**Mass Transfer in Multiphase Systems**

Badie I. Morsi and Omar M. Basha

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60516

#### **Abstract**

Mass transfer in reactive and non-reactive multiphase systems is of vital impor‐ tance in chemical, petrochemical, and biological engineering applications. In this chapter, theories and models of mass transfer in gas-liquid, gas-solid and gasliquid-solid systems with and without chemical reactions are briefly reviewed. Literature data on the mass transfer characteristics in multiphase reactors over the last two decades with applications to the Fischer-Tropsch (F-T) synthesis are summarized. Moreover, the F-T reactions are described and an overview of the use of Slurry Bubble Column Reactors (SBCRs) and Multitubular Fixed Bed Reactors (MTFBRs) for low temperature F-T (LTFT) synthesis are discussed. The important factors affecting the hydrodynamic (gas holdup, bubble size/distribu‐ tion) and mass transfer parameters (volumetric mass transfer coefficients) in SBCRs for F-T synthesis, including operating conditions, gas-liquid-solid properties, reactor geometry and internals as well as gas distributors are also discussed. The discussion reveals that the performance of the LTFT SBCR operating in the churnturbulent flow regime is controlled by the resistance in the liquid-side film and/or the F-T reaction kinetics depending on the operating conditions prevailing in the reactor. Also, there is a great need to understand the behavior and quantify the hydrodynamics and mass transfer in SBCRs operating with syngas (H2 + CO) and F-T reactor wax in the presence of active catalyst (iron or cobalt) under typical F-T synthesis conditions in a large SBCR with an inside diameter ≥0.15m.

**Keywords:** Mass Transfer, Multiphase Systems, Fischer Tropsch, Slurry Bubble Col‐ umn

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **1. Introduction**

Mass transfer in multiphase (gas-liquid-solid) systems is one of the most critical processes occurring in chemical, petrochemical, and biological engineering applications. Generally, it entails transport of species among phases through diffusion (physical) and/or chemical reactions in a special unit operation (reactor), allowing such a process to take place. Chemical reactions, often used to speed up the mass transfer rate, occur whenever species of different chemical potentials are brought into contact. In multiphase systems, the species mass transfer rate is controlled not only by the system pressure and temperature, but also by the conductance of mass transfer, concentration gradients, reaction kinetics, activation energy, etc. In some cases, either the conductance of mass transfer or the reaction kinetics could control the overall mass transfer rate; and the slowest one will be the rate limiting or controlling step. For instance, oxygen transfer from the feed (gas) to the aqueous solution (liquid) in bioreactors could be the overall rate limiting step [1]. In any case, understanding mass transfer behavior in multiphase systems requires, among others, precise knowledge of all aspects affecting the overall mass transfer rate [2].

### **2. Mass transfer theories**

There are different theories dealing with mass transfer among phases, such as the two-film theory, the penetration theory and the surface renewal theory. These theories are briefly discussed below.

#### **2.1. Two-film theory**

This is the oldest theory for gas-liquid mass transfer developed by Lewis and Whitman in 1924 [3]. The theory postulates the existence of a film of a thickness (δ) in both the gas and liquid phases separated by an interface. It is based on the following assumptions: (1) the mass transfer occurs by molecular diffusion through the film, beyond which the concentration (*CAb*) is homogeneous; (2) the mass transfer through the film occurs under steady state conditions; and (3) the flux is small and the mass transfer occurs at low concentration. Accordingly, for convective mass transfer, the concentration profile is linear as shown in Figure 1 and the liquidside mass transfer coefficient is expressed by Equation (1):

$$k\_{\perp} = \frac{D\_{AB}}{\mathcal{S}\_{\perp}} \tag{1}$$

One should remember that the actual concentration profile is nonlinear as can be seen in Figure 1. In turbulent flow, however, attempts were made to relate the mass transfer coefficient with the turbulent diffusivity, which obviously is different from that in the laminar flow. Surpris‐ ingly, some experimental results were modeled with limited success using this simplistic model, where *kL* values were found to be proportional to the diffusivity to the power one. However, one should keep in mind that the film theory does not provide a direct means for estimating the film thickness.

different from that in the laminar flow. Surprisingly, some experimental results were modeled with limited success using

conditions in many industrial processes. The penetration theory expresses the liquid-side mass transfer coefficient in

concentration (ܥ (is homogeneous; (2) the mass transfer through the film occurs under steady state conditions; and (3) the flux is small and the mass transfer occurs at low concentration. Accordingly, for convective mass transfer, the concentration profile is linear as shown in Figure 1 and the liquid-side mass transfer coefficient is expressed by Equation

concentration (ܥ (is homogeneous; (2) the mass transfer through the film occurs under steady state conditions; and (3) the flux is small and the mass transfer occurs at low concentration. Accordingly, for convective mass transfer, the concentration profile is linear as shown in Figure 1 and the liquid-side mass transfer coefficient is expressed by Equation

One should remember that the actual concentration profile is nonlinear as can be seen in Figure 1. In turbulent flow,

should keep in mind that the film theory does not provide a direct means for estimating the film thickness.

Figure 1. Schematic of two film theory **Figure 1.** Schematic of two film theory

(1):

(1):

݇ ൌ ಲಳ ఋಽ (1)

݇ ൌ ಲಳ ఋಽ (1)

#### **2.2. Penetration theory 2.2. Penetration theory**

**1. Introduction**

190 Mass Transfer - Advancement in Process Modelling

transfer rate [2].

discussed below.

**2.1. Two-film theory**

estimating the film thickness.

**2. Mass transfer theories**

Mass transfer in multiphase (gas-liquid-solid) systems is one of the most critical processes occurring in chemical, petrochemical, and biological engineering applications. Generally, it entails transport of species among phases through diffusion (physical) and/or chemical reactions in a special unit operation (reactor), allowing such a process to take place. Chemical reactions, often used to speed up the mass transfer rate, occur whenever species of different chemical potentials are brought into contact. In multiphase systems, the species mass transfer rate is controlled not only by the system pressure and temperature, but also by the conductance of mass transfer, concentration gradients, reaction kinetics, activation energy, etc. In some cases, either the conductance of mass transfer or the reaction kinetics could control the overall mass transfer rate; and the slowest one will be the rate limiting or controlling step. For instance, oxygen transfer from the feed (gas) to the aqueous solution (liquid) in bioreactors could be the overall rate limiting step [1]. In any case, understanding mass transfer behavior in multiphase systems requires, among others, precise knowledge of all aspects affecting the overall mass

There are different theories dealing with mass transfer among phases, such as the two-film theory, the penetration theory and the surface renewal theory. These theories are briefly

This is the oldest theory for gas-liquid mass transfer developed by Lewis and Whitman in 1924 [3]. The theory postulates the existence of a film of a thickness (δ) in both the gas and liquid phases separated by an interface. It is based on the following assumptions: (1) the mass transfer occurs by molecular diffusion through the film, beyond which the concentration (*CAb*) is homogeneous; (2) the mass transfer through the film occurs under steady state conditions; and (3) the flux is small and the mass transfer occurs at low concentration. Accordingly, for convective mass transfer, the concentration profile is linear as shown in Figure 1 and the liquid-

*AB*

<sup>=</sup> (1)

*L*

One should remember that the actual concentration profile is nonlinear as can be seen in Figure 1. In turbulent flow, however, attempts were made to relate the mass transfer coefficient with the turbulent diffusivity, which obviously is different from that in the laminar flow. Surpris‐ ingly, some experimental results were modeled with limited success using this simplistic model, where *kL* values were found to be proportional to the diffusivity to the power one. However, one should keep in mind that the film theory does not provide a direct means for

*L*

*<sup>D</sup> <sup>k</sup>* d

side mass transfer coefficient is expressed by Equation (1):

The "penetration theory" or "Higbie's model" [4] assumes that each liquid element at the gas-liquid interface is exposed to the gas for a short time, as schematically shown in Figure 2. The basic assumptions of the theory are: (1) mass transfer from the gas into a liquid element occurs under unsteady-state conditions once they are in contact; (2) each of the liquid elements stays in contact with the gas for same time period; and (3) equilibrium exists at the gas-liquid interface. This theory was considered an improvement from the two-film theory since mass transfer occurs under unsteady-state conditions in many industrial processes. The penetration theory expresses the liquid-side mass transfer coefficient in terms of the contact time ሺߠሻ and the molecular diffusivity of the gas in the liquid according to Equation (2). ݇ ൌ ʹ ቀಲಳ గఏ ቁ Ǥହ (2) The "penetration theory" or "Higbie's model" [4] assumes that each liquid element at the gasliquid interface is exposed to the gas for a short time, as schematically shown in Figure 2. The basic assumptions of the theory are: (1) mass transfer from the gas into a liquid element occurs under unsteady-state conditions once they are in contact; (2) each of the liquid elements stays in contact with the gas for same time period; and (3) equilibrium exists at the gas-liquid interface. This theory was considered an improvement from the two-film theory since mass transfer occurs under unsteady-state conditions in many industrial processes. The penetration theory expresses the liquid-side mass transfer coefficient in terms of the contact time (*θ*) and the molecular diffusivity of the gas in the liquid according to Equation (2). Figure 1. Schematic of two film theory **2.2. Penetration theory** The "penetration theory" or "Higbie's model" [4] assumes that each liquid element at the gas-liquid interface is exposed to the gas for a short time, as schematically shown in Figure 2. The basic assumptions of the theory are: (1) mass transfer from the gas into a liquid element occurs under unsteady-state conditions once they are in contact; (2) each of the liquid elements stays in contact with the gas for same time period; and (3) equilibrium exists at the gas-liquid interface. This theory was considered an improvement from the two-film theory since mass transfer occurs under unsteady-state

$$k\_1 = 2\left(\frac{\mathbf{D}\_{AB}}{\pi\theta}\right)^{0.9} \tag{2}$$

Figure 2. Schematic of Higbie's model **Figure 2.** Schematic of Higbie's model

݇ ൌ ʹ ቀಲಳ

గఏ ቁ

(2)

**2.3. Surface renewal theory**

#### **2.3. Surface renewal theory**

The surface renewal theory, developed by Danckwerts [5], applies mathematics of the penetration theory to a more plausible situation, where the liquid is pictured as two regions, a large well mixed bulk region and an interfacial region, which is renewed so fast that it behaves as a thick film as shown in Figure 3. The basic assumptions of the theory are (1) liquid elements at the interface are being randomly swapped by fresh elements from the bulk; (2) at any moment, each of the liquid elements at the interface has the same probability of being substi‐ tuted by a fresh element; and (3) mass transfer from the gas into the liquid element during its stay at the interface takes place under unsteady-state conditions. Thus, instead of using a constant contact time (*θ*), the differential liquid volume at the gas-liquid interface is renewed due to the turbulence around the interface, referred to as the surface renewal frequency (*s*). The surface renewal theory expresses the liquid-side mass transfer coefficient in terms of the surface renewal frequency (*s*) and the molecular diffusivity of the gas in the liquid according to Equation (3). The surface renewal theory, developed by Danckwerts [5], applies mathematics of the penetration theory to a more plausible situation, where the liquid is pictured as two regions, a large well mixed bulk region and an interfacial region, which is renewed so fast that it behaves as a thick film as shown in Figure 3. The basic assumptions of the theory are (1) liquid elements at the interface are being randomly swapped by fresh elements from the bulk; (2) at any moment, each of the liquid elements at the interface has the same probability of being substituted by a fresh element; and (3) mass transfer from the gas into the liquid element during its stay at the interface takes place under unsteady-state conditions. Thus, instead of using a constant contact time ���, the differential liquid volume at the gas-liquid interface is renewed due to the turbulence around the interface, referred to as the surface renewal frequency (*s*). The surface renewal theory

$$k\_{\perp} = \left(D\_{AB}\mathbf{s}\right)^{0.5} \tag{3}$$

expresses the liquid-side mass transfer coefficient in terms of the surface renewal frequency (*s*) and the molecular

**Author Variable Diffusivity Exponent** 

Versteeg et al. [6] *kL* 0.33-0.5 Davies et al. [7] *kL* 0.46-0.60 Kuthan and Broz [8] *kL* 0.51-0.64 Kozinski and King [9] *kL* 0.5-0.6 Linek et al. [10] *kL* 0.46-0.66

In the absence of chemical reactions, the gas (A) diffuses into a liquid (B) and the mass transfer rate can be expressed

The steady-state mass transfer flux through the liquid film can be described according to the film theory by Equation (5).

Figure 3. Schematic of surface renewal theory **Figure 3.** Schematic of surface renewal theory

�� � ��������� (3)

In all three theories, *DAB* is the molecular diffusivity of the gas (solute A) into the liquid (solvent B) at infinite dilution (up to 5 mol% of the solute in the solvent). However, one should keep in mind that the diffusivity depends to a large extent on the temperature, solvent viscosity as well as on the solvent composition and nature. A number of investigators related *kL* to *DAB* in the form *kL*α (*DAB*) m as given in Table 1. In all three theories, *DAB* is the molecular diffusivity of the gas (solute A) into the liquid (solvent B) at infinite dilution (up to 5 mol% of the solute in the solvent). However, one should keep in mind that the diffusivity depends to a large extent on the temperature, solvent viscosity as well as on the solvent composition and nature. A number of investigators related *kL* to *DAB* in the form *kL*α (*DAB*) m as given in Table 1.

Table 1. *kL* relationship with diffusivity

**3.1. Gas-liquid systems**

���� ��� (4)

��� �� � ����

**3. Mass transfer with chemical reaction**

using the following diffusivity equation:


The surface renewal theory, developed by Danckwerts [5], applies mathematics of the penetration theory to a more **Table 1.** *kL* relationship with diffusivity

**2.3. Surface renewal theory**

192 Mass Transfer - Advancement in Process Modelling

to Equation (3).

The surface renewal theory, developed by Danckwerts [5], applies mathematics of the penetration theory to a more plausible situation, where the liquid is pictured as two regions, a large well mixed bulk region and an interfacial region, which is renewed so fast that it behaves as a thick film as shown in Figure 3. The basic assumptions of the theory are (1) liquid elements at the interface are being randomly swapped by fresh elements from the bulk; (2) at any moment, each of the liquid elements at the interface has the same probability of being substi‐ tuted by a fresh element; and (3) mass transfer from the gas into the liquid element during its stay at the interface takes place under unsteady-state conditions. Thus, instead of using a constant contact time (*θ*), the differential liquid volume at the gas-liquid interface is renewed due to the turbulence around the interface, referred to as the surface renewal frequency (*s*). The surface renewal theory expresses the liquid-side mass transfer coefficient in terms of the surface renewal frequency (*s*) and the molecular diffusivity of the gas in the liquid according

> ( ) 0.5

Figure 3. Schematic of surface renewal theory

Table 1. *kL* relationship with diffusivity

**3.1. Gas-liquid systems**

m as given in Table 1.

���� ��� (4)

��� �� � ����

**Figure 3.** Schematic of surface renewal theory

the form *kL*α (*DAB*)

*kL* to *DAB* in the form *kL*α (*DAB*) m as given in Table 1.

In all three theories, *DAB* is the molecular diffusivity of the gas (solute A) into the liquid (solvent B) at infinite dilution (up to 5 mol% of the solute in the solvent). However, one should keep in mind that the diffusivity depends to a large extent on the temperature, solvent viscosity as well as on the solvent composition and nature. A number of investigators related *kL* to *DAB* in

**3. Mass transfer with chemical reaction**

using the following diffusivity equation:

�� � ��������� (3)

diffusivity of the gas in the liquid according to Equation (3).

*L AB k Ds* = (3)

plausible situation, where the liquid is pictured as two regions, a large well mixed bulk region and an interfacial region, which is renewed so fast that it behaves as a thick film as shown in Figure 3. The basic assumptions of the theory are (1)

on the temperature, solvent viscosity as well as on the solvent composition and nature. A number of investigators related

In the absence of chemical reactions, the gas (A) diffuses into a liquid (B) and the mass transfer rate can be expressed

The steady-state mass transfer flux through the liquid film can be described according to the film theory by Equation (5).

