Optimization of the adsorption and desorption processes of nickel octaethylporphyrin in carbon-based adsorbents

Abstract Despite being little explored for petroporphyrins recovery from oils and bituminous shales, adsorption and desorption processes can be feasible alternatives to obtain a similar synthetic material, and to characterize their original organic materials. Experimental designs were used to analyze the effects of qualitative (e.g., type of adsorbent, solvent, and diluent) and quantitative (e.g., temperature and solid/liquid ratio) variables on the adsorptive and desorptive performance regarding nickel octaethylporphyrin (Ni-OEP) removal using carbon-based adsorbents. The evaluation variables, adsorption capacity (qe ) and desorption percentage (%desorption ) were optimized by means of the Differential Evolution algorithm. The most efficient adsorbent for removing/recovery Ni-OEP was activated-carbon coconut shell, in which dispersive π-π type and acid-base interactions were likely formed. The highest values of qe and %desorption were obtained using toluene as solvent, chloroform as diluent, 293 K as temperature, and 0.5 mg.mL-1 as solid/liquid ratio for adsorption, and a higher temperature (323 K) and lower solid/liquid ratio (0.2 mg.mL-1) for desorption. The optimization process resulted in qe of 6.91 mg.g-1 and %desorption of 35.2%. In the adsorption-desorption cycles, approximately 77% of the adsorbed porphyrins were recovered. The results demonstrated the potential of carbon-based materials as adsorbent materials for obtaining porphyrin compounds from oils and bituminous shales.


