Cation Segregation in an Oxide Ceramic with Low Solubility: Yttrium ...
Modeling of CO2 Solubility in Crude Oil during Carbon ... · Web viewAppendix A. Tables Table A-1....
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Appendix A. Tables Table A-1. The predicted CO 2 solubility in dead oil by the newly developed GEP-based model considering the impact of reservoir temperature, saturation pressure, oil molecular weight, and oil specific gravity MW (gr/ mole) γ T( o C) P S (MPa) R S, exp (mole fractio n) R S, pred (mole fractio n) ARD a Subset 1 330 0.9433 33 18.33 17.37 0.6098 0.5686 75 6.7440 16 Train 2 440 0.9718 41 28 5.52 0.5674 0.5189 54 8.5381 88 Train 3 386 0.9496 64 21.11 6.32 0.6 0.5790 44 3.4927 14 Train 4 386 0.9496 64 21.11 10 0.629 0.6479 47 3.0122 9 Train 5 386 0.9496 64 21.11 8 0.629 0.6240 28 0.7905 05 Train 6 386 0.9496 64 140 6.41 0.28 0.2842 75 1.5268 25 Train 7 222 0.8654 43 48.89 1.81 0.16 0.1743 72 8.9822 1 Train 8 222 0.8654 43 48.89 5.26 0.42 0.4361 77 3.8515 94 Train 9 205 0.8382 7 29.44 2.07 0.2601 0.2661 17 2.3134 34 Train 10 373 0.8995 54.44 3.8 0.356 0.3370 5.3097 Train 1
Transcript of Modeling of CO2 Solubility in Crude Oil during Carbon ... · Web viewAppendix A. Tables Table A-1....
Appendix
A. Tables
Table A-1. The predicted CO2 solubility in dead oil by the newly developed GEP-based model considering
the impact of reservoir temperature, saturation pressure, oil molecular weight, and oil specific gravity
MW(gr/mole)
γ T(oC) PS
(MPa)RS, exp
(mole fraction
)
RS, pred
(mole fraction)
ARDa Subset
1 330 0.943333 18.33 17.37 0.6098 0.568675 6.744016 Train
2 440 0.971841 28 5.52 0.5674 0.518954 8.538188 Train
3 386 0.949664 21.11 6.32 0.6 0.579044 3.492714 Train
4 386 0.949664 21.11 10 0.629 0.647947 3.01229 Train
5 386 0.949664 21.11 8 0.629 0.624028 0.790505 Train
6 386 0.949664 140 6.41 0.28 0.284275 1.526825 Train
7 222 0.865443 48.89 1.81 0.16 0.174372 8.98221 Train
8 222 0.865443 48.89 5.26 0.42 0.436177 3.851594 Train
9 205 0.83827 29.44 2.07 0.2601 0.266117 2.313434 Train
10 373 0.899555 54.44 3.8 0.356 0.337097 5.309709 Train
11 386 0.949664 21.11 12.4 0.629 0.650421 3.405621 Train
12 246 0.84985 73.89 1.37 0.1157 0.105476 8.836402 Train
13 463 0.975862 48.89 2.78 0.251 0.264833 5.511129 Train
14 196 0.857576 32.22 5.45 0.53 0.526285 0.700946 Train
15 458 0.98675 54.44 12.8 0.65 0.672084 3.397589 Train
16 424 0.973847 25.56 6.99 0.598 0.583992 2.342513 Train
17 196 0.857576 32.22 6.69 0.623 0.593097 4.79988 Train
18 280 0.912315 42 6.99 0.548 0.548157 0.028579 Train
19 370 0.945224 93.33 4.97 0.328 0.29609 9.728649 Train
20 350 0.950941 93.33 7.86 0.423 0.419286 0.877899 Train
21 246 0.84985 73.89 14.28 0.697 0.695691 0.187747 Train
1
22 350 0.950941 43.33 2 0.196 0.202575 3.354798 Train
23 358 0.944593 48.89 6.87 0.508 0.512957 0.975816 Train
24 345 0.858617 48.89 3.18 0.313 0.317044 1.292135 Train
25 424 0.973847 25.56 1.83 0.222 0.236432 6.501049 Train
26 222 0.865443 48.89 2.31 0.2 0.218172 9.085915 Train
27 246 0.84985 73.89 7.93 0.496 0.490319 1.145267 Train
28 490 0.967786 140 8.36 0.344 0.368733 7.189737 Train
