Optimization and kinetic modeling of waste lard methanolysis in a continuous rec

Marija R.Miladinović,Ivan J.Stojković,Ana V.Veličković,Olivera S.Stamenković,Ivana B.Banković-Ilić,Vlada B.Veljković,3,*

1 University of Niš,Faculty of Technology,Bulevar oslobođenja 124,Leskovac 16000,Serbia

2 University of Belgrade,Faculty of Technology and Metallurgy,Karnegijeva 4,Belgrade 11000,Serbia

3 Serbian Academy of Sciences and Arts(SASA),Knez Mihailova 35,Belgrade 11000,Serbia

Keywords:Biodiesel Kinetics Optimization Reciprocating plate reactor Waste lard

ABSTRACT Continuous biodiesel production from a waste pig-roasting lard,methanol and KOH was carried out in a reciprocating plate reactor(RPR)using a factorial design containing three process factors,namely methanol/lard molar ratio,catalyst loading,and normalized height of the reactor.The main goals were to optimize the influential process factors with respect to biodiesel purity using the response surface methodology and to model the kinetics of the transesterification reaction in order to describe the change of triacylglycerols(TAG)and fatty acid methyl esters(FAME)concentrations along the RPR height.The first-order rate law was proved for both the reaction and the mass transfer.The model of the changing reaction mechanism and mass transfer of TAG was also applicable.Both kinetic models agreed with the experimental concentrations of TAG and FAME determined along the RPR height.

1.Introduction

Biodiesel can be produced from various oily feedstocks by transesterification of triacylglycerols(TAG)or esterification of free fatty acids(FFA)with alcohol commonly using a catalyst.Because of overall benefits coming with biodiesel,it is necessary to develop novel procedures that would use low-cost oily raw materials,such as waste lipid feedstocks or non-edible oils,more effective reactor types,continuous operation and the optimized reaction conditions.In line with this,the present study is focused on the use of low-cost waste lard and the reciprocating plate reactor(RPR)for continuous biodiesel production by base-catalyzed transesterification.

Waste animal fats(WAF)from meat processing are potential lowcost raw materials to produce biodiesel[1,2].Waste and raw lard[3-9],beef tallow[10-12],and poultry fat[13-15]are commonly used as feedstocks.The lard transesterification is conducted in the presence of homogeneous[3-5]and heterogeneous[6]catalysts and enzymes[7],as well as supercritical conditions of methanol[8]and a two-step process[9].Usually,stirred batch reactors are used while continuous reactors are rarely employed.Among novel reactors,continuous RPRs[16,17]can especially be suitable for upgrading biodiesel production processes because the interfacial contact area between the immiscible reactants is maximized for interfacial mass transfer at relatively small power consumption.The positive characteristics of RPRs are the frequent renewal of the interfacial contact area and uniform liquid-liquid dispersion[18].Also,its advantages are the almost plug flow,effective twophase mixing,and fast KOH-catalyzed transesterification reaction at the room temperature[16,17].Statistical and kinetic modeling and optimization have rarely been applied for improving the WAF transesterification reaction conditions.The pseudo-first-order kinetics is proved for the batch KOH-catalyzed waste lard methanolysis[3],whereas the same reaction conducted in a packed-bed reactor follows a combination of the laws of changing-and first-order reaction rate in respect of TAG and methyl esters,respectively[6].

In this paper,the continuous biodiesel synthesis from waste lard obtained from pig roasting,methanol and KOH as a catalyst was studied in an RPR at 60 °C using a factorial design.The main goals were the optimization of the methanol/lard(M/L)molar ratio,catalyst loading and height of the column reactor in respect to fatty acid methyl esters(FAME)content in the ester phase flowing out of the reactor using the response surface methodology(RSM)and the test of the existing kinetic models describing the change of the conversion degree of TAG(xA)along the height of the RPR.

2.Materials and Methods

2.1.Waste lard

Waste lard was obtained from a roasted-piglet shop.Before use,the waste lard was first cooled to remove water from the solidified lard,which was heated in a furnace at 100°C for 2 h and filtered through a cotton material[3].The used waste lard had a low content of FFA(0.53%,i.e.1.06 mg KOH·g-1)and water(0.20%),thus being suitable for direct base-catalyzed methanolysis.Its saponification and iodine values were 195.3 mg KOH·g-1and 57.5 g I2/100 g,respectively.The fatty acid composition of waste lard is given in Table 1.

