Iraqi Journal of Chemical and Petroleum Engineering 

 Vol.17 No.3 (September 2016) 57- 73 

ISSN: 1997-4884 

 
 
 
 
 

Experimental Study and Mathematical Modelling of Zinc Removal 

by Reverse Osmosis Membranes 

 
Ahmed Faiq Al-Alawy and Miqat Hasan Salih 

Chemical Engineering Department, College of engineering, University of Baghdad 

 

Abstract 

In this study, aromatic polyamide reverse osmosis membranes were used to 

remove zinc ions from electroplating wastewater. Influence of different operating 

conditions such as time, zinc concentration and pressure on reverse osmosis process 

efficiency was studied.  The experimental results showed, concentration of zinc in 

permeate increase with increases of time from 0 to 70 min, and flux of water through 

membrane decline with time. While, the concentrations of zinc in permeate increase 

with the increase in feed zinc concentration (10–300 mg/l), flux decrease with the 

increment of feed concentration. The raise of pressure from 1 to 4 bar, the zinc 

concentration decreases and the flux increase. The highest recovery percentage was 

found is 54.56% for reverse osmosis element, and the highest rejection of zinc was 

found is 99.49%. Experimental results showed that the concentrations of zinc ion in 

permeate was lower than the permissible limits (i.e. ˂ 10 ppm). A mathematical 
model describing the process was investigated and solved by using MATLAB 

PROGRAM. Theoretical results were consistent with the experimental results 

approximately 90%. 

 

Keywords: Heavy metals, Reverse osmosis, Zinc ions, Mathematical modelling. 

 

Introduction 

The world's population and the 

consequent desire for water supply 

increase, conservation of the 

invaluable and increasingly rare 

resource of water and sustainable 

development will require recycling and 

reuse.  Then, water resource 

sustainability interests suggest 

exploring the possibility of reusing 

treated water as a promising source of 

water [1]. 

The development of industries such as 

tanneries, mining operations, paper 

industries, metal plating facilities, 

batteries, fertilizer industries, 

petroleum refining, photographic 

process industry, textile industry and 

pesticides etc., a considerable amount 

of wastewater containing heavy metals 

is discharged into the water, 

particularly in developing countries 

[2]. The high solubility in the aqueous 

environments, heavy metals can be 

absorbed by living organisms. They 

enter the food chain, high 

concentrations of heavy metals may 

accumulate in human body [3, 4]. 

Heavy metals are elements having 

atomic weights between 63.5 and 

200.6, and a specific gravity greater 

than 5.0 [5]. Zinc organizes many 

University of Baghdad 

College of Engineering 

Iraqi Journal of Chemical and 

Petroleum Engineering 

 



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biochemical processes and is important 

for the physiological functions of 

living tissue. High concentrations of 

zinc cause prominent health problems, 

such as nausea, skin irritations, 

vomiting, anemia and stomach cramps. 

It is a trace element that is essential for 

human health [6]. The maximum 

contaminant level (standards) of zinc 

metal in water is 0.6-5 mg/l in Hong 

Kong SAR for Environmental 

Protection Department (EPD) [7], <10 

mg/l for Egyptian Environmental 

Standards Law (93/62)/ and Decree 

(44/2000) [8] and 2 mg/l for the Iraq 

regulation limits [9]. Thus, heavy 

metals removal from discharge water 

becomes an increasingly important 

matter globally. Toxic heavy metals of 

particular interest in industrial 

wastewaters treatment involve zinc, 

chromium, mercury, copper, nickel, 

cadmium and lead [10, 11].  

Different methods have been 

discussed for removing heavy metals 

from waters such as: coagulation, 

chemical precipitation, using ion 

exchange resins, flocculation, 

floatation, adsorption, electrochemical 

processes,  and membrane methods [7, 

12]. Membrane separation 

technologies have been specified to be 

a promising and feasible option for 

removal of heavy metal due to their 

ease of operation and high efficiency. 

