Assessing Waste Cooking Oils for the Production of Quality Biodiesel

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Biofuels and Biomass

Assessing waste cooking oils for the production of quality biodiesel using an electronic nose and a stochastic model. Adriano Francisco Siqueira, Igor Gomes Vidigal, Mariana Pereira Melo, Domingos Sávio Giordani, Pollyanna Souza Batista, and Ana Lucia Gabas Ferreira Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b04230 • Publication Date (Web): 19 Feb 2019 Downloaded from http://pubs.acs.org on February 24, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

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Energy & Fuels

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Assessing waste cooking oils for the production of quality

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biodiesel using an electronic nose and a stochastic model

3

Adriano F. Siqueiraa, Igor G. Vidigalb, Mariana P. Meloa, Domingos S. Giordanib,

4

Pollyanna S. Batistab, Ana L. G. Ferreiraa*

5

a

6

Universidade de São Paulo, 12602-810, Lorena, SP, Brazil

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b

8

de São Paulo, 12602-810, Lorena, SP, Brazil

Departamento de Ciências Básicas e Ambientais, Escola de Engenharia de Lorena,

Departamento de Engenharia Química, Escola de Engenharia de Lorena, Universidade

*Corresponding

author.

E-mail address: [email protected] (A.L.G. Ferreira): Tel. +55 12 3159 5315 ACS Paragon Plus Environment

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ABSTRACT

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Around 1% of waste cooking oil (WCO) is currently recycled to make biodiesel in Brazil,

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mainly because used oils can acquire physicochemical characteristics that render them

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unsuitable as raw materials. In order to make biofuel production from waste oils and fats

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more efficient and economically feasible, it is important to develop simple, rapid and low-

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cost methods for testing the quality of WCOs. With the objective of establishing the

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applicability of stochastic modelling of e-nose profiles in assessing the suitability of WCO

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for biodiesel production, the synthesized biodiesel samples from 36 pre-used frying oils,

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obtained from domestic and commercial premises, were analyzed regarding ester content,

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acidity index, density, viscosity and iodine index. Olfactory profiles of the WCO sources

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were obtained using a Cyranose® chemical vapor-sensing instrument and interpreted by

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application of stochastic modelling and quadratic discriminant analysis. The predictive

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model obtained by stochastic analysis exclusively from the olfactory profiles of the

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samples of WCO allowed the latter to be classified according to their ability to generate

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biodiesel that would be compliant with standard specifications and with an overall

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accuracy greater than 80%. Our results demonstrated that stochastic modeling is a

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promising tool for predicting the quality of biodiesel based only on the WCO olfactory

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profiles and its origin, since it allows qualitative assessments of the principal biodiesel

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properties and eliminates the need for complex and time-consuming laboratory tests.

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Keywords: Biofuel, electronic nose, stochastic model, waste cooking oil

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Energy & Fuels

1.

Introduction The production and consumption of fossil fuels worldwide has increased

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remarkably since the discovery of petroleum but during the past two decades the scenario

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has changed as a consequence of global economic crises and increased awareness of the

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effects of climate change. In this context, the search for new sources of energy has

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gathered apace with research and development of biofuels, including biodiesel, gaining

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priority in many emerging countries for environmental, economic, social and strategic

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reasons1,2.

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Biodiesel was introduced into Brazil in 2002 and it has since become mandatory to

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add a proportion of the biofuel to all diesel fuels sold in the country. Conventional diesel

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oil must currently contain 10% of biofuel, but this is expected to increase to 15% in future

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years3. The main challenge to the economical and sustainable production of biodiesel is the

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supply of raw material, since this factor impacts highly on the final cost. Soybean oil is the

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main raw material for biodiesel production in Brazil, followed by bovine fat and other fatty

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materials, principally frying oil, cottonseed oil and palm oil. However, the disadvantages

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of vegetable oils are that they require large agricultural areas and more than 60 days for

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cultivation, harvesting and processing, and there is the possibility that their production

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could jeopardize the availability of raw material for food preparation4.