2.2.Chemicals

Methanol(HPLC grade)and KOH(＞85%purity)were obtained from LGC Promochem(Wesel,Germany)and Centrohem(Belgrade,Serbia),respectively.HCl(36.8%)was from Moslab(Belgrade,Serbia),whereas n-hexane and 2-propanol(both of HPLC grade)were from Carlo Erba(Italy)and Fisher Chemical(Leicestershire,UK),respectively.The esters of fatty acids(palmitic,stearic,oleic and linoleic),monoolein,diolein,and triolein,used as HPLC standards,were from Sigma Aldrich.

2.3.Equipment

Fig.1 shows the experimental set-up that included the RPR and auxiliary equipment,whereas Table 2 presents the main geometric characteristics of the reactor and the applied working conditions.

A set of 65 perforated plates,fastened to the central shaft,was moved up-and-down through a 2.54 cm i.d.glass column by a motor.The glass column was placed in a glass shell through which distilled water recirculated from a bath,kept at 60°C,by a pump.The amplitude(10 mm)and frequency(2 Hz)of reciprocating plate movement were selected from the earlier studies[16,17].The reservoirs of the reactants were placed on digital scales.A methanol solution of KOH and waste lard(preheated at about 40°C)were transported from the reservoirs by the piston pumps.The two liquid streams were mixed before a heater,where the joint stream was heated up to 60°C,then fed to the column bottom through a nozzle and flew upward through the column.Seven valves,set along the column,were used for sampling the reaction mixture.The outlet reaction mixture flowed to a gravitational separator where the alcoholic and ester phases were separated and transported apart to the reservoirs.

Table 1 Fatty acid composition of the waste lard①

Fig.1.Schematicdrawingoftheexperimental set-up:1—RPR;2—drivemotor;3—thermostated chamber with pump;4—reservoir for KOH solution in methanol;5—reservoir for waste lard;6—digital scale;7—piston pump;8—heater;9—gravitational separator;10—reservoir for alcoholic phase;11—reservoir for crude biodiesel.

2.4.Procedure and reaction conditions

The transesterification of waste lard was performed at 4.5:1,6.0:1 or 7.5:1 M/L molar ratio,0.5%,0.75%or 1.0%(of waste lard)KOH loading and 60 °C.Methanolic KOH solutions of various concentrations were prepared prior to use.The input mass flow rates of the methanolic KOH solution and the waste lard matched the predetermined M/L molar ratio and KOH loading.The samples were collected at eight sampling points from the top to the bottom of the column,right away quenched by adding the 11 vol% aqueous HCl solution to neutralize KOH and centrifuged(15 min;3500 r⋅min-1;700×g).The upper FAME layer was separated,dissolved in a solution of 2-propanol and n-hexane(5:4 v/v)in the 1:200 ratio,filtered using a 0.45 μm filter,and analyzed by HPLC.TAG conversion degree(xA)was calculated from the TAG content of the samples taken from the reactor and the inlet mixture of the reactants(TAG and TAG0,respectively):

Table 2 Geometric characteristics of the RPR and the operating conditions

2.5.Experimental design

A factorial design containing three process factors,namely M/L molar ratio,catalyst loading and normalized height of the reactor(h/h0,where h is the distance of a sampling point from the column bottom and h0is the reactor height),was conducted.The actual(uncoded)and coded levels of the M/L molar ratio,catalyst loading,and normalized reactor height are given in Table 3.Table 4 shows the experimental matrix of the applied experimental design involving 55 runs.The statistical significance of process factors and the twofactor interactions were assessed based on the F-and p-values with a confidence level of 95%using the analysis of variance(ANOVA).The factorial design was performed by the Design Expert software.