Versteeg et al. [6] *kL* 0.33-0.5 Davies et al. [7] *kL* 0.46-0.60 Kuthan and Broz [8] *kL* 0.51-0.64 Kozinski and King [9] *kL* 0.5-0.6 Linek et al. [10] *kL* 0.46-0.66

**Author Variable Diffusivity Exponent** 

#### liquid elements at the interface are being randomly swapped by fresh elements from the bulk; (2) at any moment, each of the liquid elements at the interface has the same probability of being substituted by a fresh element; and (3) mass transfer **3. Mass transfer with chemical reaction**

#### from the gas into the liquid element during its stay at the interface takes place under unsteady-state conditions. Thus, instead of using a constant contact time ���, the differential liquid volume at the gas-liquid interface is renewed due to **3.1. Gas-liquid systems**

the turbulence around the interface, referred to as the surface renewal frequency (*s*). The surface renewal theory expresses the liquid-side mass transfer coefficient in terms of the surface renewal frequency (*s*) and the molecular In the absence of chemical reactions, the gas (A) diffuses into a liquid (B) and the mass transfer rate can be expressed using the following diffusivity equation:

$$\frac{\partial \mathbf{c}\_A}{\partial t} = -D\_{AB} \frac{\partial^2 \mathbf{c}\_A}{\partial \mathbf{x}^2} \tag{4}$$

The steady-state mass transfer flux through the liquid film can be described according to the film theory by Equation (5).

$$J\_i = k\_{L,i} a (\mathbf{C}\_i^" - \mathbf{C}\_{i,L}) \tag{5}$$

Where *Ci* \* represents the solute concentration at the gas-liquid interface, *Ci*,*<sup>L</sup>* is the solute concentration in the liquid bulk, *kL* is the liquid-side mass transfer coefficient, and *a* represents the gas-liquid interfacial area.

In all three theories, *DAB* is the molecular diffusivity of the gas (solute A) into the liquid (solvent B) at infinite dilution (up to 5 mol% of the solute in the solvent). However, one should keep in mind that the diffusivity depends to a large extent In the presence of chemical reactions, the film theory was also used to interpret gas-liquid mass transfer, however, modifications were required since the actual concentration profiles are no longer linear as can also be seen in Figure 4. This is due to the fact that chemical reactions could vary from slow to extremely fast, whereby instantaneous reactions occur at the interface; fast reactions occur in a narrow zone within the liquid film, and slow reactions spread through the film as well as the liquid bulk. Thus, in order to account for the effect of the chemical reaction on the solute mass transfer, an enhancement factor (*E*), defined as the ratio of the absorption rate with and without the reaction, is introduced as follows:

$$E = \frac{\text{Mass transfer rate with chemical reaction}}{\text{Mass transfer rate without chemical reaction}} \tag{6}$$

$$
\mu A + \mathfrak{n}B \to \mathcal{P}(\mathfrak{product})\tag{7}
$$

$$-r\_A = k\_{m,n} \mathbf{C}\_A^m \mathbf{C}\_B^n \tag{8}$$

$$Ha = \frac{\sqrt{\frac{2}{(m+1)}k\_{w,u}C\_{A,l}^{m-1}C\_{B,bulk}^{n}D\_{A,B}}}{k\_L} \tag{9}$$

**3.2. Gas-solid systems**

**1**

**10**

**100**

**1000**

materials. The application of both of models were extensively discussed by Levenspiel [12].

**0.1 1 10 100 1000**

Figure 5. Enhancement factor for a first order gas-liquid reaction based on the numerical solution by van Krevelen and Hoftijzer [11]

**1000**

**20 14 11**

Gas-solid reactions are widely used in industrial applications. There are two main scenarios for gas-solid reactions, either the solid particles remain unchanged in size during reaction or they shrink with time as the reaction proceeds. The former scenario is described using the Continuous Reaction Model (CRM) as shown in Figure 6. This model assumes that the gaseous reactants react inside the solid particle, where its volume remains constant. On the other hand, the Shrinking

progressively moves inwards, continuously reducing the size of the core of unreacted solids and leaving behind reacted

Figure 6. Schematic of the Continuous Reaction Model (CRM) **Figure 6.** Schematic of the Continuous Reaction Model (CRM)

Figure 7. Schematic of the Shrinking Core Model (SCM) **Figure 7.** Schematic of the Shrinking Core Model (SCM)

7. Reaction of the reactants to form products.

#### **3.3. Gas-liquid-solid systems 3.3. Gas-liquid-solid systems**

Figure 8 depicts a schematic of the concentration profile for mass transfer in three-phase systems, where the reactants in the gas-phase diffuse through the liquid-phase in order to reach the catalyst active sites to react, and then the products have to travel back to the gas-phase or to the liquid-phase. The following steps describe the mass transfer process: Figure 8 depicts a schematic of the concentration profile for mass transfer in three-phase systems, where the reactants in the gas-phase diffuse through the liquid-phase in order to reach the catalyst active sites to react, and then the products have to travel back to the gas-phase or to the liquid-phase. The following steps describe the mass transfer process:

4. Transfer of the reactants through the liquid bulk, then to the liquid film surrounding the catalyst particle. 5. Transfer of the reactants through liquid film surrounding the catalyst particles to the particle surface.

9. Transfer of the products from the particle external surface through the liquid-film surrounding the particle. 10. Transfer of the products from the liquid-film surrounding the particle through the liquid bulk. Depending of the

1. Transfer of the reactants from the gas-phase bulk to the gas-side film. 2. Transfer of the reactants through the gas-side film to the gas-liquid interface 3. Transfer of the reactants form the gas-liquid interface through the liquid-side film.

8. Diffusion of the products through the particle to its external surface.

conditions, products could remain the liquid-phase.

6. Diffusion of the reactants inside the particle pores to the catalyst active sites.

11. Transfer of the gaseous products from the liquid bulk through the liquid-side film. 12. Transfer of the gaseous products from the liquid-side film to gas-liquid interface. 13. Transfer of the gaseous products from the gas-liquid interface to the gas-phase.


Figure 5. Enhancement factor for a first order gas-liquid reaction based on the numerical solution by van Krevelen and Hoftijzer [11]

**1000**

**20 14 11**

Gas-solid reactions are widely used in industrial applications. There are two main scenarios for gas-solid reactions, either the solid particles remain unchanged in size during reaction or they shrink with time as the reaction proceeds. The former scenario is described using the Continuous Reaction Model (CRM) as shown in Figure 6. This model assumes that the gaseous reactants react inside the solid particle, where its volume remains constant. On the other hand, the Shrinking Core Model (SCM), shown in Figure 7, assumes that the gas-phase reacts with the particle and the reaction front progressively moves inwards, continuously reducing the size of the core of unreacted solids and leaving behind reacted

Figure 8 depicts a schematic of the concentration profile for mass transfer in three-phase systems, where the reactants in

have to travel back to the gas-phase or to the liquid-phase. The following steps describe the mass transfer process:

4. Transfer of the reactants through the liquid bulk, then to the liquid film surrounding the catalyst particle. 5. Transfer of the reactants through liquid film surrounding the catalyst particles to the particle surface.

9. Transfer of the products from the particle external surface through the liquid-film surrounding the particle. 10. Transfer of the products from the liquid-film surrounding the particle through the liquid bulk. Depending of the

materials. The application of both of models were extensively discussed by Levenspiel [12].

**0.1 1 10 100 1000**

Figure 6. Schematic of the Continuous Reaction Model (CRM)

**Figure 6.** Schematic of the Continuous Reaction Model (CRM)

Figure 7. Schematic of the Shrinking Core Model (SCM)

7. Reaction of the reactants to form products.

1. Transfer of the reactants from the gas-phase bulk to the gas-side film. 2. Transfer of the reactants through the gas-side film to the gas-liquid interface 3. Transfer of the reactants form the gas-liquid interface through the liquid-side film.

to the liquid-phase. The following steps describe the mass transfer process:

8. Diffusion of the products through the particle to its external surface.

conditions, products could remain the liquid-phase.

6. Diffusion of the reactants inside the particle pores to the catalyst active sites.

Figure 8 depicts a schematic of the concentration profile for mass transfer in three-phase systems, where the reactants in the gas-phase diffuse through the liquid-phase in order to reach the catalyst active sites to react, and then the products have to travel back to the gas-phase or

11. Transfer of the gaseous products from the liquid bulk through the liquid-side film. 12. Transfer of the gaseous products from the liquid-side film to gas-liquid interface. 13. Transfer of the gaseous products from the gas-liquid interface to the gas-phase.

**3.3. Gas-liquid-solid systems**

**3.3. Gas-liquid-solid systems**

**Figure 7.** Schematic of the Shrinking Core Model (SCM)

**3.2. Gas-solid systems**

196 Mass Transfer - Advancement in Process Modelling

**1**

**10**

**100**

**1000**


An example of processes where the products remain in the liquid phase is the synthesis of cyclohexanol and cyclohexanone by cyclohexane oxidation. These products remain in the liquid phase and their separation is achieved by simple distillation.

Steps 1-4 and 11-13 are evaluated considering the specific gas-liquid interfacial area (*a*) and the mass transfer coefficients in the gas-side film (*kG*) and/or the liquid-side film (*kL*). Steps 5 and 10 are accounted for through the particle specific surface area and solid-side mass transfer coefficient (*kS*). Steps 6 and 8 are determined by the Knudsen diffusivity (*Dκ*) and the effective diffusion (*Deff* ) in the catalyst particle, using Equations (10) and (11) as:

$$D\_{\kappa} = 97r\_p \sqrt{\frac{T}{M\_L}}\tag{10}$$

$$D\_{\rm eff} = \varepsilon\_{\rm cat} \frac{D\_{\rm AB}}{\tau\_{\rm cat}} \tag{11}$$

the gas-phase diffuse through the liquid-phase in order to reach the catalyst active sites to react, and then the products Where *rp* represents the catalyst pore radius; *εcat* is the catalyst void fraction; *τcat* is the tortuosity in the particle; and *ML* is the molecular weight of the liquid phase.

$$\mathbf{P}\_s = \mathbf{R}\_{\text{cat}} \sqrt{\frac{k\_{\text{reaction}}}{D\_{\text{eff}}}} \tag{12}$$

$$\eta = \frac{1}{\Phi\_s} \left( \frac{1}{\tanh\left(3\Phi\_s\right)} - \frac{1}{3\Phi\_s} \right) \tag{13}$$

$$r\_i = A \cdot \eta \cdot \exp\left(\frac{-E\_{app}}{RT}\right) \cdot \mathbb{C}\_{L,H\_2} \tag{14}$$

### **4. Measuring gas-liquid mass transfer in multiphase systems**

Physical and chemical methods were used to measure the gas-liquid interfacial area (*a*) and mass transfer coefficients (*kL*) in multiphase systems. The gas-liquid interfacial area was measured using different physical and chemical methods. Physical methods, including photography, light reflection and light scattering were used, however, they were restricted to transparent contactors having low gas holdup. Other physical methods, including γ–ray radiography and real time neutron radiography were also used to estimate *a*. While the aforementioned methods reveal the gas bubble contributions to *a*, other techniques were devised to determine the impact of gas-liquid interface ripple on *a*. For instance, Muenz and Marchello [14] measured the wave frequency using a stroboscope and determined the interface amplitude through analysis of the refractive surface properties via a photovolt photometer and densitometer. Moreover, Vazquez-Una et al. [15] used a CDD camera viewing the surface at a 45° angle to calculate through digitized images analysis the wavelength,λ. They deter‐ mined the surface peak-to-peak amplitude and frequency from the surface displacement recorded using a vertically oriented laser triple-range distance-measuring device.

The chemical methods, on the other hand, were used to measure the gas-liquid interfacial area using a fast chemical reaction, where the reaction kinetics should be known in order to calculate *a*. Midoux and Charpentier [16] thoroughly reviewed various chemical reactions for measuring the gas-liquid interfacial area *a*.

The reactions are quantified for the catalyst by the Thiele modulus (Φs), which is valid for first

Figure 8. Concentration profiles for mass transfer into a slurry with a catalytic particles [13]

*eff*

(��� and the effective diffusion ������in the catalyst particle, using Equations (10) and (11) as:

*<sup>D</sup>* <sup>=</sup> (12)

An example of processes where the products remain in the liquid phase is the synthesis of cyclohexanol and cyclohexanone by cyclohexane oxidation. These products remain in the liquid phase and their separation is achieved by

Steps 1-4 and 11-13 are evaluated considering the specific gas-liquid interfacial area (*a*) and the mass transfer coefficients in the gas-side film (*kG*) and/or the liquid-side film (*kL*). Steps 5 and 10 are accounted for through the particle specific surface area and solid-side mass transfer coefficient (*kS*). Steps 6 and 8 are determined by the Knudsen diffusivity

Where �� represents the catalyst pore radius; ���� is the catalyst void fraction; *τcat* is the tortuosity in the particle; and �� is

The reactions are quantified for the catalyst by the Thiele modulus (Φ�), which is valid for first order irreversible

Where ��������� is the reaction rate constant for a first order reaction, and *Rcat* is the particle radius. For particles smaller than 200 microns and having a small Thiele modulus, for all practical purposes, the effectiveness factor *η* is close to

Step 7 represents the chemical reaction of the reactants on the catalyst active sites. A typical first order reaction, which is

(13)

(14)

order irreversible reaction, and the effectiveness factor (*η*), Equations (12) and (13).

**Figure 8.** Concentration profiles for mass transfer into a slurry with a catalytic particles [13]

Φ *reaction s cat*

h

simple distillation.

198 Mass Transfer - Advancement in Process Modelling

�� � ����� �

���� � ����

Φ� � �������������� ���� (12)

� � � �� � � ��������� � � ��� �(13)

unity.

�� (10)

��� ���� (11)

practical purposes, the effectiveness factor *η* is close to unity.

the molecular weight of the liquid phase.

first order reaction, which is usually found in hydrogenation processes, is:

The effectiveness factor in this equation is obtained from Equation (13).

usually found in hydrogenation processes, is:

*<sup>k</sup> <sup>R</sup>*

( ) 11 1 Φ*s s tanh* 3 *<sup>s</sup>* 3Φ

Where *kreaction* is the reaction rate constant for a first order reaction, and *Rcat* is the particle radius. For particles smaller than 200 microns and having a small Thiele modulus, for all

Step 7 represents the chemical reaction of the reactants on the catalyst active sites. A typical

*app*

ç ÷ è ø

*i L H E*

*r A exp C RT* h

æ ö - = ×× × ç ÷

reaction, and the effectiveness factor (*η*), Equations (12) and (13).

<sup>2</sup> ,

æ ö <sup>=</sup> ç ÷ - <sup>F</sup> è ø

Physical and chemical methods were also used to measure the volumetric mass transfer coefficient (*kLa*) since it was found that the liquid-side mass transfer coefficient (*kL*) is strongly dependent on the turbulence induced in the multiphase systems. Among the physical methods is the transient physical gas absorption (TPGA) technique, which appears to be a simple and direct method for measuring *kLa*. For instance, Chang and Morsi [17] developed a powerful model to describe the transient pressure decline, based on a modified Peng-Robinson equation of state (EOS) and mass balance. In their method, the decline of the total pressure of the system with time was recorded, and in conjunction with total mole and volume balances, *kLa* values were obtained under high pressures and temperatures for numerous gases (CO, H2, CH4, CO2, N2, He, etc.), into the liquids (hexane, toluene, cyclohexane, methanol, silicon oil, molten wax, polyalphaolefins, etc.) in the absence and presence of solids (glass beads, alumina, Puralox, iron oxides, etc.). The improvement brought by this model was discussed elsewhere [18]. The chemical methods for measuring *kLa* were reviewed by Danckwerts et al. [5], Astarita [19] and Charpentier [20]. In these methods, a slow chemical reaction with known kinetics was employed to obtain *kLa*. The problems encountered in using these methods were due to the difficulty in controlling temperature and the lack of reliable kinetics.