INTRODUCTION
Regarding the process of assessing the quality of oil sources, the biomarkers distribution is an important factor to be considered (Affouri & Sahraoui 2017).
Porphyrins are an important class of biomarkers used to investigate the degree of oil maturity (Yang et al. 2018). Porphyrin structures are tetrapyrrolic, heterogeneous and aromatics, the result of the transformation of primary chloropigments which occurs during the processes of oil formation and maturation (Ramírez-Pradilla et al. 2019. The porphyrins are present in the most polar fractions of petroleum, asphaltenes, and resins (Mousavi et al. 2019). In bituminous shales, the porphyrins are commonly found in oil and mainly distributed in etioporphyrins (ETIO), deoxophylloerythroetioporphyrins (DPEP), and rhodoporphyrins (RHODO) (Dechaine & Gray 2010). Actually, the most abundant metalloporphyrins oil are nickel and oxovanadium porphyrins (Liu et al. 2015a, Zhao et al. 2015. Despite being found in the form of trace elements in oil (Poirier et al. 2016, Sama et al. 2018, Sugiyama & Williams-Jones 2018, these compounds are capable of altering the oil physical-chemical properties (Silva et al. 2017), promoting corrosion of pipes and equipment (Wang et al. 2016). They also poison the catalysts employed (Etim et al. 2016(Etim et al. , 2019, harming the quality and yield of refining products (Sorokina et al. 2010), hence contributing to environmental pollution (Sama et al. 2018).
Provided the damages caused to the oil processing, the removal and recognition of the porphyrinic species, and others nitrogen and sulfur contaminants , from their origin oil is highly recommended. Qualitative and quantitative analyses of petroporphyrins are necessary to identify the oil properties as well as the potential damage to the refining. Meanwhile, their recovery allows the application of their optical and electronic properties (Gottfried 2015, Hipps & Mazur 2018, Jurow et al. 2010, Kuzmin et al. 2018, Lee et al. 2017. The use of synthetic porphyrins and metalloporphyrins is observed in areas related to surface science (Hipps & Mazur 2018), such as catalysis (Kuzmin et al. 2018), and in mechanisms involving energy transfer, due to their photoelectronic properties, being potential components of electronic devices, such as wires and diodes (Jurow et al. 2010). Moreover, the photodynamic activity of sedimentary porphyrins, such as oxovanadium ethioporphyrin, has already been observed (Ribeiro et al. 2005).
Among the porphyrins separation and isolation methods currently employed, the extractive and chromatographic methods are predominant (Kumolo et al. 2019, Liu et al. 2015b, Mironov et al. 2017, 2018a, b, Rytting et al. 2018, Woltering et al. 2016, Yakubov et al. 2017. Although the high efficiency of these methods, they are associated with some disadvantages such as the high consumption of solvents and inputs (Li et al. 2020), and the limited treatment and supply . The use of adsorption processes can be a more sustainable alternative, although it has been little explored for this purpose (Chen et al. 2013(Chen et al. , 2017. Chen et al. (2013Chen et al. ( , 2017) evaluated the possible interaction mechanisms between porphyrins and asphaltenic compounds using kinetic, equilibrium and thermodynamic adsorption studies of nickel (Ni-OEP) and oxovanadium octaethylporphyrins (VO-OEP) on asphaltene. Chen et al. (2018) analyzed the polyaromatic nuclei function of the adsorbents used by comparing the results obtained in previous studies (Chen et al. 2013(Chen et al. , 2017, with the adsorption of the same porphyrins onto graphene. No study has suggested the recovery of petroporphyrin compounds. Extensive use of carbon-based materials as adsorbents is observed in the removal of several pollutants (Bin-Dahman & Saleh 2020). However, its use for the adsorption of petroporphyrins from oil is still scarce. The related studies focused on discussing the properties and mechanism of self-assembled structures formation of metaloporphyrins adsorbed onto graphitic materials (Gruden-Pavlović et al. 2007, Hipps & Mazur 2018, Ogunrinde et al. 2006).
However, their use for the removal of nitrogenous components is recurrent in the literature (Carvalho et al. 2020, Feng et al. 2015, Ferreira et al. 2019, Han et al. 2015, Wen et al. 2017. The performance of these materials is directly associated with their surface chemistry and pore structure (Wen et al. 2017). The presence of acidic functional groups in their structure may favor the adsorption of basic nitrogen regions, such as those available in the porphyrinic molecule (Lee et al. 2017), forming acid-base interactions (Han et al. 2015). Although the presence of functional groups on the adsorbent surface can be a facilitator for the adsorptive process, the recovery of the adsorbate through the subsequent desorption process can be difficult (Prado et al. 2016). Some works revealed the high efficiency of toluene and chloroform in the regeneration of adsorbent materials used in the removal of organic contaminants from liquid fuels (Almarri et al. 2009Koriakin et al. 2010, Sano et al. 2004, Shah et al. 2017. The knowledge of the physical-chemical and textural characteristics of the materials is not the only important factor for controlling the adsorptive and desorptive processes (Moskvin 2016). The study of the interactions between the operational parameters in the system's behavior is also a key factor to be considered. The statistical designs are widely used to optimize and model the experiments in the industrial sector since improvements in performance, reliability, capacity, and yield of processes were previously observed (Regti et al. 2017).
The recognized importance of porphyrin compounds in surface science applications increased the scientific interest and market value of these materials. The difficulty of separating petroporphyrin compounds and the possibility of using them as alternatives to their synthetic analogues also contribute to their high added value. The price of synthetic VO-OEP is around USD 2.72/mg, while the synthetic Ni-OEP reaches USD 4.35/mg (Sigma Aldrich 2021). The lack of studies regarding petroporphyrin recovery processes can be a limiting factor for the development of optimized operational conditions. In this context, the present study aimed to evaluate the influence of experimental conditions, adsorbents' carbonic structure, solvent types, temperature, and solid/liquid ratio on the performance of Ni-OEP adsorption/ desorption processes through experimental designs. The results obtained were quantified using the variables responses to adsorption capacity at equilibrium (q e ) and desorption percentage (% desorption ), which were statistically treated and optimized.
The adsorption and desorption experiments were carried out in batch, under agitation in a rotary shaker (Ethik Technology, 430/RDB), at 120 rpm. The concentrations of porphyrin solutions were determined using an ultravioletvisible spectrophotometer (BEL Photonics 1105). Residual solutions were analyzed in a spectrophotometer in triplicate values. The adsorbents were characterized by X-ray diffraction (XRD), nitrogen adsorption and desorption (N 2 ) and infrared spectroscopy (IR). XRD analysis was performed on a Shimadzu DRX-6000 diffractometer with a copper source, at 40 kV and 20 mA. Measurements were performed in a 2θ range from 5 to 80 deg, with 0.02 deg/step. The adsorbents specific areas and porosity were analyzed through the adsorption and desorption of N 2 , at 77 K, using the ASAP 2020 Plus 1.03 (Micromeristic) equipment, in the relative pressure range (P/P 0 ) from 10 -3 to 1. The specific area was determined by the Brunauer -Emmett -Teller (BET) multipoint technique (Brunauer et al. 1938). The total pore volume per total single point pore volume, (P/P 0 = 0.98), while the micropore volume was determined by the t-plot method (Lippens & De Boer 1965). The average pore diameter was determined by the Barrett-Joyner-Halenda (BJH) method (Barrett et al. 1951). The functional groups on the surface of the adsorbent materials were analyzed using MIR analysis, performed on a PerkinElmer spectrophotometer (model Spectrum 400), in a wavelength range from 4000 to 450 cm -1 .

