TURBULENT REGION PERFORMANCE OF REVERSE OSMOSIS DESALINATION TUBES Experience at Coalinga Pilot Plant JUDY ROSENFELD AND S I D N E Y LOEB Department of Engineering, University of California, Los Angeles, Calij.
Equations describing the turbulent region performance of reverse osmosis desalination tubes are developed. The characteristic performance quantities, desalinized water flux and desalination ratio, are expressed
as functions of experimentally determinable membrane coefficients and of operating conditions. Experimental data from a tubular pilot plant, now in operation at Coalinga, Calif., were utilized to examine the validity of the equation relating desalination ratio to membrane properties and operating conditions, The experimental results appeared to support this equation, which is based on the concentration polarization studies of Sherwood and Brian and on the salt diffusion work of Merten.
EVERSE
osmosis is being given serious consideration as a
R means for economic desalination of sea water or brackish
water, largely because of the development of membranes having an appreciable flux of highly desalinized water (4, 6). These high flux membranes, while ameliorating some problems, have emphasized others, notably concentration polarization problems. The bulk flow of brine normal to and toward the membrane carries with it water and salt; the salt is mostly rejected by the membrane. The resultant accumulaticn of salt a t the boundary layer near the membrane interface-Le., concentration polarization-becomes progressively higher until salt back-diffusion, and salt flow through the imperfectly semipermeable membrane equals salt carried by bulk flow to the membrane. Concentration polarization is deleterious because it causes decreased water flux, a decrease in degree of desalination, and possible precipitation of sparingly soluble salts. The extent of concentration polarization is recognized to be a function of both membrane properties and operating conditions, such as brine velocity, Reynolds number, etc. However, the quantitative influence of operating conditions on membrane performance has been difficult to measure experimentally because most desalination membranes have been flat, a geometry such that the influence of discontinuities at the sides and end of the membrane cannot be discounted. T o minimize these discontinuities, Sherwood (70) has employed a tubular membrane, mounted on a short porous cylinder rotating within a pressurized brine solution. The Reynolds number obtained from such a rotating cylinder is derived from the angular velocity and the radius of the rotating cylinder. The long round tube with internal brine flow is an ideal geometry for minimizing discontinuity effects. Furthermore the Reynolds number is calculated directly. A means has recently been reported of fabricating reverse osmosis desalination tubes for possible commercial application ( 3 ) . I t is the goal of this study to relate the performance (flux and desalination) obtained from such tubes to turbulent flow operating conditions. As a first step the experimental performances of tubes in daily use at the pilot plant in Coalinga, Calif., are compared herein with performances predicted by Sherwood (9) and Brian (7). The developments of these investigators have led to 122
IBEC PROCESS DESIGN A N D DEVELOPMENT
equations containing the salt concentration at the membrane solution interface, a position which is experimentally accessible only with great difficulty. Therefore, for the purpose of comparison with experimental results, performance equations are expressed herein in terms involving the readily measurable salt concentrations in bulk brine and in the desalinized water, and in particular, their ratio, defined as the desalination ratio. This term is of particular interest to the reverse osmosis investigator as a sensitive criterion of the membrane’s desalination capacity. I t was found useful in the derivation of these equations to utilize the salt permeability coefficient described by Merten (7). Derivation of Performance Equations
Concentration Polarization a n d Its Relation to Other Salt Concentration Terms. Concentration polarization is determined from a mass balance on the salt flow carried to the interface by brine bulk flow, by the diffusional back flow of salt, and by salt flow through the interface due to the fact that the membrane is imperfect. The concentration polarization ratio in the turbulent region is given by Brian (7) as:
and
where CB
= salt concentration in the bulk brine on the saline
side of the membrane, grams/cc. cw = salt concentration at the interface between the membrane and the brine, grams/cc. C W / C B = concentration polarization ratio C D = salt concentration in the desalinized water from the membrane, grams/cc.