The liquid-side mass transfer coefficient (*kL*) could be indirectly calculated, knowing both the gas liquid interfacial area (*a*) and the volumetric mass transfer coefficient (*kLa*) determined using any of the physical methods described above. However, one must measure *kLa* and *a* simultaneously, i.e., under the same hydrodynamics in order to calculate a meaningful value of *kL*. This is because as mentioned above *kL* strongly depends on the turbulence induced in the multiphase system. The liquid-side mass transfer coefficient (*kL*) was also calculated using a chemical reaction with known kinetics and a contactor with known surface area (gas-liquid interface). The knowledge of the total absorption rate, equilibrium solubility, and reaction kinetics would enable the calculation of *kL* [20]. Again, the difficulty in this method resides in the stability of the liquid film on the surface area of the contactor.

### **5. Literature data on gas-liquid mass transfer in multiphase systems**

The effects of mass transfer on three-phase reactor performance have been extensively investigated in the literature. Earlier studies on the mass transfer in F-T systems focused on the significance of hydrogen mass transfer compared to the overall reaction resistance. This was due to the fact that F-T kinetics over iron catalyst were reported to be first order with respect to hydrogen. The principal mass transfer resistance occurs in the slurry-phase and the extent of the effect of gas-liquid mass transfer on the reactor performance has been argued. Satterfield and Huff [21] concluded that the hydrogen mass transfer was the limiting step for reactor productivity, whereas Deckwer [22] showed that the mass transfer resistance was smaller when compared with the kinetics resistance. Inga and Morsi [23] and Sehabiague and Morsi [24] reported that F-T SBCRs operating under a kinetically-controlled regime at low catalyst concentrations could move to a mass transfer-controlled regime at high catalyst concentrations, where the reactor performance quickly declines. Nonetheless, it is generally agreed that the mass transfer strongly depends on the bubble size, where smaller bubbles result in a greater gas-liquid interfacial area, which improves the overall mass transfer.

The volumetric mass transfer coefficients, derived from the inlet and outlet concentrations of absorption experiments, were influenced by the dispersion in both phases [13]. Since the dispersion is strongly dependent on the column size and geometry, the developed equations for the calculating the volumetric mass transfer coefficients appear to include geometric parameters, such as the column diameter and sparger characteristics. Behkish et al. [25, 26] measured the volumetric mass transfer coefficients (*kLa*) for H2, CO, N2, CH4 and He in Isopar-M (an isoparaffinic liquid mixture of C10 – C16) in the presence of alumina particles under high pressures (up to 30 bar), temperatures (up to 473 K), gas velocities (up to 0.39 m/s) and solid concentrations (up to 36 vol.%). While the experiments by these authors were conducted under typical F-T operating conditions, they did not use gas mixtures, mimicking the syngas; and the composition of their Isopar-M varies greatly from that of the molten wax produced in the SBCR once a steady-state operation is reached.

More recently, Sehabiague et al. [24] have measured the volumetric mass transfer coefficients for N2 and He, in C12-C13, paraffins mixture, light F-T cut, heavy F-T cut in a 0.3 m ID SBCR under high pressures (up to 30 bar), temperatures (up to 500 K) in the presence of Alumina, Puralox Alumina and Iron oxide particles (up to 20 vol.%) at various superficial gas velocities (up to 0.27 m/s). Table 2 summarizes the literature studies and correlations for kLa in multi‐ phase reactors over the past 20 years.


chemical reaction with known kinetics and a contactor with known surface area (gas-liquid interface). The knowledge of the total absorption rate, equilibrium solubility, and reaction kinetics would enable the calculation of *kL* [20]. Again, the difficulty in this method resides in

**5. Literature data on gas-liquid mass transfer in multiphase systems**

in a greater gas-liquid interfacial area, which improves the overall mass transfer.

SBCR once a steady-state operation is reached.

phase reactors over the past 20 years.

The volumetric mass transfer coefficients, derived from the inlet and outlet concentrations of absorption experiments, were influenced by the dispersion in both phases [13]. Since the dispersion is strongly dependent on the column size and geometry, the developed equations for the calculating the volumetric mass transfer coefficients appear to include geometric parameters, such as the column diameter and sparger characteristics. Behkish et al. [25, 26] measured the volumetric mass transfer coefficients (*kLa*) for H2, CO, N2, CH4 and He in Isopar-M (an isoparaffinic liquid mixture of C10 – C16) in the presence of alumina particles under high pressures (up to 30 bar), temperatures (up to 473 K), gas velocities (up to 0.39 m/s) and solid concentrations (up to 36 vol.%). While the experiments by these authors were conducted under typical F-T operating conditions, they did not use gas mixtures, mimicking the syngas; and the composition of their Isopar-M varies greatly from that of the molten wax produced in the

More recently, Sehabiague et al. [24] have measured the volumetric mass transfer coefficients for N2 and He, in C12-C13, paraffins mixture, light F-T cut, heavy F-T cut in a 0.3 m ID SBCR under high pressures (up to 30 bar), temperatures (up to 500 K) in the presence of Alumina, Puralox Alumina and Iron oxide particles (up to 20 vol.%) at various superficial gas velocities (up to 0.27 m/s). Table 2 summarizes the literature studies and correlations for kLa in multi‐

The effects of mass transfer on three-phase reactor performance have been extensively investigated in the literature. Earlier studies on the mass transfer in F-T systems focused on the significance of hydrogen mass transfer compared to the overall reaction resistance. This was due to the fact that F-T kinetics over iron catalyst were reported to be first order with respect to hydrogen. The principal mass transfer resistance occurs in the slurry-phase and the extent of the effect of gas-liquid mass transfer on the reactor performance has been argued. Satterfield and Huff [21] concluded that the hydrogen mass transfer was the limiting step for reactor productivity, whereas Deckwer [22] showed that the mass transfer resistance was smaller when compared with the kinetics resistance. Inga and Morsi [23] and Sehabiague and Morsi [24] reported that F-T SBCRs operating under a kinetically-controlled regime at low catalyst concentrations could move to a mass transfer-controlled regime at high catalyst concentrations, where the reactor performance quickly declines. Nonetheless, it is generally agreed that the mass transfer strongly depends on the bubble size, where smaller bubbles result

the stability of the liquid film on the surface area of the contactor.

200 Mass Transfer - Advancement in Process Modelling


**Table 2.** Recently published gas-liquid mass transfer empirical correlations applicable to multiphase reactors

### **6. Applications to Fischer-Tropsch synthesis**

**System Conditions Correlation Reference**

*<sup>H</sup>*<sup>2</sup> : *kL <sup>d</sup>*<sup>32</sup>

*CO* : *kL <sup>d</sup>*<sup>32</sup>

*kL*

<sup>⋅</sup> *<sup>ρ</sup><sup>l</sup>* <sup>026</sup>*µl* 0.12*ε<sup>g</sup>* 1.21*DAB* 0.5

*σl* 0.52*ρ<sup>g</sup>* 0.06*ug* 0.12*dp*

*DAB* =1.546×10−<sup>2</sup>

*DAB* =8.748×10−<sup>2</sup>

(1 <sup>−</sup> *<sup>ε</sup><sup>g</sup>* ) =6.14×10<sup>4</sup> <sup>⋅</sup>

*ηg M wl* ) −2.84

> 1.82*ρ<sup>g</sup>* 0.27*ug*

*µl* 0.25*σ<sup>l</sup>*

<sup>2</sup> <sup>−</sup>*Cv*

0.387Γ0.173

<sup>3</sup> <sup>−</sup>1675.7*dp* + 0.176*XW*

0.976*M wg* 0.02

0.1 ×*exp*

*kL <sup>a</sup>* =7.99×10−<sup>9</sup> *<sup>ρ</sup><sup>l</sup>*

−1.3*Cv* + 0.8*Cv*

( *PT PT* − *PS* ) 0.242 ( *dC dC* + 0.3 )

**Table 2.** Recently published gas-liquid mass transfer empirical correlations applicable to multiphase reactors

0.05*<sup>T</sup>* 0.68 <sup>Γ</sup>0.11( *dC*

*Eu* 0.052*Re* 0.076*Sc* <sup>−</sup>0.231

*Eu* <sup>−</sup>0.012*Re* 0.024*Sc* <sup>−</sup>0.133

*dC* + 1 )

Yang et al. [34]

0.4 Lemoine et al. [35]

Sehabiague et al. [24]

(*ρgug*)0.49 ×*exp* −2.66*CV* Behkish et al. [36]

dp :177−210 µm <sup>ρ</sup><sup>s</sup> :8900 kg / <sup>m</sup><sup>3</sup> dC :0.05 m , hC :0.5 m

202 Mass Transfer - Advancement in Process Modelling

T:293−523 K P:1−5 MPa dp :134 µm C*<sup>v</sup>* : 5− 20 vol.% dC :0.037 m , hC :0.48 m

ug :0.0035−0.574 m / s Cv : 0 −36 vol.% T: 275−538 K P: 0.1−15 MPa <sup>ρ</sup><sup>s</sup> :700−4000 kg / <sup>m</sup><sup>3</sup> dp :5−300 µm <sup>ρ</sup><sup>l</sup> :633.4−1583 kg / <sup>m</sup><sup>3</sup> µl :0.189−398.8 mPa⋅ s σ<sup>l</sup> :8.4−75 mN / m dC : 0.0382−5.5 m

Same as Lemoine et al. [35] *kL <sup>a</sup>* =0.18*Sc* 0.6( *<sup>ρ</sup><sup>l</sup>*

ug :0.14−0.26 m / s C*<sup>v</sup>* : 0 −20 vol.% T: 330−530 K P: 8−30 MPa <sup>ρ</sup><sup>s</sup> :3218−4000 kg / <sup>m</sup><sup>3</sup> dp :1.5−140 µm <sup>ρ</sup><sup>l</sup> :631.3−779.5 kg / <sup>m</sup><sup>3</sup> µl :0.27−9.96 mPa⋅ s σ<sup>l</sup> :13−27 mN / m dC :0.3 m m, hC :3 m

H2/CO - Paraffin oil - Silica gel

H2, CO, N2, CH4- Isopar-M, Hexanes – Glass beads, Iron Oxide

H2, CO, N2, CH4,-Isopar-M, Hexanes – Glass beads, Iron Oxide

He, N2 – Paraffins mixture, C12-C13, Light F-T Cut, Heavy F-T- Cut – Alumina, Puralox Alumina, Iron oxide

This Chapter focuses on the Fischer-Tropsch (F-T) synthesis process as an example of industrial multiphase systems. In this process, the syngas (CO + H2) react in the presence of a catalyst, conventionally iron or cobalt, to produce synthetic hydrocarbon products, primarily linear alkanes and alkenes. The overall F-T process involves three main steps: syngas generation, F-T catalytic reactions and product upgrading. Syngas generation involves converting the carbonaceous feedstock into a H2-CO mixture via reactions with steam and optionally oxygen or air. Solid feedstocks, such as coal and biomass, are converted in a gasifier, of which various types have been already in industrial applications [37-40]. Different gasification processes and technologies have also been discussed in the literature [41-52]. Natural gas, on the other hand, is converted to syngas in a reformer using either partial oxidation (POX), steam methane reforming (SMR) or auto-thermal reforming (ATR).

Although many metals have been identified to catalyze F-T reactions, only iron (Fe) and cobalt (Co) have been used in industrial applications [39, 52]. Iron catalyst is cheap and has a high water-gas-shift (WGS) activity, however, it is prone to severe attrition and the water produced during the reaction appeared to decrease its activity [53, 54]. Cobalt-based catalyst, on the other hand, has higher activity than iron catalyst since it is not strongly inhibited by water. It is more resistant to attrition and as such has a longer life in the reactor than iron catalyst. Cobalt-based catalyst, however, is more expensive and has no WGS activity [53, 55]. During Cobalt catalyzed F-T reaction, the oxygen from CO dissociation is converted to H2O, as shown in Equation (15). Conversely, iron catalyst has a high affinity for the WGS reaction as shown in Equation (16), resulting in the conversion of a significant portion of oxygen from CO dissociation into CO2.

$$F-T: \text{CO} + 2H\_2 \rightarrow \text{-CH}\_2- + H\_2\text{O} \tag{15}$$

$$\text{WGS}: \text{CO} + H\_2\text{O} \leftrightharpoons H\_2 + \text{CO}\_2\tag{16}$$

Thus, the extent of the WGS reaction has to be closely considered as it affects the H2/CO ratio in the F-T process.

#### **6.1. Multiphase Reactors for F-T synthesis**

Depending on the reaction temperature, the F-T process is referred to as low temperature F-T (LTFT) or high temperature F-T (HTFT). The temperature of the LTFT ranges from 180 to 260 o C and the syncrude produced is wax consisting mostly of long chain hydrocarbons, while the temperature of the HTFT process is between 290 and 360 o C and the products are mostly short chain hydrocarbons and gases. Therefore, the final products of the LTFT process consist mostly of diesel fuel, while gasoline production has been the focus of the HTFT [56]. The LTFT syncrude product is easy to upgrade by a hydroprocessing step and a fractionation step to obtain naphtha and middle distillate, whereas the HTFT syncrude requires more complex


**Table 3.** F-T Plants: catalysts and reactor technologies [53, 57]

refinery facilities [56]. It should be noted that recent R&D and commercial efforts have been focused on the LTFT due to the current drive for using more diesel engines than gasoline engines, the excellent quality of sulfur-free F-T diesel, and perhaps the mild conditions of the process.

Reactor technologies used for commercial applications of the F-T synthesis are summarized in Table 3. The HTFT reactors include fixed fluidized-bed reactors (FFBRs) and circulating fluidized-bed reactors (CFBRs), whereas multitubular fixed-bed reactors (FBRs) and slurry bubble column reactors (SBCRs) are used for the LTFT process. Also, LTFT micro-channel reactors for small-scale applications have been recently receiving considerable attention, even though no commercial applications are yet available.

In multi-tubular FBRs, the syngas flows through small diameter tubes packed with catalyst at small voidage, resulting in a high pressure drop and an increased operating cost. These reactors have comparatively complex heat transfer characteristics and their maximum production capacity is limited by the amount of heat which can be removed. Hot spots would ultimately result in carbon deposition on the catalyst surfaces and serious plugging of the reactor tubes. These types of reactors, however, have been used to carry out LTFT by Germany during WWII, Sasol since 1950's and Shell at the Bintulu GTL (Malaysia) and more recently at the Pearl GTL (Qatar) [41, 53, 57, 58].

SBCRs, on the other hand, have a simpler design and allow for much higher heat removal efficiencies than multitubular FBRs due to the presence of a large volume of the liquid-phase. Its advantages include a much greater flexibility than FBRs and its capital cost is 20 - 40% lower than that of multitubular FBRs [59]. However, the high mechanical shear on the catalyst, resulting in particles attrition and the lack of a reliable system for the fine particles separation from the liquid products, have delayed commercial deployment of SBCRs until the 1990's. Conversely, microchannel reactors have a stationary catalyst bed combined with enhanced heat and mass transfer characteristics. Also, they are typically aimed at exploiting a different market than conventional reactors where their small size is an advantage. A schematic of both SBCR and FBR multiphase reactors is shown in Figure 9 aimed at exploiting a different market than conventional reactors where their small size is an advantage. A schematic of both SBCR and FBR multiphase reactors is shown in Figure 9

Figure 9. Schematic of SBCR and FBR reactors for F-T **Figure 9.** Schematic of SBCR and FBR reactors for F-T

based particles as solid-phase).

refinery facilities [56]. It should be noted that recent R&D and commercial efforts have been focused on the LTFT due to the current drive for using more diesel engines than gasoline engines, the excellent quality of sulfur-free F-T diesel, and perhaps the mild conditions of the

Reactor technologies used for commercial applications of the F-T synthesis are summarized in Table 3. The HTFT reactors include fixed fluidized-bed reactors (FFBRs) and circulating fluidized-bed reactors (CFBRs), whereas multitubular fixed-bed reactors (FBRs) and slurry bubble column reactors (SBCRs) are used for the LTFT process. Also, LTFT micro-channel reactors for small-scale applications have been recently receiving considerable attention, even

In multi-tubular FBRs, the syngas flows through small diameter tubes packed with catalyst at small voidage, resulting in a high pressure drop and an increased operating cost. These reactors have comparatively complex heat transfer characteristics and their maximum production capacity is limited by the amount of heat which can be removed. Hot spots would ultimately result in carbon deposition on the catalyst surfaces and serious plugging of the reactor tubes. These types of reactors, however, have been used to carry out LTFT by Germany during WWII, Sasol since 1950's and Shell at the Bintulu GTL (Malaysia) and more recently at the Pearl GTL

SBCRs, on the other hand, have a simpler design and allow for much higher heat removal efficiencies than multitubular FBRs due to the presence of a large volume of the liquid-phase. Its advantages include a much greater flexibility than FBRs and its capital cost is 20 - 40% lower than that of multitubular FBRs [59]. However, the high mechanical shear on the catalyst, resulting in particles attrition and the lack of a reliable system for the fine particles separation from the liquid products, have delayed commercial deployment of SBCRs until the 1990's.

though no commercial applications are yet available.

process.

