The impact of biodiesel fuel on ethanol / diesel blends

The interest in biofuels was stimulated by the fossil fuel depletion and global warming. This work focuses on the impact of biodiesel fuel on ethanol/diesel (ED) fuel blends. The soybean methyl ester was used as a representative composition of typical biodiesel fuels. The heating and evaporation of ethanol–biodiesel–diesel (EBD) blends were investigated using the Discrete–Component (DC) model. The Cetane Number (CN) of the EBD blends was predicted based on the individual hydrocarbon contributions in the mixture. The mixture viscosity was predicted using the Universal Quasi-Chemical Functional group Activity Coefficients and Viscosity (UNIFAC–VISCO) method, and the lower heating value of the mixture was predicted based on the volume fractions and density of species and blends. Results revealed that a mixture of up to 15% biodiesel, 5% ethanol, and 80% diesel fuels had led to small variations in droplet lifetime, CN, viscosity, and heating value of pure diesel, with less than 1.2%, 0.2%, 2%, and 2.2% reduction in those values, respectively.


Introduction
The energy demand is sharply increasing along with the increases in worldwide population and global fossil fuel consumption.Currently, more than 99% of the transport sector is powered by combustion engines, which contribute to around 14% of greenhouse gas emissions (GGE) [1].Due to the need for reducing GGE, which contribute to global warming, and the depletion of fossil fuels, governments and industries are aiming to shift from the dependency on fossil fuels to renewable energy sources (e.g., biofuels) [2,3].The mixture of biofuels (e.g., biodiesel and ethanol) with fossil fuels in standard propulsion systems can reduce GGE and lead to complete combustion [4][5][6].According to the UK Department for Transport, the British Government has increased the percentage of bio/fossil fuel blends from 4.75% (currently) to 9.75% in 2020 [7].Therefore, it is important to investigate the feasibility of increasing the bio-/fossil-fuel fractions.
There have been numerous studies on bio-fossil fuel blends for automotive applications, such as ethanol-gasoline, biodiesel-diesel, and ethanol-diesel (ED) blends [8][9][10].The ED blend, however, is found to be not practical due to the poor solubility of ethanol in diesel and the negative impact of ethanol on the Cetane Number (CN) [11][12][13][14][15]. Therefore, researchers have started to add some agents to stabilize the mixture and attain the required CN [16,17].Dimethyl ether (C 2 H 6 O) is a suitable CN booster when it is mixed with diesel, as it has a CN of greater than 55 [18].However, we believe that this molecule cannot be used in diesel engines effectively due to its lower values of molecular weight, boiling point, and density, which makes it evaporate much faster than diesel fuel molecules.Among other different agents, biodiesel is a chemically-convenient additive to mix with ED fuel [19].The most recent studies conducted have focused on the ethanol-biodiesel-diesel (EBD) fuel blend.For instance, Kwanchareon et al. [17] studied the GGE and the CN of this fuel blend.The presence of biodiesel in EBD blend resulted in a significant reduction in the Carbon monoxide (CO) and Hydrocarbon (HC) emissions of internal combustion engines (ICE) compared to the ED blend.In [20], the solubility of EBD blend was investigated at two different temperatures, which showed that the solubility of ethanol increased when increasing the temperature.Beatrice et al. [21] studied the influence of blending 10% biodiesel, 20% ethanol, and 70% diesel fuels on ICE performance.In the latter study, the smoke and Nitrogen Oxides (NO X ) emissions were found to be significantly less than those of pure diesel.The impact of EBD blend on emissions was investigated experimentally in [22], where results showed that the EBD blend had lower NO X emissions compared to those of pure diesel.Similarly, in [23][24][25][26][27], the EBD blend was CN-richer and its combustion produced less NO X emissions than diesel combustion.According to [19,28], up to 25% of biodiesel and 10% of ethanol could be blended with diesel effectively.In brief, previous studies on EBD blends only focused on the solubility, toxic emissions, heating value and CN of these blends.The impact of such blends on droplet heating and evaporation, with consideration to full fuel compositions, has not been investigated to the best of our knowledge.
The heating and evaporation of multi-component fuel droplets are essential processes for various combustion applications [29,30].These processes have been widely investigated and different models have been proposed in [31,32], and validated in [33][34][35][36].Some studies have been made to envisage the feasibility of blending biofuels with fossil fuels in terms of heating and evaporation [35,37].In this paper, the new key findings are the investigation into mixing different fractions of EBD blends with consideration of their droplet lifetimes and surface temperatures, viscosities, and CN.The basic equations of heating and evaporation model and types of fuels, used in the current analysis, are described in Section 2. The results and their discussion are provided in Section 3. The findings are concluded in Section 4.

Model
Our analysis of the blended fuel droplet heating and evaporation is based on the Discrete-Component (DC) model for a spherically symmetric droplet.The heat and mass transfer equations are solved analytically in this model, using the Effective Thermal Conductivity (ETC) and Effective Diffusivity (ED) models, as will be described later in this section.In the latter models, several physics inside droplets associated with fuel heating and evaporation are considered, for example, temperature and species gradient, and recirculation due to moving droplets [29,32].
The transient heat transfer equation for the temperature T = T(t, R) in the liquid phase in a spherical droplet is [32]: where R is the distance from the center of the droplet (assumed to be spherical), T is the temperature, t is time in seconds, and κ is effective thermal diffusivity accounting for the recirculation inside droplet, defined as: c l is the liquid specific heat capacity, ρ l is the liquid density, and k eff is the effective thermal conductivity, defined as: where k l is the liquid thermal conductivity, and χ is the recirculation coefficient [38].χ varies between 1 (when Peclet number Pe d(l) = Re d(l) Pr l < 10) and 2.72 (for Pe d(l) > 500).The analysis based on Equation ( 3) is described as the Effective Thermal Conductivity (ETC) approach.
Energies 2019, 12, 1804 3 of 11 The initial and boundary conditions are introduced as: where T s = T s (t) is the surface temperature of droplet, R d is the droplet radius, h is the heat transfer coefficient, and T g = T g (t) is the ambient temperature.To take into account the effect of evaporation, the ambient temperature (T g ) is replaced by the so-called effective temperature (T eff ): where L is the latent heat of evaporation and .R de is the rate of change of droplet radius due to evaporation.The mass fraction diffusion of liquid species i is described as: where D eff is the effective diffusivity.The D eff and the diffusion coefficient in the liquid phase are correlated by the following equation: χ Y is the coefficient of recirculation inside droplet.The analysis based on Equation ( 7) is known as the Effective Diffusivity (ED) approach.The droplet evaporation is estimated using the following correlation: .
where D v is the coefficient of vapor diffusion in the gas phase, ρ total = ρ g + ρ v is the total mixture density of vapor and gas, Sh iso is the Sherwood number of isolated droplets, B M = Y vs −Y ∞ 1−Y vs is the Spalding mass transfer number, Y vs is the vapor mass fraction in the vicinity of the droplet, and Y ∞ is the far-field vapor mass fraction, with Y vs = i Y vis and Y vis being the vapor mass fractions of group and individual species (i), respectively.Y vis is determined using the vapor molar fractions on the surface of droplet (X vis ), as: where p is the ambient air pressure, X lis is the molar fraction in the liquid phase of i th species at the droplet surface, γ i is the Activity Coefficient (AC) of the i th species, and p * vis is the saturated pressure of the i th species in the absence of other species.
Due to the presence of ethanol, which forms a highly non-ideal solution when it mixes with diesel fuel, the Universal Quasi-Chemical Functional group Activity Coefficients (UNIFAC) model is used to predict the AC of 106 components of the EBD blends.In fact, AC is used to correct the vapor pressure of each individual component.The UNIFAC model is presented in greater detail in [39].However, as this is the first study to deal with the UNIFAC model for the EBD blend to the best of our knowledge, we have included two tables in Appendix A for the UNIFAC groups' parameters and their interaction parameters [40].
The diesel fuel used in this work conforms to standard European Union fuel (EN590).It consists of 98 components divided into nine groups according to their chemical structures.Molar fractions of various components of this fuel and their physical properties are inferred from [41].Biodiesel is represented by soybean, formed of seven methyl ester components.The molar fractions and physical properties of these components are inferred from [42,43].Soybean is a type of biodiesel fuel which refers to single alkyl esters of a long-chain fatty acid derived from vegetable oils.The physical properties of ethanol (anhydrous) are inferred from [35].The physical properties for each component are calculated, with appropriate blending rules, to form the average properties of the blend.

Heating and Evaporation
The impact of different fractions of EBD blends (the EBD blends are referred to as Ex/By/Dz, where x, y and z are the fractions of ethanol, biodiesel and diesel fuels, respectively) on the lifetimes and surface temperatures of droplets is studied using the DC model.Following [36], the droplet with initial temperature T d = 360 K was assumed to be moving in stationary air at an axial velocity of U d = 10 m/s.The initial radius of droplet was assumed to be equal to 12.66 µm.The ambient temperature and pressure were assumed to be constant and equal to T g = 800 K and p g = 30 bar, respectively.The evolutions of droplet radii are shown in Figure 1, and their surface temperatures are presented in Figure 2.

Heating and Evaporation
The impact of different fractions of EBD blends (the EBD blends are referred to as Ex/By/Dz, where x, y and z are the fractions of ethanol, biodiesel and diesel fuels, respectively) on the lifetimes and surface temperatures of droplets is studied using the DC model.Following [36], the droplet with initial temperature  = 360 K was assumed to be moving in stationary air at an axial velocity of  = 10 m/s.The initial radius of droplet was assumed to be equal to 12.66 µm.The ambient temperature and pressure were assumed to be constant and equal to  = 800 K and  = 30 bar, respectively.The evolutions of droplet radii are shown in Figure 1, and their surface temperatures are presented in Figure 2. As presented in Figure 1, the droplet lifetime decreased as the fractions of biodiesel, ethanol, or both fuels increased at the expense of diesel fuel.This decrease was 0.7% when a blend of E5/B5/D90 was used, and further decreased by 0.9% when 10% of ethanol was mixed with 90% of diesel.This reduction reached up to 1.2% when the total fraction of biofuels was 20% (15% biodiesel and 5% ethanol).Predictions showed that pure biodiesel and pure ethanol had 11.7% and 43.3%, respectively, less droplet lifetime than pure diesel.This shorter droplet lifetime was ascribed to the fact that ethanol and biodiesel had higher vapor pressures than diesel, which made them evaporate faster than pure diesel.

Heating and Evaporation
The impact of different fractions of EBD blends (the EBD blends are referred to as Ex/By/Dz, where x, y and z are the fractions of ethanol, biodiesel and diesel fuels, respectively) on the lifetimes and surface temperatures of droplets is studied using the DC model.Following [36], the droplet with initial temperature  = 360 K was assumed to be moving in stationary air at an axial velocity of  = 10 m/s.The initial radius of droplet was assumed to be equal to 12.66 µm.The ambient temperature and pressure were assumed to be constant and equal to  = 800 K and  = 30 bar, respectively.The evolutions of droplet radii are shown in Figure 1, and their surface temperatures are presented in Figure 2. As presented in Figure 1, the droplet lifetime decreased as the fractions of biodiesel, ethanol, or both fuels increased at the expense of diesel fuel.This decrease was 0.7% when a blend of E5/B5/D90 was used, and further decreased by 0.9% when 10% of ethanol was mixed with 90% of diesel.This reduction reached up to 1.2% when the total fraction of biofuels was 20% (15% biodiesel and 5% ethanol).Predictions showed that pure biodiesel and pure ethanol had 11.7% and 43.3%, respectively, less droplet lifetime than pure diesel.This shorter droplet lifetime was ascribed to the fact that ethanol and biodiesel had higher vapor pressures than diesel, which made them evaporate faster than pure diesel.As presented in Figure 1, the droplet lifetime decreased as the fractions of biodiesel, ethanol, or both fuels increased at the expense of diesel fuel.This decrease was 0.7% when a blend of Energies 2019, 12, 1804 5 of 11 E5/B5/D90 was used, and further decreased by 0.9% when 10% of ethanol was mixed with 90% of diesel.This reduction reached up to 1.2% when the total fraction of biofuels was 20% (15% biodiesel and 5% ethanol).Predictions showed that pure biodiesel and pure ethanol had 11.7% and 43.3%, respectively, less droplet lifetime than pure diesel.This shorter droplet lifetime was ascribed to the fact that ethanol and biodiesel had higher vapor pressures than diesel, which made them evaporate faster than pure diesel.
Similarly, droplet surface temperature decreased with increasing biofuels fractions.A reduction of up to 0.5% was predicted for the E5/B5/D90 blend compared to the pure diesel.This decrease reached up to 1% for the E5/B15/D80 blend.However, the reduction was significant for pure biodiesel and pure ethanol, which were up to 10.6% and 39.4%, respectively, compared to pure diesel.This was attributed to the higher heat of capacity of biodiesel and ethanol, as components with higher heat capacity have lower temperature rise.
According to the predicted deviations in droplet surface temperatures and lifetimes between pure diesel and its EBD blends, it can be said that up to 15% biodiesel, 5% ethanol, and 80% diesel can replace the diesel fuel without any modification to the automotive system.

Cetane Number and Viscosity
In order to further illustrate the feasibility of mixing different fractions of biofuels with diesel, some important characteristics were investigated.CN is one of the most important characteristics of diesel fuel, as it measures the combustion quality of diesel fuel [44].The presence of ethanol in diesel results in a reduction in its CN and viscosity, which is another important property that influences the quality of atomization and combustion [26,45].Therefore, biodiesel fuel was used to compensate the decrease in the aforesaid two properties [16].The impact of biodiesel fuel on the CN of ethanol-diesel blends was predicted using the formula suggested in [46].The CN of pure diesel fuel (CN D ) was predicted using the formula suggested in [47], as follows: For each species group, v i is the total volume fraction, β i is the blending parameter, and CN i is the cetane number of that group.The CN number for each component is inferred from [47][48][49][50].It should be emphasised that the n-alkanes and iso-alkanes groups were merged together in [41] to form one group due to their similar physical properties.For the predictions of the CN, however, these two groups were considered separately due to the impact of varying component structures (straight chain or branched) on the CN.The predictions of the CN D , using Equation (10), is presented in Table 1.Note that the last three groups of diesel fuel presented in [41], have been ignored due to their small volume fractions (1.8% tricycloalkanes, 0.8% diaromatics, and 0.5% phenanthrenes).The CN number of each component present in biodiesel fuel was predicted using the formula suggested in [51], which was based on the carbon number of the component and the number of double-bonds existing in each component.Then, the following formula, which was suggested in [52], was used for the predictions of the CN of biodiesel fuel (CN B ).Note that CN B depends on molecular structure.Methyl lineolate (C 19 H 34 O 2 ), for instance, has very low CN (23).Based on this, not all types of biodiesel can compensate the reduction of CN caused by ethanol.However, SME fuel had small fractions of methyl lineolate which made it an appropriate fuel to boost the CN B of the blend.
where CN i and w i are the CN number and mass fraction, respectively, of component i in the biodiesel fuel.
The CN of the EBD blend was predicted using the formula suggested in [46] and compared with the volume fraction mixing rule for the predictions of CN of EBD blends.The latter formula suggested in [46] illustrates that each 1 vol.% of ethanol causes a decrease in CN by 0.6 units which will be well compensated by 0.55 units for each 1 vol.% of biodiesel.The impact of different fractions of ethanol and biodiesel on the CN of the EBD blend is shown in Table 2. Zöldy [46] suggested a correlation to predict the viscosity of EBD blends based on several experimental measurements [46].Such an approach may not predict the viscosity of our analyzed blends.A more rigorous approach will need to be considered to predict the viscosity of a blend of species with different structures.Therefore, we used the UNIFAC-VISCO method which is described as [40]: where η m is the mixture viscosity and η i is the viscosity of i th component, respectively.V m and V i are the volumes of the mixture and i th component, respectively, , and All the terms and parameters appearing in Equation (12) and their related terms are the same as those for the UNIFAC model (see [39] for more details).The application of Equation (12) for the predictions of the EBD viscosity is summarized in Table 3.As can be seen from Tables 2 and 3, the addition of 15% biodiesel and 5% ethanol resulted in up to 0.2% and 2% reduction in the CN and viscosity, respectively, compared to pure diesel, which can be Energies 2019, 12, 1804 7 of 11 sacrificed in diesel engines.In fact, the presence of biodiesel compensated the reduction in the CN and viscosity caused by ethanol, as the E10/D90 blend had approximately 10.8% and 7% less CN and viscosity, respectively, compared to pure diesel.

Heating Value
The impact of biodiesel and ethanol additions on the heating value (HV) of diesel was predicted for different EBD blends using the following formula [54]: where HV D , HV B , and HV E refer to the heating values (in MJ/kg) of diesel, biodiesel, and ethanol respectively; and v D , v B , and v E refer to the volume fractions of diesel, biodiesel, and ethanol respectively.ρ D , ρ B , ρ E , and ρ blend refer to the densities of diesel, biodiesel, ethanol, and their blend, respectively.The solution to Equation ( 13) was compared to the experimental data of [17], and presented in Figure 3 (see Table A2 for the blends in x-axis of Figure 3).where HV , HV , and HV refer to the heating values (in MJ/kg) of diesel, biodiesel, and ethanol respectively; and  ,  , and  refer to the volume fractions of diesel, biodiesel, and ethanol respectively. ,  ,  , and  refer to the densities of diesel, biodiesel, ethanol, and their blend, respectively.The solution to Equation ( 13) was compared to the experimental data of [17], and presented in Figure 3 (see Table A2 for the blends in x-axis of Figure 3).[17], for ethanol, biodiesel, diesel, and their blends.The x-axis blend cases are illustrated in Table 4. Table 4.The cases of EBD blends used in Figure 3.As shown in Figure 3, the predicted HVs were in agreement with the experimental data.The HV of ethanol (case 13) was very low due to its small structure.The addition of biodiesel had Figure 3.The predicted heating value, experimentally measured in [17], for ethanol, biodiesel, diesel, and their blends.The x-axis blend cases are illustrated in Table 4. Table 4.The cases of EBD blends used in Figure 3.As shown in Figure 3, the predicted HVs were in agreement with the experimental data.The HV of ethanol (case 13) was very low due to its small structure.The addition of biodiesel had compensated the reduction in HV caused by ethanol.For instance, E10/D90 (case 3) had 3% less HV compared to pure diesel, while E5/B5/D90 had only 0.5 less HV compared to pure diesel.Predictions showed that our target blend (E5/B15/B80) has 2.2% less HV compared to pure diesel, which can be tolerated in diesel engines.

Conclusions
The combining of biofuels with fossil fuels has received significant attention during the last two decades due to the depletion of fossil fuels and the need for reducing the GGE which contribute to global warming.In this study, we investigated the feasibility of mixing different fuel fractions of biodiesel and ethanol with diesel in terms of heating and evaporation characteristics, Cetane Number (CN), viscosity, and heating value.The aforesaid characteristics and properties are essential for the design of engines to ensure their good performance.
Predictions revealed that the presence of biodiesel at the expense of ethanol (e.g., 5% biodiesel and 5% ethanol, instead of only 10% of ethanol) compensated the reduction in droplet lifetime, surface temperature, CN, viscosity, and even the heating value.It was found that a blend of 15% biodiesel, 5% ethanol, and 80% diesel fuels led to less than 1.2%, 0.2%, 2%, and 2.2% reduction in droplet lifetime, CN, viscosity and heating value, respectively, compared to those of pure diesel fuel.
It can be concluded that the presence of biofuels with up to 20% in diesel fuel can be used in engines designed for pure diesel with minimal, or no, modification requirement.In Table A1, there are six groups in ethanol, biodiesel, and diesel fuels, and each group interacts with the other five groups.In contrast to our previous work [39], this table includes the van der Waals Energies 2019, 12, 1804 9 of 11 volumes and surface areas of biodiesel fuels (methyl-esters).The a mn between these groups, including those for biodiesel fuel (group 11), are shown in Table A2 [40].

Figure 2 .
Figure 2. The evolution of droplet surface temperatures for the same fuels and their blends as in Figure 1.

Figure 2 .
Figure 2. The evolution of droplet surface temperatures for the same fuels and their blends as in Figure 1.

Figure 3 .
Figure3.The predicted heating value, experimentally measured in[17], for ethanol, biodiesel, diesel, and their blends.The x-axis blend cases are illustrated in Table4.

Table 1 .
The volume fractions and parameters of each group of diesel fuel and their predicted Cetane Number (CN).

Table 2 .
Predicted CN of biodiesel, diesel, ethanol, and their blends.

Table A1 .
Van der Waals volumes (R k ) and surface areas (Q k ) for various molecules and atoms.

Table A2 .
The m-group and n-group interaction parameters (a mn ) in K, used in the UNIFAC and UNIFAC-VISCO models.