Adsorbent
The adsorbent used in this study was synthesized from a 20 µm mesh enriched smectite clay fraction and silica from rice husk ash as starting materials. It led to a product which structure was largely described in previous work (Kepdieu et al. 2023) as a delaminated/exfoliated porous material with a specific surface area of 300 m2/g.
Palm oil
The palm oil used in this study is locally purchased from Master Foods Co., Cameroon. It was kept in the dark chamber at a low temperature (˜20°C) to avoid any degradation by oxidizing and photocatalytic reaction (Woumfo et al. 2007; Syamila et al. 2019).
Batch adsorption
For RSM studies, preliminary experiments help to choose the factor’s domains as time (from 20 to 60 min), temperature (from 60 to 90°C) and adsorbent dosage (from 1 to 2%) for design of experiment. The batch tests were performed in a thermostatically controlled reflux reactor following a method described in some previous works (Ayu Putranti et al. 2018; Baptiste et al. 2020). 5 g of oil was introduced in the reactor and when the indicated temperature value (60, 75 or 90°C) was reached. A known amount of adsorbent was added and the mixture was stirred at 250 rpm for a fixed time following the runs provided by the matrix of experiences. The mixture was filtered under vacuum using Whatman paper N°1. The oil was allowed to settle for 20 min and 1000 mg of the supernatant was then used to determine the FFA left in the treated oil.
For kinetics, the study was conducted in a larger range of time (from 0 to 90 min) and the data were compared to three models. On the same line, the influence of temperature and adsorbent dosage on the removal of FFAs was also evaluated. For 5 g of oil, the adsorbent dosage varied as 1, 1.5, 2, 2.5 and 3% at t = 90 min and the temperature values were 60, 75 and 90°C.
Assessment of FFAs content of treated oil supernatant
The oil was tested for acidity using the American Oil Chemists’ Society (AOCS) method Ca 5a–40 (1989) adapted by Japir et al. (Japir et al. 2017). First of all, 1000 mg of the treated oil sample were placed in a dried conical flask. Approximately 10 mL of pre-neutralized ethanol were then added to the sample. Afterward, 4 drops of 1% phenolphthalein indicator was then added to the mixture. The flask was subsequently placed on a hot plate and heated until a temperature of around 40°C was attained. The mixture was then titrated with alcoholic potassium hydroxide solution (0.05 N) until a pink color emerged for at least 30 s. Indeed, if molecules of FFAs are labeled with the formula RCOOH, the acid-base reaction which occurs between them and alcoholic KOH is total and the balance equation of the reaction is Eq. (1).
$$RCOOH + {(K}^{+}+ {OH}^{-})\to RCO{O}^{-}+{K}^{+}+{H}_{2}O$$
1
For treated sample, the FFA content expressed as Current Acid Value was determined using Eq. (2) (Akinola et al. 2010; Medeiros Vicentini-Polette et al. 2021).
$$\text{C}\text{u}\text{r}\text{r}\text{e}\text{n}\text{t} \text{a}\text{c}\text{i}\text{d} \text{V}\text{a}\text{l}\text{u}\text{e}=\frac{{\text{C}}_{\text{K}\text{O}\text{H}}{\text{V}}_{\text{é}\text{q}}{\text{M}}_{\text{K}\text{O}\text{H}}}{{\text{m}}_{0}}$$
2
Where \({C}_{KOH}\) is the molar concentration of the alcoholic KOH solution (0.05 mol/L), \({V}_{eq}\)the equivalent Volume of the pre-neutralized ethanol (mL), \({M}_{KOH}\)molar mass of KOH (56.1 g/mol) and \({m}_{o}\)the weight of the treated oil sample (1000 mg). The FFA content was determined in oil by titration of the supernatant after treatment and the quantity adsorbed (response) was calculated and expressed as Acid value drop (AV drop) in Eq. (3)
AV drop = Initial Acid value - Current Acid value (3)
Box-Behnken Design/Response Surface Methodology
In this study, RSM was applied to evaluate the effects of three independent variables contact time (X1), temperature (X2), and adsorbent dosage (X3), on the FFAS removal efficiency expressed as AV drop. Experimental adsorption design was established using Box-Behnken Design (BBD) implemented in Minitab 21. It is a three-factors and levels (–1, 0, 1) system consisting of 15 experimental runs. They were designed to optimize Acid Value (AV) drop in palm oil. The ranges of the considered variables as well as the corresponding levels in coded and uncoded values are summarized in Table 1.
Table 1
Designation of factors and levels in coded and uncoded values
Temps | Temperature | Adsorbent dosage |
X1 | t/min | X2 | T/°C | X3 | d (%) |
-1 | 20 | -1 | 60 | -1 | 1 |
0 | 40 | 0 | 75 | 0 | 1.5 |
1 | 60 | 1 | 90 | 1 | 2 |
If the natural variables (uncoded units) are labeled as U1, U2 and U3 corresponding to dimensionless coded variables X1, X2 , X2 respectively, the conversion of natural variables (Uij) into coded ones (Xij) is done following Eq. (4) (Merabet et al. 2009; Zolgharnein et al. 2015).
$${X}_{ij}=({U}_{ij}-{U}_{j}^{0})/\varDelta {U}_{j}$$
4
Where \({X}_{ij}\), \({U}_{ij}\) and \({U}_{j}^{0}\)are the values of the coded variable, the natural variable and the natural value at the center of the domain of factor j at the ith experiment respectively.\(\varDelta {U}_{j}\) is the half variation step of the factor domain of the natural variable.
The effect of the processing parameters as well as their interactions were investigated on the adsorption of FFAs by calculating the coefficients of the linear terms bi and the coefficient of interactions bij (i ≠ j) between factors i and j using Equations (5) and (6).
