Appendix B

Appendix B
Specifications of spiral-wound modules
Characteristics 4" Roga 4160-HR
A, m3/m2.s.Pa 20.85x10-13
L, m 0.88
W, m 1.43
Leaves 3
hb, m 7×10-4
hp, m 3×10-4
K 0.5
Lmix, m 0.006
D, m2/s 1.6× 10-9
kfb x 10-8, 1/m2 18.3673
kfp x 10-10, 1/m2 0.744444

Appendix A (C++ Program)

#include
#include
#include
void main()
{
clrscr();
double Qf,S,Jv,Pf,Cf,U;
double L,W;
cout<<"Enter Qf:"; cin>>Qf;
cout<<"Enter L:"; cin>>L;
cout<<"Enter W:"; cin>>W;
cout<<"Enter Pf:"; cin>>Pf;
cout<<"Enter Cf:"; cin>>Cf;
cout<<"Enter U:"; cin>>U;
int n=5,m=5,i,j=1;
S=2*(L*W)/(m*n);
Jv=2.1528*pow(10,-7); //Assumed value of volumetric flux
//double phi=1.00392; //Assumed value of phi
int leaves=3;
double Qb[6][6];
double Cb[6][6];
double Ub[6][6];
double k[6][6];
double Pb[6][6];
double Pp[6][6];
double kfb=18.3673*pow(10,(8));
double hp=.0003;
double nf;
double JV[6][6];
double phi[6][6];
double R[6][6];
double F[6][6];
double Cp[6][6];
double Qpt=0;
double Cpt=0;
cout<<"Enter nf:"; cin>>nf;
double mu=9.02*pow(10,(-4));
double A=2.085*pow(10,(-12));
double B=1.1*pow(10,(-7));
double hb=7*pow(10,(-4));
Pp[5][1]=101325;
Ub[5][1]=U;
Cb[5][1]=Cf;
Pb[5][1]=Pf;
Qb[5][1]=Qf/(n*leaves); //initializing value
for(j=1;j<6;j++) i="4;i">0;i--)
{
Qb[i][j]=Qb[i+1][j];
}
}
for(j=1;j<6;j++) i="4;i">0;i--)
{
Cb[i][j]=Cb[i+1][j];
}
}
for(j=1;j<6;j++) i="4;i">0;i--)
{
Ub[i][j]=Ub[i+1][j];
k[i][j]=k[i+1][j];
}
}
for(j=1;j<6;j++) i="4;i">0;i--)
{
Pb[i][j]=Pb[i+1][j];
}
}
for(j=1;j<6;j++) i="4;i">0;i--)
{
Pp[i][j]=Pp[i+1][j];
}
}
for(j=1;j<6;j++) i="4;i">0;i--)
{
JV[i][j]=JV[i+1][j];
}
}
for(j=1;j<6;j++) i="4;i">0;i--)
{
phi[i][j]=phi[i+1][j];
}
}
for(j=1;j<6;j++) i="4;i">0;i--)
{
F[i][j]=F[i+1][j];
}
}
for(j=1;j<6;j++) i="4;i">0;i--)
{
R[i][j]=R[i+1][j];
}
}
for(j=1;j<6;j++) i="4;i">0;i--)
{
Cp[i][j]=Cp[i+1][j];
}
}
for(j=1;j<6;j++)
{
Qpt=Qpt+(5*JV[5][j]*S*leaves);
}
Qpt=Qpt*0.85;
cout<<"\nPredicted value of Qpt=";
cout<for(j=1;j<6;j++)
{
Cpt=Cpt+((5*JV[5][j]*Cp[5][j]*S*leaves)/Qpt);
}
Cpt=Cpt/36.48;
cout<<"\nPredicted value of Cpt=";
cout<// //display
getch();
// //display
cout<<"\n\n\n";
cout<<"\t\t\t\t\tQb matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\tCb matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\tUb matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\tK matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\tPb matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\tPp matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\tJV matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\tphi matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\tF matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\tR matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<cout<<"\t\t\t\t\Cp matrix displayed\n";
cout<<"\n\n\n";
for(i=1;i<6;i++)
{
cout<<"\n\n";
for(j=1;j<6;j++)
{
cout<

