Investigating the Effects of Ultrasonic Frequency and Membrane Technology on Biodiesel Production from Chicken Waste

In this study, the experiments were carried out under different operating conditions to evaluate the effect of ultrasound waves on biodiesel production from chicken feet oil. A two-step esterification–transesterification mechanism was employed to improve the biodiesel quality. The continuous (methanol-to-oil molar ratio and KOH catalyst amount) and discrete (frequencies, 25 and 45 kHz) variables were investigated using the experimental design method. The five-level three-factor response surface method (RSM) was assisted to optimize the biodiesel synthesis variables. Applying RSM based on the central composite design (CCD), a polynomial equation was fitted to the experimental data with the aid of Design-Expert software. The model accuracy was checked by analysis of variance (ANOVA). The results showed the highest yield of 89.74% could be achieved by using an M/O molar ratio of 12, a KOH concentration of 1 wt%, and an ultrasound frequency of 45 kHz. Finally, a mathematical model of biodiesel production in a membrane system was developed. The reaction rate constant was calculated as a function of ultrasonic frequency. Compared with the conventional method, the membrane system has significantly improved chicken feet biodiesel production’s reaction rate. The membrane is more effective at higher frequencies than at lower ones.


Introduction
One of societies' major issues is their need for fossil fuels and the continuing pollution growth due to their consumption. Diesel fuel is the greatest energy-dense transportation fuel, which causes many environmental problems such as air pollutant emissions and climate change [1,2]. Therefore, the economic output of petroleum products will decrease in the future. Considering these problems, researchers have been interested in alternative fuels [3]. Biodiesel is a green fuel produced from renewable sources [4]. It has several benefits compared with fossil fuels: 1-It has a renewable energy source. 2-It is nontoxic and decomposable. 3-It contains less pollutants (no sulfur). 4-It has lower toxic gas emissions. 5-It is relatively nonflammable due to its high ignition point [5].
Biodiesel production from animal fat and vegetable oil could enhance the fuel viscosity and combustion characteristics [6]. Therefore, it could be applied in typical diesel engines without modifications [7]. The most critical concern for biodiesel generation is the selection of suitable raw material. reaction with methanol was done in the presence of a sulfuric acid catalyst in an ultrasonic reactor. The results showed that a high conversion of 90% could be obtained at ambient operating conditions. It clearly illustrated the impact of cavitation phenomena as an excellent way to enhance the biodiesel production process. Teixeira et al. (2009) [20] performed a comparison of the transesterification reaction in conventional and ultrasound-assisted (20 kHz and 400 W) reactors. It was observed that the ultrasound-assisted reactor could significantly reduce the reaction time and increase the yield of biodiesel production. Santos et al. (2009) [21] produced biodiesel from soybean oil using an ultrasonic bath. As a result, a conversion yield of 91.8% was obtained within 30 min. In another study, they investigated biodiesel production from tilapia fish oil through a low-frequency (40 kHz) ultrasonic device with a power of 60 W at 30 • C [22]. The response surface method (RSM) was utilized to evaluate the biodiesel yield at different operating conditions. They concluded that the most important factor for biodiesel production in an ultrasonic reactor was the alcohol-to-oil molar ratio. Yin et al. (2015) [23] performed experiments on soybean oil using ultrasound waves, resulting in an esterification efficiency of 96.1%. Singh et al. (2017) [24] worked on the production of biodiesel from algae oil. The higher conversion was attained by the ultrasonic method (98%) compared with the simple transesterification process (91%). Suryanto et al. [25] investigated the process of transesterification to produce biodiesel from cottonseed oil in an ultrasonic device. Ultrasound technology has been revealed to decrease the reaction time and the amount of essential catalyst and alcohol needed for the reaction.
Various edible oils have been applied in biodiesel production, such as rapeseed, sunflower, soybean, and palm oil. However, these edible oil feedstocks are not economical Energies 2021, 14, 2133 3 of 21 due to their wide applications in the food industry. Therefore, nonedible oils, waste animal fats, and waste cooking oils have been considered as potential sources for biodiesel production [26][27][28].
Gole et al. [29] performed experiments to produce biodiesel from nonedible oils. In their study, the advantages of using an ultrasonic device were discussed. It was concluded that it is possible to produce biodiesel with the ultrasonic technique at a lower temperature and time than the mechanically agitated systems. Moreover, the decreased reaction temperature results in energy consumption reduction in biodiesel fabrication. Choudhury et al. (2014) [30] conducted studies on biodiesel production from Jatropha oil. Jatropha is recognized as one of the most prominent herbs. The product is produced by esterification with a sulfuric acid catalyst and transesterification with calcium oxide catalyst. They found that the highest yield could be obtained with the catalyst concentration of 5.5 wt% and alcohol-to-oil molar ratio of 11.
The production cost of virgin vegetable oils is higher than that of animal fats. Therefore, the feedstock costs for biodiesel can be reduced by using animal fats [31]. Animal fats such as tilapia fish [22], chicken skin [32], beef, and sheep tallow [33,34] are used for biodiesel production.
Abid et al. [32] began to produce biodiesel by extracting oil from chicken waste. The esterification process's optimum conditions were the methanol-to-oil (M/O) molar ratio of (3:1) and 1 wt% of catalyst concentration at 65 • C. Also, excellent catalytic performance was observed in the transesterification reaction at 60 • C.
One of the disadvantages of common technologies in biodiesel production is high methanol consumption due to the reversible reaction of the transesterification process [35,36]. Therefore, the reaction time and production cost increase in conventional systems. Another disadvantage is the significant loss of unreacted alcohol and water during the biodiesel purification [37]. In order to offset these drawbacks, the membrane technique is proposed as a promising modification method [36]. Membranes are widely employed for the separation of an individual component (e.g., hydrogen, CO 2 , CH 4 , H 2 S, etc.) from gas mixtures [38][39][40][41][42]. For biodiesel production, the membrane is used for the selective separation of biodiesel as a liquid product. Biodiesel permeates through the membrane, and the unpermitted components (especially alcohol) are recycled back to the reactor. Furthermore, biodiesel purification by membrane could decrease water consumption and increase fuel quality [43][44][45].
Sokac et al. [37] worked on polymeric membranes for biodiesel purification. The membranes included polyethersulfone, polyacrylonitrile, polypropylene, and regenerated cellulose. They showed that the polyacrylonitrile membrane could have a good performance in separating biodiesel produced by lipase-catalyzed transesterification [37]. Alves et al. [46] used a 30 kDa membrane for biodiesel purification. Higher permeations were achieved at higher pressures in membranes with greater pore sizes. They concluded that membrane technology is a suitable alternative for biodiesel purification [46].
Poly(ether sulfone) hollow fiber membranes (PES-HFM) were selected as a membrane in work prepared by Noriega [47]. The process was experimentally tested and modeled [47,48]. Results showed that high-quality biodiesel could be obtained in a membrane reactor. The purity was 10 times more than the conventional reactor [48].
Talaghat et al. [49] modeled a continuous membrane tubular reactor used for biodiesel generation in the presence of an alkaline catalyst. They compared membrane and conventional reactors. The highest conversion was achieved in a membrane reactor with a methanol/oil ratio of 24 [49].
Cao et al. [50,51] used filtanium ceramic membrane for canola oil biodiesel purification. The retentate was recycled into the reactor. High-purity biodiesel was produced in their work.
In another work, they modeled the process and evaluated the reaction rate constants [52]. NaOH catalyst with different weight percents (0.05, 0.1, and 0.5 wt%) and a Energies 2021, 14, 2133 4 of 21 methanol/oil ratio of 24:1 were used in their work. They showed that the application of membrane technology could increase the reaction rate.
As mentioned, there is no study on the effect of ultrasonic baths with different frequencies on biodiesel production from animal fat oil. This study aims to investigate the effect of the M/O molar ratio, catalyst concentration, and ultrasonic frequency on the production of chicken feet oil biodiesel. In the following, the appropriate model was selected to optimize the operating conditions and efficiency of biodiesel production by central composite design (CCD), which is one of the subsets of the response surface methodology (RSM) method. In the following, a membrane system is proposed and modeled to increase the process's time consumption.

