M ODELING A R EACTIVE B ATCH D EODORIZER

2.2.1.1 Mathematical Equations

Previously in this chapter, the basic equations that describe conventional steam distillation were presented. Here, an extension of this standard model including chemical reactions is given. A scheme of a lab-scale batch deodorizer is shown in Figure 2.2.1

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In this process, a still (batch deodorizer) is fed and then heated until the deodor- ization temperature is reached. Then, the injection of sparge steam begins promoting the volatilization of the undesirable substances, which are condensed and collected in a receiver. In this way, the whole deodorization time can be divided in two parts: heating (in absence of water) and stripping with sparge steam at constant tempera- ture, which is allowed by the presence of small amounts of condensed steam that are dissolved into the oil. Despite this low level, water has a strong infl uence in the vapor–liquid equilibria of the whole multicomponent mixture.

The total and component molar balances for the reactive batch deodorizer are given by dL dt = − +V ∆ , (2.2.1)Rt and d d t L x t V y R i i i · ·

(

)

_{= − +}

₍

₎

_{, (2.2.2)}

where L is the total moles of liquid in the still, V is the molar vaporization rate in moles/time, x_i and yi are the liquid and vapor molar fractions of component i in the

liquid and vapor phases, respectively, ∆R_t is the total change of number of moles caused by reaction course (moles) at a given time, and (R_i )_t is the number of moles of component i produced (or consumed) by the reaction (moles) at time t.

∆R and (Ri )t can be calculated using the relations below:

∆R _t Ri i t

( )

= ⎛ ⎝⎜ ⎞ ⎠⎟

∑

(2.2.3) (R_i)_t= (k_i)_{t ·} (x_i · L)t, (2.2.4) Heat Steam Distillate To the vacuum Condenser

FIGURE 2.2.1 Scheme of a lab-scale batch deodorizer.

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where (ki)t is the constant of reaction of component i at time t.

For the distillate, the total and component molar balances are as follows: d d D t = , (2.2.5)V and d d D t V y i i = · , (2.2.6) where D is the total moles of distillate and D_i represents the moles of component i in the distillate.

The molar vaporization rate, V, is a function of the heat supplied by the heating source to vaporize the volatiles and the vaporization enthalpy of the mixture. Ceriani and Meirelles [9] estimated an average molar vaporization value to be an input in the simulation program, based on the total amount of distillate formed during the experimental trials of Petrauskaitè et al. [1]. In this way, it was not necessary to do energy balances in their simulations.

2.2.1.2 Vapor–Liquid Equilibria and Vaporization Effi ciency

The variables xi and yi that appear in Equation 2.2.2 are related to each other by the

vapor–liquid equilibria at each instant:

y x f P i i i i o i = · · · γ φˆ . (2.2.7)

For the system in discussion the total pressure is low; thus, assuming non-ideal gas behavior, the reference or standard-state fugacity fi

o_{of Equation 2.2.7 is given by} f P exp V P – P RT i o i vap i sat i L i vap = ⋅ ⎛

(

)

⎝ ⎜ ⎞_⎠⎟ ·φ · _{, (2.2.8)}

where R is the ideal gas constant, T is the absolute temperature of the system, Pi vap and φ_isat _{are, respectively, the vapor pressure and the fugacity coeffi cient of the pure} component i, and Vi

L

is the liquid molar volume of component i. The exponential term corresponds to the Poynting factor.

At each time, Equation 2.2.9 is solved to determine the conditions in which the sum of the partial pressure of n compounds is equal to the system total pressure. During the heating period, the boiling point temperature of the fatty mixture should be determined by solving Equation 2.2.9. During the stripping period, the boiling temperature of the mixture is already set, and Equation 2.2.9 is solved to calculate

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the water concentration in the liquid phase at the chosen temperature and pressure conditions: f P xi f i i o i = –

∑

ˆ , i= n 1 · γ · φ (2.2.9)

Ceriani and Meirelles [11] studied the vapor–liquid equilibria of fatty systems in detail. In their work, the fugacity coeffi cients were calculated using the virial equation trun- cated at the second term in combination with the appropriate mixing rules. Critical properties and acentric factors of the pure components, needed to calculate second virial coeffi cients, were estimated using Joback’s technique for critical volumes and pressures and Fedor’s group contributions for critical temperatures [12]. The V_iL values for fatty compounds were obtained using the model developed by Halvorsen et al. [13]. The activity coeffi cients were determined using UNIFAC, and the vapor pressures were estimated by the group contribution equation suggested by Ceriani and Meirelles [11].