Ultrafiltration (UF) and reverse 

osmosis (RO) are now being 

increasingly used for heavy metals 

removal from wastewater. 

Nanofiltration (NF) is less investigated 

intensively than RO for heavy metals 

removal because that RO is more 

effective to remove the divalent ions 

from wastewater than NF[13]. 

RO was the first membrane 

process to be widely commercialized. 

RO membranes are used to separate 

low molecular weight compounds and 

salts from water because they are 

highly permeable to water and highly 

impermeable to colloids, 

microorganisms, organic molecules 

and salts [14].  RO is one of the 

effective technologies to remove 

almost all pollutants, especially those 

with low concentrations. RO 

technology is also used today in large 

water treatment plants. It produces 

good quality of potable water from 

seawater and brackish water resources, 

reduce water salinity and improve 

polluted water sources for industrial 

applications. In addition, the 

application of series of RO membrane 

elements covers household units to 

produce higher quality of drinking 

water [15]. 

In this study, the effect of time, 

feed concentration and pressure on flux 

and permeate concentration, and 

comparison between experimental and 

theoretical results have been studied 

for reverse osmosis membranes to 

remove zinc ions from wastewater. 

 

Mathematical Model  

Spiral wound element is the most 

popular type of membrane element in 

use. Water passes through the element, 

some water passes into the permeate 

channel, resulting in continuously 

changing conditions over the length of 

the element [16]. 

 

1. Steady State Calculations 
In the solution-diffusion model, the 

transport of solvent and solute are 

independent of each other. The flux of 

solvent through the membrane is 

linearly proportional to the pressure 

difference across the membrane [17]: 
 

                                    …(1) 
 

Where:    is the flux of water (l/m
2
.h), 

   is the permeability coefficient of 
pure water (l/m

2
.h.bar),    is the 

applied pressure driving force (bar) and 

   is the osmotic pressure of the 
solution (bar). 

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Ahmed Faiq Al-Alawy and Miqat Hasan Salih 

 
 

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Solution osmotic pressure is related to 

its dissolved solute concentration and 

is predicted from Van't Hoff equation 

as: 
 

                                           …(2) 
 

Where:   is the osmotic coefficient 
(dimensionless), i is the number of 

dissociated ions per molecule (Van’t 

Hoff factor) (dimensionless), T is the 

temperature (K), Rg is the universal gas 

constant (l.bar/mole.K) and C is the 

concentration of solute (mg/l). 
 

The Van't Hoff factor is inserted to 

more than deviations from ideal 

solution behavior that implicates finite 

volume occupied by molecules of 

solute and their mutual attraction as in 

Vander Waals attraction [18]. 

The solute flux through the membrane 

is proportional to the solute 

concentration difference across the 

membrane [17]: 
 

                                            …(3) 
 

Where:    is the solute mass flux 
(mg/m

2
.h),    is the permeability 

coefficient of salt (m/h) and    is the 
concentration gradient across 

membrane (mg/l). 
 

And: 
 

   
  

  
                                         …(4) 

 

Where:    is the concentration in 
permeate (mg/l). 
 

By measuring the solute concentrations 

in feed solution (  ) and also in 
permeate solution (  ), the rejection is 
calculated from the rejection data as 

follows [11]: 
 

     
  

  
)                                 …(5) 

 

Where:   is the solute rejection 
(dimensionless) and    is the 
concentration in feed solution. 
 

At steady state, in the case with no 

accumulation of mass, the flux of 

solute to the membrane surface can be 

balanced by solute fluxes flowing 

away from the membrane and through 

the membrane as following[16]: 
 
  

  
          

  

  
              

                                                      …(6) 

 

Where: M is the solute mass (mg), t is 

the time (s),    is the solute diffusion 
coefficient in water (m

2
/s), z is the 

distance perpendicular to the surface of 

membrane (m) and a is the surface area 

of membrane (m
2
). Equation 6 can be 

not only applied at the surface of 

membrane but also at any plane in the 

boundary layer because the net flux of 

solute must be constant everywhere in 

the boundary layer to prevent the 

solute accumulation in that layer. 

