Orr, F. M. - Theory of Gas Injection Processes Episode 15 docx

Compositions reported in the table are in volume fractions... Table B.10: Displacement details for Fig.. Composition routes and saturation and flow velocity profiles for displacement of a

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): x CO2 = 0.8235, x C4 = 0.0874,

x C10 = 0.0891, y CO2 = 0.8833, y C4 = 0.0719, y C10 = 0.0285 Phase compositions on the injection

tie line (mole fractions): x CO2 = 0.6554, x C4 = 0., x C10 = 0.3446, y CO2 = 0.9817, y C4 = 0.,

y C10= 0.0448 Compositions reported in the table are in volume fractions.

Line Rarefaction c-b 0.8660 0.0764 0.0576 0.7100 1.0000 0.9981

Table B.10: Displacement details for Fig 5.23a Composition routes and saturation and flow velocity profiles for displacement of a C4/C10mixture 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, x C4 = 0.1651, x C10= 0.3464, y CO2 = 0.9454, y C4 = 0.0514, y C10 = 0.0033 Phase compositions on the injection tie line (mole fractions): x CO2 = 0.4976, x C4 = 0., x C10 = 0.5024,

yCO2 = 0.9964, y C4 = 0., y C10 = 0.0036 Compositions in the table are reported in mole fractions.

Line Rarefaction c-b 0.6368 0.1282 0.2350 0.5500 1.0054 0.5560

c-b 0.6175 0.1330 0.2495 0.5000 1.0054 0.7704

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): x CO2 = 0.4884, x C4 = 0.1651, x C10 = 0.3464, y CO2 = 0.9454, y C4 = 0.0514,

yC10 = 0.0033 Phase compositions on the injection tie line (mole fractions): x CO2 = 0.4976,

x C4 = 0., x C10 = 0.5024, y CO2 = 0.9964, y C4 = 0., y C10 = 0.0036 Compositions in the table are

reported in mole fractions

Line Rarefaction c-b 0.7028 0.1118 0.1855 0.5200 1.0000 0.6753

c-b 0.6937 0.1140 0.1923 0.5000 1.0000 0.7663

c-b 0.6713 0.1196 0.2091 0.4500 1.0000 1.0429

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 = 0

K-values are constant: K1 = 2.5, K2 = 1.5, K3 = 0.5, and K4= 05 µ liq /µ vap = 5

Constant State e 0.5442 0.3477 0.0000 0.1081 0.8304 1.0000 0.7707

d-c 0.3620 0.2757 0.2356 0.1267 0.5400 1.0000 0.8911

d-c 0.3590 0.2746 0.2372 0.1292 0.5300 1.0000 0.9429

d-c 0.3560 0.2735 0.2388 0.1316 0.5200 1.0000 0.9968

d-c 0.3530 0.2724 0.2404 0.1341 0.5100 1.0000 1.0529

d-c 0.3500 0.2713 0.2421 0.1366 0.5000 1.0000 1.1111

Constant State b 0.4904 0.0000 0.3034 0.2062 0.3550 1.0000 1.2421

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 = 1 K-values are constant: K1 = 2.5, K2 = 1.5, K3 = 0.5, and K4= 05 The

viscosity ratio, µ liq /µ vap, is 5

Constant State e 0.8788 0.0000 0.0000 0.1212 0.8442 1.0000 0.7840

d-c 0.6025 0.0356 0.2451 0.1166 0.6500 1.0000 1.1140

d-c 0.5719 0.0674 0.2435 0.1173 0.6400 1.0000 1.1191

d-c 0.5437 0.0962 0.2420 0.1180 0.6300 1.0000 1.1241

d-c 0.5179 0.1225 0.2408 0.1188 0.6200 1.0000 1.1290

d-c 0.4942 0.1462 0.2398 0.1198 0.6100 1.0000 1.1337

d-c 0.4725 0.1677 0.2390 0.1208 0.6000 1.0000 1.1382

d-c 0.4528 0.1869 0.2384 0.1218 0.5900 1.0000 1.1426

d-c 0.4349 0.2040 0.2381 0.1230 0.5800 1.0000 1.1467

d-c 0.4188 0.2190 0.2379 0.1243 0.5700 1.0000 1.1506

d-c 0.4043 0.2321 0.2379 0.1257 0.5600 1.0000 1.1541

d-c 0.3915 0.2432 0.2381 0.1272 0.5500 1.0000 1.1573

d-c 0.3803 0.2524 0.2384 0.1288 0.5400 1.0000 1.1600

d-c 0.3706 0.2598 0.2391 0.1305 0.5300 1.0000 1.1624

d-c 0.3625 0.2652 0.2399 0.1324 0.5200 1.0000 1.1643

d-c 0.3558 0.2688 0.2409 0.1345 0.5100 1.0000 1.1657

d-c 0.3506 0.2705 0.2422 0.1367 0.5000 1.0000 1.1665

c-b 0.3410 0.2681 0.2469 0.1440 0.4700 1.0000 1.2978

c-b 0.3380 0.2670 0.2485 0.1465 0.4600 1.0000 1.3638

Chapter 7–Multicomponent Displacements

Table B.14: Displacement details for Fig 7.5 (no volume change) Composition route for a dis-placement 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 Point CO2 CH4 C4 C10 C16 C20 S1 Flow Vel. ξ/τ

