1

Membranes in Wastewater Treatment Computation Model

Francisco de Oliveira e Carmo Mascarenhas (1)

May 2017

(1) Instituto Superior Técnico – Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisbon, Portugal

ABSTRACT: Wastewater Treatment by Membrane Technology gives rise to the innovative MBR-

Membrane Bioreactors System. This type of system differs from Conventional systems due to the use

of an alternative membrane filtration system rather than a Secondary Decanter. The quality of the

effluent produced by this type of systems allows them to comply with the stipulated parameters of

reuse without the need for additional treatment. For this reason, its use has been accentuated by the

increase in environmental concerns and control of water use.

This dissertation intends to study the Design Computation Model of two alternatives of this type of

systems. In particular, in relation to the Pre-Packaged Type and the Modified Ludzak-Ettinger with

Cascade Sludge Recirculation system, it is intended to list the equations and design criteria necessary

for the definition of the Volumes and Parameters that relate to the materialization and operation of

these systems while Secondary Treatment solutions. Based on this, a search is made for the

constitution of a Computational Algorithm which, according to the input of the system's operating data,

can automatically define a solution as output and which constitutes as close as possible a preliminary

dimensioning guide of the Presented.

These systems differ mainly in the values and criteria of the published parameters for the sizing of the

common phases and in the order in which the equations are used in the associated Algorithm. For the

purpose of Preliminary Dimensioning, the practical application of the Modeling that is presented lacks

the qualitative and quantitatively more demanding definition of the values of the parameters and the

criteria involved as well as the conditions of their use.

KEYWORDS: MBR, Membrane Filtration, Reuse, Design Modeling, Pre-Packaged, Modified Ludzak-

Ettinger

1. Introduction

The discharge of wastewater into water lines

implies the prior treatment of them. In case the

reuse of the secondary effluent produced in the

aforementioned process is considered, it is

necessary to subject it to a higher level of

treatment.

Activated Sludge Treatment consists generally

in the use of a Biological Reactor and a

Separation Reactor. This technology evolved

on the passage of treated liquid from the

Biological Reactor by very thin membranes

which in this way replace the separation

achieved through a Secondary or Tertiary

2

Decanter and allow it to cope with the

aforementioned quality demand.

The treatment of waste water by membrane

process presents several practical applications

and the present dissertation intends to deepen

the study of MBR systems as a waste water

treatment solution and the development of the

calculation model associated to its design.

Namely, of a Pre-Packaged and a Modified

Ludzak-Ettinger MBR systems.

2. MBR - Membrane Bioreactor Systems

The MBR technology came into being in the

60's and has evolved since then. The design of

the configurations used in such systems has

followed this trend, allowing them to

consolidate as a wastewater treatment solution

adopted with reflection on the volume of the

facilities and the wastewater flows treated

nowadays.

2.1. Configurations

Regarding the commercial application of MBR

systems, two different types of configurations

have been developed with respect to the

condition of the membranes: Submerged or

Immersed MBRs and External MBRs. The

types of membrane modules used in these

configurations are: Flat Sheet, Hollow Fiber

and Multi Tubular.

2.2. Filtration

The pore size of the membranes used

commercially in the separation of biosolids in

membrane bioreactors lie in the region of the

Ultrafiltration and Microfiltration, from 0,05 to

0,2 μm. Submerged MBR aerobic systems

operating within this filtration range, play the

most important role in Large scale.

2.3. Materials

The materials used in membranes may be

ceramic or polymeric and should allow good

endurance and structural resistance even with

a large concentration of pores with

homogeneous diameters.

2.4. Applications

MBR systems are used both in municipal and

industrial wastewater treatment when

advanced treatment and a compact system is

required (Hai, Yamamoto and Lee, 2014).

Generally, municipal tributaries are usually

easier to treat since they have lower

concentrations of BOD and COD and are more

homogeneous. At the opposite extreme, the

industrial tributaries present great variability

and high concentrations of substances difficult

to remove by biological treatment.

In addition to biological treatment, they are

naturally predisposed for advanced treatments

like the removal of Nutrients.

This type of treatment has been successfully

implemented in wastewaters both with large

percentage of easily biodegradable organic

matter and moderate biodegradation.

However, effluents rich in oils and fats continue

to be the weak point of this type of systems

because of the fouling of the membranes

caused by these substances.