2.6.Kinetic modeling

For the kinetic modeling of the KOH-catalyzed wastelard methanolysis,the existence of heterogeneous and pseudo-homogeneous regimes,where the overall reaction was controlled by the mass transfer and chemical reaction,respectively was assumed.Such behavior was recognized for the methanolysis of sunflower oil catalyzed by KOH in the same RPR[16].Two reaction mechanisms were tested:(1)the pseudo-first-order reaction in both regimes and(2)the changing mechanism coupled with the TAG mass transfer in the entire reactor.The methanolysis occurs through the conversion of TAG to FAME and glycerol via diacylglycerols(DAG)and monoacylglycerols(MAG).Since the consumption of the intermediates is faster than that of TAG,they are not considered.Hence,the overall reversible methanolysis reaction is shown as follows:

where A,B,R,and S designate TAG,methanol,FAME,and glycerol,respectively.

The flow through the RPR was ideal plug flow as proved by the previous tests under the same operating conditions[16,17].Since the FFA content in the waste lard was only 0.53%,the FFA neutralization was neglected.Saponification of TAG could also be ignored as the high M/L molar ratio was employed.

2.6.1.Pseudo-first-order reaction in heterogeneous and homogeneous regimes

2.6.1.1.Heterogeneous regime.The overall reaction rate was controlled by the TAG mass transfer resistance in the lower part of the RPR.Hence,the TAG conversion rate is equal to the rate of TAG mass transfer into methanol drops.On the basis of the assumed plug flow,the rate equation is as follows[16]:

where kcis the TAG mass transfer coefficient,a is the average specific interfacial area(their product kca is known as the volumetric TAG mass transfer coefficient),cAis the TAG concentration in the lard phase,cA,sis the TAG concentration at the interface,and τ is theresidence time(τ=hS/v0,where S is the cross-sectional area,h is the reactor height,and v0is the volumetric flow rate).As cA,s=0 and cA=cA0(1-xA),then after an appropriate rearrangement and integration,the following equation was derived[16]:

Table 3 Experimental range and levels of each process factor

The kca-values were found from the slope(h0Skca/v0)of the dependency of-ln(1-xA)on h/h0.

2.6.1.2.Pseudo-homogeneous regime.Being slower than the TAG mass transfer,the reaction limited the overall process rate in the pseudohomogeneous regime.Assuming the plug flow through the RPR and the irreversible pseudo-first-order of the reaction,the following kinetic equation was used:

where kappis the apparent reaction rate constant(pseudo-first-order)that incorporates the catalyst concentration.After an appropriate rearrangement and integration,the following equation was derived:

where C1is the integration constant.The value of kappwas calculated from the slope(h0Skapp/v0)of the dependency-ln(1-xA)versus h/h0.

2.6.2.Changing mechanism coupled with TAG mass transfer

Miladinović et al.[19]originally developed this model for the heterogeneously-catalyzed sunflower oil methanolysis.The changing mechanism has already been assumed for homogeneous alkalicatalyzed methanolysis[20].Besides the TAG concentration,this model involves the effect of the FAME concentration on the overall reaction rate.FAME act as a co-solvent that improves the interfacial contact area,thus enhancing the TAG mass transfer rate.This model was integrated into the steady-state mass balance of the plug flow RPR to yield the following equation[21]:

where kmis the apparent reaction rate constant,K is the model parameter that takes the TAG affinity to the catalytic species(methoxide ions)into account,cRis the concentration of FAME and cR0is the hypothetic initial concentration of FAME that corresponds to the initially available catalytic species near the interfacial area,which is introduced to avoid the fact that cR=0 for τ=0.If cAand cRare expressed in term of xA,Eq.(7)can be transformed as follows:

For the heterogeneous regime,where K ≪cA,a simplified equation is obtained:

The parameters of Eqs.(8)and(9)were calculated from the experimental values of xAby the Polymath software.These equations and software were also applied for calculating the xA-values along the reactor height,which were then used to calculate cAand cR(=3cA0xA).

2.7.HPLC analysis

The chemical composition of the ester phase was analyzed by the HPLC method[22].FAME content was determined with an experimental error in the replicated runs of±1.0%.