F1
=
N,,
= = = =
UB
R ;D
water flux, c:c./sq. cm. sec. In the subsequent discussion, water flux is assumed equal to total flux, since the salt concentration in the total flux is low (dimensionless) Schmidt No. for salt diffusion bulk brine velocity, cm./sec. interfacial salt rejection Chilton-Colburn (dimensionless) mass transfer factor frequently used in turbulent flow. For round tubes j D =: f / 2 , where f is the friction factor, and is some function of Reynolds number. Following Shewood we have used the function of Drew, Koo, and McAdams (2)
When the membrane rejects all salts ( R = I ) , Equation 1 reduces to that given tiy Sherwood (9) :
is the osmotic pressure a t the membrane-brine interface, atm. A D is the osmotic pressure of the desalinized water, atm. A is the water permeability coefficient, cc./sq.cm. sec., atm. AW
The water permeability coefficient is fairly constant with pressure up to a critical pressure above which it may decrease due to membrane compaction. T h e coefficient is also a direct function of operating temperature. Equation 9 contains the difficultly measurable interfacial osmotic pressure, aw, due to concentration polarization. Therefore, we invoke Equation 6 where, since:
-
cw - - rw TB
CB
-=
exp K
(3)
CB
we have :
where for conciseness we have defined K, the concentration polarization exponent, as: (4) T h e concentration polarization ratio can be determined directly only with considerable difficulty because cW, the concentration at the interface, is difficult to measure. A term more useful for descrilbing membrane performance, and one which can be readily rneasured under operating conditions, is the desalination ratio, 23,) defined as: (5) The desalination ratio has the further virtue of describing the desalination capacity of a membrane in dimensionless form. Finally, the magnitude of D, is sensitive to differences in desalinizing capacity. The relation between the concentration polarization ratio and the desalination ratio is obtained by combining Equations 1, 2, 4, and 5, to give:
where rBis the bulk brine osmotic pressure, atm. This equation may be simplified by using Equation 5 to eliminate rD (where again T D / T ~ N C D / C B ) , to give the transcendental equation : F1
=
- TB
[
A
AP
(exp K) (l
-
$1
Water flux is a function of the membrane properties through the water permeability coefficient, A , of the boundary layer characteristics through K, and of feed brine concentration through rBand the desalination ratio, D,. Several limiting cases can be discerned from Equation 11. For a perfectly semipermeable membrane (Dl= rn ) : F1
=
A(AP
- i ~ exp g K)
F1
= AAP
(13)
FI
M e m b r a n e Performance as a Function of M e m b r a n e Properties and Oper,ating Conditions. I n the following derivations it is assumedl with Lonsdale et al. (5) that the water and salt fluxes are simply diffusional. Sherwood (70) and Michaels (8) have presented equations which allow for pore flow as well as simple diffusional flow, but the Coalinga pilot plant operating conditilons and experimental evidence therefrom, presented below, do not warrant use of the possibly more exact equations. WATERFLUX,F1. T h e water flux equation is: F1
=
A[AP
-
-
(rw
~ d ) ]
(9)
-+
1) :
Equation 14 can be rearranged from the definition of desalination ratio to be:
(7) and substituting Equations 5 and 6 to give, after simplifying:
(12)
For a completely nonselective membrane (D, = l), or for a pure liquid (rB= 0):
When concentration polarization is negligible (exp K
The relation between interfacial salt rejection, R, and desalination ratio is given by writing Equation 2 as:
(11)
A [AP -
(TB
- AD)]
(1 5)
Equation 14 or 15 is useful for evaluating A experimentally. The water flux is measured under high flow conditions such that exp K + 1. If a pure liquid is used, A can also be evaluated from Equation 13 under low flow conditions. DESALINATION RATIO,D,. Equation 5 is written:
Substitute Equation 6 :
Solve for D,:
where
AP is the hydraulic pressure drop across the membrane, atm. VOL. 6
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123
I n order to eliminate C W , the concentration at the brinemembrane interface, we consider the driving force for salt flux. According to Merten (7) the salt flux may be expressed as a function of concentration gradient:
where F z is the salt flux, grams/sq. cm. sec. B is the salt permeability coefficient, cm./sec. As discussed before, the use of Equation 19 implies that salt flux occurs through a simple diffusion mechanism. Therefore in this equation, only one coefficient occurs, analogously to Equation 9. The salt permeability coefficient is determined by membrane properties and by the nature of the ionic species being desalinized. Furthermore the coefficient may also be a direct function of temperature, as is the water permeability coefficient. When concentration polarization is negligible, cB and Equation 19 becomes: cW
Fa = B(CB -
(20)
CD)
Obviously, from values of A and B so determined, the validity of Equations 11 and 23 can be checked by making performance tests under a variety of operating conditions and comparing the fluxes and desalination ratios experimentally obtained with those predicted. This method of validation is especially suitable for laboratory tests, since concentration polarization can be controlled or virtually eliminated by varying brine velocity and/or tube diameter, and since other operating conditions can be varied independently over a wide range. I t is planned to conduct tests under such controlled conditions in a later part of this study. For a given membrane, values of A and B are appropriate only a t the operating pressure and temperature a t which they were determined, and for the ionic species being desalinized. Operating conditions which can be varied for given values of A and B include bulk brine salt concentration, bulk brine velocity, and tube diameter. These restrictions and limits suggest an alternate experimental means for examining the validity of Equations 11 and 23. Let Equation 23 be solved for B:
T o express D,in terms of measurable quantities, Equation 19 is solved for cW, and substituted into Equation 18 to give:
D, =
F2 fl BcD exp K
(21)
However, to a good approximation:
!! p F , CD
Substitute Equation 22 in Equation 21 to give:
D, =:
F1
~
B exp K
fl
The desalination ratio is a function of membrane properties through the salt permeability coefficient, B , of concentration polarization through K, and of water flux through PI. When concentration polarization effects are negligible (exp K -h 1):
D,-3
B
+1
Application and Validity of Equations
If the above developments are valid, Equations 11 and 23 can be used to predict performance of a given membrane under various operating conditions, once the permeability coefficients are determined. These coefficients can be calculated from Equations 14 (or 15) and 20 by performing a high brine velocity experiment such that the concentration polarization is negligible. (The value of A may also be determined at low brine velocities from Equation 13, if pure water is used,)
-% FILTER
10000 GPO FEEDBRINE
F1
B=
(0, - 1) exp K
B can be calculated from Equation 25 without the necessity of a high brine velocity experiment. Now for a given operating temperature and pressure and given ionic species in the brine, B should be invariant with the other operating changes cited above, if Equation 25 is valid. This alternative method of examining the validity of Equation 25 is especially appropriate for a number of tubes in series. Therefore, this method was used in conjunction with available experimental data from a pilot plant consisting of a number of such tubes in series. The plant has been in operation at Coalinga, Calif., since June 4, 1965. Experimental Results at Coalinga Pilot Plant
The Coalinga pilot plant, shown schematically in Figure 1 and pictorially in Figure 2, consists of 112 tubes in series, each tube being 10 feet long and nominally 1 inch in diameter. The plant operates at 41 atm. on feed brine having about 2500 p.p.m. of dissolved solids with the composition given in Table I. The feed brine input rate is 10,000 g.p.d. (gallons per day) from which nominally 5000 g.p.d. of fresh water is produced. Hence from one end of the plant to the other, the brine salt concentration is approximately doubled, while Reynolds number and brine bulk velocity are approximately halved. Furthermore the membranes are not all fabricated identically. A spectrum of membrane properties is attained in the Coalinga plant by varying the temperatures to which the membranes have been heated in hot water, the last step in the fabrication process. As described above, these changes are useful for examining the variation of plant performance with operating conditions, BACK PRESSURE REGULATOR
DESALINIZING SECTION
,-.
- /
TUBE STATION 112 . TUBEISTATION 1 1 1
CONCENTRATED BRINE 5000 GPD 4 0 5 0 4 7 0 0 PPM SALTS ~
2500 PPM SALTS
OPERATING PRESSURE,41 ATM DESALINIZED WATER 5000 GPD 1 5 0 . 3 0 0 P P M SALTS
Figure 1. 124
Flow diagram of Coalinga pilot plant
I&EC PROCESS DESIGN A N D DEVELOPMENT
(25)
14~r
96-981
I
,201
/
19-21
c
2
loot 00
384-86.
