Aerosol and Air Quality Research, 17: 330–339, 2017 Copyright © Taiwan Association for Aerosol Research ISSN: 1680-8584 print / 2071-1409 online doi: 10.4209/aaqr.2016.09.0397 

 

Using Box Modeling to Determine Photodegradation Coefficients Describing the Removal of Gaseous Formaldehyde from Indoor Air Ming-Wei Lin1, Ching-Song Jwo1, Hsin-Jr Ho1, Liang-Yü Chen2* 1 Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 106, Taiwan 2 Department of Biotechnology, Ming Chuan University, Taoyuan 33343, Taiwan

ABSTRACT

Human exposure to volatile organic compounds (VOCs) indoors is receiving increasing attention. Formaldehyde (HCHO) is the most common VOC emitted from household materials and is associated with many health risks, including sick building syndrome. In this study, a simple box model was developed and applied to help understand the fate and degradation mechanisms of HCHO in the indoor environment. The model was validated using observations from an air handling system under different conditions. A UV/TiO2 filter reactor was installed in a closed box with the air conditioning unit. Three parameters, temperature, relative humidity, and circulation wind speed, were investigated for their effects on the performance of the air handling system. Our results show that the operation mode of the air handling system has a greater effect on the removal of HCHO than any of the air conditioning parameters. From a kinetic perspective, the removal of gaseous HCHO from a constant-volume box clearly represents a zero-order reaction. After UV irradiation with a TiO2 filter for 2 hours, the removal efficiency of gaseous HCHO increases to approximately 90%. Contributions to the removal of gaseous HCHO from natural dissipation, photodegradation, and photocatalytic oxidation decomposition are 12%, 30%, and 58%, respectively. Our results have implications for reducing indoor air pollution and reducing stress on air conditioning systems. Meeting these goals is beneficial for human health and energy conservation in modern society. Keywords: Heterogeneous catalysis; Titanium dioxide; Air cleaning; Reaction kinetics. INTRODUCTION

Human exposure to indoor concentrations of volatile organic compounds (VOCs) is receiving more and more attention from scientists working in environmental medicine and public health (Hellweg et al., 2009; Collinge et al., 2013; Rosenbaum et al., 2015). In urban areas, people are more likely to ingest, absorb, or breathe in large amounts of harmful chemicals because these chemicals are more prevalent indoors than in outdoor environments (Geiss et al., 2011; Kim et al., 2015).

As air pollutants, VOCs are potentially hazardous byproducts or outgassing products from sources including upholstery, smoking, candle and incense burning, household cleaning activities, cooking, furnishings, printers, building materials, and electronic devices (Panagopoulos et al., 2011; Chaudhary and Hellweg, 2014). Formaldehyde (HCHO) is one of the most common VOCs, and the World Health * Corresponding author.

Tel.: +886-3-3507001 ext. 3773; Fax: +886-3-3593878 E-mail address: loknath@mail.mcu.edu.tw

Organization (WHO) has set a 30-minute exposure limit for HCHO of 0.08 ppm (Salthammer et al., 2010; Golden, 2011). The main exposure pathways for formaldehyde are inhalation of gaseous HCHO from the air or absorption of aqueous HCHO through the skin (Gelbke et al., 2014). Workplaces, including chemical plants and places where industrial chemicals are used, professional health care facilities, forensics laboratories, and mortuaries may present elevated risks of HCHO exposure (Demou et al., 2009).

Ventilation is a generally effective means of ameliorating air quality that works by diluting the concentrations of indoor pollutants, but it causes energy use by indoor air handling systems to increase (Bari et al., 2011; Ciuzas et al., 2016). Specialized air cleaners can be used to address air pollution problems in office buildings or factory workshops. Air filtration can remove specific chemicals or particles from the air and accompanying aerosols. The resulting residues on filters can then be aggregated, collected or transformed. The use of air purifying apparatus to filter out and decompose pollutants is simple in principle and more efficient than ventilation as a means of resolving indoor air quality issues (Schleibinger and Ruden, 2009; Han et al., 2012, Ciuzas et al., 2016).

