Novel dispersed plug flow model for UASB reactors focusing on sludgedynamics

1 Sergey Kalyuzhnyi*, Vyacheslav Fedorovich* and Piet Lens**1

*Department of Chemical Enzymology, Chemistry Faculty, Moscow State University, 119899j Moscow, Russia; email:svk@enz.chem..msu.ro! **Sub-Department of Environmental Technology, Wageningen University, 6700 EV Wageningen,

The Netherlands

1 ABSTRACTi

f A new approac.h to model UASB-reactors, referred to as a one-dimensional dispersed plug flow model, wasj developed. This model focuses on the sludge dynamics along the reactor height, based on the balance.. between dispersion, sedimentation and convection using one-dimensional (with regard to reactor height),: equations. A univers~l description of ??th the hydrod~amics and sludge dynamics w~s elaborated by

applYIng known physIcal laws and emplTlcal relations denved from expenmental observations. In addition,! the developed model includes (i) multiple-reaction stoichiometry, (ii) microbial growth kinetics, (iii)j equil~brium chemis~ in the liquid phase, (iv) major solid-liquid-gas interactions, and (v) material balancesI for dIssolved and solid components along the reactor height. The parameters of the integrated model have

been identified with a set of experimental data on the start-up, operation performance, sludge dynamics andsolute intermediate concentration profiles of a UASB reactor treating cheese whey. A sensitivity analysis of

j the model was performed with regard to the key model parameters, which showed that the output of theJ dispersed plug flow model was most influenced by the sludge settleability characteristics and the growth1 properties (especially~) of both protein-degrading bacteria and acetotrophic methanogens.,

KEYWORDS

Dispersion; mathematical model; partial derivatives; plug flow; sedimentation; UASB reactor

\ INTRODUCTION1I;1" The UASB reactor is currently the most popular reactor design for the high rate anaerobic treatment of

industrial wastewater (Franklin, 2001). The heterogeneous sludge distribution along the UASB reactorheight excludes the application of the majority of the numerous mathematical models developed forcompletely mixed anaerobic digestion systems, as these models assume a homogeneous biomass distributionand hydrodynamic pattern within the reactor. The objective of the present work was to develop an integratedmathematical model for the UASB reactor concept, combining sludge dynamics, solid-liquid-gasinteractions and hydrodynamics with biological conversions (multiple reaction stoichiometry, microbialgrowth kinetics) and liquid phase equilibrium chemistry. The integrated model was subsequently fitted toexperimental data on the start-up and operational performance of a UASB reactor treating cheese whey (Yanet al., 1989; Yan et al., 1993). Finally, a sensitivity analysis of the key model parameters was performed.

BRIEF DESCRIPTION OF MODEL DEVELOPMENT

J In the present model, all processes (physical, chemical, microbiological) inside the reactor are considered todepend only on the vertical axis of the reactor (distance z from input, z varies from 0 to H) and time t. Thus,

j all the process characteristics in a fixed reactor cross-section CSz are assumed to be uniform. In general, the

I

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tiY"

space distribution of the concentration of any component N (soluble or suspended) along the reactor height zcan be written on the basis of the dispersed plug flow concept by the following equation:a a a a~N(z, t) = -a;:-[D(z, t) . ~N(z, t)] - ~[W (z, t) . N(z, t)] + r(z, t) - M (z, t) (1)

The first term in the right part ofEq. (1) characterises the degree of mixing by gas-induced dispersion. Thesecond tenD determines a convective transport of component N in the vertical direction. The third and fourthterms are the net biotransformation rate and transfer rate to the gas phase for component N, respectively.

