Author's Accepted Manuscript

Dynamic multidimensional modelling of sub-merged membrane bioreactor fouling

A. Boyle-Gotla, P.D. Jensen, S.D Yap, M. Pidou, Y.Wang, D.J. Batstone

PII: S0376-7388(14)00404-9DOI: http://dx.doi.org/10.1016/j.memsci.2014.05.028Reference: MEMSCI12936

To appear in: Journal of Membrane Science

Received date: 31 January 2014Revised date: 15 May 2014Accepted date: 17 May 2014

Cite this article as: A. Boyle-Gotla, P.D. Jensen, S.D Yap, M. Pidou, Y. Wang, D.J.Batstone, Dynamic multidimensional modelling of submerged membranebioreactor fouling, Journal of Membrane Science, http://dx.doi.org/10.1016/j.memsci.2014.05.028

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Dynamic multidimensional modelling of submerged membrane bioreactor fouling

A. Boyle-Gotla a, P.D. Jensen a, S.D Yap a, M. Pidou a, Y. Wang b, D.J. Batstone a*

aAdvanced Water Management Centre, University of Queensland, Level 4, Gehrmann Laboratories

Building (60), Brisbane, QLD 4072, AUSTRALIA bThe UNESCO Centre for Membrane Science and Technology, School of Chemical Engineering,

University of New South Wales, Sydney, NSW 2052, AUSTRALIA

*Corresponding author: Tel: +61 (0)7 3346 9051; Fax: +61 (0)7 3365 4726. Email address:

damienb@awmc.uq.edu.au

Abstract

Existing membrane fouling models are limited to simple hydraulic profiles which is a limitation

particularly for planar membranes. Here, we present a new model that allows for a distributed shear

profile, with dynamic linking of flux and transmembrane pressure (TMP). Shear profile is calculated

using a multi-phase computational fluid dynamic approach, and is applied to a distributed parameter

model to simulate membrane fouling profile and flux distribution. This allows for simulation of

complex flux-step experiments, or situations where non-uniform shear is present. The model was

applied to filtration experiments conducted in a pilot-scale anaerobic membrane bioreactor treating

slaughterhouse wastewater comprising 1950 ± 250 mg/L total solids and was able to effectively fit

experiments under dynamic critical flux conditions. Cake compressibility was a key parameter, and

was estimated at 870 ± 80 Pa. Non-uniform gas distribution decreased critical flux from 12 LMH to

8.5 LMH. This emphasises the importance of local flow conditions on membrane fouling behaviour

and that performance can depend heavily on reactor configuration and hydraulics.

Keywords

Fouling, multiphase, CFD, anaerobic membrane bioreactor, model

Abbreviations

MBR Membrane bioreactor

AnMBR Anaerobic MBR

SMBR Submerged MBR

TMP Transmembrane pressure

CFD Computational fluid dynamics

TS Total solids

1.0 Introduction

Submerged membrane bioreactors (SMBR) are an established alternative to conventional clarifier

based wastewater treatment technology with a number of advantages [1]. These include the removal

of a separate clarification step and hence reduced footprint, better control over solids inventory and

solids retention time, a more concentrated biomass and hence a higher space loading rate, and

improved effluent quality due to elimination of solids through the membrane. Disadvantages are

largely energy consumption related to membrane fouling management and permeate collection. The

high cost of membranes and their replacement; which can be 50% of total capital expenditure [1], as

well as energetic and chemical costs of fouling control and cleaning, provides strong motivation to

predict and manage membrane fouling effectively.

Membrane fouling is the accumulation of largely insoluble material on or within the membrane [2],

reducing membrane flux at a given transmembrane pressure (TMP) or conversely, increasing TMP at

a given flux. It is possible to control membrane fouling during operation by gas sparging to create

shear across the membrane and thus remove foulant. Physical and chemical cleaning operations are

also used to periodically clean membranes, but require an interruption to process operation and are

therefore less desired.

