Mathematical modelling of wastewater treatment

technologies in industrial water circuits

Mid Term Conference, Oviedo

14th June, Oviedo

P. Grau, I. Lizarralde and L. Sancho

� Rising costs and scarcity of water encourages the study of new water treatment technologies and strategies for reusing water in water networks in mills

� The wide variety of technologies, the different water qualities at each point in the network and the multiple sources/sinks make difficult to find the optimum solution

Introduction and Objectives

difficult to find the optimum solution

� The use of mathematical models and simulation tools can be very helpful on this task

� Objective:

� To develop a library of mathematical models able to reproduce the behaviour of some traditional and novel wastewater treatments

Part of the WQMT

DatabasesStudy by

dynamic/ steady-state simulations:Steady-state model

library

SOFTWARE TOOL

Dynamic model library

•Water treatment technologies

•Integrated water circuits

Optimum water circuits

library

Library of Unit-Process models

Water – Solids separation

Unit Processes

Settler

DAF

Biological Unit Processes

Activated Sludge unit

MBR

MBBR

MF, UF

NF, RO

3FM

FACT

Evapoconcentrator

Electrodialysis

Anaerobic unit (UASB)

Denutritor

Chemical Unit processes

AOPs

Disinfection (O3, Cl2, UV)

Coagulation-flocculation

Mathematical structure of the models

� IWM: common method to construct mathematical models that guarantees mass and heat energy continuity

� Definition of a Common Components List

� Gathers all relevant components/measurements in internal processes in the mills and wastewater treatment technologiesprocesses in the mills and wastewater treatment technologies

� Definition of mass and heat balances for all components

� Definition of operational and capital costs functions

Modelling of Biological units

� Describe the COD removal:

� Aerobic conditions:

� ASU, MBR, MBBR

� Anaerobic conditions:

� UASB (COD and SO4= removal)

� COD removal is described according to the endogenous respiration model (Lawrence and McCarty 1970)

SS XBH Xend So

XBH growth -1 YH -(1-YH)

XBH decay -1 fend -(1-fend)

respiration model (Lawrence and McCarty 1970)

� Steady-state equations are generated applying mass balances to the control volume of each biological technology

BH

SS

S

H

H XSK

S

Y += ·

µρ

BHH Xb ·=ρ

Biological models: Activated Sludge Unit (ASU)

Mass balance

l/mg3500TSS max ≈

d8SRT ≈

Effluent Quality Variables related with costs

CSTRSETTLERInflow Effluent

Waste

CSTRSETTLERInflow Effluent

Waste

+

+

+

−+

+

−

= SRT·Xf

SRT·XSRT·b1

)BODBOD·(Y·SRT·SRT·b·f

SRT·b1

)BODBOD·(Y·SRT

·TSS

1HRT 0,II

TSS_COD

0,IH

ef0HHend

H

ef0H

maxmin

( )[ ]( ) ( )nsHH

Hnsseff

f1bSRT

b·SRTf1KBOD

−−−µ

+−=

( ) ( )

−+

−= LM,BHHend

CODHASUreq X·b·f1

HRT

S·Y1·

1000

VDO

SRT

VQ ASU

w =inf

minASU

Q

HRTV =

Effluent Quality Variables related with costs

Biological models: Membrane Bioreactor (MBR)

Mass balance

l/mg10000TSS max ≈

d35SRT ≈

Effluent Quality Variables related with costs

+

+

+

−+

+

−

= SRT·Xf

SRT·XSRT·b1

)BODBOD·(Y·SRT·SRT·b·f

SRT·b1

)BODBOD·(Y·SRT

·TSS

1HRT 0,II

TSS_COD

0,IH

ef0HHend

H

ef0H

maxmin

( )[ ]( ) ( )nsHH

Hnsseff

f1bSRT

b·SRTf1KBOD

−−−µ

+−=

( ) ( )

−+

−= LM,BHHend

CODHMBRreq X·b·f1

HRT

S·Y1·

1000

VDO

SRT

VQ MBR

w =inf

minMBR

Q

HRTV =

Effluent Quality Variables related with costs

Comparison between ASU and MBR

0.80

1.00

1.20

1.40

1.60

1.80

2.00

BO

De

f (m

gC

OD

/l)

ASU

MBR

Effluent Quality Variables related with costs

0.30

0.40

0.50

0.60

0.70

0.80

HR

T (

d)

ASU

MBR

0.00

0.20

0.40

0.60

0.80

0 5000 10000 15000 20000 25000 30000

Mass Flux (kg/d)

BO

De

f (m

gC

OD

/l)

0.00

0.10

0.20

0 5000 10000 15000 20000 25000 30000

Mass Flux (kg/d)

0.00

5000.00

10000.00

15000.00

20000.00

25000.00

30000.00

0 5000 10000 15000 20000 25000 30000

Mass Flux (kg/d)

