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An analysis of reverse osmotic characteristics of B-9 hollow fiber module
Desahkarion,
21 (1977) 257-274
Els.evierScientific Publishing Company, Amsterdam - Printed in The Netherlands
@
AN
ANALYSIS
HOLLOW
FIBER
OF
REVERSE
OSMOTIC
CHARACTERISTICS
OF
B-9
MODULE*
H. OHYA’ Division
of Chemistry,
NationaI
Research Council
of Cattaifu, Ottawa KIA
OR9
(Can&a)
AND
H. NAKA.JIMA=, K. TAKAG13, S. KAGAWA Kant0 Gakuin
University,
Kanazawaku,
Yokohama
AND
Y. NEGISH14
(Japan)
(Received September 29, 1974; in revised form January 11, 1977)
SUMMARY
Reverse osmosis experiments were carried out with a B-9 hollow fiber membrane module to obtain its reverse osmotic characteristics. Analysis of the data based on the general equations for radial reverse osmosis unit gives membrane characteristic constants, A = 1.9 - 2.3 x lO_’ g - mole H20/cm2 - atm - s, and of A on (D,,/K6) = 1.65 - 2.85 x 10e6 cm/s. A relatively large dependency pressure and a tendency for (D,,,/K6) to increase with pressure were observed. These two facts may imply that there might be some imperfections on the surface of the hollow fiber membrane. The average mass transfer coefficient is about one half to one tenth of the value with a spiral wound module, 0.55 - 2.1 x 10-4 cm/s_ SYMBOLS
A Ao
-
‘B
-
C
-
c1,c2c3
-
pure water
permeability
constant,
g - mole H,O/cm’
- atm - s
pure water permeability constant at zero pressure difference, g - mole H20/cm2 - atm - s osmotic pressure proportionality constant, atm. molar density of solution, g mole/cm3 solute concentration in the bulk solution, the concentrated boundary l
solution on the high pressure side of the membrane, and in the permeate solution on the atmospheric pressure side of the mem-
l
Experimentswere carried out at Yokohama University and theory devetoped at the National
Research Council of Canada. 1 Visiting Scientist from Yokohama National University, Yokohama, Japan. 2 Now with Tsukishima MachineriesCo., Chuoku, Tokyo, Japan. 3 Now with Bio-Engineering Co., Sumidaku. Tokyo, Japan. J Now -with Yokohama National University.
258
H. OHYA
brane, respectively, at any point on the membrane, fraction value of c1 at the outer surface of the distributor
flh k L.
P
-
4 r
-
ri R
-
r0
ii 3, v: .VW x a
-
a0 /3
-
II 0
-
1.0
-
v
-
Superscript Subscript I_nt.
-
f?t al.
ppm or mole
cle: solute transport constant, cm/s temperature correction factor for pure water flux rate proposed by Sourirajan (fC) = v(T)/v(25T) membrane area per unit volume of fluid space in the reverse osmosis unit, cm-’ mass transfer coefficient on the high pressure side of membrane, cm/s length of the bundle of hollow fibers, cm averaged operating pressure, atm quantity defined by Eq. (7) radius, cm outer radius of the distributor, cm quantity defined by Eq. (1 I) outer radius of the hollow fiber bundle, cm average radial fluid velocity, cm/s value of P at the outer surface of the distributor pure water fiux rate, (= AP/c), cm/s water flux rate, cm/s = aR quantity defined by Eq. (12) quantity defined in Eq. (24) quantity defined in Eq. (25) dimensiomess osmotic pressure n(cy)/B fractional permeate recovery dimensionless membrane permeability = (D,,JIGi)/u: dimensionless mass transfer coefficient = @I: kinematic viscosity, cm*/s
averaged value
logarithmic mean of the outer surface of the distributor periphery of the bundfe
and the
INTPIODUCTION
Reverse osmosis
for desalting
water has by now been well established
RQ CHARACTERISTICS
OF B-9 HOLLOW FIBER MODULE
259
-although research continues for improvement in membranes, hardware and plant operating procedures. There are essentially four different reverse osmosis membrane configurations which have been successfully developed by different groups of workers. These are (i) the Bat membrane, (ii) tubular membrane, (iii) spiralwound membrane, and (iv) hollow fiber membrane configurations. The effect of concentration polarization on the performance of a membrane in a reverse osmosis unit is well recognized in general terms, and hence, in every design, an attempt is -made to minimize concentration polarization in the membrane unit. The problem of concentration polarization has also been well discussed both theoretically and experimentally for thin channel and tubular systems. Only very few experimental studies have been reported on the mass transfer coefficient obtained in the actual operation of the different membrane configuration. The desired and the actually obtainable mass transfer coefficient should be the most important consideration in the development of a suitable design concept for saline water and sea water conversion. Membrane characteristics and average mass transfer coefficients of spiral-wound membrane module have been studied (I). Extremely compact design and a wider range of pH for practical operation are the advantages in the case of a hollow fiber module as compared to cellulose acetate membranes. But a few studies were carried out on the hollow fiber modules. Cooke (2) reported some of the experimental results on Nylon hollow fiber module developed by DuPont. Orofino (3) reported development of cellulose acetate hollow filament technology for a reverse osmosis desalination system in which fluid flow characteristics inside and outside of hollow fiber was treated. Chen and Petty (4) treated the same topics. Hermans (5) accounted for the shell side pressure drop and developed analytical expressions for the productivity of both parallel and radial flow systems. Davis and Orofino (6) have treated both systems on the basis of Hermans’ work. Gill and Bansal (7) and Bansal and Gill (8) developed a more rigorous mathematical model of the hollow fiber system on the assumption of negligibIe concentration polarization and a constant rejection coefficient. It is the purpose of this paper to study membrane characteristics aud average mass transfer coefficient using the hollow fiber membrane module. CONFIGURATION
OF THE HOLLOW
FIBER MODULE
DuPont, with its extensive background in polymer chemistry and fiber technology, has been developing the hollow fiber module concept since mid-60’s, and the first large scale demonstration of the practicability of treating brackish water supplies by the system began in Plains, Texas, in 1969. The first B-9 permeator was introduced in late 1970 (9). The hollow fiber system of DuPont utilizes a tightly packed ‘bundle of
H. OKYA
260
Fig.
I.
et cd.
Schematic representation of DuPont B-9 hollow fiber module.
