Process for producing esters and biolubricants, catalysed by fermented solid

Abstract

The present invention relates to a process for producing esters comprising reaction of methyl biodiesel or free fatty acids with a polyhydroxylated alcohol, in the presence of a biocatalyst, which is a fermented solid containing lipases of Rhizomucor miehei produced by culturing the microorganism on agricultural waste by solid state fermentation.

Claims

1. A process for producing biolubricant esters, comprising: a) culturing a microorganism on agricultural waste by solid state fermentation to obtain a biocatalyst; and b) reacting methyl biodiesel or free fatty acids with a polyhydroxylated alcohol in the presence of the biocatalyst obtained from step a) to generate one or more biolubricant esters, wherein the agricultural waste is cottonseed cake or palm oil cake; the biocatalyst comprises a fermented solid produced by the solid state fermentation of the agricultural waste by the microorganism; and the methyl biodiesel is soya biodiesel or castor oil biodiesel.

2. The process according to claim 1, wherein the reaction of the methyl biodiesel with the polyhydroxylated alcohol in step c) is a transesterification reaction.

3. The process according to claim 1, wherein the reaction of the free fatty acids with the polyhydroxylated alcohol in step c) is a hydroesterification reaction.

4. The process according to claim 1, wherein the biocatalyst is used at a concentration from 10 to 30 percentage by weight (wt %).

5. The process according claim 1, wherein a molar ratio from 2:1 to 5:1 of the polyhydroxylated alcohol to the methyl biodiesel or the free fatty acids is used.

6. The process according to claim 1, wherein the free fatty acids are obtained by reaction of soya oil or castor oil with a biocatalyst.

7. The process according to claim 6, wherein the biocatalyst comprises a plurality of lipases.

8. The process according to claim 1, wherein the polyhydroxylated alcohol is neopentyl glycol, trimethylolpropane or pentaerythritol.

9. The process according to claim 1, wherein the microorganism is a fungus.

10. The process according to claim 9, wherein the fungus is Rhizomucor miehei.

11. The process according to claim 1, wherein the one or more esters are generated in step c) by adding the biocatalyst, in the form of a lyophilizate, to a mixture comprising the methyl biodiesel or free fatty acids and the polyhydroxylated alcohol.

12. The process according to claim 1, wherein the fermented solid is reused at least once.

13. The process according to claim 1, wherein the process further comprises: d) purifying the one or more esters produced by reacting the methyl biodiesel or the free fatty acids with the polyhydroxylated alcohol.

14. The process according to claim 1, wherein the agricultural waste is palm oil cake.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) FIG. 1 shows the synthesis of biolubricants based on the reaction between soya biodiesel and neopentyl glycol alcohol catalysed by the lipases of R. miehei present in the fermented solid of palm oil cake.

(2) FIG. 2 shows the reuse of the fermented solid of palm oil cake in the synthesis of biolubricant based on the reaction between soya biodiesel and neopentyl glycol alcohol.

(3) FIG. 3 shows the synthesis of biolubricant based on the reaction between castor oil biodiesel and trimethylolpropane alcohol catalysed by the lipases of R. miehei present in the fermented solid of palm oil cake.

(4) FIG. 4 shows the synthesis of biolubricant based on the reaction between castor oil biodiesel and neopentyl glycol alcohol catalysed by the lipases of R. miehei present in the fermented solid of cottonseed oil cake.

(5) FIG. 5 shows the synthesis of biolubricant based on the reaction between the free fatty acids of castor oil and neopentyl glycol alcohol catalysed by the lipases of R. miehei present in the fermented solid of cottonseed oil cake.

(6) FIG. 6 shows the synthesis of biolubricant based on the reaction between the free fatty acids of soya and neopentyl glycol alcohol catalysed by the lipases of R. miehei present in the fermented solid of cottonseed oil cake.

(7) FIG. 7 shows the activity of the fermented solid (SEP) of palm oil cake, after reuse several times, without washing with solvent, in the synthesis of biolubricants.

DETAILED DESCRIPTION OF THE INVENTION

(8) Unless they are defined otherwise, all the technical and scientific terms used here have the same meaning as understood by a person versed in the subject matter to which the invention relates. The terminology used in the description of the invention has the sole purpose of describing particular embodiments, and is not intended to limit the scope of the teaching. Unless stated otherwise, all the numbers expressing quantities, percentages and proportions, and other numerical values used in the specification and in the claims, must be understood as being qualified, in all cases, by the term about. Thus, unless stated otherwise, the numerical parameters shown in the specification and in the claims are approximations that may vary, depending on the properties to be obtained.

