What single, pure compound would best replace petrol?

Question

Petrol for use as automotive fuel is produced by blending of different product streams of oil refining. It consists of hundreds of different compounds, and the exact composition can vary widely. Certainly, not all components are absolutely necessary. Is there a single pure compound that could be used instead and that is similar or even superior to typical petrol?

In order to limit the scope of this question, I only consider pure hydrocarbons ($\ce{C_xH_y}$), i.e. no alcohols, ethers, amines, nitro compounds, or other compounds containing hetero atoms. I am only asking about fuel for spark ignition (Otto) engines, i.e. not about diesel fuel.

The relevant criteria for the comparison shall be only the knock resistance and the energy content of the compounds. Other properties may be ignored.

For similar compounds, there may be a tendency for fuel with a higher knock resistance to have a lower energy content. The challenge is to find a single pure compound with a suitable balance of knock resistance and energy content, with better values than found for typical petrol.

The knock resistance shall be expressed as research octane number (RON). Currently, the most important petrol blends in most countries have an RON of 95. However, blends with an RON of up to 102 are widely available. Therefore, the candidate compound should have at least an RON of 102.

The energy content shall be expressed as specific enthalpy of combustion $\Delta_\mathrm ch^\circ$ at a temperature of $T=25\ \mathrm{^\circ C}$. If necessary, this value can be directly calculated from the molar enthalpy of formation $\Delta_\mathrm fH_\mathrm m^\circ$ or the molar enthalpy of combustion $\Delta_\mathrm cH_\mathrm m^\circ$. For this purpose, the generated water shall be assumed to be in liquid form (although this assumption is not representative for vehicle engines and may favour small saturated compounds). The energy content of petrol can vary. For example, typical average values for $\Delta_\mathrm ch$ given by Aral in Germany are

• Regular (RON = 91): $-44.2\ \mathrm{MJ/kg}$
• Super (RON = 95): $-43.5\ \mathrm{MJ/kg}$
• Super Plus (RON = 98): $-42.7\ \mathrm{MJ/kg}$

Therefore, the candidate compound should have at least an energy content corresponding to about $\Delta_\mathrm ch^\circ=-44\ \mathrm{MJ/kg}$.

In order to limit the choice, the candidate compound shall be a liquid at room temperature. The boiling point should be below $210\ \mathrm{^\circ C}$, preferably between $70\ \mathrm{^\circ C}$ and $150\ \mathrm{^\circ C}$. The melting point should be well below $0\ \mathrm{^\circ C}$.

By way of comparison, the following table shows the relevant parameter values for the reference compounds that are used for the octane number (heptane and 2,2,4-trimethylpentane) as well as for one candidate compound (2,2,3-trimethylbutane) that I have already found.

$$ \small\begin{array}{llllllll} \hline \text{Compound}&\text{Formula}&\Delta_\mathrm fH_\mathrm m^\circ&\Delta_\mathrm cH_\mathrm m^\circ&\Delta_\mathrm ch^\circ&\mathrm{RON}&T_\mathrm{mp}&T_\mathrm{bp} \\ &&\text{in}\ \mathrm{kJ/mol}&\text{in}\ \mathrm{kJ/mol}&\text{in}\ \mathrm{MJ/kg}&&\text{in}\ \mathrm{^\circ C}&\text{in}\ \mathrm{^\circ C} \\ \hline \text{Heptane}&\ce{C7H16}&-224.2&-4817&-48.1&\hphantom{00}0&\hphantom{1}{-90.55}&98.4 \\ \text{2,2,4-Trimethylpentane}&\ce{C8H18}&-259.2&-5461&-47.8&100&-107.3&99.22\\ \text{2,2,3-Trimethylbutane}&\ce{C7H16}&-236.5&-4805&-48.0&112&\hphantom{1}{-24.6}&80.86 \\ \hline \end{array}$$

I would be interested in answers that search through literature data and find better candidate compounds as well as in answers that use a theoretical approach to estimate where to find the best compounds.

