RESERVOIR ENGINEERING A empirical correlatio for oil FVF predictio GHASSAN H. ABDUL-MAJEED ad NAEEMA H. SALMAN Petroleum ad Miig Egieerig Departmet Uiversity of Baghdad Baghdad, Iraq ABSTRACT A ew empirical correlatio for predictig oil FVF at bubble poit pressure is developed from 42 experimetally obtaied oil FVF o 9 oil-gas mixtures collected from four differet upublished sources. Whe applied to all data, the ewly developed correlatio clearly out-performs the existig oil FVF correlatios, based o low values of average per cet differece, absolute average per cet differece, ad stadard deviatio. The preset ad the existig correlatios are evaluated withi pre-determied rages of oil API gravity. Five mai rages of this parameter are selected for best correlatios. Itroductio The oil formatio volume factor, Bo, is a factor used to estimate the chage i volume of oil as it udergoes a chage i pressure ad temperature. The chage i volume is a combiatio of thermal expasio, compressibility effects, ad mass trasfer, which is represeted by gas evolvig from or goig ito solutio. Therefore oil FVF is the volume of oil at P ad T occupied by oe stock tak barrel (STB} of oil ad the gas i solutio. Several empirical correlatios have bee published that ca be used to estimate Boat ad below bubble poit pressure (Pb). The most widely used correlatios are show i Table 1. The scope of the proposed research cosisted of developig a ew correlatio for estimatig Boat ad below Pb. Data Acquisitio ad Preparatio The aalysis of 9 bottom-hole fluid samples were made available for this study. The data bak used (cosistig of a total of 425 PVT tests), is obtaied from four differet upublished sources. I these sources, the flash separatio data were used i cojuctio with the values of the flash ad differetial process to calculate the combiatio formatio volume factor. The calculatios were performed assumig that the relatioship betwee the flash ad differetial liberatio processes is costat at ay reservoir pressure (the procedure of calculatios is described, i detail, i Ref. 2, p. 18). Each of the PVT tests is examied for ureasoable values. If the observed FVF for a PVT test seemed ureasoable whe Keywords: Physical fluid property, PVT tests, Multiple regressio aalysis, Statistics. compared to the FVFs estimated by all the existig FVF correlatios (i.e. the per cet errors of all the correlatios are greater tha loojo}, the PVT test is elimiated from the data set. As a result, five data poits are removed. The revised data bak ow cotais 42 data poits (Table 2). A brief descriptio of the revised data bak is give i Table 3. Developmet of the Correlatio Usig o-liear multiple regressio aalysis, the followig relatio is developed from 42 experimetally obtaied oil FVF o 9 differet oil-gas mixtures: Bo =.9657876 + 4.8141x1S F - 6.8987x1Q-IO F2 + 7. 