3.Results and Discussion

3.1.Statistical modeling and optimization

For both full and reduced quadratic model equations,the significant lack of fit and the coefficient of variation were higher than 10%(Tables S1 and S2,Supporting information),thus indicating that both these model equations did not exactly represent the observed FAME content and their reproducibility was uncertain in the experimental region employed[23].Therefore,despite the high coefficient of determination,their use for modeling FAME content could not be advised[24].While the full cubic equation was aliased,its simplified form without the statistically insignificant terms,called here reduced cubic equation,was found to be significant(F-value=74.7 and p-value＜0.0001)and with the insignificant lack of fit(p=0.509)(Table 5).This model was represented by the following regression equations:

-Actual:

-Coded:

The quality of the fit of the experimental data by the reduced cubic model was assessed on the basis of several statistical criteria.The R2-value of 0.944 highlighted the goodness of fit of the derived reduced cubic model since it could explain 94.4% of FAME content variation,whereas only 5.6%of the variation resulted from the uncontrolled factors.The-value of 0.910 agreed with thevalue of 0.932,thus demonstrating a very good predictive ability of the reduced cubic model.The coefficient of variation of 7.8%pointedout a good reproducibility of this model.The relatively small value(±7.1%,55 data)of the mean relative percentage deviation(MRPD)demonstrated a good agreement between the actual and predicted data.The Kolmogorov-Smirnov normality test(statistic=0.171＞p=0.072,degrees of freedom=55)confirmed at the 0.05 level that the data were normally distributed.Besides that,the analyzed data had no outlier value.

Table 5 ANOVA results for the response surface reduced cubic model

The normalized reactor height(X3),i.e.the residence time,having the highest F-value,affected FAME content more significantly than the catalyst loading and the M/L molar ratio.The higher significant impact of the catalyst loading on FAME content,compared to the influence of M/L molar ratio,was also noticed for the methanolysis of refined lard catalyzed by KOH[4].As concluded from Eq.(11),the M/L molar ratio affected FAME content negatively unlike the positive effect of the catalyst loading and the reactor height.Therefore,the larger the catalyst loading and the residence time,the higher the FAME content.The positive effect of catalyst loading on FAME content resulted from the dependency of the reaction rate constant on it,where the reaction rate constant was enhanced with increasing the catalyst loading.Also,the positive and statistically significant impact of catalyst concentration on FAME formation was determined for the alkali-catalyzed transesterification of used frying oil under batch conditions[25].The increase of residence time due to the increase of the reactor height resulted in higher FAME content due to a longer time contact between the reactants and the catalyst.FAME concentration also increased along the height of a liquid-liquid film reactor where the palm oil methanolysis catalyzed by NaOH was carried out[26].The influence of the M/L ratio appeared to be more complex and dependent on the other two factors.A positive effect of the methanol/tallow molar ratio on ester yield was observed during the KOH-catalyzed methanolysis in a batch reactor[27].However,due to increasing the solubility of the generated glycerol,the high amount of methanol could cause the reversible reaction resulting in lower FAME content[28,29].

Eq.(11)has three significant two-factor interaction terms affecting FAME content,which involve all three process factors.Hence,these factors did not independently influence FAME content,i.e.the effect of a process factor depended on the specific level of the other two.Among the significant two-factor interactions,the interaction between the catalyst loading and the M/L molar ratio had the most significant impact on FAME content,whereas the quadratic term of catalyst loading was more influential on FAME content than that of M/L molar ratio.The interactions between catalyst loading and M/L molar ratio or normalized reactor height were negative while that between M/L molar ratio and normalized reactor height had a positive and significant impact on FAME content.This negative effect of the interaction between catalyst loading and M/L molar ratio could be probably attributed to decreasing the catalyst concentration and increasing the glycerol solubility in a larger methanol amount,thus promoting the backward reaction.As the reactor height increased,saponification of FAME and TAG could be promoted with increasing the catalyst loading,thus causing the negative effect of the interaction between these two influential process factors.With increasing the reactor height,the residence time and the zone of the uniform emulsion of very fine drops increased,which favored the FAME synthesis at higher M/L molar ratios.Which of these two-way interactions would prevail depended on the relative importance of their influence under the certain combination of the individual process factors.

