Investigation of Breakthrough Curves of Citric Acid Adsorption

Citric acid is the most widely used organic acid in the field of foods and beverages as an acidulant as well as in pharmaceutical and chemical products. Generally, surface or submerged fungal fermentation mainly with aspergillus niger is utilized for citric acid production. However, the submerged fermentation method is the most used method for citric acid production.1,2 The method of calcium salt precipitation is an established process for citric acid purification. a series of precipitation and isolation reactions using Ca(OH)2 and H2SO4 can be exploited for citric acid separation from fermentation broths.3,4 However, this process includes several batch treatments in which huge amounts of chemical reagents and a large amount of heat are required. These negative factors have directed many investigators to find new techniques to separate or purify citric acid from fermentation broths, such as adsorption and electro-dialysis.5,6 Electro-dialysis as an electrochemical separation process charged the membranes electrically. For separation of ionic species from aqueous solutions, electrical potential difference is used. The electro-dialysis was used in citric acid recovery. However, the main problem is that the costs of this technique were determined to be approximately 50 % higher compared to the current industrial citric acid recovery process. The use of electro-dialysis requires the development of new processes to decrease waste formation and enhance productivity.7 Purification of organic acids, particularly citric acid, by adsorption process has lower production costs compared to other methods. Attention has been drawn to the novel use of synthetic ion-exchange resins in separation and purification of organic acids.8,9 This set of adsorbents acts selectively and other components of solution remain intact. After saturation of solid adsorbent at the end of a separation operation period, it is recovered by elution with water, acid or base. Although the principle of organic acids separation by ion-exchange method is known, there are many details that require development and increment. Thus, it seems that Simulated Moving Bed (SMB) by using chromatography method on the base of countercurrent continuous contact between feed and adsorbent is appropriate and effective.10,11 SMB is a continuous chromatographic method which requires determined parameters like ion-exchange resins properties, adsorption equilibrium data, and operating characteristics of bed. One of the best methods to specify and optimize operating parameter is to prepare a fitting mathematical model from actual processes. Generally in such models, mass transfer in liquid layer outside the resin particles is negligible. The general ion-exchange reaction of resin is presented in eq. 1.12–14


INTRODUCTION
Citric acid is the most widely used organic acid in the field of foods and beverages as an acidulant as well as in pharmaceutical and chemical products. It is generally produced by surface or submerged fungal fermentation mainly with aspergillus niger. However, the highest citric acid production has been obtained with the submerged fermentation method 1-2 . Citric acid is typically purified by a firmly established process known as the method of calcium salt precipitation. Citric acid can be separated from fermentation broths by a series of precipitation and isolation reactions using Ca(OH)2 and H2SO4 [3][4] . However, this process contains several batch treatments, which require large amounts of chemical reagents and a considerable amount of heat. These negative factors have directed many investigators to find new techniques to separate or purify citric acid from fermentation broths such as adsorption and electro-dialysis [5][6] .
Electro-dialysis as an electrochemical separation process charged membranes electrically. For separation of ionic species from aqueous solutions, electrical potential difference is used. The electro-dialysis was used in citric acid recovery. However, the main problem is costs of this technique were determined to be approximately 50% more in comparison with that of current industrial citric acid recovery process. The use of electrodialysis requires the development of new processes to decrease waste formation and enhance productivity 7 .
Purification of organic acids particularly citric acid by adsorption process has lower production costs in comparison with that of other methods. Newly using synthetic ionexchange resins in separation and purification of organic acids has paid attention [8][9] . This set of adsorbent act selectively and other component of solution remain intact. After saturation of solid adsorbent at the end of a separation operation period, its recovery is done by elution with water, acid or base. Although the principle of organic acids separation by ion-exchange method has known, but there are many details that requires development and increment.
Thus, it seems that Simulated Moving Bed (SMB) by using chromatography method on the base of countercurrent continuous contact between feed and adsorbent is appropriate and effective [10][11] . SMB is a continuous chromatographic method which requires determined parameters like ion-exchange resins properties, adsorption equilibrium data and operation characteristics of bed. One of the best methods to specify and optimize operating parameter is preparing fitting mathematical model from actual processes. Generally in such models, mass transfer in liquid layer outside the resin particles is negligible. The general ion-exchange reaction of resin is presented in equation 1 [12][13][14] . (1) For acids with more than one carboxyl group and also for R-N in the equation 1 base resins are appropriate 15 .
Estimation of breakthrough curves is required for successful design of an adsorption column. For a fixed-bed randomly packed adsorption column in which is fed from the top of the bed at a constant flow rate by an aqueous solution containing an organic pollutant, the mass transfer balance equation for predicting fixed-bed dynamics is [16][17][18][19] : where ε is the void fraction in the column, C is the concentration, t is the time, U0 is the superficial velocity, Z is the column depth, q is the concentration in the stationary phase, Dp is the diffusivity.
The overall mass balance on the adsorbed solute is: where p is the adsorption rate.
The initial and boundary conditions for the equation 2 are: where C0 is the initial concentration and DL is the axial dispersion coefficient.

4
The following assumptions associated with the equation 2:  No chemical reactions take place in the column.
 Radial and axial dispersions are negligible.
 The flow pattern is the ideal plug flow.
 The temperature in the column is constant with time.
In present study, experimental breakthrough curves for citric acid adsorption from aqueous solution onto ion-exchange resin at different temperatures have been obtained. Then, several mathematical models have been developed and analyzed to predict system properties based on experimental data.