Despite the reduced pore size of the

membranes, they are not sufficient alone to

remove dissolved solids, metals or traces of

contaminants such as hormone or

pharmaceutical compounds which therefore

require specific additional treatment

(Membrane BioReactors WEF Manual of

Practice No. 36, 2012 ).

3

2.5. Operation

The Microfiltration and Ultrafiltration processes

are operated either by positive or negative

pressure to extract the permeate. The volume

of this permeate generated per unit area of

membrane per unit time is known as Flux and

has a major influence over the design of the

membrane unit and the scouring system

(Tchobanoglous et al., 2014). The choice of

this design parameter is usually made through

the recommendation of the manufacturer with

unfavorable consequences on the efficiency

and operation costs and the life of the

membranes the higher the Flow value adopted.

There are mainly two types of Filtration

concerning the physical membranes: the

Impact Filtration where the effluent is forced

perpendicularly against the membrane and the

Tangential Filtration where the effluent flows

parallel to it.

The Flat Sheet systems operate according to a

sustainable permeability in which the

conditions are chosen for a stable and lasting

operation. On the other hand, Hollow Fiber

systems operate according to an intermittent

pattern in which the flow used is higher than

can be supported by the operating conditions

of the filtration cycle, requiring the use of

recovery measures such as backwash and

maintenance cleaning frequently (Judd, 2010).

The membrane fouling phenomenon can be

partly prevented and partly reversed by

physical and chemical techniques aimed at

maintaining the process efficiency and the

extension of membrane life. The techniques

used depend on the configuration adopted

since not all types of membranes support the

known cleaning methods.

2.6. Costs

MBR systems are still a costly and

inappropriate solution with low economic

efficiency. The most important factors in the

evaluation of the solution to be adopted are

Capital or Investment Costs and Operating

Costs. It is necessary for the solution to be

characterized by a balance between the two.

A solution that requires a large investment

usually results in more robust equipment that

needs less maintenance resulting in lower

values of operating costs. On the other hand, a

solution with lower investment, for example

through operation with higher values of flow

and therefore of smaller area of membranes,

will result in a more accentuated fouling,

implying a higher frequency and intensity of

cleaning and a shorter service life of

membranes resulting in higher maintenance

costs (Judd, 2010).

MBR systems are generally a more costly

solution than Conventional Systems and, in the

treatment of more advanced objectives of

reuse and nutrient removal, both technologies

present the same finantial arguments in the

long run (Young et al., 2012)

3. Activated Sludge Processes

The principle associated with activated sludge

systems is the maintenance in suspension of

the microorganisms responsible for the

biological treatment.

The mixture present in the Biological Reactor,

is called Mixed Liquor and contains living

microorganisms which consumes the organic

matter and inert solids also present and

causes the formation of the active unit of

treatment – the activated sludge.

4

3.1. Concepts

The main Concepts in Activated Sludge

Processses are:

The Sludge Retention Time - mean time of

permanence of the activated sludge solids in

the system; The Food to Microrganism ratio -

relation between the quantities of Available

Substrate and Suspended Biomass; and

Hydraulic Retention Time - duration of each

unit phase (Tchobanoglous et al., 2014).

3.2. Operations and Control

There are also some operational practices that

need to be carried to ensure the health of the

system:

Sludge Disposal - to maintain the desired

concentration of SSLM; Sludge Recirculation -

the redistribution of the microorganisms for

maintaining their concentration and system

efficiency; and the Control of The Oxygen

Concentration to optimize the system

performance.

4. MBR Technology Modeling

The computation modeling of the reactions that

translate the treatment process are the main

purpose of this chapter.

These are based on treatment kinetics

involving the processes and respective rates of

Microorganism Growth and Substrate

Utilization as well as Cell Degradation,

Biomass Production and Transfer Between

Media. Also, it needs to be taken into account

the dynamic nature of the system considered

for this kinetics: the Biological Reactors where

the treatment is actually processed. In a

system with dynamic boundaries:

Accumulation = Influence - Effluency +

Generation – Depletion

The core Design of an MBR treatment system

is the design of the components of membrane

filtration, tank volume and aeration

capacity(Hai, Yamamoto and Lee, 2014) .

