INTRODUCTION
Biodiesel, renewable diesel (“green” diesel) and sustainable aviation fuel (SAF) are three types of biomass-to-liquid fuels that can be made from vegetable oils, animal fats or waste cooking oils. Biomass-based diesel (BBD) such as biodiesel and renewable diesel are suitable for combustion in compression-ignition (diesel) engines. Production of these BBD has increased in the U.S. and throughout the world in recent years as efforts to develop renewable alternatives continue to be ramped up.
The Clean Fuels Alliance of America (CFAA) reported that 1.6 billion gal of total BBD were produced in the U.S. in 2022 (CFAA, 2022). This industry trade group has published its goal of ramping up production to 6 billion gal of BBD by 2030, a quantity that could eliminate 35 MMT of CO2-equivalent greenhouse gas emissions per year. As of January 2023, the U.S. Energy Information Administration estimated that biodiesel plant production capacity was 2.1 billion gal annually in the U.S. (EIA, 2023).
While renewable diesel may be used in blend ratios up to 100 vol%, this fuel is more expensive to produce than biodiesel (Lane, 2023). Production of renewable diesel is a multi-step continuous process that requires high-purity hydrogen gas, expensive metal catalysts, high pressures and temperatures and the liquid fuel needs to be separated by condensation from light fractions in the product stream (Gutiérrez-Antonio et al., 2015). In contrast, biodiesel is typically produced in one step under relatively mild conditions (ambient pressures and low temperatures [~ 60 °C]) and uses inexpensive base catalysts (Amin, 2019). Conversion time is relatively short (1-2 h) ameliorating the common use of batch or semi-batch process equipment.
The production of renewable diesel in the U.S. has increased significantly in the past five years. Partially as a result, increases in biodiesel production have slowed down. However, biodiesel is still relevant in many parts of the world where refining capacity for renewable diesel production is limited or nonexistent. Countries such as Argentina, Brazil and Indonesia are continuing to increase their national production levels of biodiesel.
Currently, the ASTM fuel specification D6751 for biodiesel as a blending stock for mixing with conventional diesel fuel (petrodiesel) limits its content to 20 vol% (‘B20’) (ASTM, 2021). In recent years, governmental incentives favoring greener fuels as well as consumer demand have been the main driving forces for expanding biodiesel blend ratios in petrodiesel to ‘B50’ and higher. As a result, one of the major concerns with biodiesel, its relatively poor oxidative stability, is receiving increased attention.
When stored at the terminal or in fuel tanks and systems, biodiesel can be exposed to oxygen present in ambient air, making it susceptible to oxidative degradation, especially if it is exposed periodically to heat. Biodiesel is a fatty derivative that is primarily composed of alkyl esters of fatty acids obtained from the feedstock lipid. The most common form of biodiesel is fatty acid methyl esters (FAME). The FAME are composed of saturated, monounsaturated and polyunsaturated esters (SFAME, MUFAME and PUFAME). Reactivity of biodiesel with oxygen increases when its degree of unsaturation increases. While unsaturated FAME are significantly more reactive to oxygen than SFAME, linoleates are 40 times more reactive than oleates in neat systems without an added initiator (Frankel, 2005a).
Oxidative degradation can adversely affect the fuel quality of biodiesel by altering its kinematic viscosity (KV), acid value (AV) or peroxide value (PV). As a safeguard, the ASTM biodiesel fuel specification D6751 includes a minimum limit for oxidative stability as measured by induction period (IP) under accelerated conditions (ASTM, 2021). The IP is generally defined as the time period where the oxidation of biodiesel shifts from the formation of primary products (hydroperoxides) to the degradation of primary products to secondary products (acids, alcohols, aldehydes, ketones, lactones and aromatics) (Frankel, 2005a; Kamal-Eldin and Yanishlieva, 2005; White, 2000). Once this level of degradation is present, it is likely that its KV and AV increase above their respective maximum limits (6.0 mm² s−1 at 40 °C and 0.50 mg KOH g−1), diminishing the overall fuel quality.
When a Rancimat instrument is used to analyze oxidative stability, the result is term ‘IPR’ (in h). According to ASTM specification D6751, this parameter is measured at T = 110 °C while the fuel sample is sealed in a test tube with 10 L h−1 air steadily bubbled through it (ASTM, 2021). If the sample yields IPR = 3 h or longer, it is within specification, with respect to the oxidative stability. If not, then the biodiesel should be treated with antioxidants until it can pass the specification.
The IPR is measured under tight laboratory conditions that include steadily bubbling the sample with air and an elevated measurement temperature 110 °C (ASTM, 2021). However, most realistic storage conditions will have lower temperatures, generally between 25 and 45 °C, and little if any constant contact with fresh air (oxygen). One common method used by the fats and oils industry is to measure IPR data for the product at three or more temperatures and extrapolate the results to obtain “shelf-life” data at lower temperatures.
A simple formula used by the fats and oils industry to estimate the shelf-life of products is described by the Model A linear type equation (Dunn, 2008; Farhoosh, 2007; Frankel, 2005c; Nakatani et al., 2001):
ln(IPR) = A0 + A1(T) (1)
where IPR = induction period measured isothermally by a Rancimat instrument (in h), A0 and A1are constants determined by linear regression analysis of ln(IPR) versus T data and T = temperature (in K). For a given FAME mixture such as biodiesel, measuring IPR for a series of elevated temperatures. Once the experimental data is analyzed to obtain coefficients A0 and A1, then Model A type equations for a given FAME can be extrapolated to T = 25 °C (298.15 K) to calculate shelf-life (SLA) as follows:
ln(SLA) = A0 + A1(298.15) (2)
where SLA is obtained by taking an inverse natural logarithm of the results from Eq. 2.
An alternative method for estimating the shelf-life of biodiesel and other fatty derivatives is to employ Model B type equations (Eq. 3) to extrapolate the results:
ln(IPR) = B0 + B1(T)−1 (3)
where B0 and B1 are constants determined by linear regression analysis of ln(IPR) versus T−1 data (Dunn, 2008). Analogous to Model Atype equations, the IPR of FAME are measured for a series of elevated temperatures, and the results analyzed to complete Eq. 3 and extrapolate it to calculate shelf-life (SLB) at 25 °C (298.15 K) using the following equation:
ln(SLB) = B0 + B1(298.15)−1 (4)
where SLB is also obtained by taking an inverse natural logarithm of the outcome.
Another advantage of using the Model B approach is that it may be used to calculate the activation energy (Ea) and frequency factor (Z0) for oxidation of biodiesel (Dunn, 2008). These parameters are useful in determining the reaction rate constant (kT):
kT = Z0[exp{−Ea(RgT)−1}] (5)
where Rg = gas constant (8.3144 J mol−1 K−1). The Eacan be estimated from the following equation:
Ea = Rg(B1) (6)
where coefficient B1 is defined in Eq. 3 and Ea is in kJ mol−1.
The collision frequency factor can be estimated if the reaction kinetic model is known. For example, if the kinetics follow a first order model:
f(α) = (1 − α) (7)
where α = degree of conversion, then Z0 can be calculated as follows:
Z0 = −ln(1 − α)[exp{−B0}] (8)
Equation 8 can be generalized for different kinetic models by substituting g(α) for −ln(1 − α) where g(α) is defined as:
g(α) = ∫f(α)−1dα (9)
where the boundary limits 0 and α* are defined as α at t = 0 and IP (Dunn, 2008; Khawam and Flanagan, 2006; Zhang et al., 2013).
The main objective of the present work is to develop model equations for estimating the shelf-life of biodiesel at T = 25 °C (298.15 K) from the experimental IPR-T data. Regression analyses were performed to obtain coefficients A0 and A1 in Eq. 1 for Model A type equations, and B0 and B1 in Eq. 3 for Model Btype equations. One model equation of each type was developed for each of five FAME mixtures: canola, palm and soybean oil-FAME (CaME, PME and SME), methyl oleate (MeC18:1) and methyl linoleate (MeC18:2). Experimental IPR data were measured at five temperatures for the first four FAME and at six temperatures for MeC18:2. Once the data were gathered and the Model A and B type correlations determined, the results were extrapolated according to Eqs. 2 and 4 to calculate SLA and SLB data for each FAME at 298.15 K. The final results were compared with each other and shelf-life data for biodiesel from the literature to assess how realistic the predictions from SLA and SLB were.