Integrating Equation 6 across the 

thickness of the boundary layer with 

the boundary conditions: C(0) =    
and C(  ) =    , where     is the feed 
concentrate channel concentration and 

   is the membrane surface 
concentration. 
 

  ∫
  

    

   

  
    ∫   

  

 
          …(7) 

 

Integrate Equation 7 as: 
 

  (
     

      
)  

    

  
                       …(8) 

 

     

      
  

    
                      …(9) 

 

The concentration polarization is 

expression used to characterize the 

accumulation of rejected solute at the 

membrane surface so that the 

concentration of solute at the wall of 

membrane is greater than of the bulk 

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solution of feed. The convective flow 

of solute to the surface of membrane is 

greater than the diffusion back to the 

bulk feed solution; so that, the solute 

concentration at the wall of membrane 

increases [19]. Negative effects of 

concentration polarization involve 

[20]: 

1- Changes in membrane separation 
properties. 

2- Declines in the flux of water 
because of increased in osmotic 

pressure at the wall of membrane. 

3- Enhanced fouling by colloidal or 
particulate materials in the feed 

which plug the surface of membrane 

and decrease the flux of water.  

4- Increases in the flux of solute over 
the membrane due to increased 

concentration gradient across the 

membrane. 

5- The solute precipitation if the 
concentration of surface exceeds its 

solubility limit, leading to particle 

fouling or scaling on membrane and 

reduced the flux of water.  

Concentration polarization is defined 

as the ratio of the solute concentrations 

of membrane and feed concentrate 

channel as: 
 

  
  

   
                                       …(10) 

 

Where:   is the concentration 
polarization factor (dimensionless). 
 

Combining Equation 10 with 

Equations 5 and 9 gives the following 

expression: 
 

                 ⁄ )        …(11) 
 

Schock and Miquel [21] found that the 

mass transfer coefficient of 

concentration polarization could be 

calculated from equations below:  
 

          
  
  

                    

 …(12) 

   
      

 
                                  …(13) 

 

   
 

    
                                     …(14) 

 

Where:    =       is the mass 
transfer coefficient of concentration 

polarization (m/h),    is the hydraulic 
diameter (m), Re is the Reynold 

number (dimensionless), Sc is the 

Schmidt number (dimensionless),   is 
the velocity in the feed channel (m/h), 

  is the density of feed water (kg/m
3
) 

and μ is the dynamic viscosity of feed 

water (kg/m.s). 
 

As shown in Figure 1 the center plane 

of a differential slice of membrane 

performs the surface of membrane. 

The feed concentrate channel overhead 

the membrane, the permeate channel 

below the membrane. 
 

 
Fig. 1: Differential slice of membrane element 

 

The water and solute fluxes are 

expressed by Equations 1 and 3, but 

the concentration differential, osmotic 

pressure differential and applied 

pressure differential rely on the 

position in the pressure vessel [16]: 
 

                  

   [(          )  (         )]   
…(15) 

 

                 (         )                                                             
…(16) 

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Where:      is the concentration at the 

surface of membrane,               
and      is the osmotic pressure at the 
surface of membrane. 
 

The flow of permeate and flow of mass 

of solute through the membrane are 

equal to the flux multiply by the area 

of membrane for the differential 

element. The accumulative water and 

solute transfer across the membrane is 

predicted by integrating the flow 

between the feed end and the position z 

in the pressure vessel, as: 
 

     ∫          
 

 
                     …(17) 

 

     ∫              
 

 
                    …(18) 

 

Where: w is the width of feed 

concentrate channel (m) and      is the 
solute mass transferred (mg/s). 
 

