Copper Removal by Acid-Conditioned Zeolite, Part I: Equilibrium, and Numerical Simulations

Heavy metal water pollution is one of the most pressing environmental problems of the last decades. Wastewater from many industrial processes contain high concentrations of metals and have very acid pH. Thus, technologies to remove heavy metals from aqueous solutions are costly or suffer deterioration when in contact with substances with acid pH. Natural zeolites have demonstrated to be a low-cost heavy metal adsorbent. This study aimed to determine basic parameters for efficient copper removal by aluminosilicates. A Zeolite was conditioned with concentrated H2SO4 to further develop the experiments to test 12 equilibrium isotherms (Freundlich, RedlichPaterson, Sips, Halsey, Dubinin-Radushkevich, Flory-Huggins, Langmuir, Temkin, Elovich, Fowler-Guggenheim, Henry's and Kiselev) and pHpzc. Maximum removal was obtained with neutral pH values; the Freundlich model had the best performance. The removal efficiency increased as the initial concentration of the solution increased. The pH value at the point of zero charge was 2.9.

are in contact with the zeolite pores (S. Wang & Peng, 2010b). An acid treatment to a zeolite, which supplies H + , causes a partial rupture of the Al-O-Al and Al-O-Si bonds through the dealuminization, as indicated by lower Si/Al ratios, with this it is suggested that the Al-O-and Si-O-dealuminizated bonds are potential ion exchange sites (Paul, Dynes, & Chang, 2017). Zeolites can be modified by means of treatments such as chemical attacks. An acidic treatment can improve its adsorption capacity and expand its pore system. Acid attack dealuminizes the structure because it attacks and weakens Al-O bonds, causing defects and vacancies in the skeleton. These treatments increase the size and quantity of the zeolite pores, increasing the surface area and adsorption capacity. Acid treatment can be used as a simple and economical method to increase the adsorption capacity of natural zeolites (X. Wang, Ozdemir, Hampton, Nguyen, & Do, 2012). The drainages produced by mining are usually very acidic pH, which can have an effect on the crystalline structure of zeolites; therefore, it is important to know the degree of affectation of the adsorption capacity of a zeolite (Clinoptilolite) once it has been put in contact with a solution with extreme acidic pH values. Solution pH affects both the adsorbent aqueous chemistry and surface binding sites (Demiral & Güngör, 2016). The objective of this study was to determine the basic design parameters of a treatment process for copper removal and the degree of affectation of the adsorption capacity after acidconditioning.

Reagents
All the reagents used for the preparation of the standard solutions were made with reactive grade products. The Cu(II) standard solution was prepared with Penta Hydrated Copper Sulphate (CuSO4 · 5H2O).

Preparation of the adsorbent material
For this study, a mineral zeolitic material extracted from a deposit that is located in the vicinity of the city of Aldama, Chihuahua, Mexico (28 ° 48 '36 "N, 105 ° 54' 3.0" W) was used. The samples were crushed and passed through a metal sieve. The material that went through a No. 10 mesh (U.S. STD. Sieve), with an opening of 2 mm was used for the study. The samples were conditioned by an immersion in concentrated sulfuric acid (H2SO4) for 24 hours, after conditioning they were decanted and washed with distilled water and dried in an oven.

Methodology
All laboratory material was presoaked with 5% HNO3, then rinsed with distilled water and dried in the oven at 106 0 C. The batch tests were carried out in a 150 mL Erlenmeyer flask and mixed in an oscillatory shaker. Adsorption experiments were carried out in triplicate at a constant agitation speed. 3 g of zeolite with a variation no greater than +/-0.005 g was added to 100 ml of the solution of known concentration. The pH values were adjusted with HNO3 and NaOH 0.1 N according to the case and with the necessary amount until the desired pH value was adjusted. Once the test was finished, the samples were separated on Number 1 Whatman filter paper. The concentration of residual metals was measured by ICP-OES Perkin Elmer OPTIMA 8300. The percentage of removal was calculated with the following expression: (1) = * (2) 2.5 Sorption Studies 2.5.1 Effect of the pH of the solution A 7-level, 3-repetition one-way experimental test was performed. The pH values used were 2, 3, 4, 5, 6, 7 and 8. To 100 mL of solution at 50 mg L -1 Cu(II) concentration 6 g of the adsorbent material was added and the mixture was stirred for 24 hours to ensure that the equilibrium was reached. 2.5.2 Maximum Sorption Capacity A constant mass of 3 g of zeolite was used in a volume of 100 mL of a solution containing a specific concentration.
The pH value was adjusted to the optimum range obtained in concentration diagram of copper species in aqueous solution, the range was 4.0-4.5. A 5-level, 3-repetition one-way experimental test was performed to observe the reproducibility of the results; the average value obtained in this procedure was used. The concentrations used for each metal were 50, 100, 150, 200 and 250 mg L -1 . The agitation time was 24 hours. The pH was adjusted to the range 4.0-4.5.

