Modeling the Phenanthrene Decomposition Adsorbed

Water Air Soil Pollut (2015) 226:200 DOI 10.1007/s11270-015-2378-6

Modeling the Phenanthrene Decomposition Adsorbed in Soil by Ozone: Model Characterization and Experimental Validation J. Rodriguez-Aguilar & A. Garcia-Gonzalez & T. Poznyak & I. Chairez & A. Poznyak

Received: 26 November 2014 / Accepted: 27 February 2015 # Springer International Publishing Switzerland 2015

Abstract This paper analyzes the mathematical modeling procedure to describe the decomposition of adsorbed phenanthrene in prototypical and real soil samples (sand and agricultural soil, respectively) by ozone. The modeling scheme considered a set of ordinary differential equations with time varying coefficients. This model used the adsorbed ozone in the soil, the ozone reacting with the contaminant and the phenanthrene concentration in the soil sample. The main parameters involved in the mathematical model included a time varying ozone saturation function (ksat(t)) and reaction constants (kr). These parameters were calculated using the ozone concentration variation at the reactor output, named as ozonogram, and the measurements of phenanthrene decomposition through ozonation. The model was validated using two series of experiments: (1) soil saturated with ozone in the absence of the

J. Rodriguez-Aguilar : T. Poznyak (*) Superior School of Chemical Engineering, Instituto Politécnico Nacional (ESIQIE-IPN), Edif. 7, UPALM, C.P. 07738 Mexico, DF, Mexico e-mail: [email protected] A. Garcia-Gonzalez Tecnológico de Monterrey, Guadalajara, Mexico I. Chairez Professional Interdisciplinary Unit of Biotechnology, Instituo Politécnico Nacional (UPIBI-IPN), Mexico, Mexico A. Poznyak Department of Automatic Control, CINVESTAV-IPN, Mexico, Mexico

contaminant and (2) soil artificially contaminated with phenanthrene. In both cases, the proposed parametric identification method yields to validate the mathematical model. This fact was confirmed by the correspondence between numerical simulations and experimental data. In particular, total decomposition of phenanthrene adsorbed in two different systems (ozone-sand and ozone-agricultural soil) was obtained after 15 and 30 min of reaction, respectively. This difference was obtained as a consequence of soil physicochemical characteristics: specific surface area and pore volume. The ozonation reaction rate constants of phenanthrene in the sand and agricultural soil were calculated using the same parameter identification scheme. Keywords Soil ozonation . Mathematical modeling . Simulation . Phenanthrene decomposition . Kinetic parameters calculation

1 Introduction Successful applications of ozone in water treatment have motivated researching propositions to investigate the potential application of this oxidant gas to clean up contaminated soil (Pierpoint et al. 2003). The main attention has been focused on eliminating adsorbed polycyclic aromatic hydrocarbons (PAHs) from soil. This family of chemical compounds is highly recalcitrant, insoluble in water, and tends to be accumulated on solid surfaces.

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Besides, the level of toxicity and possible teratogenic activity (Lee and Kim 2002; O’Mahony et al. 2005; Rivas 2006; Takayama et al. 2006; Yu et al. 2007; Poznyak et al. 2007; Rivas et al. 2008) have become PAHs into a real and challenging environmental problem. Ozonation has been proposed as a contaminated soil remediation technique applied directly as gas, dissolved in water, and also combined (in sequence) with other treatments such as biodegradation (Kulik et al. 2006; Derudi et al. 2007). However, this treatment method has not been extended considering the number of open questions regarding the interaction dynamics between ozone and contaminants adsorbed on the soil surface. Mathematical modeling of ozonation of soil samples may contribute to increase the understanding of this interaction dynamics. Characterization based on mathematical models of soil remediation by ozone remains as an active field in environmental researching. On counterpart, in the ozone-based wastewater treatment, it is possible not only to find mathematical models representing the ozone mass transfer in agreement to the corresponding experimental data, but also mathematical models where the decomposition of a contaminant or a mixture of contaminants by ozone is explained (Bin and Roustand 2002; Poznyak et al. 2005; Poznyak et al. 2006). Mathematical modeling of ozonation in solid phase is a tough task. Heterogeneous soil composition, variety of particle geometry, the combination of solid phase with the gaseous phase (twophase system), or with liquid phase (three-phase system) are some difficulties that appear when the aforementioned model must be determined. Even though, the scientific community continue studying two-phase system (gas-solid) modeling (Kulik et al. 2006; Dong et al. 2008a, b). Just a few works regarding the specific case of ozone mass transfer in soil have been reported (Heechul 2002; Kim and Heechul 2002; Shin 2004). Moreover, the modeling complexity is strongly augmented in the case of the presence of pollutants adsorbed in the soil. In this case, it is necessary to take into account the contaminant decomposition dynamics simultaneously to the ozone mass transfer. A step ahead of the modeling process is to consider the presence of natural organic matter,