BREAKTHROUGH CURVES
Equations that heretofore offered for describing breakthrough curves are kind of complicated expressions that just can describe ideal, symmetrical breakthrough curves and for other possible shapes of these curves are unable to generate acceptable results. These equations in some cases were obtained from mass balances along with simplification assumptions 20-21 that often were offered for gas breakthrough curves, or are including additional fitting parameters to better describe asymmetric (skewed) breakthrough curves like Wood equation and other are only mathematical equations that generate "S" shape curves [22][23] .
In this research work, it was tried to derive mathematical equations that not only can predict symmetrical "S" shape breakthrough curves but also can describe other curves that deviate from. Furthermore, several models in different forms such as fractional, polynomial and exponential are developed and statistically analyzed. Finally, three new mathematical fitting models, two implicit and one explicit, in following forms are developed for prediction breakthrough curves.

Implicit models
Developed implicit models are shown in equations 7 and 8. These equations can be divided to two categories including two and three parameter models. Parameters A, B, J, n, and r are fitting constant parameters that must be determined by regression of the experimental data.
where A, B, J, n and r are constants.

Explicit model
Using explicit equations because of their simple usage has preference, but often it seems difficult to develop explicit equations with a suitable simplicity that possesses enough generality. Implicit models usually have better performance for describing different experimental data curves in comparison with that of explicit models. But, implicit models require trial and error calculations in order to solve them. In this section, implicit equations were transformed to their analog explicit equations. Afterwards, an explicit equation was determined by replacing C/C0 with t/tF in equation 8.
where tF is the time that C/C0 reaches to 0.999 and D', E' and m' are constants.

EXPERIMENTAL
In preliminary experiments, several types of weak and strong basic anionic resins such as, IRA-92, IRA-93, IRA-420 and IRA-458 were examined and finally amberlite IRA-93 was selected because of its high performance and compatibility in acid adsorption. Then, experiments were planned to investigate temperature effect on IRA-93 adsorption capacity.
The experimental apparatus consists of a glass column (ID=1 cm, height=20 cm) and a bed (volume=15 cm 3 ). A schematic diagram of used apparatus is depicted in figure 1. The volumetric flow rate of acid in adsorption and desorption is constant and is equal to 1.5 ml/min. Moreover, the experiments were carried out at three temperatures (20, 35, and 55ºC) in which about 25 samples were analyzed for each temperature. The influent solution contains %20wt of citric acid and elution process is performed by 0.   In this way, number 1 is added to logarithmic term which makes that available at evident point (0 , 0). The constants of all models were obtained by ordinary least square method using the "Eviews software" version 3.1 25 . In Eviews software, several examinations are performed for analyzing and fitting of data that are described as follows: 1. R-squared: The R-squared (R 2 ) statistic measures the success of the regression in predicting the values of the dependent variable within the sample. The statistic will equal one if the regression fits perfectly.
where MRPE is the mean absolute percent error, N is the number of data points, (C/C0)Exp is the experimentally measured relative concentration, and (C/C0)Equ is the relative concentration determined using equations. use. On the first look, it seems that implicit equations are very difficult to use but, this kind of models are simple to determine the unknown value of the equation. Also, they are more precise than other models for breakthrough curves. Moreover, Table 3  In aqueous solution, weak dispersion forces dominate interactions between organic compounds and hydrophobic surfaces. Therefore, the adsorption can be considered reversible. It is proposed citric acid adsorption on IRA-93 contains four steps: diffusion through the bulk liquid, film diffusion, intra-particle diffusion, and adsorption on the solid surface. Generally, the bulk liquid diffusion and adsorption steps happen quickly and therefore, they are not rate-limiting. Intra-particle diffusion is in the pore space (i.e., pore diffusion) or along the adsorbent surface in the pores (i.e., surface diffusion). Intra-particle diffusion studies investigating the adsorption of organic compounds showed that surface diffusion typically dominates over pore diffusion. Therefore, the citric acid adsorption by IRA-93 is also controlled by surface diffusion [26][27] .     In addition, sensitivity analysis has been done for equation 9 and results have been presented on figure 9. According to Figure, Equation 9 has a good performance to a change of 20 percent of time (see slopes of the curves).

Figure 9.
Furthermore, our data has been evaluated using other researcher's models. Three different models derived by Adams-Bohart, Yoon-Nelson, and Chern have been chosen in order to assess our model [18][19] . The results were shown on table 6. According to table 6, we improved the MRPE around 12.12% using equation 9. Moreover, equation 9 is easy to use.   0 ln 1

CONCLUSION
An experimental investigation was performed to obtain the adsorption breakthrough curves for citric acid at 20, 35, and 55 0 C. amberlite IRA-93 resin was used as adsorbent.
Furthermore, implicit and explicit models were utilized in order to correlate breakthrough curves. The results were then analyzed and summarized as follows.
Weak basic resins are more appropriate to adsorb citric acid onto adsorbent than strong basic resins because of their higher mechanical strength and low cost. In addition, adsorbate diffusivity in resin increases as a result of temperature increase. Then, it could be recommended that low and high temperatures are not appropriate conditions for adsorption process and middle temperature could be recommended as process design based on low diffusivity at low temperatures and resin degradation at high temperature.
Because of their structure, implicit mathematical models have good flexibility to describe various breakthrough curves with different steepness and shapes even for unusual "S" shape type and also can predict alteration of various adsorption breakthrough curves, but explicit model generates smooth "S" shape curves. As a result, logarithmic models show better conformity with experimental data in comparison with that of non-logarithmic corresponding models. Since the numerical values of time are much greater than concentration ratio, taking logarithm of time reduces its amount and arise propriety in equation and consequently logarithmic models give better results which this is very obvious.
To probe the accuracy of the models, our models were compared with other researchers' experimental data. Totally, 18 breakthrough curves have been investigated. The results show that our models can describe breakthrough curves with a wide range of data. Furthermore, we compared our model with Adams-Borhat, Yoon-Nelson, and Chern's models and the results were in satisfactory agreement.