Appendix B 271 Table B.9: Displacement details for Initial Oil Composition C in Fig 5.22 The viscosity ratio on the initial tie line is M = 1.268, and on the injection tie line, M = 4.586 The molar volumes used to convert mole fractions to volume fractions were CO2 , 150.978 cm3 /gmol, C4 , 101.886, C10 , 215.013 Phase compositions on the initial tie line (mole fractions): xCO2 = 0.8235, xC4 = 0.0874, xC10 = 0.0891, yCO2 = 0.8833, yC4 = 0.0719, yC10 = 0.0285 Phase compositions on the injection tie line (mole fractions): xCO2 = 0.6554, xC4 = 0., xC10 = 0.3446, yCO2 = 0.9817, yC4 = 0., yC10 = 0.0448 Compositions reported in the table are in volume fractions Segment Injection Gas Trailing Shock Constant State Intermediate Shock Initial Tie Line Rarefaction Leading Shock Initial Oil B Point e e d d d c c c-b b a a CO2 1.0000 1.0000 0.9557 0.9557 0.9752 0.8663 0.8663 0.8660 0.8658 0 C4 0 0 0.0763 0.0763 0.0764 0.0764 0.3008 0.3008 C10 0 0.0443 0.0443 0.0248 0.0574 0.0574 0.0576 0.0578 0.6992 0.6992 S1 1.0000 1.0000 0.9799 0.9799 0.9799 0.7162 0.7162 0.7100 0.7074 0 Flow Vel 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 ξ/τ 1.0000 0.7366 0.7366 0.7366 0.9647 0.9647 0.9647 0.9981 1.0120 1.0120 1.0000 272 Appendix B Table B.10: Displacement details for Fig 5.23a Composition routes and saturation and flow velocity profiles for displacement of a C4 /C10 mixture by CO2 at 1000 psia and 160◦ F with volume change The viscosity ratio on the initial tie line is M = 8.319, and on the injection tie line, M = 10.68 The molar volumes used to convert mole fractions to volume fractions were CO2 , 308.685 cm3 /gmol, C4 , 104.509, C10 , 216.278 Phase compositions on the initial tie line (mole fractions): xCO2 = 0.4884, xC4 = 0.1651, xC10 = 0.3464, yCO2 = 0.9454, yC4 = 0.0514, yC10 = 0.0033 Phase compositions on the injection tie line (mole fractions): xCO2 = 0.4976, xC4 = 0., xC10 = 0.5024, yCO2 = 0.9964, yC4 = 0., yC10 = 0.0036 Compositions in the table are reported in mole fractions Segment Injection Gas Trailing Shock Injection Tie Line Rarefaction Constant State Intermediate Shock Initial Tie Line Rarefaction Leading Shock Initial Oil Point f f e d-e d-e d d c c-b c-b c-b b a a CO2 1.0000 1.0000 0.8620 0.8490 0.8104 0.7982 0.7982 0.6670 0.6580 0.6368 0.6175 0.6085 0 C4 0 0 0 0.1207 0.1229 0.1282 0.1330 0.1352 0.2868 0.2868 C10 0 0.1380 0.1510 0.1896 0.2018 0.2018 0.2124 0.2191 0.2350 0.2495 0.2562 0.7132 0.7132 S1 1.0000 1.0000 0.8658 0.8500 0.8000 0.7829 0.7829 0.6197 0.6000 0.5500 0.5000 0.4754 0 Flow Vel 1.0000 1.0000 0.9823 0.9823 0.9823 0.9823 0.9823 1.0054 1.0054 1.0054 1.0054 1.0054 0.6318 0.6318 ξ/τ 1.0000 0.0379 0.0379 0.0447 0.0710 0.0820 0.3535 0.3535 0.4033 0.5560 0.7704 0.8981 0.8981 0.6318 Appendix B 273 Table B.11: Displacement details for Fig 5.23b Composition routes and saturation and flow velocity profiles for displacement of a C4 /C10 mixture by CO2 at 1000 psia and 160◦ F with no volume change The viscosity ratio on the initial tie line is M = 8.319, and on the injection tie line, M = 10.68 The molar volumes