**F-T Plant**

German CTL (14 plants active at end of WWII)

**Date of Operation**

Hydrocol GTL 1951-1957 HTFT FFB

**Table 3.** F-T Plants: catalysts and reactor technologies [53, 57]

Sasol I CTL/GTL 1955-present

204 Mass Transfer - Advancement in Process Modelling

PetroSA GTL 1992-present

1935-1962 LTFT FB

**Reactor**

HTFT CFB LTFT FB, SBCR

> HTFT CFB LTFT SBCR

Shell Bintulu 1993-present LTFT FB Co/Zr/SiO2 Sasol Oryx GTL 2007-present LTFT SBCR Co/Pt/Al2O3 Shell Pearl GTL 2011-present LTFT FB Co/Zr/SiO2

Sasol Synfuels CTL 1980-present HTFT FFB Fused Fe (similar to Sasol I HTFT CFB catalyst)

**Technology Catalysts**

Co/ThO2/kieselguhr (100:18:100) before 1938 Co/ThO2/MgO/kieselguhr (100:5:8:200) after 1938

Fused Fe3O4/Al2O3/K2O (97:2.5:0.5) Later replaced by Magnetite with 0.5% K2O

Magnetite with 0.5% K2O Precipitated Fe/SiO2/K2O/Cu (100:25:5:5)

Fused Fe (same as Sasol Synfuels) Co based catalyst

(Qatar) [41, 53, 57, 58].

#### **6.2. Mass transfer in SBCRs for F-T synthesis 6.2. Mass transfer in SBCRs for F-T synthesis**

In general, the longer the molecules stay in the catalyst pores, the heavier the hydrocarbons become, significantly reducing their diffusivities, which could be considered as one of the main reasons for catalyst deactivation, referred to as fouling, in F-T synthesis [53]. In most applications, however, it is often assumed that when the products leave the solidliquid interface, there is no major effect of their presence on the reaction rate. With these considerations, it can be concluded that the steps that affect the overall reaction rate of the process are the gas-liquid mass transfer step and the reaction on the catalyst active sites. This means that a major impact on the optimization of a gas-liquid or a gas-liquidsolid reactor could be done by increasing the catalyst activity and/or improving the mass transfer rate between the gas and the liquid phases. It should be mentioned, however, that the relative importance of the mass transfer, in certain processes depends on the catalyst activity, operating conditions, and reactor configuration [2]. Figure 8 shows the concentration profiles for mass transfer into a slurry system, and as such, it could be used to explain the mass transfer behavior in SBCRs. In F-T synthesis, since the diameter of catalyst particles used are in the range of 30 to 90 μm [60], the interfacial area between the liquid and the catalyst particles becomes very large and accordingly the In general, the longer the molecules stay in the catalyst pores, the heavier the hydrocarbons become, significantly reducing their diffusivities, which could be considered as one of the main reasons for catalyst deactivation, referred to as fouling, in F-T synthesis [53]. In most applica‐ tions, however, it is often assumed that when the products leave the solid-liquid interface, there is no major effect of their presence on the reaction rate. With these considerations, it can be concluded that the steps that affect the overall reaction rate of the process are the gas-liquid mass transfer step and the reaction on the catalyst active sites. This means that a major impact on the optimization of a gas-liquid or a gas-liquid-solid reactor could be done by increasing the catalyst activity and/or improving the mass transfer rate between the gas and the liquid phases. It should be mentioned, however, that the relative importance of the mass transfer, in certain processes depends on the catalyst activity, operating conditions, and reactor configu‐ ration [2].

resistance to the mass transfer due to steps 4, and 9 can be neglected. Steps 3 and 10 can also be neglected if the reactor is operated in the churn-turbulent flow regime due to the efficient mixing in this flow regime. Also, since the products formed in the F-T reactor are wax and as such the gas-phase consists mainly of the reactants (CO and H2), one can neglect the resistance associated with steps 1-2 and 13. Thus, the main resistances controlling the behavior of F-T synthesis in SBCRs are (1) the reaction kinetics (step 7), and (2) the gas-liquid mass transfer through the liquid-side film (steps 3 and 12). **7. Factors affecting the hydrodynamics and mass transfer in F-T SBCRs** Figure 8 shows the concentration profiles for mass transfer into a slurry system, and as such, it could be used to explain the mass transfer behavior in SBCRs. In F-T synthesis, since the diameter of catalyst particles used are in the range of 30 to 90 µm [60], the interfacial area between the liquid and the catalyst particles becomes very large and accordingly the resistance to the mass transfer due to steps 4, and 9 can be neglected. Steps 3 and 10 can also be neglected if the reactor is operated in the churn-turbulent flow regime due to the efficient mixing in this flow regime. Also, since the products formed in the F-T reactor are wax and as such the gasphase consists mainly of the reactants (CO and H2), one can neglect the resistance associated

**7.1. Effect of molecular weight and density of the gas-phase**

The hydrodynamics (gas holdup, bubble size/distribution) and mass transfer characteristics (volumetric mass transfer coefficients) in SBCRs for F-T synthesis are affected by numerous factors ranging from the physicochemical properties of the gas-liquid-solid system to the operating conditions and reactor geometry. Unfortunately, the majority the experimental studies found in the literature on the hydrodynamics and mass transfer in SBCRs used air-water-glass beads systems under ambient conditions; and only few data are available under F-T conditions for H2, CO, N2 and He in F-T molten wax in the presence and absence of inert solid particles, including iron oxides, alumina and Puralox [24]. None of these studies, however, cover all the conditions encountered in an industrial F-T reactor (T > 450 K, P > 20 bar, UG > 0.15 m/s, CV > 10 vol%, mixture of hydrocarbons as liquid-phase, H2 and CO as gas-phase, micron sized Fe or Cowith steps 1-2 and 13. Thus, the main resistances controlling the behavior of F-T synthesis in SBCRs are (1) the reaction kinetics (step 7), and (2) the gas-liquid mass transfer through the liquid-side film (steps 3 and 12).

### **7. Factors affecting the hydrodynamics and mass transfer in F-T SBCRs**

The hydrodynamics (gas holdup, bubble size/distribution) and mass transfer characteristics (volumetric mass transfer coefficients) in SBCRs for F-T synthesis are affected by numerous factors ranging from the physicochemical properties of the gas-liquid-solid system to the operating conditions and reactor geometry. Unfortunately, the majority the experimental studies found in the literature on the hydrodynamics and mass transfer in SBCRs used airwater-glass beads systems under ambient conditions; and only few data are available under F-T conditions for H2, CO, N2 and He in F-T molten wax in the presence and absence of inert solid particles, including iron oxides, alumina and Puralox [24]. None of these studies, however, cover all the conditions encountered in an industrial F-T reactor (T > 450 K, P > 20 bar, UG > 0.15 m/s, CV > 10 vol%, mixture of hydrocarbons as liquid-phase, H2 and CO as gasphase, micron sized Fe or Co-based particles as solid-phase).

#### **7.1. Effect of molecular weight and density of the gas-phase**

The density of the gas-phase has been reported to increase the gas holdup [61, 62], and denser gases led to higher gas holdups. It was also reported that an increase of gas density resulted in the shrinkage of the gas bubbles [63]. The impact of the molecular weight of the gas phase is similar to that of the gas density. Indeed, an increase of the molecular weight will translate into an increase of gas density and as such will lead to higher gas holdup and smaller gas bubbles [64]. It is, however, important to note that the increase of gas holdup with density/ molecular weight is not true under all conditions. Clark [65] for example reported that at low gas velocities below 0.05 m/s (corresponding to the homogeneous or bubbly flow regime), the gas holdup of N2 was smaller than that of H2.

#### **7.2. Effect of density, viscosity and surface tension of the liquid phase**

The effect of the liquid density on the gas holdup has been studied by several investigators, but still remains unclear. Some investigators reported an increase [66, 67] of gas holdup with increasing the liquid density, while others reported a decrease [62, 68]. The volumetric mass transfer coefficient was found to decrease with decreasing liquid density [69, 70]. Increasing the liquid viscosity has been found to decrease the gas holdup [61, 67, 68] and increase the gas bubbles size [71]. The volumetric mass transfer coefficient has been reported to decrease with increasing the liquid-phase viscosity [69, 70]. The liquid surface tension was reported to have a similar effect to that of the liquid viscosity on gas holdup, i.e., an increase of liquid surface tension leads to a decrease of gas holdup [61, 68]. Also, an increase of liquid surface tension leads to the formation of larger gas bubbles [71] and smaller volumetric mass transfer coeffi‐ cients [69].

#### **7.3. Effect of size, density and wettability of solid particles**

Slurry suspensions of denser solid particles led to lower the gas holdup [72] than similar suspensions of particles with lower density. Increasing the size of solid particles was found to increase [72] the gas holdup for non-wettable solid particles, however, it was found to decrease [72, 73] the gas holdup for wettable solid particles. The solid particles diameter was reported, in some cases, to have no significant effect [74] on the gas holdup. The wettability of the solid particles has no clear effect on the gas holdup. In some cases, it was found to increase the gas holdup [72] and in others to decrease it [74].

#### **7.4. Effect of operating conditions**

with steps 1-2 and 13. Thus, the main resistances controlling the behavior of F-T synthesis in SBCRs are (1) the reaction kinetics (step 7), and (2) the gas-liquid mass transfer through the

**7. Factors affecting the hydrodynamics and mass transfer in F-T SBCRs**

phase, micron sized Fe or Co-based particles as solid-phase).

**7.1. Effect of molecular weight and density of the gas-phase**

**7.2. Effect of density, viscosity and surface tension of the liquid phase**

gas holdup of N2 was smaller than that of H2.

cients [69].

The hydrodynamics (gas holdup, bubble size/distribution) and mass transfer characteristics (volumetric mass transfer coefficients) in SBCRs for F-T synthesis are affected by numerous factors ranging from the physicochemical properties of the gas-liquid-solid system to the operating conditions and reactor geometry. Unfortunately, the majority the experimental studies found in the literature on the hydrodynamics and mass transfer in SBCRs used airwater-glass beads systems under ambient conditions; and only few data are available under F-T conditions for H2, CO, N2 and He in F-T molten wax in the presence and absence of inert solid particles, including iron oxides, alumina and Puralox [24]. None of these studies, however, cover all the conditions encountered in an industrial F-T reactor (T > 450 K, P > 20 bar, UG > 0.15 m/s, CV > 10 vol%, mixture of hydrocarbons as liquid-phase, H2 and CO as gas-

The density of the gas-phase has been reported to increase the gas holdup [61, 62], and denser gases led to higher gas holdups. It was also reported that an increase of gas density resulted in the shrinkage of the gas bubbles [63]. The impact of the molecular weight of the gas phase is similar to that of the gas density. Indeed, an increase of the molecular weight will translate into an increase of gas density and as such will lead to higher gas holdup and smaller gas bubbles [64]. It is, however, important to note that the increase of gas holdup with density/ molecular weight is not true under all conditions. Clark [65] for example reported that at low gas velocities below 0.05 m/s (corresponding to the homogeneous or bubbly flow regime), the

The effect of the liquid density on the gas holdup has been studied by several investigators, but still remains unclear. Some investigators reported an increase [66, 67] of gas holdup with increasing the liquid density, while others reported a decrease [62, 68]. The volumetric mass transfer coefficient was found to decrease with decreasing liquid density [69, 70]. Increasing the liquid viscosity has been found to decrease the gas holdup [61, 67, 68] and increase the gas bubbles size [71]. The volumetric mass transfer coefficient has been reported to decrease with increasing the liquid-phase viscosity [69, 70]. The liquid surface tension was reported to have a similar effect to that of the liquid viscosity on gas holdup, i.e., an increase of liquid surface tension leads to a decrease of gas holdup [61, 68]. Also, an increase of liquid surface tension leads to the formation of larger gas bubbles [71] and smaller volumetric mass transfer coeffi‐

liquid-side film (steps 3 and 12).

206 Mass Transfer - Advancement in Process Modelling

Increasing temperature has been found to increase the gas holdup [36] through the decrease of both liquid surface tension and viscosity. Increasing temperature was also reported to increase the volumetric mass transfer coefficient [66] due in part to the increase of the gas diffusivity. On the other hand, the gas holdup was found to increase with pressure [75] which was attributed to the increase of the gas density. The volumetric mass transfer coefficient was also found to increase with pressure [75, 76]. Moreover, numerous experimental studies have shown that increasing the superficial gas velocity led to the increase of the gas holdup [62, 67] and the volumetric mass transfer coefficient [75, 76].

#### **7.5. Effect of liquid and slurry velocity**

The effect of liquid superficial velocity on the gas holdup has been investigated by several authors; and increasing liquid velocity was found to decrease the gas holdup in the absence [77] and presence [73, 74] of solid particles.

#### **7.6. Effect of solid loading**

The presence of fine micron-size catalyst particles in the liquid-phase greatly affects the properties of the slurry-phase, such as density and viscosity. While a few studies [24, 77] have found an increase of gas holdup with increasing solid concentration, adding more particles has mostly been found to decrease the gas holdup [63, 70, 73] by increasing the slurry viscosity. A decrease of the volumetric mass transfer coefficient and the formation of larger gas bubbles due to the increase of the rate of bubbles coalescence was also reported when increasing the solid loading [70]. It was also observed, particularly at low solid concentrations [78] that the volumetric mass transfer coefficient appeared to increase with increasing solid concentration. It should be noted that these results have to be considered along with the effects of the physical properties of the solids used, such as shape, size and wettability.

#### **7.7. Effect of reactor geometry**

The Reactor geometry has a strong influence on the gas holdup. In SBCRs, 3 zones can be identified where the gas holdups are significantly different. The first zone corresponds to the bottom of the reactor in the vicinity of the gas sparger, which is strongly affected by the sparger design. The second zone is the bulk region. The third zone is the top region, where the gas holdup will behave very differently from the bulk region, if foaming occurs. It is important to note that if the reactor is long enough the effect of the first and third regions on the total gas holdup will become negligible [79]. The effect of column diameter on the gas holdup has been found to be strong in the case of small diameter reactors with diameter ≤ 0.15 m [80], however, several investigators have found that this effect would level off or disappear for diameters ≥ 0.15 m [69, 79]. Moreover, the length to diameter (L/D) ratio is frequently used instead of the reactor length when studying the effects of reactor geometry on the hydrodynamics. Several studies found that the gas holdup remained unaffected when the length to diameter ratio was ≥ 6 [24, 79].

#### **7.8. Effect of gas distributor**

The design of the gas distributor, the number of openings, their sizes and their orientations play an important role in affecting the hydrodynamics and mass transfer in the SBCRs not only within the bottom region at the vicinity of the gas distributor, but also in the bulk region. The initial bubble size and distribution at the orifice could be controlled by the sparger character‐ istics, but due to the balance between coalescence and breakup of gas bubbles, the initial bubble size created at the gas sparger would not describe the behavior of gas bubble size distribution in the entire column [71]. Under the same operating conditions, different designs of the gas sparger were found to give different volumetric mass transfer coefficient values [81]. For two different designs of the gas distributor, increasing the size of the openings was found to decrease gas holdup due to the formation of larger gas bubbles [36]. However, several investigators have reported that the gas sparger had a minimal effect on the bubble sizes and gas holdup if the orifice diameters were > 0.001-0.002 m [71, 79]. This suggests that for a certain size of the openings, the gas bubble size and gas holdup reach a maximum and a minimum value, respectively.

