Numerical Assessments of Flow and Advective Transport Uncertainty for Performance Measures of Radioactive Waste Geological Disposal in Fractured Rocks
Abstract
:1. Introduction
2. Materials and Methods
2.1. Mathematical Formulations
2.1.1. Conservation and State Laws
2.1.2. Fracture Generation
2.1.3. Computational Grids and Representation of Fractures on a Grid
2.1.4. Particle Tracking Algorithms
2.1.5. Performance Measures
2.2. Reference Case
2.2.1. Conceptual Disposal Facility
2.2.2. Hydrogeological Conceptual Model
Units | Lithology or Material | Distributions/Attitude and Width | Range of Hydraulic Conductivity (m/s) | Recommended Hydraulic Conductivity (m/s) | Porosity (-) |
---|---|---|---|---|---|
R0 | Regolith | 70 m thickness of the topmost domain | 5.0 × 10−6–1.0 × 10−4 | 1.0 × 10−5 | 1.0 × 10−3 |
R# | Granitic gneiss | - | 4.1 × 10−12–1.0 × 10−9 | 1.0 × 10−10 | 5.4 × 10−3 |
F1 | Fault | N64E/70N, 200 m width | 3.0 × 10−8–1.0 × 10−4 | 5.0 × 10−6 | 1.0 × 10−2 |
F2 | Fracture zone | N80E/50S, 20 m width | 3.0 × 10−8–1.0 × 10−4 | 5.0 × 10−6 | 1.5 × 10−2 |
MT | Backfill material | - | - | 1.0 × 10−10 | 4.0 × 10−1 |
DT | Backfill material | - | - | 1.0 × 10−10 | 4.0 × 10−1 |
DH | Buffer material | - | - | 1.0 × 10−12 | 4.0 × 10−1 |
EDZ | Granitic gneiss | - | 3.3 × 10−9–3.3 × 10−7 | 3.3 × 10−8 * | 1.0 × 10−4 |
Fracture Domain | R0 | R# | |
---|---|---|---|
Elevation | Depth below surface < 70 m | Depth below surface > 70 m | |
Fracture clusters (Pole trend, pole plunge, κ, P32, rel) | Cluster 1 | (198, 18, 18, 26%) | (65, 17, 20, 15%) |
Cluster 2 | (155, 4, 15, 24%) | (344, 38, 18, 24%) | |
Cluster 3 | (264, 23, 16, 18%) | (281, 29, 16, 30%) | |
Cluster 4 | (98, 81, 11, 32%) | (174, 22, 17, 10%) | |
Cluster 5 | - | (175, 75, 19, 21%) | |
Fracture intensity(P32) | 2.4 | 0.3 | |
Fracture size | , | ||
Fracture location | Stationary random (Poisson) process | Stationary random (Poisson) process | |
Fracture transmissivity (T, m2⁄s) | T = 1.51 × 10 −7 × (L0.7); is the equivalent size (m) of a square fracture. | ; is the equivalent size (m) of a square fracture. | |
Fracture Aperture (e, m) |
3. Numerical Examples
3.1. Workflow for the Study
3.2. DFN Generation, Fracture Connectivity Analysis, and Intersections between Fractures and Repository
3.3. The Computational Grid and Effective Flow Properties Field for the Base Case
4. Results and Discussions
4.1. Steady-State Flow, Particle Tracking, and Calculation of PMs for the Base Case
4.2. Sensitivity of Hydrogeological Units and EDZ on Flow, Particle Tracking, and PMs
4.3. The Stochastic Simulations for 49 DFN Realizations
4.3.1. Effective Fracture Number
4.3.2. Remaining DHs Based on Rejection Criteria for the Q1 Path
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Number of DH Intersected by Isolated Fractures | Number of DH Intersected by Connected Fractures | Number of DH with Rejection Criteria | Remained Number of DH for Q1 Path |
---|---|---|---|
47 | 365 | 217 | 148 |
Cases | Base Case | R0_5.0 × 10−6 | R0_1.0 × 10−4 | R#_1.0 × 10−12 | R#_1.0 × 10−9 | F#_1.0 × 10−8 | F#_1.0 × 10−4 | EDZ_3.3 × 10−9 | EDZ_3.3 × 10−7 |
---|---|---|---|---|---|---|---|---|---|
Maximum Qeq (m3/year) | 8.72 × 10−5 | 9.01 × 10−5 | 6.08 × 10−5 | 4.12 × 10−5 | 1.91 × 10−4 | 7.39 × 10−5 | 6.07 × 10−5 | 7.67 × 10−5 | 7.53 × 10−5 |
Minimum Qeq (m3/year) | 4.55 × 10−5 | 4.69 × 10−5 | 1.32 × 10−5 | 5.88 × 10−6 | 1.49 × 10−4 | 4.55 × 10−5 | 3.76 × 10−5 | 4.62 × 10−5 | 4.48 × 10−5 |
Maximum F (year/m) | 4.78 × 107 | 6.15 × 107 | 7.61 × 108 | 5.91 × 108 | 2.33 × 107 | 6.17 × 107 | 6.83 × 107 | 5.33 × 107 | 5.29 × 107 |
Minimum F (year/m) | 2.51 × 106 | 2.54 × 106 | 5.78 × 106 | 1.51 × 107 | 7.77 × 105 | 1.41 × 106 | 4.29 × 106 | 2.24 × 106 | 1.88 × 106 |
Realization number * | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 |
Fracture number ** | 8,320,632 | 8,341,248 | 8,156,556 | 8,278,347 | 8,285,150 | 8,300,106 | 8,239,884 | 8,225,342 | 8,252,640 |
Realization number | 11 | 21 | 31 | 41 | 51 | 61 | 71 | 81 | 91 |
Fracture number * | 8,195,941 | 8,253,067 | 8,237,262 | 8,265,553 | 8,385,158 | 8,264,897 | 8,301,048 | 8,241,552 | 8,230,608 |
Realization number | 12 | 22 | 32 | 42 | 52 | 62 | 72 | 82 | 92 |
Fracture number * | 8,273,013 | 8,231,334 | 8,253,960 | 8,279,343 | 8,308,163 | 8,206,153 | 8,269,453 | 8,219,716 | 8,210,454 |
Realization number | 13 | 23 | 33 | 43 | 53 | 63 | 73 | 83 | 93 |
Fracture number * | 8,235,503 | 8,353,253 | 8,258,874 | 8,214,399 | 8,304,313 | 8,186,264 | 8,205,598 | 8,238,796 | 8,295,528 |
Realization number | 14 | 24 | 34 | 44 | 54 | 64 | 74 | 84 | 94 |
Fracture number * | 8,246,436 | 8,204,342 | 8,267,200 | 8,245,352 | 8,247,883 | 8,243,216 | 8,273,206 | 8,241,587 | 8,228,915 |
Realization number | 10 | 20 | 30 | 40 | - | - | - | - | - |
Fracture number * | 8,182,334 | 8,269,977 | 8,191,695 | 8,283,339 | - | - | - | - | - |
Parameters | Effective Fracture Number * | Realization Number |
---|---|---|
Min | 8,156,556 | 03 |
Max | 8,385,158 | 51 |
M | 8,253,971 | 32 |
SD | 45,126 | - |
M − 3 SD | 8,118,592 | - ** |
M − 2 SD | 8,163,718 | 03 |
M − 1 SD | 8,208,845 | 92 |
M + 1 SD | 8,299,098 | 06 |
M + 2 SD | 8,344,224 | 02 |
M + 3 SD | 8,389,351 | 51 |
Realization number * | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 |
Number of DH ** | 138 | 128 | 139 | 153 | 150 | 147 | 167 | 113 | 133 |
Realization number | 11 | 21 | 31 | 41 | 51 | 61 | 71 | 81 | 91 |
Number of DH | 132 | 141 | 152 | 168 | 142 | 142 | 143 | 153 | 114 |
Realization number | 12 | 22 | 32 | 42 | 52 | 62 | 72 | 82 | 92 |
Number of DH | 125 | 125 | 126 | 121 | 132 | 128 | 165 | 132 | 122 |
Realization number | 13 | 23 | 33 | 43 | 53 | 63 | 73 | 83 | 93 |
Number of DH | 138 | 112 | 133 | 130 | 140 | 146 | 130 | 148 | 139 |
Realization number | 14 | 24 | 34 | 44 | 54 | 64 | 74 | 84 | 94 |
Number of DH | 128 | 115 | 129 | 124 | 132 | 117 | 152 | 146 | 144 |
Realization number | 10 | 20 | 30 | 40 | - | - | - | - | - |
Number of DH | 148 | 142 | 149 | 126 | - | - | - | - | - |
Parameters | Remaining Number of DH * | Realization |
---|---|---|
Min. | 112 | 23 |
Max. | 168 | 41 |
M | 137 | 1, 13 |
SD | 14 | - |
M − 3 SD | 96 | - ** |
M − 2 SD | 109 | 23 |
M − 1 SD | 123 | 92 |
M + 1 SD | 150 | 5 |
M + 2 SD | 164 | 72 |
M + 3 SD | 178 | - ** |
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Yu, Y.-C.; Shen, Y.-H.; Lee, T.-P.; Ni, C.-F.; Lee, I.-H. Numerical Assessments of Flow and Advective Transport Uncertainty for Performance Measures of Radioactive Waste Geological Disposal in Fractured Rocks. Energies 2022, 15, 5585. https://doi.org/10.3390/en15155585
Yu Y-C, Shen Y-H, Lee T-P, Ni C-F, Lee I-H. Numerical Assessments of Flow and Advective Transport Uncertainty for Performance Measures of Radioactive Waste Geological Disposal in Fractured Rocks. Energies. 2022; 15(15):5585. https://doi.org/10.3390/en15155585
Chicago/Turabian StyleYu, Yun-Chen, Yu-Hsiang Shen, Tsai-Ping Lee, Chuen-Fa Ni, and I-Hsien Lee. 2022. "Numerical Assessments of Flow and Advective Transport Uncertainty for Performance Measures of Radioactive Waste Geological Disposal in Fractured Rocks" Energies 15, no. 15: 5585. https://doi.org/10.3390/en15155585
APA StyleYu, Y.-C., Shen, Y.-H., Lee, T.-P., Ni, C.-F., & Lee, I.-H. (2022). Numerical Assessments of Flow and Advective Transport Uncertainty for Performance Measures of Radioactive Waste Geological Disposal in Fractured Rocks. Energies, 15(15), 5585. https://doi.org/10.3390/en15155585