&EPA
          United States
          Environmental Protection
          Agency
            Industrial Environmental Research
            Laboratory
            Research Triangle Park NC 27711
EPA-600/2-79-195
October 1979
          Research and Development
Hyperfiltration Processes
for Treatment
and  Renovation
of  Textile Wastewater

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                                          EPA-600/2-79-195

                                                October 1979
Hyperfiltration  Processes for Treatment
 and Renovation of Textile Wastewater
                             by

                     S. M. Ko and J. A. Tevepaugh

                    Lockheed Missiles and Space Co.
                Huntsville Research and Engineering Center
                       Huntsville, AL 35807
                      Contract No. 68-02-2614
                          Task No. 009
                    Program Element No. 1BB-610
                   EPA Project Officer: Max Samfield

                Industrial Environmental Research Laboratory
              Office of Environmental Engineering and Technology
                   Research Triangle Park, NC 27711
                          Prepared for

                U.S. ENVIRONMENTAL PROTECTION AGENCY
                   Office of Research and Development
                       Washington, DC 20460

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                           ABSTRACT

     A computer program for design and simulation of a multi-
stage hyperfiltration system for renovation of textile waste-
water has been developed.  The program is capable of practical
design, parametric simulation and cost projection of the multi-
stage hyperfiltration system with tapered innerstages.  The
mathematical model is formulated based on Sourirajan's prefer-
ential sorption and solute diffusion theory.  Experimental
rejection and flux data of a test hyperfiltration module are
required as input parameters.   Empirical correlations and test
results available from recent EPA-sponsored programs are uti-
lized to calculate membrane transport parameters.  Computed
results for sample cases using cellulose acetate and dynamic
membranes are presented.  Various design and operating para-
meters are considered in the numerical computations to show
effects of these parameters on economics of the system.  This
simulation program has been developed in a general manner and
is readily adaptable for evaluation of other R0*/hyperfiltration
applications.
  *  Reverse  Osmosis
                               11

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     This report was submitted in fulfillment of Contract



68-02-2614,  Task 009, by the Lockheed Missile § Space



Company Huntsville Research § Engineering Center under the



sponsorship  of the U.S. Environmental Protection Agency.   This



report covers the period November 19, 1978 to August 31,  1979



and work was completed as of August 31, 1979.
                              111

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                 TABLE OF CONTENTS


Abstract  	
                      	    11

Acknowledgements 	




   1.  Introduction	    ^

   2.  Conclusions    	    4

   3.  Theory of Hyperfiltration 	    6

   4.  Transport Parameters  	   12

   5.  Membrane Systems Model  	   18

   6.  Parametric Results    	   38
References

Appendices
A.  Experimental Rejection/Flux Data   ....

B.  "Prediction of Osmosis Membrane Separation
    Efficiencies for Solutes in Dilute Aqueous
    Solutions 	

C.  Computer Code Listing 	   j
                                                    48
                                                    08
                         IV

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                      FIGURES


Number                                          Page
  1.    Concentration profiles of water and
        solute for steady state operation of
        reverse osmosis process 	     7

  2.    A tubular hyperfiltration module  ...    20

  3.    Concentration profile of the
        differential hyperfiltration module
        under steady state      	        26

  3b.   Summary of hyperfiltration model  ...    27

  4.    Schematic diagrams of tapered multistage
        hyperfiltration systems 	    34

  5.    Flow chart of the three-stage hyper-
        filtration design program 	    36

  6.    Performance simulation of a single
        tubular hyperfiltration module  ....    39

  7.    Effect of design product rate factor and
        rejection on unit cost    	    43

  8.    Effect of operating temperature and
        pressure on unit cost     	    44
                          v

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                       TABLES


Number
          Summary of Computer Design             40
          Simulation Results for Two
          Sample Hyperfiltration Systems
          of One Million Gallons Per Day
          Capacity
                         VI

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                 LIST OF SYMBOLS


  A     pure water permeability of membrane

 A      constant
  o
  B     constant

  C     molar concentration of solution

 Ci     solvent concentration in membrane

 C?     concentration of water in solution on low
        pressure side

 G£     molar concentration of boundary solution

AC2     solute concentration gradient across
        membrane

 C,     molar concentration of product solution

AC.     difference in solute concentration in feed
        and product solutions

CAI     molar concentration of solute in bulk

        molar concentration of solute in product

CAM     solute concentration in membrane

  D     diffusivity

 DI     solvent diffusion coefficient

 D?     solute  diffusion coefficient

DAB     diffusivity of solute in feed solution

        diffusivity of solute in membrane phase

  f     Fanning friction factor

  F     flow rate
                        VII

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 g      conversion factor

 J-L     solvent flux

 ^2     solute flux

  K     mass transfer coefficient

  1     effective thickness of concentrated
        boundary layer

  L     channel length

 L^     solute permeability

 Lg     filtration coefficient

 m^     molarity of feed solution

 mj     molarity of product solution

  M     average  molecular weight of solution

 MA     molecular weight of component

 Mg     molecular weight of water

 NA     solute flux

 Ng     solvent flux

  P     bulk pressure

 AP     difference in bulk pressure across
        membrane

 PR     product rate

PWP     pure water permeability

  Q     permeability

  r     tube radius

 rj     rejection

  R     gas constant
                         Vlll

-------
 R      Reynolds number
  "
  S     solute transport parameter

 S.     surface area

 Sc     Schmidt number

 Sh     Sherwood number

  t     channel thickness

  T     temperature

TCM     mass transfer coefficient of solute

  u     average axial velocity

 v      permeation velocity

 V1     partial molar volume of water

  x     axial distance

XA2     mole  fraction of solute in concentrated
        boundary solution on high pressure side of
        membrane

X»,     mole fraction of solute in product solution

  a     constant

  B     constant

  6     solubility parameter

 
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                       ACKNOWLEDGEMENTS

     The authors are grateful to Dr. J.L. Gaddis of Clemson
University and Dr. C.A. Brandon of Carre, Inc., for their
contribution to this study, in particular, their comments
on the mathematical model.  The EPA project officer was
Dr. Max Samfield and his support and interest in this study
is gratefully acknowledged.

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                      1.   INTRODUCTION


     Hyperfiltration (also termed reverse osmosis) as a textile

wastewater treatment and renovation process has been studied

under EPA/IERL/RTP* sponsorship to investigate the technical

feasibility and the economic practicability of the separation

process.  A recent investigation (Ref.l) of a pilot scale hyper-

filtration facility at LaFrance Industries, a division of Riegel

Textile Corporation, successfully demonstrated the feasibility

of dynamic hyperfiltration membranes for the in-plant recycle

and reuse of composite textile dyeing and finishing wastewater.

The applicability of the concept to a variety of composite

textile wastewaters has been confirmed in a more recent study

(Ref.2) at eight different textile mills encompassing eight

different subcategories of the textile mills point source

category (Ref.3).  The scope of these studies, however, was

limited to testing and evaluating a few commercial membranes

using plant composite wastewater and the mixed dyehouse effluent.

Furthermore, optimization of process parameters in regard to more

favorable economics, energy conservation, byproduct recovery and

effluent control of the process system were not investigated in

detail.

*  Environmental Protection Agency. Industrial Environmental
   Research Laboratory, Research Triangle Park, N.C.

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      Textile  finishing wastewater  contains  a variety  of  chemi-



 cals  depending  upon  the particular dyeing and  finishing  opera-



 tions.   The type  of  chemicals  in the wastewater greatly  affects



 the performance of the membranes.   The  effectiveness  of  mem-



 branes  is  also  sensitive  to  the temperature of the wastewater



 being treated.  In the interest of energy recovery, high temp-



 erature  operation of the  process is desirable.  Thus, a  para-



 metric  investigation of the  separation  process directed  toward



 efficient  and cost effective design of  the  treatment  system is



 required to provide the optimum performance and design informa-



 tion  essential  in the development  of a  full-scale system.  Since



 experimental investigations  of these parameters are not  practical,



 such  a parametric study necessitates a  theoretical analysis of



 fundamental mechanisms involved in  the  hyperfiltration process



 and the development of a  computer  model of  the process system.



 Unfortunately, however, direct extension of general reverse



 osmosis theory to mixed solute systems  is complicated due to



 nonavailability of pertinent fundamental physiochemical  proper-



 ties of both membranes and solutes, and possible complex inter-



 actions of chemicals in such a system.  Thus, the transport



properties of solutes in  the composite wastewater must be calcu-



 lated from experimental flux and rejection data.   Where  such



data are not available, these transport parameters may be esti-



mated using empirical correlations   (Refs.4 and 5).








     In the following sections a discussion  of hyperfiltration

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theory and associated transport parameters is followed by a



description of a computer model for design and simulation of a



multi-stage hyperfiltration system.  Results of a parametric



study of the multi-stage system using the computer model are



presented and significant conclusions summarized.  In Appendix



A, experimental membrane rejection and flux data are presented in



tabular and graphic form.  A report authored by Mr. A. Schindler



of Research Triangle Institute on osmosis membrane separation



efficiencies is included as Appendix B.   A listing of the com-



puter code is contained in Appendix C.

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                         2.   CONCLUSIONS

     Governing equations describing the hyperfiltration of solvents
and solutes can be derived from phenomenological considerations.
These equations can be used to predict the performance of actual
membranes provided experimental data and correlations are available
for determining membrane transport parameters.  These parameters
are membrane and solute dependent.

     A mathematical model formulated from Sourirajan's preferential
sorption and solute diffusion theory is adequate for predicting
membrane performance.  The computer code provides reasonable design
and simulation results (pressure, flow rate, rejection, recovery
factor, concentration polarization) for a single module with mul-
tiple innerstages using both cellulose acetate and dynamic mem-
branes.  Given accurate cost information,  the economic model real-
istically depicts the impact of various design parameters on unit
cost.

     The computer model is capable of predicting system perfor-
mance as well as analyzing system economics to find an optimum set
of design parameters.  Reliability of the computer results is
largely dependent on the availability of rigorous cost information

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for the system as well as the accuracy of the test module data and



membrane specifications.

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                3.   THEORY OF HYPERFILTRATION







Phenomenology






     Hyperfiltration (reverse osmosis) is a separation process



which utilizes the selective sorbability of the solvent from a



solution by semipermeable,  microporous membranes.   Figure 1 shows



a schematic of steady state concentration profiles of the solvent



(water) and the solute across the membrane.  Due to relatively



high affinity of the membrane to solvent molecules, a concentra-



tion gradient is established in the interface region.  Adsorbed



pure water molecules are permeated through the microporous struc-



ture of the membrane at a rate which is determined by the charac-



teristics of the membrane and the pressure exerted to overcome



the osmotic pressure.








     Solute, on the other hand, diffuses to both directions from



the interface.  The selective permeation of water molecules will



develope high solute concentration in the vicinity of the inter-



face and thus develop a maximum concentration.  This provides a



driving force for the solute diffusion in both directions from



the interface.

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                          Concentration
Interface


Water
Concentration
Profile-
                        Solute
                        Concentration
                        Profile
                                                                 Bulk Feed Solution Under
                                                                 Operating Gauge Pressure
                                                               Concentrated Boundary
                                                               Solution

                                                               Preferentially Sorbed
                                                               Interfacial Region
                                                              Dense Microporous
                                                              Membrane -Surface
                                                                . Spongy Porous Membrane
                                                          Product Solution at
                                                          Atmospheric Pressure
           Figure 1.  Concentration profiles of water and solute for steady state
                      operation of reverse osmosis process.

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It is necessary to define a quantity to express the overall degree
of permeation in general, regardless of the actual transport
mechanism.  Permeability may be defined in terms of concentration
or pressures  in the general forjn,
where
                   Q = permeability
                  S^ = area
                   F = flow rate

The concentration gradients of solutes and the solution pressure
are important forces primarily responsible for inducing fluxes of
solute and solvent.

Each flux can be associated with the various forces using a
finite number of the linear phenomenological coefficients.  Dif-
fusion models are generally one of two types, diffusion or pore.
The diffusion model  is very convenient, particularly in the case
where the molecular size of a chemical species is of the same
order as that of another species from which it is to be separated.
If the molecular sizes are quite different as in ultrafiItration,
a porous membrane with a suitable average pore size is commonly
chosen to effect the separation (pore model).  The membrane is
viewed as a homogeneous medium with a finite thickness.  When
the membrane is associated with a solution, the membrane phase
itself is considered as a solution in which the "component" of the
membrane segment is  very sluggish and almost stationary.   Thus,
                                8

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     Three transport coefficients are involved in the transport



process.  The relative magnitude of these coefficients will de-



termine the shape of concentration gradients and the efficiency



of the hyperfiltration process.  They are:





        • Water permeability constant through the membrane



        • Solute transport coefficient through the membrane



        • Mass transfer coefficient of the solute in the solution





These transport coefficients can be obtained from a set of ex-



perimental measurements of the product water rate, pure water



permeability of the membrane (normally given by the membrane



manufacturer) and solute separation efficiency.  The mass trans-



fer coefficient of the solute can also be obtained from empirical



correlations published in the literature.







Preferential Sorption/Diffusion Theory





     Permeation is a phenomena in which a species or component



is passing through another substance, usually but not necessarily



by means of diffusion.  In fact, permeation is a phenomenological



definition which encompasses a variety of transport mechanisms.



Driving forces which cause permeation include:





        • concentration gradient



        • pressure gradient



        • electric potential



        • temperature gradient

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the well established solution theory can be applied directly to

the system.



Nonequilibrium Flow Model


     Katchalsky and Curran (Ref.6) developed equations governing

membrane permeability from phenomenological considerations of

nonequilibrium flow.  The solvent flux N?,  was determined to be,


        NB = LB  (Ap-aAir)


and similarly the solute flux, N., was determined to be,
where,
        L_ = filtration coefficient (represents velocity of
             fluid per unit pressure difference)
        L  = solute permeability (measured at NR = 0)


         o = Staverman reflection coefficient (measure of
             membrane selectivity depending on properties
             of both the membrane and solute)

        AP = difference in bulk pressure across the membrane

        Air = difference in osmotic pressure across the membrane

           = solute concentration in membrane
       AC. = diiference in solute concentration in feed and
             product solutions
                              10

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Substituting for NR, the solute flux may be written,






        N  = CL   ^PCl-o) -aAir(l-o)]   + L^A
         A    AMB




For the special case of a nonselective membrane (^ = 0) ,  the solute




flux is,







        NA ' CAMVP * VCA




For the special case of an ideal semipermeable membrane, o=l,



and the solute flux reduces to the expression







        NA ' LAACA






     The coefficients, L , Lfi, and a can  be determined from ex-



perimental measurements.  Thus, membrane permeability can be cal-



culated from phenomenological considerations provided the neces-



sary constants can be determined experimentally.
                               11

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                  4.   TRANSPORT PARAMETERS




     Two parameters have been suggested by Sourirajan for char-

acterizing membranes.  These parameters are the pure water per-

meability constant, A, and a mass transfer coefficient, D^/Re.

The parameter, A, is a measure of the overall porosity of a film

and is independent of any solute.  The parameter, DAM/K6, is a

mass transfer coefficient with respect to solute transfer.




Permeability



     The parameter, A, is pressure dependent according to the

relationship,

                    A = Ao exp (- aP)



where A0 is A at P=0 and a is  a constant.   The parameter,

A  (gm-moles-water/cm^-sec-atm),  may be further defined,

                PWP                 NR
        A = 	  =  	!	
             MBxSAx3600xP      P- MXA  )+ "(XA  )
                                      L*        *J


where ,


    PWP   = pure water permeability (gm/hr)


      M   = molecular weight of water (gin/mole)



                               12

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       S  = surface area of membrane (cm")
        r\

        P = operating pressure (atm)


       NL = solvent water flux (gm-mole/cm-sec)
        B

        TT = osmotic pressure (atmj


      X   = mole fraction of solute in concentrated boundary

            solution on high pressure side of membrane


      XA, = mole fraction of solute in product solution
       f\ J



the term, NR, may be obtained from the following equation,



                                1
          = (PR)
1-
                                   (l-f)MA
                         Mg-S-3600
where ,
     (PR) = product rate (gm/hr-cm2)


       IR-, = molarity of feed solution (moles of solute/1000 gm

            water, m]_ = ppm/1000MA  where MA is the solute

            molecular weight)
        f = separation = 1 --- = rejection

                             ml

       m, = molarity of product solution



Values for the terms, N_ and X.  at different pressures are not
                       D      AT

usually available for commercial membranes.  In order to obtain


approximate values for A, the osmotic pressure,  f (XA ) was
                                                     •D

assumed zero and the osmotic pressure,  " (X  ) was assumed equal
                                           A2

to  ^(X  ), the i smotic pressure of the  feed solution.