used to convert mole fractions to volume fractions were CO2 , 308.685 cm3 /gmol, C4 , 104.509, C10 , 216.278 Phase compositions on the initial tie line (mole fractions): xCO2 = 0.4884, xC4 = 0.1651, xC10 = 0.3464, yCO2 = 0.9454, yC4 = 0.0514, yC10 = 0.0033 Phase compositions on the injection tie line (mole fractions): xCO2 = 0.4976, xC4 = 0., xC10 = 0.5024, yCO2 = 0.9964, yC4 = 0., yC10 = 0.0036 Compositions in the table are reported in mole fractions Segment Injection Gas Trailing Shock Injection Tie Line Rarefaction Constant State Intermediate Shock Initial Tie Line Rarefaction Leading Shock Initial Oil Point f f e d-e d-e d d c c-b c-b c-b c-b b a a CO2 1.0000 1.0000 0.8974 0.8831 0.8721 0.8566 0.8566 0.7208 0.7119 0.7028 0.6937 0.6713 0.6619 0 C4 0 0 0 0.1073 0.1095 0.1118 0.1140 0.1196 0.1219 0.2868 0.2868 C10 0 0.1026 0.1169 0.1279 0.1434 0.1434 0.1719 0.1786 0.1855 0.1923 0.2091 0.2161 0.7132 0.7132 S1 1.0000 1.0000 0.8260 0.8000 0.7800 0.7513 0.7513 0.5593 0.5400 0.5200 0.5000 0.4500 0.4288 0 Flow Vel 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 ξ/τ 1.0000 0.0573 0.0573 0.0723 0.0855 0.1076 0.5242 0.5242 0.5941 0.6753 0.7663 1.0429 1.1833 1.1833 1.0000 274 Appendix B Chapter 6–Four-Component Displacements Table B.12: Displacement details for Fig 6.7 and 6.8 (no volume change) Composition route (in volume fractions) for a displacement of an oil with composition a, C1 = 0, C2 = 0, C3 = 0.491852, and C4 = 0.508148 by gas with composition f, C1 = 0.625, C2 = 0.375, C3 = 0, and C4 = K-values are constant: K1 = 2.5, K2 = 1.5, K3 = 0.5, and K4 = 05 µliq /µvap = Segment Injection Gas Trailing Shock Zone of Constant State Intermediate Shock Crossover Tie Line Rarefaction Intermediate Shock Zone of Constant State Leading Shock Initial Oil Point f f e e e e d d d-c d-c d-c d-c d-c d-c d-c c c b b b b a a C1 0.6250 0.6250 0.5442 0.5442 0.5442 0.5442 0.3695 0.3695 0.3680 0.3650 0.3620 0.3590 0.3560 0.3530 0.3500 0.3489 0.3489 0.4904 0.4904 0.4904 0.4904 0.0000 0.0000 C2 0.3750 0.3750 0.3477 0.3477 0.3477 0.3477 0.2784 0.2784 0.2778 0.2768 0.2757 0.2746 0.2735 0.2724 0.2713 0.2709 0.2709 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 C3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2316 0.2316 0.2324 0.2340 0.2356 0.2372 0.2388 0.2404 0.2421 0.2427 0.2427 0.3034 0.3034 0.3034 0.3034 0.4918 0.4918 C4 0.0000 0.0000 0.1081 0.1081 0.1081 0.1081 0.1205 0.1205 0.1218 0.1242 0.1267 0.1292 0.1316 0.1341 0.1366 0.1375 0.1375 0.2062 0.2062 0.2062 0.2062 0.5081 0.5081 S1 1.0000 1.0000 0.8304 0.8304 0.8304 0.8304 0.5651 0.5651 0.5600 0.5500 0.5400 0.5300 0.5200 0.5100 0.5000 0.4963 0.4963 0.3550 0.3550 0.3550 0.3550 0.0000 0.0000 Flow Vel 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 ξ/τ 1.0000 0.2741 0.2454 0.2454 0.7707 0.7707 0.7707 0.7707 0.7940 0.8415 0.8911 0.9429 0.9968 1.0529 1.1111 1.1334 1.1334 1.1334 1.1334 1.2421 1.2421 1.2421 1.0000 Appendix B 275 Table B.13: Displacement details for Fig 6.9 and 6.10 (no volume change) Composition route for a displacement of an oil with composition C1 = 0.1, C2 = 0.1809, C3 = 0.3766, and C4 = 0.3425 by pure CH4 , C1 = K-values are constant: K1 = 2.5, K2 = 1.5, K3 = 0.5, and K4 = 05 The viscosity ratio, µliq /µvap , is Segment Injection Gas Trailing Shock Zone of Constant State Intermediate Shock Nontie-Line Rarefaction Tie-line Rarefaction Leading Shock Initial Oil Point f f e e e e d d d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c c c c-b c-b c-b b b a a CH4 1.0000 1.0000 0.8788 0.8788 0.8788 0.8788 0.6370 0.6370 0.6358 0.6025 0.5719 0.5437 0.5179 0.4942 0.4725 0.4528 0.4349 0.4188 0.4043 0.3915 0.3803 0.3706 0.3625 0.3558 0.3506 0.3472 0.3472 0.3440 0.3410 0.3380 0.3360 0.3360 0.1000 0.1000 C2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0011 0.0356 0.0674 0.0962 0.1225 0.1462 0.1677 0.1869 0.2040 0.2190 0.2321 0.2432 0.2524 0.2598 0.2652 0.2688 0.2705 0.2703 0.2703 0.2692 0.2681 0.2670 0.2663 0.2663 0.1809 0.1809 C3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2471 0.2471 0.2470 0.2451 0.2435 0.2420 0.2408 0.2398 0.2390 0.2384 0.2381 0.2379 0.2379 0.2381 0.2384 0.2391 0.2399 0.2409 0.2422 0.2436 0.2436 0.2453 0.2469 0.2485 0.2496 0.2496 0.3766 0.3766 C4 0.0000 0.0000 0.1212 0.1212 0.1212 0.1212 0.1160 0.1160 0.1160 0.1166 0.1173 0.1180 0.1188 0.1198 0.1208 0.1218 0.1230 0.1243 0.1257 0.1272 0.1288 0.1305 0.1324 0.1345 0.1367 0.1389 0.1389 0.1415 0.1440 0.1465 0.1481 0.1481 0.3425 0.3425 S1 1.0000 1.0000 0.8442 0.8442 0.8442 0.8442 0.6603 0.6603 0.6600 0.6500 0.6400 0.6300 0.6200 0.6100 0.6000 0.5900 0.5800 0.5700 0.5600 0.5500 0.5400 0.5300 0.5200 0.5100 0.5000 0.4908 0.4908 0.4800 0.4700 0.4600 0.4533 0.4533 0.0000 0.0000 Flow Vel 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 ξ/τ 1.0000 0.2850 0.2850 0.2850 0.7840 0.7840 1.1088 1.1088 1.1090 1.1140 1.1191 1.1241 1.1290 1.1337 1.1382 1.1426 1.1467 1.1506 1.1541 1.1573 1.1600 1.1624 1.1643 1.1657 1.1665 1.1668 1.1668 1.2337 1.2978 1.3638 1.4085 1.4085 1.4085 1.0000 276 Appendix B Chapter 7–Multicomponent Displacements Table B.14: Displacement details for Fig 7.5 (no volume change) Composition route for a displacement of an oil with composition CO2 = 0.005, CH4 = 0.350, C4 = 0.250, C10 = 0.195, C16 = 0.125, and C20 = 0.075 by pure CO2 Phase behavior calculated with the Peng-Robinson EOS (see Tables 3.1 and 3.2) Segment Injection Gas Trailing Shock Zone of Constant State Intermediate Shock Zone of Constant State Intermediate Shock Zone of Constant State Intermediate Shock Tie-Line Rarefaction Intermediate Shock Zone of Constant State Leading Shock Initial Oil Point h h g g g g f f f f e e e e d d c c b b b b a a CO2 1.0000 1.0000 0.9804 0.9804 0.9804 0.9804 0.9615 0.9615 0.9615 0.9615 0.9224 0.9224 0.9224 0.9224 0.8011 0.8011 0.7789 0.7789 0.0055 0.0055 0.0055 0.0055 0.0050 0.0050 CH4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.4399 0.4399 0.4399 0.4399 0.3500 0.3500 C4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1048 0.1048 0.1119 0.1119 0.2211 0.2211 0.2211 0.2211 0.2500 0.2500 C10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0398 0.0398 0.0398 0.0398 0.0481 0.0481 0.0554 