Equivalent Pore Channel Model for Fluid Flow in Rock Based on Microscale X-ray CT Imaging
Abstract
:1. Introduction
2. Specimen and Microscale X-ray CT Imaging
3. Development of the Pore Channel Model
3.1. Ternary Segmentation
3.2. Analysis and Determination of Representative Pore Shape
3.3. Application of Tortuous Flow Path
3.4. Construction of 3D Domain and Its Properties
4. Numerical Modeling and Results
5. Discussion
5.1. Effect of Tortuosity Factor
5.2. Comparison with Direct Numerical Simulation
6. Conclusions
- Representative streamline channels of five types of sandstones were determined from a ternary image segmentation to distinguish apparent and indistinct pores. Threshold intensity values of the micro-CT images were examined through matching experimentally measured pore volumes from MIP tests with the CT image voxel volumes.
- In two dimensions, a shape perturbation theory was applied to extend the pore channel flow for the case of irregular pores with a shape-dependent flow resistance. The results of micro-CT image analysis of pore perimeter, area, and rugosity were used for determining the parameters in the perturbation theory. A representative pore shape for each of the different sandstones could be derived.
- In three dimensions, the effect of tortuosity was modeled by expressing the flow as sinusoidal curves expressing the degree of tortuosity, average distance and propagation angle of connected pores along the z-axis. Each factor was also investigated through image analysis, and the results indicated a dependence on the chosen object region, i.e., whether the pore phase was defined as only the apparent pores or the combination of apparent and indistinct pores.
- Distinct 3D domains of apparent and indistinct pores were constructed through combining a 2D section with representative pore shapes and a 3D tortuous flow path. Both the Stokes and Brinkman equations were solved to compute the interaction flow regime with the two domains. A coupling simulation was achieved and evaluated against the experimental results in the Darcy flow regime.
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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Pore Characteristics | Boise | Berea | Buff Berea | Bandera | Linyi |
---|---|---|---|---|---|
Average mean pore diameter (μm) | 2.61 (±0.31) | 0.75 (±0.03) | 1.00 (±0.04) | 0.24 (±0.01) | 0.13 (±0.01) |
Average median pore diameter (µm) | 43.39 (±2.99) | 11.69 (±0.18) | 17.76 (±0.59) | 5.03 (±1.30) | 7.01 (±0.60) |
Average porosity | 29.5 (±0.76) | 21.1 (±0.35) | 23.8 (±0.71) | 20.7 (±0.82) | 10.1 (±0.44) |
Voxel size (µm) | 10 | 4.138 | 4.138 | 3.396 | 3.847 |
Pore Phase | Title | Boise | Berea | Buff Berea | Bandera | Linyi |
---|---|---|---|---|---|---|
Intensity value | Ia | 87 | 85 | 97 | 87 | 107 |
Is | 131 | 128 | 143 | 118 | 121 | |