Determination of pHpzc
The pH value at which the net surface charge was zero is known as pHPZC. At pH < pHpzc, the zeolite surface has a net positive charge, while at pH > pHpzc the surface has a net negative charge (Al-Degs, El-Barghouthi, El-Sheikh, & Walker, 2008a;Chutia, Kato, Kojima, & Satokawa, 2009;Fiol & Villaescusa, 2009;Mohammadian, Rabieh, & Zavvar, 2018). The knowledge of point of zero charge of the studied materials provides information about the possible attraction and repulsion between sorbent and sorbate (Fiol & Villaescusa, 2009). For the determination of the pH at the point of zero charge (pHpzc) the equilibrium batch method was used, also known as the conventional method (Kalhori, Al-Musawi, Ghahramani, Kazemian, & Zarrabi, 2017;Zavareh, Farrokhzad, & Darvishi, 2018). A series of solutions of NaCl 0.1M had their pH value adjusted in a range between 2 to 11 by adding diluted HNO3 or NaOH. The exact value of each of the solutions is called the initial pH (pHi). A sample of the zeolite (0.2 g) was weighed and added to a volume of 100 mL of the aforementioned solutions. The suspensions were shaken for 48 hours at room temperature to ensure their complete equilibrium. Once the agitation was finished, the samples were filtered to separate the adsorbent and the liquid phase; the final pH value (pHf) was quantified.
The pHpzc is the point where the curve of pHf versus pHi intersects the plot line pHi = pHf (Al-Degs, El-Barghouthi, El-Sheikh, & Walker, 2008b;Mourid, Lakraimi, El Khattabi, Benaziz, & Berraho, 2017;Sun, Zhang, Wang, & Wu, 2013;Tabassi, Harbi, Louati, & Hamrouni, 2017 Where: n is the data number, qi,cal are the equilibrium values calculated with the mathematical expression (mg g -1 ) and qi,exp are values obtained experimentally (mg g -1 ) (Demiral & Güngör, 2016;Rajabi et al., 2016;Rangabhashiyam, Anu, Giri Nandagopal, & Selvaraju, 2014). An average relative error lower or equal than 5% was considered adequate. 2.5.4.2 Chi-square ( 2 ) To identify the best fitted isotherm model, we examined the linear Chi-square values (2) along with the linear regressions (R 2 ). The Chi-square statistical test is basically the sum of the squared errors of the differences between the experimental data and the data obtained by calculations using the models. Each square difference is divided by the corresponding data obtained by calculations using the models. If the values obtained using a model are similar to the experimental values, the value of 2 will be very small and close to zero. High values of 2 imply a high bias between the experiment and the model. Therefore, analyzing the data set of the Chi-square test possibly confirms the isotherm that best fits the Sorption system. The mathematical expression of the Chi-square test is explained below (Tran, You, & Chao, 2016).
If values 2 ≤ 0.05 between the experimental data and the data obtained by calculations using the models then they have a statistically significant association.

Effect of pH and pHpzc
The pH value at which the net surface charge is zero, is known as pHPZC. When pH < pHpzc, the zeolite surface has a net positive charge, and when pH > pHpzc the surface has a net negative charge (Al-Degs et al., 2008b;Chutia et al., 2009;Fiol & Villaescusa, 2009;Mohammadian et al., 2018). The pHpzc is the point where the curve pHfinal vs pHinitial intersects the line pHinitial = pHfinal (Al-Degs et al., 2008b). The knowledge of point of zero charge of the studied materials provides information about the possible attraction and repulsion between sorbent and sorbate (Fiol & Villaescusa, 2009). The point of zero charge is the pH at which the surface of adsorbent is globally neutral, i.e., contains as much positively charged as negatively charged surface functions. Below this value, the surface is positively charged; above this value, it is negatively charged. So normally, it is always easier to adsorb a cation on a negatively charged surface, and an anion on a positively charged surface. However, other interactions may be stronger than purely electrostatic forces, making the effect of surface charge not so important. Additionally, a cation is often complexed with ligands, some of them being possibly negatively charged. Therefore, in such a case, the cation is in fact a negative complex, which may adsorb very well on a positively charged surface. The surface chemistry of any material is determined by the acidic or basic character of their surface. It knows that acidic means a positive surface charge and basic means negative surface charge. So, it is very important to know the surface charge of the material in the aqueous media, especially in adsorption studies because a high surface area material may be produced but if the surface charge of the material is opposite to adsorption due to the fact of being the same charge as the adsorbate, then the pH conditions must be modified and pH conditions that show the best adsorption must be found. The pH at which the surface charge of the material is zero in the aqueous media must also be found, or in other words the pHpzc (pHpoint of