This lesson introduces general principles of ion exchange reactions and setup simulations for ion exchange reactions in well-mixed batch reactors using CrunchFlow.
By the end of this lesson, you should be able to:
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If you have any questions, please post them to our Questions? discussion forum (not e-mail), located in Canvas. The TA and I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.
Ion exchange reactions occur when ions in water exchange with those electrostatically bound to the solid phase. They occur commonly in the presence of iron oxides, organic matters, and clay minerals with large surface area. Ion exchange reactions are important in determining natural composition in surface waters (e.g., rivers, lakes) and ground water. They can alter water composition and trigger other reactions including mineral dissolution and precipitation. For example, in the coastal freshwater aquifer, Na+ in seawater displaces presorbed Ca2+ from solid phase (Figure 1). In this reaction, Ca2+ is replaced by Na+ and the water changes from Na-rich to Ca-rich (Appelo and Willemsen, 1987; G., 2008; Slomp and Van Cappellen, 2004) while the solid surface change from Ca-rich to Na-rich. In northeastern United States, the use of road salt as deicer increases the salinity of fresh water and mobilize metals through ion exchange reactions (Kaushal et al., 2005).
Applications of ion exchange reactions in industry include drinking water softening (Figure 2), desalination, ultra-pure water production (Rodrigues, 1986), and chromatography. In petroleum refining processes, ion exchange reactions are often used to purify, separate, and dry natural gases (Marinsky and Marcus, 1995). Natural gas extraction in the Marcellus shale has led to the production of large quantity of wastewater with high metal concentrations. Ion exchange is commonly used to remove metals such as Ba2+ and Sr2+ (Gregory et al., 2011).
Ion exchange reactions occur when ions exchange their positions at the soid-surface – water interface. These reactions are typically assumed reversible and occur instantaneously at time scales ranging from microseconds to hours. Ion exchange is typically represented in the following form:
Here (s) and (aq) refer to solid and aqueous phases, respectively; X- denotes the negatively charged surface sites that bound cations Au+ and Bv+, with u and v being the charges of A and B, respectively. In this reaction, A and B are cations that compete for sorption sites (Appelo and Postma, 1993; Sposito et al., 1981; Vanselow, 1932). The equilibrium constant Keq of reaction (1) can be expressed as
Here the parentheses [ ] represent activities. Aqueous concentrations are easily related to activities through concentration and activity coefficients. Activities of ions on solid phases are typically expressed as a fraction of the total, either as molar fraction or as equivalent fractions. The total number can be based on the number of exchange sites or as the number of exchangeable cations.
The units meq is often used in ion exchange calculations. An meq is the number of ions that sums a specific quantity of electrical charges. For example, an meq of K+ is about 6.02 x 1020 positive charges. On the other hand, an meq of Ca2+ is also 6.02 x 1020 positive charges, however only 3.01 x 1020 ions because Ca2+ has two positive charges. For an ion Ii+ with a charge of i, the equivalent fraction bI is calculated as:
where I, J, K are exchangeable cation with charges i, j, k, respectively. A molar fraction $\beta_{I}^{M}$ is obtained by the following form:
Here TEC is the total exchangeable cations in mmol/kg sediment, not cation exchange capacity. The use of fractions should give the summation of fractions being 1, that is, .
Three common conventions used in writing ion exchange equilibrium constants are Gaines-Thomas convention, Gapon convention, and Vanselow convention. If the ion exchange is between cations of the same valence (homovalent exchange), the convention does not make a difference. If the exchange is between cations of different valences (heterovalent), the convention makes a difference. For example, the ion exchange reaction between Na and Ca can be written as follows:
With
Here if the equivalent fraction of the exchangeable cations is used for $β$ values, the Gaines-Thomas convention is followed (Graines and Thomas, 1953). If we use molar fractions for $β$ values, we follow the Vanselow convention (Vanselow, 1932). If the activities of cations on exchange sites are expressed as a fraction of the number of exchange sites (X-), we follow the Gapon convention, the reaction will be written as follows:
Where
Here the activities are expressed in terms of the mole fraction of the total number of exchangeable sites. To fully understand the difference between different conventions and calculation, please go over Example 6.3 in chapter 6 of Appelo and Postma (2005).