Heterogeneous photocatalysis on titanium dioxide (TiO2)

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in the presence of ultraviolet (UV) light is an emerging technique for chemical removal and microbe inactivation (Peral and Ollis, 1992; Chen et al., 2012; Ortega Méndez et al., 2015). This technique is based on the generation of reactive radical species that are destructive to organic pollutants and microorganisms (Liang et al., 2013). The use of TiO2 nanoparticles as photocatalytic reactors has many advantages, including high photocatalytic activity and reactive surface area, abrasion resistance, low operating temperature, and good thermal stability (Yang et al., 2010; Zhou et al., 2014; Pramod and Pandey, 2015).

Filters incorporating TiO2 and activated carbon have been used to remove nitrogen oxide and toluene at ppb levels from indoor air (Ao and Lee, 2004, 2005). A photochemical reactor incorporating TiO2 was applied in a continuous laminar flow that forced air to pass over the reactor (Chen et al., 2012). These studies provide useful experimental models for studying the effectiveness of air conditioning systems in reducing air pollution at moderate energy cost. However, the competition between adsorption onto and reemission from activated carbon air purifiers results in poor overall removal efficiencies (Obee and Brown, 1995). Frequent adjustments to the temperature and humidity of the environment are necessary to avoid secondary pollution caused by reemission from activated carbon fabric (Niu et al., 1998).

Box modeling techniques are applied widely on large scale environmental issues and engineering fields (Liu et al., 2000; Afram and Janabi-Sharifi, 2014; Sossan et al., 2016). Indoor air quality can be affected by VOCs, tinny particulates, microbes, or various types of hazardous pollutants which present a health risk to people. Rigorous mathematical modeling of fluid dynamics leads to a system of partial differential equations describing chemical behavior (Sanongraj et al., 2007). To understand the fate and dynamics of a chemical pollutant entering an air-conditioned environment, a conceptual box model is proposed, as shown in Fig. 1. Simplifying assumptions are made with respect to the relative concentrations of species in our model.

Mass balance provides an approach for identifying unknown concentrations and reaction rates. The initial mass of HCHO in a closed system is the sum of the initial mass of formaldehyde and the additional mass that can be derived from chemical transformation of other chemical species present in the system, expressed as HCHOinput = Ʃ (HCHO)+ + CHOtransf. The transformation of HCHO involves decomposition, polymerization, and oxidation to other chemicals (Salthammer et al., 2010). The photocatalytic oxidation of HCHO first forms the intermediate product carboxylic acid (HCOOH), which then oxidizes to carbon dioxide (CO2). The amounts of oxygen and water in the air have important impacts on the overall photocatalytic reaction efficiency of air cleaner units containing TiO2 catalysts (Yang et al., 2010). Therefore, the aerosol term of HCHO is emphasized in our model to reflect the effect of water molecules in the photochemical reactions. Based on other studies (Han et al., 2012; Lo et al., 2015; Yu et al., 2015), three air conditions of temperature, relative humidity and wind speed are considered as the principal factors on the removal of gaseous VOCs indoors.

To appraise the cleaning performance of modern air handling system needs to model the air purifier units either by the data driven or physics based approaches. Our aim is to investigate the effects of air conditioning parameters on the removal of HCHO by heating, ventilation, and air conditioning (HVAC) systems. Thus, we develop and assess a simple box model representing an air handling chamber with a photocatalytic air purifier. The model includes a set of air conditioning parameters and describes the behavior of HCHO species using the principles of mass balance and chemical kinetics. Three processes of HCHO removal could be distinguished and evaluated as a natural dissipation, a photodegradation, and photocatalytic oxidation decomposition within our experimental validation. This study presents results that describe the heterogeneous catalytic reaction of these species in detail and helps engineers to design air handling units to achieve improved

Fig. 1. Mass balance and transformations of HCHO for the photoreaction experiments with box modeling. Three processes were proposed to remove the gaseous HCHO in this conceptual box.

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control strategies on the indoor air quality and the energy consumption efficiency (Afram and Janabi-Sharifi, 2014; Sossan et al., 2016). EXPERIMENTAL METHODS Materials and Chemicals

Titanium dioxide (TiO2-1125A) was purchased from Yong-Zhen Technomaterial Co. LTD (Taiwan). Commercial-grade polyvinyl acetate (PVA-666) binder was purchased from Gunway Co. (Taiwan). Formaldehyde was purchased from Sigma Aldrich (USA). All chemicals were ultrapure grade and were used without further purification. Ultrapure water produced by a Milli-Q system (Millipore, USA) was used as a solvent.

