**5. Adsorption**

In the last years there has been a great progress in adsorbent design and cyclic adsorption process developments, thus making adsorption an important separation tool (King, 1980). Adsorption is usually performed in columns packed with adsorbent but it can also be performed in stirred tanks with the adsorbent in suspension. The latter are usually known as bleachers since their most common application is the bleaching of edible oils with clays.

The high separating power of the chromatographic effect, achieved in adsorbent-packed columns, is a unique advantage of adsorption as compared to other separation processes. The high separating power is caused by the continuous contact and equilibration between the fluid and sorbent phases. If no diffusion limitations are considered, each contact is equivalent to an equilibrium stage (theoretical plate) and several hundreds or more of such equilibrium stages can be achieved within a short column. Adsorption is thus ideally suited for purification applications and difficult separations.

The adsorptive separation is achieved by one of three mechanisms: adsorption equilibrium, steric effect and kinetic effect. Most processes, especially those in solid-liquid phase, operate with the principle of adsorption equilibrium and hence they are called equilibrium

Adsorption in Biodiesel Refining - A Review 437

equilibrium values of the bulk concentration of the adsorbate in the liquid phase and the

maximum or saturation load. At low pressures or in dilute solutions, the Langmuir isotherm

\* *K CL*

All isotherms should reduce to the Henry's law form at extreme dilution. Since high dilution is the condition for many systems that need to be purified to extremely small amounts of certain impurities, the Henry's constant becomes the most important factor for purification. Both *KL*

adsorbent surface. Thus bond energy becomes critical for purification. Strong bonds are typical

Fig. 2. Adsorption isotherm for silica TrySil 3000 at three different temperatures (Manuale,

Zeldowitsch (1934) and previously Freundlich (1906) supplied an equation that is widely

1/ \* \* *<sup>n</sup>*

In this formula *q\** and *C\** are the equilibrium adsorbate concentrations in the solid and fluid phase, respectively. Zeldowitsch obtained this formula assuming an exponentially decaying

basis. Freundlich's isotherm is customarily used to express the equilibrium concentration of metals and colorant bodies (chlorophylls, carotenes, etc.) in oils (Liu et al., 2008; Toro-Vázquez & Proctor, 1996) and is expected that it should also be convenient for the same adsorbates in biodiesel precursor oils and fats. In the case of the biodiesel product probably the fit of the data of adsorption of some impurities could also be good, but in this case the oil has already been refined before entering the transesterification reactor and in so diluted

2011). 70 °C (■), H=44.6. 90 °C (●), H=31.4. 110 °C (), H=18.3.

used to describe the data for heterogeneous adsorbents (Eq. 4).

condition the Henry's linear isotherm could better apply.

function of site density with respect to

*H* is proportional to the bond energy between the adsorbate molecule and the

is the fractional coverage of the surface and *qm* the

\* \* *q K CL mq HC* (3)

*<sup>F</sup> q KC* (4)

*H*, while Freundlich proposed it on an empirical

*H*=-5.7 kCal mol-1.

(2)

*H)*. For physical

and *H* are proportional to the exponential of the heat of adsorption *(-*

reduces to a linear form, or Henry's law form (Eqs. 2-3).

of adsorbate-adsorbent systems in ultrapurification.

concentration in the solid phase.

adsorption,

separation processes. In this processes the amount of adsorbate retained is primarily determined by the thermodynamic adsorbate-adsorbent activity with little regard to mass transfer phenomena. The steric effect derives from the molecular sieving properties of zeolites and other molecular sieves and can be taken as an extreme case of adsorption controlled by mass transfer phenomena. In this case either small or properly shaped molecules can diffuse into the adsorbent while other molecules are partially or totally excluded. Typical examples are the separation of linear and branched alkanes (Silva et al., 2000) or the dehydration of aqueous ethanol (Teo & Ruthven, 1986), both performed using molecular sieves. Kinetic separation is achieved by virtue of the differences in diffusion rates of different molecules. This kind of separation is mostly found in gas-gas separation as in the separation of the component gases of air (Ruthven & Farooq, 1990).

In the case of the biodiesel feedstock and product, the low elution rates in the packed columns makes the dynamic separation (kinetic effect) of no use for a practical separation. In the case of the steric effect this is expected to work fine for molecules differing widely in size and this could be the case for molecules of the organic and polar phases normally found at the outlet of the transesterification reactors. Triglycerides, diglycerides, monoglycerides, free fatty acids and fatty acid methyl esters have high molecular weights and long acyl chains and they are the main components of the organic phase. On the other side glycerol, water and methanol have small molecular sizes and could be retained in packed beds containing suitable adsorbents. Because of their relative high vapor pressure, water and methanol need a relatively few number of thoretical plates to be separated from the organic phase by distillation/evaporation (Zhang et al., 2003) and this is indeed the preferred method of water and methanol removal. However some reports on the use of hygroscopic adsorbents for biodiesel drying can be found (Lastella, 2005). Removal of glycerol from biodiesel using adsorbents has already been proved but only equilibrium adsorption on open pore adsorbents has been tried (Yori et al., 2007; Mazzieri et al., 2008). The use of the steric effect in the adsorption of water on zeolites has however been proposed for the drying of the methanol to be recycled to the biodiesel process (McDonald, 2001).

This leaves equilibrium adsorption as the main principle behind the adsorption refining of biodiesel and makes the adsorption isotherm as the main piece of information for the accurate design and scale-up of adsorption units. In this sense, though a lot of information is available for adsorption of impurities from plant oils (biodiesel feestock) in relation to bleaching with clays (Hussin et al., 2011) or silicas (Rossi et al., 2003) only scarce information for purification of biodiesel by adsorption has been published (Manuale et al., 2011; Schmitt Faccini et al., 2011; Vasques, 2009; Mazzieri et al., 2008).

#### **6. Adsorption isotherms**

The function that describes the relation between the amount of adsorbate on the solid and its liquid-phase concentration is called adsorption equilibrium isotherm. Different functions can be used to describe this equilibrium. The Langmuir-type isotherm remains to be the most widely used for practical applications (Eq. 1).

$$\theta = \frac{q^\*}{q\_m} = \frac{K\_L C^\*}{1 + K\_L C^\*} \tag{1}$$

Only liquid phase applications will be discussed in this review and therefore also only liquid phase isotherms. The constant *KL* is called Langmuir constant. *C\** and *q\** are the

separation processes. In this processes the amount of adsorbate retained is primarily determined by the thermodynamic adsorbate-adsorbent activity with little regard to mass transfer phenomena. The steric effect derives from the molecular sieving properties of zeolites and other molecular sieves and can be taken as an extreme case of adsorption controlled by mass transfer phenomena. In this case either small or properly shaped molecules can diffuse into the adsorbent while other molecules are partially or totally excluded. Typical examples are the separation of linear and branched alkanes (Silva et al., 2000) or the dehydration of aqueous ethanol (Teo & Ruthven, 1986), both performed using molecular sieves. Kinetic separation is achieved by virtue of the differences in diffusion rates of different molecules. This kind of separation is mostly found in gas-gas separation as in

In the case of the biodiesel feedstock and product, the low elution rates in the packed columns makes the dynamic separation (kinetic effect) of no use for a practical separation. In the case of the steric effect this is expected to work fine for molecules differing widely in size and this could be the case for molecules of the organic and polar phases normally found at the outlet of the transesterification reactors. Triglycerides, diglycerides, monoglycerides, free fatty acids and fatty acid methyl esters have high molecular weights and long acyl chains and they are the main components of the organic phase. On the other side glycerol, water and methanol have small molecular sizes and could be retained in packed beds containing suitable adsorbents. Because of their relative high vapor pressure, water and methanol need a relatively few number of thoretical plates to be separated from the organic phase by distillation/evaporation (Zhang et al., 2003) and this is indeed the preferred method of water and methanol removal. However some reports on the use of hygroscopic adsorbents for biodiesel drying can be found (Lastella, 2005). Removal of glycerol from biodiesel using adsorbents has already been proved but only equilibrium adsorption on open pore adsorbents has been tried (Yori et al., 2007; Mazzieri et al., 2008). The use of the steric effect in the adsorption of water on zeolites has however been proposed for the drying of the

This leaves equilibrium adsorption as the main principle behind the adsorption refining of biodiesel and makes the adsorption isotherm as the main piece of information for the accurate design and scale-up of adsorption units. In this sense, though a lot of information is available for adsorption of impurities from plant oils (biodiesel feestock) in relation to bleaching with clays (Hussin et al., 2011) or silicas (Rossi et al., 2003) only scarce information for purification of biodiesel by adsorption has been published (Manuale et al., 2011; Schmitt

The function that describes the relation between the amount of adsorbate on the solid and its liquid-phase concentration is called adsorption equilibrium isotherm. Different functions can be used to describe this equilibrium. The Langmuir-type isotherm remains to be the

> \* \* 1 \* *L m L q K C q KC*

Only liquid phase applications will be discussed in this review and therefore also only liquid phase isotherms. The constant *KL* is called Langmuir constant. *C\** and *q\** are the

(1)

the separation of the component gases of air (Ruthven & Farooq, 1990).

methanol to be recycled to the biodiesel process (McDonald, 2001).