Flow rate of water in the feed 

concentrate channel decreases as the 

permeate is produced. At any point in 

the channel the flow rate can be 

predicted by [16]: 
 

                                   …(19) 
 

The concentration of solute in the feed 

concentrate channel can be calculated 

by doing a mass balance on solute as: 
 

      
         

     
                        …(20) 

 

The flux of water and solute are 

influenced by solute concentration at 

the membrane surface and 

concentration polarization. Both 

velocity and flux are changing,   must 
be determined by Equation 11 as a 

function of position, as the following 

equation: 
 

    ( 
    
     )                …(21) 

 

The velocity in the feed concentrate 

channel which mass transfer 

coefficient     depends on it can be 
calculated from the following 

equation: 
 

   
     

  
                                    …(22) 

 

Where h is the height of feed 

concentrate channel (m). 
 

The concentration of solute at the 

surface of membrane as a function of 

position expressed as: 

 

                                            …(23) 
 

The feed channel pressure drops 

because of the head loss, head loss 

changes across the length of the 

membrane. Turbulent conditions are 

maintained, so head loss in the channel 

is given by the expression: 
 

        
                                …(24) 

 

Where:    is the feed concentrate 
channel head loss (bar),     is the head 
loss coefficient (bar.s

2
/m

3
),   is the 

velocity of water in feed concentrate 

channel (m/s) and L is the length of the 

channel (m). 
 

The concentration of permeate can be 

determined from the ratio of the fluxes 

of solute and water per Equation 4 as: 
 

     
    

    
                                   …(25) 

 

2. Unsteady Steady State 
Calculations 

Recovery can be expressed as the 

volume of permeate divided by the 

initial volume of feed. This expression 

applied in batch concentrating mode. 

For the overall system, the expression 

is [22]: 
 

   
  

  
                             …(26) 

 

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Where:    is the recovery 
(percentage),    is the volume of 
permeate (l) and   

  is the initial feed 

volume (l). 
 

Reverse osmosis unit in continuous 

operation consists of a tank for feed, a 

tank for product and the membrane 

element. The concentrate is recycled 

back to the tank of feed and the 

permeate is separately collected in the 

product tank as shown in Figure 2 [23]. 

 

 

 
Fig. 2: Reverse osmosis system 

 

Material balance equation applied for 

the  product tank as: 
 

     
          

  
                      …(27)  

 

      is the product average 
concentration (mg/l). 
 

Expansion of equation 27 yields: 
 

       
      

  
      

   

  
    …(28) 

 

Initial conditions, at t=0,   =0, 
     =  =0. The variation in the 
product volume corresponds to the 

production rate of membrane as: 
 
   

  
                                        …(29)  

 

Substitution to Equation 28: 
 
      

  
 

            

  
                  …(30) 

 

Material balance on the membrane 

element gives: 
 

                              …(31) 
 

Analogous material balance equation 

can be obtained around the feed tank: 
 

          
          

  
           …(32) 

 

Developing this equation gives: 
 

          
    

  
    

     

  
    …(33) 

 

Where,     is the volume in the tank of 
feed at a time t, with a concentration in 

the tank    . The tank of feed is 
assumed well mixed [22] so: 
 

                                            …(34) 
 

And: 
 

                                           …(35) 
 

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The variation in the feed tank volume 

with time corresponds to the 

production rate as: 
 

 
   

  
                                    …(36) 

 

Integrating equation 36 with the initial 

condition: t=0,      
  

 

     
                                …(37) 

 

Substituting these expressions in 

Equation 33: 
 
   

  
 

         

   
       

                          …(38) 

 

Knowing that the system of interest is 

closed, the conservation of mass 

reveals that the solute mass in feed 

tank at initial time is equal to the sum 

of various streams and tank: 
 

   
  
       

  

          
                           …(39) 

  

Substituting    by its expresssion in 
Equation 30: 
 
      

  
 

            

  
       

  
            

…(40) 
 

Equation 38 and 40 are the outcome of 

material balances on the product tank, 

feed tank, and membrane element. The 

solution of this set of ordinary 

differential equations requires the 

values of     and   .    and    are 
obtained from the steady state 

equations 4 and 17 as initial values for 

the ordinary differential equations 

when the concentration and product 

rate of permeate change with position 

of module. The solution of Equation 38 

gives the concentration of feed as 

function of time. The solution of 

Equation 40 gives the solute average 

concentration in product tank and the 

volume of water by Equation 39. The 

equations of the mathematical model 

can be solved by using MATLAB 

PROGRAM. 

