3.2. Impact of Operating Conditions on Copper Adsorption
3.2.1. Contact Time Effect
The Cu(II) removal versus contact time is shown in
Figure 3. One can see that the adsorption rate was rapid: within the initial 60 min. Beyond, the removal process slows down, reaching a constant value around 92%.
In fact, 70% of copper was removed during a contact time around 60 min. Then, the removal rate of copper decreased for a contact time comprised between 60 and 180 min. For longer residence times, the adsorbent becomes saturated and no enhancement of the sorption capacity is recorded. The fast adsorption rate can be attributed to the availability of active sites at the beginning, as well as to the functional groups present on the surface [
45]. Thus, the resistance of mass transfer was low in the first stage of the process and increased with the contact time, which led to the sorption rate decrease.
3.2.2. Particle Size Effect
In order to assess the particle size influence on the adsorptive capacity of olive cakes, five ranges of particle sizes (from 0.5 to 2.8 mm) were used (
Figure 4).
According to
Figure 4, the retention of cupric ions was decreased by about 33% between fine powder smaller than 0.5 mm and particles with a diameter superior to 2.8 mm. In fact, the smaller are the particle sizes, the greater are the rates of diffusion and of adsorption. This finding was highlighted in several previous studies which indicated that the increase of particle size leads to a decrease in the rate of adsorption since the internal mass transfer zone becomes larger, which reduces the intra-particle diffusion [
36].
In addition, it should be mentioned that the size of particles affects not only the kinetic of the adsorption process but also the capacity of the adsorbent to remove pollutants. In fact, the reduction of the size of particles enhances the specific surface and, thus, the quantity of the retained adsorbate and the efficiency of the adsorption process.
3.2.3. pH Effect
The pH solution is one of the most significant factors affecting the adsorption process since it controls the surface charge density of the adsorbent and the metal species. The effect of pH solution on the removal of the cupric ions from aqueous solution by olive mill solid residues is shown in
Figure 5.
The removal yield of copper rose with the increase of pH from 3 to 5.25 and reached a maximum at pH equal to 5.25. After that, the amount of copper adsorbed decreased when the pH values moved from 5.25 to 9.125.
The high removal percent (90%) of copper at acidic pH (5.25) can be explained by the high solubility of the divalent ionic form of copper (Cu
2+) at this pH. Similar results were highlighted by Hawari et al. who found that the high adsorption capacity of copper by olive mill solid residues was obtained at pH 5 [
41].
At low pH values (<5.25), and due to the high H
+ concentration, the competition between H
+ and Cu
2+ ion species for the sites of adsorbent slows down the adsorption. However, at pH values higher than the optimum value (5.25), Cu
2+ ions tend to precipitate out of solution as hydroxides (Cu(OH)
2) according to the following reaction [
46]:
The solubility constant K
sp of copper hydroxide (Cu (OH)
2) can be written as follows:
In fact, most heavy metal hydroxides are relatively insoluble at certain pH [
47]. The pH which allows the formation of the hydroxide deposit was calculated according to Equation (5) and it was found equal to 5.59.
It should be mentioned that the removal yield of copper is still not negligible at high values of pH solution (around 77.33%). Similar finding was highlighted by Hawari et al. [
41].
In addition, it should be mentioned that pH influences not only the chemical properties of copper in aqueous solution but also the chemical properties of the functional groups of the oil mill solid waste.
Indeed, oxygen functional groups (hydroxyl, ether, and carbonyl) revealed by FTIR are to be correlated with the maximum removal rate obtained at pH 5.25. At a pH < 6, acid groups at the surface are more likely to be involved. This also would explain the pH-dependence observed. In fact, at this value, olive residues have a negative charge due to the excess of negatively-charged functional groups. This negative charge is probably due to the pKa of hydroxyl (10) and of phenol (22), above the value of the optimum pH (5.25). As for carbonyl, the pKa (4) is below to the optimum pH. Thus, this metal removal (depending on pH) is itself dependent on the ligands responsible for the uptake of copper, for instance carboxyl and phenol functional groups.
On the issue of these results, it can be concluded that the removal efficiency of cupric ions depends strongly on pH solution which indicates that electrostatic interactions and/or ion exchange are possible mechanisms of copper biosorption [
6,
41].
3.2.4. Initial Concentration Effect
The influence of the initial concentration of copper on the adsorption process is shown in
Figure 6.
It is clear that the increase of initial concentration of copper leads to a decrease in the copper removal efficiency. In fact, around 21% of the removal capacity was lost when copper concentration increased from 20 to 320 mg/L. This result can be explained by the saturation of the adsorption sites which is due to the presence of a high quantity of cupric ions.