hollow fibers within a high pressure vase1 in a shelt-and-tube type configuration. The holloti fibers serve as the membrane element and as their own support against the pressure of the feed water. The open ends of each fiber loop are potted in a header where the product water from the interior of each fiber exits. A model of the DuPont 33-9 permeator has the following dimensions; shell 41/2 inches i.d., by 4 ft long, made of fiber reinforced plastics and pressure rated at 650 psi; active length of looped fiber 5 ft; fiber size 42 microns i.d. by 85 microns o.d., and nominal surface area of I9IcIoft’. The use of hollow fibers permits the development of an extremely compact device, because membrane surface area per unit volume is approximately 3300 ft2 mt?mbFane area per ft3 module compared with 300 for spiral module. Fig. i iltustrates a Ltinch B-9 permeator. The pressurized aqueous feed solution enters the permeator through a very porous tubular distributor focated at the center of the permeator. The solution moves radially from the distributor toward the outer she11 of the permeator, and around the outer side of the fibers. The pressure then forces the pure water through the fiber walls into the bore of the fiber, and this water moves along the bore of each fiber to the tube sheet end, where fibers have been cut to aHow the pure water to escape.The solutes in the solution move to the outer perimeter and are taken out of the permeator through the reject port. EQUATIOrJS
FOR THE RADIAL
REVERSE OSMOSIS UNIT
Ohya and Sourirajan (IO) derived general equations for iinear ffow reverse osmosis system such as spiral wound module and, plate and frame module on the Kimura-Sourirajan analysis (II) which is based on a two parameter model of membrane permeation and the film theory OR the membrane surface of the high pressure side for reverse osmosis transport. These equations are found to be useful
RO CHARAClXRISTlCS
OF B-9 HOLLOW
261
FIBER MODULE
to obtain reverse osmotic characteristics of practical reverse osmosis modules (I, 12). The following series of equations shows how to derive general equations for a radial flow reverse osmosis system such as B-9, B-10, corresponding to the general equations for a linear flow system. Using the general equations obtained, we will be able to analyse experimental data on a radial flow type module to obtain reverse osmotic characteristics such as pure water permeability constant A, solute permeability constant (DAM/K&, and the averaged mass transfer coefficient k on the outer surface of hollow fiber, and also to use those constants for design purpose of a reverse osmosis system in large scale with radial flow type modules. The mechanisms of fluid flow, permeation and separation which occur inside such a radial flow system will be very complicated. It is not our purpose to analyse this complexity, but rather to provide a much simpler and more convenient model from the practical standpoint of engineering of reverse osmosis systems. Consider the reverse osmosis process in which feed flows only radially from the distributor located at the center toward the perimeter. Let us assume (i) identical radial velocity at same radius, (ii) uniform distribution of flow along the distributor, (iii) no pressure drop inside the bore of hollow fiber, and (iv)
averaged pressure and mass transfer coefficient. Fig. 2 illustrates a model of hollow fiber module of length L and radius r, with a distributor of radius rI_ Let l/h be defined as membrane area per unit volume of the bundle of hollow fibers. Let iTOand E be the average velocity of feed and at a radius r respectively. From the solution and solute material balance over a differential shell of thickness Ar at radius r and length L, the following equations are obtained.
at the outer surface of the distributor,
27rrLE = 2n(r + Ar)L
ii + $
Ar) + a,,,2mLAr
$
(1)
Taking the limit as Ar goes to zero, this gives
2nrLiicl
--
= 2n(r + Ar)L
1 d(riic,) dr
r
VW =
C3h
d(lic,)
iic, + dr
At-
+ c3 -0, 2iirLAr h (4)
where c1 and c3 are the concentration of the bulk soiution and that of the permeate respectively, and vW is the flux of water through the membrane. The following basic equations have been derived for reverse osmosis membrane (II, 13) VW= u:, (1 Cl
=
c3q
Y(C, -
G)>
(3 (6)
Distributor 1
i ??\
Pri WI”.
cz
Feed
vw
Cl
~
$ Fig. 2. Model of Fad&I reverse osmosis unit.
where
c2 = 1 + (yC,
+ of3
(8)
Eqs. (5) to,@) are applicable at any point on the membm~e surface in the reverse osmosis separation system.
:
CS OF B-9 HOLLOW
RO CHARACXEREXI
Using
Eq. (5), Eq. (2) may be rewritten
a
dA
R
dR
--=
FIBER MODULE
1
-yy(c2
-
263
in a dimensionless
form as follows.
C,)
where
R
=-r r0
a=T
(11)
Eoh
(12)
rob Executing differentiation of the left hand side of the Eq. (4), it may be rewritten in a dimensionless form by substituting Eq. (9) as follows
d G -G--c3
dA
1-A
dR
(13)
dR
Relationship between cI and Z3 is given by the overall solute material the system corresponding to a specified fraction (A) product recovery 1 = C,(l
-
A) +C,
A
balance
for
(14)
Eqs. (9) (13) and (14) are the basic equations of the radial type reverse osmosis unit. These Eqs. (9), (13) and (14) have some analytical solutions in some special cases.
Case I: A0 + co, 0 = 0.0 This
case
is an
approximation
to
practical
cases
where
concentration
polarization effects are negligible and where complete separation is achieved. Using Eqs. (6), (7), (S), (14) for the special case, the following relationships are obtained. c3 = 0 c2 = Cl
(1%
And also 1 = (1 -
AK
(16)
H. OHYA c?I d.
264 Substituting
Eq. (16) into (13), one can obtain
dCI -
c2*
’
dR
dR
Substituting Eq. (17) into (9), and using the reiations~p of Eq. (15), one cau obtain
Using an initial condition of C!, = 1 at R = 1, Eq. (I 8) may be integrated to give
ylnC, + 1 - _& + ylu.+LZL.-.= - YCI 1 This equation shows the relationship using Eq. (16).
$-
(19)
between Ci and R, and A can be obtained
Case 2: y = 0
This case is an approximation to practical cases where the osmotic pressure of the solution is negligible. From Eqs. (7) and (9), q and dA/dR for the case may be expressed as I
4=1++exp-
( ;ie )
(20) (21)
Using an initial condition of A = 0 at R = I, Eq. (21) may be integrated to give A =&(R'-
1)
G0
Substituting Eqs. (2 1) and (22) into Eq. (13), and using an initial condition C, = 1 at R. = 1, it may be integrated to give 1
In C, = tog 2a - fog/R2 - (I “I-2JX)I
(231
Numerical solutions of Eqs. (9) and (13) may be obtained by the numerical integration using an electronic computer for any specikd combinations of y, 0, X0, and rx.And the numerical solutions for the above two cases can be compared with analytical solutions.
RO CHARACXERCXl~
OF B-9 HOLLOW
The reverse osmosis pressure pumping
FIBER MODULE
265
system consisted of a solution feed system, a high B-9 hollow fiber module. A flow diagram is shown
unit, and a
in Fig. 3. Tap water pretreated with activated carbon to decrease the concentration of chlorine to less than 0.1 ppm was forced to go through hollow fiber membrane three times to give ultrapure water which had an electric conductivity less than distilled water. This ultrapure water was used to obtain pure water permeability measurement_ An aqueous sodium chloride solution whose concentration was 2,775 ppm to 3,650 ppm was used to obtain reverse osmosis characteristics of the module. In both cases, water was recirculated, returning the concentrate and the permeate to the feed tank. No attempt was made to keep the feed temperature constant. Concentrations of feed, permeate and concentrate have been determined using an electrical conductivity meter. Flow rates of feed, permeate and concentrate were atso measured. The pure water permeation data at different temperatures have been corrected to 25°C using the temperature correction factorsf$s pioposed by Sourirajan (24). results of pure water permeability measurement The experimental measurement in are shown in Table I and those of reverse osmosis Table II.
TAP WATER
PURE NIATER
:
TANK
:
,--...---4 ,,_m.____%
Fig. 3. Row diagram of experimental
system.
23 23 23 23 20 18 18 13 12 8
19,5 20 21 22 1605 16,s 17 11 7 5,s
* Ps, = 0.5 (&I t PC43 ++ corrected by the Sourirajan metliod
SF-l-l -2 -3 -3 -5 -6 -7 -8 -9 -10
Presswe [arm] Inlet Olrtlet
11.5 11.8 12.0 12.5 9.5 12.8 9.5 12.8 9 12.8
21.3 21.5 22 22.5 18.3 17,3 17.5 12 9.5 6.75
Temp
I”Cl
Avenge*
PURE WATER PERMEABILITY EXPERIMENTAL RESULT3
TABLE I
472 483 487 486 411 386 379 274 234 178
680 603 455 373 604 376 301 435 602 390 337 347 352 356 278 216 256 203 156 132
PWP(25”C)” [l//w]
Flow rate [I/h] Feed Penttearc
1,94 1,95 1.95 1.88 1.96 1,95 1.89 1.99 2.15 2.30
A L-moleHzO/cmz alms] x 10-T
28 28 28 28 24 23
SF-2-l -2 -3 “4 -5 -6
:; 23 23 18 13
Met
-7 :; -JO -11 -12
Pressm
tt0.
