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Ind. Eng. Chem. Res. 1997, 36, 2346-2352
Efficient Sorption Processes by Fibrous Sorbents Gerard van Zee* and Jan de Graauw Laboratory for Process Equipment, Delft University of Technology, Leeghwaterstraat 44, 2628 CA, Delft, The Netherlands
Sorption separation processes, by which a solute is removed from a gas or liquid stream by preferential sorption into a solid sorbent, traditionally utilize spherical or granular sorbent particles. This study examines the performance of fiber sorbents by model analyses. It concentrates on an efficiency parameter, defined to compare the combined space and power consumption efficiency of sorption operations. It is shown that the utilization of fiber sorbents may increase the efficiency of a sorption process by approximately 1 magnitude order as a result of the high void fraction of a packed fiber bed. The advantages of the efficiency improvement are investigated for the most common sorption operation modes. 1. Introduction Sorption separation processes depend on favorable retention of the separated components by a solid sorbent. The sorbents available are mostly porous spherical solid particles of a diverse chemical nature. Applications are equally wide-ranging as the sorbents applied, including many product separations in the process industries and removal of undesired compounds from effluent streams. In a number of recent publications the development of novel fibrous sorbent materials has been reported (Suzuki (1994), Shikaleeva (1993), Goto (1987), Kobuke et al. (1990)). This study investigates the performance of fibrous sorbent materials by simple model studies. The approach followed is based on the definition of an efficiency parameter, which represents a measure for the space and power consumption efficiency of sorption operations. This efficiency parameter is expressed as a function of sorbent properties and operating conditions, thus providing a method to compare the efficiency of sorption operations and sorbent types in a consistent manner. In section 2 the general properties of sorption operations and sorbent bed types are discussed briefly and the main performance variables are introduced. Section 3 discusses the separation effectiveness of typical sorption operation modes, and section 4 is concerned with evaluation of the efficiency parameter and analysis of the advantages of fibrous sorbents. Conclusions are given in section 5. 2. Elementary Process Description A wide range of sorption process types and equipment variants exists (Wankat, 1978). To accomplish some degree of general applicability of the results of this work, the performance of fiber sorbents will be investigated for typical modes of operation. Most applied sorption processes can be described by one of the following operation modes: (1) true continuouscounter current operation (CC); (2) fixed bed in cyclic operation (FB); (3) simulated moving bed (SMB); (4) continuous crossflow operation (XF). The basic process diagrams of these four operation modes are shown in Figure 1. * Author to whom correspondence is addressed. Telephone: 31-15-2786678. Fax: 31-15-2786975. E-mail: G.vanZee@ wbmt.tudelft.nl. S0888-5885(96)00684-7 CCC: $14.00
Figure 1. Principle of operation of four sorption operation modes.
2.1. Bed Types and Properties. The efficiency analysis focuses on the properties of the sorbent bed. For granular sorbents both packed beds and fluidized beds are considered and for fibrous sorbents only packed beds are considered, because a fluid bed obviously cannot be realized with fibers. The following characteristic values for the porosity of the three bed types are assumed: (A) granular packed bed, 0.3-0.4 (Schweitzer, 1988); (B) fluidized bed, 0.5-0.8 (Slater, 1975); (C) fiber bed, 0.85-0.95. The fiber bed is considered to be isotropic, consisting of cylindrical fibers oriented randomly in space. This type of ideal arrangement can be approached by packings of stacked fiber felts. Because of the length of a fiber relative to its diameter, it is possible to make use of a “self-induced” spacing of a fiber bed, in order to attain high bed porosities. The porosity range ) 0.850.95 has been chosen here, as these are normal values © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2347
for a felt of polymer fibers without mechanical compression exerted onto it. The fluid-side mass-transfer coefficient depends on the bed properties and can be obtained from empirical relations for forced convection mass and heat transfer. Many data correlations have been published. Reviews indicate that the majority of the correlations available yield similar results, both for granular particles (Dwivedi and Upadhyay, 1977) and for fibrous media (van Zee, 1996). Individual representative expressions were used for fibrous and granular sorbents, which are presumed to provide reliable estimates. Equation 1 represents a correlation for mass transfer in packed and fluidized granular beds, valid for the range 2 < Re < 2000 (Snowden and Turner, 1967).