0.0554 0.1648 0.1648 0.1648 0.1648 0.1950 0.1950 C16 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0246 0.0246 0.0246 0.0246 0.0236 0.0236 0.0236 0.0236 0.0289 0.0289 0.0336 0.0336 0.1055 0.1055 0.1055 0.1055 0.1250 0.1250 C20 0.0000 0.0000 0.0196 0.0196 0.0196 0.0196 0.0139 0.0139 0.0139 0.0139 0.0141 0.0141 0.0141 0.0141 0.0172 0.0172 0.0200 0.0200 0.0633 0.0633 0.0633 0.0633 0.0750 0.0750 S1 1.0000 1.0000 0.9148 0.9148 0.9148 0.9148 0.8548 0.8548 0.8548 0.8548 0.7476 0.7476 0.7476 0.7476 0.5074 0.5074 0.4292 0.4292 0.1359 0.1359 0.1359 0.1359 0.0000 0.0000 Flow Vel 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 ξ/τ 1.0000 0.0091 0.0091 0.0091 0.0188 0.0188 0.0188 0.0188 0.1083 0.1083 0.1083 0.1083 0.6755 0.6755 0.6755 0.6755 1.2046 1.2046 1.2046 1.2046 2.0237 2.0237 2.0237 1.0000 Appendix B 277 Table B.15: Displacement details for Fig 7.6 (no volume change) Composition route for a displacement of an oil B in Table 7.2 by Gas C in Table 7.2 Phase behavior calculated with the Peng-Robinson EOS (see Tables 3.1 and 3.2) Volume fractions reported are those for the components shown in Fig 7.6 Segment Injection Gas Trailing Shock Shock 14 Shock 13 Shock 12 Shock 11 Shock 10 Shock Shock Shock Shock Shock Shock Shock Shock Shock Initial Oil Point 14 14 13 13 12 12 11 11 10 10 9 8 7 6 5 4 3 2 1 CO2 0.0240 0.0240 0.0238 0.0238 0.0237 0.0237 0.0235 0.0235 0.0232 0.0232 0.0230 0.0230 0.0229 0.0229 0.0229 0.0228 0.0228 0.0228 0.0226 0.0226 0.0226 0.0226 0.0228 0.0228 0.0233 0.0233 0.0160 0.0160 0.0160 0.0160 0.0150 0.0150 CH4 0.8011 0.8011 0.7895 0.7895 0.7787 0.7787 0.7511 0.7511 0.7237 0.7237 0.6995 0.6995 0.6916 0.6916 0.6827 0.6784 0.6737 0.6737 0.6554 0.6554 0.6508 0.6508 0.6365 0.6365 0.6423 0.6423 0.6460 0.6460 0.6367 0.6367 0.4600 0.4600 C2 0.0708 0.0708 0.0709 0.0709 0.0712 0.0712 0.0719 0.0719 0.0725 0.0725 0.0732 0.0732 0.0734 0.0734 0.0736 0.0737 0.0738 0.0738 0.0744 0.0744 0.0745 0.0745 0.0760 0.0760 0.0468 0.0468 0.0469 0.0469 0.0469 0.0469 0.0500 0.0500 C5 0.0117 0.0117 0.0129 0.0129 0.0139 0.0139 0.0166 0.0166 0.0194 0.0194 0.0219 0.0219 0.0227 0.0227 0.0237 0.0241 0.0245 0.0245 0.0187 0.0187 0.0195 0.0195 0.0239 0.0239 0.0256 0.0256 0.0258 0.0258 0.0261 0.0261 0.0400 0.0400 C9 0.0017 0.0017 0.0025 0.0025 0.0033 0.0033 0.0060 0.0060 0.0119 0.0119 0.0331 0.0331 0.0336 0.0336 0.0354 0.0366 0.0380 0.0380 0.0457 0.0457 0.0485 0.0485 0.0655 0.0655 0.0724 0.0724 0.0734 0.0734 0.0748 0.0748 0.1300 0.1300 C20 0.0000 0.0000 0.0072 0.0072 0.0037 0.0037 0.0033 0.0033 0.0033 0.0033 0.0037 0.0037 0.0040 0.0040 0.0043 0.0045 0.0047 0.0047 0.0059 0.0059 0.0064 0.0064 0.0094 0.0094 0.0106 0.0106 0.0108 0.0108 0.0110 0.0110 0.0200 0.0200 S1 1.0000 1.0000 0.9463 0.9463 0.9105 0.9105 0.8249 0.8249 0.7391 0.7391 0.6474 0.6474 0.6156 0.6156 0.5789 0.5606 0.5405 0.5405 0.4576 0.4576 0.4340 0.4340 0.3261 0.3261 0.2952 0.2952 0.2911 0.2911 0.2839 0.2839 0.0000 0.0000 Flow Vel 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 ξ/τ 1.0000 0.1323 0.1323 0.1819 0.1819 0.2616 0.2616 0.3103 0.3103 0.3439 0.3439 0.4175 0.4175 