Conclusions

It was found that for lower values of the reflection coefficient, the overall permeate produced is much higher and the permeate concentration differs substantially from that obtained for σ = 1 where the SK model mathematically is reduced to the solution-diffusion model. Since the SK model is known to be the most accurate membrane transport model, the present model for spiral-wound modules may provide more accurate results for design and analysis for reverse osmosis systems

Significance of reflection coefficient

It may be noted that when σ= 1, the SK model mathematically is reduced to a two-parameter model such as the solution-diffusion model. The membrane characteristics used for simulation are given in Appendix B. The effect of the variation of the feed parameters and σ on the permeate flow rate and concentration are shown in Figs. 5-8. For simulation purposes the membrane hydrodynamic permeability and the solute permeability are taken as 20.8x10 -13 m3/m2.s.Pa and 1.11xl0 -7 m*s respectively.
In Graph 1, the permeate flow rate is seen to decrease with increasing feed concentration. This is because the osmotic pressure increases with increasing feed concentration. This reduces the driving force for the mass transfer, thus leading to lower volumetric flux. The value of the permeate flow rate can also be seen to be increasing as σ decreases. This is along the expected lines as lower σ values imply lower contribution of the osmotic pressure in the flux, Eq. (3).
From Graph 2 the value of (Cpt/Cf) x 100 falls with an increasing feed flow rate from 5 x 10-5 to 20 x 10 -5 m3/s, and after this the (Cp,/Cf) x 100 values almost remain constant when the feed flow rate is increased beyond 20x10-5 m3/s. This is because, as the velocity in feed channel is increased, the mass transfer coefficient also increases and thus the concentration polarization decreases, leading to lower permeate concentrations. But at a higher feed flow rate the concentration polarization becomes negligible, and therefore the permeate concentration does not change noticeably. The value of (Cpt/Cf) × 100 changes quite noticeably with respect to σ. This is because for lower σ values the membrane is leaky and allows more solute to pass through it compared to tight membranes where σ values are


Graph 1: Permeate flow rate Vs Feed concentration



Graph 2: Ratio of permeate to feed concentration Vs. Feed flowrate

closer to 1. At a feed flow rate of 5x 10-5 m3/s, the differences in the (Cpt/Cf) × 100 values for σ = 1 and σ = 0.9 can be almost 400%.
Since the driving force for mass transfer increases for higher feed pressures, the permeate flow rate is seen to increase with increasing feed pressure, as shown in Graph 3. However, the effect on permeate flow rate with respect to σ is not significant. On the other hand, the value of (Cpt/Cf)xl00 decreases significantly as the feed pressure is increased up to 20 bar, and after that the permeate concentration decreases marginally with increasing feed pressure for σ values up to 0.98 where as for lower values of σ , the permeate concentrations


Graph 3: Permeate flow rate Vs. Feed pressure

actually increase with increasing feed pressures. From the above results and discussion, the role of the reflection coefficient (σ) can be investigated.
It is noticed that for membranes with a higher reflection coefficient, both the permeate flow rates the permeate concentrations are lower. As the value of σ decreases, the permeate concentration goes up and the permeate flow rates are also increased.


Graph 4: Ratio of permeate to feed concentration Vs. Feed pressure

In conclusion, it can be said that the membranes with high reflection coefficients have lower permeabilities but higher selectivities.

Estimation of parameters

The data of Taniguichi were analyzed using a computer program. The membrane hydrodynamic permeability of the Roga module can be estimated from the pure water permeability data, and the value of A was taken to be 20.80x10-13 m3/m2.s.Pa as given by Taniguichi.

Table 1
Estimation of parameters for the Roga 4160 spiral-wound module using Taniguichi’s data predicted at nF =1

Predicted: B = 1.08 x 10-7 m/s, σ = 0.988, k = 1.06 x 10-4 Ub0.4834 m/s. Fixed: A = 20.80x10-13 m3/m2.s.Pa


Table 2
Estimation of parameters for the Roga 4160 spiral-wound module using Taniguichi’s data predicted at nF =1.5


Predicted: B = 1.127 x 10-7 m/s, σ = 0.988, k = 1.07 x 10-4 Ub0.4834 m/s. Fixed: A = 20.80x10-13 m3/m2.s.Pa

