Water and Wastewater Engineering
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11-56 WATER AND WASTEWATER ENGINEERING
Hazen, A. (1892) Annual Report of the Massachusetts State Board of Health, Boston.
Hibler, C. P., C. M. Hancock, L. M. Perger, J. G. Wergrzyn, and K. D. Swabby (1987) Inactivation
of Giardia Cysts with Chlorine at 0.5 C to 5 C, American Water Works Association Research
Foundation, Denver, Colorado.
H udson, H. E. (1981) Water Clarification Processes Practical Design and Evaluation, Von Nostrand
Reinhold, NewYork, 1981, pp. 180–182, 233–234.
Kawamura, S. (2000) Integrated Design and Operation of Water Treatment Facil
ities, 2nd ed., John
Wiley & Sons, NewYork, pp. 194–292.
Kramer, M. H., B. L. Herwaldt, G. F. Craun, R. L. Calderon, and D. D. Juranek (1996) “Waterborne
Diseases 1993 and 1994,” Journal of American Water Works Association, vol. 88, no. 3, pp. 66–80.
LeGouellec, Y. A., D. A. Cornwell, and M. J. MacPhee (2004) “Treating Microfiltration Backwash,
Journal of American Water Works Association, vol. 96, no. 1, pp. 72–83.
Logan, B. E. et al. (1995) “Clarification of Clean-Bed filtration Models, Journal Environmental
Engineering, vol. 121, no. 12, pp. 869–873.
Monk, R. D. G. (1984) “I
mproved Methods of Designing Filter Boxes,” Journal of American Water
Works Association, vol. 76, no. 8, pp. 54–59.
Monk, R. D. G. (1987) “Design Options for Water Filtration,” Journal of American Water Works
Association, vol. 79, no. 9, pp. 93–106.
MWH (2005) Water Treatment: Principles and Design, John Wiley & Sons, Hoboken, New Jersey,
pp. 882, 892–894.
Rajagopalan, R. and C. Tien (1976) “Trajectory Analysis of Deep-Bed Filtration with Sphere-in-Cell Porous
Media Model,” American Institute of Chemical Engineeri
ng Journal, vol. 22, no. 3, pp. 860–868.
Reynolds, T. D. and P. A. Richards (1996) Unit Operations and Processes in Environmental Engineering,
PWS, Boston, pp. 287–288, 320.
Richardson, J. F., and W. N. Zaki (1954) “Sedimentation and Fluidization, Part I, Transactions of the
Institute of Chemical Engineers (Brit.), vol. 32, pp. 35–53.
Robeck, G. G, K. A. Dostal, and R. L. Woodward (1964) “Studies of Modification in Water Filtration,”
Journal Ameri
can Water Works Association, vol. 56, no. 2, p. 198.
Rose, H. E. (1945) “On the Resistance Coefficient–Reynolds Number Relationship of Fluid Flow through
a Bed of Granular Material,” Proceedings of the Institute of Mechanical Engineers, vol. 153, p. 493.
Trussell, R. R. and M. Chang (1999) “Review of Flow Through Porous Media as Applied to Headloss in
Water Filters,” Journal of Environmental Engineering, vol. 125, pp. 998–1,006.
Yao, K. M., M. T. Habibian and C.R. O’Melia (1971) “Water and Waste Water Filtration: Concepts and
Applications,” Environmental Science and Technology, vol. 5, no. 11, pp 1,105–1,112.
12-1
12-5 CHAPTER REVIEW
12-6 PROBLEMS
12-7 DISCUSSION QUESTIONS
12-8 REFERENCES
MEMBRANE FILTRATION
12-1 INTRODUCTION
12-2 MEMBRANE FILTRATION THEORY
12-3 PROPERTIES OF MF AND UF
MEMBRANES
12-4 MF AND UF PRACTICE
12
CHAPTER
12-2 WATER AND WASTEWATER ENGINEERING
12-1 INTRODUCTION
The membrane used in membrane filtration is a synthetic material that is semipermeable; that is,
it is highly permeable to some constituents and less permeable to others. To remove a constituent
from the water, the water is pumped against the surface of a membrane, resulting in a separation
of product and waste
streams as shown in Figure 12-1 .
Membranes can be described by a variety of criteria including (Jacangelo et al., 1997):
• Membrane pore size,
• Molecular weight cutoff (MWCO),
• Membrane material and geometry,
• Targeted materials to be removed,
• Type of water quality to be treated, and/or
• Treated water quality.
Along with these criteria, m
embrane processes can als o be categorized broadly into pressure
driven and electrically driven processes. This discussion is limited to pressure driven membrane
processes. Figure 12-2 summarizes the various pressure driven membrane processes an
d selected
materials removed by each. As used in water treatment, membranes are classified into two broad
categories: (1) those that are used to separate ions from solution, that is, reverse osmosis (RO)
and nanofiltration (NF) and (2) those that are used to separate suspended partic
les from water,
that is, microfiltration (MF) and ultrafiltration (UF). RO and NF were presented in detail in
Chapter 9. This chapter focuses on MF and UF.