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It is possible to reuse waste cooking oil (WCO) generated in food frying processes

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for producing biodiesel. This is an attractive proposition because it comprises a renewable

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resource, avoids disposal in the environment with the consequent devastating effects, and

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represents an opportunity for businesses to increase revenue5-7. Approximately 7 million

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tons of soybean oil were consumed in Brazil in 2017, and is the main source of WCO in

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the country8. However, around 1% of WCO is currently recycled to make biodiesel in

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Brazil, mainly because its physiochemical characteristics differ, depending on the use of 3 ACS Paragon Plus Environment

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the oil, mainly due to domestic or professional use that could render it unsuitable as a raw

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material for biofuel production9,10. The characteristics of WCOs vary according to the

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conditions of the frying process during which the oil may be degraded and modified with

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respect to odor, color, viscosity and acidity. Although a number of reliable

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physicochemical methods are available to monitor the quality of a WCO and its suitability

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for biodiesel production, they are generally time consuming and demand large amounts of

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solvents and chemical reagents. In order to make biofuel production from waste vegetable

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oils more efficient and economically feasible, it is important to develop simple, rapid and

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low-cost methods for testing the quality of biofuel and associating it with the

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characteristics of WCOs. In this context, electronic noses (e-noses) have been employed

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for quality control in many fields including those associated with agriculture, biomedicine,

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cosmetics, food, military and the environment. E-noses are multisensor devices that mimic

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the mammalian olfactory system and provide the aroma profile of sample mixtures without

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identifying individual chemical species within the mixture11-13. In a recent publication13, we developed a stochastic model capable of obtaining

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useful information from e-nose profiles. This information could be useful in assessing the

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quality and suitability of WCO for producing biodiesel. In order to test this hypothesis, in

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the present study we have: (i) used 36 WCO samples and biodiesel samples synthesized

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therefrom, (ii) recorded the olfactory profiles of the WCOs using an e-nose, and (iii)

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applied our stochastic model and quadratic discriminant analysis to the olfactory profiles in

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order to identify WCOs that would be suitable for the generation of biodiesels compliant

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with the specifications of the Brazilian Petroleum Authority (Agência Nacional de

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Petróleo, Gás Natural e Biocombustíveis; ANP).

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2.

Experimental

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Energy & Fuels

2.1.

Characterization of WCOs Thirty-six samples of WCOs generated by food frying were collected from

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domestic (nd = 18) and commercial (nc = 18) premises located in the municipality of

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Lorena, SP, Brazil. Samples were filtered through filter paper and homogenized prior to

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analysis. Acidity and peroxide indices, determined according to the methods described by

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the American Oil Chemists’ Society14,15, and density, recorded using an Anton Paar (Graz,

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Austria) model DMA™ 35N EX digital density meter, were measured at 20 ºC with 2 mL

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samples. Absolute fluid viscosity was determined as a function of shear stress rate at 40 ºC

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with ~1 mL samples using a Brookfield Viscometers (Harlow, UK) model LVDVIII

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viscometer and a CP-42 cone. Color was evaluated at 25 ºC using a HunterLab (Reston,

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VA, USA) ColorQuest XE benchtop spectrophotometer and EasyMatch QC software. The

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instrument was calibrated in the total transmittance mode for color assessment of

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translucent liquids and configured for measurements using a D65 standard light source and

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a 10° viewing angle (D65/10° color space). Assessments were performed using a 50 mm

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path length cuvette in order to obtain values based on the CIELAB system according to the

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color axes L *, a * and b *16. All analyses were performed in triplicate.

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2.2.

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Synthesis and characterization of biodiesel Although production of biodiesel from high acid oils has been reported to be better

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achieved from homogeneous acid or some specific heterogeneous catalysts, in this work

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the more industrially employed basic homogeneous catalysis was used to evaluate the

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biodiesel produced under the more usual conditions of production17. Transesterification of

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a 100 g sample of a WCO was carried out at 60 ºC in a 300 mL jacketed reactor vessel

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fitted with a mechanical stirrer set at 400 rpm. The catalyst, potassium hydroxide, was

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dissolved in ethanol (9:1 alcohol: oil molar ratio) to form the alkoxide and subsequently 5 ACS Paragon Plus Environment

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added to the reactor vessel at a mass ratio of 1% catalyst to oil. After 2 h of reaction time,

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the product mixture was transferred to a decantation funnel in order to separate the heavy

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(glycerol and wash water) and light (ethyl esters or biodiesel) phases. The biodiesel was

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washed with distilled water until the washings showed the same pH as distilled water and

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then left to stand for 2 h. The biofuel was reduced to dryness at 80 ºC for 40 min in a rotary

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evaporator, and drying was completed by the addition of anhydrous sodium sulfate.

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Samples of biodiesel were assessed for quality compliance according to ANP

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specifications regarding acidity index (≤ 0.5 mg KOH g-1), viscosity (3 – 6 mm2 s-1) and

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density (850 – 900 kg m-3) as described above, while ester concentration (≥ 96.5%) was

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determined by nuclear magnetic resonance (NMR) spectroscopy18 and iodine index was

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calculated using the Hübl method19.

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2.3.

Analysis of olfactory profiles of WCOs The olfactory profiles of the WCO samples were determined using a Sensigent

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(Baldwin Park, CA, USA) Cyranose® 320 chemical vapor-sensing instrument, which

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utilizes a NoseChip® array of 32 nanocomposite sensors and advanced pattern recognition

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algorithms to detect substances based on the electrical resistances of the sensors. The

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sensors act in response to the vapor headspace to which they are exposed, as explained in

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the work of Giordani et al. (2008)11. The time during which the sensor was exposed to

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vapor is large enough to reasonably assume that the concentration of volatile substances is

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constant13. The WCO samples were stabilized at 23 ºC prior to analysis, and ten replicates

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of each sample were analyzed to provide the olfactory profiles.

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2.4.

Stochastic modeling

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Energy & Fuels

The model used to extract information from the signals generated by the e-nose was

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that proposed by Siqueira et al. (2018)13 and described by the stochastic differential

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equation:

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𝑑𝑋𝑡 = 𝑎 + 𝑒𝑘𝑡 𝑑𝑡 +

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where 𝑋𝑡 is the electronic measurement of the e-nose signal at time t, 𝑊𝑡is the Brownian

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motion to reproduce the signal noise, and a, b, c, k and p are model parameters.

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The typical e-nose signal with respect to time may be described by the average signal plot

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(corresponding to the solid line in Fig. 1), which shows an initial rapid increase in signal

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followed by a linear behavior, called “plateau”. In the stochastic model, 1/k indicates the

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approximate time when the signal reaches the “plateau”, 𝑎 represents the slope of the

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“plateau” (which can be positive, negative or zero), and b is the signal strength at the start

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of the “plateau”. The model parameters 𝑐 and 𝑝 are related to the widths of the 95%

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confidence intervals (CI95) of the e-nose measurements (corresponding to the two dashed

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lines in Fig.1). The larger the 𝑐 value, the greater the variability of the signal, whereas a

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larger 𝑝 value indicates lower variability of the signal noise. The estimators of the model

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parameters have been described by Siqueira et al. (2018)13, and these authors have shown

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that the combination (𝑎 + 𝑏𝑘) may be proportional to the concentration of volatile

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substances present in the sensor region.

(

𝑏𝑘

)

𝑐

142 143

𝑑𝑊𝑡

(𝑡 + 1)𝑝

(1)

(FIGURE 1 NEAR HERE)

2.5.

Statistical analyses

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Quadratic discriminant analysis (Box's M-test, p value < 0.0001) with cross-

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validation was employed to examine the possibility of predicting compliance of a biodiesel

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with ANP specifications based on the origin of a WCO and the parameters of its olfactory

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profile. All analyses were performed using R software version 3.2.5 (R Foundation,

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Vienna, Austria) and Minitab version 16 (Minitab, State College, PA. USA).

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3.

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3.1.

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Results and discussion Characteristics of WCOs and biodiesels produced therefrom Knowledge of the physicochemical properties of a WCO is essential in order to

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assess the suitability of the material for the production of biodiesel, since these

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characteristics influence the transesterification reaction and, consequently, the quality of

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the biofuel so formed20. The acidity indices of the WCO samples were highly variable and

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ranged from 0.39 to 12.59 mg KOH g-1 (Table 1). High acidity indices result from

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oxidation and hydrolysis reactions that oils undergo during the frying process or storage21.

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According to some studies, acidity indices above 1 mg KOH g-1 may cause deactivation of

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the catalyst, thus impeding the transesterification reaction and resulting in a reduction in

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the yield of esters, the generation of large amounts of soap, and the production of low

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quality biodiesel22. Considerable variability was also observed in the peroxide indices of

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the WCO samples, which ranged from 1.98 to 71.82 meq kg-1, indicating that many

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samples had undergone considerable oxidative degradation. The kinematic viscosity of

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WCO samples varied between 33.15 and 61.84 mm2 s-1, values that were much higher than

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those (29.80 - 47.80 mm2 s-1) reported previously by Tiosso et al.20. However, the oil

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samples evaluated in the present study had all been subjected to the complex chemical

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reactions that occur during the frying process.

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(TABLE 1 NEAR HERE)

Regarding the color of WCO samples, substantial variations were observed in the

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measurements on all CIELAB axes, with lightness L* ranging from 0.05 to 68.98 (where 0

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indicates extremely dark and 100 completely colorless), while the chromaticity coordinates 8 ACS Paragon Plus Environment

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Energy & Fuels

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a* and b* ranged from -5.79 to 31.45 and from 0.04 to 70.92, respectively. Although the

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chromaticity coordinates can assume positive or negative values, the great majority of

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positive values recorded in the present study indicate that the color of the WCOs tended to

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towards the red (a*) and yellow (b*) sections of the chroma scales.

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According to Lobo et al.21, it is possible to obtain information about the quality of a

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biodiesel, including the selection of appropriate raw material, the production and storage

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process, and the nature of its emissions, through application of a range of analytical

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methods. In the present study, samples of biodiesel synthesized from WCOs were assessed

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according to the main descriptors included in ANP specifications, namely ester content,

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acidity index, density, viscosity and iodine index.

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The ester content of a biodiesel is particularly important since it is associated with

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the efficiency of the transesterification reaction. The synthesized biodiesels exhibited ester

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contents that varied between 0 and 100%, although 75% of the samples contained at least

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96.5% of esters and complied with ANP specifications23-24 (Table 1). The acidity indices of

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the synthesized biodiesels varied between 0.14 and 6.3 mg KOH g-1 with 59% of the

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samples exhibiting values higher than the acceptable limit of 0.5 mg KOH g-1. Increased

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acidity suggests the presence of water in the reaction medium, since acids are formed by

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hydrolytic reactions, and this is associated with a reduction in the quality of biodiesel

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because it causes corrosion and accelerates aging in diesel engines21.

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The iodine index of a biodiesel indicates the degree of unsaturation of the biofuel, a

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factor that influences density, viscosity and oxidative stability21. Values of the iodine index

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of the synthesized biodiesels varied between 72.84 and 113.37 g I2 100 mg-1 with 100% of

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the samples exhibiting values up to the acceptable limit of 120 g I2 100 mg-1 (Table 1). The

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densities of biodiesel samples were in the range 810 – 930 kg m-3 with 91% presenting

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values within the acceptable limits of 850 to 900 kg m-3. According to Basso et al.25,

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density influences the efficiency of atomization of the diesel in the fuel injector of the

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engine.

Page 10 of 25

Viscosity not only affects atomization efficiency of the biofuel but also its

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distribution in the engine and is, therefore, an important variable for monitoring the

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conversion yield of the transesterification process. A reduced viscosity suggests a high

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conversion yield into esters26, whereas increased viscosity indicates that the WCO was

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incompletely transesterified or that the biodiesel was not adequately purified. The presence

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of contaminants, residual soaps and products of oxidative degradation are further factors

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responsible for increased viscosity21. The kinematic viscosities of the synthesized

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biodiesels tested in the present study varied widely in the range 4.67 – 57.53 mm2 s-1,

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although 81% of the samples presented values within the acceptable limits of 3 to 6 mm2

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s-1.

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3.2.

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Olfactory profiles of WCOs and stochastic analyses Sensors 17, 18 and 28 of the Cyranose® 320 chemical vapor-sensing instrument

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were selected for the assessment of olfactory profiles because they exhibited typical signal

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acquisition behavior (cf. Fig. 1) as described by Siqueira et al.13. Of the 360 e-nose profiles

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analyzed, i.e. 10 profiles for each of the 36 WCOs, a total of 317 exhibited acceptable

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goodness-of-fit to the stochastic model as shown by the CI95 and R-squared values (>

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0.976) presented in Fig. 2.

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(FIGURE 2 NEAR HERE)

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Mean values of the model parameters 1/k, p and a + bk of the olfactory profiles

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produced by sensors 17, 18 and 28 (Fig. 3) revealed distinct differences between WCO

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samples that generated biodiesels that were compliant with ANP specifications (group

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BD1) and those that generated biodiesels that were non-compliant (group BD0). Thus, 10 ACS Paragon Plus Environment

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Energy & Fuels

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olfactory signals emitted by sensors 17 and 28 for the BD0 group of WCOs tended to reach

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the plateau of the signal/time plot more rapidly than those of the BD1 group as

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demonstrated by the smaller 1/k values (Fig. 3a and 3b). Moreover, the signals emitted by

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sensors 18 and 28 for the BD0 group exhibited more variability in comparison with those

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of the BD1 group as demonstrated by the smaller 𝑝 values (Fig. 3c and 3d). Finally, the

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mean concentration of volatile substances around sensor 28 (as determined by 𝑎 + 𝑏𝑘) was

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higher in the BD0 group compared with the BD1 group (Fig. 3e). One possible explanation

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for these results is the presence of moisture in BD0 samples, which generated more rapid

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and variable signals and a higher concentration of volatiles around the sensors. According

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to Sabudak & Yildiz6, the presence of water in a WCO promotes the formation of free fatty

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acids that hinder the production of biodiesel using the method employed in this study. The

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presence of free fatty acid requires pretreatment in the biofuel process in order to reduce

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this compound5,27. Therefore, the technique proposed here can help in reducing the volume

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of residual oil destined to the pretreatment, decreasing their costs.

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(FIGURE 3 NEAR HERE)

3.3.

Characteristics of synthesized biodiesels according to stochastic modeling

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The prediction of obtaining quality biodiesel from the OGR, even before the

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production process begins, is extremely important, both economically and environmentally.

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In Siqueira et al.13 the stochastic model presented in (1) was used to analyze the olfactory

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profile produced by an electronic nose, which enabled the origin of the OGR to be identified,

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residential neighborhoods and commercial restaurants. The aim of the present study is to

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predict the quality of the biodiesel that will be produced from WCO.

243

Quadratic discrimination analysis with cross-validation was employed in order to

244

examine the possibility of predicting whether a synthesized biodiesel would be compliant

245

with ANP specifications based on the parameters of the olfactory profile (provided by e11 ACS Paragon Plus Environment

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Page 12 of 25

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nose sensors 17, 18 and 28) and the origin (domestic or commercial) of the WCO. The

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stochastic parameters that were significant for discriminant analysis are identified in Table

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2, from which it may be observed that their distribution was balanced between the sensors.

249

(TABLE 2 NEAR HERE)

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The confusion matrices obtained by quadratic discriminant analyses of 317 e-nose

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profiles for the parameters ester content, acidity index, density and viscosity are presented

252

in Table 3. The overall accuracy for ester content was around 80%, with 82% of profiles of

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WCOs that produced biodiesel with compliant ester content (≥ 96.5%) identified correctly

254

and 76% of the non-compliant profiles rightly classified. For acidity index, the overall

255

accuracy was 80%, with 87% of compliant profiles (synthesized biodiesel with ≤ 0.5 mg

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KOH g-1) and 75% of non-compliant profiles identified correctly. Regarding density, the

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overall accuracy was 92%, with 93% of compliant profiles (synthesized biodiesel in range

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850 – 900 kg m-3) and 80% of non-compliant profiles rightly classified. For viscosity, the

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overall accuracy was 89%, with 91% of compliant profiles (synthesized biodiesel in range

260

3 – 6 mm2 s-1) and 80% of non-compliant profiles identified correctly. Finally, for all

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descriptors of biofuel quality, the overall accuracy was 84%, with 79% of compliant

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profiles (synthesized biodiesel with all descriptors according to ANP specifications) and

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86% of non-compliant profiles identified correctly (synthesized diesel non-compliant with

264

respect to one or more ANP specifications).

265 266

(TABLE 3 NEAR HERE)

Our results demonstrate that stochastic modeling is a promising tool in the

267

prediction of biodiesel quality based on the olfactory profile of a WCO, since it allows

268

qualitative assessments of the parameters of interest. Application of our stochastic model

269

in association with quadratic discriminant analysis presented a predicting quality of

270

biodiesel, according to ANP specifications, based on the profiles provided by an e-nose

271

device. The predictive model described herein is efficient and has the advantage of 12 ACS Paragon Plus Environment

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Energy & Fuels

272

eliminating the need for complex and time-consuming laboratory tests. The development

273

of e-noses for specific applications such as biodiesel production would greatly improve the

274

efficiency and economic viability of the processes while allowing the diversification of raw

275

materials to include other types of food waste, thus engendering a positive impact on both

276

society and the environment.

277 278 279

4.

Conclusions Our results demonstrate that stochastic modeling is a promising tool in the

280

prediction of biodiesel quality based on the olfactory profile of a WCO, since it allows

281

qualitative assessments of the parameters of interest. Application of our stochastic model

282

in association with quadratic discriminant analysis presented a predicting quality of

283

biodiesel, according to ANP specifications, based on the profiles provided by an e-nose

284

device. The predictive model described herein is efficient and has the advantage of

285

eliminating the need for complex and time-consuming laboratory tests. The development

286

of e-noses for specific applications such as biodiesel production would greatly improve the

287

efficiency and economic viability of the processes while allowing the diversification of raw

288

materials to include other types of food waste, thus engendering a positive impact on both

289

society and the environment.

290

Author Information

291

Corresponding author

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*Ana Lucia Gabas Ferreira, E-mail: [email protected], Department of Basic and

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Environmental Sciences, Engineering School of Lorena, University of São Paulo, Brazil.

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Acknowledgements 13 ACS Paragon Plus Environment

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This work was financed by Fundação de Amparo à Pesquisa do Estado de São Paulo

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(FAPESP; grant number 2014/25001-2) and in part by the Coordenação de

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Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

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Figure legends Fig. 1. Typical behavior of an e-nose signal. The individual data points represent the discrete signals acquired from the e-nose, the solid line represents the average signal plot, while the dashed lines represent the 95% confidence intervals calculated according to equation 1. Fig. 2. Interval plots of the 95% confidence intervals of mean R2 values representing the goodness-of-fit to the stochastic model of olfactory profiles obtained from e-nose sensors 17, 18 and 28. Fig. 3. Interval plots of the 95% confidence intervals of means of the variables 1/k, p and a + bk, established from olfactory profiles produced by sensors 17, 18 and 28, showing distinct differences between samples of waste cooking oil that generated compliant biodiesels (group BD1) and those that did not (group BD0).

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Figure 1

393 394 395 396 397 398 399 400 401

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Figure 2

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(a)

(b)

(c)

(d)

(e)

Figure 3 402

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Graphical Abstract

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405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420

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Table 1 Characteristics of waste cooking oil and biodiesel synthesized therefrom. ANPa descriptors Acidity index (mg KOH g-1) Peroxide index (meq kg-1) Density (kg m-3) Viscosity (mm2 s-1) Color L* a* b* Ester content (%) Iodine index (g I2 100 mg-1) a Brazilian

Waste cooking oil mean ± SDb 1.78 ± 2.56 18.36 ± 16.15 917 ± 6.4 42.69 ± 7.62

Synthesized biodiesel mean ± SD 0.91 ± 1.14 NA c 880 ± 20 8.66 ± 10.71

No. of biodiesel samples compliant with ANP nb (%) 14 (39%) NA 29 (81%) 33 (92%)

43.36 ± 13.68 6.93 ± 8.25 49.37 ± 13.80 NA NA

NA NA NA 90.51 ± 24.73 99.11 ± 9.96

NA NA NA 27 (75%) 36 (100%)

Petroleum Authority (Agência Nacional de Petróleo, Gás Natural e

Biocombustíveis). b

standard deviation.

c

not applicable.

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Table 2 Results of quadratic discriminant analyses with cross-validation showing parameters of the stochastic model that were significant for predicting the main descriptors of synthesized biodiesels included in the specifications of the Brazilian Petroleum Authority (ANP). Stochastic model Biodiesel descriptorsb parametersa Ester content Acidity index Density a X X X b c X Sensor 17 k X X p 𝑎 + 𝑏𝑘 X X 1/k X a b X X c X Sensor 18 k X X p X 𝑎 + 𝑏𝑘 X X 1/k a X X X b X X c Sensor 28 k X p 𝑎 + 𝑏𝑘 X 1/k X Origin X X X (domestic/commercial) E-nose sensors

a Stochastic

(

differential equation: 𝑑𝑋𝑡 = 𝑎 +

421

b

422

quadratic discriminant analysis.

𝑏𝑘 𝑒

)𝑑𝑡 +

𝑘𝑡

𝑐

Viscosity X

All descriptors X

X X

X

X X

X X X X

X X X X

X X X X

X X X

X

X

𝑑𝑊𝑡

(𝑡 + 1)𝑝

X denotes the parameters of the stochastic model that were considered as predictors in the

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Table 3 Confusion matrices obtained by quadratic discriminant analyses of 317 e-nose profiles for ester content, acidity index, density and viscosity showing the efficiency of the stochastic model in predicting the compliance of synthesized biodiesels with the specifications of the Brazilian Petroleum Authority (ANP).

Predicted class Ester contenta Actual class

0 1

Totals in predicted classes

1 19 195

103

214

Predicted class

Acidity indexa Actual class

0 1

Totals in predicted classes

0 140 17

1 47 113

157

160

Predicted class

Densitya Actual class

0 1

Totals in predicted classes

0 24 19

1 6 268

43

274

Predicted class

Viscositya Actual class Totals in predicted classes All descriptors

0 60 43

0 1

0 48 24

1 12 233

72

245

Predicted class

Totals in actual classes 79 238

Totals in actual classes 187 130

Totals in actual classes 30 287

Totals in actual classes 60 257

Totals in actual classes

0 1 0 169 27 196 Actual class 1 25 96 121 Totals in predicted 194 123 classes a Class 1 - oils compliant with ANP specifications regarding the descriptor indicated, (i.e. ester content ≥ 96.5%, acidity index ≤ 0.5 mg KOH g-1, density 850 – 900 kg m-3 or viscosity 3 – 6 mm2 s-1). Class 0 - oils non-compliant with ANP specifications regarding the descriptor indicated.

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