The value of nF may change from 1 to 1.7 depending on the module and the operating conditions. The remaining four parameters (B,σ, ka and kb) were estimated. The results obtained by using only the first five experimental data and for values of nF =1 and nF =1.5 are shown in Tables 1 and 2 respectively. From these tables we note that the values of B (solute transport parameter) and σ are 1.089 x 10-7 m/s and 0.988, and 1.127 x 10-7 m/s for nF =1 and nF =1.5 respectively. The estimated value of B was compared with Taniguichi data (for two-parameter model (σ =1)).B was supposed to lie between 1.08 x 10-7 m/s to 1.46 x 10-7 m/s. Using mass transfer coefficient parameter estimation program, the mass transfer correlation may be written as
k = 1.06 x 10-4 Ub0.4834 m/s at nF = 1
k = 1.07 x 10-4 Ub0.4919 m/s at nF = 1.5
Whereas correlation given in the literature for this module for similar conditions may be written as
k = 1.08 x 10-4 Ub0.5 m/s
This shows that the results from the present parameter estimation program are in excellent agreement with the results available in the literature. The maximum error between predicted and reported values of Cpt and Qpt are 4.19 % and 4.54 % respectively. It can be also seen that errors in values of Qpt and Cpt are almost same for Table 1 and Table 2. Therefore, the change in value of nF from 1 to 1.7 may not create significant changes as far as estimation of membrane parameters are concerned. Using the estimated parameters from Table 1, the remaining data of taniguichi are predicted as shown in Table 3.Now; the maximum errors are only 4.22 % and 3.70 % for Q¬pt and Cpt respectively. From the above results of parameter estimation and prediction, we may conclude that the model works fine for a spiral-wound module.

Table 3
Permeate characteristics of Taniguichi’s data predicted using parameters estimated in Table 1

Solute Transport Parameter (B) and Hydraulic Transport Parameter (A)

The hydraulic transport parameter (A) and the solute (TDS) transport parameter (B) need to be determined for the membrane used in the pilot-scale element. An iterative algorithm (Appendix C) is used to determine A and B values from pilot-scale experimental data. Initially the assumed A and B values (close to the actual) along with the operating conditions (i.e. feed pressure (Pf), feed flow rate (Qf) and feed TDS concentration (Cf)) are used as inputs to the deterministic process model developed in the previous part, to predict the values of permeate flow rate (Qp) and permeate TDS concentration (Cp). The predicted values for above parameters are compared with the experimental results to determine converge1 and converge2 values as follows:
converge1 =Qp (predicted)/Qp (observed) (21)
converge2 =Cp (predicted)/Cp (observed) (22)
The converge1 and converge2 values approach unity as A and B reaches the accurate values. Therefore, the convergence criteria are based on the deviation of converge1 and converge2 values from unity:
E1 = 1 - converge1, and E1 ≤ 0.001 (24)
E2 = 1 - converge2, and E2 ≤ 0.001 (25)
If the assumed values of A and B satisfy the convergence criteria, they are considered acceptable. Otherwise the assumed values are changed as follows:
A = A/converge1 (26)
B =B/converge2 (27)
Same procedure is repeated using the new A and B values until the convergence criteria stated in equation (24) and (25) are satisfied.
Alternatively, the transport parameters can be estimated by using Simplex search method from a given set of experimental data. An initial guess for each of the model parameters to be estimated is used to initialize the estimation of parameters. The predicted exit permeate flow rates and concentrations obtained based on the initial guess are compared with experimental values. If the values chosen for the parameters are not correct, the values are refined so that the predicted and experimental permeate conditions are as close as possible. The Simplex search algorithm is given in Appendix D.

Governing Equations for Deterministic Process Model contd

(E)Pressure Drop
The flow pattern in feed channel and permeate channel are oriented in orthogonal directions (as described in section before). The pressure drop in these two channels over an infinitesimal element ‘Δx’ & ‘Δy’ can be calculated by the following equations (Senthilmurugan, Ahluwalia et al., 2005):

Pb(i-1,j) – Pb(i,j) = 2kfbnFU¬b(i,j)nF-1μ Δx2∑1i-1[Jv(i,j)/hb] (7)