Water Air Soil Pollut (2015) 226:200

metals, metal oxides, and moisture on the soil surface. In particular, derivation of mathematical model under this condition is much more complicated, because these components affect severely the ozonation kinetics (Dong et al. 2008a, b; Chiang et al. 2002; Lima et al. 2002; Haapea and Tuhkanen 2006). As expected, all the previous models describing ozone mass transfer in soil simultaneously with the pollutant degradation were represented by partial differential equations (Luster-Teasley et al. 2010). In the present study, the mathematical modeling of the phenanthrene decomposition in soil by ozone was designed under a framework of time varying lumped parameters included in an ordinary differential equation set. The comparison of numerical simulations and experimental data obtained from two solid phases (ozone-sand and ozone-agricultural soil) was used as the validation scheme to the proposed model in this study. The same mathematical modeling process was simultaneously used to determine the phenanthrene decomposition reaction rate when the contaminant was adsorbed in the same soils.

2 Materials and Methods 2.1 Preparation of the Model Soils The size distribution of soil particles was obtained using a selective screening. This distribution was 0.07–>3.35 mm in diameter for both soils: sand and agricultural soil. All the experiments were executed with particles of size 0.18 mm. This condition was satisfied with the treatment of both soils. Model soils were prepared before the treatment with ozone. These solids were washed with distilled water for 0.5 h and then with ethanol for additional 0.5 h under continuous mixing. After the washing, the soil samples were baked during 24 h at 80 ° C to eliminate solvent. These samples were exposed to high temperature environment (550 °C) by 24 h to eliminate organic matter, according to the method reported by McKeague (1976).


2.2 Artificial Contamination of Model Soils with Phenanthrene The phenanthrene decomposition experiments were executed using two different concentrations of contaminant (0.02 and 1.5 mg/g). This condition was evaluated over the samples of both soils. The phenanthrene concentrations were obtained using 100 g of dry sand and soil that were washed with 100 mL of phenanthrene-methanol solutions with concentrations of 25 and 1500 mg/L, respectively. In a second step, remaining methanol was evaporated at 60 °C. Contaminant distribution in the model soil was controlled by UV–Vis spectrum variation (spectrophotometer Perkin Elmer— Lambda 2B) of phenanthrene extracted in methanol from the treated soil. Extraction method was Soxhlet with 2 g of treated soil in 30 mL of methanol after 3 recirculation cycles. Extracts of phenanthrene were obtained from sand and soil samples taken randomly at different locations. Average initial concentrations of phenanthrene in solid phases were 0.021 and 1.5 mg/g (±0.20), respectively. Contaminated samples of 30 g were ozonized according to the strategy presented in the following section. 2.3 Ozonation Procedure 2.3.1 In the Absence of Phenanthrene The study of ozone mass transfer in the soils without contaminant was carried out in glass micro-reactor (25 mL) by the Bfluidized bed^ principle. Initial ozone concentration was 6 mg/L (±0.2) with a fixed gas flow of 0.1 L/min. Ozone concentration was obtained by an automatic UV ozone generator (40 w). Gaseous phase ozone concentration at the reactor outlet was measured by an ozone analyzer BMT 964 BT (BMT Messtechnik, Berlin). This sensor was interfaced with a PC using an acquisition data module (National Instrument, NIDaq USB board 6008). This system registered the ozone concentration online with a sampling period of 0.01 s. These measurements were used to determine the current ozonation degree by means of the ozonogram. The online registration was finished when the