RESULTS
Rm
EXPERIMENTAL
TABLE II
25 26.5 27 27 22s 19s 20 21 21.5 21s 16,s 11
Outlet
[Kg/cm3
G]
OF SODIUM
26.5 27.3 27.f 27.5 23,3 21,3 21.5 22 22.3 22.3 17.3 12
SOLUTION
Feed
3,500 3,500 3,200 2,775 3,500 3,500 3,500 3,500 3,300 3,100 3,625 3,650
Il.5 12.2 15 12.6 13 19 17.5 16‘5 15.8 15 16 16.5
SEPARATION
[“a
Tentp
AQUEOUS
Average [utm]
CHLORIDE
7,900 12,000 19‘ooo 14,750 12,ooo 7,500 7,600 10,500 11,750 15,500 8,700 6,m
270 420 700 510 480 270 290 415 !m 750 413 388 342 335 322 316 271 345 328 304 283 252 325 156
254 If5 46.8 56.7 97.8 330 274 147 90 48 146 217
1.40 1.38 I .2R 1.36 1.35 1.15 1.20 1.23 1.25 1.28 1.24 1.23
Corfcenfruriorf[ppot] Flow rate [i/h] fT”6 Cotrcerrtrare Permeate Pertnrate Concerrtrale
1.082 1.082 0.9887 0.8572 1.082 1.082 1,082 1,082 1.0197 0.9578 1.1204 1.1281
Mole fracthht of feed x lo-”
H. 0HyA et al,
268 RESULTSAND ANALYSIS
Pure water permeability A Adopting the nominal membrane surface area 1,900 ft* (= 1.77 x lo6 cm2), ,vaIues of A at several averaged pressures are calculated from the pure water permeation data which have been corrected to 2!Y’C with the correction factors given by Sourirajan as shown in Fig. 4. The pure water permeation da& do not seem to be influenced by flow rate if one takes the average applied pressure. The cateulated pure water permeabilities are plotted against the averaged pressure in Fig. 5 from which values of A are found to be 1.9 - 2.3 x IO-’ g - moles H20/cmZ - atm - s. This value is about l/to of the value obtained with Loeb-Sdurirajan type cellulose acetate membranes_ Pure water perm~b~ity constant A decreases when the operating pressure is increased. This may be due to the mechanical compaction of the hollow fiber membrane, and due to the pressure drop inside the hollow fiber of which maximum value may reach to about
Fig. 4. Pure water permeability data at difTerent fiow rates, vs. averaged operating pressure. PWP were corrected at 25°C using Sourirajan’s temperature correction factor.
Fig. S_ F.&d of operating pressure on pure water permeabiity constant.
RO CFKABA~
CS OF
B-9HOLLOW
269
FIBER MODULE
one atm. or less than 5% of the operating pressure at 500 I/h of permeation rate, assuming all fluid flow through the 3 feet length of 42 i-d. hollow fiber, calculated from Poiseulle’s law at 25°C. And the quantity of the ratio of actual flow rate per fiber end to the flow rate that would be observed if there were no pressure losses due to product flow inside the hollow proposed by Orofino (3), is calculated as 0.979 for this B-9 module, K = 3.55 x IO-” [cm/s/dyne/cm*] from Fig. 5, D = 85, I =
100 cm, symbols refer to his definition_ This change can be expressed bg the type cellulose acetate
Eq. (24) which is the same as in the case of Loeb-Sourirajan membranes (II). A = AoesmP
(24)
where A,,isa pure water permeability at zero pressure difference. The value of the exponent aO, 0.01 ‘is quite high as compared with that of porous asymmetric cellulose acetate membrane_ Analysis of the results of reverse osmosis experiments listed in Table 11 to obtain performance characteristics of the module is carried out based on the general equation for radial reverse osmosis process discussed above. According to the equations, yield A, dimensionless concentration of the concentrate c,, of the permeate t?j and non-dimensional equipment radius X (= aR), are uniquely defined by the basic reverse osmosis nondimensional
parameter,
y, 0, and 10.
Calculations (i) Calculate pure water flux rate 13: corresponding to each operating temperature and pressure, and E,,, feed rate divided by surface area of the distributor 581.2 cm2 (= K x 2.5 cm x 74 cm). (ii) Calculate a, X (= aR), and y (= B cf/p), assuming that osmotic pressure of feed solution is directly proportional to the mole fraction of solute_ (i-d., n(cl) = B cl). (iii) Assuming 8 to be zero, obtain first approximate value of (I.@,,, corresponding to a set of values for a, X, y, and A (= permeate rate/feed rate), using numerical solutions of Eq. (5) to (14). obtained in step (iii), and c, (= concentration (iv) Using the value of(M),,, of the permeate/concentration of the feed), obtain first approximate value of (e),,, corresponding to a set of values for a, X, y, and (%I)l,,_ (v) Obtain second approximate value of (no),,, for a set of data for (O& A, a, X, and y_ (vi) Obtain second approximate value of (e),,, for a set of data (A@,,,, &, a, X, and y, and compare the calculated Au, with Aobs. If the agreement between Au, and AOti is not satisfactory, repeat the steps (v) and (vi) until satisfactory agreements are obtained, such as 0.5% of relative error depending on the experimental error. (vii)
Calculate (D&KS)
(=
8 x 0:) and
k (= M x u:)_
SF-2-1 -2 -3 4 -5 -6 -7 -8 -9 -10 -11 -12
0.574 0,744 0,873 0,848 0,735 OS 11 0,545 0,674 0,759 0,840 0,606 0,420
0.285 0‘215 0.176 0.178 0.176 0.323 0.288 0.216 0,178 0.143 0.177 0,177
0.0975 0,230 0.199 0.130 0,095 0.066 0.115 0.137
0,192 0,117 0.0745 6.21 6.45 6.97 6.56 5.85 6.44 6.32 6.21 6,lt s.97 4.88 4.50
10.61 7.71 5.85 6.28 6.97 11.60 10.54 8.03 6.75 5.56 8,110 11.73 0.077 0,120 0.219 0,184 0,137 0.077 0,083 0.118 0,151 0,242 0,114 0,106
3.8 3.3 2.7 1.6 1.8 5.0 3.3 2.6 2.0 1.7 3.0 6.1
0,036s 0.0428 0.0478 0.0393 0.0384 0.0400 0.0376 0.0421 0.0424 0.0497 0.0442 0.0548
AQUEOUS !iOLUTION SEPAR/.TION
0,101 0.098 0.090 0.077 0.115 0.128 0.127 0.123 0.114 0.107 O.lfj2 0,236
ANALYTICAI. RESULTS OF THE EXPERIMENTAL RESULTS OF Nad
TABLE 111
2.70 2.00 1.17 1.03 I,25 3,33 2.31 1.72 1.30 0,935 ,1.845 3.00 0.0335 2.78 0.0338 2.22 0.0412 1.26 0.0342 1.07 0.0336 1.29 0.0368 3.50 0.0339 2.42 0.0373 t ,78 0.0372 1.34 0.0429 0.925 000384 1.94 0.0479 3.04
0.0336 1.68 0.0388 1,29 0.0421 0.813 0.0348 0.675 0.0340 0.73t 0.0372 2J4 0.0345 1.46 0.0377 I.07 0.037 1 0,794 0,0427 .0.557 0.0391 0.901 o&479 LOS
2.08 2.18 2.87’ 2.24 1.96 2.37 2.14 2.32 2.27 2.56 1.87 l&7
271
RO CHARACTERISTICS OF B-9 HOLLOW FIBER MODULE The calculated tion
results are given in Table
III, from which a 2nd approxima-
of 10 and 0 gives satisfactory results in many cases. (DAM/K@ and mass transfer coeficient k
Solute permeability
The calculated solute permeabilities are plotted against the averaged pressure in Fig. 6 from which values of (DAM/K@ are found to be around 1.65 - 2.85 x lO_’
cm/s which is about one tenth the value obtained
with Loeb-Sourirajan
type
cellulose acetate membrane. The solute permeability constant (DAM/K6) increases when the averaged operating pressure increases. This change can be expressed by Eq. (25) which is the same as in the case of cellulose acetate membranes (II). (DAM/K@ = (DAM/K&
P-’
(25)
The value of j3 for cellulose acetate membrane is usually positive, but it is very interesting to note here that the value of /3 for aromatic polyamide membrane is negative. In Fig. 7 the calculated average mass transfer coefficients are plotted against (fi)*_l?l_the logarithmic mean value of the radial fluid velocity at the surface of the distributor and at the periphery of the bundle of the hollow fiber. (iQl_,,_may be expressed by the following equation
~I0f.m.= 110_
(q-
In
From this figure, values which is about one half module (I), and also to @),.,.- The relationship equation
4
of Czare found to be around 2.2 - 0.55 x IO- cm/s to one tenth of the values obtained with a spiral wound be directly proportional to the logarithmic mean velocity between li and (ii),_,_ may be expressed by the foilowirig
E = 9 x lo-s(C),.,_
(27) 301
3
E “0 L
3.0 25 -
z = 2.0 ii
:.5,f<.