Adsorbent selection
In order to evaluate the performance of CSAC, G and GO in the adsorption of nickel porphyrin, Ni-OEP solutions in toluene were subjected to initial adsorption tests, varying the adsorbent used. The experiments were carried out in batches, in which an initial porphyrin concentration of 8 μg.mL -1 was used, with 10 mL volumes and 5 mg adsorbent doses. The systems were kept under agitation (120 rpm) in a rotary shaker for 24 h at 298 K. The adsorption capacities at equilibrium (q e ) were calculated by Equation 1, which is given below: where C 0 is the initial solution concentration; C e is the solution concentration at equilibrium; V is the solution volume; and M is the adsorbent mass.
The saturated adsorbents were subjected to subsequent desorption processes with chloroform in order to select the best adsorbent for Ni-OEP adsorption and desorption. After adsorption, the saturated adsorbents were dried in an oven (353 K, 24 h) and underwent batch desorption tests. Doses of 1 mg were used, in contact with 5 mL of diluent, being kept under the same conditions of stirring (120 rpm), time (24 h) and temperature (298 K) as the adsorption tests. The desorption percentages (% desorption ) were calculated by Equation 2, which is given below: where q e is the adsorption capacity at equilibrium (mg.g -1 ); and q e,des is the desorption capacity at equilibrium (mg.g -1 ), being calculated by Equation 3: where C d is the solution concentration at the end of the desorption; V dil is the diluent volume; and M S is the mass of the saturated adsorbent.
The highest values obtained for q e and % desorption were determinant to select the most efficient adsorbent for both adsorption and desorption of Ni-OEP, within the experimental conditions employed.

Experimental designs
Once the best adsorbent material was selected, the influence of solvent, diluent, temperature and solid/liquid ratio of adsorption and desorption on q e and % desorption was evaluated using experimental designs. Batch adsorption and desorption tests were performed under experimental conditions similar to those used in the initial tests. 10 mL of solutions with initial concentrations of 8 μg.mL -1 were subjected to the adsorption process for 24 h, under agitation at 120 rpm, changing the analyzed variables according to the experimental designs. While the volumes of diluent used in the desorption were 5 mL, they were also kept under agitation at 120 rpm for 24 h.
The results obtained were analyzed using statistical treatment. The regression equations were obtained as a function of the quantitative variables evaluated, and the conditions of temperature and solid/liquid ratio of both adsorption and desorption were optimized.

Qualitative experimental design
The effects of qualitative variables (solvent and diluent) on q e and % desorption were analyzed using a qualitative factorial design 2 2 . The levels of the variables evaluated are shown in Table I.
The results obtained in the qualitative tests, which the adsorption capacity in the equilibrium and the percentage of desorption were evaluated, allowed the elucidation of the performance of each solvent and diluents used in the adsorption and desorption processes, respectively.

Quantitative experimental design
The effects of quantitative variables, temperature, and solid/liquid ratio on q e and % desorption were analyzed using quantitative experimental designs. First, the influence of temperature (T ads ) and solid/liquid ratio ((S/L) ads ) on the adsorption process performance was evaluated, being measured by the q e value. An orthogonal central composite (CCOD) design was used, with 2 central points and 2 2 axial points (2.1.10). The levels used for the variables evaluated are shown in Table II. The effects of adsorption (T ads ) and desorption (T des ) temperatures and adsorption ((S/L) ads ) and desorption ((S/L) des ) solid/liquid ratios on % desorption were evaluated by means of CCOD, with 2 central points and 2 3 axial points (4.1.26). The levels used for the variables evaluated are shown in Table III.

