Scientia Iranica Vol. 14 No. 4 pp 358{368 c Sharif Univerity of Technoloy Auut 2007 Reearch Note Evaluation of Empirically Derived PVT Propertie for Middle Eat Crude Oil M.N. Hemmati and R. Kharrat 1 PVT propertie are important parameter in reervoir enineerin. Correlation are ued whenever experimentally derived PVT data are not available and data from local reion are expected to ive better approximation to etimated PVT value. Thi paper evaluate the mot frequently ued empirical black oil PVT correlation for application in the Middle Eat. A will be dicued Empirical PVT Correlation for Middle Eat crude oil have been compared a a function of commonly available PVT data. Correlation have been compared for: Bubble point preure; olution a oil ratio at bubble point preure and oil formation volume factor at bubble point preure. Often thee propertie are required for oil eld computation when there are no experimental or laboratory meaurement available. For comparion of correlation a wide rane of data ha been covered. Approximately ve hundred Preure-Volume-Temperature (PVT) report have been ued in the comparion correlation. The PVT correlation can be ordered with repect to their accuracy: (a) Bubble point preure: The reult of Al-Marhoun and Standin are imilar to Hanafy Dindoruk; (b) Oil formation volume factor: Petroky Glao and Dokla correlation produce imilar reult while Al-Marhoun Standin and Hanafy prediction are dierent and (c) Solution a oil ratio: Standin and Al-Marhoun reult are the ame however Dindoruk Glao and Petroky correlation are le accurate. Error bound of the obtained correlation are calculated and compared to Middle Eat crude oil. All reervoir uid property correlation available in the petroleum enineerin literature were compared with thi databae. INTRODUCTION The calculation of reerve in an oil reervoir or the determination of it performance and economic require a ood knowlede of the uid phyical propertie. Bubble point preure GOR and OFVF are of primary importance in material balance calculation. Ideally thee propertie are determined from laboratory tudie on ample collected from the bottom of the well bore or from the urface. Such experimental data are however not alway available becaue of one or more of thee reaon: a) Sample collected are not reliable b) Sample have not been taken becaue of cot avin c) PVT analye are not available when needed. Thi ituation often occur in production tet interpretation well. In uch cae PVT propertie mut be determined *. Correpondin Author The Reearch Center of Petroleum Univerity Tehran I.R. Iran. 1. The Reearch Center of Petroleum Univerity Tehran I.R. Iran. by uin empirical derived correlation. Obviouly the accuracy of uch correlation i critical for the abovementioned calculation and it i not often known in advance. Depite the reat number of work performed in the pat 50 year on PVT correlation each of them eem to be applicable with a ood reliability only in a well-dened rane of reervoir uid characteritic. Thi i becaue each correlation ha been developed by uin ample belonin to a retricted eoraphical area with imilar uid compoition and API ravity. In particular for oil with ravity le than 22 API the literature i very poor and nearly abent for oil with ravity le than 10 API. DATA DESCRIPTIONS More than 50 Middle Eat oil eld were elected for thi tudy. Thee eld were elected becaue they produce the crude of black oil in nature and the availability of complete PVT report that are neceary for the evaluation and development of the black oil
