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Gas-lift digester configuration effects on mixingeffectiveness

Khursheed Karima,�, Gregory J. Thomaa, Muthanna H. Al-Dahhanb

aRalph E. Martin Department of Chemical Engineering, University of Arkansas, 3202 Bell Engineering Center, Fayetteville, AR 72701, USAbDepartment of Energy Environmental and Chemical Engineering, Washington University, Saint Louis, MO 63130, USA

a r t i c l e i n f o

Article history:

Received 30 September 2006

Received in revised form

20 March 2007

Accepted 30 March 2007

Available online 13 June 2007

Keywords:

Baffle

Digester

Draft tube

Gas-lift

Mixing

nt matter & 2007 Elsevie.2007.03.042

thor. Tel.: +1 479 5752484;kkarim@uark.edu (K. Kar

a b s t r a c t

Computational fluid dynamics simulations were used to study the effect of bottom

configuration and a hanging baffle on the mixing inside a gas-lift digester filled with non-

Newtonian sludge. The Navier–Stokes and continuity equations were solved numerically

using commercially available finite element method-based solver. The results from this

simulation were found to be in good agreement with previously reported experimental

findings. At a gas recirculation rate of 84.96 l/h, the poorly mixed zones inside a flat bottom

digester were about 33.6% of the digester volume, while in the case of digesters with 251

and 451 conical bottoms poorly mixed zones were about 31.9% and 29.6%, respectively.

The power law viscosity index, n, did not have a significant effect on the mixing pattern

under the conditions studied. Introduction of a hanging baffle in combination with a 451

hopper bottom resulted in reduction of the poorly mixed zone by a factor of three

compared to a flat bottom without baffle configuration. Although the introduction of

a hanging baffle was able to significantly reduce the size of the poorly mixed zones

inside a gas-lift digester, further optimization of the digester geometry may lead to

additional improvements.

& 2007 Elsevier Ltd. All rights reserved.

1. Introduction

The fact of limited fossil fuel resources, coupled with the

concern of increasing environmental pollution due to the use

of fossil fuels, has led to the exploration of renewable energy

sources. Biomass is a large and geographically widespread

renewable energy resource, which includes animal wastes

(from cattle, poultry and hog farms), crop/agricultural resi-

dues (e.g. bagasse from sugarcane, corn fiber, rice straw and

hulls, and nutshells), wood, wood waste (e.g. sawdust, timber

slash, and mill scrap), municipal waste, etc. Anaerobic

digestion of biomass (animal wastes, crop/agricultural resi-

dues, municipal sludge, etc.) using microorganisms is an

effective means of generating methane rich biogas—a poten-

tial source of energy. Anaerobic digestion technology for

r Ltd. All rights reserved.

fax: +1 479 5757926.im).

methane production from biomass has been known since the

17th century and has been used in the USA since the 1970s.

However, the failure rate for anaerobic digesters is still very

high (Lusk, 1998). These failures are believed to be mainly due

to poor design, construction, operation, as well as inadequate

mixing. Digester mixing is needed to break scum, to prevent

stratification, and to homogenize the contents of digesters

(substrate and microorganisms, temperature, and pH). Mixing

of an anaerobic digester can be accomplished by mechanical

mixers, biogas recirculation, or by slurry recirculation.

Digesters mixed by biogas recirculation, known as gas-lift

digesters, are becoming popular and many successful studies

have been reported in the literature (Morgan and Neuspiel,

1958; Kontandt and Roediger, 1977; Lee et al., 1995; Reinhold

and Markl, 1997; Karim et al., 2005; Borole et al., 2006).

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Gas inlet pipe

(0.64 cm internal diameter)

Sealing

Gas Recirculation

29.5

cm

22.2

cm

Sludge level

4.4 cm

14 c

m

Draft tube

Hangers

20.32 cm

4 c

m

3.25 cm plane

18.57 cm plane

Bottom

Computational Geometry

Axis of symmetry

4.4 cm

14 c

m4 c

m 4.4 cm

14 c

m4 c

m

Hanging baffle

configuration

θ

Fig. 1 – Bench-scale 8-in flat bottom digester. The figure on the right shows the computational geometry used for the 2D axial

symmetric CFD simulations.