Membrane life can be enhanced by operating the SMBR below its ‘critical flux’; or the flux below

which resistance to flow is governed by inherent membrane, rather than cake resistance [2]. Critical

flux is generally determined in flux-step experiments, where membrane flux is step-wise increased

and the corresponding TMP continuously measured [1, 3]. Critical flux is assessed as the flux at

which the fouling rate (or rate of TMP increase, dP/dt) increases substantially above the baseline [4].

Overall resistance to flux is dominated by membrane resistance at subcritical flux and controlled by

the resistance of the fouling layer at supercritical flux. Therefore, operation of an MBR below its

critical flux is inherently more stable, with minimal periodic cake removal required (e.g. through

backflushing). Critical flux is influenced by membrane shear, membrane properties, solids properties

and membrane configuration [2]. It is therefore important to predict membrane and cake formation

behaviour under subcritical, supercritical, and in transition fluxes.

Membrane fouling in MBRs is most commonly assessed via experimental analysis [5]. This faces a

number of challenges:

(1) The outcomes of a flux-step analysis are generally only applicable to MBR setups and process

conditions similar to those tested in the experiment. In particular, lab-scale studies have limited

applicability to full-scale applications due to different hydrodynamics [5].

(2) Hydrodynamics around the membrane creates surface shear on the membrane responsible for

fouling control. Techniques for hydrodynamic characterisation include the use of dye particles

[4, 6, 7], flow velocimetry [4, 8] and particle image velocimetry [9, 10]. These techniques

however, cannot easily be implemented in large scale systems that have large volumes, variable

flows and opaque fluids. They are also intrusive to flow and often restricted by the lack of space

in reactor systems [11].

(3) Experimental analysis is generally limited to studying the impact of a small number of process

variables at a given time and therefore may fail to account for the combined effects or

interactions of the many process factors that affect membrane fouling [5]. These include; sludge

properties such as solids concentration, stickiness, floc size, compressibility of cake layer and

viscosity; and process parameters such as membrane flux, applied TMP and gas sparging

intensity; which can vary between systems and over time.

Therefore, model based analysis is an important tool for fouling characterisation and effective fouling

control, which allows for determination of platform independent fouling characteristics and a better

fundamental understanding of controlling mechanisms.

Deterministic modelling of membrane fouling is at a comparatively early stage compared to general

wastewater process and hydrodynamic modelling, partly due to its complexity. The default model

approach is the use of lumped (non-distributed) parameter models which sufficiently characterise

simple fouling behaviour [12-14]. These models however, are inapplicable in membranes with non-

uniform shear and cake distributions and provide limited insight into transitionary behaviour from

satisfactory to unsatisfactory performance. A fractal permeation model was proposed by Meng et al

[15] which estimates cake layer permeability by using fractal theory to characterise its microstructure.

This model however has limited use as a predictive model as it is unable to estimate the impact of

changing operational parameters and reactor conditions on cake resistance. Li and Wang [16]

developed a semi-analytic, sectional resistance-in-series (RIS) fouling model which can be used to

simulate dynamic sludge film formation on the membrane and its effect on TMP. This model

considers net cake accumulation on the membrane to be dependent on the balance between

accumulation due to membrane flux, which encourages solids deposition, and detachment due to

shearing. This model can predict flux, cake thickness, for a given transmembrane pressure and bulk

liquid shear, on the basis of parameters such as membrane resistance, solids stickiness and

compressibility. Further expansions and modifications to the model have since been made: Wu et al

[17] included the effect of variable particle size solids, Zarragoitia-Gonzalez et al [18] integrated the

model with the Activated Sludge Model No.1 (ASM1) to predict the impact of biologically produced

soluble and insoluble products on membrane fouling and Mannina et al [19] further included deep bed

filtration theory to predict COD removal by the accumulated cake layer.

The sectional RIS fouling model and its extensions still have a number of limitations:

(a) The model geometry is 1-D and hence cannot assess the impact of variable shear and non-

uniform fouling across the membrane surface

(b) Maximum shear intensity is correlated with aeration intensity via an empirical laminar

correlation, and is therefore inaccurate for the prediction of shear in generally turbulent

conditions. Shear profile along membrane length is also approximated by a sine function rather

than a deterministic shear profile.