Sh )
0.86 0.5 0.33 Re Sc
separation effectiveness fE is specific for a mode of operation. In section 3 the appropriate expressions are discussed for the sorption operation modes to be considered. Column Volume. The required column volume is given by
F V ) ZA ) (HTU)(NTU) u
(5)
Power Consumption. The minimum power consumed for transportation of a noncompressible fluid phase is given by WL ) F∆P. According to Darcy’s law, the pressure drop of flow in a porous medium in the laminar flow region is given by
(1)
ub µ dP )dz kp
(6)
where Sh ) kLd/DL; Re ) Fubd/µ; Sc ) µ/(FDL); D ) fluid phase diffusion coefficient; and F ) fluid phase density. The velocity ub in Re represents the superficial flow velocity with respect to the bed. For fibers the following correlation was selected, which has been reported for mass transfer to a single fiber in the flow regime 4 < Re < 40 (Schmal et al., 1986):
ub represents the flow velocity with respect to the bed, kp bed permeability, µ dynamic viscosity, P pressure, and z length coordinate. It has been derived theoretically for a porous medium (de Nevers, 1991) that the permeability is given by
Sh ) 0.7Re0.4Sc0.33
kp ) 3/Ka2
(2)
The specific surface area of the sorbent bed is given by a ) s(1 - )/d, where d represents the particle diameter and s is a particle shape factor equal to s ) 4 for fibers and s ) 6 for spheres. The affinity of the sorbate for the sorbent is usually expressed by a distribution coefficient mSL, which is defined as mSL ) CS/CL at equilibrium. For the present study mSL is considered to be equal for fibers and spheres. Furthermore, mSL is assumed to be concentration independent, and flow rates are assumed to be constant. The latter two conditions are normally approximated in dilute systems. 2.2. Separation Performance. The concept of transfer units, utilizing the parameter’s height of a transfer unit HTU and number of transfer units NTU, presents a convenient basis for separation process modeling
(7)
K is a constant that depends on the bed structure. For granular particles a value K ) 5 is generally accepted. For porous fiber structures at ) 0.9 experimental data indicate K ) 9 (Coulson and Richardson, 1968). Normally, for sorption processes involving sorbent transport, the transport velocity of the sorbent is small with respect to the flow velocity, which means that the power consumption of sorbent transport is negligible and the flow velocities with respect to the bed (ub) and to a fixed point (u) are approximately equal. Thus, the total power consumption is given by W ) F∆P, which, by combination with eqs 3, 6, and 7, can be expressed as
W)F
µu Ku Z ) Fµ 3 a2(NTU)(HTU) kp
(8)
HTU ) u/koL NTU ) Z/HTU
(3)
In these definitions u represents the superficial flow velocity and Z represents the bed length. The parameter koL represents the overall mass-transfer coefficient. The present study will be restricted to sorbents for which the contribution of the solid phase to the total mass-transfer resistance can be neglected, which results in koL ) kL. Additionally, it is assumed that the feed or initial concentration in the sorbent CS,in ) 0, and we define the separation effectiveness fE and the sorbent lading or utilization fM as
fE ) 1 -
fM )
CL,Z C0L
CS,out mSLC0L
(4)
The number of transfer units NTU required to attain a
Efficiency Parameter. Sorption equipment combining high power and space efficiencies exhibits high values for an efficiency parameter Q, defined by the following expression, which results from combination of eqs 5 and 8:
Q)
( )
1 µF2 3 ) WV NTU2 HTU2Ka2
(9)
This dimensionless parameter is a measure for the compactness and mechanical energy economy of a sorption operation and essentially independent of the throughput and viscosity of the feed. For a given value NTU, the efficiency parameter Q is a function only of the sorbent bed properties, the flow velocity, and the mass-transfer coefficient. The number of transfer units required is determined by the separation effectiveness requested, depending on the mode of operation. The parameter Q is therefore suitable for efficiency comparison of different operation modes and sorbent types for a specified separation duty.
2348 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
Substitution in eq 9 of HTU by eq 3 and koL by eq 1 reveals the key efficiency variables for granular sorbents. We obtain
Q ∝ /ud
(10)
Hence, upon first consideration it appears that highvoidage, fine particles and low-flow velocities generally are favorable properties of a sorption process. Choosing both u and d small, however, may lead to unrealistically wide and short columns. In order to prevent the assignment of values to variables in subsequent calculations to result in efficient, but unrealistically shaped, columns, a constraint must be designated. This is done by assigning a fixed value to the length/width ratio of the column R. This ratio, expressed in the variables introduced previously, is given by:
R)
Z d u3/2 ) NTU koLs(1 - ) F1/2 A1/2
(11)
where A represents the cross-sectional area of the column perpendicular to the flow direction.