The MBR technologies chosen as the object of

this study, constitute the most consolidated

solutions: a compact pre-packaged

configuration with Membranes of the Flat

Sheet type and a Modified Ludzak-Ettinger

configuration with Cascade-type recirculation

and Hollow Fiber membranes. The design of

the compact, pre-packaged type system is

relatively simpler than the one required for the

modified Ludzak-Ettinger configuration which,

additionally, targets the Desnitrification.

From here, the main equations used in the

Design Model are presented.

4.1. Biological Treatment

Nitrification and

Removal of BOD

The calculations of this Section must be made

based on the kinetic ratios of nitrification for

both Systems.

Sludge Retention Time

𝜇!"# = 𝜇!"#,!"#𝑆!"!

𝑆!"! + 𝐾!"!

𝑆!𝑆! + 𝐾!,!"#

− 𝑏!"#

𝑆𝑅𝑇!"# = (𝐹𝑆)1

𝜇!"#

Biomass Production

𝑁!" = 𝑆!"#! − 𝑆!"!! − 0,12𝑃!,!"#,!!"

𝑃!,!"#,!"" =𝑄𝑌 𝑆! − 𝑆1 + 𝑏 𝑆𝑅𝑇

+𝑓! 𝑏 𝑄𝑌 𝑆! − 𝑆 𝑆𝑅𝑇

1 + 𝑏 𝑆𝑅𝑇

5

𝑃!,!!" =

=

𝑄𝑌 𝑆! − 𝑆1 + 𝑏 𝑆𝑅𝑇

0,85+

𝑓! 𝑏 𝑄𝑌 𝑆! − 𝑆 𝑆𝑅𝑇1 + 𝑏 𝑆𝑅𝑇

0,85

+𝑄𝑋!,! + 𝑄 𝑆𝑆𝑇! − 𝑆𝑆𝑉!

SSV and SST Mass

SST Mass = 𝑋!!" 𝑉 = 𝑃!,!!" 𝑆𝑅𝑇

Pre-Packaged MBR Aeration Tank Volume

𝑉!"#$!%#&'( = 𝑉!!" + 𝑉!"!

𝑉!!" =𝑃!,!"" 𝑆𝑅𝑇𝑋!""

Modif ied Ludzak-Ett inger MBR Pre-

Aeration Tank Volume

𝑉!"# =𝑃!,!"" 𝑆𝑅𝑇 − 𝑋!"#$%& !"! 𝑉!"#$%& !"!

𝑋!"#

Pre-Packaged MBR Activated Sludge

Recirculat ion Rate

𝑅𝐴𝑆 =1

𝑋!"#$%& !"!𝑋!"#

− 1

Alkal inity

𝐶𝑎𝐶𝑂!𝑡𝑜 𝑎𝑑𝑑 𝑚𝑔 𝐶𝑎𝐶𝑂!

𝐿=

=70 − 𝑖𝑛𝑓𝑙𝑢𝑒𝑛𝑡 𝐶𝑎𝐶𝑂!

+ 7,14×𝑁!" − 3,6× 𝑁!" − 𝑁!

DeNitrification

The Calculations presented in this section are

meant to be used for the Modified Ludzak-

Ettinger MBR alone.

Internal Recycle

𝑄 𝑁!" = 𝑆!"!! · 𝑄 + 𝑆!"!! · 𝐼𝑅 · 𝑄

𝐼𝑅 =𝑁!"𝑆!"!!

− 1

Anoxic Zone Biomass Concentration

𝑋!"#$ = 𝑋!"#𝐼𝑅

𝐼𝑅 + 1

Act ive Anoxic Biomass Concentration

𝐹! =𝑃!!𝑃!,!""

𝑋!"#$,!"#$%! = 𝐹! · 𝑋 !"#$

F/M b

𝐹 𝑀! =𝑄𝑆!

𝑋!"#$,!"#$%! 𝑉!"#$

𝑉!"#$ = 0,20 𝑉!"# = 0,20 𝑉!"# + 𝑉!"!

SDNR - Specif ic DeNitr i f icat ion Rate

For F/Mb>0,50

𝑆𝐷𝑁𝑅! = 𝑏! + 𝑏! 𝑙𝑛 𝐹/𝑀!

For F/Mb≤0,50

𝑆𝐷𝑁𝑅! = 0,24 𝐹/𝑀!

SDNRadj - AdjustedSpecif ic DeNitr i f icat ion

Rate

For IR=2

𝑆𝐷𝑁𝑅!"# = 𝑆𝐷𝑁𝑅! − 0,0166 𝑙𝑛𝐹𝑀!