Aiming at the achievement of the maximum FAME content in the range of up to 100%,the optimal process factors in the used experimental ranges were found by solving Eq.(11).Table 6 presents only 10 combinations of the optimal process conditions,showing that the optimal catalyst loading was in the range of 0.9%to 1%,the optimal M/L molar ratio was close to either the lowest or highest level(4.5:1-4.7:1 and 7.3:1-7.4:1,respectively)and the optimal reactor height corresponded to the reactor outlet.

Table 6 Optimum reaction conditions on the basis of the reduced cubic model

Fig.2 shows the outlet FAME content as a function of the catalyst loading and the M/L molar ratio in the form of 3D and contour plots resulted from the developed reduced cubic model.The contour plot shows that the outlet FAME content larger than 96.5%could be achieved in the whole range of M/L molar ratio if the catalyst loading was high enough(shadowed area).Therefore,the minimum M/L molar ratio was the additional criterion for selecting the optimal process conditions.In this way,the optimal process conditions ensuring the maximum outlet FAME content higher than 99%were as follows:the catalyst loading of 0.9%(of lard mass)and the M/L molar ratio of 4.5:1.The experimentally obtained FAME content under the same M/L molar ratio and somewhat higher catalyst loading(1.0%of lard mass)was 96.2%,indicating that the model overestimated the FAME content in the design area determined by high catalyst loading and either low or high M/L molar ratio.Hoque et al.[30]reported the optimal range of M/L molar ratio for the batch methanolysis of various feedstocks including animal fat in the range between 4.8:1 and 6.5:1.

3.2.Kinetic analysis

3.2.1.Model of pseudo-first order reaction

Eqs.(4)and(6)describe the variation of xAalong the height of the RPR for the methanolysis of waste lard catalyzed by KOH.Fig.3 demonstrates a linear dependency of In(1-xA)on h/h0.Except for the lowest catalyst and methanol amounts(0.5%of waste lard and 4.5:1 M/L molar ratio,respectively),where only the heterogeneous regime was observed,for the other combinations of catalyst loading and M/L molar ratio,both regimes existed.In that case,the initial part of the reactor(approximately one-third of the reactor)was characterized by a slow reaction rate because of a small rate of TAG transfer from the bulk of waste lard towards the waste lard-methanol contact area.For this regime,kca did not depend on the catalyst concentration and the M/L molar ratio,i.e.kca=0.036 min-1.As the formed FAME behaved as a cosolvent while DAG and MAG acted as emulsifiers,the pseudohomogeneous system was formed in the upper column part,where the overall process rate was controlled by the chemical reaction rate.At all M/L molar ratios applied,the value of kapp(Table S3,Supporting information)increased linearly with increasing the catalyst amount(Fig.4).The slope of the straight line corresponded to the reaction rate constant k1=4.70 L·(mol·min-1)-1(R2=0.995).

3.2.2.Model of changing mechanism and mass transfer limitation

After calculating the parameters of Eq.(7),they were divided by the initial methanol concentration(km/cB0and K/cB0)and then correlated with the catalyst concentration[19].Fig.5 confirms the linear relations for km/cB0and K/cB0with the catalyst concentration with the slope representing the reaction rate constant(k2=4.54 L2·mol-2·min-1and the modified TAG affinity for catalytic species(K′=8.73 L·mol-1).The k2-value for the waste lard methanolysis in the RPR is nearly a hundred times higher than the value(0.045 L2·mol-2·min-1for the quicklimecatalyzed methanolysis of sunflower oil in a stirred batch reactor at 60°C[19].

Fig.6 shows the dependency of cR0on the M/L molar ratio and the catalyst concentration.At a constant M/L molar ratio,this parameter increased with the increase of the catalyst concentration up to approximately 0.10 mol·L-1and remained constant with further increasing the catalyst amount.On the other hand,with increasing the M/L molar ratio,this parameter decreased because of the dilution of the reaction mixture by the high methanol amount,which decreased the catalyst concentration in the reaction system.