-0.01

0

0.01

0.02

0.03

0.04

0 0.02 0.04 0.06 0.08 0.1 0.12

Radius (m)

Axia

l V

elo

city (

m/s

)

Grid size 2mm

Grid size 1mm

Grid size 0.5mm

Grid size 2mm

Grid size 1mm

Grid size 0.5mm

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 0.02 0.04 0.06 0.08 0.1 0.12

Radius (m)

Axia

l V

elo

city (

m/s

)

Fig. 2 – Axial velocity profile for 28.32 l/h gas recirculation

rate at (A) 3.25 cm and (B) 18.75 cm above the digester

bottom for the mesh sizes of 2, 1, and 0.5 mm.

WAT E R R E S E A R C H 4 1 ( 2 0 0 7 ) 3 0 5 1 – 3 0 6 03052

In a gas-lift reactor many parameters can influence the

mixing efficacy, including biogas recycling rate, bottom

clearance of the draft tube, slope of the hopper bottom, draft

tube to tank diameter ratio, position of the biogas injection

(sparger) and its design, solids loading rate, etc. (Couvert

et al., 1999; Kojima et al., 1999). The importance of mixing in

achieving efficient biogas production has been noted by many

researchers (Casey, 1986; Lee et al., 1995; Smith et al., 1996).

However, no information is available in the literature about

the optimum mixing intensity and duration other than a

power input of 0.2–0.3 HP/1000 cu ft (5.26–7.91 W/m3), which

has been empirically recommended by the EPA for proper

digester mixing (US EPA, 1979).

Recently an effort was made by Karim et al. (2004) to

characterize the mixing inside a gas-lift flat bottom digester

containing mixed primary and secondary sludge, using

non-invasive flow-sensing techniques, computer automated

radioactive particle tracking (CARPT) and computed tomo-

graphy (CT). The flat bottom configuration was found to

have solids deposition at the bottom close to the digester

wall. The study further revealed that the unmixed zones

(i.e., the regions in the digester relatively isolated from the

main recirculation pattern through the draft tube) could not

be reduced significantly even after increasing the gas

recirculation rate from 28.32 to 84.96 l/h. Most of the released

gas through a single-point sparger was confined inside the

draft tube, and there was almost no gas hold-up in the

annular section. To identify an optimal digester configuration

with improved mixing (reduction in separated recirculation

zones) more experiments need to be performed. Since the

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WAT E R R E S E A R C H 41 (2007) 3051– 3060 3053

experimentation with the non-invasive techniques, CARPT

and CT (Karim et al., 2004), is time consuming and costly,

computational fluid dynamics (CFD) simulations can be used

as an alternative approach for digester configuration optimi-

zation. However, CFD simulations need to be validated

against experimental findings before they can be implemen-

ted with confidence. In one of such effort Vesvikar et al. (2005)

performed CFD simulations for an air–water system and

compared their results with the experimental findings of

Karim et al. (2004). The simulated flow pattern inside the

reactor agreed reasonably well with the experimental ob-

servation; however, the simulated velocity data did not match

with the experimentally observed velocity results. One of the

possible reasons behind this finding could be the fact that

Vesvikar et al. (2005) did not consider the non-Newtonian

characteristics of the digester slurry.

The present paper is focused on simulating the mixing of a

non-Newtonian fluid (sludge) in the bench-scale gas-lift

digester reported by Karim et al. (2004) using CFD. Although

non-ideal properties of sludge were considered in the present

exercise, some simplification of the problem was made based

-0.04

-0.02

0

0.02

0.04

0.06

0 0.02 0.04

Axia

l V

elo

city (

m/s

)A

xia

l V

elo

city (

m/s

)A

xia

l V

elo

city (

m/s

)

E

-0.08

-0.04

0

0.04

0.08

0.12

0.16

0 0.02 0.04

Radial

-0.02

0

0.02

0.04

0.06

0.08

0 0.02 0.04

Fig. 3 – Plot showing comparison of computed and experimenta

gas recirculation rates at 3.25 cm above the digester bottom. Th

on earlier findings. Karim et al. (2004) experimentally

observed that most of the released gas was confined inside

the draft tube, and there was almost no gas hold-up in the

annular section. Based on this observation, the mixing

pattern inside the gas-lift digester was simulated as a single

phase using an inlet velocity at the top of the draft tube as a

boundary condition. The paper reports the comparison of the

CFD simulation results with the experimental findings of

Karim et al. (2004), and discusses the effect of gas recircula-

tion rate, reactor bottom configuration, and a hanging baffle

on the flow pattern inside the gas-lift digester.