− 0,078

For 3≤IR≤4

𝑆𝐷𝑁𝑅!"# = 𝑆𝐷𝑁𝑅! − 0,029 𝑙𝑛𝐹𝑀!

− 0,012

Anoxic Tank Volume

𝑁𝑂! = 𝑉!"#$ 𝑆𝐷𝑁𝑅!"# 𝑋!"#$,!"#$%!

6

Phosphorus Removal

This can be achieved without further design

simply by adding precipitation salts into the

Mixture and operating a Standard Filtration

Procedure.

4.2. Membrane Unit

Membrane Area

𝐴! =𝑄𝐽

Pre-Packaged MBR Membrane Unit Volume

𝑉!"! =𝐴!"!𝜙

Modif ied Ludzak-Ett inger MBR Membrane

Tank Volume

𝑉!"! !"#$ =𝐴!"!𝜙

+ 𝜔 · 𝐴!"!

4.3. Aeration System

Pre-Packaged MBR Oxygen Demand

𝑅! = 𝑄 𝑆! − 𝑆 − 1.42𝑃!,!"# + 4.57𝑄 𝑁!"

Modif ied Ludzak-Ett inger MBR Oxygen

Demand

𝑅! = 𝑄 𝑆! − 𝑆 − 1.42𝑃!,!"#

+4.57𝑄 𝑁!" − 2.86𝑄 𝑁!" − 𝑁!

Membrane Scouring Aeration

𝑄!",!"!#$%&%' = NEA! · 𝐴! = NEA! · 𝐴! · 𝐽

For Kubota Flat Sheet,

NEA! = 0.0044 · J + 0.708

For Zenon Hollow Fiber

NEA! = 0.0052 · J + 0.3257

Oxygen Transfer Rate

𝑂𝑇𝑅! = 𝑆𝑂𝑇𝑅𝜏𝛽Ω𝐶!"#⋇ − 𝐶

𝐶!"#⋇ 𝛼 𝐹

Alpha Factor

For Coarse Bubble

𝛼 = 1,2888 · 𝑒!!,!"#"·!"##

For Fine Bubble

𝛼 = −0,03𝑀𝐿𝑆𝑆 + 0,71

Aeration FlowRate

𝑄!" =𝑆𝑂𝑇𝑅

𝑆𝑂𝑇𝐸 60𝑚𝑖𝑛/ℎ 𝑘𝑔𝑂!/𝑚!𝑎𝑟

Adit ional Pre-Packaged MBR Oxygen

Transfer Rate in S itu Demand

𝑂𝑇𝑅! = 𝑅! − 𝑅!"#$%&'()

Adit ional Modif ied Ludzak-Ett inger MBR

Oxygen Transfer Rate in S itu Demand in

Membrane Tank

𝑂𝑇𝑅! = 0,95𝑅! − 𝑅𝐴𝑆 · 𝑄 ∗ (𝐶!"#$%&'( !"!

− 𝐶!"#$%&'( !"é !"#$)

Adit ional Modif ied Ludzak-Ett inger MBR

Oxygen Transfer Rate in S itu Demand in

Pre-Aeration Tank

𝑂𝑇𝑅! = 0,05𝑅!

Pre-Packaged MBR Sludge Wasting Rate

𝑄! =𝑉!"#$!%#&!"

𝑆𝑅𝑇

Modif ied Ludzak-Ett inger MBR Sludge

Wasting Rate

𝑄! =𝑅𝐴𝑆

1 + 𝑅𝐴𝑆 𝑉!"é!!"#$!%#&'( + 𝑉!"!#$%&%'𝑆𝑅𝑇!"#ó!"#$

5. Computation Model

5.1. Algorithm 1.Definition of input data into the system:

Characteristics of the system influent, Effluent

requirements, Biological treatment data,

Membrane unit and Aeration system;

7

2. Determination of the Growth Rate of

Nitrifying Bacteria and corresponding Aerobic

Sludge Retention Time;

3. Definition of Ammonia Oxidation - Nox;

4. Iterative determination of Biomass

Production and Quantity of Ammonia to

oxidize;

5. Calculation of SSV and SST mass in

Aerobic Tanks;

6. Determination of Tank Volume:

6.1. Determination of the Pre-Aeration Tank

Volume (Modified Ludzak-Ettinger System);