3.2.3.Simulation of TAG and FAME variation

For the lowest KOH concentration(0.5%of waste lard)and the lowest M/L molar ratio(4.5:1),when the reaction rate was limited only by the TAG mass transfer,Eqs.(4)and(9)were applied for calculating xA,cAand cRcR.The actual and predicted values of cAand cRare compared in Fig.7(a)and Fig.8(a).An acceptable agreement between the actual and predicted values was pointed out by the MRPD-values of±25.2%and±15.9%,respectively.For the other reaction conditions,xAwas calculated by Eqs.(4),(6)and(8).As it can be seen in Figs.7(b)and(c)and 8(b)and(c),the models fitted adequately the experimental data under these reaction conditions(catalyst loading of 0.75% and 1.00%of waste lard and M/L molar ratio of 6.0:1 and 7.5:1),which was also indicated by even lower MRPD-values of±9.2%and±11.8%for models of pseudo-first-order reaction and changing mechanism coupled with mass transfer,respectively.Figs.7 and 8 show that the increase of FAME content in the middle part of the reactor was higher than in the highest part of the reactor(h/h0＞0.70),where the increase of FAME content was＜2%.The similar behavior was observed in the case of the palm oil methanolysis performed in a liquid-liquid film reactor[26].

Fig.3.The linear dependence of-ln(1-xA)on the normalized reactor height at different M/L molar ratios:a)4.5:1,b)6.0:1 and c)7.5:1(catalyst loading,%of waste lard:0.50—circles,0.75—triangles and 1.00—squares;mass transfer-controlled regime:open symbols and chemical reaction controlled regime:solid symbols).

Fig.4.Dependence of apparent reaction rate constant on the catalyst concentration for different M/L molar ratios:●4.5:1;▲6.0:1;■7.5:1.

The same model was verified for the sunflower oil methanolysis conducted in the same RPR at 6.0:1,20°C and 1.0%KOH[16](Fig.S1,Supporting information;MPRD:±6.4%).The validity of the model for waste and sunflower oil indicated its potential for modeling the kinetics of any transesterification reaction.

3.3.Comparison of performance RPR with other reactor types

It was encouraging to compare the performances of the RPR and other reactor types,as well as the catalytic capabilities of KOH and other catalyst types(NaOH,quicklime bits)applied in the methanolysis of various feedstocks under similar process conditions.Table 7 presents an overview of the conversion(or esters yields),capacity and operating conditions in several reactor types,such as stirred[11],reciprocating plate[16,31,32],ultrasonic[33],zigzag micro-channel[34],metal foam[35]and packed-bed[6,21]reactors.

Fig.5.The linear dependences of km/cB0(●)and K/cB0(■)on the catalyst concentration for all M/L molar ratios(R2=0.95 and 0.98,respectively).

Fig.6.The variation of cR0with catalyst concentration at various M/L molar ratios:●4.5:1;▲6.0:1;■7.5:1.

The capacity of the present RPR for the waste lard methanolysis performed under the optimal process conditions with the best FAME content of 96.2% was 120 kg·d-1.Compared to it,a batch pilot reactor used for the KOH-catalyzed methanolysis of beef tallow had higher capacity(800 kg·d-1),a slightly lower conversion(＞95%)within a long reaction time(3 h)at slightly higher catalyst amount and temperature[11].Although the use of ultrasonic irradiation in a tubular reactor has certain benefits of lower temperature(38-40 °C)[33],this process required larger methanol/oil molar ratio(7.5:1 and 6.0:1 for edible and palm oil,respectively)and longer residence time(30 min)to achieve FAME content over 95%than the process in the RPR.A zigzag micro-channel reactor had higher reaction efficiency(99.5%FAME yield in 28 s)than the RPR under the optimal reaction conditions,which could be attributed to the more intensive mass transfer due to passive mixing at the micro-scale[34].However,its capacity(0.28 kg·d-1)was much smaller than that of the RPR and hence,an excessive number of reactors should be applied.Metal foam reactor can also reduce the residence time(3.26 min)for achieving a high ester yield(95.2%)at the increased methanol/oil molar ratio(10:1)but it has smaller capacity(13.2 kg·d-1)[35].The shorter residence time for reaction completion and higher production capacity are advantages of the RPR over a packed-bed reactor for the waste lard methanolysis[6].On the other hand,the disadvantage referred to the methyl ester separation from KOH.At a lower reaction temperature(20°C),a lower FAME content(78%-80%)was achieved by the KOH-catalyzed sunflower oil methanolysis carried out in the same RPR under the same other reaction conditions[16].FAME content of over 99%was achieved with the same reaction carried out in a series of two RPRs with a gravitational separator between the reactors[31].

