Correlation for Vapor Pressure of Mixture

Availale online at www.ejournals.uofk.edu Proceedings Vol. 6 pp. 202-212 7th Annual Conference for Postgraduate Studies and Scientific Research Basic Sciences and Engineering Studies - University of Khartoum Theme: Scientific Research and Innovation for Sustainale Development in Africa Correlation for Vapor Pressure of Mixture Ali A. Raah, Nagi A. Osman Department of Chemical Engineering, Faculty of Engineering, University of Khartoum Khartoum, Sudan (E-mail: raahs@yahoo.com) Astract: This paper aims to find empirical equation to calculate the vapor pressure of the mixture of crude oil from Sudan and taking advantage of some of the PVT properties that are measured experimentally. Where the data is retrieved from many fields and different wells to get the relationship etween vapor pressure and properties availale Emphasis was placed on thermodynamic properties have a direct effective on the vapor pressure, and has to take useful of the density of the mixture at the oiling pressure measured in the laoratory to calculate these properties using the equations are availale in advance (Raiza Duert) and then use the method of regression analysis using the Excel program to find a relationship etween vapor pressure and properties calculated on the asis of the density at the oiling of the mixture and the molecular weight of the mixture. Where the results were compared with some of the empirical equations used to calculate the vapor pressure of some of the world raw materials used other properties of non-thermodynamic properties as a function of vapor pressure. The study found positive results in dependence on the thermodynamic properties of a direct impact on the vapor pressure and through the use of some statistical metrics to compare other equations which proved the quality of the idea where the error etween the measured pressure and the calculated error rate dropped Keywords:Merowe Dam; Specific Water Consumption S.W.C; Routing, Operation Rule Curve; Megawatt INTRODUCTION The ule point is essential in reservoir simulation and in design of transport and separator equipment.there are asically one experimental method and threetheoretical methods for ule point pressure of reservoir fluid. Constant mass expansion tests (CME) is the experimental test for ule point pressure. The prediction methods are correlation and equation of state. The availale correlations of the prediction of ule pressure include Standing, Lasater, Glas, Stunn and Farshad, Vazquez and Beggs, AL Marhounand Hanafy et al correlation. All these correlation incorporate four input feature from datasets (1) reservoir temperature, (2)API (3) gas specific gravity and (4) solution gas oil ratio. The first three parameters are readily availale from composition analysis. The fourth parameter is determined experimentally from differential lieration test. Hence, these models are not predictive, as experimental phase equilirium data are needed.hence these correlations are used only to verify experimental data. Quick prediction of the ule point pressure with minimum information remained difficult task. The ule point pressure can e predicted from equation of state using ule point calculation procedure. There are a numer of equations of state availale such as PR, SRK,However, all of the availale cannot e used as a quick procedure for the prediction of ule point pressure of reservoir fluids. It is the purpose of this paper is to provide correlation for the prediction of mixture vapor pressure. The equation, with data of compositional analysis only, facilitates the calculation of ule point pressure. The Model The vapor pressure of mixtureis considered to e a function of critical temperature, critical pressure, ule point temperature, centric factorand gas oil ratio as P P(, Tc, Pc, T,, Rs ) (1) 202

The parameters in the mixture characterization procedure are calculated directly from measured gas oil ratio data for the hydrocaron fractions. In turn the critical temperature, critical pressure, ule point temperature is function of density at ule point pressureas given y Riazi and Dauert (1987), equation (3) The molecular weight of mixture are calculate y using equation (2) mixture a exp 1.008M 42.43 M mixutr mixutr...(2) f e M c dm M......(3) wherea to f, are constants for ule point temperature as follows Tale (1) Parameter A c D f E T (k) 6.77857 0.401673 1.58262 3.77409 2.98403-4.2588 To calculation critical temperature and critical pressure is function of specific gravity and ule point temperature as given y Riazi and Dauert: a exp f e M c dm M......(4) where a to f, are constants for critical temperature and critical pressure as follows y tale (2) Tale (2) Parameter A C D f E P c 4.5203*10 4-0.8063 1.6015-1.8078*10-3 -0.3084 0 T c 544.4 0.2998 1.0555-1.3478*10-4 -0.61641 0 Hence equations(1) and(2) can e written as P P( P, T, T,, R, M, ) c c Thea centricfactor in this work calculate as function in (T c, P c ) y using equation (6) Where: Pc 3log 14.70 1 Tc 7 1 T.. (6) ω = Acentric factor P c = Critical pressure, psia T c = Critical temperature, Rᴼ T c = Normal oiling point, Rᴼ S W (5) Using the principles of corresponding state equation (5) can e reduced further to P P( P, T, T, R,, ) (7) c c There are many formulations for vapor pressure such as Antoine and Wagner equations of vapor pressure of pure components. In this work is adoptedthe model y using Microsoft Excel(regressionlogarithmic) to express vapor pressure of mixture. s Ln P = a + lnt c T c P c e R S d ω f (8) Where: P = The ule point pressure (ar) T c = Critical temperature k P c = Critical pressure ar T P = The ule point pressure k R s = Gas oil ratio (scf/st) ɷ = a centric factor 203