A brief description of MF and UF provides a delineation of their differences.
Feed stream
Semipermeable
membrane
Waste stream containing
particulate matter (reject o
r
concentrate)
Product stream
(permeate)
FIGURE 12-1
S chematic of separation process through semipermeable mebrane.
MEMBRANE FILTRATION 12-3
• Ultrafiltration ( UF ). UF membranes cover a wide range of MWCOs and pore sizes. Opera-
tional pressures range from 70 to 700 kPa, depending on the application. “Tight” UF mem-
branes (MWCO 1,000 daltons * ) may be employed for removal of some organic materials
from freshwater, while the objective of “loose” membranes (MWCO 50,000 daltons
, 70
to 200 kPa) is primarily for liquid/solid separation, that is, particle and microbial removal.
• Microfiltation ( MF ). A major difference between MF and loose UF is membrane pore size;
the pores of MF ( 0.1 m or greater) are approximately an order of magnitude greater
than those of UF. The primary application for this me
mbrane process is particulate and
microbial removal.
12-2 MEMBRANE FILTRATION THEORY
Mechanisms of Filtration
A s shown in Figure 12-3a , some particles are removed by simple mechanical screening because
the particle is larger than the smallest opening through which the water flows. This is the dominant
mechanism for membrane filters. Additional mechanisms that remove particles are adsorption and
cake formation.
Natural organic matter (NOM) adsorbs onto membrane surfaces as shown in F igure 12-3b
(Jucker and Clark, 1994). In the early stages of filtration with a clean membrane this may be an
important mechanism for removing soluble and insoluble materials that have dimensions that
are much smaller than the mem
brane pore size. Although the adsorption c apacity is quickly
exhausted, the adsorbed material can reduce the size of the pores and, thus, increase the ability of
the membrane to capture particles smaller than the nominal pore size.
* A dalton (Da) is a unit of mass equal to 1/16 the mass of the lightest and mos t abundant isotope of oxygen. Typical solu tes
used for the determination of MWCO are sodium chloride, magnesium sulfate, and dextrose.
Operating
pressures
(kPa)
Size
(micrometers)
Separation
processes
700
Reverse
osmosis
Nano-filtration
Ultrafiltration
Microfiltration
Conventional filtration
processes
0.01 0.1 1.0 10 100 1,000
200 70 35
0.001
FIGURE 12-2
S chematic comparison of selected separation processes.
12-4 WATER AND WASTEWATER ENGINEERING
Particles that are removed by straining build up a cake on the membrane surface ( Figure 12-3c ).
The cake acts as a filtration medium. It improves the efficiency of the filter because it collects
particles smaller than the nominal pore size of the membrane.
Models of Membrane Filtration
The basic models for describing membrane performance are based on the concept of rejection.
The fraction of material removed from the permeate stream is described in the form of a simple
efficiency equation:
R
C
C
1
permeate
feed
⎛
⎝
⎜
⎞
⎠
⎟
(12-1)
where R rejection, dimensionless
C
permeate
permeate concentration, mg/L or particles/L
C
feed
feed water concentration, mg/L or particles/L
This equation may also be expressed in a logarithmic form (“log-removal”):
LR log
feed
permeate
C
C
⎛
⎝
⎜
⎞
⎠
⎟
(12-2)
or as percent removal
% removal
LR
100
100
10
⎛
⎝
⎜
⎞
⎠
⎟
(12-3)
Particles
Membrane
surface
Pores
Coating on wall
by small particles
Finer particles
trapped by cake
(a)
(b)
(c)
FIGURE 12-3
Mechanisms of membrane filtra-
tion: ( a ) Straining, ( b ) adsorption,
( c ) cake filtration.
MEMBRANE FILTRATION 12-5
Ferry (1936) developed a model for straining based on the hypothesis that particles following
a streamline near the edge of a pore opening impact the membrane surface and are captured, and
those particles in the streamline near the center of the pore escape. Ferry’s model is analogous to
Yao’s model (Yao et al., 1971). Based
on a statistical analysis of this model, rejection is a func-
tion of the particle size (MWH, 2005):
R
d
d
d
d
121 1
2
part
pore
part
pore
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
44
(12-4)
where d
part
particle diameter, m
d
pore
effective pore diameter, m
Mathematical modeling of cake filtration results in equations similar to that for granular fil-
tration such as those of Carmen (1937) and Rose (1945).
