Phase Behavior Introduction to Phase Behavior F.E. Londono M.S. Thesis (2001)

Transcription

1 Natual Gas Engineeing Phase Behavio Intoduction to Phase Behavio F.E. Londono M.S. hesis (001).. Blasingame, exas &M U. Depatment of Petoleum Engineeing exas &M Univesity College Station, X t-blasingame@tamu.edu Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 1

2 SPE 7571 Simplified Coelations fo Hydocabon Gas Viscosity nd Gas Density Validation and Coelation of Behavio Using a Lage-Scale Database F.E. Londono, R.. che, and.. Blasingame Depatment of Petoleum Engineeing exas &M Univesity College Station, X (979) t-blasingame@tamu.edu Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide

3 Executive Summay In this wok we developed new and efined coelations fo the density and viscosity behavio of hydocabon gases. he following esults ae noted: Gas Density new EOS coelations: Danchuk, et al. (11 constants): 0.81 pecent E Nishiumi, et al. (15 constants): pecent E Gas Viscosity new/efined coelations: Lee, et al. "efit" (10 constants):.73 pecent E Implicit Model (4 constants):.65 pecent E 1atm Model (7 constants): 1.57 pecent E Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 3

4 Executive Summay Gas Density (z-facto) a. z vesus p p fomat (Poettmann). b. z vesus p p / p fomat (Poettmann). he "Standing and Katz" z-facto chat is defined using data pesented by Poettmann (hydocabon gases only). he calibation of an "Equation of State" fo gas density should be made using these data as well as data fo natual gas mixtues. his wok consides two sepaate foms of a modified-bwr EOS: Danchuk, et al. (11 constants) Nishiumi, et al. (15 constants) Explicit elations fo gas density (o z-facto) do not povide the accuacy o consistency of EOS fomulations. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 4

5 Executive Summay Gas Viscosity a. g / 1atm vesus p fomat (Ca, et al.). he "Ca, et al." gaphical coelation fo gas viscosity is based on the "Law of Coesponding States." We found (as did Jossi, et al. and Lee, et al.) that gas viscosity is best coelated with gas density (and tempeatue). b. g / 1atm vesus p p fomat (Ca, et al.). c.residual viscosity vesus Reduced Density (Jossi, et al. ). Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 5

6 Outline Executive Summay Rationale fo his Wok Oientation Databases and Coelation Gas Density 14,88 total points EOS Calibation: 5960 Poettmann, 96 pue Pseudocitical Coelations: 603 mixtue points Gas Viscosity 5675 points ll g coelations: 50 pue, 3155 mixtue points ll 1atm coelations: 30 pue and mixtue points Summay of Results Recommendations fo Futue Wok Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 6

7 Rationale fo his Wok his wok evolved fom a need to veify and extend the coelations used to estimate the density and viscosity of hydocabon gases and gas mixtues. he pimay issues involved in this wok ae: he need to focus on elatively simple models fo gas density and gas viscosity (e.g., the Law of Coesponding States (coelations based on citical o pseudocitical behavio)). he need fo the models to be defined using pue components as well as natual gas mixtues. he need to povide a clea validation of existing models, as well as the applicability of new models defined fo gas density and gas viscosity. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 7

8 Oientation Issues: Viscosity and density ae equied in all fluid flow calculations g is not constant. g = f (M w, p, and ). g is not constant. g = f (M w, p, and ). Gas Viscosity: Used fo all pessue dop and flow calculations. Extend ange (pessue and tempeatue). Gas Density: Used fo all volumetic calculations. Extend ange (pessue and tempeatue). Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 8

9 Oientation Wok ppoach fo Gas Viscosity Use existing coelations as a stating point: Lee, Gonzales, and Eakin (semi-empiical). Jossi, Stiel, and hodos (esidual viscosity). Optimization of the Lee, et al. and Jossi, et al. models ae poposed. Oiginal coelations compae well with database. "Refitted" coelations pefom well fo all anges. We also povide new empiical/semi-analytical elations fo hydocabon gas viscosity. Mixtues: Pseudocitical paametes fo gas mixtues. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 9