Materials and Methods Materials
Chicken feet oil is the raw material used for biodiesel production. The chicken feet were placed in a dish, and some warm water was added, brought to boil, and simmered for 4-5 h [53]. The prepared liquid was cooled to a temperature at which it converted into solid and liquid phases. The solid fraction (oil) was then separated from the liquid. Table 1 shows some characteristics of the prepared chicken feet oil. The acid number and FFA content of the chicken feet oil were measured as 3 mg KOH/g and 1.5%, respectively. It is worth mentioning that sulfuric acid and potassium hydroxide were employed as catalysts for the esterification and transesterification processes. Methanol was chosen as the alcohol for biodiesel production [2]. Figure 1 shows a schematic of the experimental setup. The Elma ultrasonic bath model TI-H5 was applied for biodiesel synthesis. The ultrasound device could operate with two frequencies (25 kHz and 45 kHz), sound power level up to 100 W, and the temperature range up to 70 • C. The reaction took place in a triple-neck flask equipped with condenser reflux (for returning the condensed alcohol vapor to the reactor), mechanical stirrer (at 500 rpm), and a digital thermometer (German Model 1048.30 TFA).

Experimental Setup
A hydrostatic weighing digital balance (AND model HR-200, 0.1 mg sensitivity) and a centrifuge (TL 320 model) were used to weigh samples and separate glycerol from biodiesel, respectively.
The gas chromatography analysis was applied to reveal fatty acid compositions in the biodiesel. The Agilent 6890 GC was connected to an MS detector. The GC method conditions were as follows: •  A hydrostatic weighing digital balance (AND model HR-200, 0.1 mg sensitivity) an a centrifuge (TL 320 model) were used to weigh samples and separate glycerol from bio diesel, respectively.
The gas chromatography analysis was applied to reveal fatty acid compositions i the biodiesel. The Agilent 6890 GC was connected to an MS detector. The GC metho conditions were as follows: •

Experimental Protocol
Due to the high percentage of FFAs in chicken feet oil (Table 1), a two-step esterifica tion-transesterification mechanism should be considered to improve biodiesel quality The esterification procedure was handled based on the research of Alptekin and Canakc [8]. In order to investigate the effectiveness of the ultrasound system, the reactions wer performed in an ultrasonic water bath with two frequencies (25 and 45 kHz).