Answer 1

Higher $\mathrm{RON}$ seems possible. Yet the boiling point rises accordingly while heat of combustion remains roughly the same. Here are two compounds that fit all posed criteria.

\begin{array}{|c|c|c|c|c|} \hline \mathbf{Molecule} & \mathrm{mp\ \mathrm{(^\circ C)}} & \mathrm{bp\ \mathrm{(^\circ C)}} & \Delta_\mathrm cH_\mathrm m^\circ\ (\mathrm{kJ/mol}) \ \text{@}25\ ^\circ \mathrm{C} & \mathrm{RON} & \mathrm{MON}\\ \hline \ce{1,3,5-TMB^{[a]}} & -44.7^{[1]} & 164.65(15)^{[1]} & -5193.1(1.3)^{[2]} & 137^{[3]} & 124^{[3]} \\ \ce{2,2,3,3-TMH^{[b]}} & -54^{[4]} & 160^{[5]} & -5405^{[6]} & 112.8^{[3]} & 92.4^{[3]} \\ \hline \end{array}

_{[a] 1,3,5-trimethylbenzene, [b] 2,2,3,3-tetramethylhexane}

Theoretical predictions of $\mathrm{RON}$

Tareq A. Albahri$^{[7]}$ summarises in his paper the usage of statistics $\mathrm{RON}$ and $\mathrm{MON}$.

The research octane number $\mathrm{RON}$, which is representative of the fuel performance during low-speed city driving, is more often reported in the literature than the motor octane number $\mathrm{MON}$, which is representative of the fuel performance during high-speed highway driving.$^{[7]}$

Theoretical intercalculation between the two characteristics is possible.$^{[7]}$ This work was done by Jenkins$^{[8]}$. First predictions of $\mathrm{RON}$ itself were and are still largely empirical$^{[7]}$. These models use regression techniques to assign effective octane numbers to various organic groups. Albahri examplifies the procedure via Anderson, Sharkey, and Walsh$^{[7]\ [9]}$.

Anderson et al.,$^{[9]}$ for example, developed an empirical model for calculating the RON based on chromatographic analysis of gasoline.$^{[7]}$

In their model, the gasoline is divided into 31 hydrocarbon groups or pseudocomponents, all of which are assigned an “effective” octane number that is estimated by regression of experimental data. The octane number of gasoline is calculated by adding the contribution of octane number[s] from each group.$^{[7]}$

Many similar methods include those proposed by Van Leeuwen et al.$^{[10]}$, Sasano$^{[11]}$, and Lugo et al$^{[12]}$, Ramadhan and Al-Hyali$^{[13]\ [14]}$, Nelson$^{[15]}$, Baird$^{[16]}$, Twu and Coon$^{[17]\ [18]}$, Rusin et al.$^{[19]}$, Habib$^{[20]}$, Cotterman and Plunkee$^{[21]}.$ Some of these fail to differentiate between isomers, or are valid in specific mixtures.$^{[7]}$ Additionally,

Although these techniques [by Van Leeuwen et al$^{[10]}$, Sasano$^{[11]}$, and Lugo et al$^{[12]}$] give reasonably accurate results, they are usually too time consuming for planning studies and often the compositional data are not available.$^{[7]}$

• Tareq A. Albahri's method of SGC (structural group contribution)

After considerable testing, Albahri found that the best equation to take into account contributions of different groups is$^{[7]}$

\begin{split} \mathrm{ON} &= f\left(\sum_{i}\mathrm{\left(ON\right)_i}\right)^{-1}+ a + b\left(\sum_{i}\mathrm{\left(ON\right)_i}\right) \\ &\quad + c\left(\sum_{i}\mathrm{\left(ON\right)_i}\right)^2 + d\left(\sum_{i}\mathrm{\left(ON\right)_i}\right)^3 + e\left(\sum_{i}\mathrm{\left(ON\right)_i}\right)^4 \end{split}

where $\mathrm{ON}$ is either $\mathrm{RON}$ or $\mathrm{MON}$, and $\left(ON\right)_i$ is the contribution from the $i$th group. Note how the powers increase from left to right.

The coefficients still have experimental basis.$^{[7]}$ This equation is a modified version of what Albahri put forward a year earlier.$^{[22]}$ For many compounds the difference between the estimate and experimatal data is just $5$.$^{[7]}$ If the $\left(ON\right)_i$ are known, one only needs the knowledge of the structure of the molecule to apply Albahri's method.

