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.