\({\text{b}}_{\text{i}}=\frac{{\sum }_{1}^{\text{N}}{\text{X}}_{\text{i}\text{n}}{\text{Y}}_{\text{n}}}{\text{N}}\) (1 ≤ n≤N) (5)
\({b}_{ij}=\frac{{\sum }_{1}^{N}{X}_{in}{{X}_{jn}Y}_{n}}{N}\) (1 ≤ n≤N) (6)
where\({X}_{in}\) and \({X}_{jn}\) are the values of the coded variables of factor i and j respectively.
The polynomial regression model used to describe the effects of the processing parameters is based on Taylor series and given in Eq. (6) (Khuri and Mukhopadhyay 2010; Turan et al. 2011; Zulfiqar et al. 2016; Kumar and Das 2017; Jawad et al. 2020; Dbik et al. 2022).
$$Y={b}_{0}+\sum _{i}{b}_{i}{X}_{i}+\sum _{i}\sum _{j}{b}_{ij}{X}_{i}{X}_{j}+\sum _{i}\sum _{j}\sum _{l}{b}_{ijl}{X}_{i}{X}_{j}{X}_{l}+\dots$$
6
Where Y and \({b}_{0}\)represent the theorical response of a test and that at the center of the experimental domain respectively. with 1 ≤ n ≤ k, 1 ≤ i ≤ j ≤ k and 1 ≤ i ≤ j ≤ l ≤ k.
In the, present study, a simple second order form of Eq. (6) for three factors is considered and given in Eq. (7).
$$Y={b}_{0}+{b}_{1}{X}_{1}+{b}_{2}{X}_{2}+{b}_{3}{X}_{3}+{b}_{11}{X}_{1}^{2}+{b}_{22}{X}_{2}^{2}+{b}_{33}{X}_{3}^{2}+{b}_{12}{X}_{1}{X}_{2}+{b}_{13}{X}_{1}{X}_{3}+{b}_{23}{X}_{2}{X}_{3}$$
7
Regression and graphical analysis were done using Minitab21 Software. Analysis of variance (ANOVA) was done on the regression model and on the model coefficients to test their significance, and adequacy. Thus, parameters such as the correlation coefficient R2, R2 (Adjusted), F-value, and P-value (probability) were generated to determine the relevance and suitability of the predicated model.
Kinetic studies
For kinetics studies, a non-linear approach was done considering Equations. (8) and (9) where Qe and Qt represented the quantities of FFAs adsorbed at equilibrium and at a time t respectively. AVe, the acid value of the oil at equilibrium, AVt; the acid value of the oil after treatment for time t (min) and m, the mass of oil.
$${Q}_{e}= \frac{{AV}_{0} -{{AV}_{ }}_{e}}{m}$$
8
$${Q}_{t}= \frac{{AV}_{0} -{{AV}_{ }}_{t}}{m}$$
9
Using the classical equations of the pseudo-first order, pseudo-second order and intra-particle diffusion models as reported by many authors (Ahmad et al. 2009; Pohndorf et al. 2016; Baptiste et al. 2020; Kurtulbaş et al. 2021) and introducing in the acid value parameter, the kinetics equations in their non-linear form have been re-written and presented in Equations (10)-(12).
\(({\text{A}\text{V}}_{0} -{{\text{A}\text{V}}_{ }}_{\text{t}})=({\text{A}\text{V}}_{0} -{{\text{A}\text{V}}_{ }}_{\text{e}})[1-\text{exp}\left(-{\text{K}}_{1}\text{t}\right)]\) (Pseudo-1st order) (10)
\(({\text{A}\text{V}}_{0} -{{\text{A}\text{V}}_{ }}_{\text{t}})=\frac{{\text{K}}_{2}{({\text{A}\text{V}}_{0} -{{\text{A}\text{V}}_{ }}_{\text{e}})}^{2}\text{t}}{1+{\text{K}}_{2}({\text{A}\text{V}}_{0} -{{\text{A}\text{V}}_{ }}_{\text{e}})\text{t}}\) (Pseudo-2nd order) (11)
$$({\text{A}\text{V}}_{0} -{{\text{A}\text{V}}_{ }}_{\text{t}})= {K}_{id}*{t}^{\frac{1}{2}}+\gamma \left(Intraparticle diffusion\right)$$
12
Where K1 (min-1), K2 (mg-1.g.min) and \({K}_{id}\) (in mg/min0.5) are the kinetic constants of the pseudo-1st order, pseudo-2nd order and intraparticle diffusion respectively; \(\varvec{\gamma }\) (mg/g) is associated to the boundary layer thickness.
In order to validate the best fitting to the model with more accuracy, the determination coefficient and the root mean square deviation designated by R2 and RMSD have been calculated using Equations (13) and (14).
$${R}^{2}=1-\frac{{\sum }_{k=1}^{n}{({v}_{exp,k}-{v}_{mod,k)}}^{2}}{{\sum }_{k=1}^{n}{({v}_{mod,k}-{\widehat{v}}_{exp,k)}}^{2}}$$
13
$$RMSD=\sqrt[2]{\frac{\sum _{k=1}^{n}{({v}_{exp,k}-{v}_{mod,k)}}^{2}}{n}}$$
14
Where: \({\text{v}}_{\text{e}\text{x}\text{p},\text{k}}\) and \({\text{v}}_{\text{m}\text{o}\text{d},\text{k})}\) are the exprimental and the expected values of the “kth” test.\({\widehat{\text{v}}}_{\text{e}\text{x}\text{p}}\) is the average exprimental value. n is the total number of tests.