Ind. Eng. Chem. Res. 1991,30, 1886-1892
1886
Nomenclature A = surface area of the particle (m2) F = flow rate (m3/s) kf = liquid-phase mass-transfer coefficient (m/s) Deff= effective diffusivity (m2/s) Dmol= molecular diffusivity (m2/s) Bi = Biot number (RkflD,,) B = constant [l - (l/Bi)], in Spahn and Schlunder model Co = initial concentration of solute in liquid phase (kg/m3) D, = particle diameter (m) Q, = concentration of adsorbate on adsorbent (kg/kg) X = variable of integration of eqs 5-8 2 = bed height (m) Z, = distance coordinate h = bed height from solutions for eqs 4-6 Re = Reynolds number [(D,ufp)/(l- e ) ~ ] uf = superficial velocity (m/s) T = temperature (K) Sc = Schmidt number ( F / D , , ~ ) V = molar volume of solute at normal boiling point (m3/kg mol) x = 2.6 for water M = molecular weight of solvent S = mass of adsorbent (kg)
Greek Symbols { = dimensionless bed height [(D,~&3)/(FR2ZeJlZ, et = particle density (kg/m3) t
= porosity
7
= dimensionless solid-phase concentration
p =
density of solution (kg/m3)
= viscosity (kg/m.s) E = dimensionless liquid phase concentration (C/Co)
p
Acknowledgment
P.K.P. is thankful to the University Grants Commission, New Delhi, India, for an award of a senior research fellowship. Literature Cited Brauch, V.; Schlunder, U. E. The scale-up of activated carbon columns for water purification, based on results from batch tests. 11. Chem. Eng. Sci. 1975, 30, 539-48. Cech, S.; Chudoba, J. Effect of activated sludge on the rate of removal of organic substances and their biodegradability. Vodni
Hospod B 1987,37(2),40-6; Chem. Abstr. 1987, 106,201184. Ceh, S. J.; Chudoba, J. Biological degradation of morpholine. Khim. Tekhnol. Vody. 1987, 9(5), 451-453; Chem. Abstr. 1988, 108, 43263. Cooney, D. 0. External film and particle phase control of adsorber breakthrough behavior. AIChE J . 1990, 36, 1430-32. Deshmukh, S. W.; Pangarkar, V. G. Recovery of organic chemicals from effluents by adsorption over polymeric adsorbents. Indian Chem. Eng. 1984,26(3),35-8. Fox, P.; Suidan, M. T.; Pfeffer, J. T. Anaerobic treatment of a biologically inhibitory wastewater. J . Water Pollut. Control Fed. 1988, 60(1), 86-92. Gyunter, L. I.; Shatalaev, I. F.; Bakulin, N. D. Evaluation of the toxicity of components of wastewaters from petrochemicals production. Vodosnabzh. Sanit. Tekh. 1983, 7, 26; Chem. Abstr. 1983, 99, 127819. Isaeva, G. Ya.; Borvenko, V. V.; Repkina, V. I. Removal of morpholine from wastewaters. Khim. Prom-St. 1976, 7, 507-10; Chem. Abstr. 1977, 86, 21391. Kaczvinsky, J. R., Jr.; Saitoh, Koichi; Fritz, James S. Cation-Exchange Concentration of Basic Organic Compounds from Aqueous Solution. Anal. Chem. 1983, 55, 1210-15. Kataoka, T.; Yoshida, H.; Ueyama, K. Mass transfer in laminar region between liquid and packing material surface in the packed bed. J . Chem. Eng. (Jpn.) 1972, 5(2), 132. Martin, J. R.; Activated carbon product selection for water and wastewater treatment. Ind. Eng. Chem. Prod. Res. Deu. 1980,19, 435-41. Martin, R. J.; Iwugo, K. 0. Recovery of a-picoline from water by the activated carbon adsorption process. Stud. Enuiron. Sci. 1982,19, 265-83. Nikolenko, N. V.; Nechaev, E. A.; Pavlyuchik, G. S. Some principles of selection of sorbents for purification of sewage. Kolloidn. Zh. 1986, 48, 823-5; Chem. Abstr. 1986, 105, 177839. Radeke, K. H. Adsorption method for treating wastewater. Ger. Pat. 212028, 1984; Chem. Abstr. 1985, 102, 100325. Rota, R.; Wankat, P. C. Intensification of pressure swing adsorption processes. AlChE J . 1990,36, 1299-1311. Spahn, H.; Schlunder, E. U. The scale-up of activated carbon columns for water purification, based on results from batch tests. I. Chem. Eng. Sci. 1975,30,529-37. Stevens, H. W.; Skov, K. A rapid spectrometric method for determining ppm of morpholine in boiler water. Analyst 1965,90,182. Stuber, H. A.; Leenheer, J. A. Selective Concentration of Aromatic Bases from Water with a Resin Adsorbent. Anal. Chem. 1983,55, 111-15. Wankat, P. C. Intensification of sorption processes. lnd. Eng. Chem. Res. 1987, 26, 1579-1585. Wilke, C. R.; Chang, P. Correlation of diffusion coefficients in dilute solutions. AZChE J. 1955, I , 264-270. Received for review February 12, 1991 Accepted March 26, 1991
Mixed-Bed Ion-Exchange Modeling with Amine Form Cation Resins Edward J. Zecchini and Gary L. Foutch* School of Chemical Engineering, Oklahoma S t a t e University, Stillwater, Oklahoma 74078
A model for the operation of a mixed-bed ion-exchange (MBIE) column with the cation resin in the amine form is developed. The development is aimed specifically a t removal of ionic contaminants a t parts-per-billion concentrations. The model considers film diffusion limited exchange with bulk-phase neutralization and correction for amine and hydroxide concentrations. The effect of pH and inlet concentration on the cation resin exchange rate is addressed. Predictions for ammonia cycle exchange compare favorably with previously published data. Amine cycle operation with morpholine is also discussed. The model can be used to evaluate alternative amines to ammonia, provided that the necessary physical property data are available.
Introduction Electrical power generating facilities encounter corrosion and erosion of metallic surfaces due to ionic contaminants present within the steam cycle. These contaminants are 0888-5885/91/2630-1886$02.50/0
removed from the steam cycle by cationic and anionic ion exchange resins, which, combined in a single unit (mixed bed), produce ultrapure water. The typical ionic concentrations encounter in power plants are in the parts-per0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 8,1991 1887 billion range. One method for improved corrosion control is the introduction of a weak base into the water stream to increase the pH which, in turn, reduces the corrosion of the metallic surfaces. This base has historically been ammonia. In recent years alternatives to ammonia have been considered. One alternative increasing in usage is morpholine (C,H,ONH). The major factors that affect the selection of a weak base are (1)dissociation constant, (2) distribution coefficient, (3) degradation characteristics, and (4) toxicity. The dissociation constant reflects the extent to which the base ionizes when dissolved in water. The larger the dissociation constant, the more effective the weak base is at pH control. A comparison of the dissociation constants for ammonia, (AMP) as morpholine, and 2-amino-2-methyl-l-propanol functions of temperature has been performed by Sawochka et al. (1988). Their results show that, to attain the same pH with morpholine as with ammonia, a higher concentration of base must be used. For AMP less base is needed, but preliminary tests have shown it to be less effective than morpholine or ammonia for corrosion control due to its high degradation rate. The distribution coefficient is the ratio of the concentration of base in the steam phase to that in the water phase, when both phases are present. A low distribution coefficient is desirable to provide decreased corrosion rates in process equipment where two-phase operation occurs (Sawochka, 1988). The base must also be thermally stable because of the wide range of process conditions within the steam cycle. Some bases are unstable under certain conditions, and the effects of their degradation products must then be considered. Finally, the base should not be toxic since material handling is necessary and spills may occur. The effect an additive has on water stream purification must be considered when evaluating an amine. An important ion-exchange factor is the selectivity coefficient for sodium to amine on the cationic resin. The selectivity coefficient relates the interfacial and resin-phase concentrations of the two species as
Where the bar denotes resin phase and the * denotes interfacial concentration. If Ki is less than 1,the resin tends to prefer ion B. In amine form operation the selectivity coefficient directly relates to the ability of the ion-exchange system to remove ionic contaminants, such as sodium. Some fossil fuel electrical power generating facilities and most pressurized water reactor (PWR) nuclear power generating facilities use some form of pH control agent. The Electrical Power Research Institute (EPRI) recommends that feed water pH be maintained in the range of 9.3-9.6 in the absence of copper alloys and 8.8-9.2 when copper alloys are present (Sawochka, 1988). This requires ion-exchange systems to handle aminated water. This can be accomplished by MBIE in either hydrogen cycle operation or with the cation resin in the amine form (i.e., ammonia cycle). Hydrogen cycle exchange starts with the cationic resin in the hydrogen form, while amine cycle exchange begins with the resin in the amine form. Both forms exchange either hydrogen or amine ions for other cations present in the water stream being purified. For both cycles, the anionic resin begins in the hydroxide form with hydroxide ions being exchanged for other anions present in the water stream. The released hydrogen, or amine, and hydroxide then establish a new equilibrium based on the water, or amine, dissociation.
Current models for ammonia cycle exchange are of the mass-action equilibria type. The model developed by Bates and Johnson (1984) uses an empirical plate height method and equilibrium calculations to simulate an ammonia-form MBIE unit. Models of this type are useful to industry because of their empirical basis, but they represent only limiting cases that may be improved on by more theoretical models. Consideration of low inlet concentrations ( 1, then the liquid-phase resistance (film diffusion) is predominant. Morpholine cycle exchange also yields values of T greater than 1. These evaluations are true even for the most unfavorable conditions encountered in the systems. As a result, assuming film diffusion control is reasonable. The objective of this work is to develop a model for amine cycle MBIE at low concentrations, less than lo4 M. This article presents the model development and evaluation as it applies to ammonium- and morpholinium-form cation-exchange resins in a MBIE column. Model Development The model developed here addresses the inclusion of an amine into a typical MBIE system operating in the amine cycle. The ions considered during the exchange process are Na+, NH4+ (or alternate amine), OH-, and C1-. The equations derived to describe the various conditions involved are highlighted. Assumptions. The number of assumptions involved with this development have been limited to produce as general a model as possible. MBIE has been considered from a mass-transfer-limitation viewpoint with film diffusion control, which was justified earlier. Exchange resistance due to particle diffusion is not accounted for in the derived flux expressions. Also, the rates of reactions are assumed to be instantaneous compared to the rate of exchange. Other assumptions are uniform bulk- and resin-phase compositions for a given particle, equilibrium at the particle-film interface, bulk-phase neutralization,
1888 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991
negligible hydrogen ion concentration, activity coefficients equal to unity, pseudo-steady-state mass transfer, isothermal operation, and plug flow. Simplifying assumptions have been employed only as necessary. The plug flow assumption has been used by Kataoka et al. (1972) and Haub and Foutch (1986a,b). The negligible hydrogen ion concentration is a direct result of operation in the 9.0-9.8 pH range, since this gives hydrogen ion concentrations of 10-9-10-9.8 M. The dissociation of ammonia affects the bulk-phase concentrations of the amine (dissociated and undissociated) and hydroxyl ions. The reaction between the dissociated amine and hydroxide has been restricted to the bulk phase to accommodate the release of these species from the cation and anion resins, respectively. The bulk-phase concentrations of these ions are corrected on the basis of the exchange process and the amount of undissociated amine present. The equilibrium reaction is given as amine+ + OH-
-
amine
+ H20
The reaction consumes released amine and hydroxyl ions in order to maintain equilibrium. In turn, the bulk-phase concentrations affect the exchange process by changing the concentration driving force across the film and the effective diffusivity of all species present. This shows the coupled nature of the exchange. The release or removal of various ions affects the bulk concentrations of the other constituents through the amine equilibrium relation. This equilibrium is expressed as (Gamine+) (COH-) KB = (2) CNH~ Flux Expressions. The flux expressions, and thereby the concentration of the bulk and resin phases, are derived by using the Nernst-Planck equation. This expression incorporates the typical concentration driving force and includes an electrical potential effect due to differing ionic mobilities. The flux is related using these equations by a diffusion coefficient. The Nernst-Planck equation for ion (i) is (3) Equation 3 is used in conjunction with the static-film model. Other methods for handling multicomponent liquid film mass transfer have been discussed by Frey (1986). He describes the benefits of matrix generalization methods while indicating that they are also more difficult to apply. Both film models and matrix methods gave good agreement with exact calculations. Further work (Frey and Wong, 1989) describes the use of matrix theory for several applications including ion exchange. The matrix procedure was better than the film models for the concentration range of 10-4-10-1 mequiv/cm3, higher than the concentration range of interest for this model. Using a different film model may be appropriate, but the simpler static-film model has been shown to work reasonably well (Kataoka et al., 1973). The resulting expression for the flux of sodium through the film surrounding the cation resin is
Equation 4, combined with a similar expression for the flux of the chloride ion for the anion resin, allows the application of the static film model to define the effective diffusivity for each species.
Particle Rates and Effective Diffusivities. The particle rate expression given by the static film model is a ( c i ) / a t = Ki'a,(Cio - ci*) (5) where ( Ci)is the resin-phase concentration of species i. This can be related to the flux across the film due to pseudo-steady-state exchange as (6) a(ci)/at = -vi)aS This relation can be used to define the effective diffusivity for species i since the constant in the rate expression is K' = De/6 (7) where De is the effective diffusivity and 6 is the film thickness. The resulting expression for De is (8) De = -6Ji/(Cio - Ci*) The expression for the flux, eq 4, can be used in eq 8, and the result is an explicit expression for the effective diffusivity as
The resin-phase and liquid-phase compositions are more conveniently expressed in fractional notation as Yi = ( C i ) / Q for the resin fraction and xi = Ci/CT for the liquid-phase concentration fraction. In these relations, Q is the total resin capacity and CT is the total inlet counterion (or co-ion) concentration. CT is used for comparison purposes and to keep a consistent basis. The actual fractional concentrations, which vary with bed depth, are determined at each distance increment within the column and used in the flux evaluation. These concentrations are then corrected to the CT basis for the next material balance calculation. The selectivity coefficient can be used to eliminate the interfacial concentration in favor of the resin-phase fraction when combined with the film concentration equation. Fluid flow effects are incorporated depending on the particle Reynolds number using either Carberry's (1960) or Kataoka's (Kataoka et al., 1972) equation for the nonionic mass-transfer coefficients. These coefficients are included in the rate equation by using the Ri factor, where Ri is the ratio of electrolyte to nonelectrolyte mass-transfer coefficients:
Ri= (De/Di)2/3= K,'/Ki
(10) Ki is the nonionic mass-transfer coefficient in the packed bed based on species i and indicates the extent to which the differing ionic mobilities effect the exchange process. Kataoka et al. (1973) showed that the two-thirds power of the diffusivity ratio correlated very well, which agrees with the results of Pan and David (1978). Adding this relation to the previously defined particle rate yields ayi/at = K ~ R ~ ~ ~ c ~-( XXi *~) /O8 (11) Material Balances. The overall material balances for the column are evaluated to determine the concentration profile within the column and the effluent concentration history. The column material balance is
for one resin. The fact that the column is a mixed bed of cationic and anionic resins requires that the volume fraction of each resin be incorporated into the balances.
Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 1889 This is accomplished by defining two system parameters, FCR (cation resin volume fraction) and FCA (anion resin volume fraction), which allows for the inclusion of a third, inert resin, sometimes used as a separation aid. These parameters allow both resins to be considered simultaneously. The form of the equations can be improved by a transformation to the dimensionleas independent variables used by Kataoka and Yoshida (1976). These new variables are
Table I. Temperature-Dependent Values Ionic Diffusion Coefficienta DN, = (RT/F)(23.00498 + 1.064167' + 0.0033196ZV Dh = (RT/F)(1.405492' + 39.1537) DOH= (RT/P)(104.74113 + 3.80754411 D a = (RT/F)(39.6493 + 1.391762' = 0.00331967V Dissociation Constants species K, = exp(-(4470.99/2' - 6.0875 + 0.1706T))" HZO KB = 10(-(4.8601 + 6.31 X' 10dT - 5.98 X 10-T')) NH3 morpholine KB = lo(-(5.7461 8.095 X lO?l' - 0.013881p))
+
p
and (I
The resulting material balance equations are
where FCj is the volume fraction of the resin over which the balance is performed. A basis for the new variables must be selected; this case has been based on the parameter values for sodium. This requires the chloride material balance equation to use sodium-based independent variables, which changes the form of the equation slightly. The particle rate equations must be transformed to the new independent variables. aYNa/aT = 6RNa(XNao - XN~*) (16) and
Hence, the material balance equation can be written in the form
- - - --ayi = ratei axi
at
a7
where the rate equation is given by the particle rate expression. This resultant system of equations can be solved by the method of characteristics. The numerical technique evaluates these equations along curves of constant 7 and 5. This requires the ability to solve a system of ordinary differential equations. Their solution is accomplished by using the Adams-Bashforth (fourth order) explicit method in 7 and Adams-Bashforth-Moulton (fourth order) in 5. The basic calculation procedure is to set the inlet conditions for the column, calculate all of the constant system properties (Di,Ki), and then solve the differential equations. The order of solution is to integrate in 5 at constant I and then step in 7 . The outlet concentrations, resinphase composition, and outlet pH are continuously monitored. Temperature Effects. The model contains several temperature-dependent properties. Divekar et al. (1987) modified the model developed by Haub and Foutch (1986a,b) to account for temperature effects. Those equations have been supplemented with additional ones required for this work. Those that can be incorporated for different temperatures have been fit in the typical zone of operation (20-90 "C). Table I summarizes the temperature-dependent properties considered and the equations used to evaluate them. The diffusion coefficients use the limiting ionic mobilities given by Robinson and Stokes (1969). The diesociation constants were fitted to the curves presented by Sawochka et al. (1988).
Bulk Solution Viscosity = 1.5471 - 0.03171092' + 2.3345 X lO4P
Divekar et al. (1987).
Table 11. Model Parameters Bulk Phase viscosity ( p ) temperature (9 capacities (Qc, Q.) selectivity coeff
flow rate column diam packed height void fractn (e)
Resins particle d i m (dp,dp.) Column Conditions cation resin vol. fractn (FCR) anion resin vol. fractn (FCA) init resin-phase concn (ri;t = 0)
Inlet Conditions sodium and chloride concn ionic diffusion coeff (D's) PH
The necessary equations and parameters have been determined for the MBIE column under consideration. These can now be compared with existing data to evaluate the capability of the model to describe amine cycle ion exchange. Discussion The necessary model parameters are summarized in Table 11. These are system- or species-dependent properties that can be obtained from manufacturers' data or the literature. This is the major advantage of a theoretical model: existing parameters can be used to compare with experimental results and examine hypothetical situations. Rates of Exchange. The ratio of electrolyte to nonelectrolyte mass-transfer coefficients (Ri) describes the effect that differing ionic mobilities have on the exchange process. Ri depends on the diffusivities of the exchanging species and the resin characteristics. Ammonium has a higher self-diffusion coefficient than sodium, so when ammonium is the exiting species from the resin the rate of exchange should be enhanced. The ratio of self-diffusion coefficients of sodium and ammonium is nearly 1, and this, coupled with the unfavorable and near-unity value of the selectivity coefficient, results in very limited sodium loadings for forward exchange, where the remainder of the resin is in the ammonium form. The dimensionless rate of exchange for equivalent inlet sodium concentrations in the ammonia cycle is shown in Figure 1. Morpholine, on the other hand, has a lower diffusivity than sodium, so the value of R j will be less than 1. This tends to retard the exchange process. The actual value of the selectivity coefficient varies greatly from resin to resin, particularly as a function of divinylbenzene cross-linkage (Myers and Boyd, 1956). The rate of exchange of sodium for morpholine on Ambersep 252 (K$ - 2.1) and Ambersep 200 (K$ = 15) (McNulty, 19901, for the same conditions used in Figure 1, is shown in Figure 2. The rate is positive over a larger loading range
1890 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 2.00r
0.00
cka= 1 x
1000
I
\ '
IO-~M
\
-
0.05 0.10 0.15 0.20 0.25 0.30 FRACTION OF SODIUM IN THE RESIN
Figure 1. Rate of exchange of sodium for ammonium on a single particle a t various pH values.
TIME (minutes)
Figure 4. Comparison of time for 2 fig/ kg breakthrough between this work and Bates and Johnson AMMLEAK model (1984). 4.01
~~
CATlONiANlON
.
=
y" 3.0 01 1
I
2
0.00
0.20 0.40 0.60 0.80 1.00 FRACTION OF SODIUM IN THE RESIN
Figure 2. Rate of exchange of sodium for morpholine on a single particle at various pH values on Ambersep 200 and 252 cation resins.
0.0;
2.01
0.0 1 0
2000
4000
6000
I
8000
TIME (minutes)
Figure 5. Predicted sodium breakthrough for ammonia cycle exchange at various cation-to-anion resin ratios for pH 9.6.
1
2000
4000 6000 TIME iminutesr
8000
0 01 r,
2000
4000
6000
8000
TIME minutes;
Figure 3. Predicted sodium breakthrough for ammonia cycle exchange with a step change in inlet concentration compared to Bates and Johnson (1984), experimental.
Figure 6. Predicted sodium breakthrough for ammonia cycle exchange a t 25,40, and 60 O C for temperature-independent selectivity.
than for ammonia due to the favorable selectivity coefficient. Ambersep 200 has a significantly higher selectivity coefficient for sodium over morpholine, and the range of positive rates has increased considerably when compared with Ambersep 252. The rate for Ambersep 200 remains positive for a wider range of sodium loadings and then drops off sharply as the equilibrium loading is exceeded. This implies that morpholine, although unfavorable to Ri, compared with ammonia, has advantages for sodium exchange. Column Simulations. Column conditions equivalent to those used by Bates and Johnson (1984) have been studied with our model so that the results of their AMMLEAK model can be compared with the one developed here. The pH conditions vary from 9.2 to 9.8 for ammonia cycle exchange, and inlet sodium concentrations have been evaluated from 10 pg/kg to 1 mg/kg. This gives a wide range of conditions for model evaluation. Bates and Johnson (1984) conducted one experimental run on a l-mcolumn at pH 9.4 to compare model predictions with actual data. The AMMLEAK model overpredicts the time for breakthrough based on an intermittent condenser leak of 1 mg/kg. The model developed here is compared with their experimental data in Figure 3. The predicted curve at pH 9.4 agrees quite well with
their experimental data, which has an accuracy of the experimental pH of fO.O1 (Bates, 1990). A comparison of AMMLEAK predicted times to 2 pg/kg breakthrough, for constant sodium inlet concentrations, and the present model predictions are given in Figure 4. The current model underpredicts the time at each inlet concentration for pH 9.4. The AMMLEAK model predicts breakthrough times reasonably well for ammonia cycle exchange due to the small impact of Ri.AMMLEAK failings become more evident when the possibility of hydrogen cycle exchange is considered. The effect of cation-to-anion resin ratio on ammonia cycle exchange is shown in Figure 5. The net effect of an increase in the cation resin volume fraction is to increase the bed capacity for sodium. The increase in breakthrough times for sodium is evident from this figure. The possible breakthrough of chloride becomes important only at very high cation resin fractions since the selectivity coefficient for chloride on the anionic resin is 16.5. This observation will change when the morpholine cycle is considered. Breakthrough curves for 25,40, and 60 O C are shown for total ammonia concentration equivalent to pH 9.6 at 25 "C, in Figure 6. The net effect of increased operating temperature is to increase the breakthrough time for sodium. This prediction does not account for the tempera-
Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 1891
0.0015
I
AMBE RSEP/
I
TlME (minutes)
TIME (minutes)
Figure 7. Predicted sodium breakthrough curves for morpholine cycle exchange a t various pH values and conditions equivalent to Figure 3.
Figure 9. Comparison a t sodium breakthrough in morpholine cycle for Ambersep 200 and Ambersep 252. 1500
c= ,;
.soot 1 \
I
0.1 ppm
I I I
* o oO I
""9
2 cn
CHLORIDE
I
"" 0
8000
/ ,
9000
10000
SODIUM
11000
12000
TIME (minutes)
ob
10000
20000 30000 TIME (minutes)
40000
Figure 8. Comparison of time for 2 Hg/kg breakthrough for ammonia cycle and morpholine cycle operation.
ture dependence of the resin selectivity coefficient due to a lack of experimental information. Industrial-scale ionexchange units are typically run at temperatures in the range of 40-60 "C. ke mentioned, the use of morpholine instead of ammonia for pH control has two drawbacks. First, its dissociation constant is nearly an order of magnitude lower than that for ammonia. This requires nearly an order of magnitude increase in the bulk-phase concentration of morpholine to attain the same pH. This results in increased amine cost. Second, morpholine has degradation products that are known to have a negative effect on steam cycle chemistry. However, the favorable selectivity for sodium over morpholinium and the reduced corrosion rates outweigh these problems. (Sadler et al., 1988). The same conditions used to evaluate the ammonia cycle have been applied for the morpholine cycle. The selectivity coefficient for Ambersep 252 (2.1)was used in these model evaluations. This allows the comparison of both cycles on essentially equal ground. The breakthrough characteristics equivalent to those in Figure 3 for ammonia are shown for morpholine in Figure 7. The predicted breakthrough time has increased because the column is sufficiently large to overcome the unfavorable diffusivity effect. The condition of constant sodium inlet concentration is compared with breakthrough times to a 2 pg/kg limit for ammonia and morpholine in Figure 8. This figure implies that morpholine has the potential for longer MBIE unit service times than ammonia under the same process conditions. A comparison between Ambersep 252 and 200 is shown in Figure 9. The increased selectivity coefficient greatly increases the breakthrough time, as one would expect. In the case of Ambersep 200,chloride breakthrough must also be considered since the anionic resins have typically 60% of the exchange capacity of the cation resins. This operational scheme is when the model can be used to select the optimum cation-to-anion resin ratio. The possibility of chloride breakthrough prior to sodium is shown in Figure 10. Here the chloride has reached the inlet concentration
Figure 10. Breakthrough curves for sodium and chloride in morpholine cycle a t pH 9.6 for Ambersep 200 cation resin.
level before the sodium breakthrough has fully developed. The level of contamination considered acceptable influences which species must be tracked. The sodium concentration rises sooner than chloride, but when breakthrough occurs, the chloride concentration rises rapidly. Conclusions The model presented here compares favorably with both the existing experimental data and the mass action equilibria model of Bates and Johnson (1984). The major advantage of the present model is the ability to make predictions based on available parametric data. Additionally, the model can be modified to evaluate other alternative amines and their effects on ion exchange solely on the basis of the experimental values for the system properties. The Wilke-Chang (1955) equation can be used to estimate self-diffusion coefficients for species that are not readily available within the literature. The comparisons between ammonia and morpholine as pH-control agents show morpholine, operating in the morpholine cycle, is a viable alternative to ammonia. The major drawback of morpholine is its degradation within the steam cycle and the effects that these degradation products have on the corrosion and exchange processes. Current applications of the model are limited by the accuracy of the available data. Most of the parameters used within the model are accurate to only two significant digits. This combined with the tremendous effect an error in a parameter, such as the capacity of the resin, can have on the predicted MBIE behavior, suggests that more reliable data are needed for these system parameters. Acknowledgment
This work has been partially funded by a grant from the National Science Foundation, RIT-8610676. We are grateful for this support. Nomenclature a, = interfacial surface are (L2/L3) Ci= concentration of species i (mequiv/L3)
1892 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991
C,* = concentration of species i in t h e resin (mequiv/L3) C , O = concentration of species i i n the bulk (mequiv/L3) d, = particle diameter (L) D, = diffusivity of species i (L2/t) De, = effective diffusivity for species i (L2/t)
F = Faraday's constant (C/mol) FCA = anion resin volume fraction FCR = cation resin volume fraction J, = flux of species i in t h e film (mequiv/(t L2)) K B = dissociation constant for base B K , = mass-transfer coefficient (including flow) ( L / t ) K,' = mass-transfer coefficient (excluding flow) (L/t)
K t = resin selectivity for i compared t o j
K , = dissociation constant of water Q = capacity of t h e resin (mequiv/L3) R = universal gas constant R' = ratio of resin concentration to bulk concentration R, = ratio of mass-transfer coefficients T = temperature or T criteria t = time (t) t , = external diffusion time t , = internal diffusion t i m e u = superficial velocity ( L / t ) XA*= fractional interfacial concentration of species A x, = bulk-phase concentration fraction of species i y , = fraction of species i o n the resin 2, = charge of species i Greek Letters 6 = film thickness (L) t = void fraction 4 = electrical potential (mL2/(t C)) F = viscosity of t h e bulk phase ( m / ( L t ) ) T = dimensionless combined time-distance variable 6 = dimensionless distance variable Superscripts O = bulk-phase value * = interfacial value ' = overall value Subscripts a = anion resin A = species A B = species B/base B c = cation resin C1 = chloride H = hydrogen i = species i j = species j N a = sodium OH = hydroxide w = water Am = ammonium/morpholinium Registry No. NH3, 7664-41-7; Morpholine, 110-91-8.
Literature Cited Bates, J, C. Nuclear Electric, UK, personal communication, 1990. Bates, J. C.; Johnson, T. D. The Development of a Computer Model, AMMLEAK, for Sodium Leakage from HN,+/OH- Form Mixed
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