Mathematical modeling of a single stage ultrasonically assisted distillation process

Ultrasonics Sonochemistry 24 (2015) 184–192

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Mathematical modeling of a single stage ultrasonically assisted distillation process Taha Mahdi a,b,d, Arshad Ahmad a,b,⇑, Adnan Ripin a,b, Tuan Amran Tuan Abdullah a,b, Mohamed M. Nasef a,c, Mohamad W. Ali a,b a

Institute of Hydrogen Economy, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia Faculty of Chemical Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia Malaysia Japan International Institute of Technology, Universiti Teknologi Malaysia, 54100 Kuala Lumpur, Malaysia d Midland Refineries Company, Ministry of Oil, Daura, Baghdad, Iraq b c

a r t i c l e

i n f o

Article history: Received 4 February 2014 Received in revised form 31 October 2014 Accepted 5 November 2014 Available online 13 November 2014 Keywords: Mathematical modeling Ultrasound Azeotrope Ethyl acetate/ethanol Vapor–liquid equilibrium

a b s t r a c t The ability of sonication phenomena in facilitating separation of azeotropic mixtures presents a promising approach for the development of more intensified and efficient distillation systems than conventional ones. To expedite the much-needed development, a mathematical model of the system based on conservation principles, vapor–liquid equilibrium and sonochemistry was developed in this study. The model that was founded on a single stage vapor–liquid equilibrium system and enhanced with ultrasonic waves was coded using MATLAB simulator and validated with experimental data for ethanol– ethyl acetate mixture. The effects of both ultrasonic frequency and intensity on the relative volatility and azeotropic point were examined, and the optimal conditions were obtained using genetic algorithm. The experimental data validated the model with a reasonable accuracy. The results of this study revealed that the azeotropic point of the mixture can be totally eliminated with the right combination of sonication parameters and this can be utilized in facilitating design efforts towards establishing a workable ultrasonically intensified distillation system. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction In process industries, distillation is still one of the preferred processes despite its difficulties in separating mixtures with very close boiling points and those that form azeotrope. To overcome this limitation, variety of frontier technologies have been explored [1]. For example, dividing-wall column has been introduced to separate more components in a single distillation unit, thereby offering energy savings along with substantial capital and space reduction [2,3]. Furthermore, it is also possible to implement this separation technique with azeotropic distillation [4], or extractive distillation [5], so that it can be integrated into single column configuration. However, this process is marred by high pressure drop and temperature difference caused by the increase in the boiling point [6]. Another new approach is to intensify the process by adding ultrasonic equipment to the distillation system. Using cavitation as a source of energy input for chemical processes to generate ⇑ Corresponding author at: Institute of Hydrogen Economy, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia. E-mail address: [email protected] (A. Ahmad). http://dx.doi.org/10.1016/j.ultsonch.2014.11.005 1350-4177/Ó 2014 Elsevier B.V. All rights reserved.

rapidly formed and disappearing hot-spots under nearly ambient conditions offer potential improvements to conventional distillation. The whole process of generation, growth and collapse of cavities occurs rapidly, of the order of few microseconds, and this phenomenon alters physical properties of the mixtures and enhances the mass [7] and heat [8] transfer, thus offering further exploitation to intensify vapor–liquid separation. As a foundation for the development of ultrasonic distillation process, studies on vapor–liquid equilibrium (VLE) under ultrasonically intensified environment have been carried out. These include experimental works on the VLE of methanol–water [9], MTBEmethanol [10] and cyclohexane-benzene [11]. In all cases, positive changes on the VLE characteristics were observed and sonication effects have been proven to alter the relative volatility of azeotropic mixtures, thus enabling higher purity separation in a single distillation column. To facilitate further development, a mathematical model describing the process is needed so that comprehensive design study of the ultrasonic distillation system can be carried out. In this paper, this issue is addressed. A mathematical model that represents a single stage vapor–liquid equilibrium system with intensification using ultrasonic waves is derived and validated.