The parametersaoveare otained using equation (2) and (5) and using the data direction. Experimental Data Experimental PVT data were supplied y the Ministry of Energy and Mining, Sudan, for a numer of wells representing different reservoirs. The data include compositional analysis of single caron numers of up to Eicosanes plus (C20+) and Hexatriacontanes plus (C36+) and PVT of CME of ottom hole samples. The data also include ule point pressure,reservoir temperature, and specific gravity of the reservoir fluid. Tale 3:The Data Description for ule Point Pressure Numer of Data Properties Min Max MEDIAN 65 Reservoir temperature ( F) 107.6 239 167.180 65 Bule point pressure (psig) 36 3812 579.000 65 density at P (gm/ml) 0.4763 0.8945 0.80095 65 density @60(gm/ml) 0.82 0.945 0.887 65 Specific gravity 0.481 0.904 0.808 65 Viscosity @P (centipoises) 0.61 407 8.04 65 Formation volume 1.01 1.8317 1.0685 65 Total gas oil ratio (scf/stb) 1.2 770.17 74.925 65 Gas oil ratio at P (scf/stb) 1.108 896.53 81.802 65 Gas specific gravity (air = 1) 0.577 1.427 0.70245 65 Molecular weight 38.74 367.165 171.6 65 API 18.315 41.08202 28.02649 204

Tale 4: Summary of Calculate Parameters using Equations 2, 3, 4 and6 NO P(ar) Density @P Spec. Gravity Mw T C (K) T (K) P c (ar) Centric factor 1. 6.069 0.895 0.904 367.165 866.050 685.972 8.713 0.558 2. 20.897 0.836 0.844 218.584 729.916 552.623 15.812 0.567 3. 18.276 0.837 0.845 219.878 731.459 554.157 15.720 0.567 4. 163.034 0.869 0.877 284.988 799.500 621.814 11.924 0.583 5. 18.690 0.793 0.801 164.398 655.850 480.166 20.449 0.504 6. 103.448 0.785 0.793 156.526 643.190 468.146 21.281 0.492 7. 108.345 0.802 0.810 173.798 670.233 493.983 19.516 0.518 8. 6.690 0.831 0.839 211.235 720.980 543.748 16.347 0.561 9. 4.621 0.873 0.882 296.250 809.688 631.844 11.399 0.580 10. 33.103 0.837 0.846 221.184 733.009 555.698 15.628 0.568 11. 27.586 0.849 0.858 241.895 756.449 579.050 14.269 0.580 12. 61.862 0.787 0.795 158.508 646.435 471.213 21.067 0.495 13. 59.586 0.788 0.796 159.659 648.300 472.981 20.944 0.497 14. 44.138 0.784 0.792 155.595 641.654 466.697 21.382 0.491 15. 219.241 0.697 0.704 98.044 524.424 364.241 29.261 0.407 16. 53.310 0.807 0.815 179.580 678.717 502.204 18.972 0.526 17. 262.897 0.694 0.701 97.026 521.822 362.185 29.433 0.407 18. 33.103 0.807 0.815 179.464 678.549 502.040 18.983 0.526 19. 27.586 0.816 0.824 190.447 693.980 517.105 18.007 0.539 20. 34.483 0.807 0.815 179.464 678.549 502.040 18.983 0.526 21. 53.310 0.829 0.838 208.529 717.614 540.411 16.550 0.558 22. 27.586 0.849 0.858 241.895 756.449 579.050 14.269 0.580 23. 6.690 0.859 0.867 261.269 776.667 599.185 13.142 0.585 24. 6.621 0.839 0.847 223.502 735.736 558.411 15.468 0.570 25. 43.793 0.778 0.786 149.928 632.107 457.740 22.015 0.482 26. 91.862 0.707 0.714 103.114 537.030 374.355 28.422 0.412 27. 34.483 0.807 0.815 179.464 678.549 502.040 18.983 0.526 28. 6.552 0.859 0.868 263.242 778.643 601.150 13.035 0.585 29. 69.034 0.476 0.481 38.744 306.913 234.546 40.100 1.198 30. 2.483 0.710 0.717 104.478 540.323 377.038 28.202 0.413 31. 11.310 0.802 0.810 173.467 669.740 493.507 19.548 0.518 32. 48.966 0.702 0.709 100.655 530.988 369.477 28.825 0.409 33. 39.448 0.704 0.711 101.776 533.759 371.707 28.641 0.410 205

