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Journal of Membrane Science 298 (2007) 110–116

Abiotic transport in a membrane aerated bioreactor

Eric McLamore a,1, W. Andrew Jackson b,2, Audra Morse b,∗a 550 Stadium Mall Dr., West Lafayette, IN 47907, United States

b Texas Tech University, Civil and Environment Engineering, Box 41023, Lubbock, TX 79409-1023, United States

Received 8 August 2006; received in revised form 14 February 2007; accepted 5 April 2007Available online 8 April 2007

bstract

Abiotic transport characteristics of a nitrifying membrane-aerated bioreactor were empirically analyzed and a model was developed. Therientation of the membranes in the bioprocessor is novel and the membrane/reactor length ratio is much larger than similar reactors for enhancedass conversion. While mass conversion may be improved due to increases in total specific surface area, abiotic transport was characterized to

nsure transport properties were similar to other membrane aeration bioprocessors. The developed model indicated that oxygen mass transfer andutrient convection may limit bioreactor performance. Peclet numbers indicated that the bioreactor could be modeled as a complete-mix reactor forn initial approximation, but further research should be conducted to characterize non-ideal hydraulic behavior. The random “coiled” orientationf the membranes provided enhanced surface area for microbial attachment, but may have caused flow misdistribution issues. In contrast to abioticodeling, experiments with nitrifying biofilm indicated sufficient electron acceptor and nutrient transport for the operational conditions tested.

t was concluded that the complex nature of the silicon membrane geometry and assumption of parameter interdependency caused the under

rediction of bioreactor transport. This model is intended to establish a platform for future models attempting to predict transport conditions ineveloping robust bioprocessors under stringent size, mass and energy restrictions. The random coiled geometry of the membranes is a viableption for long-lifetime bioprocessors requiring high specific surface area.

2007 Elsevier B.V. All rights reserved.

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eywords: Membrane bioreactor; Abiotic transport; Graywater; Mass transfer;

. Introduction

A membrane aerated bioreactor (MABR) was designedonstructed and operated at Texas Tech University to promoteitrification within a two stage denitrification–nitrificationystem [1]. The two stage denitrification–nitrification systems the biological component within a larger advanced lifeupport (ALS) system designed for the reclamation of humanastewater for long duration space mission such as the Earth’s

oon, Mars, or beyond [1,2]. The waste stream simulated

ygiene, shower/laundry water, urine and humidity condensatefrom both humans and machine exhaust) [3]. The surfactants,rganics and salts contained within the wastestream all poten-

∗ Corresponding author. Tel.: +1 806 742 2801x284; fax: +1 806 742 3449.E-mail addresses: emclamor@purdue.edu (E. McLamore),

ndrew.jackson@ttu.edu (W.A. Jackson), audra.n.morse@ttu.edu (A. Morse).1 Tel.: +1 806 239 9556; fax: +1 765 496 3449.2 Tel.: +1 806 742 2801x230; fax: +1 806 742 3449.

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376-7388/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.memsci.2007.04.005

rocessor

ially affect bioreactor transport, and detailed models shouldnclude these effects.

Due to predicted energy and size restrictions for long durationpace missions, process performance was optimized during theesign phase based on maximizing biological conversion effi-iency. This set of design decisions included random “coiled”rientation of the membranes to increase surface area for micro-ial growth and oxygen transfer. Oxygen transport from theumen to the active attached biofilm via sorption and diffusion iscritical parameter as O2 is the electron acceptor necessary foritrification. Transport characteristics of other MABR systemssing silicon rubber membranes have been previously investi-ated by many researchers [4–7]; however, Cote et al. [7] notedhat empirical mass transfer coefficients were significantly dif-erent from those reported in the literature. It is the aim of thiset of experiments to characterize the transport properties within

he novel MABR.

It was assumed that all significant nutrient transport occurredia convection (advection and/or dispersion), while all electroncceptor (oxygen) transport occurred via diffusion. Additionally,

embrane Science 298 (2007) 110–116 111

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he effect of surfactants, organics and salts on MABR massransfer was quantified via the α-factor and β-factor correction

ethod reported by [8]. In terms of mass transfer, the α-factor ismass transfer coefficient correction factor for wastes contain-

ng surfactants and high concentrations of organics. The β-factors an oxygen solubility correction factor for wastes containingalts and organics in high concentration [8]. It was assumedhat surfactants had the greatest effect on mass transfer due tooating/surface interaction with the hydrophobic silicone mem-ranes.