 

Experimental Work 
Synthetic wastewater containing the 

desired concentrations of Zn
+2

 were 

prepared by dissolving the desired 

amount of zinc chloride (ZnCl2, 

Minimum assay 97%, M.W. 136.28, 

CAS-NO. 7646-85-7 UN 2331, 

INDIA) in deionized water of 

conductivity 1-2 µs/cm. 

Commercially spiral-wound ultra low 

pressure aromatic polyamide reverse 

osmosis membrane element is used in 

this work, can work under ultra low 

pressure to attain as high permeate 

flow rate and salt rejection as low 

pressure membrane element can, the 

specifications of this module are given 

in Table 1. 

Schematic diagrams of lab-scale RO 

system used in these experiments are 

shown in Figure 3. Feed solution was 

prepared in feed vessel by dissolving 

the ZnCl2 in 8 liter of deionized water. 

Pressure gauge (Range: 0-10 bar) is 

used in the feed line to indicate the 

operating pressure, the feed solution 

drawn from the feed vessel by 

centrifugal pump (Model: 15 GR-18, 

Rated power: 150 W, Rated voltage: 

220-240 V, Rated current: 0.58 A, 

Rated speed: 2860 r/min, Frequency: 

50/60 Hz, Highest head: 15 m, Rated 

head: 10 m, Max. capacity: 25 l/min, 

Rated capacity: 10 l/min, Insulation 

class: B) then the solution is 

introduced into the spiral-wound 

reverse osmosis element by means of a 

high pressure pump (Model: HF-6050, 

Max. outlet pressure: 125 psi, Open 

flow: 1.2 l/min, VOLTS: 24 VDC, 

AMPS: 0.26 A). The feed temperature 

was varied by submersible electrical 

coil (Rated power: 1000 W, Rated 

voltage: 220V). The feed flow rate was 

controlled by rotameter (Range: 10-

100 l/h) and keeping constant at 40 l/h. 

The concentrate stream is recycled to 

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the feed vessel and mixed with the feed 

stream. The water flux was obtained by 

dividing the permeate volume by the 

product of effective area of membrane 

and time. The concentration of heavy 

metal ion (Zn
+2

) was measured by an 

atomic absorption spectrometry (Buck 

210/211, U.S.A., Perkin Elmer, 

Sr.Nr:1159 A). After recording the 

results, the solution was drained by a 

drain valve and the system was washed 

by deionized water.

 
Table 1: Specification of reverse osmosis element 

Model VONTRON-ULP 1812-50 

Type of membrane 
Ultra low pressure aromatic polyamide 

reverse osmosis membrane element 

Active membrane area, m
2
 0.36 

Average permeated flow, m
3
/d 0.19 

Stable rejection rate, % 97.5 

Minimum rejection rate, % 96 

Testing pressure, Mpa 0.41 

Concentration of testing solution (NaCl), ppm 250 

pH of testing solution 7.5 

Recovery of single membrane element, % 15 

Maximum working pressure, Mpa 2.07 

Maximum feed water temperature, °C 45 

Maximum feed water SDI 5 

Free chlorine concentration of feed water, ppm <0.1 

pH range of feed water during continuous operation 3-10 

pH range of feed water during chemical cleaning 2-12 

 
Fig. 3: Schematic diagram of lab-scale RO system 

 

Results and Discussion 
The aromatic polyamide membrane 

permeability (  ) for pure water was 

experimentally determined by a 

hydraulically low pressure RO process. 

The pure water flux through the 

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membrane was determined with range 

of pressures according to Equation 1 

when     . 
As shown in Figure 4, the data shows a 

linear relationship between water flux 

and driving force. Aromatic polyamide 

compound membrane permeability for 

pure water is determined from the 

slope of this curve, the value of    
was obtained 6.736 l/m

2
.bar.h. 