Optimization
The regression equations obtained for the variables evaluated were used in combination with the Differential Evolution algorithm (Storn & Price 1997), to determine the conditions of T ads/des and (S/L) ads/des , which simultaneously maximize q e and % desorption . Provided it is multiobjective optimization problem, the weighted sum method (Marler & Arora 2010) was used to obtain a single solution point. It was performed by applying weights to the response variables. This method was applied to an optimization code available in the MATLAB 2020 simulation program, similar to the methodology used by Silva et al. (2015). The optimization results obtained were evaluated to verify the consistency of the response surfaces constructed for q e and % desorption variables. They were validated through new adsorption and desorption tests.

Adsorption-desorption cycles
Consecutive cycles of Ni-OEP adsorption and desorption were carried out in batches to evaluate the porphyrin recovery capacity and regeneration of the selected adsorbent after successive processes. The q e/des and % removal/ desorption were evaluated at each adsorptiondesorption cycle. The experimental conditions used to concern temperature and solid/liquid ratio corresponded to those obtained by the optimization process.

Adsorbent characterization
The diffraction patterns obtained for the adsorbent materials are shown in Figure 2. The GO formation was confirmed by the presence of a broad peak at 2θ = 10.34°, corresponding to the Table II. Levels of the factors used in the study of the effect of the adsorption temperature and solid/liquid ratio on the adsorption of Ni-OEP in CSAC, using a CCOD 2.1.10 (α = 1.078).

Factor
Code Level  Figure 3.
The constitution of the materials basic structure is revealed by the presence of bands at wavelengths close to 1632 cm -1 in the spectra, characteristics of C═C stretches. The C─C stretches, identified by bands at 1384 cm -1 , might be associated with the presence of branches in the carbonic skeleton, mainly in CSAC and GO materials. In these functionalized materials, bands close to 1090 cm -1 are also evident, characteristic of C─O bonds. It suggests the presence of epoxy groups on their surfaces. Carbonyl groups (C═O), characteristic of the band close to 1725 cm -1 , may indicate the presence of carboxylic or aldehydic functional groups in the synthesized GO structure. The bands at 3445 cm -1 , common to the three materials evaluated, are characteristic of hydroxyl-type groups (O─H), indicating the likely presence of moisture or alcohols in the structures of the functionalized materials (CSAC and GO). The predominance of acidic functional groups on the surface of the GO is remarkable, as has already been observed (Channei et al. 2018). The peaks corresponding to the acid groups distributed on the surface of the GO are similar to those obtained by acid treatment of carbon-based materials (Saleh 2011). While basic and acidic functional groups can be found on the surface of other materials, with higher peak intensities of polar groups observed for CSAC.  The values obtained for specific area, total pore volume, micropore volume and average pore diameter are shown in Table IV, and the N 2 adsorption/desorption isotherms are illustrated in Figure 4. Higher values of specific area, total volume of pores and micropores were observed for activated carbon in relation to graphical materials. Considering the    (Figures 4b and 4c) are also indicative of the low presence of pores on the surface of graphitic materials. In general, micropores are more favorable adsorption sites for the formation of adsorbateadsorbent interactions (i.e., when the adsorbate molecule and adsorbent pore sizes are compatible) (Liu et al. 2020). The Ni-OEP molecules have an estimated surface area of 26.7 Å 2 (PubChem 2019), presenting a twofold measurement of their approximate values dimensions (~ 5.17 Å). Provided the materials' average pore diameters are larger than 20 Å, it is possible to infer the diffusion of adsorbate molecules in the micropores of the adsorbents.
Due to the predominance of micropores on the CSAC porous surface, it was initially supposed that the use of activated carbon is associated with results of greater adsorption capacity results in comparison to the use of other materials.