Although nutrient transport via hydrodynamics, electroncceptor transport via mass transfer and biochemical reactionsere assumed to be independent processes for this model, they

re highly dependent on one another. In addition, shell side massransfer strongly depends on system geometry and [9] noted thathe non-ideal behavior of the shell-side fluid causes significanterturbations in mass transfer performance. Biofilm growth andhus hydrodynamic efficiency is dependent on electron acceptorvailability. The assumption was made that these processes arendependent in order to construct a model describing general

ABR behavior, and only abiotic modeling is presented herein.he biological portion of the model based on Monod kineticsith multiple substrates will be presented in a subsequent paper.odels using strategies similar to those herein should build on

hese correlations by including the inter-dependency of transportnd transformation.

. Materials and methods

The following design decisions concerning reactor size, con-guration, specific surface area and operational conditions (suchs flow rates) were dictated by realistic NASA mission durationnd equivalent system mass guidelines [1,10].

.1. MABR system

The MABR is composed of 0.635 × 10−2 m (1/4 in.) thickcrylic plastic that is 54.7 cm long with an outside diameter of0.2 cm. The total volume and working volume of the MABRre 4465 and 3865 mL, respectively, generating a packing ratiof 0.87. The MABR consists of 150 non-porous Silastic® brandilicon membranes (Dow Corning Co., Midland, MI) that allowxygen to diffuse from the lumen side of the membrane and acts support media for biofilm growth. The silicon membranesave an outside diameter of 0.17 cm and an inside diameter of.08 cm. The silicon tubing is attached to stainless steel pres-ure taps (Scanivalve Corp., Liberty Lake, WA) that are pottedhrough a rubber mat and connect the silicon membranes to theressurized air cavities (membrane sheets). The spacing in theABR is novel in that the membranes are arranged in a ran-

om coiled packing fashion and the membrane length to reactorength ratio (rz) is much larger (2.3) than other MABRs. Fig. 1epresents a schematic of the MABR.

The module was operated in flow-through gas mode withuilding air providing fractional oxygen transfer. The mem-ranes occupied 13% of the empty bed volume (before biofilmormation). The total specific surface area for oxygen transfer

EcRt

Fig. 1. MABR system profile.

n the MABR was approximately 186 m2/m3. The membranesere oriented in a random fashion with an rz ratio of approxi-ately 2.3. Some specific membrane surface area (9 cm2) was

ost due to contact of membranes in the random packing andonnection with stainless steel pins. The amount of membranepecific surface area lost was estimated based on the approxi-ate number of membrane contacts and the tangential length ofsingle membrane–membrane interaction.

.2. Bromide tracer studies

Nutrient transport was quantified and modeled using abi-tic continuous flow tracer studies. The liquid was relativelysothermal (20–24 ◦C) during all studies. The tracer selectedor use in the experiment was sodium bromide (40 mg Br−/L).ffluent bromide samples were collected at 10% hydraulic reten-

ion time (Θs) intervals; influent samples were also collected tonsure that no contamination occurred within the holding tankuring the experiment. Bromide was measured using ion chro-atography (DX-600, Dionex, Sunnyvale, CA) on an AS12A

olumn. The mean superficial fluid velocity ranged from 0.26o 3.82 mm/min. The tracer studies were conducted for trans-

embrane air pressures of 17.9 and 24.8 kPa. Only the resultsor a transmembrane pressure of 17.9 kPa are presented, asarying this parameter had no significant effect on convection.xperiments were conducted for three mean Θ to obtain full

sharacterization of system residence time distribution (RTD).TD curves were developed and analyzed to obtain values of

he mean Θs (tm) following procedures in Weber and Digiano

1 embr

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12 E. McLamore et al. / Journal of M

11]. The F curve (F(τ)) as defined in Eq. (1) is:

(τ) =∫ τ

0E(t) dt (1)

here E(t) is the fraction of particles with exit age “t” (Eq. (2))nd is equal to:

(t) = C(t)/C�∫ ∞0 (C(t)/C�) dt

(2)

The value of tm is based on non-ideal flow conditions andas estimated from the F-curve to account for the effects of

hanneling and preferential flow [11]. Nutrient transport wasodeled using a packed bed correlation (Eqs. (3)–(5)) taken

rom Cussler [12]:

C

C0= erf(β1) + exp [Pe erf(β2)] , (3)

1 = 0.25εeff

(x2

tm− v2tm

), (4)

2 = 0.25εeff

(x2

tm+ v2tm

)(5)

he εeff values were obtained by fitting the data to the hydro-ynamic model above where Pe is the ratio of axial convectiono radial diffusion and describes the relative influence of con-ection on total hydrodynamic transport. It should be noted thate = (vL)/εeff.

