1 Prediction of Phase Equilibrium Related Properties by Correlations Based on Similarity of Molecular Structures N. Brauner a, M. Shacham b, R.P. Stateva c and G. St. Cholakov d a School of Engineering, Tel-Aviv University, Tel-Aviv, Israel b Dept. Chem. Engng, Ben-Gurion University, Beer-Sheva, Israel c Inst. Chem. Engn., Bulgarian Academy of Sciences, Sofia, Bulgaria d University of Chemical Technology and Metalurgy, Sofia, Bulgaria

2 The Needs  Phase equilibrium related properties (vapor pressure, activity coefficients etc.) are essential for risk assessment, environmental impact assessment and process and product design  The number of the compounds used at present by the industry or those of its immediate interest ~100,000. Those theoretically possible and may be of future interest several tens of millions.  DIPPR 801 database contains ~2100 compounds (33 constant properties, 15 temperature dependent properties)

3 Equations Commonly Used in Phase Equilibrium Computations Model : The vapor-liquid equilibrium ratio K (K-value) for the i-th component is given by: - activity coefficient in the liquid phase -standard-state fugacity in the liquid phase - fugacity coefficient in the vapor phase. calculation requires -pure component saturation pressure of a pure liquid at specified temperature and pressure. To calculate the Soave-Redlich-Kwong or Peng-Robinson EoS with mixing rules are employed.

4 Equations Commonly Used in Phase Equilibrium Computations In the EoS, the properties of the pure compounds required are the critical temperature (T c ) and pressure (P c ), and the acentric factor (ω). We have developed several methods to predict these properties. They are described elsewhere.* The mixing rules require binary interaction parameters: *Bruaner et al. AIChE J, 54(4), (2008). where A brief demonstration of the method proposed by us for prediction of the binary interaction parameters k ij is included in the paper in the proceedings. In this presentation the emphasis is on the prediction of vapor pressure

5 Vapor Pressure Prediction Methods  “Corresponding States” methods Require constant, pure component property data (such as T b, T c, P c and acentric factor) for the target compound (the compound for which vapor pressure need to be estimated).  “Quantitative Structure Property Relationships” (QSPR’s), based on the use of molecular descriptors Only molecular structure based data of the target compound are used, however these methods are limited to prediction of the vapor pressure for one temperature value. Our objective was to develop new methods for predicting vapor pressure for a wide range of temperatures while using only structural information for the target molecule

6 A Generalized Algorithm for Prediction of Saturation Temperatures (1)  Similarity group selection - Identify compounds that are structurally similar to the target compound (i.e., members of homologous series, or apply the TQSPR algorithm*).  It is assumed that data for the normal boiling temperature (T b ) are available for members of the similarity group, and for a few of them (at least two compounds) experimental data and/or models for vapor pressure are available.  Selection of the predictive descriptor - Use a stepwise regression program to identify a molecular descriptor that is co- linear with T b for the similarity group. *Shacham et al. Chem. Eng. Sci. 62 (22), 6222 (2007)

7 Plot of T b versus the descriptor VEv1* for the 1-alkene series. *A 2D eigenvalue-based descriptor: eigenvector coefficient sum from van der Waals weighted distance matrix, calculated by the Dragon program ξ- the selected descriptor

8 A Generalized Algorithm for Prediction of Saturation Temperatures (2)  Recalling that T b is the saturation temperature (T s ) at atmospheric pressure suggests that the same descriptor is also collinear with T s at other pressures  Predictive compounds selection - Select two (or three) predictive compounds, closest to the target compound (in terms of the selected descriptor value) and preferably located on opposite sides of the target compound. Experimental data and/or models for vapor pressure must be available for the selected predictive compounds (e.g., Antoine, Riedel or Wagner).  Model applicability range - determine the applicability range of the predictive model to be developed based on the common vapor pressure range where data are available for all predictive compounds.

9 Vapor pressure versus temperature of the predictive and target compounds. ♦, 1-decene (predictive); ▲, 1-undecene (target); ●, 1-dodecene (predictive).

