668
Ind. Eng. Chem. Fundam. 1986, 2 5 , 668-677
Nomenclature c = solute concentration, dimensionless F =
solute concentration in the inner domain, dimensionless
c, = solute concentration in the outer domain in phase i (i = 1, 2), dimensionless c’ = solute concentration, mol/cm3
c( = characteristic solute concentration, mol/cm3 D = solute diffusivity, dimensionless D’ = solute diffusivity, cmz/s D, = solute diffusivity in the outer domain, dimensionless D,’ = solute diffusivity in phase i (i = 1, 2), cm2/s E = interaction energy divided by RT, dimensionless E, = asymptotic limits of E in the phase i (i = 1, 2), dimension 1ess i = solute flux, dimensionless j = solute flux in the inner domain, dimensionless j , = solute flux in the outer domain in phase i (i = 1, 2), dimensionless j ‘ = solute flux, mol/(cm2 s) J(O)= integration constant, dimensionless K = equilibrium partition coefficient, dimensionless L = macroscopic length scale, cm L, = distance of the bounding surface from the interface in phase i (i = 1, 2), cm m = exponent in eq 15, dimensionless R = gas constant, erg/(mol K) R’ = total resistance, s/cm R,’ = resistance in phase i (i = 1, 2), s/cm R{ = interfacial resistance, s/cm RI = interfacial resistance, dimensionless t = time, dimensionless t’ = time, s T = temperature, K LZ = dummy integration variable, dimensionless y = coordinate normal to the interface, dimensionless y’ = coordinate normal to the interface, cm = coordinate normal to the interface in the inner domain, dimensionless Greek Letters d = parameter defined in eq 5 , dimensionless K~ = constant in eq 15 for phase i (i = 1, 2), dimensionless = microscopic length scale, cm
Superscripts
’ = dimensional quantities k = perturbation quantities ( k = 1, 2, ...) Subscript
i
=
denotes bulk phase (i = 1, 2)
Literature Cited Blank, M. J . Phys. Chem. 1964, 6 8 , 2793. Bockman, D. D. Ind. Eng. Chem. Fundam. 1969, 8 , 77. Brenner, H.; Leal, L. G. AIChE J . 1978a, 2 4 , 246. Brenner, H.; Leal, L. G. J . Colloid Interface Sci. 1978b, 6 5 , 191. Brenner, H.; Leal, L. G. J . Colloid Interface Sci. 1982. 88, 136. Brown, A. H. Br. Chem. Eng. 1965, 10,622. Carey, B. S.; Scriven, L. E.; Davis, H. T. AIChE J . 1980, 26, 705. Cullen, E. J.; Davidson, J. F. Chem. Eng. Sci. 1956, 6 , 49. Davies, J. T. I n Advances in Chemical Engineering;Drew, T. B., Hoopes. J. W., Jr., Vermeulen, T., Eds.; Academic: New York, 1963; VoI. IV, pp 1-50. Davies, J. T.; Myers, G. R. A. Chem. Eng. Sci. 1961, 16, 5 5 . Davies, J. T.; Rideal, E. Interfacial Phenomena; Academic: New York, 1961. Dickinson. E. J . Colloid Interface Sci. 1978, 6 3 , 461, England, D. C.; Berg, J. C. AIChE J . 1971, 17, 313. Falls, A. H.; Scriven, L. E.; Davis, H. T. J . Chem. Phys. 1983, 78, 7300. The Scientific Papers of J . Williard Gibbs; Longmans Green: London, 1906; VOl. I . Goodrich, F. C. I n The Modern Theory of Capillarity; Goodrich, F. C., Rosanov, A. J., Eds.; Akademi-Verlag: West Berlin, 1981a; pp 19-34. Goodrich, F. C. Proc. R . SOC.London, A 1981b, 3 7 4 , 341. Healy, R. N.; Reed, R. L. SOC.Pet. Eng. J . 1974, 491. Hutchinson, E. J . Phys. Colloid Chem. 1948, 52, 897. Larson, R. S. J . Colloid Interface Sci. 1982, 8 8 , 487. Lee, S.H.; Chadwick, R. S.; Leal, L. G. J . FluidMech. 1979, 9 3 , 705. Lindland, K. P.: Terjesen, S . G. Chem. Eng. Sci. 1956, 5 , 1. Ly, L-A. Nguyen; Carbonell, R. G.; McCoy, B. J. AJChE J . 1979, 25, 1015. Mahanty, J.; Ninham, 8. W. Dispersion Forces; Academic: New York, 1976. Milliken, J. D.; Zollweg, J. A.; Bobalek, E. G. J . Colloid Interface Sci. 1980, 77, 41. Mudge, L. K.;Heideger, W. J. AIChE J . 1970, 16, 602. Nayfeh. A. H. Introduction to Perfurbation Techniques; Wiley: New York, 1980. Plevan, R. E.; Quinn, J. A. AIChE J . 1966, 12, 894. Scott, E. J.; Tung, L. H.; Drickamer. H. G. J . Chem. Phys. 1951, 79, 1075. Shaeiwitz, J. A.; Raterman. K. T. Ind. Eng. Chem. Fundam. 1982, 2 1 , 154. Ward, A. F. H.; Brooks, L. H. Trans. Faraday SOC. 1952, 4 8 , 1124. Ward, W. J.; Quinn, J. A. AIChE J . 1965, 7 1 . 1005. Whitaker, S.; Pigford, R. L. AIChE J . 1966, 12, 741.
Received for review September 13, 985 Revised manuscript received July 10, 986 Accepted July 17, 986
Surface Fractionation of Multicomponent Oil Mixtures James W. Peterson and John C. Berg’ Department of Chemical Engineering, BF- 10, University of Washington, Seattle, Washington 9 8 195
An investigation is made of fractionation which occurs in oil mixtures as they spread over water under the control of surface forces. Its Occurrence is suggested in the literature, but the evidence is scant and fragmentary. Carefully controlled experiments using mixtures of poly(dimethylsi1oxane) and tetradecane were undertaken to verify or disprove the existence of the phenomenon. The results provide positive evidence of fractionation and indicate that a preferential spreading mechanism is involved. Additional fractionation measurements are made of a mixture of toluene, octane, and decane. This system also exhibits fractionation trends, indicating preferential spreading. A mathematical model is developed which describes the process as a multistage, batch-charged separation and yields good fits to the fractionation data. Oil film thickness profiles needed in the model were obtained by a new method using polychromatic interference fringes.