      Al


                               13

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Solute Mass Transfer Coefficient





     The parameter, D^/Kd, is pressure dependent according to



the relationship,



                    DAM/K6  aP





where   g is a constant.  For many solutes, D«,,/KS is independent



of feed concentration and feed flow rate at any given operating



pressure.  The solute mass transfer coefficient is further de-



fined ,
            D
             AM
                  N
                   B
            K6
                        I-XA-
where,
        D
         AM
= diffusivity of solute in membrane phase (ff/sec)
          K = mass transfer coefficient  (.cm/sec)



          6 = solubility parameter



         C? = molar density of boundary  solution  (gnTmole/cnrM



         Cj = molar density of product solution  (gm'mole/cm^)






Values for the term, C-,, at different pressures  are  not  usually



available for commercial membranes.   In  order  to  obtain  approxi-



mate values for DAM/K 6,  it was assumed  that C2  is equal to  the



molar density of pure water, X. 7  is  equal  to X.,,  and  the  mole
                              i\ £               f\ -*•


fractions, XA, are,

                            -6  M

                X. = ppmxlO       ^

                               ( M  )
                                MA
                               14

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Mass Transfer Coefficient



     The mass transfer coefficient of the solute in solution is


given by the expression,
                      TCM =
                              ShD
                               2r


where,

        Sh = Sherwood number  (mass diffusivity/molecular

             diffusivity)


         D = diffusivity


         r = tube radius



Sherwood number depends on membrane geometry and flow conditions,


i.e., whether the flow is turbulent or  laminar.  The flow  is


considered turbulent for Reynolds numbers greater  than  2100


(based on hydraulic diameter).  For turbulent  flow, the Sherwood


number is assumed independent of axial  distance from the tube


entrance and for a tubular membrane is  calculated  with  an  ex-


pression developed by Gill and Sherwood,


                   7/81/4            '    60   l1n'5
                      ,,
        Sh = O.lSRe   Sc





where,


        Re = Reynolds number


        Sc = Schmidt number
0.127
              .875
            Re
 and  for  a  sheet membrane  is  calculated  with  an  expression  de-


 veloped  by Linton  and  Sherwood,
                               15

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                   7/12    Sct      0.333
        Sh = 0.44Re      (	)
                            2L
         t = channel thickness

         L = channel length


For laminar flow,  the Sherwood numher is a function of axial

distance and for a tubular membrane is calculated with an ex-

pression developed by Lebeque and modified by Sourirajan,

                     ReScZr   °'3"
        Sh = 1.95  (	)
                       x


and for a sheet membrane,

                     ReScZt   °'"3
        Sh = 2.24  (	)
                       x


where x is the axial distance from the tube entrance.



Macroscopic Parameters


     Several macroscopic parameters are required in order to

define the membrane transport.  The diffusion model for membrane

transport assumes that Pick's law is obeyed and that uncoupled

flow occurs (the flow of one component is unaffected by the

flow of other components within the membrane I.  The solvent  flux,

J,, is given by the expression,

              D1C1V1
        J  = —±~—i—   (AP-A n )
         1     RTX

                               16

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where,  C,  = solvent concentration in membrane

        D  = solvent diffusion coefficient

        Vi  = partial molar volume of water

        AP = bulk pressure difference across the membrane

        ATT  = osmotic pressure difference across the membrane

         R = gas constant

         T = temperature

         \  = mass transfer coefficient on high pressure side
             divided by the solute mass transfer coefficient


The solute flux, J  , is given by the expression,

              -D2k(AC,)
where,

         k = distribution coefficient  tg/cnT3 of solute in
             the membrane divided by the g/cnP of solute in
             the surrounding solution)

        D2 = solute diffusion coefficient

       AC9 = solute concentration gradient across the membrane


Performance of the membrane  is also characterised by the rejec-
tion, r j ,
D2k
                1
                 +
                    D,C1V1  f A P- ATT )

where,
        C* = concentration of water  in  solution on  the  low
          1   pressure  side of the membrane

     The  utilization of  the preceding parameters  in  the membrane

systems model  is described in the following  chapter.
                              17

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                 5.   MEMBRANE SYSTEMS MODEL

 In the following paragraphs a mathematical model of hyperfiltra-
 tion processes is  developed.  The model includes a mathematical
 description of membrane behavior and the economics of a hyper-
 filtration system.  A description is presented of the hyperfil-
 tration system to  be simulated and the computer code developed
 from the mathematical model.

Mathematical Model

     The model described herein is based on Sourirajan's prefer-
 ential sorption and solute diffusion theory (Ref.7) which applies
 simple boundary film theory (Refs. 8 and 9)  to obtain the con-
 centration polarization of the solute (Ref. 10) .  The effect of
pressure drop due  to friction losses and momentum changes on the
performance of the system (Refs. 11  and 12) is included in the
model.

Membrane model:  The model described herein is based on Sourirajan's
preferential sorption and solute diffusion theory  (Ref. 1 )  which
applies simple boundary film theory (Refs. 2 and 3) to obtain
                              18

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the concentration  polarization  of  the  solute  (Ref.4).   The  effect



of pressure  drop due  to  friction  losses  and momentum changes  on



the performance of the system  (Refs.5  and  7)  is  included  in the



model.




      Consider  a tubular  hyperfiltration  module  shown in Fig. 2.



From  the  overall material  balance  for  the  differential  control



volume, the  change in average  axial  velocity  (u)  can be written
 as
                    .du	Z_                              (5.la)

                    dx ~  r   w
where  v   is  the  permeation  velocity  of product  water through the
        w
membrane  in  ft/sec.   Similarly,  the  solute material  balance can



be written as       , ._CA,»    ->
                    d (u  Al)	Z_ v  r

                  	to	 "  r   w °A3                 (5.2a)
where  C    and C    are  the  molar  densities  of solute in the hulk

       Al      A3

and  the product, respectively.



     Now,  an expression for the pressure drop in a tube in terms



of friction losses  and momentum changes may be obtained from an



energy balance (Ref. 5).



                             u2f    u_ du.                   (5.3a)

                              7 + gc
                            .UJL , 2 Vw 5                  (5.3b)

                             gcr     gcr
or substituting (5.]a)yields
                               19

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 where  C  is the molar density of  solution (Ib mole/ft3), M  is  the

 average  molecular weight of solution,  f is  the Fanning friction

 factor,  and gc is the conversion  factor.
Membrane
                     \
                 Product
                 Water
                                            Feed
                                            P'CA1.U
\   \
w
                                                      dx
               t   t
               Reject
                                                           'A 2
 \   I
Product
 Water
               Fig. 2 - A Tubular Hyperfiltration Module
                                 20

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     By solving Eqs. ' 5J.a) and ( 5. 3h)simul taneous ly,  one  can  com-



pute output variables, u, P and CA]  for  the  differential  volume



for a given set of dependent variables,  prod .> f  rate  i v  i and



solute transport (C.-).  These dependent  v;in thles  car.  he related
                   A J


to the feed rate (u), the system operating pressure  iP   and  the



concentration of feed streani 'f^i' by  transper4  mechanisms  of



solute in the high pressure side of  the  membraru .




     The transport of product water  through  The  membrane  (Refs.



1  and 4) is proportional to the effective opei.-iting  pressure of



the system (see Fig. 2a),
             N
              B
[" -  «lx   - 'Ix   |]
        A 2     A 3 -J
4ai
where A is the pure water permeability of  t;ie membrane,  n  is  the



osmotic pressure at given solute concentrat;  n  .-inJ  r  i-  the  sv^-



tem operating pressure, NR  is the product  K.itei  flu.x  through  the


membrane.   XA2 and XA3 are  the mole  fraction- nf  the  solute  at



the high pressure and product water  sides  of  the  membrane.   l-.qua-



tion ( i.4a)can be written in terms of mole  fraction  by  assuming



a linear dependency of osmotic pressure  on  mole  fraction.  This



is true for most dilute solutions.




                        ir = BX                            i 5. 4b)





where B is a constant with  units  of pressure.   Substituting, we



have                      T    B            1

                 NB  = AP I1 - & (CA2 -  CA3>J              (3.40
                               21

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or dividing both sides of Eq. (5.4c)by C,
              v   - !!§. _ AP r    B ,r     .,   n
               w-  C  -  C  V  ~ PC (CAZ ~ CA3}\           (5-4d)
     The transport of the solute through  the membrane  is given
by (Ref. 1)

                 NA  ' ft?)                    (5.5a)

where CA2* a"d CA3* are the molar densities of  the solute  in  the
membrane phase in equilibrium with  the respective solution  phases,
                                                            "\
DAM is the diffusivity of solute in  the membrane phase  in  ft /sec,
and &tis the effective thickness of  membrane.   The equilibrium
concentration can be written as

                         CA = KCA*                       (5.5b)

where K is a characteristic constant determined by the  properties
of membrane and solute.  Substituting (5.5b)into (5. 5a)yields
                                                 (5.5C)
  .    v
 I K^ ) is the solute transport parameter  (ft/sec) uniquely
determined by the characteristics of specific membrane/solute
combination.

Dividing ( 5. 5c)by ( 5. 4c)yields
                               22

-------
or
            CA2 " CA3
                                   D
     Now, for a simultaneous  solution of equations (5-4d)and fS.SD

one must have an  expression  for the solute concentration in the

boundary layer  (CA2) .   The net rate of solute transport to the

membrane within the  thin  boundary layer is given by (Refs. 1 and


4),
              C
          N  -- A_3_ /N   + N  ) = Bulk flux — solute diffusion flux back
           A    C    A    B          „   to the bulk
               CA                 d  A
                                   —
*-'•*•        UL»    1 A** ..  I  A 1 -r-\ I      I  - ' A ' ~ ' U 1                  / —  ,

                                            ;A3              (5'6al
with boundary conditions


                     CA  = CA1   at  y=0


                     CA  = CAZ   at  y = ^


where  DATD  is  the  diffusivity of solute in the  feed  solution,  and
        AD
 /  is  the  effective thickness of the concentrated boundary  layer


      Solving  the  differential equation ( 5. 6a )and  defining  the

mass  transfer coefficient of solute in the feed  solution,
                                                           (5.6bj
                                23

-------
we have
                   log.
                       'CAZ-CA3\    NA+NB
                                        kC
                                                           (5.6c)
or solving for N.
                   NA= k
From ( 5. 5c)and( 5. 6d)we write
                           - C
                          CA2 - CA3

                          CA1 * CA3
                                          CA , - C
                                                 A3
                            A3


Substituting( 5. 5d)into( 5- 6e)and solving for C., yields
where
                       CA  = C   q ,
                        Al    A3
                                             Al
                                                           (5.6d
                                                           (5.be
q   =  1 +
                   y  cA31 0
                                exP
                                          CA3+ 9)
                                                           ( 5.6f
               y


               9
                       B
                      CP
                             w
                                                           (5.6gJ
                      K6

               v  *=  AP.
                w    C


     The set of equations summarized in Fig. 3b can be solved

simultaneously to obtain output conditions of the differential

section for a given input (or initial) conditions at the  inlet


of the differential section.  By repeating the procedure  one can
                               24

-------
compute the overall performance of the module.


     To predict the overall performance of the hyperfiltration

system, the following input data are required:


  1. Design specifications for the system, i.e., geometry of the
     module,

  2. Initial process conditions at the inlet of the system, i.e.,
     flow rate, feed concentration, pressure, temperature and pH,

  3. Physical properties of feed stream, i.e., viscosity and
     osmotic pressure (IT)  as functions of solute concentration
     and temperature,

  4. An empirical expression for the mass transfer coefficient
     (k) as a function of Reynolds number, arid   Schmidt number
     (Section 4),
  5. Membrane parameters:

     a. Permeability constant (A) as a function of pressure and
        temperature,  (Section 4), and

     b. Solute transport parameter (DAM/K6)  as a function of
        pressure, temperature and pH   (Section  4).


     Items 1 and 2 are defined by the system design specifica-

tions.   Item 3 may be obtained from published data in the litera-

ture.  In the event when these data are not available from the

literature, experimental measurements are necessary.  Item 4 can

be obtained from the literature.  Item 5, membrane parameters,

must be obtained through a series of experimental measurements.

Variables to be monitored in an experimental system for this

purpose are solute rejection, product rate and  system pressure.

The experimental data then can be used to compute membrane para-

meters using the system  of equations presented  in Fig. 3b.
                               25

-------
                                          Preferentially Sorbed
                                          Interfacial Region
       Concentrated Boundary
       Solution
                                    Bulk Feed Solution
                                    Under Operating
                                    Pressure
c
o
in
O
cu
fl)
«
            7^=*
          x   *->
'A3 /
               A 2
      /
      3A3
             Concentration
                     Product Solution at
                     Atmospheric Pressure

                       Spongy  Porous Membrane
                       or Membrane Support
                                      Dense Microporous
                                      Membrane Surface
     Fig. 3- Concentration Profile of the Differential Hyperfiltration
             Module Under Steady State (c^2 and CA \ denote solute
             concentrations in the membrane phase  in equilibrium
             with respective concentrations in the liquid phases.)
                                 26

-------
List of Equations
            .

          dx    r
                                            dx
              •  CM
              e r
              ec
                             2 Vw u
                              re
      v   = v
                         A3
CA! = CA3  '+^
                            J	 exp (-
       X =
                         *    B
            Fig.Sb- Summary of the Hyperfiltration Model
                                    27

-------
     Consider a tubular hyperf iltration module shown in Fig. 1.



From the overall material balance for the differential control



volume, the change in average axial velocity (uj can be written a;
                           du"    2

                           dx- ~-  7 vw
where v^ is the permeation velocity of product water  (permeate



through the membrane (ft/sec).  Similarly, the solute material



balance can be written as
                      _      Al)    2

                          cfx     ~ r  vv  A3               (S.2a)





where C^, and C^ are the molar concentrations of solute  in the



bulk and the product, respectively.






     Now, an expression for the pressure drop in a tube in terms



of friction losses and momentum changes may be obtained from an



energy balance (Ref. 11).




                       dp       u2f   u du
                     - j — = CM - + - -= —
                       dx       g(,r   gc dx





or substituting (1) yields




                                  £ -2V™U                (5.3a,
where C is the molar density of solution  (Ib mole/ft  ), M  is  the



average molecular weight of solution, f is the Fanning  friction



factor, and g  is the conversion factor.





     By solving Eqs. (5. la), ( 5. 2a) and (5.3a) simultaneously, one



can compute output variables, u, P and CAI for the differential






                               28

-------
volume for a given set of dependent variables, product rate (v )
                                                              W


and solute transport (CA3) •   These dependent variables can be



related to the feed rate  (u) , the system operating pressure (P)



and the concentration of  feed stream (CA1) by transport mechan-



isms of solute and permeate (product water) through the membrane



and associated concentration polarization of solute in the high



pressure side of the membrane.  To obtain the expressions for vv



and CA7, let us consider  a differential section of the tubular
     f\ O


hyperfiltration module shown in Fig.3a.  The figure shows a



schematic of steady state concentration profile of the solute



across the membrane.  Due to relatively high affinity of the mem-



brane to solvent (water) molecules, a concentration gradient is



established in the interface region.  Adsorbed water molecules



are permeated through the microporous structure of the membrane



at a rate which is determined by the characteristics of the mem-



brane and the pressure exerted to overcome the osmotic pressure.



Solute, on the other hand, diffuses to both directions from the



interface.  The preferential sorption of water molecule will



develop high solute concentration right in the vicinity of the



interface and thus develop a maximum concentration.  This pro-



vides a driving force for the solute diffusion to both directions



from the interface.





     The transport of product water through the membrane (Refs.



7 and 10) is proportional  to the effective operating pressure of



the system.  The effective pressure is defined to he the differ-



ence between the operating pressure and the osmotic pressure




                               29

-------
 exerted  by  the  concentrated  boundary  layer.   Assuming  a  linear

 dependency  of osmotic pressure  on mole  fraction, we  obtain  the

 following expression.   Detailed derivation  of the  expression  is

 available in Ref.  13.
                        N
                         B    AP f   B
                  Vw  =  —  = ~C~ L1 " PC (CA2 ' CA

 NB  is  the  permeate water  flux  through the membrane (lh mole/ft 2

 -sec),  C is  the molar concentration  of  the  bulk solution  (lb-mole/

 ft  ),  A is the pure water permeability  of the  membrane  (Ib  mole/

 ft   -sec-psi), P  is the operating  pressure  (psi), and B  is  a  pro-

 portionality constant for osmotic  pressure  (psi)*.


     The expression for CA3  can  be obtained by integrating  the

 differential equation obtained from  a differential  solute material

 balance within the concentrated  boundary  layer.   A  detailed- deriv-

 ation  and  solution of the boundary equation are presented in  Ref.

 13.  The resulting expression  is:

   C
                  B/CP + CS/AP     |" k/S (C   B/CP + SC/AP)
 S  is  the  solute  transport  parameter*  (ft/sec)  and  k  is  the  mass

 transfer  coefficient  of  the  solute  in  the  solution phase  (ft/sec)
 Note  that  the  constant  B is  a very small number for organic
 solutes  found  in  textile wastewaters.   For such cases, the
 osmotic  pressure  term can be neglected and the flux can be
 written  simply  as:  v  =  AP/C.

*S  is used to denote the  solute transport parameter which is rep-
 resented by (DAM/K6)  by Sourirajan (Ref.  7).   DAM is the  diffu-
 sivity of solute in the  membrane phase  (ft2/sec).   K is a  charac-
 teristic constant  which  represents preferential sorbability of
 the solute  on a given  membrane surface.   S is  uniquely determined
 by the characteristics  of specific membrane/ solute combination.