 

 
Fig. 4: Operating pressure vs. water flux (Q

F
 = 30 l/h, T = 26 

o
C and t=10 min) 

  

The membrane permeability (  ) for 
salt (ZnCl2) was experimentally 

determined under a range of feed 

concentrations according to Equation 

3. 

As shown in Figure 5, the data show a 

linear relationship between mass flux 

of solute and driving force. Membrane 

permeability for salt is determined 

from the slope of this curve, the value 

of    was obtained 2.498*10
-4
 m/h.

 

 
Fig. 5: Concentration difference vs. solute flux (QF=40 l/h, T=26 

o
C , t=30 min and P=2 bar) 

 

Figure 6 show the effect of time on the 

concentration of zinc ion in permeate. 

The heavy metal ions concentration in 

the product gradually increased with 

the increase in operating time. This 

behavior can be explained by the 

increase of the feed concentration with 

time in the recirculation mode led to 

increase in concentration polarization 

and this cause an increase in the zinc 

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6

W
a

te
r 

F
lu

x
 (

Jw
),

 L
M

H
 

Pressure, bar 

0

50

100

150

200

250

0 200 400 600 800 1000

S
o

lu
te

 F
lu

x
 (

J s
),

 m
g

/m
2
.h

 

CF - CP, mg/l 

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passage, this behavior is agreement 

with Xiuzhen [13]. The first 30 

minutes resulted in the increase in 

permeate concentration of 17.72% and 

the final 40 minutes resulted in the 

increase in permeate concentration of 

52.58%.

 

 
Fig. 6: Effect of operating time on permeate concentration of zinc ions (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, 

P = 2 bar, CZn+2=300 mg/l) 

 

 
Fig. 7: Effect of operating time on rejection of zinc ions (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, P = 2 bar, 

CZn+2=300 mg/l) 

 

As shown in Figure 7 the rejection 

rates of zinc ions have been randomly 

decreased and increased in spite of that 

the concentration of zinc ions in 

permeate has been increased with time, 

this behavior due to the increase in 

feed concentration (feed concentration 

has been changed with time) because 

of the recirculation mode. The 

rejection for zinc ion at first three 

minutes when the feed concentration 

approximately constant (300 mg/l) is 

99.49%. 

Figure 8 shows the effect of time on 

flux. It can be easily observed that the 
flux from reverse osmosis unit 

decrease with increase in operating 

time. The continuous decrease of the 

flux was mainly due to the gradual 

increase in the viscosity of solution 

0

2

4

6

8

10

0 10 20 30 40 50 60 70 80

C
P
 Z

n
+

2
, 

m
g

/l
 

Time, min 

98

98.2

98.4

98.6

98.8

99

99.2

99.4

99.6

0 10 20 30 40 50 60 70 80

R
e

je
ct

io
n

, 
%

 

Time, min 

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and to heavy metal deposition onto the 

membrane surface with increasing feed 

concentration and osmotic pressure 

gradually, which led to further 

membrane fouling and severe 

concentration polarization. Resistance 

against water flux through the 

membrane increased due to the 

boundary layer on the membrane 

surface formed by heavy metals. 

Furthermore, increasing osmotic 

pressure because of concentration 

polarization led to a decrease in the 

driving force through the membrane. 

This behavior is agreement with 

Xiuzhen and Zhi [13, 24]. The increase 

in time to 70 min resulted in the flux 

decline of  6.226%.

 
Fig. 8: Effect of operating time on flux (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, P = 2 bar, CZn+2=300 mg/l) 

 

Figure 9 shows the effect of time 

recovery percentage of permeate. The 

recovery percentage increase according 

to equation 26 because the 

accumulation volume of permeate has 

been increased as time increased. The 

increase in time to 70 min resulted in 

the increase of water recovery from 

8.3125 to 54.5625%. 