.3. Oxygen transfer studies

Oxygen mass transfer experiments were conducted usingoth distilled, deionized water (DI water) and an early planetaryase (EPB) waste stream to correct for α-factor and β-factorrrors. The two main surfactants within the EPB waste streamere an anionic surfactant (sodium laureth sulfate, or SLES)

nd an amphoteric surfactant (disodium cocoamphodiacetate,r DSCADA). Each of these was assumed to alter oxygen trans-er, but the precise mechanism has not been determined at thisime. A complete description of the waste stream may be foundn McLamore et al. [1].

Oxygen mass transfer experiments were conducted by fillinghe shell side of the MABR with de-oxygenated DI water at aonstant flowrate. Air was de-oxygenated by boiling and purgingith nitrogen gas until the dissolved oxygen (DO) concentrationas less than 1.0 mg/L at a temperature of 20.0 ± 2.0 ◦C. Air was

upplied within the lumen of each silicon membrane at constantransmembrane pressure until the bulk fluid did not indicate a DOhange greater than 2%. DO was monitored in the influent andffluent of the reactor throughout the experiment using a Ther-oOrion DO probe (Thermo Orion model 9708, Waltham, MA)

nd a DO-compatible Orion pH meter (IQ Scientific, Carlsbad,A). Mass transfer coefficients and associated parameters were

btained following common practices outlined in Cussler [12]nd Metcalf and Eddy [8]. The range of operational parametersor the transmembrane pressure ranged from 2.6 to 24.8 kPa. Itas assumed that deformation of the silicon did not affect the

E

ane Science 298 (2007) 110–116

tructural integrity of the membranes. Due to operation at rel-tively high transmembrane pressure, it was assumed that thexygen concentration profile along the longitudinal length ofhe membrane was constant [4].

The overall mass transfer coefficient (koa) is the sum of thendividual mass transfer resistances from the gas, membrane andiquid [7,13]. The lumped parameter approach using koa wassed to describe mass transfer across the interfacial area. Theas coefficient (kG) describes mass transfer through the gas film,he membrane coefficient (kM) describes gas-specific diffusioncross the length of the membrane and the liquid coefficient (kL)escribes mass transfer at the liquid boundary layer-bulk liquidnterface (see below). The resistance for each boundary layer ishe reciprocal of the mass transfer coefficient and is presented inq. (6) [13]. The value used of Henry’s constant (H) for oxygenas 41644.575 × 105 Pa (41,100 atm) [8].

1

koa= 1

kL+ 1

HkM+ 1

kG(6)

Gas-phase resistance for gases with low solubility (suchs oxygen) is typically negligible in systems of this type1/kG ≪ 1/(αMG/αML)kL); thus, only the membrane, liquid andverall resistances are presented [12]. The values of kM (Eq. (7))ere obtained following procedures from Cote et al. [7] using:

M = DG(αMG)

o.d. ln(o.d./i.d.)(7)

Determination of koa via non-linear regression was usedo take into account the decrease in local driving force dueo increased bulk liquid DO concentration. Determination ofmpirical mass transfer parameters allowed electron acceptorransport to be characterized within the unique MABR geometry.

.4. MABR model

One-phase bulk flow within the MABR allowed transporto be modeled by a combination of abiotic mass transfer andydrodynamic analysis. The model assumes that nutrient trans-ort via convection, electron acceptor transport via diffusionnd biochemical reaction are independent processes. Steadytate hydraulic conditions were assumed to exist within theystem. This is a valid assumption as this model considersulk transport-transformation processes (macroscale). Follow-ng common practice, the advection and dispersion transporterms in Eq. (1) were quantified via abiotic inert tracer exper-ments and the mass transfer term was determined by meansf abiotic aeration experiments. Transversal dispersion wasssumed to be far less significant than axial dispersion, andhus was neglected in the model. Lumen side mass transferynamics are not discussed herein but can be modeled usingeat transfer analogy for ideal gases. Using general reactor the-ry documented in Weber and Digiano [11] and Levenspiel [14],

q. (8) was the starting point of model development:

δC

δt= −vxδC

δz+ εx

δ2C

δx2 ± koa(DO2 ) ± rBIO (8)

embrane Science 298 (2007) 110–116 113

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The first two terms describe nutrient advection–dispersion,nd the third term describes electron acceptor mass transfer. TheBIO term in Eq. (8) is zero during the abiotic modeling process.xygen deficit is the difference between the dissolved oxygen

oncentration in the bulk liquid and the saturated dissolved oxy-en concentration at a given temperate. This simplified approachs based on bulk fluid transport and related biotransforma-ion. Dimensionless parameters commonly used to characterizeonvection were calculated based on techniques presented inussler [12]. To investigate the process performance predictionsade by the abiotic transport model, steady state values of nitri-cation rate were analyzed at various Θs; aiding in establishingnd validating MABR bioconversion limitations (if any).

. Results and discussion

Abiotic transport characteristics were empirically determinedor a MABR within a two-stage N-D system designed to treat

urine-containing wastestream. The novel orientation of theembranes was designed to provide excessive surface area foricrobial attachment while enhancing dispersion. The orien-

ation of the membranes required that a detailed analysis ofransport phenomenon be conducted for accurate system processnalysis. Analysis of oxygen and nutrient transport characteris-ics of the MABR module are presented separately below. The

odel assumed independent convection and diffusion. Detailednalysis of transport including preferential flow, laminar stream-ines, multi dimensional dispersion and lumen side mass transfers not presented herein. RTD analysis allowed values of tm to bestimated for general characterization of channeling and Eq. (3)as used to estimate values of ε and Pe. Mass transfer coef-cients along with α and β correction factors were estimatedeparately and combined to form the model.

.1. Tracer study results

The results from the abiotic RTD analysis are presented belowTable 1). The Reynolds number (Re) represents the ratio ofnertial and viscous forces and was calculated using techniquesommon to literature. The presence of preferential flow and/orydraulic channeling is apparent by noting the significant dif-erence between the Θs and the value of tm determined by RTDnalysis. The tm is less than the Θs for the lower velocitiesnd greater than the Θs for the higher velocities. This inconsis-ency indicates that detailed hydrodynamic analysis is required

t each test condition to fully characterize MABR convection.he tm value obtained from the F-curve was used with the corre-ponding velocity to obtain values of εx and Pe based on Eq. (3)Fig. 2). The R2 values represent the correlation of the model and

able 1ABR hydrodynamics

iquid velocity (cm/min) Re Θs (min) tm (min) Pe R2

2.60 0.33 1930 1200 13.0 0.9295.5 5.69 193 180 2.3 0.8990.6 3.99 161 192 3.7 0.9378.2 8.54 129 174 2.2 0.911

ftSsgm

TM

α

β

Fig. 2. Hydrodynamic modeling of nutrient transport (v = 0.26 mm/min).

he data using Eq. (3). Although the Re values seem extremelyow, the lower limit on axial dispersion described by the modelPe = 13) indicates the reactor may never reach near-ideal plugow behavior (Pe = 100). The upper limit on axial dispersion in

he MABR (Pe = 2.2) suggests the reactor may be modeled ascomplete-mix reactor (CMR), where convection is dominatedy the presence of forced convection (from pumping) and axialispersion is considered to be moderately low.

A typical plot of the nutrient transport model and empiricalata is presented in Fig. 2. The test conditions for this specificxperiment were a velocity of 0.26 mm/min and transmembraneressure of 17.9 kPa. As indicated in Table 1, the R2 for theodel was 0.929 for this experiment. The largest error in theodel occurred during the initial lag region on the F(t) graph.ue to the relatively high R2 value for each of the test conditions

n Table 1, this approach was deemed acceptable for the abioticransport model.

.2. Oxygen mass transfer results

Mass transfer experiments were conducted using DI water,urfactants (SLES + DSCADA) and the EPB wastewater as sol-ents to correct for α-factor and β-factor errors. The α-factor iscorrection for the overall mass transfer coefficient (wastewa-

er/DI water) and the β-factor is a correction for the O2 saturationoncentration (wastewater/DI water). All mass transfer experi-ents were conducted in abiotic conditions. Typical α and β

actors for this type of system operated on municipal wastewa-er are 0.6 and 0.9, respectively [8]. The correction factors for

LES + DSCADA and early planetary base wastewater are pre-ented in Table 2 (both relative to DI water). The α-factor wasreater for the early planetary base wastewater as compared tounicipal wastewater, which may be due to the contribution of

able 2ass transfer correction factors

Wastewater Surfactants (SLES + DSCADA)