#### **7.9. Effect of reactor internals**

Since F-T synthesis is an exothermic reaction, cooling tubes are needed in the reactor in order to remove the heat released by the reaction. The presence of those internals will affect the performance of the reactor in terms of hydrodynamics and mass transfer. Saxena et al. [82] have studied 3 different configurations of internals representing 1.9%, 2.7% and 14.3% of the column cross sectional area and could not find any clear effect of the number of internals on the gas holdup. O'Dowd et al. [83] found slightly higher gas holdup value in a column equipped with cylindrical baffles occupying 15% of the cross-sectional area than in an unbaffled column of the same size. However, the difference lies within the range of errors of their experimental measuring technique. Also, another study [84] reported slightly higher gas holdup value when internals representing 5% of the cross section area were present. Yamashita [85] studied the effect of the separation distance between the internals and found out that gas holdup decreased when the separation distance was small (0.006 m) and increased when the separation distance was greater than 0.008 m. He attributed the decrease and increase in gas holdup values to the reduction of the radial mobility of gas bubbles and to the increase in interstitial gas velocity, respectively. Indeed, it is important to note that the slight increase in gas holdup reported in the above mentioned studies might be the result of the increase of interstitial velocity inside the reactor when adding internals.

### **8. Concluding remarks**

holdup will behave very differently from the bulk region, if foaming occurs. It is important to note that if the reactor is long enough the effect of the first and third regions on the total gas holdup will become negligible [79]. The effect of column diameter on the gas holdup has been found to be strong in the case of small diameter reactors with diameter ≤ 0.15 m [80], however, several investigators have found that this effect would level off or disappear for diameters ≥ 0.15 m [69, 79]. Moreover, the length to diameter (L/D) ratio is frequently used instead of the reactor length when studying the effects of reactor geometry on the hydrodynamics. Several studies found that the gas holdup remained unaffected when the length to diameter ratio was

The design of the gas distributor, the number of openings, their sizes and their orientations play an important role in affecting the hydrodynamics and mass transfer in the SBCRs not only within the bottom region at the vicinity of the gas distributor, but also in the bulk region. The initial bubble size and distribution at the orifice could be controlled by the sparger character‐ istics, but due to the balance between coalescence and breakup of gas bubbles, the initial bubble size created at the gas sparger would not describe the behavior of gas bubble size distribution in the entire column [71]. Under the same operating conditions, different designs of the gas sparger were found to give different volumetric mass transfer coefficient values [81]. For two different designs of the gas distributor, increasing the size of the openings was found to decrease gas holdup due to the formation of larger gas bubbles [36]. However, several investigators have reported that the gas sparger had a minimal effect on the bubble sizes and gas holdup if the orifice diameters were > 0.001-0.002 m [71, 79]. This suggests that for a certain size of the openings, the gas bubble size and gas holdup reach a maximum and a minimum

Since F-T synthesis is an exothermic reaction, cooling tubes are needed in the reactor in order to remove the heat released by the reaction. The presence of those internals will affect the performance of the reactor in terms of hydrodynamics and mass transfer. Saxena et al. [82] have studied 3 different configurations of internals representing 1.9%, 2.7% and 14.3% of the column cross sectional area and could not find any clear effect of the number of internals on the gas holdup. O'Dowd et al. [83] found slightly higher gas holdup value in a column equipped with cylindrical baffles occupying 15% of the cross-sectional area than in an unbaffled column of the same size. However, the difference lies within the range of errors of their experimental measuring technique. Also, another study [84] reported slightly higher gas holdup value when internals representing 5% of the cross section area were present. Yamashita [85] studied the effect of the separation distance between the internals and found out that gas holdup decreased when the separation distance was small (0.006 m) and increased when the separation distance was greater than 0.008 m. He attributed the decrease and increase in gas holdup values to the reduction of the radial mobility of gas bubbles and to the increase in interstitial gas velocity, respectively. Indeed, it is important to note that the slight increase in

≥ 6 [24, 79].

**7.8. Effect of gas distributor**

208 Mass Transfer - Advancement in Process Modelling

value, respectively.

**7.9. Effect of reactor internals**

The knowledge of hydrodynamic and mass transfer parameters in multiphase systems is critical for the development of numerous industrial processes, and therefore proper under‐ standing, measurement and quantification of these important parameters remains an area of significant interest from research and industrial perspectives. An important example of multiphase systems is the F-T synthesis and although interest in the design and scaleup of SBCRs for low temperature F-T has soared over the past two decades, there still remain significant knowledge gaps, which are yet to be investigated, particularly relating to investi‐ gation of the hydrodynamic and mas transfer parameters, such as gas holdup and *kLa*, under high pressures and temperatures typical to those of F-T industrial process. Such studies at elevated pressures and temperatures remain very limited when compared with the plethora of other studies conducted using air-water systems under ambient conditions. Thus, there is a great need for more studies to further understand the complex and intricate behavior of such multiphase systems and to investigate the effect of various operating parameters on the interphase mass transfer.


### **Nomenclature**


### **Author details**

Badie I. Morsi\* and Omar M. Basha

\*Address all correspondence to: morsi@pitt.edu

Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA, USA

### **References**


Fr Froude number T Temperature (K)

*εcat* Catalyst void fraction *π* 3.14

δ<sup>L</sup> Liquid film thickness (m) *ρ* Density (kg/m3

*µ* Viscosity (kg/m∙s) *ϕ* Thiele modulus

cat Catalyst l Liquid g Gas s Solid

and Omar M. Basha

\*Address all correspondence to: morsi@pitt.edu

*neering Chemistry,* vol. 16, pp. 1215-1220, 1924.

*η* Effectiveness factor *σ* Surface tension (N/m) *θ* Contact time τcat Tortuosity of the particle

Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh,

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) ub Gas bubble rise velocity (m·s-1)

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*g* Gravitational acceleration, (m/s2

210 Mass Transfer - Advancement in Process Modelling

Ji Molar flux of species i (kmol·s -1·m-2)

**Greek Letters**

**Subscripts**

**Author details**

Badie I. Morsi\*

PA, USA

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## **Ion Exchange Fundamentals and New Challenges**

Maria Angélica Simões Dornellas de Barros, Marcelino Luiz Gimenes, Melissa Gurgel Adeodato Vieira and Meuris Gurgel Carlos da Silva

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60864

#### **Abstract**

Ion exchange is a stoichiometric phenomenon commonly used in water treatment as an end-of-pipe technique. Such process is highly influenced by mass transfer conditions and may be modeled by adsorption equations. Although widely applied in industries its theo‐ ry has not been completely understood and depends on the exchanger characteristics. Moreover, competitive systems may add complexity and decrease removal efficiency and exchanger selectivity mainly in dynamic systems. In this chapter some general theory was presented and some detailed examples involving alginate biopolymer, bonechar and zeolite in single and competitive systems were discussed in batch and continuous state.

**Keywords:** ion exchange, kinetics, equilibrium data, fixed bed, multicomponent systems

### **1. Introduction**

Ion exchange processes are the processes in which a solid phase (ion exchanger) reacts in a double exchange reaction when in contact with a liquid phase with electrolytes. Actually, this should not be considered as a true chemical reaction as it involves the redistribution of ions between two phases by diffusion. Chemical factors are almost negligible with small amount of heat, often less than 2 kcal/mol [1].

In an ion exchange process, the balancing ion (the one previously detected in the solid phase) is replaced by the counter ion (previously in the liquid phase) always when the exchange has a higher affinity to the counter ion. It is important to emphasize that the stoichiometric replacement involves charges. Nevertheless, normality is much more adequate to describe the phenomenon than molarity. Figure 1 presents examples of the monovalent and divalent exchange processes. In this diagram, it is easy to see the importance of charges in the stoichio‐ metric process.

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The first citation of an application of ion exchange can be found in Aristotle's, but the ion exchange processes became well known in the nineteenth century. In the 1930s, they were strengthened when organic cation exchangers were discovered. Nowadays, anion exchange resins are also commercially obtained [2].

Ion exchange is considered as an end-of-pipe technique used in wastewater and one of the best available techniques to remove heavy metal ions, which is of a great concern due to the toxic compounds constantly presented in bodies of water.

With such general aspects in mind, this chapter has the main goal to discuss the ion exchange phenomenon through already published results. Theory and fundamental aspects will be briefly revised.

balancing cation, B is the monovalent counter ion, and C is the divalent counter ion. **Figure 1.** Cationic exchange examples. IE– is the ionic exchanger charge. A is the balancing cation, B is the monovalent counter ion, and C is the divalent counter ion.

Ion exchange is generally controlled by diffusion, a consequence of the material

is the ionic exchanger charge. A is the

#### structure. Ion exchange framework, size of the beads, and any other physical chemistry characteristics have important roles in this process. Nevertheless, in all cases, it is **2. General theory**

followed by the diffusion of the ion inside the solid phase and the diffusion in the surrounding solution. Actually, the ion exchange process occurs in the following steps [2]: 1. Dissociation of the electrolytes in the bulk phase, originating the denominated counter ion 2. Diffusion of the counter ion from the bulk phase towards the interphase film Ion exchange is generally controlled by diffusion, a consequence of the material structure. Ion exchange framework, size of the beads, and any other physical chemistry characteristics have important roles in this process. Nevertheless, in all cases, it is accomplished by transfer of ions to and from the interphase boundary, the exchange itself followed by the diffusion of the ion inside the solid phase and the diffusion in the surrounding solution.

accomplished by transfer of ions to and from the interphase boundary, the exchange itself

3. Diffusion of the counter ion through the interphase film 4. Diffusion of the counter ion inside the ion exchanger Actually, the ion exchange process occurs in the following steps [2]:

Figure 1. Cationic exchange examples. IE

**2. General theory** 


The first citation of an application of ion exchange can be found in Aristotle's, but the ion exchange processes became well known in the nineteenth century. In the 1930s, they were strengthened when organic cation exchangers were discovered. Nowadays, anion exchange

Ion exchange is considered as an end-of-pipe technique used in wastewater and one of the best available techniques to remove heavy metal ions, which is of a great concern due to the toxic

With such general aspects in mind, this chapter has the main goal to discuss the ion exchange phenomenon through already published results. Theory and fundamental aspects will be

Ion exchange is generally controlled by diffusion, a consequence of the material structure. Ion exchange framework, size of the beads, and any other physical chemistry characteristics have important roles in this process. Nevertheless, in all cases, it is accomplished by transfer of ions to and from the interphase boundary, the exchange itself followed by the diffusion of the ion inside the solid phase and the diffusion in the

balancing cation, B is the monovalent counter ion, and C is the divalent counter ion.

**Figure 1.** Cationic exchange examples. IE– is the ionic exchanger charge. A is the balancing cation, B is the monovalent

Actually, the ion exchange process occurs in the following steps [2]:

3. Diffusion of the counter ion through the interphase film 4. Diffusion of the counter ion inside the ion exchanger

**2.** Diffusion of the counter ion from the bulk phase towards the interphase film

inside the solid phase and the diffusion in the surrounding solution. Actually, the ion exchange process occurs in the following steps [2]:

**3.** Diffusion of the counter ion through the interphase film

**4.** Diffusion of the counter ion inside the ion exchanger

1. Dissociation of the electrolytes in the bulk phase, originating the denominated

Ion exchange is generally controlled by diffusion, a consequence of the material structure. Ion exchange framework, size of the beads, and any other physical chemistry characteristics have important roles in this process. Nevertheless, in all cases, it is accomplished by transfer of ions to and from the interphase boundary, the exchange itself followed by the diffusion of the ion

2. Diffusion of the counter ion from the bulk phase towards the interphase film

5. Association between the counter ion and the functional group of the exchanger 6. Dissociation of the balancing ion and functional group of the exchanger 7. Diffusion of the balancing ion inside the exchanger towards the surface 8. Diffusion of the balancing ion through the interphase film

**1.** Dissociation of the electrolytes in the bulk phase, originating the denominated counter

is the ionic exchanger charge. A is the

resins are also commercially obtained [2].

220 Mass Transfer - Advancement in Process Modelling

briefly revised.

compounds constantly presented in bodies of water.

Monovalent ion exchange

Divalent ion exchange

**2. General theory** 

counter ion, and C is the divalent counter ion.

**2. General theory**

ion

surrounding solution.

counter ion

Figure 1. Cationic exchange examples. IE


Basically, the mechanism of ion exchange processes has some possible rate-controlling steps. The most important ones are related to steps 3 and 8, 4 and 7, 5 and 6. Steps 3 and 8 deal with film resistance and should be minimized through adequate agitation. The mass transfer in this case is defined by the diffusion coefficients. Steps 4 and 7 are related to intraparticle diffusion and depend on the physic-chemical properties of the system. Small particles of the ion exchanger may decrease such resistances. Steps 5 and 6 are the ion exchange processes properly. Almost always, the film and/or intraparticle resistances are considered the most important rate-controlling steps. Many kinetic models take into account these characteristics. More information regarded to kinetics can be seen elsewhere [3, 4]. The regeneration of the saturated ion exchanger may be also modeled [5]. It must be emphasized that many models are used to describe both adsorption and ion exchange mechanisms. Despite of the mathe‐ matical similarity, the significant differences related to these mechanisms should be in mind.

Besides kinetic data, ion exchange equilibrium data are also of great value. Isotherms may be classified in five different types [6], as shown in Figure 2.

Isotherm shapes indicate whether or not the ion is solution is preferably exchanged. However, they provide no information on the type of exchange sites or even whether they have similar energies. This is outstanding information as it is directly related to the ion exchange mecha‐ nism. The Kielland plot is an interesting thermodynamic tool to understand such process. Ion selectivity and the thermodynamic properties may be obtained from such data.

The Kielland plot may be obtained through log *K* | *<sup>B</sup> <sup>A</sup>* (equilibrium constant through the balancing ion A and the counter ion B) and *x*A(Z). Linear Kielland plots are a consequence of exchangers with only one kind of exchange site [7]. Nonlinear plots indicate different sites and different cavities where the exchanged cation occupies different positions in the framework [6].

Although batch operations where isotherms may be obtained are rarely used in industries, they are very common when investigating mechanisms such as the ones in equilibrium through isotherms. Continuous systems are almost often well suited for industrial purposes when scale-up process is needed. Continuous ion exchange uses packed beds where the mass transfer is of great importance. As the feed solution passes through the ion exchange packed bed, the outlet solution has different concentrations of the incoming ion as a function of time. Plots of the ratio outlet concentration of the incoming ion/concentration of the incoming ion in the feed solution versus time are well known as breakthrough curve. Mass balances in the column as well as the mass transfer parameters are reported elsewhere [8,9].

**Figure 2.** Ion exchange isotherms: *x*a(z): equivalent fraction of the counter ion in the exchanger; *x*a(s): equivalent fraction of the counter ion in solution [6]. (a) Favorable isotherm; (b) isotherm with reversal behavior, from favorable to unfav‐ orable; (c) unfavorable isotherm; (d) incomplete favorable isotherm; (e) isotherm with hysteresis.

Besides the use of adsorption models, ion exchange systems may be more correctly represented by the mass action law (MAL). This is the most characteristic property of ion exchange and can be used as one of the possible modeling equations. Actually, it expresses the typical double exchange reaction where the balancing ion in the exchanger is replaced by the in-going ion according to the stoichiometry.

MAL is based on the definition of the chemical equilibrium of the chemical reactions first proposed by Cato Guldberg and Peter Waage in 1864. It was defined as the equilibrium constant *K*, which is the relationship of the activity coefficient of reagents and products in equilibrium at a given temperature.

If the chemical reaction presented in Eq. (1) is considered:

$$
\mathbf{b}B + \mathbf{c}\mathbf{C} \to \mathbf{d}D + \mathbf{e}E \tag{1}
$$

The equilibrium constant may be written as follows:

$$K = \frac{\left\lceil \begin{smallmatrix} a\_D \ \overline{\Box}^d \cdot \left\lceil \begin{smallmatrix} a\_E \ \overline{\Box}^e \end{smallmatrix} \right\rceil^e \end{smallmatrix} \right\rceil}{\left\lceil \begin{smallmatrix} a\_B \ \overline{\Box}^b \cdot \left\lceil \begin{smallmatrix} a\_C \ \overline{\Box}^c \end{smallmatrix} \right\rceil \end{smallmatrix} \right\rceil} \tag{2}$$

where *a* stands for the ionic activity of each ion presented in Eq. (1).

