available in the literature to predict these properties for petroleum ... explicit models for simulating the kinetics and dynamics of ....

ENHANCED METHOD FOR PREDICTING THE PROPERTIES OF PETROLEUM FRACTIONS Tareq A. Albahri Chemical Engineering Dept. - Kuwait University P.O.Box 5969 - Safat 13060, Kuwait [email protected] Introduction The properties of petroleum and its fractions are usually determined experimentally in the laboratory. Several methods are available in the literature to predict these properties for petroleum fuels from their bulk properties such as the boiling point and the specific gravity for example. Although accurate enough, these methods are not suitable for incorporation into the molecularly explicit models for simulating the kinetics and dynamics of petroleum refining processes. In previous work1 we have developed a molecularly explicit characterization model (MECM) that allows for the simulation of the molecular composition of petroleum fractions using a pre-selected set of pure components. What is lacking, however, is the ability to predict the properties of the various streams as the molecular composition changes during processing by physical separation or chemical reaction. This work focuses on the development of such a property estimation method from the molecular composition of complex, multicomponent mixtures such as petroleum. Technical Development In our previous work on the simulation of light petroleum fractions1 we have found that not all the properties of the petroleum fuel are required to be optimized against those from the pure components. In fact only the ASTM D86 Distillation, the PNA content and the RVP were sufficient to provide a feasible solution. All the other properties calculated form the bulk properties of the petroleum fraction and those from the pure components in them were almost alike. This lead us to believe that the properties of a petroleum fraction can be estimated from the above three properties alone. The concept of the proposed model is that the global properties of a petroleum fraction such as the boiling point, the vapor pressure and the paraffins, naphthenes, and aromatics content must be equal to those calculated from the pure components contained in that petroleum fraction. When both bulk and pure component properties are available, the composition of the petroleum fraction may be predicted using optimization algorithms as simplified in Figure 1. The predicted composition of a limited set of pure components may then be used to predict the other properties of the petroleum fuel using appropriate mixing rules. C3

RVP ASTM D86 or TBP Distillation PNA

MECM Model C11

Detailed composition of 68 predefined molecules

Mixing Rules

API MW RI H/C Viscosity Surface Tension Other properties

Figure 1. Simplified schematic representation of the proposed model. Experimental values of the RVP and PNA are always desirable as inputs. However, when these are not available they may be predicted using methods available in the literature2,3 making the ASTM D86 distillation or the true boiling point (TBP) the minimum model input required.

The internally calculated properties are the molecular weight, the Reid vapor pressure (RVP), the true vapor pressure at 100°F, the specific (API) gravity, the cubic average boiling point (CABP), the mean average boiling point (MeABP), the volumetric average boiling point (VABP), the weight average boiling point (WABP), the molar average boiling point (MABP), the Watson characterization factor (Kw), the refractive index, the carbon to hydrogen ratio (C/H), the kinematic viscosity at 100 and 210°F, the surface tension, the aniline point, the true and pseudo critical temperatures and pressures, the critical compressibility factor, the acentric factor, the freezing point, the heat of vaporization at the normal boiling point, the net heat of combustion at 77°F, the isobaric liquid heat capacity at 60°F, the isobaric vapor heat capacity at 60°F, the liquid thermal conductivity at 77 ºF, and the paraffins, naphthenes, and aromatics content. These properties are calculated for the petroleum fraction using well established methods in the literature or were developed specifically for this project1. The same properties are calculated from the pure component composition using the appropriate mixing rules from the literature. When the pure component properties are not available in databases they were estimated using group contribution methods available in the literature or were developed specifically for this project1. The difference between the values obtained from the two different methods for the true boiling point and the PNA content are minimized in the objective function the purpose of which is to calculate the values of xi which is the mole fraction of the pure components in the petroleum fraction. This is shown in Equation 1 where both PNA and Tb of the pure components are a function of xi. The composition of the light ends was determined using the RVP which is converted to the true vapor pressure at 100 °F and then using simple bubble point calculations. The First line in the objective function represents the sum of errors in the boiling points of the pure components and the corresponding value on the true boiling point (TBP) curve. The pure component concentrations are determined by minimizing the following modified objective function,

∑ ((Tb j −T ′b j ) × Wo j =1 n

S = +

(( PNA

− PNA′

)

×

×100

Tb j )

W 1 ×100 PNA

2

)

(1) 2

where j is the index number of the molecule and n is the total number of molecules. PNAi and PNA'i refer respectively to the actual and predicted paraffin, naphthene, and aromatic content of the petroleum fraction. Tbj and T'bi refer respectively to the boiling point of the pure component j and the corresponding value on TBP curve. W1 and Wo are weighting factors and S is the objective function to be minimized. An optimization algorithm based on the least square method was used to minimize the objective function while calculating the concentration of the pure components. The nonlinear regression algorithm minimizes the sum of the difference between the fuels bulk properties and those estimated from pure components. Using the Microsoft Excel Solver tool and the global optimization algorithm, convergence was achieved in less than one minute for all cases on a Pentium IV-1.7 GHz PC. Discussion The model was tested to predict the properties of 30 petroleum naphtha samples ranging in API from 35 to 91, IBP from 62 to 267 °F and FBP from 152 to 312 °F. Some of these results are shown in Table 1 and Figures 2 to 4. The MECM model proves to be a powerful tool for simulating the properties of petroleum fuels.

