Improved Efficiency in Preparative Chromatographic Columns Using a Moving Feed Phllllp C. Wankat School of Chemical Engineering, Purdue University, West Lafayene, lndiana 47907
A new operational method for preparative chromatographic columns is proposed. The technique uses a feed injection point which moves at a velocity V F E Eup~ the column during the time the feed containing two (or more) solutes to be separated is injected. Solvent or carrier gas is continuously fed at the origin of the column. If VFEE, is chosen to lie between the concentration wave velocities of two solutes, the separation of these two solutes will be greatly enhanced. The local equilibrium model of adsorption is used to analyze the technique and compare it with the usual preparative method. The moving feed point technique is predicted to have improved resolution with higher capacity. The solutes can also be concentrated instead of diluted as is the usual case. In some cases solutes can be separated with continuous injection of feed to the column. Possible methods for applying the technique and the relation to simulated counter current operation are discussed.
The usual method of operating fixed beds for preparative chromatography and chromatographic adsorption systems is to use a large pulse of feed followed by a longer period with only carrier gas or solvent. In this paper a new technique which will enhance the normal separation is proposed. This technique consists of moving the injection point inside (or up) the column as the pulse of feed is added. The solvent or carrier gas are continuously fed to the column a t the origin of the column. This method will enhance the separation and the separation will be optimized if the velocity of movement of the injection point is chosen so that it lies between the velocities of the solutes being separated. This technique will allow more throughput of feed than usual preparative operation since it is thermodynamically more efficient. In some insiances it is possible to obtain a multicomponent separation with continuous injection of feed. The moving feed point technique can be applied to a variety of chromatographic techniques such as gas-liquid chromatography, gas-solid chromatography, liquid-solid chromatography, gel permeation, countercurrent distribution, thin-layer chromatography, or paper chromatography. The local equilibrium model of adsorption will be used to study the application of a moving feed point to chromatographic separations and to compare this technique with the usual preparative method. Then the application of the method for continuous separation will be illustrated.
Local Equilibrium Model The local equilibrium model has been extensively applied to adsorption operation (see Vermeulen et al. (1973) or Sherwood et al. (1975)) and to cyclic operation of sorption columns (Baker and Pigford, 1971). For dilute systems the solute mass balance developed by Baker and Pigford (1971) is ac a-
at
ac * a4 + (1 - a)€+ ps (1- a ) ( l- €1 + at at
ffu
ac -
az
where Baker and Pigford’s nomenclature is used. Equation 1 assumes a constant carrier velocity u , and this is strictly applicable only to dilute liquid systems or dilute, isothermal gas systems with a negligible pressure drop. With the usual assumptions of local equilibrium between solid and fluid, negligible dispersion effects, negligible heat of adsorption, and 468
Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
solutes independent of each other, the mass balance simplifies to ac [a (1- a)€]-
+
+ ps(l - a)(l at
t)
dc + au - = 0 at az
dq -
(2)
Since the amount of solute adsorbed is a function of concentration and temperature, eq 2 can be manipulated to
where uc =
(YU
a
+ (1 - a ) c+ (1- a)(i- c)p,aq/ac
(4)
is the solute wave velocity which is in general a function of temperature, concentration, and the particular solute being studied. The solute wave velocity ucmust be less than or equal to the carrier velocity u . For isothermal operation the right-hand side of eq 3 is zero and the resulting equation is easily solved by the method of characteristics. Appropriate initial and boundary conditions are (t = 0 , o I2 IL) c = c&) (5) and either c = CF
(0
< t 5 tF9
= VFeedt)
(6)
for the moving feed case or c = CF
(0 < t 5 tF, z = 0 )
(7)
for the stationary feed case. For isothermal conditions the solution to eq 3 is obtained as dc _ -0 dt when dz _ - uc dt Thus concentration is constant along characteristic lines given by eq 9. For linear isotherms of the form q = A(T)c*
(10)
ucis constant and all characteristics have constant slopes. The solution for two solutes assumed to not interact are shown in
Time-
'F
'F
Time
-
Figure 1. Characteristics for moving feed point system for solutes with linear equilibria: slope of feed injection line = VFeed; slope of characteristic lines = U A or UB.