73x1Q-4 T where F = Rs1.2 Gag-.147 oa -5.222 The same uits apply for Rs, Gag, Gao, ad T as i the equatios show i Table 1. The developed correlatio meets approximately, the requiremet for the formatio volume factor of 1. at 6 F ad atmospheric pressure (R = ). Figure 1 is a plot of the observed Bo values vs the estimated Bo values for the data used. Statistical Results The followig statistical parameters are used to determie the relative accuracy of the preset correlatio: PD = [- Estimated J x 1 E PDi APD = _i_=_l E IPDil AAPD = _i_=_l SD = ~.J E(PDi) 2 - [E PDi] 2 The preset correlatio ad the existig correlatios of Stadig(}>, <2>, Glaso(3), ad Al-Marhou<4> are tested Paper reviewed ad accepted for publicatio by the Editorial Board of the Joural of Caadia Petroleum Techology. 8 The Joural of Caadia Petroleum Techology
8.5r------------------l AI-Marhou c CD t- VJ ~.a.a ABSOLUTE AVERAGE PERCENT ERROR 4.5 CD -u 2 E ~ Ill w 1.5 1 AI-Marhou 1.25 1.5 I. 75 Bo, bbi/stb FIGURE 1. vs estimated oil FVF for all PVT data (this study). STANDARD DEVIATION agaist the experimetal PVT data used i this study. Table 4 gives a summary of the statistical results. It is apparet that both the Glaso ad correlatios ted to uderpredict the FVFs, while the Al-Marhou correlatio overpredicts the FVFs. Based o lowest values of APD, AAPD, ad SD, the preset correlatio gives the best performace. Besides determiig the cumulative statistical figures for the 42 PVT tests, we evaluated the preset ad the existig correlatios withi specific rages of oil API gravity. Because the oil API gravity has a major effect o the oil FVF [Amyx eta!. (5)], TABLE 1. The existig Bo correlatios Stadig (1947) 1.175 Bo =.972 + 1.47x1-4 x Rs Gag + 1.25 T] (1976) ForAPI~3 [ ~ Gao Bo = 1 + 4.677x1-4 Rs +.1751x1-4 FF- 1.816x1-8 Rs FF ForAPI>3 Bo = 1 + 4.67x1-4 Rs +. x1-4 FF -.1337x1 o-s Rs FF FF = (T-6) x ( API ) Gag Glaso (198) Bo = 1 + Atilog (-6.585 + 2.91329 CF -.27683 CF2) CF = Log [ ( G~ ) ' 526 +.968 T] ' Gao AI-Marhou (1985) Bo =.57495 + 73532x1-4 Tr + 2.4545x1-3 FM + 37676x1-5 FM2 FM = Rs.538 Gag-.145526 Gao-5.22726 T = temperature, deg. F Tr = temperature, deg. R Gag = gas specific gravity (air= 1) Gao = oil specific gravity (water= 1) Rs = solutio gas-oil ratio, scf/stb > -25 25-3 3-35 35-4 >4 (7) (1) (48) (32) (65) (91) RANGES OF OIL API GRAVI1Y (NUMBER OF PVT TESTS IN EACH GROUP PARENTHESES) FIGURE 2. Statistical results for PVT data grouped by oil API gravity. TABLE 2. Complete set of data, Bo No. Rs (m3fm3) 1 6 2 28.5 3 7.5 4 8.37 5 67 6 6.95 7 3.6 8 5.88 9 3.6 1 7.13 197 71 13 31.17 14 13.36.455 16 9.8 17 13.18 18 3.92 19 2.9 2 4.81 21 1 22.5 23 8. 