Pp(i,j+1) – Pp(i,j) = 2kfp μ Δy2 ∑j+1n[Jv(i,j)/hp] (8)

where Pb = pressure in bulk solution side [Pa; ML-1T-2]; Pp = pressure in permeate channel (permeate side) [Pa; ML-1T-2]; Δx = element along x axis [m; L]; Δy = element along y axis [m; L]; μ = dynamic viscosity [Pa•s; ML-1T-1]; Jv = permeate flux [m3/(m2•s);LT-1]; hb = depth of feed channel [m; L]; hp = thickness of permeate channel [m; L]; nF =dimensionless constant parameter[dimensionless]; kfb = friction parameter for feed channel [(1/m2); L-2]; kfp = friction parameter for permeate channel [(1/m2); L-2].
The applicable boundary conditions for the above equations are as follows:
Pf = Pf0, at x = 0 (9)
Pp = Patm, at y = 0 (10)
Where Patm = atmospheric pressure (assumed to be equal to pressure in permeate at outlet) = 1.013×105 Pascal. Above pressure drop equations are derived based on the assumption that the Darcy’s law is applicable for flow through narrow channels and the dimensionless constant nF = 1.


(F) Material Balance and Performance
The local grid area through which the fluid flows and the feed flow rate at the entry grid point of the feed channel may be written as:-
S(i,j) =2*(L*W)/(m*n) (11)
Qb(1,j) = Qf/n*leaves (12)
Where S=membrane (grid) surface area [m2; L2]; Qb=flow rate in bulk solution side [m3/s; L3T-1]; Qf = input feed flow velocity [m3/s; L3T-1]; leaves =3.
The finite difference form of the overall material balance is given by :
Qb(i+1,j) – Qb(i,j) = -Jv(i,j)*S(i,j) (13)
And the bulk solution at inlet is:
Cb(1,j) = Cf0 (14)
Similarly the solute material balance equation and the permeate concentration in finite difference formulation may be written as follows:
Cb(i,j) Qb(i,j) = Cb(i+1,j) Qb(i+1,j) + S(i,j) Cp(i,j) Jv(i,j) (15)
Cp(i,j) = [φ(i,j) (1-R(i,j)Cb(i,j)]/[ φ(i,j) + R(i,j) (1- φ(i,j) )] (16)



Where,
R(i,j) = [(1 – F(i,j))σ]/[1- σ F(i,j)] (17)
F(i,j) = exp[-Jv(i,j)(1- σ)/B] (18)
Where Cb & Cp are solute concentrations at bulk solution side and permeate side respectively [kg/m3; ML3]; R= rejection [dimensionless]; F=flow parameter defined by eq. (18); B=solute permeability of the membrane [m/s; LT-1].
Finally, the total quantity of permeate Qpt and the average concentration of permeate Cpt may be estimated by following equations:
Qpt =∑mi=1 ∑nj=1 (Jv(i,j) S(i,j))*leaves (19)
Cpt =∑mi=1 ∑nj=1 Cp Jv(i,j) S(i,j)*leaves/Qpt (20)
Equation (1) to (18) was solved using C++ program to obtain the values of Qpt and Cpt. The program code is given in the Appendix A. The spiral-wound module Roga 4160-HR was studied. The specifications of this module can be found in Appendix B.

Governing Equations for Deterministic Process Model contd

(C) Concentration Polarization
Concentration polarization is one of the most important factors limiting performance of nearly all membrane separation processes (Strathmann, 1981). CP effect leads to increased flow resistance and the solute passage through the membrane, thereby reducing permeate flux and rejection of solutes. Therefore, designing of a reverse osmosis system requires a fair prediction of CP phenomenon. The steady state concentration of solute at the membrane wall (i.e. in the CP layer) can be determined by following nonlinear relationship (Marinas and Urama, 1996).

The equation for concentration polarization in finite difference form can be given by :
φ(i,j)=[Cm(i,j) – Cp(i,j)]/[Cb(i,j) – Cp(i,j)]=exp[Jv(i,j)/k(i,j)] (4)
where Cm = concentration of solute adjacent to membrane wall [mol/m3; ML-3]; Cp = concentration of solute in permeate [mol/m3; ML-3]; Cf = concentration of solute in the feed solution [mol/m3; ML-3]; Jv = volumetric flux of water through membrane [m3/ (m2•s); LT-1]; and k = mass transfer coefficient [m/s; LT-1]. In this study, CP layer is assumed to be fully developed, and a simple non-linear mathematical equation with a lumped parameter approach is used to predict the degree of concentration polarization, as compared to various numerical models based on distributed parameter approaches (Bhattacharya and Hwang, 1997; Kim and Hoek, 2005).

