### 1. Introduction

^{−7}cm/s. Even with such hydraulic conductivity, the dispersion of organic contaminants from clay liners can be significant. Using absorbents in the landfill liners structure can reduce contaminants’ dispersion through the retardation mechanism. The retardation factor (R) illustrates the effect of retarding the transfer of pollutant in the adsorption process. The adsorption level of organic contaminants by natural soil and clay depends on their solubility and the organic carbon content [2]. In organophilic (modified) clay, ion exchange process leads to convert ordinary bentonite to modified one. In this process, inorganic ions present in the double layer of ordinary bentonite such as sodium, calcium, magnesium are replaced by organic-based cation compounds like the quaternary ammonium salts (QAS). These changes convert the bentonite property from hydrophilic to organophilic (hydrophobic) that makes it suitable to absorb hydrocarbon. The organic contaminant adsorption capacity of organoclay increases with the increase in the number of carbons associated with the QAS. In previous studies, it had been stated that contaminant advection rate as well as dispersion rate will decrease considerably with the increase of the adsorption capacity in liner by organophilic clay without any need of raising the liner thickness [3, 4]. Several studies have been conducted on the factors affecting the permeability and adsorption for different compounds. Daniel [5] indicated that in a mixture of sand and bentonite, hydraulic conductivity decreases significantly while the percentage of bentonite increase from 0 to 8% in a way that it's amount reduces from 10

^{−4}to 10

^{−8}cm/s. He also observed that less reduction occurs in hydraulic conductivity when the amount of bentonite was increased. Investigation of adsorption isotherm of organic compounds on ordinary bentonite and organophilic clays shows that the absorption of benzene, toluene, ethylbenzene and xylene by organophilic clay were 75%, 87%, 89% and 89% on average, respectively [6]. Irene [7] was examined five different percentages of bentonite and organophilic clays. The results revealed that sample containing 20% bentonite and 20% organophilic clays had the lowest permeability (10

^{−8}cm/s). In addition, the best adsorption of Total Organic Carbon (TOC) was obtained for sample containing 20% organophilic clay and 80% sand. Jhamnani [2] also reported a permeability of 1.6 × 10

^{−8}cm/s for a sample with 20% bentonite, 20% organophilic clay and 60% sand. He also asserted that the highest adsorption capacity of TOC was allocated to a sample with 15% bentonite, 10% organophilic clay and 75%. Moreover, Sharafi and Bazigar [8] showed that the adsorption capacity of organophilic clay is evidently greater than that of ordinary clay. The results indicated the adsorption capacity of hydrocarbons (Crude oil, Kerosene, Gasoline and Toluene) range from 4 to 10 g/g of adsorbent [8]. In another study, Abdelwahab [9] measured the removal of contaminants in four adsorbents including activated carbon, bentonite, modified activated carbon, and organophilic bentonite. His evaluation on the effect of pH, contact time, and contaminant concentration led to the discovery of the fact that the removal efficiencies of hydrocarbons (diesel) are 67–90% and 75–99.3% for modified activated carbon and modified bentonite, respectively. Guddada [10] stated that not only the minimum bentonite required in the reduction of hydraulic conductivity is at least 12%, but also he also believed that the saturated hydraulic conductivity of the mixture of sand and bentonite reduces with the increase in bentonite content. In this study, the best result of permeability was obtained for a sample with 15% bentonite and 85% sand. Sarkar et al. [11] studied the adsorption capacity of ordinary bentonite (Witheroo Bentonit) and HW2CEC (Witheroo Bentonite modified by hexadecyl trimethyl ammonium). Comparing ordinary bentonite (0.19 mg/kg) and organophilic (11.79 mg/kg), revealed an increase in phenol adsorption. It was probably because of the modification by long chain organic compounds. Badv and Ashrafi [1] revealed that the sample containing 40% of bentonite and 60% of sand has the lowest permeability (1.91 × 10

^{−11}m/s) and the addition of bentonite more than 20% does not present a significant effect in reducing permeability as all pores are filled due to swelling of the bentonite. Sharafi et al. [12] compared the adsorption of organic compounds in ordinary and organophilic clays. The results show that adsorption of organophilic clay for gasoline and toluene (9 g/g) has been almost twice more than kerosene (4.8 g/g). Moreover, the amount of hydrocarbon adsorption on organophilic clay is equivalent to five times of its own weight. While the adsorption capacity of ordinary clay has been reported to be 5 (for toluene) to 8 times (for kerosene and gasoline) lower than organophilic clay.

^{−9}cm/s) that the ordinary bentonites (1.2 × 10

^{−6}cm/s) against crude oil. They conclude using of modified clays instead of ordinary clays in the GCLs structure is more viable [15]. Zhu et al. [16] investigated organo-clays (OCs) as sorbents of hydrophobic organic contaminants. After studying OCs structure, they evaluated the sorptive characteristics of the OCs. They showed the effect of layer charge on the sorption of benzene by two different modified montmorillonites with low and high charge characteristics. In this research, sorption isotherms of several samples were also investigated.