(9) The present inventors solved the problem of the prior art by providing a process for producing esters that comprises reacting methyl biodiesel or free fatty acids with a polyhydroxylated alcohol, in the presence of a biocatalyst, wherein the biocatalyst is a fermented solid, produced by culturing a microorganism in agricultural waste by solid state fermentation.

(10) In a first aspect, the present invention involves the production of low-cost lipases for use in the synthesis of biolubricant esters. For this purpose, agricultural wastes are used as the culture medium in the solid state fermentation process.

(11) Solid state fermentation makes it possible to use low-cost raw materials as the culture medium for microorganisms, having a single fermentation medium. In this process, the substrates not only supply nutrients for culture of the microorganisms, but also serve as support for growth of the cells.

(12) In the context of the present invention, the term agricultural waste(s) is to be understood as solid residues (cakes) of oleaginous raw materials. Preferably, solid residues from the extraction of palm oil and cottonseed oil are used.

(13) The term inoculum is to be understood as cells of microorganisms, in the form of spores or vegetative cells, used for initiating the fermentation process. Preferably, the microorganism is a filamentous fungus. More preferably, the fungus is of the genus Rhizomucor. Even more preferably, the fungus is of the species Rhizomucor miehei.

(14) The term fermenter is to be understood as a chamber with controlled temperature and humidity for development of the microorganism on the cakes.

(15) The term fermented solid is to be understood as the dry fermented cake at the end of the solid state fermentation process containing the biomass of the microorganism and lipases.

(16) In one embodiment, water is added to the palm oil cake or cottonseed oil cake, the substrate for solid state fermentation, in the proportion ideal for the fermentation process, and then the inoculum is mixed in.

(17) The moistened and inoculated cake is then incubated in the fermenter, during which the microorganism grows and, as a result of its metabolism, produces a set of lipases with high synthesis capacity.

(18) At the end of solid state fermentation, the fermented cake is submitted to a drying step before being used in catalysis of the reactions. Preferably, drying is carried out by lyophilization or by forced aeration.

(19) The low-cost enzymatic biocatalyst produced by the solid state fermentation process is used in transesterification or hydroesterification reactions for production of the biolubricant esters.

(20) In the transesterification process, methyl biodiesels are reacted with polyhydroxylated alcohols, producing the biolubricant esters. Preferably, the methyl biodiesel is soya methyl biodiesel or castor oil methyl biodiesel. Preferably, the polyhydroxylated alcohol is neopentyl glycol, trimethylolpropane or pentaerythritol.

(21) In one embodiment, the transesterification reaction is carried out in the biodiesel:alcohol molar ratio from 2 to 5 and optionally 1 to 3% (w/w) of water. The fermented solid is used as a biocatalyst in a concentration from 10 to 30% (w/w). The reaction is carried out in the reactor, with stirring, at a temperature from 30 to 50 C., at atmospheric pressure.

(22) In a preferred embodiment, the reactor used is a controlled-temperature stirred tank at atmospheric pressure, in which the transesterification reaction takes place.

(23) In these conditions, methyl esters are transesterified with the alcohol, producing the biolubricant esters and methanol as a by-product. Said product is separated at the end of the process.

(24) The hydroesterification process consists of a first hydrolysis reaction and a second reaction of esterification.

(25) In one embodiment, the first reaction (hydrolysis) comprises mixing an oleaginous oil and a buffer, in a ratio of 1:1 volume/volume, followed by addition of a lipase in a proportion from 1 to 2% w/v of the weight of oil.

(26) The reaction is carried out in the reactor with stirring, at a temperature from 30 to 40 C., at atmospheric pressure. In these conditions, the oil is hydrolysed and the free fatty acids and glycerol are produced as by-products. The free fatty acids are separated from the buffer, from the glycerol and from the lipase before being used in the esterification reaction.

(27) In a preferred embodiment, the oleaginous oil is soya oil or castor oil and the lipase is a commercial lipase from Candida rugosa or lipases obtained from dormant castor oil plant seeds.

(28) In a preferred embodiment, the reactor used is a controlled-temperature stirred tank at atmospheric pressure, in which the hydrolysis reaction takes place.