Introduction
It has been suggested (e.g., Phillips and Groseva, 1975; Fazal, 1975) that a separation process occurs during the
* To whom correspondence should be addressed. 0196-4313/86/1025-0668$01.50/0
surface-tension-controlled spreading of oil mixtures on water. This “surface fractionation” occurs as some components of the mixture apparently spread faster and farther than others. There are numerous possible causes for the existence of variations in the local composition of a spreading oil film. By limiting our interest to calm water
0 1986 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
surfaces and relatively short times and by ruling out the possibility of chemical or biological degradation, we can reduce the list of important possibilities to three: (1) evaporation, (2) dissolution into the subphase, and (3) preferential spreading. Until a few years ago, evaporation and dissolution were considered the sole causes of such variations. Then Berridge et al. (1968) reported observations of thin films or “flashes”, presumably composed of surface-active components, spreading much faster than the bulk volume of the crude oils which they were studying. While others have since made passing mention of a separation based on differential spreading, only the studies of Phillips and Groseva (1975) and Fazal (1975) deal with the subject directly. Phillips and Groseva (1975) described radial spreading experiments which they conducted with 0.1 mL of equimolar toluene, n-octane, .ad n-decane spreading on water in a shallow dish. The oil system was specifically chosen to place the anticipated preferential spreading effects in opposition to those expected from evaporation and dissolution. Although the analysis of the spreading samples was rudimentary, the trends of the results suggested the existence of horizontal concentration gradients. Toluene was in preponderance in the outer regions of the oil film and decane near the center. Octane appeared to have a maximum concentration at intermediate radii. These qualitative results were interpreted to indicate that the spreading effects controlled the local concentration and were thus of greater magnitude than the evaporative and solubility effects. Fazal’s work (1975) was similar in approach. While more attention was given to the details of the experimental method, his selection of equivolume p-cymene, n-octane, and n-decane lost the earlier workers’ advantage of counterdirected spreading and evaporative effects. The results display trends like those of the earlier study, with toluene being replaced with the less volatile p-cymene. However, no conclusions regarding preferential spreading can be inferred because the spreading effects cannot be differentiated from those due to evaporation or dissolution. In both of the works cited the qualitative nature of the experiments precludes definite interpretation of the results. Doubt is cast on the conclusions by several weaknesses in the methods of preparation and analysis. The evidence presented in favor of surface fractionation by preferential spreading is thus inconclusive. The primary objective of the present work is to establish, by a process of careful observation and quantitative measurement, whether or not surface fractionation can occur by a mechanism of preferential spreading. During the experimental development, attention is given to identifying relationships between the observed fractionation and the properties of the individual components of the oil mixtures. The earlier studies proposed that the spreading properties of the pure components should control the fractionation process. This and other possibilities are considered. Additional objectives are the development of a practical descriptive model of surface fractionation effects and the elucidation of mechanistic details of the fractionation process. Materials and Methods Oil and Water. As the objectives of the experiments were to measure quantitatively the effects of preferential spreading, means were sought to eliminate or reduce the impact of the competing effects of volatility and solubility. A binary oil mixture was desired which was composed of readily analyzed, nonvolatile oils of similar density, mis-
669
cible with each other but each highly insoluble in water, and possessed of opposing spreading characteristics. Many possibilities for a nonspreading oil existed. Any of the CI4 to CI6 alkanes would meet the requirements. Tetradecane was selected because it was readily available in pure form. The selection of a spreading component, however, was not as simple. None of the obvious choices, such as alkanes or other common crude oil components, possessed the required positive spreading coefficient along with low volatility and low solubility in water. A readily available oil which did meet all of the criteria was poly(dimethy1siloxane) (PDMS), a silicone oil. An interesting additional feature of PDMS as the spreading component was the capability of choosing among compounds having widely different viscosities while maintaining all other physical characteristics of the oils nearly constant. The selected oils, tetradecane from Kodak and PDMS (in 5-, 50-, and 500-cSt grades) from Dow Corning, were carefully characterized with respect to surface and interfacial tensions and densities. The absence of a published standard of purity or cleanliness for the PDMS required the precaution of filtering it through packed columns of activated Florisil to remove any trace surfactants. The Florisil used in the columns was activated by heating to 675 “C for 60 h, and the glass columns were thoroughly cleaned and rinsed with purified water before and after each use. After these preparations, measurements were made of the pure oils, of each one after saturation with water, and of mixtures of each of the three grades of PDMS with tetradecane over a wide range of proportions. A Mettler/Paar Model DMS45 density meter was used for density measurements at room temperature (19 “C) and at 35 “C, and constants were determined for an assumed inverse linear dependence of density on temperature. Surface tensions were measured at room temperature by using the Wilhelmy slide method. Interfacial tensions a t room temperature were determined by the drop-weight method. In addition to the work done with the nonvolatile PDMS-tetradecane system, experiments were conducted with the volatile system studied earlier by Phillips and Groseva (1975): toluene, n-octane, and n-decane. Toluene used in the experiments was chromatographic grade, obtained from Burdick and Jackson. The octane and decane were standard analytical grades from MCB and Kodak, respectively. Characterization of these oils and certain mixtures of them for surface and interfacial tensions and densities was done as described for the nonvolatile oils. The water used in the experiments also required characterization. Three different grades of water were used during the course of the study. Tap water was used for all noncritical washing. Deionized water was treated by filtration, demineralization, and reverse osmosis and typically contained an ionic equivalent of less than 10 ppm NaC1. Stored in polyethylene containers, this water was used for noncritical dilutions and rinses during lab procedures. Purified water was deionized and subsequently double-distilled. Stored only in acid-cleaned glass containers, this water routinely possessed a surface tension in excess of 72 dyn f cm. Purified water was used for all washing, rinsing, and dilutions for procedures and equipment that were sensitive to surfactant contamination. Nonvolatile Fractionation Experiments. The experimental apparatus designed for fractionation studies consisted of a circular nonwetting polypropylene dish 38 cm in diameter and 2 cm deep, as shown in Figure 1. A set of five stainless steel rings fit into the dish, dividing it into six concentric regions, from each of which a sample
870
Ind. Eng. Chem. Fundam.. Vol. 25, No. 4. 1986
I
I
,
I
Figure 1. Fractionation apparatus.