zero charge) of the adsorbent material. To determine pHpzc or the pH where the surface charge of the adsorbent material is zero, the pH drift method was used, which graphs the final pH (y axis) vs Initial pH (x axis). The pH is an important factor for the sorption process (Ben-Ali, Jaouali, Souissi-Najar, & Ouederni, 2017;Zanin et al., 2017). To determine the range of values where copper sorption was favored, tests were carried out in batches maintaining constant the temperature, stirring, contact time, metal concentration, and adsorbent dose. Figure 1 shows the removal efficiency (%) and quantity of sorbed Cu(II) per gram of zeolite versus pH. The pH value that reached the highest copper removal was 7, but it is important to emphasize that the values of removal obtained with the values of pH 6, 7 and 8 do not present significant differences from the statistical point of view with a value of significance of 5%. According to a diagram of pHdependent copper species, it is observed that copper at a pH value ≥5.5 begins to precipitate, whereby the removal of the copper is done by the precipitation of the same; it is necessary to take care that its precipitation is not quantified as a removal by adsorption. When the pH range was between 2-5, the removal capacity remained very low and there were very slight increases in the removal, but an abrupt increase was observed when the pH value increased to 6. The low removal capacity at low values pH may be due to a competition between hydrogen ions and metal ions for the same sorption sites (Ben-Ali et al., 2017;Demirbas, 2009). When alkaline pH values were achieved, the sorption capacity decreased with respect to the values obtained in the neutrality. At high pH values, sorption decreased since the exchange sites were not activated under basic conditions (Hossain, Ngo, Guo, & Nguyen, 2012). In our results, the pH value at which the maximum removal is achieved is the neutral, remaining practically constant with increasing pH, this behavior agrees with the findings of by Abdel Salam et. al. (2011), since in their study the sorption capacity remained constant, although the pH value increased. Previous studies (Hossain et al., 2012;Ltaief, Siffert, Fourmentin, & Benzina, 2015) found that the removal of this metal reached its maximum sorption in neutral values and decreased with increasing pH values, which is contrary to what was in this study. Ksakas et. al. (2018) found that the pH at which the maximum sorption was achieved was placed in 6 units. Hesnawi et. al. (2017) concluded that the elimination efficiency for copper increased strongly from 7% to 99% in a pH range of 2.0 to 7.0, and then no further elimination was observed at a pH higher than 7.0, our results observed that the removal was directly proportional to the increase in the pH value, staying unaltered by increasing the pH. Kocaoba et. al. (2007) found that at a pH value of 6, the removal of copper was 88.9% and in this study for that same pH value the removal was 95.89%. Zanin et. al. (2017), conducted an assay to remove copper from an effluent of the graphic printing industry by means of zeolites, removing 96% at a pH of 4.0, in the present study at that pH value only 33.18% was removed, but at a value of 7, 96.88% was removed; the variations were attributed to the difference of the liquid matrix from which the metal in question is adsorbed. Wang et. al. (2008) found that the maximum sorption capacity was reached at a pH value of 7, coinciding with the findings of this study. Figure  2 shows the determination of pHpzc. From this figure the value of pHpzc = 2.9 was obtained. In a previous study, the pHPZC value in a zeolite was determined after an acid treatment was performed and the value decreased from 7.9 without treatment to 2.7 with treatment (Valdés, Tardón, & Zaror, 2010). The electrical charge of the natural surface of the zeolite depends on the permanent negative charge of its aluminosilicate structure, due to the isomorphic substitution of aluminum (Al +3 ) by silicon (Si +4 ) and the pH of the solution, which influences the protonation/deprotonation of the superficial functional groups. The modification of the functional groups of the surface by chemical pretreatment of the raw ore can change the value of pHpzc (Mitrogiannis et al., 2017).

Amount of Cu(II) sorbed and removal efficiency (%) on the zeolite at different initial concentrations
The amount of copper removed per unit mass of adsorbent increases as the initial concentration increases, this since the amount removed is given as a function of the initial and final concentrations; if increasing these amounts, but keeping the amount of adsorbent constant, is reflected in an increase in the amount of sorbed metal ion per unit mass of the adsorbent, however, the percentage of removal decreases this because there are no more surface exchange sites of the adsorbent, this behavior was similar to that presented by Abdel Salam et. al. 2011. Figure 3 shows the amount of copper sorbed and the removal efficiency by the zeolite at different initial concentrations of the same metal.

