Development of Property Models with Uncertainty Estimate for Reliable Product-Process design

Transcription

1 Development of Property Models with Uncertainty Estimate for Reliable Product-Process design Amol Hukkerikar a, Bent Sarup b, Jens Abildskov a, Gürkan Sin a, and Rafiqul Gani a a CAPEC, Department of Chemical Engineering, Technical University of Denmark, Lyngby, Denmark. b Vegetable Oil Technology Business Unit, Alfa Laval Copenhagen A/S, Søborg, Denmark.

2 Outline Motivation Objective Overview Methodology for property modeling and uncertainty analysis Results Conclusions 2

3 Motivation Physical and thermodynamic property data and property models are vital pre-requisites for performing tasks such as, 1) Process design, simulation and optimisation 2) Computer aided molecular/mixture (product) design (CAMD) The accuracy & reliability of product/process design largely depends on the accuracy of the involved thermo-physical properties. For the estimation of pure component properties, group-contribution (GC) methods have been widely used; but how good is their accuracy? This issue is highlighted for pure component properties in this work. In addition to the accuracy, it is also necessary to know the uncertainties (prediction error) of the estimated property values. With this information, it is possible to perform better-informed product/process design by taking into account these uncertainties. 3

4 Objective Develop a systematic methodology to provide more reliable predictions with a revised and improved sets of model parameters for GC (groupcontribution) based and CI (atom connectivity index) based models to estimate properties of pure components and to quantify the uncertainties (for eg. 95% confidence intervals) of the estimated property values. 4

5 Overview of property modeling and uncertainty analysis Experimental data Property Prediction model Molecular structure information Application of models Parameter estimation Model parameters Uncertainty analysis Prediction error Marrero and Gani GC-method based property models CI method based property models 5

6 Overview of property modeling and uncertainty analysis Experimental data Property Prediction model Molecular structure information Application of models Parameter estimation Model parameters Uncertainty analysis Prediction error Maximum-likelihood estimation theory 6

7 Marrero and Gani (MG) method The MG method based property prediction model has the form, The function f (X) is a function for a target property X. For normal melting point: f (X) = exp (T m / T mo ) For normal boiling Point: f (X) = exp (T b / T bo ) For critical temperature: f (X) = exp (T c / T co ) For critical pressure: For critical volume: f (X) = (P c P c1 ) 0.5 P c2 f (X) = V c V co Details of other MG method based property prediction models can be found in the following references. J. Marrero, and R. Gani, Fluid Phase Equilibria, (2001), J. Marrero, and R. Gani, Industrial and Engineering Chemistry Research, (2002), Kolska et al., Industrial and Engineering Chemistry Research (2005), E. Conte et al., Industrial and Engineering Chemistry Research, (2008), A. Hukkerikar et al., Fluid Phase Equilibria, (2012), doi: /j.fluid

8 Marrero and Gani (MG) method Step-wise approach The parameter estimation is performed at three levels. The contributions of the higher levels act as corrections to the approximations of the lower levels. 1 st Level estimation First-order group Contribution (w =0; z = 0) 2 nd Level Estimation Second-order group contribution (w =1; z = 0) 3 rd Level Estimation Third-order group contribution (w =1; z = 1) Reference: J. Marrero, and R. Gani, Fluid Phase Equilibria, (2001),

9 Marrero and Gani (MG) method - Simultaneous approach The parameter estimation is performed in a single step by considering all three terms (first order, second order and third order group term). The definition of function f (X) for each property is the same as used in the step-wise approach. First-order group contribution term Second-order group contribution term Third-order group contribution term 9

10 Atom Connectivity Index (CI) method This method allows creation of new groups through the regressed contributions of the connectivity indices. The CI method based property prediction model is: The function f (X) is a function for a target property X. v o 1 v and are the zeroth- and the first-order connectivity indices. A i represents the occurrences of the i th atom in the molecular structure. a i is the contribution of atom i. b and c are adjustable parameters and d is a model constant. If the molecular structure of a given component is not completely described by any of the available groups, CI method can be employed together with GC method (known as GC + approach) to create the missing groups and to predict their contributions. Reference: Gani et al., Industrial and Engineering Chemistry Research, (2005), 44,

11 Methodology for parameter estimation and uncertainty analysis Maximum-likelihood estimation theory The minimization of a cost function, S(P * ) i.e. sum of the squares of the difference between the experimental value and estimated value, X exp X pred 2 * exp pred * min N P j j P S X X j1 yields the values of model parameters P *. The covariance matrix COV (P * ) for the estimated parameters is given by, * SSE * * P P T P COV J J dof 1 The Jacobian matrix J(P * ) is given by, J P * pred X P * P * The covariance matrix for estimated property value is then obtained by, pred P * P * P * COV X J COV J T References: Seber and Wild, (1989). Nonlinear Regression, New York: Wiley. Sin et al., Computers and Chemical Engineering, (2010), 34,