Injection Gas h 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000 Trailing h 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 0.0091 Shock g 0.9804 0.0000 0.0000 0.0000 0.0000 0.0196 0.9148 1.0000 0.0091 Zone of g 0.9804 0.0000 0.0000 0.0000 0.0000 0.0196 0.9148 1.0000 0.0091 Constant State g 0.9804 0.0000 0.0000 0.0000 0.0000 0.0196 0.9148 1.0000 0.0188 Intermediate g 0.9804 0.0000 0.0000 0.0000 0.0000 0.0196 0.9148 1.0000 0.0188 Shock f 0.9615 0.0000 0.0000 0.0000 0.0246 0.0139 0.8548 1.0000 0.0188 Zone of f 0.9615 0.0000 0.0000 0.0000 0.0246 0.0139 0.8548 1.0000 0.0188 Constant State f 0.9615 0.0000 0.0000 0.0000 0.0246 0.0139 0.8548 1.0000 0.1083 Intermediate f 0.9615 0.0000 0.0000 0.0000 0.0246 0.0139 0.8548 1.0000 0.1083 Shock e 0.9224 0.0000 0.0000 0.0398 0.0236 0.0141 0.7476 1.0000 0.1083 Zone of e 0.9224 0.0000 0.0000 0.0398 0.0236 0.0141 0.7476 1.0000 0.1083 Constant State e 0.9224 0.0000 0.0000 0.0398 0.0236 0.0141 0.7476 1.0000 0.6755 Intermediate e 0.9224 0.0000 0.0000 0.0398 0.0236 0.0141 0.7476 1.0000 0.6755 Shock d 0.8011 0.0000 0.1048 0.0481 0.0289 0.0172 0.5074 1.0000 0.6755 Tie-Line d 0.8011 0.0000 0.1048 0.0481 0.0289 0.0172 0.5074 1.0000 0.6755 Rarefaction c 0.7789 0.0000 0.1119 0.0554 0.0336 0.0200 0.4292 1.0000 1.2046 Intermediate c 0.7789 0.0000 0.1119 0.0554 0.0336 0.0200 0.4292 1.0000 1.2046 Shock b 0.0055 0.4399 0.2211 0.1648 0.1055 0.0633 0.1359 1.0000 1.2046 Zone of b 0.0055 0.4399 0.2211 0.1648 0.1055 0.0633 0.1359 1.0000 1.2046 Constant State b 0.0055 0.4399 0.2211 0.1648 0.1055 0.0633 0.1359 1.0000 2.0237 Leading b 0.0055 0.4399 0.2211 0.1648 0.1055 0.0633 0.1359 1.0000 2.0237 Shock a 0.0050 0.3500 0.2500 0.1950 0.1250 0.0750 0.0000 1.0000 2.0237 Initial Oil a 0.0050 0.3500 0.2500 0.1950 0.1250 0.0750 0.0000 1.0000 1.0000

Table B.15: Displacement details for Fig 7.6 (no volume change) Composition route for a dis-placement 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 compo-nents shown in Fig 7.6

Segment Point CO2 CH4 C2 C5 C9 C20 S1 Flow Vel. ξ/τ

Injection Gas 0.0240 0.8011 0.0708 0.0117 0.0017 0.0000 1.0000 1.0000 1.0000 Trailing 0.0240 0.8011 0.0708 0.0117 0.0017 0.0000 1.0000 1.0000 0.1323 Shock 0.0238 0.7895 0.0709 0.0129 0.0025 0.0072 0.9463 1.0000 0.1323 Shock 14 14 0.0238 0.7895 0.0709 0.0129 0.0025 0.0072 0.9463 1.0000 0.1819

14 0.0237 0.7787 0.0712 0.0139 0.0033 0.0037 0.9105 1.0000 0.1819 Shock 13 13 0.0237 0.7787 0.0712 0.0139 0.0033 0.0037 0.9105 1.0000 0.2616

13 0.0235 0.7511 0.0719 0.0166 0.0060 0.0033 0.8249 1.0000 0.2616 Shock 12 12 0.0235 0.7511 0.0719 0.0166 0.0060 0.0033 0.8249 1.0000 0.3103