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measured ozone concentration increased up to the same value fixed at the reactor’s input (this condition was kept unchanged for all experiments). Data analysis was done using a program developed in the MATLAB software platform. More details on the ozonation system can be consulted either in (Poznyak et al. 2005) or (Poznyak et al. 2007). This system includes the oxygen tank, a UV ozone generator, the glass micro-reactor (10 cm3), the bypass system with electro-valves, the ozone analyzer connected to the data acquisition system and the PC. The ozone removal was executed by a reactor purged with oxygen flow. This procedure was performed before and after each experiment.

2.3.2 In the Presence of Phenanthrene Ozonation of the contaminated soil was carried out in the same reactor described above, but with the ozone concentration of 30 mg/L and the gas flow of 0.5 L/min. In this case, ozone was produced from dry oxygen by a corona discharge type ozone generator HTU500G (Azco Industries Limited, Canada). Different experiments were proposed with ozonation finishing after different periods of time: 1, 3, 5, 7, 10, 20, 30, and 60 min. These measurements were used to evaluate the ozone saturation dynamics and the phenanthrene decomposition in the course of ozonation. Phenanthrene stripping degree was determined using the blank test with oxygen flow (without ozone) during 30 min. The phenanthrene stripping degree ( dQtotal ðtÞ Qads ðtÞ < Qmax ads dQreact ads ðtÞ < α dt ¼ > dt : dQtotal ðtÞ otherwise dt

ð18Þ

where ksat(t) can be calculated from Eq. (7), considering (13) and (17). To calculate kr, the value of kr as its least-square estimate k*r was considered. Therefore, the value of this parameter is the ( k sat

react ðtÞ

¼

dQreact ads ðtÞ max Qreact dt 0

ads ‐Qreact

ads ðtÞ

−1 Qreact Qreact

In Eq. (20), it is needed the time variation of c(t), Qads_react(t) and their rates of change; c(t) function is represented by a regression model of double exponential, which is obtained from the set of punctual extractions of phenanthrene. As it is presented in the results section, the remaining data are obtained from Eq. (12). The parameter γ is used to avoid any possible division by 0. Finally, to determine ksat_react(t), a similar procedure described to ksat(t) is used. This value is the solution of the following pair of equations: ads ðtÞ

< Qmax react

ads

max ads ðtÞ ¼ Qreact

ads

ð21Þ

2.7 Experimental Validation

procedure considered that each solid phases should be exposed to ozone. Then, the corresponding ozonograms were recorded and filtered. The last step of this process used the set of experimental data that were adjusted to the following sigmoidal equation:

Ozonogram is the key information needed to validate the mathematical models presented above. Therefore, a brief study about sensor sensitivity is proposed in order to evaluate if this experimental approach allows us to differentiate the ozonogram of each solid phase without overlapping. The comparison was carried out after applying a simple first-order low pass filter over all data sets. The

C in ð22Þ eðt−x0 Þ 1þ d The unknown parameters x0 and d were calculated by means of nonlinear regression techniques that were implemented in the software OriginPro (version 7.0). The values of these parameters with confidence intervals are compared (p=0.05) in Table 1. It is worth to

Taking into account Eqs. (16) and (18), one gets enough information to obtain the function values of (21).

C out ðtÞ ¼ C in −

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Table 1 Values of parameter x0 and d with their confidence intervals Phase

x0

Confidence interval (p=0.05)

d


Empty reactor

42.00

41.976–42.024

5.87

5.855–5.897

Sand

46.95

46.914–46.991

7.43

7.406–7.473

Soil I

47.63

47.595–47.664

7.16

7.136–7.198

Soil II

68.69

68.654–68.735

9.78

9.745–9.816

remark that this associated statistical model for ozonogram represented by (22) was employed only to analyze the sensitivity of the proposed experimental method, and it was not considered in the structure of the proposed mathematical models OP and OWP.