T. Mahdi et al. / Ultrasonics Sonochemistry 24 (2015) 184–192

This is followed by a simulation study to investigate the process characteristics and determination of optimal operating condition for separation this system. 2. Mechanism of ultrasonic separation 2.1. Mechanisms of bubble collapse Acoustic cavitation is a phenomenon by which ultrasonic waves induce bubbles formation, growth and collapse [12]. The collapse normally takes place when the bubble reaches critical size referred to as the resonance size. Depending on the operating condition, the growth-collapse process may end up in two possible scenarios. Firstly, if they are smaller than the resonance size, bubbles tend to migrate from the minimum pressure, also known as pressure node to the maximum pressure referred to as antinode. This is driven by primary Bjerknes forces, and will lead to a condition whereby bubbles are collapsing inside the liquid and generating high temperature [13]. This causes the formation of radicals and highly reactive intermediates within the bubbles during the collapse. For this reason, they are called ‘‘active’’ cavitation bubbles. This condition facilitates various chemical pathways, thus enhancing sonochemical reactions [14]. Recently, numerous papers have reported enhancement effect of ultrasound on biodiesel synthesis with basic strength of catalyst [15–17]. They established the mechanism of this enhancement by discrimination of the physical and chemical effects of cavitation bubbles in the system on transesterification of oil with alcohol using a catalyst. Secondly, if they are larger than the resonance size, they will be forced to the node to become ‘‘inactive’’. These bubbles eventually float out of the liquid due to buoyancy forces and collapse at the liquid surface [18]. Similar observation is reported in a study involving ethanol/water mixture, where the bubble travel through the liquid mixture and collapse in the fountain jet formed at the liquid surface releasing the alcohol vapor in the bubble [19]. These phenomena have significant impact on mechanical and physical processes such as cleaning and vapor–liquid separation processes. However, certain combination of operating conditions may also create exceptions. For example, a study by Matula [20] revealed that at 20 kHz and 1.8 bar, the bubble is repelled from the antinode even if the size is smaller than the resonance size. Other researchers [21,22] also proposed an alternative mechanism based on capillary wave. In this hypothesis, a liquid is parametrically excited by ultrasound waves such that capillary waves are formed on the surface. As the amplitude of these waves increase, the capillary become instable and small liquid droplets pinch off from the crests (peaks) of the capillary wave causing atomization. Oscillation and collapses of the cavitation bubbles enhance the capillary wave perturbations and thus facilitate the pinch-off of droplets mist formation [23]. However, the visible mist was produce by mixture droplets which is depend on the physical properties of a mixture and operation conditions. If the boiling points of the components of a mixture are close, the percentages of these components in the droplet mist are also close; and vice versa [21,22]. Therefore, in the present system this theory is futile to break the azeotrope. 2.2. Factor influencing the mechanisms of bubble collapse Many literatures have examined the effect of physical properties of mixtures and operating conditions on the activity of acoustic cavitation bubbles [24–30]. In summary, there are three important conditions that may cause cavitation bubbles to lose their activities. The first condition is concerned about the influence of ultrasonic frequency on the cavitation bubbles. At lower frequencies,

185

since the cycle of expansion and compression is slower, larger bubbles are produced. Moreover, when the population of bubbles is high, which typically happen at high sonication intensity, some of the bubbles coalesce to form larger bubbles [24]. As a consequence, the bubbles have larger surface area of contact with the surrounding liquid, thus allowing more light molecules to diffuse into the bubble, thus increasing its vapor pressure, which in turn further increase the bubble size. When the bubble is larger than the resonance size, it will be pushed toward the nodes by primary Bjerknes forces and becoming inactive [26,27]. The second condition is related to the operating temperature. An increase in the bulk liquid temperature leads to a reduction in bubbles’ activities due to two reasons [25–27]. Firstly, dissolved gases in the liquid evaporate to the surface at high temperature, thus reducing the bubble population. Secondly, as temperature of the bulk liquid increases, the liquid vapor pressure inside a cavitation bubble is increased, leading to an increase of the bubble size. When the size exceeds the resonance size and become ‘‘inactive’’ as mentioned previously. The third condition is related to decomposition of components in the presence of hydrocarbons [28,29]. When molar heat of hydrocarbons is much larger than that of gases inside the bubble, the temperature generated during the bubble collapse decreases monotonously to an extent that it is unable to dissociate hydrocarbons inside the bubble, thus making it inactive. This is contrary to the observation by Yasui et al. [30,31] when the liquid environments were aqueous. In their work involving aqueous methanol environment, they reported that as the bubbles collapsed methanol molecules were dissociated inside a bubble. Similarly, when pure water is used, water vapor dissociated inside the heated bubble and chemical species such as OH radical and H atom are created inside the bubble during the violent collapse of bubbles [31]. Based on the above arguments, ‘‘inactive’’ conditions are established when the operating conditions are at low frequency, high temperature, and hydrocarbons. It is also important to note that the ultrasonic wave generates micro-point vacuum condition within the liquid during bubbles formation. In this condition, azeotrope of the vapor components inside the bubbles is altered, resulting in changes in vapor liquid equilibrium. This is confirmed by a various studies that proved the breaking of azeotrope under vacuum pressure condition [32,33]. To understanding the mechanism of the enhancement separation of the system in this process, these bubbles eventually float out of the liquid due to buoyancy forces and collapse at the liquid surface in the fountain jet releasing the vapor in the bubble to the vapor phase. Thus, the mole fractions of the vapor inside the bubbles are considering equal to those in the vapor phase. These are the scenarios considered in this study.