was taken. The rings were 3.9 cm tall, constructed of 24-gauge sheet stainless steel, and ranged in diameter from 6.5 to 32.5 cm in 6.5-cm increments. The rings were friction-fit into a round plate of acrylic plastic which was in turn suspended from an arm-and-cam device. The cam raised and lowered the plate and rings while the arm held them in a plane parallel to the surface of water in the dish. The arm also pivoted, allowing the acrylic plate to be swung out of the way so that the dish was accessible. The surfaces of the rings were plasma-coated with a polymer of hexafluoroethane, courtesy of the 3M Co., to discourage wetting by the oil mixtures. In preparation for an experiment, all equipment was thoroughly cleaned. The dish was filled with purified water such that the miniscus stood above the lip of the dish. A Teflon bar was used to sweep the surface of the dish twice to remove any contaminants. As each sweep was made, the buildup of dust particles and contaminants in front of the bar was removed by aspiration. After the second sweep, the aspiration was continued in order to lower the water level in the dish, preventing overflow problems later in the procedure. The acrylic plate with steel rings attached was then suspended above the center of the waterfilled dish, with the bottoms of the rings approximately 1 em above the water. A small sample of a PDMS-tetradecane mixture ranging from 20 to 100 pL was deposited on the water surface by a glass microliter syringe via Teflon and stainless steel tubing. The tip of the stainless steel tubing was lowered through a hole in the center of the acrylic plate to a height of 1-2 mm above the water surface. The end of the tubing was ground a t an angle to promote the detachment of drops. Oil deposition took place over a period of about '/, 8, care being taken that the oil did not form a jet or cause undue disturbance of the water surface. After a short period of spreading, from 3- to 20-9 duration, the suspended rings were abruptly and simultaneously lowered by the cam through the water surface until they rested on the bottom of the dish. Immediately af-
terward, the surfaces of the sample regions were flooded with chromatographic-grade toluene, applied via polypropylene wash bottles. This was found to be necessary to prevent significant losses by evaporation of even the nonvolatile mixtures. The steel rings were then detached from the acrylic plate, the plate swung out of the way, and the toluene-diluted oil samples collected from the water surface of each sample region by aspiration. To assure quantitative sample collection from each region, the vertical ring walls were rinsed at least twice with small additional amounts of toluene from the wash bottles. Satisfactory collection from all six regions typically required 1h a n d resulted in toluene-diluted samples ranging from 30 to 80 mL in volume. The dilute samples were placed in separatory funnels where the entrained water phases settled and were drained off. The toluene phases were then placed in open beakers in a fume hood and concentrated by evaporation of the toluene to a volume of less than 1 mL. The evaporation was accelerated through use of a heat lamp and a series of filtered air jets directed a t the samples. A known volume of cyclohexane in toluene was then added to each sample as an internal standard, and the samples were analyzed by gel permeation chromatography (GPC) with refractive index (RI) detection. The samples were injected in 150-pL lots into a Perkin-Elmer Model-601 high-performance liquid chromatograph (HPLC) and flowed through an Alltech 100 A pore size p-Spherogel column a t an approximate rate of 0.5 mL/min. Column effluent passed through a differential RI detector, producing signal peaks a t approximately 11, 15, and 18min after injection for the PDMS, tetradecane, and cyclohexane, respectively. The signals were recorded by both a chart recorder and a digital data system based on a Hewlett-Packard HP-87 computer. The digitized data were collected at 1-s intervals and were later numerically integrated to yield absolute volume information on the two unknown components based on the known cyclohexane volume. At least two chromatograms were obtained of each experimental sample, including a control sample of the initial oil mixture. Calibration samples containing known volumes of all three solutes were included in the analyses on a regular basis. During the development of the analytical technique it was found that the responses of the refractive indices of tetradecane and PDMS to changes in temperature were opposite to that of the toluene solvent. Decreases in temperature caused the already large RI of toluene to increase while the indices of the two solutes decreased. The resulting increase in differential RI between the solvent and each solute produced an increase in sensitivity of the RI detector. This improvement was realized by operating the temperature-stabilizing water bath of the detector a t 5 "C. With some small modifications to the detector housing to prevent fogging of the optics, an enhancement in the detectability of the solutes was obtained. The additional sensitivity proved valuable when working with some of the samples which contained very small concentrations of tetradecane (less than 50 ppm). Volatile Fractionation Experiments. As will he discussed later, the nonvolatile experiments resulted in smaller fractionation effects than had been expected based on previous studies. This prompted a series of fractionation experiments using the toluene-octane-decane mixture which had been the subject of one of the earlier works. The objective of these additional experiments was the acquisition of quantitative data for the volatile mixture under the tightest evaporative controls possible. The re-
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986 671
sults could then be compared with the qualitative data from the earlier work and with the results obtained with the nonvolatile mixtures. The experimental apparatus and methodology used for the nonvolatile experiments was modified with additional evaporative controls and a suitable change in analytical technique for use with the volatile oils. Spreading tests at room temperature indicated that virtually all of a 1OO-kL sample of equivolume toluene-octane-decane evaporated from the water surface in the 38-cm dish within 30 s. To cut these losses, three types of control were utilized: (1) reduce vapor pressures by lowering temperature, (2) reduce partial pressures by dilution, arid (3) slow mass transport rate from the water surface by limiting air convection. The first of these was accomplished by conducting experiments within a refrigerated room. Ambient temperature was maintained between 3 and 5 "C, and all materials and equipment were brought to this temperature prior to an experiment. The second type of control was already implemented in the solvent-flooding step of the nonvolatile procedure. Initial experiments indicated, however, that the 1-min flooding time was not rapid enough for use with the volatile mixture. This flooding time was cut to less than 10 s by using a series of flasks and tubes to flood all six regions simultaneously. For the volatile experiments, chromatographic-grade hexane was used as the flooding solvent. The third loss-control method was built into the apparatus. The acrylic plate served to slow air convection near the water surface from the time the rings were lowered until flooding was completed. The plate was then removed and collection of the samples by aspiration proceeded as it had for the nonvolatile experiments. Complete sample collection required 30-40 min. Rinsing of the steel rings was not needed because the volatile oils showed no tendency to cling as the PDMS had. Evaporative losses remaining after implementation of these controls could not be further reduced. However, a correlation was made for losses occurring after the samples were diluted with hexane. The hexane loss was found by using a measured volume of hexane to flood each sample region and measuring the volume of hexane collected from each. The Rayleigh equation was then used to find the fraction of loss sustained by the toluene, the octane, and the decane based on their relative volatilities referenced to hexane. Following collection, the samples were allowed to settle in stoppered flasks for 20-30 min. A known volume of n-nonane was added to each sample as an internal standard, and the samples were poured into a graduated cylinder for measurement of collected hexane. The hexane phase was decanted from the graduate into a beaker, covered, and stored at 3-5 "C until analyzed (within 8 h). The water phase and any undecanted hexane phase were discarded. This hexane phase loss did not affect the analytical accuracy because the nonane standard was added prior to decantation. With no further preparation, samples were analyzed by gas chromatography with flame ionization detection. The instrument used was a Perkin-Elmer Model 3920 GC with a 10 f t by 1/8 in. stainless steel column packed with 20% SP2100 and 0.1% Carbowax 1500 on 100/120 Supelcoport. Helium carrier passed through an oxygen trap and an activated-carbon bed before flowing into the column at 30 mL/min. Upon injection of a 1-pL sample, a temperature program was started which held the column at 110 "C for 4 min and then raised the temperature a t 16 "C/min to a final temperature of 210 "C. The final temperature was
maintained for 4 min before resetting to 110 "C. During this program, the sample components eluted in boiling point order: hexane-toluene-octane-nonane-decane. For some samples an 8 "C/min temperature ramp was used to broaden and shorten the decane peak. The data acquisition and analysis system used for the HPLC was transferred to the GC with only slight modification. Absolute volume information for each sample component resulted from the analysis. Again, at least two chromatograms were obtained for each sample region and the initial control sample. Calibration samples of known concentration were included with each experiment, and solvent null samples were injected between experimental samples to guarantee the absence of cross-contamination. After developing the additional evaporative controls needed for the volatile oil experiments, several of the techniques were used in a final series of nonvolatile oil experiments. These experiments differed from the earlier nonvolatile procedure in that they were conducted at an ambient temperature of 3 "C and that flooding was accomplished within 10 s. As will be seen, this final series of experiments provided important additional information which the earlier nonvolatile experiments had not been accurate enough to resolve.