                               30

-------
     The set of equations,  (5.la)  -  (5.3a),  (5.4d), and  (5.7),
can be numerically  solved  to  obtain  output  conditions  from  the
differential section  of  the module for  a  given  input  (or  initial)
conditions at  the inlet  of the  differential  section.   By  re-
peating the procedure one  can compute the overall performance of
the module.
     The relative magnitude of  the three  transport  coefficients
v,ill determine the  shape of concentration profile and  the
efficiency of the hyperfiltration process.  The transport coef-
ficient can be  obtained from a set of experimental measurements
of the product  water rate,  pure water permeability of the mem-
brane (normally given by the membrane manufacturer)  and solute
rejection efficiency.   These parameters  are temperature and
pressure dependent.   The dependencies can be expressed by the
following equations  (Refs.  14 and 15.):
                         A oc  exp(-aP)

                       S « P~P exp(-y/T)
a , 3  and T are constants, which can be calculated from experi-
mental results.  Empirical correlations  published in the litera-
ture can be used to  calculate the solute mass transfer coeffi-
cient (Ref.  16).
                              31

-------
Economic model:  The incremental cost  for producing unit  quan-
tity of permeate water  is considered to analyze  the system  eco-
nomics.  The cost elements contributing to  the incremental  product
cost are amortized capital cost, UCC ($/Kgal), and 0§M costs
($/Kgal).  The amortized capital cost  is calculated based on  the
installed system capital cost per unit membrane  area  ($/ft2 of
membrane surface).  The 0§M costs include membrane replacement
cost.  UMRC  ($/Kgal), pumping power cost, UPP  ($/Kgal), and other
0§M costs, UMOMC ($/Kgal).  The credits to  the product cost are
credit from  recovered water, CRW ($/Kgal),  and credit  from  recov-
ered energy, CRE ($/Kgal).  The credit from  recovered  chemicals
from the concentrate usually requires  additional process  modi-
f i cat ion<^.
     The unit incremental cost for product uater, UCPW ($/Kgall,
is  written as:
       UCPW = UCC + UMRC + UPP + UMOMC  -  CRW - CRE          (6)
The unit costs  can be obtained from vendors or actual estimations.

Description of  System and Method

     In practical applications of the reverse osmosis process, a
certain multistage  design concept is desirable to achieve desired
levels  of product recovery and solute rejection.   Three such con-
cepts  with  tapered  inner stages  are presented in  Fig.  4.
                              32

-------
Note that the innerstages are tapered with respect to the number
of modules rather than the physical shape of the membrane support
structure.  The tapered innerstage design increases efficiency
of the system since it reduces the concentration polarization
in the boundary layer.  The feed rate at the inlet of each
module is maintained at the design value by reducing the number
of modules within an innerstage.  The number of modules for an
innerstage is determined by the flow rate fed to the particular
innerstage.   As the bulk flow rate decreases due to permeation
of water through the membrane, the level of polarization in a
module increases.  Minimizing the concentration polarization
increases the efficiency of solute rejection as well
as the product rate.  The rejection increases due to reduced
solute concentration in the boundary layer while higher effective
operating pressure is responsible for the improvement in the
product rate.
     The single stage concept employs direct recycle of a portion
of the reject stream to concentrate the reject  to the specified
design value.  In this case,  the system is operated  at a some-
what higher concentration than  the concentration of  the  feed.   In
the two-stage concept shown  in  Fig. 4b, the first stage  is used
as a purification stage, and  the second as a concentration stage.
Since the permeate from  the  second stage has a  higher concentra-
tion than the design product  concentration, it  is recycled to
the first stage.  In the two-stage case, the concentration of
the combined feed to the first  stage is lower  than  the incoming
                               33

-------
          a. Single Stage
                                     Recycle
    Feed

1



r



n
y






r=i j=i
£r L^T
— i 	
j







                                                           ^Reject
                                                            (Concentrate)
                                    Permeate
          b.  Two Stage
Feed.
                                    Recycle
                                                                   Reject
                                                                   (Com i • n •
                                                                     trate)
                        1 'Permeate
         c. Three Stage
Feed
                                                                   Reject
                                                                   (Concen-
                                                                     t ratri
                          Permeate
Fig. 4- Schematic Diagrams of Tapered Multistage Hyperfiltration Syst

                                    34
ems

-------
feed concentration to the hyperfiItration system.   An additional
stage is employed in the three-stage concept.   The purpose of
this stage is to concentrate the permeate from the second stage
hack to the feed concentration.   This scheme provides higher
Astern efficiency because of the reduced numher .it' modiues
required for the system.

     For a given design rejection and product  recovery factor,
the best system efficiency can be obtained when the recycle flow
rate is the minimum and the concentration of the recycle stream
is the same as the feed stream.   Numerical results indicated that
the three-stage concept reduces  the total number of modules by
30 and 10 percent over the single and two-stage system, respec-
tively.  For this reason, the three-stage concept is chosen as
the system model.

     For the reasons discussed above the tapered innerstage
design is chosen for the system design purposes.  Note that the
innerstages are tapered with respect to the number of modules
rather than the physical shape of the membrane support structure.

     A schematic flow chart for the design simulation of the
three-stage tapered hyperfiltration system is shown  in Fig.5.
A computer program developed to solve the system of  equations
presented in the previous section was utilized to obtain design
and economic results for the staged system.  The numerical
procedure for simulation of a single module employs  an iterative
                              35

-------
               (   Start    J
            Input Module Geometry,
            Operating Conditions and
            Test Module Data.
            Calculate Membrane
            Parameters
            Assume a Value for
            Stage 1 Permeate
            Water Concentration,
            Calculate Performance
            of Stage  1 Innerstages.
            Calculate Performance
            of Stage  2 Innerstages.
                                            Calculate Performance
                                            of Stage 3 Innerstages.
Calculate Total
Number of Modules
and Costs.
                                                    C    End     J
Fig. 5 - Flow Chart of the Three-Stage Hyperfiltration Design Program
        (Subscripts  P, R and F  denote permeate, rejected concentrate,
        and feed, respectively.)
                                     36

-------
scheme based on the Newton-Raphson method over a number of



finite subsections of the module.   A similar iterative procedure



is utilized to match the concentrations and flow rates to and



from each stage.
                              37

-------
                    6.    PARAMETRIC RESULTS



     The numerical results of a single module performance simula-

tion are shown in Fig.  6.  The case shown in the figure simulates

a tubular Westinghouse  module with a cellulose acetate membrane on

the inside tube wall.   The operating conditions and the geometry

are indicated in the figure.  The pressure drop for the 100 ft.

module is approximately 1 percent.  The initial rejection is 96

percent and slightly decreases as the concentration polarization

increases by 8 percent.  Approximately 10 percent of the feed i«

recovered as permeate water and the resulting decline of the tl
-------
           £   4.0
           £ *""
Rejection
1.0
0,95
-
-
                 0.1
           S °
           > 4->
           O U
           U ft
           4) [^
           c
           .2 O   74
           4_J ._.   &. t
           rt ti
           SM   2.3
                 2.2
                                       _L
                                                 JL
                              20       40       60
                                     Tube  Length (ft)
                                          80
100
Fig. 6 - Performance Simulation of a Single Tubular Hyperfiltration Module
        (Feed Rate = 10 gpm, Temperature =  70 F, Tube  Diameter =  1  in.,
        Cellulose Acetate Membrane  (by Westinghousc) with  Flux r 4.75 x
        10"5 ft/sec, Feed Concentration -  2.0 x 10'5 lb-molc/ft3)
                                      39

-------
                                 Table 1

    SUMMARY OF COMPUTER DESIGN SIMULATION RESULTS FOR TWO
         SAMPLE HYPERFILTRATION SYSTEMS OF ONE MILLION
                     GALLONS PER DAY CAPACITY

Item

Design Parameters
Test Tube Rejection
Test Tube Flux (ft/sec) ^
Permeability (Ib-mole/ft -sec-psi)
Solute Transport Parameter (ft/sec)
Design Tube Diameter (in.)
Design Tube Length (ft)
Design Product Recovery Factor
Design Rejection
Design Feed Concentration (Ib-mole/ft )
Design Temperature (F)
Design Pressure (psi)
Design Results
Number of Innerstages, Stage 1
Stage 2
Stage 3
Number of Modules, Stage 1
Stage 2
Stage 3
Total Number of Modules
Total Membrane Area (ft^)
Economic Results'""
Total Installed Capital Cost ($)
Capital Amortization Cost (cents/Kgal
Membrane Replacement Cost (cents/Kgal)
Pumping Power Cost (cents/Kgal)
Other O&M Costs (cents/Kgal)
Credit for Recovered Water (cents/Kgal)
Credit for Recovered Energy (cents/Kgal)
Total Unit Cost (cents/Kgal)
Cellulose
Acetate
Membrane

0.96
4.75 x 10 Q
2.07 x 10"^
1.23 x 10
1
100
0.8
0.95
2.0 x 10
70
600

19
1 1
42
846
213
204
1,263
31,727

539,350
24
79
15
10
40
0
88
ZR(IV)-PAA
Dynamic
Membrane

0.96 ,
11.3 x 10 "J
2.88 x 10"7
2.53 x 10"
1
100
0.8
0.95 ,
2.0 x 10
150
1,000

7
5
15
339
101
99
539
13,540

2,301,700
102
2
25
20
40
67
42
"The unit cost basis are obtained from a recent study estimation (Ref. 2).  More
 detailed cost breakdown is described in the reference
                                   40

-------
for two sample one million gallons per day hyperfiltration systems.



One is a Cellulose Acetate (CA) membrane system (Westinghouse)



operating at 600 psi and 70 F.  The other is a Zr(IV)-PAA (poly-



acrylic acid) dynamic membrane system (Selas) operating at 1000



psi and 150 F.  These two membranes are selected because of readily



available design and cost information (Refs. 1 and 2) .   The trans-



port parameters are calculated from experimentally measured rejec-



tion and flux data from the references.  The two systems are de-



signed for a product recovery factor and rejection of 0.8 and 0.95,



respectively.  The unit cost  information was obtained from vendors



and recent study estimations  (Refs. 1 and 2) .





     The computed total numbers of modules of 1 in. in diameter



and 100 ft long for the CA and dynamic membranes are  1263 and 539,



respectively.  The corresponding membrane areas required are 31,727



and 13,540 sq. ft.  The higher surface area  requirement  for the  CA



membrane system is due  to  the smaller permeability of water through



the membrane.  The unit cost  for producing  a thousand gallons of



permeate water is 88 cents for the CA system and  42 cents  for  the



dynamic membrane  system.   It  is noted that  the  major  cost  element



for the CA system is the membrane  replacement cost, while the  capi-



tal amortization  cost makes  the largest  cost contribution.   The



credit from  recovered energy  is significant  enough  to cause  the



dynamic membrane  to  be  attractive.   It  should be  noted  that  the



design and operation conditions used  are for illustration purposes



and do not represent a  typical case.
                                41

-------
     To demonstrate the range of applicability of the developed
model and to investigate the effects of various design parameters
on the economics of the system, a series of parametric studies wa:
performed.  The results are shown in Figs. 7 and 8.

     Figure 7 shows the effects of design product rate factor and
solute rejection on the unit cost.  The effect of design product
rate factor on the unit cost is relatively moderate.  The design
rejection factor has a more pronounced effect on the cost of the
dynamic membrane system.  Significantly lower unit cost can be
obtained at slightly lower design rejection for the dynamic mem-
brane.  On the other hand, the effect of design rejection is less
significant in the CA membrane.  Thus, a proper combination of
these two membrane systems may be desirable when a higher design
rejection is necessary due to more stringent quality requirements
for reuse of the permeate water.

     Figure 8 shows the effects of operating temperature on the
unit cost with operating pressure as a parameter.  Due to charac-
teristics  of the membranes, the effects are shown only for the
respective applicable operating temperature and pressure ranges.
It is shown that the unit cost is generally lower at higher temp-
erature and pressure.  Unit cost is a stronger function of- temp-
erature and pressure than product recovery factor and rejection
(Fig.7).

     The unit cost does not include credit from possible reuse of
the chemicals contained in the concentrated reject stream.  A net
                               42

-------
            1.4
            l.Z
            1.0
          •o
o

w>
            0.6
tn
O
'J
2 0.4
c
D
            0.2
            	Cellulose Acetate Membrane (Westinghouse)

            	  Zr(IV)-PAA Dynamic Membrane (Selas)

            DREJ = Design Rejection              DREJ
                -DREJ

                 0.97^
                   °-95^^— -*
                                                             0.95
                                                              0.93
                       0.6     0.75      0.8      0.85
                            Design Product Rate Factor
                                                  0.9
Fig. 7 - Effect of Design Product Rate Factor and Rejection on Unit Cost
        (Feed Rate = 10 gpm, Tube Diameter = 1 in., Temperature - 70 F
        for CA Membrane and 150 F for Dynamic Membrane, Pressure =
        600 psi for CA  Membrane and 1000 psi for Dynamic  Membrane)
                                   43

-------
   3.5
   3.0
   2.5
3
T3
O
nl
cm
   1.5
CO
O
O

X  1.0
c
P
   0.5
	Cellulose Acetate Membrane  (Westinghouse)


	  Zr(IV)-PAA Dynamic Membrane (Solas)

P = Operating Pressure (psi)
                                                          1000
          60       80      100      120       140      160

                  Operating  Temperature (F)
Fig. 8- Effect of Operating Temperature and Pressure on Unit Cost

        (Feed Rate = 10 gpm.  Tube Diameter = 1  in.,  Design Rejection

        = 0.95, Design  Product Rate Factor = 0.8)
                                    44

-------
saving can be realized if the chemical credit is included in the
computation of the unit cost.  Although high temperature and
pressure operation is desirable in the interest of achieving lower
unit cost or even net savings, it is limited by excessive main-
tenance costs at high operating temperature and pressure.
Membrane lifetime is diminished by operation at high temperatures
and very high pressures (several hundred atmospheres) thus in-
creasing maintenance costs.  For the range of temperatures and
pressures investigated, a flat estimated average maintenance cost
was assumed.  At higher temperatures and pressures, a functional
relationship between these operating variables and maintenance
cost should be developed and included in the computations.
                               45

-------
                            REFERENCES


 1.   Brandon,  C.A.,  and J.J.  Porter,  "Hyperfiltration for Renovation
     of Textile Finishing Plant Wastewater," EPA-600/2-76-060, March
     1976.

 2.   Brandon,  C.A.,  J.J.  Porter and D.K.  Todd,  "Hyperfiltration for
     Renovation of Composite Wastewater at Eight Textile Finishing
     Plants,  " EPA-600/2-78-047, March 1978.

 3.   Development Document for Effluent Limitations Guidelines and
     New Source Performance Standards for the Textile Mills Point
     Source Category," EPA-440/l-74-022-a, June 1974.

 4.   Shindler, A., Unpublished results developed under EPA/RTP  spon-
     sorship.

 5.   Spencer,  H.G.,  and J.L.  Gaddis,  "Hyperfiltration of Nonelectro-
     lytes: Dependence of Rejection on Solubility Parameters,"  Paper
     presented at EPA Symposium on Textilw Industry Technology, 5-8
     December 1978.

 6.   Katchalsky, A.  and P.P.  Curran,  Nonequilibrium Thermodynamics
     in Biophysics,  Harvard University Press, Cambridge Massachu-
     setts, 1965.

 7.   Sourirajan, S., Reverse Osmosis, Academic Press, New York,
     1970,  pp. 176-184.

 8.   Sourirajan, S., Reverse Osmosis, Academic Press, New York,
     1970,  pp. 185-188T

 9.   Brian, P.L.T.,  "Mass Transport in Reverse Osmosis," in Desalin-
     ation by Reverse Osmosis, edited by Ulrich Merten,  The MIT
     Press, Cambridge,1971.

10.   Pusch, W., "Concentration Polarization in Hyperfiltration
     Systems," in Reverse Osmosis Membrane Research, edited by
     H.K. Lonsdale and H.E. Podall, Plenum Press, New York, 1972,
     pp. 43-57.
                                                                  \
11.   Griffith, W.L., R.M. Keller, and K.A. Kraus, "Parametric Study
     of Hyperfiltration in Tubular Systems with High Permeability
     Membranes," Desalination. Vol. 4, 1968, pp. 203-308.
                                46

-------
12.   Johnson,  J.S.,  Jr.,  L.  Dresner and K.A.  Kraus,  "Hyperfiltra-
     tion (Reverse Osmosis)," in Principles of Desalination,  edited
     by K.S.  Speigler,  Academic Press,  New York,  1966,  pp.  345-439.

13.   Ko, S.M., and P.G. Grodzka, "Study of Hyperfiltration  Proces-
     ses for  Treatment  and Renovation of Textile  Wastewater," to
     be published.