Faccini et al., 2011; Vasques, 2009; Mazzieri et al., 2008).

most widely used for practical applications (Eq. 1).

**6. Adsorption isotherms** 

equilibrium values of the bulk concentration of the adsorbate in the liquid phase and the concentration in the solid phase. is the fractional coverage of the surface and *qm* the maximum or saturation load. At low pressures or in dilute solutions, the Langmuir isotherm reduces to a linear form, or Henry's law form (Eqs. 2-3).

$$
\theta = \mathsf{K}\_L \mathsf{C}^\* \tag{2}
$$

$$q = \mathcal{K}\_L \mathcal{C}^\* q\_m = \mathcal{H} \mathcal{C}^\* \tag{3}$$

All isotherms should reduce to the Henry's law form at extreme dilution. Since high dilution is the condition for many systems that need to be purified to extremely small amounts of certain impurities, the Henry's constant becomes the most important factor for purification. Both *KL* and *H* are proportional to the exponential of the heat of adsorption *(-H)*. For physical adsorption, *H* is proportional to the bond energy between the adsorbate molecule and the adsorbent surface. Thus bond energy becomes critical for purification. Strong bonds are typical of adsorbate-adsorbent systems in ultrapurification.

Fig. 2. Adsorption isotherm for silica TrySil 3000 at three different temperatures (Manuale, 2011). 70 °C (■), H=44.6. 90 °C (●), H=31.4. 110 °C (), H=18.3. *H*=-5.7 kCal mol-1.

Zeldowitsch (1934) and previously Freundlich (1906) supplied an equation that is widely used to describe the data for heterogeneous adsorbents (Eq. 4).

$$q^\* = K\_F \subset \mathbb{C}^{\*1/n} \tag{4}$$

In this formula *q\** and *C\** are the equilibrium adsorbate concentrations in the solid and fluid phase, respectively. Zeldowitsch obtained this formula assuming an exponentially decaying function of site density with respect to *H*, while Freundlich proposed it on an empirical basis. Freundlich's isotherm is customarily used to express the equilibrium concentration of metals and colorant bodies (chlorophylls, carotenes, etc.) in oils (Liu et al., 2008; Toro-Vázquez & Proctor, 1996) and is expected that it should also be convenient for the same adsorbates in biodiesel precursor oils and fats. In the case of the biodiesel product probably the fit of the data of adsorption of some impurities could also be good, but in this case the oil has already been refined before entering the transesterification reactor and in so diluted condition the Henry's linear isotherm could better apply.

Adsorption in Biodiesel Refining - A Review 439

Mazzieri et al. (2008) used the multicomponent Langmuir isotherm to express the simultaneous adsorption of glycerol and monoglycerides. They found that adsorption of glycerol is not influenced by the presence of small amounts of water and soaps. Conversely the presence of MGs and/or methanol lowers the adsorption capacity of glycerol because of

It is generally recognized that transfer of adsorbates from the bulk of a liquid occurs in two stages. First molecules diffuse through the laminar film of fluid surrounding the particles and then they diffuse inside the pore structure of the particle. Most authors assume that the concentration gradient of any species along the film is linear and that the mass transfer to the adsorbent surface is proportional to the so-called film coefficient, *kf* (Eq. 8). In this equation, *q* is the adsorbent concentration on the solid particle, *rp* is the particle radius and

*<sup>p</sup>* is the average density of the particle. *C* is the concentration of the adsorbate in the bulk of the fluid and *Cs* the value of adsorbate concentration on the surface. *kf* is often predicted with the help of generalized, dimensionless correlations of the Sherwood (*Sh*) number that correlate with the Reynolds (*Re*) and Schmidt (*Sc*) numbers and the geometry of the systems.

3 *<sup>f</sup>*

*q k*

 

*Sh Sc*

*Sc*

*t r* 

*m r k*

*D*

values of *DM* are presented in Table 4.

*p p*

<sup>3</sup> 0.6 <sup>2</sup> 2.0 1.1 Re *p f*

*M*

*D* 

In the case of the homogeneous surface diffusion model (HSDM) the equation of mass transport inside the pellet it that of uniform Fickian diffusion in spherical coordinates (Eq. 11). Sometimes this model is modified for system in which the diffusivity is seemingly not constant. The most common modification is to write the surface diffusivity, *Ds*, as a linear function of the radius, thus yielding the so-called proportional diffusivity model (PDM). A detailed inspection of the available surface diffusivity data indicates that surface diffusivity is similar but expectedly smaller than molecular diffusivity, *DM*. Some

> 2 2

In the case of fatty substances there is not much reported data on the values of surface diffusivity. Yang et al. (1974) found that stearic acid had a surface diffusivity on alumina of about 10-9-10-11 m2s-1 depending on the hydration degree of the alumina. Allara and Nuzzo

*s q qq <sup>D</sup> t rr r* 

(1985) reported values of *Ds* of 10-10-10-11 for different alkanoic acids on alumina.

2

*C C*

*s*

1

(8)

(11)

(10)

(9)

**7. Mass transfer kinetics and models for adsorption in the liquid phase** 

the competition of MGs for the same adsorption sites.

The most popular is that due to Wakao and Funazkri (1978) (Eq. 9).

To avoid indefinite increase in adsorption with concentration, the so-called Langmuir-Freundlich isotherm is sometimes proposed (Sips, 1948) (Eq. 5). This isotherm can be derived from the Langmuir isotherm by assuming each adsorbate molecule occupies *n* sites. It can also be considered as the Langmuir isotherm on nonuniform surfaces.

$$\mathbb{P}\left(q^\* \neq q\_m\right) = \frac{K\_{LF} \gets \ast^{1/n}}{1 + K\_{LF} \gets \ast^{1/n}} \,. \tag{5}$$

Langmuir's formula has been successfully used to express the adsorption of glycerides from biodiesel over silica gel (Mazzieri et al., 2008). In the case of free fatty acids (FFAs) Nawar and Han (1985) also concluded that the Langmuir isotherm was followed by octanoic acid adsorption on silica. The better adjustment of free fatty acid (oleic, linoleic, etc.) adsorption over several solids by the Langmuir model (in comparison to Freundlich's) has also been reported by Proctor and Palaniappan (1990) and Cren et al. (2005, 2010).

The Langmuir and Langmuir-Freundlich isotherms for adsorption of single components are readily extended to an *n*-component mixture to yield the extended multicomponent Langmuir isotherm (Yang, 1997) (Eq. 6) and the so-called loading ratio correlation (LRC) (Yon & Turnock, 1971) (Eq. 7). In these equations it is assumed that the area occupied by one molecule is not affected by the presence of other species on the surface. This is not thermodynamically consistent but the equations remain nonetheless useful for design.

$$\mathbf{M}(q\_i \triangleq / q\_{m,i}) = \frac{\mathbf{K}\_{L,i} \cdot \mathbf{C}\_i \triangleq \mathbf{}}{\mathbf{1} + \sum \mathbf{K}\_{L,i} \cdot \mathbf{C}\_i \triangleq \mathbf{1}} \tag{6}$$

$$\mathbf{M}\left(q\_i \triangleq / q\_{m,i}\right) = \frac{\mathbf{K}\_{LF,i} \mathbf{C}\_i \star^{1/n}}{1 + \sum \mathbf{K}\_{LF,i} \mathbf{C}\_i \star^{1/n}}\tag{7}$$

Fig. 3. Adsorption of glycerol over silica (Mazzieri et al., 2008). (■) Pure biodiesel. (□) Biodiesel spiked with water (944 ppm). (○) Biodiesel spiked with soap (270 ppm). () Biodiesel spiked with MG (7500 ppm). () Biodiesel spiked with methanol (12000 ppm).