Figure 2. Characteristics for usual preparative separation for solutes with linear equilibria; characteristic line slopes U A or UB.
Figure 1 for a moving feed and in Figure 2 for the usual preparative case. The figures are drawn with equal periods for injection of feed. In Figure 1the moving feed line has a slope of VFeed, and the characteristics for solutes A and B have slopes U A and U B , respectively. U A and U B are the concentration wave velocities for solutes A and B and are calculated from eq 4. In Figure 1carrier is continuously fed to the bottom of the column and the feed containing the solutes to be separated is injected from time zero to t ~This . pulse of feed is then repeated after sufficient time has been allowed to separate the solutes. The material to be separated is not continuously injected a t the bottom of the column, but instead the point of injection is continuously moved inside the column a t a velocity VFeed. At the end of the pulse the point of injection is a t LF where LF = VFeed t ~ . In Figure 2 the characteristics for solutes A and B again have slopes U A and U B ,respectively. Carrier is again continuously fed to the bottom of the column. The pulses of material to be separated are also fed to the bottom of the column. This is equivalent to having VFeed = 0. The cross-hatched region in Figure 2 represents a region where the solutes are not separated even when zone spreading phenomena are ignored. Note that Figure 1does not contain a region where the solutes are not separated. In order to obtain the same separation as in Figure 1 the next pulse in Figure 2 must start a t a later time. For the velocity of the moving feed shown in Figure 1 the two solutes do not intermix although considerable intermixing must occur in the usual preparative system shown in Figure 2. T o avoid intermixing and thus enhance the separation we must have
the column as they do in Figure 2. Even though these bands have the same column length to achieve separation the resolution will be better in Figure 1.This must be true since zone spreading, which is not predicted by the local equilibrium theory, is proportional to the square root of the total migration distance (King, 1971), and the total migration distance for these two band edges is considerably longer in the usual preparative case. In the moving feed point system the leading edge of the band for solutes which move slower than VFeed (solute B in Figure 1)consists of material which was injected last. This is the opposite of what usually occurs. Since the leading edge of band A and the trailing edge of band B both travel the full column length in both systems, the band spreading for these parts of the product should be comparable for both techniques. However, the moving feed system can either process more feed with the same resolution by putting successive pulses closer together (as shown in Figure 1)or the same amount of feed can be processed with much better resolution. This additional capacity occurs because in the moving feed system the necessary waiting time between feed pulses is the time between the start of each feed pulse while in the usual preparative system the necessary waiting time is the time between the end of one pulse of feed and the beginning of the next pulse. This difference in waiting time is evident when the figures are compared. The solution by the method of characteristics shows that the concentration will be constant along a characteristic, but this concentration still must be determined. The moving feed point system will change the concentration of solute depending upon the solute velocity and the velocity of the feed point. The appropriate concentration can be determined by a macroscopic mass balance over a length of column from 0 to L F ,the maximum depth of insertion of the feed point into the column. Solute is input from t = O to t = t~ = LF/VFeed a t a rate of F moles of solute per minute. For solute B which moves slower than the feed point, U B < VFeed, the solute exits the control volume from t = t~ to t = LF/UB.This can be seen from Figure 1.For the slow moving solute the concentration can be calculated from the mass balance as
UA
> VFeed > UB
(11)
The criteria shown in eq 11 can be explained by reference to Figure 1. If VFeed is less than U B then the feed injection line will lie under what is currently the lower characteristic for solute B. The characteristics for solute A leaving the feed line must cross this B characteristic. Thus there will be a region where the solutes are not separated and are intermixed. The limiting case is where VFeed = 0 and the results are shown in Figure 2. The cross-hatched region in Figure 2 shows where there is no separation of the solutes. If VFeed is greater than U A then the feed injection line will lie above what is currently the upper characteristic for solute A. In this case the B characteristics leaving the feed line will intersect this A characteristic. The resulting cross-hatched region without any separation will then lie below the feed line. If eq 11is satisfied a region without separation does not exist. With proper selection of the velocity of the feed injection point the solute bands can be made narrower than in the usual preparative case and more feed can be processed through the column. This is evident when Figures 1and 2 are compared. The feed point velocity in Figure 1 was chosen so that the trailing edge of the solute A band and the leading edge of the solute B band have the same remaining distance to travel in