Film Thickness and Velocity Profile Measurements. During the development of a descriptive model for surface fractionation, which is described later, the need for a predictive model of volumetric flow in a spreading oil film became evident. This need was met through time-motion studies of the thicknesses and velocities of axisymmetric spreading oil films identical with those used in the nonvolatile fractionation experiments. High-speed color motion pictures were taken of 50- and 100-pL samples of PDMS-tetradecane mixtures spreading over clean water surfaces in the 38-cm dish. Time-motion analyses of floating Teflon tracer particles sprinkled on one side of the dish yielded velocity data at various radii in the spreading oil. On the other half of the dish, the lighting was arranged so that colorful interference fringes could be recorded by the high-speed camera. The oil film thickness profiles were determined by analysis of the color and location of these fringes. The problems of constructive interference of multiple wavelengths when using polychromatic light for interference measurements were dealt with through an analysis of all wavelengths present, using techniques of color measurement described by MacAdam (1981) and by Billmeyer and Saltzmann (1981). The result of this color analysis was a set of computer-generated tables and graphs, detailed elsewhere (Peterson, 1985), which described the apparent color of light produced by reflection through an oil film as a function of its thickness. The physical parameters necessary to generate this information were the refractive indices of the oil and water phases, the angle of incidence of the light, and the power spectrum of the light source. A Descriptive Model The approach taken in developing a descriptive model for surface fractionation was to follow the classical chemical engineering formalism for separation processes. Surface fractionation was represented as an unsteady-state multistage separation with a batch-charged first stage. The first, or center, stage is charged with a fixed volume, Yo, of a binary oil mixture described by initial concentration, Xo. The oil fractionates as it spreads toward the boundary of the first stage and crosses it. The oil which enters the second stage is no longer a t the initial concentration. Instead, the concentration of the oil leaving stage 1, Y,, is
672
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
related to the current overall concentration of oil in stage 1, X,, by the separation coefficient, CY. The separation coefficient is defined by the relationship Y, = a X , / [ l + ( a - l)]X, (1) Prior to any oil leaving stage 1,its overall concentration will be equal to the initial concentration, X, = X,. As oil crosses the boundary of the stage, however, the overall concentration of the first stage changes and at any time will be described by the Rayleigh equation for a differential separation ..
rl-
r
a
11
where Xl and V , are the current overall concentration and volume in stage 1, Xo and Voare the initial concentration and volume, and CY is the separation coefficient defined in eq 1. Equation 2 must be solved iteratively for XI, but it converges rapidly. A similar separation occurs as the oil film spreads through the second and subsequent stages. The second stage may be described at any time by a differential material balance. During a differential time element, dt, the overall change of oil volume in the second stage is dV2 = -dV, - (output to next stage) (3) Prior to the edge of the oil film reaching the outer boundary of stage 2 , the output is zero and dV2 = -dV,. When the oil film does pass the outer boundary, the output to the next stage is defined by eq 3 as output = dV, - dV,. At any time, then, the material balance on a given component in stage 2 is d(X2V2) = Y,(-dV,) - Y,(-dV, - dV2) (4) This can be rearranged to yield the differential change in the concentration, X2 d(X,) = [(Yz - X,) dVz
+ (Yz - YJ
dVil/V,
(5)
Performing similar balances on a generalized stage i (i the form
> 1) produces
1-1
d(XJ = [(Y, - Xi) dV1 + (Y, - yl-l)CdVll/V, ( 6 ) J=1
Converting eq 6 into finite-difference form and utilizing eq 1 produce
ax, =
{( + ax,
( a - 1)X,
1
(+ 1
.
(CY
-
)
-x,AVi +
1)X, - 1 + (a CYxi-l - l)xi-l)$VI)/.