10 Oientation Wok ppoach fo Gas Density Existing z-facto (i.e., density) elations ae not sufficient (compaed to ou data): Pessue/tempeatue anges need efinement. Optimization of the Danchuk, et al. EOS and the Nishiumi, et al. EOS models ae poposed using standad and pue component data. Use the Danchuk, et al. EOS as a stating point. Fo natual gases we stat with the following models fo pseudocitical vaiables: Sutton Eqs. ( pc and p pc ). Pipe, et al. Eqs. ( pc and p pc ). Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 10

11 Database: Souces Data obtained fom seven souces: Gonzalez meican Petoleum Institute (1970) Lee meican Petoleum Institute (1965) Diehl IFP (Fance) (197) Golubev Math/Physics Lab (Russia) (1959) Stephan Pudue Reseach Foundation (1979) Setzmann J. Phys. Chem. Ref. Data (1991) Poettmann Dilling and Pod. Pactices (195) Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 11

12 Database: Data used fo Coelations Golubev data was only used fo compaison these data deviated fom all othe data. Stephan gas viscosity data was not used lack of gas density data. empeatue Range: 3 < < 650 deg F. Pessue Range: 14.7 < p < 15,000 psia. Methane-pentane (light hydocabons), and natual gas mixtues. Databases:, (database) (at 1 atm) (database-no data) z-facto (Poettmann, et al.) Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 1

13 Database Validation: Gas Viscosity/Density Gas Viscosity: Jossi, Stiel, and hodos (Jossi, et al.) "esidual viscosity" and "educed density" coelation. Lee, Gonzalez, and Eakin (Lee, et al.) Genealized coelation based on tempeatue, density, and molecula weight. Gas Density: Danchuk and bou-kassem (DK-EOS) 11- constant (BWR-type) EOS. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 13

14 Gas Viscosity: Jossi, et al. Oiginal Coelation Viscosity at 14.7 psia (cp) Molecula weight Citical tempeatue (deg K) ve. bs. Eo: 4 pecent Reduced density Citical pessue (atm) 8 constants Pue components only X 10 6 μ g μo C 1 3 Mw pc X ρ ρ ρ ρ 4 Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 14

15 Gas Viscosity: Jossi, et al. Pue Data Only Statistics: Pue components only. 50 points. veage bsolute Eo 5.01 pecent. Standad Deviation cp. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 15

16 Gas Viscosity: Lee, et al. Oiginal Coelation Gas density (g/cc) empeatue (deg R) Molecula weight 10 constants ve. bs. Eo: % (at low p) to 4 % (at high p) 4 natual gases plus pue components μ g 4 Y 1x10 K exp Xρ K M M X w w Y M w X Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 16

17 Gas Viscosity: Lee, et al. Pue/Mixtue Data Statistics: Pue components and gas mixtues points. veage bsolute Eo 3.16 pecent. Standad Deviation cp. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 17

18 Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Pseudoeduced tempeatue Reduced density Pseudoeduced pessue 11 constants ve. bs. Eo: pecent 1500 data points z ) exp( ) ( z 0.7 p Gas Density: DK EOS Oiginal Coelation Slide 18

19 Gas Density: DK EOS Pue/Mixtue Data Statistics: Sutton Eqs. fo ( pc and p pc ) 6574 points. veage bsolute Eo 8.05 pecent. Standad Deviation Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 19

20 New/Revised Coelations fo Gas Viscosity Gas Viscosity: "Refit" Models Jossi, et al. "esidual viscosity/educed density" Lee, et al. "tempeatue, density, and M w " Gas Viscosity: "New" Models "Implicit" model combination of the Jossi, et al. "esidual viscosity" fomulation and the Lee, et al. "tempeatue, density, and M w " fomulation. "Viscosity at 1 atm model" used as efeence viscosity fo "implicit" model (above). Summay of Gas Viscosity Models Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 0

21 Gas Viscosity: Jossi, et al. Revised Coelation Statistics: Pue components only. 50 points. veage bsolute Eo 3.94 pecent. (5.01 pecent oiginal) Standad Deviation cp. ( cp oiginal) Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 1

22 Gas Viscosity: Lee, et al. Revised Coelation Statistics: Mixtues/pue components points. veage bsolute Eo.73 pecent. (3.16 pecent oiginal) Standad Deviation cp. ( cp oiginal) Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide

23 Implicit Model fo Gas Viscosity: g - 1atm = f (,) a.residual viscosity vesus Reduced Density (Jossi, et al. ). b.residual viscosity vesus Density (this wok ). Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 3

24 Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Density (g/cc) empeatue (deg F) Gas viscosity at 1 atm (cp) 4 constants ) ( 1 f atm g 3 3 ) ( h g f e d c b a f 1 0 a a a a he b, c, d, e, f, g, and h vaiables ae defined in the same fom as the a vaiable. Implicit Model fo Gas Viscosity: Slide 4

25 Implicit Model fo Gas Viscosity: Statistics: Mixtues/pue components points. veage bsolute Eo.65 pecent. Standad Deviation cp. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 5

26 Compaison: Gonzalez, et al. Sample 3 Data Implicit Model fo Gas Viscosity Compaed with Lee, et al. Coelation fo Gas Viscosity veage bsolute Eo.65 pecent. (Lee, et al.: optimized.73 pecent, oiginal 3.16 pecent ) Standad Deviation cp. (Lee, et al.: optimized cp, oiginal cp) 5675 points. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 6

27 Gas Viscosity at 1 atm: New Model Gas specific gavity (ai = 1.0) empeatue (deg F) 7 constants ln( 1atm ) a 0 1 b a 1 1 ln( ln( g g ) ) b a ln( ) ln( ) b a 3 3 ln( ln( g g ) ln( ) ) ln( ) Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 7

28 Gas Viscosity at 1 atm: Pue/Mixtue Data Statistics: Mixtues/pue components. 30 points. veage bsolute Eo 1.57 pecent. Standad Deviation 5.6x10-6 cp. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 8

29 Summay: Gas Viscosity Models Gas viscosity models Jossi, et al. 4 oiginal model, epoted data Lee, et al. 5 oiginal model, epoted data Jossi, et al. 4 oiginal model, with ou database Lee, et al. 5 oiginal model, with ou database Optimized Jossi, et al. 4 model, with ou database Optimized Lee, et al. 5 model, with ou database Residual gas viscosity, implicit model Gas viscosity at 1 atm, model Numbe of data points veage absolute eo, pecentage Sum of squaes esiduals, cp Standad deviation, cp to x10-6 Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 9

30 Revised Coelations fo Gas Density Gas Density: EOS Models (calibate using standad (Poettmann) and pue component data) Danchuk and bou-kassem (DK-EOS) Nishiumi and Saito (NS-EOS) Gas Density: Mixtue Coelations Quadatic elations fo pseudocitical tempeatue and pessue wee fitted using mixtue data. Summay of Gas Density Models Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 30

31 Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Reduced density Pseudoeduced tempeatue (1) DK-EOS with Poettmann data () DK-EOS with Poettmann data + pue components z ) exp( ) ( Gas Density: DK-EOS Revised EOS z 0.7 p Slide 31

32 Gas Density: DK-EOS Pue/Poettmann Data Statistics: 5960 points. (1) 856 points. () veage bsolute Eo 0.41 pecent. (1) 0.81 pecent. () Standad Deviation cp. (1) cp. () Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 3

33 Gas Density: DK-EOS Mixtue Coelations pc Only fo use with the optimized DK-EOS g g p pc g 9.05 g Only fo use with the optimized DK-EOS Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 33

34 Gas Density: DK-EOS Mixtue Coelations Statistics: 603 points. veage bsolute Eo 3.06 pecent. Standad Deviation cp. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 34

35 Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Reduced density Pseudoeduced tempeatue (1) NS-EOS with Poettmann data () NS-EOS with Poettmann data + pue components z Gas Density: NS-EOS Revised EOS z 0.7 p ) )exp( ( * * 1 Slide 35

36 Gas Density: NS-EOS Pue/Poettmann Data Statistics: 5960 points. (1) 856 points. () veage bsolute Eo 0.46 pecent. (1) 0.73 pecent. () Standad Deviation cp. (1) cp. () Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 36

37 Gas Density: NS-EOS Mixtue Coelations pc Only fo use with the optimized NS-EOS g g p pc g g Only fo use with the optimized NS-EOS Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 37

