Lin S.D. Water and Wastewater Calculations Manual

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16.1 Process description and operations

The membrane processes were originally developed based on the theory

of reverse osmosis. Osmosis is the natural passage of water through a

semipermeable membrane from a weaker solution to a stronger solution,

to equalize the concentration of solutes in both sides of the membrane.

Osmotic pressure is the driving force for osmosis to occur. In reverse

osmosis, an external pressure greater than the osmotic pressure is

applied to the solution. This high pressure causes water to ﬂow against

the natural direction through the membrane, thus producing high-quality

demineralized water while rejecting the passage of dissolved solids.

The driving force for a membrane process can be pressure, electrical

voltage, concentration gradient, temperature, or combinations of the

above. The ﬁrst two driving forces are employed for water and waste-

water membrane ﬁltrations. Membrane processes driven by pressure are

microﬁltration (MF), utraﬁltration (UF), nanoﬁltration (NF), and reverse

osmosis (RO); while processes driven by electric current are electro-

dialysis (ED) and electrodialysis reversal (EDR). ED is originally used

for medical purposes. EDR is generally used for water and wastewater

treatments. The vacuum-driven process typically applies to MF and UF

only.

Microfiltration. Microfiltration uses microporous membranes that

have effective pore sizes in the range of 0.07 to1.3 ␮m and typically

have actual pore size of 0.45 ␮m (Bergman, 2005). The particle-

removal range is between 0.05 and 1 ␮m. Flow through a microp-

orous membrane can occur without the application of pressure on the

feed side of the membrane, but in most water and wastewater appli-

cants, a small pressure difference across the membrane produces sig-

niﬁcant increases in ﬂux, which is required for water production. MF

membranes are capable of removing particles with sizes down to 0.1

to 0.2 ␮m. As granular filtration, MF system filters out turbidity,

algae, bacteria, Giardia cysts, Cryptosporidium oocysts, and all par-

ticulate matters in water treatment (Bergman, 2005; Movahed, 2006a,

2006b). It is also most often used to separate suspended and colloidal

solids from wastewater.

Ultrafiltration. Ultrafiltration uses membranes that have effective

pore sizes of 0.005 to 0.25 ␮m (Bergman, 2005). UF units are capable

of separating some large-molecular-weight dissolved organics, col-

loids, macromolecules, asbestos, and some viruses from water and

wastewater by pressure (Qasim et al., 2000; Bergman, 2005, Movahed,

2006b). The UF process is designed to remove colloidalized particles,

in the range from 0.005 to 0.1 ␮m (Movahed, 2006a). It is not effec-

tive for demineralization purposes; however, most turbidity-causing

Public Water Supply 445

particles, viruses, and most organic substances such as large molec-

ular NOMs (natural organic matters, with coagulation) and proteins

are within the removal range of UF.

In the case of food processing, UF units can be used to separate pro-

teins and carbohydrates from the wastewater. The proteins and carbo-

hydrates may then be reused in the process or sold as a by-product.

Another use of UF units is the separation of emulsiﬁed fats, oils, and

grease from wastewater (Alley, 2000). The UF process retains nonionic

material and generally passes most ionic matter depending on molecu-

lar weight cutoff of the membrane.

Both MF and UF membrane systems generally use hollow ﬁbers that

can be operated in the outside-in or inside-out direction of ﬂow. Low pres-

sure (5 to 35 psi or 34 to 240 kPa) or vacuum (–1 to –12 psi or –7

to –83 kPa for outside-in membranes only) can be used as the driving

force across the membrane (Movahed, 2006a; Bergman, 2005). MF and

UF membranes are most commonly made from various organic polymers

such as cellulose derivatives, polysulfones, polypropylene, and polyvinyli-

dene ﬂuoride (PVDF). Physical conﬁgurations of MF and UF mem-

branes include hollow ﬁber, spiral wound, cartridge, and tubular

constructions. Membrane technologies are also widely used for waste-

water treatment (Movahed, 2006a).

Most MF and UF facilities operate with high recoveries of 90% to

98%. Full-scale systems have demonstrated the efﬁcient performance

of both MF and UF as feasible treatment alternatives to conventional

granular media ﬁltrations. Both MF and UF units can also be used as

a pretreatment for NF or RO or to replace the conventional media

ﬁltration.