(29) In one embodiment, the second reaction (esterification) is carried out by mixing free fatty acids and a polyhydroxylated polyol alcohol, in the molar ratio of free fatty acids to alcohol from 2 to 5 and optionally 1 to 3% (w/w) of water. The fermented solid is used as a biocatalyst in a concentration from 10 to 30% (w/w). The reaction is carried out in the reactor with stirring, at a temperature from 30 to 50 C., at atmospheric pressure.

(30) In a preferred embodiment, the reactor used is a controlled-temperature stirred tank at atmospheric pressure, in which the esterification reaction takes place.

(31) In these conditions, the free fatty acids are esterified with the polyol, producing the biolubricant esters and water as by-product.

(32) The biolubricant esters obtained by the process of the present invention were analysed with respect to their physicochemical properties, displaying satisfactory physicochemical characteristics in line with the biolubricants currently available.

(33) The viscosity of the biolubricants is the most important property of these fluids, as it is directly related to the formation of the film that will protect metallic surfaces against attack.

(34) The viscosity index is a parameter for the behaviour of the viscosity of oils at temperature. The higher the value, the smaller are the changes in viscosity of the oil with temperature changes. Normally, the value of the viscosity index is determined by calculations that take into account the viscosity of the product at 40 C. and at 100 C.

(35) The flow point measures the minimum temperature at which the oil still flows and is a test used for assessing the behaviour of lubricating oils when subjected to low temperatures.

(36) The physicochemical properties such as viscosity, viscosity index and flow point of biolubricants are higher compared to the mineral-base lubricants.

(37) The properties and performance of the biolubricants of the present invention may be further improved by using additives that are compatible with the lubricants, and preferably that are non-toxic and biodegradable.

(38) The esters produced by the process of the present invention are especially useful in lubrication applications in which the maximum operating temperatures are below 120 C., but in which the ambient temperature remains above 40 C.

(39) The biolubricants of the present invention may be used as motor oil, hydraulic fluid, rolling fluid, etc.

(40) The present invention will be further illustrated by the following examples, which are not to be regarded as limiting. As will be obvious to a person skilled in the art, the invention is not limited to these particular embodiments.

EXAMPLES

Example 1Production of the Fermented Solid

(41) The fermented solid of Rhizomucor miehei was obtained as a result of fermentation of cottonseed oil cake (crushed) or palm oil cake (crushed and sievedparticles smaller than 1.18 mm). The fermentations were carried out in beakers containing 15 g of cake with water content adjusted to 65 and 50%, for the palm oil cake and cottonseed oil cake, respectively. Each beaker containing the cake was sterilized at 121 C. for 15 minutes in an autoclave and the cake was inoculated with 10.sup.7 spores of R. miehei per gram of solid (dry weight) and incubated at 30 C. in a climate chamber with relative moisture of 90%, for 72 h. At the end of fermentation, the fermented medium was lyophilized and stored at 4 C. until used. Fermented solids of R. miehei were obtained by solid state fermentation using palm oil cake or cottonseed oil cake as raw materials, with hydrolytic activity of 172 U/g and 291 U/g, respectively.

Example 2Hydrolytic Activity

(42) The hydrolytic activity of the fermented solid was estimated from the change in absorbance in spectrophotometry promoted by hydrolysis of the substrate p-nitrophenyl laurate (p-NFL) at a concentration of 25 mM in solution of acetonitrile/dimethyl sulphoxide (DMSO) 1:1. For the reaction of hydrolysis of the substrate, an aliquot of 250 L of the solution of p-NFL was diluted in 2.2 mL of sodium phosphate buffer pH 7.0 (25 mM) in the cell, which was acclimatized at 30 C. for 2 minutes. After this time, an aliquot of 50 L of the liquid enzymatic extract was added, and the absorbance was monitored in the spectrophotometer (SHIMADZU UV-1800) at 412 nm. One enzyme unit (U) corresponds to the amount of enzyme capable of producing 1 mol of p-nitrophenol per minute, in the test conditions. The activity is calculated using Equation 1:

(43) $\begin{array}{cc}\mathrm{Activity}\left(U\text{/}\mathrm{mL}\right)=\frac{Df{V}_f}{V_s}& \left(\mathrm{Equation}1\right)\end{array}$
where: =change in absorbance (Abs) in the time interval t (in minutes) elapsed during the phase of linear increase in absorbance; D=dilution of the enzyme solution; f=conversion factor (0.094 mol.Math.L.sup.1), obtained by constructing a standard curve of p-NFL at a concentration varying between 0.01 and 0.2 mol.Math.mL.sup.1; Vf=reaction volume, which is the volume of the solution of p-NFL in the buffer and the volume of the sample (mL); Vs=volume of the enzyme solution used in the test (mL).