29 358 0.944593 48.89 3.25 0.299 0.294557 1.485983 Train
30 490 0.967786 21 6.1 0.6 0.573718 4.380377 Train
31 345 0.858617 48.89 10.59 0.667 0.688862 3.277724 Train
32 205 0.83827 29.44 1.38 0.1915 0.184597 3.604682 Train
33 370 0.945224 93.33 11.59 0.553 0.553245 0.044319 Train
34 440 0.971841 28 0.89 0.1 0.121598 21.59771 Train
35 490 0.967786 21 12.36 0.622 0.653278 5.028538 Train
36 440 0.971841 28 4.35 0.4491 0.450196 0.244091 Train
37 458 0.98675 54.44 2.77 0.251 0.246358 1.849386 Train
38 246 0.84985 73.89 21.48 0.795 0.796307 0.164398 Train
39 222 0.865443 40.56 4.76 0.44 0.440956 0.217239 Train
40 222 0.865443 48.89 8.45 0.6 0.598359 0.273439 Train
41 280 0.912315 42 3.54 0.313 0.336927 7.644425 Train
42 205 0.83827 29.44 5 0.5638 0.526492 6.617196 Train
43 440 0.971841 28 1.58 0.1875 0.204602 9.121043 Train
44 386 0.949664 140 10.84 0.43 0.431205 0.280314 Train
45 280 0.912315 42 8.2 0.618 0.599093 3.059371 Train
46 350 0.950941 93.33 16.28 0.625 0.660699 5.71177 Train
47 440 0.971841 28 3.03 0.3302 0.349335 5.795006 Train
48 236 0.858617 71.11 8.9 0.531 0.535767 0.897829 Train
49 222 0.865443 40.56 7.24 0.6 0.581838 3.026943 Train
50 222 0.865443 48.89 5.58 0.45 0.455729 1.27302 Train
51 246 0.84985 73.89 27.38 0.847 0.818376 3.379444 Train
52 330 0.943333 18.33 4.03 0.459 0.46518 1.34635 Train
2
53 246 0.84985 73.89 4 0.298 0.283584 4.837604 Train
54 236 0.858617 71.11 14.05 0.675 0.694093 2.82852 Train
55 330 0.943333 18.33 13.78 0.6082 0.608189 0.001862 Train
56 373 0.899555 54.44 7.54 0.555 0.548467 1.177148 Train
57 490 0.967786 140 4 0.2 0.200003 0.001343 Train
58 196 0.857576 32.22 3.79 0.4 0.407539 1.884868 Train
59 358 0.944593 121.1 3.79 0.215 0.195381 9.124899 Train
60 370 0.945224 62.78 15.17 0.681 0.710148 4.280213 Train
61 386 0.949664 21.11 3.75 0.5 0.440562 11.88764 Train
62 330 0.985376 48.89 7.69 0.498 0.520508 4.519748 Train
63 490 0.967786 21 5.4 0.574 0.54467 5.109744 Train
64 463 0.975862 48.89 5.23 0.457 0.431083 5.67109 Train
65 222 0.865443 40.56 4.43 0.4 0.417835 4.458727 Train
66 458 0.98675 54.44 9.21 0.584 0.580706 0.56404 Train
67 424 0.973847 25.56 3.51 0.385 0.39444 2.451918 Train
68 236 0.858617 71.11 3.22 0.235 0.236599 0.680429 Train
69 350 0.950941 43.33 3.17 0.294 0.301195 2.44735 Train
70 463 0.975862 48.89 10.71 0.669 0.64487 3.606907 Train
71 345 0.858617 48.89 6.15 0.495 0.517082 4.46109 Train
72 490 0.967786 21 10.28 0.622 0.650878 4.64269 Train
73 358 0.944593 121.1 15.81 0.571 0.592576 3.778569 Train
74 222 0.865443 48.89 9.31 0.66 0.630679 4.44259 Train
75 490 0.967786 21 3.17 0.356 0.400952 12.6271 Train
76 490 0.967786 21 8 0.621 0.625335 0.697988 Train
77 330 0.943333 18.33 3.47 0.4084 0.423728 3.753087 Train
78 330 0.985376 48.89 3.57 0.283 0.296087 4.62432 Train
79 358 0.944593 121.1 7.75 0.366 0.359981 1.644571 Train
80 450 0.952862 23 2 0.2854 0.27866 2.36159 Train
81 330 0.943333 18.33 4.61 0.5062 0.501518 0.924994 Train
82 450 0.952862 23 3 0.3824 0.380338 0.539337 Train
3
83 205 0.83827 29.44 4.21 0.4719 0.469626 0.481845 Train
84 490 0.967786 140 6.36 0.3 0.296974 1.008655 Train
