Nomenclature
literature Cited
D
Browne, C. A., “Handbook of Sugar Analysis,” Table I, Wiley, New York, 1912. International Critical Tables, Vol. 111, p. 79, McGraw-Hill, New York, 1928. Kelly, F. H. C., J . Appl. Chem. (London) 4, 411 (1954). Meyer, W., Olsen, R. S.,Kalwani, S.L., IND.ENG.CHEM.PROCESS DESIGN DEVELOP. 6, 55 (1967). Plato, F., Domke, J., Harting, H. Z., Ver. deut. Zucker-Ind. 50, 1079 (1900). Shurts, E. L., Ph.D. thesis, University of Michigan, Ann Arbor, 1955. Shurts, E. L., White, R. R., A.I.Ch.E. J . 3, 183 (1957). RECEIVED for review February 9, 1968 ACCEPTED May 20, 1968
Do S SR
X
= = = =
XR
= =
p ps
= =
AV =
diameter of resin bead in sugar-salt solution diameter of bead in water sucrose concentration in external solution, wt. sucrose concentration within bead on resin-free base, wt. yo NaCl concentration in external solution, wt. yo NaCl concentration within bead on resin-free base, wt. 7 0 density of sugar-salt solution a t 25’ C., g./ml. density of solution containing same yo sucrose but no NaC1 a t 25’ C., g. ml. decrease in total volume on mixing resin and solution, % initial volume air-dry resin
S T A G E W I S E R E V E R S E OSMOSIS PROCESS DESIGN SHOJl K I M U R A , * S . SOURIRAJAN, AND H A R U H I K O O H Y A
Division of Applied Chemistry, National Research Council of Canada, Ottawa, Canada
Reverse osmosis i s treated as a general separation process which can be operated in stages, if necessary. Equations developed for stagewise reverse osmosis process design are based on the Kimura-Sourirajan analysis of the reverse osmosis data for water and solute transport through the Loeb-Sourirajan type porous cellulose acetate membranes, The analysis involves the specification of the membrane in terms of the pure water permeability constant, A, and the solute transport parameter, (DA.w/K6). Expressions connecting the concentrations of the feed solution entering and leaving the unit stage on the high pressure side of the membrane, and of the membrane-permeated product solution leaving the atmospheric side of the membrane are derived as functions of A, (Da.BI/KG), operating pressure, molar density of the solution, average mass transfer coefficient, and volumetric fraction of product recovery. Following the formalism of the multistage distillation process, the cascade theory i s applied to the multistage reverse osmosis process, and expressions for the minimum number of stages and minimum reflux ratio are derived. The ideal cascade theory is then used to establish a practical criterion for multistage reverse osmosis process design. To minimize concentration polarization effects on product concentration, membrane area per unit product rate, and power consumption due to frictional pressure drop, a unit stage i s considered as a combination of several inner stages connected in series. Assuming complete mixing of the feed solution between adjacent inner stages, equations are developed for unit-stage and two-stage reverse osmosis process design. Application of the design equations i s illustrated by a set of calculations with particular reference to saline water conversion.
HE reverse osmosis process can be operated as either a Tsingle-stage or multistage process where the membranepermeated product from one stage constitutes the feed for another stage. The general effect of concentration polarization is to bring about a continuous change in product rate and solute separation in the direction of feed flow from the start to the end of the reverse osmosis operating unit. Consequently a multistage operation may be necessary for at least some applications; it may also be necessary to build a number of inner stages in series within each primary stage to break the boundary concentration profile by effecting complete mixing of the feed fluid between every two adjacent inner stages.
Present address, Department of Chemical Engineering, University of Tokyo, Tokyo, Japan.
Thus whatever be the number of primary stages, and inner stages within each primary stage needed for a particular application, stagewise analysis offers a general approach to reverse osmosis process design. Some equations governing stagewise reverse osmosis process design are developed below with particular reference to saline water conversion. These equations are based on the KimuraSourirajan analysis of the reverse osmosis data reported earlier (Kimura and Sourirajan, 1967, 1968a) for water and solute transport through the Loeb-Sourirajan type porous cellulose acetate membranes. This analysis, which follows from an application of the simple film theory and pore diffusion model for reverse osmosis transport, leads to the specification of the membrane in terms of its pure water permeability constant, A , and the solute transport parameter, ( D A M / K 6 ) . BothA and VOL. 8
NO. 1
JANUARY 1 9 6 9
79
(DA,/K6) are dependent on the porous structure of the membrane surface and hence they are different for different membranes; both are functions of operating pressure, and in addition, (DAAv/K8)depends on the chemical nature of the solute. At a given operating pressure, the value of ( D A M / K 8 ) is independent of feed concentration and feed flow rate for sodium chloride and many other inorganic and organic solutes. Basic Transport Equations
For porous cellulose acetate membranes which have a preferential sorption for water from aqueous feed solutions, the Kimura-Sourirajan analysis gives rise to the following basic equations for the solvent and solute transport through the membrane at a given operating procedure.
where u w is the fluid velocity component in the j-directionLe., the direction perpendicular to the membrane surface. Equating the right side of Equations 8 and 10.