Equation 1 2 will represent a more concentrated and hence a narrower solute band as long as VFeed/UB < 2. This increase in concentration is reasonable since the time period during which the solute emerges from the column is shorter than the time it is fed into the column. For solute A which moves faster than the feed point, U A > VFeed, the solute exits the control volume from t = LF/UAto t = t ~This . is also illustrated in Figure 1.The corresponding mass balance gives
Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
469
I
I
Diffuse Wave
Diffuse Wave L
'F
Time
+
Figure 3. Characteristics for moving feed point system for solutes
locities are concentration dependent, a variety of other patterns are possible. The nonlinear isotherms cause tailing of the peaks and reduce resolution, but the use of a moving feed band will still improve separation. The concentration produced by the moving feed line for the nonlinear isotherm case can be calculated from a macroscopic balance similar to that used previously except the balance is now complicated by the presence of shock waves and diffuse waves. Three cases are possible. If U A I c A - ~ > VFeed (solute A in Figure 3) then U s h A is also greater than VFeed and the mass balance is
with favorable nonlinear equilibria: slope of feed injection line = VFeed; shock waves slopes are UshA and U s h s ; diffuse wave slopes are concentration dependent and are equal to U A and UB.
For the usual preparative separation VFeed = 0 and all solutes move faster than VFeed. Equation 13 then reduces to c = F / uaA,, which is the expected feed concentration if VFeed = 0. The increased concentrations predicted by eq 12 and 13 could be utilized to concentrate and separate solutes which appear as minor impurities. Equations 12 and 13 predict infinite concentrations when the solute wave velocity equals VFeed. This prediction is physically impossible and implies that the assumption of a linear isotherm is no longer valid. With a favorable nonlinear isotherm such as the Freundlich or Langmuir types the solute wave velocity will increase as the concentration increases, the solute wave will move ahead of the feed point, and infinite concentrations are not predicted. These infinite concentrations are also physically impossible because of dispersion effects. For nonlinear isotherms of the Freundlich or Langmuir type the solution given by eq 8 and 9 is still valid but u, is now concentration dependent. If a dilute fluid is displaced by a concentrated fluid a shock wave occurs (e.g., see Sherwood et al., 1975).The velocity of this shock wave can be obtained from a macroscopic mass balance as
(14) 1 refers to conditions after the shock wave has where j passed (fluid is concentrated) and j to conditions before the shock. The shock wave velocity thus depends upon both the concentrations and the form of the equilibrium isotherm. Since the concentration jump across the shock is finite eq 14 does not reduce to eq 4. Instead, ush lies between the values of u, calculated at concentrations c, and at c,+l. If a concentrated fluid is displaced by a dilute fluid a diffuse wave results since the concentration wave velocity decreases as the concentration decreases. The results for nonlinear isotherms are shown in Figure 3 for a system where the two solutes do not interact. In Figure 3 a shock wave occurs where solute A displaces fluid which contains no A. The velocity of this shock wave, u & A , can be calculated from eq 14. Note that
+
> uShA > uAlCA-0
where u A l C A = C , h A is the solute wave velocity calculated from eq 4 when the concentration is CshA, the solute concentration after the shock wave. U A c ~A - c ~ is the solute wave velocity calculated from eq 4 when solute A is infinitely dilute. The diffuse wave occurs because the wave velocity is concentration dependent. Each line in the diffuse wave fan corresponds to a different concentration of solute A. Solute B also generates a similar shock wave and diffuse wave. Figure 3 is an illustration of one possible pattern for the solute waves. Since the solute wave veuAlCA=CshA
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Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
Equation 15 is nonlinear in the concentration behind the shock wave, CshA, since U s h A depends on CshA. The form of eq 15 will depend on the isotherm employed. If VFeed = 0 eq 15 reduces to C s h A = F/uaA, as expected. If u ~ I ~ ~< -VFeed o and U s h B < VFeed (solute B in Figure 3) the mass balance is
where CAVG is the average concentration of the diffuse waves which range from C s h B to zero. CAVG is calculated as
CAVG
=
(t2 - t l )
where is the time at which the slowest moving diffuse wave reaches