Nanoﬁltration. “Nano” means one-thousandth of a million (10

⫺9

). One

nanometer (1 nm) ⫽ 10

⫺9

m ⫽ 10

⫺3

␮m. Nanoﬁltration uses membranes

that have a larger effective pore size (0.0009 to 0.005 ␮m or about 1 to

5 nm) than that of RO membranes (Qasim et al., 2000; Bergman, 2005).

NF and RO separation properties are typically expressed in molecular

weight cutoff (MWCO) as the unit of mass in daltons. The typical masses

used for NF and RO are 200 to 1000 daltons and <100 daltons, respec-

tively (Movahed, 2006c).

The typical feed pressures for NF system are 50 to 150 psi (340 to 1030

kPa) (Bergman, 2005). The osmotic pressure equation still applies to NF,

but the osmotic pressure difference across the membrane will be lower.

It could be 10 to 20 psi (Movahed, 2006c). The osmotic pressure differ-

ential across the membrane is taken into account in the equation for

water transport through the membrane.

The major equipment for an NF process is similar to that for an RO

system, and includes a membrane module with support system, a

446 Chapter 5

high-pressure pump and piping, and a concentrate-handling and dis-

posal system. The NF is only periodically backwashed by using either

water or air as with a granular filtration system. Membranes are

usually cleaned automatically as required.

New development. NF processes reject molecules in the range from

0.001 to 0.01 ␮m. Such a process can be used for softening and for reduc-

tion of total dissolved solids (TDS) and TOC. A lower-pressure RO tech-

nology called nanoﬁltration, also known as “membrane softening,” has

also been widely used for treatment of hard, high-color, and high-organic-

content feedwater (Movahed, 2006a). NF also removes NOM, disinfec-

tion by-products (DBPs), and radionuclides (Movahed, 2006a; Crittenden

et al., 2005).

Cregorski (2006) reported that in early 2006, researchers at the

Lawrence Livermore National Laboratory created a membrane made of

carbon nanotubes and silicon which may offer an even less-expensive

desalination technology. The nanotubes, special molecules made of

carbon atoms in a unique arrangement, are hollow and more than 50,000

times thinner than a human hair. Billions of these tubes act as pores in

the membrane allowing liquids and gases to rapidly pass through while

the tiny pore size blocks larger molecules.

The research team was able to measure ﬂows of liquids by making a

membrane on a silicon chip with carbon nanotube pores, ideal for desali-

nation. The membrane was created by ﬁlling with a ceramic matrix

material into the gaps between aligned carbon nanotubes. The pores are

so small that only six water molecules could ﬁt across their diameter.

According to Olgica Bakajin, lead scientist for the National Laboratory

nanotube membrane research project, “The gas and water ﬂows that we

measured are 100 to 10,000 times faster than what classical models

predict. In regards to desalination, the process is usually performed

using an RO membrane process, which does require a large amount of

pressure and energy. According to the research team, the more perme-

able nanotube membranes could reduce energy costs of desalination by

up to 75% compared to current RO technology. We hope that this tech-

nology will be ready for the market soon”.

Reverse osmosis. Reverse osmosis is a membrane separation process,

which through the application of pressure, reverses the natural phe-

nomenon of osmosis. Osmosis is the ﬂow of water from an area of low

ionic concentration to an area of high ionic concentration. Under an

applied pressure, water is forced through a semipermeable membrane

from an area of high concentration to one of low concentration. The

semipermeable membrane rejects the solutes in the water while allow-

ing the clean water to pass through.

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The effective pore sizes of RO membranes range from 0.1 to 1.2 nm

(0.0001 to 0.0012 ␮m) (Qasim et al., 2000; Bergman, 2005). This pore

size allows the passage of only water. In order for RO to take place,

the applied pressure must be greater than the naturally occurring

osmotic pressure. Osmotic pressure is a characteristic of the solution

and is a function of the molar concentration of the solute, the number

of ions formed when the solute dissociates, and the solution

temperature.

Reverse osmosis modules have been developed in four different types

of designs: plate and frame, large tube, spiral wound, and hollow ﬁber.