Sorption Isotherms
The equilibrium data, which are generally known as sorption isotherms, are the main requirement for the understanding of the sorption mechanisms. The sorption isotherms are important to describe how the adsorbate molecules or ions interact with superficial adsorption sites. Therefore, the correlation of the data in equilibrium using either a theoretical or empirical equation is essential for adsorption interpretation and prediction (Demiral & Güngör, 2016). Adsorption isotherms are expressed in an equation in which the relationship between the amount of the solute adsorbed by the adsorbent and the concentration of the solute in the liquid phase, they are important because they describe how an adsorbate interacts with an adsorbent and these are critical for the design of an adsorption process. Several isotherm models have been developed to describe the relationship of the metal concentration that has been adsorbed on the solid phase with metal concentration in the solution in equilibrium for a specific temperature ( In almost all adsorption studies of metals with zeolites, Freundlich and Langmuir were the isotherms models used (Abdel Salam et al., 2011;Erdem, Karapinar, & Donat, 2004;Hesnawi, R. Jamal, F. Eswayah, A. Maga, 2017;Kocaoba, Orhan, & Akyüz, 2007;Ksakas, Tanji, El Bali, Taleb, & Kherbeche, 2018;Ltaief et al., 2015;Merrikhpour & Jalali, 2013;Panayotova, 2001;Sprynskyy, Buszewski, Terzyk, & Namiesnik, 2006;Taamneh & Sharadqah, 2017;Zanin et al., 2017) which are the most often used to predict the maximum adsorption capacity (Moussout, Ahlafi, Aazza, & Maghat, 2018). 3.3.1 Henry's isotherm This isotherm model appropriately describes the adsorption process for low concentrations, such that none of the adsorbate molecules have interaction with adjacent molecules (Ayawei, Ebelegi, & Wankasi, 2017). The concentrations in the phases are related to a linear expression. It is expressed with: ( = 0 12 3 ( (5) Where: qe is the quantity of Cu(II) ions sorbed per gram of zeolite (mg g -1 ); KHE is the equilibrium constant of Henry's and Ce is the equilibrium concentration of the metal ions in the solution (mg L -1 ). Figure 4 shows the graph of Henry's model, the value of R 2 , %ARE and  2 are not satisfactory ( Table 1). The results indicate that the copper adsorption does not present a linear behavior.  (7) The values of the constants qm and KL are defined by the slope and the intercept point of the adjusted line of graphing on the Ce abscissa and ordinates Ce/qe respectively (Fardjaoui, El Berrichi, & Ayari, 2017;Kankrej, Kulkarni, & Borhade, 2017;Subramani & Thinakaran, 2017;Y. Wu & Wang, 2016;Zhang, Jin, Shen, Lynch, & Al-Tabbaa, 2018).
The characteristic of the Langmuir isotherm is that it can express a dimensionless constant called Equilibrium Parameter or Separation Factor, which is expressed with the following equation: : = ; 7'4 5 .< Where: RL is the equilibrium parameter.
The RL values indicate what type of adsorption can be expected. RL1 is unfavorable, RL = 1 the adsorption is linear, RL = 0 is irreversible and 0RL1 is favorable for adsorption (Humelnicu, Băiceanu, Ignat, & Dulman, 2017;Zendelska, Golomeova, Blazev, Krstev, & Golomeov, 2014). Figure 5 shows the graph for the Langmuir model. The value of R 2 is adequate but the values of %ARE and  2 are high ( Table 1), this model is not very suitable for copper adsorption. With respect to RL the values indicate that the adsorption is favorable but the value is near to zero which indicates a possible irreversibility of the adsorption. The values of the Langmuir KL and qm constants observed in the results of this study and in Panayotova, 2001, are in the same range, not presenting significant differences. For this isotherm model Ksakas et. al. (2018) present very significant differences that could be attributable to the physical-chemical characteristics of the materials. The maximum adsorption capacity obtained using the Langmuir model by Wang, et. al. (2008), (23.3 mg Cu(II) g -1 of zeolite) is higher than the 9.08 mg Cu(II) g -1 of Zeolite obtained in the results of this study but is within the range of results presented in previous studies. Inglezakis et. al. (2016) determined that the equilibrium of copper in a Zeolite was not favorable being perimetrally opposed to the results of this study. (9) Where: KF is the Freundlich constant in (L g -1 ) and nF is the Freundlich exponent related to the intensity of adsorption; is dimensionless. The equation of this model can be linearized as follows: @ = @ 0 = 9 ? @ 3 The values of the constants (KF and nF) are defined by the intercept and the slope of the graph line in the ordinate ln qe and in the abscissa ln Ce respectively. The range of values of 1/nF is between 0 and 1 showing the degree of non-linearity between the concentration of the solution and the adsorption. If the value of 1/n is equal to 1, the adsorption is linear (Fardjaoui et al., 2017;Kankrej et al., 2017;Subramani & Thinakaran, 2017;Y. Wu & Wang, 2016;Zhang et al., 2018). In this case the results show non-linearity on the adsorption onto zeolite. Figure 6 shows the graph for the Freundlich model. The value of R 2 is excellent, this model being the one that presents the best fit, with which we can express the existence of a heterogeneous adsorption on the surface of the Zeolite. The values of the suitability coefficients (Table 1) %ARE and  2 are very low which indicates a high correlation between the results obtained experimentally and those that calculated from the models. Hesnawi et. al. (2017) affirmed that if the value of the Freundlich constant was such that 0.1<1/n<1, adsorption was considered favorable, for both studies it was determined that the adsorption