12 0.0232 0.7237 0.0725 0.0194 0.0119 0.0033 0.7391 1.0000 0.3103 Shock 11 11 0.0232 0.7237 0.0725 0.0194 0.0119 0.0033 0.7391 1.0000 0.3439

11 0.0230 0.6995 0.0732 0.0219 0.0331 0.0037 0.6474 1.0000 0.3439 Shock 10 10 0.0230 0.6995 0.0732 0.0219 0.0331 0.0037 0.6474 1.0000 0.4175

10 0.0229 0.6916 0.0734 0.0227 0.0336 0.0040 0.6156 1.0000 0.4175 Shock 9 9 0.0229 0.6916 0.0734 0.0227 0.0336 0.0040 0.6156 1.0000 0.4899

9 0.0229 0.6827 0.0736 0.0237 0.0354 0.0043 0.5789 1.0000 0.4899 Shock 8 8 0.0228 0.6784 0.0737 0.0241 0.0366 0.0045 0.5606 1.0000 0.5719

8 0.0228 0.6737 0.0738 0.0245 0.0380 0.0047 0.5405 1.0000 0.5719 Shock 7 7 0.0228 0.6737 0.0738 0.0245 0.0380 0.0047 0.5405 1.0000 0.6555

7 0.0226 0.6554 0.0744 0.0187 0.0457 0.0059 0.4576 1.0000 0.6555 Shock 6 6 0.0226 0.6554 0.0744 0.0187 0.0457 0.0059 0.4576 1.0000 0.7632

6 0.0226 0.6508 0.0745 0.0195 0.0485 0.0064 0.4340 1.0000 0.7632 Shock 5 5 0.0226 0.6508 0.0745 0.0195 0.0485 0.0064 0.4340 1.0000 0.8923

5 0.0228 0.6365 0.0760 0.0239 0.0655 0.0094 0.3261 1.0000 0.8923 Shock 4 4 0.0228 0.6365 0.0760 0.0239 0.0655 0.0094 0.3261 1.0000 1.0263

4 0.0233 0.6423 0.0468 0.0256 0.0724 0.0106 0.2952 1.0000 1.0263 Shock 3 3 0.0233 0.6423 0.0468 0.0256 0.0724 0.0106 0.2952 1.0000 1.1088

3 0.0160 0.6460 0.0469 0.0258 0.0734 0.0108 0.2911 1.0000 1.1088 Shock 2 2 0.0160 0.6460 0.0469 0.0258 0.0734 0.0108 0.2911 1.0000 1.4111

2 0.0160 0.6367 0.0469 0.0261 0.0748 0.0110 0.2839 1.0000 1.4111 Shock 1 1 0.0160 0.6367 0.0469 0.0261 0.0748 0.0110 0.2839 1.0000 1.7069

1 0.0150 0.4600 0.0500 0.0400 0.1300 0.0200 0.0000 1.0000 1.7069 Initial Oil 0.0150 0.4600 0.0500 0.0400 0.1300 0.0200 0.0000 1.0000 1.0000

Table B.16: Displacement details for Fig 7.7 (no volume change) Composition route for a dis-placement 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 Point N2 CH4 C4 C10 C16 C20 S1 Flow Vel. ξ/τ

Injection Gas 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000 Trailing 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 0.0003 Shock 0.9808 0.0000 0.0000 0.0000 0.0000 0.0192 0.9344 1.0000 0.0003 Zone of 0.9808 0.0000 0.0000 0.0000 0.0000 0.0192 0.9344 1.0000 0.0003 Constant State 0.9808 0.0000 0.0000 0.0000 0.0000 0.0192 0.9344 1.0000 0.0011 Intermediate 0.9808 0.0000 0.0000 0.0000 0.0000 0.0192 0.9344 1.0000 0.0011 Shock f 0.9475 0.0000 0.0000 0.0000 0.0365 0.0160 0.8558 1.0000 0.0011 Zone of f 0.9475 0.0000 0.0000 0.0000 0.0365 0.0160 0.8558 1.0000 0.0011 Constant State f 0.9475 0.0000 0.0000 0.0000 0.0365 0.0160 0.8558 1.0000 0.0190 Intermediate f 0.9475 0.0000 0.0000 0.0000 0.0365 0.0160 0.8558 1.0000 0.0190 Shock e 0.8855 0.0000 0.0000 0.0581 0.0389 0.0175 0.7614 1.0000 0.0190 Zone of e 0.8855 0.0000 0.0000 0.0581 0.0389 0.0175 0.7614 1.0000 0.0190 Constant State e 0.8855 0.0000 0.0000 0.0581 0.0389 0.0175 0.7614 1.0000 0.4622 Intermediate e 0.8855 0.0000 0.0000 0.0581 0.0389 0.0175 0.7614 1.0000 0.4622 Shock d 0.7907 0.0000 0.0964 0.0572 0.0384 0.0173 0.6954 1.0000 0.4622 Zone of d 0.7907 0.0000 0.0964 0.0572 0.0384 0.0173 0.6954 1.0000 0.4622 Constant State d 0.7907 0.0000 0.0964 0.0572 0.0384 0.0173 0.6954 1.0000 1.1980 Rarefaction d 0.7907 0.0000 0.0964 0.0572 0.0384 0.0173 0.6954 1.0000 1.1980