Experimental Protocol
Due to the high percentage of FFAs in chicken feet oil (Table 1), a two-step esterificationtransesterification mechanism should be considered to improve biodiesel quality. The esterification procedure was handled based on the research of Alptekin and Canakci [8]. In order to investigate the effectiveness of the ultrasound system, the reactions were performed in an ultrasonic water bath with two frequencies (25 and 45 kHz).

Esterification
Esterification of oils and fats is one of the advanced techniques used to modify glycerides' basic structure. As mentioned, this process should be performed for the oils with high FA content (0.5 to 5% by mass) [32]. The esterification reaction was performed for the prepared chicken feet oil with 1.5% FA. The reaction was catalyzed by H 2 SO 4 to convert FFAs to methyl ester.
The esterification process was performed with 6:1 M/O molar ratio, 1 wt% of catalyst concentration, 1 h reaction time, and 60 • C reaction temperature in a 25 kHz ultrasonic system. The produced mixture was kept in a funnel overnight to separate oil from water and alcohol. Figure 2 shows the photo of a prepared sample placed in a separating funnel. The yellow phase represents the esterified oil and the colorless phase represents the separated water. Afterward, the esterified oil was heated (110 • C, 1 h) to evaporate standing water and alcohol [8].
concentration, 1 h reaction time, and 60 °C reaction temperature in a 25 kH system. The produced mixture was kept in a funnel overnight to separate oil and alcohol. Figure 2 shows the photo of a prepared sample placed in a separa The yellow phase represents the esterified oil and the colorless phase represe arated water. Afterward, the esterified oil was heated (110 °C, 1 h) to evapora water and alcohol [8].

. Transesterification Reaction
The flask was filled with prepared oil from the esterification process, me 15:1 M/O molar ratios), and KOH (0.5 to 2.5 wt%). The reaction was carried o 500 rpm mechanical agitation, and a reaction time of 1.5 h in an ultrasonic sys kHz and 45 kHz frequencies. After the transesterification reaction, the produ was centrifuged for 10 min at 2000 rpm to separate glycerol and biodiesel lay tained mixture was settled and the biodiesel was washed with distilled water the washed biodiesel was heated (110 °C) to eliminate the excess water and m Figure 3 shows an image of the produced sample placed in a separating fun

Transesterification Reaction
The flask was filled with prepared oil from the esterification process, methanol (3:1-15:1 M/O molar ratios), and KOH (0.5 to 2.5 wt%). The reaction was carried out at 60 • C, 500 rpm mechanical agitation, and a reaction time of 1.5 h in an ultrasonic system with 25 kHz and 45 kHz frequencies. After the transesterification reaction, the produced mixture was centrifuged for 10 min at 2000 rpm to separate glycerol and biodiesel layers. The obtained mixture was settled and the biodiesel was washed with distilled water. Afterward, the washed biodiesel was heated (110 • C) to eliminate the excess water and methanol [8]. Figure 3 shows an image of the produced sample placed in a separating funnel after the transesterification reaction. The yellow phase represents the produced biodiesel and the dark phase represents the glycerol. Energies 2021, 14,2133 transesterification reaction. The yellow phase represents the produced bio dark phase represents the glycerol. The biodiesel yield could be calculated using the following formula [5

Yield =
Total weight of methyl ester Total weight of oil in the sample × 100

Experimental Design and Statistical Analysis
The response surface methodology (RSM) comprises statistical techniqu mathematics used to model the processes based on the experimental data. The site design (CCD) approach-based response surface methodology (RSM) is u the response variable [53,55]. In this work, the Design-Expert software was ut analyze, and optimize the production process. The process variables, as well levels for CCD, are listed in Table 2. Two continuous variables (M/O molar ra amount) and one discrete variable (frequency) were considered.  The biodiesel yield could be calculated using the following formula [54]: Total weight of methyl ester Total weight of oil in the sample × 100 (1)