The capabilities of ions to compete for exchange sites are governed by their affinity to the surface of the exchangers. Selectivity coefficients have been reported in literature for common ions including Na+, K+, Ca2+, and Mg2+, however rarely for trace metals. The larger the selectivity coefficient, the higher affinity of the ion to the solid phase and the more competitive for exchange. In general, ions have high affinity to exchange sites when they have higher valence, are less solvated with water molecules, and react strongly with the surface sites. The following Table 1 lists selectivity coefficients reported in literatures for ion exchange on kaolinite (Appelo and Postma, 2005; Bundschuh and Zilberbrand, 2011).
No. | Ion exchange reaction | log K |
---|---|---|
1 | $2 \mathrm{Na}-X+\mathrm{Mg}^{2+} \Leftrightarrow \mathrm{Na}^{+}+\mathrm{Mg}-X_{2}$ | 0.60 (0.44 ~ 0.78) |
2 | $2 \mathrm{Na}-\mathrm{X}+\mathrm{Ca}^{2+} \Leftrightarrow \mathrm{Na}^{+}+\mathrm{Ca}-X_{2}$ | 0.80 (0.44 ~ 0.104) |
3 | $2 \mathrm{Na}-X+\mathrm{Ba}^{2+} \Leftrightarrow \mathrm{Na}^{+}+\mathrm{Ba}-X_{2}$ | 0.91 (0.44 ~ 0.104) |
4 | $2 \mathrm{Na}-X+\mathrm{Sr}^{2+} \Leftrightarrow \mathrm{Na}^{+}+\mathrm{Sr}-X_{2}$ | 0.91 (0.44 ~ 0.104) |
For typical ion exchangers, the sequence of affinity is as follows: Ba2+> Pb2+ > Sr2+ > Ca2+ > Ni2+ > Cd2+ > Cu2+ > Co2+> Zn2+ > Mg2+ > Ag+> Cs+ > K+ >NH4+ >Na+ >H+. When there are multiple cations co-exist in the solution, the surface exchange site composition is largely determined by the cation aqueous concentration and their affinity to the exchange sites. To calculate the exchange site composition, that is, the mole fraction of each cation on the exchange site, please follow the example 6.4 in chapter 6 of Appelo and Postma (2005).
The cation exchange capacity (CEC, meq/kg solid) is a measure of the solid phase capacity for ion exchange reactions (Meunier, 2005). The CEC of different porous media are very much associated with their clay content, organic carbon, and grain size. Different materials have different CEC values. CEC values of clay minerals such as muscovite, illite, kaolinite, and chlorite are high for their grain sizes smaller than 2 μm (Drever, 1982). In general, organic matter has the highest CEC values (1500 - 4000 meq/kg). Iron oxides play a vital role in natural processes and controls nutrient availability and heavy-metal mobility (Houben and Kaufhold, 2011). Iron oxides, such as goethite and hematite, have CEC values from 40 to 1000 meq/kg. Many solid materials have iron oxides or organic matters coated on their surface and therefore have large CEC values. For soils, CEC value is a function of solution pH depending on hydrolysis reactions of surface sites. In general, cation exchange occurs due to the broken bonds around the crystal edges, the substitutions within the lattice, and the hydrogen of exposed surface hydroxyls that may be exchanged. Higher pH values give rise to more negative charges on clay, resulting in higher CEC. CEC values increase as the grain size decreases due to the large surface area associated with smaller grains.
Minerals | Grain size (μm) | Surface area (m2/g) | CEC (meq/kg) |
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Kaolinite | 0.1-5.0 | 5-20 | 30-150 |
Illite | 0.1-2.0 | 15-40 | 150-400 |
Montmorillonite | 0.01-1.0 | 600-800 | 800-1200 |
Marcellus Shale flow back and produced waters typically contains high concentrations of metals, including Na(I), Ca(II), Mg(II), Sr(II), and Ba(II) (Chapman et al., 2012). The release of Marcellus Shale waste water into natural soils and sediment can lead to ion exchange reactions and partition of surface sites between major cations. Here we set up a batch experiment in CrunchFlow to model the major cations exchange on clay surface from Marcellus shale produced water.
Assume that we have the following Marcellus water in a 300 ml batch reactor. The water is in equilibrium with partial pressure of CO2 at 3.15×10-4 atmosphere. Please note that the concentrations are in ppm and in mol/kgw. Both can be used directly in CrunchFlow.