I suggest reading both papers by Albahri since they include tables of data and an example calculation.

Here is a selection of $\left(ON\right)_i$ values.$^{[22]}$

• QSPR Model for octane number prediction

In a research article by Al-Fahemi, Albis, Gad, a quantitative structure-property relationship (QSPR) is performed. This includes establishing a correlation relation between $\mathrm{ON}$ and various physical parameters.$^{[23]}$ Again the model is based upon regression rather than derivation from first principles.

\begin{align} \mathrm{ON} = & - (193.53 \pm 319.19) + (1.47 \pm 1.01)M\\ & - (53.06 \pm 31.47)E_H - (8.67 \pm 2.73)B_P\\ & - (24.94 \pm 19.44)M_R - (50.52 \pm 26.92)\log P\\ & + (4.33 \pm 3.09)C_P + (3.72 \pm 2.04)C_V + (5.17 \pm 2.08)C_T\\ \end{align}

where

• $M$ is molecular mass,
• $E_H$ is hydration energy,
• $B_P$ is boing point,
• $\log P$ $-$ octanol/water distribution coefficient,
• $M_R$ is molar refractivity,
• $C_P$, $C_V$, $C_T$ is the critical point (pressure, volume and temperature, respectively).$^{[23]}$

TL; DR

There is no model to date that estimates or derives a result for $\mathrm{ON}$ from first principles. Different models depend more or less on multiparameter regression analysis and experimental data. Nevertheless, the methods of Albahri and others have predictive capability. Often the difference beteen estimated and experimental octane numbers is less than $5$.

Or as Albahri mentions,

Octane number is one of the most difficult properties to estimate or correlate because of its complex dependency on the molecular structure of the compound.$^{[7]}$

An estimation technique of the octane rating of pure hydrocarbons, though essential, is nonexistent.$^{[7]}$

So for your second question, I suggest applying Albahri's method because

• widest applicability among hydrocarbons,
• relatively easy to use,
• few $\mathrm{RON}$s are known from experiments,
• Al-Fahemi et al.'s procedure requires many parameters which will be a pain to track down (if known at all).

Qualitative considerations$^{[3]\ [7]}$

• shorter alkane chain $\ce{->}$ higher $\mathrm{ON}$ (but higher volatility)

• branching of alkane $\ce{->}$ higher $\mathrm{ON}$

• aromaticity in hydrocarbon $\ce{->}$ higher $\mathrm{ON}$ (but tends to burn sooty with carcinogenic byproducts)

• effects on $\mathrm{RON}$ and $\mathrm{MON}$ can be very different

Arithmetic average of $\mathrm{RON}$ and $\mathrm{MON}$ $-$ anti-knock index or $\mathrm{AKI}$ $-$ is also used.

$$\mathrm{AKI} = \frac{\mathrm{RON} + \mathrm{MON}}{2}$$

---

• _{$[1]$ T.F. Ardyukova, I.K. Korobeinicheva, A.I. Rezvukhin. Atlas of Spectra of Aromatic and Heterocyclic Substances. $(1973)$, 7.}
• _{$[2]$ W. H. Johnson, E.J. Prosen, F.D. Rossini. 'Heats of combustion and isomerization of the eight $\ce{C9H12}$ alkylbenzenes', Journal of Research of NIST, $(1945)$, 35, pp 141$-$146.}
• $[3]$ A. Demirbas, M. A. Balubaid, A. M. Basahel, W. Ahmad, M. H. Sheikh. 'Octane Rating of Gasoline and Octane Booster Additives'. Petroleum Science and Technology, $(2015)$, 33(11), pp 1190$-$1197. DOI: 10.1080/10916466.2015.1050506.
• _{$[4]$ Jean-Claude Bradley Open Melting Point Dataset. (January 29, 2017)}
• _{$[5]$ R. Stenutz. 2,2,3,3-tetramethylhexane. A collection of tables for chemistry. (January 29, 2017)}
• _{$[6]$ Pure Components Data. (Excel file.) Petroleum Engineering, Texas A&M University. (January 29, 2017)}
• $[7]$ Tareq A. Albahri. 'Structural Group Contribution Method for Predicting the Octane Number of Pure Hydrocarbon Liquids'. Industrial & Engineering Chemistry Research $2003$, 43(24). DOI: 10.1021/ie020306+.
• _{$[8]$ G. I. Jenkins. 'Calculation of the motor octane number from the research octane number'. Journal of the Institute of Petroleum, $1968$, 54, 14.}
• _{$[9]$ Anderson, P. C.; Sharkey, J. M.; Walsh, R. P. 'Calculation of the Research Octane Number of Motor Gasoline from Gas Chromatographic Data and a New Approach to Motor Gasoline Control'. Journal of the Institute of Petroleum, $1972$, 58, 83.}
• _{$[10]$ J. A. Van Leeuwen, R. J. Jonker, R. Gill. 'Octane Number Prediction Based on Gas Chromatographic Analysis and Nonlinear Regression Techniques'. Chemometrics and Intelligent Laboratory Systems, $1994$, 25(2), pp 325$-$340. DOI: 10.1016/0169-7439(94)85051-8.}
• _{$[11]$ Y. Sasano. 'Measuring Research Octane Number of Gasoline by Gas Chromatograph'. JP Patent 09138613, $1997$.}
• _{$[12]$ H. J. Lugo, G. Ragone, J. Zambrano. 'Correlations between Octane Numbers and Catalytic Cracking Naphtha Composition'. Industrial & Engineering Chemistry Research, $1999$, 38, 2171.}
• _{$[13]$ O. M. Ramadhan, E. A. S. Al-Hyali. 'New Experimental and Theoretical Relation to Determine the Research Octane Number (RON) of Authentic Aromatic Hydrocarbons that Could be Present in the Gasoline Fraction'. Petroleum Science and Technology, $1999$, 17, 623.}
• _{$[14]$ O. M. Ramadhan, E. A. S. Al-Hyali. 'Aromatic Hydrocarbons in Some Iraqi Gasoline and Their Influence in the Value of the Research Octane Number'. Petroleum Science and Technology, $1999$, 17, 607.}
• _{$[15]$ W. L. Nelson. 'Octane Numbers of Naphthas'. Oil and Gas Journal, $1969$, 67, 122.}
• _{$[16]$ C. T. Ch Baird. Address: De la Haute-Belotte 6, 1222 Vezenaz, Geneva, Switzerland. Unpublished results.}
• _{$[17]$ C. H. Twu, J. E. Coon. 'Predict Octane Numbers Using a Generalized Interaction Method'. Hydrocarbon Processing, $1996$, 71,}
• _{$[18]$ C. H. Twu, J. E. Coon. 'Estimate Octane Numbers Using an Enhanced Method'. Hydrocarbon Processing, $1997$, 76, 65.}
• _{$[19]$ M. H. Rusin, H. S. Chung, J. F. Marshall. 'A Transformation Method for Calculating the Research and Motor Octane Numbers of Gasoline Blends'. Industrial and Engineering Chemistry Research. $1981$, 20, 195.}
• _{$[20]$ E. T. Habib. 'Effect of Catalyst, Feedstock, and Operating Conditions on the Composition and Octane Number of FCC Gasoline'. ACS Symposium Division of Petroleum Chemistry, Miami, FL, Sept $1989$.}
• _{$[21]$ R. L. Cotterman, K. W. Plunkee. 'Effects of Gasoline Composition on Octane Number'. ACS Symposium Division of Petroleum Chemistry, Miami, FL, Sept $1989$.}
• $[22]$ Tareq A. Albahri. 'Structural Group Contribution Method for Predicting the Octane Number of Pure Hydrocarbons and Their Mixtures'. Fuel Chemistry Division Preprints, $2002$, 47(2), 532
• $[23]$ Jabir H. Al-Fahemi, Nahla A. Albis, Elshafie A. M. Gad. 'QSPR Models for Octane Number Prediction'. Journal of Theoretical Chemistry, $2014$, vol 2014, article ID: 520652, 6 pages. DOI: 10.1155/2014/520652.