(c) The flux-pressure interaction is solved by iteration of the differential equation solution at a

defined time point. This does not allow dynamic analysis of the flux-pressure interaction.

In particular, interaction of these limitations does not allow for detailed analysis of the interaction of

fouling and flux distribution across a broader permeable domain.

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A rheological model was based on AnMBR sludge after 30 days batch operation at 33°C [20], which

is similar to the system studied in this analysis (52-65 days operation at 34°C). The study found that

the Bingham model best describes sludge rheology at intermediate shear rates (500 to 800 s-1). The

corresponding correlation Eq. (1) that relates sludge viscosity with total solids (TS) concentration is

valid for TS concentrations between 1.2 and 22.3 g/L and at a temperature of 22°C.

0.001 . (1)

Viscosity obtained from the above correlation was adjusted for a temperature of 34°C using an

Arrhenius relationship [21], μT34/μT22=θ(34-22) (temperature correction coefficient, θ = 0.98, obtained

from a water viscosity vs. temperature relationship). Therefore, at a TS concentration of 2 kg/m3 and a

temperature of 34°C, viscosity was estimated to be 0.008 Pa s.

Fluid turbulence was modelled using a k- ε turbulence model, which is the most widely validated of

the existing Reynolds Stress turbulence models [22, 23]. Default values of the empirical turbulence

constants are used in the CFD analysis, as described by the ANSYS CFX manual which is in

accordance with the standard values provided by Rodi [22]. Additional models include the use of a

Grace drag model for gas-liquid momentum transfer, Tomiyama lift force model and Sato’s model for

turbulence enhancement in bubbly flows.

The AnMBR domain was meshed using ANSYS meshing software. The mesh comprises a total

approximately 2.7 million elements and is within quality recommendations (orthogonal quality >0.1,

skewness <0.95). The solver was run in transient mode with timesteps of 0.01 s for a total duration of

120 s or until the model reached steady state; i.e. no variation in monitored parameters (fluid velocity,

maximum and average wall shear). The maximum residual target was 1 × 10-3.

2.2 Fouling model

Sectional approach

The membrane experiences non-uniform shear along its length and width, therefore resulting in

uneven cake accumulation and flux across the membrane surface. To assess the space-variable shear,

the membrane surface was discretised into a grid (finite element approach) comprising 34 × 23 or 782

sections.

Cake accumulation and corresponding increase in TMP

Cake accumulation rate, (dMc/dt), over each membrane section (i,j), is described by a conservation

equation, with the major mass transfer components of convective flux due to permeate movement

through the membrane (positive) and loss due to transverse liquid shear (negative) related to gas

sparging and cross-flow [2]. This conservation equation is described in Eq. (2).

Accumulation = Attachment - Detachment (2)

Solids attachment rate in Eq. 2 describes convective movement of solids towards the membrane,

which increases with membrane flux, J, and sludge solids concentration, C and decreases with

transverse lift (lift coefficient, Kl) and membrane shear intensity, G. The lift coefficient Kl, is a

function of the particle drag coefficient, Cd and particle size, dp (Kl = Cd × dp).

Solids detachment rate in Eq. 2 is a function of sludge stickiness, α, in the numerator and sludge

compression, γ, and filtration time, θf, in the denominator. Therefore, at a given shear intensity, G, a

stickier cake layer (described by a higher stickiness coefficient, α) is more difficult to detach. Higher

sludge compression and longer filtration times also reduce sludge detachment rate.

The accumulated cake layer provides an additional resistance to flow at each membrane section, Rc,ij,

which is calculated by Eq. (3).

, , , (3)

Resistance for each membrane section is calculated using the resistance-in-series approach, which

describes overall resistance, Rij, as the sum of inherent membrane resistance, Rm and cake layer

resistance, Rc,ij, and is given by Eq. (4).

, (4)

Rm is the primary contributor to total resistance at low flux when foulant accumulation is minimal to

non-existent, and the flux versus TMP relationship is linear. At high flux, foulant build-up on the

membrane increases total resistance and therefore the flux versus TMP relationship deviates from

linearity. The transition point is at the critical flux. The strong form of the critical flux definition states

that membrane resistance is the resistance to pure water, while the weak form defines membrane

resistance as the total resistance at subcritical flux [2]. The weak form is applied here.