(44) The hydrolytic activity expressed per gram of dry cake (U/g) was calculated from Equation 2:

(45) $\begin{array}{cc}\mathrm{Activity}\left(U\text{/}g\right)=\frac{\left(U\text{/}\mathrm{mL}\right)V_t}{m}& \left(\mathrm{Equation}2\right)\end{array}$
where: Vt=volume of buffer used in extraction of the enzyme; m=dry weight of cake.

Example 3Transesterification Reaction

Example 3.1Soya Biodiesel and Neopentyl Glycol Alcohol

(46) The reaction between soya biodiesel and neopentyl glycol alcohol resulted in a product with conversion of 85.5% after 48 h of reaction catalysed by the fermented solid of R. miehei produced on palm oil cake.

(47) The reaction of soya biodiesel with neopentyl glycol alcohol took place in the molar ratio from 2:1 to 3.1:1 alcohol/biodiesel, 10 to 30% (w/w) of biocatalyst, with water content from 1 to 2.5% (w/w) and temperature from 35 to 50 C. with stirring at atmospheric pressure (FIG. 1).

(48) The product of the reaction between soya biodiesel and neopentyl glycol alcohol catalysed by the lipases of the fermented solid of palm oil cake was produced in considerable volume (200 ml) and was characterized, to determine the properties of the biolubricant produced (Table 1). With the exception of the acidity index, all the other properties assessed were satisfactory.

(49) TABLE-US-00001 TABLE 1 Characteristics of the biolubricant produced in the reaction between soya biodiesel and neopentyl glycol alcohol. Test Result Moisture (ppm) 884.4 Viscosity 100 C. (mm.sup.2/s) 4.290 Viscosity 40 C. (mm.sup.2/s) 15.41 Viscosity index 206 Fluidity ( C.) 6 Acidity index (mgKOH/g) 19.8 Rotary pump (min) 30

(50) The fermented solid of palm oil cake was assessed with respect to reuse in reactions between soya biodiesel and neopentyl glycol. After a reaction time of 24 h or 72h, the enzyme was washed with solvent (hexane or ethanol) followed by filtration in a Buchner funnel and incubation overnight in a desiccator. At the end of this procedure, the enzyme was used again in the reaction as described in example 1. The fermented solid of palm oil cake can be reused at least once after washing with hexane or ethanol (FIG. 2). Reuse without washing with solvent was also tested. In this case, the product, after reaction for 72 h, was removed at the top of the reactor after decanting the fermented solid. Then fresh reaction medium was added to the reactor, equivalent in weight to the weight of product withdrawn (FIG. 7).

Example 3.2Castor Oil Biodiesel and Alcohols Trimethylolpropane and Pentaerythritol

(51) Reaction between castor oil biodiesel and the alcohols trimethylolpropane and pentaerythritol resulted in a product with conversion of 52% in 72 h, respectively. The reactions were carried out with fermented solid of R. miehei produced on palm oil cake as biocatalyst.

(52) Reaction of castor oil biodiesel with the alcohols trimethylolpropane and pentaerythritol took place in the molar ratio from 2 to 3.75:1 alcohol/biodiesel, 10 to 30% (w/w) of biocatalyst, with water content from 1 to 3% (w/w) and temperature from 30 to 50 C. with stirring at atmospheric pressure (FIG. 3).

Example 3.3Castor Oil Biodiesel and Neopentyl Glycol Alcohol

(53) Reaction between castor oil biodiesel and neopentyl glycol alcohol resulted in a product with conversion of 91% in 96 h. The reactions were carried out with fermented solid of R. miehei produced on cottonseed oil cake as biocatalyst.

(54) Reaction of castor oil biodiesel with neopentyl glycol alcohol took place in the molar ratio from 2 to 4:1 alcohol/biodiesel, 10 to 30% (w/w) of biocatalyst, with water content from 1 to 3% (w/w) and temperature from 30 to 50 C. with stirring at atmospheric pressure (FIG. 4).

(55) The product of the reaction between castor oil biodiesel and neopentyl glycol alcohol catalysed by the lipases of the fermented solid of palm oil cake was produced in considerable volume (200 ml) and was characterized, to determine the properties of the biolubricant produced (Table 2). With the exception of the acidity index, the other properties were satisfactory.