di%_ a P
0
I
0'
21)
0’ 0
E
$No%’ 0’
h
20
B [ah]
1.0
2
x
O _.,*..
/
O,Q
I0
_..._ 30
lx
O
0.a
al
(nlh
QzQ3
Pvrccl
Fig. 6. Effet of operating pressure on solute permeability constant (D&k& Fig. 7. Correlation of mass transfer coefficients and @)I.~..
272
H. OHYA
et al.
DISCUSSION
The pure water permeability constant A of B-9 hollow fiber membrane is about one tenth of the value obtained with Loeb-Sourirajan type cellulose acetate membrane. But the corresponding value of aceis about three times larger than the value obtained with the cellulose acetate membrane. These observed values of A and a0 in the case of B-9 hollow fiber membrane might imply that B-9 membrane is much tighter than the ce1luiose acetate membrane and tends to become still tighter by pressurization, and that the bore also tends to become small by pressurization. The solute permeability constant of sodium chloride increases when the average operating pressure increases. This phenomenon is quite the reverse of that observed with the cellulose acetate membrane. But only one case of the same phenomenon is reported in separating aqueous sodium nitrate solution with a very tight cellulose acetate membrane (I I). These two facts seem to suggest that B-9 hollow fiber membrane has imperfections which are not small enough to separate solute from the bulk solution. On increasing the pressure the amount of water which permeates through imperfections becomes relatively higher, resulting in the apparent increase of the solute permeability constant. Applegate and Antonson (16) tried to explain the same phenomenon observed with DP-1 membranes by the solution-diffusion and im~rfection membrane theory. Fig. 8 shows the relationship between A and (D&K&) for B-9 hollow fiber membrane and for CA-NRC-18 type cellulose acetate membrane (26). From this figure one may say that B-9 membrane has rather larger value of (DAAf/Kb) than the extrapolated (D&M) for CA-NRA-18 type cellulose acetate membrane at the same A value of B-9 hollow fiber. The calculated mass transfer coefficient shows rather good performance of this module. The low value of Reynolds number based on the diameter of hollow fiber 8.5~, the average flow rate 0.3 cm/s as shown in Fig. 7, JI = 0.01 poise, iVae = 0.255, indicates that the flowing condition on the membrane surface can be comp1eteIy laminar in nature. It is interesting to note that the value of k is high and is one half of the value obtained with a spill-wound module in spite of the low value for Reynolds number. The high value of k together with low value of A gives rather higher value of M about 1 - 3 especially when flow rate is high. From our previous discussion on a single stage desalination of sea water (17), this high value of R8 may be attractive enough to be applicable to single stage desalination if the properties of the hollow fiber are improved to give a lower value of (D,,,/KG) and high pressure resistability. In fact, the B-10 module is already put to commercial use for the purpose of a single stage desalination of sea water. It will be quite interesting to analyse the reverse osmotic characteristics of the B-10 module.
RO CHARACIERBTICS OF B-9 HOLUlW FIBER MODULE
273
Fig, 8. (DA.&@ VS.pure water perm=bility cwstant for the B-9 hollow fiber membrane and CA-NRC-18
membrane.
CONCLUSION Reverse osmotic characteristics
of the B-9 hollow fiber module was analyzed
to obtain pure water ~rmeabil~ty constant A and sodium chloride permeability constant (DAM/-K6),based on the general equations for radial reverse osmosis unit. The values of A = 1.9 N 2.3 x IO-’ g - mofefcm’ atm - s, and (D&G) = 1.65 N 2.85 x IO-” cm/s are obtained. The value of A is about one tenth of the value obtained with Loeb-Sourirajan type cellulose acetate membranes, and the value of the exponent do, in Eq. (24) is 0.01 and is quite high as compared with that of the cellulose acetate membrane. A relatively large dependency of A on pressure and smali value of A might imply that B-9 membrane is much tighter than the cellulose acetate membrane, and that radius of the bore might tend to become small by pressurization. The value of (DAM/K@ increases wben the average operating pressure increases_ This phenomenon which is quite the reverse of that observed with the celhtlose acetate membrane, might imply that B-9 hollow fiber membrane has some imperfections on the membrane surface. The average mass transfer coefficient is about one half to one tenth of the value with a spiral-wound module, 0.55 ro 2.1 x 1P cm/s. The authors are grateful to Kachita Co. for the financial support of the experiment& apparatus, and to Shinko-Faudler for offering the B-9 hollow fiber
H. OHYA
274
it Cd
module. One of the authors (H-0.) thanks the National Research Council of Canada for a summer appointment. The authors are grateful to Dr. V. S. Sastri for his help in writing the paper and to the staff of the hational Research Council Computation Center for their help in processing the calculations.
REFERENCES
I. H. OWYA AND Y. TANXGUCHI, 2. 3. 4. 5. 6. 7. 8. 9. IO. 11. 12. 13. 14. 15. 16. 17.
Desaharion, 16 (1975) 359. W. COOKE, ibid., 7 (1969/1970) 31_ T. OR~FINO, Ofice o$Saline Water, Res. Devel. Prog. Rept. No. 549. 1970. C. CHEN AND C. PEI-IY, Desahation, 12 (1973) 281. J. HERMANS, Membrane Digest, 1 (1972)45. J. DAVIS AND T. ORORNO, 163rd ACS Meeting, Boston, April 1972. W. GILL AND B. BANZAL, Am. Inst. Gem. Eag. J., 19 (1973) 823. B. BANUL AND W. GILL, Am. Inst. Chem. Eng. Symp. Ser., No. 144. 70 (1974) 136. DUPONT DE NEMOURS & Co., Kirkpatrick Chemical Engineering Award Winners Report, Chem. Eng.. 78 (1971) 54. H. OHYA AND S. SOURIRAJAN, Am. Insr. Chem. Eng. 1., 15 (1969) 829. S. KIMURA AND S. SOURWAJAN. ibid., 13 (1967) 497. H. OHYA, T_ MORIYAMA, S. SUZUKI AND S. ISHIZAKA. Desalinafion, 16 (1975) 235. S. KIMUFCA,S. SOURIRAJAN AND H. OHYA, Ind. Eng. Chem. Process Design Develop.. 8 (1969) 79. S. SOURIRAJAN. Reverse Osmosis, Academic Press, New York, N.Y., 1970. ‘I’. S. GOVINDAN AND S. S~LJRIRAJAN,Ind. EnR. Chem. Process Design Develop., 5 (1966) 422. L. APPLEGATE AND C. ANTONSON, ACS Polymer Preprint, 12(2) (1971) 385. H. OHYA AND S. SOURIRAJAN, Desalination, 6 (1969) 153.