Since this study mainly focuses on the impact of shear due to gas sparging on fouling or cake layer

development, pore fouling is neglected in the model development.

In constant flux conditions, the increase in total overall resistance due to cake accumulation leads to

an increase in TMP. Darcy’s law is used to describe the flux-pressure relationship, J=P/μR. Therefore,

for a membrane section, individual flux, Jij, and individual resistance, Rij, are related to TMP by Eq.

(5).

(5)

Dynamic flux-pressure interaction and the prediction of critical flux

During a flux-step experiment, dynamic increase in cake accumulation leads to a dynamic increase in

TMP to maintain a period of constant flux during a flux-step. A control loop is used to model this

dynamic response, where the rate of increase in TMP is equal to the error (or the difference between

flux setpoint and actual flux) multiplied by a proportional gain. This flux-pressure feedback loop

enables the fixing of overall flux and the simulation of dynamic pressure increase due to increase in

cake accumulation. The effect on TMP with stepwise increase in flux and the prediction of critical

flux is hence made possible.

Model parameters

Rm can be estimated by linear regression of dP/dt vs. flux below subcritical flux; and is therefore

estimated as the total resistance at sub-critical flux.

Li and Wang used a constant rc in their model. However, sludge cake is highly compressible [18, 24,

25] and its properties will vary with time during filtration in a constant flux scenario due to the

increase in applied TMP. Therefore, rc for a compressible material can be described by the empirical

Eq. (6) [26].

1 (6)

rc0 is the value of specific cake resistance at zero pressure and is assumed to vary between typical

values of 3 × 1012 m/kg to 3 × 1014 m/kg for averagely dewaterable sludge [27]. A midrange value of

5 × 1013 m/kg was adopted in this study. The compressibility coefficient, c, can vary from 0 (non-

compressible) to 1 (highly compressible). Activated sludge at 35°C was found to have a

compressibility coefficient of approximately 1 [25], and this value was therefore adopted in this work.

The compressibility parameter, Pa, is the TMP at which rc is double its initial value, rc0. The value of

Pa is sludge specific as sludge cake compressibility can vary with floc size, sludge type, sludge

conditioning, operating temperature and pH [13, 24, 28, 29]. Therefore, Pa was estimated via

parameter estimation during model calibration using a non-linear least squares parameter estimation

method (Levenberg-Marquardt algorithm) with TMP as fitted output and residual sum of squares (J)

as objective function. Parameter uncertainty was estimated from a two-tailed t-test (95% confidence

interval) on the parameter standard error calculated from the objective-parameter Jacobian at the

optimum (i.e., linear estimate) [30].

Flow near the sparger and membrane module is expected to be fully turbulent (Newton regime),

where particle drag coefficient, Cd, is approximately equal to 0.44 [31].

A typical value of the stickiness coefficient, α, of 0.5 was considered in this study. The remaining

model parameters, erosion rate coefficient, β, and compression coefficient, γ; (which is the actual rate

of sludge compression measured as rate of change of solids concentration in cake layer and not to be

confused with compressibility coefficient, c); were adopted from Li and Wang [16].

Fouling model parameter values are summarised in Table 1.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 1: Fouling model parameters

Symbol Definition Value Units Notes/References

i,j Section number

Mc Accumulated cake mass Eq. 2 g/m2

G Shear rate s-1 From CFD

C Total solids concentration 2 kg/m3

J Membrane flux L/m2 h or LMH

t Filtration time mins

Vf Volume of filtrate J × t m3

R Overall resistance Eq. 4 m-1

Rm Membrane resistance 1 × 1011 m-1 Measured

Rc Cake resistance Eq. 3 m-1

rc Specific cake resistance Eq. 6 m/kg [26]

rc0 Initial specific cake resistance 5 × 1013 m/kg [27]

c Compressibility coefficient 1 [ ] [25]

P Transmembrane pressure Eq. 5 Pa

Pa Pressure at which rc= 2 x rc0 870 ± 80 Pa Estimated

dp Particle diameter 60 μm Measured

Cd Drag coefficient 0.44 [ ] [31]