(D) Mass Transfer Coefficient
Several mass transfer coefficient relationships have been developed in the past, as briefly reviewed by Gekas and Hallstrom (1987). The mass transfer through RO membrane is influenced by geometry of spacers (turbulence promoters), geometry of feed flow channel (thickness), fluid properties (dynamic viscosity and velocity) and the solute properties (diffusivity). The presence of the turbulence promoters in spiral wound module needs to be accounted for, because it leads to increased mass transfer as the laminar boundary layer thickness reduces due to turbulence. Considering above factors, an empirical equation that includes the effect of all of the above parameters would best serve the purpose of developing a design and simulation model.
Therefore, a generic empirical equation developed by Winograd et al. (1973) to predict the mass transfer in narrow channels in presence of turbulence promoters is used in this study, based on a sensitivity analysis presented in later part of this study (Winograd, Solan et al., 1973):
k = 0.753[K/(2-K)]^0.5(D/hb) Sc^(-1/6)(Pe.hb/Lmix)^0.5 (5)
Also the variation in the mass transfer coefficient at local grid points may be given as:
k=ka [Ub(i.j)]^kb (6)
where, k = mass transfer coefficient [m/s; LT-1]; K = 0.5 = efficiency of mixing net [dimensionless]; D = diffusion coefficient [m2/s; L2T-1]; hb = thickness of the feed channel [m; L]; hp = thickness of permeate channel [m; L]; Sc = Schmidt number =μ/ρD,[dimensionless]; Pe = Peclet number = 2hbUb/D, [dimensionless]; Lmix= 0.006 m=characteristic length of mixing net [m; L].Ub =feed solution velocity on bulk side [m/s;LT-1].

Governing Equations for Deterministic Process Model Continued

(B) Water and Solute Transport
A phenomenological Spiegler and Kedem model was used to predict water and solute transport as follows (Spiegler and Kedem, 1966):
Jv(i,j) = A{[Pb(i,j) – Pp(i,j)] – σ α φ(i,j) [Cb(i,j)-Cp(i,j)] (3)
where Jv = volumetric water flux [m3/m2•s; LT-1]; A = hydraulic transport parameter [m/(Pa•s); M1L2T]; B = solute transport parameter [m/s; LT-1]; σ = reflection coefficient which indicates the degree of water/solute coupling [dimensionless]; P = hydraulic pressure [Pa; ML-1T-2]; C = superficial aqueous-phase solute concentration which is assumed to be in equilibrium with concentration of solute in the membrane phase [mol/m3; ML-3]; i = index number along x axis; j = index number along y axis; φ = concentration polarization; α=osmotic pressure proportionality=2RT.

Governing Equations for Deterministic Process Model

(A) Spiral Wound Element Model
The membrane leaf (consisting of filtration channel i.e. a feed flow channel and a permeate flow channel) is divided in m = 5 and n = 5 segments (oriented in orthogonal directions), each of distance Δx and Δy respectively to form a grid, as shown in Figure 1.The dimensions of the finite element i.e. Δx and Δy are obtained as:
Δx =L/m (1)
Δy =W/n (2)
where L = length of the membrane leaf (along the spiral wound module) [m; L]; W = width of membrane leaf (orthogonal longitudinal axis of spiral wound module) [m; L].The input parameters to model Qf0, Pf0 and Cf0, are the operating parameters for the element of the grid as shown in fig below

Various RO Modules

Four types of membrane modules are available in the marketplace: plate and frame, tubular, spiral-wound and hollow-fiber. The spiral-wound module occupies the largest market share because of its relative ease of cleaning, fabrication technology and very large surface area per unit volume. When compared with the hollow-fiber module in terms of the method of fabrication and cost, the spiral wound is the best. The flow of feed and permeate in a spiral-wound module is shown in Fig. 4. A typical spiral-wound module may have a packing density of 250 m2/m3. The flow channel size is on the order of 0.05 cm. The continuous change of flow in the spiral-wound module allows good mixing of the feed solution.

