Characterizing Pure and Undefined Petroleum Components

Transcription

1 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 8 Charaterizing Pure and Undefined Petroleum Components Hassan S. Naji King Abdulaziz University, Jeddah, Saudi Arabia Website: Abstrat-- In ompositional reservoir simulation, equations of state (EOS) are extensively used for phase behavior alulations. Proper haraterization of petroleum frations, however, is essential for proper EOS preditions. In this paper, the most ommon haraterization methods for pure and undefined petroleum frations are presented. A set of equations for prediting the physial properties of pure omponents is proposed. he equations require the arbon number as the only input. hey aurately alulate properties of pure omponents with arbon numbers in the range 6-50 while eliminating disrepanies therein. Correlations for haraterizing the undefined petroleum frations assume speifi gravity and boiling point as their input parameters. If moleular weight is input instead of boiling point, however, the same moleular weight equation is rearranged and solved nonlinearly for boiling point. his maes their use more onsistent and favorable for ompositional simulation. 1. INRODUCION Physial properties of pure omponents were measured and ompiled over the years. Properties inlude speifi gravity, normal boiling point, moleular weight, ritial properties and aentri fator. Properties of pure omponents are essential to the haraterization proess of undefined petroleum frations. Katz and Firoozabadi (1978) presented a generalized set of properties for pure omponents with arbon number in the range Whitson (198) modified this set to mae its use more onsistent. His modifiation was based on Riazi and Daubert (1987) orrelation for undefined petroleum frations. able I presents a listing of this set. G&P Engineering (006) presented a omplete set of data for pure omponents. able II presents a listing of this set. Equations of state are extensively used in ompositional reservoir simulators. Flash alulations are neessary to alulate vapor and liquid mole frations and ompositions at eah new pressure and hene at eah time step. Deep inside the proess of flash alulations, pure omponent properties play an important role in these alulations. After tangling a lot with flash alulation problems, Naji 008, it has been onluded that the smoothness of properties is really important for the onvergene of the solution. hat is, onvergene is learly affeted by the set of pure omponent properties when all other fators are ept onstant. his is why we dediated this researh to dig deeper and mae lear the feasible sets of pure omponent properties. In both data sets, eah property was plotted versus arbon number and the plot was fit by regression methods. he fit equations for Katz-Firoozabadi and for the G&P physial properties are given next. hose equations have proved onsistent when applied for splitting and lumping petroleum plus frations, see Naji, 006. When two-phase flash alulations were diretly applied to unmanaged pure data sets, onvergene problems were enountered. Suh problems, however, were eliminated when those orrelations were implemented, see Naji KAZ-FIROOZABADI DAA SE Katz and Firoozabadi (1978) presented a generalized set of properties for pure omponents with arbon number in the range Whitson (198) modified this set to mae its use more onsistent. His modifiation was based on Riazi and Daubert (1987) orrelation for undefined petroleum frations. able I presents a listing of this set.. G&P ENGINEERING DAA SE G&P Engineering (006), in their software PhysProp v , presented a omplete set of physial properties for pure omponents. able II presents a listing of this set IJE-IJENS April 010 IJENS

2 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No: RIAZI-DAUBER CORRELAIONS Riazi and Daubert (1987) developed a set of equations to evaluate properties of undefined petroleum frations. Given speifi gravity () and boiling point ( b ) or moleular weight (MW) of the petroleum fration, physial properties are estimated as follows: Moleular Weight If speifi gravity () and boiling point (b) of the petroleum fration are given, moleular weight (MW) is estimated as follows: MW exp.097x x10 (1) Where: /1.8 () b Normal Boiling Point In ase boiling point ( b ) of the petroleum fration is not nown and moleular weight (MW) is given instead, the above equation is rearranged and solved iteratively for. he objetive funtion for the nonlinear solver is given by: f exp x x10 MW 0 () p V Critial emperature exp 9.14x10 Critial Pressure x10 exp 8.505x10 Critial Volume x exp.64x x x x10 4 (4) (5) (6) Critial Compressibility Critial ompressibility may be onveniently alulated by the real gas equation-of-state at the ritial point as follows: Z pv MW R pv MW 10.7 (7) Watson Fator he Watson fator is alulated from its definition as follows: IJE-IJENS April 010 IJENS