In general, the value of W(z,t) for any component N is determined by the balance between the upwardvelocity W up(z,t) and the apparent settling velocity W s(z,t):

IW(z,t) = W up(z,t) - W s(z,t) (2)

Vertical velocity of sludge aggregates. Under neglecting solid hold-up, the upward velocity can beapproximated to:

VRWup= HRT.CS (3)

The expression for W s(z,t) for sludge solids can be derived from the Stokes law under Re < 2 (the region inwhich VASE reactors usually operate):

2[\fI) . Pag(t) - Pl.].g .dag(t)Ws(z,t) = 18.,,(z,t) (4)

where \VI represents the influence of gas entrapment and attachment on the apparent aggregate density.Though the sludge suspensions in VASE reactors behave like non-Newtonian liquids, they can be referred toas pseudo-Newtonian liquids and several empirical formulas to calculate their viscosity ,,(z,t) are availablein engineering practice (Darton, 1985). In our model, the following formula was used:,,(z,t) ="L exp[A1 E(Z,tf"5] (5)The solid hold up E(Z,t) given in Eq. 5 can be calculated from its physical definition:

( ) VSSIoI (z, t) (6)£ z,t =( ACag ) ( MCag )1-- . 1-- 'p (t)

100 100 ag

Since the aggregate density Pag(t) usually does not vary significantly during an experimental run with onetype of wastewater (Hulshoff Pol, 1989), the aggregate density is assumed to be constant in the currentversion of the model. Additionally, aggregates were assumed to have a spherical form and the same (butvariable with time) diameter dag(t) within the entire reactor (see below). These simplifying assumptions wereintroduced to make the model workable, although it does not reflect completely the reality. The averagegranule diameter was found to have a positive relation with the sludge loading rate and the influentconcentration (Hulshoff Pol, 1989). Both parameters are often related and determine the substratepenetration depth and thus, indirectly the aggregates size. Since it is rather problematic to formalise theobserved dependencies between the average aggregate diameter and the factors mentioned above, a moresimple relation derived from the net sludge growth/decay (Chang and Rittman, 1987) was used in the model:

d[d (t)] d t H{ I( /lj(Z,t)-bj),Xj(Z,t) ] .CS.dz

ag= \fI .~.ll J (7)dt 2 3 VSSR (t)

Dispersion of sludge aggregates. A formulation for D(z,t) in the blanket zone of VASE reactors wasproposed (Narnoli and Mehrotra, 1997) on the basis of the so-called diffusion concept:

D(z,t) = A2.[q(z, t) .(1- exP(-~) ] 2 (8)

, q(z, t)This expression has been found to be valid on the basis of experimental observations available in literatureabout solids concentrations in the sludge blanket zone of VASE reactors. It should be noted that Eq. (8) is

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I similar to several expressions proposed earlier for the calculation of the dispersion coefficients in three-phase fluidised beds reactors (Darton, 1985). In all these formulations, the value of D(z,t) is highly

: dependent on the surface gas production q(z,t). In our model, Eq. (8) was used to describe the dispersion ofsolids throughout the reactor height.

(i Soluble components. For fluidised bed systems, the formula for the calculation of the dispersion coefficients1 D(z,t) of solutes was shown to be not principally different from the dispersion coefficients of the suspended

~ solids (Darton, 1985) due to the physical link between solids and liquid dispersion. Therefore, Eq. (8) wasused in the model for the description of solute dispersion coefficients throughout the reactor height. Due tothe negligible settling velocity of solutes, the upward velocity Wup (Eq. 3) exclusively determines theirvertical velocity.

Gaseous components. Although anaerobic reactors have a gas hold up, it is usually relatively low, e.g.,; varying between 0.01-0.05 of the reactor volume depending on the surface gas production (Buffiere et al.,I 1998). To avoid an excessive intricacy, the gas hold up is neglected in the current version of the model,

~ except for its influence on the apparent density of sludge aggregates (parameter 'VI, see Eq. 4). The gaseousj components (methane, hydrogen carbon dioxide and ammonia) are treated in the model as solutes withI taking into account their transfer to the gas phase, which is considered as an ideally mixed medium. Studies

on bubble columns have shown that the mass transfer coefficient kLa mainly depends on the surface gasproduction q(z,t) and various formulations have been proposed (Darton, 1985; Zhukova, 1991) for the

j description of this dependency. The following formula was used in the present model to describe the mass-J transfer coefficients of components from the liquid to gas phase (Zhukova, 1991):

i kLa(z,t) = ~. [~] A' (9)