-Factor 0.75 ± 0.02 1.03 ± 0.04-Factor 0.81 ± 0.03 0.92 ± 0.08

114 E. McLamore et al. / Journal of Membrane Science 298 (2007) 110–116

Table 3MABR mass transfer coefficients

QL (cm/min) PO2 (kPa) koa (DI water) (×10−5 min−1) koa (EPB) (×10−5 min−1) Sh (DI water) Sh (EPB)

2 24.8 17.3 ± 2.5 15.9 ± 1.2 2.94 2.7124 17.8 14.2 ± 3.8 12.7 ± 0.9 3.32 3.08223

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he surfactants. The β-factor was less for the early planetaryase wastewater compared to municipal wastewater but similaro that for surfactants.

The effect of solvent type on oxygen mass transfer followedxpected trends. The presence of surfactants increased overallxygen mass transfer and increased total oxygen solubility. Theull strength EPB wastestream reduced overall mass transfer andxygen solubility. This was most likely due to the presence ofigh concentrations of organics and salts present in urine.

The mass transfer coefficients and related Sherwood num-ers (Sh) are presented in Table 3 (Sh = koaL/D). The membraneontributed 28 ± 8% of the total mass transfer resistance1/km = 2.13 × 104). As was expected, the major mass trans-er resistance in the MABR was in the liquid boundary layer.he individual mass transfer results are near values reported

n current literature [6,13]. Increasing oxygen partial pressureignificantly increased mass transfer (p-value = 0.08 for a 95%onfidence interval) within the operating conditions tested (17.9nd 68.9 kPa). The values of koa and Sh for both the early plan-tary base wastewater and DI water are presented in Table 3 tourther highlight α and β effects on oxygen transport.

The relatively high bulk liquid DO concentration (5.0 mg-O/L) throughout the experiments indicated that mass transfer

s sufficient to initiate nitrification as the minimum DO necessaryo support nitrification is approximately 2 mg/L [8]. Analysisndicates that only relatively large changes in hydrodynamicsill significantly increase the overall oxygen mass transport in

he system (Fig. 3). Increasing the velocity outside the rangef mission guidelines would intuitively enhance mass transfer,ut this source of energy consumption would be undesirable to

Fig. 3. MABR mass transfer as a function of velocity.

acp

atttwr

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ma

18.5 ± 1.4 3.32 3.1514.1 ± 0.8 2.41 2.1724.7 ± 1.0 4.73 4.21

ASA [10]. Thus, it is not foreseeable that such an increase inurbulence would be energy efficient for the proposed operatingonditions.

To verify that the results in Table 3 followed expected massransfer trends reported in literature [12,13] a correlation relatingxial Reynolds (Reaxial), Sherwood and Schmidt (Sc) numbersas developed. The correlations were developed for laminarow and moderate convection following procedures outlined

n Cussler [12] and Nielson and Villadsen [15]. The correla-ion is presented as Eq. (9), a Sh value of 2.0 being the lowerimit on mass transfer for negligible convective transport (or zeroulk fluid flow) near a surface. Note that the product of the Shnd Reaxial numbers is the Peclet number. The R2 value for theollowing correlation is 0.94.

h = 2 + 0.92(Re0.52axial)(Sc0.33) (9)

Correlations of this type are system-specific and highlympirical having “little value outside the range of the underlyingata material” [15]. According to Cussler [12], “the accuracy ofhese correlations is on the order of thirty percent.” These typesf models are, however, extremely useful in modeling futureystems and provide a framework for continuing models.

.3. MABR transport model

The final model, therefore, may be used for the given condi-ions requiring only bulk DO concentration, Re, and Sc numberss the only variables to predict overall system transport viaonvection and diffusion. The final abiotic model (Eq. (10)) isresented below.

δC

δt= C0[0.5 erf(β1) + exp[Pe erf(β2)]] ± (DO2 )

×(

DG

o.d.

)(2 + Re0.52

axial + Sc0.33) (10)

Holding all reactor geometry, fluid properties and temper-ture constant, the above transport model describes nutrientransport as a function of liquid velocity and Pe. The massransfer varies as a function of liquid velocity and DO2 . Fromhe hydrodynamic experiments presented earlier, values of Peithin the tested range may be estimated by the following linear

elationship (R2 = 0.93) (Eq. (11)):

e = −32.3v + 12.9 (11)

In accordance with abiotic mass transfer experiments, theodel predicts potential transport limitations at the specified Θs,

s indicated by low Sh (2.3–4.5) and Sc (0.50–0.91) numbers.