Comparison of correlations Statistical Error Analysis Mean Asolute per- cent error, minimum /maximum asolute per- cent error, standard deviation and correlation coefficient were computed for each correlation Tale (5) shows the statistical error analysis results of the ule-point pressure correlations. This work correlation gives low values of Mean Asolute Per-cent Error (MAPE) and standard error of 34.236percent and 0.235percent, respectively. Lower value of MAPE indicates a etter accuracy of the correlation. The correlation coefficient of the correlation is almost equal to 1.0(0.995). This shows that a good agreement exists etween experimental and calculated ule point pressure. In comparison withother known correlations, this work correlation gives lowest AAPRE and standard Error. This shows that this work correlation predicts etter ule point pressure for Sudanese crude oil than any other known correlations. Tale5: Summary of Statistical Measures for P for Common Correlations Correlation Crude Oil MAPE (E a ) MPE(E i ) Ea max Ea min R 2 Standing California 29.82832 20.06147 136.5053 4.554 0.972 Marhoun Middle Eastern 39.34317 26.96057 91.74487 2.563 0.951 Glaso s North Sea 39.67769-14.9779 98.60902 0.2377 0.959 Petrosky and Farshad Gulf of Mexico 348.9783 182.713 3680.016 1.6711 0.951 Dolka& Omer U.A.E 13.1 6.554071 54.09005 0.581 0.985 Hanafy et al Egyptian 48.75457 3.381003 347.5444 5.3685 0.986 Marhoun Saudi Araian 48.06217 14.41428 211.4398 2.2247 0.940 Vasquez-Beggs API 30 27.37511 27.32164 71.33314 0.5882 0.985 API 30 41.38263 41.38263 59.30116 28.814 0.741 AdAlshakoor, Ali and Nagi Sudanese 11.27562 3.617619 35.37696 0.4739 0.994 RESULTS AND DISCUSSION The parameters of mixture for samples 1 to 33 is calculated using equation (2), (3), (4) and (7). The regression analysis is facilitated using the Microsoft excel. The results of regression with respect to the constants of equation (8) shown Tale (6) shows the statistical parameters of regression Tale 6: The constant a to f of equation (8) Constants a B C d f e Value -3.76394 0.5135262 10 2-0.506739 10 2-3.974 6.124552 0.803255 206