(56) TABLE-US-00002 TABLE 2 Characteristics of the biolubricant produced in the reaction between castor oil biodiesel and neopentyl glycol alcohol. Test Result Moisture (ppm) 541.9 Viscosity 100 C. (mm.sup.2/s) 86.57 Viscosity 40 C. (mm.sup.2/s) 8.854 Viscosity index 66 Fluidity ( C.) 39 Acidity index (mgKOH/g) 87.5 Rotary pump (min) 29 Rancimat (h) 6.5

(57) The fermented solid of cottonseed oil cake was assessed with respect to reuse in the reactions between castor oil biodiesel and neopentyl glycol. After a reaction time of 24 h, the enzyme was washed with solvent (ethyl ether or ethanol) followed by filtration in a Buchner funnel and incubation overnight in a desiccator. At the end of this procedure, the enzyme was used again in the reaction as described above. The cotton SEP can be reused at least once after washing with ether or ethanol.

Example 4Reactions of Hydroesterification

Example 4.1Free Fatty Acids (FFAs) of Castor Oil and Neopentyl Glycol Alcohol

(58) Reaction between FFAs of castor oil and neopentyl glycol alcohol resulted in a product with conversion of 65% in 96 h. The reactions were carried out with fermented solid of R. miehei produced on cottonseed oil cake as biocatalyst.

(59) Reaction of FFAs of castor oil with neopentyl glycol alcohol took place in the molar ratio from 2 to 4:1 alcohol/FFAs, 10 to 30% (w/w) of biocatalyst, with water content from 1 to 3% (w/w) and temperature from 30 to 50 C. with stirring at atmospheric pressure (FIG. 5).

(60) The product of the reaction between the FFAs of castor oil and neopentyl glycol alcohol catalysed by the lipases of the cotton SEP was produced in considerable volume (200 ml) and was characterized, to determine the properties of the biolubricant produced (Table 3). With the exception of the acidity index, all the other properties assessed were satisfactory.

(61) TABLE-US-00003 TABLE 3 Characteristics of the biolubricant produced in the reaction between FFAs of castor oil and neopentyl glycol alcohol. Test Result Moisture (ppm) 873.5 Viscosity 100 C. (mm.sup.2/s) 152.2 Viscosity 40 C. (mm.sup.2/s) 13.04 Viscosity index 73 Fluidity ( C.) 33 Acidity index (mgKOH/g) 100.4 Rotary pump (min) 42 Rancimat (h) 114.5

Example 4.2Soya Free Fatty Acids (FFAs) and Neopentyl Glycol Alcohol

(62) Reaction between the soya FFAs and neopentyl glycol alcohol resulted in a product with conversion of 82% in 72 h. The reactions were carried out with fermented solid of R. miehei produced on cottonseed oil cake as biocatalyst.

(63) Reaction of soya FFAs with neopentyl glycol alcohol took place in the molar ratio from 2 to 4:1 alcohol/FFAs, 10 to 30% (w/w) of biocatalyst, with water content from 1 to 3% (w/w) and temperature from 30 to 50 C. with stirring at atmospheric pressure (FIG. 6).

(64) The product of the reaction between the soya FFAs and neopentyl glycol alcohol catalysed by the lipases of the cotton SEP was produced in considerable volume (200 mL) and was characterized, to determine the properties of the biolubricant produced (Table 4). With the exception of the acidity index, fluidity and moisture, all the other properties assessed were satisfactory.

(65) TABLE-US-00004 TABLE 4 Characteristics of the biolubricant produced in the reaction between Soya FFAs and neopentyl glycol alcohol. Test Result Moisture (ppm) 2150.3 Viscosity 100 C. (mm.sup.2/s) 20.27 Viscosity 40 C. (mm.sup.2/s) 5.034 Viscosity index 191 Fluidity ( C.) 15 Acidity index (mgKOH/g) 105.5 Rotary pump (min) 28 Rancimat (h) 3.08

Example 5Determination of the Acidity of the Reactions

(66) The content of free fatty acids in the oils and products was determined by neutralization titrimetry. The free fatty acids, about 0.2 g of the sample, were titrated with 0.04 mol.Math.L.sup.1 NaOH solution in a Mettler model DG20 automatic titrator up to a pH of 11.0 and the acidity of the sample was determined from Equation 3.