was favorable, but there are significant differences between the numerical values of 1/nF in both studies. Taamneh and Sharadqah (2017) and Ksakas et. al. (2018) found that the values of the constant 1/nF of the Freundlich model and the one observed in this investigation are in the same range but the value of the constant KF presents very different values among the aforementioned investigations. Erdem et. al. (2004) expressed that if the value of the Freundlich constant nF was between 2 and 10, good adsorption was shown, in this investigation the value of said constant was 2.85, which can be said to be a good adsorption. The value of the Freundlich constant KF, in this research and in Erdem, et. al. (2004) do not present significant differences. Figure 6. Freundlich Isotherm Model for Cu(II) onto Zeolite 3.3.4 Temkin isotherm The Temkin isotherm model contains a factor that explicitly considers the adsorption interactions between the species and the adsorbate. This model assumes that: (i) the adsorption heat of all the molecules in the layer decreases linearly with the coverage due to adsorbent-adsorbate interactions, and (ii) the adsorption is characterized by a uniform distribution of the binding energies, up to maximum binding energy (Demiral & Güngör, 2016;Kankrej et al., 2017;Subramani & Thinakaran, 2017;Zhang et al., 2018). The Temkin isotherm model is presented in linear form with the following equation: Where: B = RT / bT, KT is the Temkin Binding Equilibrium Constant (L mg -1 ), R is the universal gas constant (8.314 x 10 -3 KJ mol -1 o K -1 ), T is the absolute temperature o K, bT is the constant of the isotherm, which is related to the adsorption heat and B gives the adsorption heat (J mol -1 ). The Temkin isotherm model is presented in linear form with the following equation: = A B 0 C 9 A B 3 (12) To obtain the constants B and KT that are defined by the slope and the intercept respectively of the straight line of graphing qe in the ordinates and abscissas Ln Ce. Figure 7 shows the graph for the Temkin model. The value of R 2 is high, although not comparable with other models and the values of %ARE and  2 (Table 1) are high, so the correlation between the experimental and calculated data is not very convenient.
Where: qe is the quantity of ions sorbed in mol per gram of zeolite (mol g -1 ), qs is the saturation capacity of the isotherm (mol g -1 ), βD-R is the Dubinin-Radushkevich constant (mol 2 0 K -1 J -2 ) and ε is correlated with the following expression: The magnitude of E is used to estimate the type of adsorption process. The adsorption process is a chemical ion exchange if the magnitude of E is between 8 and 16 KJ mol -1 . If the value of E is greater than 16 KJ mol -1 it is mainly a diffusion. In turn, when the magnitude of E is less than 8 KJ mol -1 , the type of adsorption can be defined as a physical process (Demiral & Güngör, 2016;Kaveeshwar et al., 2018;Rajabi et al., 2016). Figure 8 shows the graph for the Dubinin-Radushkevich model. R 2 , % ARE and  2 presented adequate values, but below other models. The value of E ( The constants of the Redlich-Paterson isotherm can be determined from graphing between Ce/qe versus Ce β RP. However, its application is very complex since it includes 3 unknown parameters αRP, KRP and βRP. Therefore, a minimization procedure is adopted to obtain the maximum value of the coefficient of determination R 2 , between the theoretical data for qe obtained from the linearized form of the Redlich-Peterson Isotherm equation and the experimental data (Benzaoui et al., 2017). By trial and error, values of  are adopted to obtain an optimal line. In the specific range, the values of  are limited and it is easy to obtain the correct value (F. C. Wu et al., 2010). Figure 9 shows the performance of Redlich-Peterson Isotherm model. Using Microsoft Excel, a mathematical algorithm was used to maximize the value of R 2 , obtaining a maximum value of 0.99978 with a value of the coefficient βRP = 0.651, this value explains the deviation of the Langmuir model, since when this value approaches 1 it is the same as the Langmuir model. The values of %ARE and  2 ( Table 1) are adequate. The use of this model validates what was obtained by the Freundlich model. The ratio of KR/αR indicates the adsorption capacity of the monolayer (Kaveeshwar et al., 2018), in this case it is much lower (1.82 mg Cu g -1 Zeolite) than that obtained by the Langmuir model (9.08 mg g -1 ) which corroborates for that the type of adsorption Freundlich is the best suited.

.7 Sips Isotherm
The Sips isotherm is a combined form of Langmuir and Freundlich isotherms applied for the prediction of heterogeneous adsorption systems. The Sips model avoids the inconveniences and limitations of the Langmuir or Freundlich models. At low concentrations, the adsorbate becomes Freundlich's isotherm and, therefore, does not obey Henry's law (Vijayaraghavan, Padmesh, Palanivelu, & Velan, 2006). At high concentrations the Sips isotherm is reduced to the Langmuir isotherm (Dlugosz & Banach, 2018). The equation of the Sips isotherm is characterized by containing a dimensionless heterogeneity factor, βs. If βs = 1, the Sips equation is reduced to the Langmuir equation, which indicates that the adsorption process is homogeneous. The constant of isotherms of Sips (βs) confirms whether the surface of the adsorbent is of heterogeneous nature or not (Sogut & Caliskan, 2017). The Sips isotherm is expressed with the following equation: Where: Ks is the equilibrium constant of the Sips isotherm (L mg -1 ), as is the maximum adsorption capacity (mg g -1 ) and βs is the model exponent (dimensionless). The linear form of the Sips isotherm is: B' . = O\ B'3 . 9 B'0 ] N \ .