Many types of membranes for RO have been developed, but cellulose

acetate and polyamide are currently the most widely used membrane

materials in RO systems. Typical membranes are approximately 100 ␮m-

thick having a surface skin of about 0.2-␮m thickness that serves as the

rejecting surface. The remaining layer is porous and spongy, and serves

as backing material. The hollow ﬁne ﬁbers have outer and inner diam-

eters of 50 and 25 ␮m, respectively (Qasim et al., 2000).

Reverse osmosis processes are mostly used for demineralization in

industrial water supply or for desalinization of seawater and brackish

water in drinking water supply. The RO cartridges have been widely

installed for tap water at homes and ofﬁces in Asian countries, such as

Taiwan and Japan. Even coin-operated RO water supplies are popular

on streets.

Reverse osmosis membrane technology has been successfully used

since the 1970s for brackish and seawater desalination. In comparison

with other membranes, the RO membrane rejects most solute ions and

molecules, while allowing water of vary low mineral content to pass

through (Movahed, 2006b). Of course, this process also works as a bar-

rier for cysts, bacteria, viruses, NOMs, DBPs, etc.

In the RO process, the feedwater is forced by hydrostatic pressure

through membranes while impurities remain behind. The puriﬁed water

(permeable or product water) emerges at near atmospheric pressure. The

waste (as concentrate) remains at its original pressure and is collected

in a concentrated mineral stream. The pressure difference is called

osmotic pressure that is a function of the solute concentration, charac-

teristics, and temperature. The operating pressure ranges from 800 to

1200 psi (5520 to 8270 kPa or 54.4 to 81.6 atm) for desalting seawater

and from 300 to 600 psi (2400 to 4100 kPa or 20.4 to 40.8 atm) for brack-

ish water desaltation (Montgomery Consulting Engineers, 1985;

Bergman, 2005).

The RO process produces a concentrated reject stream in addition

to the clean permeate product. By-product water or the “concentrate”

may range from 10% to 60% of the raw water pumped to the RO unit.

For most brackish water and ionic contaminant removal applications,

448 Chapter 5

the concentrate is in the 10% to 25% range, while for seawater, it could

be as high as 50%. Typical RO/NF elements are in spiral wound ele-

ment configuration, while EDR is in stacks containing membrane

sheets.

Electrodialysis reversal. Electrodialysis is an electrochemical sepa-

ration process in which ions are transferred through ion exchange

membrane by means of an electrical driving force. When a DC volt-

age is applied across a pair of electrodes, positively charged ions move

toward the cathode, while negatively charged ions move toward the

anode. Membranes are placed between the electrodes to form several

compartments. Flow spacers are placed between the membranes to

support the membranes and to create turbulent flow. Water flows

along the spacers’ ﬂow paths across the surface of the membranes,

rather than through the membranes as in RO (von Gottberg, 1999).

Impurities are electrically removed from the water. EDR is an ED

process, except by reversing polarity two to four times per hour; the

system provides constant, automatic self-cleaning that enables

improving treatment efficiency and less downtime for periodic

cleaning.

The conﬁguration of EDR is in stacks containing membrane sheets.

The nonpressure EDR has also been widely used for removal of dis-

solved substances and contaminants. In the United States, RO and

EDR ﬁrst have been used for water utilities ranging from 0.5 to 12 MGD

(1.94 to 45.4 m

/d); most are located in the East Coast and West Coast

(Ionic, 1993).

16.2 Design considerations

Membrane ﬁltration technologies have emerged as viable options for

addressing current and future drinking water regulations related to the

treatment of surface water, groundwater under the inﬂuence, and water

reuse applications for microbial, turbidity, NOM, and DBP removal.

Membrane systems are now available in several different forms and

sizes, each uniquely ﬁtting a particular need and application.

The basic theory, process fundamentals, membrane fouling, and

process design for membrane ﬁltration are given elsewhere (Crittenden

et al., 2005; Bergman, 2005). The design engineer must understand the

fundamentals of membrane material, modules, fouling, scaling, and per-

formance to evaluate new technologies with the objective of the project.

Design assistance is often available from the equipment manufacturers.

Membrane processes that satisfy treatment objectives at the lowest

possible life-cycle cost should be selected. The following procedures

Public Water Supply 449

should be considered in membrane system selection (Bergman, 2005;

Crittenden et al., 2005; Qasim et al., 2000):

■

Review the historical water quality data.