LF, and is the time a t which the last characteristic of concentration of C s h g reaches LF. t l and t2 are shown in Figure 3. C B ~ * = (t) L~ is evaluated by finding the time that different characteristics in the diffuse wave intersect the z = LF line, and calculating the concentration, CB, which will make U B equal to the slope of the characteristic. This calculation of is similar to the calculation of a breakthrough curve for nonlinear isotherms (Sherwood et al. (1975)). For the third case uD
ICD-O < VFeed but u D I c=c.hD > VFeed
and u s h D > VFeed. This case was not illustrated but would have the solute wave straddling the line generated by the feed point. The mass balance for this case is
where C A V G is ~ the appropriate average of the concentrations of the diffuse waves. In this last case there will be mixing of solutes near the feed point, but it will be less than would occur with the usual preparative feed. The results shown in Figures 1to 3 are for separation of two solutes. Systems with more than two solutes can also be separated. The moving feed point system will minimize mixing and enhance separation compared to the usual preparative system. For a three solute system VFeed is chosen to lie in between the wave velocities of the least strongly held solute, A,
and the most strongly held solute, B, U A > VFeed > UB. This criterion will prevent the occurrence of a region where there is no separation of A and B. For the intermediate solute, D, we will have U D VFeed. Then in Figures 1to 3 the additional solute would lie between solutes A and B. Obtaining good resolution between all components becomes more difficult as the number of components is increased. This is true for both the moving feed point system and the usual preparative system. However, with the moving feed system VFeed can be optimized for the most difficult separation by picking VFeed so that it lies between the wave velocities of the two solutes that are hardest to separate. A very interesting application of the moving feed point system is the possibility of multicomponent separation with continuous feed to the column. This is illustrated in Figure 4 for two noninteracting solutes both of which have linear isotherms. The technique requires proper timing of the feed injections so that feed is always being injected into the column at some point, but the trailing edge of solute B does not overlap with the leading edge of solute A. In addition, the solutes being separated must have wave velocities that are not too different. If they are too different the solute bands will overlap at the outlet of the column unless a period without any feed is used. Both of these criteria are satisfied in Figure 4. Additional solutes can be separated if they have wave velocities between those of solutes A and B. This method could also be used with feed simultaneously input a t two points in the column for part of each cycle. It is not necessary that the inequality given in eq 11 be satisfied, but the thermodynamic efficiency is better if this inequality is satisifed, since irreversible mixing of the solutes is minimized. Application of the continuous multicomponent separation technique will be aided by use of high performance chromatographic packings which minimize spreading of the bands.
-
Discussion The moving feed point system is applicable to other systems besides chromatography in columns. Actual application in open systems such as thin layer chromatography or paper chromatography would be relatively easy since the surface is readily accessible. Commercially available streakers could be modified to provide the desired moving feed point for these systems. Alteration of counter-current distribution equipment to allow feed to different tubes should also be relatively easy. In columns the system could be implemented by changing the location of a syringe inside a porous tube. Alternately, a segmented column could be used and movement of the feed could be obtained by switching feed locations. A segmented column would be similar to but simpler than the commercially available Sorbex system (Broughton, 1968; de Rosset et al., 1976). The moving feed technique is related to the simulated counter-current flow technique (Broughton, 1968; de Rosset et al., 1976) developed and used for commercial adsorption separation. Around the feed injection point solute A moves up and solute B down relative to the feed injection point. Thus an observer located a t the feed point will observe a countercurrent separation of A from B. However, this simulated counter-current separation is not continued, but instead a fixed bed chromatographic separation is used for the remainder of the separation. Thus the separation is time dependent instead of steady state as in a truly counter-current process, but the system can separate multicomponent mixtures instead of being limiting to binary separations. The moving feed system does not utilize adsorbent as effectively as a counter-current or simulated counter-current system since there are time periods when adsorbent near the origin is doing nothing. Also adsorbent is not being used effectively when a band of pure solute is in the column. However, the
L
t
Z
Time
-+
Figure 4. Characteristics for moving feed point system with continuous feed. Both solutes have linear equilibria.