2. Digester geometry

The geometry of the digester used for the CFD simulations

was same as the one reported by Karim et al. (2004), which is

reproduced with some modification in Fig. 1. As shown in the

figure, the digester consisted of a 20.32-cm (8-in) diameter

cylindrical tank with a flat bottom, and was equipped with an

axial draft tube (4.4 cm internal diameter). For all simulations

0.06 0.08 0.1 0.12

CFD

xperimental (Karim et al.,2004)

CFD

Experimental (Karim et al.,2004)

CFD

Experimental (Karim et al.,2004)

0.06 0.08 0.1 0.12

Position (m)

0.06 0.08 0.1 0.12

l axial velocity profiles for (A) 28.32, (B) 56.64 and (C) 84.96 l/h

e draft tube has a radius of 2.2 cm.

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the draft tube inlet was located 4 cm above the bottom of the

digester. The gas was sparged in the draft tube through a

small tube (0.5 cm inner diameter, 0.65 cm outer diameter)

positioned in the center of the draft tube. Initially the

mixing pattern inside the digester was simulated for three

different gas flow rates (Qg) of 28.32, 56.64, and 84.96 l/h (1, 2

and 3 ft3/h). The corresponding superficial gas velocities

inside the draft tube were 0.51, 1.02, and 1.55 cm/s, which is

equivalent to superficial gas velocities of 0.02, 0.05, and

0.07 cm/s with respect to the tank cross section. The simula-

tions were performed to evaluate the effects of digester

bottom configurations (flat, 251 and 451 hopper) and a hanging

baffle on the mixing pattern and dead zones distribution.

3. Mathematical model

Digester sludges are generally considered to have non-New-

tonian properties (Seyssiecq et al., 2003). Therefore, for the

modeling purpose the liquid inside the digester (digestant)

was assumed to have power law viscosity for pseudoplastic

-0.08

-0.04

0

0.04

0.08

0.12

0.16

0.2

0 0.02 0.04Axia

l V

elo

city (

m/s

)

-0.08

-0.04

0

0.04

0.08

0.12

0.16

0.2

Axia

l V

elo

city (

m/s

)

-0.08

-0.12

-0.04

0

0.04

0.08

0.12

0.16

0.2

Axia

l V

elo

city (

m/s

)

0 0.02 0.04

0 0.02 0.04

Radia

Fig. 4 – Plot showing comparison of computed and experimental

gas recirculation rate at 18.75 cm above the digester bottom. Th

and dilatant conditions with constant density close to that of

water. Solutions for the flow field in the digester were sought

for non-Newtonian fluid using the incompressible Navier–

Stokes application mode in Comsols 3.2, a commercial finite

element package. The instantaneous transport equations of

mass and momentum conservation can be written as follows:

r � u ¼ 0, (1)

rquqt�r � Zðruþ ðruÞTÞ þ rðu � rÞuþrp ¼ F, (2)

where Z denotes the dynamic viscosity (M L�1 T�1), u the

velocity vector (LT�1), r the density of the fluid (M L�3), p

the pressure (M L�1 T�2) and F is a body force term (M L�2 T�2).

The expression for the viscosity can be selected from the

power law model according to Eq. (3).

t ¼ m0kgn, (3)

where s is the shear stress, m0 is a constant viscosity, g is the

corresponding shear rate, k is the consistency and n is the

power index. For n ¼ 1, the power law reduces to Newtonian

form. For no1, the power law describes pseudoplastic, or

0.06 0.08 0.1 0.12

CFD

Experimental (Karim et al., 2004)

CFD

Experimental (Karim et al., 2004)

CFD

Experimental (Karim et al., 2004)

0.06 0.08 0.1 0.12

0.06 0.08 0.1 0.12

l Position (m)

axial velocity profiles for (A) 28.32, (B) 56.64, and (C) 84.96 l/h

e draft tube has a radius of 2.2 cm.

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WAT E R R E S E A R C H 41 (2007) 3051– 3060 3055

shear thinning behavior, and for n41, dilatant or shear

thickening behavior is described.

Karim et al. (2004) experimentally observed that most of the

released gas was confined inside the draft tube, and there was

almost no gas hold-up in the annular section. Therefore, in

the present study the mixing pattern inside the gas-lift

digester, but outside the draft tube, was simulated as a single

phase, and the liquid velocity at the top of the draft tube was

used as a boundary condition. The flow inside the draft tube

was assumed to be at steady state. The liquid recirculation

velocity through the draft tube was calculated from a

correlation (Eq. (4)) reported by Kojima et al. (1999). As per

the correlation the liquid recirculation velocity through a

short draft tube,

U ¼ 0:401� vg �DT

DiD

!224

35

0:564

�ðD2

T �Do2D Þ

Di2D

" #�0:182

, (4)

where U denotes the liquid recirculation velocity (m/s)

through the draft tube, vg denotes the superficial gas velocity

with respect to tank diameter (m/s), DT is tank diameter (mm),

DiD is the inner diameter (mm), and Do

D is the outer diameter of

the draft tube (mm).