To avoid indefinite increase in adsorption with concentration, the so-called Langmuir-Freundlich isotherm is sometimes proposed (Sips, 1948) (Eq. 5). This isotherm can be derived from the Langmuir isotherm by assuming each adsorbate molecule occupies *n* sites.

\* ( \*/ ) 1 \*

*LF m n LF*

Langmuir's formula has been successfully used to express the adsorption of glycerides from biodiesel over silica gel (Mazzieri et al., 2008). In the case of free fatty acids (FFAs) Nawar and Han (1985) also concluded that the Langmuir isotherm was followed by octanoic acid adsorption on silica. The better adjustment of free fatty acid (oleic, linoleic, etc.) adsorption over several solids by the Langmuir model (in comparison to Freundlich's) has also been

The Langmuir and Langmuir-Freundlich isotherms for adsorption of single components are readily extended to an *n*-component mixture to yield the extended multicomponent Langmuir isotherm (Yang, 1997) (Eq. 6) and the so-called loading ratio correlation (LRC) (Yon & Turnock, 1971) (Eq. 7). In these equations it is assumed that the area occupied by one molecule is not affected by the presence of other species on the surface. This is not thermodynamically consistent but the equations remain nonetheless useful for design.

\* ( \*/ ) 1 \*

\* ( \*/ ) 1 \*

*q q K C*

Fig. 3. Adsorption of glycerol over silica (Mazzieri et al., 2008). (■) Pure biodiesel. (□) Biodiesel spiked with water (944 ppm). (○) Biodiesel spiked with soap (270 ppm). () Biodiesel spiked with MG (7500 ppm). () Biodiesel spiked with methanol (12000 ppm).

,

, , 1/ ,

*K C*

*LF i i i mi n*

*K C*

*Li i*

,

*LF i i*

*Li i*

1/

*n*

*q q K C* (6)

(7)

*K C*

1/ 1/

*n*

*q q K C* . (5)

It can also be considered as the Langmuir isotherm on nonuniform surfaces.

reported by Proctor and Palaniappan (1990) and Cren et al. (2005, 2010).

,

*i mi*

Mazzieri et al. (2008) used the multicomponent Langmuir isotherm to express the simultaneous adsorption of glycerol and monoglycerides. They found that adsorption of glycerol is not influenced by the presence of small amounts of water and soaps. Conversely the presence of MGs and/or methanol lowers the adsorption capacity of glycerol because of the competition of MGs for the same adsorption sites.

#### **7. Mass transfer kinetics and models for adsorption in the liquid phase**

It is generally recognized that transfer of adsorbates from the bulk of a liquid occurs in two stages. First molecules diffuse through the laminar film of fluid surrounding the particles and then they diffuse inside the pore structure of the particle. Most authors assume that the concentration gradient of any species along the film is linear and that the mass transfer to the adsorbent surface is proportional to the so-called film coefficient, *kf* (Eq. 8). In this equation, *q* is the adsorbent concentration on the solid particle, *rp* is the particle radius and *<sup>p</sup>* is the average density of the particle. *C* is the concentration of the adsorbate in the bulk of the fluid and *Cs* the value of adsorbate concentration on the surface. *kf* is often predicted with the help of generalized, dimensionless correlations of the Sherwood (*Sh*) number that correlate with the Reynolds (*Re*) and Schmidt (*Sc*) numbers and the geometry of the systems. The most popular is that due to Wakao and Funazkri (1978) (Eq. 9).

$$\frac{\partial q}{\partial t} = \left(\frac{3k\_f}{r\_p \rho\_p}\right) \left(\mathbf{C} - \mathbf{C}\_s\right) \tag{8}$$

$$\text{Sh} = \frac{2r\_pk\_f}{D\_m} = \left(2.0 + 1.1 \text{Sc}^{\frac{1}{3}} \text{ Re}^{0.6}\right) \tag{9}$$

$$Sc = \frac{\mu}{D\_M \rho} \tag{10}$$

In the case of the homogeneous surface diffusion model (HSDM) the equation of mass transport inside the pellet it that of uniform Fickian diffusion in spherical coordinates (Eq. 11). Sometimes this model is modified for system in which the diffusivity is seemingly not constant. The most common modification is to write the surface diffusivity, *Ds*, as a linear function of the radius, thus yielding the so-called proportional diffusivity model (PDM). A detailed inspection of the available surface diffusivity data indicates that surface diffusivity is similar but expectedly smaller than molecular diffusivity, *DM*. Some values of *DM* are presented in Table 4.

$$\frac{\partial \hat{q}}{\partial t} = D\_s \left( \frac{\partial^2 q}{\partial r^2} + \frac{2}{r} \frac{\partial q}{\partial r} \right) \tag{11}$$

In the case of fatty substances there is not much reported data on the values of surface diffusivity. Yang et al. (1974) found that stearic acid had a surface diffusivity on alumina of about 10-9-10-11 m2s-1 depending on the hydration degree of the alumina. Allara and Nuzzo (1985) reported values of *Ds* of 10-10-10-11 for different alkanoic acids on alumina.

Adsorption in Biodiesel Refining - A Review 441

fatty acids over silicas (Manuale, 2011). FFA adsorption was found to be rather slow despite the small diameter of the particles used (74 microns). This was addressed to the dominance of the intraparticle mass transfer resistance. This resistance was attributed to a working mechanism of surface diffusion with a diffusivity value of about 10-15 m2 s-1. The system could be modeled by a LDFM with an overall coefficient of mass transfer, *KLDF*=0.013-0.035 min-1 (see Table 5). These values compare well with those obtained for the adsorption of

*Adsorbent T, °C KLDF, min-1 Adsorbent T, °C KLDF, min-1 Silica TrySil 3000* 70 0.035 *Silica TrySil 300B* 70 0.032

Table 5. Values of the LDF overall mass transfer coefficient for the silica adsorption of free

The authors provided a further insight into the internal structure of the LDF kinetic parameter by making use of the estimation originally proposed by Ruthven et al. (1994) for

large difference between them. In the case of the adsorption of oleic acid from biodiesel it

that the silica-FFA system is strongly dominated by intrapellet diffusion (Manuale, 2011).

3 15 *p p*

*r r*

*LDF f s*

*KkD*

2

The LDF model was first proposed by Glueckauf and Coates (1947) as an "approximation" to mass transfer phenomena in adsorption processes in gas phase but has been found to be highly useful to model adsorption in packed beds because it is simple, analytical, and physically consistent. For example, it has been used to accurately describe highly dynamic PSA cycles in gas separation processes (Mendes et al., 2001). Yet, a difference is sometimes found in the isothermal batch uptake curves on adsorbent particles obtained by the LDFM and the more rigorous HSDM. The LDF approximation has also been reported to introduce some error when the fractional uptake approaches unity (Hills, 1986). In practice however saturation values might never be approached because adsorption capacity is severely decreased due to unfavourable thermodynamics in the saturation range. The precision of LFDM can be also improved by using higher

*Breakthrough curve.* It is the "S" shaped curve that results when the effluent adsorbate concentration is plotted against time or volume. It can be constructed for full scale or pilot testing. The breakthrough point is the point on the breakthrough curve where the effluent adsorbate concentration reaches its maximum allowable concentration, which often corresponds to the treatment goal, usually based on regulatory or risk based numbers.

90 0.019 90 0.022 110 0.013 110 0.018

*f D*

(13)

 *total*) is sometimes questioned because of the

*total*1700 seconds (experimental) indicating

*D*) and the film transfer time (

is the porosity of

*f*)

sodium oleate over magnetite, 0.002-0.03 min-1 (Roonasi et al., 2010).

fatty acids from biodiesel at different temperatures (Manuale, 2011).

the pellet. The additivity of the intrapellet diffusion time (

*f*0.07 seconds (estimated) and

1

to give the total characteristic time (1/*KLDF*=

order LDF models (Álvarez-Ramírez et al., 2005).