Figure 2. Diagram of breakthrough patterns.
minimum breakthrough time tr is given by Suzuki (1990)
mSL(1 - ) mSL(1 - ) + ≈Z u u
tr ) Z 3. Separation Effectiveness By eq 9 the sorption efficiency has been expressed as a function of the number of transfer units NTU. In order to allow comparison of sorbent performance for different operation modes, the relationship between NTU and the separation effectiveness fE must be known. For the operation modes of interest such expressions are available for specific conditions. 3.1. Countercurrent Operations (CC). For a countercurrent sorption process, under perfect plug flow conditions, the separation effectiveness fE depends only on NTU and the stripping factor S. The latter is equal to S ) FSmSL/FL, where FL and FS are the volumetric flow rates of the continuous and sorbent phases, respectively. The present study will be limited to the situation S ) 1 and perfect plug flow conditions, for which the relation between fE and NTU is given by Perry and Green (1984):
NTUCC fE ) NTUCC + 1
(12)
The sorbent lading at S )1 is equal to fM ) fE. 3.2. Fixed-Bed Operations (FB). An important characteristic parameter for a fixed-bed sorption operation is the breakthrough time or cycle time tc. The breakthrough curve and the concentration pattern in the column at t ) tc are depicted in Figure 2. Unfortunately, the relationship between NTU and the separation effectiveness fE is rather complicated for fixedbed operations. It can be approximated, however, by the following relation, provided NTU > 40 (Ruthven and Ching, 1993):
fE )
(
1 1 + erf 2 2
)
xNTUFB(1 - tc/tr) 2xtc/tr
(13)
The parameter tr represents the minimum breakthrough time. The actual breakthrough time tc is equal to tr in the absence of mass-transfer resistance. The
(14)
Omitting the term + in the nominator is normally allowed for realistic values of , as usually mSL . 1. The ratio (tc/tr) in eq 13 determines the width of the mass-transfer zone and the sorbent utilization fM. For well-developed breakthrough curves the mass balance over the column is approximately given by
F(C0Ltc -
∫0t CL,Z dt) ) c
1 A (Z - ∆ZMTZ) + ∆ZMTZ ((1 - )mSL + )C0L (15) 2
[
]
For not too small values for fE the effluent term ∫t0c CL,Z dt ≈ 0 so that eq 15 reduces to
tc
1 u ≈ Z - ∆ZMTZ 2 mSL(1 - ) +
(16)
from which it is clear that ∆ZMTZ ≈ 2(1 - tc/tr)Z and therefore fM ≈ ((Z -∆ZMTZ) + 1/2∆ZMTZ)/Z ≈ tc/tr. In order to achieve effective utilization of the sorbent packed in the column, normal operation conditions are chosen such that a narrow breakthrough curve is obtained, which implies that NTU > 40 and tc/tr is fairly close to unity. 3.3. Simulated-Moving-Bed Operations (SMB). The separation effectiveness of a simulated-moving-bed sorption operation depends on the number of column segments in the sorption section, equal to the total number of port connections on the sorption section of the column minus 1. Because of the irregular boundary conditions that apply to the mathematical description, an expression for fE is not available. Some calculated results for simulated-moving-bed separation performance for various values n are given by Svedberg (1976). For the case n ) 1, the simulated-moving-bed operation mode is identical to the fixed-bed operation mode. For large n its behavior approaches true countercurrent operation. 3.4. Cross-flow Operations (XF). The cross-flow mode of operation has a two-dimensional concentration pattern. As for the counter-current operation mode, fE
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2349
Figure 3. NTU as a function of the separation effectiveness fE. Table 1. Case Parameters parameter general feed throughput separation effectiveness column shape bed porosity additional for fixed-bed operation distribution coefficient breakthrough time min. breakthrough time
value assumed F ) 100 m3/h fE ) 0.9 RCC ) 5; RFB, RXF ) 1 bed types A, B, C (section 2) mSL ) 100 tc ) 8 h tr ) tc/fE
is only a function of NTU and the stripping factor S. For S ) 1 and n ) 1 passes, it is given by Sherwood et al. (1975):
fE(n)1) ) 1 - NTUXF ×
∫01∫01exp(- NTUXF(y + z))I0(2NTUXFxyz) dz dy
(17)
where I0 represents the Bessel function of the first kind of zero order. With an increasing number of passes, the theoretical performance characteristics approach countercurrent operation, but for n > 1 no expression is available and the NTU required to meet a specified value fE can only be determined by numerical approximations. Figure 3 presents plots for NTU as a function of fE according to the expressions given above. The difference between the operation modes is considerable and grows with increasing effectiveness fE. The curve plotted for fE ) tc/tr for fixed-bed operations corresponds to a sorbent lading fM ) fE, as is the case for countercurrent and cross-flow operations at S ) 1. 4. Efficiency Comparison for Sorption Operations The influence of the bed properties on the efficiency Q can be illustrated well by a case analysis. To this purpose, the efficiency Q was computed for a set of design specs, listed in Table 1. The parameter values used represent common sorbent and system properties for sorption processes. For the continuous phase the physical properties of water were assumed, with DL ) 10-9 m2/s. Choosing a minimum breakthrough time tr
Figure 4. Sorption efficiency Q as a function of the bed porosity for different operation modes.