According to Ceriani and Meirelles [11], even at the low pressures that prevail in stripping units of the vegetable oil industry, it is necessary to include in the vapor–liquid calculations the fugacity coeffi cient φ_isat _{for water and fatty acids, because of the high} values of P_ivap _{at equilibrium temperatures in these cases. Ceriani and Meirelles [11]} also found that UNIFAC r3/4 _{[14] gave better predictions of vapor–liquid equilibrium} data than original UNIFAC [15] and UNIFAC r2/3 _{[16]. An earlier work of Fornari et al.} [14] had similar conclusions for systems composed of vegetable oils and hexane.

One should note that Equation 2.2.7 assumes that the liquid and vapor phases are in equilibrium at each instant, which means that the steam becomes totally saturated with the volatiles as it passes through the oil in the still. The concept of vaporization effi ciency is a measure of completeness with which the steam bubble becomes satu- rated with volatile substances during its passage through the oil layer. In 1941 Bailey [17] proposed a mathematical model for vaporization effi ciency applied to steam (batch) deodorization that is still used today. At that time, the author discussed that a complete mathematical treatment of the phenomenon should consider two effects of the hydraulic pressure on the rising bubble: continuous variation on its surface area (the bubble expands signifi cantly) and its internal pressure. In fact, because the pressure above the free surface of the liquid (Po_{) is suffi ciently low, 133 to 800}

Pa for steam deodorization, the bubble formed at the orifi ce grows signifi cantly as it ascends in a varying pressure fi eld. As a consequence, the rising bubble expands with the decreasing external pressure, and the partial pressure of the solute, which is zero at the bottom, increases as the bubble moves toward the free surface. In an earlier work, Coelho Pinheiro and Guedes de Carvalho [18] modeled the stripping of pentane from sunfl ower seed oil using experimental results from the system at 298 K and pressures of 0.3 to 100 kPa. A detailed review about vaporization effi - ciency during steam distillation and deodorization can be found by referring to Ceri- ani and Meirelles [19].

2.2.1.3 Estimation of the Oil Composition

From computational simulation studies of steam deodorization and steam deacidi- fi cation, it is possible to extract important information about the composition of the

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products (refi ned oil and distillate) throughout the stripping process, understanding the effects of the processing variables on the distribution of each compound or class of compounds. However, in order to achieve results with good quality, it is necessary to do an accurate estimation of the oil composition, in terms of its major compounds, such as TAG, and minor compounds, such as DAG, MAG, FFA, and nutraceuticals.

Oil composition is usually given in terms of fatty acids, as a result of the analysis by gas–liquid chromatography of the prepared methyl esters from the fatty acids attached to the glycerol part of TAG [20]. Statistical procedures, such as the one developed by Antoniosi Filho et al. [21], are capable of converting the fatty acid composition of the oil in its probable TAG composition with satisfactory accuracy, considering the distribution of the fatty acids in the three positions of the glycerol molecule. As inputs of this method, it is necessary to inform the percentage of tri- saturated TAG that usually appear in the oil, the mass concentration of fatty acids, and their molecular weights. The compositions in DAG and MAG can be estimated from the probable TAG composition, following the stoichiometric relations of the hydrolysis reactions in the following way: each TAG is split into 1,2- and 1,3-DAG; each DAG is then split into MAG.

Concentrations of minor compounds can be easily found in the literature [22] for a variety of oils.

In document Extracting Bioactive Compounds for Food Products Theory and Applications (Page 40-44)