**8. Experimental breakthrough curves** 

was shown that

gas phase adsorption (Eq. 13). *Ds* is the intrapellet surface diffusivity and

Fig. 4. Homogeneous surface diffusion (left) and linear driving force (right) models.


Table 4. Values of molecular diffusivity of several biodiesel impurities.

$$\frac{\partial q}{\partial t} = K\_{LDF} (q \, \text{\*} - q\_{av} \, \text{)}\tag{12}$$

In the case of the linear driving force model (LDFM) all mass transfer resistances are grouped together to give a simple relation (Eq. 12). *qav* is the average adsorbate load on the pellet and is obtained by the time-integration of the adsorbate flux. *q\** is related to *C\**, through the equilibrium isotherm. It must be noted that in this formulation *qs=q\** and *Cs=C\**, indicating that the surface is considered to be in equilibrium. In the case of adsorption for refining of biodiesel, the LDF approximation has been used to model the adsorption of free

Fig. 4. Homogeneous surface diffusion (left) and linear driving force (right) models.

*Triolein, Tristearin* 70 Triolein, tristearin 1-2x10-10 Callaghan & Jolley (1980) *Sodium oleate* 25 Sodium oleate 3.3x10-10 Gajanan et al. (1973) *Sodium palmitate* Sodium palmitate 4.8x10-10 Gajanan et al. (1973) *Glycerol* 130 Biodiesel 6.18x10-9 Kimmel (2004)

> (\* ) *LDF av <sup>q</sup> K qq <sup>t</sup>*

In the case of the linear driving force model (LDFM) all mass transfer resistances are grouped together to give a simple relation (Eq. 12). *qav* is the average adsorbate load on the pellet and is obtained by the time-integration of the adsorbate flux. *q\** is related to *C\**, through the equilibrium isotherm. It must be noted that in this formulation *qs=q\** and *Cs=C\**, indicating that the surface is considered to be in equilibrium. In the case of adsorption for refining of biodiesel, the LDF approximation has been used to model the adsorption of free

(12)

*Molecule T, °C Solvent DM, m2 s-1 Reference Stearic acid* 130 Nut oil 4.2x10-10 Smits (1976) *Oleic acid* 130 Nut oil 3.7x10-10 Smits (1976) *Monoolein* 25 Water 1.3x10-10 Geil et al. (2000)

Table 4. Values of molecular diffusivity of several biodiesel impurities.

fatty acids over silicas (Manuale, 2011). FFA adsorption was found to be rather slow despite the small diameter of the particles used (74 microns). This was addressed to the dominance of the intraparticle mass transfer resistance. This resistance was attributed to a working mechanism of surface diffusion with a diffusivity value of about 10-15 m2 s-1. The system could be modeled by a LDFM with an overall coefficient of mass transfer, *KLDF*=0.013-0.035 min-1 (see Table 5). These values compare well with those obtained for the adsorption of sodium oleate over magnetite, 0.002-0.03 min-1 (Roonasi et al., 2010).


Table 5. Values of the LDF overall mass transfer coefficient for the silica adsorption of free fatty acids from biodiesel at different temperatures (Manuale, 2011).

The authors provided a further insight into the internal structure of the LDF kinetic parameter by making use of the estimation originally proposed by Ruthven et al. (1994) for gas phase adsorption (Eq. 13). *Ds* is the intrapellet surface diffusivity and is the porosity of the pellet. The additivity of the intrapellet diffusion time (*D*) and the film transfer time (*f*) to give the total characteristic time (1/*KLDF*=*total*) is sometimes questioned because of the large difference between them. In the case of the adsorption of oleic acid from biodiesel it was shown that *f*0.07 seconds (estimated) and *total*1700 seconds (experimental) indicating that the silica-FFA system is strongly dominated by intrapellet diffusion (Manuale, 2011).

$$\frac{1}{K\_{LDF}} = \frac{r\_p}{3k\_f} + \frac{r\_p^2}{15\varepsilon D\_s} = \tau\_f + \tau\_D \tag{13}$$

The LDF model was first proposed by Glueckauf and Coates (1947) as an "approximation" to mass transfer phenomena in adsorption processes in gas phase but has been found to be highly useful to model adsorption in packed beds because it is simple, analytical, and physically consistent. For example, it has been used to accurately describe highly dynamic PSA cycles in gas separation processes (Mendes et al., 2001). Yet, a difference is sometimes found in the isothermal batch uptake curves on adsorbent particles obtained by the LDFM and the more rigorous HSDM. The LDF approximation has also been reported to introduce some error when the fractional uptake approaches unity (Hills, 1986). In practice however saturation values might never be approached because adsorption capacity is severely decreased due to unfavourable thermodynamics in the saturation range. The precision of LFDM can be also improved by using higher order LDF models (Álvarez-Ramírez et al., 2005).

#### **8. Experimental breakthrough curves**

*Breakthrough curve.* It is the "S" shaped curve that results when the effluent adsorbate concentration is plotted against time or volume. It can be constructed for full scale or pilot testing. The breakthrough point is the point on the breakthrough curve where the effluent adsorbate concentration reaches its maximum allowable concentration, which often corresponds to the treatment goal, usually based on regulatory or risk based numbers.

Adsorption in Biodiesel Refining - A Review 443

equations are the "clean bed" initial condition and the Danckwertz boundary conditions for

*L p*

0, *<sup>C</sup> z L*

In order to solve a specific problem of adsorption, mass transfer kinetics equations must be added, such as those of the HSDM or LDFM. The film equation is customarily replaced in the general equation of flow along the bed (Eq. 14) and thus the total system is reduced. The system still remains rather complex and in most instances can only be solved numerically. For faster convergence and accuracy special methods can be used, such as orthogonal collocation, the Galerkin method, or finite element methods. The general solution of the system is a set of points of *C* as a function of *z*, *t* and *r*. Often much of this information is not necessary and only the fluid bulk concentration at the bed outlet as a function of time, i.e.

In order to obtain analytical breakthrough curves some simplifications can be made. For example the first implication of a high intrapellet diffusion resistance in liquid-solid systems (as in biodiesel refining) is that the Biot number that represents the ratio of the liquid-to-solid phase mass transfer rate, takes very high values. In Biot's equation (Eq. 18), *q0* is the equilibrium solid-phase concentration corresponding to the influent concentration *C0* and *rp* is the particle radius. The film resistance in high *Bi* systems can be disregarded; their breakthrough curves being highly symmetrical. Experimental symmetrical curves have indeed been found for the adsorption of glycerol over packed

> 0 0 *f P s P*

*k rC*

*D q* 

Another simplification is related to the longitudinal dispersion term in Eq. 14. *DL* is usually calculated together with the film coefficient *kf* by using the Wakao & Funazkri (1978) correlations for the mass transfer in packed beds of spherical particles (Eqs. 9 and 19). Due to the dependence of *Sc* on the molecular diffusivity, the value of *DL* is dominated by *DM*. The importance of *DL* in systems of biodiesel flowing in packed bed adsorbers could be disregarded in attention to the value of the axial Péclet number (Eq. 22), since *Pe* > 100 in these systems. For very big *Pe* numbers the regime is that of plug flow (no backmixing) and when *Pe* is very small the backmixing is maximum and the flow equations are reduced to

*Bi*

the equation of the perfectly mixed reactor (Busto et al., 2006).

*z*

*C C uC <sup>q</sup> <sup>D</sup> t zt z*

(14)

<sup>0</sup> *CtC* (0, ) (15)

(16)

*C z*( ,0) 0 (17)

(18)

( )1 <sup>0</sup> *<sup>B</sup>*

*B*

*<sup>B</sup>* is the bed porosity. The last three

*B*), where *U* is the empty bed space velocity and

2 2

(*u=U/*

a closed system.

the "breakthrough" curve, is reported.

beds of silica (Fig. 6).

Fig. 5. Adsorption colum zones. Relation to breakthrough curve.