(21) The coefficients of the Sips isotherm are calculated plotting ln (qe) versus ln (Ce), where βs is the slope (Dlugosz & Banach, 2018;Foo & Hameed, 2010;Vijayaraghavan et al., 2006). A rearrangement of the Sips equation can be expressed as follows: It should be plotted ln (Ce) versus ln (qe) and the inverse of the slope will be βs and the inverse Ln of the intercept will represent Ks (Hamdaoui & Naffrechoux, 2007b;Kaveeshwar et al., 2018;Sogut & Caliskan, 2017). Another linear form of this isotherm is expressed as follows: The coefficients of the equation may be calculated graphing Ln(Ks/qe) versus Ln(Ce) (Foo & Hameed, 2010). Figure 10 shows the performance of this model. Table 1 shows the results of R 2 , % ARE and  2 which are very good. For this model, the exponent βs is numerically the same as the exponent n of the Freundlich model, in the same way the numerical values of the constants of Freundlich and Sips are equal, with which the heterogeneous adsorption is corroborated. Wang et. al. (2008) for its study used concentrations not higher than 50 mg L -1 Cu(II), which can be considered low concentrations, and at low concentrations the Sips isotherm becomes the Freundlich model (Vijayaraghavan et. al., 2006), for this reason, the Freundlich coefficients 1/n obtained in the results of the present study are very similar to the coefficient n of the Sips model calculated by Wang, et. al. (2008). The constants of the isotherm may be calculated graphing ln (qe) versus ln (1/Ce) and from the straight line obtained, the slope is nH and the intercept represents KH (Kaveeshwar et al., 2018). Figure 11 illustrates the performance of this model. The values of R 2 , % ARE and  2 are excellent (Table 1), with which it may be affirmed that the adsorption of copper is in multilayers and the ions are relatively far from the surface.

Harkins-Jura isotherm
The Harkins-Jura model describes a multilayer adsorption and the existence of a heterogeneous distribution of the pores of the surface of the adsorbent. The model is defined with the following expression: Where: BHJ is a model constant and AHJ is another model constant. Graphing 1/q 2 e versus log(Ce) the model constants are calculated with slope AHJ and intercept BHJ (Kaveeshwar et al., 2018). Figure 12 shows the performance of this model. Although the value of R 2 is 0.94, which indicates a high correlation, the values of % ARE and  2 are very high (Table 1), indicating that there is no adequate correlation between the data obtained experimentally and those calculated with this model. Considering the results of the Halsey model and the R 2 value of this model it is affirmed that the adsorption is in multilayers, but the pore distribution of the adsorbent is not heterogeneous.
Where: qm is the maximum adsorption capacity of Elovich (mg g-1) and KE is the equilibrium constant of Elovich (L mg -1 ). KE and qm are calculated from the intercept and slope respectively of the straight line of ln (qe/Ce) versus qe (Ayawei et al., 2017;Farouq & Yousef, 2015;Kaveeshwar et al., 2018;Rangabhashiyam et al., 2014). Figure 13 illustrates the performance of this model. The value of R 2 is convenient but the values of % ARE and  2 are high (Table 1) discarding the suitability of this model. The maximum adsorption capacity of this model is well below that obtained by the Langmuir model.
The linear form is expressed: @ e f = @ 0 =1 9 B =1 @'1 N g. Where: KFH is the equilibrium constant of Flory-Huggins (L mg -1 ), nFH is the exponent of the model and θ is the coverage parameter of the adsorbent surface. The constant KFH can be used to calculate the spontaneity of Gibbs free energy (Rangabhashiyam et al., 2014). For its calculation is used the following equation (Foo & Hameed, 2010): hi = K B 0 =1 (31) For the calculation of the isotherm parameters, log θ/C0 versus log (1-θ) should be plotted, where the slope and the intercept represent nFH and KFH respectively. Figure 14 presents the graph for this model. This model expresses the degree of coverage of the adsorbate on the surface of the adsorbent, the coverage values θ range from 0.966 to 0.77 and these values vary inversely proportional to the initial concentration of the adsorbate. nFH is the number of adsorbates that are occupying the adsorption sites (Ayawei et al., 2017), therefore according to the results ( Table  2) a limited number of adsorbates are found in the adsorption sites.  Table. 2. Isotherm model constants and correlation coefficients for Cu (II) adsorption onto Zeolite 3.3.12 Fowler-Guggenheim Isotherm It is one of the simplest equations that consider the lateral interaction of the adsorbate molecules. Its general form is expressed below:    Vol.9, No.3, 2019 between the molecules of the adsorbate (KJ mol -1 ) (Farouq & Yousef, 2015;Hamdaoui & Naffrechoux, 2007a).