J As

1 Biotransformation kinetics. The present model simulates the anaerobic treatment of soluble organicwastewater, which can be represented by a three-step process: acidogenesis, acetogenesis andmethanogenesis. Each of these steps is carried out by separate groups of bacteria. The kinetic description ofbiotransformations was adapted from our previous model (Kalyuzhnyi and Fedorovich, 1998)

RESULTS AND DISCUSSION

The parameters of the integrated model have been identified with a set of experimental data on the start-up,operation performance, sludge dynamics and solute intermediate concentration profiles of a UASB reactor.treating cheese whey (Yan et al., 1989; 1993). The results of superimposing experimental data and model

I predictions are presented in Figs. 1-4. In general, the predictions agree with the experimen~all,>: recorde~ data1 during the start-up period (Fig. 1) as well as with the reported steady-state performance Indicators (FIg. 2), and sludge characteristics (Fig. 3) under the various OLR applied. The model overestimates the effluent VSS! during the start-up period (Fig. 1 b) and a cumulative VSS washout during the first 4 OLR applied (Fig. 3b).1 However, a satisfactory agreement between the simulations and the experimental observations was obtained1 for the total quantity ofVSS in the reactor (Fig. 3~). On ~he other hand, the model under~stimates the steady-I state effluent COD during the last 3 OLR applIed (FIg. 2a) and as a result overestImates the methane)1 production in the same periods (Fig. 2b). These discrepancies can be mainly attributed to a simplified

description of the VSS dynamics and, consequently, not quite accurate description of sludge transport along~ the reactor height in the dispersed plug flow model.j~j Satisfactory agreement between model and experiment has also been obtained for the COD- and pH profile

along the reactor height (Fig. 4). The major discrepancies were found at the OLR of 7.62 g COD/dm3/day for1 both pH- and COD-profiles (Figs. 4b and d), namely, a prolonged plug-flow region was experimentally~ observed in the bottom of the sludge bed whereas the model predicts this region as more n~ow. The reasonj might be related. to the i~adequate description of .dispersion at the reactor bottom, I.e., the model1 overestimates dunng last penod the surface gas productIon..

1 125

~ 100 1 6~ ..,. - Modelg ~ ~ ~ e.- 75 ~ 12 .

- -. .u ~

-6 50 .::. 0 8 b~ ~ Experiment ~.Q 25 - Model ~ 0.48 0 > 0

0 5 10 15 20 25 30 0 5 10 15 20 25 30Time, days Time, days

Fig. 1. Model versus experiment during start-up period for (a) total COD removal and (b) effluent VSS.

~.., ~ 3e 0.5 ~ 2 5~ .., .

~ 0.4 a e 2 b~

= 0.3 -. 1 5.. .., .

§ 0.2 .§ 1U 0.1 ~ 0.5

0 0 00.91 1.99 3.54 5.76 7.62 0.91 1.99 3.54 5.76 7.62

OLR, g COD/dm3/day OLR, g COD/dm3/day IFig. 2. Model versus experiment during operation under steady-state conditions: (a) effluent COD; (b) C~

production.~~ 200 "' 50

"' r/j.s 150 a ~ 40C,j - 30~ 100 g 20

I

.: 50 ~ 10~ 0 ~ 0> Start 0.91 1.99 3.54 5.76 7.62 0.91 1.99 3.54 5.76 7.62

OLR, g COD/dm3/day OLR, g COD/dm3/day

Fig. 3. Model versus experiment: (a) total VSS in reactor at the end of each the OLR applied; (b) integralVSS wash-out during each period.