(7)
This is the form of the material balance used in the descriptive model. The fractionation model thus consists of eq 2 and 7. Solutions to the equations were obtained in a step-by-step sequence of calculations wherein the spreading event was divided into a series of small time increments. For each time increment beginning with the first, the volumes and volume changes for each radial stage were determined. These were then used in the modeling equations, along with the last current concentrations for each stage, to determine the changes in concentration of each stage during the time increment. In each time increment, the calculations begin with the first stage and move outward to the edge of the oil film. The current concentration of each stage at the end of the time increment was found by
adding the calculated changes to the last current value of concentration, and the process was repeated for the next time increment. The final result of the computations was a complete history of volumes and concentrations for each radial stage. Performance of the calculations required a knowledge of the volumetric flow field of the spreading oil film and the selection of three model parameters: (1)the separation coefficient, (2) the number and size of radial stages, and (3) the number and size of time increments. Knowledge of the volumetric flow field was obtained from oil film thickness profile models developed from measurements already described. Of the three modeling parameters, the separation coefficient was varied to produce the best fit to the data. The other two were selected based on experimental conditions and computational efficiency. Since the model separation was continuous, the ideal was to use as many stages as possible. There was a limit, however, to the number of stages which could be reasonably used. This limit was forced on the model by the requirements of the finite-difference material balance equations. The equations assume that the volume of a stage is much larger than its change in volume over a given time increment. This required that the number of time increments be more than twice the number of radial stages. The number of time increments chosen was limited only by computation time and available computer memory. In application, these limits did not present a problem. The computations were performed on a Hewlett-Packard HP-87 computer using 10 radial stages and 50 time increments. Various values of the separation coefficient, CY, were used, and the results compared with experimental data from the PDMS-tetradecane fractionation experiments.
Res ul t s Characterization of the pure oils and oil mixtures was careful and complete. A summary of the measured properties of the pure oils appears in Table I. The values obtained were very close to those reported in the literature, indicating the purity of the starting materials. Interesting to note are the identical values of the spreading coefficient, S, for the three grades of PDMS. Also noteworthy is the fact that the values of S for PDMS and tetradecane are more extreme than those of toluene and decane. Results of characterizations of mixtures are too voluminous to be displayed here, but they can be summarized. Binary mixtures of toluene and decane were used for comparison with the three grades of PDMS in tetradecane. The densities of all mixtures were linear with concentration, indicating no changes of volume on mixing. Surface and interfacial tensions as functions of concentration for PDMS-tetradecane mixtures displayed strong adsorption of the PDMS on both air and water interfaces, the 5-cSt PDMS being somewhat less adsorbing than the 50- and 500-cSt grades. For the toluene-decane mixtures the adsorption of toluene at the oil/water interface was much weaker than that of PDMS in tetradecane. Also, although the toluene has a positive spreading coefficient, its surface tension was higher than those of octane and decane, and it displayed negative adsorption at the oil/air interface when in a mixture with decane. All nonvolatile fractionation experiments involved initial mixtures of 25.5 mol% PDMS. Bulk mixture spreading coefficients were roughly 9 dynlcm. Equations by Fay (1969) indicate that, for oil with these properties, interfacial tensions will control spreading of oil films less than 3 mm thick. Thus, for the volumes used in the experiments, interfacial tension control of spreading was assured.
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
673
Table I. Experimentally Determined Oil PropertiesD oil PDMS (5 cSt, dry) PDMS (5 cSt, wet) PDMS (50 cSt, dry) PDMS (50 cSt, wet) PDMS (500 cSt, dry) PDMS (500 cSt, wet) tetradecane (dry) tetradecane (wet) toluene (dry) toluene (wet) octane (dry) octane (wet) decane (dry) decane (wet)
bo,
dyn/cm 19.5 19.2 20.8 20.6 20.8 20.8 26.7 26.7 28.9 28.9 21.8 22.0 24.0 24.2
S, dynlcm 11.7 11.7 11.0 11.0 11.5 11.5 -4.1 -4.1 6.8 6.8 0.6 0.6 -2.9 -2.9
aoiwrdyn/cm
41.9 41.2 40.5 50.2 37.1 50.2 51.5
p = ( A + Bn-' (1.06912 1.1433 X 10-3T)-' (1.06912 1.1433 X 10-3T)-' (1.01821 + 9.7067 X 10-4T)-1 (1.01821 + 9.7067 X 10-4T)-' (1.01046 + 9.4428 X 10-4T)-' (1.01046 9.4428 X 10-4T)-' (1.28714 + 1.2083 X 10-'T)T)-' (1.28714 + 1.2083 X 10-3T)-' (1.13036 + 1.214 X 10-37"-' (1.13036 1.214 X 10-3T)-' (1.39259 1.593 X 10-3T)-' (1.39259 + 1.593 X 10-3T)-' (1.34309 1.394 X (1.34309 + 1.394 X 10-4T)-'
g/cm3 0.9172 0.9172 0.9650 0.9650 0.9722 0.9722 0.7633 0.7633 0.8670 0.8670 0.7028 0.7028 0.7302 0.7302
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radius
rodius (cm)
Figure 2. Composition profiles of 50-cSt PDMS with tetradecane ( T = 22 O C ) .
Of the three viscosity grades used, the mixtures containing 50-cSt PDMS proved the most convenient to work with and displayed the clearest trends. Initial oil volumes of 25 FL were found to result in the optimal balance between experimental response and analytical accuracy. Spreading times of approximately 4 s produced maximum apparent fractionation. This length of time corresponded to the time required for the leading edge of the colorful oil film to reach the fifth sample region. Thus, the sixth region contained only an invisibly thin film of oil. Results of experiments conducted at room temperature are shown in Figure 2, plotted as mole fraction PDMS vs. radial distance from the center of the dish. The data for each sample region are plotted as the root-mean-square radius of the region. The trend of increasing PDMS fraction with increasing radial distance is very plain. An exception to this trend appears in the sixth sample region, where the data are very scattered. A separate experiment confirmed that the results in this region were affected by adsorption of some of the PDMS on the edge of the plastic dish. The volumes of oil in this region were so small that only a few hundred nanoliters of adsorbed PDMS would be sufficient to cause the excursions seen in the data. For this reason, the sixth region is excluded from further discussion. An experimental bias can be detected in Figure 2 in that the local concentration never falls significantly below the initial value in the inner sample regions. This indicates that some tetradecane was missing from the overall material inventory. The numerical data indicate that, while the PDMS collection efficiencies were roughly 98%, those of the tetradecane were only 90%. The tetradecane losses, which proved to be caused by evaporation chiefly before flooding was accomplished, were remedied in the final series of experiments using the
10
L
15
volue - -
p
A
20
(cm)
Figure 3. Composition profiles of BO-cSt PDMS with tetradecane (T= 5 "C). 061
,
'
,
'
1
'
'
7
0
t
0.5t C
0
50 4 e
L
9
B
3 02
t
v
" 20 radius (cm) Figure 4. Composition profiles of equivolume mixtures of toluene (O), octane (01, and decane ( A ) . 0.1;'
"
'
5
"
"
IO
"
"
15
'
"
evaporative control techniques developed for the volatile oils. The results, shown in Figure 3, continue to display the trend of increasing PDMS fraction with increasing radial distance, while also clearly indicating tetradecane enrichment in the inner sample regions. Collection efficiencies for both components in these experiments were 97% or better. Results of the volatile fractionation experiments appear in Figure 4. The overall trends shown are similar to those reported by Phillips and Groseva (1975), but of lesser magnitude. Toluene increases in concentration with increasing radial distance, while the decane fraction decreases. Octane displays a maximum in the intermediate regions. Despite the efforts made to control and correct for evaporation, significant losses occurred, mostly during the period of spreading and prior to flooding with hexane.