Apparent pore | Average pore area (m2) | 1.17 × 10−8 (± 2.41 × 10−9) | 1.87 × 10−9 (±0.31 × 10−9) | 3.81 × 10−9 (±0.67 × 10−9) | 1.16 × 10−9 (±0.21 × 10−9) | 1.96 × 10−9 (±0.57 × 10−9) |
Average Perimeter (μm) | 433 (±55.8) | 159 (±15.1) | 239 (±26.3) | 129 (±14.4) | 152 (±25.2) | |
Average Hydraulic D (μm) | 66.4 (±4.17) | 31.7 (±1.87) | 41.2 (±2.54) | 24.1 (±1.38) | 26.2 (±2.05) | |
Indistinct pore | Average pore area (m2) | 1.63 × 10−8 (±4.01 × 10−9) | 3.04 × 10−9 (±0.50 × 10−9) | 4.56 × 10−9 (±0.91 × 10−9) | 1.35 × 10−9 (±0.27 × 10−9) | 1.18 × 10−9 (±0.51 × 10−9) |
Average Perimeter (μm) | 1341 (±316.2) | 380 (±55.9) | 597 (±112.1) | 273 (±60.3) | 153 (±44.4) | |
Average Hydraulic D (μm) | 42.8 (±1.57) | 27.7 (±1.06) | 28.2 (±1.06) | 13.9 (±5.51) | 13.9 (±8.88) |
Boise | Berea | Buff Berea | Bandera | Linyi |
---|---|---|---|---|
| | | | |
<Pap> | <Pap> | <Pap> | <Pap> | <Pap> |
C = 21.1 (±1.3) | C = 17.7 (±0.7) | C = 19.8 (±1.0) | C = 18.3 (±0.9) | C = 18.0 (±1.2) |
k = 4 (±2) | k = 3 (±0.3) | k = 3 (±0.4) | k = 3 (±0.4) | k = 4 (±0.5) |
l = 4.51 (±0.38) × 10−5 | l = 1.93 (±0.14) × 10−5 | l = 2.64 (±0.21) × 10−5 | l = 1.50 (±0.13) × 10−5 | l =1.69 (±0.17) × 10−5 |
ε = 0.31 (±0.106) | ε = 0.30 (±0.095) | ε = 0.37 (±0.084) | ε = 0.27 (±0.094) | ε = 0.22 (±0.084) |
<Pindis> | <Pindis> | <Pindis> | <Pindis> | <Pindis> |
C = 115.2 (±25.7) | C = 49.79 (±6.8) | C = 83.2 (±14.6) | C = 75.7 (±14.2) | C = 35.3 (±5.4) |
k = 9 (±3) | k = 5 (±1.5) | k = 7 (±2.3) | k = 8 (±2.4) | k = 9 (±2.2) |
l = 6.99 (±0.48) × 10−5 | l = 3.00 (±0.17) × 10−5 | l = 3.67 (±0.23) × 10−5 | l = 2.02 (±0.11) × 10−5 | l = 1.92 (±0.13) × 10−5 |
ε = 0.36 (±0.101) | ε = 0.38 (±0.084) | ε = 0.39 (±0.077) | ε = 0.32 (±0.097) | ε = 0.19 (±0.086) |
Tortuous Characteristics | Boise | Berea | Buff Berea | Bandera | Linyi |
---|---|---|---|---|---|
Tortuosity | 1.44 | 1.99 | 1.77 | 1.72 | 2.75 |
Tortuous propagation angle (°) | 47.4 (±2.6) | 61.2 (±1.2) | 63.8 (±6.7) | 58.0 (±0.4) | 48.7 (±2.5) |
Avg. z-axis distance of connected pore (mm) | 0.1135 (±1.41 × 10−4) | 0.06034 (±6.55 × 10−6) | 0.05518 (±9.14 × 10−6) | 0.04635 (±2.71 × 10−6) | 0.0529 (±5.29 × 10−6) |
Tortuous flow path | |
Indistinct Pore Properties | Boise | Berea | Buff Berea | Bandera | Linyi |
---|---|---|---|---|---|
Derived permeability (m2) | 1.06 × 10−11 | 3.49 × 10−12 | 3.52 × 10−12 | 8.49 × 10−13 | 3.75 × 10−13 |
Porosity | 0.186 | 0.147 | 0.157 | 0.124 | 0.063 |
Property | Value | Description | |
---|---|---|---|
μ | 2.842 × 10−5 Pa·s | Dynamic viscosity | |
vs | 7.29 × 10−6 m/s | Superficial velocity | |
vi | Boise | 2.51 × 10−5 m/s | Interstitial inlet velocity |
Berea | 3.46 × 10−5 m/s | ||
Buff Berea | 3.08 × 10−5 m/s | ||
Bandera | 3.56 × 10−5 m/s | ||
Linyi | 7.35 × 10−5 m/s | ||
P0 | 10 MPa | Initial outlet pressure |
Results | Boise | Berea | Buff Berea | Bandera | Linyi | |
---|---|---|---|---|---|---|