Tale 7: The Vapor Pressure of Mixture for TheSample 1 to 33Otained to Develop Correlation Equation (8) No Rs (scf/stb) T C (k) T ( k) P c (ar) Ω P (ar)meas P (ar) calc E a 1 5.2 866.05 685.972 8.713 0.558 6.069 5.947 2.004 2 28.1 729.916 552.623 15.812 0.567 20.897 20.884 0.058 3 24.5 731.459 554.157 15.72 0.567 18.276 18.733 2.499 4 333 799.5 621.814 11.924 0.583 163.034 152.091 6.712 5 26.3 655.85 480.166 20.449 0.504 18.69 17.804 4.74 6 170 643.19 468.146 21.281 0.492 103.448 77.857 24.738 7 179.2 670.233 493.983 19.516 0.518 108.345 85.304 21.266 8 5.6 720.98 543.748 16.347 0.561 6.69 5.666 15.304 9 4.6 809.688 631.844 11.399 0.58 4.621 4.801 3.905 10 62.83 733.009 555.698 15.628 0.568 33.103 39.968 20.738 11 52.33 756.449 579.05 14.269 0.58 27.586 34.998 26.868 12 110.6 646.435 471.213 21.067 0.495 61.862 55.463 10.344 13 109.3 648.3 472.981 20.944 0.497 59.586 55.131 7.476 14 78.6 641.654 466.697 21.382 0.491 44.138 41.775 5.353 15 641 524.424 364.241 29.261 0.407 219.241 187.217 14.607 16 85.6 678.717 502.204 18.972 0.526 53.31 47.794 10.347 17 770.17 521.822 362.185 29.433 0.407 262.897 216.774 17.544 18 62.83 678.549 502.04 18.983 0.526 33.103 37.271 12.591 19 52.331 693.98 517.105 18.007 0.539 27.586 32.957 19.468 20 72.15 678.549 502.04 18.983 0.526 34.483 41.651 20.788 21 86.5 717.614 540.411 16.55 0.558 53.31 50.886 4.548 22 52.33 756.449 579.05 14.269 0.58 27.586 34.998 26.868 23 4.4 776.667 599.185 13.142 0.585 6.69 4.792 28.373 24 4.5 735.736 558.411 15.468 0.57 6.621 4.82 27.205 25 77.7 632.107 457.74 22.015 0.482 43.793 40.635 7.212 26 312.7 537.03 374.355 28.422 0.412 91.862 106.007 15.398 27 72.15 678.549 502.04 18.983 0.526 34.483 41.651 20.788 28 7.61 778.643 601.15 13.035 0.585 6.552 7.435 13.487 29 154 306.913 234.546 40.1 1.198 69.034 68.74 0.427 30 3.2 540.323 377.038 28.202 0.413 2.483 2.68 7.948 31 19.9 669.74 493.507 19.548 0.518 11.31 14.585 28.953 32 145 530.988 369.477 28.825 0.409 48.966 56.926 16.257 33 111.05 533.759 371.707 28.641 0.41 39.448 46.033 16.693 Ea max 28.953 Ea min 0.058 MAPE 13.985 207

Tale (6) shows The Vapor Pressure of Mixture for The Sample 1 to 31Otained Using Equation (8) is Validated NO Rs (scf/stb) T c (K ) P c (ar ) T (K ) Ω P (ar) measuring P (ar) Calculate E a 1 98 639.81876 21.503432 685.97154 0.4890148 49.65517 49.89052 0.474 2 57.2 587.19835 25.036046 552.62263 0.4420631 30.2069 29.22874 3.238 3 70.86 683.45452 18.670725 554.15666 0.530152 40.41379 41.53531 2.775 4 63.12 715.38596 16.685643 621.81424 0.5565694 33.44828 39.55796 18.266 5 67.28 713.53972 16.798053 480.16626 0.5551969 35.86207 41.54858 15.857 6 163.2 315.23875 39.905281 468.14551 1.0793588 88.75862 77.02046 13.225 7 57.2 587.19835 25.036046 543.74832 0.4420631 30.2069 29.22874 3.238 8 79.227 666.95558 19.727476 631.84381 0.5149204 48.48276 44.20441 8.824 9 78.54 660.64046 20.136862 555.69762 0.5089381 48.34483 43.41056 10.206 10 10.4 705.34187 17.300824 579.0495 0.548841 8.896552 9.178705 3.171 11 63.9 662.57295 20.011315 471.21299 0.5107748 30.27586 36.90841 21.907 12 83.3 689.28557 18.302026 472.98107 0.5353357 40.89655 47.72577 16.699 13 60.5 674.53568 19.239583 466.69661 0.5220051 29.03448 36.05724 24.188 14 19.95 822.16865 10.771796 364.24146 0.5736237 16.89655 15.22506 9.893 15 19.97 832.27993 10.277255 502.20352 0.5662237 14.48276 14.76862 1.974 16 144.9 565.30255 26.518746 362.18457 0.4263106 65.24138 59.39435 8.962 17 103.1 717.98608 16.527855 502.04015 0.5584628 64 58.84231 8.059 18 94.8 695.38159 17.91942 517.10526 0.5406085 57.24138 53.42869 6.661 19 84.5 661.28359 20.095054 502.04015 0.5095499 56.89655 46.09034 18.993 20 4.8 819.19162 10.919673 540.41114 0.5754305 7.103448 4.885731 31.220 21 1.2 819.19162 10.919673 579.0495 0.5754305 2.482759 1.604434 35.377 22 4 438.60975 34.609871 599.18509 0.4464042 4.137931 3.653413 11.709 23 144.7 311.70976 39.991072 558.41109 1.1268911 62.2069 68.15358 9.560 24 706.6 433.73172 34.885305 457.74006 0.4535815 257.2414 237.2546 7.770 25 27.3 561.0696 26.80495 374.35541 0.423655 15.72414 15.44129 1.798817 26 166.568 559.4378 26.9152 502.04015 0.422669 69.44828 65.84972 5.181632 27 134.3273 580.0938 25.51723 601.14959 0.436613 68.96552 57.28509 16.93662 28 109.3 648.30047 20.94386 234.54611 0.4971365 59.58621 55.34402 7.119 29 78.6 641.65444 21.382012 377.03783 0.4907696 44.13793 41.93614 4.988 30 110.6 646.43489 21.066617 493.50682 0.495348 61.86207 55.67677 9.999 E a max 35.377 E a min 0.474 MAPE 11.3 THROUGH THE STUDY CAME TO THE CONCLUSION FOLLOWS: 1- Acute shortage of data and not availale in large and one of the prolems faced Search 2. The presence of more than one field, and more than well in addition to the diversity of geographical locations led to a variation in the readings of the data and the existence of differences in each 3. Has to take advantage of the measured data within the narrow represented y the density at a pressure oiling point in addition to the 208