corresponding to tc/tr ) fE for the fixed-bed mode of operation makes the conditions such that the sorbent lading fM is equal for all modes of operation, thus rendering the separation duty performed identical for all operation modes. The counter-current and cross-flow sorption operations have 5 degrees of freedom, given S ) 1. By Table 1 four parameters have been fixed. Determination of the separation performance therefore requires one additional variable to be assigned a value. For countercurrent and cross-flow operations a flow velocity u ) 0.005 m/s was used as an additional constraint. The fixed-bed operation mode has 7 degrees of freedom and also seven variables have been fixed in Table 1. 4.1. Comparison of Bed Types. Figure 4 presents the values for Q thus computed as a function of the bed porosity for packed granular beds (A), fluidized beds (B), and packed fiber beds (C). It shows that application of fibrous sorbents results in high values for the efficiency Q, which is a consequence of the high void fraction of a packed fiber bed. Improvement of the combined space and power consumption efficiency by 1 magnitude order with respect to packed granular beds appears possible. The efficiency improvement for fibers appears to be independent of the operation mode. This is explained as follows. From the expression for the efficiency Q given by eq 9, by combination with eq 11 and either eq 1 for spherical particles or eq 2 for fibers, the following relationships can be derived for Q, in which koL and d have been eliminated.
Q)
(
) ( )
0.015 D0.5/Sc0.167 NTU u0.33
1.33
1 RF1/2
0.67
(18)
for packed beds of spherical sorbent particles at ) 0.4, and
Q)
(
) ( )
0.103 D0.6/Sc0.067 NTU u0.375
1.25
1 RF1/2
0.75
(19)
2350 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
Figure 5. Influence of the flow velocity on the efficiency Q of countercurrent sorption operations.
Figure 6. Relative performance fY of sorption operation modes as a function of the separation effectiveness fE.
for packed fiber beds at ) 0.9. Apart from the constant, these relationships for packed fiber and granular beds are almost identical functions, which implies that the ratio of Q for fibers and spherical packed beds is determined predominantly by the ratio of the constants, so that roughly Qfibers ≈ 7Qspheres for any mode of operation, provided the flow velocities to be applied for fibers and spheres are of the same order. Figure 5 reflects the effect of variation of the flow velocity on the parameters Q, W, and V for countercurrent operations, for both packed granular beds (at ) 0.4) and fiber beds ( ) 0.9). This figure shows a strong decrease of the required column volume, a strong increase of the power consumption, and a slight decrease of the efficiency Q as the flow velocity grows. The required column volume is independent of the bed properties for a given R, which follows directly from eqs 5 and 11:
sorbent, the power consumption can be equal for both sorbent types, which then yields a smaller column volume for fibers. Cross-flow and fixed-bed operations exhibit a similar effect of the flow velocity, though at other values for Q and W. For fixed-bed operations, however, the flow velocity is not an independent variable, as
(Fu)
V)R
3/2
(20)
Note that a high flow velocity must be compensated by fine particles, as dictated by eq 11. If u is increased with R fixed, the column length Z decreases and therefore d must be smaller in order to maintain Z/HTU ) NTU. For countercurrent operations the higher efficiency Q of fibrous sorbents can be used effectively to reduce either the space occupation or the power consumption, depending on the flow velocity applied. Figure 5 makes clear that, if the same flow velocity is applied for fibers and for spheres, the power consumption is smaller for fibers, whereas the required column volumes are equal. Alternatively, at a higher flow velocity for the fiber
uFB )
(
)
mSL RfEFBF1/2(1 - ) tc
2/3
(21)
which is derived by combination of eqs 11 and 14 and tr ) tc/fE and demonstrates that the column volume required for fixed-bed operations is actually larger for fibers than for granular sorbents. The higher bed porosity of a packed fiber bed demands a lower flow velocity and therefore a higher column volume, provided mSL is equal for the two sorbent types. As opposed to countercurrent and cross-flow operation, utilization of fiber sorbents does not result in more compact fixedbed equipment. However, despite the larger column size, Q is higher for fibers so that the power consumption of fixed-bed operations can be reduced considerably. For countercurrent sorption operations utilizing a fluidized bed, which also appear to be more efficient than packed granular bed operations in Figure 4, it should be realized that mixing is normally an important factor and countercurrent behavior can be approximated only by dividing the column into a fairly large number of stages. In addition, the bed porosity of a fluidized bed is a function of the flow velocity and the particle diameter. This dependency prohibits the combined application of high flow velocities and small particles and obstructs the design of compact fluid bed equipment as a result.