Considering the big number of variable model parameters (in total 33) and the rather arbitrary fixation of theseed sludge characteristics (in total 5), one can expect significant difficulties in the parameter identification.So, it was of primary importance to investigate the model sensitivity to these parameters. A sensitivityanalysis of the model was performed with regard to the seed sludge characteristics and the key modelparameters. The sensitivity analysis showed that the output of the dispersed plug flow model was mostinfluenced by the sludge settleability characteristics and the growth properties (especially ~m) of bothprotein-degrading bacteria and acetotrophic methanogens (data not shown).

The developed model allows to derive additional information about the UASB reactor investigated. As anexample, Fig. 5 presents the calculated concentration profiles of the total VSS and the aceticlasticmethanogens (the most important bacteria in the system) along the reactor height at the end of each the OLRapplied. Fig. 5a clearly shows that the height of the high-density sludge zone (sludge bed) variessignificantly under the various operational regimes applied. Namely, this height significantly decreasedduring the first two periods of operation due to increased sludge wash out during this period (Fig. 3b).However, continuous improvement of the settling characteristics of the remaining sludge led to a gradualincrease of the sludge bed height followed by a substantial elevation of VSS concentration in this zone (Fig.5a). Interestingly, at a 10w'OLR of 1.91 g COD/dm3/day, there is a sharp distinction between the sludge bed(high and constant solid concentration) and the sludge blanket (lower and gradually decreasing solidconcentration). This sharp distinction disappears during the subsequent increases of the OLR (Fig. 5a). Thus,

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due to the continuous description of sludge dynamics along the reactor height, the dispersed plug-flowmodel is able to predict the position as well as the granular sludge concentration gradient at the boundarybetween the sludge bed and blanket zones in a VASE reactor. According to our knowledge, none of thepreviously reported models of VASE reactors possess this ability without any arbitrarily division of thereactor volume into different zones with postulated mixing regimes. It should also be noted that thatsubsequent increases of the OLR led to a significant enrichment of the sludge by aceticlastic methanogens(Fig. 5b), which agrees with many other experimental observations. However, the model also predicts thateven a sludge substantially enriched by aceticlastic methanogens (e.g., at the end of experiment) can notcope with a heavy overloading of the reactor, as indicated by a simulation where the OLR was doubled incomparison with the OLR applied during the last period (data not shown). In the latter case, the reactorfailed because the VF A production exceeded the assimilative methanogenic capacity of the sludge.

7 ::a Co 5 b

3 3

0 3.5 7 10.5 14 0 3.5 7 10.5 14Reactor height, dm Reactor height, dm

,; .., 15 .., 15leef ~ 10 t 10 di", C ~

Q 5 Q 50 0u 0 u 0

0 3.5 7 10.5 14 0 3.5 7 10.5 14Reactor height, dm Reactor height, dm

Fig. 4. Model versus experiment for the pH (a-b) and COD (c-d) profiles along the reactor height after anIoperating period of3 HRTs at an OLR (g COD/dm3/day) of (a,c) 5.76 and (b,d) 7.82 (points - experimental

data; lines - model).

.., ..,E 45 e 15~ 0.91 ~ 0.91 I"' 30 a 1.99 ~ 10 b 1.99~ 3.54 ~ 3.54> 15 - - - 5.76 >- 5 - - - 5.76'3 7.62 ~ 7.62= 0 0~

0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14Reactor height, dm Reactor height, dm

Fig. 5. Model simulations of the concentration profiles of (a) total vSS and (b) aceticlastic methanogensalong the reactor height at the end of each OLR applied (figures on the plots refer to the applied OLR,expressed in g COD/dm3/day).