0.4899 0.4899 0.5719 0.5719 0.6555 0.6555 0.7632 0.7632 0.8923 0.8923 1.0263 1.0263 1.1088 1.1088 1.4111 1.4111 1.7069 1.7069 1.0000 278 Appendix B Table B.16: Displacement details for Fig 7.7 (no volume change) Composition route for a displacement of an oil with composition N2 = 0.005, CH4 = 0.350, C4 = 0.250, C10 = 0.195, C16 = 0.125, and C20 = 0.075 by pure CO2 Phase behavior calculated with the Peng-Robinson EOS (see Tables 3.1 and 3.2) Segment Injection Gas Trailing Shock Zone of Constant State Intermediate Shock Zone of Constant State Intermediate Shock Zone of Constant State Intermediate Shock Zone of Constant State Rarefaction Rarefaction Leading Shock Initial Oil Point f f f f e e e e d d d d d-c d-c c c b b a a N2 1.0000 1.0000 0.9808 0.9808 0.9808 0.9808 0.9475 0.9475 0.9475 0.9475 0.8855 0.8855 0.8855 0.8855 0.7907 0.7907 0.7907 0.7907 0.3839 0.1502 0.0145 0.0145 0.0142 0.0142 0.0050 0.0050 CH4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.4049 0.6306 0.7295 0.7295 0.7221 0.7221 0.3500 0.3500 C4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0964 0.0964 0.0964 0.0964 0.1031 0.1097 0.1240 0.1240 0.1265 0.1265 0.2500 0.2500 C10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0581 0.0581 0.0581 0.0581 0.0572 0.0572 0.0572 0.0572 0.0554 0.0567 0.0689 0.0689 0.0711 0.0711 0.1950 0.1950 C16 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0365 0.0365 0.0365 0.0365 0.0389 0.0389 0.0389 0.0389 0.0384 0.0384 0.0384 0.0384 0.0364 0.0365 0.0438 0.0438 0.0456 0.0456 0.1250 0.1250 C20 0.0000 0.0000 0.0192 0.0192 0.0192 0.0192 0.0160 0.0160 0.0160 0.0160 0.0175 0.0175 0.0175 0.0175 0.0173 0.0173 0.0173 0.0173 0.0164 0.0164 0.0196 0.0196 0.0204 0.0204 0.0750 0.0750 S1 1.0000 1.0000 0.9344 0.9344 0.9344 0.9344 0.8558 0.8558 0.8558 0.8558 0.7614 0.7614 0.7614 0.7614 0.6954 0.6954 0.6954 0.6954 0.6500 0.5518 0.3849 0.3849 0.3626 0.3626 0.0000 0.0000 Flow Vel 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 ξ/τ 1.0000 0.0003 0.0003 0.0003 0.0011 0.0011 0.0011 0.0011 0.0190 0.0190 0.0190 0.0190 0.4622 0.4622 0.4622 0.4622 1.1980 1.1980 1.2999 1.3998 1.5047 1.5047 1.7323 1.7323 1.7323 1.0000 Appendix B 279 Table B.17: Displacement details for Fig 7.9 (with volume change) Composition route for a displacement of an oil with composition CO2 = 0.005, CH4 = 0.350, C4 = 0.250, C10 = 0.195, C16 = 0.125, and C20 = 0.075 by pure CO2 Phase behavior calculated with the Peng-Robinson EOS (see Tables 3.1 and 3.2) Segment Injection Gas Trailing Shock Zone of Constant State Intermediate Shock Zone of Constant State Intermediate Shock Zone of Constant State Intermediate Shock Tie-Line Rarefaction Intermediate Shock Zone of Constant State Leading Shock Initial Oil Point h h g g g g f f f f e e e e d d c c b b b b a a CO2 1.0000 1.0000 0.9714 0.9714 0.9714 0.9714 0.9452 0.9452 0.9452 0.9452 0.8969 0.8969 0.8969 0.8969 0.7826 0.7826 0.7595 0.7595 0.0054 0.0054 0.0054 0.0054 0.0050 0.0050 CH4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.4299 0.4299 0.4299 0.4299 0.3500 0.3500 C4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1108 