3 1 b K International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 0 (8) Aentri Fator (Edmister s Correlation) p log b 1 1 (9) Aentri Fator (Korsten s Correlation) p log b (10) Where b and are in R, p is in psia, and V is in ft /lb. 5. KESLER-LEE CORRELAIONS Kesler and Lee (1976) developed a set of equations to evaluate properties of undefined petroleum frations. Given speifi gravity () and boiling point ( b ) or moleular weight (MW) of the petroleum fration, physial properties are estimated as follows: Moleular Weight If speifi gravity () and boiling point (b) of the petroleum fration are given, moleular weight (MW) is estimated as follows: MW 1,7.6 9,486.4 Where: /1.8 (1) b Normal Boiling Point In ase boiling point ( b ) is not nown and moleular weight (MW) is given instead, the above equation is rearranged and solved iteratively for. he objetive funtion for the nonlinear solver is given by: f 1,7.6 9, MW (11) (1) IJE-IJENS April 010 IJENS

4 Critial emperature International Journal of Engineering & ehnology IJE-IJENS Vol:10 No: (14) p Critial Pressure exp (15) Aentri Fator K K K 8.59br br p ln ln br br ln br br br Where: 6 br br br (16) b br (17) 1 b K (18) Critial Compressibility Fator Z (19) Critial Volume (General Definition) R Z V (0) MWp Where b and are in R, p is in psia, and V is in ft /lb. 6. CAVE CORRELAIONS Cavett (196) developed a set of equations to evaluate properties of undefined petroleum frations. Given speifi gravity () and boiling point ( b ) of the petroleum fration, moleular weight and ritial properties are estimated as follows: Moleular Weight (Soreide Correlation) he Soreide orrelation for true boiling point is solved iteratively for moleular weight (MW). he objetive funtion for the nonlinear solver is written as follows: IJE-IJENS April 010 IJENS

5 f 4 MW x10 MW Where: exp International Journal of Engineering & ehnology IJE-IJENS Vol:10 No: x10 MW x10 MW 0 (1) b 1. 8 () Normal Boiling Point (Soreide Correlation) x10 MW exp x10 MW x10 MW 0 () p Critial emperature F x x x10 Critial Pressure x x x10 API F x API F x10 API F x10^ x10 F 4 8 API F x10 API API F 10 Critial Volume (Reidel Correlation) 4 API F x10 9 F F x10 F F 6 F (4) (5) MWP V (6) Where: API 11.5 F b (7) Aentri Fator (Korsten s Correlation) p log b (8) 7. WU CORRELAIONS wu (1984) used the ritial properties ba-alulated from vapor pressure data to get orrelations for the undefined petroleum frations. Given speifi gravity () and boiling point ( b ) in R of the undefined petroleum fration, moleular weight and ritial properties are estimated as follows: (Note that quantities are alulated in SI units. o onvert them to the English system, is multiplied by 1.8, p is multiplied by , and V is multiplied by ) IJE-IJENS April 010 IJENS

6 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 Critial emperature f 1 f (9) 0 1 Where: 0 f x x x x / / (1) exp () () /1.8 (4) b 0 1 / (5) (0) V Critial Volume f 1 f V (6) 0 1 V V Where: V (7) f V V / / (8) V exp (9) V p Critial Pressure 0 V 0 / V 1 f 1 f p (40) 0 / p p Where: p (41) f p p ( / ( / /1000) /1000) p exp (4) Moleular Weight 1 f M 1 f MW exp (44) Where β is obtained by solving the following nonlinear equation: M p (4) IJE-IJENS April 010 IJENS

7 f f International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 4 exp M M / (46) / (47) M exp (48) M If speifi gravity () and moleular weight (MW) of the petroleum fration were given instead, the boiling point ( b ) in R is alulated as follows: b 1. 8 (49) Where is estimated by solving Eq. 45 iteratively and β is alulated by rearranging Eq. 44 as follows: lnmw 1 1 (50) f M f M Other parameters are the same as given by Eq (45) Z Critial Compressibility Fator (General Definition) p V R (51) p V 8.14 Aentri Fator (Edmister s Correlation) p log (5) Aentri Fator (Korsten Correlation) p log (5) 8. REGRESSION MODELS FOR HE KAZ-FIROOZABADI DAA SE When plotting Katz and Firoozabadi (1978) properties versus arbon number, disrepanies for C0-C were observed for ritial properties and aentri fator as shown in Figures 5-8 original data. herefore, these data sets were fit via regression models as a funtion of arbon number. he fit data is more onsistent than the original data. he regression models are give n by: Speifi Gravity n n (54) Normal Boiling Point b 4 4 n.870x10 n x10 n n n (55) IJE-IJENS April 010 IJENS