3 Results and Discussion 3.1 Experimental Validation of the Mathematical Models Tables 1 depicts the calculated parameters x0 (R2 =0.9998) and d involved in the model given by (22) for each one of the soils. As one can notice, there is no overlapping between the confidence intervals. This condition implies that at least, for the fixed experimental conditions, it is possible to ensure that each ozonogram is specific for each phase. Furthermore, ozone sensor possesses enough sensibility to characterize them. It is not possible to guarantee this situation under any other experimental conditions. Figure 2 depicts the evaluation of regression model (22) with parameters of Tables 1. As can be seen, the ozonogram profiles of sand and soil (CO) are almost the same. However, the obtained parameters pointed out the difference between them. This can be explained by similar selected particle sizes of both soils. It should be noticed that data used for comparison purposes came from different experiment to those used in the parametric identification method described in the theoretical section.

concentration reached the ozone concentration produced by the reactor in a period of time smaller than 1000 s. Figure 3b shows the rate of change of ozone amount adsorbed on the solid phase (dQ(t)/dt) calculated from Eq. (8) and the information coming from ozonograms. Integrating with respect to time dQ(t)/dt (Runge-Kutta 4th order with integration step of 0.01 s) and by Eq. (9), it is possible to derive the current adsorption Qads(t) (Fig. 3c). Figure 3d depicts the ksat(t) evolution calculated from Eq. (7) and the data in Fig. 3b, c. Recalling that ksat(t) is proportional to saturation rate of change dQads(t)/dt and inversely proportional to the difference between maximum amount of ozone and the current amount of ozone accumulated in the soil, it is possible to appreciate that ksat(t) has a completely different behavior for each soil studied. This can be explained by different physicochemical characteristics of soils such as permeability and porosity. Despite ozonograms depicted in Fig. 3a, seem to be equal each other for sand and soil OWP samples, their identified parameters pointed out their true differences. In particular, the time varying

3.2 Parameter Calculation and Simulation of Model OWC Figure 3a depicts the ozonogram for the empty reactor and all the three soils. In all cases, the ozone

Fig. 2 Ozonograms of each solid phase approximated by the sigmoidal model


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Fig. 3 Ozonogram comparison of empty reactor, sand, soil I, and soil II (a); experimental rate change of Qads(t), dQads(t)/dt from equation (b); behavior of adsorption Qads(t) for different solid phases (c); ksat(t) evolution (d)

function ksat(t) quantifies accurately such differences without the complete knowledge of their physicochemical characteristics. However, an extensive study considering the control of specific geometric parameters must be carried out, in order to establish the correlation with the ksat(t) behavior. The acceptable correspondence (percentage relative means square error less than 5 %) between simulated Cout(t) and the ozonograms for each solid phase confirmed the high representative of function ksat(t) to characterize the type of soil. Table 2 summarizes the maximum values of Qads(t), dQads(t)/dt, and the calculated ksat(t) for each model soils in the absence of phenanthrene . The calculated ksat(t) was tested by the numerical solution of model OWC for each soil considered in this study. The comparison of the simulation results with the

experimental data is shown in Fig. 4a–c. These figures compare experimental information and calculated ozonograms for baked sand, soil CO, and soil OWC. The convergence between experimental ozonograms and simulation results is appreciated in Fig. 4. The mean square error produced by this modeling procedure is 3.56×10−6. Table 2 Characteristic parameters calculated for each soil without contaminant Solid phase Qadsmax [mol] max dQads/dt [mol/s] ksatmax [s−1] Sand Soil I Soil II

1.18×10−6

2.83×10−8

10.91×10−2

−6

−7

7.92×10−2

−8

9.97.1×10−2

5.87×10

−6

1.38×10

1.25×10 3.30×10

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Fig. 4 Experimental and modeled ozonograms: a sand, b soil I, and c soil II