Kl Lift coefficient Cd × dp m Calculated

β Erosion rate coefficient of sludge cake 3.5 × 10-4 [ ] [16]

α Stickiness coefficient 0.5 [ ] [16]

γ Compression coefficient 2.5 × 10-5 kg/(m3s) [16]

ni,j Number of membrane sections 782

μ Sludge dynamic viscosity 0.008 Pa s [20]

T Temperature 34 °C

θf Filtration period in a cycle 15 mins

3.0 Experiments

The model developed here is calibrated and validated against two batch filtration experiments on a

pilot scale AnMBR with fully digested slaughterhouse wastewater.

Fig. 2: Experimental setup of the pilot scale AnMBR

The AnMBR comprised a 200 L bioreactor (0.47 m diameter by 0.865 m wetted height) (Fig. 2) with

two vertical mounted submerged A4 flat sheet membranes (Aquatec-Maxcon Pty Ltd, Australia).

These were installed in an acrylic frame fitted with a gas sparger unit located 20 mm from the bottom

of the membranes. Constant flux was maintained using a peristaltic pump on the permeate stream.

Pressure change was continuously monitored by means of a pressure transducer (model Druck PTX

1400, GE) situated at the permeate stream. The permeate stream was recirculated into the bioreactor

to maintain the liquid level within the reactor. Furthermore, temperature was controlled via an RTD

sensor (model SEM203 P, W&B Instrument Pty.), and was maintained at the operating temperatures

of the AnMBR (34 °C). Both pressure transducer and temperature output signal (4-20 mA) were

logged via PLC onto a computer. Circulation at the bottom of membrane bioreactor was achieved

using a Masterflex pump (model: 253G-200E-W1219) at flow rate of 613 L/h to avoid particle

settling.

Membranes were systematically cleaned prior to each measurement. Cleaning protocol included

physical cleaning with tap water and a soft sponge, after which they were soaked in 0.5 wt% sodium

hypochlorite and subsequently 0.2 wt% citric acid for 2 hours each. The membranes were rinsed again

and stored in tap water until they were next required. Clean water permeability was measured

subsequently to evaluate permeability recovery prior to the next trial.

Experiment 1 comprised a substrate (high protein red stream of slaughterhouse wastewater) to

inoculum (sludge from an anaerobic WWTP) ratio of 90: 10 by volume. The membrane was operated

under constant cross flow of nitrogen gas at 2 L/min, corresponding to 0.6 m/h. Permeate rate was

incrementally increased in steps of 2 LMH, terminating at a final flux of 14.2 LMH.

Experiment 2 comprised a substrate to inoculum ratio of 80:20 by volume. The membrane was

sparged with 3.5 L/min of nitrogen gas, corresponding to 1.05 m/h. Permeate rate was incrementally

increased in steps of 4 LMH, with a final flux of 16.9 LMH. Results from Experiment 2 were used to

calibrate the model.

TS concentrations were 1950 ± 250 mg/L, and flux step durations were 15 minutes. Particle size was

measured in Experiment 2 using a Malvern Mastersizer. Mean particle size (50th percentile) was

measured at 60 μm. The same particle size was assumed in experiment 1 as both experiments used

substrate and inoculum from the same source.

Experimental conditions in Experiments 1 and 2 are summarised in Table 2.

Table 2: Summary of experimental conditions

Experiment 1 Experiment 2

Gas sparge rate [L/min] 2 3.5

Flux step size [LMH] 2 4

Final flux [LMH] 14.2 16.9

Flux step duration, θf [min] 15 15

TS concentration [mg/L] 1700 2200

Mean particle diameter [μm] 60 60

Temperature [°C] 34 34

4.0 Results and discussion

4.1 Visualisation of membrane fouling in 2D

The shear intensity profiles expressed on the membrane surface at 2 L/min and 3.5 L/min are shown

in Figs. 3a and b, respectively. Qualitatively, the results show a marked difference in membrane shear

intensity between the two gas flow rates. The shear profiles follow a typical pattern of decreasing in