This result implies that only small fraction would be retained if Cu2+ concentration is high. Olive mill solid waste is was more efficient at low concentrations where the cupric ions are totally or predominantly retained and, if the Cu2+ concentration becomes very large, only a small fraction was retained. Nevertheless, it should be noticed that the concentrations of cupric ions in industrial wastewaters do generally not reach such the high values tested in the present study. As an example, the wastewaters of tanneries contain a concentration of cupric ions less than 30 mg/L which is in the same order of magnitude of the concentrations used in this work and for which where a high removal yield was recorded.
3.3. Kinetic Study
Several kinetic models were applied namely pseudo-first order, pseudo-second order, Elovich, and Brouers-Sotolongo models. Model parameters were determined by the non-linear fitting method and experimental, as well as fitted curves were presented in
Figure 7.
According to
Figure 7, it is clear that the kinetic uptake of copper was faster during the first 60 min and became constant after a contact time of 180 min (q
t = 18.4 mg/g). This last same value was also reached by Tchoumou et al. [
45].
The fast sorption in the first stage can be explained by the abundance of the functional sites. This is advantageous at industrial scale since it allows treating heavy-metal contaminated water with a minimum of contact time and with lower operation costs. Afterwards, adsorption sites become saturated and the sorption rate decreases.
With such capacity and given the average produced and non-recovered quantity of olive cake in Tunisia, around 1.84 kTons of copper could be removed from contaminated waters. This last quantity, being more important than that actually produced by the Tunisian industries, possible import routes to neighboring countries could be envisaged.
In order to assess the best fitted kinetic model, four error functions (SSE, HYBRID, MPSD, and R2) were calculated.
According to the results reported in
Table 5, Brouers Sotolongo is the best fitting model since the correlation coefficient R
2 (0.998) exhibited the highest value and SSE (0.198), HYBRID (0.011) and MPSD (0.0006) the lowest. Besides, the adsorption capacity (18.93 mg/g) calculated on the basis of this model was the closest to the experimental value (18.4 mg/g).
Using the parameters of the Broeurs-Sotolongo model (γ, n and τ), the half sorption time (τ
50%) can be determined according to the following equation [
48,
49]:
The half sorption time is as the time at which the half of the adsorbate has been removed. This parameter was found to be 31.56 min in this study. This result is in adequacy with the experimental output since the first step of the sorption reaction occurs within 60 min, during which 76% of copper was removed.
The comparison of the pseudo-first and the pseudo second order models, as the most used kinetic models, showed that the latter model fit less the kinetic uptake of copper compared to the former. This indicates that the adsorption kinetic was not governed by chemical mechanisms.
For Bohli et al., the pseudo-first order model also gave quite good prediction with R
2 = 0.970 (q
e,cal = 0.145 mmol/g) but the pseudo-second order (q
e,cal = 0.139 mmol/g) was more suitable (R
2 = 0.999) for copper removal by activated carbon issued from olive stone waste [
50].
On other side, Elovich prediction was the worst with the highest SSE, HYBRID and MPSD and the lowest R2. According to the assumptions of this model, it can be deduced that desorption reactioncan occur and the dominant adsorption mechanism cannot be chemical sorption. This finding strengthened the conclusion highlighted through the analysis of the poor fitting of the pseudo-second order model to the experimental data.
The four kinetic models cited above inform us about the sorption rate but they did not give information about the adsorption mechanisms and the controlling step of the copper adsorption by olive mill waste. For this purpose, film and intraparticle diffusion models were applied to estimate which step controls more the overall adsorption rate. Intraparticle (K
in, C) and film (K
f, D
f) diffusion model parameters were determined by the non-linear method using the solver add-in facility for Microsoft Excel (USA) (and were reported in
Table 6.
The effective diffusion coefficient of the copper onto olive residues (D) can be calculated from the intraparticle rate sorption (K
in) by using the following equation:
where D is in (cm
2/s) and r is the mean radius of adsorbent particles (cm).
The free diffusivity D
0 (m
2/s) of the copper in diluted solutions can be determined according to Stokes-Einstein equation:
where:
The calculated ratio D/D0 (10−3) indicates that the diffusivity of copper inside olive mill residues was reduced by a factor of 1000 compared to its diffusivity in diluted solutions. This finding indicates the high hindrance of copper by the adsorbent which is expected since the physical properties of olives residues were limited (BET surface, porosity).