14.   Sourirajan,  S., Reverse Osmosis, Academic Press,  New York,
     1970,  pp. 191-ZOT;

15.   Gaddis,  J.L., Private communication dated 24 May  1978.

16.   Hwang,  S.T.,  and K.  Kammermeyer, Membranes in Separations,
     Wiley-Interscience,  New York, 1975, pp.  351-359.
                                47

-------
                         Appendix A

             EXPERIMENTAL REJECTION/FLUX DATA
The experimental rejection data presented in Tables 1-8 and
Figs. A-l through A-18 were obtained from:   CARRE, Inc.,
"Compilation of Toxic Rejection Data for Membranes".  Prepared
for EPA, December, 1977.
                            48

-------
                                              Table 4-1

               REJECTION OF SPECIFIC COMPOUNDS BY THE SELAS DYNAMIC Zr(IV)-PAA MEMBRANE
                                  OPERATING ON TEXTILE WASTEWATER
Solution (underlined
solutes in consent
decree)
COD
BOD
TOC
Dissolved Solids
Total Solids
Volitile Solids
Color
Phenol
Iron
Nickel
Chromium
Zinc
Copper
Manganese

Rejection
(%)
71 - 99
74 - 99
82 - 98
62 - 99
63 - 96
70 - 99
89 - 100
86 - 100
97 - 99
80 - 98
89 - 99
94 - 99
92 - 99
90 - 98
pH
5.2 - 12
5.2 - 12
5.2 - 12
5.2 - 12

5.2 - 12
5.2 - 12
6.6 - 9.6
5.2 - 9.6
5.2 - 9.6
5.9 - 12
5.2 - 7.5
5.2 - 9.3
6.1 - 7.4
Concentration
(mg/1)
1600 - 7100
25 - 2300
175 - 2000
670 - 128000
2500 - 215000
370 - 2700
120 - 3400*
0.66 - 315
8.25 - 20
0.7 - 3.87
0.7 - 23
2.1 - 18
1.2 - 5.5
0.5 - 1.02
70-80%
1
3
0
2

2
1
1
0
0
0
0
0
0
Number
80-90%
7
6
6
8

6
1
2
0
3
1
0
0
0
of Data
90-100%
27
29
26
21

21
19
4
6
7
7
13
14
4
Total
35
38
32
32
40
29
21
7
6
10
8
13
14
4
*Concentration in Pt-Co Units

 Data compiled from:   Brandon,  C.  A.,  Porter, J.  J.,  and Todd,  D.  K.,  "Hyperfiltration for
                      Renovation of Composite Wastewater at Eight  Textile Finishing Plants."
                      Final  Report, EPA Grant No.  S802973,  Clerason University report in
                      preparation.

-------
                                             Table A-2
                        REJECTION OF SPECIFIC COMPOUNDS  BY THE WESTINGHOUSE
                                TUBULAR CELLULOSE ACETATE MEMBRANE
                                 OPERATING ON TEXTILE WASTE WATER
Solute (underlined
. solutes in consent
decree)
COD
BOD
TOG
Dissolved Solids
Volatile Solids
Color
Phenol
Iron
Nickel
Chromium
Zinc
Copper
Manganese

Rejection
<%)
89-99
87-99
82-96
82-97
90-98
91-98
9-99
96.5
_
-
_
-
67-99

PH
5.8-7.1
5.8-7.1
5.8-6.2
5.8-7.1
5.8-7.1
5.8-7.1
6.8-7.1
5.8

-

-
5.8-7.1

Concentration
(mg/1)
1765-8664
128-1800
345-1800
2804-6303
630-3504
220-2000*
0.54-0.65
8.48

—

-
0.12-1.34

70-80%
0
0
0
0
0
0
0
0

_

_
1

Number
80-90%
2
2
1
0
0
0
0
0

_

_
2

of Data
90-100%
6
6
4
3
5
5
1
1

_

—
1

TOTAL
8
8
5
3
5
5
2
1

_

_
5

Concentration in Pt-Co Units
Data compiled from:
Brandon, C. A., Porter,  J.  J.,  and Todd,  D.  K.,  "Hyperfiltration for
Renovation of Composite  Wastewater at Eight  Textile Finishing Plants."
Final Report, EPA Grant  No. S802973,  Clemson University report in
preparation.

-------
                                             Table A-3
                            REJECTION OF SPECIFIC COMPOUNDS BY THE UOP
                              SPIRAL-WOUND CELLULOSE ACETATE MEMBRANE
                                 OPERATING ON TEXTILE WASTE WATER
Solute (underlined
solutes in consent
decree)
COD
BOD
TOC
Dissolved Solids
Volatile Solids
Color
Phenol
Iron
Nickel
Chromium
Zinc
Copper
Marganese

*Concentration in Pt
Rejection
(%)
89-99
89-100
83-99
90-99
89-99
98-100
20-98
94-99
80-83
97
89-99
92-99
98-99

-Co Units.
PH
5.2-9.4
4.9-9.4
4.9-9.4
4.9-8.0
4.9-7.2
3.6-8.0
6.8-7.1
5.2-6.8
5.2-6.8
6.8
3.6-7.5
3.6-7.5
4.9-6.2


Concentration
(mg/1)
27-2303
500-8664
232-2000
670-12120
630-3504
65-2000*
0.54-35.0
8.25-12.0
1.02-1.20
3.6
3.02-18.3
1.78-5.51
0.47-1.32


70-80%
0
0
0
0
0
0
0
0
0
0
0
0
0


Number o
80-90%
2
1
3
0
1
0
1
0
2
0
1
0
0

f Data
90-100%
18
21
11
22
13
17
1
5
0
1
9
6
5

TOTAL
20
22
14
22
14
17
3
5
2
1
10
6
5


Data compiled from:
Brandon, C. A., Porter, J. J., and Todd,  D.  K., "Hyperfiltration for
Renovation of Composite Wastewater at Eight  Textile Finishing Plants.
Final Report, EPA Grant No. S802973, Clemson University report in
preparation.

-------
                                              Table A-4
                            REJECTION OF SPECIFIC COMPOUNDS BY THE DUPONT
                              MEMBRANE OPERATING ON TEXTILE WASTE WATER
Solute (underlined
solutes In consent
decree)
COD
BOD
TOC
Dissolved Solids
Volatile Solids
Color
Phenol
Iron
Nickel
Chromium
Zinc
Copper
Manganese

Rejection
(%)
98.3
98.4
97.2
99.2
96.7
99.1

85

-

95.7
_

*Concentration in Pt-Co Units.
PH
6.4
6.4
6.4
6.4
6.4
6.4

6.4

_

6.4
—


Concentration
(mg/1)
2776
1138
1058
8906
1950
1571*

1.0

_

0.92



Numbe
70-80%
0
0
0
0
0
0

0

^

0



r of Data
80-90% 90-100%
0
0
0
0
0
0

1

_

0



1
1
1
1
1
1

0

_

1



TOTAL
1
1
1
1
1
1

1



1



Data compiled from:
Brandon, C. A., Porter,  J.  J., and Todd, D.  K.,  "Hyperfiltration for
Renovation of Composite  Wastewater at Eight  Textile Finishing Plants."
Final Report, EPA Grant  No. S802973, Cletnson University report in
preparation.

-------
                                                    Table A-5
                                      REJECTION OF SPECIFIC COMPOUNDS BY THE
                                           UNION CARBIDE 3NJR MEMBRANE
                                        OPERATING ON TEXTILE WASTE WATER
Solute (underlined
solute In consent
decree)
COD
BOD
TOC
Dissolved Solids
Volatile Solids
Color
Phenol
Iron
Nickel
Chromium
Zinc
Copper
Manganese

Rejection
(%)
mm
mm
15.2
7.3
55.7

/


61.0
5A.1
55.9

PH
_
-
8.1
8.1
8.1




8.1
8.1
8.1

Concentration
(mg/D

-
330
23853
804




0.172
1.6A
0.397

Number
70-80%
—
-
0










of Data
80-90%
-
-
0










90-100%
-
-
0










TOTAL
-
-
1
1
1




1
1
1

O«
        *Concentration in Pt-Co Units.
        Data compiled from:
Brandon, C. A., Porter, J. J., and Todd,  D.  K.,  "Hyperfiltration for
Renovation of Composite Wastewater at Eight  Textile Finishing Plants."
Final Report, EPA Grant No. S802973, Clemson University report in
preparation.

-------
                                             Table A-6
                               REJECTION OF SPECIFIC  COMPOUNDS  BY  THE
                                    SELAS Zr(IV)-Na2S103 MEMBRANE
                                  OPERATING ON  TEXTILE WASTE WATER
Solute (underlined
solute in consent
	 decree)
COD
BOD
TOG
Dissolved Solids
Volatile Solids
Color
Phenol
Iron
Nickel
Chromium
Zinc
Copper
Manganese

"Concentration in Pt-C
Rejection
(%)
71-98
88-98
85-92
41-97
81-98
99-100
16-97
67-95
90.6
93-100
89-99
94-100
99.7
o Units
PH
7.1-10.7
7.1-10.7
8.0-10.7
7.1-10.7
8.0-10.7
7.4-10.7
7.1-8.1
7.1-10.7
7.1
7.1-10.7
7.1-10.7
7.1-10.7
7.1

Concentration
(n.R/1)
933-17,800
295-6200
330-440
17810-23853
213-10870
4000-30,000*
1.4-241
2.9-9.02
2.12
0.129-1.38
1.64-7.76
0.243-1.59
3.97
Nu
70-80%
1
0
0
0
0
0
0
1
0
0
0
0
0
mber of
80-90%
1
1
2
0
1
0
0
1
0
0
2
0
0
Data
90-100%
2
4
2
1
2
3
1
1
1
5
3
5
1
TOTAL
4
5
4
5
3
3
3
4
1
5
5
5
1

Data compiled from:
Brandon, C. A., Porter, J.  J.,  and Todd,  D.  K.,  "Hyperfiltration for
Renovation of Composite Wastewater at Eight  Textile Finishing Plants."
Final Report, EPA Grant No. S802973,  Clemson University report in
preparation.

-------
                                             Table A-7
                              REJECTION OF SPECIFIC COMPOUNDS BY THE
                             WESTINGHOUSE TUBULAR POLYSULFONE MEMBRANE
                                 OPERATING ON TEXTILE WASTE WATER
Solute (underlined
solute in consent
decree)
COD
BOD
TOC
Dissolved Solids
Volatile Solid
Color
Phenol
Iron
Nickel
Chromium
Zinc
Copper
Manganese

*Concentration in Pt-
Rejection
(%)
17-75
65-71
A9-82
23-69
30-72
25-96
11-24
48-97
15.8
82-93
33-99
76-97
50-75

Co Units
PH
3.6-12
6.4-12
5.9-12
3.6-12
3.6-11.6
5.9-12
6.4-7.0
3.6-9.2
3.6
5.9-12.0
3.6-7.0
3.6-12.0
5.9-7.0


Concentration
(mg/1)
468-5020
1180-1800
762-1338
3705-12840
370-2698
200-3409*
0.140-0.210
3.80-7.75
0.76
1.4-23.0
3.60-9.91
0.92-5.51
0.08-0.40


Number of Data
70-80% 80-90% 90-100%
2
1
2
0
1
1
0
1
0
0
0
2
1


0
0
1
0
0
2
0
0
0
2
0
0
0


0
0
0
0
0
2
0
1
0
3
4
6
0


TOTAL
8
2
8
9
8
8
3
3
1
5
6
8
5


Data compiled from:
Brandon, C. A., Porter, J.  J., and Todd,  D.  K.,  "Hyperfiltration for
Renovation of Composite Wastewater at Eight  Textile Finishing Plants."
Final Report, EPA Grant No. S802973, Clerason University report in
preparation.

-------
                                                  Table  A-8
                                   REJECTION OF SPECIFIC COMPOUNDS BY THE
                                   Zr(IV)-PAA MEMBRANE ON  STAINLESS STEEL
                                      OPERATING ON TEXTILE WASTE WATER
Solute (underlined
solute in consent
decree)
COD
BOD
TQC
Dissolved Solids
Total Solids
Volatile Solids
Color
Phenol
Iron
Nickel
Chromium
Zinc
Copper
Manganese
Rejection
(%)




38-88



0-97

11-100

48-99

PH














Concentration
(mg/1)




3000-9200



0.65-7.10

12-281

0.07-0.96

Numbe
70-807.




6



0

3

0

r of Dat
80-90%




2



3

0

2

a
90-100%




0



5

4

5

TOTAL




10



10

9

9

Cn
      *Concentration in Pt-Co Units
      Data compiled from:
Brandon, C. A., Porter, J.  J.,  and Todd,  D.  K.,  "Hyperfiltration for
Renovation of Composite Wastewater at Eight  Textile Finishing Plants."
Final Report, EPA Grant No. S802973,  Clemson University  report in
preparation.

-------
 100




  90




  80




  70
c
o

73 cr»
.£, **0

ec

S« 50




  40




  30




  20




   10

         O SELAS Zr (IV)-PAA


         • WESTINGHOUSE   TUBULAR  CELLULOSE  ACETATE


         AUOP


         D WESTINGHOUSE   TUBULAR  POLVSULFONE.
                                       X  DUPONT


                                       O  SELAS Zr (IV)-No2SI03
               500
1000
1500        2000        2500

         Concentration (mg/l)
3000
6200
         Figure A-l  Percent Rejection versus Concentration for Biochemical Oxygen Demand   (BOD ).

-------
00
  100

  90

  80

  70
c
o
'•C 60
O)
-—^
0)
cr
jo 50

  40

  30

  20

  10
                O SELAS Zr (IV)-PAA
                • WESTINGHOUSE   TUBULAR  CELLULOSE  ACETATE
                A UOP
                D WESTINGHOUSE   TUBULAR  POLYSULFONE ULTRAFILTRATION
                                        X  OUPONT
                                        0  SELAS Zr (IV)-No2SI03
                               A o A CD
                            00
                               o
                               O
                                00  $   AO
                                                                                                              00
                                                                                                           I  // I //I
                     1000
2000
                                       3000
4000        5000
Concentration (mg/l)
6000
7000
8000
                Figure A-2  Percent Rejection  versus Concentration  for Chemical Oxygen  Demand (COD).

-------
  100




  90




  60




  70
c
o


I 60
«T
cc

5? 50




  40




  30




  20




   10




   0
O SELAS Zr (IV)-PAA


• WESTIN6HOUSE   TUBULAR  CELLULOSE  ACETATE


A UOP


O WEST1NGHOUSE  TUBULAR  POLYSULFONE ULTRAFILTRATION
      O  A
                           • 3 NJR ON UCC


                           X OUPONT


                           e SELAS Zr (IV)-Na2Si03







                           o _     O  A
      250
                            500
750
 1000        1250

Concentration (mg/l)
1500
1750
2000
Figure  A-3  Percent Rejection versus Concentration  for Total Organic  Carbon (TOC).

-------
  100

   90

   80

c  70
g
.£. 60
o>
tr.
&  50

   40

   30

   20

   10
      O SELAS Zr (IV)-PAA
      • WESTINGHOUSE   TUBULAR  CELLULOSE  ACETATE
      A UOP
      0 WESTINGHOUSE   TUBULAR  POLYSULFONE ULTRAFILTRATION
                                                                    B 3 NJR ON UCC
                                                                    X DUPONT
                                                                    « SELAS Zr (IV)-No2SI03
a
              J	1	'    '
                                  O

                                  O
                                           O
                                           0
                                           O
                                           Q
                                                J_
                                                  A A
                                                 0O      O
                                                  J	L
_L
                                                                    J	L
                                                                                                 i   //t
0
                           5000
                                            10000
                                          Concentrotion (mg/l)
                                                                       15000
              Figure A-4  Percent  Rejection versus  Concentration for  Dissolved Solids.

-------
      100

      90

      60
       70
ON   OC
     u
     •>
     •5-60
       50

       40

       30

       20

       10
             O SELAS Zr (IV)-PAA
             • WESTINGHOUSE   TUBULAR   CELLULOSE   ACETATE
             A UOP
              O WESTINGHOUSE   TUBULAR   POLYSULFONE ULTRAFILTRATION
00
              o /^o
                                            •  3 NJ R ON UCC
                                            X  DUPONT
                                            a  SELAS  Zr (IV)-No2Si03
                                                                                                  it.	I
                    500
     1000
1500        2000        2500
          Concentration (mg/l)
3000
3500 " 10870
                       Figure A-5   Percent Rejection  versus Concentration for Volatile  Solids.

-------
            O SELAS Zr (IV)-PAA


            • WESTINGHOUSE  TUBULAR CELLULOSE ACETATE

            A UOP

            0 WESTINGHOUSE  TUBULAR POLYSULFONE  ULTRAFILTRATION
                                                                 3NJR ON UCC


                                                                 SELAS Zr (IV)-Na2Si03
100


90



80
                       •   • D


                           o
                                       a
        O     9


        a
    o
O*   ^*  en
NJ   'ST  60
    a:
    ^o
    ^  50
40



30



20



10



 0
  0
                                JL
                                      _L
             _L
                                                                    _L
                                                                                                         JL
                                                                                                       J_
                   1000
                        2000
3000        4000       5000

            Concentration (mg/l)
                                                                         6000
                                                                                            7000
eood^soooo
                            Figure A-6  Percent Rejection versus Concentration for Color.

-------
a
      100




       90




       80




       70
    o

    .£.  60
    «>
       50





       40





       30





       20





       10





       0
                   O  SELAb Zr(IV)-PAA                          D WESTINGHOUSE TUBULAR  POLYSULFONE ULTRAFILTRATION


                   •  WESTINGHOUSE TUBULAR CELLULOSE ACETATE    «SELAS Zr (IV)-No2Si03


                   A  UOP
                      A
 0


A     O
         0
       0.25
0.50
0.75
                                                          J_
                                                                      JL
                                                          1.00         1.25


                                                        Concentration (mg/l)
                                                                                                 \
1.50'
                                                                                               -J	1
50   100  150  200 250"3I5
                          Figure  A-7  Percent Rejection  Versus Concentration for  Phenol.