adsorbent usage is better than in a usual preparative chromatographic column. The efficiency of any separation can be increased by eliminating or reducing any irreversible steps. In preparative chromatography there is an unavoidable iccrease in entropy due to mixing. For an ideal solution the entropy increase due to mixing is given as A S = Z(x, In x i ) This entropy increase occurs when solutes are mixed with each other and when they are mixed with solvent or carrier gas. The moving feed system limits mixing of solutes while as shown in Figure 2 this mixing must occur in the usual preparative chromatography separation. The moving feed system also dilutes the solutes less than the usual chromatographic system and thus decreases mixing with solvent. Other irreversible steps such as dispersion and diffusion in pores are still present in the moving feed point system. The combination of less mixing and better adsorbent utilization explains why improved separations are expected with the moving feed system when compared to the usual chromatographic column. The moving feed point system could also be useful for removing a single solute from solution. This would be particularly true if the solute were present in trace amounts since the solute concentration can be greatly increased by choosing VFeed = Utrace comp. The local equilibrium model used here does not include zone spreading due to dispersion or mass transfer rate limitations. Zone spreading can be modeled by a staged model. We have modified the counter-current distribution model (King, 1971) for both the usual preparative case and the moving feed case by summing a series of solutions for a single pulse of feed. This model is exact for a counter-current distribution apparatus and is an approximate model of column behavior. Alternatively, the nonequilibrium models applied to adsorption (Sherwood et al., 1975; Vermeulen et al., 1973) could be applied to this system. A more complete model would also have to take into account changes in the carrier velocity u which could be appreciable in gas systems, and the effect of solutes which compete for adsorption sites. Other nonlinear isotherms such as BET type isotherms could also be considered. The behavior of thin-layer or paper chromatography can be estimated by calculating solute velocities from R F values. For continuous multicomponent separations in a twodimensional apparatus a method analogous to the moving feed point can be used (Wankat, 1977). In a two-dimensional apparatus a feed line that is slanted into the apparatus is used, but the feed line is stationary. Acknowledgment The use of facilities at the University of California, Berkeley, while on sabbatical is gratefully acknowledged. Nomenclature A = solid-fluid equilibrium distribution parameter for linear isotherm, eq 10 A , = cross-sectional area of column, cm2 Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
471
c = fluid concentration, mol/L c* = fluid concentration in equilibrium with solid-phase concentrations, mol/L D M = mass molecular diffusivity, cm2/min E D = eddy axial dispersion, cm2/min F = solute feed rate, mol/min L = lengthofbed,cm q = solid-phase concentration, mol/kg of dry solid t = time,min t 1, t 2 = times that diffuse wave intersects z = L F ,eq 18 and 19 and Figure 3, min UA, UB, uc, U D
= solute wave velocity for solutes A, B, D or for a general case (c), cm/min u = interstitial fluid velocity, cm/min VFeed = velocity of feed injection point, cm/min z = axial distance, cm
Greek Letters = interparticle void fraction e = intraparticle void fraction ps = structural density of solid, kg/cm3
Subscripts A, B, D = solute species AVG = averaged solute concentration, eq 17 c = concentration-related value F = feed j = conditions before shock wave j t 1 = conditions after shock wave sh = shock Literature Cited Baker, B., Pigford, R. L., hd. Eng. Chem., Fundam., 10, 283 )1971). Broughton, D. B., Chem. Eng. Prog., 64 (8),60 (1968). de Rosset, A. J., Neuzil, R. W., Korous, D. J., I&. Eng. Chem.,Process Des. Dev., 15, 261 (1976). King, C. J., "Separation Processes", McGraw-Hill, New York, N.Y.. 1971. Sherwood, T. K., Pigford, R. L., Wilke, C. R., "Mass Transfer", McGraw-Hill, New York, N.Y., 1975. Vermeulen, T. G., Klein, G., Hiester, N. K., In R. H. Perry and C. H. Chilton, Ed., "Chemical Engineer's Handbook", 5th ed,Sect. 16, McGraw-Hill, New York, N.Y., 1973. Wankat, P. C., Separat. Sci., 12, (1977).