24.221 25 3.85 26 14.6 27 13.54 28 13.36 29 1. 3 7.5 31 8.27 32 8.37 33 9.44 34 5.9 35.47 36.4 37 14.7 38 6.56 39 63.5 Temperature (DC) 51 48.9 5 43.34 35 29.45 36.1 97.23 44 132.23 92.23 5.56 49 39 35 44.45 57.23 44 5 45.6 53.34 46 43.34 41.1 47.8 35.6 4.6 45 46 67.2 68.9 API (degree) 14.2 14.9 14 14.5 13.2 13 13.9 14.2 14.6 14 14.8 1.3 13 13.8 14 14.3 13.2.8 1.8 1.9 1 1 1 26.5 28.4 Gas (Sp. Gr.) 7 1.89.85.85.8 1..63 3 1.69 3 7 1.64.64.525.547 Bo 1 1.91 1.48 1.43 1.36 1.38 1.28 1.43 1.73 1.276 1. 1.9 1.13 1.6 1 1.37 1.32 1.38 1.74 1.51 1.64 1.44 1.75 1.66 1.63 1.44 1.49 1.49 1.51 1.56 1.18 1.17 Estimated Bo by the ew Eq. 1 1.69 1.64 1.66 1.48 1.45 1.43 1.34 1.48 1.22 1.8 1.185 1.133 1 1.69 1.47 1.41 1.46 1.6 1.79 1.69 1.56 1.76 1.65 1.6 1.61 1.45 1.59 1.59 1.51 1.184 1.197 November-December 1988, Volume 27, No.6 9
TABLE 2. Complete set of data, Bo (Cot'd) Estimated Estimated Rs Temperature API Gas Bo by the Rs Temperature API Gas Bo by the No. (m3fm3) (OC) (degree) (Sp. Gr.) Bo ew Eq. No. (m3fm3) (OC) (degree) (Sp. Gr.) Bo ew Eq. 4 98.5 81.1 29.585 1.29 1.293 3 163.86 71. 4.1 8 1.485 1.5 41 41.86 63.9 23.4.598 1.3 1.137 4 9.44 73.34 34.9 91 1.79 1.16 42 53.8 64.45 23.553 1.142 1.8 5 7 86. 32.6 6 1.35 1.319 43 6.31 87.23 28.1.58 1.35 1.329 6 295.66 97.22 51 1.962 1.947 44 45.42 66. 22.8.581 1.136 1.145 7.85 42.8 34.1.8 1.63 1.75 45 9.44 62.23 26.9.5 1.8 1.88 8 49 57.8 36.3.8 1.18 1.172 46 4.5 87.23 28.2 7 1.3 1.341 9 913 71 37.3 71 1.31 1.31 47 32.42 628 28.616 1. 1.7 13 189. 86. 44.9.83 1.679 1.648 48 8.55 54.45 3.661 1.7 1.77 131 72.31 65.6 37.4 9 1.243 1.243 49.58 54.45 26.678 1.5 1.8 132 52 14.8 1.838 1 5 24.58 45.56 19.6 1.69 1.8 133 14.95 5 14.5 1.855 1.721 51 19.41 45.56 19.3 17 1.62 1.73 134 1 4 13 1.67 3 52 66.8 79.45 28.9.6 1.21 1.217 135 28 3 1 8 53 32.6 55.56 21.6 18 1. 1.17 136 2 62.8.66 1.816 1.925 54 64.48 93.34 27.8.63 1.22 1.229 137 47 7 13.2.67 1.147 1.1335 55 52.36 55.56 28.2.674 1.145 1.3 138 52 65 14.1 7 1.5 1.133 56 74.27 86. 29.1 8 1.238 1.241 139 54 72 8 1.1 1.147 57.85 93.89 25.6 19 1. 1.14 14 13 49 1.829 1.69 58 85.5 61.67 21.5 9 1.224 1.196 141 4.2 35.67 1.56 1.4 59 13.54 71. 24.3 1 1. 