-------
  100

  90

  80
c 70
o
  40

  30

  20

  10
   •
  0
               O SELAS Zr (IV)-PAA
               • WESTINGHOUSE TUBULAR CELLULOSE  ACETATE
               A UOP
       	1	1	1	1	(	i
   0                      0.001                    0.002                    0.003
                                                 Concentration  (mg/l)
                   Figure A-8  Percent  Rejection versus Concentration  for  Mercury.

-------
tn
  100

  90


  80

  70
c
o

.I60
cc
& 50

  40


  30


  20


   10

   0
             O SELAS Zr (IV)-PAA

             • WESTINGHOUSE  TUBULAR CELLULOSE ACETATE
                                                                  0 SELAS Zr (IV}-No2Si03
              O WESTINGHOUSE TUBULAR  POLYSULFONE ULTRAFILTRATION
                             O   AOA A A
                           O  O
                        A O   .
                        OQ   A
                             D   •
              Q
                     0.25
                            0.50        0.75           1.00          1.25
                                               Concentration (mg/l)
3.97
                       Figure A-9  Percent Rejection  versus Concentration for Manganese.

-------
        OSELAS Zr (IV)-PAA


        • WESTIN6HOUSE  TUBULAR  CELLULOSE ACETATE

        AUOP

        OWESTINGHOUSE  TUBULAR POLYSULFONE ULTRAFILTRATION
c
o
  100*



  90



  60



  70
S! 60

V
DC

5« 50




  40




  30




  20




  10
                    A          D


                            O
         O
                                            h
                                                                  X DUPONT


                                                                  OSELAS Zr (IV)-No2Si03
                                                               n    o
    0
                            10
15
                                                    20
                                                                25
                                                 Concentration  (mg/l)
                                    30
                                                                                        35
                                                                                                    40
                   Figure A-10  Percent Rejection versus  Concentration  for  Iron.

-------
        OSELAS Zr (IV)-PAA

        • WESTINGHOUSE  TUBULAR CELLULOSE ACETATE
        AUOP

        OWESTINGHOUSE  TUBULAR POLYSULFONE ULTRAFILTRATION
  100


  90

  80


 . 70
o
"o
o

A
    o
    A
      o

     o
                                                      eSELASZr (IV)-PAA
^
  50

  40
  30


  20
   10

   0
               0.25
               0.50
0.75          1.00         1.25
         Concentration (mg/l)
1.50
1.75
2.00
                     Figure A-ll  Percent  Rejection versus Concentration for Nickel.

-------
OO
 100

 90

 80

; 70
       "o
       5-60
      cc
         50

         40

         30

         20

         10
               • WESTINGHOUSE  TUBULAR  CELLULOSE  ACETATE
               AUOP
               DWESTINGHOUSE TUBULAR  POLYSULFONE  ULTRAFILTRATION
                 e e
                                                              • 3NJR ON UCC
                                                              e SELAS Zr (IV)-Na2SI03
J-   °A
                    O
                    o
                                                                                                 o
                                                                                                 0
                                                                                         Oo
                                                                                           o
                                                                                                _L
                                                                                          -L
                                                                             o
                                                                             D
                                                                        _L
                                                                                                       _L
           0
           0.25
050
                                      0.75         1.00         1.25
                                                Concentration lmg/1)
I.507
                                                                                                10   15    20  25
                         Figure A-12   Percent Rejection versus Concentration for  Chromium.

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  100




  90



  80
  70
'=-60

-------
 "100

  90

  80

o 70
-0  o
o  «>
      60
      50^
  40

  30

  20

  10

   0
             0 SELAS Zr(IV)-PAA

             • WESTINGHOUSE   TUBULAR  CELLULOSE   ACETATE

             A UOP
             • WESTINGHOUSE   TUBULAR  POLYSULFONE  ULTRAFILTRATION
                0
                 0
              A

          M
          A*

          o
                                      h
                                                                    • 3NJRONUCC

                                                                    X OUPONT
                                                                    0 SELAS Zr(IV)-Na2SI03
                                                                                         0
                                                                                      o  a
                                                         i
                                                                     i
                                                                                                   -//-
O50
                               1.00
1.50         2.00         2.50
         Concentration (mg/l)
                                                                            3.00
3.50
5.51
                          Figure A-1A   Percent Rejection versus Concentration for Cooper.

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  100



   90




   80
I  70
u
o
0>
   60




   50




   40



   30




   20




   10
              O  2000 SERIES  SELAS Zr(IV)-PAA


              A  4000 SERIES  SELAS Zr (IV)-PAA


              A  4000 SERIES  STAINLESS STEEL-PAA
                            _L
                                        JL
                                                                            J_
                                                                                        J_
                                                                                            0°
                                                                                                    JL
    0
2500
5000
7500        10000       12500

      Concentration  (mg/l )
                                                                           15000
                                                                        17500
                                                                        20000
                  Figure A-15   Percent Rejection versus  Concentration for Total' Solids.

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  100
   90         °*
   80
   70
o
55
        A
           O  2000 SERIES  SELAS Zr(IV)-PAA

           A  4000 SERIES  SELAS Zr(IV)-PAA

           A  4000 SERIES  STAINLESS STEEL Zr (IV)-PAA
           AO
                               A                                       °      °   °  °
       8
60


50


40


30
   A


20U>


10
        0 A
    0           0.25         0.50          0.75         1.002 345           10           15           20
                                                Concentration (mg/l)
                      Figure A-16   Percent Rejection versus Concentration  for Copper.

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100

 90

 80
          O 2000 SERIES—SELAS  2r(IV)-PAA

          A 4000 SERIES —SELAS  Zr(IV)-PAA

          A 4000 SERIES-STAINLESS STEEL Zr (IV)-PAA
                         AO
                        O  O
                           A

70
 60

 50

 40

 30

 20
         o
         o
 10
             0.50
                                        234
                                           Concentration (mg/e)
               Figure A-17  Percent  Rejection versus Concentration for Iron.

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   90


   80


|  70
O

£  60
5*

   50


  40


  30


  20


   10
  O  2000 SERIES "-SELAS Zr(IV)-PAA

  A 4000 SERIES—SELAS Zr(IV)-PAA

  A 4000 SERIES —STAINLESS STEEL Zr(IV)-PAA
 A     O
    A
        A             A
     O          A
O

O O
        50
                            100
150         200         250
       Concentration (mg/l)
300
350
400
          Figure A-18   Percent Rejection versus Concentration for Chromium.

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                     Appendix B

     PREDICTION OF OSMOSIS MEMBRANE SEPARATION
EFFICIENCIES FOR SOLUTES IN DILUTE AQUEOUS SOLUTIONS
                         75

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                                             V
                                              1 •      3-
                                             - < j -.    1

                                                    I
     RTI/1430/29-01F
                                .   ..  A...I :,•. .jj   e.  L  ;r    r» ;.  - -    >     jj.  y
                               .>.-..;:iK.jJ ^ij^ii^.y^r»^S2a^^it<,^>^%>i^^t^^
                       PREDICTION OF OSMOSIS MEMBRANE  SEPARATION

                 EFFICIENCIES FOR SOLUTES  IN DILUTE  AQUEOUS  SOLUTIONS
                                          by

                                    Anton Schindler

                              Research Triangle Institute
                                    P. 0. Box 12194
                    Research Triangle Park, North Carolina   27709
                           Contract No. 68-02-2612, Task 29


                          EPA Task Officer:  Dr. Max Samfield

                     Industrial Environmental Research Laboratory
                       Office of Energy, Minerals, and Industry
                           Research Triangle Park, NC  27711
                                     Prepared for

                        .U.  S.  ENVIRONMENTAL PROTECTION AGENCY
                          Office of Research and Development
                                Washington, DC   20460
                                            76
RESEARCH  TRIANGLE   PARK,  NORTH   CAROLINA  277
09

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                              CONTENTS
                                                                         Page
List of Figures	         78
List of Tables	         79
List of Symbols	         80
Sections
I         Abstract	         81
II        Conclusions  and  Recommendations  	         82
III       Introduction	         ^4
IV        Solute Parameters  	         89
V         Prediction of  Solute Separation  	         9G
References	
                                        77

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                  LIST OF SYMBOLS
F  .  	  cohesive energy
 con
e  .  	  cohesive energy density
 con
K	dissociation constant of an acid
K	  .  dissociation constant of a base
 b
M	  molecular weight of solute
p  	  pressure
R	solute rejection in reverse osmosis
RO 	  reverse osmosis (hyperfiltration)
S  	  Small number
V  	  molar volume
a  	  degree of dissociation
6  	  solubility parameter (general)
6  	  solubility parameter of solvent
6  	  solubility parameter of polymer
5. . .	solubility parameter of solute
5  	  solubility parameter of membrane
A	difference between solubility parameters
 iin  '                                              , .   , .     i  \
                            of solute and membrane  (absolute value;
o  	  Hammet constant
o*	Taft constant
Av 	  band shift for hydroxyl groups in  infrared
                            spectra
                           80

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                                   SECTION I

                                   ABSTRACT

     The EPA has set maximum concentration levels for many environmental
pollutants in water.   Most of these pollutants are nonelectrolytes  being
present in low concentrations albeit still exceeding the maximum permissible
level.   Hyperfiltration possesses a high potential for large volume separation
of pollutants in industrial  unit operation effluents.   The objective of this
report was to present a critical evaluation of methods permitting the predic-
tions of separation efficiencies in hyperfiltration for different ncn-elec-
trolytes from their chemical structure.   The evaluation was based on two
criteria important for practical applications:  universality and facile
accessibility of the required correlation parameters.
                                     81

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                                    SECTION II

                           CONCLUSIONS AND RECOMMENDATIONS

      The most extensive investigations of establishing correlations between
 solute parameters and hyperfiltration efficiency (solute rejection) were
 carried out by Sourirajan and Matsuura on cellulose acetate membranes.   Al-
 though this work represents  extremely valuable contributions to the problem
 by initiating and stimulating the search for  predictibi1ity parameters  in
 hyperfiltration,  the choice  of solute parameters was very unfortunate  for
 practical  applications.   Generally,  the  parameters  lack  universality,  i.e.,
 solutes possessing  the  same  parameter value but being of  different  chemical
 structure  exhibit different  behavior  in  hyperfiltration.   As a  consequence,
 as many individual  correlations  have  to  be established as there are structural-
 ly distinguishable  groups  of  solutes.   In addition  most  of the  solute para-
 meters  proposed  are  not accessible  for compounds of which only  the  chemical
 structure  is  known.
      The above objections  were circumvented in the  correlation  studies  of
 Spencer and Gaddis  by selecting  the  solubility parameter  of the solute  as the
 correlation parameter for  predicting  hyperfiltration efficiencies.   These
 correlations  represent the best  and  simplest  approach toward predicting
 membrane performance so far obtained.  For practical  applications the method
 only  requires knowledge of the solubility parameters of  solute  and  membrane.
 The latter  value, which would be  nearly  impossible  to calculate, can be
 obtained from a small number of  hyperfiltration tests performed with solutes
 covering a  fair range of solubility parameter  values.  Solubility parameters
 of solutes  are either accessible  from  extensive compilations in the literature
or can  be calculated from the chemical structure  and  the  density of the
solute.
      In  all fairness toward Sourirajan and Matsuura  it has  to be pointed out
that  the correlation by Spencer and Gaddis practically fails  in  the case of

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cellulose acetate membranes.  One may conclude that the hyperfiltration
properties of cellulose acetate membranes cannot be described by one-para-
metric correlations comprising solutes of widely differing chemical structures.
Since cellulose acetate membranes represent the most commonly used membrane
type, further investigations, especially of commercial membranes, are required.
     Presently, predictions of membrane performances according to Spencer and
Gaddis are solely based on estimates of solute distributions between membrane
and feed solution.   Transport properties of the hyperfiltration system are
not considered in this treatment.   This deficiency permits the use of a
single parameter in the correlation but necessarily restricts the applicabil-
ity of the correlation to a limited pressure range.
     Despite this minor deficiency the correlation proposed by Spencer and
Gaddis presently represents the simplest and the most generally applicable
method for predicting hyperfiltration performance of membranes with the
exception of cellulose acetate membranes.   With the latter type of membranes
the correlation is  not satisfactory although it is still  applicable with some
reservations.   Especially the facile accessibility of the required solubility
parameters of the solutes should  make the  correlation method of Spencer and
Gaddis the preferred one for practical  applications.
                                    83

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                                    SECTION III

                                   INTRODUCTION

     Reverse osmosis (RO) is an efficient water purification process of low
energy consumption.   In the application of RO for water desalination membrane
characterization with respect to solute separation does not present too
severe a problem due to the predictable composition of the feed solution.
Complications arise in the application of RO for purification of industrial
wastewaters containing organic impurities.  The great number of possible
organic compounds which can be present in industrial wastewater precludes, at
least at the present time, the application of experimental data to describe
membrane performance.  It is therefore pertinent to investigate the possibil-
ity of predicting membrane performance in RO from easily accessible solute
parameters which can be related to the chemical structure of the solute.
     The most extensive investigations in this direction were carried out by
Sourirajan and Matsuura.   These authors based the choice of characteristic
solute parameters on their sorption-capillary flow model describing membrane
performance (Figure 1).  According to this model, RO is governed by inter-
facial phenomena on the feed side of the RO membrane, Ke., either the water
or the solute is preferentially sorbed on the feed-membrane interface.  As a
consequence, the membrane surface will be in contact with a solution differing
in concentration from the bulk of the feed.  If water is preferentially
sorbed then an interfacial layer results on the feed side  of the membrane
which is depleted in solute with respect to the bulk of the feed (Figure  1A).
This interfacial layer of low solute concentration  is then  transported  through
the capillaries of  the membrane by the applied pressure (Figure IB).   Contin-
uous removal of the interfacial layer by  flow  under pressure (hydraulic  flow)
and reformation of  the layer by preferential sorption of water  results  in a
permeate of lower solute concentration than the feed, _Le. , the membrane
rejects the solute.
                                       84

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THE SOLUTION \






nuM "
PRESS
4
H,O No'Cr H,0
HjO No*Cr H,0




HjO No*Cr HjO
HjO No*Cr HjO
'HjO H,0 HjO
k HjO H,0 HZO
''»olou» »br»;»«ct M'
- S*!1^0"^., H,
JURE

No4CI" HtO
No^cr H,O




No*CI~ H,0
No*CI~ HZ0
HtO H,0
H^O H?0
0 ^,0,, ,,IV13'«:
o ^^"^vj-t











PORE v
\ CRITICAL
\ SIZE
                                                                (A)
   DEMINERAUZEO  WATER  AT  THE
j[          INTERFACE  	_J[


    POROUS          POROUS \T
     FILM            FILM
                                                                (B)
                                               CRITICAL  PORE  DIAMETER
                                               ON  THE  AREA OF  THE  FILM

                                               AT  THE  INTERFACE
Figure 1.  Schematic representation of the  sorption-capillary  flow mechanism
           in  hyperfiltration.   (A) Sorption  mechanism on feed-membrane
           interface, (B) Transport mechanism.
                                         85

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     Solutes which exhibit sorption behavior comparable to that of water or
solutes which are even more strongly sorbed than water will not be separated
under RO conditions.
     According to the model of Sourirajan and Matsuura the membrane perform-
ance in RO is a function of solute-solvent-membrane interaction at the inter-
face.  These interactions are assumed to arise from the polar-, steric,  non-
polar- and/or ionic character of each of the three components in the RO
system.  Proper selection of interaction parameters should provide means for
predicting RO separations for a wide range of different solutes.   Indeed,
Surirajan and Matsuura succeeded in establishing correlations between RO
performance and solute parameters by restricting themselves to water as  the
solvent and cellulose acetate as the membrane material.  With these constraints
RO performance should be a sole function of solute properties characterized
by some physicochemical parameters.
     Solute parameters for predicting solute separations in RO should meet
two conditions.  First, in agreement with the proposed model of membrane
transport, the parameters should be relevant in describing sorption phenomena.
Secondly, it should be possible to calculate the parameters from the known
chemical structure of the solute, .i.e., the parameters should be accessible
from group contributions.
     Five solute parameters were investigated by Sourirajan and Matsuura in
their correlation studies.
     1.   Band shifts in IR spectra of OH groups (Av)
     2.   Dissociation constants of carboxylic acids (K )
     3.   Hammett constants of aromatic compounds (a)
     4.   Taft constants of aliphatic compounds (a*)
     5.   Small's number (S))
     All of the parameters are not applicable to all solutes but the latter
have to be classified into chemically related groups.  Inside each group of
solutes good correlation between the applicable solute parameter and solute
separation in RO could be experimentally established.
     It must be pointed out that the good correlations between solute para-
meters and solute separations in RO observed for many  solutes does not  repre-
sent a proof for the validity of the sorption-capillary flow mechanism  proposed
                                         86