Experimental Design and Statistical Analysis
The response surface methodology (RSM) comprises statistical techniques and applied mathematics used to model the processes based on the experimental data. The central composite design (CCD) approach-based response surface methodology (RSM) is used to optimize the response variable [53,55]. In this work, the Design-Expert software was utilized to design, analyze, and optimize the production process. The process variables, as well as the pertinent levels for CCD, are listed in Table 2. Two continuous variables (M/O molar ratio and catalyst amount) and one discrete variable (frequency) were considered. The five-level three-factor RSM ( Table 2) was applied to optimize the transesterification reaction parameters. Totally, 20 experiments were performed to evaluate the effect of the variables on biodiesel yield.
The Design-Expert software proposed the following polynomial model as the best fitting to experimental results: where the parameters Y, X i , β 0 , β i , β ij , and ň stand for the response factor (fatty acid methyl ester (FAME) contents), the independent factor, the intercept, the first-order model coefficient, the coefficient for the interaction between i and j, and power transform, respectively.
The optimum value of ň should be determined by the Box-Cox plot's minimum point [56]. Figure 4 illustrates the Box-Cox plot. As can be seen, the minimum occurred at ň = 3.
Energies 2021, 14,2133 The five-level three-factor RSM ( Table 2) was applied to optimize the transe tion reaction parameters. Totally, 20 experiments were performed to evaluate the the variables on biodiesel yield.
The Design-Expert software proposed the following polynomial model as fitting to experimental results: where the parameters Y, Xi, β0, βi, βij, and ƛ stand for the response factor (fatty acid ester (FAME) contents), the independent factor, the intercept, the first-order mo ficient, the coefficient for the interaction between i and j, and power transform tively. The optimum value of ƛ should be determined by the Box-Cox plot's m point [56]. Figure 4 illustrates the Box-Cox plot. As can be seen, the minimum occ ƛ = 3. The coefficients of Equation (2) were determined by the CCD approach for feet oil biodiesel. Equation (3) is obtained in terms of coded values to estimate diesel yield as a function of the M/O molar ratio (A), catalyst concentration (B), quency (C). The coded levels of variables are provided in Table 2.  Table 2. Table 3 lists the results of the CCD experimental design matrix for the transesterification reaction. Clearly, a good consistency was seen between the actual response and the predicted values obtained from Equation (3). The analysis of variance (ANOVA) was employed to analyze the proposed response surface model ( Table 4). The model accuracy was checked using the coefficient of determination (R 2 ), F-value, and p-value. Particularly, R 2 should be close to unity. This proximity indicates a better correlation between the experiment and the predicted values. Besides, statistical significance was checked by calculating the F-value and p-value [57].
The model p-value (0.0014) and F-value (10.3) confirmed that the proposed model has statistical significance demonstrating the experiment's obtained results. Furthermore, the lack of fit with an F-value of 0.41 and a low p-value of 0.8334 shows that the lack of fit is not significant.

Effect of Process Variables on Biodiesel Production
The effect of catalyst amount, M/O molar ratio, and their reciprocal interaction on the synthesis of chicken feet biodiesel with the ultrasonic frequency of 25 kHz are illustrated in Figure 5. The biodiesel yield is moderately influenced by the methanol/oil molar ratio at low catalyst concentration. Conversely, the impact of methanol/oil molar ratio is considerable at a high catalyst concentration. The maximum acquisition of FAME content is achieved with a high methanol/oil molar ratio and 1% of catalyst concentration (w/w). The model p-value (0.0014) and F-value (10.3) confirmed that the proposed model has statistical significance demonstrating the experiment's obtained results. Furthermore, the lack of fit with an F-value of 0.41 and a low p-value of 0.8334 shows that the lack of fit is not significant.

Effect of Process Variables on Biodiesel Production
The effect of catalyst amount, M/O molar ratio, and their reciprocal interaction on the synthesis of chicken feet biodiesel with the ultrasonic frequency of 25 kHz are illustrated in Figure 5. The biodiesel yield is moderately influenced by the methanol/oil molar ratio at low catalyst concentration. Conversely, the impact of methanol/oil molar ratio is considerable at a high catalyst concentration. The maximum acquisition of FAME content is achieved with a high methanol/oil molar ratio and 1% of catalyst concentration (w/w).  The influence of KOH catalyst amount, M/O molar ratio, and reciprocal interaction on chicken feet biodiesel synthesis using an ultrasonic frequency of 45 kHz are shown in Figure 6. It could be observed that FAME content increases with a decrease in catalyst concentration and methanol/oil molar ratio. The highest methyl ester content is achieved with a catalysis level of 1 wt% and an oil/methanol molar ratio of 1:12.
The influence of KOH catalyst amount, M/O molar ratio, and reciprocal interaction on chicken feet biodiesel synthesis using an ultrasonic frequency of 45 kHz are shown in Figure 6. It could be observed that FAME content increases with a decrease in catalys concentration and methanol/oil molar ratio. The highest methyl ester content is achieved with a catalysis level of 1 wt% and an oil/methanol molar ratio of 1:12. The comparison between the results of Figures 5 and 6 shows that the higher fre quency (45 kHz) could give an increased yield of biodiesel at lower catalyst amount.

Optimization
The optimum value of the response surface, catalyst amount, and M/O molar rati were obtained by considering the desirability function approach as presented in Figure 7 The results showed that the maximum yield of 89.74% could be obtained with the catalys amount of 1 wt%, M/O molar ratio of 12:1, and ultrasonic frequency of 45 kHz.
In order to check the validity of the results obtained by Figure 7, an experiment wa set at these conditions. The experimental yield of mutton bone biodiesel was estimated a 89.74%, which showed good consistency with the desirability function result (90.14%).  The comparison between the results of Figures 5 and 6 shows that the higher frequency (45 kHz) could give an increased yield of biodiesel at lower catalyst amount.