38 Gas Density: NS-EOS Mixtue Coelations Statistics: 5118 points. veage bsolute Eo.55 pecent. Standad Deviation cp. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 38

39 Summay: Gas Density Models z-facto models Numbe of data points veage absolute eo, pecentage Sum of squaes esiduals Standad deviation DK-EOS 6 oiginal model, epoted data NS-EOS 7 oiginal model, epoted data.300 Bill-Beggs 9 oiginal model, epoted data DK-EOS 6 - Sutton, 0 with ou database DK-EOS 6 - Pipe, et al. 1 with ou database DK-EOS 6 with Poettmann, et al. 16 database DK-EOS 6 with Poettmann, et al. 16 database - pue components DK-EOS 6 - New pseudocitical equations, with mixtues - pue components NS-EOS 7 with Poettmann, et al. 16 database NS-EOS 7 with Poettmann, et al. 16 database - pue components NS-EOS 7 - New pseudocitical equations, with mixtues - pue components Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 39

40 Conclusions: Geneal he new and evised coelations pesented in this wok fo gas viscosity, gas density, and gas viscosity at 1 atm ae appopiate fo all gas esevoi engineeing applications. lthough cabon dioxide, nitogen, and helium wee pesent in some mixtues, ou gas viscosity and gas density coelations match the database vey well. By extension, these coelations should wok well fo pactical applications whee small amounts of non-hydocabon impuities ae pesent. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 40

41 Gas Viscosity: Summay of Coelations Gas Viscosity Models veage bsolute Eo Oiginal Jossi, et al. 4.00, c, p c, M w, 1atm Oiginal Lee, et al. Oiginal Jossi, et al. (mix/pues) Oiginal Lee, et al. (mix/pues).00 to 4.00 Numbe of Data Points Vaiables Notes Only pue components Only fo <.0 g,, M w 4 natual gas samples, pue comp Less accuate fo g > 1.0 aces of CO, N, He , c, p c, Deviation at high viscosities (0. M w, 1atm cp) g,, M w Deviation at high viscosities (0.15 cp) Optimized Jossi, et al , c, p c, Some deviation of the data M w, 1atm Optimized Lee, et al g,, M w Deviation at high viscosities (0. cp) New esidual gas viscosity g,, 1atm Seveal gas mixtues, pue comp aces of CO, N, He New gas viscosity at 1 atm , g Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 41

42 Gas Density: Summay of Coelations Models fo z-facto veage absolute eo Numbe of data points Vaiables Notes Oiginal DK-EOS ,, p 0. < p <30 and 1 < < 3 p < 1 and 0.7 < < 1 (only) Oiginal NS-EOS.300,, c, v c, E,, y( ) DK-EOS - Sutton (mix/pues) DK-EOS - Pipe, et al. (mix/pues) Optimized DK-EOS (Poettmann) Optimized DK-EOS (Poettmann/pues) Optimized DK-EOS (mixtues/pues) Optimized NS-EOS (Poettmann) Optimized NS-EOS (Poettmann/pues) Optimized NS-EOS (mixtues/pues) ,, p, g ,, p, g ,, p ,, p he coefficients = f () Not fo 1.3 > > 1.0 and 3.0 > p > 1.0 Gas composition to calculate pc, and p pc ,, p New quadatic equations fo pc, and p pc , , , New quadatic equations fo pc, and p pc Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 4

43 Futue Wok: Ou ecommendations fo futue wok ae: dditional investigations should include the explicit effects of highe concentations of non-hydocabon components such as hydogen sulfide, wate, hydogen, cabon dioxide, and nitogen fo both gas viscosity and gas density (z-facto). his wok also could be extended to gas condensate liquids, fo both liquid viscosity and the "two-phase" z-facto. Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 43

44 Natual Gas Engineeing Phase Behavio Intoduction to Phase Behavio F.E. Londono M.S. hesis (001) (End of Pesentation).. Blasingame, exas &M U. Depatment of Petoleum Engineeing exas &M Univesity College Station, X t-blasingame@tamu.edu Natual Gas Engineeing 6 May - 30 May 014 (U. Kavala/GREECE) om BLSINGME t-blasingame@tamu.edu exas &M U. Slide 44