CONCLUSIONS

This paper presented a newly developed dispersed plug flow model of VASE reactors based on thecombination of sludge dynamics and bacterial metabolism. According to our knowledge, this is the firstsuccessful attempt in the creation of models of a new generation which are able to simulate complex spaceheterogeneous dynamics, not only of solutes but also of the granular sludge (e.g., immanent formation and

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development of sludge bed and blanket zones, sludge wash-out) inside VASE reactors. The second princildifference of the presented model with the models of VASE reactors proposed before is that it givesuniversal description of both hydrodynamics and solids dynamics by continuous equations throughout treactor volume. The third prominent feature of the dispersed plug flow model is that it relies solely 4internal mechanisms of the bioprocesses to predict sludge washout from the reactor. This feature is a distinadvantage over the world-wide used approach to model anaerobic reactors with a fixed sludge retenti<time. The latter was routinely transferred from the activated sludge reactor models but can no longer 1valid, at least, for the description of high-rate anaerobic reactors because of the principal differences betwe(these treatment systems. The above-mentioned abilities of the described dispersed plug flow model malthis type of mathematical models a powerful tool for the design and control ofUASB reactors.

Despite its conceptual advantages over the models proposed thus far, the described model also used somassumptions and empirical equations, which have to be further fine-tuned. It should, nevertheless, be notethat so far no alternative mathematical expressions are available for the empirical relations adopted in thpresent paper to describe the time dependency of the average aggregate diameter and sludge density. Furtheresearch to derive these relations is required to fine-tune the developed mathematical model. The parametesensitivity analysis showed that the growth properties of protein-degrading bacteria and acetotrophilmethanogens (especially ~m) as well as the sludge settleability characteristics are the parameters, whiclinfluence an VASE reactor most. The kinetic properties of the bacteria involved in anaerobic digestion havcreceived extensive attention in the literature. In contrast, internal sludge dynamics in VASE reactors hav(been studied scarcely, which hampers further comprehensive validation, justification and development ofth(dispersed plug flow model. Therefore, further elucidation of internal mechanisms of the functioning ojVASE reactors, which allow to upgrade the present model, requires new comprehensive experimentalstudies including both traditionally measured "black box" characteristics (overall reactor performance, gasproduction etc.), supplemented with detailed documentation of the profiles of COD, VFA, VSS, specificmetabolic activity, aggregate diameter and density along the reactor height.

REFERENCES

Buffiere P., Fonade C. and Moletta R. (1998). Mixing and phase hold-ups variations due to gasproduction in anaerobic fluidized-bed digesters: influence on reactor performance. Biotechnol. Bioeng., 60,36-43.

Chang H.T. and Rittman B.E. Mathematical modeling ofbiofilm on activated carbon. (1987). Environ.Sci. Technol., 21, 273-280.

Darton R.C. (1985). The physical behaviour of three-phase fluidized beds. In: Fluidization, J.F.Davidson, R. Clift, and D. Harrison (eds.), 2nd edn, Academic Press, London, New York, pp. 495-525.

Franklin R.J. (2001). Full scale experiences with anaerobic treatment of industrial wastewater. In:Anaerobic digestion for sustainable development. Papers of the farewell seminar of prof Gatze Lettinga, J.van Lier and M. Lexmond (eds.), Wageningen, the Netherlands, pp.2-8.

Hulshoff Pol L.W. (1989). The phenomenon of granulation of anaerobic sludge. Ph.D. thesis,Wageningen Agricultural University, The Netherlands.

Kalyuzhnyi S. V .and Fedorovich V. V. (1998). Mathematical modelling of competition betweensulphate reduction and methanogenesis in anaerobic reactors. Biores. Technol. 65,227-242.

Narnoli S.K. and Mehrotra I. (1997). Sludge blanket of VASE reactor: mathematical simulation. Wat.Res., 31,715-726.

Yan J.Q.; Lo K.V. and Liao P.H. (1989). Anaerobic digestion of cheese whey using up-flow anaerobicsludge blanket reactor. Bioi. Wastes, 27, 289-305.

Yan J.Q., Lo K.V. and Pinder K.L. (1993). Instability caused by high strength of cheese whey in aVASE reactor. Biotechnol. Bioeng., 41,700-706.

Zhukova, T.B. (1991). Investigation and modeling of bubble column reactors. ftogi Nauki i Tekhniki,Ser. Processes and Apparatuses of Chemical Technology, v. 18, VINITI Press: Moscow.

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