4. Properties of fluid/digestant and boundaryconditions

Understanding of the rheological properties of sludge is not

only important in the design of pumping and piping facilities

Fig. 5 – Plot showing (A) experimental velocity filed (reproduced

84.96 l/h gas recirculation rate. The draft tube has a radius of 2.

but also critical for controlling treatment processes like

digester mixing. However, this important property has not

received the deserved attention until recently, mainly due to

the difficulties associated with the measurement of viscosity

of biological sludges. Animal waste slurries or municipal

waste sludge is a biological suspension of particles having

irregular shapes and various sizes that change with time and

with environmental conditions. Dilute slurry may have

rheological properties very close to water (Newtonian beha-

vior); however, with increasing solids concentration, it

exhibits non-Newtonian flow character.

Since the results of this simulation are compared with the

experimental findings of Karim et al. (2004), it would have

been best to use their reported fluid properties. Unfortunately,

the rheological properties of the fluid used in that study were

not measured. Therefore, the fluid properties used in the

present simulations were taken to be similar to those of

sewage sludges, as described by James and Jayaranaiwachira

(2000). In the case of pseudoplastic conditions r, m0, k, and n

were assumed to have values as 1005 kg/m3, 1 Pa s, 0.009, and

0.8, respectively. For dilatant conditions r, m0, k, and n were

assumed to have values of 1100 kg/m3, 1 Pa s, 0.008, and 1.2,

respectively.

Simulations were solved for a 2D axially symmetric reactor

with a uniform upward velocity given by Eq. (4) at the top of

the draft tube, no slip at all walls, and a neutral condition at

the bottom of the draft tube. The neutral condition is defined

by a vanishing total stress tensor, which models the fluid

behavior as if there were no boundaries present at that

surface.

from Karim et al., 2004) and (B) computed velocity field for

2 cm.

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5. Results and discussion

5.1. Mesh independence of the solution

To show the mesh independence of the numerical solution,

axial velocity profiles at 3.25 and 18.75 cm above the tank

Fig. 6 – Velocity field for 251 and 451 conical bottom digesters (A

baffle.

bottom for 28.32 l/h gas recirculation rate for three different

global mesh sizes of 2, 1, and 0.5 mm are shown in Fig. 2. The

smallest mesh size of 0.5 mm resulted in 1,454,133 degrees of

freedom, which required 38 h runtime on a 16 GB RAM UNIX

server. A mesh size of 0.25 mm in the inlet region was also

tested, but the simulation could not converge due to memory

constraints. Although reasonable overall grid independence

and B) without hanging baffle and (C and D) with hanging

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WAT E R R E S E A R C H 41 (2007) 3051– 3060 3057

was achieved at 0.5 mm grid size, slight grid dependence was

observed just below the draft tube (at the radial positions less

than 0.015m, Fig. 2A), and above the draft tube close to the

digester wall (at 0.09 m radial position, Fig. 2B). As mentioned

earlier the draft tube had an internal radius of 0.022m, and was

positioned 0.04 m above the digester bottom. Nonetheless, the

simulated velocity profiles were observed to be consistent with

the CARPT data as shown in Fig. 3. Since the purpose of this

study was to evaluate the effect of digester geometry on the

flow field outside the draft tube, which was observed to be

consistent across the mesh sizes tested, the remaining

simulations were solved with a mesh having a maximum

element size of 1 mm. A comparison of the simulation results

with experimental data is reported in the following section.

5.2. Effect of gas recirculation rates

The effect of three different gas recirculation rates of 28.32,

56.64 and 84.96 l/h on the axial velocity profile as a function of

radial position at 3.25 and 18.75 cm above the digester bottom

(i.e., 0.75 cm below and above the draft tube) is shown in

Figs. 3 and 4. Fig. 4 shows a positive velocity above the draft

tube region and a negative velocity close to the wall of the

digester. Negative velocity indicates that the flow direction

near the digester tank wall was downward. The magnitude of

the upward and downward velocities increased with increas-

ing gas flow rates although the flow pattern was not

significantly affected. Specifically the recirculation patterns

Fig. 7 – Velocity contours and streamlines for the flat bottom geo

Numerical values on the figure show velocity in m/s. The shade

and apparent degree of mixing was not noticeably changed.