Theory of Membrane Filter Hydraulics
Flux. Pure water transport across a clean porous membrane is directly proportional to the trans-
membrane pressure (TMP) and inversely proportional to the dynamic viscosity. The volumetric
flux (m
3
/h · m
2
of membrane surface area) is modeled using a modified form of Darcy’s law
(AWWA, 2005):
J
Q
A
P
R
m
()( )
(12-5)
where
J volumetric water flux through membrane, m
3
/h · m
2
or m/h
Q volumetric flow rate of pure water, m
3
/h
A surface area of clean membrane, m
2
P transmembrane pressure, kPa
dynamic viscosity of water, Pa · s
R
m
membrane resistance coefficient, m
1
This form differs from Darcy’s law in that the absolute value of the pressure differential is used
rather than the pressure gradient.
The volumetric flow rate of water across a single pore can be modeled using Poiseuille’s law:
Q
rP
z
pore
4
8( )
(12-6)
where Q
pore
volumetric flow rate of pure water across a single pore, m
3
/h
r radius of pore, m
P transmembrane pressure, kPa
dynamic viscosity of water, Pa · s
z
pore length, m
Becau se pores in commercial water treatment membranes are not perfectly cylindric al,
a dimensionless tortu
osity factor is added to Equation 12-6 . To represent the total flow rate,
12-6 WATER AND WASTEWATER ENGINEERING
Equation 12-6 is mu ltiplied by the surface area and pore density per unit area (AWWA,
2005):
Q
rP
z
A
pore
4
8( )
(12-7)
where
pore
pore density per unit area, number/m
2
tortuosity factor, dimensionless
B y analogy, the membrane resistance coefficient ( R
m
) can be expressed as
R
z
r
m
8
4
()
pore
(12-8)
This equation provides some insight into the factors that influence the design of a membrane
filter. The flow rate is directly proportional to the pore density and inversely proportional to water
viscosity, tortuosity, and thickness of the membrane. The most important factor affecting flow rate
is the pore size because flow rate is d
irectly proportional to the 4th power of pore radius. Therefore,
small increases in pore radius can result in large increases in filtered water flow. Perhaps more
importantly, because commercial membranes employed in water treatment have a distribution of
pore sizes, the larger pores will transport a disproportionate quantity of water and particles.
Membrane Fouling.
Fouling of MF/UF membranes may be defined as the gradual reduction in
filtrate water flow rate at constant pressure, or an increase in transmembrane pressure to maintain
a constant flux. Fouling may be caused by particulate matter, dissolved organic matter, or biologi-
cal growth. It may be reversible or irrevers
ible. The fouling is termed irreversible if the loss in
flux cannot be recovered by backwashing and cleaning operations (Jacangelo and Buckley, 1996).
These are illustrated in Figure 12-4 . There are a number of models that have been developed in an
attempt to describe the decline in permeate flux.
The first class of models is c
alled resistance-in-series. These models apply a resistance value
to each of three components thought to contribute to membrane fouling. It is assumed that each
component contributes to hydraulic resistance and that they act independently from one another.
The following two equations
are typical of the form of the models:
J
P
RRR
m irr
()
(12-9)
J
P
RRR
mca
()
(12-10)
where
J volumetric water flux through membrane, m
3
/h · m
2
or m/h
P
transmembrane pressure, kPa
dynamic viscosity of water, Pa · s
R
m
membrane resistance coefficient, m
1
R
ir
irreversible membrane resistance coefficient, m
1
MEMBRANE FILTRATION 12-7
R
r
reversible membrane resistance coefficient, m
1
R
c
cake layer membrane resistance coefficient, m
1
R
a
adsorptive fouling membrane resistance coefficient, m
1
The second class of models is descriptive of the change in flux as a function of time. That is,
they are equations developed to fit experim ental data. In form, they represent the fact that flux
declines toward a steady-state value. They are summarized in Table 12-1 .
The third class of m
odels is mec hanistic. That is, they attempt to describe pore adsorption,
pore blocking, or cake formation as function of time. Collectively they have been termed the
blocking laws. They are summarized in Table 12-2 .
12-3 PROPERTIES OF MF AND UF MEMBRANES
Membrane Material
The most common MF and UF membrane materials are organic polymers. The characteristics of
the polymers are summarized in Table 12-3 on page 12-9.
Most synthetic membranes are hydrophobic. They must be stored wet or be filled with a
wetting agent. If allowed to dry, they will experience a change in
structure that will result in a
reduction in potential flux.
Polysulfone membranes are one of the most widely u sed because of their high tolerance to
pH and resistance to oxidants. They can withs tand temperatures up to about 75 C. In addition,
Initial transmembrane flux
Backwashing
Chemical cleaning
Chemical cleaning
Irreversible
fouling
Backwashing Initial transmembrane pressure
Irreversible
fouling
Transmembrane fluxTransmembrane pressure
Time
FIGURE 12-4
S chematic of partial restorations of transmembrane flux and pressure by chemical
cleaning of MF membranes. The abscissa scale is compressed and the ordinate scale
is expanded for illustration of the deterioration in performance.