OPERATINGTEMPERATURE.29.C OPERATING PRESSURE,41 ATM
2-
97-89 13-15
I -
0
I
I
I
I
I
72
76
00
E4
E8
MEMBRANE H E A T I N G T E M P E R A T U R E , 'C
1.1 8.0 7.8 iron, p.p.m. 0.018 0.06 0.012 Nil Hydroxide, p.p.m. Nil Nil Boron, p.p.m. 2.15 3.50 2.25 Carbonates (Goa), p.p.m. Nil Nil Nil Bicarbonates (HCOJ, p.p,m, 161.7 315.2 24.4 Chlorides (CI), p.p.m. 262.4 517.1 14.5 Sulfates (SO*),p.p.m. 1260.5 2942.9 34.2 Nil Phosphates (PO,), p.p.rn. Nil Nil Silica (SiO,), 9.p.m. 49.2 92.8 8.4 Iron and alumina (RnOs),p.p.m. 1.2 2.8 0.8 .. Calcium (Ca), p.p.m. 128.1 29P.4 6.9 Magnesium (Mg), p.p.m. 89.0 199.1 1.0 Sodium (Na). D.D.m. 521.0 1168.0 66.0 Total d i s k l d sblids, p,p,rn. 2417.6 5592.8 220.8 Total hardness (as CaCOa), p.p.rn. 692.4 1511.1 25.2 Total incrustating solids, p,p.m, 742.8 1613.3 34.4 Free carbon dioxide, p.p.m. 5 6 1
Figure 3. Influence of membrane heatina temoerature on membrane tube performance
~
and the validity of Equation 25. Figure 3 shows plant performance at various tube stations as a function of membrane heating temperature, and Figure 4 shows B, obtained from the insertion of experimental data into Equation 25, as a function of operating conditions, membrane heating temperature being a parameter. As can he seen in Figure 4, the salt permeability coefficientwas relatively invariant with position in the plant in spite of variation of operating conditions, approximate values of which are given on the abscissa of Figure 4 and in Table 11. Although the range of operating conditions was narrower than desired, the relative constancy of the B coefficient may be regarded as support for Equation 25 and therefore of the developments of Sherwood, Brian, and Merten, from which the equation was derived. Without the introduction of the concentration polarization exponent, the calculated values ofB at a single membrane heating temperature would have varied from each other considerably more than shown in Figure 4. In Figure 5, the salt permeability coefficient is given as a function of membrane heating temperature. This figure also
r
,
MEMBRANE HEATINTEMPERATURE.OC
TUBE TATION
__
._ I"
C I?
Cg BULK ERlNE SALT CONCENTRATION. PPM
2.380 IO0
~
uB
;E:;;INEVELOClTY,
B,O€O
NRL REYNOLDS NUMBER
,0029
j,
CWILTOY-COLEURN j - FICTOR
1,
3,480 68
19,WO 0.0032
AVERAGE
Figure 4. Influence of operating tions on salt permeability coefficient VOL 6
NO. 1
JANUAna
l l y l
,-.,
Table II. Experimental and Calculated Data
Operating temperature, 29 C. Operating pressure, AP, 41 atm. Schmidt number, A'sse,585 Performance Desalinized water
Membrane tube internal diameter, D , 2 . 2 9 cm. Kinematic viscosity, v , 8 . 2 x 10-3 sq. cm./sec. Average diffusion coefficient, D,, 1 . 4 X lod6 sq. cm./sec.