8 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 5 Moleular Weight p MW n x10 n x10 n n n n Critial emperature n x10 n x10 n x10 n n n Critial Pressure n 1.9x10 n x10 n x10 n n n (56) (57) (58) Aentri Fator 4 n x10 n x10 n (59) V Critial Volume n x x x x n x10 n x10 n n x10 n x10 n n x10 n n 1 1 n 50 (60) Critial Compressibility Critial ompressibility may be onveniently alulated by the real gas equation -of-state at the ritial point as follows: Z p V MW R (61) p V MW 10.7 Watson Fator he Watson fator is alulated from its definition as follows: 1 b K (6) 9. REGRESSION MODELS FOR HE G&P ENGINEERING DAA SE When plotting G & P Engineering (006) properties versus arbon number, disrepanies for C17-C1 were observed for ritial properties and aentri fator as shown in Figures 1-16 original data. herefore, this data set was fit via regression models as a funtion of arbon number. he fit data is more onsistent than the original data. he models are given by: n Speifi Gravity n (6) IJE-IJENS April 010 IJENS

9 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 6 Normal Boiling Point b 4 4 n x10 n x10 n n n (64) Moleular Weight MW n n (65) p V Critial emperature 5 5 n x10 n x10 n x10 n n n Critial Pressure n 8.87x10 n x10 n x10 n n n Aentri Fator 5 n x10 n x10 n x10 n Critial Volume n 1.685x10 n x10 n x10 n x10 n x10 4 (66) (67) (68) (69) Critial Compressibility Critial ompressibility may be onveniently alulated by the real gas equation -of-state at the ritial point as follows: Z pv MW R pv MW 10.7 (70) Watson Fator he Watson fator is alulated from its definition as follows: 1 b K (71) 10. CONCLUSIONS After tangling with many data bans for the physial properties of pure omponents, a set of regression models, for prediting the physial properties of pure omponents (paraffins/ alanes), were devised. he only required input is the arbon number. Predited properties inlude: speifi gravity, normal boiling point, moleular weight, ritial properties and aentri fator. he models are used to alulate physial properties of pure omponents with arbon numbers in the range A worthwhile aspet of the fit models, however, is that they aurately dupliate the original data sets while eliminating disrepanies therein. his maes their use more onsistent and favorable for ompositional reservoir simulation purposes IJE-IJENS April 010 IJENS

10 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 7 he most ommon orrelations for haraterizing undefined petroleum frations, that were presented in literature and have gotten a wide aeptane in the oil industry, are revised. he only required input parameters are speifi gravity and normal boiling point or moleular weight. Calulated properties inlude: normal boiling point (if moleular weight is supplied), moleular weight (if normal boiling point is supplied), ritial properties and aentri fator. b MW γ ω K p Z V 11. NOMENCLAURE = normal boiling point, R = moleular weight, lb/lb-mole = speifi gravity = aentri fator = Watson haraterization fator = ritial temperature, R = ritial pressure, psia = ritial ompressibility fator = ritial volume, ft /lb REFERENCES [1] Cavett, R.H., "Physial Data for Distillation Calulations-Vapor- Liquid Equilibrium," Pro. 7 th Meeting, API, San Franiso, 196, pp [] G & P Engineering Software, PhysProp, v , 006. [] Katz, D.L., and Firoozabadi, A., Prediting phase behavior of ondensate/rude oil systems using methane interation oeffiients: JP: [4] Kesler, M. G., and Lee. B. I., "Improved Predition of Enthalpy of Frations," Hydroarbon Proessing, Marh 1976, pp [5] Naji, H.S., 006. A polynomial Fit to the Continuous Distribution Funtion for C 7+ Charaterization: Emirates Journal for Engineering Researh (EJER) 11(), 7-79 (006). [6] Naji, H.S., 008. Conventional and Rapid Flash Calulations for the Soave-Redlih Kwong and Peng-Robinson Equations of State: Emirates Journal for Engineering Researh (EJER), 1(), (008). [7] Press, W. H., euolsy S. A., Fettering W.., and Flannery B. P., "Numerial Reipes in C++, he Art of Sientifi Computing," Seond Edition, Cambridge University Press (00), 9. [8] Riazi, M. R. and Daubert,. E., "Charaterizing Parameters for Petroleum Frations," Ind. Eng. Chem. Res., Vol. 6, No. 4, 1987, pp [9] wu, C.H., An Internally Consistent Correlation for Prediting the Critial Properties and Moleular Weights of Petroleum and Coal- ar Liquids: Fluid Phase Equilibria 16, 17. [10] Whitson, C.H., 198. Charaterizing hydroarbon plus frations: SPEJ : IJE-IJENS April 010 IJENS