The parameters of the equation are calculated by graphing ln [Ce(1-θ)/θ] versus θ. From this straight line the intercept and the slope represent KFG and W respectively.
The charge and heat of adsorption vary linearly. When the values of W are greater than zero, it indicates that the interaction between the adsorbate molecules is attractive, but if the values of W are negative, the interaction is repulsive; if W = 0 there is no interaction (Farouq & Yousef, 2015). As shown in Table 2, the value of W was -33,430, indicating a repulsive interaction between the adsorbed molecules, and showing a decrease in the adsorption heat. The values of R 2 are close to 0.95, which shows a good correlation, but the suitability between the experimental data and those calculated with the model are not acceptable since the values of %ARE and  2 are very high. Figure 15 shows the performance of this model. When plotting lnqe versus Ce, the slope and the intercept are KJ and qm respectively. Figure 16 shows the performance of this model. The value of R 2 is low compared to the other models studied and the values of %ARE and  2 are high ( Table 2). The results indicate that adsorption by a monolayer was not feasible.  Vol.9, No.3, 2019 3.3.14 Kiselev Isotherm This model is known as the model of the localized monomolecular layer and is only valid when θ ≥ 0.68. Its linear expression is: = 0 e 9 0 0 (36) Where: Ki is Kiselev constant (L mg -1 ) and Kn is the equilibrium constant of complex formation between the molecules of the adsorbate. Constants are calculated by plotting 1/[Ce*(1-θ)] versus 1 / θ where the slope and the intercept represent Ki and Ki*Kn respectively (Ayawei et al., 2017). Figure 17 illustrates the performance of this model. The use of this model is valid since the lower value of θ was 0.77 but the values of R 2 , % ARE and  2 ( Table 2) are unacceptable. This model does not describe in any way the behavior of the adsorption for this study.

Isotherms, and Maximum Adsorption Capacity
Merrikhpour and Jalali (2012) (Merrikhpour & Jalali, 2013) made a summary of previous studies on the adsorption of copper by Zeolites and found that this was in the range of 0.69 to 12.7 mg Cu(II) g -1 Zeolite; in this study it was 9.08 mg Cu(II) g -1 Zeolite. This value is within the range of previous studies. The adsorption capacity in this study was superior to that reported in studies reviewed by the aforementioned authors. Hesnawi et. al. (2017) (Hesnawi, R. Jamal, F. Eswayah, A. Maga, 2017 found that the maximum adsorption capacity obtained by means of the Langmuir model for copper was 1.08 mg g -1 of zeolite, being very low compared to that obtained in this study, but Taamneh and Sharadqah (2017) reported a value of 14.3 mg Cu(II) g -1 of zeolite, this being the highest value reported. Atkovska et. al. (2018) (Atkovska, Lisichkov, Ruseska, Dimitrov, & Grozdanov, 2018) made a summary of several studies of the removal of copper by natural zeolites and concluded that these removed 75% of this metal, which is low in comparison with what was found in this study since the maximum adsorption stood at 96.15%. In the present study it was observed that increasing the temperature increased the adsorption of copper, which is consistent with what was observed by Panayotova (2001). The effect of temperature is a significant physicalchemical parameter, since temperature can change the capacity of adsorption. If the capacity of adsorption increases with increasing temperature, the adsorption process is endothermic (Al-Degs et al., 2008b;Santos et al., 2017;Yagub, Sen, Afroze, & Ang, 2014). This may be due to the increased mobility of the adsorbate molecules and a possible increase in the number of exchange sites (Malamis & Katsou, 2013;Yagub et al., 2014). The adsorption isotherms show how the adsorbate interacts with the adsorbent and how equilibrium is reached. According to the models used in this study it can be concluded that the interaction between adsorbent and adsorbate does not exhibit a linear behavior, as expressed with Henry's model, since experimental data with this model do not have good correlation. The adsorption surface is not homogeneous and the sorption process is not performed in a monolayer, as formulated in the Langmuir model; but it can be expressed as a heterogeneous process with an exponential distribution of its active sites and their adsorption energies, as demonstrated with the Freundlich model. The results obtained with the Freundlich model validate the non-linearity observed with the Henry's model, since the Freundlich model also shows a lack of linearity and this model was the one that presented the best correlation (R 2 =0.999) of all the models used in this study. The Freundlich model explains in an excellent way the process observed in the laboratory tests. The Temkin constant, bT, which is related to the heat of sorption, presented low values (lower than 8 KJ mol -1) which indicates a weak interaction between the adsorbent and the adsorbate, which suggests an ion exchange sorption process. The results achieved with the Dubinin-Radushkevich model confirm and validate what was derived of the Temkin constant, namely that an ion exchange was performed, since the magnitude of the constant E derived from the Dubinin-Radushkevich model also indicate an ion exchange. The results obtained from the Redlich-Peterson model confirm that the data fit better to what is mentioned in the Freundlich model, more than what was observed in the