The computed magnitude of the velocity in the region outside

the draft tube was very close to the experimental data of

Karim et al. (2004), as shown in Figs. 3 and 4. This confirms

the validity of the results obtained using the simplifications

discussed earlier, and in particular the estimation of the draft

tube velocity using Eq. (4). Fig. 5 presents a comparison of the

experimentally observed velocity field (Fig. 5A, reproduced

from Karim et al., 2004) with the computed velocity field

(Fig. 5B). The experimentally observed overall flow pattern

was clearly reproduced through the simulation. Both plots

show a large zone at the bottom where there is poor mixing of

the reactor contents as indicated by very low velocities.

5.3. Effect of bottom configuration

Conical bottoms have been found to be effective in improving

mixing effectiveness (Choi et al., 1996). In the present study

the effect of two conical bottom configurations, with 251 and

451 cone angles were simulated. In order to maintain the

same design HRT, the height of the digester was increased to

offset the loss in volume associated with the conical bottom.

The draft tube position and length were not changed. The

velocity fields, for a pseudoplastic sludge material are shown

in Figs. 6A and B. The figures demonstrate that the conical

bottoms resulted in only slight improvement (up to 4%

reduction in poorly mixed zone, as explained under the last

subsection) in the mixing compared to the flat bottom

metry (A) without hanging baffle and (B) with hanging baffle.

d area is the area considered to be poorly mixed.

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WAT E R R E S E A R C H 4 1 ( 2 0 0 7 ) 3 0 5 1 – 3 0 6 03058

configuration. A lack of sensitivity to conical bottoms was

also observed while considering the digestant as a dilatant

fluid, and thus the flow fields for dilatant case are not

presented in this paper.

5.4. Effect of hanging baffle

Since the change in the bottom configuration of the digester

had only limited effect in improving mixing, we chose to

evaluate the inclusion of an inclined baffle hanged from the

digester’s roof (referred in the text as hanging baffle). Figs. 6A

and B show that the simulated velocity fields had eddy

formation at the top of the digester (upper right region) as

Fig. 8 – Velocity contours and streamlines for 251 (A and B) an

hanging baffle. Numerical values on the figure show velocity in

the fluid begins to circulate back to the bottom entrance of the

draft tube. Therefore, it was envisioned that the introduction

of a hanging baffle in the eddy zone should force the flow to

move closer to the digester wall, which will eventually

minimize the poorly mixed zone inside the digester. To test

this hypothesis, simulations were performed for flat and

conical bottom configurations with a hanging baffle of 5.5 cm

length and inclined at 451 to the digester walls. The simulation

results, shown in Figs. 6C and D, clearly demonstrate the

benefit of the hanging baffle. As anticipated, the introduction

of the hanging baffle forced the flow to move close to the

digester wall, and considerably reduced the proportion of

poorly mixed zones as explained in the following section.

d 451 (C and D) conical bottom digesters with and without

m/s.

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WAT E R R E S E A R C H 41 (2007) 3051– 3060 3059

5.5. Evaluation of mixing effectiveness

Digesters are designed to operate with a specified hydraulic

residence time (HRT). This ensures that there is sufficient

time for the biological processes to adequately treat the

influent material. The efficacy of the digester is reduced by

either short-circuit flow or by regions of the digester that do

not actively mix—that is regions of flow field that may

circulate at low velocities but are disconnected from the

main recirculation pattern through the draft tube as shown by

the closed streamline in the lower right region of the digester

in Figs. 7A and B.