6.2. Determination of the Aerobic Volume of

the Aeration Tank (Pre-Packaged System);

7. Calculation of Sludge Recirculation Rate

(Modified Ludzak-Ettinger System);

8. Calculation of Internal Recycle Rate

(Modified Ludzak-Ettinger System);

9. Determination of the Biomass Concentration

in the Anoxic Tank (Modified Ludzak-Ettinger

System);

10. Estimation of the Active Fraction of the

Biomass Concentration in the Anoxic Tank

(Modified Ludzak-Ettinger System);

11.First estimate of Anoxic Volume (Modified

Ludzak-Ettinger System);

12. Calculation of the Food to Microrganisms

Ration of the Active Fraction of the Biomass

Concentration in the Anoxic Tank (Modified

Ludzak-Ettinger System);

13. Calculation of the Specific Denitrification

Rate (Ludzak-Ettinger Modified System);

14. Anoxic Volume Calculation (Modified

Ludzak-Ettinger System);

15. Alkalinity Check (Modified Ludzak-Ettinger

System);

16. Determination of the Membrane Area;

17. Determination of the Membranes Volume:

17.1. Determination of the Membrane Tank

Volume (Modified Ludzak-Ettinger System);

17.2 Determination of the Aeration Tank

Volume (Pre-Packaged System);

18. Calculation of the Total Oxygen Demand

for Biological Treatment;

19. Determination of the Specific Aeration

Requirement of the membranes;

20. Determination of Air Flow for Scouring of

Membranes and their Transfer Rates in Situ;

21. Definition of the remaining In Situ Transfer

Charges required:

21.1. Concerning the Membrane and Pre-

Aeration tanks (Ludzak-Ettinger Modified

System);

21.2. Concerning the Aeration tank (Pre-

Packaged System);

22. Calculation of the corresponding Standard

Oxygen Transfer Rates;

23. Determination of the required airflow:

23.1. In Pre-Aeration and Membrane Tanks

(Ludzak Ettinger Modified System);

23.2. In the Aeration Tank (Pre-Packaged

System);

24. Calculation of Sludge Recirculation Rate;

25. Calculation of Sludge Wasting Rate;

26. Presentation of Results.

8

5.2. Results

The tank volumes resulting from the Algorithm

application are oversized. Even so, the greater

simplicity of the Compact Pre-Packaged

system is reflected in the smaller dimensions

of the resulting tank volumes. On the other

hand, the inclusion of Denitrification process in

the Modified Ludzak-Ettinger system results in

a significant reduction in aeration

requirements, with consequences on operating

costs, and also has a positive influence on the

need for correction of Alkalinity.

Although the Safety factor can be changed as

a safety principle used for good measure, the

inhibition consequences of the operation

Project Temperature would be more difficult to

overcome.

6. Conclusions and Future

Recommendations

The Sizing of MBR Systems as a Secondary

Treatment System does not present, at

Biological level, significant differences in

relation to the Conventional Systems.

Due to the numerous applications and

configurations of MBR systems, it is difficult to

generalize not only the calculation models

associated with their design, but also the

choice of parameter values used in them. The

relatively short maturation time associated with

Membrane Technology has direct

consequences in the design of this type of

systems that depends a lot on the

manufacturer's recommendations for each

specific case.

The studied alternatives use the same type of

equations with respect to the common phases:

Nitrification and Removal of Organic Matter;

Filtration by Membranes and Aeration System.

The differences are mainly focused on the

values used and the order in which the

systems are dimensioned.

It can be concluded that the presented models

constitute a preliminary and comparative

analysis between the chosen configurations

and do not present the necessary rigor that is

required for the implementation of a treatment

system lacking concrete dimensioning data for

each specific case.

Once the Dimension Model equations have

been listed, it would be interesting in the future

to collect and compile the values of the

parameters used in specific cases of

Membrane Unit design and in the Aeration

System for these and other technologies

depending on the Manufacturer, Type and

Influent Flow, Membrane Type and Operating

Parameters. Subsequently, the models could

be evaluated and adjusted comparing the

theoretical values obtained by the application

of the algorithm that results from this

Dissertation with the practical values of

Analysis of Effluents and Effluents Treated in

WWTP of similar configurations.

As recommendations for future works, it is also

advisable to model other configurations

associated to MBR systems and to study the

effect of the design temperature in this type of

systems.

9

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