1.14 142 18 53 1.69 1.61 1.77 6 47.2 1378 23 8 1.213 1.247 143 1.1 45 1.5.82 1.69 1 61 26 44.45 22.5 5 1.73 1.83 144 4.8 83 9.9 1.3 1.186 62 22.98 55.56 29.6 9 1.1 1. 145 7.3 8 1.82 1.961 63 26 57.8 3.67 1.99 1.1 146 22 39 13.8.81 1.77 1.633 64.22 5.3 71 1.48 1.69 147 25 44 14 1.85 1.73 65 18.3 5 24.4 2 1.319 1.38 148 79 14.8 7 1.91 1.188 66 3 44.45 21.9 67 1.65 1.77 149 3.9.63 1.591 1.453 67 4.7 41.1 25 64 1.17 1.13 7 56.66 1.735 68 24.22 35 24.6 8 1.61 1.69 1.2 46 1.88 1.77 1.63 69 36.87 65.56 27.9.648 1.13 1.138 2 9.1 55.9.9 1.785 1.73 7 28.32 32.22 17.3 1 1.74 1.64 3 8.9 48 13.1.92 1.73 1.633 71 5.94 29.45 25.6.84 1. 1. 4.6 13 9 1.66 1.516 72 77. 71.67 28.835 1.228 1.22 5 14 6 2 73 89.23 67.8 27.8.855 1.24 1.236 6.2.8 1.642 1.55 74 74.63 7 27.846 1.224 1.2 7 13.9.82 75 13.36 95.56 24.6.866 1.1 1.138 8 3 84.84 1.9 1.133 76 1.33 34.45 26.1 1.2 1.43 1.49 9 5.6 66 1.9 7 1.85 1.856 77 27.43 6 27.8.914 1.4 1.2 16 26 5 8 1.84 1.838 78 36.16 69.45 26.98 1.14 1.138 161 27.6 44.67 1.769 1.776 79 279 69.45 27.5.922 1.2 1.5 162 17.8 1 1.56 1.56 8 52.54 68.9 29.3.844 1.17 1.173 163 17.9 41.1 13.2.66 1.64 1.622 81 27.25 63.33.96 1.98 1.19 164 1.5 4.6 1.69 1.54 82.85 96.67 26.4.95 1.18 1.144 165 177.4 9.6 38.4 73 1.55 1.552 83.47 5.56 27.4.926 1.7 1.75 166 16.51.6 41.4 1.49 1.434 84 69.82 55.56 3.3.931 1.2 1.19 167.5 78.34 45.3 31 1.338 1.395 85 52.9 7.56 28.4.857 1.27 1.173 168 3.17 45.6 38.8.836 1.423 1.43 86 1.33 95.56 27.6.857 1. 1.135 169 27.3 6 43.2 79 139 131 87 29.3 66. 26.5.93 1.14 1.1 17 231.4 69.45 49.4 81 2 182 88 65.1 42.22 26.5 1.36 1.17 1.147 171 283.2 47.8 44.8 7 198 1.8 89 31.88 71. 28.1.937 1.133 1.135 172 94.4 71. 38.1.838 1.318 1.39 9 3.1 7 26.5.936 1.8 1.8 173 28 96 44.9.589 1.668 131 91 26.89 58.9 28.4.935 1. 1. 174 245.3 75.6 46.6.82 19 184 92 131 92.22 19 1. 1.7 1.131 175 282.13 45.6 45 6 18 197 93 4.25 38.9 28.3.996 1.4 1.14 176 7.88 4.9.8 1.462 1.475 94 41 1 3.3.933 1.193 1.197 177 5.94 77.8 35.1 71 1.189 1.2 95 6.59 63.34 27.1.813 1.7 1.85 178 8.52 86 38.8.839 1.47 1.51 96 18.52 58.9 28.4.963 1.1 1.96 179 4.96 16. 47 83 1.549 1.616 97 17.99 76.67 29.8 1.4 1.19 1.1 18 63.94 9.6 36.4.814 1.25 1.252 98 76.94 17.22 32.4.873 1.327 1.287 181 183.81 7.22 39.6 6 1.62 1.619 99 26.18 88.34 28.8.971 1.145 1. 182 64. 19.45 38.1.83 1.276 1.286 1 18.167 63.34 24.3 1.4 1.95 1.99 183 64.83 18.9 38.3.8 1.28 1.288.14.56 28.5.94 1.14 1.6 184 64.83.6.834 1.282 1.286 17.633 98.34 23.1 1.37 1.2 1.146 185 41 65 42.3.875 1.181 1.2 13 76.5 19.45 2.967 1.3 1.273 186 48.27 71 44.5.863 1.192 1.213 14 17.63 98.34 23.1 1.37 1.2 1.146 187 73.2 82.2 38.1.845 1.273 1.27 6.914 5 29.3.934 1.2 1.237 188 16 1 37.1.888 1.16 1.179 16 13.54 6 29 1.4 1.84 1.91 189 82. 