A stainless steel filter (21 × 21 × 1.5 mm) was used as a mesh supporting substrate in the air purifier unit to decrease chemical adsorption. The mesh filters were used in our experiments without film modification, except in those experiments that examined the photocatalytic oxidation mode of the air handling system. Setup of Air Conditioning Box with Photoreactor

As shown in Fig. 2, a recirculating air system with a photoreaction unit was used to examine the removal kinetics of formaldehyde pollution in indoor environments. The air conditioning recirculation tank used in this study was constructed from existing laboratory equipment, including an air conditioning unit (P.A. Hilton Ltd., UK) with a vapor compression cooling device, heating coil, fan, and humidifier. The mixing chamber’s surface is polished and chemically inert, and inhibits adsorption. The system also allowed operation at various wind speeds, temperatures and humidity levels.

A photoreactor with four mesh filters was designed as an air purifier for photodegradation and photocatalytic oxidation operations in this study. Five UV lamps (TUV 10W SLV/25,

Philips Lighting) were placed on the upper layer of filters to achieve maximal irradiation area. The UV lamps are designed to meet a specification of 28(D) × 331(L) mm, with a maximum wavelength of 253.7 nm (UVC germicidal). The irradiation intensity was validated using a multi-sense optical radiometer (MS-100, Ultra-Violet Products Ltd., UK). Preparation of the TiO2 Filter

Part of the stainless steel filters were selected and cleaned before they were coated with TiO2 film. Commercial oily binder (PVA-666) was mixed with water in a 1:9 (volume/volume) ratio, and used to evenly coat the stainless steel filter, which was then set to dry at 50°C. The nano-TiO2 solution was diluted to 3%, placed in an ultrasonic oscillator for 10 to 20 minutes to ensure uniformity, and then placed into a solvent tank for 5 to 10 minutes. The TiO2 nanoparticles were evenly attached to the surface. Then, the stainless steel filter was dried in a 100°C oven for 10 minutes, until completely dry. The ignition technique was used to ensure that the modified films were evenly distributed. The TiO2 nanoparticles were completely immobilized on the surfaces of the stainless steel filters. Experimental Design

The experimental variables were grouped with the air conditioning parameters and the operation modes. The air conditioning parameters were temperature, relative humidity, and internal wind speed, as described in Table 1. In total, 18 sets of experimental conditions were investigated. The air purifier unit could be operated in one of three modes, and these modes are listed and coded in Table 2.

These operation modes are designed as cumulative hierarchy sets in our experimental model. The efficacies of operation modes in gaseous HCHO removal (Δ[HCHOg]) are counted with the relationship that is F-D-S (100) ⊂ F-L-S (110) ⊂ F-L-T (111).

Fig. 2. Schematic illustration of the air handling system, which includes a recirculation air tank, an air conditioning unit, and an air purifier unit.

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Table 1. Air conditioning parameters used in box chamber.

Control Variables Control Constants Temperature (°C) 18, 20, 22, 24, 26,28

RH = 50%, WS = 0.7 m s–1

Relative Humidity (%) 40, 50, 60

Temp. 22°C Temp. 25°CWS = 0.7 m s–1

Wind Speed (m s–1) 0.4, 0.7, 1.4

Temp. 22°C Temp. 25°CRH = 50%

Gaseous HCHO Measurement Five milliliters of 37% HCHO aqueous solution were

injected into the recirculation air system as shown in Fig. 2. The liquid HCHO was then released from the solution as gaseous HCHO and was introduced into the air purifier unit and the mixing chamber by the recirculating air flow. The residual gaseous HCHO in the air was detected by an electrochemical sensor (FormaldemeterTM 400, PPM Technology Ltd., Wales, UK). The Formaldemeter contains an internal sampling system that has a detection range of

10 ppb to 10 ppm and a resolution of 1 ppb. This instrument was thoroughly recalibrated less than a month before our experiments. The concentration of gaseous HCHO within the apparatus was measured every 15 minutes and recorded for kinetic calculations.