intensity with increased proximity from the sparger unit. At a gas sparge rate of 2 L/min, membrane

shear intensity ranges from 3.6 s-1 to 13.6 s-1. This gradient in shear is reduced at the higher sparge

rate of 3.5 L/min, with minimum shear intensity increasing to 6.2 s-1 but maximum shear intensity

remaining unchanged at 13.3 s-1. Although maximum shear has not increased at the higher gas flow

rate, quali

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experience non-uniform planar shear; i) with a single orifice sparger located centrally below the

membrane and; ii) with a plate sparger similar to experiment 2, but with only 23 % of the sparger

active at the right hand side of the unit, i.e. 200 mm blocked, 60 mm unblocked. Both sparger units

were located 20 mm from the bottom of the membrane. The overall gas flow rate for both scenarios

was set at 3.5 L/min, similar to Experiment 2.

Simulated shear and corresponding cake profiles at these scenarios are displayed in Figs. 5a -d. The

membrane experiences shear where it overlaps gas flow; i.e., at membrane areas immediately above

the single orifice sparger (Fig. 5a) and above the unblocked portion of the plate sparger in (Fig. 5c).

This leads to cake profiles as shown in Figs. 5b and d, with higher shear regions comprising lower

accumulated cake mass (~2 g/m2 in both cases) and the negligible shear region comprising the

majority of accumulated cake (~9 g/m2 in both cases). In contrast, the shear profile at full sparger

coverage in Experiment 2 (Fig. 3b) is more uniform along membrane width (x-axis) with all

membrane sections experiencing at least 5 s-1 shear intensity, and therefore comprising a more

uniform cake thickness (Fig. 3d).

Fig. 5e displays the change in TMP with step-wise increase in flux over time at the above scenarios

and at uniform sparging (fully functional sparger in Experiment 2). At low subcritical flux, the impact

of non-uniform sparging on TMP is minimal, but at supercritical flux, TMP increases at a faster rate

than with uniform sparging. Fig. 5f displays the rates of TMP increase (fouling rates), at the non-

uniform and uniform sparging scenarios and demonstrates that final non-uniform fouling rates reach 2

(single orifice) to 4 (blocked sparger) times the fouling rate at uniform sparging (unblocked sparger).

This can be attributed to a lower active membrane area, defined here as the percentage of membrane

receiving > 5 s-1 shear intensity, in the single orifice (39%) and blocked plate sparger (30%), than in

the uniform gas coverage scenario (100%). Critical flux, or the flux where a deviation from linearity

in dP/dt is observed, decreases from approximately 12 LMH in uniform shear to 8.5 LMH in the

blocked plate sparger.

The membrane experiences the highest area-average shear intensity with the single orifice sparger

(8.4 s-1), followed by the unblocked (7.4 s-1) and blocked gas spargers (6.0 s-1). It is interesting to note

that membrane performance is lower with the single orifice sparger than with the unblocked sparger,

despite receiving higher shear. This therefore suggests that increasing shear intensity alone may be

insufficient for fouling control if membrane coverage by the sparger unit is poor.

The extent of membrane coverage by the sparger is important as it directly relates to the extent of

active membrane surface. Model simulations at various non-uniform shear profiles, with overall gas

flow rate maintained at 3.5 L/min, revealed a non-linear (power-law) relationship between active

membrane

Confidenc

Fouling ra

acceptable

Fig. 5: Filtr

orifice spar

uniform an

e area and fou

ce intervals fo

ate is unaffect

e as long as th

ration behaviou

rger; c) shear in

nd non-uniform

uling rate. Th

or the non-lin

ted above 80%

he proportion

ur at non-unifor

ntensity and d) c

shearing; and

his profile is d

near regression

% membrane

n of inactive m

rm shear scenar

cake accumulat

f) fouling rate a

displayed in F

n model are d

coverage. Th

membrane is m

rios: a) Shear in

tion with a heav

at uniform and

Fig. 6 at 12 LM

displayed as e

his suggests th

maintained be

ntensity and b)

vily blocked pla

non-uniform sh

MH only, for

error bars at e

hat non-unifo

elow a certain

cake accumula

ate sparger; e) T

hearing.