4. Benefited from the pre-existing relationship () at the expense of the critical temperature and critical pressure and temperature at the oiling point and the calculation of molecular weight 5- Considered thermodynamics of the factors mentioned properties to affect direct impact on the vapor pressure of the crude mixture a,, c coefficients of the aove equation having the following values:a = 0.816 = 0.172 c = 0.989 Al MarhounCorrelations (1988) (Middle Eastern crude oil) c d e S g 0 P ar T 6- Compare the results proved the high quality of which was otained compared with the linear correlations exist, which depends on the properties availale in the data 7. Use the properties thermodynamics direct link characteristic proven APPENDIX A: PVT CORRELATIONS StandingCorrelations (1981) Standing (1981) expressed the graphical correlation y the following expression P = 18.2 [(Rs/γ g ) 0.83 (10) a 1.4] where T temperature, R γ o stock-tank oil specific gravity γ g gas specific gravity a e coefficients of the correlation having the following values: a5.38088 10 3 c1.87784 e1.32657 0.715082 d 3.1437 With Where a = 0.00091 (T 460) 0.0125 (API) P =ule-point pressure psia T =system temperature, R Glaso s Correlations (North Sea crude oil)(1980) log (P )=1.7669+1.7447 log(p* ) 0.30218 [log(p* )] 2 where P* is a correlating numer and defined y the following equation: where: RS P t API g R s gas soluility, scf/stb tsystem temperature, F. a γ g average specific gravity of the total surface gases (air = 1) c The Petrosky-Farshad Correlations (Gulf of Mexico crude oil) P 112.727R 0.8439 g 0.577421 s (10) X Where the correlating parameter X is 1391.051...2.42 X = 7.916 (10 4 ) (API) 1.5410-4.561(10-5 ) (T - 460) 1.391 where P =pressure, psia T =temperature, R Al-Marhoun 1985 (Saudi Araian Oil) 2 9 2 P 64.138910 0.702362 10 X 2.278475 10 X Where 0.722569 1.879109 3.046569 1.302347 s g o X R T In this work(2015) (Sudanese crude oil) 209