Optimization
The optimum value of the response surface, catalyst amount, and M/O molar ratio were obtained by considering the desirability function approach as presented in Figure 7. The results showed that the maximum yield of 89.74% could be obtained with the catalyst amount of 1 wt%, M/O molar ratio of 12:1, and ultrasonic frequency of 45 kHz. The comparison between the results of Figures 5 and 6 shows that the highe quency (45 kHz) could give an increased yield of biodiesel at lower catalyst amount.

Optimization
The optimum value of the response surface, catalyst amount, and M/O molar were obtained by considering the desirability function approach as presented in Figu The results showed that the maximum yield of 89.74% could be obtained with the cat amount of 1 wt%, M/O molar ratio of 12:1, and ultrasonic frequency of 45 kHz.
In order to check the validity of the results obtained by Figure 7, an experiment set at these conditions. The experimental yield of mutton bone biodiesel was estimat 89.74%, which showed good consistency with the desirability function result (90.14%  In order to check the validity of the results obtained by Figure 7, an experiment was set at these conditions. The experimental yield of mutton bone biodiesel was estimated as 89.74%, which showed good consistency with the desirability function result (90.14%).

Analysis
A set of analyses was carried out to determine the biodiesel sample's properties with optimal conditions and compare the results with the standards.

FA Contents
The qualitative criteria of biodiesel and the acceptable impurity in it are determined by the standards [58]. For instance, the maximum allowable methyl ester content in a biofuel is about 5 mg/kg (ppm) in the transport sector.
In order to determine FAs composition in biodiesel, the GC analysis was performed. The analysis was carried out using the library of the National Institute of Standards and Technology (NIST) with more than 62,000 patterns ( Figure 8).

Analysis
A set of analyses was carried out to determine the biodiesel sample's properties wit optimal conditions and compare the results with the standards.

FA Contents
The qualitative criteria of biodiesel and the acceptable impurity in it are determine by the standards [58]. For instance, the maximum allowable methyl ester content in a bio fuel is about 5 mg/kg (ppm) in the transport sector.
In order to determine FAs composition in biodiesel, the GC analysis was performed The analysis was carried out using the library of the National Institute of Standards an Technology (NIST) with more than 62,000 patterns ( Figure 8). As illustrated in Figure 9, GC/MS chromatogram analysis of biodiesel had 18 peak with retention time ranging from 13.95 to 20.85 min. As shown, the presence of phyto chemicals is clear. Totally, 18 FAME compounds were determined in the chicken feet o biodiesel (Table 5). Elaidic acid (47.98%), palmitic acid (19.18%), and palmitoleic aci (16.45%) were the three main ingredients. As illustrated in Figure 9, GC/MS chromatogram analysis of biodiesel had 18 peaks with retention time ranging from 13.95 to 20.85 min. As shown, the presence of phytochemicals is clear. Totally, 18 FAME compounds were determined in the chicken feet oil biodiesel (Table 5). Elaidic acid (47.98%), palmitic acid (19.18%), and palmitoleic acid (16.45%) were the three main ingredients. Clearly, there were seven saturated FAs such as methyl tetradecanoic acid (1.13%), methyl pentadecanoic acid (0.13%), methyl hexadecanoic acid (19.18%), methyl heptadecanoic acid (0.2%), methyl octadecanoic acid (8.14%), methyl eicosanoic acid (0.13%), and cyclooctene, 3-ethenyl (0.22%). Moreover, 11 unsaturated FAs were found in the biodiesel.

Physicochemical Characterization
The properties of chicken feet oil biodiesel like density, acid value, saponification value, iodine value, cetane number, flash, fire, and cloud points were examined based on the ASTM standard procedures. The kinematic viscosity test was done based on ASTM D92-85 using a Canon-Fenske Routine Viscometer at 40 • C. The standard values and experimental results are compared in Table 6. Clearly, the obtained values from the analysis are within the standard range. The findings support a good performance of biodiesel fuel prepared from chicken feet oil.

Modeling of Chicken Feet Biodiesel Production in a Membrane Reactor System
In this section, attempts have been made to propose a membrane system to decrease the transesterification reaction time. The system has the potential to separate biodiesel (FAME) and recycle it to the reactor. Therefore, the biodiesel purification and reaction rate enhancement will take place simultaneously.

Determination of the Reaction Kinetics
The physical ultrasonic wave effects on reactants (methanol and triglyceride) are dissimilar. Thus, individual reaction rate orders should be taken into account for the reactants in the transesterification reaction. Equation (4) Grant and Gude [59] proposed the following reaction rate for ultrasonic transesterification reaction: In this work, the reaction rate constant is considered as a function of ultrasonic bath frequency: The constants of Equations (5) and (6) are calculated based on the model fitting of experimental results and signified in Table 7.