674
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
C
5
IO
I5
23
(cm)
radius
F i g u r e 5. Representative velocity profiles as a function of radius for 100 bL of BO-cSt PDMS with tetradecane.
scaled radius, (r/t3'4) F i g u r e 7. Thickness as a function of radius scaled with (time)3!4 for 100 uL of 50-cSt PDMS with tetradecane.
5
I5
IO
radius
2C
!err)
F i g u r e 6. Representative thickness profiles as a function of radius for 100 ,uL of 50-cSt PDMS with tetradecane.
Overall collection efficiencies ranged from about 80% for decane to between 50% and 60%' for toluene and octane. As expected, the effect of the losses on the concentration profiles were counter to those of preferential spreading. Again, experimental difficulties rendered the data from the sixth ring unusable. Only the inner five rings are presented in the figure. Representative profiles of the oil film thickness and velocity vs. position, with time as a parameter, are shown in Figures 5 and 6. These measurements were made for 50- and 100-pL volumes of 25.5 mol% mixtures of all three viscosity grades of PDMS in tetradecane. Inspection of the thickness profiles in Figure 6 suggests that with appropriate scaling they might coincide. Use of a radius reduced by time to the 3 / 4 power was consistent with theoretical developments by Fay (1969) and Camp (1985) and produced the outstanding results seen in Figure 7. The measurements thus provided an experimental confirmation of the earlier theoretical treatments. A further development by Fay (1969) relates oil film leading-edge position, R , to time to the 3 / 4 power. Using a radius reduced by R , shown in Figure 8, results in a slight degradation of fit but is much easier to use in subsequent modeling. Empirical modeling of the thickness profiles was sufficient for purposes of flow field predictions. Inspection of the reduced profiles suggested a power-law function of the form h = A(r/R)"
(8)
where h is the film thickness, r / R is the reduced radius, and A and B are empirically determined constants. Values for A and B were found by linear least-squares fit of log ( h )to log ( r / R ) . Curves determined by this method are displayed in Figures 7 and 8. Lacking data for the central portion of the oil film, where the film was thick and did not display colorful fringes, a horizontal profile was assumed. At any given time the thickness of this inner region and the point of intersection between the inner and outer regions were both fixed by
--* . **j
." ..,L
.--
I
,
02
OO-
~
. -..-.
~
-.
L
04
00
06
reduced radius
,-
_
10
(r/R)
F i g u r e 8. Thickness profile model for 50 eL of BO-cSt PDMS with tetradecane. T a b l e 11. Summary of T h i c k n e s s P r o f i l e Models and Constants thickness profile h = A(r/R)B V = 2 ~ J h ( r ) rd r oil film volume outer region
:1;"
50 25
grade. cSt 500 50 5 500 50 50
27rA RB(B
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2) (r)B+21:;
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V , NUL 100
=
A 4.5946 X 5.2884 X 1.6187 X 4.6170 X 5,4638 X 2.1155 X
I? lo-'
lo-' 1O-I
lo-' lo-* 10.'
-3.9398 -2.4256 -1.5827 -1.7937 -1.7720 -2.7114
the constraint that the total volume of the profile must equal its initial volume. The inner portion of the thickness model does not exhibit similsrity and is therefore not shown in the figures. A summary of the thickness model and constants, along with the resulting oil film volume model, is given in Table 11. The values given for 25-pL spreads from the volumetric data of fractionation experiments. It was assumed that the same profile development and similarity would apply to this volume of oil as i t had to 50 and 100 pL. The film volume models in Table I1 were used directly in the fractionation model calculations. With 10 radial stages and 50 time increments, a separation coefficient of a = 1.1produced a good fit with the data from both series of nonvolatile experiments. Model results are shown in
Ind. Eng. Chern. Fundarn., Vol. 25, No. 4 , 1986
v)
08-
E L (1
-
06-
L
O0
-.1
I
-1-1 -1 A 5 IO 15
L_
zo
radius ( c m )
Figure 9. Fractionation modeling of data from the PDMS-tetradecane series ( T = 5 “C, spread time 4.00 9). (---) (Y = 1.2; (-) (Y = 1.1; (- - -) (Y = 1.05.
Figure 9 as a solid line plotted with the experimental data. In this figure the data points represent average compositions computed from the equations over the sample regions used in the experiments. Also shown in the figure as dashed lines are modeling results for a values of 1.05 and 1.2. Comparison of the three modeled curves gives an indication of the sensitivity of the model to changes in the value of cy. A value of cy = 1 would produce no fractionation at all.