3. Mathematical modeling The mathematical model developed here is focusing on the use of ultrasound in facilitating a distillation process. To simplify model development efforts, a number of assumptions on the physical characteristics of the bubble are made. The cavitation bubble is assumed to be spherically symmetric and is initially composed of mixture of gas (air) and liquid vapor. The surrounding liquid is assumed incompressible, with constant and uniform dynamic viscosity, and is at steady-state condition. The non-equilibrium condition is during the growth of a bubble which is very short time (microsecond). During this time, the bubble is unstable due to the amount of material that gets into the bubble (during expansion) is larger than what comes out of the bubble (during compression). Therefore the final number of molecules inside the bubble will be calculated at equilibrium condition. The validity of the model

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is also limited to certain conditions such as low frequency, high temperature of bulk liquid and this system is of hydrocarbons mixture.

2

R

d R dt

2

þ

 2 3 dR PðRÞ  P1 ¼ 2 dt q

ð8Þ 2

3.1. Vapor–liquid equilibrium One of the major assumptions made in the present investigation is that that bubbles occur inside the liquid, whose size is uniform, and they filled with a vapor in equilibrium with the bulk solution and the bubbles enriched with ethyl acetate due to surface excess, and can be represented by Rault’s law. Thus, the relationships between vapor compositions in the bubble and the compositions in the bulk liquid, is denoted by:

P  yi ¼ ci  xi  P oi

ð1Þ

Here, P is the pressure of the system, yi and xi are mole fractions in vapor and liquid phase respectively, ci is the activity coefficient and P oi is the vapor pressure of i component. Under ultrasonic influence, it is the vapor composition that will be seriously impacted, and when this can be estimated, the liquid composition can be computed by using Eq. (1). The activity coefficient can be determined using suitable model depending on the type of liquid system involved. For the ethanol/ethyl acetate mixture considered here, NRTL model is chosen. Other information needed to determine the VLE compositions are obtained by looking into the details of bubble dynamics and sonication phenomena. NRTL model was chosen because of its suitability for liquid– liquid systems containing alcohols and non-polar hydrocarbon liquids such as ETAC [34]. The activity coefficients for the NRTL model of binary mixture were determined using the following equations:

ln c1 ¼

x22

ln c2 ¼ x21



G21 x1 þ x2 G21



G12 x2 þ x1 G12

2

2

s21 þ

s12 þ

G12 s12

! ð2Þ

ðx2 þ x1 G12 Þ2 G21 s21 ðx1 þ x2 G21 Þ2

! ð3Þ

G12 ¼ ea12 s12

ð4Þ

G21 ¼ ea21 s21

ð5Þ

The parameters a12 and a21 are non-randomness parameters, and in usual cases, a12 is set equal to a21. In practice, the nonrandomness parameter a12 is set to 0.3 for the case of liquid–liquid nonideality and for non-aqueous systems [34]. Therefore, this value was adopted for this case study:

s12 ¼

g 12  g 22 RT

ð6Þ

s21 ¼

g 21  g 11 RT

ð7Þ

Here R is the gas constant and T the absolute temperature, and g21 and g11 are energies of interaction between a 1–2 and 1–1 pair of molecules, respectively. Again in common practice, the value of g12 is set equal to g21. 3.2. Rayleigh–Plesset equation The study on bubble dynamics can be traced back to the early works of Rayleigh [35], in which, the collapse of an empty spherical bubble from an initial radius, Ro, to a new radius R at time t was considered. By equating the work accomplished by the hydrostatic pressure to the kinetic energy of the fluid surrounding the bubble, the motion of the bubble wall can be represented by Eq. (8):