85 370 0.945224 62.78 2.28 0.191 0.190766 0.122618 Train
86 358 0.944593 121.1 9.66 0.43 0.426473 0.820348 Test
87 373 0.899555 54.44 10.62 0.658 0.656683 0.200153 Test
88 350 0.950941 43.33 5.45 0.455 0.454878 0.026753 Test
89 370 0.945224 62.78 10.15 0.598 0.594806 0.534035 Test
90 386 0.949664 21.11 0.5 0.1 0.078613 21.38727 Test
91 463 0.975862 48.89 12.29 0.677 0.678683 0.248652 Test
92 386 0.949664 140 12.79 0.486 0.485077 0.189999 Test
93 424 0.973847 25.56 5.2 0.542 0.505988 6.6443 Test
94 490 0.967786 140 10.48 0.42 0.435579 3.709189 Test
95 236 0.858617 71.11 5.94 0.38 0.398229 4.7972 Test
96 222 0.865443 40.56 7.93 0.65 0.611624 5.903947 Test
97 358 0.944593 48.89 10.32 0.632 0.639044 1.114503 Test
98 440 0.971841 28 7.58 0.609 0.602748 1.026622 Test
99 330 0.943333 18.33 10.35 0.6065 0.627402 3.446346 Test
100 490 0.967786 140 12.44 0.511 0.489874 4.134206 Test
101 386 0.949664 140 2 0.1 0.098787 1.213248 Test
102 330 0.943333 18.33 5.5 0.5948 0.545732 8.249499 Test
103 196 0.857576 32.22 7.17 0.68 0.614469 9.636953 Test
104 370 0.945224 62.78 5.66 0.418 0.407062 2.616801 Test
105 386 0.949664 21.11 2.05 0.3 0.282257 5.914271 Test
106 386 0.949664 21.11 1.32 0.2 0.19384 3.07978 Test
Average absolute relative deviation (%) 3.7810
a ARD is the absolute relative deviation which is defined as follows:
4
Table A-2. The predicted CO2 solubility in live oil by the newly developed GEP-based model considering
the impact of reservoir temperature, saturation pressure, bubble point pressure, oil molecular weight, and
oil specific gravity
MW
(gr/mole)
γ T(oC)
Pb
(MPa)
PS
(MPa)
RS, exp
(mole fraction
)
RS, pred
(mole fraction)
ARDa Subset
1 112.3 0.8348 64.4 11.91 18.62 0.53 0.544175 2.674549 Train
2 87.5 0.7208 54.4 11.45 13.79 0.297 0.311781 4.976821 Train
3 154.2 0.8708 63 4.9 11.9 0.5629 0.535743 4.824403 Train
4 127 0.8348 73.9 18.52 23.06 0.3987 0.369078 7.429757 Train
5 149.6 0.8654 41.1 4.84 8.33 0.44 0.432796 1.637296 Train
6 87.5 0.7208 54.4 11.45 14.66 0.4 0.398497 0.375751 Train
7 164.2 0.8448 61 3.5 8.3 0.4749 0.473959 0.198164 Train
8 211.5 0.8816 65 2.15 7.54 0.433 0.436759 0.868195 Train
9 133.2 0.8498 76.7 16.26 19.54 0.255 0.260018 1.967691 Train
10 211.5 0.8816 65 2.15 11.94 0.61 0.639953 4.910345 Train
11 120.3 0.737 123.9 17.61 32.76 0.68 0.64571 5.042705 Train
12 87.5 0.7208 54.4 11.45 15.52 0.48 0.47228 1.608368 Train
13 211.5 0.8816 65 2.15 5.08 0.27 0.272525 0.935278 Train
14 164.2 0.8448 61 3.5 12.8 0.7201 0.706948 1.826457 Train
15 211.5 0.8816 65 2.15 4.3 0.2 0.208905 4.452343 Train
16 115.7 0.8348 67 6.2 11.11 0.4413 0.442427 0.255369 Train
17 391.6 0.9663 28 2.71 8.44 0.5844 0.638193 9.20479 Train
18 211.5 0.8816 65 2.15 4 0.175 0.182589 4.336458 Train
19 127 0.8348 73.9 18.52 30.73 0.6996 0.699314 0.040867 Train
20 211.5 0.8816 65 2.15 9.66 0.52 0.545838 4.968855 Train
21 115.7 0.8348 67 6.2 13.05 0.5699 0.552705 3.017232 Train
22 120.3 0.737 123.9 17.61 27.59 0.5 0.500002 0.000426 Train
5
23 149.6 0.8654 41.1 4.84 7.22 0.32 0.323527 1.102341 Train
24 120.3 0.737 123.9 17.61 20.69 0.2 0.199562 0.219125 Train
25 176.7 0.8816 59 2.9 11.4 0.6313 0.623064 1.304608 Train