O
Membrane Heating Temp. OC. 72
Tube Stations Date of Included Data (7965) in Data 6/25 1-3 8/31 84-86 76 6/25 7-9 8/31 87-89 80 6/25 13-15 8/31 90-92 84 6/25 16-18 8/31 93-95 88 6/25 19-21 8/31 96-98 a Calculated from Van't H o f s
Bulk Brine Operating Conditions Salt concn. CB, Osmotic g./cc. pressure,a Velocity,
Permeability Coeflcients Dimensionless Groups Ratio Chilton- Concn. water/ DesalinaColburn polariza- Water, salt, A , em./ Salt, B , sq. cm. tion factor. tion sec. ratio, x 106 = T B , A/B, Reynolds jD, exponent, see. atm. cm./sec. UB, x 105 X IO5 atrn.-l p.p.m. atm. cm./sec. NO., hTEe X lo3 K X lo3 D, 42 0.15 2.48 4.5 2180 0.97 114 0.53 6.3 2.9 31,000 42 0.17 3180 1.70 2.65 3.8 73 20,000 0.79 7.0 3.2 2300 1.0 2.18 8.2 18 0.31 104 29,000 2.9 0.51 5.5 3300 1.8 70 2.18 6.1 22 0.26 19,000 3.2 0.68 5.8 2410 1.69 16.3 1.1 98 7.3 0.59 28,000 2.9 0.42 4.3 9.1 0.51 1.75 11.8 3490 1.9 67 19,000 0.57 4.6 3.2 1.50 30.7 2470 1.1 3.5 1.1 98 26,000 3.0 0.36 3.8 1.38 22.2 3630 2.0 64 4.1 0.90 0.45 3.7 18,000 3.3 1.02 94.2 2530 0.85 3.1 1.1 95 2.6 3.0 0.25 26,000 3810 0.95 136 2.1 64 18,000 0.51 4.9 0.32 2.5 3.3 law and interpolation to Libtain concentration at tube station indicated. $ux, F,~.cc./
,
I
I t can be seen from Figure 5 that the rate of decrease of A with membrane heating temperature is much less than that of B. This fact accounts for the great improvement in membrane selectivity with increased membrane heating temperature, and can be understood quantitatively by considering the influence of A and B on the desalination ratio when concentration polarization effects are absent. Equation 15 is substituted into Equation 24 to give:
As can be seen, the desalination ratio is linear with the ratio A / B , which may be considered an index of the intrinsic desalinizing capacity of the membrane. A similar equation has been presented by Lonsdale, Merten, and Riley ( 5 ) . Conclusions
Equations have been developed from the analyses of Sherwood, Brian, and Merten, describing the key membrane performance quantities, desalinized water flux and desalination ratio, as functions of the membrane permeability coefficients, A and B , and of turbulent flow operating conditions in tubes. The validity of the equations should ultimately be tested by reverse osmosis experiments for determination of the membrane permeability coefficients under conditions where concentration polarization is negligible, after which experiments should be made under a variety of operating conditions such that observed fluxes and desalination ratios can be compared with those calculated from the equations containing these permeability coefficients. As a preliminary to the above experiments, experimental data from the Coalinga tubular pilot plant have been utilized to examine the equation relating desalination ratio to membrane coefficients and operating conditions. The experimental results appeared to support the equation.
F
68
72
76
80
04
88
MEMBRANE HEATING TEMPERATURE,OC
Figure 5. Influence of membrane heating temperature on permeability coefficients
shows values of the water permeability coefficient, A , obtained from insertion of Coalinga experimental data into Equation 11. These data are given in Table 11, and as shown there, A was also fairly constant with position in the plant. However, the osmotic pressure of the bulk brine, T ~is ,small throughout the Coalinga plant compared to AP, and the experimental values of exp K are always less than 3. Thus, at every station :
Acknowledgment
Under these conditions, variations in operating conditions available at Coalinga could have little influence on the value of the water permeability coefficient, and are therefore not useful for evaluating the validity of Equation 11. 126
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
This study was supported by funds provided by the California State Legislature. They are administered through the University of California's Statewide Water Resources Center located on the Los Angeles Campus of the university.
The Coalinga plant was designed by Edward Selover as an efficient tool for conducting individual tube experiments. Harry Baldwin obtained all the data reported on the Coalinga plant, which he operates. T h e city officials of Coalinga have been most cooperative, in particular Glenn Marcussen, City Manager, and Reginald Phelps, Director of Public Works. Thanks are expressed to Harry Lonsdale of General Atomics for appropriate suggestions on the inclusion of salt flux and the salt permeability Coefficient in the development of the equations.