5 42.5 8 1.337 1.417 17 6 5 23.9 1.182 1.94 1.147 19 34.55 63.9 45.1.863 1.2 1.164 18 2 98.9 2 1.22 1.8 1. 191 327 17.8 37.2 1 1.19 1.26 19 29 17.2 29.9 1.148 1.174 1.183 192.58 51. 42.3 938 1.365 1.379.85 54.5 29 1.19 1.87 1.86 193 66.26 63.9 45.3.866 1.239 1.26 1 21.26 13.34 27.9 1.351 1.545 1.483 194 142.5 136 48.3 8 1.62 1.632 2 6.1 56. 36.9.83 1.364 1.362 195 144.45 19.45 43.897 1.566 1.541 3 144.8 55.6 41.4.822 1.41 1.449 196 16.39. 36.5.826 1.13 1.9 4 135.2 72.8 41.4.817 1.433 1.447 197 93 33.34 36.9.87 1.255 1.246 1 135.36 76 41.5.826 1.438 1.453 198 65.55 68.9 37.5.848 1.25 1.229 6 9.49 6 41.5.88 1.56 1.58 199 56.82 76.67 38.848 1.223 1.22 7 8.24 6 42.88 1~5 1.59 2 45.95 1 33.836 1.222 1.233 8 226.2 75.6 43.5 3 13 1 21 913 17.22 53.4 92 1.385 1.462 9 178.82 132.8 49.3 78 1 22 38.69 5 31 925 1.219 1.228 245.26 75.6 46.6.82 19 184 23 168.31 5 46.8 7 1.625 1.645 1 28 96 44.9.589 1.668 131 24 5.5 54.45 43.9.917 1.163 1.193 2 18.47 75.6 35 85 1.337 1.332 25 19 3.9 45.5.834 1.693 1.694 The Joural of Caadia Petroleum Techology
TABLE 2. Complete set of data, Bo(Cot'd) Estimated Estimated Rs Temperature API Gas Bo by the Rs Temperature API Gas Bo by the No. (m3fm3) (OC) (degree) (Sp. Gr.) Bo ew Eq. No. (m3fm3) (OC) (degree) (Sp. Gr.) Bo ew Eq. 26 7.84 6.67 32.5.837 1.7 1.177 289 56.46 58.9 33.3.99 1.182 1.176 27 3 41.67 44.3.824 1.425 1.481 29 27.96 71.67 34.2.998 1.13 1.137 28 91.14 63.34 42.876 1.39 1.313 291 5.34 32.1.963 1.28 1.49 29 571 61. 36.5.873 1.19 1.195 292 164.4 77.8 43.8.942 1.591 1.55 21 69.64 6.67 35.2.89 1.295 1.295 293 23.69 25.56 4 1.41 1.86 1.73 2 95.83 5 38.9.873 1.365 1.363 294 27.43 75.56 42.5.993 1.16 1.4 2 13 18.34 34.1.697 1.98 1.161 295 37.4 38.8 1.34 1. 1.8 213 13.18 6. 36.9.93 1.61 1.173 296 17.99 88.9 44.8.933 1.144 1.3 214 197.9 68.89 41.5.831 1.5 1.53 297 133.6.56 46.9 1.41 1.495 1.529 2 133.6 66.67 45.864 1.444 1.465 298 57.9 44.45 43.2 1.13 1.27 1.195 ' 216 6.84 578 41.4.841 1.351 1.375 299.29 96. 33.6.942 1.17 1.142 " 217.17 46. 38.9 4 1.297 1.31 3 3.1 78.9 36.1 1.27 1.4 1.4 218 56 56.67 4.4.877 1.6 1.185 31 133.6.56 46.9 1.41 1.495 1.529 219 4.96 578 41.5.878 1.462 1.477 32 1.99 33.4.894 1.43 1.349 22 5.5 71. 37.3.969 1.186 1.192 33 9.44 95.6 35.4.969 1. 1.137 221 7.93 578 41.2.873 1.383 1.41 34 75.875 71. 48.6 1.9 1.316 1.314 222 54.9 9.45 4.3.85 1.265 1.282 35 1.69 143.34 39.6.96 1.162 1.28 223 91.55 78.34 38.3.865 1.291 1.3 36 31.17 29.45 53.931 1.1 1.4 224 61.45 48.89 4.3.863 1.192 1.22 37 14.2 66.67 46.6.988 1.362 1.385 225 64.48 31. 