Mathematical Modeling of the Membrane Reactor System
The diagram for the proposed membrane system is presented in Figure 9. The reactants containing methanol and triglyceride are fed in a well-stirred tank. The products are then directed to a membrane module. The biodiesel is permeated through the membrane to allow the recycling of the retentate (especially alcohol) to the reactor. This will lead to producing high-purity biodiesel as a final product. In this work, a filtanium ceramic membrane (TAMI, Nyons, France) made of titanium oxide support and the active layer was considered [51]. Equation (7) is used for estimating the kinetics of the ultrasound-assisted biodiesel production from chicken feet oil. In order to obtain this equation, a perfect mixture for the recycled stream is assumed, leading to the uniform properties (temperature, concentration, etc.) for the recycled stream. On the other hand, the feed mass flow rate is considered equal to the product mass flow rate [52]. The diagram for the proposed membrane system is presented in Figure 9. The reactants containing methanol and triglyceride are fed in a well-stirred tank. The products are then directed to a membrane module. The biodiesel is permeated through the membrane to allow the recycling of the retentate (especially alcohol) to the reactor. This will lead to producing high-purity biodiesel as a final product. In this work, a filtanium ceramic membrane (TAMI, Nyons, France) made of titanium oxide support and the active layer was considered [51]. Equation (7) is used for estimating the kinetics of the ultrasound-assisted biodiesel production from chicken feet oil. In order to obtain this equation, a perfect mixture for the recycled stream is assumed, leading to the uniform properties (temperature, concentration, etc.) for the recycled stream. On the other hand, the feed mass flow rate is considered equal to the product mass flow rate [52].
In Equation (7), ⩒o ut ṁTotal-in, FMethanol-in, FTG-in, and MWTG, ρout are permeate flow rate of the (L/min), mass flow rate of the feedstock, methanol molar rate in the feed stream (mol/min), triglyceride molar rate in the feed stream (mol/min), triglyceride molecular weight (g/mol), and product density (g/mL), respectively.
The components molar balance is provided in the following. Triglyceride is supposed not to be presented in the reactor outlet stream. Hence, the molar accumulation rate of triglyceride is as follows: For FAME, glycerol, and methanol, the mole balances are presented in Equations (9)- (11). where: In Equations (8)- (14), V0, [x], r, t, Fx-in, and Fx-out are reactor volume (L), concentration of component x (mol/L), reaction rate ((mol/min)/L), time (t), and flowrate of component x in feed and product streams (mol/min), respectively. Two distinct phases are assumed to be formed: methanol, glycerol, and FAME are presented in a single mobile phase and triglyceride is formed in another phase. The mobile phase volume (Vmobile) can be calculated by Equation (13).
The concentration of FAME in the mobile phase passing through the membrane could be obtained from Equation (14). The diagram for the proposed membrane system is presented in Figure 9. The reactants containing methanol and triglyceride are fed in a well-stirred tank. The products are then directed to a membrane module. The biodiesel is permeated through the membrane to allow the recycling of the retentate (especially alcohol) to the reactor. This will lead to producing high-purity biodiesel as a final product. In this work, a filtanium ceramic membrane (TAMI, Nyons, France) made of titanium oxide support and the active layer was considered [51]. Equation (7) is used for estimating the kinetics of the ultrasound-assisted biodiesel production from chicken feet oil. In order to obtain this equation, a perfect mixture for the recycled stream is assumed, leading to the uniform properties (temperature, concentration, etc.) for the recycled stream. On the other hand, the feed mass flow rate is considered equal to the product mass flow rate [52].
In Equation (7), ⩒out, ṁTotal-in, FMethanol-in, FTG-in, and MWTG, ρout are permeate flow rate of the (L/min), mass flow rate of the feedstock, methanol molar rate in the feed stream (mol/min), triglyceride molar rate in the feed stream (mol/min), triglyceride molecular weight (g/mol), and product density (g/mL), respectively.
The components molar balance is provided in the following. Triglyceride is supposed not to be presented in the reactor outlet stream. Hence, the molar accumulation rate of triglyceride is as follows: For FAME, glycerol, and methanol, the mole balances are presented in Equations (9)- (11). where: In Equations (8)- (14), V0, [x], r, t, Fx-in, and Fx-out are reactor volume (L), concentration of component x (mol/L), reaction rate ((mol/min)/L), time (t), and flowrate of component x in feed and product streams (mol/min), respectively. Two distinct phases are assumed to be formed: methanol, glycerol, and FAME are presented in a single mobile phase and triglyceride is formed in another phase. The mobile phase volume (Vmobile) can be calculated by Equation (13).