11 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 8 ABLE I KAZ-FIROOZABADI GENERALIZED PHYSICAL PROPERIES AS MODIFIED BY WHISON IJE-IJENS April 010 IJENS

12 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 9 ABLE II PHYSICAL PROPERIES AS PRESENED BY G&P ENGINEERING SOFWARE (V ) IJE-IJENS April 010 IJENS

13 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 40 Fig. 1. Katz-Firoozabadi original and fit speifi gravities of pure omponents plotted versus omponent arbon number Fig.. Katz-Firoozabadi original and fit normal boiling points of pure omponents plotted versus omponent arbon number IJE-IJENS April 010 IJENS

14 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 41 Fig.. Katz-Firoozabadi original and fit moleular weights of pure omponents plotted versus omponent arbon number Fig. 4. Katz-Firoozabadi original and fit ritial temperatures of pure omponents plotted versus omponent arbon number IJE-IJENS April 010 IJENS

15 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 4 Fig. 5. Katz-Firoozabadi original and fit ritial pressures of pure omponents plotted versus omponent arbon number Fig. 6. Katz-Firoozabadi original and fit aentri fators of pure omponents plotted versus omponent arbon number Fig. 7. Katz-Firoozabadi original and fit ritial volumes of pure omponents plotted versus omponent arbon number IJE-IJENS April 010 IJENS

16 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 4 Fig. 8. Katz-Firoozabadi original and fit ritial ompressibility fators of pure omponents plotted versus omponent arbon number Fig. 9. Katz-Firoozabadi original and fit Watson fators of pure omponents plotted versus omponent arbon number Fig. 10. G & P Engineering original and fit speifi gravities of pure omponents plotted versus omponent arbon number IJE-IJENS April 010 IJENS

17 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 44 Fig. 11. G & P Engineering original and fit normal boiling points of pure omponents plotted versus omponent arbon number Fig. 1. G & P Engineering original and fit moleular weights of pure omponents plotted versus omponent arbon number Fig. 1. G & P Engineering original and fit ritial temperatures of pure omponents plotted versus omponent arbon number IJE-IJENS April 010 IJENS

18 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 45 Fig. 14. G & P Engineering original and fit ritial pressures of pure omponents plotted versus omponent arbon number Fig. 15. G & P Engineering original and fit aentri fators of pure omponents plotted versus omponent arbon number Fig. 16. G & P Engineering original and fit ritial volumes of pure omponents plotted versus omponent arbon number IJE-IJENS April 010 IJENS

19 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 46 Fig. 17. G & P Engineering original and fit ritial ompressibility fators of pure omponents plotted versus omponent arbon number Fig. 18. G & P Engineering original and fit Watson fators of pure omponents plotted versus omponent arbon number Fig. 19. Normal boiling points of pure omponents plotted versus omponent arbon number for various orrelations IJE-IJENS April 010 IJENS

20 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 47 Fig. 0. Moleular weights of pure omponents plotted versus omponent arbon number for various orrelations Fig. 1. Critial temperatures of pure omponents plotted versus omponent arbon number for various orrelations Fig.. Critial pressures of pure omponents plotted versus omponent arbon number for various orrelations IJE-IJENS April 010 IJENS

21 International Journal of Engineering & ehnology IJE-IJENS Vol:10 No:0 48 Fig.. Aentri fators of pure omponents plotted versus omponent arbon number for various orrelations Fig. 4. Critial volumes of pure omponents plotted versus omponent arbon number for various orrelations Fig. 5. Critial ompressibility fators of pure omponents plotted versus omponent arbon number for various orrelations IJE-IJENS April 010 IJENS