26 154.2 0.8708 63 4.9 7.2 0.2643 0.229595 13.13083 Train
27 176.7 0.8816 59 2.9 12.6 0.6741 0.671084 0.447368 Train
28 100 0.8251 66 11.6 14.7 0.3411 0.307933 9.723586 Train
29 164.2 0.8448 61 3.5 7.2 0.3937 0.393432 0.067952 Train
30 100 0.8251 66 11.6 17.01 0.5062 0.467402 7.664503 Train
31 176.7 0.8816 59 2.9 8.4 0.4733 0.473044 0.054148 Train
32 133.2 0.8498 76.7 16.26 27.13 0.6 0.615522 2.586959 Train
33 211.5 0.8816 65 2.15 8.62 0.48 0.49538 3.204209 Train
34 133.2 0.8498 76.7 16.26 24.14 0.5 0.503825 0.765051 Train
35 100 0.8251 66 11.6 14.2 0.3009 0.266459 11.44611 Train
36 211.5 0.8816 65 2.15 6.93 0.4 0.400404 0.101019 Train
37 154.2 0.8708 63 4.9 10.4 0.4773 0.455947 4.473619 Train
38 115.7 0.8348 67 6.2 10.28 0.3695 0.386653 4.642165 Train
39 164.2 0.8448 61 3.5 5.2 0.1705 0.207654 21.79102 Train
40 149.6 0.8654 41.1 4.84 5.56 0.11 0.108793 1.097315 Train
41 211.5 0.8816 65 2.15 6 0.34 0.339745 0.075107 Train
42 112.3 0.8348 64.4 11.91 17.24 0.455 0.467245 2.691134 Train
43 164.2 0.8448 61 3.5 9.5 0.5603 0.549042 2.009318 Train
44 87.5 0.7208 54.4 11.45 12.29 0.12 0.12373 3.10841 Train
45 149.6 0.8654 41.1 4.84 6.11 0.19 0.188369 0.858528 Train
46 120.3 0.737 123.9 17.61 24.14 0.375 0.370028 1.325922 Train
47 133.2 0.8498 76.7 16.26 21.93 0.4 0.400339 0.084714 Train
48 80.7 0.6748 65.6 10.75 13.5 0.4035 0.325692 19.28328 Train
49 115.7 0.8348 67 6.2 9.17 0.2765 0.301799 9.149845 Train
6
50 133.2 0.8498 76.7 16.26 18.68 0.2 0.20002 0.009859 Train
51 127 0.8348 73.9 18.52 28.16 0.6042 0.613337 1.512312 Train
52 80.7 0.6748 65.6 10.75 12.37 0.2022 0.20818 2.957646 Train
53 120.3 0.737 123.9 17.61 31.04 0.61 0.60238 1.2491 Train
54 211.5 0.8816 65 2.15 3.23 0.11 0.109708 0.265477 Train
55 115.7 0.8348 67 6.2 8.2 0.1865 0.2159 15.76395 Train
56 133.2 0.8498 76.7 16.26 20.12 0.3 0.297366 0.878025 Train
57 176.7 0.8816 59 2.9 8 0.4434 0.4489 1.240462 Train
58 87.5 0.7208 54.4 11.45 17.24 0.577 0.592928 2.760446 Train
59 112.3 0.8348 64.4 11.91 13.79 0.195 0.203774 4.499448 Train
60 133.2 0.8498 76.7 16.26 17.24 0.1083 0.084955 21.55547 Test
61 154.2 0.8708 63 4.9 17.01 0.6809 0.73292 7.639901 Test
62 154.2 0.8708 63 4.9 9.2 0.3944 0.381508 3.268725 Test
63 154.2 0.8708 63 4.9 14.4 0.6471 0.643944 0.487753 Test
64 176.7 0.8816 59 2.9 9.9 0.5409 0.554194 2.457779 Test
65 391.6 0.9663 28 2.71 4.23 0.2424 0.2424 4.88E-05 Test
66 391.6 0.9663 28 2.71 5.75 0.4415 0.42259 4.283132 Test
67 176.7 0.8816 59 2.9 4.5 0.1631 0.173896 6.619207 Test
68 133.2 0.8498 76.7 16.26 21.17 0.36 0.3594 0.166689 Test
69 112.3 0.8348 64.4 11.91 20.69 0.6 0.639622 6.60369 Test
70 87.5 0.7208 54.4 11.45 16.38 0.53 0.536509 1.228152 Test
71 112.3 0.8348 64.4 11.91 15.17 0.322 0.324273 0.705888 Test
72 149.6 0.8654 41.1 4.84 9.44 0.53 0.522963 1.327753 Test
73 164.2 0.8448 61 3.5 10.1 0.5967 0.58247 2.384751 Test
74 127 0.8348 73.9 18.52 20.7 0.2028 0.201327 0.726154 Test
Average absolute relative deviation (%) 3.7642
7
a ARD is the absolute relative deviation which is defined as follows:
8
B. Figures
GEP-based Emera and Sarma
Mehrotra and Svrcek Chung et al.
AARD
(%)
(a)
GEP-based Emera and Sarma
Mehrotra and Svrcek Chung et al.
RMSE
(b)
GEP-based Emera and Sarma
Mehrotra and Svrcek Chung et al.
R²
(c)
Figure B-1. Statistical quality measures of the GEP-based model in comparison with other commonly used
literature correlations in dead oil: (a) AARD (%), (b) RMSE, and (c) R2
9
GEP-based Emera and SarmaMehrotra and Svrcek Chung et al.
AARD
(%)
(a)
10
0.04
0.08
0.12
0.16
0.2
0.24
GEP-based Emera and SarmaMehrotra and Svrcek Chung et al.
RMSE
(b)
GEP-based Emera and SarmaMehrotra and Svrcek Chung et al.
R²
(c)
Figure B-2. Statistical quality measures of the GEP-based model in comparison with other commonly used
literature correlations in live oil: (a) AARD (%), (b) RMSE, and (c) R2
10
Experimental dataGEP-based, training setGEP-based, test set
Data index
CO2
solu
bilit
y (m
ole
frac
tion)
(a)
Experimental dataEmera and Sarma
Data index
CO2
solu
bilit
y (m
ole
frac
tion)
(b)
Experimental dataMehrotra and Svrcek
Data index
CO2
solu
bilit
y (m
ole
frac
tion)
(c)
Experimental dataChung et al.
Data index
CO2
solu
bilit
y (m
ole
frac
tion)
(d)
Figure B-3. Experimental and predicted CO2 solubility values versus data index in dead oil for different
models: (a) GEP-based model, (b) Emera and Sarma, (c) Mehrotra and Svrcek, and (d) Chung et al.
11
Experimental dataGEP-based, training setGEP-based, test set
Data index
CO2
solu
bilit
y (m
ole
frac
tion)
(a)
Experimental dataEmera and Sarma
Data index
CO2
solu
bilit
y (m
ole
frac
tion)
(b)
0 20 40 60 800
0.2
0.4
0.6
0.8
1
Experimental dataMehrotra and Svrcek
Data index
CO2
solu
bilit
y (m
ole
frac
tion)
(c)
0 20 40 60 800
0.2
0.4
0.6
0.8
1
Experimental dataChung et al.
Data index
CO2
solu
bilit
y (m
ole
frac
tion)
(d)Figure B-4. Experimental and predicted CO2 solubility values versus data index in live oil for different
models: (a) GEP-based model, (b) Emera and Sarma, (c) Mehrotra and Svrcek, and (d) Chung et al.
12
Figure B-5. Comprehensive error analysis of CO2 solubility calculation by GEP-based correlation in
comparison with the suggested model of Emera and Sarma in dead oil.
13
Object 20
Emera and Sarma, Bou-Mikael (2002) GEP-based, Bou-Mikael (2002)
Emera and Sarma, Dong et al. (2001a) GEP-based, Dong et al. (2001a)
Emera and Sarma, Srivastava et al. (2000) GEP-based, Srivastava et al. (2000)
Emera and Sarma, Srivastava et al. (1995) GEP-based, Srivastava et al. (1995)
Emera and Sarma, Novosad and Costain (1990) GEP-based, Novosad and Costain (1990)
Emera and Sarma, Chaback (1988) GEP-based, Chaback (1988)
Emera and Sarma, Turek et al. (1984) GEP-based, Turek et al. (1984)
Emera and Sarma, Brinlee and Brandt (1982) GEP-based, Brinlee and Brandt (1982)
Emera and Sarma, Simon et al. (1978) GEP-based, Simon et al. (1978)
AARD (%)
Mol
ecul
are
wei
ght (
gr/m
ole)
127127115.7115.7100100176.7176.7164.2164.2154.2154.2391.6391.6211.5211.5133.2133.2149.6149.680.780.7112.3112.3120.3120.387.587.5
Figure B-6. Comprehensive error analysis of CO2 solubility calculation by GEP-based correlation in
comparison with the suggested model of Emera and Sarma in live oil
14
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