*Mass Transfer Zone.* The mass transfer zone (*MTZ*) is the area within the adsorbate bed where adsorbate is actually being adsorbed on the adsorbent. The *MTZ* typically moves from the influent end toward the effluent end of the adsorbent bed during operation. That is, as the adsorbent near the influent becomes saturated (spent) with adsorbate, the zone of active adsorption moves toward the effluent end of the bed where the adsorbate is not yet saturated. The *MTZ* is generally a band, between the spent adsorbent and the fresh adsorbent, where adsorbate is removed and the dissolved adsorbate concentration ranges from *C°* (influent) to *Ce* (effluent). The length of the *MTZ* can be defined as *LMTZ*. When *LMTZ*=*L* (bed length), it becomes the theoretical minimum bed depth necessary to obtain the desired removal. As adsorption capacity is used up in the initial *MTZ*, the *MTZ* advances down the bed until the adsorbate begins to appear in the effluent. The concentration gradually increases until it equals the influent concentration. In cases where there are some very strongly adsorbed components, in addition to a mixture of less strongly adsorbed components, the effluent concentration rarely reaches the influent concentration because only the components with the faster rate of movement are in the breakthrough curve. Adsorption capacity is influenced by many factors, such as flow rate, temperature, and pH (liquid phase). The adsorption column can be considered exhausted when *Ce* equals 95 to 100% of *C°*.

#### **9. Model equations for flow in packed beds**

We should start by writing the general equation for flow inside a packed bed, isothermal, and with no radial gradients (Eqs. 14-17). In these equations, *u* is the interstitial velocity

Fig. 5. Adsorption colum zones. Relation to breakthrough curve.

considered exhausted when *Ce*

**9. Model equations for flow in packed beds** 

*Mass Transfer Zone.* The mass transfer zone (*MTZ*) is the area within the adsorbate bed where adsorbate is actually being adsorbed on the adsorbent. The *MTZ* typically moves from the influent end toward the effluent end of the adsorbent bed during operation. That is, as the adsorbent near the influent becomes saturated (spent) with adsorbate, the zone of active adsorption moves toward the effluent end of the bed where the adsorbate is not yet saturated. The *MTZ* is generally a band, between the spent adsorbent and the fresh adsorbent, where adsorbate is removed and the dissolved adsorbate concentration ranges from *C°* (influent) to *Ce* (effluent). The length of the *MTZ* can be defined as *LMTZ*. When *LMTZ*=*L* (bed length), it becomes the theoretical minimum bed depth necessary to obtain the desired removal. As adsorption capacity is used up in the initial *MTZ*, the *MTZ* advances down the bed until the adsorbate begins to appear in the effluent. The concentration gradually increases until it equals the influent concentration. In cases where there are some very strongly adsorbed components, in addition to a mixture of less strongly adsorbed components, the effluent concentration rarely reaches the influent concentration because only the components with the faster rate of movement are in the breakthrough curve. Adsorption capacity is influenced by many factors, such as flow rate, temperature, and pH (liquid phase). The adsorption column can be

equals 95 to 100% of *C°*.

We should start by writing the general equation for flow inside a packed bed, isothermal, and with no radial gradients (Eqs. 14-17). In these equations, *u* is the interstitial velocity (*u=U/B*), where *U* is the empty bed space velocity and *<sup>B</sup>* is the bed porosity. The last three equations are the "clean bed" initial condition and the Danckwertz boundary conditions for a closed system.

$$\frac{\partial \mathbf{C}}{\partial t} - D\_L \frac{\partial^2 \mathbf{C}}{\partial z^2} + \frac{\partial (\mu \mathbf{C})}{\partial z} + \frac{1 - \varepsilon\_B}{\varepsilon\_B} \rho\_p \frac{\partial q}{\partial t} = 0 \tag{14}$$

$$\mathbf{C}(0,t) = \mathbf{C}^0 \tag{15}$$

$$\frac{\partial \mathbf{C}}{\partial z} = \mathbf{0}, \quad z = \mathbf{L} \tag{16}$$

$$\mathbf{C}(z,0) = 0\tag{17}$$

In order to solve a specific problem of adsorption, mass transfer kinetics equations must be added, such as those of the HSDM or LDFM. The film equation is customarily replaced in the general equation of flow along the bed (Eq. 14) and thus the total system is reduced. The system still remains rather complex and in most instances can only be solved numerically. For faster convergence and accuracy special methods can be used, such as orthogonal collocation, the Galerkin method, or finite element methods. The general solution of the system is a set of points of *C* as a function of *z*, *t* and *r*. Often much of this information is not necessary and only the fluid bulk concentration at the bed outlet as a function of time, i.e. the "breakthrough" curve, is reported.

In order to obtain analytical breakthrough curves some simplifications can be made. For example the first implication of a high intrapellet diffusion resistance in liquid-solid systems (as in biodiesel refining) is that the Biot number that represents the ratio of the liquid-to-solid phase mass transfer rate, takes very high values. In Biot's equation (Eq. 18), *q0* is the equilibrium solid-phase concentration corresponding to the influent concentration *C0* and *rp* is the particle radius. The film resistance in high *Bi* systems can be disregarded; their breakthrough curves being highly symmetrical. Experimental symmetrical curves have indeed been found for the adsorption of glycerol over packed beds of silica (Fig. 6).

$$\text{Bi} = \frac{k\_f r\_p \text{C}^0}{D\_s \rho\_P q^0} \tag{18}$$

Another simplification is related to the longitudinal dispersion term in Eq. 14. *DL* is usually calculated together with the film coefficient *kf* by using the Wakao & Funazkri (1978) correlations for the mass transfer in packed beds of spherical particles (Eqs. 9 and 19). Due to the dependence of *Sc* on the molecular diffusivity, the value of *DL* is dominated by *DM*. The importance of *DL* in systems of biodiesel flowing in packed bed adsorbers could be disregarded in attention to the value of the axial Péclet number (Eq. 22), since *Pe* > 100 in these systems. For very big *Pe* numbers the regime is that of plug flow (no backmixing) and when *Pe* is very small the backmixing is maximum and the flow equations are reduced to the equation of the perfectly mixed reactor (Busto et al., 2006).

Adsorption in Biodiesel Refining - A Review 445

*system References* 

(1974)

silica

Neretnieks (1980)

. (22)

(23)

(24)

 *> 5/2 + Np/Nf*)

*<sup>q</sup> <sup>C</sup>* (25)

Weber & Chakravorti

(21)

*resistance Adsorption Biodiesel* 

Table 6. Breakthrough models for square and linear isotherms. CD: constant diffusivity.

*<sup>Q</sup> N Q <sup>Q</sup>*

<sup>1</sup> 1/3 2/3 15 2 (1 ) 15 tan 1 ln 1 (1 ) (1 ) 3 3 <sup>2</sup>

0

<sup>15</sup> ( /) *<sup>s</sup>*

*p B <sup>D</sup> <sup>z</sup> <sup>N</sup>*

*<sup>z</sup> N k*

*r u*

1 3

<sup>0</sup> *<sup>s</sup> <sup>q</sup> <sup>C</sup> <sup>Q</sup>*

 is the dimensionless time variable, *Q* is the fractional uptake, *Np* is the pore diffusion dimensionless parameter and *Nf* is the film dimensionless parameter. The constant pattern

except in the initial region when the pattern is developing. The simplified expression for

For glycerol adsorption over silica Yori et al. (2007) provided a sensitivity study based on Weber and Chakravorti's model. These results are plotted in Figures 7 and 8. The influence of the pellet diameter (*dp*) can be visualized in Figure 7 at two concentration scales. For small diameter (1 mm) the saturation and breakthrough points practically coincide and the traveling *MTZ* is almost a concentration step. For higher diameters the increase in the time of diffusion of glycerol inside the particles produces a stretching of the mass front and a more sigmoidal curve appears. The breakthrough point was defined as *C/C0*=0.01 because for common *C0* values (0.1-0.25% glycerol in the feed) lowering the glycerol content to the quality standards for biodiesel (0.002%) demands that *C/C0* at the outlet is equal or lower than 1% the value of the feed. The results indicate that for a 3 mm pellet diameter the breakthrough time is reduced from 13 h to 8 h and that for a 4 mm pellet diameter this value is further reduced to 4.5, i.e. almost one third the saturation time. It can be inferred that the

 

*p*

*u r*

*<sup>D</sup> <sup>C</sup> tzu*

Linear Yes Fick, CD Reversible FFA-silica Rasmusson &

Isotherm *Film* 

*resistance* 

*Intrapellet* 

Square Yes Fick, CD Irreversible Glycerol-

<sup>5</sup> 2.5 ln 1

*N*

*p f*

*<sup>Q</sup> <sup>N</sup>*

*p*

2 3

*p*

.