0.1108 0.1182 0.1182 0.2243 0.2243 0.2243 0.2243 0.2500 0.2500 C10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0523 0.0523 0.0523 0.0523 0.0542 0.0542 0.0619 0.0619 0.1681 0.1681 0.1681 0.1681 0.1950 0.1950 C16 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0350 0.0350 0.0350 0.0350 0.0318 0.0318 0.0318 0.0318 0.0329 0.0329 0.0378 0.0378 0.1076 0.1076 0.1076 0.1076 0.1250 0.1250 C20 0.0000 0.0000 0.0286 0.0286 0.0286 0.0286 0.0198 0.0198 0.0198 0.0198 0.0190 0.0190 0.0190 0.0190 0.0196 0.0196 0.0226 0.0226 0.0646 0.0646 0.0646 0.0646 0.0750 0.0750 S1 1.0000 1.0000 0.9052 0.9052 0.9052 0.9052 0.8432 0.8432 0.8432 0.8432 0.7434 0.7434 0.7434 0.7434 0.5332 0.5332 0.4496 0.4496 0.1576 0.1576 0.1576 0.1576 0.0000 0.0000 Flow Vel 1.0000 1.0000 0.9979 0.9979 0.9979 0.9979 0.9954 0.9954 0.9954 0.9954 0.9808 0.9808 0.9808 0.9808 0.9798 0.9798 0.9798 0.9798 0.8879 0.8879 0.8879 0.8879 0.8572 0.8572 ξ/τ 1.0000 0.0061 0.0061 0.0061 0.0127 0.0127 0.0127 0.0127 0.0750 0.0750 0.0750 0.0750 0.5376 0.5376 0.5376 0.5376 1.0228 1.0228 1.0228 1.0228 1.9081 1.9081 1.9081 1.0000 Index volume change, 61 multicomponent no volume change, 13 volume change, 12 quaternary no volume change, 135 ternary no volume change, 75, 77 volume change, 120 constant K-value, 37–40, 78, 79, 131 quaternary, 41, 138–149 ternary, 40, 84–87, 93–96, 132, 133 continuity equation, convection, convection-dispersion equation, 15, 16 Courant, 43 Crane, 238 critical locus, 37 critical point, 36–38 critical tie line, 118, 119, 130, 206–208, 210, 212 Abbot, 40 Abbott, 22 Amundson, 2, 43, 70 Aris, 2, 43, 70 Aziz, ii Batycky, ii, 238 Bedrikovetsky, 70, 130, 176 binodal curve, 36 binodal surface, 37 Blunt, ii, 238 boundary condition, 14 Braun, 74 Buckley, 53, 70 capillary pressure, Cer´, 130 e characteristics, 47 chemical potential, 10, 25 Chumak, 176 coherence, 80 component recovery, 67–69, 127–129 composition path, 75, 80, 83, 84 geometry, 87 nontie line, 84 nontie-line liquid locus, 82 vapor locus, 82 tie-line, 81 compositional simulation, 155, 176, 213–230, 235–237 condensing gas drive, 2, 73–75, 106–114, 119, 130, 132, 133 condensing/vaporizing gas drive, 3, 135, 155– 158, 161, 164, 168, 170, 176, 212 conservation equations, 5–13 binary no volume change, 44 Dake, 43, 70 Datta-Gupta, 238 diffusion, 5, 7, 9, 175 dilution line, 36, 73, 74, 102, 108, 218, 223, 225–228, 230 Dindoruk, i, 40, 70, 74, 127, 130, 172, 176, 187, 199, 212 dispersion, 3, 5–7, 12, 51, 175 numerical, 3, 213, 216–218, 221–230 dispersive distance, 223–230, 236, 238 divergence theorem, Dumor´, 74, 130 e eigenvalue nontie-line, 79, 188, 255, 256, 258 tie-line, 79, 193, 255, 256, 258 280 Index eigenvalue problem quaternary no volume change, 136 volume change, 171 ternary, 86 no volume change, 78 volume change, 120 eigenvector nontie-line, 80 tie-line, 80, 81 enhanced oil recovery, enthalpy, 22, 23 entropy, 22, 23 entropy condition, 52, 54, 58, 64, 69, 92, 98– 99, 108, 121, 255–265 envelope curve, 78, 79, 93–95, 187–193, 256 equal eigenvalue point, 83, 87, 88, 102, 111, 142, 