A "Reference Series" Method for Prediction of Properties of Long-Chain Substances Inga Paster and Mordechai Shacham Dept. Chem. Eng. Ben-Gurion University of the Negev Beer-Sheva, Israel Neima Brauner School of Engineering Tel-Aviv University Tel-Aviv, Israel

The Needs  Physical property data are extensively used in chemical process design, environmental impact assessment, hazard and operability analysis, and additional applications.  Measured property values are available only for a small fraction of the chemicals used in the industry, as reactants, products or side products. Long chain substances pose special challenges, as their critical constants cannot be measured because of thermal instability.  Currently Asymptotic Behavior Correlations (ABC) are used for predicting properties of long chain substances.  ABCs represent the change of properties as nonlinear functions of n C (and/or molecular mass).

Presently Used ABC Correlations 1. Marano and Holder, Ind. Eng. Chem. Res. 36, 1887 (1997) Y is the property, 5 or 6 adjustable parameters 2. Gao et al., Fluid Phase Equilibria, 179, 207(2001) 5 adjustable parameters: For many homologous series only a few, inaccurate property data points are available in the low carbon number range. The use of nonlinear models with adjustable parameters based on such data for long range extrapolation is very risky and unreliable.

Property Behavior at the limit n C → ∞*  Properties that approach a finite value for large carbon numbers (e.g., normal boiling and melting points, critical temperature).  Properties which are additive in nature, with a monotonic incremental change with increasing the n C. (e.g., critical volume, molar volume).  Consistency between different homologous series at the limit. The same property approaches the same value for different series.  In approaching the limit the difference between the property values for different homologs should monotonically decrease *Marano and Holder, Ind. Eng. Chem. Res. 36, 1887 (1997)

* AIChE J, 57(2), 423–433 (2011) Related Previous Work*  Molecular descriptors collinear with a particular property are identified based on available experimental data.  From among these, the ones whose behavior at the limit n C → ∞ is similar to the property behavior are used for prediction.  A linear QSPR in terms of the selected descriptor, with an optional additional correction term which exponentially decays with n C, can be developed. Development of (linear) QSPRs with good extrapolation capabilities for high carbon number (n C ) substances in homologous series. Methodology Property Descriptor

The Objective of this Research 1.To establish relationships between properties of a reference series, for which the largest amount and the highest precision property data are available and the properties of a target series for which a smaller number and lower precision data points are available. 2.To use this relationship in order to determine whether the property data available for the target series is sufficient for obtaining reliable predictions. 3.To use the relationship, if the test in (2) positive, in order to predict property data for the reference series by interpolation and both short and long range extrapolations 4.Various aspects of the proposed method will be demonstrated by predicting normal boiling temperature (approaches a finite value for large carbon numbers) and critical volume (monotonic incremental change with increasing carbon number.

Ideal Gas Enthalpy of Formation (H f ) for n-alkanes and n- mercaptans H f decreases monotonically with increasing n C Source: DIPPR database (Rowley et al. 2010), experimental data in bold

Modeling the H f data of n-alkanes with the linear QSPR: R 2 = The H f of the reference series can be adequately represented as a linear function of n C for long range extrapolation Used for model derivation

The relationship between n-Alkane and n- mercaptan, H f data for 3 ≤ n C ≤ 12 The predicted and experimental data points are indistinguishable. The proposed relationships can be used for long range extrapolation Prediction by linear equation β 0 = (3.772 ± 0.12)E+07; β 1 = ± 0.006; R 2 = Proposed by Peterson, Ind. Eng. Chem. Res., 2010,

Normal Boiling Temperatures (T b ) for n-alkanes and n- alkanoic acids From various literature sources: Source: DIPPR database (Rowley et al. 2010), experimental data in bold

Fitting a Linear QSPR to the n-Alkane T b data for 9 ≤ n C ≤ 20 The linear QSPR obtained: T b = (± 15.6) (± 26.0) IVDE R 2 = The descriptor IVDE has the highest correlation with the n-alkane T b data. This descriptor belongs to the "information indices", and it can be calculated (for the n-alkane series from: (Requirement [1071 K – 1091 K]

Fitting a Linear QSPR to the n-Alkane T b data for 9 ≤ n C ≤ 20 In this case a linear QSPR cannot be used for long range extrapolation

Fitting a Nonlinear QSPR to the n-Alkane T b data for 9 ≤ n C ≤ 20 β 0 = ± 11.9; β 1 = ± 11.4; β 2 = 1/(45.1 ± 0.9) R 2 = The nonlinear model represents both the available data and the asymptotic behavior excellently

The relationship between n-Alkane and n-Alkanoic acid T b data for 3 ≤ n C ≤ 13 The experimental data of n-alkanoic acids is smooth, the linear relationship can be used for interpolation and short range extrap. Prediction by linear equation β 0 = ± 5.79; β 1 = ± 0.015; R 2 = 0.999

The relationship between n-Alkane and n-Alkanoic acid T b data for 3 ≤ n C ≤ 13 The nonlinear relationship represents adequately the available data and converges to the correct limiting value. Prediction by the equation: β 0 = ± 0.03; β 1 = ± 0.04; β 3 = ± 0.005; R 2 =

Prediction of T b for a “Target” homologous series  Plot the available T b data of the target series versus the corresponding n-alkane data. Based on the smoothness of the curve and the number of available data points determine whether long range extrapolation is feasible.  Use nonlinear regression to obtain the coefficients of the equation:  To predict T b for a member of the target series of a particular n C introduce the corresponding T b data of the n-alkane series (if available) or a predicted value obtained using the equations provided, into the above equation.

Special Challenges in (Long Chain) Property Prediction  Insufficient amount of property data for the reference and/or the target series  Available property data for the reference and/or the target series is too noisy.  The property value for n C → ∞* is not known  Phase change at the standard state (usually T = 298 K and P = 1 bar) appears at high n C with no corresponding property data are available. This may happen for properties specified at a standard state (For example: heat of combustion). The influence of the phase change must be considered in extrapolation.

Critical Volume (V c ) for n-alkanes and n-alkanoic acids V c changes monotonically with increasing n C Source: DIPPR database (Rowley et al. 2010), experimental data in bold

Modeling the V C data of n-alkanes with the linear QSPR: Super-linear change with n C (Suggested by Marano, Gao et al.)

The relationship between n-Alkane and n-Alkene V C data for 3 ≤ n C ≤ 10 The deviation of the DIPPR pred. data can be explained by the high unceratainty (up to 25%) of these data. Prediction by linear equation β 0 = 0; β 1 = ± 0.006; R 2 =

Checking the Consistency of the Available V C data for the Target Series The plot of V Cr – V Ct versus V Ct should yield a straight line with slope of (1- β 1 ) for consistent data Slope = = Slope = unclear

Conclusions  For properties that approach a finite value for large n C a linear function of the descriptor with the highest correlation with the available data often able to provide good predictions only for interpolation and short rage extrapolation. A nonlinear expression containing the descriptor and the property value at n C → ∞*, that provides good prediction in long range extrapolation, has been developed.  The linear relationship between properties of corresponding members of different homologous series, may be valid only locally. A new nonlinear relationship which holds in very wide ranges has been developed.  It has been shown that the reference series approach enables optimal utilization of the available property data for checking the consistency of such data and prediction of properties in the short and long range.