35.6.932 1. 1.165 38 17.81 76.67 35.943 1.94 1.5 226 2.137 46.67 38.1.849 1.38 1.58 39 9.8 49.45 46.1 1.19 1.73 1.78 227 142.132 86. 41.9.834 1.52 1.489 31 41.5 57.8 42.6.933 1.16 1.168 228 13.48 5 38.6.834 1.4 1.383 3 3.92 628 35.3 1.18 1.44 1.82 229. 55 32.1.936 1.73 1.83 3 43.46 1.6 45.1.822 1.249 1.263 23 43.64-35.937 1.139 1.5 313 23.33 58.33 41.6 1.95 1.7 1.8 i' 231 17.99 38.9 44 5 1.484 1.537 314 3 2.8 33 1.73 1.92 1.1 232 7.4 3.22 38.4.859 3 3.1 41.67 56.2 1. 1.456 1.499 233 5.34 136.67 36.1 98 1.2 1.188 316 14.25 91. 55.2.84 1.134 1.7 234 6.84 38.8.851 1.43 1.432 317 27.43 34.4 1.17 1.17 1.88 235 1.63 13.34 33.3 8 1.8 1.136 318 38.83 63.34 43.9 1.58 1.174 1.17 336 18.43 458 44.696 1.56 1.571 319 43.46 1.6 45.1.822 1.249 1.263 237 167.96 41. 44.4 3 1.483 1.529 32 43.1 67.45 42.883 1.198 1.189 238 63.6 6. 4.99 1.316 1.313 321 41 41.67 44.5 1. 1.167 1.148 239 52.9 6. 39.89 1.271 1.284 322 25.47.6 41.1.827 1.28 1.2 24 1.1 13.9 38.9.93 1.391 1.373 323 174 16. 32.9 1.278 1.55 1.497 241 16.3 2.23 36.1 69 1.8 1.187 324 44.17 94.45 5 1 1.259 1.284 242 296.4 83.89 51.628 2.42 1.928 325 148 428 44.5 1.137 1.77 1.79 243 143 59.45 37.6 84 1.321 1.318 326 5.23 88.34 46.6 1.148 1.264 1.245 244 144.98 7 41.8.94 1.471 1.469 327 3.384 98.9 3.9 1.259 1.83 1.131 245 133.5 142.23 41.846 1.573 1.533 328 3.175 62.23 36.6 1.288 1.414 1.413 246 3.74 77.8 4 6 1.385 1.414 329 2479 87.23 32.1 1.3 16 1.593 247 13.89 98.34 33.3.816 1.19 1.148 33 54.69 76 23 1.25 1.174 248 86.4 37.9 62 1.342 1.344 331 41 76 23 1.162 1.3 249 174.37 7.56 48.5.83 1.563 1.63 332 31.98 76 23 1.139 1.138 25 62.16 7.23 3.839 1.33 1.31 333 23.998 76 23 1.1 1.6 251 45.42 83.34 37.9 7 1.24 1.23 334 17.64 76 23 1.4 1.7 252 34.55 4.56 41.2.954 1. 1.2 335 76 23 1.95 1.97 253 13 62.23 4.3.92 1.4 1.382 336 84.93 82.2 17.9 1.264 1.29 254 8.86 6 43.6.914 1.263 1.287 337 74 82.2 17.9 1.2 1.196 255 718 71. 46.3.9 1.251 1.291 338 64.87 82.2 17.9 1.2 1.182 256 1.86 23.89 32.6 1.8 1.33 1.38 339 54.99 82.2 17.9 1.17 1.168 257 588 52.8 41.2.95 1.23 1.22 34 45.1 82.2 17.9 1.174 1.5 258 45.24 35.56 39.99 1.5 1.135 341 341 82.2 17.9 1.2 1.142 259 9.84 56. 44.1.94 1.424 1.429 342 23.88 82.2 17.9 1.7 1.8 26 69.64 7.8 5.5.887 1.344 1.387 343 17.83 82.2 17.9 1. 1.2 261 9.. 41.8.924 '1.367 1.36 344 82.2 17.9 1.8 1. 