Adsorbent selection
The q e and % desorption values obtained for each adsorbent material (CSAC, G and GO) employed in the initial Ni-OEP adsorption and desorption are shown in Table V. The values obtained were compared to the values observed in the literature for the use of other carbon-based materials, such as graphene and asphaltene.
As can be seen in Table V, the highest values of adsorption capacity are associated with the use of activated carbon (5.73 mg.g -1 ). Compared to G and OG, this result may be associated with more favorable surface chemistry of CSAC, due to higher values of specific total area, pore distribution and presence of micropores.  the formation of more specific and intense adsorbent-adsorbent interactions during the adsorption process. The larger specific areas and volumes of micropores are associated with greater numbers of active sites available for adsorption. The higher content of oxygenated functional groups on the GO surface may have been a facilitator and limiting factor in the adsorption process, justifying the proximity of the adsorption capacity values in equilibrium with graphite. Acid-base interactions were potentially formed between the acid-character functionalized regions of GO and the basiccharacter nitrogenous regions of nickel porphyrins. However, these functional groups may have limited the access of Ni-OEP molecules to the interlayer space of the oxidized material (Feng et al. 2015), impairing the establishment of adsorbent-adsorbent interactions.
Despite the lower result of adsorption capacity, the use of graphite (G) is associated with a higher rate of Ni-OEP recovery with chloroform, reaching % desorption values close to 50%. This performance may be related to the presence of less intense interactions between the nonfunctionalized graphitic surface and the metallic porphyrin, facilitating the desorption process. Due to the presence of acidic functional groups (carboxylics, epoxy and hydroxides) on the GO surface, intense interactions with the basic nitrogen regions of Ni-OEP, with chemisorption or reactive adsorption characteristics as already reported for other aromatic compounds (Barroso-Bujans et al. 2010), may have hindered the desorption process. The tendency of porphyrinic molecules to form aggregates through π-π type stacks (Kumolo et al. 2019, Rytting et al. 2019, associated with high values of the CSAC specific area may be related to the significant desorption percentage obtained for the material, which was close to 31%. Chen et al. 2017, 2018 did not evaluate porphyrin recovery processes.
Considering the higher values of q e and % desorption obtained for CSAC, this material was chosen as adsorbent material in the subsequent experimental designs.

Qualitative experimental design
The adsorption capacity and desorption percentage values obtained with the factorial type 2 2 design experiments are shown in Table VI.
According to the results obtained, we found that the change in the solvent used in the initial Ni-OEP solution did not cause significant changes in q e , which ranged from 5.38 mg.g -1 , obtained with the use of toluene, to 5.07 mg.g -1 , obtained with the use of chloroform. Although the change of solvent (-1 to +1) caused a decrease in q e of 0.28 mg.g -1 , there was no significant effect on the response variable. The differences observed in Table VI. Qualitative design matrix and respective results of q e , in mg.g -1 , and % desorption , in %, with adsorption initial solution of 8 μg.L -1 , at T ads/des of 298 K, (S/L) ads of 0.5 mg.mL -1 and (S/L) des of 0.2 mg.mL -1 , both under agitation of 120 rpm for 24 h.

Experiment
Solvent Diluent q e (mg.g -1 ) % desorption (%) the experimental q e might be a consequence of the greater porphyrin solubility in chloroform (Freeman et al. 1990). This provides a competitive medium for the adsorbent molecules, which have affinity with both the adsorbent active sites and the solvent molecules. This inverse relationship between solubility and the extent of adsorption capacity has been previously reported for the adsorption of aromatic compounds on activated carbon (Villacañas et al. 2006). Regarding the desorptive processes outcomes, despite the greater solubility of porphyrin in dichloromethane in comparison to chloroform (Freeman et al. 1990), the % desorption highest values were obtained using chloroform as diluent, reaching values close to 31%. The change of diluent (-1 to +1) led to a 14.2% decrease in % desorption , indicating that the use of chloroform is more efficient in recovering porphyrin by desorption in relation to dichloromethane. The change of solvent (-1 to +1) led to a decrease of 8.7% in the % desorption , which indicates that the use of toluene in the adsorption process favors a greater desorptive performance. The linear interaction between solvent and diluent led to a 7.4% increase in the % desorption . Although the variables effects are more noticeable in the results of experimental % desorption , these effects were considered as little significant in the response variable during statistical analysis.
As the effects of the independent qualitative variables were little significant on the response variables, toluene and chloroform were selected as the most suitable solvent and diluent, respectively. The experimental results obtained and the possibility of working in a higher temperature range in subsequent procedures were considered for this decision.