Evaluation of Empirically Derived PVT Propertie 359 Table 1. Data decription for bubble point preure GOR and bubble point oil FVF correlation. Number of Point PVT Property Minimum Maximum Mean 499 Bubble point preure pia 130 5156 2370.5 499 Solution GOR SCF/STB 26 2266 715.15 499 FVF bbl/stb 1.03 2.54 1.41 499 Temperature F 74 290 165 499 Stock tank oil ravity API 18.80 68.50 31.53 499 Ga ravity (air=1) 0.523 1.50 0.94 Table 2. Rane for bubble point preure olution GOR and oil FVF correlation. Propertie Standin [1] Al-Marhoun [2] Glao [3] Petroky-Farhad [4] Tank oil ravity API 16.5 to 63.8 19.4 to 44.6 22.3 to 48.1 16.3 to 45 Bubble point preure pia 130 to 7000 130 to 3573 165 to 7142 1574 to 6523 Reervoir temperature F 100 to 258 74 to 240 80 to 280 114 to 288 Oil FVF at bubble point bbl/stb 1.024 to 2.15 1.032 to 1.997 1.025 to 2.588 1.1178 to 1.6229 Solution GOR SCF/STB 20 to 1425 26 to 1602 90 to 2637 217 to 1406 Total urface a ravity (air=1) 0.59 to 0.95 0.752 to 1.367 0.65 to 1.276 0.5781 to 0.8519 Separator preure pia 256 to 465-415 (mean) - Separator temperature F 100 (mean) - 125 (mean) - Reervoir preure pia - 20 to 3573-1700 to 10692 correlation. From thee oileld 499 laboratory PVT analye were obtained and ued to compare the correlation. Decription of the data utilized in comparion of each correlation are hown in Table 1 and the rane of input data ued by each author in developin hi correlation i provided in Table 2. COMPARISON OF CORRELATIONS Statitical Error Analyi Averae percent relative error averae abolute percent relative error minimum /maximum abolute percent relative error tandard deviation and correlation coecient were computed for each correlation. Bubble Point Preure Table 3 how the tatitical error analyi reult of the bubble-point preure correlation. Al-Marhoun' [2] correlation ive low value of Abolute Averae Percent Relative Error (AAPRE) and tandard deviation of 6.999 percent and 9.26 percent repectively. A lower value of AAPRE indicate a better accuracy of the correlation. The correlation coecient of the correlation i almot equal to 1.0(0.977). Thi how that a ood areement exit between experimental and calculated bubble point preure. In comparion with other known correlation Al-Marhoun' correlation ive lowet AAPRE and tandard deviation. Thi how that Al-Marhoun' correlation predict better bubble point preure for Middle Eat crude oil than any other known correlation. The cro plot of the experimental aaint the calculated bubble point preure uin correlation are preented in Fiure 1 throuh 7. Mot of the data point of the Al-Marhoun correlation fall very cloe to the perfect correlation of a 45 line. A raphical plot of reidual (the dierence between experimental and calculated bubble point preure) and experimental bubble point preure (hown in Fiure 1) demontrated a uniform ditribution of error with mot of the data point fallin within a 500 pia reidual line. Bubble Point Oil FVF The tatitical error analyi reult of the bubble point oil FVF correlation are compared in Table 4. The Petroky correlation [4] ive a better accuracy in etimatin bubble point oil FVF for Middle Eat crude oil. Amont the correlation both Petroky [4] and Glao [3] correlation eem to be ood correlation their abolute averae deviaton and tandard deviation are very cloe and ive the lowet value of AAPRE. AAD and tandard deviation for Glao
360 M.N. Hemmati and R. Kharrat Table 3. Summary of tatitical meaure for P b for common correlation. Parameter Petroky [4] Glao [3] Standin [1] Al-Marhoun [2] Dindoruk [5] Dokla [6] Hanafy [7] % AAD 42.33 23.45 10.49 6.999 42.43 17.87 22.64 % ARE -18.25 20.94 6.185-4.14 38.54-0.197 17.83 % Max Dev. 784.5 73.13 70.08 43.66 114.21 197.81 192.34 % Min Dev. 0.013 0.281 0.009 0.021 1.010 0.043 0.111 Std. Dev. 112.75 26.87 14.41 9.26 45.25 26.87 34.69 r 0.882 0.865 0.927 0.977 Minu 0.903 0.930 Fiure 1. Cro plot and reidual plot of P b (Al-Marhoun [2]) baed on Middle Eat PVT data. Fiure 2. Cro plot and reidual plot of P b (Standin [1]) baed on Middle Eat PVT data. Fiure 3. Cro plot and reidual plot of P b (Petroky [4]) baed on Middle Eat PVT data.