It is obvious that monocomponent ion exchange only occurs when the solid in is contact with synthetic solutions. Other solutions, mainly wastewaters, always contain significant amount or other ions that may be also exchanged. That is why selectivity and affinity properties of the ion exchanger in relation to the specific incoming ion should be considered no matter if it is continuous or batch system. Of course, in such a case, modeling is more complex. Some examples of MAL can be seen in reference [10].

### **3. Ion exchangers**

Besides the use of adsorption models, ion exchange systems may be more correctly represented by the mass action law (MAL). This is the most characteristic property of ion exchange and can be used as one of the possible modeling equations. Actually, it expresses the typical double exchange reaction where the balancing ion in the exchanger is replaced by the in-going ion

**Figure 2.** Ion exchange isotherms: *x*a(z): equivalent fraction of the counter ion in the exchanger; *x*a(s): equivalent fraction of the counter ion in solution [6]. (a) Favorable isotherm; (b) isotherm with reversal behavior, from favorable to unfav‐

orable; (c) unfavorable isotherm; (d) incomplete favorable isotherm; (e) isotherm with hysteresis.

MAL is based on the definition of the chemical equilibrium of the chemical reactions first proposed by Cato Guldberg and Peter Waage in 1864. It was defined as the equilibrium constant *K*, which is the relationship of the activity coefficient of reagents and products in

> *d e D E b c B C*

*a a*

*a a* é ùéù <sup>×</sup> ë ûëû <sup>=</sup> éùéù × ëûëû

*K*

*bB cC dD eE* +® + (1)

(2)

according to the stoichiometry.

222 Mass Transfer - Advancement in Process Modelling

equilibrium at a given temperature.

If the chemical reaction presented in Eq. (1) is considered:

The equilibrium constant may be written as follows:

Ion exchangers are porous matrixes from different sources, with positive or negative excess charge, insoluble in aqueous solutions and in many organic solvents. The excess charge of the matrix should be compensated by the balancing ions, which may be replaced by the in-going ion depending on the selectivity and affinity of the exchanger to the ions involved.

Mechanical resistance as well as regeneration capacity is quite important when packed beds are considered. There are acid and basic exchangers being the anionic exchangers that have basic superficial groups and cationic exchangers those containing superficial acid groups. Exchangers may be also classified according to complete or incomplete dissociation based on the pH range where the exchange process is efficient.

Ion exchangers can be natural such as alginate, clay, algae, or even some zeolites. Alginate occurs in seaweeds as calcium alginate and is present in the cells of brown algae. Actually, the term alginate designates salts of alginic acid and its derivatives.

Clays are fine powders constituted by hydrated aluminosilicates that often tend to agglomer‐ ate. In clay materials alumina is presented in octahedral form whereas silica is found as tetrahedrons. Such materials are thermally stable and can be greatly improved by pillaring process. Zeolites are also aluminosilicates. Nevertheless, they have an open three-dimensional framework with interconnecting cavities. Both materials can be used as adsorbents, ion exchangers, catalysts, or catalysis support.

Natural exchangers have some disadvantages such as low exchange rate and rather poor mechanical properties and low abrasion resistance, which restrict their application, mainly in packed beds without any previous treatment.

Exchangers obtained specifically from synthetic materials are available commercially being. Zeolites and resins are the most famous representatives of such class. Many zeolites are related to cationic exchange process. Nevertheless, zeolites can act as anionic exchangers if tailored.

Resins are known since 1935. They can be used as ion exchangers or catalysts. Ion exchange resins may be found as in acids and bases, acting, therefore, as anionic or cationic exchangers. Cationic resins generally contain sulfonic acid groups, whereas anionic resins are commonly found in quaternary ammonium groups.

### **4. Experimental results of ion exchange**

#### **4.1. Case study: Metallic ion in calcium alginate biopolymer**

#### *4.1.1. Copper kinetics study of calcium alginate particles in a static system*

Calcium alginate biopolymer was prepared by dropping sodium alginate into solution of calcium chloride (3% w/w) under continuous agitation. Calcium alginate particles formed (mean diameter, 1083 µm) were washed and dried to be used in adsorption/ion exchange experiments [11].

Kinetic studies were carried out using single nitrate solutions of Cu2+, Cd2+, Pb2+, and Ni2+ of 3 mmol/L (Vetec, Brazil) and a bicomponent equimolar solution of Cu2+and Cd2+ (1 mmol/L for each metal). Values of pH were corrected using NH4OH and HNO3.

All runs were conducted in finite baths at 25°C using 1 g of alginate immersed in 0.1 L of metallic solutions. Samples of these solutions were taken at different running times, and after filtration, the concentration of solutions was analyzed through atomic absorption spectropho‐ tometry.

Mathematical modeling of the ion diffusion process in ion exchanger provided relevant information on mass transfer that is essential to the ion exchange/adsorption system design. The diffusion process in a solid matrix was described for the second Fick's law. In the spherical coordinate system, the concentration gradients are negligible in the angular direction, and the second Fick's law is represented by Eq. (3):

$$\frac{\partial \mathcal{O}}{\partial t} = D\_e \frac{1}{r} \frac{\partial}{\partial \left(r \frac{\partial q}{\partial r}\right)} \left(r \frac{\partial q}{\partial r}\right) \tag{3}$$

where *q* is the ion capacity in ion exchanger (mg/g), *D*<sup>e</sup> is the ion diffusion coefficient in the adsorbent/ion exchanger (cm2 /s), *t* is time (s), and *r* is the radial direction (cm).

In this modeling, it was considered that the adsorbent was initially free of metal, the ion diffusivity was constant, the concentration in the fluid phase was homogeneous, and external resistance in the liquid film was negligible due to the agitation. The initial and boundary conditions used are described by Eqs. (4)–(6):

$$\text{at } t = \text{ } 0: q = q\_0 \tag{4}$$

$$\text{at } r = \mathbb{R} \text{ and } t > \begin{array}{c} 0 \text{:} q = 0 \\ \end{array} \tag{5}$$

$$\text{at } r = \ 0 \\ \frac{\partial q}{\partial r} = 0$$

The average concentration of the metal ion exchanger is given by Eq. (7):

$$\frac{\overline{q}\left(t\right) - q\_{\text{eq}}}{q\_0 - q\_{\text{eq}}} = \Theta \sum\_{j=1}^{\text{o}} \left( \frac{1}{\mathcal{V}\_j^2} e^{-\mathcal{V}\_j \cdot \overline{\rho}\_M} \right) \tag{7}$$

where

**4. Experimental results of ion exchange**

224 Mass Transfer - Advancement in Process Modelling

second Fick's law is represented by Eq. (3):

conditions used are described by Eqs. (4)–(6):

adsorbent/ion exchanger (cm2

experiments [11].

tometry.

**4.1. Case study: Metallic ion in calcium alginate biopolymer**

*4.1.1. Copper kinetics study of calcium alginate particles in a static system*

each metal). Values of pH were corrected using NH4OH and HNO3.

Calcium alginate biopolymer was prepared by dropping sodium alginate into solution of calcium chloride (3% w/w) under continuous agitation. Calcium alginate particles formed (mean diameter, 1083 µm) were washed and dried to be used in adsorption/ion exchange

Kinetic studies were carried out using single nitrate solutions of Cu2+, Cd2+, Pb2+, and Ni2+ of 3 mmol/L (Vetec, Brazil) and a bicomponent equimolar solution of Cu2+and Cd2+ (1 mmol/L for

All runs were conducted in finite baths at 25°C using 1 g of alginate immersed in 0.1 L of metallic solutions. Samples of these solutions were taken at different running times, and after filtration, the concentration of solutions was analyzed through atomic absorption spectropho‐

Mathematical modeling of the ion diffusion process in ion exchanger provided relevant information on mass transfer that is essential to the ion exchange/adsorption system design. The diffusion process in a solid matrix was described for the second Fick's law. In the spherical coordinate system, the concentration gradients are negligible in the angular direction, and the

> 1 *e q q D r trr*

where *q* is the ion capacity in ion exchanger (mg/g), *D*<sup>e</sup> is the ion diffusion coefficient in the

In this modeling, it was considered that the adsorbent was initially free of metal, the ion diffusivity was constant, the concentration in the fluid phase was homogeneous, and external resistance in the liquid film was negligible due to the agitation. The initial and boundary

/s), *t* is time (s), and *r* is the radial direction (cm).

¶ æ ö ¶ <sup>=</sup> ç ÷ ¶ ¶ è ø (3)

<sup>0</sup> at 0 : *t qq* = = (4)

at and 0 : 0 *rR t q* = >= (5)

¶

¶

$$F o\_{\
u} = \frac{D\_{\rm ef} t}{R^2} ; \mathcal{Y}\_{\rangle} = j\pi$$

where *γ* is the *j* component of the activity coefficient, *D*ef is the effective diffusivity (m2 /s), and *R* is the radius of the particle (m).

The metal concentration in the fluid phase is obtained from an overall mass transfer balance, represented by Eq. (8):

$$C\left(t\right) = \left(C\_0 V - m\_s \overline{q}\left(t\right)\right) / V \tag{8}$$

where *C*0 is the initial concentration of metal in the fluid phase (mg/L), *q*¯ is the metal incoming average capacity in the adsorbent (mgmetal/galginate), *m*s is the mass of bioadsorbent/ion exchanger (g dry basis), and *V* is the volume of the solution (dm3 ).

The method "golden search" was used to determine the effective diffusion coefficient of ions in bioadsorbent/ion exchanger to minimize the objective function given by Eq. (9):

$$F\_{\text{obj}} = \sum\_{j=1}^{n} \left( \mathbf{C}\_{\text{//}}^{\text{MOD}} - \mathbf{C}\_{\text{//}}^{\text{EXP}} \right)^2 \tag{9}$$

where *n* is the number of experimental data, *Cj* EXP is the ion concentration in solution deter‐ mined experimentally (mEq/L), and *Cj* MOD: ion concentration in the solution calculated by the model (mg)

Figure 3 shows experimental results of the kinetics of the process and results obtained with the mathematical modeling for different metals in this study. The metal ions nickel, lead, and copper showed adsorption and desorption, indicating the competitiveness of metal ions (with calcium present in alginate) by the occupation of the active sites. The model used does not consider this competitiveness, but only the adsorption of the ions of interest, resulting in slightly different values when compared to the experimental data.

Table 1 shows the quantities of metal ions removed from the single solutions by adsorption/ion exchange process. It appears that nickel was less adsorbed (0.92 mmol Ni/gcalcium alginate) in equilibrium. Indeed, alginic acid has a greater affinity for calcium than for nickel [12]. In a study of removal of different metals using calcium alginate, it was obtained the following amounts adsorbed: 0.247 mmol Cu/g, 0.138 mmol Cd/g, and 0.247 mmol Pb/g [13]. Although the conditions used were different from those used in this work, it can be seen that the alginate showed the same order of adsorptive capacity, or Cu2+ > Pb2+ > Cd2+; in the case of this study (Table 1), it was Cu2+ > Pb2+ > Cd2+ > Ni2+.

**Figure 3.** kinetic curves for different metal ions in monocomponent solutions for the adsorption/ion exchange into cal‐ cium alginate particles.


**Table 1.** Adsorbed amount (mmolmetal/galginate) of different metals in the process of adsorption/ion exchange using single solutions.

The results obtained in finite bath for copper-cadmium binary mixture are shown in Figure 4. It is observed that copper was significantly more removed than cadmium. The adsorbed amount of copper and cadmium was 1.746 mmol Cu/gcalcium alginate and 0.661 mmol Cd/gcalcium alginate, respectively. The greater affinity of calcium alginate to copper may be due to the chemical parameters listed in Table 2. The higher the electronegativity and the reduction potential and the lower the ionic radius, the easier the ion exchange/adsorption [14]. In this case, copper is more susceptible to ionic interaction with the alginate than cadmium because it presents all the favorable parameters to the ion exchange.

**Figure 4.** Kinetics of copper and cadmium in binary solution in the adsorption/ion exchange by calcium alginate particles.


Source: reference [11].

consider this competitiveness, but only the adsorption of the ions of interest, resulting in

Table 1 shows the quantities of metal ions removed from the single solutions by adsorption/ion exchange process. It appears that nickel was less adsorbed (0.92 mmol Ni/gcalcium alginate) in equilibrium. Indeed, alginic acid has a greater affinity for calcium than for nickel [12]. In a study of removal of different metals using calcium alginate, it was obtained the following amounts adsorbed: 0.247 mmol Cu/g, 0.138 mmol Cd/g, and 0.247 mmol Pb/g [13]. Although the conditions used were different from those used in this work, it can be seen that the alginate showed the same order of adsorptive capacity, or Cu2+ > Pb2+ > Cd2+; in the case of this study

**Figure 3.** kinetic curves for different metal ions in monocomponent solutions for the adsorption/ion exchange into cal‐

**Table 1.** Adsorbed amount (mmolmetal/galginate) of different metals in the process of adsorption/ion exchange using single

The results obtained in finite bath for copper-cadmium binary mixture are shown in Figure 4. It is observed that copper was significantly more removed than cadmium. The adsorbed amount of copper and cadmium was 1.746 mmol Cu/gcalcium alginate and 0.661 mmol Cd/gcalcium

**Copper Cadmium Nickel Lead** 4.658 1.792 0.987 3.106

slightly different values when compared to the experimental data.

(Table 1), it was Cu2+ > Pb2+ > Cd2+ > Ni2+.

226 Mass Transfer - Advancement in Process Modelling

cium alginate particles.

solutions.

**Table 2.** Chemical properties of divalent cations.

The diffusion capacity of the metal ions in the alginate particles analyzed was evaluated considering the Fick's law, and the respective values are shown in Table 3. It is observed that the cadmium showed higher diffusion capacity, and nickel is the metal resulting in an increased resistance to intraparticle diffusion; thus, the metal adsorption order was Cd2+ > Cu2+ > Pb2+ > Ni2+. However, experimental results obtained with single and binary solutions were Cu2+ > Pb2+ > Cd2+ > Ni2+ and Cu2+ > Cd2+, respectively, indicating that this parameter cannot solely describe the metal affinity of alginate. Therefore, it becomes necessary to evaluate other properties of the ion exchanger/adsorbent.


**Table 3.** Diffusion capacity of metal ions in calcium alginate.

#### *4.1.2. Copper equilibrium study of calcium alginate particles in a static system*

The isotherm of Langmuir model (L) is widely used due to its simplicity and theoretical basis and is expressed by Eq. (10). The parameter *b* is the ratio between the rate of adsorption and desorption and is directly related to Henry's constant. High values of *b* indicate high affinity of the ions by the active sites of the material. The parameter *q*max indicates the total number of active sites available, and *q*\* and *C*\* represent the metal removal capacity at equilibrium in the solid and liquid phases, respectively. Adsorption is very favorable when values of *b*.*C*\* >> 1; however, if *b*.*C*\* < 1, the isotherm is almost linear.

$$\eta^\* = \frac{q\_{\text{max}} \cdot b \cdot \mathbb{C}^\*}{1 + b \cdot \mathbb{C}^\*} \tag{10}$$

The Freundlich isotherm is an empirical adjustment of a model, which considers that the energy of the active sites of the adsorbent material is heterogeneous and that the adsorption process is reversible. It corresponds to the exponential distribution heats of adsorption and is expressed by Eq. (11), where *k*d and *n* are constants in the model. This model does not predict the saturation of the adsorbent, allowing an infinite number of layers covering the ionic adsorbent [15]. When *n* < 1, it is typically a liquid adsorption [16].

$$
\mathfrak{q}^\* = k\_{\rm d} \cdot \mathbb{C}^{\*\mathbb{N}} \tag{11}
$$

Figure 5 shows the equilibrium data in finite bath by contacting 1 g of hydrated alginate with 100 mL of metal solution with different initial concentrations [11]. The Langmuir isotherm model (Equation 10) and the Freundlich model (Equation 11) were fitted to the experimental equilibrium data as shown in Figure 5, and the respective values of model parameters are presented in Table 4.