12 Continued... The confidence interval of parameters, P *, at α t significance level (usually a value of 0.05) is given as, P P diag COV P 1 t * * *. t dof, t 2 The confidence interval of the predicted property value, level is given as, X pred, at α t significance X T P * P * P *., t pred pred 1 diag J COV J t dof 2 t X Following 21 pure component properties were considered for the analysis: 1. Normal melting point, 2. Normal boiling point, 3. Critical temperature, 4. Critical pressure, 5. Critical volume, 6. Standard enthalpy of formation, 7. Standard enthalpy of vaporization (298 K), 8. Standard enthalpy of vaporization (Tb), 9. Standard Gibbs energy, 10. Standard enthalpy of fusion, 11. Entropy of vaporization (Tb), 12. Liquid surface tension (298 K), 13. Liquid viscosity (300 K), 14. Flash point, 15. Auto ignition temperature, 16. Hansen solubility parameters, 17. Hildebrand solubility parameter, 18. Aqueous solubility, 19. Octanol/water partition coefficient, 20. Acentric factor, and 21. Liquid molar volume (298K). 12

13 CAPEC database used for parameter estimation (class-wise description) Class of pure components T b T c P c V c T m G f H f H fus LogK ow F p δ D δ P δ H H v H vb S vb δ Ait ω V m Hydrocarbons Oxygenated Nitrogenated Chlorinated Fluorinated Brominated Iodinated P containing Sulfonated Si containing Multifunctional Total no. of components Reference: T. Nielsen et al., J. Chem. Eng. Data, 46 (2001)

14 Results: 1.1 Model performance statistics Performance of MG Method Based Property Prediction Models Property Exptl. data points Corr. Coeff. R 2 % of data points within ±5% error SD AAE ARE No. of parameters regressed T b K T c K P c bar V c cc/mol T m K G f kj/mol ** 227 H f kj/mol ** 233 H fus kj/mol ** 244 H v kj/mol H vb kj/mol Total no. of parameters = 424 (first-order groups = 220, second-order groups = 130, third-order groups = 74) T b = Normal boiling point, T c = Critical temperature, P c = Critical pressure, V c = Critical volume, T m = Normal melting point, G f = Gibbs free energy, H f = Enthalpy of formation, H fus = Enthalpy of fusion, H v = Enthalpy of vaporisation (298K), H vb = Enthalpy of vaporisation (T b ). SD = Standard deviation, AAE = Average Absolute Error, ARE = Average Relative Error ** These values are not given as these properties contain both +ve and ve values. 14

15 Results: 1.1 Model performance statistics Performance of MG Method Based Property Prediction Models Property Exptl. data points Corr. Coeff. R 2 % of data points within ±5% error SD AAE ARE No. of parameters regressed T b K T c K P c bar V c cc/mol T m K G f kj/mol ** H f kj/mol ** 233 H fus kj/mol ** 244 H v kj/mol H vb kj/mol

16 Results: 1.2 Model performance statistics Performance of MG Method Based Property Prediction Models Property Exptl. data points Corr. Coeff. R 2 % of data points within ±5% error SD AAE ARE No. of parameters regressed LogKow ** 376 LogWs Logmg/L ** 370 F p K AiT K HSP-D MPa 1/ HSP-P MPa 1/ HSP-H MPa 1/ ST mn/m Visc mpa-s SolP MPa 1/ Omega V m cc/mol Total no. of parameters = 424 (first-order groups = 220, second-order groups = 130, third-order groups = 74) LogKow = Octanol/water partition coefficient, LogWs = Aq. solubility, F p = Flash point, AiT = Auto ignition temperature, HSP = Hansen solubility parameter, ST = Surface tension, Visc = Viscosity, SolP = Hildebrand solubility parameter, Omega = Acentric factor, V m = Liquid molar volume (298K); SD = Standard deviation, AAE = Average Absolute Error, ARE = Average Relative Error ** ARE is not reported ad these properties contain both +ve and ve experimental property values. - ARE is not reported as these properties contain very small experimental values 16

17 Results: 2. Model performance For most properties, the average prediction error is lower than (or comparable to) the average measurement error. Comparison of model prediction error with reported measurement error Property Data-points (DIPPR) Avg. measurement error * Data-points (This work) Avg. prediction error (with revised parameters) Normal boiling point K 1306 < Critical temperature K 402 < Critical pressure bar 293 < Critical volume cc/mol 234 < Normal melting point K 1385 < Gibbs free energy kj/mol 258 < Enthalpy of formation kj/mol 668 < Enthalpy of fusion kj/mol 520 < Flash point K 111 < * Reference: DIPPR 801 database 17

18 Results: 3.1 Reliability of property prediction models Plot of Tb and Tc for n-alkanes Plot of Tc/Tb for a large data-set For n-alkanes, the ratio Tc / Tb is greater than unity. For a wide range of components considered in the data-set, the ratio Tc /Tb was found greater than unity. 18

19 Results: 3.2 Reliability of property prediction models Plot of Tc/Pc for n-alkanes Plot of critical compressibility factor for n-alkanes Zc max = for components with Tc > 100 K The ratio Tc/Pc is important in many engineering calculations. This ratio is reliably predicted with a good accuracy. Z c = R T c / V c P c The predicted critical compressibility factor values of n-alkanes are consistent with the theoretical foundation. Reference: Poling et al., The properties of gases and liquids, McGraw Hill, New York,