Equation 11 shows that for any given solution system, C A and c A 3 (hence X.42 and X A 3 ) are uniquely related for specified at a given operating pressure. This values of A and (DA.>~/KS) has been illustrated experimentally for a number of membranesolution systems (Kimura and Sourirajan, 196813, d ; Sourirajan and Kimura, 1967). Eliminating CA2 from Equations 9 and 10 using Equation 11, C A I may be expressed as CAI
SOLVEKT TRANSPORT
(12)
cA3q
where
NE = A[P - T(XA2) f T(XA3)l
(1)
SOLUTETRANSPORT (3) For the present analysis, the following simplifying assumptions are made : The molar density of the solution is essentially constant-Le., CI = c z = c 3 = c-the osmotic pressure of the solution is proportional to the mole fraction of solute-Le., ~ ( X A =) BXA-and the solute flux across the membrane is h r g or X A 1. small compared to solvent flux-i.e., N A All these assumptions are valid for the system sodium chloride% ' water at least up to a concentration of 1.OM ( ~ 5 . 5 weight 2 NaCl), and can be considered acceptable for engineering calculations up to a concentration of 2.OM ( ~ 1 0 . 4 7weight % NaCI). They do not restrict the scope of the following analysis, but they simplify the equations involved in illustrating the effect of process and design variables relating to sea water and brackish water conversion. Defining
-
’
#
I
SUBSCRIPTS 1 2
= = = =
i orj i,m
stage stage stage stage
1 2 i or j , respectively i, inner stage m
SUPERSCRIPTS = channel inlet = average over X
literature Cited
Benedict, M., Pigford, T. H., “Nuclear Chemical Engineering,” p. 384, McGraw-Hill, New York, 1957a. Benedict, M., Pigford, T. H., “Nuclear Chemical Engineering,” p. 385, McGraw-Hill, New York, 1957b. Benedict, M., Pigford, T. H., “Nuclear Chemical Engineering,” p. 386, McGraw-Hill, New York, 1957c. Bray, D. T., Menzel, H. F., Office of Saline TVater, U. S. Department of the Interior, TVashington, D. C., Research and Development Progress Rept. 176 (1966).
Johnson, K. D. B., Grover, J. R., Pepper, D., Desalination 2, 40 (1967). Kimura, S., Sourirajan, S., A.Z.Ch.E. J . 13, 497 (1967). Kimura, S., Sourirajan, S., IND. ENG. CHEM.PROCESS DESIGN DEVELOP. 7,41 (1968a). Kimura, S., Sourirajan, S., IND. ENG. CHEM.PROCESS DESIGN DEVELOP. 7,197 (196813). Kimura, S., Sourirajan, S., IND. ENG. CHEM.PROCESS DESIGN DEVELOP. 7, 539 (1968~). Kimura, S., Sourirajan, S., IND. END. CHEM.PROCESS DESIGN DEVELOP. 7, 548 (1968d). Knudsen, J . G., Katz, D. L., “Fluid Dynamics and Heat Transfer,’’p. 100, McGraw-Hill, New York, 1958a. Knudsen, J. G., Katz, D. L., “Fluid Dynamics and Heat Transfer,” p. 207, McGraw-Hill, New York, 195813. Sourirajan, S., Govindan, T. S., First International Symposium on Water Desalination, Washington, D. C., October 1965, Office of Saline IYater, U. S. Department of the Interior, Vol. 1, pp. 251-74. Sourirajan, S., Kimura, S., IND. ENG. CIIEM.PROCESS DESIGN DEVELOP. 6 , 504 (1967). RECEIVED for review January 29, 1968 ACCEPTED July 1, 1968 Issued as N.R.C. No. 10450
S E P A R A T I O N OF W A X A N D OIL BY CENTRIFUGATION NORMAN N. L I ESSOResearch and Engineering Go., Linden, N . J . 07039
W a x and oil are separated b y Centrifugation. Chill rates more than 100 times those used in conventional processes can b e employed to achieve large capacity. Plate-type crystals give highest initial settling rate and w a x compaction. Crystal needles can b e changed into aggregates for improving centrifugation efficiency b y using modifiers.
for dewaxing by freezing, the wax crystals are It has been customary to add a crystal modifier (crystal-modifying surfactant) to the oil before freezing and to use a high solventdilution ratio (Chamberlin et al., 1949; Frolich, 1935; Moser, 1938; Selson, 1958; Salmon and Pullen. 1964). Using crystal modifiers causes Ivax crystals to aggregate and thus improves the filtration, and adding solvent (or recycled product oil) to the waxy oil decreases the viscosity of the wax-oil mixture for easy filtration. The purpose of this bvork was to study the separation of wax and oil by centrifugation, and specifically, to examine the effects of chilling rate, crystal modifier concentration, and solvent dilution ratio (volume ratio) on centrifugation efficiency in the dewaxing of Solvent 100 Neutral (SIOON). A major advantage of centrifugation over filtration is that high chill rate can be used to achieve large process capacity. For filtration, it is usually necessary to control the chill rate to a very low value in order to obtain large wax crystals. For example, in ketone de\vaxing. a chill rate of l o to 2’ F. per minute is used (Nelson, 1958), Lvhereas in the process of direct chilling in combination with centrifugation (Li, 1968; Li and Torobin, 1967; Torobin. 1966) as illustrated by Figure 1, the chill rates can be higher than 100’ F. per minute and still produce wax crystals large enough to be separated from oil by centrifugation. T h e centrifuge can be used for viscous lubricating oils, because N A PROCESS
I usually separated from other liquor by filtration.
the viscosity of the oil can always be adjusted by solvent dilution. T h e temperature difference between the product pour point and the dewaxing temperature is at least as good as those obtainable in the current filter press operations. T h e basic factor that affects the centrifugation efficiency is the shape, o r “habit,” of the crystals (Chamberlin et al., 1949; Nelson, 1958). A supplemental study was therefore carried
-pjry: COOLANT
WAXY SLURRY
(CONTINUOUS PHASE)
D E W A X E D OIL
CEYTRIFUGE WAX
CHILLING
TOWER
COOLANT
1 I
WAXY OIL + SOLVENT (DISPERSED PHASE)
Figure 1. Dewaxing by continuous direct chilling and centrifugation VOL 8
NO. 1
JANUARY 1 9 6 9
89