The concentration of FAME in the mobile phase passing through the membrane could be obtained from Equation (14). Total−in In Equation (7), The diagram for the proposed membrane system is presented in Figure 9. The reactants containing methanol and triglyceride are fed in a well-stirred tank. The products are then directed to a membrane module. The biodiesel is permeated through the membrane to allow the recycling of the retentate (especially alcohol) to the reactor. This will lead to producing high-purity biodiesel as a final product. In this work, a filtanium ceramic membrane (TAMI, Nyons, France) made of titanium oxide support and the active layer was considered [51]. Equation (7) is used for estimating the kinetics of the ultrasound-assisted biodiesel production from chicken feet oil. In order to obtain this equation, a perfect mixture for the recycled stream is assumed, leading to the uniform properties (temperature, concentration, etc.) for the recycled stream. On the other hand, the feed mass flow rate is considered equal to the product mass flow rate [52].
In Equation (7), ⩒o ut ṁTotal-in, FMethanol-in, FTG-in, and MWTG, ρout are permeate flow rate of the (L/min), mass flow rate of the feedstock, methanol molar rate in the feed stream (mol/min), triglyceride molar rate in the feed stream (mol/min), triglyceride molecular weight (g/mol), and product density (g/mL), respectively. The components molar balance is provided in the following. Triglyceride is supposed not to be presented in the reactor outlet stream. Hence, the molar accumulation rate of triglyceride is as follows: For FAME, glycerol, and methanol, the mole balances are presented in Equations (9)- (11). where: In Equations (8)- (14), V0, [x], r, t, Fx-in, and Fx-out are reactor volume (L), concentration of component x (mol/L), reaction rate ((mol/min)/L), time (t), and flowrate of component x in feed and product streams (mol/min), respectively. Two distinct phases are assumed to be formed: methanol, glycerol, and FAME are presented in a single mobile phase and triglyceride is formed in another phase. The mobile phase volume (Vmobile) can be calculated by Equation (13).
The concentration of FAME in the mobile phase passing through the membrane could be obtained from Equation (14).
out ,ṁ Total-in , F Methanol-in , F TG-in , and MW TG , ρ out are permeate flow rate of the (L/min), mass flow rate of the feedstock, methanol molar rate in the feed stream (mol/min), triglyceride molar rate in the feed stream (mol/min), triglyceride molecular weight (g/mol), and product density (g/mL), respectively.
The components molar balance is provided in the following. Triglyceride is supposed not to be presented in the reactor outlet stream. Hence, the molar accumulation rate of triglyceride is as follows: For FAME, glycerol, and methanol, the mole balances are presented in Equations (9)- (11).
where: F FAME−out = [FAME] out × Energies 2021, 14,2133 The diagram for the proposed membrane system is presen tants containing methanol and triglyceride are fed in a well-stirre then directed to a membrane module. The biodiesel is permeate to allow the recycling of the retentate (especially alcohol) to the producing high-purity biodiesel as a final product. In this work, a brane (TAMI, Nyons, France) made of titanium oxide support considered [51]. Equation (7) is used for estimating the kinetics of the ultra production from chicken feet oil. In order to obtain this equation recycled stream is assumed, leading to the uniform properties tion, etc.) for the recycled stream. On the other hand, the feed ma equal to the product mass flow rate [52].
In Equation (7), ⩒o ut ṁTotal-in, FMethanol-in, FTG-in, and MWTG, ρout a the (L/min), mass flow rate of the feedstock, methanol molar (mol/min), triglyceride molar rate in the feed stream (mol/min weight (g/mol), and product density (g/mL), respectively. The components molar balance is provided in the following. not to be presented in the reactor outlet stream. Hence, the mo triglyceride is as follows: ( ) = + × For FAME, glycerol, and methanol, the mole balances are pr (11).
In Equations (8)- (14), V 0 , [x], r, t, F x-in , and F x-out are reactor volume (L), concentration of component x (mol/L), reaction rate ((mol/min)/L), time (t), and flowrate of component x in feed and product streams (mol/min), respectively. Two distinct phases are assumed to be formed: methanol, glycerol, and FAME are presented in a single mobile phase and triglyceride is formed in another phase. The mobile phase volume (V mobile ) can be calculated by Equation (13).
The concentration of FAME in the mobile phase passing through the membrane could be obtained from Equation (14).
MATLAB 2016a software was applied for system modeling. The modified Rosenbrock method (ode23s) was assisted to solve the set of ODEs. Table 8 presents the system specifications for the membrane system. The system conditions are similar to those used for experimental tests.  [52]. They produced biodiesel from canola oil using a 6 L membrane reactor system [52]. Figure 10 shows the comparison of experimental and calculated FAME concentration variation in the membrane reactor. MATLAB 2016a software was applied for system modeling. The modified Rosenbrock method (ode23s) was assisted to solve the set of ODEs. Table 8 presents the system specifications for the membrane system. The system conditions are similar to those used for experimental tests.  [52]. They produced biodiesel from canola oil using a 6 L membrane reactor system [52]. Figure 10 shows the comparison of experimental and calculated FAME concentration variation in the membrane reactor. As can be seen in Figure 10, the model has a good capability to predict the FAME concentration in the membrane reactor.