_{6}H

_{5}OH) was used as an organic contaminant. Phenol and its derivatives are used in a variety of industries including oil refineries, petrochemical industry, mines, and pesticides. Through unsafe discharge of the wastewater of these industries, they cause environmental contamination. The effects resulted from being exposed to phenol are associated with adsorption amount and contact time which varies from inflammation and skin burning to toxicity along with reduced blood pressure, increased heart beats, and coma.

### 2. Materials and Methods

### 2.1. Materials

^{3}, solubility 84 g/L and pH (20°C) 5 [19].

### 2.2. Analytical Methods

#### 2.2.1. Compaction test

#### 2.2.2. Batch equilibrium absorption test and adsorption isotherm

*C*is the concentration of the pollutant in solution at equilibrium (mg/L),*q*is the adsorbed materials per unit weight of the solid phase (adsorbent) at equilibrium (mg/g);*q*is the maximum of_{m}*q*(mg/g),*K*is the distribution coefficient,_{d}*K*is the Langmuir constant which is related to adsorption capacity and energy or net enthalpy of adsorption._{L}*K*and_{f}*n*are the constants of the Freundlich isotherm which depend on the adsorption capacity and intensity.

#### 2.2.3. Sample preparation and analysis of phenol

_{4}Cl was added to 142.5 mL of concentrated ammonium and then, it was increased to a volume of 250 mL using distilled water), one mL of 4-amino anti pyrine and 1 mL potassium ferri- cyanide was added to both blank and contaminated samples. After calibration with the blank sample, the others were analyzed for phenol concentration using HACH LANGE spectrophotometer (DR 2800- Germany) by the U.S.EPA method 420.1 [24]. It was able to detect a wide range of pollutant concentration (0.005 -5 mg/L) at 510 nm.

#### 2.2.4. Hydraulic conductivity

K = Coefficient of permeability (m/s),

a = Area of the burette (m

^{2}),L = Length of soil column (m),

A = Area of the soil column (m

^{2}),*h*_{1}= Primary height of water (m),*h*_{2}= Secondary height of water (m),t = Time required to get head drop of Δh (s).

#### 2.2.5. Molecular diffusion theory

_{D}, is written as the following equation for steady-state conditions, as the first Fick's law [31].

*J*

*is the mass flux of solute (M/L*

_{D}^{2}T),

*C*is the solute concentration (M/L

^{3}),

*D*

*is the free-solution diffusion coefficient (L*

_{o}^{2}/T), and ${\scriptstyle \frac{\partial c}{\partial x}}$ is the concentration gradient in the “x” direction.

_{0}) of chemicals is lower than that free solution. Then, the Eq. (6) is modified by the effective diffusion coefficient (D*).

##### (8)

$$1/R\hspace{0.17em}\left({D}_{x}\frac{{\delta}^{2}c}{\delta {x}^{2}}-{V}_{x}\frac{\delta c}{\delta x}\right)=\frac{\delta c}{\delta t}$$V

_{x}= pore velocity in the x direction.*D*is dispersion coefficient, includes two components of molecular diffusion and mechanical dispersion._{x}*R*= retardation factor, where

_{b}= bulk density, and

*K*

*is the distribution coefficient which is calculated by the following relation.*

_{d}*f*

*is the organic carbon fraction of soil,*

_{oc}*K*

*is the partition coefficient of a compound between organic carbon and water.*

_{oc}##### (11)

$$C(x,t)=\frac{{C}_{o}}{2}\left(erfc\left(\frac{RX-{V}_{X}t}{2\sqrt{{RD}_{x}t}}\right)+\text{exp}\left(\frac{{V}_{x}X}{{D}_{x}}\right)\times erfc\left(\frac{RX+{V}_{X}t}{2\sqrt{{RD}_{x}t}}\right)\right)$$*C*

*is the initial concentration of phenol (2,000 mg/L),*

_{0}*C*is the output concentration, t = time and x = passing distance of the contaminants in the soil. By knowing the mentioned variables/ parameter,

*D*

*can be estimated by a trial and error procedure.*

_{x}_{x}is chosen as the best combination in terms of dispersion.

#### 2.2.6. Cost analysis to find the best combination

- Defining objective function: This is a single formula that accurately describes what model should be optimized. In this research, an objective function is minimizing cost by a linear optimization approach. The average cost of bentonite and organophilic clays were assumed to be 60 and 267.5 $/ton, respectively [32].

- Selecting variables: In this research, the percentages of bentonite and organophilic clays were chosen as variables. The optimal value of the objective function can be determined by changing the variables.

- Defining constraints: These formulas define the limits on the values of the variables. The constraints are 1) permeability of less than 10

^{−9}m/s [33] and 2) allowable phenol leakage of less than 137 mg/L [34]. To define such constraints, the related functions were obtained from multiple regression analyses of the examined samples in Minitab software. Several functions were analyzed to reach the best correlation. The best formula was selected by its highest determination coefficient (R^{2}).