Discussion The data in Figure 2 provide supporting evidence for fractionation by preferential spreading but fall short of completely verifying this mechanism because of the evaporative losses suffered by the tetradecane during sample collection. The concentration profiles shown in Figure 3, however, could not have been the result of evaporation or dissolution. We conclude that they were caused by preferential spreading and that this mechanism of fractionation is confirmed. A comparison of the fractionation observed in the PDMS-tetradecane system with the qualitative results reported for toluene-octane-decane by Phillips and Groseva (1975) suggested that the volatile ternary system fractionated more than the nonvolatile binary. This was contrary to our expectations for two reasons: (1) the driving force for fractionation was presumed much larger in the binary system due to the greater difference in spreading coefficients, and (2) evaporation should have worked against preferential spreading in the volatile system. The unexpectedly small fractionation of the PDMS-tetradecane prompted the decision to make quantitative measurements of toluene-octane-decane. As noted earlier, the concentration profiles exhibited by the volatile experiments agreed with those reported by Phillips and Groseva (1975) in direction but not in magnitude. The current results display significantly less fractionation than did those of the earlier work. It is difficult to draw any conclusions from this comparison due to lack of information concerning the earlier experiments. One conclusion that can be reached is that the careful methods and evaporative controls used in the current experiments resulted in much less scatter in the data and a more accurate picture of the actual compositional trends than were evident in the earlier results. Comparison of the toluene-octane-decane profiles with those of the nonvolatile mixture reveals that the fractionation effects of the ternary system, while smaller than those reported in earlier literature, are still larger than
675
those displayed by the binary system. This departure from the expected behavior suggests that the fractionation of the binary mixture was hindered or that the the ternary mixture enhanced by some effect which had not been considered. A review of the properties and spreading behavior of the mixtures and their components disclosed several characteristics other than spreadability in which the mixtures differed and which might be capable of affecting their fractionation. The first two of these were closely related: viscosity and molecular weight. As will be discussed later, the mechanism by which fractionation occurs may involve the establishment of convective flows within the thick regions of the oil films. The higher viscosity of the PDMS mixtures would tend to inhibit such flow, thereby hindering fractionation. Likewise, the higher molecular weight of the PDMS will hinder its movement on a molecular level. A third characteristic in which the mixtures differed was their spreading configuration. The toluene-octane-decane mixture spread as a very unstable thick oil film: a combination of large and small lenses dispersed in a monolayer and moving very rapidly. In contrast, the PDMS-tetradecane mixtures spread as a much thinner, continuous film whose thickness profiles have been shown. Both the increased thickness and the rapid chaotic movement of the volatile oil film may have contributed to flow patterns which enhanced fractionation. Another characteristic difference was the evaporative loss experienced by the mixtures. The rate of loss in the ternary system was higher than for the binary, and the ternary losses affected the spreading toluene more than the nonspreading decane. The rapid loss of toluene and octane from the monolayer or thin film allowed the thicker film or lenses to continue “spreading” and creating a new thin film, even after the water surface was covered. This effectively enlarged the size of the dish, allowing the fractionation to continue over a “longer distance” and perhaps enhancing the separation. The evaporative losses, then, while working against fractionation in one way, may have been promoting it in another. With regard to the descriptive model, the limited amount of quantitative fractionation data available precluded the development of correlations between the values of a and the properties of the oils. As has just been discussed, however, the data indicated that a did not depend only on the equilibrium spreading properties of the component oils. Viscosity, molecular weight, and volatility of the pure oils and the spreading dynamics of the mixtures were also indicated as relevant variables. Attempting to draw together the disparate information now available into a unified mechanism proved a difficult task. One of the difficulties was that the existing theoretical developments of interfacial-tension-controlled spreading include an assumption which makes surface fractionation impossible. The assumption is that the velocity of the oil film does not vary in the vertical direction; that is, the film moves in “plug flow”. This assumption rules out the possibility of convective flows within the oil film. Under this restriction, fractionation could occur by only two means: (1)the spreading component must diffuse radially outward through the mixture, or ( 2 ) fractionation is simply an artifact of strong adsorption of the spreading component at an interface combined with the increased interface-to-volume ratio in the outer, thinner regions of the oil film. Neither of these mechanisms was found to be adequate to produce fractionation on the scale evident in the experiments.
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Ind. Eng. Chern. Fundam., Vol. 25, No. 4, 1986
We conclude that some form of convective flow must take place within the spreading oil film in order for the components of a mixture to be distributed in the manner observed experimentally. The probable driving forces for this convection are drag from the moving subphase boundary layer and the interfacial tension gradient which drives the spreading. The convection minimizes any concentration gradients which occur in the thick regions of the oil film and helps maintain equilibrium between the bulk of the oil film and the interface. The adsorption equilibrium which is established, however, is not capable of producing fractionation. The inventory of adsorbing species which is a t the interface is only a miniscule fraction of that contained in the bulk of even the thinnest visible oil film. The presence or removal of the interfacial inventory would not significantly impact the overall concentration. Apparently, the separation brought about by the influence of interfacial forces is not an equilibrium separation but rather a rate-controlled one. Consideration of the dynamic behavior of spreading oil films suggests that the transition from visible film to monolayer may be the rate-controlled process responsible for the separation. This transition has been studied by Camp (1985). The location of the transition in the spreading oil film is characterized as the "acceleration zone". In their work on the spreading of liquids on solids, Neogi and Miller (1982) call upon a process of surface diffusivity to explain the movement of the leading solid-liquid interline as a liquid spreads. In this development, the no-slip condition a t the interline is overcome on a molecular level by rapid surface diffusion which effectively moves the interline forward. Assuming that the adsorption of species is fast enough to remain in equilibrium, Neogi and Miller gave an expression for the mass average velocity at the interline for the molecules of each species Vq -(Ds/ntkT)(dP/dx) (9) =L
where Vs is the surface velocity of the species, D s is its surface diffusivity, and nI, is its molecular density. The potential which drives the spreading is represented by P. In a similar treatment of liquids spreading on liquids, the transition from visible film to monolayer may be considered analogous to the solid-liquid interline. The molecules of each species entering the monolayer would do so a t the rate specified in eq 9. Assuming that the potential gradient is the same for all species, the difference in their velocities across the transition is accounted for by variations in nI, and LIS. The dependence of the molecular density, nI, on bulk density and molecular weight is obvious. The nature of the surface diffusivity, however, is not known. The experimental evidence suggests that there is a correlation between the value of D s and the spreading properties of an oil, but the nature of this correlation cannot be determined from the limited data available. It seems likely that the diffusivity term may also be dependent on molecular weight and configuration. A mechanism involving the two features discussed, convection in the thick film and fractionation a t the transition from visible film to monolayer, will accommodate all six of the variables identified in the experiments as possibly influencing fractionation. Two of the variables, viscosity and oil film thickness, directly affect the convection needed to sustain fractionation. Two more, the molecular weight and spreading properties of the components, influence the fractionation through eq 9. Another variable, the spreading configuration of the oil mixture, affects the length of the visible-to-monolayer interline.
Since the fractionation process would occur at this interline, increasing its length would enhance the effects observed. The sixth and final variable identified as possibly affecting fractionation is the volatility of the spreading oils. The monolayer-production-dependent mechanism proposed would be affected by large evaporative losses. For the case of confined spreading, evaporation of the monolayer would allow continued production of new monolayer beyond the initial spreading period. This extended monolayer production would enhance the fractionation achieved by the volatile system relative to that of a nonvolatile system. The fractionation mechanism described is highly speculative, but it does address all of the relationships between oil properties, spreading behavior, and fractionation which we have observed.