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 by Sourirajan and Matsuura.  Indeed, this mechanism has met strong criticisms
 by several authors.   Nevertheless, the established correlations are experi-
 mental facts and consequently demonstrate the existence of relationships
 between specific solute parameters and solute properties under RO conditions.
 From this point of view the investigations of Sourirajan and Matsuura repre-
 sent extremely valuable contributions by initiating and stimulating the
 search for predictbility parameters in RO although the underlying theory can
 be considered only as a working hypothesis.
      According to the sorption-capillary flow model of the authors it is only
 the sorbed layer on  the membrane interface at the feed side which participates
 in the hydraulic flow through the membrane,  ^.e., the composition of the
 sorbed layer determines the composition of the effluent.
      According to hydrodynamic  theories the  first molecular layers on a
 liquid-solid interface  do  not particpate in  the flow of the liquid but remain
 at rest,  _i.e.,  the flow of the  liquid encompasses only subsequent layers.
 One has now to consider that forces which govern  preferential  sorption of
 either water or solute  on  the membrane  interface  are of short-range,  i.e.,
 their acting distance will  not  extend beyond one  or two molecular layers.   At
 larger distances  the  solution will  be of uniform  concentration  since  at this
 distance  a  solute molecule  will  be  unaware of the presence  of the membrane
 surface.  Since  the layer  being  affected in  its composition by  sorption will
 not participate  in the  hydraulic  flow,  it is  difficult to  understand  how the
 composition  of  this layer  should  determine the  composition  of the solution
 flowing through  the membrane capillaries  (pores)  under hydraulic  pressure.
      The  solute parameters  on which the  correlation  studies of  Sourirajan and
 Matsuura  are based are  not  specific for  sorption  processes  but  are of  general
 validity  in describing  interactions between  solutes  and solvents.  Consequently,
 the same  correlations could be expected  to exist  if  the RO  process were  based
 on a  solution-diffusion model in which the partition of the solute between
 aqueous solution and membrane plays the  decisive  role.  A solute  which  is
 strongly sorbed on the membrane surface will  also migrate into  the membrane
due to  the favorable interaction with the membrane material, i.e., the parti-
tion coefficient of such a solute will be relatively high.   As  a  consequence
of the  relatively high solute concentration in the membrane the solute rejec-
tion will be low.
                                       87

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     Solutes which are less compatible with the membrane material will  possess
a low partition coefficient, j..e.,  a low equilibrium concentration will
establish inside the membrane.   Such solutes will be highly rejected by the
membrane.
     Compatibility (miscibility) of solvents and polymers is described best
by their respective solubility parameters.   Although these parameters are not
providing quantitative relationships with respect to the amounts of solute
imbibed by the membrane, they permit a relative classification of different
solutes with respect to their compatibilities with a given membrane material.
It is somewhat surprising that no direct use of solubility parameters was
made by Sourirajan and Matsuura in their correlation studies inasmuch as
                  2
Spencer and Gaddis  could demonstrate good correlations to exist for a number
of different membranes.  Indeed, the correlations obtained by Spencer and
Gaddis for different membranes could be unified thus permitting a comparison
of rejection properties of different membrane materials with respect to a
given solute.
                                      88

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                                   SECTION IV

                                SOLUTE PARAMETERS

     A considerable number of different solute parameters were investigated
by Sourirajan and Matsuura1'3'6 with respect to their correlation with solute
rejection under RO conditions.   Unfortunately, nearly all of these parameters
do not meet the most important conditions required for practical  applica-
tions: universality and facile accessibility.
     The condition of universality of a parameter would mean that solutes
differing in their chemical structure but possessing the same parameter value
should exhibit very similar rejection properties with respect to the same
membrane.  If this condition is not met but correlations exist only for
solutes belonging to the same structurally related group (e.g.,  alcohols,
aldehydes, ketones, esters, ethers, etc.) prediction of membrane performance
requires as many individual correlations as there are structurally distin-
guishable groups.  This unfortunate situation exists for nearly all of the
solute parameters investigated by Sourirajan and Matsuura.  For example a
Taft  number of zero corresponds to solute separations of 60% with aldehydes,
50% with ethers, 30% with esters, and 20% with ketones.   The same pronounced
differences are observed with Small numbers  in the case of hydrocarbons.
      The second condition of facile accessibility of the solute parameter  is
also  not always met by the parameters selected by Sourirajan and Matsuura.
Very  often practical applications of RO will be concerned with compounds of
which only the chemical structure is known,  and this sparse information  has
to suffice for the estimation of the correlation parameters.  Under these
conditions the choice of solubility parameters by Spencer and Gaddis   is of
advantage.  Solubility parameters for an extremely  large  number of  solvents
are listed in the literature, e.o.. , Hoy7 lists close to  700 compounds.
Values for unlisted compounds can be estimated from  the  chemical  structure by
means of the additivity rule for group "  or atomic    contributions to  the
molar attraction constant.
                                           89

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     The different solute parameters investigated by Sourirajan and Matsuura
and by Spencer and Gaddis are discussed in subsequent sections.
A.   Polar Parameters
     The polar parameters describe the proton-donating or the proton-accepting
properties of the solute.  Numerical values related to these properties can
be derived from (i) infrared spectra of alcohols and phenols, (ii) dissocia-
tion constants of carboxylic acids, and (iii) reaction rates under standard
conditions.
     (1)   Infrared Spectra
     Infrared spectra supply numerical values for the strength of hydrogen
bond formation under standard conditions.  If the solute is a proton-donor
(alcohols  or phenols) spectroscopic measurements are performed with diethyl
ether as the proton-acceptor.  The relative shift, 6v (acidity), in the
absorption maximum of the hydroxyl group represents a quantitative measure for
the hydrogen bonding ability of the solute, j^.e., the larger Av, the stronger
the acidity of the solute.
     If the solute is a  proton-acceptor (aldehydes, ketones, ethers, or
esters) deuterated methanol  (ChUOD) is used as  the standard proton-donor.  In
this case  the relative shift in the absorbance  maximum of the OD group, Av
(basicity), expresses the hydrogen bonding ability of the solute, j..e. , the
larger Av, the stronger  the  basicity of the solute.
     (2)   Dissociation Constants
     In the case  of carboxylic acids, amines, and aminoacids,  the acidity or
the basicity of the solute is quantiatively described by its dissociation
constants, Kg or  Kb, respectively.
           Acid:     HA + H20   ^        H30+ +  A                  (1)
                    Ka = LH30+][A"]/[HA]                          (2)

           Base:     B +  H20          "  HB+ + OH~                 (3)
                    Kb = [HB+][OH"]/[B]                           (4)
     The  degree of dissociation,  a, expressed as  the  fraction  of  total  acid
«r base  being present  in ionized  form is  then given by
                    K =  a2c/(1"a)                            (5)

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     The degree of dissociation of weak acids and weak bases is pH dependent
which has to be considered in the prediction of solute separation by RO.
     (3) Hammet or Taft Numbers
     Hammett numbers describe the polar effect of substitutents in m- or p-
position of aromatic compounds.  The values are obtained either from equili-
brium determinations or from rate measurements under standard conditions.   In
the first case dissociation constants of differently m- or p-substituted
benzoic acids are compared.  If K  and K are the dissociation constants of
unsubstituted and substituted benzoic acid, respectively, the Hammett constant
o, is given by:
                    a = (l/p)lg(K/K0)                            (6)
where p is a constant, in this case referring to measurements of dissociation
constants.  The value of p changes with the kind of physico-chemical measure-
ment, e.cj., if one compares rate constants of ester hydrolysis, but taking
this change into account the same o value is obtained for each substituent.
     Taft numbers are defined analogously for aliphatic and o-substituted
aromatic compounds.   Also in this case the Taft number o* is a measure of the
polar effect of the substituent.
     Both solute parameters,  Hammett and Taft numbers represent group contri-
butions, _[•£., for solutes possessing more than one substituent, Hammett or
Taft number of the solute are equal to the sum of the Hammett or Taft numbers
of each of the substituent groups.   Consequently, it is possible to calculate
Hammett or Taft numbers if the chemical structure of the solute is known.
     Since the dissociation constants, K,, represents the total polar effect
                                        a
of the acid molecule and a or o* represent the contribution of the substitu-
tent groups to this total effect, a relationship exists between K  and o or
                                                                 d
a* for aromatic and aliphatic monocarboxylic acids, respectively.   From this
relationship dissociation constants of monocarboxylic acids can be estimated
from the chemical structure of the acid.
     There exists also a correlation between o or o* numbers and spectro-
scopically determined Av values for reasons analogous to those given for the
correlation between K  and o or o*.
                     d
     Because of the existing relationships between different polar parameters
correlation of solute separation in RO with either the Hammett or the Taft
number of the solute will  suffice.
                                         91

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  B.    Small  Numbers
       Hydrocarbon solutes  are  hydrophobia and essentially non-polar.  The
  cellulose acetate membrane  has both polar and non-polar character.  The polar
  character of  the membrane arises  from hydroxyl and ester groups and is respon
  sible for the ability  of  hydrogen bond formation.  The non-polar character
  arises  from the  hydrocarbon backbone and the hydrocarbon groups in the ester
  part.   Consequently, the  membrane may be expected to attract both the polar
  solvent (water)  and the non-polar solute (hydrocarbon).  According to the
  sorption-capillary flow mechanism of Sourirajan and Matsuura the relative
  extents of  these attractions  determine the solute separation in RO.
       For the  purpose of correlation of RO data both the molar solubility of
  the  solute  in water or the Small number of the solute were used to express
  the  degree  of hydrophobicity  or of non-polar character of the solute.   From a
  practical point  of view,  it was desirable to use a solute parameter which can
  be calculated from the chemical structure of the solute.  This is the case
 with  Small  numbers but not with solubilities which require experimental
  determinations.
       The Small numbers are related to the cohesive energies of liquids, E
 which are defined as the  energies necessary to break all the intermolecular
 contacts per  mole of the  liquid.   The cohesive energy of a liquid is closely
 related  to  its molar heat of evaporation, AH
                     Ecoh = AHvap ' PAV      V3P                  (7)
 Quantities derived from the cohesive energy of a liquid are,  vis.:
      the cohesive energy density:   e  .  = (E  ./V) ,               (8)
the solubility parameter:  6 = (E/V)1/2,  and
                                      con
                                                                  (9)
      the molar attraction constant (Small  Number):
      S = (VEcoh)1/2= V6

      In the above expressions V is the molar volume at standard temperature
 Of 298 K (25°C) and is given by molecular  weight divided by density.   The
 dimension of the solubility parameters is  [J1/2 m3/2] with 1.0 (J/m3)1/2 =
 4.88 x 102 (cal/cm3)172.
      In the final analysis  the calculation of solubility parameters or Small
 numbers revolves  around obtaining  the  value  of  the  heat of evaporation from
vapor  pressure  data.   The procedure used in  the  calculation  of  solubility
parameters  for  680  compounds  from  vapor pressure data  is  outlined by Hoy.7
                                       92

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     The additive property of the cohesive energy, E  ., was demonstrated as
                        11       8
early as 1928 by Dunkel.    Small  demonstrated the usefulness of the molar
attraction constant as an additive quantity.   His set of values is still
                                                       7-9
frequently used with some refinements by other authors.      A comparison  of
values derived by different authors is given by Van Krevelen.    The latter
author also devised a list of atomic attraction constants   which considerably
simplify calculations.
     Generally, solubility parameters derived from vapor pressure data should
be preferred in correlation studies over those calculated by the additivity
method from group contributions.  The total cohesive energy, E, which holds a
liquid together and which is derived from vapor pressure data, can be divided
into contributions from dispersive forces (London forces), E., dipole-dipole
forces, E , and hydrogen bonding forces, E..
                    E - Ed+ EP * Eh                             <">
Multiplying this equation by the molar volume of the compound one obtains
                    VE = VEd + VEp + VEh                         (12)
or with VE = S  from equ.  10
                    s2 = sd + Sp + Sy                            (13)
     The value of S calculated from group contributions strongly depends  on
the way the individual group values were derived with respect to equ.(13).
For example, Small obtained a value of 170 for the OH group which was derived
from the contribution of an ether oxygen (70) and a hydrocarbon hydrogen
(100).  This value represents only the contribution to the cohesive energy
derived from dispersion forces but neglects the considerably high contribution
resulting from hydrogen bonding which does not exist in hydrocarbons from
which the value of 100 for hydrogen was derived.   According to Konstam and
           Q
Feairheller  the value for a single OH group is 399 which yields good agree-
ment between calculated and experimental solubility parameters of alcohols
(see Table I).
     Problems arise with compounds containing more than one functional group.
In some cases,  e.g.,  OH in diols, Cl in CC12 or CC13, modified group contibu-
tions are reported,   but generally the additive method yields ambigous results
if applied to polyfunctional compounds.
                                          93

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Table 1.   COMPARISON OF  SOLUBILITY PARAMETERS  OF  SELECTED
          COMPOUNDS OBTAINED BY DIFFERENT  METHODS
Compound
Alcohols
Methanol
Ethanol
n-Propanol
i-Propanol
n-Butanol
n-Pentanol
3-Pentanol
Ethyl eneglycol
Propyleneglycol
Glycerol
Benzylalcohol
Esters
~~ Methyl acetate
Ethylacetate
Ethylbenzoate
Ketones
Acetone
Butanone
Aldehydes
Acetaldehyde
Propionaldehyde
Acids
Acetic acid
Propionic acid
Butyric acid
Acrylic acid
Ethers
Diethylether
Isopropylether
Amines
	 DTethylamine
Tri ethyl ami ne
Tri ethyl enetetramine
Ethylenediamine
fjydrocarbons
"ii-Hexane
Cyclohexane
Benzene
Toluene
Molac Volume
(mVkmol)

40.66
58.60
75.11
78.8?
91.53
99.41
104.27
55.92
73.70
73.19
103.82

79.88
98.54
144.20

74.01
90.19

57.13
73.44

57.26
74.99
92.45
69.30

104.78
142.33

104.30
139.95
149.83
66.57

131.61
108.79
89.42
106.88
Solubility Parameter in (J/m3)1/2 x 103
Hoy
(Ref. 7)

29.7
26.2
25.0
23.4
23.8
22.8
20.8
34.9
30.7
36.3
24.7

19.4
18.3
20.0

19.7
19.4

20.2
19.3

26.7
25.6
24.5
26.4

15.4
14.5

16.5
15.2
22.8
25.3

14.9
16.8
18.8
18.3
VanKrevelen
(Ref. 10)

31.9
27.0
24.8
22.0
23.4
24.4
21.0
34.5
30.0
34.9
25.8

17.0
16.6
19.0

20.7
20.1

21.8
20.8

-
-
-
•

15.8
15.6

17.6
15.0
25.1
23.0

14.9
16.6
18.6
18.2
Konstam et. al .
(Ref. 9)

30.9
26.1
24.1
22.2
22.7
23.6
21.0
32.5
27.7
34.3
25.0

18.9
18.1
19.8

21.1
20.3

22.1
20.9

26.4
23.8
22.3
24.4

19.1
17.2

-
-
-
29.6

14.9
16.9
17.0
18.2
                             94

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     The usefulness of solubility parameters for predicting solute rejections
                                           p
in RO was pointed out by Spencer and Gaddis  and is based on the fact that
these parameters describe the solubility of a solute in a polymer.   According
to theoretical  concepts developed by Hildebrand   the solubility parameters
of solvent, 6 ,  and polymer, 6 , determine the compatibility of both.   The
larger the difference    6-6    the less compatible the components whereas
close similarity of 6  and 6g assures complete miscibility.
                                     95

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                                    SECTION V

                         PREDICTION OF SOLUTE SEPARATION

A.   Polar Parameters of Sourirajan and Matsuura
     Although several of the polar parameters selected by Sourirajan and
Matsuura show good correlations with solute rejections in RO,  these results
are more of academic interest and are not useful for practical  applications.
     Band shifts in infrared spectra cannot be predicted from the chemical
structure of the solute but would require individual determinations.  Further-
more, the range from zero rejection to over 80% rejection is compressed
inside a range of 20 units in Av, thus small changes in the parameter cause
extremely large changes in the rejection value.
     A similar criticism applies to the use of Taft numbers.  Also  in this
case the Taft number would have to be known to three significant digits to  be
useful for predicting solute rejections.  In addition, as pointed out previous-
ly, structurally different compounds possessing the same Taft number exhibit
widely differing rejection properties.  Consequently, a great number of
correlation curves would be required for practical applications.
B.   Small Numbers
     Small numbers of different aliphatic and aromatic hydrocarbons were
correlated with their rejection properties by Sourirajan and Matsuura.   No
correlation existed between Small numbers and rejections if all of  the com-
pounds were considered.   Some improvement could be obtained by grouping the
solutes according to chemically related groups, e.g., paraffins, olefins,
aromatics, etc.
     The usefulness of Small numbers as correlative parameters is doubtful.
With structurally related compounds for which correlations are observed, the
Small numbers generally increase linearly with molecular weight as  a conse-
quence of their additive nature.  Such a dependence is shown in Figure 2 for
hydrocarbons, but also exists for alcohols, esters, ketones, etc.   Because of
                                     96

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              130
              120
              110
              100
               90
               BO
               70 -
                                   (SMALL NUMBER; x  io"2
                                      10      11      12
13
Figure 2.  Molecular weight  dependence  of Small  numbers for structurally
           related compounds, Aliphatic (+),  cycloaliphatic (A),  and  .
           aromatic (°) hydrocarbons.
                                       97

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this  linear  relationship molecular weights of solutes can be substituted for
Small  numbers without change in the shape of the correlation curve, i.e.,
correlation  of  solute rejection with molecular weight of the solute will be
as  good  as correlation with Small numbers.
C.    Solubility Parameters
      Correlation of solute rejections, R., in RO with solubility parameters
of  the solute,  6^, was proposed by Spencer and Gaddis (2).   This correlation
is  based on  the assumption that the concentration of solute available for
transport across the membrane depends on the difference between the solubility
parameters of solute, 6^, and membrane material, 6 .
                              *1. •  ai - 6M      "              04)
Consequently, R. should be a function of A.  and a membrane should exhibit
                i                          im
maximum  rejection properties for solutes which differ strongly in the 6^
value from that of the membrane material.  Contrarily, minimum rejection or
no  rejection at all will be observed with solutes possessing 6. values equal
to  that  of the  membrane.
      Correlation plots of R. vs 6. for three different membranes were found
in  good  agreement with the predicted dependence of R. on 6-.  The plots
exhibited minima which permitted the estimation of the 6  values of the three
membranes.   It  was further observed .that close to 100% rejection is obtained
                                               01/0
if  the 6^ value of a solute differed ±0.01 (J/m )    from the 6m value of the
membrane.  Inside the intermediate range of 6. values the R. values showed a
linear correlation with respect to 6..
      Since the  A^ values observed for onset of 100% rejection were found to
be  the same  for the three membranes, their correlation plots could be super-
imposed  by changing the independent variable 6. to A. , I.e., by using the 6
values as the common origin.  The resulting correlation plot in its gener-
alized form  is  shown in Fig. 3.
      The correlation by Spencer and Gaddis between R. and 6- represents the
best  and simplest correlation so far obtained for predicting membrane per-
formance in  RO.   For practical applications the method only requires know-
ledge  of 6.j  of  the solute (See Section IV-B) and of 6m of the membrane.  The
latter value, which would be nearly impossible to calculate, can be obtained
from few hyperfiltration tests with solutes of differing 6. values.