■

Identify overall project goals and deﬁne the correct treatment.

■

Evaluate source water quality characteristics and select pretreat-

ment processes.

■

Assess the need for bench or pilot testing.

■

Select membrane system after consultation with the equipment man-

ufacturers and pilot testing.

■

Select feedwater pretreatment or disinfection requirements (methods

to control fouling).

■

Select the basic performance criteria: plant capacity, salinity of feed-

water, ﬂux rate, recovery rate, rejection, applied pressure, system

life, performance level, feedwater temperature, and permeate solute

concentration based on the best and worst conditions.

■

Determine product water quality and quantity requirements and

blending options (for example, split-ﬂow treatment).

■

Establish process design criteria and develop speciﬁcations for major

system components.

■

Calculate system size.

■

Select the type of membrane and determine the array conﬁguration.

■

Determine ancillary and support facilities, such as transfer piping,

pumping facilities, chemical storage facilities, laboratory space, build-

ings, energy recovery system, and electrical systems.

■

Determine power requirement.

■

Evaluate hydraulic grade line and waste wash water disposal options.

■

Select permeate posttreatment requirements.

■

Estimate system economics, including amortization of capital and

operation and maintenance cost, supplies and chemicals, and con-

centrate disposal.

■

Select equipment and procedures for process monitoring.

16.3 Membrane performance

The osmotic pressure theoretically varies in the same manner as the

pressure of an ideal gas (James Montgomery Consulting Engineers,

1985; Conlon, 1990):

(5.145a)p 5

nRT

450 Chapter 5

or (Applegate, 1984):

␲ ⫽ 1.12 T ⌺ m (5.145b)

where ␲ ⫽ osmotic pressure, psi

n ⫽ number of moles of solute

R ⫽ universal gas constant

T ⫽ absolute temperature, ⬚C ⫹ 273

␯ ⫽ molar volume of water

⌺m ⫽ sum of molarities of all ionic and nonionic constituent in

solution

At equilibrium, the pressure difference between the two sides of the

RO membranes equals the osmotic pressure difference. In low solute con-

centration, the osmotic pressure (␲) of a solution is given by the following

equation (US EPA, 1996):

␲ ⫽ C

RT (5.145c)

where ␲ ⫽ osmotic pressure, psi

⫽ concentration of solutes in solution, mol/cm

or mol/ft

R ⫽ ideal gas constant, ft ⋅ lb/mol K

T ⫽ absolute temperature, K ⫽⬚C ⫹ 273

When dilute and concentrated solutions are separated by a mem-

brane, the liquid tends to ﬂow through the membrane from the dilute

to the concentrated side until equilibrium reaches sides of the membrane.

The liquid and water passages (ﬂux of water) through the membrane are

a function of pressure gradient (Allied Signal, 1970):

⫽ W (⌬P ⫺⌬␲) (5.146)

and for salt and solute ﬂow through a membrane:

⫽ S (C

⫺ C

) (5.147)

where F

, F

⫽ liquid and salt ﬂuxes across the membrane,

respectively, g/cm

/s or lb/ft

/s; cm

/cm

/s or gal/ft

W ⫽ ﬂux rate coefﬁcients, empirical, depend on

membrane characteristics, solute type, salt type,

and temperature, s/cm or s/ft

⌬P ⫽ drop in total water pressure across a membrane,

atm or psi

⌬␲ ⫽ osmotic pressure gradient, atm or psi

⌬P ⫺⌬␲ ⫽ net driving force for liquid pass through

membrane

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, C

⫽ salt concentrations on both sides of membrane,

g/cm

or lb/ft

⫺ C

⫽ concentration gradient, g/cm

or lb/ft

The liquid or solvent ﬂow depends upon the pressure gradient. The

salt or solute ﬂow depends upon the concentration gradient. Also, both

are inﬂuenced by the membrane types and characteristics.

The terms “water ﬂux” and “salt ﬂux” are the quantities of water

and salt that can pass through the membrane per unit area per

unit time. The percent of feedwater recovered terms water recovery

factor, R:

(5.148)

where Q

⫽ product water ﬂow, m

/d or gpm

⫽ feedwater ﬂow, m

/d or gpm

Water recovery for most RO plants is designed in the range of 75% to 90%

for brackish water and of 30% to 50% for seawater (Movahed, 2006c).