21 (1977) 257-274
Els.evierScientific Publishing Company, Amsterdam - Printed in The Netherlands
@
AN
ANALYSIS
HOLLOW
FIBER
OF
REVERSE
OSMOTIC
CHARACTERISTICS
OF
B-9
MODULE*
H. OHYA’ Division
of Chemistry,
NationaI
Research Council
of Cattaifu, Ottawa KIA
OR9
(Can&a)
AND
H. NAKA.JIMA=, K. TAKAG13, S. KAGAWA Kant0 Gakuin
University,
Kanazawaku,
Yokohama
AND
Y. NEGISH14
(Japan)
(Received September 29, 1974; in revised form January 11, 1977)
SUMMARY
Reverse osmosis experiments were carried out with a B-9 hollow fiber membrane module to obtain its reverse osmotic characteristics. Analysis of the data based on the general equations for radial reverse osmosis unit gives membrane characteristic constants, A = 1.9 - 2.3 x lO_’ g - mole H20/cm2 - atm - s, and of A on (D,,/K6) = 1.65 - 2.85 x 10e6 cm/s. A relatively large dependency pressure and a tendency for (D,,,/K6) to increase with pressure were observed. These two facts may imply that there might be some imperfections on the surface of the hollow fiber membrane. The average mass transfer coefficient is about one half to one tenth of the value with a spiral wound module, 0.55 - 2.1 x 10-4 cm/s_ SYMBOLS
A Ao
-
‘B
-
C
-
c1,c2c3
-
pure water
permeability
constant,
g - mole H,O/cm’
- atm - s
pure water permeability constant at zero pressure difference, g - mole H20/cm2 - atm - s osmotic pressure proportionality constant, atm. molar density of solution, g mole/cm3 solute concentration in the bulk solution, the concentrated boundary l
solution on the high pressure side of the membrane, and in the permeate solution on the atmospheric pressure side of the mem-
l
Experimentswere carried out at Yokohama University and theory devetoped at the National
Research Council of Canada. 1 Visiting Scientist from Yokohama National University, Yokohama, Japan. 2 Now with Tsukishima MachineriesCo., Chuoku, Tokyo, Japan. 3 Now with Bio-Engineering Co., Sumidaku. Tokyo, Japan. J Now -with Yokohama National University.
258
H. OHYA
brane, respectively, at any point on the membrane, fraction value of c1 at the outer surface of the distributor
flh k L.
P
-
4 r
-
ri R
-
r0
ii 3, v: .VW x a
-
a0 /3
-
II 0
-
1.0
-
v
-
Superscript Subscript I_nt.
-
f?t al.
ppm or mole
cle: solute transport constant, cm/s temperature correction factor for pure water flux rate proposed by Sourirajan (fC) = v(T)/v(25T) membrane area per unit volume of fluid space in the reverse osmosis unit, cm-’ mass transfer coefficient on the high pressure side of membrane, cm/s length of the bundle of hollow fibers, cm averaged operating pressure, atm quantity defined by Eq. (7) radius, cm outer radius of the distributor, cm quantity defined by Eq. (1 I) outer radius of the hollow fiber bundle, cm average radial fluid velocity, cm/s value of P at the outer surface of the distributor pure water fiux rate, (= AP/c), cm/s water flux rate, cm/s = aR quantity defined by Eq. (12) quantity defined in Eq. (24) quantity defined in Eq. (25) dimensiomess osmotic pressure n(cy)/B fractional permeate recovery dimensionless membrane permeability = (D,,JIGi)/u: dimensionless mass transfer coefficient = @I: kinematic viscosity, cm*/s
averaged value
logarithmic mean of the outer surface of the distributor periphery of the bundfe
and the
INTPIODUCTION
Reverse osmosis
for desalting
water has by now been well established
RQ CHARACTERISTICS
OF B-9 HOLLOW FIBER MODULE
259
-although research continues for improvement in membranes, hardware and plant operating procedures. There are essentially four different reverse osmosis membrane configurations which have been successfully developed by different groups of workers. These are (i) the Bat membrane, (ii) tubular membrane, (iii) spiralwound membrane, and (iv) hollow fiber membrane configurations. The effect of concentration polarization on the performance of a membrane in a reverse osmosis unit is well recognized in general terms, and hence, in every design, an attempt is -made to minimize concentration polarization in the membrane unit. The problem of concentration polarization has also been well discussed both theoretically and experimentally for thin channel and tubular systems. Only very few experimental studies have been reported on the mass transfer coefficient obtained in the actual operation of the different membrane configuration. The desired and the actually obtainable mass transfer coefficient should be the most important consideration in the development of a suitable design concept for saline water and sea water conversion. Membrane characteristics and average mass transfer coefficients of spiral-wound membrane module have been studied (I). Extremely compact design and a wider range of pH for practical operation are the advantages in the case of a hollow fiber module as compared to cellulose acetate membranes. But a few studies were carried out on the hollow fiber modules. Cooke (2) reported some of the experimental results on Nylon hollow fiber module developed by DuPont. Orofino (3) reported development of cellulose acetate hollow filament technology for a reverse osmosis desalination system in which fluid flow characteristics inside and outside of hollow fiber was treated. Chen and Petty (4) treated the same topics. Hermans (5) accounted for the shell side pressure drop and developed analytical expressions for the productivity of both parallel and radial flow systems. Davis and Orofino (6) have treated both systems on the basis of Hermans’ work. Gill and Bansal (7) and Bansal and Gill (8) developed a more rigorous mathematical model of the hollow fiber system on the assumption of negligibIe concentration polarization and a constant rejection coefficient. It is the purpose of this paper to study membrane characteristics aud average mass transfer coefficient using the hollow fiber membrane module. CONFIGURATION
OF THE HOLLOW
FIBER MODULE
DuPont, with its extensive background in polymer chemistry and fiber technology, has been developing the hollow fiber module concept since mid-60’s, and the first large scale demonstration of the practicability of treating brackish water supplies by the system began in Plains, Texas, in 1969. The first B-9 permeator was introduced in late 1970 (9). The hollow fiber system of DuPont utilizes a tightly packed ‘bundle of
H. OKYA
260
Fig.
I.
et cd.
Schematic representation of DuPont B-9 hollow fiber module.