-------
       0.4 -
       0.2 '
                                                                  16
Figure 3.  Dependence of solute rejection on  the  difference  between the
           solubility parameters of solute and membrane.   Data  from
           Ref. 2.
                                       99

-------
      The correlation  shown in Fig. 3 does not include f^ values obtained with
 cellulose acetate membranes.  Such values are shown in Fig. 4.  Also in this
 case 100% rejection approximately corresponds to a A-  value of 0.01 (J/m3)1''2
 but the scatter  of data  is considerably stronger than for the three combined
 membranes of Fig. 3.  Solute rejection by cellulose acetate membranes can be
 predicted only with some reservations.
      As pointed  out by Spencer and Gaddis (2) their approach toward predicting
 membrane performance  in  RO is solely based on estimating the distribution of
 the solute between the separating membranes and the bulk of the feed.   This
 treatment does not include a parameter describing the transport properties of
 the hyperfiltration system.
      A possible  effect of a changing transport parameter is indicated if one
 compares rejection data  obtained with the same membrane at widely differing
 pressures.   In Table  II, data by Chian and Fang (13) are presented which were
 obtained with a  polyamide membrane at three different operating pressures.
 In  Fig.  5 the rejection  values are plotted versus 6. values of the solutes.
 Although data are insufficient to permit the estimation of the 6  value of
                                  r                             m
 the membrane, they clearly demonstrate that at low pressure the rejection is
 much less sensitive to changes in 6. than at high pressure.  Probably for this
 reason the correlation between Ri and 6, is somewhat lost at higher pres-
 sures.
 0.    Molecular Weight
      The value of solute molecular weights, Mi, as a parameter for predicting
 the rejection of non-electrolytes in RO was pointed out by Spencer et aj
 (14).   Most highly rejecting hyperfiltration membranes effectively reject
 non-electrolytes in the molecular weight range exceeding a limiting value of
 about 70.   This  is demonstrated for data by Cadotte et al_ (15) shown in Fig.
 5.   Solutes with molecular weights exceeding a value of 60 exhibit an average
 rejection of 93.2 ± 4.1%.
      Hyperfiltration results presented in Fig. 5 are replotted in Fig. 7 in
 dependence  of solute molecular weights.   Data obtained at lowest operating
pressure show very weak correlation but the correlation improves by going to
 higher pressures.  If one neglects two solutes, methanol and methyl acetate,
which show  decreasing rejection with increasing pressure, the average re-
jection for solutes with M^ >60 is 91%.
                                       100

-------
          Table 2.  EFFECT OF OPERATING PRESSURE ON SOLUTE REJECTION
                    BY A POLY(AMIDE)MEMBRANE.
Solute
Methanol
Ethanol
i-Propanol
Acetone
Diethylether
Glycerol
Aniline
Me thy! acetate
Acetic acid
Phenol
Formaldehyde
Molecular
Weight
(kg/kmol)
32
46
60
58
74
92
93
74
60
94
30
Solubility
Parameter9
(J/m3/1/2 x 103
29.7
26.2
25.0
19.7
15.4
36.3
(21.3)
19.4
26.6
(23.5)
(28.5)
Percent Solute Rejection at
Operating Pressure in MPa
2.75
28
36
90
53
58
88
47
57
31
45
21
4.13
19
28
89
72
90
88
78
54
70
80
52
10.34
5
57
95
72
92
88
82
45
82
89
69
a Solubility parameters from Ref.  7,  values in parenthesis calculated
  according to Ref.  10.
  Rejection values from Ref. 13.
                                     101

-------
              0.4
               0.2 •
                12   14    16   18   20   22    24    26    28   30

                              (SOLUBILITY PARAMETER)  X 103
32    34
Figure 4.   Solute rejection by cellulose  acetate membranes  in  dependence
            of the solubility parameters of the solute.  Data  from Ref. 2.
                                           102

-------
              .6
               .4
               .8
               .6
               .2
                   O

                   5
                   01
                   LU
                   ec
                                                    PRESSURE
                                                     2.U MPa
                                                    PRESSURE
                                                   '	1
                    O
                    3
                    c
                                                     PRESSURE
                      (SOLUBILITY PARAMETER) X 103
                14
16    18    20    22    24    26
                                                   28
                                  30    32    34   36
Fiaure 5    Solute rejections for three operating  pressures in dependence
         '   on  the solubility parameters of the  solutes.  Data from
            Table II.
                                          103

-------
1.0
                                      MOLECULAR WEIGHT
     30
40
SO
60
                      70
                                         80
                                    90
                                    100
                                    110
120
Figure 6.  Solute rejection  in dependence on the molecular weight of solutes
           for NS-1 membrane at  5.52 MPa  operating pressure.  Data from
           Ref. 15.  Alcohols  (<>), aldehydes and ketones (•), amines (A),
           and esters  (A).
                                        104

-------
                     PRESSURE: 2-76 MP»
                     PRESSURE: 4.13 MPi
                     PRESSURE: 10.34 MPi
                   .  O


                     i
                  U  3
                     c
                                         MOLECULAR WEIGHT
                           20
                                     40
                                               60
                                                         80
                                                                  100
Figure 7.  Solute rejection for three  operating pressures  in dependence

           nn  thp mnlprular weiaht of  the  solute.  Data  from Table II.
                                          105

-------
     As demonstrated by Spencer and Gaddis,  (2) no correlation between R.  and
M. exists for cellulose acetate membranes.   With other membrane systems the
molecular weight of the solute can be considered to represent a useful para-
meter for estimating solute rejection in RO.
                                        106

-------
References
 1.   S.  Sourirajan and T. Matsuura, in "Reverse Osmosis and Synthetic Membranes",
     S.  Sourirajan, Ed., National Research Council of Canada Publication,
     Ottaw, Canda, 1977, Chapter 2.
 2.   H.  G. Spencer and J. L. Gaddis, EPA Grant Number R805777-1.
 3.   T.  Matsuura and S. Sourirajan, J. Appl. Polymer Sc. ,  1_5, 2905  (1971).
 4.   T.  Matsuura and S. Sourirajan, J. Appl. Polymer Sci., V7,  1043 (1973).
 5.   T.  Matsuura and S. Sourirajan, J. Appl. Polymer Sci., ±6,  1663 (1972).
 6.   T.  Matsuura and S. Sourirajan, J. Appl. Polymer Sci., ]7,  3683 (1973).
 7.   K.  L. Hoy, J. Paint Techn., 42, 76 (1970).
 8.   P.  A. Small, J. Appl. Chem., 3, 71 (1953).
 9.   H.  H. Konstam and W. R. Feairheller, AIChE J. , J_6, 837 (1970).
10.   D.  W. Van Krevelen and P. J. Hoftyzer, "Properties of Polymers",  Elsevier
     Publishing Co., Amsterdam,  Netherlands, 1972, Chapter 8.
11.   M.  Dunkel, Z. physik. Chem., A138. 42  (1928).
12.   J.  H. Hildebrand and R. L.  Soctt, "The Solubility  of  Non-Electrolytes",
     Reinhold, New York, 1959.
13.   E.  S. K. Chian and H. H.  P. Fang, Annual  Report  1973, U.  S.  Army Medical
     Res. and Development Command,  Contract No. DADA  17-73-C-3025.
14.   H.  G. Spencer, J.  L. Gaddis, and  C. A. Brandon,  Membrane  Separation
     Technology Seminar, Clemson University, Clemson,  S.C.,  1977.
15.   J.  E. Cadotte, C.  V. Kopp,  K.  E.  Cobian,  and L.  T.  Rozelle,
     Progress Report June 19 to  Office of Water Research  and  Technology, U.
     S.  Dept. of  the Interior.
                                      107

-------
     Appendix C



COMPUTER CODE LISTING
        108

-------
      REAL LTU»E.LCHNL.LCHNT.LTU1T
      REAL f1AREA.nRC.HOnC
      DlfltNSION PIN(9«.3).CIN(99.3>.POUT(99.3>,COUT(99.3>.CPRI1<99,3>.
     *   RF<99.3>.FTRJC99.3>.FTPm99.3>.CPHOA(99.3>.ISTG<3>.FINC99.3).
     X   NTB(99,3>,NTBS<99.3>
C
      COflnON/PRAH'IftDUl,DIF.I
      COimON/TGEOn/      LTUIT.RTUIT.UCHNT.TCHNT.LCHNT
      COfHION/TCOND/CFDT.OFDT.TFDT.PFDT
      COWtONsCOND'OFEED, TFEED
      COnnON/GEOfl/RTUIE. LTUBE, RFCTH, UCHNL. TCHNL. LCHNL, ATUBE. ACHNL. RMVDR
      COn«ONxHSPEC/PERH,STP
C
C     INPUT SECTION
C     READ TVPE OF HODUU(TUWU« HEfWRANE-l. SHEET
 !••• CONTINUE
      RCAD(S,3> INDUL
      IF (IHDUL.EO.*) CO TO 8M«
      READ(5.4) TREJ.TFLUX
      CO TO  , inOUL
   Z» READ(5,a)LTUlT.RTUIT
      CO TO ZZ
   81 READCt.2) UCHNT,TCHNT,LCHNT
   22 COMTINUE
      RCAD(f.E) DIF.CFDT,QFDT,TFDT,PFOT,I
C     READ INITIAL CONDITIONS
      RIAD<».1 )PTEED,OfEED.CFEE0.TFEED
C     READ *V«TCH fPfCIFICATION
      00 TO (3»,31). IRDUL
   M RIADd.t) RTUM.LTUtf.tFCTR

-------
               QO TO 38
            31 READ(S,2) UCHNL.TCHNL.LCHhL.RFCTR
            38 CONTINUE
               READtS,2> DPRF.DFLOU.DREJ
         C     READ COHSTANTS FOR TRANSPORT COEFFICIENTS
               READ(5,3> UCC.UnRC.UflOHC.EPUflP.ERATE.UUC.UEC
         C
             1 FORRAT<2F1«.4,E1«.4,F1».4)
             a FORrtAT<8Fl«.4>
             3 FORRATU6IS)
             4 FORIV>T(F1».4.E1«.4>
             5 FORflAT<3Eie.4.4FI».4>
               TFLUX-TFLUX«',F1».4)
              00 TO f0
           97 IMITC(C,M> UCHNT.TCHNT.LCHNT

-------
   6* FORHATC WIDTH- '.Fl». 4. 3X. 'THICKNESS-'. Fl«. 4. ax," LENGTH- -,F1». 4)
   b9 CONTINUE
      URITE(6,fil>
   61 FORHATI/.' TEST CONDITIONS')
      URITE<6,62> CFDT.OFDT.TFDT.PFDT
   62 FWMATC CFDT-'.E1«.4.'OFDT-'.F1».4. 'TFDT- • ,F1».4. 'PFDT- ' .F19.4 )
      URITE(6,5»)
      URITE(6.51> PERH.STP
   59 FORHAK/. ' TRANSPORT PARAHETER')
   51 FOUfWTC PERn€AiILITV'.E15.g,3X. 'SOLUTE TRNS.  PARA. •' .ElS.B.ax,
     >       'FT/SEC')
C     CALCULATE TU»E CROSS SECTION AREA AMD HYDROLIC  RADIUS
      GO TO (33.34), IHDUL
   33 ATUlE-3.141S93*RTU»E**a.
      RHVM-RTUBEX3.
      60 TO 35
   34 ACHNL'UCHNLSTCHNL
      RHVDR-TCHHL/B.
   35 CONTINUE
C
C
      CR-CFEED«( I .-DPRF+DPRP*DREJ )/< 1. -DPRF )
      CP-CFEEDt(l.-DREJ)
C
      1*1
      CIN(I.J)-CFIED
C
  1*4 COMTZNUI

-------
 c
 c
       CALL nODULCPlN.
      «   RFCI.J))
       ircl.CT.l ) CO TO  151
       FTRJ(1,J>-1.-RFC1.J>
       FTPHCl,J)-l.-FTRJ«(1.-RF(I,J»
       FTPI1CI,J>-1.-FTRJ(I.J>
       CPPKV»(I,J)-FTPH(I-l,J)tCPnOA(I-l.J)/FTPM(I.J)
      s    +j))«cpRHti,j)-'FTpn(r. j)
 c
   153 CONTINUE
       IFCJ.E0.3) CO TO  15*
      IF(CPHO«(I.J).LT.CP) IP-I
      IF(COUT(I,J).GT.CR)  GO TO  153
      CO  TO 149
   150 IF(COUT(I,J).6T.CFEED> CO  TO  158
   140 CONTINUE
      PIN(I*1.J)-POUT(I.J)
      CIN
      I-I+l
      CO TO 154
C
  1B3 CONTINUC
      III-I

-------
  155 CONTINUE
      ISTG(8)-III-IX
      ISTG(1)-IX
C
c
      ISTCl-ISTC(l)
      ISTOa-ISTC(S)
c
      00 157 I-1.ISTG2
      PIN
      COUT(I.2)-COUT(IX+I.l >
      IF(I.CT.l) GO TO 158
      FTRJ(1,2»-1.-RF(1,2)
      FTPHC1.8)-1.-FTRJ(1.8)
      60 TO 157
  158 FTRJ(I.8)«FTRJ(I-1.8)«C1.-RF(I.8))
      FTPB(I.8)-1.-FTRJ(I,8)
      CPflOA(I.3)-FTPPI(I-l,2)«CPnOA(I-l,a)/F7Pn(I,2)
     *   *1
      JO
      PJH
-------
       CIH< I. J >-CPHOA< ISTOa, 8 )
       GO TO 154
   1C9 CONTINUE
       MSTC-J
       ItTQU)-!
       IST63-ISTQO)
 C
 C
       ***-FTPmiSTGl,l>/U.-FTRJCISTCl.l>*FTPf1
       Mi-FTRJ( ISTOi, 1 >*FTPfU ISTOZ,8)*FT»»m ISTC3. 3 )/
      S   (l.-FT»J(I«T01.1)*FTPH(I6TCa.a)«FTRJ(IST03.3))
      CX'AAA/CCOCPnOA ( IST01 , 1 )+MtxCCCICPfKW( ISTC3, 3 >
      E-CX-CF
      TOL*«.*1«*CFEED
      IF(MS(E).LT.TOL) 00 TO 1M
      IF(E.LT.«.) IX-IX+1
      IFCE.OT.t.) IX-IX-1
      00 TO 156
C
C
  16* CONTINUE
      FINU.l).DFLOU'tFTPmiSTG2,2>SFTRJ{IST03,3>)
      FIM(1.8).FTdJ(I«T01.1>«FIN(l,l)
      MTMT-*
      BO 197 J-1,3
      M IM  i-i,irroj
      tra.io.t)  oo TO

-------
  188 CONTINUE
      NTBCI.J)*FIN(I.J)/OFEED>1
      IF(I.GT.l) 00 TO 17*
      NTMU.JI-NTBd.J)
      00 TO 1M
  17* NTBS
  1S7 CONTINUE
C
C
      gRITtca.M)
   94 FORNAT<'ISUHNARV OF DESIGN AND PERFORMANCE OF THE SYSTEM',///.
     X   ' MODULE DESIQN SPECIFICATIONS AND OPERATING CONDITIONS'.
     S   IX.'SPECIFIED'>
      00 TO <9*.9*>. INDUL
   96 URITECS.W) RTUBE,LTUBE.RFCTR.OFEED,TFEED.PFEED
   9S FORHATt/.' TVPE OF MEMBRANE-',11X.'TUBULAR',/,
     X   ' RADIUS OF TUB£-',1*X.E18.K.' FT'./.
     X   ' LENGTH OF TUBE-'.1»X.E18.S.' FT'./,
     X   ' TUBE UALL ROUGHNESS FACTOR-'.FS.I,/.
     X   ' TUBE FEED RATE-',1«X,E1S.S.' QPM',/.
     X   ' FEED TEMPERATURE-', W,FB.I.' DEO F',/.
     X   ' PUMP OUTLET PRESSURE-'.RX.FB.I,' PSIO')
      00 TO 97
C
   9« URITE(S,M> MCHNL.TCHNL.LCMNL.RFCTR.OFEED.TFEED.PFEED
   M FORfMTC/,' TVPE OF NEHBRANE-SMEET OR SPIRAL MOUND'./,
     X   ' WIDTH OP CHANNEL-'.Ell.f,' FT'/,