12-8 WATER AND WASTEWATER ENGINEERING
TABLE 12-1
General forms of time-dependent membrane flux equations
Flux equation Linearized form Comments
(a) J
t
J
0
e
kt
ln
0
J
t
J
kt
⎛
⎝
⎜
⎞
⎠
⎟
Flux declines exponentially as
foulants accumulate. Flux
assumed to drop to zero at
infinite
time, which may not
occur in practice.
(b) J
t
J
ss
(J
0
J
ss
)e
kt
ln
J
t
J
ss
JJ
ss
kt
0
⎛
⎝
⎜
⎞
⎠
⎟
Similar to Eq. (a), except flux
drops to a steady-state flux J
ss
at t
infinite time.
(c) J
t
J
0
(kt)
n
ln ln
J
t
J
nkt
0
⎛
⎝
⎜
⎞
⎠
⎟
()
Cannot be used for initial stages
of filtration because infinite
flux is predicted at time t 0.
Sometimes expressed as a
function of the volume of
permeate (kt V) instead of as a
function of time.
(d)
J
J
kt
t
n
0
1()
ln ln
J
t
J
nkt
0
1
⎛
⎝
⎜
⎞
⎠
⎟
()
The series resistance model can be
written in this form with n 1.
Source: Adapted from MWH, 2005.
(continued)
TABLE 12-2
Blocking filtration laws
Flux equation Major features and assumptions
Pore sealing (complete blocking filtration law) • Models blockage of the entrance to pores by particles
retained at the membrane surface.
(1.5CJ
0
t/
P
d
P
)
J
t
J
0
e
• Each retained particle blocks an area of the membrane
surface equal to the particles cross-sectional area.
c
concentration of particles • Flux declines in proportion to the membrane area that
has been covered.
• No superposition of particles occurs. Each particle lands
on the membrane surface and not on other particles
, so
flux reaches zero when a monolayer of particles has been
retained.
Internal pore constriction (standard blocking
filtration law)
• Models the reduction of the void volume within the
membrane.
J
J
t
0
(1 CJ
0
t/L
P
)
2
• Assumes the membrane is composed of
cylindrical pores of constant and uniform
diameter.
L membrane thickness, m
• Particles deposit uniformly on the pore walls; pore
volume decreases proportionally to the volume of
particles deposited.
MEMBRANE FILTRATION 12-9
to polysulfone (PS), polyethersulfone (PES) and polyvinylidene difluoride (PVDF) are also in
common use (AWWA, 2005).
Membrane Configuration
Hollow fiber membranes ( Figu re 12-5 ) are the most common configuration for MF and UF fil-
tration applications (U.S. EPA, 2005). The fibers have an outside diam eter ranging from 0.5 to
2 mm, and a wall thickness ranging from 0.07 to 0.6 mm. Unlike NF and RO membranes, the
membrane filters operate over a repeating filtration cycle like granular filters. After filtration for
a set duration, the accumulated
solids are removed by backwashing with air and/or water. Once
clean, the filter is put back into service.
All of the hollow fiber membranes fall into one of two categories: positive pressure driven
and negative pressure (vacuum) driven. The positive pressure systems are configured in pressure
vessels. The vacuum systems are submerged in bas
ins containing the feed water.
TABLE 12-3
Characteristics of selected membrane materials
Membrane material Type Hydrophobicity
Oxidant
tolerance
pH
range
Fouling
resistance/
cleanability
PVDF MF/UF Modified hydrophilic Very high 2–11 Excellent
PP MF Slight hydrophobic Low 2–13 Acceptable
Polyethersulfone (PES) UF Very hydrophilic High 2–13 Very good
Polysulfone (PS) UF Modified h
ydrophilic Moderate 2–13 Good
Cellulose acetate (CA) UF Naturally hydrophilic Moderate 5–8 Good
( Source: AWWA, 2005.)
Pore sealing with superposition (intermediate
blocking filtration law)
• Models blockage of the entrance to pores by particles
retained at the membrane surface.
J
J
t
0
(1 1.5CJ
0
t/
P
d
P
)
• Extension of the complete blocking filtration law.
• Relaxes the “monolayer” assumption in the complete
blocking filtration law by allowing particles to land on
previously retained particles or on the membrane surface
by evaluating the probability that a particle will block a
pore.
Cake filtration law • Models the formation of a cake on the surface of a
membrane using the resistance serie
s model.
J
J
Jt
t
C
0
0
0 5
12() CR
m
/
.
• The retained particles have no impact on the membrane
itself, that is, no pore blocking or pore constriction.
c
specific cake resistance
Source: Adapted from MWH, 2005.