1/3

2

*f f*

condition is fulfilled in most of the span of the breakthrough experiments (

dominant pore diffusion (high *Bi*) can be obtained by setting (*Np/Nf*)=0.

*p m*

*r q*

2 15 1 *S B*

Fig. 6. Left: appearance of breakthrough curves as a function of the Biot number. Right: breakthrough curve for glycerol adsorption over silica (Yori et al., 2007).

$$\frac{D\_L}{2\,\mu r\_p} = \frac{20}{\text{Re}\,\text{Sc}} + 0.5\tag{19}$$

$$Pe = \frac{\mu L}{D\_M} \tag{20}$$

Another degree of complexity is posed by the nature of the isotherm equilibrium equation. Langmuir and Langmuir-Freundlich formulae are highly linear and propagate this nonlinearity to the whole system. However some simplifications can be done depending on the strength of the affinity of the adsorbate for the surface and the range of concentration of the adsorbate of practical interest.

Sigrist et al. (2011) have indicated that Langmuir type isotherms for systems with high adsorbate/solid affinity can be approximated by an irreversible "square" isotherm (*q=qm*), while systems in the high dilution regime can be represented by the linear Henry's adsorption isotherm. Combining the linear isotherm or the square isotherm with the equations for flow and mass transfer along the bed, inside the pellet and through the film, analytical expressions for the breakthrough curve of biodiesel impurities over silica beds can be found (Table 6) (Yori et al., 2007).

For the square isotherm, the Weber and Chakravorti (1974) model is depicted in equations 21-25. A square, flat isotherm curve yields a narrow *MTZ*, meaning that impurities are adsorbed at a constant capacity over a relatively wide range of equilibrium concentrations. Given an adequate capacity, adsorbents exhibiting this type of isotherm will be very cost effective, and the adsorber design will be simplified owing to a shorter *MTZ*. Weber and Chakravorti took a further advantage of this kind of isotherm and simplified the intrapellet mass transfer resolution by supposing that the classical "unreacted core" model applied, i.e., that the surface layers could be considered as completely saturated and that a mass front diffused towards the "unreacted core".

.

444 Biodiesel – Feedstocks and Processing Technologies

Fig. 6. Left: appearance of breakthrough curves as a function of the Biot number. Right:

2 Re *L p D* 

*r Sc*

<sup>20</sup> 0.5

*M uL Pe*

Another degree of complexity is posed by the nature of the isotherm equilibrium equation. Langmuir and Langmuir-Freundlich formulae are highly linear and propagate this nonlinearity to the whole system. However some simplifications can be done depending on the strength of the affinity of the adsorbate for the surface and the range of concentration of the

Sigrist et al. (2011) have indicated that Langmuir type isotherms for systems with high adsorbate/solid affinity can be approximated by an irreversible "square" isotherm (*q=qm*), while systems in the high dilution regime can be represented by the linear Henry's adsorption isotherm. Combining the linear isotherm or the square isotherm with the equations for flow and mass transfer along the bed, inside the pellet and through the film, analytical expressions for the breakthrough curve of biodiesel impurities over silica beds can

For the square isotherm, the Weber and Chakravorti (1974) model is depicted in equations 21-25. A square, flat isotherm curve yields a narrow *MTZ*, meaning that impurities are adsorbed at a constant capacity over a relatively wide range of equilibrium concentrations. Given an adequate capacity, adsorbents exhibiting this type of isotherm will be very cost effective, and the adsorber design will be simplified owing to a shorter *MTZ*. Weber and Chakravorti took a further advantage of this kind of isotherm and simplified the intrapellet mass transfer resolution by supposing that the classical "unreacted core" model applied, i.e., that the surface layers could be considered as completely saturated and that a mass front

(19)

*<sup>D</sup>* (20)

breakthrough curve for glycerol adsorption over silica (Yori et al., 2007).

adsorbate of practical interest.

be found (Table 6) (Yori et al., 2007).

diffused towards the "unreacted core".


Table 6. Breakthrough models for square and linear isotherms. CD: constant diffusivity.

$$\begin{split} \tau - N\_p &= \frac{15}{\sqrt{3}} \tan^{-1} \left[ \frac{2 \left( 1 - Q \right)^{1/3}}{\sqrt{3}} + 1 \right] - \frac{15}{2} \ln \left[ 1 + \left( 1 - Q \right)^{1/3} + \left( 1 - Q \right)^{2/3} \right] + \\ &+ 2.5 - \frac{5 \,\pi}{2 \sqrt{3}} + \left( \frac{N\_p}{N\_f} \right) \ln \left( Q + 1 \right) \end{split} \tag{21}$$

$$
\pi = \left[\frac{15\,\text{\AA}\,D\_s}{r\_p^2}\right] \left[\frac{C^0}{q\_m}\right] \left(t - z\,/\,u\right). \tag{22}
$$

$$N\_p = \left[\frac{15\ \varepsilon \, D\_S}{r\_p^2}\right] \left[\frac{1-\varepsilon\_B}{\varepsilon\_B}\right] \left(\frac{z}{u}\right) \tag{23}$$

$$N\_f = k\_f \left[ \frac{1 - \varepsilon}{\varepsilon} \right] \left( \frac{3 \, z}{\mu \, r\_p} \right) \tag{24}$$

$$Q = \frac{q}{q\_s} = \frac{\text{C}}{\text{C}^0} \tag{25}$$

 is the dimensionless time variable, *Q* is the fractional uptake, *Np* is the pore diffusion dimensionless parameter and *Nf* is the film dimensionless parameter. The constant pattern condition is fulfilled in most of the span of the breakthrough experiments ( *> 5/2 + Np/Nf*) except in the initial region when the pattern is developing. The simplified expression for dominant pore diffusion (high *Bi*) can be obtained by setting (*Np/Nf*)=0.

For glycerol adsorption over silica Yori et al. (2007) provided a sensitivity study based on Weber and Chakravorti's model. These results are plotted in Figures 7 and 8. The influence of the pellet diameter (*dp*) can be visualized in Figure 7 at two concentration scales. For small diameter (1 mm) the saturation and breakthrough points practically coincide and the traveling *MTZ* is almost a concentration step. For higher diameters the increase in the time of diffusion of glycerol inside the particles produces a stretching of the mass front and a more sigmoidal curve appears. The breakthrough point was defined as *C/C0*=0.01 because for common *C0* values (0.1-0.25% glycerol in the feed) lowering the glycerol content to the quality standards for biodiesel (0.002%) demands that *C/C0* at the outlet is equal or lower than 1% the value of the feed. The results indicate that for a 3 mm pellet diameter the breakthrough time is reduced from 13 h to 8 h and that for a 4 mm pellet diameter this value is further reduced to 4.5, i.e. almost one third the saturation time. It can be inferred that the

Adsorption in Biodiesel Refining - A Review 447

\* *f p*

The breakthrough curve for the linear isotherm model is depicted in equations (26-28). This is the Q-LND (quasi log normal distribution) approximation of Xiu et al. (1997) and Li et al. (2004), of the general solution of Rasmusson and Neretnieks (1980). This approximation is known to be valid in systems of high Bi. *y* is the adimensional adsorbate concentration in the

The Rapid Small Scale Column Test (RSSCT) was developed to predict the adsorption of organic compounds in activated carbon adsorbers (Crittenden et al., 1991). The test is based upon dimensionless scaling of hydraulic conditions and mass transport processes. In the RSSCT, a small column (SC) loaded with an adsorbent ground to small particle sizes is used to simulate the performance of a large column (LC) in a pilot or full scale system. Because of the similarity of mass transfer processes and hydrodynamic characteristics between the two columns, the breakthrough curves are expected to be the same. Due to its small size, the RSSCT requires a fraction of the time and liquid volume compared to pilot columns and can thus be advantageously used to simulate the performance of the large column at a fraction of the cost (Cummings & Summers, 1994; Knappe et al., 1997). As such, RSSCTs have emerged as a common tool in the selection of adsorbent type and process parameters. Parameters of the large column are selected in the range recommended by the adsorbent vendor. The RSSCT is then scaled down from the large column. Based on the results of the RSSCT, the designer develops detailed design and operational parameters. The selection

 Mean particle size: the designer must find an adequate mesh size, 100-140, 140-170, 170- 200, etc., that can be used to successfully simulate the large column. Too small particles

 Internal diameter (ID) of column: 10-50 mm ID columns are preferred to keep all other column dimensions small and more important, to reduce the amount of time and eluate

RSSCT scaling equations have been developed with both constant (CD) and proportional (PD) diffusivity assumptions. The two approaches differ if *Ds* values are independent (for CD) or a linear function (for PD) of the particle diameter, *dp*. Equations 29-30 can be used to select the small column (SC) RSSCT parameters based upon a larger column (LC) that is being simulated. *t* is the time span of the experiment for a common outlet concentration. For CD and PD scenarios the values for *X* are zero and one, respectively. Additional *X* values

2

*x*

, ,

*EBCT d t EBCT d t*

*SC p SC SC LC p LC LC*

 

used. The *dSC/dp,SC* should be higher than 50 to keep wall effects negligible.

 and 

number (*Pe*), the modified Biot number (*Bi\**) and the time parameter ().