Component | Conc. (ppm) | Molar (mol/kgw) |
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pH | 7.02 | |
Co2 (aq) | Co2(g), 3.15e-4 atm | |
Na(I) | 7900.0 | 3.43e-1 |
Ca(II) | 2774.0 | 6.94e-2 |
K(I) | 82.5 | 2.11e-3 |
Mg(II) | 239.0 | 9.83e-3 |
Ba(II) | 183.0 | 1.34e-3 |
Sr(II) | 6.5 | 7.38e-5 |
C1(-I) | charge |
“Charge” means that the ion concentration is calculated from charge balance.
The water is in equilibrium with a sediment with kaolinite being the major clay with a specific surface area of 13.9 m2/g and a CEC value is 100.0 meq/kg (the units in CrunchFlow is eq/g). The kaolinite occupies 0.005 of the total volume.
The selectivity coefficient of the cations are as follows in the database (values from (Appelo and Postma, 1993; Li et al., 2010)):
No. | Ion exchange reaction | log K |
---|---|---|
1 | $\mathrm{Na}X\Leftrightarrow\mathrm{Na}^++X^-$ | 0.0 |
2 | $\mathrm{K} X \Leftrightarrow \mathrm{K}^{+}+X^{-}$ | -0.69 |
3 | $\mathrm{Ca} X_{2} \Leftrightarrow \mathrm{Ca}^{2+}+2 X^{-}$ | -0.39 |
4 | $\mathrm{Mg} X_{2} \Leftrightarrow \mathrm{Mg}^{2+}+2 X^{-}$ | -0.30 |
5 | $\mathrm{Ba} X_{2} \Leftrightarrow \mathrm{Ba}^{2+}+2 X^{-}$ | -0.45 |
6 | $\operatorname{Sr} X_{2} \Leftrightarrow \mathrm{Sr}^{2+}+2 X^{-}$ | -0.45 |
To set up CrunchFlow simulation please read CrunchFlow manual page 62 – 63 for details. Please also refer to the Exercise 5: Cs exchange on Hanford sediments.
You will need to set up the ION_EXCHANGE key word block in the input file to define the name of the exchange site and give parameters related to ion exchange in the CONDITION block. In addition, you will also need to define exchange reactions and equilibrium constants in the “Begin Exchange” block. For example, if you call your exchange site “XKao”, then you have the following block:
ION_EXCHANGE
exchange XKao- on Kaolinite
convention Vanselow
END
The first line specifies name of the exchange site and the mineral that the exchange is on. The second line specify the calculation convention that is used.
As an extension of the example 4.1, we can look at different parameters and understand how they change the cation concentrations on the exchange site. Please include all Cl- and OH- aqueous complexes as in example 4.1. Please calculate the major cation concentrations on the exchange site (K, Na, Ca, Mg, Ba, Sr) by changing only the parameter discussed in each sub-question, with all other parameters being the same as those in example 4.1. For each sub questions, please plot major cation concentrations on the exchange site as the changing parameter.
For each question, calculate the mole fraction of each species on the exchange site, and the mole fraction of each species compared to its own original total mass. Please make a table and a figure comparing different species. Which one has the largest percentage of its own mass on exchange sites? Why?
Which parameter(s) have the largest impact on ion exchange reactions? In lesson 3 we learned that pH is important for surface complexation reactions. Does it make a difference for ion exchange reactions?
Read the paper (Valocchi et al., 1981). Native groundwater in the injection test of this paper had the composition of $Na^+=\ 86.5,\mathrm{\ Mg}^{2+}=18.2,\text{ and }\mathrm{Ca}^{2+}=11.1\mathrm{\ mmol}/\mathrm{L}$. Injected water has 14.66 meq Cl-/L. Selectivity coefficient were (Gaines and Thomas convention, activity = molal concentration) $\mathrm{K}_{\text{Na\Mg}}=0.54\text{ and }\mathrm{K}_{\text{Na\Ca}}=0.41$. Sediment $\mathrm{CEC}=750\mathrm{\ meq}/\mathrm{L}$ pore water. Calculate
Ion exchange is an important chemical process in natural and engineered systems. Understanding ion exchange reaction is important for us to understand and predict the reactive transport and fate of chemicals in nature. Here we introduce the reaction thermodynamics of ion exchange, and the set up of ion exchange simulation in a well-mixed batch reactor in CrunchFlow.
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