hollow fibers within a high pressure vase1 in a shelt-and-tube type configuration. The holloti fibers serve as the membrane element and as their own support against the pressure of the feed water. The open ends of each fiber loop are potted in a header where the product water from the interior of each fiber exits. A model of the DuPont 33-9 permeator has the following dimensions; shell 41/2 inches i.d., by 4 ft long, made of fiber reinforced plastics and pressure rated at 650 psi; active length of looped fiber 5 ft; fiber size 42 microns i.d. by 85 microns o.d., and nominal surface area of I9IcIoft’. The use of hollow fibers permits the development of an extremely compact device, because membrane surface area per unit volume is approximately 3300 ft2 mt?mbFane area per ft3 module compared with 300 for spiral module. Fig. i iltustrates a Ltinch B-9 permeator. The pressurized aqueous feed solution enters the permeator through a very porous tubular distributor focated at the center of the permeator. The solution moves radially from the distributor toward the outer she11 of the permeator, and around the outer side of the fibers. The pressure then forces the pure water through the fiber walls into the bore of the fiber, and this water moves along the bore of each fiber to the tube sheet end, where fibers have been cut to aHow the pure water to escape.The solutes in the solution move to the outer perimeter and are taken out of the permeator through the reject port. EQUATIOrJS
FOR THE RADIAL
REVERSE OSMOSIS UNIT
Ohya and Sourirajan (IO) derived general equations for iinear ffow reverse osmosis system such as spiral wound module and, plate and frame module on the Kimura-Sourirajan analysis (II) which is based on a two parameter model of membrane permeation and the film theory OR the membrane surface of the high pressure side for reverse osmosis transport. These equations are found to be useful
RO CHARAClXRISTlCS
OF B-9 HOLLOW
261
FIBER MODULE
to obtain reverse osmotic characteristics of practical reverse osmosis modules (I, 12). The following series of equations shows how to derive general equations for a radial flow reverse osmosis system such as B-9, B-10, corresponding to the general equations for a linear flow system. Using the general equations obtained, we will be able to analyse experimental data on a radial flow type module to obtain reverse osmotic characteristics such as pure water permeability constant A, solute permeability constant (DAM/K&, and the averaged mass transfer coefficient k on the outer surface of hollow fiber, and also to use those constants for design purpose of a reverse osmosis system in large scale with radial flow type modules. The mechanisms of fluid flow, permeation and separation which occur inside such a radial flow system will be very complicated. It is not our purpose to analyse this complexity, but rather to provide a much simpler and more convenient model from the practical standpoint of engineering of reverse osmosis systems. Consider the reverse osmosis process in which feed flows only radially from the distributor located at the center toward the perimeter. Let us assume (i) identical radial velocity at same radius, (ii) uniform distribution of flow along the distributor, (iii) no pressure drop inside the bore of hollow fiber, and (iv)
averaged pressure and mass transfer coefficient. Fig. 2 illustrates a model of hollow fiber module of length L and radius r, with a distributor of radius rI_ Let l/h be defined as membrane area per unit volume of the bundle of hollow fibers. Let iTOand E be the average velocity of feed and at a radius r respectively. From the solution and solute material balance over a differential shell of thickness Ar at radius r and length L, the following equations are obtained.
at the outer surface of the distributor,
27rrLE = 2n(r + Ar)L
ii + $
Ar) + a,,,2mLAr
$
(1)
Taking the limit as Ar goes to zero, this gives
2nrLiicl
--
= 2n(r + Ar)L
1 d(riic,) dr
r
VW =
C3h
d(lic,)
iic, + dr
At-
+ c3 -0, 2iirLAr h (4)
where c1 and c3 are the concentration of the bulk soiution and that of the permeate respectively, and vW is the flux of water through the membrane. The following basic equations have been derived for reverse osmosis membrane (II, 13) VW= u:, (1 Cl
=
c3q
Y(C, -
G)>
(3 (6)
Distributor 1
i ??\
Pri WI”.
cz
Feed
vw
Cl
~
$ Fig. 2. Model of Fad&I reverse osmosis unit.
where
c2 = 1 + (yC,
+ of3
(8)
Eqs. (5) to,@) are applicable at any point on the membm~e surface in the reverse osmosis separation system.
:
CS OF B-9 HOLLOW
RO CHARACXEREXI
Using
Eq. (5), Eq. (2) may be rewritten
a
dA
R
dR
--=
FIBER MODULE
1
-yy(c2
-
263
in a dimensionless
form as follows.
C,)
where
R
=-r r0
a=T
(11)
Eoh
(12)
rob Executing differentiation of the left hand side of the Eq. (4), it may be rewritten in a dimensionless form by substituting Eq. (9) as follows
d G -G--c3
dA
1-A
dR
(13)
dR
Relationship between cI and Z3 is given by the overall solute material the system corresponding to a specified fraction (A) product recovery 1 = C,(l
-
A) +C,
A
balance
for
(14)
Eqs. (9) (13) and (14) are the basic equations of the radial type reverse osmosis unit. These Eqs. (9), (13) and (14) have some analytical solutions in some special cases.
Case I: A0 + co, 0 = 0.0 This
case
is an
approximation
to
practical
cases
where
concentration
polarization effects are negligible and where complete separation is achieved. Using Eqs. (6), (7), (S), (14) for the special case, the following relationships are obtained. c3 = 0 c2 = Cl
(1%
And also 1 = (1 -
AK
(16)
H. OHYA c?I d.
264 Substituting
Eq. (16) into (13), one can obtain
dCI -
c2*
’
dR
dR
Substituting Eq. (17) into (9), and using the reiations~p of Eq. (15), one cau obtain
Using an initial condition of C!, = 1 at R = 1, Eq. (I 8) may be integrated to give
ylnC, + 1 - _& + ylu.+LZL.-.= - YCI 1 This equation shows the relationship using Eq. (16).
$-
(19)
between Ci and R, and A can be obtained
Case 2: y = 0
This case is an approximation to practical cases where the osmotic pressure of the solution is negligible. From Eqs. (7) and (9), q and dA/dR for the case may be expressed as I
4=1++exp-
( ;ie )
(20) (21)
Using an initial condition of A = 0 at R = I, Eq. (21) may be integrated to give A =&(R'-
1)
G0
Substituting Eqs. (2 1) and (22) into Eq. (13), and using an initial condition C, = 1 at R. = 1, it may be integrated to give 1
In C, = tog 2a - fog/R2 - (I “I-2JX)I
(231
Numerical solutions of Eqs. (9) and (13) may be obtained by the numerical integration using an electronic computer for any specikd combinations of y, 0, X0, and rx.And the numerical solutions for the above two cases can be compared with analytical solutions.
RO CHARACXERCXl~
OF B-9 HOLLOW
The reverse osmosis pressure pumping
FIBER MODULE
265
system consisted of a solution feed system, a high B-9 hollow fiber module. A flow diagram is shown
unit, and a
in Fig. 3. Tap water pretreated with activated carbon to decrease the concentration of chlorine to less than 0.1 ppm was forced to go through hollow fiber membrane three times to give ultrapure water which had an electric conductivity less than distilled water. This ultrapure water was used to obtain pure water permeability measurement_ An aqueous sodium chloride solution whose concentration was 2,775 ppm to 3,650 ppm was used to obtain reverse osmosis characteristics of the module. In both cases, water was recirculated, returning the concentrate and the permeate to the feed tank. No attempt was made to keep the feed temperature constant. Concentrations of feed, permeate and concentrate have been determined using an electrical conductivity meter. Flow rates of feed, permeate and concentrate were atso measured. The pure water permeation data at different temperatures have been corrected to 25°C using the temperature correction factorsf$s pioposed by Sourirajan (24). results of pure water permeability measurement The experimental measurement in are shown in Table I and those of reverse osmosis Table II.
TAP WATER
PURE NIATER
:
TANK
:
,--...---4 ,,_m.____%
Fig. 3. Row diagram of experimental
system.
23 23 23 23 20 18 18 13 12 8
19,5 20 21 22 1605 16,s 17 11 7 5,s
* Ps, = 0.5 (&I t PC43 ++ corrected by the Sourirajan metliod
SF-l-l -2 -3 -3 -5 -6 -7 -8 -9 -10
Presswe [arm] Inlet Olrtlet
11.5 11.8 12.0 12.5 9.5 12.8 9.5 12.8 9 12.8
21.3 21.5 22 22.5 18.3 17,3 17.5 12 9.5 6.75
Temp
I”Cl
Avenge*
PURE WATER PERMEABILITY EXPERIMENTAL RESULT3
TABLE I
472 483 487 486 411 386 379 274 234 178
680 603 455 373 604 376 301 435 602 390 337 347 352 356 278 216 256 203 156 132
PWP(25”C)” [l//w]
Flow rate [I/h] Feed Penttearc
1,94 1,95 1.95 1.88 1.96 1,95 1.89 1.99 2.15 2.30
A L-moleHzO/cmz alms] x 10-T
28 28 28 28 24 23
SF-2-l -2 -3 “4 -5 -6
:; 23 23 18 13
Met
-7 :; -JO -11 -12
Pressm
tt0.