Ln P = a + lnt c T c P c e R S d ω f where P = The ule point pressure (ar) T c = Critical temperature k a ecoefficients of the correlation having the following values: P c = Critical pressure ar T = The ule point pressure k R s = Gas oil ratio (scf/stb) Ω = a centric factor Constants A B C D F E Value -3.76394 0.5135262 10 2-0.506739 10 2-3.974 6.124552 0.803255 Dokla and OsmanCorrelations (United Emirates crude oil) E a = 1 n d n d i=1 E i P = 8363.86R s 0.724047 γ 0.107991 γ g 1.01049 T + 459.67 0.952584 APPENDIX B: Statistical Error Analysis 1. MEAN PERCENT ERROR(MPE): It is the measure of the relative deviation from the experimental data, defined y: E r = 1 E n i d i=1 WhereE i is the relative deviation of an estimated value from an experimental value. E i = x exp x est 100 i = 1,2.. n x d exp 2. MEAN ABSOLUTE PERCENT ERRO(MAPE)R: It measures the relative asolute deviation from the experimental values, defined y: n d 3. MINIMUM AND MAXIMUM MEAN ABSOLUTE PERCENT ERROR: To define the range of error for each correlation, the calculated asolute percent relative error values are scanned to determine the minimum and maximum values. They are defined y: n E a max = max d i=1 Ei 4-STANDARD DEVIATION: n E a min = min d i=1 Ei Standard deviation, (sx), of the estimated (otained from the correlation) relative to the experimental values can e calculated using the following equation: Symol x represents physical properties.a lower value of standard deviation means a smaller degree of scattering. The accuracy of the correlation is determined y the value of the standard deviation, where small value indicates higher accuracy. The value of standard deviation is usually expressed in percent. 5. THE CORRELATION COEFFICIENT: It represents the degree of success in reducing the standard deviation y regression analysis, defined y: r 2 n xy ( x)( y) = n x 2 ( x) 2 n y 2 ( y) 2 SUMMARY OUTPUT Regression Statistics Multiple R 0.989118 R Square 0.978354 Adjusted R 0.974345 210

Square Standard Error 0.183316 Oservations 33 ANOVA Df SS MS F Significa nce F Regression 5 41.00834 8.201669 244.0633 1.39E-21 Residual 27 0.907326 0.033605 Total 32 41.91567 Coefficien ts Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -16.5074 20.58553-0.80189 0.429617-58.7454 25.73067-58.7454 25.73067 X Variale 1-53.3704 87.97887-0.60663 0.549166-233.888 127.1474-233.888 127.1474 X Variale 2 55.54224 90.30736 0.615036 0.543681-129.753 240.8376-129.753 240.8376 X Variale 3 5.490668 8.728312 0.629064 0.534594-12.4183 23.39968-12.4183 23.39968 X Variale 4-5.37325 9.493279-0.56601 0.576064-24.8518 14.10535-24.8518 14.10535 X Variale 5 0.803359 0.026493 30.3238 2.16E-22 0.749 0.857717 0.749 0.857717 RESIDUAL OUTPUT Oservation Predicted Y Residuals 1 1.781016 0.022172 2 3.017204 0.02238 3 2.90802-0.00244 4 5.048971 0.044991 5 2.897048 0.030923 6 4.380011 0.259061 7 4.455376 0.229943 8 1.715599 0.184963 9 1.620454-0.08991 10 3.665536-0.1659 11 3.532011-0.2147 12 4.038978 0.08593 13 4.031916 0.055508 14 3.758203 0.029116 15 5.20756 0.182614 16 3.870829 0.105302 17 5.347306 0.224455 18 3.622216-0.12258 211

19 3.490036-0.17272 20 3.733333-0.19287 21 3.912386 0.063744 22 3.532011-0.2147 23 1.554889 0.345673 24 1.549234 0.340965 25 3.735569 0.043907 26 4.666355-0.14607 27 3.733333-0.19287 28 1.996325-0.1166 29 4.234678-7.1E-05 30 0.994014-0.08464 31 2.689226-0.26351 32 4.032396-0.14128 33 3.825787-0.1508 REFERENCES [1]. Riazia, M. R. and Dauert, T. E., Characterization Parameters for Petroleum Fractions, Ind. Eng. Chem. Res., 1987, Vol. 26, No. 24, pp. 755 759. [2]. Glaso, O., Generalized Pressure-Volume- Temperature Correlations, JPT,May 1980, pp. 785 795. [3]. Marhoun, M. A., PVT Correlation for Middle East Crude Oils, JPT, May 1988, pp. 650 665. [4]. Standing, M. B., Volumetric and Phase Behavior of Oil Field Hydrocaron Systems, pp. 125 126. Dallas: Society of Petroleum Engineers, 1977. [5]. Sutton, R. P., and Farshad, F. F., Evaluation of Empirically Derived PVT Properties for Gulf of Mexico Crude Oils, SPE Paper 13172, presented at the 59th Annual Technical Conference, Houston, Texas, 1984. [6]. Vasquez, M., and Beggs, D., Correlations for Fluid Physical Properties Prediction, JPT, June 1980, pp. 968 970. 212