Langmuir model. With the use of the coefficient of the Redlich-Peterson model it was found that the calculation of the Freundlich coefficient was adequate, since according to the relationship (1-βRP)=1/nF, the experimental results were validated, and the results obtained in both exponents are significantly the same. In order to confirm a heterogeneous adsorption shown with the Freundlich model, the Sips model was used, showing a perfect analogy between the Sips coefficient (βs) and the Freundlich model exponent, with which the heterogeneous sorption process is validated. The Halsey model presents a good correlation (R2=0.999) with the values obtained experimentally, which suggests that the adsorbent material has a heterogeneous nature in its pores and its active sites, in addition to a multilayer adsorption. With the Harkin-Jura model a good correlation (R 2 =0.94) with the experimental data was observed; therefore, the existence of a multilayer adsorption and of a pore distribution on the surface of the heterogeneous adsorbent is suggested. With the use of the Elovich model, the multilayer adsorption is reaffirmed, taking into account that the experimental data present a good correlation (R 2 =0.96). With the use of the last three mentioned models it can be concluded that the adsorption process is carried out in multilayer, with a heterogeneous distribution. The Flory-Huggins model was used in order to know the characteristic degree of surface coverage of the adsorbent by the adsorbate. The processes of general coverage indicate that 15% of the binding sites on the surface of the adsorbent were covered by metal ions during the sorption process. The Fowler-Guggenheim model was selected to determine what type of lateral interaction between the adsorbate molecules would be manifested. According to the results of this model, it follows that there is a lateral repulsion between the molecules of the adsorbate. The model Javanovic had a poor fit to the experimental data, therefore, the assumptions made in this model are discarded, and an approximation to a localized sorption in a monolayer is not feasible, which again validate the experimental observations in the Freundlich model of a heterogeneous sorption. This model also expresses that there is no interaction between molecules, which is discarded and confirms the interaction expressed in the Fowler-Guggenheim model. The Kiselev model clearly shows a very low correlation with the experimental data, whereby a sorption is discarded by means of a localized monomolecular layer. (52) Where: t is time, c is concentration, D tensor of the dispersion coefficient and v speed vector (Auset & Keller, 2004;Sahimi, 2011;Zheng & Bennett, 2002). The general transport model incorporates 3 processes: • Advection. Driven by the flow of the liquid. • Dispersion. Caused by the heterogeneity of the material. • Adsorption. The main parameter is the adsorption coefficient KD (Zheng & Bennett, 2002)  Where: KD is the adsorption coefficient (length 3 mass -1 ), ρ is the density (mass length -3 ), η porosity of the material (dimensionless), c concentration (mass length -3 ), t time (time),ν fluid velocity (length time -1 ), x distance (length), and D Diffusivity coefficient (length 2 time -1 ). The first term of equation (51)  3.5.2 Simulation software A simulation was carried out through the software COMSOL Multiphysics ® . COMSOL is a software package to solve and analyze finite element, especially coupled to physical or multiphysics phenomena. It includes a complete environment to model almost any physical phenomenon that can be described using ordinary differential equations (ODE's) and partial differential equations (PDE's) (COMSOL Incorporated, 2015). 3.5.3 Parameter For this problem a cylindrical column with a diameter of 1 m with a height (Z) of 10 m was used. This column was packed with the zeolitic material. Acid drainage with 50 mg L -1 of CU(II) was fed from the bottom at a constant speed of 0.001 m seg -1 . The porosity of the material was measured by means of the liquid displacement technique using an Ohaus® Pioneer analytical balance. The porosity of the material was determined at 0.4242 and the density was measured by the weighing technique of a given volume with volumetric material and quantified in 915.27 Kg m -3 . The values of the constants (KF and n) of the isotherm for Freundlich calculated in this study were the ones that best adjusted to the experimental data and therefore the most recommended for its use, they were calculated according to what is stated in the subsection 3.2.3 and la Figure 5. Effective Diffusivity Coefficient was calculated according to the model of Millington and Quirk. The values used for Fluid Diffusion Coefficient and Dispersion Tensor were those provided in the COMSOL support material. Table 3 shows the parameters for simulation. The simulation was carried out assuming that the column was completely filled with a concentration solution of 50 mg L -1 of Cu(II). Table 3. Parameters for Numerical Simulation The following figure show the concentration of Cu(II) at a certain time at the exit of the column where the simulation was performed.

Conclusions
The optimum pH value for the removal of copper is neutral. The sequence of the isotherms was: Freundlich > R-P > Sips = Halsey > D-R > Flory-Huggins > Langmuir > Temkin > Elovich > Fowler-Guggenheim > Henry's > Kiselev. Copper removal is feasible through a Zeolite that was subjected to intense acid treatment.