3.3 Parameter Calculation and Simulation of Model CO Figure 5a shows the experimental ozonograms of baked sand without and with phenanthrene in comparison with empty reactor. The high degree of similarity between profiles of ozonograms for empty reactor and baked sand demonstrates how this information can be used to characterize soils. This fact demonstrates the small absorbance of ozone on the surface of baked sand that can be explained by its low porosity. Based on the UV–Vis absorbance variation at 254 and 292 nm of phenanthrene extracts in methanol (results not shown), the complete contaminant

decomposition was obtained during the period of time when ozonation was carried out (Fig. 5b). Experimental data of the phenanthrene decomposition were adjusted by the following equation (Kahan et al. 2006; Perraudina et al. 2006): phenanthrene concentrationðtÞ ¼ aebt þ cedt

ð23Þ

Calculated parameters obtained by the proposed method (R2 =0.9996) are presented in the second and third columns of Table 3. The fourth and fifth columns of Table 3 summarizes the calculated parameters from experimental data to


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Fig. 5 Ozonograms of baked sand without and with phenanthrene in comparison with empty reactor (a); decomposition of phenanthrene: experimental and regression model data (b)

characterize model CO, considering α=0.5, and Qads(t) as is presented in Table 2 (R2 =0.994). The simulation of phenanthrene decomposition in the soils was carried out using the data presented in Table 3. Figure 6 depicts the results for each one of the involved variables in Model CO. As one can appreciate, there are small differences between experimental values and numerical simulation for Cout(t), particularly (Fig. 6a). One can assume that one of the main causes to justify this difference is the by-products formation trough the phenanthrene decomposition, which is a phenomena not considered in the modeling process, but their presence provoke an increment of the consumed ozone. In spite of this situation the convergence of the model is highly acceptable. One should consider that the assumed condition of α=0.5 implies that the adsorption of ozone and its reaction is happening at the same rate of change until Qads(t) achieves its maximum value. At this point, all the parameters needed to perform the calculation of the reaction rate constant kr between Table 3 Parameters calculated for the decomposition of phenanthrene

Parameter

Value

ozone and phenanthrene was already obtained by the procedure presented in Eq. (20). This constant must characterize the phenanthrene decomposition by ozone in a porous medium such as the baked sand and agricultural soil. The obtained constant was kr =14.01×104 g/ mg s. This value is twice larger than that found by the authors for the anthracene 6.10×104 g/mg s (Poznyak et al. 2007). This difference is expected because the phenanthrene is more reactive with ozone according to its chemical structures. The same condition was achieved when the decomposition of the same contaminants was considered when they were dissolved in water.

4 Conclusions The proposed calculated function ksat(t) involves a set of factors such as porosity, particle geometry, density, and etc. Considering all these properties


Value

Deviation ±0.001

A

0.009

(−0.001, 0.020)

0.010

B

−1.248

(−2.893, 0.395)

4.430

±0.016

C

0.010

(0.001, 0.022)

0.010

±0.065

D

−0.245

(−0.441, −0.049)

0.721

±0.012

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Fig. 6 Comparison between simulation (model CO) and experimental data of baked sand: a Cout(t), b Qads(t), c Qreact_ads(t), and d c(t)

into a lumped factor let us to characterize the ozone saturation from a quantitative point of view, but without the necessity of carrying out the complete determination of these properties. The proposed saturation model (model OWC) confirms that the k sat (t) is representative for each solid phase. On the other hand, the presence of the ozonation by-products provokes the general model (model CO) partially diverges from the experimental values. The value of the reaction constant of the phenanthrene decomposition under experimental conditions was determined as kr =14.01×104 g/

mg s. The proposed simplified mathematical model can be considered as an alternative tool in the characterization of the ozone mass transfer from a global point of view, and it can be applied in the description of the decomposition of a contaminant in soil treated by ozone.

Acknowledgments The authors thank the Department of Graduate Study and Investigation of the National Polytechnic Institute of Mexico (Project No. 20080171) and the National Counsel of Science and Technology of Mexico—CONACyT (Project No. 49367) for the supporting of this investigation.


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