### 3. Results and Discussion

### 3.1. Sorption Isotherms

^{−4}C

^{1.25}.

### 3.2. Hydraulic Conductivity

_{80}M

_{20}is 1,000 times greater than S

_{80}B

_{20}. While, when bentonite amount is increased to 30% (S

_{70}B

_{30}), the permeability coefficient declines around three times in comparison with S

_{80}B

_{20}. It suggests that bentonite increasing over 20% has only a minor effect on permeability coefficient; because a major part of sand pores has probably been filled due to bentonite swelling. The S

_{70}B

_{30}is the most impermeable compound. The difference in permeability coefficient in S

_{80}B

_{20}and S

_{60}B

_{20}M

_{20}may not be merely due to the presence of organiphilic clay in S

_{60}B

_{20}M

_{20}. It could also be because of the variation in the nature of both clays. In the samples containing bentonite, similar results are also observed in the study of Komine [40], Badv and Ashrafi [1]. Irene [7] pointed out the mixture consist of 20% bentonite, 20% organophilic clay, and 60% sand gain the lowest permeability (10

^{−10}m/s). Irene [7] also reveals that the soil specimen with more organoclays provide higher adsorption capacity. It is also proposed that the presence of bentonite reduces hydraulic conductivity of admixture. The same trend was observed by Jhamnani et al. [2], who obtained the best permeability coefficient (1.6 × 10

^{−10}m/s) at the same mixing percentage.

The structure and texture of clay: Komine [40] has stated that swelling of Montmorillonite is one of the major causes of diminished hydraulic conductivity by bentonite. Therefore, the physical properties of soil are a regional function and case dependent [40].

Compression efforts: Other factors that can influence hydraulic conductivity are proper compression effort on the soil sample which can be effective in reducing permeability due to crushing clay flocs and decreasing soil porosity.

The type of solution used in the measurement of permeability: Clay minerals are sensitive to chemicals where the presence of some chemicals can affect the clay structure and properties. In various other studies, researchers also examined clays permeability. They explored that solution such as solid waste leachate causes higher permeability in clay. Moreover, the presence of Ca

^{2+}ion can increase hydraulic conductivity. This observation could be attributed to the shrinkage of Montmorillonite structure [41]. In the other researches performed by Irene [7] and Jhamnani [2], the permeability of TOC-contaminated solutions was studied. Their reported permeability coefficients were 0.4 × 10^{−8}and 1.8 × 10^{−8}(cm/s), respectively. The difference between the results of these researches and the present study can stem from the fact that different solutions had been applied.

### 3.3. Dispersion Coefficient

_{x}) and retardation factors (R) for different compounds of sand, bentonite, and organophilic clay is given in Fig. 3. In these compounds, D

_{x}varies between 1.85 × 10

^{−10}and 7.99 × 10

^{−10}m

^{2}/s. The lower D

_{x}shows the lower capability of the contaminant's movement.

^{−6}to 10

^{−7}cm/s, advection is the dominant mechanism. While in sites with lower permeability of 10

^{−8}cm/s, the dispersion phenomenon is influential. As mentioned before, the diffusion coefficient (D*) is governing with high diffusion in fine soils. On the other hand, the mechanical dispersion coefficient (D

_{m}) is governing with low diffusion in coarse soil [31]. The permeability values (Fig. 2) and the rate of reduction in the concentration of the output contaminant (Fig. 3) confirm that the diffusion phenomenon is the predominant mechanism in the samples of the present study.

_{80}B

_{20}and S

_{80}M

_{20}, respectively. Moreover, adding organophilic clay led to suddenly increase in the retardation factor. When 20% of organophilic clay was replaced with 20% of bentonite, the retardation factor was significantly increased which makes predictable the considerable descending trend of diffusion factor. This behavior can be explained by the great ability of organophilic clay to adsorb organic compounds. Comparing D

_{x}of S

_{80}M

_{20}(16.63) and S

_{60}B

_{20}M

_{20}(15.58), it can observe that as the organophilic clay percentage increases, the dispersion coefficient decreases. Furthermore, taking the adsorption capacity of bentonite for samples sand S

_{80}B

_{20}and S

_{70}B

_{30}, reduction in dispersion coefficient is expected. Eventually, the S

_{60}B

_{20}M

_{20}with the highest adsorption level succeeded in obtaining the lowest dispersion coefficient, thereby introducing itself as the best compound in terms of dispersion.

### 3.4. Cost Analysis to Find the Best Combination

^{−9}m/s, phenol leakage of 137 mg/L, and cost of 13.64 $/ton.

### 4. Conclusions

^{−9}m/s, phenol leakage of 137 mg/L, and cost of 13.64 $/ton. Although the use of organophilic clay might appear not to be economical, it should be noted that the costs expended for running the projects against environmental damages which will be irrecoverable in the future can be considered trivial.