**Figure 5.** Cu adsorption isotherm in calcium alginate fitted by the Langmuir and Freundlich models.


**Table 4.** Parameters of Langmuir and Freundlich models.

increased resistance to intraparticle diffusion; thus, the metal adsorption order was Cd2+ > Cu2+ > Pb2+ > Ni2+. However, experimental results obtained with single and binary solutions were Cu2+ > Pb2+ > Cd2+ > Ni2+ and Cu2+ > Cd2+, respectively, indicating that this parameter cannot solely describe the metal affinity of alginate. Therefore, it becomes necessary to evaluate other

**/min)**

The isotherm of Langmuir model (L) is widely used due to its simplicity and theoretical basis and is expressed by Eq. (10). The parameter *b* is the ratio between the rate of adsorption and desorption and is directly related to Henry's constant. High values of *b* indicate high affinity of the ions by the active sites of the material. The parameter *q*max indicates the total number of active sites available, and *q*\* and *C*\* represent the metal removal capacity at equilibrium in the solid and liquid phases, respectively. Adsorption is very favorable when values of *b*.*C*\* >> 1;

> max \* \* 1 \* *q bC <sup>q</sup> b C* × × <sup>=</sup> + ×

The Freundlich isotherm is an empirical adjustment of a model, which considers that the energy of the active sites of the adsorbent material is heterogeneous and that the adsorption process is reversible. It corresponds to the exponential distribution heats of adsorption and is expressed by Eq. (11), where *k*d and *n* are constants in the model. This model does not predict the saturation of the adsorbent, allowing an infinite number of layers covering the ionic

Figure 5 shows the equilibrium data in finite bath by contacting 1 g of hydrated alginate with 100 mL of metal solution with different initial concentrations [11]. The Langmuir isotherm model (Equation 10) and the Freundlich model (Equation 11) were fitted to the experimental equilibrium data as shown in Figure 5, and the respective values of model parameters are

<sup>d</sup> \* \**<sup>n</sup> q kC* = × (11)

(10)

properties of the ion exchanger/adsorbent.

**Metal Diffusion capacity (cm2**

**Table 3.** Diffusion capacity of metal ions in calcium alginate.

however, if *b*.*C*\* < 1, the isotherm is almost linear.

presented in Table 4.

adsorbent [15]. When *n* < 1, it is typically a liquid adsorption [16].

*4.1.2. Copper equilibrium study of calcium alginate particles in a static system*

Copper 7.44E–06 Cadmium 8.38E–05 Lead 2.19E–06 Nickel 4.57E–07

228 Mass Transfer - Advancement in Process Modelling

According to Table 4, both models could satisfactorily adjust the equilibrium experimental data for copper ions. The isotherm obtained in Figure 5 can be classified as type I [17], which is characteristic of the Langmuir isotherm where adsorption occurs only in monolayer. Moreover, these models have also been adequately used to describe the process of removing metal ions using calcium alginate (Ca-Alginate) particles [18,19].

In the ion exchange process involving the binary system of copper and cadmium ions in calcium alginate (systems Cu2+-Ca2+, Cd2+-Ca2+, and Cu2+-Cd2+), it was considered only the presence of the higher affinity ion, or for the Cu2+-Ca2+ system, only the presence of Cu2+ species, for Cd2+-Ca2+system, the presence of Cd2+ species, and for the Cu2+-Cd2+ system, the presence of copper [11]. Many single adsorption isotherms were evaluated for the binary systems, as shown in Table 5 and in Figure 6.


**Table 5.** Adsorption isotherm models used for the binary system by considering only the presence of the ion of higher affinity.


**Table 6.** Parameters obtained for the single component isotherm models for the system Cu2+–Ca2+.

All models resulted in satisfactory determining coefficient values (*R*<sup>2</sup> ), indicating proper fit to the experimental data (Table 6).

The Sips model was successfully used to represent the removal of copper and cadmium ions in Ca-Alginate particles, mainly when compared to Langmuir and Freundlich models [19]. It happened due to the heterogeneity of the surface of the adsorbent, especially for metals of lower-affinity with the alginate.

**Model Parameters Equation**

Freundlich *q*max, *n q* \* =*k*<sup>d</sup> ⋅*C*\*

Toth *<sup>q</sup>*max, *b*, *<sup>n</sup> <sup>q</sup>* \* <sup>=</sup> *<sup>q</sup>*max*<sup>C</sup>* \* *<sup>b</sup>* 1/*<sup>n</sup>*

Radke–Praunitz *<sup>q</sup>*max, *b*, *<sup>n</sup> <sup>q</sup>* \* <sup>=</sup> *<sup>q</sup>*max*<sup>C</sup>* \* *<sup>b</sup>*

*q*max ⋅ *b* ⋅*C* \* 1 + *b* ⋅*C* \*

*n*

*q*max*bC* \* 1 + *bC*\* *n*

(1 + *bC*\*

(1 + *BC* \*)*<sup>n</sup>*

*q*max*bC*\* *n*

1 + *bC*\* *n*

**Table 5.** Adsorption isotherm models used for the binary system by considering only the presence of the ion of higher

**Model Parameters** *Fobj R2*

b (L/mEq) = 0.139

*K* (mEq/g) = 2.020 *n* = 0.658

*q*max(mEq/g) = 20.7841 b(L/mEq) = 0.091 *n* = 1.1331

*q*max(mEq/g) = 13.207 b(L/mEq) = 0.108 *n* = 1.1455

*q*max(mEq/g) = 40.555 b(L/mEq) = 4.677 *n* = 2.139

*q*max(mEq/g) = 25.332 b(L/mEq) = 0.077 *n* = 0.847

All models resulted in satisfactory determining coefficient values (*R*<sup>2</sup>

**Table 6.** Parameters obtained for the single component isotherm models for the system Cu2+–Ca2+.

*<sup>n</sup>* )1/*<sup>n</sup>*

0.069 0.990

1.054 0.982

0.56198 0.991

0.566 0.990

0.549 0.991

0.592 0.988

), indicating proper fit to

Langmuir *q*max, *b q* \* =

230 Mass Transfer - Advancement in Process Modelling

Redlich–Peterson *q*max, *b*, *n q* \* =

Sips *q*max, *b*, *n q* \* =

Langmuir *<sup>q</sup>*max (mEq/g) = 14.540

affinity.

Freundlich

Toth

Sips

Redlich–Peterson

Radke–Prausnitz

the experimental data (Table 6).

Although in the system involving the Cd2+-Ca2+ ions, experimental data have been acceptable adjusted, the interference of calcium on Cd2+-Ca2+ system was higher when compared to Cu2+- Ca2+system, indicating that the alginate had a higher affinity for copper than for cadmium [11,20].

and Cd2+ adsorption isotherms for Ca-Alginate system (c) in monocomponent system [11,20]. **Figure 6.** Cu2+ adsorption isotherms for Ca-Alginate system (a), Cd-Alginate system (b), and Cd2+ adsorption isotherms for Ca-Alginate system (c) in monocomponent system [11,20].

Table 6. Parameters obtained for the single component isotherm models for the system

0.069 0.990

1.054 0.982

0.56198 0.991

Model Parameters *F*obj *R*<sup>2</sup>

b (L/mEq) = 0.139

*K* (mEq/g) = 2.020

b(L/mEq) = 0.091

*q*max(mEq/g) = 20.7841

*n* = 0.658

*n* = 1.1331

Langmuir *<sup>q</sup>*max (mEq/g) = 14.540

Cu2+–Ca2+.

Freundlich

Redlich–Peterson

Figure 6. Cu2+ adsorption isotherms for Ca-Alginate system (a), Cd-Alginate system (b),

#### *4.1.3. Copper removal in dynamic system: adsorption and desorption cycles*

The study of removing copper ions in the calcium alginate particles porous bed column was assessed through adsorption and desorption cycles. The experiments were performed in a glass column (internal diameter, 1.4 cm) filled with 9.80 g of calcium alginate particles to reach a bed height of 13.3 cm. Flow tests were performed with 3 mL/min for adsorption and desorption cycles. The initial concentration of copper used in the adsorption step was 4.72 mmol/L. In the desorption step, calcium chloride solution with a concentration of 18 mmol/L was employed as eluent. The amount of copper removed in the column experiment was calculated by the Eq. (12). The experimental conditions were defined from fluid dynamic preliminary studies.

$$Q = \frac{\mathcal{C}\_0 F}{1000m} \cdot \int\_0^t \left(\frac{\mathcal{C}\_0 - \mathcal{C}}{\mathcal{C}\_0}\right) \cdot dt \tag{12}$$

where *C*<sup>0</sup> is the initial concentration of metal (mmol/L), *C*(*t*) is the metal concentration at time *t* (mmol/L), *F* is the volumetric flow of the solution (mL/min), *m* is the mass of alginate (g), *Q* is the metal removal capacity at time *t* (mgmetal/gbioadsorvente), and *t* is time (min).

**Figure 7.** Kinetics of adsorption of copper ions in porous bed (Initial copper concentration 4.72 mmol/L).

Aliquots were withdrawn periodically, and the pH of feed metallic solution was moni‐ tored throughout the process, which was maintained between 4 and 4.5. The copper removal kinetics is shown in Figure 7. From the breakthrough curve, the complete saturation of the bed was reached at 140 min of process. The total amount of copper removed given by Eq. (12) was 2.83 mmol/g.

*4.1.3. Copper removal in dynamic system: adsorption and desorption cycles*

preliminary studies.

232 Mass Transfer - Advancement in Process Modelling

The study of removing copper ions in the calcium alginate particles porous bed column was assessed through adsorption and desorption cycles. The experiments were performed in a glass column (internal diameter, 1.4 cm) filled with 9.80 g of calcium alginate particles to reach a bed height of 13.3 cm. Flow tests were performed with 3 mL/min for adsorption and desorption cycles. The initial concentration of copper used in the adsorption step was 4.72 mmol/L. In the desorption step, calcium chloride solution with a concentration of 18 mmol/L was employed as eluent. The amount of copper removed in the column experiment was calculated by the Eq. (12). The experimental conditions were defined from fluid dynamic

> 0 0 <sup>0</sup> <sup>0</sup> 1000 *<sup>t</sup> CF C C <sup>Q</sup> dt m C* æ ö - =× × ç ÷

is the metal removal capacity at time *t* (mgmetal/gbioadsorvente), and *t* is time (min).

**Figure 7.** Kinetics of adsorption of copper ions in porous bed (Initial copper concentration 4.72 mmol/L).

Aliquots were withdrawn periodically, and the pH of feed metallic solution was moni‐ tored throughout the process, which was maintained between 4 and 4.5. The copper removal kinetics is shown in Figure 7. From the breakthrough curve, the complete saturation of the

è ø

where *C*<sup>0</sup> is the initial concentration of metal (mmol/L), *C*(*t*) is the metal concentration at time *t* (mmol/L), *F* is the volumetric flow of the solution (mL/min), *m* is the mass of alginate (g), *Q*

ò (12)

Copper was desorbed from alginate employing calcium chloride solution with a concentration of 18 mmol/L. Initially, it is known that alginate has a greater affinity for copper than the alginate. However, when alginate is saturated with copper ions and comes into contact with a solution containing a high concentration of calcium, copper alginate may desorb ions and adsorb calcium ions to achieve chemical equilibrium. However, in this case, which the ions being adsorbed has a lower affinity, the process occurs only when calcium is present in solution at high concentrations. The kinetics of this process step is in Figure 8. The flow rate used, as well as in adsorption cycle, was 3 mL/min. The calcium alginate recovery was 97%. The equilibrium time of the desorption system was close to 150 min.

**Figure 8.** Kinetics of copper desorption in bed of porous calcium alginate particles.

#### **4.2. Case study 2: Equilibrium and dynamic studies of Mn2+ and Cr3+ in bone char**

It is already known that metal ions, like manganese and chromium, when present in waste‐ waters may contaminate the environment if not adequate treated. In particular, high concen‐ trations of manganese ion in water promote corrosion of pipes, and as this metal is toxic to the brain, it may cause neurological disorders. The hexavalent chromium ion is another highly toxic metal present in wastewater, which is related to cancer diseases. The trivalent chromium specie is less toxic than the hexavalent one, and it can be easily oxidized in wastewater treatment through reduction of manganese ions. The removal of these metals from wastewater can be carried out by adsorption/ion exchange processes using bone char [21].

Bone char is an untypical kind of activated carbon due to its animal origin. It is com‐ posed by around 10% carbon and 90% calcium phosphate. Figure 9 illustrates the bone char structure. The calcium phosphate in bone char is present as hydroxyapatite— Ca10(PO4)6(OH)2 [22] with a calcium-to-phosphate ratio of 1.67, and unit cell dimensions of *a* = *b* = 9.432 Å and *c* = 6.881 Å [23].

**Figure 9.** The hydroxyapatite structure viewed along the *c*-axis. The yellow polyhedrons represent the phosphate groups [23].

Cation exchange in bone char may occur preferentially with calcium ions, depending on radius and electronegativity of the incoming ion [24]. Under this consideration, bone char can be quite useful material to be used for removal of both Mn2+ and Cr3+ through calcium ion exchange.

#### *4.2.1. Materials*

The bovine bone char was crushed, sieved (20–28 mesh Tyler, average particle diameter of 0.725 mm), and elutriated with abundant water to remove fine particles and finally dried at 80°C for 24 h. The exchanger particulate material was characterized through N2 adsorption, scanning electron microscopy (SEM), and infrared spectrophotometry (FTIR). Zero point charge (ZPC) was obtained based on references [25, 26].

Solutions of 15 mEq/L of CrCl3.6H2O and MnCl2.4H2O were used in single metal removal. Binary solutions containing 7.5 mEq/L of each cation were also used.

#### *4.2.2. Results and discussion*

N2 isotherm showed that the bone char was predominantly mesoporous material with hysteresis and a BET area of 100 m2 / g, which is a typical for this kind of solid material (Figure 10).

Scanning electron microscopy (SEM) of the bone char sample (Figure 11) presented heteroge‐ neity morphology of particles and channels similar to results already reported [27].

FTIR spectrum presented in Figure 12 depicts a characteristic band at 1380 cm–1 attributed to <sup>ν</sup>NO3 group, bands at 3450 cm–1, 603 cm–1 due to –OH group vibration, band at 1640 cm–1 due

**Figure 10.** Nitrogen adsorption–desorption isotherm at 77K of bone char.

Bone char is an untypical kind of activated carbon due to its animal origin. It is com‐ posed by around 10% carbon and 90% calcium phosphate. Figure 9 illustrates the bone char structure. The calcium phosphate in bone char is present as hydroxyapatite— Ca10(PO4)6(OH)2 [22] with a calcium-to-phosphate ratio of 1.67, and unit cell dimensions of

**Figure 9.** The hydroxyapatite structure viewed along the *c*-axis. The yellow polyhedrons represent the phosphate

Cation exchange in bone char may occur preferentially with calcium ions, depending on radius and electronegativity of the incoming ion [24]. Under this consideration, bone char can be quite useful material to be used for removal of both Mn2+ and Cr3+ through calcium ion exchange.

The bovine bone char was crushed, sieved (20–28 mesh Tyler, average particle diameter of 0.725 mm), and elutriated with abundant water to remove fine particles and finally dried at 80°C for 24 h. The exchanger particulate material was characterized through N2 adsorption, scanning electron microscopy (SEM), and infrared spectrophotometry (FTIR). Zero point

Solutions of 15 mEq/L of CrCl3.6H2O and MnCl2.4H2O were used in single metal removal.

N2 isotherm showed that the bone char was predominantly mesoporous material with

Scanning electron microscopy (SEM) of the bone char sample (Figure 11) presented heteroge‐

FTIR spectrum presented in Figure 12 depicts a characteristic band at 1380 cm–1 attributed to <sup>ν</sup>NO3 group, bands at 3450 cm–1, 603 cm–1 due to –OH group vibration, band at 1640 cm–1 due

neity morphology of particles and channels similar to results already reported [27].

/ g, which is a typical for this kind of solid material

charge (ZPC) was obtained based on references [25, 26].

Binary solutions containing 7.5 mEq/L of each cation were also used.

*a* = *b* = 9.432 Å and *c* = 6.881 Å [23].

234 Mass Transfer - Advancement in Process Modelling

groups [23].

*4.2.1. Materials*

*4.2.2. Results and discussion*

(Figure 10).

hysteresis and a BET area of 100 m2

**Figure 11.** Micrograph obtained by SEM of the bone char.

to CO3 2−, and a band at 1038 cm–1 attributed to the molecular vibration of PO4 3– [22]. The balancing cations of such groups may be exchanged when in contact with electrolyte solutions.

The superficial zero point charge (ZPC) was pH 7.9. As the pH values solutions was 5–6, the surface charge was predominated by positively charged ≡CaOH<sup>2</sup> + and neutral ≡POH<sup>0</sup> sites. The surface charge was then positive [28].

**Figure 12.** FTIR Spectrum of the bone char samples.

Single and bicomponent isotherms were obtained at 25°C, 30°C, and 40°C. Although bone char is a typical ion exchanger, ions may be also retained by adsorption mechanism. Actually, it is difficult to find out an equation that presents, mathematically, the contribution of all phe‐ nomena involved. Classical adsorption equations such as the Langmuir, Freundlich, and Langmuir–Freundlich models are commonly used [2].

Single isotherms are shown in Figure 13. Chromium isotherms are more favorable than the manganese ones. This can be seen through the steeper shape and higher amounts of ion retained, which is a consequence of higher ion charge and electronegativity [24].

Temperature seemed to have a higher influence in chromium removal when temperature was increased to 40°C. Probably, a reduction of the hydration radius occurred exposing the electronegativity and promoting the exchange process. According to the amount retained observed qualitatively in all temperatures, the selectivity order is Cr3+ > Mn2+.

Cr3+ and Mn2+ ions may be located in site II, at the edge of the hydroxide channel of the hydroxyapatite. In site II, there would be a shift of the ion. In site I, Cr3+ and Mn2+ ions would be compressed within the local cluster.

The ion exchange process may be expressed as follows [24]:

( ) 2+ 2+ 3+ 2+ 2 3 CaHOAP + Mn = MnHOAP + Ca 3CaHOAP + 2Cr = Cr HOAP + 3Ca

+

and neutral

Figure 12: FTIR Spectrum of the bone char samples.

The superficial zero point charge (ZPC) was pH 7.9. As the pH values solutions

 Single and bicomponent isotherms were obtained at 25°C, 30°C, and 40°C. Although bone char is a typical ion exchanger, ions may be also retained by adsorption mechanism. Actually, it is difficult to find out an equation that presents, mathematically, the contribution of all phenomena involved. Classical adsorption equations such as the

Single isotherms are shown in Figure 13. Chromium isotherms are more favorable

of ion retained, which is a consequence of higher ion charge and electronegativity [24].

was 5–6, the surface charge was predominated by positively charged ≡CaOH2

Langmuir, Freundlich, and Langmuir–Freundlich models are commonly used [2].

sites. The surface charge was then positive [28].

≡POH<sup>0</sup>

Figure 13. (a) Mn2+ isotherms; (b) Cr3+ isotherms. ( )25C, ( ) 30C, ( ) 40C. **Figure 13.** (a) Mn2+ isotherms; (b) Cr3+ isotherms. (∎)25°C, (▲) 30°C, (●) 40°C.

Due to pH < ZPC, replacements below may also happen:

Single and bicomponent isotherms were obtained at 25°C, 30°C, and 40°C. Although bone char is a typical ion exchanger, ions may be also retained by adsorption mechanism. Actually, it is difficult to find out an equation that presents, mathematically, the contribution of all phe‐ nomena involved. Classical adsorption equations such as the Langmuir, Freundlich, and

Single isotherms are shown in Figure 13. Chromium isotherms are more favorable than the manganese ones. This can be seen through the steeper shape and higher amounts of ion

Temperature seemed to have a higher influence in chromium removal when temperature was increased to 40°C. Probably, a reduction of the hydration radius occurred exposing the electronegativity and promoting the exchange process. According to the amount retained

Cr3+ and Mn2+ ions may be located in site II, at the edge of the hydroxide channel of the hydroxyapatite. In site II, there would be a shift of the ion. In site I, Cr3+ and Mn2+ ions would

> CaHOAP + Mn = MnHOAP + Ca 3CaHOAP + 2Cr = Cr HOAP + 3Ca

( )

3+ 2+ 2 3

2+ 2+

retained, which is a consequence of higher ion charge and electronegativity [24].

observed qualitatively in all temperatures, the selectivity order is Cr3+ > Mn2+.

Langmuir–Freundlich models are commonly used [2].

**Figure 12.** FTIR Spectrum of the bone char samples.

236 Mass Transfer - Advancement in Process Modelling

The ion exchange process may be expressed as follows [24]:

be compressed within the local cluster.

0 2+ + + 0 +3 +2 + POH + Mn = POMn + H POH + Cr = POCr + H º º º º

Moreover, besides the ion exchange, the multilayer adsorption may occur as the typical plateau of ion exchange monolayer is not seen in the isotherms. In agreement with such phenomena, experimental data may be better represented by the Langmuir–Freundlich isotherms [29]. Tables 7 and 8 show such results.


**Table 7.** Equilibrium parameters for manganese ions.


**Table 8.** Equilibrium parameters for chromium ions.

The binary isotherms are shown in Figure 14. As expected, chromium is again more retained, although the shape of the isotherms is completely different. This is a consequence of compe‐ tition of both ions for site II.

**Figure 14.** Isotherms for Mn2+/Cr3+ binary system in bone char.

Again, the Langmuir–Freundlich model was the one that best represents bicomponent exchange in bone char sample, as seen in Table 9 with the lowest objective function. The parameter *bi* for the bicomponent adjustment for the Langmuir–Freundlich model is lower than the ones estimated for the single isotherms due to the competition to site II. Nevertheless, *q*max are much higher than the single values, indicating a physisorption process where more ions are retained with weaker energy.


Cr3+ = subscript 1; Mn2+ = subscript 2.

**Parameter**

**Langmuir**

238 Mass Transfer - Advancement in Process Modelling

Freundlich

**Table 8.** Equilibrium parameters for chromium ions.

**Figure 14.** Isotherms for Mn2+/Cr3+ binary system in bone char.

tition of both ions for site II.

Langmuir–Freundlich

**25°C 30°C 40°C**

*q*max 1.507 ± 0.082 1.305 ± 0.097 1.836 ± 0.066 *B* 0.287 ± 0.033 0.450 ± 0.087 1.090 ± 0.121 *R*² 0.9772 0.9217 0.9612

*k*<sup>f</sup> 0.381 ± 0.011 0.444 ± 0.019 0.897 ± 0.020 *N* 0.531 ± 0.020 0.452 ± 0.031 0.408 ± 0.019 *R*² 0.9886 0.9627 0.9678

*q*max 1.792 ± 0.216 1.263 ± 0.589 3.789 ± 0.013 *B* 0.261 ± 0.036 0.503 ± 0.029 0.318 ± 0.145 1/*n* 0.779 ± 0.052 0.871 ± 0.049 0.571 ± 0.091 *R*² 0.987 0.989 0.983

The binary isotherms are shown in Figure 14. As expected, chromium is again more retained, although the shape of the isotherms is completely different. This is a consequence of compe‐

**Table 9.** Model parameters for Mn2+/Cr3+ binary system.

#### **4.3. Case study 3: Dynamic ion exchange in multicomponent solution**

Zeolites NaY and NaX are well-known ion exchangers. In this study, these zeolites were used for chromium uptake from bicomponent solutions. As it will be seen, multicomponent ion exchange in dynamic systems may provide some overshooting (*C*/*C*o > 1) related to a sequential ion exchange, where a more preferable cation with lower diffusion will be exchanged not by the balancing ion but by the competing ion previously retained [32].

#### *4.3.1. Materials and methods*

NaY has the unit cell composition of Na51(AlO2)51(SiO2)141 on a dry basis, and a cation exchange capacity (CEC) of 3.90 mEq/g NaX zeolite has a unit cell composition of Na81(AlO2)81(SiO2)111, which corresponds to a higher cation exchange capacity of 5.96 mEq/g.

First, the zeolite samples were added to 1 mol/L solution of NaCl four times at 60°C under stirring. Samples were then washed at the end of each addition with 2 L of hot deionized water and finally oven-dried at 100°C. Such procedure aimed to originate a homoionic sodium zeolite. Samples were pelletized (average diameter size of 0.180 mm).

Reagent-grade CrCl3 9H2O, MgCl2 6H2O, CaCl2 2H2O, and KCl were used to obtain binary solutions, always containing chromium and another cation in an equivalent ratio of 1:1. The concentration of chromium solution was 18 mg/L. .

The dynamic runs were conducted in a packed bed of a clear glass tube 0.9 cm ID and 30 cm long. The zeolite pellets were located in the middle of the column that operated isothermally at 30°C. The packed bed was composed of 1.60 g of NaY or 1.04 g of NaX in order to provide the same cation exchange capacity, whereas the system was fed at 9 mL min–1 of ion solution. Although the packed bed heights were different for NaY and NaX zeolites, experiments conducted with the same cation exchange capacity will generate results to compare the performance of the zeolites, mainly when uptake efficiency is aimed.

#### *4.3.2. Results of the dynamic binary runs*

Breakthrough curves of metals ions in packed beds of NaY and NaX zeolites are presented in Figures 15 to 17. In all cases, except for the Cr/Mg system in NaX zeolite, some overshooting could be seen as *C*/*C*<sup>o</sup> reached values higher than 1. In such cases, the incoming ions were first uptaken. As their hydrated radii are smaller than the one for chromium, their diffusion into the zeolitic channels were improved. Rapidly, the incoming ions were exchanged. Chromium ions are much more preferred due to the trivalent charge, and after reaching the exchanging sites, they could replace the ion previously retained.

Besides the sequential ion exchange, it is also important to emphasize the influence of the ion exchanger. NaY and NaX zeolites are isomorph materials, and the only difference between them is the charge density in the packed bed. Denser sites of NaX may promote higher attraction with electrostatic instability due to repulsion of ions closely attracted. As a conse‐ quence, the ratio of chromium uptake up to its breakpoint time (tb)/cation exchange capacity (CEC) is less retained than in NaY system, as it can be seen in Table 10.

**Figure 15.** Breakthrough curves for the Cr-Mg competitive system: (a) NaY and (b) NaX.

exchange in dynamic systems may provide some overshooting (*C*/*C*o > 1) related to a sequential ion exchange, where a more preferable cation with lower diffusion will be exchanged not by

NaY has the unit cell composition of Na51(AlO2)51(SiO2)141 on a dry basis, and a cation exchange capacity (CEC) of 3.90 mEq/g NaX zeolite has a unit cell composition of Na81(AlO2)81(SiO2)111,

First, the zeolite samples were added to 1 mol/L solution of NaCl four times at 60°C under stirring. Samples were then washed at the end of each addition with 2 L of hot deionized water and finally oven-dried at 100°C. Such procedure aimed to originate a homoionic sodium

Reagent-grade CrCl3 9H2O, MgCl2 6H2O, CaCl2 2H2O, and KCl were used to obtain binary solutions, always containing chromium and another cation in an equivalent ratio of 1:1. The

The dynamic runs were conducted in a packed bed of a clear glass tube 0.9 cm ID and 30 cm long. The zeolite pellets were located in the middle of the column that operated isothermally at 30°C. The packed bed was composed of 1.60 g of NaY or 1.04 g of NaX in order to provide the same cation exchange capacity, whereas the system was fed at 9 mL min–1 of ion solution. Although the packed bed heights were different for NaY and NaX zeolites, experiments conducted with the same cation exchange capacity will generate results to compare the

Breakthrough curves of metals ions in packed beds of NaY and NaX zeolites are presented in Figures 15 to 17. In all cases, except for the Cr/Mg system in NaX zeolite, some overshooting could be seen as *C*/*C*<sup>o</sup> reached values higher than 1. In such cases, the incoming ions were first uptaken. As their hydrated radii are smaller than the one for chromium, their diffusion into the zeolitic channels were improved. Rapidly, the incoming ions were exchanged. Chromium ions are much more preferred due to the trivalent charge, and after reaching the exchanging

Besides the sequential ion exchange, it is also important to emphasize the influence of the ion exchanger. NaY and NaX zeolites are isomorph materials, and the only difference between them is the charge density in the packed bed. Denser sites of NaX may promote higher attraction with electrostatic instability due to repulsion of ions closely attracted. As a conse‐ quence, the ratio of chromium uptake up to its breakpoint time (tb)/cation exchange capacity

.

the balancing ion but by the competing ion previously retained [32].

which corresponds to a higher cation exchange capacity of 5.96 mEq/g.

zeolite. Samples were pelletized (average diameter size of 0.180 mm).

performance of the zeolites, mainly when uptake efficiency is aimed.

(CEC) is less retained than in NaY system, as it can be seen in Table 10.

concentration of chromium solution was 18 mg/L.

*4.3.2. Results of the dynamic binary runs*

sites, they could replace the ion previously retained.

*4.3.1. Materials and methods*

240 Mass Transfer - Advancement in Process Modelling

**Figure 16.** Breakthrough curves for the Cr-Ca competitive system: (a) NaY and (b) NaX.

**Figure 17.** Breakthrough curves for the Cr-K competitive system: (a) NaY and (b) NaX.


*U*tb Cr / CEC= ratio of chromium uptake up to chromium breakpoint time (tb) and the cation exchange capacity of the column.

**Table 10.** Amount of chromium ions retained up to the breakpoint of 5% of the feed concentration.

### **5. General conclusions**

Ion exchange is a much more complex phenomenon than adsorption as many ion exchangers may also act as adsorbents, increasing the difficulty in understanding the sorption removal.

Moreover, electrolytes add complexity in fluid phase and also in the solid phase. Ion charges and hydration energy of the incoming ions as well as charge density of the ion exchanger are undoubtedly factors that deserve detailed investigation, mainly for scaling-up proposals.

### **Author details**

Maria Angélica Simões Dornellas de Barros1 , Marcelino Luiz Gimenes1 , Melissa Gurgel Adeodato Vieira2 and Meuris Gurgel Carlos da Silva2

1 Chemical Engineering Department, State University of Maringá, Maringá, PR, Brazil

2 School of Chemical Engineering, University of Campinas, Campinas, SP, Brazil

### **References**


**System** *<sup>U</sup>***tb**

242 Mass Transfer - Advancement in Process Modelling

**5. General conclusions**

**Author details**

**References**

Maria Angélica Simões Dornellas de Barros1

Melissa Gurgel Adeodato Vieira2

Elsevier, 2007.

ard. Mater., 2009, 162, 2–3, 616.

*U*tb

column.

**Cr / CEC System** *<sup>U</sup>***tb**

Cr / CEC= ratio of chromium uptake up to chromium breakpoint time (tb) and the cation exchange capacity of the

Ion exchange is a much more complex phenomenon than adsorption as many ion exchangers may also act as adsorbents, increasing the difficulty in understanding the sorption removal.

Moreover, electrolytes add complexity in fluid phase and also in the solid phase. Ion charges and hydration energy of the incoming ions as well as charge density of the ion exchanger are undoubtedly factors that deserve detailed investigation, mainly for scaling-up proposals.

, Marcelino Luiz Gimenes1

and Meuris Gurgel Carlos da Silva2

[2] Zagorodni, A.A., Ion Exchange Materials Properties and Applications, Great Britain,

[3] Febrianto, J., Kosasih, A., N., Sunarco, J., Ju, Y-H., Indraswati, N., Ismadji, S., J. Haz‐

1 Chemical Engineering Department, State University of Maringá, Maringá, PR, Brazil

2 School of Chemical Engineering, University of Campinas, Campinas, SP, Brazil

[1] Helferich, F., Ion Exchange, EUA, Dover Publications Inc., 1995.

,

Cr-NaY 0.69 Cr-NaX 0.71 Cr/Mg-NaY 0.54 Cr/Mg-NaX 0.27 Cr/Ca-NaY 0.51 Cr/Ca-NaX 0.31 Cr/K-NaY 0.66 Cr/K-NaX 0.41

**Table 10.** Amount of chromium ions retained up to the breakpoint of 5% of the feed concentration.

**Cr / CEC**