d-c 0.3839 0.4049 0.1031 0.0554 0.0364 0.0164 0.6500 1.0000 1.2999

d-c 0.1502 0.6306 0.1097 0.0567 0.0365 0.0164 0.5518 1.0000 1.3998

c 0.0145 0.7295 0.1240 0.0689 0.0438 0.0196 0.3849 1.0000 1.5047 Rarefaction c 0.0145 0.7295 0.1240 0.0689 0.0438 0.0196 0.3849 1.0000 1.5047

b 0.0142 0.7221 0.1265 0.0711 0.0456 0.0204 0.3626 1.0000 1.7323 Leading b 0.0142 0.7221 0.1265 0.0711 0.0456 0.0204 0.3626 1.0000 1.7323 Shock a 0.0050 0.3500 0.2500 0.1950 0.1250 0.0750 0.0000 1.0000 1.7323 Initial Oil a 0.0050 0.3500 0.2500 0.1950 0.1250 0.0750 0.0000 1.0000 1.0000

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 Point CO2 CH4 C4 C10 C16 C20 S1 Flow Vel. ξ/τ

Injection Gas h 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000 Trailing h 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 0.0061 Shock g 0.9714 0.0000 0.0000 0.0000 0.0000 0.0286 0.9052 0.9979 0.0061 Zone of g 0.9714 0.0000 0.0000 0.0000 0.0000 0.0286 0.9052 0.9979 0.0061 Constant State g 0.9714 0.0000 0.0000 0.0000 0.0000 0.0286 0.9052 0.9979 0.0127 Intermediate g 0.9714 0.0000 0.0000 0.0000 0.0000 0.0286 0.9052 0.9979 0.0127 Shock f 0.9452 0.0000 0.0000 0.0000 0.0350 0.0198 0.8432 0.9954 0.0127 Zone of f 0.9452 0.0000 0.0000 0.0000 0.0350 0.0198 0.8432 0.9954 0.0127 Constant State f 0.9452 0.0000 0.0000 0.0000 0.0350 0.0198 0.8432 0.9954 0.0750 Intermediate f 0.9452 0.0000 0.0000 0.0000 0.0350 0.0198 0.8432 0.9954 0.0750 Shock e 0.8969 0.0000 0.0000 0.0523 0.0318 0.0190 0.7434 0.9808 0.0750 Zone of e 0.8969 0.0000 0.0000 0.0523 0.0318 0.0190 0.7434 0.9808 0.0750 Constant State e 0.8969 0.0000 0.0000 0.0523 0.0318 0.0190 0.7434 0.9808 0.5376 Intermediate e 0.8969 0.0000 0.0000 0.0523 0.0318 0.0190 0.7434 0.9808 0.5376 Shock d 0.7826 0.0000 0.1108 0.0542 0.0329 0.0196 0.5332 0.9798 0.5376 Tie-Line d 0.7826 0.0000 0.1108 0.0542 0.0329 0.0196 0.5332 0.9798 0.5376 Rarefaction c 0.7595 0.0000 0.1182 0.0619 0.0378 0.0226 0.4496 0.9798 1.0228 Intermediate c 0.7595 0.0000 0.1182 0.0619 0.0378 0.0226 0.4496 0.9798 1.0228 Shock b 0.0054 0.4299 0.2243 0.1681 0.1076 0.0646 0.1576 0.8879 1.0228 Zone of b 0.0054 0.4299 0.2243 0.1681 0.1076 0.0646 0.1576 0.8879 1.0228 Constant State b 0.0054 0.4299 0.2243 0.1681 0.1076 0.0646 0.1576 0.8879 1.9081 Leading b 0.0054 0.4299 0.2243 0.1681 0.1076 0.0646 0.1576 0.8879 1.9081 Shock a 0.0050 0.3500 0.2500 0.1950 0.1250 0.0750 0.0000 0.8572 1.9081 Initial Oil a 0.0050 0.3500 0.2500 0.1950 0.1250 0.0750 0.0000 0.8572 1.0000

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, 9

Cer´e, 130

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

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, 8

convection, 5 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 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, 8

Dumor´e, 74, 130 eigenvalue nontie-line, 79, 188, 255, 256, 258 tie-line, 79, 193, 255, 256, 258 280