Methodology for the Development of Empirical Models Relating ¹³C NMR Spectral Features to Fuel Properties

Abstract

Effective formulation of new gasoline or diesel fuels for internal combustion engines would benefit from the development of reliable models for predicting key fuel properties based on a set of molecular descriptors obtained from a single measurement. This is particularly relevant in the case of renewable fuels, where the available fuel sample quantity may be limited. In this work, we present a statistically based methodology for building empirical models to predict multiple properties from onedimensional 13 C nuclear magnetic resonance (NMR) spectra measured on around 200 μL of a liquid fuel. NMR spectra contain information about the molecular composition of a sample and the carbon types and molecular substructures therein. Our approach uses this information to build sparse, interpretable models, where the predicted properties are linked to specific molecular features. The approach takes into consideration the constrained nature of the features making up the one-dimensional NMR spectrum, which, after standardization, represents a relative fuel composition. We point to the limitations in interpretability that arise when building this type of empirical predictive model and suggest how these limitations may be diminished. Among the many properties important for maximizing engine performance and minimizing emissions, we build models that predict derived cetane number and distillation temperatures, as these are of particular interest because of their links to fuel economy, drivability, and engine-out emissions. The results suggest that the properties of interest may be impacted by only a few of the 27 13 C NMR regions represented in the data, pointing to new directions for further testing in the development of improved fuels.

Formulation of 7-Component Surrogate Mixtures for Military Jet Fuel and Testing in Diesel Engine

“…CN and DCN correlations have been developed based on compound category, − functional group classification within molecules (e.g., aromatic bond, double bond, quaternary carbon, etc. ), − 1 H NMR to get carbon types, − 13 C NMR, and physical properties . ASTM methods (ASTM D976 or D4737) estimate CN using density and distillation curve temperature information and call the estimate a cetane index. , Machine learning and neural networks have also been used to predict the CN of diesel and gasoline from IR spectroscopy data, , the CN of hydrocarbons with and without oxygenates using molecular descriptors (e.g., polar surface area, average bond enthalpy, etc.…”

“…CN and DCN correlations have been developed based on compound category, 74−76 functional group classification within molecules (e.g., aromatic bond, double bond, quaternary carbon, etc. ), 77−79 1 H NMR to get carbon types, 80−82 13 C NMR, 83 and physical properties. 84 ASTM methods (ASTM D976 or D4737) estimate CN using density and distillation curve temperature information and call the estimate a cetane index.…”

Correlation between the Molecular Structure and Viscosity Index of CTL Base Oils Based on Ridge Regression

“…However, the coefficients of the regression model did not guarantee the consistency with the actual positive and negative correlations due to the significant multicollinearity among different molecular structures, which increased the variance of the coefficients of the input variables and made the prediction model unrepresentative of the true regulation. 26 For severe multicollinearity, the common possible solutions are (1) grouping input variables and combining or splitting highly correlated variables, (2) using stepwise regression methods to filter and eliminate input variables, and (3) using ridge regression methods to introduce a small amount of bias to reduce sensitivity to sample data. 27,28 Studies on the relationship between base oils with various structures and bulk properties could provide the right direction for base oil production and processing.…”

“…With small sample sizes, most studies have focused on simple linear statistical methods to determine regression models of dependent variables with multiple explanatory variables. − Based on experimental samples, the strongly correlated variables were selected as input features for modeling by measuring the linear correlation between the input structures and VI, which implied that the relationship between the representative variables with strong correlation coefficients and VI was confirmed. However, the coefficients of the regression model did not guarantee the consistency with the actual positive and negative correlations due to the significant multicollinearity among different molecular structures, which increased the variance of the coefficients of the input variables and made the prediction model unrepresentative of the true regulation . For severe multicollinearity, the common possible solutions are (1) grouping input variables and combining or splitting highly correlated variables, (2) using stepwise regression methods to filter and eliminate input variables, and (3) using ridge regression methods to introduce a small amount of bias to reduce sensitivity to sample data. , …”