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Reformulation of Gasoline To Replace Aromatics by Biomass-Derived Alkyl Levulinates Gourav Shrivastav,†,‡,∥ Tuhin S. Khan,*,†,∥ Manish Agarwal,*,§ and M. Ali Haider*,† †

Renewable Energy and Chemical Laboratory, Department of Chemical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India ‡ Department of Chemistry, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India § Computer Services Centre, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India S Supporting Information *

ABSTRACT: In the search for a “green gasoline”, a new reformulation strategy, having no or reduced amount of aromatics, is proposed. Biomass-derived alkyl levulinates (ALs) are prospected as oxygenated additives as well as blending components to circumvent the use of aromatics and methyl tertiary butyl ether (MTBE) in gasoline. By utilizing molecular dynamics (MD) simulations, the thermophysical and dynamical behavior of gasoline blends with four alkyl levulinates, viz. methyl levulinate (ML), ethyl levulinate (EL), propyl levulinate (PL), and butyl levulinate (BL), was scrutinized and compared with those of MTBE−gasoline mixtures. It is shown that, at 300 K and 1 atm, ALs in conventional gasoline can be used for reformulation with amounts up to 18 mol % while maintaining the density, viscosity, and compressibility within the recommended limits. However, this amount can be further increased to 35 mol % by modification of aromatic content. Among the studied oxygenates, BL was observed to have the lowest miscibility in water as compared to other ALs studied. The methodology may be applied to study similar biomass-derived oxygenates for their applicability as a fuel additive or blend. KEYWORDS: Biomass, Oxygenates, Alkyl levulinates, Gasoline, Molecular dynamics

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INTRODUCTION Gasoline is a complex hybrid of various hydrocarbon families, viz. paraffins (16 wt %), isoparaffins (30 wt %), olefins (16 wt %), naphthenes (8 wt %), and aromatics (30 wt %).1 The octane rating of gasoline fuel is one of the most vital parameters for its use, in addition to other desired properties. Before the 1970s, toxic organo-lead compounds were used to improve the octane ratings. Since leaded fuel was discontinued due to its toxicity, expensive catalytic reforming units, converting paraffins (mostly C6 and C7) into aromatics, were employed which helped in improving the octane ratings. The aromatics thus produced have benzene and its alkyl derivatives, e.g. toluene, ethylbenzene, and xylene, as the main constituents. All of these are well-known toxic and carcinogenic compounds, having adverse environmental impacts.2−7 Therefore, the United States, with their amendments to the “Clean Air Act” in 1990, have called for regulations to reduce aromatics, leading to the reformulation of gasoline and thereby reducing the toxic content.8 Similar regulations and resolutions have been proposed in all major countries worldwide.9 In this regard, several ideas have been proposed, the foremost of which constitute the use of oxygenated additives, facilitating clean combustion by enhancing the local concentration of oxygen. It © 2017 American Chemical Society

has been reported that higher oxygen content leads to a reduction of unburned hydrocarbon emission.10 While hydroxyl based oxygenates such as ethanol, butanol, and bioethanol have been observed to show lower CO emission levels during engine testing,11−13 carbonyl based oxygenates such as acetone were reported to produce higher CO emission.10 Emission of NOx is dependent on the engine and temperature conditions, and in general, an increment of oxygen content at low loads maintains (or slightly reduces) the level of NOx emissions.10 For decades, MTBE, an oxygenated additive, has been widely used to improve octane ratings. However, now it is proven to be carcinogenic14,15 and a major contaminant of groundwater,16 owing to its high aqueous miscibility. Hence, an environmentally benign oxygenated additive is required for the reformulation of gasoline. Herein, biomass-derived ALs are suggested as an alternative, with a novel reformulation strategy, which may serve the desired dual purpose, to replace and reduce the aromatic content as well as complete elimination of MTBE in gasoline. Received: April 27, 2017 Revised: June 21, 2017 Published: July 8, 2017 7118

DOI: 10.1021/acssuschemeng.7b01316 ACS Sustainable Chem. Eng. 2017, 5, 7118−7127

Research Article

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generalized united atom force field TraPPE-UA (Transferable Potentials for Phase Equilibria-united atom) are known to produce accurate results for a number of systems, including alkanes (acyclic and cyclic), alkenes, ethers, ketones, aldehydes, and esters.42−47 While in some studies deviations in transport properties are calculated to be higher than expected, the qualitative behavior is predicted to the desired accuracy.34 In the present study, the thermophysical and dynamical behaviors of conventional and proposed gasoline blends with four alkyl levulinates (alkyl 4-oxopentanoates), i.e. ML, EL, PL, and BL, are investigated. Figure 1 shows the chemical structure of the studied oxygenates. The obtained results are systematically compared with those obtained from fuel blends containing MTBE and aromatics.

The proposed reformulation strategy provides a generic framework for the study of biomass-derived oxygenates in the design of a relatively greener gasoline. An array of biomassderived compounds, i.e. levulinic acid (LA), dimethyltetrahydrofuran (DMTHF), methylfuran (MF), dimethylfuran (DMF), ethoxymethylfurfural (EMF), nonanones, etc., have been investigated both theoretically and experimentally,17−23 with recent interest in exploring ALs as additives for diesel.24 Levulinates have been traditionally used in fragrances and as food flavors25,26 and, thus, are expected to be environmentally and biologically benign. Noncompatibility of ALs with existing diesel engines causes a major hindrance in their commercial applications.27 However, recent experimental reports have suggested their suitability as an additive to gasoline.23,28 In addition to octane ratings, the vapor pressure of the reformulated gasoline is an important property to be checked before its application. The volatility of gasoline should remain low for warm weather conditions and should stay in a higher range in cold weather conditions, for better driveability.28 In the study of McCormick and co-workers, three blend stocks of gasoline with various oxygenates, which include ethanol, ML, EL, and BL, were prepared volumetrically to achieve a nominal weight percent of oxygen.28 Subsequently, the effect of the presence of oxygenates on vapor pressure, distillation temperature, octane ratings, density, viscosity, and solubility was investigated.28 ML, EL, and BL blending were measured to introduce relatively mild lowering of vapor pressure. ML blending up to 20 vol % produced no significant effect on the lowering of gasoline’s vapor pressure.28 In addition, the relatively mild lowering in gasoline’s vapor pressure caused by ALs is expected to reduce the evaporative emission, eliminating expensive removal of light-end components. An improvement in the antiknock index (average of research and motor octane number) with blending amount of alkyl levulinates in regular gasoline was reported.28 This is further confirmed by Tian et al., suggesting the superior antiknock properties of ALs, compared to gasoline.29 This can be elucidated by focusing on the combustion properties of levulinates. ML is proposed to undergo H-abstraction reactions with hydroxyl and methyl radicals from fuels to give stable intermediates.29,30 The intermediates undergo subsequent beta-scission and H atomtransfer to yield methyl acrylate and methyl vinyl ketone as the final products.30 The formation of stable intermediates consequently slows down the overall reaction rate and thereby improves the antiknocking properties of ALs as compared to conventional gasoline.29 While the engine efficiency of ALs blended with gasoline remained to be tested, ALs have shown similar engine efficiencies with respect to diesel.31 Hence ALs may improve the octane ratings while maintaining other properties and can be used as gasoline blend stocks. In general, the reformulation strategies of gasoline reported so far in several reports were focused toward MTBE replacement while keeping the same aromatic content.32,33 The study presented here proposes a unique reformulation approach, in which ALs may be used as conventional additives as well as blending components, replacing aromatics. Moreover, ALs with higher oxygen content are expected to provide comparable octane ratings to that of MTBE.21 Using MD simulations, the study explores the extent to which ALs can be added, without significantly altering the behavior of gasoline. Molecular simulations have been used to predict the thermophysical, dynamic, and fluid-phase equilibria properties of fluids, including fuels.34−41 MD simulations with the

Figure 1. Chemical structure of studied oxygenates.

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COMPUTATIONAL DETAILS

Two compositions of gasoline were used: gasoline with aromatic content (AG) and gasoline with no aromatic content (NAG). The latter was the novel reformulation serving the dual purpose. AG was based on an “ideal” composition given in ref 35 and has aromatics, normal paraffins, isoparaffins, naphthenes, and olefins. In comparison, the composition of NAG was the same as that of AG, except the aromatics were removed and other compounds were increased. In addition to pure systems, four variants of each oxygenate in AG and NAG with mole fractions (x) = 0.1, 0.2, 0.3, and 0.4 were studied with a total number of 10,000 molecules. These mole fractions for MTBE correspond to the range ≈1.5−7.25 wt % while, for ALs, this range corresponds to ≈4.75−18.25 wt %. Protocols discussed by Christensen et al.28 advise a 3.7 wt % oxygen to be the maximum limit fuel for the conventional gasoline combustion engine. However, it should be noted that this limit is set for the application of ethanol and other similar oxygenates. For structurally different ALs, this limit may change significantly. Furthermore, flexible fuel vehicles with an internal combustion engine have been designed to take higher oxygen content, such as 85% ethanol, and are likely to be applicable for the reformulated gasoline with higher content of ALs proposed in this study. The representative compositions of the conventional gasoline AG, its formulation, and proposed gasoline NAG are tabulated in Table 1. A similar procedure was used to prepare the other studied formulations. Potential Energy Surface. Gasoline and its additives were modeled using a united-atom approach under the TraPPE-UA force field.42 Although the original TraPPE-UA force field considers the bonds to be fixed; here, the harmonic potential was used to maintain 7119

DOI: 10.1021/acssuschemeng.7b01316 ACS Sustainable Chem. Eng. 2017, 5, 7118−7127

Research Article

ACS Sustainable Chemistry & Engineering

Subsequently, reverse nonequilibrium molecular dynamics (rNEMD) simulations in the NVE ensemble were performed for 0.5 ns to generate initial conditions. This was subsequently followed by 10 ns of rNEMD simulations in order to estimate the viscosity at 300 K.55 The box was divided into 20 slabs, and velocities were exchanged for every 100 time steps using 10 swaps as implemented in LAMMPS. Rigid aromatic molecules were not used for the velocity exchange. Data was collected for every 1000 steps to compute the viscosity. For the computation of diffusivity, data from the NPT simulation was used. Self-diffusion constants were estimated using the Einstein relation, mathematically given as39

Table 1. Composition of AG Gasoline, NAG Gasoline, and AG Formulation Containing 0.1 Mole Fraction of Oxygenatea Components

AG

NAG

AG with AL/MTBE

Paraffins Pentane Hexane Heptane Octane Isoparaffins Isopentane Isohexane Isoheptane Isooctane Olefins Pent-2-ene Hex-2-ene Naphthenes Cyclohexane Aromatics Benzene Toluene o-Xylene Oxygenate

1600 400 400 400 400 3000 700 700 800 800 1600 800 800 200 200 3600 100 1800 1700 0

2500 650 650 600 600 4500 1100 1100 1150 1150 2500 1250 1250 500 500 0 0 0 0 0

1440 360 360 360 360 2700 630 630 720 720 1440 720 720 180 180 3240 90 1620 1530 1000

D = lim

t →∞

1 ⟨|(ri(t ) − ri(0)|2 ⟩ 6t

(1)

where ri(t) corresponds to the position of carbon atom i at time t, while the angular bracket denotes the ensemble average of the mean square displacement (MSD). Mean-square displacements were calculated by parallel GPU in-house codes. The trajectory was split into 8 parts to estimate the error, which was within 0.5%−3% for all the systems. The isothermal compressibility (κT) of studied formulations of gasoline was estimated by utilizing the volumetric fluctuations obtained from NPT simulations. It is calculated using56

κT = −

⟨V ⟩2 − ⟨V ⟩2 1 ⎛⎜ ∂V ⎞⎟ = V ⎝ ∂P ⎠T ⟨V ⟩kBT 2

(2)

Here, V, P, T, and kB represent the volume, applied pressure, temperature, and Boltzmann constant, respectively. Angular brackets denote ensemble averages. Data was divided into 8 parts to estimate the error. The estimated error was ≈14%.

a

Major categories are shown in bold face. Values denote number of molecules, totaling to 10,000 in the simulation box.

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the bond stretchings as well as bond bendings of these pseudoatoms.48,49 Torsional movements were governed by triple cosine series potential. For aromatic components, a rigid model of atomic sites was used. Nonbonded interactions between united-atoms were modeled through pairwise additive standard 12−6 Lennard-Jones potential. These nonbonding interactions included the interactions of united-atoms separated by three or more bonds in the same molecule and the interaction between united-atoms of different molecules.42 Nonbonded parameters for unlike pairs of united atoms were obtained by Lorentz−Berthelots mixing rules, and electrostatic interactions were parametrized using Coulombic potential as per the TraPPE-UA model used here.47 For simulating water environment, the flexible model was used.50 In this approach, water molecules had charges situated on each of the three atoms, with flexible bonds and angle. Hydrogen atoms were used as point charges interacting only with Coulombic potential. In addition, molecules can also interact using a Lennard-Jones potential on the oxygen sites. Simulation Details. Simulations for all the systems were performed in the NPT ensemble using the GPU accelerated LAMMPS package.51−53 Equations of motion were integrated using the velocityVerlet scheme with a time step of 1 fs. The cubic periodic boundary condition was used to ensure the bulk limit. A global cutoff of 14 Å was used in the interaction potential, and long-range corrections to the energy and pressure were also included. Temperature and pressure were maintained using a Nosé-Hoover thermostat and barostat with the damping constant of 1 and 5 ps, respectively. Particle-particleparticle-mesh was used for the electrostatic calculations for compounds containing charged atoms, as implemented in LAMMPS. For all the systems, the initial configuration with randomly packed molecules was obtained using the PACKMOL software package.54 Thereafter, the system was allowed to equilibrate for 5 ns with rescaling of velocities every 10 steps followed by the production run of 11 ns. For all the simulations, temperature and pressure were maintained at 300 K and 1 atmospheric pressure, respectively. The data from the last 5 ns was used for further analysis. We confirmed that this protocol ensured equilibration of all properties. The trajectory was stored every 1000 time steps. For viscosity calculations, the system was further simulated for 1 ns each in NVT and NVE ensembles.

RESULTS AND DISCUSSION The proposed formulations of AG and NAG were tested considering the fact that when gasoline reaches the engine, it is subjected to a multitude of flow, compression, and temperature gradients. Therefore, the thermophysical and dynamic behavior of a fuel would play a crucial and decisive role. Furthermore, significant deviations from the desired limits affect the engine’s performance and emission characteristics. In order to avoid considerable modifications in the current engine styles, these properties should be maintained within standard specifications after addition of new additives. Density. Density is one such physical property and has been known to be accurate from the calculation based on MD simulations.42 The complete details of experimental and computed densities for pure ALs and MTBE are tabulated in Table 2. The computed densities for ML, BL, and MTBE were 1.004 g cm−3, 0.956 g cm−3, and 0.747 g cm−3, respectively. These values were in fair agreement with their corresponding Table 2. Data for Experimental and Simulation Densities (g cm−3) for Pure Alkyl Levulinates, MTBE, and Gasoline at 300 K and 1 atma

a

7120

Experimental

Simulation

System

Density

Density

ML EL PL BL MTBE AG NAG

1.0492528 1.0228 0.989857 0.9728 0.7458 0.694−0.79423

1.004 0.982 0.965 0.956 0.747 0.720 0.650

Superscripts represent the appropriate references. DOI: 10.1021/acssuschemeng.7b01316 ACS Sustainable Chem. Eng. 2017, 5, 7118−7127

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Figure 2. Multiplot showing the variation in density with the mole fraction of oxygenated additive in gasoline samples for (a) AG formulations, (b) NAG formulations, and (c) RAG formulation, at 300 K and 1 atm. The shaded region denotes the recommended density range.23

experimental densities of 1.05 g cm−3, 0.97 g cm−3, and 0.74 g cm−3, respectively.42 With the increase of alkyl group’s chain length in ALs, a monotonic reduction in the density was observed. It was apparent that simulation densities were only within a deviation of ≈4% of experimental densities. Considering the fact that the force field parameters were not specifically trained for ALs, the observed deviations were considered acceptable. These results complement the transferable behavior of the TraPPE-UA force field and support its employment for ALs in the present study. The density of fuel blends is a useful parameter for assessing the power of fuel and its spray characteristics during the combustion in an engine. Moreover, it plays a central role in the correlations with the other properties of the fuel, viz. octane index, kinetics, and thermodynamic properties. As per ASTM international standards, the recommended range of density for gasoline is 0.694−0.794 g cm−3 at 293 K and ambient pressure.23,35 The same range is used here to screen the studied gasoline blends, as shown in the blue shaded region in Figure 2. As the first test of these oxygenates as additives in gasoline, the densities of existing and proposed gasoline blends were computed at 300 K and 1 atm. The density for the chosen composition of neat gasoline sample AG was computed to be 0.72 g cm−3 (Table 2), which is within the range of international standards. The density variations for the AG formulations as a function of added mole fraction of oxygenates are shown in Figure 2(a). In the case of blends containing ALs, density linearly increased from 0.72 g cm−3 at x = 0 to 0.839 g cm−3, 0.835 g cm−3, 0.837 g cm−3, and 0.837 g cm−3 for ML, EL, PL, and BL, respectively, at x = 0.4. All the studied ALs demonstrated the increment in the density, and at a given mole fraction, the variation of density among the ALs was only about 1−2%. Compared to ALs−AG mixtures, an insignificant density variation, from 0.72 g cm−3 at x = 0 to 0.725 g cm−3 at x = 0.4, was seen for MTBE−AG mixtures. This difference in the density variation for AG formulations containing ALs and MTBE can be attributed to the difference in alkyl chain length. The longer the chain length, the larger is the molecular mass and, thus, the stronger will be the intermolecular forces, resulting in a higher density. Hence, the overall changes observed in density for mixtures of ALs and MTBE were ≈16% and 1%, respectively. This can be further depicted by a higher density of neat ALs than those of neat AG and MTBE, as shown in Table 2. As a result, an increase in the fraction of such additives would increase the density of the blend considerably. Since the density of MTBE is 0.746 g cm−3, close to that of AG, only small modifications in density for MTBE−AG blends were observed. Like MTBE, alcohols are of lesser density as

compared to ALs. Experiments have revealed that the change in densities of the gasoline with ALs is greater than that of alcohols.28 Furthermore, for ALs, per gram of oxygen addition in experiments increments density by ≈0.0065 g cm−3. In this study, a similar amount of variation in density (≈0.0066 g cm−3 per gram of oxygen) was observed for AG formulations. These observations indicate that only 20 mol % of ALs can be capitalized without causing the density to exceed the recommended specifications; however, MTBE can be used to a larger extent in AG. Complete removal of aromatics reduced the density significantly from 0.72 g cm−3 to 0.65 g cm−3 for neat gasoline NAG, which was clearly well below the acceptable range of density (Table 2). In Figure 2(b), the formulations of NAG feature similar uptrends in the density but lead to different consequences. Here, higher mol % of ALs can be tolerated, in contrast to those in ALs−AG mixtures. It was apparent that initially the densities were below the recommended standards and entered into the acceptable limits only when x > 0.2. In comparison, addition of 0.4 mole fraction of MTBE exhibited an increase in density from 0.65 g cm−3 to 0.69 g cm−3. This unequivocally highlighted that MTBE was unable to compensate the loss of aromatic content; however, a higher mole fraction of ALs could be used to retain the density in specified allowed limits. Since current engine design and emission specification may not allow complete removal of aromatics, progressive replacement of aromatics by MTBE and ALs was investigated next. Note that while replacing aromatics with oxygenates, the proportion of other components remains unchanged. Therefore, the role of added oxygenates can be considered as a blending component rather than an additive. For example, 10 mol % of aromatics were exactly replaced by BL by replacing 360 molecules of aromatic compounds out of 3600 (Table 1) in proportion by 360 molecules of BL. Subsequently, other blends were also prepared by replacing the 20 mol %, 30 mol %, and 36 mol % of aromatics. The highest amount of oxygenates was 36 mol %, corresponding to the exact amount of aromatics in AG. The newly proposed resultant formulation is termed as replaced aromatic gasoline (RAG), and the alterations in density are shown in Figure 2(c). Akin to the mixtures of ALs in AG and NAG, accumulation of ALs mol % in RAG increased the density from 0.72 g cm−3 at x = 0 to 0.778 g cm−3 for ML and EL whereas to 0.783 g cm−3 and 0.785 g cm−3 for PL and BL, respectively, at x = 0.36. Contrary to this, the density of MTBE−RAG blends continuously decreased from 0.72 g cm−3 to 0.67 g cm−3 at the corresponding mole fractions. This was understandable, as ALs are denser than the aromatics, which in turn are denser than MTBE. As noted before, MTBE was 7121

DOI: 10.1021/acssuschemeng.7b01316 ACS Sustainable Chem. Eng. 2017, 5, 7118−7127

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Figure 3. Representative snapshots from 20 ns simulation of oxygenate molecules in water at 300 K and 1 atm. (a, f, k) MTBE, (b, g, l) ML, (c, h, m) EL, (d, i, n) PL, and (e, j, o) BL.

dispersed even for 20 ns. The preference to form a stable dispersion followed the order ML > MTBE ≈ EL > PL > BL. This observed qualitative trend of miscibility of studied oxygenates corroborates with the experimental trends based on solubility. Experimental investigations28 have suggested ML to be miscible in water while MTBE and BL are slightly soluble, with solubilities of 5.1 and 1.3 wt % at 293 K.28,59 Furthermore, Christensen et al. have shown relatively lesser extraction of BL from gasoline to water as compared to EL and ML.28 This can be elucidated by the fact that at a given temperature and pressure, solubility in water depends on the solute−solvent interactions. The oxygenates exhibit some polarity due to the presence of oxygen which becomes subordinate with an increase in carbon chain length. Therefore, BL is expected to show a relatively lesser miscibility in water as compared to MTBE due to the longer n-alkyl chain. Considering the density behavior and miscibility, it was concluded that BL was a better additive blend candidate among the studied ALs. Furthermore, the effective C/H ratio, which is proportional to the energy density of a given component, of BL (0.90) was similar to that of the aromatic fragments (0.8−1.0), as given in Table 3. Thus, in the following discussion, only MTBE and BL are compared in the proposed NAG and RAG formulations. Viscosity. Viscosity is another property of fuels which is inter-related to the density. It affects the lubrication and atomization phenomenon during the spray, controlling the carbon deposition on the fuel filter.60 In molecular simulations, viscosities have been known to be underestimated,41,61 especially with the TraPPE-UA potential.34,62 As a result, the

deficient in compensating the loss occurring in density by removal of aromatics. At lower concentration of ALs, higher content of aromatics maintained the density, and at higher concentration, ALs themselves took over and maintained the density. As a result, it was interesting that, unlike AG and NAG blends, RAG formulations allowed access to the full concentration range of levulinates−gasoline mixtures studied here, since the densities of all four samples were within the recommended range. It is also apparent from all the formulations that variations at a given density across the four levulinates were within 1−2% (Figure 2(a)−2(c)). Therefore, in order to determine a good choice out of the four ALs studied, the effects of the other key fuel properties were considered. Solubility in Water. The miscibility in water plays a decisive role to judge the environmental impact of such oxygenated fuel additives and blends. To inspect the aggregation behavior, which is inversely proportional to solubility, of each oxygenate in water, MD simulation for a periodic cubic box consisting of 20−60 molecules of oxygenates in 10,000 water molecules was performed at 300 K and 1 atm. Subsequently, the aggregation tendency was monitored visually. Figure 3 shows representative snapshots from the simulations containing 20−40 molecules of oxygenates in water. These snapshots clearly show a greater clustering of BL in water than MTBE and other ALs. While ML and EL formed multiple small agglomerates, PL and BL quickly formed a single mass. It was observed that the BL phase separates within ≈10 ns of simulation time, while MTBE and other ALs remained 7122

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viscosity caused by the removal of aromatics. This observed behavior can be attributed to the higher viscosity of BL than MTBE, likely due to its higher density. From Figure 4(c), it is apparent that progressive replacement of aromatics with BL, in RAG formulation, increased the viscosity from 0.26 at x = 0 to 0.40 mPa s at x = 0.36, well within the allowed limit. However, the viscosity for MTBE-RAG blends continuously decreased from 0.26 to 0.183 mPa s (Figure 4(c)), indicating that the rise in viscosity due to MTBE addition was lower than the fall of viscosity due to the removal of aromatics. Viscosities for all the formulations are shown in Figure S1 in the SI. Relationship between Viscosity and Diffusivity. The Stokes−Einstein (SE) relation was examined next by computing the self-diffusivity of the gasoline blends. In general, the SE relationship can be used to determine the hydrodynamic radius of a solute in the viscous medium and is given as D = kBT/6πηr, where kB, T, η, and r represent the Boltzmann’s constant, temperature, viscosity, and hydrodynamic radius, respectively.63 Furthermore, the existence of the SE relationship in these systems can be fruitful to determine the variation of transport properties by considering the self-diffusivity rather than the viscosity. This aids in alleviating an excess computation overhead of reverse nonequilibrium MD simulation for viscosity calculations. In comparison, self-diffusivity is relatively rapidly converged, and easily obtained from equilibrium MD simulations. Here, it was computed using the Einstein relation and the estimated error was within 0.5− 3%. For all the studied formulations of AG, NAG, and RAG, a linear fit (R2 = 0.981−0.995) was observed between inverse diffusivity, 1/D, and viscosity, η, shown in Figure 5. Equations

Table 3. Effective C/H Ratio for Aromatics and Additives Used in Gasoline Blends Compounds

C

H

O

C/H

Benzene Toluene o-Xylene MTBE ML EL PL BL

6 7 8 5 6 7 8 9

6 8 10 12 10 12 14 16

0 0 0 1 3 3 3 3

1.00 0.88 0.80 0.50 1.50 1.17 1.00 0.90

acceptable experimental viscosity range of 0.37 to 0.44 mPa s, at 293 K and ambient pressure,35 cannot be used as a reference range here. Hence, a modified viscosity range is defined as follows. The lower bound was the computed viscosity for neat AG (0.26 mPa s), and the upper bound was the corresponding value for 0.23 mol % AG-BL (0.38 mPa s) blend. The choice of these limits was based on Figure 4(a), corresponding to the viscosities of the systems which have the densities in the acceptable range. Viscosities for all systems were estimated by reverse nonequilibrium MD (rNEMD) simulations to avoid convergence issues with the traditional Green−Kubo formalism.55 It should be noted that although simulations do not give good quantitative results, the qualitative behavior obtained for viscosity among ALs in AG was similar to those obtained from experiments.28 For a given amount of oxygen content, BL was observed to increase viscosity the most while ML the least. Furthermore, the ratio of increment in viscosity for BL to ML was calculated ≈2.2 from experiments28 and ≈2.3 from the simulations performed. Increasing the amount of BL in NAG showed an increase in computed viscosity from 0.175 mPa s at x = 0 to 0.449 at the x = 0.4, as shown in Figure 4(b). The relatively smaller increment was also apparent in the case of MTBE, which displayed an increase in viscosity from 0.175 mPa s at x = 0 to 0.190 at x = 0.4, as shown in Figure 4(c). It was evident that BL blending was able to bring the viscosity within the recommended limit in the range of x = 0.18 and x = 0.35; Post this range, viscosity exceeded the allowed limit (Figure 4(b)). The range of mole fraction corresponding to suitable viscosity correlated with the acceptable range of mole fraction obtained from the density profiles in corresponding blends which may be explained by the direct proportionality between the two. Similarly, the viscosity for MTBE−NAG mixtures negligibly varied from 0.175 mPa s to 0.190 mPa s (Figure 4(b)), which was inferior to the specified limit, suggesting MTBE is unlikely to compensate the decrease in

Figure 5. Correlation plot of the viscosity and inverse of diffusivity for (a) AG formulations (red star), NAG formulation (green square), and RAG formulations (blue triangle) at 300 K and 1 atm.

obtained from the linear fits are given in Table 4. This indicated that there was a direct correlation between the viscosity and inverse diffusivity in the SE relationship for the entire range of

Figure 4. Plot for the variations in shear viscosity for (a) AG formulations, (b) NAG formulations, and (c) RAG formulations at 300 K and 1 atm. The blue shaded region denotes the recommended viscosity range as described in the text. For RAG, the highest mole fraction of oxygenates is 0.36, which corresponds to the exact amount of aromatics in AG. 7123

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Table 4. Linear Polynomial Fitting Data of Inverse Diffusivity as a Function of Viscosity for AG Formulations, NAG Formulations, and RAG Formulationsa System

a

b

R2

AG NAG RAG

0.954 0.984 0.961

−0.016 −0.031 −0.035

0.995 0.982 0.991

Research Article

CONCLUSION

ALs possess good octane ratings, similar C/H ratio to that of aromatics and better local oxygen concentration than that of MTBE. Considering these facts, ALs were studied to reduce the amount of aromatics as well as MTBE in gasoline simultaneously. In order to avoid the modifications in current engine style, it was crucial to study the effect of new components on the thermophysical and dynamical behavior of gasoline. MD simulations were performed on the selected blends of gasoline with four alkyl levulinates (ML, EL, PL, and BL) with three mixing strategies, (i) increasing the amount of additives while reducing the mol % of other components of gasoline in proportion in sample AG, (ii) increasing the amount of additives while reducing the mol % of other components of gasoline in proportion in sample NAG, and (iii) increasing the amount of additives while reducing the mol % of only aromatic content of gasoline in sample AG. It was clearly demonstrated that for all the three formulations, the density of fuel increased with an increase in mole fraction of ALs. The amounts of ALs which maintained the density of blends in the specified limit were