Physical, chemical, and/or electrical driving force

Permeate

Solute or particle rejection

Feed or concentrate

Semi-permeable (selective) membrane

Accumulated, rejected material, migrating back to bulk solution

cc(x)

cp(x)Feed(Qf, cf)

Permeate(Qp, cp,out)

Concentrate (Qc, cc,out),Retentate, Rejectate

Membrane Applications in Drinking Water Treatment

Pressure-Driven Membrane Processes

• Separate by size and chemistry• Concentration, Porosity Effects

OTHER DRIVING FORCES

• Charge Gradient (Electrodialysis)• Concentration Gradient (Dialysis)• Temperature Gradient (Thermoosmosis)

PRESSURE GRADIENT

PORE DIAMETER

MEMBRANE DESIGNATION

REMOVAL EFFICIENCY

RelativeSizes

SeparationProcess

Molecular Weight (approx..)

Size, MicronsIonic Range

0.001(nanometer)

Molecular Range

0.01

MacroMolecular Range

0.1 1.0

MicroParticle Range

10 100

Macro Particle Range

1000

100 1,000 100,000 500,000

BacteriaVirusesDissolved Salts(ions)

Algae

Clays Silt

Asbestos Fibers

Cysts Sand

Conventional Filtration (granular media)

Organics (e.g., Color , NOM, SOCs)

Microfiltration

Ultrafiltration

Nanofiltration

ReverseOsmosis

Membrane Separations for Application to Drinking Water Treatment

Membrane cross section

(b)

The Two Meanings of Filtration:2. Porous Membrane Filtration

1 m

1 m

PDMAEMA-b-PFOMA layer

Microporous Polysulfone Support

40% PDMAEMA-60% PFOMA Thin-film Composite NF Membrane (Polysulfone Support Layer)

Membrane Geometry

Spiral Wound

NF/RO

Hollow Fibers

MF/UF

Tubular Elements

Spiral Elements

(a)

INORGANIC SYNTHETICS

Ceramics

Glass

Metallic

• Excellent thermal stability

• Withstands chemical attack

PLATE AND FRAME

Two MF/UF Configurations

• Encasedmembrane system

• Submerged membrane system

Pump supplies positive pressure to PUSH water through membrane media.

FeedWater

Filtrate

Pump

PressureVessel(s)

Membrane

Pump suction PULLS water through membrane media.

FeedWater

Filtrate

Pump

OpenTank

Membrane

Permeate

HF

Air

Raw Water Pump

2-12 psi

Wasting

Immersed Membranes with Gentle Crossflow

NF & RO Scottsdale Water Campus

CASCADE SYSTEM

RETENTATE

PERMEATE

FEED

PERMEATEFEED

RETENTATE

Qf

Cf

A

QP

CPQR

CR

TMP = “Transmembrane pressure (difference)”

Flux (“LMH” or “GFD”) = QQpp / A / A

(Contaminant) Rejection (%) = 1 CCpp/C/Cff

Recovery (%) = Qp/Qf

Membrane Geometry

Approximate Packing Density (m2/m3)

Capillary 5000-8000

Spiral wound 700-2000

Hollow fiber 1000-2000

Flat (plate and frame)

200-500

Tubular 100-300

Membrane Process Transmembrane Pressure, ∆Ptot (kPa)

System Recovery (%)(a)

Microfiltration 10 to 100 90 to 99+

Ultrafiltration 50 to 300 85 to 95+

Nanofiltration 200 to 1500 75 to 90+

Reverse Osmosis 500 to 8000 60 to 90

(a) Defined as the ratio of permeate flow rate to feed flow rate

LP gh

2

MF

3 2

kg m-s15,000 Pa 1.0

Pa1.53 m

kg m1000 9.81

m sL

Ph

g

2

6

RO

3 2

kg m-s4.5x10 Pa 1.0

Pa459 m

kg m1000 9.81

m sL

Ph

g

Example. What height would a column of water have to be to exert a pressure equal to 15 kPa? 4500 kPa?

Solution. From fluid mechanics:

Therefore:

Example. What is the average velocity of solution toward a membrane, if the flux is 50 LMH?

3

2

L 1 m cm cm50 100 5.0

m -h 1000 L m hVJ

Flow Through Porous Membranes

2

2f

L vh f

D g

For Laminar Flow:

64 / Ref

fP gh

Darcy-Weisbach Eqn:

For Steady Flow Through a Pore:

Hagen-Poiseuille Eqn:

2

8pore

pore

r PJ

L

2

8pores pore

memmem mem

A r PJ

A

Flow Through Porous Membranes

Driving Force

Flux

P

J

RResistance (kg/m2-s):

P

J

R

RMembrane Resistance (m:

Process Typical Volumetric

Flux, (L/m2-h)

Typical Membrane

Resistance, Rm (m1)

Microfiltration 100-250 1x1011 – 1x1012

Ultrafiltration 30-150 1x1012 – 1x1013

Nanofiltration 20-50 1x1013 – 1x1014

Reverse osmosis 5-40 5x1013 – 1x1015

Flow Through Porous Membranes

/ mem

mem

P

J

RResistivity:

1

Resistivity /V

Vmem

Jk

P

Permeability for overall flow:

/i

imem

Jk

P

Permeability for individual species:

1 m

Contaminant Rejection by Open Pores (Clean Membrane)

A B

Membrane

Pore

Contaminant Rejection by Open Pores (Clean Membrane)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Particle-to-Pore Diameter Ratio, i

Par

tic

le R

eje

cti

on

, R

i

Flat

Parabolic

Modifiedparabolic

Velocity Profile at Entrance

Increasing driving force increases flux of both water and contaminants. So, rejection of a given type of particle by a clean membrane is predicted to be independent of P or J.