20 Results: 4.1 Application example (Estimation of normal boiling point and the 95% confidence interval) Butanedioic acid, dipropyl ester Molecular structure CAS No: O O O O Molecular formula: C 10 H 18 O 4 First-order groups Occurrences Contribution CH CH CH 2 COO Second-order groups Occurrences Contribution OOC-CHm-CHm-COO (n, m in 1..2) Third-order groups Occurrences Contribution No third-order groups are involved pred T T ln b bo NiCi w M jdj z EkO k i j k K Absolute error = K K = 4.28 K Marrero and Gani (2001) method = K, Abs. Err. = K ; Constantinou and Gani (1994) method = K, Abs. Err. = K Joback and Reid (1987) method = K, Abs. Err. = K 20

21 Results: 4.2 Application example (Calculation of 95% confidence interval of predicted property value) Covariance matrix COV(P * ) with dimensions (5 5) for the groups listed T bo CH 3 CH 2 CH 2 COO OOC-CHm-CHm-COO (n, m in 1..2) T bo CH E E-05 CH E E-05 CH 2 COO E E OOC-CHm-CHm-COO (n, m in 1..2) E E E Local sensitivity J(P * ) with dimensions (5 5) of T b model δt b /δt b0 δt b /δch 3 δt b /δch 2 δt b /δch 2 COO δt b /δ OOC-CHm-CHm-COO (n, m in 1..2) The 95% confidence interval of predicted normal boiling point is calculated by, b pred pred T * * * , 2. b diag J COV J t dof P P P t T T K ± 4.79 K It can be observed that experimental value of the normal boiling point ( K) lies within predicted confidence interval indicating reliability of developed methodology. 21

22 Experimental values of Tb in K Experimental values of Tm in K Results: 4.3 Reliability of the developed methodology of property estimation and uncertainty analysis Experimental values together with calculated 95% confidence intervals Experimental values 95% confidence intervals Experimental values 95% confidence intervals Data-set of normal boiling point Data-set of normal metling point The most of the experimental values falls within calculated 95% confidence intervals. This analysis supports linear error propagation method for quantifying model prediction error. 22

23 Results: 4.3 Reliability of the developed methodology of property estimation and uncertainty analysis Comparison of the performance of Marrero and Gani (2001) method and this work (2012) 23

24 Results: 5.1 Implementation in ICAS The developed methodology was implemented in ProPred - a property estimation toolbox of ICAS (Integrated Computer Aided System) software developed by CAPEC. ProPred (Component Property Prediction Toolbox) 24

25 Results: 5.2 ProPred Property display area (method of estimation-wise) Tools available for drawing a molecular structure Drawing area to draw structure of a molecule Alternatively, molecule s structure can be drawn by importing SMILES. Step 1 Step 2 25

26 Results: 5.3 Illustrative example Component: Butanedioic acid, dipropyl ester, CAS No Step-wise method Simultanous method Molecular structure First order groups Second order groups Third order groups 26

27 Conclusions A systematic methodology for property modeling and uncertainty analysis is developed to provide more reliable predictions together with an estimate of uncertainties which is much needed information to obtain reliable product/process design. The application range, and prediction capability of earlier version of models is improved by utilizing extended CAPEC database. In addition, a new approach based on the simultanous regression is developed. The reliability of developed methodology has been tested by comparing model prediction uncertainties with the reported range of measurement uncertainties. For most properties, experimental values of properties were found within the calculated 95% confidence intervals. Motivated by these results, our current and future work is focused on 1) extension of the methodology to other important pure component properties (for eg. environmentrelated properties such as LC50, LD50 etc.) 2) sensitivity analysis of product/process design to uncertainties in property estimates. 27

28 Acknowledgments Project Supervisors: Bent Sarup, Jens Abildskov, Gürkan Sin, and Rafiqul Gani CAPEC, DTU and Alfa Laval Copenhagen A/S MULTIMOD ITN Network (project under the FP7 Programme) 28

29 Development of Property Models with Uncertainty Estimate for Reliable Product-Process design Amol Hukkerikar a, Bent Sarup b, Jens Abildskov a, Gürkan Sin a, and Rafiqul Gani a a CAPEC, Department of Chemical Engineering, Technical University of Denmark, Lyngby, Denmark. b Vegetable Oil Technology Business Unit, Alfa Laval Copenhagen A/S, Søborg, Denmark. Thank You For Your Attention Questions????

30 Effect of quantity of experimental data on the model performance Large quantity of experimental data helps to achieve improved quality parameter estimation and improved property predictions. Large quantity of experimental data helps to estimate maximum number of model parameters (group-contributions) Table 5. Effect of quantity of experimental data on quality of parameter estimation Distribution of experimental data SD in kj/mol AAE in kj/mol No. of model parameters estimated a 50% for training purpose % for training purpose % for training purpose All data-points for training purpose a The total no. of model parameters (first-order, second-order and third-order group contributions) is 424. * Reference: A. Hukkerikar et al., Fluid Phase Equilibria, (2012), doi: /j.fluid