262 75.34 85.56 42.9 1.6 1.284 1.3 345 9 76 23 1.319 1.282 263 88.52 51.67 39.9.928 1.275 1.275 346 17.96 76 23 1.31 1.262 264.67 62.8 37.91 1.1 1.14 347 986 76 23 1.286 1.246 265 13.89 6.56 37.886 1.9 1.98 348 89.23 76 23 1.23 1.23 266 376.67 48.3.885 1.217 1.235 349 8.453 76 23 1.2 1.2 267 18.52 75.6 36.8.989 1.9 1.7 35 71.91 76 23 1.233 1.2 268 246 85.6 39.6 1.38 1.2 1.7 351 63.29 76 23 1.22 1.186 269 42 3 41.4 4 1.133 1.132 352 54.675 76 23 1.171 1.172 27 49.87 75.6 37.866 1.198 1.2 353 46.36 76 23 1.16 1.8 271.67 1. 37.6.8 1. 1.172 354 36.93 76 23 1.139 1.144 272 56.46 74.45.926 1.226 1.214 355 27.6 76 23 1.6 1.131 273.29 57.8 32.895 1.76 1.88 356.32 76 23 1. 1.4 274 24.4 5 43.1.965 1.27 1.217 357 76 23 1.84 1.97 275 13 1 35.5.887 1.4 1.398 358 14.2 82.2 23.6 1.34 1.333 276 218.19 65 45.8.921 131 1.692 359 9.88 82.2 23.6 1.32 1.294 277 636 61. 42.3.921 1.239 1.233 36.97 82.2 23.6 1.29 1.269 278.82 3.34 36.5 9 1. 1.169 361 93.3 82.2 23.6 1.28 1.247 279.58 17.22 38.3.97 1.426 1.426 362 8.673 82.2 23.6 1.261 1.225 28 13 17.22 38.3.919 1.44 1.428 363 66.82 82.2 23.6 1.255 1.22 281 35.62 31. 32.953 1.1 1.94 364 57.5 82.2 23.6 1.232 1.185 282 19.41 17.8 32.9 1.138 1.169 365 47.6 82.2 23.6 1.25 1.169 283 56.46 82.22 38.8.91 1.233 1.229 366 37.39 82.2 23.6 1.183 1.4 284 143 6.56 45.927 1.35 1.374 367 25.898 82.2 23.6 1.3 1.137 285 31.35 18.34 32.6.823 1.176 1.194 368 18.85 82.2 23.6 1.135 1.7 286 24.22.56 32.8.879 1.149 1.176 369 82.2 23.6 1.1 1. 287 52.9 31. 37.2 1 1.142 1.142 37 71.85 76 1.19 1.199 288 65.55 58.9 38.8.986 1.22 1.218 371 59.245 76 1.221 1.178 November-December 1988, Volume 27, No. 6 1
TABLE 2. Complete set of data, Bo (Cot'd) Rs Temperature No. (m3fm3) ( C) 372 49.91 76 373 4.56 76 374 3 76 375 18.1 76 376 76 377 9.3 76 378.83 76 379 14.29 76 38 94.84 76 381 83.94 76 382 73.8 76 383 63 76 384 53.675 76 385 43.56 76 386 32.92 76 387 18.88 76 388 13.35 76 389 76 39 94.9 81.1 391 82.83 81.1 392 71 81.1 393 62.644 81.1 394 52.9 81.1 395 44.44 81.1 396 36 81.1 397 28. 81.1 398 198 81.1 399 13.46 81.1 4 81.1 41 63.85 87.8 42 56 87.8 43 47.93 87.8 44 41.45 87.8 45 31.18 87.8 46 21.6 87.8 47 13.22 87.8 48 87.8 49 6.14 81 41 5 81 4 91.962 81 4 8213 81 413 7.24 81 414 59 81 4 51.25 81 416 42.3 81 417 33.37 81 418 23.7 81 419 16.58 81 42 81 API (degree) Gas (Sp. Gr.) Bo Estimated Bo. by the ew Eq. 1. 1.164 1.176 1.149 1.2 1.135 1.9 1.7 1.44 1.97 1.3 1.274 1.28 1.26 1.317 1.246 1.233 1.233 1.24 1.2 1.22 1.199 1.222 1.183 1.199 1.167 1.175 1.2 1.148 1.137 1.3 1.7 1.98 1.1 1.74 1.97 1.3 1.225 1.22 1.26 1.2 1.19 1.19 1.178 1.18 1.165 1.175 1.3 1.16 1.143 1. 1.132 1.131 1.2 1.1 1.1 1.46 1.13 1.199 1.197 1.195 1.185 1.175 1.173 1.9 1.163 1.134 1.149 1. 