E. McLamore et al. / Journal of Membr

Table 4Abiotic and biotic mass transfer experiments

Test QL (cm/min) PO2 (kPa) koa (min−1) Sh (DI)

AB

Modiib

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The authors would like to thank the Center for Space Sci-ences at Texas Tech University for funding this research andthe Advanced Life Support System Research Team at NASAJohnson Space Center.

Nomenclature

C(t) tracer concentration at some time t (mg/L)C concentration of target constituent (mg/L)C0 tracer concentration at time zero (mg/L)DG gas diffusivity constant

biotic 2 24.8 17.30 2.71iotic 2 24.8 23.38 3.66

ass transfer experiments were repeated following 527 daysf biofilm growth to investigate the validity of this predictionuring normal operating conditions. Sh numbers and koa valuesn Table 4 indicate that mass transfer efficiency did not signif-cantly change following the formation of a mature nitrifyingiofilm.

In addition, biotransformation results (Fig. 4) indicated suf-cient nutrient and electron acceptor availability at all operatingonditions tested [1]. These results were similar to valueseported for other nitrifying bioreactors operated under nearlydentical conditions [16,17]. In Fig. 4, the y-axis presents NOX-

(nitrate as N plus nitrite as N) volumetric and aerial conversionate. Aerial and volumetric conversion rates were calculated ashe average daily mass of ammonium conversion per specificurface area and working volume, respectively. The effluentO (3.0 ± 0.5 mg-DO/L) and bioconversion rates (Fig. 4) dur-

ng operation indicate that MABR nitrification was kineticallyimited (removal rate was a function of Θs rather than oxygennd/or nutrient limitations). The complex random geometry ofhe “coiled” membranes enhanced overall transport at the localevel, in turn supporting the nitrifying biofilm throughout thexperiments presented in Fig. 4.

Finally, data taken from [1], tracer experiments and massransfer experiments were used to predict the NOx aerial andolumetric conversion rates as a function of Θs (using equa-ion (10)). Due to funding and time constraints, only the dataoint for Θs = 0.25 days could be completely quantified. Thisxperiment used a liquid velocity of 11.0 cm/min (Re = 0.24)nd had a tm value of 0.24 days. The Pe and R2 values (asresented in Table 1) for the experiment were 9.4 and 0.892,espectively. The predicted and actual values for NOx volumet-

3

ic conversion rate were 12,100 and 10,356 g/m -d, respectively;hile the predicted and actual values for NOx aerial conversion

ate were 4200 and 3614 mg/m2-d, respectively. The under-rediction of bioconversion by the model was most likely due to

Fig. 4. NOx-N volumetric and aerial conversion rates.

ane Science 298 (2007) 110–116 115

he interdependency amongst the individual parameters (namelyonvection and diffusion). However, if used as a first genera-ion model during biosystem design, models similar to the oneresented here can be of great value. The authors note thatuture models should incorporate the symbiotic nature of theonvection-mass transfer-reaction processes occurring withinhe bioprocessor.

. Conclusion

This abiotic model allowed MABR transport to be character-zed for biotransformation efficiency (nitrification in this case).

ABRs have been shown to be applicable to a wide array ofaste streams and models of this type will aid in maximizing

ransport; and in turn bioconversion of target contaminants. Theesults of the mass transfer and hydrodynamic analysis indi-ate that the MABR may be modeled with a CMR regime wherexial dispersion is moderately low. Although this seems counter-ntuitive based on the low Re numbers, it is most likely due toigh void space near the inlet and outlet of the reactor whereignificant mixing occurs. However, the random coiling may beesponsible for the increase in turbulence observed in the reactorhich was not predicted by the model.

cknowledgements

DO2 oxygen deficit (mg-O2/L)Dvoid diffusion coefficient within poresi.d. membrane inside diameter (cm)koa overall volumetric mass transfer coefficient

(min−1)o.d. membrane outside diameter (cm)Pe Peclet numberrBIO biological reaction rate (mg/L-min)tm liquid-phase mean residence time (min)v mean fluid velocity (cm/min)x reactor length (cm)z distance in direction of flow (cm)

Greek lettersαMG membrane/gas phase partition coefficientαML membrane/liquid phase partition coefficientεeff effective dispersion number (= Dvoid/τ)

valid fraction of pore space

1 embr

R

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16 E. McLamore et al. / Journal of M

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