Quantitative experimental design 2.1.10
The influence of the different temperature and solid/liquid ratio conditions employed in the adsorption process were evaluated through the statistical analysis of the experimental q e results. They are shown in Supplementary Material -Table SI. The determined statistical parameters are presented in the form of ANOVA distribution in Table VII.
Considering the 90% as significance level and analyzing the F and p-values, we found that only (S/L) ads (x 2 ) in the linear form (p < 0.10) had a significant effect on q e . The regression coefficients presented in Table VII show that (S/L) ads has a negative correlation with q e . In other words, smaller (S/L) ads favor higher Table VII. ANOVA parameters of quadratic polynomial regression model of q e as a function of T ads (x 1 ) and (S/L) ads (x 2 ). values of q e due to the greater availability of adsorbent molecules (present in solution) in relation to the adsorbent active sites, promoting a greater likelihood of contact and formation of interactions. Similar results were achieved for the Ni-OEP and VO-OEP adsorption on asphaltene and graphene (Chen et al. 2013(Chen et al. , 2017. On the other hand, the adsorption temperature had no significant effect on q e in the temperature range studied, in which we observed a behavior for the adsorption of heterocyclic nitrogen compounds on activated carbon (Wen et al. 2010). The evaluation of the temperature influence on adsorption can be a complex process. While the increase in temperature can reduce the solution viscosity, facilitating the diffusion of the adsorvate molecules and increasing the adsorption rate (Yao et al. 2010), such variation can also promote an increase in the adsorbate solubility in the solvent, making competitive the affinity of the adsorbate for the solvent and the adsorbent surface. Favorable temperature conditions can be better analyzed through the thermodynamic study of the process (Lamichhane et al. 2016).

Quantitative experimental design 4.1.26
The % desorption results obtained for the CCOD 4.1.26 adsorption and desorption experiments are Table VIII. ANOVA parameters of quadratic polynomial regression model of % desorption as a function of T ads (x 1 ), (S/L) ads (x 2 ), T des (x 3 ), and (S/L) des (x 4 ).

Factor
Sum of Squares presented in the matrix in Table SII. Percentages from 10.4 to 36.3% were obtained with the application of different temperature conditions and solid/liquid ratios for adsorption and desorption. The effects of the independent variables on the % desorption were evaluated through the related statistical parameters presented in Table VIII. Considering 90% as significance level, linear, quadratic and cross effects between the independent adsorption and desorption variables were verified in the % desorption . The variables referring to the desorption process had greater effects on % desorption : T des (x 3 ), in the linear form, had the greatest effect due to its higher F-value (116.31), followed by (S/L) des (x 4 ), in the linear form, with F-value of 32.16. The adsorption variables had less significant effects on the desorption performance, as summarized in quadratic and cross interactions: (S/L) ads (x 2 ), in the quadratic form, presenting an effect similar to the interaction between (S/L) ads and T des , with close F-values results (9.11 and 8, respectively), while T ads (x 1 ), in the quadratic form, presented lesser effects. The other factors considered did not have any significant effect on the % desorption .
Concerning desorption conditions, whose effects on the desorption processes performance were superior to those from adsorption variables, it was possible to establish direct relationships with % desorption . In Table VIII, it was verified that T des has a positive correlation and (S/L) des has a negative correlation with % desorption , through regression coefficients. In other words, higher T des and lower (S/L) des favor higher values of the dependent variable. It is possible that the use of higher temperatures during the desorption process influenced the increase in the agitation degree of the solvent molecules, promoting a reduction in their viscosity as well as an increase in the diffusion rate on the surface of the adsorbent (Nasuha et al. 2010) and adsorbate. This increases its energy level in relation to the adsorbed and solvated states, a necessary condition for the desorption of organic molecules (Ten Hulscher & Cornelissen 1996). The temperature can also be a key factor for the solubility increase of the porphyrinic molecules in the diluent, which increases the desorption rate. Meanwhile, the use of smaller amounts of adsorbent can facilitate the diluentadsorbent contact, as a result of a greater availability of solvent molecules in the medium (Daneshvar et al. 2017).
As regards the adsorption variables, the same relationships cannot be directly established, in which the construction of response surfaces is required. It is discussed in detail in the optimization section.