RESULTS AND DISCUSSION Microstructure and Morphology of Nano-TiO2 Film

TiO2 has a number of characteristics that make it desirable for air pollution reduction, including high activity, chemical stability and abundance in commercial photocatalysts. TiO2 exists mainly in two crystallographic phases, anatase and rutile. The lattice structure of anatase is considered to be particularly appropriate for encouraging photocatalytic activity. Fig. 3 shows the X-ray diffraction (XRD) patterns of the TiO2 powder (1125A). Two peaks corresponding to anatase were observed at 25.3° and 48.1°, ignoring diffraction peaks associated with amorphous titanium oxides. The morphology of the TiO2 film was found to have a porous

Table 2. Operation modes for experimental design.

CODE Fan UV Filter F-D-S (100) Circulation Dark Stainless Steel F-L-S (110) Circulation Irradiation Stainless Steel F-L-T (111) Circulation Irradiation TiO2 coating

Fig. 3. X-ray powder diffractogram of photocatalytic nano-TiO2 1125A. The inset shows a SEM image of the nano-TiO2 film coating on the stainless steel mesh filter.

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microstructure via scanning electron microscopy (SEM), which should enhance the capacity of this material to encourage VOC reaction.

TiO2 displays photocatalysis and photoinduced superhydrophilicity upon irradiation with light of particular wavelengths (Lee et al., 2007). Superhydrophilicity means that the surface is extremely wetted by water, and the contact angle of a water droplet is less than 10 degrees. Therefore, water molecules play a key role in determining the photodegradation and/or photocatalytic oxidation decomposition of HCHO. Effects of Temperature on HCHO Removal

Temperature is a key function of air conditioning systems and is a major factor that determines the rate of HCHO removal. As shown in Fig. 4, the concentration of gaseous HCHO decreased linearly in each operation mode. In the F-D-S (100) operation mode, which is the background mode, the effectiveness of HCHO removal does not depend on temperature. However, the efficacy of HCHO removal was significantly enhanced when the F-L-S (110) and F-L-T (111) operation modes were active. In these modes, higher temperatures promoted increased reaction rates. According to Arrhenius’ law, higher temperatures accelerate chemical reaction rates and increase the adsorption of reactants on catalyst surfaces. According to the solid catalyzed reaction

model, the temperature dependency of reactions is strongly affected by pore resistance. Generally, higher temperatures enhanced the efficiency of gaseous HCHO removal with or without TiO2 filters in this study.

Effects of Relative Humidity and Wind Speed

For multivariate testing, the effects of relative humidity and wind speed were evaluated by subgrouping the experiments according to whether they were conducted at high temperature (25°C) or moderate temperature (22°C).

The effect of relative humidity (RH) on gaseous HCHO removal is shown in Fig. 5. Notably, high relative humidity promoted the removal of gaseous HCHO removal at high temperatures under the F-L-T (111) operation mode. This result indicates that high relative humidity and high temperature enhance the photocatalytic oxidation decomposition of HCHO in the presence of TiO2 nanoparticles. Furthermore, the water molecules are a dominant factor in this reaction by the photoinduced superhydrophilicity of TiO2.

The effect of recirculation wind speed (WS) on gaseous HCHO removal is shown in Fig. 6. High wind speed promoted the efficiency of gaseous HCHO removal at high and moderate temperatures under the F-L-T (111) operation mode. This result indicates that the photocatalytic oxidation decomposition of HCHO was dominated by diffusion into

Fig. 4. Temperature effects on time series of gaseous HCHO concentrations according to operation mode. Air conditioning constants included 50% relative humidity and a wind speed of 0.7 m s–1. Three operation modes, F-D-S (100), F-L-S (110), and F-L-T (111) are described in Table 2. The terms of F, D/L, and S/T mean the fan, the dark or lighting, and the stainless steel or TiO2 coating filters used in the referred operation mode.

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Fig. 5. Relative humidity effects on time series of gaseous HCHO concentrations according to operation mode. Air conditioning constants included a wind speed of 0.7 m s–1 and temperatures of 25°C or 22°C. The coded operation modes, F-D-S (100), F-L-S (110), and F-L-T (111) are defined as the same as in Fig. 4.

the porous surface of TiO2 nanoparticles. However, although high temperatures also enhance HCHO desorption from solid surfaces, which is the reverse reaction, this effect does not appear to be significant.