The percent of salt rejection (Rej) is:

(5.149)

(5.149a)

(5.149b)

where C

and C

⫽ TDS concentrations in permeate and feedwater,

respectively.

Salt rejection is commonly measured by the total dissolved solids (TDS).

Measurements of conductivity are sometimes used in lieu of TDS. In RO

system, salt rejection can be achieved at 9% or more for seawaters; while

NF could be as low as 60% to 70% (Movahed, 2006c). Solute rejection

varies with feedwater concentration, membrane types, water recovery

rate, chemical valance of the ions in the solute, and other factors.

Example 1: A city’s water demand is 26,500 m

/d (7 MGD). What is the

source water (feedwater) ﬂow required for a brackish water RO, if the plant

recovery rate is 98%?

s1 2 Rejd

sQasim et al., 2000d

SP 5

3 100%

5 a1 2

product concentration

feedwater concentration

b 3 100%

Rej 5 100 2 salt passage sSPd

Recovery, R 5

3 100%

452 Chapter 5

solution:

rearranging:

Example 2: For a brackish water RO treatment plant, the feedwater applied

is 53,000 m

/d (14 MGD) to the membrane and the product water yields

42,400 m

/d (11.2 MGD). What is the percentage of concentrate rate?

solution:

Example 3: At a brackish water RO treatment plant, the total dissolved

solids concentrations for the pretreated feedwater and the product water are

2860 and 89 mg/L, respectively. Determine the percentages of salt rejection

and salt passage.

solution:

Step 1: Compute salt rejection using Eq. (5.149)

Step 2. Compute salt passage

Salt passage ⫽ 100% ⫺ salt rejection

⫽ (100 ⫺ 96.9)%

⫽ 3.1 %

5 96.9%

5 a1 2

2860

b 3 100

Salt rejection 5 a1 2

product conc.

feedwater conc.

b 3 100%

5 20%

Percentage of concentrate rate 5

10,600 m

53,000 m

3 100%

5 10,600 m

5 s53,000 2 42,400d m

5 Q

2 Q

Rate of concentrate produced 5 feedwater rate 2 product rate

5 7.13 MGD

5 27,000 m

5 s26,500 m

/dd 3 100/98

Recovery 5

3 100%

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Example 4: A pretreated feedwater to a brackish water RO process con-

tains 2600 mg/L of TDS. The ﬂow is 0.25 m

/s (5.7 MGD). The designed TDS

concentration of the product water is no more than 450 mg/L. The net pres-

sure is 40 atm. The membrane manufacturer provides that the membrane has

a water ﬂux rate coefﬁcient of 1.8 ⫻ 10

⫺6

s/m and a solute mass transfer rate

of 1.2 ⫻ 10

⫺6

m/s. Determine the membrane area required.

solution:

Step 1. Compute ﬂux of water

Given: ⌬P ⫺⌬␲ ⫽ 40 atm ⫽ 40 atm ⫻ 101.325 kPa/atm

⫽ 4053 kPa

⫽ 4053 kg/m ⋅ s

W ⫽ 1.8 ⫻ 10

⫺6

s/m

Using Eq (6.146)

⫽ W (⌬P ⫺⌬␲) ⫽ 1.8 ⫻ 10

⫺6

s/m (4053 kg/m ⋅ s

)

⫽ 7.3 ⫻ 10

⫺3

kg/m

⋅ s

Step 2. Estimate membrane area

Q ⫽ F

rearranging:

A ⫽ Q/Fw ⫽ (0.25 m

/s) ⫻ (1000 kg/m

)/(7.3 ⫻10

⫺3

kg/m

⋅ s)

⫽ 34,250 m

Step 3. Determine permeate TDS (C

) with above area

The TDS concentration of the product water is lower than the limit desired.

For the purpose of economy, blending some feedwater to the product water

can reduce membrane area.

5 367 mg/L

5 367 g/m

5 0.367 kg/m

Q 1 SA

1.2 3 10

m/s 3 2.6 kg/m

3 34,250 m

0.25 m

/s 1 1.2 3 10

m/s 3 34,250 m

5 F

A 5 SsC

2 C

5 SsC

2 C

5 2600 mg/L 5 2600 g/m

5 2.6 kg/m

454 Chapter 5