RESULTS
Rm
EXPERIMENTAL
TABLE II
25 26.5 27 27 22s 19s 20 21 21.5 21s 16,s 11
Outlet
[Kg/cm3
G]
OF SODIUM
26.5 27.3 27.f 27.5 23,3 21,3 21.5 22 22.3 22.3 17.3 12
SOLUTION
Feed
3,500 3,500 3,200 2,775 3,500 3,500 3,500 3,500 3,300 3,100 3,625 3,650
Il.5 12.2 15 12.6 13 19 17.5 16‘5 15.8 15 16 16.5
SEPARATION
[“a
Tentp
AQUEOUS
Average [utm]
CHLORIDE
7,900 12,000 19‘ooo 14,750 12,ooo 7,500 7,600 10,500 11,750 15,500 8,700 6,m
270 420 700 510 480 270 290 415 !m 750 413 388 342 335 322 316 271 345 328 304 283 252 325 156
254 If5 46.8 56.7 97.8 330 274 147 90 48 146 217
1.40 1.38 I .2R 1.36 1.35 1.15 1.20 1.23 1.25 1.28 1.24 1.23
Corfcenfruriorf[ppot] Flow rate [i/h] fT”6 Cotrcerrtrare Permeate Pertnrate Concerrtrale
1.082 1.082 0.9887 0.8572 1.082 1.082 1,082 1,082 1.0197 0.9578 1.1204 1.1281
Mole fracthht of feed x lo-”
H. 0HyA et al,
268 RESULTSAND ANALYSIS
Pure water permeability A Adopting the nominal membrane surface area 1,900 ft* (= 1.77 x lo6 cm2), ,vaIues of A at several averaged pressures are calculated from the pure water permeation data which have been corrected to 2!Y’C with the correction factors given by Sourirajan as shown in Fig. 4. The pure water permeation da& do not seem to be influenced by flow rate if one takes the average applied pressure. The cateulated pure water permeabilities are plotted against the averaged pressure in Fig. 5 from which values of A are found to be 1.9 - 2.3 x IO-’ g - moles H20/cmZ - atm - s. This value is about l/to of the value obtained with Loeb-Sdurirajan type cellulose acetate membranes_ Pure water perm~b~ity constant A decreases when the operating pressure is increased. This may be due to the mechanical compaction of the hollow fiber membrane, and due to the pressure drop inside the hollow fiber of which maximum value may reach to about
Fig. 4. Pure water permeability data at difTerent fiow rates, vs. averaged operating pressure. PWP were corrected at 25°C using Sourirajan’s temperature correction factor.
Fig. S_ F.&d of operating pressure on pure water permeabiity constant.
RO CFKABA~
CS OF
B-9HOLLOW
269
FIBER MODULE
one atm. or less than 5% of the operating pressure at 500 I/h of permeation rate, assuming all fluid flow through the 3 feet length of 42 i-d. hollow fiber, calculated from Poiseulle’s law at 25°C. And the quantity of the ratio of actual flow rate per fiber end to the flow rate that would be observed if there were no pressure losses due to product flow inside the hollow proposed by Orofino (3), is calculated as 0.979 for this B-9 module, K = 3.55 x IO-” [cm/s/dyne/cm*] from Fig. 5, D = 85, I =
100 cm, symbols refer to his definition_ This change can be expressed bg the type cellulose acetate
Eq. (24) which is the same as in the case of Loeb-Sourirajan membranes (II). A = AoesmP
(24)
where A,,isa pure water permeability at zero pressure difference. The value of the exponent aO, 0.01 ‘is quite high as compared with that of porous asymmetric cellulose acetate membrane_ Analysis of the results of reverse osmosis experiments listed in Table 11 to obtain performance characteristics of the module is carried out based on the general equation for radial reverse osmosis process discussed above. According to the equations, yield A, dimensionless concentration of the concentrate c,, of the permeate t?j and non-dimensional equipment radius X (= aR), are uniquely defined by the basic reverse osmosis nondimensional
parameter,
y, 0, and 10.
Calculations (i) Calculate pure water flux rate 13: corresponding to each operating temperature and pressure, and E,,, feed rate divided by surface area of the distributor 581.2 cm2 (= K x 2.5 cm x 74 cm). (ii) Calculate a, X (= aR), and y (= B cf/p), assuming that osmotic pressure of feed solution is directly proportional to the mole fraction of solute_ (i-d., n(cl) = B cl). (iii) Assuming 8 to be zero, obtain first approximate value of (I.@,,, corresponding to a set of values for a, X, y, and A (= permeate rate/feed rate), using numerical solutions of Eq. (5) to (14). obtained in step (iii), and c, (= concentration (iv) Using the value of(M),,, of the permeate/concentration of the feed), obtain first approximate value of (e),,, corresponding to a set of values for a, X, y, and (%I)l,,_ (v) Obtain second approximate value of (no),,, for a set of data for (O& A, a, X, and y_ (vi) Obtain second approximate value of (e),,, for a set of data (A@,,,, &, a, X, and y, and compare the calculated Au, with Aobs. If the agreement between Au, and AOti is not satisfactory, repeat the steps (v) and (vi) until satisfactory agreements are obtained, such as 0.5% of relative error depending on the experimental error. (vii)
Calculate (D&KS)
(=
8 x 0:) and
k (= M x u:)_
SF-2-1 -2 -3 4 -5 -6 -7 -8 -9 -10 -11 -12
0.574 0,744 0,873 0,848 0,735 OS 11 0,545 0,674 0,759 0,840 0,606 0,420
0.285 0‘215 0.176 0.178 0.176 0.323 0.288 0.216 0,178 0.143 0.177 0,177
0.0975 0,230 0.199 0.130 0,095 0.066 0.115 0.137
0,192 0,117 0.0745 6.21 6.45 6.97 6.56 5.85 6.44 6.32 6.21 6,lt s.97 4.88 4.50
10.61 7.71 5.85 6.28 6.97 11.60 10.54 8.03 6.75 5.56 8,110 11.73 0.077 0,120 0.219 0,184 0,137 0.077 0,083 0.118 0,151 0,242 0,114 0,106
3.8 3.3 2.7 1.6 1.8 5.0 3.3 2.6 2.0 1.7 3.0 6.1
0,036s 0.0428 0.0478 0.0393 0.0384 0.0400 0.0376 0.0421 0.0424 0.0497 0.0442 0.0548
AQUEOUS !iOLUTION SEPAR/.TION
0,101 0.098 0.090 0.077 0.115 0.128 0.127 0.123 0.114 0.107 O.lfj2 0,236
ANALYTICAI. RESULTS OF THE EXPERIMENTAL RESULTS OF Nad
TABLE 111
2.70 2.00 1.17 1.03 I,25 3,33 2.31 1.72 1.30 0,935 ,1.845 3.00 0.0335 2.78 0.0338 2.22 0.0412 1.26 0.0342 1.07 0.0336 1.29 0.0368 3.50 0.0339 2.42 0.0373 t ,78 0.0372 1.34 0.0429 0.925 000384 1.94 0.0479 3.04
0.0336 1.68 0.0388 1,29 0.0421 0.813 0.0348 0.675 0.0340 0.73t 0.0372 2J4 0.0345 1.46 0.0377 I.07 0.037 1 0,794 0,0427 .0.557 0.0391 0.901 o&479 LOS
2.08 2.18 2.87’ 2.24 1.96 2.37 2.14 2.32 2.27 2.56 1.87 l&7
271
RO CHARACTERISTICS OF B-9 HOLLOW FIBER MODULE The calculated tion
results are given in Table
III, from which a 2nd approxima-
of 10 and 0 gives satisfactory results in many cases. (DAM/K@ and mass transfer coeficient k
Solute permeability
The calculated solute permeabilities are plotted against the averaged pressure in Fig. 6 from which values of (DAM/K@ are found to be around 1.65 - 2.85 x lO_’
cm/s which is about one tenth the value obtained
with Loeb-Sourirajan
type
cellulose acetate membrane. The solute permeability constant (DAM/K6) increases when the averaged operating pressure increases. This change can be expressed by Eq. (25) which is the same as in the case of cellulose acetate membranes (II). (DAM/K@ = (DAM/K&
P-’
(25)
The value of j3 for cellulose acetate membrane is usually positive, but it is very interesting to note here that the value of /3 for aromatic polyamide membrane is negative. In Fig. 7 the calculated average mass transfer coefficients are plotted against (fi)*_l?l_the logarithmic mean value of the radial fluid velocity at the surface of the distributor and at the periphery of the bundle of the hollow fiber. (iQl_,,_may be expressed by the following equation
~I0f.m.= 110_
(q-
In
From this figure, values which is about one half module (I), and also to @),.,.- The relationship equation
4
of Czare found to be around 2.2 - 0.55 x IO- cm/s to one tenth of the values obtained with a spiral wound be directly proportional to the logarithmic mean velocity between li and (ii),_,_ may be expressed by the foilowirig
E = 9 x lo-s(C),.,_
(27) 301
3
E “0 L
3.0 25 -
z = 2.0 ii
:.5,f<.