Kinetics of Heterogeneous Reactions

The experimental system in this study is designed as a batch reaction in a box with limited volume. Based on the time series of gaseous HCHO concentration, the removal of HCHO appears to follow a zero order reaction (Yang et al., 2012). The reaction rate is approximately constant over the monitoring period. The integrated rate equation becomes as follows,

1

21A A

A

dC k C

dt k C

(1)

At high CA or k2CA >> 1, the apparent rate constant k+ =

k1/k2 becomes the slope of the regression line. The reactant, gaseous HCHO, was entirely introduced at the beginning of reaction monitoring. Thus, the initial concentration of gaseous HCHO was difficult to measure. Extrapolating the regression line to the beginning of the experiment, the initial concentration of gaseous HCHO can be approximated from the intercept of the regression line. The regression lines fit the data well and have R2 values > 0.95. Kinetic

parameters were calculated from the measured gaseous HCHO concentrations; these values are listed in Table 3.

The initial concentrations of gaseous HCHO, referred as [HCHOg]0, are substantial and their values occupy a narrow range. The amounts of HCHO introduced into our system were precise and accurate, that is, they were validated for each experiment. This result also suggests that the reaction kinetics were not sensitive to the air conditioning parameters, such as temperature, relative humidity, and wind speed. However, the efficiencies of the three operation modes are significantly different and distinguished by their inferred kinetic parameters. Since the apparent rate constant for the F-D-S (100) operation mode k+

100 is controlled by natural decomposition, the apparent rate constants are 2.255-fold and 5.020-fold of k+

100 for operation modes F-L-S (110) and F-L-T (111), respectively. Effects of UV Light Irradiation

Gaseous HCHO can be removed by many pathways, including the natural decomposition, adsorption onto other materials, photolysis, polymerization and photocatalytic oxidation decomposition (Li et al., 2014). Without TiO2 filters, the F-L-S (110) and F-D-S (100) operation modes can be considered to mimic indoor environments with air handling equipment, but without a photocatalytic air purifier unit. Irradiation with UV light noticeably enhanced the removal of gaseous HCHO without photocatalysts. We

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Fig. 6. Wind speed effects on time series of gaseous HCHO concentrations according to operation mode. Air conditioning constants included 50% relative humidity and temperatures of 25°C or 22°C. The coded operation modes, F-D-S (100), F-L-S (110), and F-L-T (111) are defined as the same as in Fig. 4.

Table 3. Kinetic and quantitative measurements for gaseous HCHO removal. The concentrations of gaseous HCHO at initial and after 2 hr., [HCHOg]0 and [HCHOg]2hr, are presented as the mean ± standard deviation (coefficient of variance) in ppm. The apparent rate constants, k+ = k1/k2, are presented as the mean ± standard deviation (coefficient of variance) in ppb per minute.

Operation Overall Data (18 × 3 sets) Mode [HCHOg]0 k+ = k1/k2 [HCHOg]2hr F-D-S (100) 5.34 ± 0.05 (0.95%) 5.1 ± 0.5 (9.28%) 4.78 ± 0.09 (1.95%) F-L-S (110) 4.71 ± 0.07 (1.42%) 11.5 ± 2.0 (17.39%) 3.41 ± 0.20 (5.82%) F-L-T (111) 3.77 ± 0.19 (4.98%) 25.6 ± 1.6 (6.14%) 0.75 ± 0.26 (34.5%)

suggest that the direct photolysis of gaseous HCHO and liquid HCHO in aerosol should be the mainly contributors. However, utility of filters coated with TiO2 nanoparticle film could promote the removal efficacy of gaseous HCHO to approximately 90%.

In the F-L-T (111) operation mode, photocatalytic oxidation decomposition is well known as a predominant pathway for achieving highly efficient HCHO removal. Arrhenius' equation can be used to calculate the change in activation energy (Ea) associated with a chemical reaction as the ratio of the rate constants:

,111 ,110111

110

ln a aE Ek

RTk

(2)

Here, k+

111/k+

110 is the ratio of apparent rate constants

for the F-L-T (111) and F-L-S (110) operation modes. The photocatalytic effectiveness coefficient is 2.226, and the decrease in the energy barrier is approximately 2.0 kilojoule per mole at 301-291 K in this photoreactor with TiO2 filters and UV illumination.

According to the results presented in Fig. 4, high relative humidity also promotes the removal of HCHO. The photoinduced superhydrophilicity of TiO2 film might enhance the adsorption of gaseous HCHO and liquid HCHO onto the porous film. Contributions of Each Processing on HCHO Removal

For quantitative opinions, the performance of an air cleaner could be evaluated by the total amount of gaseous HCHO removal, Δ[HCHOg] = [HCHOg]0 – [HCHOg]2hr, that are shown in Table 3. However, the measured data is derived from accumulated removals of all processes in our system.