At the same time, C parameter was equally determined and was estimated to be 5.89 mg/g. Since this parameter is different from zero, it can be deduced that the kinetic uptake of copper was not controlled by only intra-particle diffusion phenomenon and that other controlling mechanisms might be involved simultaneously. For this reason, a film diffusion model was tested and the corresponding parameters (K
f and D
f) were determined and reported in the same
Table 6. The obtained values let us conclude that film diffusion model was not the sole controlling step in copper adsorption reaction since the plot relating Bt to Ln(1-F) did not pass through the origin (data not shown). This finding suggests that another mass transfer mechanism controls the sorption uptake which is probably the intraparticle diffusion step.
In order to determine the dominating diffusion mechanisms, the Biot number (Bi) was calculated according to the following equation:
where k
f (cm/s) is the film diffusion constant, D (cm
2/s) the intraparticle diffusion coefficient, C
0 (mg/L) the initial liquid-phase concentration, d (cm) the mean particle diameter; and ρ
p (g/cm
3) the adsorbent density and q
e (mg/g) is the solid phase concentration at equilibrium.
The adsorbent density used to calculate the Biot number was adopted from a previous work of Ferhat, et al. [
51].
In previous works, three intervals of Biot number (Bi) were adopted, as follows:
- ■
If Bi ≪ 1, film diffusion is the controlling step;
- ■
If Bi ≫ 100, intra-particle diffusion is the controlling step; and
- ■
If 1 < Bi < 100, Film and intraparticle diffusion are the limiting steps.
Again, and given the Biot number comprising between 1 and 100 for the current system, film and intra-particle diffusion mechanisms control simultaneously the adsorption process of copper by olive mill solid wastes. However, given the low porosity, intraparticle diffusion would not be dominant.
Thus far, these results suggest that faster agitation of the system and the enhancement of the physical (specific surface, porosity) and chemical (functional groups) properties of the adsorbent would allow improving the overall sorption rate.
3.4. Equilibrium Study
In order to assess the affinity of the adsorbate towards the adsorbent, adsorption isotherm is usually established [
52]. In this study, several models were applied and the results are reported (
Table 7 and
Figure 8).
The experimental adsorption capacity of copper by olive mill solid residues was q
max = 23.6 mg/g. This value indicates the high potential of this bio sorbent to remove cupric ions from aqueous solution. This value was compared to other biosorbents reported in previous studies dealing with copper removal from aqueous solutions and was found higher than that of the majority of the tested biosorbents (
Table 8).
Moreover, as shown in
Figure 8, experimental isotherm curve has the ‘’L‘’ shape which indicates that the uptake of cupric ions by olive mill residues was favorable and that the competition between solvent molecules and copper is weak.
In order to determine the most appropriate model to describe copper adsorption by olive mill solid residues, an error analysis was conducted by calculating R
2, SSE, HYBRID, and MPSD values as indicated earlier. Thus, firstly, two-parameter models were compared with each other; then the two sets of models (two and three-parameter models) were compared by analyzing their corresponding error values (
Table 7).
The comparison of the two-parameter models showed that Langmuir matched the best, with the highest R
2 and the lowest SSE, HYBRID and MPSD, compared to Freundlich, Temkin, and Dubinin- Radushkevich model error values. Bohli et al. also found that Langmuir model described better the sorption of copper by activated carbon from olive stones than Freundlich model but also than Redlich-Peterson and Sips models with maximum calculated capacity q
max,cal = 17.15 mg/g and K
L= 2.37 L/mg with R
2 = 0.974 [
50].
Langmuir suitability indicates that cupric ions are adsorbed by forming a monolayer of cupric ions around the olive waste particles, a conclusion reached also by Hawari et al. [
41].
In order to improve the precision of models describing the adsorption of cupric ions, three-parameter models (Brouers-Sotolongo, Khan, Hill, Toth, and Kobble-Corrigan) were equally investigated and compared to two-parameter models. The analysis of error values led us to the conclusion that all the four three-parameter isotherms fitted better the equilibrium uptake of copper compared to two-parameter models, the lowest R
2 value (0.989) being higher than that of Langmuir model (R
2 = 0.987). Besides, and according to
Table 7, Brouers-Sotolongo isotherm was found the nearest model to equilibrium data with lowest SSE (4.243), HHYBRID (0.529), and MPSD (0.128), and with the closest R
2 to unity (R
2 = 0.993).
It should be mentioned that Khan and Toth models have the same correlation coefficient value (R2 = 0.992). However, the comparison of the SSE, HYBRID, and MPSD showed that Khan isotherm are more in adequacy with the experimental data compared to Toth model. Additionally, Hill and Koble-Corrigan have the same values of error functions and correlation coefficients. This similarity can be explained by the fact that both models have the same structure of mathematical equations.