(67) Alternatively, for samples with a larger volume, the free fatty acids, from about 0.5 to 1 g of the sample, were titrated with 0.25 mol.Math.L.sup.1 NaOH solution using phenolphthalein as indicator and the acidity of the sample was determined from Equation 3.

(68) $\begin{array}{cc}\mathrm{Acidity}\left(\%w\text{/}w\right)=\frac{VM\mathrm{AG}}{10m}& \left(\mathrm{Equation}3\right)\end{array}$
where: V=volume of sodium hydroxide used in titration of the sample (mL); M=molarity of the NaOH solution (mol.Math.L.sup.1); AG=molecular weight of the fatty acid present in highest concentration in the oil* (g); m=sample weight (g). *Soya oil=linoleic acid (280 g); castor oil=ricinoleic acid (298 g).

Example 6Determination of the Content of Methyl Esters

(69) To determine the content of the methyl ester (biodiesel) in the products of the transesterification reactions, 20 L aliquots were diluted in 480 L of n-heptane and injected in the chromatograph. A gas chromatograph was used (SHIMADZU 2010), equipped with a flame ionization detector (FID) and omegawax capillary column (length of 30 m, inside diameter 0.25 mm and film thickness 0.25 m). The conditions of the analyses were: initial temperature of 200 C. for 5 minutes, and then programmed at a rate of 20 C./min up to 260 C., remaining at 260 C. for 6 min. The temperatures of the detector and of the injector were 250 C. and 260 C., respectively. Helium was used as the carrier gas, at a flow rate of 2.0 mL/min and injection was done in split mode of 1:20. Methyl heptadecanoate was used as the internal standard and the content of esters was calculated using Equation 4.

(70) $\mathrm{Content}\mathrm{of}\mathrm{ester}\left(\%w\text{/}w\right)=\frac{{\mathrm{weight}}_{\mathrm{standard}}{\mathrm{area}}_{\mathrm{ester}}100}{{\mathrm{area}}_{\mathrm{standard}}{\mathrm{weight}}_{\mathrm{sample}}}$

Example 7Conversion in the Esterification Reactions

(71) The conversion of free fatty acids to biolubricants was monitored by the titrimetric method (acidity), in which the consumption of the FFAs was observed. The conversion of the reaction was calculated from Equation 5 or Equation 6.

(72) The results from Equation 5 are expressed in the form of percentage of FFA esterified disregarding the excess of FFA in the reactions, so that 100% conversion is equivalent to 100% of the hydroxyls of the alcohol being esterified. The results from Equation 6 are expressed in the form of percentage of FFA esterified, so that 100% conversion is equivalent to 100% of the FFAs esterified.

(73) $\begin{array}{cc}\mathrm{Conversion}\left(\%\mathrm{hydroxyls}\right)=\frac{100\left(A_i-A_f\right)\mathrm{RM}}{H{A}_i}& \left(\mathrm{Equation}5\right)\\ \mathrm{Conversion}\left(\%\mathrm{FFA}\right)=\frac{100\left(A_i-A_f\right)}{A_i}& \left(\mathrm{Equation}6\right)\end{array}$
where: A.sub.i=initial acidity (% w/w); A.sub.f=final acidity (% w/w); RM=initial molar ratio FFA/alcohol; H=number of hydroxyls in the alcohol molecule

Example 8Conversion in the Transesterification Reaction

(74) The conversion in the transesterification reaction was calculated from Equation 7. The results are expressed in the form of percentage of biodiesel transesterified, disregarding the excess of biodiesel in the reactions and the free fatty acids formed, so that 100% conversion is equivalent to 100% of the hydroxyls of the alcohol being esterified.

(75) $\begin{array}{cc}\mathrm{Conversion}\mathrm{including}\mathrm{acidity}\left(\%\mathrm{hydroxyls}\right)=\frac{100\left(E_i-\left(E_f+\left(A_f-A_i\right)\right)\right)\mathrm{RM}}{H{E}_i}& \left(\mathrm{Equation}7\right)\end{array}$
where: Ei=initial ester content (% w/w); Ef=final ester content (% w/w); Ai=initial acidity (% w/w); Af=final acidity (% w/w); RM=initial molar ratio biodiesel/alcohol; H=number of hydroxyls in the alcohol molecule

(76) It will be obvious that the above examples have only been presented for purposes of illustration, and that changes and variations thereof, obvious to a person skilled in the art, are considered to be included in the scope of the present invention, as defined in the claims given hereunder.