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Therefore, removal of gaseous HCHO in F-L-T (111) operation mode (Δ[HCHOg](111) = 4.95 ppm with TiO2 filters and UV irradiation) for 2 hours is considered as the full efficacy,. On the same estimation base, the removals of gaseous HCHO after 2 hours are 1.93 ppm and 0.56 ppm for F-L-S (110) and F-D-S (100) operation modes, respectively.

With the logical implication of set theory, the Δ[HCHOg](110) is the result of excluding the process of photocatalytic oxidation decomposition; the Δ[HCHOg](100) is the result of excluding the both processes of photodegradation and photocatalytic oxidation decomposition. If photodegradation is the dominant pathway in the F-L-S (110) operation mode, the additional removal of gaseous HCHO in the F-L-T (111) operation mode should be mainly contributed by the photocatalytic oxidation decomposition of TiO2. Considering all cases examined in this study, the fraction of photocatalytic oxidation decomposition of TiO2 achieved a level of 58%. Then, the 12% and 30% on removal of gaseous HCHO are contributed by the natural dissipation and the photodegradation, respectively. Prediction and Large Scale Application of the Box Modeling

The development of control approaches and applied strategies need to assess the interactions in detail for the different chemicals, the efficacies and the living-related activities (Hunger et al., 2010). Langmuir-Hinshelwood model is often adopted on kinetics of HCHO removal. Because of the initial rapid adsorption of HCHO onto the TiO2 photoreactor, the gaseous HCHO concentration jumps to the fixed value and the kinetic reaction is presumed as a first-order reaction (Langmuir isotherm). However, the results of data driven observation in most studies present an approximate zero-order reaction except for low concentration of HCHO (Lo et al., 2015; Yu et al., 2015). We suggest that the measurement uncertainties of rate-dependency are trade-off the accuracies of processing contributions in quantitation. Therefore, the improper data used on numerical calculation would mislead to obtain the unreasonable interpretation. Our model can clarify the contribution for each approach by kinetics and set theory.

People are exposed to the VOCs of localized, short-term and high-dose due to stay indoors for a long time. The cleaning techniques with low-energy consumption and green property (decomposable materials) are key trends in modern life. For large scale applications, the established model allows prediction of the performance of air purification units under various conditions. Further, the biological hazard controls (mold, pathogenic bacteria and virus) in indoor air quality also will be a matter of concern for people in the crowded urban space. CONCLUSION

A simple box model was used to characterize the photochemical reactions of gaseous HCHO for indoor air quality management. A series of experiments were performed with an experimental setup that mimics indoor air handing system. The effects of three air conditioning parameters,

specifically temperature, relative humidity, and recirculation wind speed, were investigated, as well as three air handler operation modes. Filter reactors with photocatalytic TiO2 nanoparticles were installed as air purifiers in this air conditioning system. Higher temperatures encourage photolysis and effectively promote the removal of HCHO. Higher circulation wind speeds also enhance HCHO removal in the presence of porous photocatalytic materials. However, higher relative humidity values attenuate the removal of HCHO by UV light degradation. Aerosol or suspended particles might participate in these photochemical reactions. Our results demonstrate that the removal of gaseous HCHO is a zero order reaction, which is a feature of heterogeneous catalytic reactions. Furthermore, kinetic analysis reveals that several different mechanisms participate in the removal of gaseous HCHO. In our experiments, natural dissipation, photodegradation, and photocatalytic oxidation decomposition remove 12%, 30%, and 58% of gaseous HCHO, respectively. Finally, our results provide a baseline for evaluating the effectiveness of air handling systems for indoor air quality management. ACKNOWLEDGMENTS

The authors thank the Ministry of Science and Technology, Taiwan, under Contracts No. MOST 103-2113-M-130-001 (grant to L-Y Chen) for supporting this work financially. We especially thank Professor Kon-Kee Liu in the Institute of Oceanography of National Taiwan University for his suggestion to use numerical modeling. REFERENCES Afram, A. and Janabi-Sharifi F. (2014). Review of modeling

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Received for review, October 6, 2016 Revised, December 3, 2016

Accepted, December 5, 2016