Optimization
The order of relative relevance of the main effects of the independent variables, and the interactions of the variables with each other, in the evaluation variables can be observed in the Pareto charts (Saleh et al. 2018), shown in Figure 5. Considering a 90% significance level, the significant effects found were: (S/L) ads (x 2 ) in q e (Figure 5a); and T des (x 3 ), (S/L) des (x 4 ), quadratic interaction of (S/L) ads (x 2 2 ), interaction between (S/L) ads and T des (x 2 .x 3 ) and quadratic interaction of T ads (x 1 2 ), in % desorption (Figure 5b), in that order. Positive coefficients reveal positive contributions of the respective factors, while negative coefficients correspond to negative contributions. Factors whose effects did not reach the dashed line had no significant effect on the response variables.
The regression equation resulting of the dependent variable q e as a function of the significant adsorption variables coded is presented in Equation 4, with R 2 close to 0.953. The adequacy of the adjustments is verified by the high determination coefficients of the regression equations obtained, close to the unit, and by the low residues between experimental and predicted values, illustrated in Figures S1 and S2.
The regression equations were used to simultaneously maximize the q e and % desorption values. The optimized conditions are shown in Table IX. They were consistent with the response surfaces behavior obtained for both response variables, as illustrated in Figures 6 and 7.
Within the pre-established conditions for the independent adsorption variables, it was possible to observe through the surface illustrated in Figure 6 that the smallest (S/L) ads resulted in the highest q e values, for any T ads value. The negative correlation between (S/L) ads and the evaluation variable qe can be easily observed, keeping T ads constant. The q e results reached values close to 7 mg.g -1 , while the lowest values reached 4 mg.g -1 for the largest (S/L) ads . The T ads did not significantly influence the q e results, keeping (S/L) ads constant.
When evaluating the response surfaces obtained for % desorption (Figure 7), we found that the use of T ads and (S/L) ads upper and lower limits favored higher % desorption values (Figure 7a). At the same time, higher T des and smaller (S/L) des maximized this response variable (Figure 7b). Although it was not possible to establish a direct correlation between the adsorption variables in % desorption , positive correlation between T des and % desorption and negative correlation between (S/L) des were observed. The use of favorable conditions of T ads/des and (S/L) ads/des resulted in % desorption experimental values close to 35%, whilst the unfavorable results reached 10%.
Thus, the optimal conditions were determined: lower T ads (293 K), lower (S/L) ads (0.50 mg.mL -1 ), higher T des (323 K) and lower (S/L) des (0.20 mg.mL -1 ), which resulted in the q e and % desorption maximized values of 6.91 mg.g -1 and 35.25%, respectively. The results in consonance with the information from the response surfaces were validated experimentally, in which a q e close to 7.12 mg.g -1 e % desorption of 37.7% were  obtained. In relation to the results predicted, the deviations did not exceed 7%.
Since the experimental results are in agreement with those predicted by the optimized conditions, it was considered that the regression equations were adequate to describe the processes behavior and to optimize the evaluation variables.

Ni-OEP desorption cycles
The adsorbent regeneration capacity is an important factor to be evaluated when studying The subsequent adsorption-desorption cycles of CSAC allowed the evaluation of this material in the removal and recovery of Ni-OEP, according to the results of % removal , q e , % desorption and q des presented in Table IX.
By means of the data shown in Table IX, there was a reduction in the removal percentage and adsorption capacity of Ni-OEP on CSAC (% removal and q e , respectively), with an increase in the number of cycles. The most significant difference was observed after the second cycle, with a reduction of approximately 78% of % removal and q e values (% removal,3 rd cycle = 0.22% removal,2 nd cycle and q e,3 rd cycle = 0.22q e,2 nd cycle ). Despite the decrease in the variables associated with the adsorption of Ni-OEP on the CSAC surface, an increase in the porphyrin desorption percentage and capacity (% desorption and q des , respectively) was observed from each cycle, gradually. Therefore, there was the desorption of Ni-OEP molecules adsorbed in previous cycles, which provides a proper rationale for the % desorption values above 100% from the 3 rd cycle onwards. Probably, as the cycles progressed, the intensity of the adsorbent-adsorbent interactions decreased, favoring desorption. This effect, known as the carry-over effect, is a recurring problem in HPLC (High-Performance Liquid Chromatography) analyzes due to interference in quantitative results per run (Mitulovic et al. 2009). However, the results obtained at the end of the regeneration cycles showed that the carryover effects are favorable to the increase of the partial results obtained per cycle.
Considering the five cycles, 22.66 mg.g -1 of Ni-OEP were adsorbed, wherein approximately 77% (17.5 mg.g -1 ) of the adsorbed porphyrins were recovered. In similar studies, nickel is reasonably removed from adsorbent materials using elution systems composed of hydrochloric acid solution (Shahat et al. 2018. However, the acid-base elution was not considered in the present study due to the recovery of only the metal ion, keeping the free base porphyrin, which is of commercial interest, still adsorbed on the material.