DO

req

(g

/d)

ASU

MBR

0

1000

2000

3000

4000

5000

6000

7000

8000

0 5000 10000 15000 20000 25000 30000

Mass Flux (kg/d)S

lud

ge p

rod

ucti

on

(kg

/d)

ASU

MBR

Biological models: (UASB)

inf

minMBR

Q

HRTV =

Mass balance

l/mg10000TSS max >

d30SRT >

CSTRSETTLERInflow Effluent

Waste

CSTRSETTLERInflow Effluent

Waste

( )

( )nsns

HH

nsHnss

eff,4SO

f1HRT

fbSRT

HRT

fbSRTf1K

S

−−

−−µ

++−

==

Effluent Quality Variables related with costs

( )

( )nsns

HH

nsHnss

eff,COD

f1HRT

fbSRT

HRT

fbSRTf1K

S

−−

−−µ

++−

=

inf44SO_CODSRB SO·fCOD==

SRT

VQ UASB

w =inf

minUASB

Q

HRTV =

Water-Solids separation Units

� Units for separation of suspended solids and colloids (TSS and TCS)

� Settler

� Dissolved Air Flotation (DAF)

� 3FM� 3FM

� MF-UF (% of dissolved particles TDS)

� Units for separation of TDS (organic and ions)

� NF-RO

� Evapoconcentrator

� Electrodyalisis

Units for separation of TSS and TCS:

Settlers and DAFs

� Water-Solid separation is based on efficiency rates for TSS and TCS

ff Q,TSS clarclar Q,TSS

slsl Q,TSS

clar

ffnss_Xclar

Q

QTSSfTSS ⋅⋅=

( )sl

ffnss_Xsl Q

QTSSf1TSS ⋅⋅−=

� Settler (>1500 mg/l) � DAF (≈≈≈≈ 1000 mg/l)

clar

ffnss_Xclar

Q

QTSSfTSS ⋅⋅=

( )sl

fffloat_Xsl Q

QTSSf1TSS ⋅⋅−=

fX_nss depends on the TSS

setteability

fX_float depends on the air/solids ratio (aS):

ffloat = 0.66aS + 0.79

Units for separation of TSS and TCS:

3FM and MF-UF

� Water-Solid separation is driven by a pressure drop across the membrane

permQ,Permeate

concQ,eConcentrat

infQ,InflowA·

)FF1(

P·LQ

pp

+

∆=

TDS·TCS·TSS·FF SCX α+α+α=

−=

100

R1·CC C

fp

� 3FM (2-5 µµµµm)

� TSS and TCS removal

� Op. Costs:

� MF-UF (0.02-0.4 µµµµm)

� TSS, TCS and % TDS removal

� Op. Costs:

concQ,eConcentrat TDS·TCS·TSS·FF SCX α+α+α=

permEEPE Q·P·KOP = permEEPE Q·P·KOP =

( ) concEEbwash QTDSTCSTSS·P·KOP ++=airairEair Q·P·KOP =

Units for separation of TDS:

RO, Evapoconcentrator and Electrodialysis

� All of them considered as instantaneous separation units:

permQ,Permeate

concQ,eConcentrat

infQ,Inflow

Reverse Osmosis

Calculation of Qperm and

TDSperm depend on the

technology used

� Electrodyalisis� Reverse Osmosis

( )A·

)FF1(

P·LQ

pp

+

∆Π−∆=

+

=

A

QB

BCC

pfp

11

76.0·)·273(19.1

−+=∆Π ∑ ∑

conc feed

ii mmT

� Electrodyalisis

pfp

QFz

INCC

⋅⋅

⋅⋅ξ−=

� Evapoconcentrator

compoundsvolatilenonfor0C

compoundsvolatileforCC

p

fp

=

=

Chemical Unit processes: Disinfection

� Inactivation related to contact time given by Chick’s law:

� k values depend on: � Disinfectant: Ozone, chloramine, chlorine, UV radiation� Pathogens: bacteria (e-coli, legionella), virus, cyst, crystosporidium,

mn

o

t HRTCkN

N··ln −=

� Pathogens: bacteria (e-coli, legionella), virus, cyst, crystosporidium, egg-nematode

� Temperature

� pH

Chloramine-Virus

-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

0.00 0.50 1.00 1.50 2.00

C·HRTln

(n/n

o)

T=5ºC

T=10ºC

T=15ºC

T=20ºC

T=25ºC

Conclusions

� A library of mathematical models able to describe a set of traditional and novel wastewater treatment technologies has been developed� Describe the fate of the most relevant and critical

components in water networks

Models are compatible and directly connectable among � Models are compatible and directly connectable among them

� Consider all relevant variables to calculate investment and operational costs associated to each treatment

� Current and future tasks� Implementation and verification of the models in the

software tool

� Calibration of the models with experimental data