Prepr. Pap.-Am. Chem. Soc., Div. Fuel Chem. 2004, 49(2),

925

120 API Gravity calculated from pure components

2

R = 0.99 100

80

30 2

28

R = 0.99

26 24 22 20 18 16 14 12 10 10

60

15

20

25

30

Surface tension calculated from global properties (dynes/cm)

Figure 4. Bar plot for the predicted surface tension from pure components for 30 petroleum naphtha samples versus that calculated from global properties using published methods.

40

20 20

40

60

80

100

120

API gravity determined experimentally

Figure 2. Bar plot for the predicted API gravity from pure components for 30 petroleum naphtha samples versus that calculated from global properties using published methods. 130 Molecular weight calculated from pure components

Surface tension calculated from pure components. (dynes/cm)

This work demonstrates that the complex nature of petroleum fuels may be modeled by a limited set of representative pure components using non-linear-regression optimization models. Considering the difficulty and limitations in predicting the properties of petroleum fuels in the currently used pseudo component techniques, the proposed method can be an effective alternative. The clear advantage of the model is its ability to compliment the molecularly explicit models for petroleum refining processing.

2

R = 0.99

120 110 100 90 80 70

Table 1. Error analysis for some of the properties investigated No. Property Av. % error Corr. Coef. 1. API gravity 2.67 0.995 2. Cubic average boiling point 1.34 0.995 3. Mean average boiling point 0.99 0.995 4. Volume average boiling point 1.34 0.995 5. Molar average boiling point 0.83 0.995 6. Mass average boiling point 1.07 0.996 7. Watson characterization factor 0.80 0.970 8. Molecular weight 2.06 0.990 9. Refractive index 0.21 0.993 10. Hydrogen content 2.57 0.965 11. Viscosity at 210 °F 4.04 0.960 12. Viscosity at 100 °F 5.41 0.972 13. Surface Tension 2.67 0.995 14. Aniline Point 4.27 0.830 15. Critical temperature 0.93 0.991 16. Pseudocritical temperature 0.80 0.989 17. Pseudocritical pressure 2.22 0.890 18. Heat of vaporization 2.07 0.948 19. Heat of combustion 0.80 20. Freezing 5.38 21. Acentric factor 3.13 0.946 22. Critical compressibility factor 0.25 0.832 23. Flash point 5.16 0.924

60 50 50

70

90

110

130

Molecular weight determined from global properties

Figure 3. Bar plot for the predicted molecular weight from pure components for 30 petroleum naphtha samples versus that calculated from global properties using published methods.

Acknowledgment This work was supported by Kuwait University, Research Grant No. EC04/01. References [1] T. A. Albahri, Am. Chem. Soc., Div. fuel chem. prep., 2004, 49(1), 327328. [2] M. R. Riazi & T. E. Daubert, Ind. Eng. Chem. Process Des. Dev., 1980, 19 (2), 289-294. [3] Jenkins, G. I. and white, M. M.. J. Inst. Petrol., 1969, 55 (543), 153.

Prepr. Pap.-Am. Chem. Soc., Div. Fuel Chem. 2004, 49(2),

926

RVP ASTM D86 or TBP Distillation PNA

MECM Model C11

Detailed composition of 68 predefined molecules

Mixing Rules

API MW RI H/C Viscosity Surface Tension Other properties

Figure 1. Simplified schematic representation of the proposed model. Experimental values of the RVP and PNA are always desirable as inputs. However, when these are not available they may be predicted using methods available in the literature2,3 making the ASTM D86 distillation or the true boiling point (TBP) the minimum model input required.

The internally calculated properties are the molecular weight, the Reid vapor pressure (RVP), the true vapor pressure at 100°F, the specific (API) gravity, the cubic average boiling point (CABP), the mean average boiling point (MeABP), the volumetric average boiling point (VABP), the weight average boiling point (WABP), the molar average boiling point (MABP), the Watson characterization factor (Kw), the refractive index, the carbon to hydrogen ratio (C/H), the kinematic viscosity at 100 and 210°F, the surface tension, the aniline point, the true and pseudo critical temperatures and pressures, the critical compressibility factor, the acentric factor, the freezing point, the heat of vaporization at the normal boiling point, the net heat of combustion at 77°F, the isobaric liquid heat capacity at 60°F, the isobaric vapor heat capacity at 60°F, the liquid thermal conductivity at 77 ºF, and the paraffins, naphthenes, and aromatics content. These properties are calculated for the petroleum fraction using well established methods in the literature or were developed specifically for this project1. The same properties are calculated from the pure component composition using the appropriate mixing rules from the literature. When the pure component properties are not available in databases they were estimated using group contribution methods available in the literature or were developed specifically for this project1. The difference between the values obtained from the two different methods for the true boiling point and the PNA content are minimized in the objective function the purpose of which is to calculate the values of xi which is the mole fraction of the pure components in the petroleum fraction. This is shown in Equation 1 where both PNA and Tb of the pure components are a function of xi. The composition of the light ends was determined using the RVP which is converted to the true vapor pressure at 100 °F and then using simple bubble point calculations. The First line in the objective function represents the sum of errors in the boiling points of the pure components and the corresponding value on the true boiling point (TBP) curve. The pure component concentrations are determined by minimizing the following modified objective function,