Summary The primary objective of this study was to verify or disprove the occurrence of surface fractionation of oil mixtures by preferential spreading. This objective was achieved by conducting several series of carefully controlled and executed experiments involving a well-characterized nonvolatile binary oil mixture. Additional fractionation experiments were conducted for the previously studied mixture of toluene, octane, and decane. These experiments were conducted under the tightest evaporative controls available. Even so, evaporative losses were significant; in excess of 40% of the octane and toluene used in the experiments was not recovered in the analysis. The trends exhibited by the toluene-octane-decane experiments confirm those of an earlier study in direction but not in magnitude. While the fractionation of this volatile system was of lesser magnitude than an earlier report led us to expect, it was significantly greater than that displayed by the nonvolatile PDMS-tetradecane mixture. Consideration of the two mixtures on the basis of spreading properties alone would result in prediction of a greater fractionation f o r the nonvolatile system. The experimental data thus indicated that the fractionation experienced by the spreading mixtures was not dependent only on the spreading properties, but also involved other characteristics of the oils, individually and as a mixture. Some of the additional variables identified as possible factors in the process were the viscosity and dynamic spreading behavior of the mixtures and the molecular weights, relative adsorptions, volatilities, and solubilities of the components. A descriptive model was developed for fractionation of a binary oil mixture. This model was based on approximating a continuous process as a multistage, batch-charged separation in which each stage achieves a separation described by the separation coefficient, a. Solution of the modeling equations required knowledge of the volumetric flow field of a spreading oil film. This was acquired by measurements of the oil film thickness profiles as a function of radius during spreading. A method was developed for evaluating oil film thickness from polychromatic interference fringes. This method was applied in time-motion analysis of color motion pictures taken of spreading oil mixtures. The resulting film thickness profiles displayed similarity when plotted as functions of reduced radius, experimentally verifying theoretical analyses done by previous workers. The similar profiles were empirically modeled by least-squares fitting of power-law curves. Volumetric flow field information for use in the fractionation model was obtained by integration of the thickness profile models. The results of the fractionation
Ind. Eng. Chem. Fundam. 1986, 25, 677-605
677
model based on this flow information agreed well with the experimental data. Finally, the mechanism responsible for surface fractionation was addressed. An assumption of the current theory for oil spreading is that the oil film moves in plug flow and no convection occurs. The implications of this assumption for fractionation were discussed, and the conclusion was reached that some form of convection must exist in order for fractionation to occur. Movement of the oil/water interface due to subphase drag and the Marangoni effect were presumed to cause this convection. The separation itself is expected to occur in the zone where the transition from visible film to monolayer takes place. As the thinner film is formed, the rates at which the various components enter it should be related to their spreading properties as well as the composition of the thicker film. A similar mechanism has been suggested by Neogi and Miller (1982) for spreading of liquids on solids. This work has unambiguously verified the existence of surface fractionation, identified some unexpected effects associated with it, set forth a descriptive model, and proposed some mechanistic speculations.
Berridge, S.A.; Dean, R. A.; Fallows, R. G.; Fish, A. I n Scientific Aspects of Pollution by the Sea; Hepple, P., Ed.; Elsevier: Amsterdam, 1968; pp 2-11. Billmeyer, F. W.; Saltzmann, M. Principles of Color Technology. 2nd ed.; Wiley: New York, 1981; Chapter 3. Camp, D. W. Ph.D. Dissertation, University of Washington, Seattle, WA, 1985. Fay, J. A. I n Oil on the Sea ; Hoult, D. P., Ed.; Plenum: New York, 1969; pp 53-63. Fazal, R. M. S. Thesis, MIT, Cambridge, MA, 1975. MacAdam, D. L. Color Measurement. Theme and Varitions: Springer-Verlag: West Berlin, 1981; Chapter 3. Neogi, P.; Miller, C. A. J . Colloid Interface Sci. 1982, 86. 525. Peterson, J. W. Ph.D. Dissertation, University of Washington, Seattle, WA, 1985. Phillips, C. R.; Groseva, V. M. Sep. Sci. 1975, 70, 111.
Acknowledgment This work was supported by Grant No. MEA 81-09226 from the National Science Foundation and by the Amer-
Received f o r review June 16, 1986 Revised manuscript received July 16, 1986 Accepted August 1, 1986
ican Chemical Society Fellowship in Colloid and Surface Chemistry, sponsored by the Procter and Gamble Co. We also thank the members of the Surfaces, Polymers, and Colloids Laboratory at the University of Washington for invaluable assistance in all phases of the work and the 3M Co. for material assistance. Registry No. Tetradecane, 629-59-4;toluene, 108-88-3;octane, 111-65-9;decane, 124-18-5.
Literature Cited
Periodic Countercurrent Operation of Sorption Processes Applied to Water Desalination with Thermally Regenerable Ion-Exchange Resins Giorgio Cartat and Robert L. Pigford’ Department of Chemical Engineering, University of Delaware, Newark, Delaware
197 76
An efficient fixed-bed process is described for water desalination with a thermally regenerated ion-exchange resin (Amberlite XD-5). Several columns are used in a “merry-go-round” cycle, during which alternating temperature swings cause sorption and desorption to occur in each bed. Various modes of operation of the process are examined experimentally and theoretically. The efficiency of the process is maximized by the proper periodic countercurrent action and by the optimal selection of flow rates and cycle times. For our system the separation factor for a four-column periodic countercurrent process can be as high as 80% of the theoretically possible value for a truly continuous countercurrent process that uses the same resin inventory. Many of the serious practical problems associated with the operation of the latter are entirely avoided, however.
Introduction Operation of continuous sorption processes in which constant countercurrent motion of the solid sorbent phase relative to the fluid phase is involved is generally difficult and has had only partial success in the past. It is difficult to maintain steady plug flow of both the solid and the fluid phases since flow nonidealities occur in practice. Furthermore, it is difficult to prevent attrition of the sorbent particles in the columns, pipes, and especially in me+ Present address: Department of Chemical Engineering, University of Virginia, Charlottesville, VA 22901.
chanical drives that are required to obtain steady movement of beds of settled solids. This may decrease the useful life of the sorbent and impose severe limitations on the particle mechanical properties, the distribution of sizes, and the allowable fluid velocities. As a consequence, the more common mode of operation employs fixed beds. The sorbent particles are tightly packed into one or more columns which are operated in a cyclic manner, each alternating between a sorption or “loading”period and a desorption or “regeneration” period. Slater (1982) has compared the relative sizes of fixed-bed and continuous sorption equipment. Under typical process conditions, conventional fixed-bed processes may require
0196-4313/86/1025-0677$01.50/00 1986 American Chemical Society