Probable adsorption mechanisms
The knowledge of the possible mechanisms involved in the adsorption of Ni-OEP on CSAC can be facilitated with the assimilation of the interactions established between the porphyrinic molecules and the other constituents of the oil asphaltenic fraction or the organic fraction of the bituminous shales. Some authors suggest Considering the aromatic base structure formed by sp 2 hybridization carbons, which is common to all adsorbents used, it is likely that dispersive interactions of the type π-π have been established not only between metalloporphyrinic molecules but between Ni-OEP molecules and the CSAC basic structure. In addition, the polar functional groups present on the surface of activated carbon may have favored the formation of a greater intensity adsorbent-adsorbent interactions of the dipoledipole or acid-base type.
Dispersive acid-base interactions are likely to be identified between acidic oxygenated functional groups present on the surface of the CSAC and the basic nitrogenous regions of the porphyrin rings (Lee et al. 2017). Some authors highlight the importance of carboxylic groups in the establishment of interactions with nitrogen compounds, improving the adsorption performance 26 of these components on activated carbon (Almarri et al. 2009, Na et al. 2011. Dispersive interactions are also potentially established between the metallic center of porphyrin, which is acidic (Lee et al. 2017) and reactive (Gottfried 2015), and functional groups of basic character on the surface of the CSAC, identified in a similar proportion to the acid groups, according to the characterization performed by Ferreira et al. 2019.
The less energetic interactions, established during the formation of multiporphyrinic aggregates on the surface of the CSAC, were more easily broken during the desorption process with chloroform. However, the more intense interactions, characteristic of the formation of porphyrinic occlusions and reactive adsorption, were the greatest obstacles to desorption (Castillo & Vargas 2016, Derakhshesh et al. 2013. Part of the remaining amount of porphyrin on the activated carbon surface can be in the form of tectons, constituents of adlayers formed during the adsorption of octaethylporphyrins on graphitic based surfaces (Hipps & Mazur 2018, Ogunrinde et al. 2006. The initially lower values of % desorption may be associated with the difficulty of breaking the most energetic interactions, which is partially reduced by the application of higher T des values and the successive adsorption cycles. The separation of petroporphyrin compounds can be facilitated by preventing the formation of occlusions (Fan et al. 2020).
In addition, the significative recovery of adsorbed and adsorbent materials allows the evolution of separation methods aiming the environmental and financial sustainability of the process. The recovered porphyrins can be used as an alternative to their synthetic counterparts in the catalytic area, while the activated carbon can be reused in new adsorption-desorption cycles. The low rate of waste generation as well as the reuse of materials and minimization of input consumption are pillars of the circular economy (Henckens et al. 2016, Londoño & Cabezas 2021.

CONCLUSIONS
The performance of Ni-OEP adsorption tests on different adsorbents and the execution of the qualitative and quantitative experimental plans allowed the selection of conditions that favor the highest q e and % desorption values. The most efficient adsorbent in removing metalloporphyrin from an initial solution with toluene was CSAC. The likely rationale for this outcome is due to the combination of its favorable surface characteristics: greater functionalization, developed micropore structure and higher values of specific surface area and pore volume. It is possible that the fraction of the adsorbed porphyrin was desorbed due to the establishment of less intense π-π type adsorbate-adsorbate interactions, whereas the more intense adsorbate-adsorbent interactions occurred by virtue of acid-base reactive adsorption characteristics, keeping part of the molecules of Ni-OEP still in the adsorbed state.
T h e co n d i t i o n s fo r s i m u l ta n e o u s maximization of the evaluation variables (q e and % desorption ) were: toluene as a solvent, chloroform as a diluent, lowest T ads (293 K), lowest (S/L) ads (0.5 mg.mL -1 ), lowest (S/L) des (0.2 mg.mL -1 ) and greatest T des (323 K), considering the preestablished conditions. The regression equations obtained, and the optimization results were adequate to the adsorption and desorption experimental data of the Ni-OEP behavior.
The results of optimized adsorption capacity and desorption percentage were reproduced in the first adsorption-desorption cycles, indicating the reproducibility of the processes under optimal conditions. At the end of the 5 cycles, approximately 77% of the Ni-OEP adsorbed on CSAC were recovered. The results obtained show the potential of study of carbonbased materials and experimental conditions in the recovery of porphyrin compounds from real oils and bituminous shales. Materials with structures similar to asphaltenic components could be interesting due to the possibility of formation of porphyrinic aggregates by π-π interaction and consequent facility of recovery of the materials.