10 A Generalized Algorithm for Prediction of Saturation Temps (3)  Select a pressure value within the applicability range of the predictive equations. Calculate the saturation temperatures of the predictive compounds using the available correlations/models (e.g., Antoine, Riedel or Wagner). For example, the Antoine equation can be solved directly for the saturation temperature at pressure P: Using the Riedel (or Wagner) equation, iterative solution of an implicit equation is required:. Point by point calculation of the saturation curve for the target compound

11 A Generalized Algorithm for Prediction of Saturation Temperatures (4)  Use the SC-QS2PR method (linear interpolation or extrapolation) to calculate T s of the target compound at the specified pressure: is the saturation temperature of the target compound, is a descriptor, the indices 1 and 2 refer to the predictive compounds and the index t refers to the target compound. For the target compound only the molecular descriptor value is needed in order to predict the saturation temperature at the prescribed pressure.

12 Prediction of T s for 1-undecene (target compound) with 1- decene and 1-dodecene predictive compounds (Interpolation)

13 Prediction of T s for n-Octanoic Acid (n-Butanoic and n- Decanoic Acids are Predictive Compounds

14 The “Two Reference Fluid” Method* P sr is the reduced vapor pressure calculated at the same reduced temperature for the predictive and target compounds. This method requires the following properties for the target compound: T c, P c, and P T = 0.7 T c There are no clear guidelines regarding the selection of the predictive compounds. *Teja, Sandler and Patel, Chem. Eng. J (Laussane) 21, 21(1981)

15 Modification of the “Two Reference Fluid” (TRF) Method The following changes are introduced in order to remove the need for properties of the target compound:  The acentric factor is replaced by a molecular descriptor which is collinear with the acentric factor for the members of the similarity group.  The reduced saturation pressure (for a particular T r ) is replaced by saturation pressure (for a particular T). The predictive compounds are selected the same way as in the SC- QS2PR method. Antoine, Riedel, Wagner etc. equations can be used for calculating Ps for the predictive compounds.

16 Plot of ω versus the descriptor TIC1* for the n-alkane series. *A 2D information index descriptor: total information content index (neighborhood symmetry of 1-order), calculated by the Dragon program

17 Prediction of P s for n-hexane (n-pentane and n-heptane predictive compounds) by the modified TRF method *T r value is for the target compound

18 Prediction of P s for n-hexane (n-pentane and n-heptane predictive compounds) by the modified TRF method *T r value is for the target compound

19 Conclusions The new QSPR-based methods for predicting vapor pressure are based on the identification of potential predictive compounds, which are structurally similar to the target compound (a similarity group) and for which data for a vapor pressure related property (e.g., normal boiling temperature or acentric factor) are available. A molecular descriptor, which is collinear with the normal boiling temperature (or acentric factor) for the members of the similarity group, is used to develop a simple structure-structure relation (short-cut QS2PR). This relation is then applied for predicting the saturation temperatures (or vapor pressure ) of the target-compound in the pressure (or temperature) range where valid vapor pressure data exist for two selected predictive compounds.

20 Advantages of the Proposed Methods Only structural information (no measured property values) are needed for the target compound; Predictive compounds similar to the target are selected in a systematic manner; The temperature - vapor pressure relationships of the predictive compounds are used only in their valid range of applicability; It is possible to predict either saturation temperature or vapor pressure giving more flexibility regarding the range and uncertainty of the predictions.

21 Presentation Outline  Categorizing the Molecular Descriptors According to the Trend of Their Change with n C for Homologous Series  Identifying Training Sets from Compounds Belonging to the Target Compounds Homologous Series  Predicting Critical Properties, Normal Boiling and Melting Temperatures, Liquid Molar Volume and Refractive Index for Five Homologous Series with and without the Use of 3-D descriptors.  Comparison of the Results and Conclusions

22 Presentation Outline  Categorizing the Molecular Descriptors According to the Trend of Their Change with n C for Homologous Series  Identifying Training Sets from Compounds Belonging to the Target Compounds Homologous Series  Predicting Critical Properties, Normal Boiling and Melting Temperatures, Liquid Molar Volume and Refractive Index for Five Homologous Series with and without the Use of 3-D descriptors.  Comparison of the Results and Conclusions