cy
Received for reuiew November 10,1976 Accepted June 13,1977
Mechanism of Antifoaming: Role of Filler Particle R. D. Kulkarni,' E. D. Goddard, and B. Kanner Union Carbide Corporation, Tarrytown, New York f059 1
A model is proposed describing the mechanism of foam bubble rupture by silicone-based antifoams containing finely divided silica as filler. It assumes that the filler particle needs to be hydrophobic for effective antifoaming action and that these hydrophobic particles are primarily responsible for bubble rupture in aqueous systems. Silicone fluids used in the antifoam act mainly as a carrier fluid which transports and exposes the active hydrophobic silica particles to the surface for rupture of the bubble. Rupture involves the creation of a surface chemical shock by rapid adsorption and local immobilization of the foaming surfactant by the hydrophobic particles. In other words, sudden adsorption and local depletion of surface molecules cause bubble rupture. During the process of bubble rupture, the hydrophobic silica particles will, by surfactant adsorption, become hydrophilic and be extracted from the antifoam phase. via the airlwater interface, into the aqueous phase. Experimental evidence is described in this paper.
Introduction Silicone antifoams, used for foam inhibition in aqueous foaming systems, contain essentially two components: (1) polydimethylsiloxane, known as silicone oil, and (2) a small proportion of finely divided filler which is often a fumed or precipitated silica of 100-2000-A particle size. Even though such compositions have been known and used for over three decades, the reason for their effectiveness is not known nor has the role of each of the components in the foam inhibition process been defined. In the literature there has, however, been scattered speculation as to the role of the above two antifoam components (Bhute, 1971; Pattle, 1950; Povich, 1975; Robinson and Wood, 1948; Ross, 1950, 1967; Ross et al., 1953; Ross and McBain, 1944; Ross and Young, 1951). It was first believed that the spontaneous spreading of silicone oil over the bubble surface is primarily responsible for bubble rupture (Pattle, 1950; Ross, 1950) and that the presence of silica filler increases the spreading pressure and improves dispersibility of silicone oil simply by reducing the interfacial tension between silicone oil and the aqueous solution. This mechanism was based 472
Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
purely on speculative ideas and was not confirmed experimentally. Recently, however, Povich (1975) has shown that the silica filler, if anything, slightly lowers the spreading pressure of silicone oil on aqueous solutions. With other factors constant, this would mean a lowering of the antifoaming efficiency which is contrary to experience. Moreover, even though it is universally agreed that the spreading of the antifoam is necessary for the antifoaming action, there is no evidence in the literature that the spreading of silicone oil is the actual cause of foam bubble rupture. Thus, spreading of antifoam fluid may be a necessary but not sufficient condition for bubble rupture (Kulkarni et al., 1977; Kulkarni and Goddard, 1977). There is much evidence supporting this argument (Bhute, 1971; Pattle, 1950; Ross, 1950; Kulkarni et al., 1977; Kulkarni and Goddard, 1977) and, indeed, a positive spreading coefficient of itself does not necessarily imply favorable foam inhibition (Pattle, 1950; Ross, 1950; Bhute, 1971). This clearly suggests that an alternative mechanism is necessary to explain the phenomenon. In recent papers ( h l k a r n i et al., 1977; Kulkarni and Goddard, 1977) we demonstrated that electrical forces can be