Plate and Frame Module




Hollow Fibre Module




Tubular Module

Spiral-wound Module

Introduction Continued

A membrane flow diagram showing influent and effluent flow, concentration and pressure of the feed, permeate and concentrate streams is presented in Fig.1below:





Fig 1: RO membrane flow diagram











Fig 1: RO membrane flow diagram

Fig 2: RO Methods

Fig 3: Schematic of (a) a simplified RO membrane process and (b) the RO process stream

Introduction Continued

Reverse Osmosis is a process used to de-mineralize water, to clean brackish water or to desalt seawater. The process consists in recovering water from a saline solution pressurized by pumping it into a closed vessel to a point grater than the osmotic pressure of the solution. Thus, the solution is pressed against a membrane so that it is separated from the solutes (the dissolved material). The portion of water that passes through the membrane reducing strongly the solute concentration is called permeate. The remaining water (brine) is discharged with a high salt concentration. Reverse osmosis is a pressure driven membrane separation process, used for removing low molecular weight solutes, such as inorganic salts or small organic molecules, from a solvent. It relies on the use of a semi permeable membrane, which allows solvent molecules to pass through it, impeding the pass of solutes. When two solutions of different concentrations are separated by such a membrane, the solvent from the lower concentration solution will move through the membrane into the concentrated one, in a process called osmosis. The osmotic flow is attributed to the tendency to equalize the both size’s solute concentrations. However, if the liquid on one side of the membrane is pure solvent, the two concentrations can never be equal. In this case, the process of osmosis continues until the chemical potentials of both solutions are equal. This happens when the pressure exerted by the concentrated solution against the membrane is high enough to prevent any further solvent flow. The hydrodynamic pressure difference between the two solutions found at chemical potential equilibrium is called the osmotic pressure difference. In a reverse osmosis process, a pressure must be applied to the concentrated solution in order to overcome the osmotic pressure and to force the solvent to cross the membrane against the concentration gradient.
The purpose of the present work is to develop a model for the spiral-wound module using a three-parameter non-linear membrane transport model by Spiegler and Kedem (SK). The pressure variations in both feed and permeate streams and the variations of concentration and the mass transfer coefficient along the length of feed and permeate channels are taken into account in the model. The value of nF in the pressure drop equation is taken from the literature. The proposed model is then used to simulate results for various operating conditions, and the significance of the third parameter, the reflection coefficient, introduced into the SK model, is further investigated. A parameter estimation program is also developed for determining membrane parameters along with the mass transfer coefficient parameters for the spiral-wound module. The data available in the literature on spiral-wound modules are further analyzed, and a correlation for the mass transfer coefficient is proposed for the Roga spiral-wound module.

Introduction(Reverse Osmosis)

In the recent years, several factors have led to the development of membrane separation technology. The most important ones are the necessity of fresh water production for drinking, domestic, agricultural, landscape or industrial uses, the requirement of higher performance level methods for waste water reclamation and reuse applications, as well as lower regulatory maximum allowed levels of contaminants. Membrane processes are often chosen in water treatment technology since these applications achieve high removals of constituents such as dissolved solids, organic carbon, inorganic ions, and regulated and unregulated organic compounds. Reverse osmosis (RO) and nanofiltration (NF) membrane processes are used around the world for potable and ultra pure water production, chemical process separations, as well as desalination of seawater (salinity around 35 g/l) and brackish water (less salty than the seawater).Reverse osmosis (RO) processes have been widely used for separation and concentration of solutes in many fields, such as chemical and biomedical industry, food and beverage processing, as well as water and wastewater treatment. With the shrinkage of water sources and the more stringent standards for drinking water quality, the applications of RO membrane in water reclamation and seawater desalination will continue to grow in the near future. Thus, a better model for describing RO process performance is highly desirable for designing and optimizing the system to further improve its cost-effectiveness. Moreover, lately there has been a growing interest in the integration of such membrane technologies for municipal and industrial water treatment, since they have been recommended as suitable for cost effective desalination and removal of a wide range of low molecular weight trace organic constituents. Organic compounds of particular interest include endocrine disruptors, human and animal antibiotics, disinfection by-products, insecticides and herbicides, and various pharmaceutical drugs. Many of these compounds have been detected in natural ecosystems at bioactive concentrations.