*HD* 

*Bi*

fluid phase,

is the adimensional time,

**10. Experimental scale-up of adsorption columns** 

and determination of the following parameters is required:

can however lead to high pressure losses and pumping problems.

have been suggested based upon non-linear relationships between *dp* and *Ds*.

*k r*

*s s*

2 *B s p LD u r* 

(27)

(28)

parameters are functions of the Péclet

(29)

pellet diameter has a strong influence on the processing capacity of the silica bed. Small diameters though convenient from this point of view are not practical. *dp* is usually 3-6 mm in industrial adsorbers in order to reduce the pressure drop and the attrition in the bed.

Fig. 7. Adsorption of glycerol from biodiesel. Breakthrough curves as a function of pellet diameter (*dp*). Breakthrough condition *C/C0*=0.01, L=2 m, *U*=14.4 cm min-1.

Fig. 8. Adsorption of glycerol from biodiesel. Left: breakthrough time as a function of *U* and *dp* (*L*=2 m, *U*=14.4 cm min-1). Right: influence of *U* and *C0* on the processing capacity (*dp*=3 mm, *L*=2 m).

The combined influence of pellet diameter and inlet velocity on the breakthrough time is depicted in Figure 8 (left). The breakthrough time seems to depend on *dp -n* (*n*>0) and also on *U-n* (*n*>0). This means that longer breakthrough times are got at smaller pellet diameters and smaller feed velocities. The processing capacity per unit kg of silica is displayed in Figure 8 (right) as a function of *dp* and the inlet velocity, *U0*. When *U0* goes to zero the bed capacity equals *qm*, and decreases almost linearly when increasing *U0*. For a typical solid-liquid velocity of 5 cm min-1 the capacity decreases at higher glycerol concentration, but the silica bed is used more efficiently because the relative *MTZ* size is reduced.

$$y(\tau) = \frac{1}{2} \mu^o \left( 1 + \text{erf} \left\{ \frac{(\ln(\tau) - \mu)}{(\sigma \sqrt{2})} \right\} \right) \tag{26}$$

pellet diameter has a strong influence on the processing capacity of the silica bed. Small diameters though convenient from this point of view are not practical. *dp* is usually 3-6 mm in industrial adsorbers in order to reduce the pressure drop and the attrition in the bed.

Fig. 7. Adsorption of glycerol from biodiesel. Breakthrough curves as a function of pellet

Fig. 8. Adsorption of glycerol from biodiesel. Left: breakthrough time as a function of *U* and

The combined influence of pellet diameter and inlet velocity on the breakthrough time is depicted in Figure 8 (left). The breakthrough time seems to depend on *dp-n* (*n*>0) and also on *U-n* (*n*>0). This means that longer breakthrough times are got at smaller pellet diameters and smaller feed velocities. The processing capacity per unit kg of silica is displayed in Figure 8 (right) as a function of *dp* and the inlet velocity, *U0*. When *U0* goes to zero the bed capacity equals *qm*, and decreases almost linearly when increasing *U0*. For a typical solid-liquid velocity of 5 cm min-1 the capacity decreases at higher glycerol concentration, but the silica

<sup>1</sup> (ln( ) ) () 1 <sup>2</sup> ( 2)

 

(26)

*dp* (*L*=2 m, *U*=14.4 cm min-1). Right: influence of *U* and *C0* on the processing capacity

bed is used more efficiently because the relative *MTZ* size is reduced.

*<sup>o</sup> y erf*

 

(*dp*=3 mm, *L*=2 m).

diameter (*dp*). Breakthrough condition *C/C0*=0.01, L=2 m, *U*=14.4 cm min-1.

$$\text{Bi}^\* = \frac{k\_f r\_p}{\text{HD}\_s \rho\_s} \tag{27}$$

$$
\Theta = \frac{\varepsilon\_B L D\_s}{\mu \left( r\_p^{-2} \right)} \tag{28}
$$

The breakthrough curve for the linear isotherm model is depicted in equations (26-28). This is the Q-LND (quasi log normal distribution) approximation of Xiu et al. (1997) and Li et al. (2004), of the general solution of Rasmusson and Neretnieks (1980). This approximation is known to be valid in systems of high Bi. *y* is the adimensional adsorbate concentration in the fluid phase, is the adimensional time, and parameters are functions of the Péclet number (*Pe*), the modified Biot number (*Bi\**) and the time parameter ().

#### **10. Experimental scale-up of adsorption columns**

The Rapid Small Scale Column Test (RSSCT) was developed to predict the adsorption of organic compounds in activated carbon adsorbers (Crittenden et al., 1991). The test is based upon dimensionless scaling of hydraulic conditions and mass transport processes. In the RSSCT, a small column (SC) loaded with an adsorbent ground to small particle sizes is used to simulate the performance of a large column (LC) in a pilot or full scale system. Because of the similarity of mass transfer processes and hydrodynamic characteristics between the two columns, the breakthrough curves are expected to be the same. Due to its small size, the RSSCT requires a fraction of the time and liquid volume compared to pilot columns and can thus be advantageously used to simulate the performance of the large column at a fraction of the cost (Cummings & Summers, 1994; Knappe et al., 1997). As such, RSSCTs have emerged as a common tool in the selection of adsorbent type and process parameters.

Parameters of the large column are selected in the range recommended by the adsorbent vendor. The RSSCT is then scaled down from the large column. Based on the results of the RSSCT, the designer develops detailed design and operational parameters. The selection and determination of the following parameters is required:


RSSCT scaling equations have been developed with both constant (CD) and proportional (PD) diffusivity assumptions. The two approaches differ if *Ds* values are independent (for CD) or a linear function (for PD) of the particle diameter, *dp*. Equations 29-30 can be used to select the small column (SC) RSSCT parameters based upon a larger column (LC) that is being simulated. *t* is the time span of the experiment for a common outlet concentration. For CD and PD scenarios the values for *X* are zero and one, respectively. Additional *X* values have been suggested based upon non-linear relationships between *dp* and *Ds*.

$$\frac{EBCT\_{SC}}{EBCT\_{LC}} = \left(\frac{d\_{p,SC}}{d\_{p,LC}}\right)^{2-\chi} = \frac{t\_{SC}}{t\_{LC}}\tag{29}$$

Adsorption in Biodiesel Refining - A Review 449

separation of the aqueous phase from the emulsion becomes difficult. In order to prevent the formation of such an emulsion in the conventional water-washing practice a large amount of water must be used. Karaosmanoglu et al. (1996) concluded that a minimum of 3- 5 grams of water per gram of biodiesel at 50 °C were needed to efficiently remove the impurities of the fuel (3000-5000 litres of water per Ton of biodiesel). These numbers should be considered typical of once-through water-washing operations but are not representative

It has been suggested that the methanol removal step needed for succesful adsorption be performed before glycerol separation and under vacuum conditions (D'Ippolito et al., 2007; Bournay et al., 2005). The data in Table 8 suggests that the best operation of dry refining is that with cyclic reversible adsorption of glycerol/glycerides in twin packed beds, as early

Water

column Steam Stripper Vacuum flash drum

mixer/settler Packed bed, bleacher

< 1 kg Tonbio-1 (cyclic bed)

of closed-loop water washing schemes. Accurate numbers are included in Table 8.