Permeability (m2) | Pore channel model | 9.49 × 10−13 | 1.04 × 10−13 | 2.17 × 10−13 | 5.01 × 10−14 | 1.80 × 10−14 |
Experiment | 1.14 × 10−12 (±1.08 × 10−13) | 1.34 × 10−13 (±4.32 × 10−15) | 2.78 × 10−13 (±1.81 × 10−14) | 3.30 × 10−14 (±1.06 × 10−15) | 2.47 × 10−15 (±8.06 × 10−17) |
Tortuous Characteristics | Boise | Berea | Buff Berea | Bandera | Linyi |
---|---|---|---|---|---|
Tortuosity | 1.93 | 3.59 | 2.54 | 2.70 | 3.96 |
Tortuous propagation angle (°) | 44.7 (±0.7) | 56.4 (±0.3) | 57.7 (±0.6) | 58.3 (±0.2) | 51.4 (±2.3) |
Avg. z-axis distance of connected pores (mm) | 0.1613 (±0.49 × 10−4) | 0.08935 (±0.99 × 10−5) | 0.07961 (±0.12 × 10−4) | 0.05961 (±0.52 × 10−5) | 0.0598 (±0.68 × 10−5) |
Tortuous flow path | |
| |
Average outlet superficial velocity (vs, 10−6 m/s): 7.185 | Average outlet superficial velocity (vs, 10−6 m/s): 7.196 |
Average pressure gradient (ΔPc, Pa): 0.0216 | Average pressure gradient (ΔPc, Pa): 0.0179 |
Results | Boise | Berea | Buff Berea | Bandera | Linyi | |
---|---|---|---|---|---|---|
Permeability (m2) | Modified pore channel model | 1.14 × 10−12 | 1.29 × 10−13 | 2.75 × 10−13 | 3.41 × 10−14 | 1.20 × 10−14 |
Experiment | 1.14 × 10−12 (±1.08 × 10−13) | 1.34 × 10−13 (±4.32 × 10−15) | 2.78 × 10−13 (±1.81 × 10−14) | 3.30 × 10−14 (±1.06 × 10−15) | 2.47 × 10−15 (±8.06 × 10−17) |
Object Phase | A z-axis Connected Pore Structure | Extract A Region of Interest | Detection of Unconnected Pores |
---|---|---|---|
Apparent pore (Pap) | | ||
Total pore (Pap + Pindis) | |
Results | Object Phase | Boise | Berea | Buff Berea | Bandera | Linyi | |
---|---|---|---|---|---|---|---|
Permeability (m2) | Direct numerical simulation | Apparent pore (Pap) | 1.01 × 10−12 | 1.45 × 10−13 | 2.92 × 10−13 | 3.04 × 10−14 | 6.22 × 10−15 |
Total pore (Pap + Pindis) | 1.26 × 10−12 | 1.98 × 10−13 | 3.74 × 10−13 | 5.60 × 10−14 | 3.15 × 10−14 | ||
Pore channel model | 1.14 × 10−12 | 1.29 × 10−13 | 2.75 × 10−13 | 3.41 × 10−14 | 1.20 × 10−14 | ||
Experiment | 1.14 × 10−12 | 1.34 × 10−13 | 2.78 × 10−13 | 3.30 × 10−14 | 2.47 × 10−15 |
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Choi, C.-S.; Lee, Y.-K.; Song, J.-J. Equivalent Pore Channel Model for Fluid Flow in Rock Based on Microscale X-ray CT Imaging. Materials 2020, 13, 2619. https://doi.org/10.3390/ma13112619
Choi C-S, Lee Y-K, Song J-J. Equivalent Pore Channel Model for Fluid Flow in Rock Based on Microscale X-ray CT Imaging. Materials. 2020; 13(11):2619. https://doi.org/10.3390/ma13112619
Chicago/Turabian StyleChoi, Chae-Soon, Yong-Ki Lee, and Jae-Joon Song. 2020. "Equivalent Pore Channel Model for Fluid Flow in Rock Based on Microscale X-ray CT Imaging" Materials 13, no. 11: 2619. https://doi.org/10.3390/ma13112619
APA StyleChoi, C.-S., Lee, Y.-K., & Song, J.-J. (2020). Equivalent Pore Channel Model for Fluid Flow in Rock Based on Microscale X-ray CT Imaging. Materials, 13(11), 2619. https://doi.org/10.3390/ma13112619