Here dR is the velocity of the cavity wall of radius R, ddt2R is the wall dt acceleration, q is the density of the liquid, P1 is the pressure in the liquid at infinity (far away from the bubble) and P(R) is the pressure in the liquid at the bubble boundary. With the inclusion of surface tension r and viscosity l effects, the equation of bubble dynamics becomes: 2

R

d R dt

2

þ

 2    3 dR 1 2r 4l dR ¼ Pi  P1   2 dt q R R dt

ð9Þ

Here, Pi is the pressure in the bubble, and this equation is frequently referred to as the Rayleigh–Plesset equation [36] and serves as a governing equation that represents the dynamics of spherical bubbles in an infinite body of liquid. 3.3. Bubble expansion Consider an initial bubble containing a very tiny mass mg of noncondensable gas (air) and liquid vapor at ambient temperature T, in a system shown in Fig. 1. The pressure of the noncondensible gas in the bubble can be estimated using the ideal gas law, and is given by [37]:

Pg ¼

mg RT

ð10Þ

M g 43 pR3o

where Mg is the molecular weight the air and R universal gas constant. The partial pressure of compositions can be estimated by assuming that it is equal to the sum of all vapor pressure of P o individual component i (Pv ¼ P i ) [38]. Note that inside the bubble, there are the noncondensible gas, the partial pressure of which is Pg and the vapor with partial pressure Pv. The combination of these two partial pressures gives the total pressure inside the bubble (i.e., Pb = Pg + Pv). At the bubble interface, the liquid pressure is lower than the pressure inside the bubble because of surface tension of the liquid phase which plays an important role in bubble dynamics as shown in Fig. 1 [39]. This phenomenon is known as Laplace pressure, and is given by the expression:

Pg þ Pv ¼ Po þ

2r R

ð11Þ

Putting Eq. (10) into Eq. (11) yields:

Po ¼ Pv o þ

mg RT M g 43 pR3o



2r Ro

ð12Þ

Po

Ro

Rmax

Pb=Pg+Pv

Fig. 1. Micro bubble.

T. Mahdi et al. / Ultrasonics Sonochemistry 24 (2015) 184–192

Eq. (12) gives the initial bubble radius Ro in mechanical equilibrium for a given liquid ambient pressure Po. A relationship between ultrasound frequency and the initial bubble radius Ro is given by Eq. (13):

Ro ¼

1 2p f

 1=2 3Po

ql

ni ¼

In the system studied here, the liquid medium is subjected to sonication effect from waves generated by the ultrasonic transducer. When a wave with pressure amplitude PA and frequency f passes through a cavitating medium, the pressure P1 in the liquid at any time t is given as [40]:

P1 ðtÞ ¼ P o  PA sinð2pftÞ

ð14Þ

where Po is the ambient pressure, and the pressure amplitude, PA of the sound field that is a function of the acoustic intensity that is given by [41]:

PA ¼

pffiffiffiffiffiffiffiffiffiffiffi 2IqC

During the rarefaction phase of the acoustic cycle, the radius of a bubble that was initially at Ro will expand to a maximum radius, Rmax. Solving the Rayleigh–Plesset equation for the maximum R gives Eq. (16) below [24]:

 1=2  1=3 2 2 2ðP A  Po Þ ¼ ðPA  P o Þ 1þ 3pf 3Po qPA

ð16Þ

where PA is the pressure amplitude, f is the acoustic frequency and q is the density of the liquid. The relationship between the pressure and bubble volume during compression or expansion can be described analytically. The expansion process is assumed isothermal and the bubble size is small enough such that the pressure and temperature inside the bubble can be assumed uniform. The instantaneous vapor pressure of components Pi is then related to the initial vapor pressure of components Pio by the following relation [42]:

Pi ¼ Pio

Ro Rmax

ð18Þ

Knowing the number of moles ni of each species involved in the system, the mole fractions of components i (yi) inside the bubble at Rmax can be determined using Eq. (19):

ni yi ¼ X ni

ð19Þ

Eq. (19) gives the vapor composition at equilibrium, and having this, the liquid composition can be computed by using Eq. (1), and the VLE is therefore defined. Due to the higher vapor pressure (Pi) of ethyl acetate compared with ethanol, we expected the value of mole fraction in vapor phase for ethyl acetate to be larger than for ethanol. 4. Simulation study The model discussed in the preceding sections is coded in MATLAB programming environment. The system considered is the ethanol/ethyl acetate mixture, which is known to form homogenous azeotropic mixture 45 mol% of ethanol, and a difference in boiling points of 1.2 °C, thus making it impossible to achieve higher purity separation in a single fractional distillation column [44]. 4.1. Model validation

3.5. Maximum bubble size



4pPi R3max 3RT

ð15Þ

where I represents intensity of the ultrasound and C is the velocity of sound through the liquid. By substituting Eq. (15) into Eq. (14), and subsequently Eq. (14) into the Rayleigh–Plesset Equation (Eq. (9)), the effect of ultrasonic intensity and frequency on the bubble size can be estimated. For the purpose of this study, the condition of interest is at equilibrium, which is assumed to be established when the bubble size is largest with bubble radius Rmax and is about to collapse at the liquid surface.

Rmax

components would also vary during this isothermal phase of bubble dynamics. Nevertheless, the condition of interests is at the maximum bubble size, and by using ideal gas law, the number of moles of components vapor (ni) inside the bubble at Rmax can be calculated by Eq. (18) [43]:

ð13Þ

3.4. Sonication effect

187

3c ð17Þ

where c is the ratio of the heat capacities of the vapor, the isothermal case is accounted for by setting parameter c to 1. Thermodynamic process described by the above equation is called a Polytropic process. 3.6. Ideal gas law Using equation of state, the number of moles of vapor components can be computed for a defined bubble size (i.e. volume), temperature and pressure. In this case, the partial pressure of components inside the bubble is assumed equal to their saturation vapor pressures. Since the partial pressure changes as the bubble is expanding, the number of moles of vapor

As a measure of fitness to validate the model developed in this study, the percentage of average absolute deviation (AAD) between the model prediction and the experimental data is used. The AAD is computed using Eq. (20) below:

qffiffiffiffiffiffiffiffiffiffi2 AAD ¼

^Þ ðyy y2

n

 100

ð20Þ

ˆ are the experimental data and model prediction where y and y respectively, and n is number of points or observations used in the analysis. This criterion is applied to conditions described by Mahdi et al. [45] and comparisons are made on the process behavior observed. 4.2. VLE behavior without sonication effect The first comparison examined is the VLE characteristics at normal atmospheric condition without the influence of sonication. Here, the model is compared with experimental data from Mahdi et al. [45], Topphoff et al. [46] and Calvar et al. [47]. The results are summarized by Fig. 2 below. It is noted that the model agree well with experimental works with AAD of 2.5% [45] 2014), 1.66% [46] and 1.9% [47]. These results indicate that the model is of reasonable accuracy in predicting the VLE curve of the system under atmospheric condition and without the influence of sonication. 4.3. Effect of sonication on VLE characteristics The effect of sonication parameters on VLE of ETOH/ETAC mixture is shown in Fig. 3. In Fig. 3(a), the influence of ultrasonic intensity on the VLE at a frequency of 25 kHz is shown. The results show that the equilibrium curve and azeotropic point of the

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The model is simulated to study the effect of sonication frequency and intensity on the azeotropic point and the relative volatility. The results are compared with experimental works previously carried out [45], and the AAD is determined to indicate how close the model agrees with the experimental works. 4.4.1. Effect of intensity Model predictions of the azeotropic points and relative volatilities against the ultrasonic intensity at a fixed frequency of 25 kHz are shown in Fig. 4. When the intensity is increased, the azeotrope point and relative volatility (aij ) are increased. The relative volatility between component i and j, are computed from individual vapor and liquid compositions using Eq. (21):

aij ¼

Fig. 2. xy-Diagram of ETOH/ETAC system without sonication and compared with literature.