Membrane Fouling

0

20

40

60

80

100

120

0 60 120 180 240 300

Time (min)

Tra

nsm

emb

ran

e P

ress

ure

(kP

a)

Backwash

Irreversible Fouling

Backwash & Chemical Cleaning

Hydraulically Irreversible Fouling

Problems Caused by NOM

Membrane Fouling

O

OHHO

HOOC COOH

OH

OH

O

COOH

COOHO

OH

HOOC

OO

O

HO

O

O

OHDBPs

+Cl2

Interference w/Activated

Carbon

NOM Fouling of an MF Membrane

Note: <3% Removal of NOM from Feed

Gel Surface

Membrane

Gel Cross-Section

Membrane support

0.0.E+00

1.0.E+12

2.0.E+12

3.0.E+12

4.0.E+12

5.0.E+12

6.0.E+12

7.0.E+12

8.0.E+12

9.0.E+12

1.0.E+13

0 50 100 150 200 250 300 350 400

Vsp (L/m2)

Rf (

m-1

)

FR: 1.64×1010

FR: 4.6×1010

Heated Aluminum Oxide Particles (HAOPs)

Al2(SO4)3+NaOHpH 7.0 110 110 ooC, 24 hrsC, 24 hrs

Particle Size Range: m, mean ~5 m, mean ~5 mm

Point of Zero Charge: pH 7.7pH 7.7

BET Surface Area: 116 m116 m22/g/g

Aluminum Content: ~25% (Al(OH)~25% (Al(OH)33HH22O)O)

0

50

100

150

200

250

300

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

Specific volume filtered, V sp (L/m2)

Tran

smem

bran

e pr

essu

re (k

Pa)

0

4.5

9

18

HAOPssurface loading

(g/m 2 as Al)

Transmembrane pressure with varying HAOPs surface loadings

DOC Concentrations in Permeate

0.0

0.2

0.4

0.6

0.8

1.0

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

Specific volume filtered, Vsp (L/m2)

No

rmal

ized

DO

C

0

4.5

9

18

HAOPssurface loading

(g/m2 as Al)

* Filtration ended at TMPs of 35~40 psi

Progressive NOM Deposition on the HAOPs Layer

Vsp: 0 L/m2 1,200 L/m2 3,600 L/m2

4,700 L/m2 7,000 L/m2 7,000 L/m2

Summary: Performance and Modeling of Porous Membranes

• Solution flux proportional to P, inversely proportional to resistance• Resistance of clean membrane can be estimated from basic fluid

mechanics• If contaminant rejection is primarily due to geometrical factors, it is

expected to be insensitive to applied pressure and flux• In practice, resistance of accumulated rejected species quickly

overwhelms that of membrane (fouling)• Frequent backwashing reduces, but does not eliminate fouling• In drinking water systems treating surface water, NOM is often a

major fouling species, even though only a small fraction of the NOM is rejected

• Approaches to reduce fouling by NOM and other species are the focus of active research

Transport Through Water-Selective, Dense (“Non-Porous”) Membranes

With no P, the concentration gradients drive water toward the feed and contaminants toward the permeate.

cw,f

55.0

0.555

55.5

0.055 Solute, 90% rejection

Osmosis of water

Pressure profile for P=0 everywhere

cw,p

cs,f

cs,p

Increasing pressure increases the “effective” concentration of any species. For an increase of P, the effective concentration is:

, exp ieff i i

V Pc c

RT

18 g/mol L0.018

1000 g/L molwV

6 17.45x10 kPawV

RT

At P= 3000 kPa: , exp 1.023ieff w w w

V Pc c c

RT

For water:

At 25oC:

Result: Even a large P increases effective concentrations by only a few percent.

The pressure required to bring the effective concentration of water up to the concentration of pure water (and thereby stop diffusion) is the osmotic pressure, . Permeate is often approximated as pure water. In this example, is a pressure that increases ceff by ~1%. Note that ceff of the solute also increases by ~1%.

cw,f 55.0

0.555

55.5

0.055

cw,p

Solute, 90% rejection

Osmosis eliminatedcw,eff,f

55.5

P = 0

P =

0.56 cs,f

cs,p

cs,eff,f

Applying a P > causes water to move in the opposite direction from passive osmosis, hence is called reverse osmosis. For P ~3000 kPa, ceff increases by ~3%, so:

cw,f 55.0

0.555

55.5

0.055

cw,p

Solute, 90% rejection

Reverse osmosis

cw,eff,f

56.5

P = 0

P >

0.57

Although increasing P causes the same percentage increase in ceff for water and solute, it has a much bigger effect on ceff for water than for solute.

cs,f cs,p

cs,eff,f

Permeate

Concentration increase due to solute rejection and slow diffusion back to bulk solution

Concentration increase in bulk concentrate due to selective water removal

Permeate

Highest salt concentrations occur right next to membrane, where precipitation (‘scaling’) is

most likely

Performance and Modeling of Dense Membranes

• Water flux occurs by diffusion, and is ~proportional to P, because changing P has big effect on cw,eff

• Solute flux occurs by diffusion, and is ~proportional to ci, because changing P has small effect on ci,eff

• Conclusion: changing P increases water transport more than solute transport, and so increases rejection (different from porous membranes)

• Fouling also occurs on dense membranes, mostly by NOM and precipitation (scaling); reduced by “anti-scalants”

• Dense membranes can’t be backwashed, because required pressures would be too high; therefore, major effort is usually devoted to pre-treatment to remove foulants

• Approaches to reduce fouling are the focus of active research