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2351
4.2. Comparison of Sorption Operation Modes. Equations 18 and 19 express the effect of variation in the key parameters NTU, R, and u. The following approximate proportionalities apply to both spherical and fibrous sorbents: Q ∝ NTU-1.3. Figure 3 shows that the distance between the curves for NTU of countercurrent operation and other operation modes increases steeply with fE. Therefore, countercurrent operation offers a particularly strong efficiency advantage as measured by the parameter Q, if deep separations (high values fE) are required. Q ∝ R-0.7. In regard to the efficiency Q design for a wide column shape is to be preferred over a tall column shape. Q ∝ u-0.35. Low flow velocities generally improve slightly the efficiency Q. As discussed above, this improvement is achieved at the cost of a relatively steep increase of the column volume (as shown by eq 20 and by Figure 5). The flow velocity to be applied to fixedbed operations is dictated by the distribution coefficient mSL and the breakthrough time required, according to eq 21. Consequently, for fixed-bed operations poor affinity of the sorbate for the sorbent (mSL small) actually improves Q but requires large columns. The choice for a particular operation mode and the optimal design is decided ultimately by costs criteria, to which the efficiency Q can act as an indicator. Figure 6 pictures the leading behavior of the efficiency parameter Q for packed granular and fiber beds in a diagram. The ordinate of the figure reflects by a parameter combination Y the relative performance fY with respect to the maximum performance attainable, i.e., for true countercurrent operation utilizing a packed fiber bed, where Y is defined on the basis of eqs 18 and 19 as
Y ) Q(uR2)0.35
(22)
and
fY )
Y Y(CC,fibers)
(23)
The figure represented in this manner is universal in that the curves indicated are only marginally dependent on process conditions and physical substance properties. For cross-flow and SMB operations with n > 1, regions are indicated in the figure, since individual curves for different values n can be determined only by numerical approximation or by experiment for a specific separation problem. 5. Conclusions The parameter Q, defined for comparison of the combined space occupation and power consumption efficiency, presents a useful tool for efficiency studies on sorption operations. An analysis shows that application of fiber sorbents can result in an improvement of the efficiency Q by roughly 1 order of magnitude with respect to conventional packed beds of spherical sorbent particles. The improvement is a consequence of the higher porosity of packed fiber beds and is approximately equal for all operation modes. For countercurrent and cross-flow operations, the higher efficiency Q for fiber sorbents can be employed effectively to reduce either the power consumption or the column volume required, depending on the choice of the flow velocity. More compact equipment can be attained by application of relatively high flow velocities
for fibers, whereas application of relatively low flow velocities results in reduction of the power consumption of sorption operations. For fixed-bed sorption operations the higher efficiency for fibers can only be effective through a reduction of the power consumption. For these operations the flow velocity to be applied depends on the sorbent properties, which causes larger column volumes to be required for fibers. Notation Dimensionless Numbers Reynolds number ) Re ) Fud/µ Schmidt number ) Sc ) µ/FD Sherwood number ) Sh ) kd/D Greek Symbols ) bed void fraction µ ) dynamic viscosity [Pa‚s] F ) phase density [kg/m3] Subscripts o ) overall value L ) property of continuous phase MTZ ) property of the mass-transfer zone in fixed-bed operations S ) property of sorbent Superscripts 0 ) feed or initial value Symbols a ) solid-phase surface area per unit column volume [m-1] A ) column cross-sectional area perpendicular to the flow direction [m2] C ) concentration [kg/m3] d ) particle diameter [m] D ) binary diffusion coefficient [m2/s] fE ) separation effectiveness: fraction sorbate removed from the feed fM ) sorbent lading (fM ) CS/mSLCL0) fY ) relative performance with respect to countercurrent operation using fiber sorbents F ) volumetric feed flow rate [m3/s] HTU ) height of a transfer unit [m] kp ) bed permeability [m2] kL ) continuous-phase mass-transfer coefficient [m/s] K ) Koze´ny constant mSL ) weight concentration distribution coefficient (CS/ CL)equil. [(kg/m3)/(kg/m3)] NTU ) number of transfer units P ) pressure [Pa] Q ) dimensionless efficiency parameter R ) column length to width ratio S ) stripping factor (S ) FSmSL/FL) s ) particle shape factor (s ) 4 for fibers; s ) 6 for spheres) tc ) cycle time, breakthrough time [s] tr ) minimum breakthrough time [s] u ) superficial (empty column) flow velocity with respect to fixed coordinates [s] ub ) superficial (empty column) flow velocity with respect to the sorbent [s] v ) (average) velocity with respect to fixed coordinates [m/s] V ) column volume [m3] W ) power consumption [W] Y ) performance weighing parameter [(m/s)0.35] Z ) column length [m]
Literature Cited Coulson, J. M.; Richardson, J. F. Chemical Engineering; Pergamon: Oxford, U.K., 1968.
2352 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 de Nevers, N. Fluid mechanics for chemical engineers; McGrawHill: New York, 1991. Dwivedi, P. N.; Upadhyay, S. N. Particle-Fluid Mass Transfer in Fixed and Fluidized Beds. Ind. Chem. Eng. Process Des. Dev. 1977, 16, 157. Goto, M. Removal and recovery of heavy metals by ion exchange fiber. J. Chem. Eng. Jpn. 1987, 20, 467. Kobuke, Y.; Oaki, T.; Tanaka, H.; Tabushi, I. Recovery of uranium from sea water by composite fiber adsorbent. Ind. Eng. Chem. Res. 1990, 9, 1662. Perry, R. H.; Green, D. Perry’s Chemical Engineers’ Handbook; McGraw-Hill: New York, 1984. Ruthven, D. M.; Ching, C. B. Modelling of chromatographic processes. In Preparative and Production Scale Chromatography; Gatenos, G., Barker, P. E., Eds.; Marcel Dekker: New York, 1993. Schmal, D.; Van Erkel, J.; Van Duin, P. J. Mass transfer at carbon fibre electrodes. J. Appl. Electrochem. 1986, 16, 422. Schweitzer, P. A. Handbook of separation techniques for chemical engineers; McGraw-Hill: New York, 1988. Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer; McGraw-Hill: New York, 1975. Shikaleeva, G. N. Dynamics of benzene vapor sorption by carbonic fibrous materials. Russ. J. Appl. Chem. 1993, 66, part 1, 1396. Slater, M. J. Assessment of Fluidised Bed Ion Exchange Equipment. J. Appl. Chem. Biotechnol. 1975, 25, 367.
Snowden, C. B.; Turner, J. C. In Proceedings of the International Symposium Fluidization; Drinkenburg, A. A. H., Ed.; Netherlands University Press: Amsterdam, The Netherlands, 1967. Suzuki, M. Adsorption Engineering; Kodaisha: Tokyo, 1990. Suzuki, M. Activated carbon fibersfundamentals and applications. Carbon 1994, 32, 577. Svedberg, V. G. Numerical solution of multicolumn adsorption processes under periodic countercurrent operation. Chem. Eng. Sci. 1976, 31, 345. van Zee, G. Counter current sorption using fiber sorbents. Ph.D. Dissertation, Delft University of Technology, Delft, The Netherlands, 1996. Wankat, P. Large scale chromatographic processes; CRC Press: Baton Rouge, LA, 1978.
Received for review October 25, 1996 Revised manuscript received February 12, 1997 Accepted February 13, 1997X IE960684C
X Abstract published in Advance ACS Abstracts, April 1, 1997.