Evaluation of Empirically Derived PVT Propertie 361 Fiure 4. Cro plot and reidual plot of P b (Glao [3]) baed on Middle Eat PVT data. Fiure 5. Cro plot and reidual plot of P b (Hanafy [7]) baed on Middle Eat PVT data. Fiure 6. Cro plot and reidual plot of P b (Dokla [6]) baed on Middle Eat PVT data. Table 4. Summary of tatitical meaure for B ob for common correlation. Parameter Al-Marhoun [2] Standin [1] Glao [3] Petroky [4] Dokla [6] Dindoruk [5] Hanafy [7] % AAD 1.96 1.93 2.157 1.45 2.608 4.39 8.55 % ARE -1.481 0.98-0.68 0.26-1.38 2.60 8.48 % Max Dev. 15.25 11.73 12.28 13.76 13.08 26.94 23.44 % Min Dev. 0.002 0.001 0.006 0.004 0.005 0.009 0.025 Std. Dev. 2.98 2.74 2.84 2.28 3.4 5.61 9.27 r 0.975 0.945 0.984 0.989 0.983 0.945 0.816
362 M.N. Hemmati and R. Kharrat Fiure 7. Cro plot and reidual plot of P b (Dindoruk [5]) baed on Middle Eat PVT data. Fiure 8. Cro plot and reidual plot of B o (Standin [1]) baed on Middle Eat PVT data. Fiure 9. Cro plot and reidual plot of B o (Al-Marhoun [2]) baed on Middle Eat PVT data. and Petroky are 2.157 and 1.45 percent 2.84 and 2.28 percent repectively. The correlation coecient i 0.984 and 0.989 repectively which i cloe to an ideal value of 1.0. Thi how that the Petroky and Glao correlation correlate better with experimental data than any other correlation. The reidual plot of the bubble point oil formation volume factor obtained from correlation are hown in Fiure 8 throuh 14. It i clear that the mot data point in Fiure 10 and 11 lie between 0:2 reidual line. A mall reidual value indicate a better accuracy of Glao and Petroky correlation in etimatin the bubble point oil FVF for Middle Eat crude oil. Solution GOR The tatitical error analyi reult of the Solution GOR correlation are compared in Table 5. It how
Evaluation of Empirically Derived PVT Propertie 363 Fiure 10. Cro plot and reidual plot of B o (Petroky [4]) baed on Middle Eat PVT data. Fiure 11. Cro plot and reidual plot of B o (Glao [3]) baed on Middle Eat PVT data. Fiure 12. Cro plot and reidual plot of B o (Dokla [6]) baed on Middle Eat PVT data. Table 5. Summary of tatitical meaure for olution GOR for common correlation. Parameter Al-Marhoun [2] Standin [1] Glao [3] Petroky [4] Dindoruk [5] %AAD 10.17 9.45 19.84 22.45 17.93 %ARE 7.83-4.73-19.55 0.53 3.68 %Max. Dev. 49.45 33.77 40.86 300.63 150.4 %Min. Dev. 0.0295 0.0009 0.248 0.152 0.0138 Std. Dev. 13.58 11.78 21.39 44.84 26.76 r 0.960 0.964 0.890 0.862 0.921
364 M.N. Hemmati and R. Kharrat Fiure 13. Cro plot and reidual plot of B o (Dindoruk [5]) baed on Middle Eat PVT data. Fiure 14. Cro plot and reidual plot of B o (Hanafy [7]) baed on Middle Eat PVT data. Fiure 15. Cro plot and reidual plot of R (Al-Marhoun [2]) baed on Middle Eat PVT data. that the Standin [1] and Al-Marhoun [2] correlation have an averae abolute deviation of 9.45% and 10.17% repectively compared to over 22% for Petroky. The correlation coecient are 0.964 and 0.96 repectively which are cloe to an ideal value of 1.0. Thi how that the Standin and Al-Marhoun correlation correlate better with experimental data than any other correlation. The maximum error and tandard deviation of thee correlation are iven in Table 5. Fiure 15 throuh 19 ive cro plot of the value etimated by the ame correlation veru the meaured experimental value. It i clear from both Table 5 and Fiure 15 throuh 19 that the Standin and Al-Marhoun correlation are quite uperior for Middle Eat crude oil than other correlation.