The Proposed Membrane System for Chicken Feet Biodiesel
The operating parameters of the proposed membrane system for chicken feet biodiesel are listed in Table 8.
The membrane system performance is evaluated by modeling. Only FAME can permeate through the membrane. Figure 11 shows the TG and FAME concentrations at optimum conditions (frequency = 45 kHz, M/O = 12, and catalyst wt% = 1). As can be seen FAME concentration (mol/lit) Figure 10. The comparison of experimental and calculated FAME concentration variation in the membrane reactor.
As can be seen in Figure 10, the model has a good capability to predict the FAME concentration in the membrane reactor.

The Proposed Membrane System for Chicken Feet Biodiesel
The operating parameters of the proposed membrane system for chicken feet biodiesel are listed in Table 8.
The membrane system performance is evaluated by modeling. Only FAME can permeate through the membrane. Figure 11 shows the TG and FAME concentrations at optimum conditions (frequency = 45 kHz, M/O = 12, and catalyst wt% = 1). As can be seen, after 15 min, a significant amount of FAME has been produced, which indicates the high efficiency of the proposed membrane system. IT means that the reaction time in the membrane system (15 min) is six times shorter than the conventional method (1.5 h). after 15 min, a significant amount of FAME has been produced, which indicates the high efficiency of the proposed membrane system. IT means that the reaction time in the membrane system (15 min) is six times shorter than the conventional method (1.5 h). The biodiesel yield, as well as TG conversion rates, are shown in Figure 12. A comparison between the biodiesel yield with Figure 8 shows that the proposed system's yield is equivalent to a single batch reactor with a reaction time of 1.5 h. Therefore, the membrane system has significantly improved the reaction rate. The biodiesel yield, as well as TG conversion rates, are shown in Figure 12. A comparison between the biodiesel yield with Figure 8 shows that the proposed system's yield is equivalent to a single batch reactor with a reaction time of 1.5 h. Therefore, the membrane system has significantly improved the reaction rate. after 15 min, a significant amount of FAME has been produced, which indicates the high efficiency of the proposed membrane system. IT means that the reaction time in the membrane system (15 min) is six times shorter than the conventional method (1.5 h). The biodiesel yield, as well as TG conversion rates, are shown in Figure 12. A comparison between the biodiesel yield with Figure 8 shows that the proposed system's yield is equivalent to a single batch reactor with a reaction time of 1.5 h. Therefore, the membrane system has significantly improved the reaction rate.  The effect of frequency on the reaction yield for the membrane system is shown in Figure 13. As can be seen, at higher frequencies, we would expect a larger effect of membrane application on the biodiesel yield and reaction rate. The effect of frequency on the reaction yield for the membrane system is shown in Figure 13. As can be seen, at higher frequencies, we would expect a larger effect of membrane application on the biodiesel yield and reaction rate. Figure 13. The effect of frequency on the reaction yield for the membrane system.

Conclusions
Due to the energy crisis and the declining fossil fuel reserves, researchers have been interested in biodiesel as an alternative fuel. In this study, an experimental setup was designed to generate biodiesel from chicken feet oil using ultrasonic waves with two frequencies (25 and 45 kHz). The chicken feet oil was subjected to the esterification-transesterification processes. The effect of M/O molar ratio and KOH catalyst amount on biodiesel yield was investigated. A polynomial model obtained by RSM analyzed the experimental data.
The desirability function approach found the optimized conditions. Results showed that the highest biodiesel yield could be achieved using a methanol-to-oil ratio of 12, the KOH amount of 1 wt%, and the ultrasonic sound frequency of 45 kHz. The predicted yield (89.74%) was in good agreement with the experimental yield (90.14%).
Finally, the biodiesel was analyzed to evaluate the biodiesel characteristics as a fuel. The analysis of density, acid value, saponification value, iodine value, kinematic viscosity, and combustion properties showed the good performance of chicken feet oil biodiesel compared to other fuels.
In this study, a membrane system is proposed to decrease the time consumption of the process. The mathematical modeling results showed the reaction time appears to be six times shorter in a membrane setup. The membrane effect is more prominent at greater frequencies than the lower ones. Consequently, membrane application is highly recommended for biodiesel production.

Conclusions
Due to the energy crisis and the declining fossil fuel reserves, researchers have been interested in biodiesel as an alternative fuel. In this study, an experimental setup was designed to generate biodiesel from chicken feet oil using ultrasonic waves with two frequencies (25 and 45 kHz). The chicken feet oil was subjected to the esterificationtransesterification processes. The effect of M/O molar ratio and KOH catalyst amount on biodiesel yield was investigated. A polynomial model obtained by RSM analyzed the experimental data.
The desirability function approach found the optimized conditions. Results showed that the highest biodiesel yield could be achieved using a methanol-to-oil ratio of 12, the KOH amount of 1 wt%, and the ultrasonic sound frequency of 45 kHz. The predicted yield (89.74%) was in good agreement with the experimental yield (90.14%).
Finally, the biodiesel was analyzed to evaluate the biodiesel characteristics as a fuel. The analysis of density, acid value, saponification value, iodine value, kinematic viscosity, and combustion properties showed the good performance of chicken feet oil biodiesel compared to other fuels.
In this study, a membrane system is proposed to decrease the time consumption of the process. The mathematical modeling results showed the reaction time appears to be six times shorter in a membrane setup. The membrane effect is more prominent at greater frequencies than the lower ones. Consequently, membrane application is highly recommended for biodiesel production.