1.135 1.88 1.6 1.88 1.3 1.33 1.275 1.3 1.256 1.28 1.235 1.25 1.22 1.22 1.2 1.19 1.183 1.18 1.17 1.171 1.6 1.5 1.143 1.136 1.9 1.19 1.1 1.8 1.13 it is expected that a aalysis of predictio errors based o rages of this parameter should poit out some of the stregths ad weakesses of the correlatios. The statistical results are show i Figure 2. The Al-Marhou correlatio shows a geeral tedecy to have more scatter for lighter oils. The Glaso correlatio seems to improve as oil API gravity decreases. The preset correlatio does quite well for heavier oils. Five mai rages of API gravity ca be selected for best correlatios. These are listed i Table 5. Coclusios The followig coclusios are draw from this study: TABLE 3. Descriptio of data used Variable Miimum Maximum Pressure, kpa (psia) API gravity, degree Temperature, oc ( F) Rs, m3fm3(scf/stb) Bo, m 3 fm3(bbl/stb).35(14. 7) 24(75) 1.28 27475(3985) 5 143(29) 296.4(1664) 2.42 TABLE 4. Statistical results for all PVT tests Correlatios APD AAPD SD Stadig Glaso AI-Marhou.23 1.32 2.55-1.5 -.24 1.66 1.91 3.3 3.57 1.4 2.62 2.44 3.63 5.25 1.91 TABLE 5. Best correlatios for selected rages of oil API gravity Oil API Gravity Best Correlatio ::::.: < ::::.:25 25 < :::3 3 < ::::.:35 >35 1. A ew empirical correlatio for estimatig oil FVF is proposed as a fuctio of solutio gas-oil ratio, gas specific gravity, oil specific gravity ad temperature. 2. The ew correlatio is based o 42 experimetally obtaied oil FVF o 9 differet oil-gas mixtures from four upublished sources. 3. Average per cet error, absolute average per cet error ad the stadard deviatio from experimetally obtaied data are lower for estimated data based o the preset correlatio tha for estimatios based o the Stadig,, Glaso ad Al Marhou correlatios. 4. The preset ad the existig correlatios are evaluated agaist selected rages of oil API gravity. The results obtaied ca be used to determie the best correlatio to use for certai coditios. REFERENCES 1. STANDING, M.B., A Pressure-Volume-Temperature Correlatio for Mixtures of Califoria Oil ad Gases; Drill. ad Prod. Prac., API, pp. 275-286, 1947. 2. VAZQUEZ, M.E., Correlatios for Fluid Physical Property Predictio; M.S. thesis, Uiversity of Tulsa, 1976. 3. GLASO,., Geeralized Pressure-Volume-Temperature Correlatios; Jour. Pet. Tech., pp. 785-795, May 198. 4. AL-MARHOUN, M.A., Pressure-Volume-Temperature Correlatios for Saudi Crude Oils; SPE Paper 13718 preseted at the SPE Middle East Oil Cof., Bahrai, March -14, 1985. 5. AMYX, J.W., BASE, D.M., ad WHITING, R.L., Petroleum Reservoir Egieerig Physical Properties; McGraw-Hill, New York, Chapter 5, 196. 2 The Joural of Caadia Petroleum Techology