 *Lurgi Crown Iron Dry* 

from wash water Rectifier column Rectifier column Not needed

bleaching n.a. Yes Not needed

consumption n.a. n.a. 11 kg Tonbio-1 (bleacher)

Table 8. Comparison of unit operations for two alkali-catalyzed processes (Lurgi, 2011; Crown Iron Works, 2011; Anderson et al., 2003) and a process with a "dry" step of adsorption of glycerol and glycerides (Manuale et al., 2011). Adsorbent comsumption calculated for glycerol removal only (0.15% in raw biodiesel) (Yori et al., 2007).

Other advantages of adsorption are the low capital investment (provided common adsorbents are used), the absence of moving parts, the simplicity and robustness of operation. Possible drawbacks are the need for disposal and replacement of the spent

Manuale et al. (2011) used bleaching silicas for the removal of FFA in biodiesel in a series of tests in a stirred tank reactor under varying temperature and pressure conditions (70 and 110 °C, 760 and 160 mmHg). Their results confirm the pattern already seen in the case of the silica refining of edible oils. For the same adsorbent and in the presence of vacuum the influence of temperature is low. For example for TriSyl 3000 in vacuo, after 90 min, and from a similar initial acidity level (1.5%), the adsorbate load at two different temperatures is: *q70 °C*=99.3%, *q110 °C*=75.0%. Similarly, for TriSyl 300B, 90 min bleaching time, 1.7-1.9% initial acidity: *q70 °C*=82.0, *q110 °C*= 69.0%. The trend is clear. Higher temperatures lead to lower

consumption 200 kg Tonbio-1 200 kg Tonbio-1 None

Water wash column

Water wash

adsorbent in the case of the use of bleaching tanks.

**12. Adsorbers operation** 

**12.1 Bleaching tanks** 

suggested (D'Ippolito et al., 2007).

Glycerol removal from biodiesel

Methanol removal from biodiesel

Methanol removal

Final polishing by

Wash water

Adsorbent

$$X = \log\left(\frac{d\_{p, \text{SC}}}{d\_{p, \text{LC}}}\right) / \log\left(\frac{D\_{s, \text{SC}}}{D\_{s, \text{LC}}}\right) \tag{30}$$

 The spatial or interstitial velocities (*U, u*) are scaled based on the relation written in Eq. 31. However, this equation will result in a high interstitial velocity of water in the small column, and hence, high head loss. Crittenden (1991) recommended that a lower velocity in the small column be chosen, as long as the effect of dispersion in the small column does not become dominant over other mass transport processes. This limitation requires the *ReSCS*c value remain in the range of 200-200,000, which is the mechanical dispersion range.

$$\frac{\mu\_{\rm SC}}{\mu\_{\rm LC}} = \left(\frac{d\_{p\_{\rm \gamma}, \rm LC}}{d\_{p, \rm SC}}\right) \tag{31}$$


Table 7. Variables for a scaled-down constant diffusivity RSSCT packed with silica gel for adsorption of glycerol. Values for the small column taken from Yori et al. (2007).

In the case of biodiesel, no results of RSSCTs designed for scale-up purposes have been published so far, though some tests in small columns have been published (Yori et al., 2007). The validity of RSSCTs holds anyway. In this sense one first step for their use for scale-up purposes would be to determine the kind of *DS-dp* relation that holds, since it is unknown whether CD or PD approaches must be used. In order to show the usefulness of the technique, a procedure of comparison between a biodiesel large column adsorber and a scaled down laboratory column is made in Table 7.

#### **11. Advantages of adsorption in biodiesel refining**

As pointed out by McDonald (2001), Nakayama & Tsuto (2004), D'Ippolito et al. (2007), Özgül-Yücel & Turkay (2001) and others, the principal advantage of the use of adsorbers in biodiesel refining is that of reducing the amount of wastewater and sparing the cost of other more expensive operations such as water washing and centrifugation. For big refiners that can afford the cost of setting up a water treatment plant the problem of the amount of wastewater might not be an issue but this can be extremely important for small refiners.

In the common industrial practice water-washing is used to remove the remaining amounts of glycerol and dissolved catalyst, and also the amphiphilic soaps, MGs and DGs. Theoretically speaking if water-washing is used to remove glycerol and dissolved catalyst only, large amounts of water should not be required. However in the presence of MGs and DGs the addition of a small amount of water to the oil phase results in the formation of an emulsion upon stirring. Particularly when this operation is performed at a low temperature

*X*

dispersion range.

, , , , log / log *p SC s SC p LC s LC*

(30)

(31)

*d D*

*d D* 

> , , *SC p LC LC p SC*

 

*u d u d*

Table 7. Variables for a scaled-down constant diffusivity RSSCT packed with silica gel for

In the case of biodiesel, no results of RSSCTs designed for scale-up purposes have been published so far, though some tests in small columns have been published (Yori et al., 2007). The validity of RSSCTs holds anyway. In this sense one first step for their use for scale-up purposes would be to determine the kind of *DS-dp* relation that holds, since it is unknown whether CD or PD approaches must be used. In order to show the usefulness of the technique, a procedure of comparison between a biodiesel large column adsorber and a

As pointed out by McDonald (2001), Nakayama & Tsuto (2004), D'Ippolito et al. (2007), Özgül-Yücel & Turkay (2001) and others, the principal advantage of the use of adsorbers in biodiesel refining is that of reducing the amount of wastewater and sparing the cost of other more expensive operations such as water washing and centrifugation. For big refiners that can afford the cost of setting up a water treatment plant the problem of the amount of wastewater might not be an issue but this can be extremely important for small refiners. In the common industrial practice water-washing is used to remove the remaining amounts of glycerol and dissolved catalyst, and also the amphiphilic soaps, MGs and DGs. Theoretically speaking if water-washing is used to remove glycerol and dissolved catalyst only, large amounts of water should not be required. However in the presence of MGs and DGs the addition of a small amount of water to the oil phase results in the formation of an emulsion upon stirring. Particularly when this operation is performed at a low temperature

*Variable Small column Large column dp* 0.3 mm 3 mm *EBCT* 105 s 2.9 h *U* 2.4 mm s-1 0.24 mm s-1 *L* 25 cm 2.5 m *trun* 3 days 300 days

adsorption of glycerol. Values for the small column taken from Yori et al. (2007).

scaled down laboratory column is made in Table 7.

**11. Advantages of adsorption in biodiesel refining** 

 The spatial or interstitial velocities (*U, u*) are scaled based on the relation written in Eq. 31. However, this equation will result in a high interstitial velocity of water in the small column, and hence, high head loss. Crittenden (1991) recommended that a lower velocity in the small column be chosen, as long as the effect of dispersion in the small column does not become dominant over other mass transport processes. This limitation requires the *ReSCS*c value remain in the range of 200-200,000, which is the mechanical separation of the aqueous phase from the emulsion becomes difficult. In order to prevent the formation of such an emulsion in the conventional water-washing practice a large amount of water must be used. Karaosmanoglu et al. (1996) concluded that a minimum of 3- 5 grams of water per gram of biodiesel at 50 °C were needed to efficiently remove the impurities of the fuel (3000-5000 litres of water per Ton of biodiesel). These numbers should be considered typical of once-through water-washing operations but are not representative of closed-loop water washing schemes. Accurate numbers are included in Table 8.

It has been suggested that the methanol removal step needed for succesful adsorption be performed before glycerol separation and under vacuum conditions (D'Ippolito et al., 2007; Bournay et al., 2005). The data in Table 8 suggests that the best operation of dry refining is that with cyclic reversible adsorption of glycerol/glycerides in twin packed beds, as early suggested (D'Ippolito et al., 2007).


Table 8. Comparison of unit operations for two alkali-catalyzed processes (Lurgi, 2011; Crown Iron Works, 2011; Anderson et al., 2003) and a process with a "dry" step of adsorption of glycerol and glycerides (Manuale et al., 2011). Adsorbent comsumption calculated for glycerol removal only (0.15% in raw biodiesel) (Yori et al., 2007).

Other advantages of adsorption are the low capital investment (provided common adsorbents are used), the absence of moving parts, the simplicity and robustness of operation. Possible drawbacks are the need for disposal and replacement of the spent adsorbent in the case of the use of bleaching tanks.