di%_ a P
0
I
0'
21)
0’ 0
E
$No%’ 0’
h
20
B [ah]
1.0
2
x
O _.,*..
/
O,Q
I0
_..._ 30
lx
O
0.a
al
(nlh
QzQ3
Pvrccl
Fig. 6. Effet of operating pressure on solute permeability constant (D&k& Fig. 7. Correlation of mass transfer coefficients and @)I.~..
272
H. OHYA
et al.
DISCUSSION
The pure water permeability constant A of B-9 hollow fiber membrane is about one tenth of the value obtained with Loeb-Sourirajan type cellulose acetate membrane. But the corresponding value of aceis about three times larger than the value obtained with the cellulose acetate membrane. These observed values of A and a0 in the case of B-9 hollow fiber membrane might imply that B-9 membrane is much tighter than the ce1luiose acetate membrane and tends to become still tighter by pressurization, and that the bore also tends to become small by pressurization. The solute permeability constant of sodium chloride increases when the average operating pressure increases. This phenomenon is quite the reverse of that observed with the cellulose acetate membrane. But only one case of the same phenomenon is reported in separating aqueous sodium nitrate solution with a very tight cellulose acetate membrane (I I). These two facts seem to suggest that B-9 hollow fiber membrane has imperfections which are not small enough to separate solute from the bulk solution. On increasing the pressure the amount of water which permeates through imperfections becomes relatively higher, resulting in the apparent increase of the solute permeability constant. Applegate and Antonson (16) tried to explain the same phenomenon observed with DP-1 membranes by the solution-diffusion and im~rfection membrane theory. Fig. 8 shows the relationship between A and (D&K&) for B-9 hollow fiber membrane and for CA-NRC-18 type cellulose acetate membrane (26). From this figure one may say that B-9 membrane has rather larger value of (DAAf/Kb) than the extrapolated (D&M) for CA-NRA-18 type cellulose acetate membrane at the same A value of B-9 hollow fiber. The calculated mass transfer coefficient shows rather good performance of this module. The low value of Reynolds number based on the diameter of hollow fiber 8.5~, the average flow rate 0.3 cm/s as shown in Fig. 7, JI = 0.01 poise, iVae = 0.255, indicates that the flowing condition on the membrane surface can be comp1eteIy laminar in nature. It is interesting to note that the value of k is high and is one half of the value obtained with a spill-wound module in spite of the low value for Reynolds number. The high value of k together with low value of A gives rather higher value of M about 1 - 3 especially when flow rate is high. From our previous discussion on a single stage desalination of sea water (17), this high value of R8 may be attractive enough to be applicable to single stage desalination if the properties of the hollow fiber are improved to give a lower value of (D,,,/KG) and high pressure resistability. In fact, the B-10 module is already put to commercial use for the purpose of a single stage desalination of sea water. It will be quite interesting to analyse the reverse osmotic characteristics of the B-10 module.
RO CHARACIERBTICS OF B-9 HOLUlW FIBER MODULE
273
Fig, 8. (DA.&@ VS.pure water perm=bility cwstant for the B-9 hollow fiber membrane and CA-NRC-18
membrane.
CONCLUSION Reverse osmotic characteristics
of the B-9 hollow fiber module was analyzed
to obtain pure water ~rmeabil~ty constant A and sodium chloride permeability constant (DAM/-K6),based on the general equations for radial reverse osmosis unit. The values of A = 1.9 N 2.3 x IO-’ g - mofefcm’ atm - s, and (D&G) = 1.65 N 2.85 x IO-” cm/s are obtained. The value of A is about one tenth of the value obtained with Loeb-Sourirajan type cellulose acetate membranes, and the value of the exponent do, in Eq. (24) is 0.01 and is quite high as compared with that of the cellulose acetate membrane. A relatively large dependency of A on pressure and smali value of A might imply that B-9 membrane is much tighter than the cellulose acetate membrane, and that radius of the bore might tend to become small by pressurization. The value of (DAM/K@ increases wben the average operating pressure increases_ This phenomenon which is quite the reverse of that observed with the celhtlose acetate membrane, might imply that B-9 hollow fiber membrane has some imperfections on the membrane surface. The average mass transfer coefficient is about one half to one tenth of the value with a spiral-wound module, 0.55 ro 2.1 x 1P cm/s. The authors are grateful to Kachita Co. for the financial support of the experiment& apparatus, and to Shinko-Faudler for offering the B-9 hollow fiber
H. OHYA
274
it Cd
module. One of the authors (H-0.) thanks the National Research Council of Canada for a summer appointment. The authors are grateful to Dr. V. S. Sastri for his help in writing the paper and to the staff of the hational Research Council Computation Center for their help in processing the calculations.
REFERENCES
I. H. OWYA AND Y. TANXGUCHI, 2. 3. 4. 5. 6. 7. 8. 9. IO. 11. 12. 13. 14. 15. 16. 17.
Desaharion, 16 (1975) 359. W. COOKE, ibid., 7 (1969/1970) 31_ T. OR~FINO, Ofice o$Saline Water, Res. Devel. Prog. Rept. No. 549. 1970. C. CHEN AND C. PEI-IY, Desahation, 12 (1973) 281. J. HERMANS, Membrane Digest, 1 (1972)45. J. DAVIS AND T. ORORNO, 163rd ACS Meeting, Boston, April 1972. W. GILL AND B. BANZAL, Am. Inst. Gem. Eag. J., 19 (1973) 823. B. BANUL AND W. GILL, Am. Inst. Chem. Eng. Symp. Ser., No. 144. 70 (1974) 136. DUPONT DE NEMOURS & Co., Kirkpatrick Chemical Engineering Award Winners Report, Chem. Eng.. 78 (1971) 54. H. OHYA AND S. SOURIRAJAN, Am. Insr. Chem. Eng. 1., 15 (1969) 829. S. KIMURA AND S. SOURWAJAN. ibid., 13 (1967) 497. H. OHYA, T_ MORIYAMA, S. SUZUKI AND S. ISHIZAKA. Desalinafion, 16 (1975) 235. S. KIMUFCA,S. SOURIRAJAN AND H. OHYA, Ind. Eng. Chem. Process Design Develop.. 8 (1969) 79. S. SOURIRAJAN. Reverse Osmosis, Academic Press, New York, N.Y., 1970. ‘I’. S. GOVINDAN AND S. S~LJRIRAJAN,Ind. EnR. Chem. Process Design Develop., 5 (1966) 422. L. APPLEGATE AND C. ANTONSON, ACS Polymer Preprint, 12(2) (1971) 385. H. OHYA AND S. SOURIRAJAN, Desalination, 6 (1969) 153.