 

 
Fig. 9: Effect of operating time on recovery percentage (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, P = 2 bar, 

CZn+2=300 mg/l) 

 

9

9.5

10

10.5

11

11.5

12

0 20 40 60 80

F
lu

x
, 

LM
H

 

Time, min 

Theo.

Exp.

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80

R
e

co
v

e
ry

, 
%

 

Time, min 

Theo.

Exp.

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Figure 10 shows the values of final 

feed vessel concentration change with 

time. It can be observed that the feed 

concentration increase with increase in 

operating time. This behavior was due 

to the recirculation mode (concentrate 

stream recycled to the feed stream). 

 

 
Fig. 10: Effect of operating time on final feed concentration (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, P = 2 bar, 

CZn+2=300 mg/l 
 

As shown in Figure 11 zinc 

concentration in permeate has been 

increased as the feed concentration 

increased, this behavior is agreement 

with Kyu [25]. The increase in feed 

concentration ion from 10 to 300 mg/l 

resulted in the increase of permeate 

concentration from  0.19 to 4.63 mg/l. 

 

 
Fig. 11: Effect of feed concentration on permeate concentration of zinc ions (Q

F
 = 40 l/h, T = 26 

o
C, pH 

= 6, P = 2 bar, t=30 min) 
 

It is clear from Figures 12 and 13 that 

the permeate flux and recovery have 

been decreased with increasing feed 

concentration. This behavior due to 

increase in osmotic pressure, decrease 

of the effective membrane pore size 

due to adsorption of solute on the 

membrane surface and the effect of 

concentration polarization, this 

behavior is agreement with Kyu [25]. 

The decrease in recovery according to 

decrease in flux. The increase in feed 

600

800

1000

1200

1400

1600

0 20 40 60 80

T
D

S
Z

n
C

l2
 F

in
a

l 
in

 f
e

e
d

, 
m

g
/l

 

Time, min 

Theo.

Exp.

0

1

2

3

4

5

0 50 100 150 200 250 300 350

C
P
 Z

n
+

2
, 

m
g

/l
 

CF Zn
+2, mg/l 

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Ahmed Faiq Al-Alawy and Miqat Hasan Salih 

 
 

05                          )6201September ( 3No. 17IJCPE Vol.             www.iasj.netonline at: Available -      
 

concentration ion from 10 to 300 mg/l 

resulted in the decrease of recovery 

from 30.81% to 24.5% and flux from 

13.694 to 10.889 LMH. 

Figure 14 show the values of final feed 

vessel concentration. It can be 

observed that the feed concentration 

increase with increase in ion feed 

concentration. This behavior due to the 

recirculation mode (concentrate stream 

recycled to the feed stream). 

 

 
Fig. 12: Effect of feed concentration on flux (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, P = 2 bar, t=30 min) 

 

 
Fig. 13: Effect of feed concentration on recovery percentage (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, P = 2 bar, 

t=30 min) 

 

Figure 15 shows that the zinc 

concentration in permeate has been 

decreased with increasing applied 

pressure which can be explained by the 

following: The decrease in 

concentration of ion in permeate with 

raise in pressure could be because of at 

higher pressure the preferential 

sorption of the membrane element for 

pure water has been increased and the 

average pore size on the membrane 

surface has been decreased, also due to 

increase in flux with increasing applied 

pressure. In other words, at low 

pressure the solute diffusive transport 

through membrane is higher than that 

of convective transport. As the applied 

pressure increases, convective 

10

10.5

11

11.5

12

12.5

13

13.5

14

0 50 100 150 200 250 300 350

F
lu

x
, 

LM
H

 

CF Zn
+2, mg/l 

Theo.

Exp.

22

24

26

28

30

32

0 50 100 150 200 250 300 350

R
e

co
v

e
ry

, 
%

 

CF Zn
+2, mg/l 

Theo.

Exp.

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 Experimental Study and Mathematical Modelling of Zinc Removal by Reverse Osmosis Membranes 
 

 www.iasj.netAvailable online at: -  6)           201 September( 3No. 7IJCPE Vol.1                               66 
 

transport becomes more important 

which make it possible to decrease the 

concentration of ion in permeate, this 

behavior is agreement with Xijun [26]. 

The increase in pressure from 1 to 4 

bar resulted in the decrease of 

permeate concentration of zinc ion of 

49.927%. 

 

 
Fig. 14: Effect of feed concentration on final feed concentration (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, P = 2 

bar, t=30 min) 

 

 
Fig. 15: Effect of applied pressure on permeate concentration of zinc ions (Q

F
 = 40 l/h, T = 26 

o
C, pH = 

6, CZn+2=300 mg/l, t=30 min) 

 

As shown in Figures 16 and 17 the 

permeate flux and recovery has been 

increased linearly with increasing 

applied pressure, this means that there 

is a little effect of concentration 

polarization in the membrane module. 

This behavior can be explained by the 

permeability equation of solution 

diffusion model (Equation 1), this 

behavior is agreement with Jae [27]. 

The increase in applied pressure from 

1 to 4 bar resulted in the increase of 

flux of 311.979%. 

Figure 18 shows the values of final 

feed vessel concentration. It can be 

observed that the feed concentration 

increase with increase in applied 

pressure. This behavior due to the 

recirculation mode (concentrate stream 

recycled to the feed stream). 

0

100

200

300

400

500

600

700

800

900

1000

0 50 100 150 200 250 300 350

T
D

S
Z

n
C

l2
 F

in
a

l 
in

 f
e

e
d

, 
m

g
/l

 

CF Zn
+2, mg/l 

Theo.

Exp.

2

3

4

5

6

7

8

0 1 2 3 4 5

C
P
 Z

n
+

2
, 

m
g

/l
 

Applied pressure, bar 

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Ahmed Faiq Al-Alawy and Miqat Hasan Salih 

 
 

66                          )6201September ( 3No. 17IJCPE Vol.             www.iasj.netonline at: Available -      
 

It can be seen from Figures 8, 9, 10, 

12, 13, 14, 16, 17 and 18 that the 

model prediction values are in good 

agreement with the experimental 

results.

 

 
Fig. 16: Effect of applied pressure on flux (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, CZn+2=300 mg/l, t=30 min) 

 

 
Fig. 17: Effect of applied pressure on recovery percentage (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, CZn+2=300 

mg/l, t=30 min) 

 
Fig. 18: Effect of applied pressure on final feed concentration (Q

F
 = 40 l/h, T = 26 

o
C, pH = 6, 

CZn+2=300 mg/l, t=30 min)

0

5

10

15

20

25

0 1 2 3 4 5

F
lu

x
, 

LM
H

 

Applied pressure, bar 

Theo.

Exp.

8

13

18

23

28

33

38

43

48

53

0 1 2 3 4 5

R
e

co
v

e
ry

, 
%

 

Applied Pressure, bar 

Theo.

Exp.

500

700

900

1100

1300

1500

0 1 2 3 4 5

T
D

S
Z

n
C

l2
 F

in
a

l 
in

 f
e

e
d

, 
m

g
/l

 

Applied pressure, bar 

Theo.

Exp.

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 Experimental Study and Mathematical Modelling of Zinc Removal by Reverse Osmosis Membranes 
 

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Conclusion 

The aromatic polyamide reverse 

osmosis membrane gives a high 

efficiency for removal of zinc ions and 

it has allowed permeation of zinc ion 

to the lower than permissible limits. 

The rejection percentage for zinc ion 

was high (i.e. ˃ 98%) for most 

experiments in this research. The 

recovery percentage for reverse 

osmosis element was 54.56%  during 

the time of 70 minutes. The polyamide 

membrane permeability for zinc 

chloride is 2.498*10
-4

 m/h. The 

theoretical flux values calculated from 

mathematical model are in a good 

agreement with the experimental 

results. 
 

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