clarity.

each point.

orm shearing i

n threshold.

ation with a sing

TMP vs time at

is

gle

Fig. 6: Foul

4.4 F

The mode

such as lo

introducti

identificat

highly use

can be eva

A key adv

membrane

therefore

CFD mod

highly dep

modelling

cake in ad

technical

membrane

coupling w

sparged sh

simulate t

relaxation

Conclusio

dimension

scenarios

pressure f

ling rate vs acti

urther mode

el can be addi

ocal geometry

ion of relaxati

tion of their o

eful in a cost

aluated in lon

vantage of the

e shear profil

avoiding repe

del however, h

pendent on lo

g hollow fibre

ddition to mem

requirements

e flux simulat

with the CFD

hear profile, a

the impact on

n, which can a

ons. The exten

nal shear and

with non-uni

feedback loop

ive membrane a

el application

itionally used

y around the m

ion periods (g

optimum valu

benefit analy

ng-term simul

e model appro

e, which can

eated CFD mo

has to be resim

ocal geometry

e membranes;

mbrane shear

in simulating

tions allows f

D model. For

and non-sparg

n membrane fo

also be simula

nsions to prev

cake profiles

iform shear on

p in the model

area at 12 LMH

ns and limita

in the study

membrane, sp

gas sparging a

ues for the ma

ysis as it allow

lations to iden

oach outlined

be scaled up

odelling and h

mulated for d

y. This model

; namely the e

[10]. The m

g the shear pr

for simulation

example, it is

ged shear pro

ouling dynam

ated using thi

vious models

s on a flat she

n the membra

l allows for th

H (15 minutes fi

ations

of the effect o

parged gas flo

at no flux); on

aximisation of

ws for dynami

ntify longer te

d here is the pr

or down prop

hence saving

different MBR

also requires

effect of fibre

main limitation

rofile through

n of dynamic

s perfectly ap

file, and then

mically in conj

is model.

presented her

et membrane

ane surface. In

he simulation

iltration)

of key design

w rate, opera

n membrane p

f membrane l

ic and realisti

erm strategies

roduction of a

portional to th

time and com

R configuratio

s further mech

e movement in

ns are the add

h CFD, but de

conditions w

ppropriate to u

n switch betwe

junction with

re allow for th

surface, ther

n addition, th

n of flux-step

n and operatio

ting flux and

performance a

ife. This mod

c operational

s (under a dyn

a two-dimens

he gas spargin

mputational re

ons as membr

hanical consid

n dislodging a

ditional softwa

coupling this

without necess

use CFD to si

een these two

h other strateg

he visualisati

efore allowin

he incorporatio

experiments a

onal parameter

the

and for the

del will also b

analysis, and

namic regime

sional

ng intensity;

esources. The

rane shear is

derations whe

accumulated

are and

from the

arily dynamic

mulate a

o profiles to

gies such as

on of two

ng analysis of

on of a flux-

and the

rs

be

d

e).

e

en

c

f

prediction of critical flux. This means inherent model parameters (such as cake compressibility and

specific resistance) can be estimated from dynamic data. This model can also be expanded for use in

true operational scenarios to model long term pressure profiles, and can therefore be particularly

useful in design and optimisation studies. A key future extension may be inclusion of mechanical

considerations needed to simulate hollow fibre membrane modules, particularly the impact of fibre

movement, and non-liquid shearing.

Acknowledgments

We thank the Australian Meat Processor Corporation (AMPC) and Meat & Livestock Australia

(MLA) for funding this project through project number 2013/5018. Apra Boyle-Gotla is the holder of

an AMPC research scholarship as well as an Australian Postgraduate Award (APA). Paul Jensen is

the holder of an AMPC research postdoctoral fellowship.

Conflict of interest

There was no conflict of interest

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Highlights

• Fouling model that predicts distributed shear, cake and flux profiles.

• Shear distribution profile predicted via multiphase computational fluid dynamics.

• Model includes dynamic linking of flux and transmembrane pressure.

• Predicts fouling dynamics with a broad range of scenarios.