The size and the settling velocity of activated sludge flocs

collected from full-scale wastewater treatment plants are

reported to be in the range of 0.06–12 mm and 0.02–2 cm/s,

respectively (Li and Ganczarczyk, 1987; Lee et al., 1996; Li and

Yuan, 2002). An approach to designate poorly mixed regions

in the digester is to identify the regions where the magnitude

of the axial velocity is lower than the settling velocity of the

floc. In the present study a typical mean floc settling velocity

was taken as 0.32 cm/s. The rationale behind adopting this

approach to identify poor mixing is that if the axial fluid

velocity is greater than the settling velocity, there will be

sufficient drag on the floc to carry it with the fluid flow. On the

other hand, if the settling velocity is larger than the fluid

velocity, then floc settling will occur in these regions. There-

fore, quantification of the poorly mixed zones in the digester

was accomplished by calculating the area enclosed by the

larger of: (i) the first stream line outside of the closed loop

streamlines, which mostly includes the region of low axial

velocity near the digester bottom, or (ii) the contour of the

magnitude of axial velocity equal to the settling velocity—as

shown by the shaded regions in Figs. 7 and 8. The figures

clearly show that the addition of the baffle results in a

compression of the closed streamlines, but lesser compres-

sion of the axial velocity contour. Axial velocity contours were

plotted for the absolute value of the axial velocity equal to the

settling velocity of the floc (0.32 cm/s). The poorly mixed

zones accumulate solids reducing the digester HRT below the

design value, which will ultimately lead to digester failure.

The effects of the digester bottom configuration and intro-

duction of a hanging baffle on the mixing effectiveness was

evaluated, and a summary of the percentage of the poorly

mixed zones inside the digester has been presented in

Table 1. Data presented in the table show that the change in

Table 1 – Summary results of CFD simulations with andwith out baffle for different digester bottom configura-tions

Bottom configuration Percentage of digester volumecalculated to be poorly mixed

Without baffle (%) With baffle

Flat bottom 33.6 21.4

251 conical bottom 31.9 15.8

451 conical bottom 29.6 11.7

digester bottom configuration resulted in about 2–4% reduc-

tion in the poorly mixed zone. However, the introduction of a

hanging baffle reduced the percentage of poorly mixed zones

by 12%, 16% and 18% in the case of flat, 251 and 451 bottom

digesters, respectively. Therefore, it is clear from the findings

of this study that a combination of a hopper bottom and a

hanging baffle would significantly improve the mixing

efficacy inside gas-lift digesters.

6. Conclusions

The fluid dynamics simulation based on the assumption of

single-phase flow outside the draft tube was successfully

used to identify the flow pattern in a gas lift digester.

Simulation results were found to be in good agreement with

the experimental finding of Karim et al. (2004). At the gas

recirculation rate of 84.96 l/h, the poorly mixed zones in the

case of flat bottom digester was about 33.6%, while in the case

of digesters with 251 and 451 conical bottoms it was about

31.9% and 29.6%, respectively. The power law viscosity index,

n, did not show significant effect on the mixing pattern under

the conditions studied. Introduction of a hanging baffle to

direct some of the fluid energy towards the poorly mixed

region in the lower corner of the digester resulted in

significant reduction of the poorly mixed zones. In combina-

tion with the 451 conical bottom, introduction of a hanging

baffle reduced the poorly mixed zone by a factor of three as

compared to the flat-bottomed without baffle configuration.

Although the introduction of a hanging baffle was able to

significantly reduce the poorly mixed zones inside a gas-lift

digester, further optimization of the digester geometry may

lead to additional improvements.

R E F E R E N C E S

Borole, A.P., Klasson, K.T., Ridenour, W., Holland, J., Karim, K.,Al-Dahhan, M.H., 2006. Methane production in a 100-L upflowbioreactor by anaerobic digestion of farm waste. Appl.Biochem. Biotechnol. 131 (1–3), 887–896.

Choi, K.H., Chisti, Y., Moo-Young, M., 1996. Comparative evalua-tion of hydrodynamics and gas-liquid mass transfer charac-teristics in bubble column and air lift slurry reactors. Chem.Eng. J. 62, 223–229.

Couvert, A., Roustan, M., Chatellier, P., 1999. Two-phase hydro-dynamic study of a rectangular air-lift loop reactor with aninternal baffle. Chem. Eng. Sci. 54 (21), 5245–5252.

James, A.E., Jayaranaiwachira, V., 2000. Simulation of non-new-tonian fluids in anaerobic digesters. In: Proceedings of XIIIthInternational Congress on Rheology, 20–25 August, Cambridge,UK, pp. 229–231.

Karim, K., Varma, R., Vesvikar, M., Al-Dahhan, M.H., 2004. Flowpattern visualization of a simulated digester. Water Res. 38(17), 3659–3670.

Karim, K., Hoffmann, R., Klasson, K.T., Al-Dahhan, M.H.,2005. Anaerobic digestion of animal waste: waste strengthversus impact of mixing. Bioresour. Technol. 96 (16),1771–1781.

Kojima, H., Sawai, J., Uchino, H., Ichige, T., 1999. Liquid circulationand critical gas velocity in slurry bubble column with shortsize draft tube. Chem. Eng. Sci. 54, 5181–5187.

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