 0.0, ε 0. 0 (non-idel). The effect of the mixing prmeter (δ ) 6

9 A. Msmli, M. Nelson, J. Kvngh In figure 6 we fix the size of the stgnnt region (ε ) nd the vlue of the residence time ( ) nd vry the mixing prmeter (δ ). The cse δ corresponds to perfect mixing whilst the cse δ 0 corresponds to the ded-volume model considered previously. Intuitively we might expect tht the concentrtion of VFA will increse s delt increses from zero to infinity. Figure 6 shows the concentrtion of voltile ftty cids (mg /l) s function of the mixing prmeter (δ ) for four vlues residence time. Prmeter vlues: 0.5, ε 0.3, [], [b] 00, [c] 300, nd [d] 000. In figure 6 (-b,d) we observe tht the performnce of the perfectly mixed rector ( δ ) is superior to the ded volume rector ( δ 0 ). However, the performnce of the rector does not lwys increse with incresing delt. For exmple, in figure 6 () the imum VFA concentrtion ( 7. 3 ) occurs when ( δ 0. 0 ). In 3, figures 6 (b & c) the VFA concentrtion initilly decreses. Thus there is rnge of vlues for the mixing prmeter over which rector with imperfect mixing between the gitted nd stgnnt regions gives lower performnce thn rector with no mixing. In figure 6 (c) the minimum VFA concentrtion occurs when ( δ min 0. 5 ). The VFA concentrtion is only lrger thn the ded-volume vlue ( δ 0) when ( δ > δ cr. 64 ). Figure 6 (c) lso exhibits very unexpected behvior. Nmely the VFA concentrtion in ded-volume rector is superior to tht in ny rector with positive vlue for the mixing prmeter ( δ > 0 ). We cn explin some of this unusul behviour by considering the stedy-stte digrm, for perfect mixing. Figure 7 shows the stedy-stte digrm for the VFA concentrtion in more detil for two cses. 7

10 A. Msmli, M. Nelson, J. Kvngh Figure7. Stedy-stte digrms showing in perfectly mixed rector the concentrtion of voltile ftty cids (mg /l) s function of the residence time (h). Prmeter vlues: 0.5, ε 0.0, δ, 70, 00, 700 3, nd For given residence time the stedy-stte vlue for perfect rector ( δ ) is redoff the stedy-stte digrm. For exmple, when 00 (h) nd 000 (h) we hve (mg /l) nd (mg /l) respectively. When δ 0 the generic model for ny biochemicl process becomes dx X0 X + f ( X), ( ε) where we hve defined n effective residence time X0 X + f ( X), (7) e e ( ε ). (8) If ε 0. 3 nd 00 then the effective residence time is 70. We see from figure 7[] tht 3 ( 70) < 3 ( 00). Therefore in this cse the performnce of the idel rector ( δ ) is better thn tht rector with ded-volume ( δ 0 ). If we tke ε 0. 3 nd 000 then the effective residence time is 700. We see from figure 7[b] tht 3 ( 700) > 3 ( 000). Therefore in this cse the performnce of the idel rector ( δ 000 ) is inferior to tht of rector with ded-volume ( δ 0, ε 0. 3 ). The effect of chnging mixing prmeter (δ ) on the imum residence time nd the imum VFA concentrtion for different vlues of membrne filtrtion rtio Figure 3 shows stedy-stte digrm for the VFA concentrtion s function of the residence time for non-idel rector. We see tht the vlues for 3, nd differ from these in n idel biorector. In figure 8 we show how these quntities vry s the mixing prmeter is incresed from zero. 8

A. Msmli, M. Nelson, J. Kvngh Figure 8 [] The imum residence time (h) nd [b] the imum rtio of VFA concentrtion s function of the membrne filtrtion. Prmeter: ε 0. 3.

11 A. Msmli, M. Nelson, J. Kvngh Figure 8 [] The imum residence time (h) nd [b] the imum rtio of VFA concentrtion s function of the membrne filtrtion. Prmeter: ε Figure 8 [] shows the imum residence time ( ) s function of the mixing prmeter (δ ) nd the membrne filtrtion rtio (). The vlue decreses shrply s the membrne filtrtion rtio is incresed from zero, it quickly reches plteu in which the vlue decreses more grdully s the vlue for () increses. The highest vlue of the imum residence time is locted when there is no mixing. Figure 8 [b] shows the imum VFA concentrtion ( 3, ) s function of the mixing prmeter (δ ) nd the membrne filtrtion rtio (). There is vlue of the mixing prmeter ( δ min ) t which the imum VFA concentrtion is minimised. If the mixing prmeter is in the region ( δ < δ min ) then the imum VFA concentrtion decreses s δ is incresed. If ( δ > δ min ) then the imum VFA concentrtion increses s δ is incresed. As noted erlier we hve δ 0) ( δ ). As the filtrtion rtio () decreses the 3, ( 3, imum VFA concentrtion decreses. We use the vlue of the mixing prmeter ( δ min ) which minimizes the imum VFA concentrtion (figure 8b) to define rector index for the imum VFA concentrtion RI 3, 3, ( δ δ min ) 00. ( δ ) The RI vlue gives the worst possible performnce of rector due to incomplete mixing. Figure 9. The dependence of the rector index (RI) upon the membrne filtrtion (). 9

12 A. Msmli, M. Nelson, J. Kvngh Figure 9 shows the reltionship between the rector-index nd the filtrtion rtio () for three sizes of the stgnnt region (ε ). As the filtrtion rtio () increses the rectorindex increses, nd s the stgnnt region increses the rector-index decreses. Thus, poor mixing is less importnt t high filtrtion rtio. In the cse ( 0, ε 0. 5 ) the minimum crbon content recovered is 90 % of tht recovered in n idel rector. ONLUSION We hve explored the behvior of membrne-coupled nerobic fermentor subject to non-idel mixing. We investigted how the imum VFA concentrtion depends upon the filtrtion rtio nd the mixing prmeters. As the filtrtion rtio increses the imum residence time decreses nd the imum VFA increses. We observed tht s the stgnnt region increses the imum residence time increses nd the imum VFA decreses. We re currently extending the work presented here by considering the effect of incomplete mixing upon the performnce of cscde of nerobic fermentors nd by undertking sensitivity nlysis of the model prmeters. AKNOWLEDGEMENT Ahmed Msmli grteful cknowledges the Sudi government through the wrding of PhD scholrship. We dedicte this pper to the memory of our collegue Dr. Grnt ox (pssed wy Mrch 0). REFERENES Dinopoulou, R.M.S Lester, G nd Lester, J.N 988, Anerobic cidogenesis of complex wstewter: Ii. kinetics of growth, inhibition, nd product formtion, Biotechnology nd Bioengineering, vol. 3, pp Fleming J.G 00, Novel simultion of nerobic digestion using computtionl fluid dynmics, PhD thesis, Mechnicl Engineering, Fculty of North rolin Stte University. Fogler, H.S 999, Elements of hemicl Rection Engineering, Prentice Hll, 3 rd ed. Kim J nd hung J 00. A mthemticl nd empiricl model of the performnce of membrne-coupled nerobic fermentor, Biodegrion, DOI 0.007/s Shuler, M.L nd Krgi, F 00, Bioprocess Engineering Bsic oncepts, Prentice Hll, nd ed. BRIEF BIOGRAPHY OF PRESENTER Ahmed is PhD student in the School of Mthemtics nd Applied Sttistics t the University of Wollongong. In 009 he gined mster degree in pplied mthemtics from UoW. In 005 he gined bchelor degree in mthemtics of eduction with distinction from Jzn University (Sudi Arbi). 0

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses