12.4. ION-EXCHANGE PROCESSES

12.4A. Introduction and Ion-Exchange Materials

Ion-exchange processes are basically chemical reactions between ions in solution and ions in an insoluble solid phase. The techniques used in ion exchange so closely resemble those used in adsorption that for the majority of engineering purposes ion exchange can be considered as a special case of adsorption.

In ion exchange, certain ions are removed by the ion-exchange solid. Since electroneutrality must be maintained, the solid releases replacement ions to the solution. The first ion-exchange materials were natural-occurring porous sands called zeolites, which are cation exchangers. Positively charged ions in solution such as Ca²⁺ diffuse into the pores of the solid and exchange with the Na⁺ ions in the mineral:

Equation 12.4-1

where R represents the solid. This is the basis for “softening” water. To regenerate, a solution of NaCl is added, which drives the reversible reaction above to the left. Almost all of these inorganic ion-exchange solids exchange only cations.

Most present-day ion-exchange solids are synthetic resins or polymers. Certain synthetic polymeric resins contain sulfonic, carboxylic, or phenolic groups. These anionic groups can exchange cations:

Equation 12.4-2

Here R represents the solid resin. The Na⁺ in the solid resin can be exchanged with H⁺ or other cations.

Similar synthetic resins containing amine groups can be used to exchange anions and OH^– in solution:

Equation 12.4-3

12.4B. Equilibrium Relations in Ion Exchange

The ion-exchange isotherms have been developed using the law of mass action. For example, for the case of a simple ion-exchange reaction such as Eq. (12.4-2), HR and NaR represent the ion-exchange sites on the resin filled with a proton H⁺ and a sodium ion Na⁺. It is assumed that all of the fixed number of sites are filled with H⁺ or Na⁺. At equilibrium,

Equation 12.4-4

Since the total concentration of the ionic groups on the resin is fixed (B7),

Equation 12.4-5

Combining Eqs. (12.4-4) and (12.4-5),

Equation 12.4-6

If the solution is buffered, so that [H⁺] is constant, the above equation for sodium exchange or adsorption is similar to the Langmuir isotherm.

The ion-exchange process functions for strong acid or strong base exchangers by replacing the ions of a solution with ions such as H⁺ or OH⁻. These replaced ions from the solution are taken up by the resin. Then, to regenerate the resin, a small amount of solution with a high concentration of H⁺ is used for cation exchangers or a high concentration of OH⁻ ions for anion exchangers. These high concentrations of H⁺ or OH⁻ for regeneration shift the equilibrium to the left, making the regeneration process more favorable.

A typical ion-exchange process for removal of metals from solution is shown for copper cation being removed from a stream containing dilute CuSO₄ and H₂SO₄:

Equation 12.4-7

For regeneration, the bed of resin is contacted with a high concentration of H₂SO₄ to shift the equilibrium to the left.

12.4C. Use of Equilibrium Relations and Relative-Molar-Selectivity Coefficients

Convenient tables for relative-molar-selectivity coefficients K have been prepared for various types of ion-exchange resins. Data are given in Table 12.4-1 for a polystyrene resin with 8% divinylbenzene (DVB) cross-linking (B8, P4) for strong-acid and strong-base resins. For cation exchangers, values are given for cation A entering the resin and displacing the cation Li⁺, and for anion exchangers, values for anion A replacing Cl⁻.

Table 12.4-1. Relative-Molar-Selectivity Coefficients K for Polystyrene Cation and Anion Exchangers with 8% DVB Cross-Linking (B8, P4)

Strong-Base Anion Exchanger (Relative to Cl− as 1.0)		Strong-Acid Cation Exchanger (Relative to Li+ as 1.0)
Cl−	1.0	Li+	1.0
Iodide	8.7	H+	1.27
Nitrate	3.8	Na+	1.98
Acetate	0.2		2.55
Sulfate	0.15	K+	2.90
Hydroxide	0.05–0.07	Mg2+	3.29
		Cu2+	3.85
		Ca2+	5.16

The equilibrium constant or selectivity coefficient for exchange of any two ions A and B can be approximated from Table 12.4-1 using values of K_A and K_B:

Equation 12.4-8

For example, for the reaction of cation K⁺ (A) displacing cation H⁺ (B),

Equation 12.4-9

Substituting into Eq. (12.4-8), K_A,B = K_A/K_B = 2.90/1.27 = 2.28.

For dilute solutions, activity coefficients are relatively constant and simple concentration units are used. For Eq. (12.4-9), the equilibrium constant is as follows:

Equation 12.4-10

where, for the resin phase, concentrations q_KR and q_HR are in equivalents/L of bulk bed volume of water-swelled resin, and for the liquid phase, concentrations and are in equivalents/L of volume of solution.

The total concentration C in the liquid solution and the total concentration Q in the resin remain constant during the exchange process because of electroneutrality in Eq. (12.4-9). Then,

Equation 12.4-11

In the case of Eq. (12.4-7), where the ion Cu²⁺ (A) replaces H⁺ (B) and the charges are unequal,

Equation 12.4-12

EXAMPLE 12.4-1. Removal of Cu2+ Ion from Acid Solution by an Ion-Exchange Resin A waste acidic stream contains copper in solution which is being removed by a strong acid–cation resin. The cation Cu2+ (A) is displacing the cation H+ (B) in the resin. A polystyrene resin similar to that in Table 12.4-1 is being used. The total resin capacity Q is approximately 1.9 equivalents/L of wet bed volume. For a total concentration C of 0.10 N (0.10 equivalents/L) in the solution, calculate at equilibrium the total equivalents of Cu2+ in the resin when the concentration of Cu2+ in solution is 0.02 M (0.04 N). Solution: The known values are C = 0.10 N or equivalents/L of Cu2+ (A) and H+ (B) in solution and Q = 1.9 equivalents/L of A and B in the resin. The equilibrium relation is Eq. (12.4-7): or, From Table 12.4-1, KA = = 3.85 and KB = = 1.27. Then, from Eq. (12.4-8), Using Eq. (12.4-12), From Eq. (12.4-11), C = 0.10 equivalents/L = + . Also, Q = 1.9 = qHR + . The values to substitute into Eq. (12.4-12) are KA,B = 3.03, = 1.9/2 − = 0.02, and = 0.10 − = 0.10 − 0.04 = 0.06. Rearranging, Solving this quadratic equation, qHR = 0.2232. Then = 1.9/2 − 0.2232/2 = 0.8384. Hence, the equivalents of Cu2+ in the resin is 2(0.8384) = 1.677 compared to a value of 1.9 when fully loaded with copper. The result shows that the removal of Cu2+ from the solution by the resin is highly favored.

12.4D. Concentration Profiles and Breakthrough Curves

1. Basic models in ion exchange

The rate of ion exchange depends on mass transfer of ions from the bulk solution to the particle surface, diffusion of the ions in the pores of the solid to the surface, exchange of the ions at the surface, and diffusion of the exchange ions back to the bulk solution. This is similar to adsorption. The differential equations derived are also very similar to those for adsorption. The design methods used for ion exchange and adsorption are similar.

2. Concentration profiles in packed beds

Concentration profiles in packed beds for ion exchangers are very similar to those given in Fig. 12.3-1a for adsorption. The typical S-shaped curves occur and pass through the bed. The major part of the ion exchange at any time takes place in a relatively narrow mass-transfer zone. This mass-transfer zone moves down the column. In Fig. 12.3-1b the breakthrough curve is shown, which is similar for adsorption and ion exchange.

3. Mass-transfer zone

As the mass-transfer zone travels down the column, the height of this zone becomes constant. This behavior is generally characteristic in cases where the ion to be removed from the feed stream has a greater affinity for the solid resin than the ion originally present in the solid. The majority of industrial ion-exchange processes fall in this category (M1). This constant height of the mass-transfer zone can then be used for scale-up, similar to adsorption scale-up.

12.4E. Capacity of Columns and Scale-Up Design Method

1. Capacity of column

The design method for fixed-bed ion exchangers is quite similar to that used for adsorption processes. Theoretical predictions of concentration profiles, the mass-transfer zone, and mass transfer may be inaccurate because of uncertainties due to flow patterns, and so forth. Hence, experiments using small packed-bed laboratory-scale columns are needed for scale-up.

The total stoichiometric capacity of the packed bed is the total shaded area in the breakthrough curve in Fig. 12.3-2. The time t_t is the time equivalent to the total capacity:

Equation 12.3-1

The usable capacity up to the break-point time t_b is the cross-hatched area from t = 0 to t_b. Then t_u, the time equivalent to the usable capacity, is

Equation 12.3-2

Numerical integration of Eqs. (12.3-1) and (12.3-2) can also be done using spreadsheets. Then the fraction of the total bed length or capacity utilized up to the break point is t_u/t_t. For a total bed length of H_T m, H_B is the length of the bed used up to the break point:

Equation 12.3-3

The length of the mass-transfer section or unused bed H_UNB in m is then

Equation 12.3-4

This H_UNB is essentially independent of the total column length. The experimental value of H_UNB is measured at the desired velocity in a small-diameter laboratory column. To design the full-scale column, the length of the bed H_B is calculated to achieve the desired capacity at the break point. Then the total column length is

Equation 12.3-5

The mass velocity of both the laboratory- and full-scale columns must be the same. The diameter of the large-scale column is calculated using the same given mass velocity.

2. Typical process variables

Some typical operating process variables are as follows. The laboratory column should be at least 2.5 cm in diameter and 0.3 m in length. Liquid flow rates commercially (W1) can be from 1 to 12 gpm/ft² (0.041–0.489 m/min) but are usually 6–8 gpm/ft² (0.244–0.326 m/min). Commercial columns are usually 1–3 m in height. Usually a freeboard of 50% or more open space is needed to accommodate bed expansion when regenerant flow is upward.

The resin gel can swell due to exchange by about 10 to 20%. Particle sizes used range from 0.2 mm to 1.0 mm. Typical moisture contents of the resins vary from 50 to 70%. The equilibrium exchange capacities of strong-acid or -base exchange resins are typically 3–5 meq/g of dry resin and 1–2 meq/ml of wet resin bed.

Regeneration flow rates are typically quite low, in the range of 0.5 to 5.0 bed volumes/h, in order to attain equilibrium while using minimum amounts of solution (W1). A bed volume is the total volume of the packed bed of resin as calculated from the column diameter and height of the packed bed.

Pressure drop can be predicted by using the equations for flow in packed beds. Typical pressure drops for beds are about 0.6 to 0.9 psi/ft height (13.6–20.4 kPa/m height) for flow rates of 6 to 8 gpm/ft². Excessive pressure drops should be avoided, since the gel-resin particles can be deformed.

A useful method for correlating experimental breakthrough curves at different flow velocities and the mass-transfer zone is as follows: Instead of plotting c/c_o versus time t, as in Fig. 12.3-1b, a plot of c/c_o versus the number of bed volumes (BV) is made. Data for different flow velocities will then tend to fall on the same curve.

3. Operating cycles

The operating cycles for ion-exchange processes in a packed bed are more complicated than those for gas adsorption. These usually consist of the following four steps, with experimental data usually needed to define each operating time (S3, W1). (1) Downflow loading of the process feed for a proper time. At the end of loading, the bed voids are filled with feed solution. (2) Displacement of the feed solution with upward flow of the regeneration solution. Thus, displacement of the occluded feed solution first occurs as a wave front. (3) Regeneration of the bed with continued upward flow of the regeneration solution. This occurs as a second wavefront. (4) Rinse upward to remove occluded regenerant from the bed. A rinse can be used instead of step (2) for recovering possibly valuable occluded process solution (W1).

For the actual design and for continuous feed flow, at least two columns are needed, so that one column is used to process the feed while the other is used for regeneration. When breakthrough occurs, the towers are switched. The total number of beds depends on the loading and regeneration times. Alternatively, a three-column system can be used for better utilization of the columns. The feed enters column 2 and then column 3 in series while column 1 is being regenerated. When breakthrough occurs in column 3, column 2 is removed for regeneration. The feed is then rerouted and goes to column 3 and then to column 1.