mixture are shifted upwards with increasing ultrasonic intensity. It is also important to note that by adding an ultrasonic cavitation effect with the frequency of 25 kHz and intensity of 500 W/cm2, the azeotropic point of ETOH/ETAC is completely eliminated. Similar trends are observed for higher intensities. For example, Fig. 3(b) shows the influence of ultrasonic frequency on the VLE at an intensity of 300 W/A cm2. This observation indicates that it is possible to realize high purity distillation separation by the assistance of sonication phenomena, thus opens the opportunity for separation in a single process unit as opposed to multiple process units configuration offered by the azeotropic and extractive distillation processes. 4.4. Sensitivity analysis Azeotropic point of the mixture can be calculated when intersect the VLE of ETOH/ETAC system curve with the standard line (45°). Each intersection between the VLE curve of the mixture and the standard line represents one azeotropic point for specific operation conditions including ultrasound intensity and frequency.

yi =xi yj =xj

ð21Þ

Since it is a derived value from the compositions, it is expected that its variations with changing ultrasonic intensity or frequency follow the same trend of azeotrope point. The azeotrope point and relative volatility of the model agree well with the experimental results for the lower range on intensity up to 300 W/cm2 with AAD of 6.8% and 6.3% respectively. Beyond this value, i.e. at higher intensity, the deviation is rather significant, giving overall AAD of 17.3% and 27.5% respectively. This condition is however not the case when the system is operating at higher frequency, as shown in Fig. 5. In this case, the AAD between the model and the experimental work are 6.1% for the azeotrope point and 6.6% for the relative volatility. Note that sonication is a rapid transient process, and during this very short period, which is in the order of microseconds, heat and mass transfer processes are very fast. Although the net changes in the operating conditions of the distillation process is small, the fast transport processes impact the interface composition of the liquid and vapor. An increase in ultrasonic intensity leads to an increase in the amount energy entering the liquid medium, thus producing more micro bubbles and creating vacuum effects inside the liquid. However, as the intensity reaches an upper limit, the tendency of cavitation bubbles to collide becomes high. Since the time available for bubbles to collapse is insufficient, they combine to form a bubble ‘cushion’ at the radiating face of the ultrasonic transducer, which in turn reduces the effect of coupling sound energy to the liquid system. This phenomenon reduces the transmission of ultrasonic energy into the liquid medium and produces less cavitational

Fig. 3. xy-Diagram of ETOH/ ETAC system with sonication at different intensity, (a) at frequency of 25 kHz, (b) at frequency of 70 kHz.

T. Mahdi et al. / Ultrasonics Sonochemistry 24 (2015) 184–192

189

Fig. 4. Comparison of model predictions and experimental observations with increasing ultrasonic intensity at frequency of 25 kHz of ETOH/ETAC system on (a) azeotropic point, (b) relative volatility.

Fig. 5. Comparison of model predictions and experimental observations with increasing ultrasonic intensity at frequency of 70 kHz of ETOH/ETAC system on (a) azeotropic point, (b) relative volatility.

and vacuum effect [24]. That explains the downward trend shown by the experimental results beyond 300 W/cm2. This phenomenon is however not accounted for in the present model, thus explains the large deviation in Fig. 4. At high frequency, the downward deviation observed by experimental works at intensity higher than 300 W/cm2 is reduced. As shown in Fig. 5 when the system operates at 70 kHz, the downward deviation is not noticeable at intensity of 400 W/cm2. This is consistent with earlier works [45], where it was concluded that at high sonication frequency, the time required to create bubbles may exceed that of the rarefaction cycle. At this condition, the overall bubbles population is reduced due to higher cavitation rate compared to bubbles production. Because of this, the ‘‘bubble cushion’’ phenomenon mentioned earlier will only occur at lower frequencies. Furthermore, to support the intended separation process, at this value and beyond, the sonication intensity must be increased with increasing frequency to create more bubbles, thus balancing the effect of frequency on azeotrope point and relative volatility. For this reason, frequencies in the range 20–50 kHz have traditionally been used for separation purposes [48]. 4.4.2. Effect of frequency Fig. 6 shows the good agreement between model prediction and experimental data on the effect of ultrasonic frequency on azeotrope point and relative volatility. The average absolute deviation of azeotrope point and relative volatility between the model predictions and experimental results is 5.4% for the azeotrope point and 4.9% for the relative volatility. The relative volatility