-------
      *    ' LENGTH Or CHANNEL-'.*«.«.' FT','.
      *    ' TU»E WALL WUOHICM FACTOR-',Ff.a./,
      *    ' row rccB MTE-'.CIB.*. - OPK'.X.
      *    ' FEED TEMPERATURE-',Fi.«,- DEO f,/,
      »    ' PU«P OUTLET PRESttttE-'.FS.t,' P»Ifl'»
    •7 CONTINUE
 C
       IMITCCC,!?)
    •7 rowwTty.' svrren DCSjOH SPECIFICATIONS «NO opgRATiwe CONDITIONS'.
      t   IX,'SPECIFIC*'>
       URlTE(«,ft> DrLOW.DKEJ.
    M FOI»MT(^,' K»I8N  FtOU
      S   ' DESIGN REJECTION-',J4X,Ft.2,/.
      *   ' DESIGN PRODUCT RECOVERY FACTOR-'.FH.3>
 C
       URlTEIf.H)
    >9 FOtlfMTt UWWMttV OF NUMERICAL RESULTS*,/,
      *    3X.'J',4X,'I'.BX.'NTt',4X,'NT»S',5X,'FIN',1»X,'PI«',»X,
      *    'POUT', iX,'CIN'.9X.'COUT',*X,'CP«OA'.ex,'FTPK'./,eBX.
     *   '(CIOU/CUFT)',/)
      DO 9* J-1,HSTO
      90 91 I«t.I»T8J
      WRITt(l,Mi /,Z.
     *   CIH(I,J>, COUTt t,4»,CP«0*
   »S CONTtNUC
   *• CONTINUt
9

-------
      WRITE (6, 93) CX.AAA.Mft
   93 FORMATC//. ' CX-'.Eia.C./,
     X   'PERMEATE FRACTION FROM STAGE 1 -'.FS.a./.
     *   'PERMEATE FRACTION FROM STAGE 3 -'.FS.8)
      nAREA-RTU»C*«.attLTU*E«FLOAT
      TCC-UCCSfMKA
C «* CAPITAL AMORTIZATION FACTO*. CAF-«.»1334S FOR IS PERCENT INTEREST
C *»* RATE AND TEN VEAR LIFE.
      CACOST-B.31S*CAF*TCC/DFLOU
C *M CALCULATE NEM1RAME REPLACEMENT COST, CENTS/KCAL.
      nRC-UnRC*I1AREAx(DFLOU>144*. )
C «» CALCULATE OTHER 0*11 COSTS. CEKTS'KGAL.
C «« CALCULATE PUHPINC POWER REOUIREHENT, KU.
      PWJ-(PFEED^3. li7*CDFLOM*FIN(1.3) )tDFLOU»OFEED*«2.*l .
     *   RTU§EM4.*
   7* FOMMTClMMfMNV Of SVSTEH ECONOMICS')
      URITI (§,?! > TCC,KT»rr,nAREA,«RC,«OHC,PCOrr,CACOST.UCRDT,

-------
00
             »    ECRDT.TCMT
           71 FORnAT',Fi*.t,
             «    x.'  punpiNQ POUEW corr.cENT«xiceAL-',Fi«.a.
             t   x.' CAPITAL AMORTIZATION C08T,CEHTSxKCAL-',Fl».8.
            *   x.' CREDIT FOR RECOVERED UATER,CENTS'K6AL-',F1«.3,
            S   /.' CREDIT FOR RECOVERED ENERGY.CENTSxKGAL-'.Fit.a,
            S   ',' TOTAL UNIT COST,C£MTS/1C«AL-'.Fl».3>
            00  TO
            CONTINUE
            STOP
            END
            SUBROUTINE FIBSPEC (TREJ,TFLUX,PERn,STP>
            COWION/TOEOn/      LTUi«.RTU»E,UCHriL,TCHNL.LCHNL
            COWWNXTCOND/ CFEED.OFEED.TFEED.PFEED
            COf*WN/PRAf|xlHDUL.DIF,l
            REAL LCHhL,LTU»E
      C
      C      CALCULATE TUBE CROSS SECTION AREA AND HVDROLIC RADIUS
            00 TO (33,34), IRDUl
        33  ATU*t-3.i41§93*RTU»E»«t.
            RHVDR.RTUttxt.
            00 TO 3C
        34  ACMHL-WCHNL«TCHNl
            RHVDR-TCHNLXI.

-------
          36 CONTINUE
       C
             00 TO (36.37>. II1DUL
          3S UBAR*OFECD'ATUBE'44I.«:C
             00 TO tt
          37 UBAR-OFEED/'ACHNL/44».i«
          3t CONTINUE
       C   CALL PROPU AND CALCULATE DENSITY AND VISCOSITVOOF SOLUTION.  IT IS
       C   ASSUNflED THAT THESE PROPERTIES ARE THE SAME AS THOSE FOR PURE WATER.
             CALL PROPU(TFEED,DENS.UIS>
       C
       C     CALCULATE REYNOLDS NUMBER
             RENR-4.»RHYDR»UBAR«DENS A> IS
M     C     CALCULATE SCHMIDT NUMBER
i-1
10           SCMi-UIS'C DENSSDIF)
             CO TOC39.4*), IHDUL
          39 X-LTUBE
             00 TO 41
          4« X'LCHNL
          41 CONTINUE
       C
       C     CALCULATE SHERWOOD NUMBER
             CALL SHUDNRUL,X,RENR,SCN*,SHNR>
       C
       C     CALCULATE MASS TRANSFER COEFFICIENT
             TCM-SMNUDIF/ (4. SRHYDft)
             P-PFEEDXiM.
             C-DOffvlf.
       e
             rrp-rrtuxsti.-TRCJIXTREJCEXPI-TTLUX/TCM>

-------
       PEim-STPtTFLUXtCtta./>
       RETURN
       END
       SUBROUTINE nO»Ul(PINTL.ClNTL.P.CAl,CA3AU.RF>
       COnHOrfCOND'OFEED. TFCED
                        , LTUWE.RFCTR. UCHNL. TCHNL, LCHML. ATU»E. ACHML.RHVDH
                       1.STP
      REAL LTU»E,LCHNL,LAnDA
      DIMENSION TCA1(3),TCA3(3),E<3).GTHET(3)
C
C     INITIALIZE VARIABLES
      X-».
      XPRNT-9.
      CA3UUS-*.*
      P-PINTL
      CO TO C3fl,4«). IHDUL
   39 UINTl-QFEED/ATUIE/448.1*
      00 TO 41
   4« UIim.*OFEED'ACHNL/44l.t6
   41 CONTINUE
      UIMt-UINTL
      CA1-CINTL
      UC-UMN*CA1
      DEFINE INTEOMTIOM fTEP SIZE
      DXX-I.1H
      PMINT INTMVAL
      DXP-t.ff

-------
    7 FORNATC1 MODULE PERFORMANCE SIMULATION RESULTS'./.ax, 'X'. 1«X.
     It   'P'.18X.'U1AR',1BX.'CA1'.18X, 'CAHMax, 'C*3'.11X,'CA3AV'.BX.
     S   'REJ'.4X.'REC',/.' '.4X.'(LI'SOFT)',iX. '(FT/SEC)'. SX.
     S   'CHOLE/CUFT)',4X.'(HOLE/CUFT)',4X.'(HOLE/CUFT)' ,4X.
     S   MBOLEXCUTT)'./)
C
C     INITIALIZE RKQ
      L-l
      CALL RKO(X.DXX,L)
C
C   CALL PROPU AND CALCULATE DENSITV AMD WISCOSITVOOF SOLUTION.  IT IS
C   ASSUMED THAT THESE PROPERTIES ARE THE SAKE AS THOSE FOR PURE WATER.
      CALL PROPU(TFEED.DENS,UIS>
C
C     CALCULATE REYNOLDS HUNKER
  1*3 REN*-4.»RHYDR«UIAR»D£NS/UIS
C     CALCULATE FANNING FRICTION FACTOR
      FFF-t.M«RFCTR/RCNRM« .8S
C     CALCULATE SCHMIDT NUMBER
      SCNR'UIS/( DENSkDIF)
C
C     CALCULATE SHCRUOOD NUflBER
      CALL SHUDNR(RTUBE,TCHm.>LCHNL.INDUL,X,RENR.SCNR,SHNR)
C
C     CALCULATE IMSfl TRANSFER COEFFICIENT
      TCN-SHNRSDIF/(4.«RHVDR)
e
C     CALCULATE HOLAR DENflTY OF fOLUTION
      C*  DCNfxll.

-------
       CALCULATE DIHENSIONLESS UAftIA*LC0
       UAHDA-TCfl'STP
       WUST«-P€R««P/C
       THETA-STP/VUSTR
 C
 C
 C     CALCULATE CA3  »V NEUTON RAPHSON METHOD
 C     INITIALIZE TRIAL FOR CA3
       TCA3U)- ».5*CA1
       TCA3(g>- ».4*CA1
 C      TOLERENCE FOR N-R CONVERGENCE
       TOL-t.MStCAl
       !!••
       DO S« I • 1,8
      TCAKI )-TCA3(I )•(!.*!. /GTHETC I >SEXP(-l.'LAflDA/GTHETCI )))
   5* Ed)-CAl-TCAl(I)
   sa n-im
C     URITE(S.B)  00 TO (1
      IF(II.ta.l*«> 00 TO (••
      TCA3(3)-TCA3
-------
                ECB»-CA1-TCA1(8>
                00 TO 58
             51  CA3-TCA31B>
                UW-WOSTRt(1.-OAfinASCA3/
                R£J-(CA1-CA3)/CA1
                RF< (UINTL-UMM >XUINTL
          C     LOGIC TO STOP PHOQRAfl
                00 TO (36,37).  IHOUL
             36  IF(X.Ce.LTUlE)  60 TO 1M
M              00 TO 3S
W           37  IF(X.BE.LCHNL)  60 TO 1M
             38  CONTINUE
          C
          C     OUTPUT SECTION
                IF  60 TO 101
          C     URITE(6,4>X.P.UBAR,CA1.CAS,CA3,CA3AU.REJ,RF-
              4  FOKHAT( F«.1.6EJS.i,EF7.3 )
                XP«NT-XPR«T»OXP
            1*1  CONTINUE
          C     EXECUTE MCO 4  TIRES
                00 1M 1-1,4
                L-8
          C
          C
          C     DEFINE DIFFERENTIAL EQUATIONS

-------
                 cc-aa.a
                 DX-l.
                 DUBAft— 1 .
                 DUG — 1 . /RHVWWC A3*UU
                 DP--DEHS*(U»ARM2.«FFFx
                CALL mCO(P,DP,L>
                CALL RKGtUBAR.DUBAR.L)
            1*3 CALL  RKG(UC,DUC,L>
          C      URITE(C,Z9>  X,DX.P,DP.U»AR.DUBAR,UC.DUC
               CAl-UCxUIAR
         C     GO TO NEXT STEP
               GO TO 1*3
           1M CONTINUE
         C     UMITE(8,4) X.P.UBAR.CA1.CA2,CA3,CA3AU,REJ,RF
4^             RCTURN
           SM IMITE(6,fi)
             6 FORTMTC/,' N-R NOT CONVERGING')
               STOP
               END
               SUBROUTINE RKGCZ.DZ.U
               DIMENSION Q(M)
               00 TO <1.8.3).L
             1  N-M
              A3-I.-AI
              M-l.x*.
              00 4  I-1,N

-------
    4
      H-D2
      J-l
      RCTUftN
    e  oo TO.J
   i«  *••.$
      I-B.
      GO TO 11
   8*  A-A8
      00 TO 12
   3*  A*A3
   ia  1-1.
   11  C*A
      00 TO 13
   4«  A-M
      ••a.
   13 J-J+1
      L-3
      !••
    3 1-1*1
      DX-HXDZ
      UC-M(DX-ltQ(I»
      Q(t)-«(I)*3.«US-CXDM
      Z-Z*M«
      RETURN
      •UMOUUNi PROPU(T,MD«,UI»)
Cttt

-------
            C«»THIS SUBROUTINE CALCULATES UISCOSITV AND DENSITV OF  UATER  AS  A FUNCT
            ION
            CSSXOF TEMPERATURE.
            CIM
                  REAL LOQT.LOOT8
                  01-M. 717753
                  08—•.U1S89MC-I
                  03—•.4M38777E-4
                  DENS*D1+D8XT+D3STX*B.
            C
            C
                  V1-82.81M3C
                  ve—It. 46959*
                  V3O.M4958S
                  IOCT-ALOC1»(T)
_                lOOTa-LOOTXU.
05               VIS-(Ul«ttSLOCT+U3*LOGT8>/36M.
                 RETURN
                 END
                 SUWtOUTINE SHUDNR
-------
 c
 C     TURBULENT FLOU CASE
 C     CHECK  TYPE OF NODULE
       00  TO  <1«.8*>,I
 C
 C     FOK TUBULAR HENBRANC
      SHNR*«.ll*AlMENRtS(7./B. >*SCNH«*.8S
      RETURN
C
C     FOR SHEET NEWKANE
   2« SHNR-».44*RENR«<7./1Z. >«(SCNRITCHNl/3./LCHW.>«(l.'3.
      RETURN
C
C     LAMINAR FLOU CASE
C     CHECK TYPE OF HODULE
  !•• 00 TO (3»,4«>,I
C
C     FOR TUBULAR HEHBRANE
   3« A3-1.9S
      SHNR-A3SCRENR*SCNR*2.SRTUBE/X)S*(1.'3. )
      RETURN
C
C     FOR SHEET FWttRAME
   4» M>l.>4
      8MNR-A4«(tEHR*»CNR«t.«TCHNl/X )«•(! ./3. )
      RETURN
      END

-------
                                  TECHNICAL REPORT DATA
                           (Please read Instructions on the reverse before completing]
1  REPORT NO.
 EPA- 600/2-79-195
                             2.
4 TITLE AND SUBTITLE
  Hyperfiltration Processes  for  Treatment and Renovation
  of Textile Wastewater
                                                         5. REPORT DATE
                                                         October 1979
                                                         6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
  S.M. Ko and J.A. Tevepaugh
                                                          8. PERFORMING Ol
9 PERFORMING ORGANIZATION NAME AND ADDRESS
  Lockheed Missiles and  Space Co.
  Huntsville Research and  Engineering Center
  Huntsville, AL  35807
                                                         10. PROGRAM ELE!

                                                             1BB-610
                                                         11. CONTRACT/GRANT NO.

                                                          68-02-2614, Task 009
12 SPONSORING AGENCY NAME AND ADDRESS
 EPA, Office of Research and Development
 Industrial Environmental Research Laboratory
 Research Triangle Park, NC 27711
                                                           TMnal; 10/78 - 8/7Q
                                                           •^ -i_im.-i~ |  ^ ._. f j .-.	1 i f , ,j
                                                         14. SPONSORING AGENCY CODE
                                                          EPA/600/13
15 SUPPLEMENTARY NOTES IERL_RTP project officer  is  Max Samfield,  Mail Drop 62, 919/
  541-2547.
16. ABSTRACT
--—	-  The report describes a computer program  developed for the design and
 simulation of a multistage hyperfiltration system for  renovation of textile waste-
 water   The program is capable of practical  design,  parametric simulation, and
 cost  proiection of the multistage hyperfiltration system  with  tapered innerstages.
 The mathematical model is based on Sourirajan's preferential sorption and solute
 Diffusion theory.  Experimental rejection and  flux data of a test hyperfiltration
 £dSe are required as inputs.  Empirical correlations and test results  available
 from  recent EPA-sponsored programs are used  to calculate  membrane transport
 parameters   Computed results for sample cases using cellulose acetate and
 5£SI membranes are presented.  Various designs and  operations are considered
 in  the computations to show their effects on system  economics    The Program
 is  readily adaptable for evaluation of other reverse osmosis/hyperfiltration
 applications.
                               KEY WORDS AND DOCUMENT ANALYSIS
                                             b.lDENTIFIERS/OPEN ENDED TERMS
  Pollution
  Textiles
  Waste Water
  Filtration
  Water Treatment
  Renovating
  Computer Programs
^DISTRIBUTION STATEMENT

  Release to Public
 "
EpA Form 2220-1 (9-73)
                           Design
                           Cost Analysis
                           Osmosis
Pollution Control
Stationary Sources
Hyperfiltration
Reverse Osmosis
                                            i?. SECURITY CLASS (This Report I
                                            20. SECURITY CLASS (This page)
14A
                                                                       07D
                                            128

-------