∑ ((Tb j −T ′b j ) × Wo j =1 n

S = +

(( PNA

− PNA′

)

×

×100

Tb j )

W 1 ×100 PNA

2

)

(1) 2

where j is the index number of the molecule and n is the total number of molecules. PNAi and PNA'i refer respectively to the actual and predicted paraffin, naphthene, and aromatic content of the petroleum fraction. Tbj and T'bi refer respectively to the boiling point of the pure component j and the corresponding value on TBP curve. W1 and Wo are weighting factors and S is the objective function to be minimized. An optimization algorithm based on the least square method was used to minimize the objective function while calculating the concentration of the pure components. The nonlinear regression algorithm minimizes the sum of the difference between the fuels bulk properties and those estimated from pure components. Using the Microsoft Excel Solver tool and the global optimization algorithm, convergence was achieved in less than one minute for all cases on a Pentium IV-1.7 GHz PC. Discussion The model was tested to predict the properties of 30 petroleum naphtha samples ranging in API from 35 to 91, IBP from 62 to 267 °F and FBP from 152 to 312 °F. Some of these results are shown in Table 1 and Figures 2 to 4. The MECM model proves to be a powerful tool for simulating the properties of petroleum fuels.

Prepr. Pap.-Am. Chem. Soc., Div. Fuel Chem. 2004, 49(2),

925

120 API Gravity calculated from pure components

2

R = 0.99 100

80

30 2

28

R = 0.99

26 24 22 20 18 16 14 12 10 10

60

15

20

25

30

Surface tension calculated from global properties (dynes/cm)

Figure 4. Bar plot for the predicted surface tension from pure components for 30 petroleum naphtha samples versus that calculated from global properties using published methods.

40

20 20

40

60

80

100

120

API gravity determined experimentally

Figure 2. Bar plot for the predicted API gravity from pure components for 30 petroleum naphtha samples versus that calculated from global properties using published methods. 130 Molecular weight calculated from pure components

Surface tension calculated from pure components. (dynes/cm)

This work demonstrates that the complex nature of petroleum fuels may be modeled by a limited set of representative pure components using non-linear-regression optimization models. Considering the difficulty and limitations in predicting the properties of petroleum fuels in the currently used pseudo component techniques, the proposed method can be an effective alternative. The clear advantage of the model is its ability to compliment the molecularly explicit models for petroleum refining processing.

2

R = 0.99

120 110 100 90 80 70

Table 1. Error analysis for some of the properties investigated No. Property Av. % error Corr. Coef. 1. API gravity 2.67 0.995 2. Cubic average boiling point 1.34 0.995 3. Mean average boiling point 0.99 0.995 4. Volume average boiling point 1.34 0.995 5. Molar average boiling point 0.83 0.995 6. Mass average boiling point 1.07 0.996 7. Watson characterization factor 0.80 0.970 8. Molecular weight 2.06 0.990 9. Refractive index 0.21 0.993 10. Hydrogen content 2.57 0.965 11. Viscosity at 210 °F 4.04 0.960 12. Viscosity at 100 °F 5.41 0.972 13. Surface Tension 2.67 0.995 14. Aniline Point 4.27 0.830 15. Critical temperature 0.93 0.991 16. Pseudocritical temperature 0.80 0.989 17. Pseudocritical pressure 2.22 0.890 18. Heat of vaporization 2.07 0.948 19. Heat of combustion 0.80 20. Freezing 5.38 21. Acentric factor 3.13 0.946 22. Critical compressibility factor 0.25 0.832 23. Flash point 5.16 0.924

60 50 50

70

90

110

130

Molecular weight determined from global properties

Figure 3. Bar plot for the predicted molecular weight from pure components for 30 petroleum naphtha samples versus that calculated from global properties using published methods.

Acknowledgment This work was supported by Kuwait University, Research Grant No. EC04/01. References [1] T. A. Albahri, Am. Chem. Soc., Div. fuel chem. prep., 2004, 49(1), 327328. [2] M. R. Riazi & T. E. Daubert, Ind. Eng. Chem. Process Des. Dev., 1980, 19 (2), 289-294. [3] Jenkins, G. I. and white, M. M.. J. Inst. Petrol., 1969, 55 (543), 153.

Prepr. Pap.-Am. Chem. Soc., Div. Fuel Chem. 2004, 49(2),

926