The mass transfer resistance existing in the inlet RPR part slows down the transesterification reaction rate.This resistance is caused by the immiscibility of waste lard and methanol[17].Hence,the dispersed drops of methanol in the inlet RPR part are large and the specific interfacial area is relatively small,causing a slow TAG mass transfer that limits the transesterification reaction rate.Intensifying the dispersion of methanol in its initial part may improve the performance of RPR.The insertion of an inert packing in the interplate spaces will intensify mixing and alleviate the mass transfer resistance.This positive effect of added spheres[36-38],Raschig rings[36,39]and pall rings[40]on mass transfer properties of RPRs has already been proved for both gas-liquid and liquid-liquid systems.This approach was proved for the rapeseed oil methanolysis conducted in a 16 cm RPR with spherical packing placed into interplate spaces when the FAME content of 98%was achieved[31].

Fig.7.Comparison of experimental and predicted values of TAG(solid symbols)and FAME(open symbols)concentration calculated by two correlations describing the TAG mass transfer and chemical reaction rates at different M/L molar ratios(a)4.5:1,(b)6.0:1 and(c)7.5:1(simulation:TAG—solid lines,FAME—dash lines;catalyst loadings,%of waste lard:0.5—circles,0.75—triangles and 1.0—squares).

4.Conclusions

The continuous KOH-catalyzed transesterification of waste lard in an RPR was modeled and optimized using RSM.The optimal M/L molar ratio and KOH loading at the reactor outlet(corresponding to the residence time of 10 min)were 4.5:1 and 0.9%of waste lard,respectively.The RPR was also proved as a promising flow reactor for the waste lard methanolysis catalyzed by KOH.The waste lard and sunflower oil methanolysis reactions catalyzed by KOH can be considered either the irreversible pseudo-first-order reactions or the reactions involving the changing mechanism and TGA mass transfer.It should be stressed that independently of the feedstock,the main problem remains the mass transfer resistance in the lower column part.Inserting an inert packing in the initial interplate spaces may alleviate the mass transfer resistance by the intensification of mixing of the immiscible reactants.

Fig.8.Comparison of experimental and predicted values of TAG and FAME concentration calculated by kinetic model for overall reaction at different M/L molar ratios:(a)4.5:1,(b)6.0:1 and(c)7.5:1(simulation:TAG—solid lines,FAME—dash lines;catalyst loadings,%of waste lard:0.5—circles,0.75—triangles and 1.0—squares).

Table 7 Comparison of various reactor and catalyst types for biodiesel production from various feedstocks with methanol

Nomenclature

a specific interfacial area,m-1

C1integration constant,Eq.(6)

cAconcentration of TAG,mol·L-1

cA0initial concentration of TAG,mol·L-1

cA,sconcentration of TAG on the interfacial area,mol·L-1

cB0initial concentration of methanol,mol·L-1

ccatcatalyst concentration,mol·L-1

cRconcentration of FAME,mol·L-1

cR0model parameter,Eq.(7),mol·L-1

h height along the reactor,m

h0total reactor height,m

K model parameter,Eq.(7),mol·L-1

K′ kinetic parameter(model combining changing mechanism and mass transfer),L·mol-1

kappapparent pseudo-first order reaction rate constant,min-1

kcTAG mass transfer coefficient,m·min-1

kca volumetric TAG mass transfer coefficient,min-1

kmapparent reaction rate constant of the model combining the changing reaction mechanism and mass transfer limitation,min-1

k1reaction rate constant(pseudo-first order model),L·mol-1·min-1

k2reaction rate constant(model combining changing mechanism and mass transfer),L2·mol-2·min-1

(-rA) TAG reaction rate,mol·L-1·min-1

S reactor cross-sectional area,m2

TAG TAG content in the FAME/lard fraction of the reaction mixture,%

v0volumetric flow rate,m3·min-1

xAdegree of TAG conversion

τ residence time,min

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2019.02.019.