Evaluation of Empirically Derived PVT Propertie 365 Fiure 16. Cro plot and reidual plot of R (Standin [1]) baed on Middle Eat PVT data. Fiure 17. Cro plot and reidual plot of R (Glao [3]) baed on Middle Eat PVT data. Fiure 18. Cro plot and reidual plot of R (Petroky [4]) baed on Middle Eat PVT data. The cro plot of the experimental aaint the calculated olution GOR uin the Standin and Al- Marhoun correlation are preented in Fiure 15 and 16. Mot of the data point of the new correlation fall very cloe to the perfect correlation of the 45 line. A raphical plot of reidual and experimental olution GOR (hown in Fiure 15 and 16) demontrated a uniform ditribution of error with mot of the data point fallin within the 200 SCF/STB reidual line. CONCLUSIONS 1. Empirical correlation for Middle Eat crude oil have been compared for bubble point preure the olution a-oil-ratio and the bubble point oil formation volume factor;
366 M.N. Hemmati and R. Kharrat Fiure 19. Cro plot and reidual plot of R (Dindoruk [5]) baed on Middle Eat PVT data. 2. The PVT correlation can be placed in the followin order with repect to their accuracy: (a) (b) (c) For bubble point preure the prediction of Al- Marhoun and Standin are imilar to Hanafy and Dindoruk; For oil formation volume factor the reult of Petroky Glao Dokla are near to each other while Al-Marhoun Standin and Hanafy correlation are le accurate; For olution a oil ratio Standin and Al- Marhoun ive ood reult while Dindoruk Glao and Petroky are le accurate. 3. Thee correlation were compared for Middle Eat crude oil but they can be ued for etimatin the ame PVT parameter for all type of oil and a mixture with propertie fallin within the rane of data ued in thi tudy; 4. The bubble point oil formation volume factor correlation provided the bet accuracy of the correlation evaluated; 5. Correlation are ued to enerate dierential liberation table for reervoir imulation; 6. Correlation can be tuned for other bain/area or for certain clae of oil. Dev. FVF GOR OFVF P P b PVT r R SCF STB Std. deviation formation volume factor a oil ratio oil formation volume factor preure pia bubble point preure pia preure volume temprature coecient of correlation olution a-oil-ratio SCF STB tandard cubic feet tock tank barrel tandard a pecic ravity (air = 1) o oil pecic ravity (water = 1) Subcript b max min o bubble point maximum minimum a oil olution NOMENCLATURE REFERENCES AAD AAPRE API ARE bbl B o B ob abolute averae deviation abolute averae percent relative error tock-tank oil ravity API aboolute relative error barrel oil formation volume factor bbl/tb oil FVF at bubble point preure bbl/tb 1. Standin M.B. \A preure-volume-temperature correlation for mixture of California oil and ae" Drillin and Production Practice API pp 275-287. 2. Al-Marhoun M.A. \PVT correlation for middle eat crude oil" JPT pp 650-665 (1988). 3. Glao O. \Generalized preure-volume-temperature correlation" JPT pp 785-795 (May 1980). 4. Petroky G.E. Jr. and Farhad F.F. \Preurevolume-temperature correlation for Gulf of Mexico