decreases with the increase of ultrasonic frequency at constant ultrasonic intensity. When the intensity is 300 W/cm2, the highest value of 2.36 is obtained at frequency of 25 kHz, while the lowest value of 1.62 is obtained at frequency of 70 kHz. Similarly, as shown in Fig. 7, good agreement between model prediction and experimental data is established for the operation at 300 W/cm2. The average absolute deviation of relative volatility between the model predictions and experimental results is 10% for the azeotrope point and 9.6% for the relative volatility. 4.4.3. Summary of the effect of ultrasonic parameters on azeotrope point and relative volatility Fig. 8 shows the plots of azeotropic point of ETOH/ ETAC mixture against ultrasound intensity from 100 to 800 W/cm2, and frequencies between 20 and 100 kHz, while Fig. 9 shows the relative volatility. The estimation of azeotropic point in Fig. 8 depends on the data in Fig. 3 and other ultrasound intensities and frequencies, when intersect the VLE of the mixture curve with the standard line (45°). The sonication intensity is found to have stronger effect on the VLE, compared to the frequency as illustrated by the steeper gradient along the intensity axis. The model also suggests the use of lower frequency so that higher relative volatility can be established, thus facilitating the intended vapor–liquid separation. 4.5. Optimization One of the key advantages of having process model is that it enables sensitivity analyses to be carried out thoroughly and

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Fig. 6. Comparison of model predictions and experimental observations with increasing ultrasonic frequency at intensity of 100 W/cm2 of ETOH/ETAC system on (a) azeotropic point, (b) relative volatility.

Fig. 7. Comparison of model predictions and experimental observations with increasing ultrasonic frequency at intensity of 300 W/cm2 of ETOH/ETAC system on (a) azeotropic point, (b) relative volatility.

Fig. 8. Azeotropic point of ETOH/ ETAC as a function of ultrasonic intensity at different frequencies.

efficiently. It also allows optimum process parameters to be determined conveniently. This can be carried out using one of the many optimization algorithms available. In this work, to identify the

optimum operating conditions, genetic algorithm (GA) is used. GA is a technique that emulates theories of biological evolution, natural selection and the survival of the fittest. It falls within the

T. Mahdi et al. / Ultrasonics Sonochemistry 24 (2015) 184–192

191

Fig. 9. Relative volatility of ETOH/ETAC as a function of ultrasonic intensity at different frequencies.

class of random optimization and has the advantage of not being susceptible to local minima, which affects the gradient-based optimization techniques. The optimization study is carried out using GA toolbox available in MATLAB and is aimed at maximizing the relative volatility. The result revealed that the optimum operating condition can be established at ultrasonic intensity of 485 W/cm2 and frequency of 26.3 kHz. At this condition, the relative volatility is 3.1. 5. Conclusion In this work, a mathematical model of a single stage vapor– liquid separation system has been established by assuming that a VLE is established when the bubble is at its maximum size and is about to collapse. The model has been validated with experimental data to a reasonable accuracy, with a limitation of not being able to represent the anticipated bubble-cushion phenomenon. This phenomenon produces less cavitational and vacuum effect which is only occurs at lower frequencies higher intensity. That is because at this condition, ultrasound waves produces more bubbles and the time available for bubbles to collapse is insufficient, thus the tendency of cavitation bubbles to collide becomes high and they combine to form a ‘bubble cushion’. It is nevertheless very useful and serves as a good starting point for further work on the design of ultrasonic-assisted distillation system, which is currently being carried out. The model is suited for distillation process that is intensified with ultrasonic phenomena at lower intensity, if lower frequency is used. If the model were to be used for a wider range of operation at lower frequency, some compensation would be needed. The model demonstrates that the azeotropic point of the mixture can be totally eliminated with the right combination of sonication parameters, and the maximum relative volatility of 3.1 can be obtained at intensity of 485 W/cm2 and frequency of 26.3 kHz. Acknowledgments The authors are grateful to Universiti Teknologi Malaysia, and the Ministry of Education for financial supports through Prototype Research Grant Scheme Vot No. 4L612 and infrastructures

provided to carry out this research. Authors are also thankful to the Midland Refineries Company, Ministry of Oil, Republic of Iraq.

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