149, 151, 185, 186, 198, 199, 258 equation of state, 21, 24, 26–28, 30, 31, 40, 150 Peng-Robinson, 28, 36, 39, 84, 150, 152, 154, 162, 218, 231 Redlich-Kwong, 41, 150, 231 van der Waals, 27, 28, 32, 35 equivelocity curve, 82, 83, 102, 119, 160 Ermakov, i, 212 flow velocity, 13 fractional flow functions, 11 fugacity, 25, 41 coefficient, 25 partial, 25–27, 31 coefficient, 26, 27, 33 Gerritsen, ii Gibbs, 21 Gibbs function, 22 gravity segregation, 175 Haajizadeh, 230, 238 Hand’s rule, 96 Hearn, 238 Helfferich, i, 70, 80, 130, 176 Helmholtz function, 22, 26 high volatility intermediate, 99, 101 Hilbert, 43 281 Hirasaki, i, 74, 130 Hutchinson, 74 HVI, 99 condensing, 106 vaporizing, 101, 147 vaporizing drive, 99 Høier, 226 initial condition, 14 Isaacson, 80 Jeffrey, 43 Jessen, i, 184, 212, 225, 238 Johansen, i, 130, 176, 255 Johns, i, 3, 70, 74, 76, 130, 176, 212 jump condition, see shock, balance King, 238 Kuo, 238 LaForce, Lake, 2, 17, 40, 70, 73 Lantz, 214 Larson, 130 Lax, 80 lever rule, 34 Leverett, 53, 70 local equilibrium assumption, low volatility intermediate, 103, 105, 221, 259 Luks, 238 LVI, 95 condensing, 109, 265 vaporizing, 103, 105, 258 Mallison, 214 Maxwell relations, 23 Metcalfe, 36, 38, 238 methane bank, 148, 152, 163, 174, 196, 201, 204 Michelsen, 27, 33, 238 minimum enrichment for miscibility, 119, 161 minimum miscibility pressure, 3, 120, 213, 217 calculation of compositional simulation, 235–238 key tie line method, 161–171, 206–210, 236 mixing cell, 230–233, 238 282 miscibility development of, see miscibility, multicontact multicontact, 2, 117–120, 158–161, 206 condensing, 119 condensing/vaporizing, 164 multicomponent, 206, 212 vaporizing, 118–119 mixing cell, 73, 210, 213, 230–233 MME, 119, 160, 161, 207, 213, 217, 230 MMP, 120, 160, 207, 213, 217, 226, 230, 233 molar density, 13 Mollerup, 27 Monroe, i, 176 negative flash, 33, 110, 152 no volume change on mixing, 13–14, 43 overall fractional flow, 14 overall molar concentration, 12 overall molar flow rate, 12 overall volume fraction, 13 Pande, i, 70, 130 path, 80 equivelocity curve, 83 geometry, 87 nontie-line, 87, 88, 93, 122, 137, 142, 149, 150, 185–193, 198 differential equation, 86 liquid locus, 82 vapor locus, 82 tie-line, 81, 87, 88, 137 path switch, 87–91, 102, 110, 114, 142, 185 Peaceman, 214 Peck, 230, 238 Peclet number, 15–17, 214, 215, 218 Pedersen, 238 plait point, 36, 37 Pope, i pressure gradient, 11, 21 Prudhoe Bay, Rankine-Hugoniot condition, see shock, balance rarefaction, 55, 75, 89, 93, 96, 221 Index nontie-line, 83, 94, 102, 103, 106, 109–111, 114, 118, 119, 122, 145, 146, 149, 155, 187, 198 tie line, 201 tie-line, 94, 102, 103, 106, 108, 110, 114, 117, 125, 147–149, 155, 185, 193, 196 Ratchford-Rice equation, 33 Reamer, 35 relative permeability functions, 45, 175 Reynolds transport theorem, Rhee, 2, 43, 70 Riemann problem, 54, 74, 80–82, 87, 89 Sage, 35 self similarity, 80 self-sharpening, 52, 69, 93, 94, 97, 98, 106, 107, 110, 117, 119, 130, 187, 210, 221, 255, 256, 258 fully, 121, 147, 152, 158, 180, 193–198 self-similar, 221 