Evaluation of Empirically Derived PVT Propertie 367 crude oil" SPE 26644 Preented at 68th Annual Meetin of the Society of Petroleum Enineer Houton Texa USA pp 3-6 (1993). 5. Dindoruk B. Peter G. and Chritman \PVT propertie and vicoity correlation for Gulf of Mexico oil" SPE Annual Technical Conference and Exhibition New Orlean Louiiana 30 September-3 Octobor. 6. Dokla M. and Oman M.E. \Correlation of PVT propertie for the UAE crude" SPE Formation Evaluation pp 41-46 (1992). 7. Hanafy H.H. Macary S.A. Elnady Y.M. Bayomi A.A. and El-Batanoney M.H. \Empirical PVT correlation applied to Eyptian crude oil exemplify inicance of uin reional correlation" SPE 37295 SPE Oileld Chem. Int. Symp. (Houton 2/18-21/97) Proc. pp 733-737 (1997). APPENDIX Known PVT Available Correlation for R Standin [1] h i p 1:2048 R = 18:2 + 1:4 10 x ; x =0:0125 API 0:00091(T 460) T = temperature R p = ytem preure pia = olution a pecic ravity. Glao [3] R = h p b = 10x API 0:989 i 1:2255 (T 460) 0:172 (p b ) x =2:8869 [14:1811 3:3093 lo(p)] 0:5. Al-Marhoun [2] R = [a b c o T d P ] e T = temperature R a = 185.843208 b = 1.877840 c = -3.1437 d = -1.32657 e = 1.398441. Petroky and Farhad [4] h R = p 112:727 + 12:340 i 1:73184 0:8439 10 x ; x=7:916(10 4 )(API) 1:5410 4:561(10 5 )(T 460) 1:3911 p = preure pia T = temperature R Dindoruk and Chritman [5] R bp = h pbp a8 + a 9 A = a1apia2 +a3t a 4! 2. a5+ 2AP Ia 6 p a 7 bp a10 10 A i a 11 Coecient Correlation Value a 1 4.86996E-06 a 2 5.7309825539 a 3 9.92510E-03 a 4 1.776179364 a 5 44.25002680 a 6 2.702889206 a 7 0.744335673 a 8 3.359754970 a 9 28.10133245 a 10 1.579050160 a 11 0.928131344 Known PVT Available Correlation for P b Standin [1] 0:83 (10) a 1:4 p b = 18:2 R a =0:00091(T 460) 0:0125(API) p b = bubble-point preure pia T = ytem temperature R. Glao [3] lo(p b ) =1:7669 + 1:7447 lo(p b ) 0:30218[lo(p b )]2 p b = ( R ) a (T ) b (API) c T = ytem temperature F a =0:816 b =0:172 c = 0:989. Al-Marhoun [2] p b = ar b c d o T e T = temperature R a =5:38088 10 3
368 M.N. Hemmati and R. Kharrat b =0:715082 c = 1:87784 d =3:1437 e =1:32657. Petroky and Farhad [4] h i 0:577421 112:727R p b = 1391:051 0:8439 (10) x x =7:916(10 4 )(API) 1:5410 4:561(10 5 )(T 460) 1:3911 p = preure pia T = temperature R. Dokla and Oman [6] p b = 0:836386 10 4 1:01049 0:107991 o T 0:952584 R 0:724047 T = ytem temperature R: Dindoruk and Chritman [5] R p bp = a 9 a 8 a 10 A = a1t a2 +a3api a 4 2. a5+ 2Ra 6 a 7 10 A + a 11 Coecient Correlation Value a 1 1.42828E-10 a 2 2.844591797 a 3-6.74896E-04 a 4 1.225226436 a 5 0.033383304 a 6-0.272945957 a 7-0.084226069 a 8 1.869979257 a 9 1.221486524 a 10 1.370508349 a 11 0.011688308 Known PVT Available Correlation for B o Standin [1] B o = 0:9759 + 0:000120 R o T = temperature R. 0:5 +1:25(T 460) 1:2 Glao [3] B o = 1:0+10 A A = 6:58511 + 2:91329 lo B ob 0:27683(lo B ob )2 B ob = R o T = temperature R. Al-Marhoun [2] 0:526 + 0:968(T 460) B o = 0:497069 + 0:862963 10 3 T +0:182594 10 2 F +0:318099 10 5 F 2 ; F = R a b c o ; a =0:742390; b =0:323294; c = 1:202040; T i the ytem temperature in R. Petroky and Farhad [4] B o = 1:0113 + 7:2046(10 5 ) R 0:3738 +0:24626(T 460) 0:5371 3:0936 ; T = temperature R. Dindoruk and Chritman [5] 0:2914 o 0:6265 B obp = a 11 + a 12 A + a 13 A 2 + a 14 (T 60) API R a 1 a 2 a A = a 3 +a4(t 60) a5 7 +a6r o a8+ 2Ra 9 a 10 (T 60) 2 Coecient Correlation a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 a 10 a 11 a 12 a 13 a 14 Value 2.510755E+00-4.852538E+00 1.183500E+01 1.365428E+05 2.252880E+00 1.007190E+01 4.450849E-01 5.352624E+00-6.309052E-01 9.000749E-01 9.871766E-01 7.865146E-04 2.689173E-06 1.100001E-05