water permeability coefficient, cc./sq. cm. sec. atm. salt permeability coefficient, cm./sec. cB salt concentration in bulk brine on saline side of membrane, grams/cc. cg = salt concentration in desalinized water from membrane, grams/cc. cw = salt concentration at interface between membrane and saline solution, grams/cc. D = membrane tube internal diameter, cm. D , = desalination ratiio, C B / C D D , = average molecular diffusion coefficient of salt in brine, sq. cm./sec. f = friction factor F1 = water flux, cc./aq. cm. sec. Used interchangeably with total flux, F = salt flux, grams/’sq. cm. sec. F1 j , = Chilton-Colburn mass transfer factor, koNsoO 6 7 / u B . Determined in this paper from j g = f / 2 , where f is function of iVRegiven by Drew, Koo, and McAdams (2) ko = mass transfer coefficient, cm./sec. ATR, = Reynolds number, D U B / V Nsc = Schmidt number, Y / D S
B
ug
K Y
?TD AW
hydraulic pressure drop across membrane, atm. interfacial salt rejection, 1 - c ~ / c w bulk brine velocity, cm./sec. concentration polarization exponent, F~Ns,O.G~/UB~O kinematic viscosity, sq. cm./sec. osmotic pressure in bulk brine on saline side of membrane, atm. = osmotic pressure in desalinized water from membrane, atm. = osmotic pressure in brine a t interface between membrane and saline solution, atm. =
= = = = =
Literature Cited
Nomenclature
A
AP
R
= = =
(1) Brian, P. L. T., “Influence of Concentration Polarization on Reverse Osmosis System Design,” First International Symposium on Water Desalination, Washington, D. C., Oct. 3-9, 1965. (2) Drew. T. B.. Koo. E. C..’ McAdams. W. H.. Trans. Am. Znst. ’ Chem. En.. 28,‘56 (1933). (3) Loeb, S., Desalination 1, No. 1, 35 (April 1966). (4) Loeb, S., Sourirajan, S., Advan. Chem. Ser., No. 38, 117 (1962). (5) Lonsdale, H. K., Merten,. U.,. Riley, . . R. L., J . Abbl. .. Polymer kci. 9, 1341’(1965).’ (6) Manjikian, S., Loeb, S., McCutchan, J. W., “Improvement in Fabrication Techniques for Reverse Osmosis Desalination Membranes,” First International Symposium on Water Desalination, Washington, D. C., Oct. 3-9, 1965. ( 7 ) Merten, U., Lonsdale, H. K., Riley, R. L., Znd. Eng. Chem. Fundamentals 3, 210 (1964). (8) Michaels, A. S., Bixler, H. J., Hodges, R. M., Jr., J . Colloid Sci. 20. 1034 (1965). ( 9 ) Sherwood, T. K.,’ Brian, P. L. T., Fisher, R. E., Dresner, L., Znd. Eng. Chem. Fundamentals4, 113 (1965). (10) Sherwood, T. K., Brian, P. L. T., Sarofim, A. F., “Research on Saline Water Conversion,” Dept. Chem. Engr., M.I.T. Rept. 295-8 (Dec. 21, 1965).
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RECEIVED for review April 18, 1966 ACCEPTED August 5, 1966
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BODMAN AND D. H. CORTEZ
Xchool of Chemical Engineering Practice, Massachusetts Institute of Technology, American Cyanamid Go., Bound Brook, N . J .
Unsteady-state heat transfer experiments were carried out in a jacketed, agitated, glass-lined vessel using as heat transfer media both single-phase and two-phase fluids: water, toluene, lubricating oil, watertoluene mixtures, and ,water-lubricating oil mixtures. Data were first obtained for the single-phase fluids and were found to agree with those of previous investigators. The rate of heat transfer to two-phase, agitated fluids was then measured and compared with the results for single-phase heat transfer. Several correlation techniques for the two-phase heat transfer results were attempted; these differed in the methods used to compute the physical properties of the two-phase mixtures. The use of bulk, volume-average properties yielded the most consistent correlation of the data. Gravitational effects at low agitator speed are discussed in some detail.
LAss-lined, jacketed kettles have been in common use for
6 many years throughout the chemical process industry. During this time, several investigators have studied heat transfer rates to single-phase liquids in jacketed, agitated vessels (7-7, 9). Results of these investigations are in reasonable agreement and they are summarized in a comprehensive
review by Uhl and Gray (72). However, the rate of heat transfer to two-phase mixtures in agitated vessels has received only cursory examination. Cummings and West (7) measured heat transfer rates for water-mineral oil mixtures in an agitated kettle equipped with a cooling coil. Because of the limited amount of two-phase data which were obtained by Cummings VOL. 6
NO. 1
JANUARY 1967
127