semishock, 52, 53, 56–58, 60, 64, 70, 92, 99, 102, 103, 106, 108, 110, 111, 114, 117, 125, 132, 147, 193, 196, 201, 256, 257 nontie-line, 151 Seto, 221, 238 shock, 43, 48 balance, 50, 63, 92, 103, 111, 145, 151, 158, 160, 163, 181, 202 evaporation, 56, 60, 65, 148, 152, 196 genuine, 103, 106, 108, 110, 111, 114, 117, 146–148, 196, 257 intermediate, see shock, nontie-line nontie-line, 92–99, 114, 119, 145, 146, 155, 160, 163, 187 phase-change, 48–55, 90–92, 121, 122 stability, 51, 52, 255 tangent, see semishock, 257 tie-line, 48–55, 64, 90–92, 121, 146–148, 152, 196 two-phase, 90, 92–98, 110, 112 velocity, 52, 106, 119 Silva, 36, 38 slim tube, 218 slim tube displacement, 16, 165, 173, 174, 210, 218 Index spreading wave, 55 Stalkup, 176, 239 streamline simulation, 238 surface developable, 150 equivelocity, 160 rarefaction, 140, 150, 151 ruled, 151 shock, 140, 151 Thiele, ii, 238 tie line, 33, 34, 36, 37 critical, 118, 119, 130, 160, 164 crossover, 135, 144–148, 150–153, 155, 157, 158, 160–164, 167, 168, 170, 174, 175, 179–181, 187, 194, 196, 206, 208, 210– 212 equation of, 32 extension, 73, 92, 110, 121, 122 initial oil, 110, 152, 181, 194, 210 injection gas, 92, 110, 152, 181, 194, 210 intercept, 76, 93, 137 intersection, 96–98, 122, 147, 151, 152, 198, 258 key, 92, 98, 110, 111, 135, 144–147, 157, 158, 160, 161, 164, 167, 168, 171, 173, 175–177, 179, 198, 207, 212 calculation of, 180–184 parametrization, 76, 77 shortest, 110, 111, 145, 146, 148, 153, 157, 160, 161, 164, 167, 168, 175, 185, 187, 193, 194, 196, 201, 202, 226, 228 slope, 37, 76, 93, 137 van der Waals, 32 van Ness, 22, 40 vaporizing gas drive, 2, 73, 74, 99–106, 221 velocity constraint, 51, 52, 58, 69, 87–89, 91–94, 99, 102, 103, 106, 111, 117, 118, 121, 129, 142, 146, 148, 149, 175, 258 flow, 11, 45, 62–64, 121, 122 rule, see velocity constraint shock, 51, 63, 70 wave, 45, 51, 57, 59, 63–65, 69, 75, 78–81, 88, 90, 102 283 indifferent, 187 velocity constraint, 64 viscous fingering, 175 volume change on mixing, 13, 122, 125 binary, 61–65 multicomponent, 201–204, 218, 220 quaternary, 135, 171–175 ternary, 120–127 Wachman, 74, 130 Walas, 40 Walsh, 238 Wang, i, 74, 131, 176, 212, 230, 238, 255 Wattenbarger, ii wave centered, 55 expansion, 55 indifferent, 119 rarefaction, 55 spreading, 55, 57, 60 Welge, 53, 70, 74 Whitson, 33, 238 Wilson equation, 32 Wingard, i Winther, 255 Yarborough, 36, 38 Zanotti, 130 Zick, 155, 176, 226 zone of constant state, 53, 59, 88, 102, 114, 128, 129, 196 ... Shock Initial Oil Point f f e e e e d d d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c d-c c c c-b c-b c-b b b a a CH4 1.0000 1.0000 0.8788 0.8788 0.8788 0.8788 0.6370 0.6370... Segment Injection Gas Trailing Shock Zone of Constant State Intermediate Shock Nontie-Line Rarefaction Tie-line Rarefaction Leading Shock Initial Oil Point f f e e e e d d d-c d-c d-c d-c d-c d-c d-c... 102, 111, 142, 149, 151 , 185, 186, 198, 199, 258 equation of state, 21, 24, 26–28, 30, 31, 40, 150 Peng-Robinson, 28, 36, 39, 84, 150 , 152 , 154 , 162, 218, 231 Redlich-Kwong, 41, 150 , 231 van der