Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells
Abstract
:1. Introduction
2. Background
3. Governing Equations
4. Proposed Solution
5. Solution with the Abandoned Well
6. Total Pressure Change and Leakage Rate
- 1.
- Define the time intervals in terms of the total time.
- 2.
- Compute the pressure change caused by injection at the abandoned well location pL,1(rl1 = R) for all time intervals.
- 3.
- For the time intervals, when pressure change pL,1(rl1 = R, t = ti) is zero, the leakage rates ql (t = ti) are also recorded as zero.
- 4.
- From the time interval, when the pressure change pL,1 (rl1 = R, t = tb) is not zero, the rest of leakage rates can be solved based on the abandoned well constraint (Equation (8)).
- 5.
7. Results
7.1. Sensitivity of Leakage Rate Discretization
7.2. Solution Verification
7.3. Sensitivity Analysis
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
a | Constant parameters related to the reservoir and fluid properties |
b | Constant parameters related to the reservoir and fluid properties |
B | Volume formation factor |
C | Rock/fluid compressibility |
h | Layer thickness |
k | Permeability |
p | Fluid pressure |
q | Fluid rate |
r | Radial distance |
t | Time |
ϕ | Porosity |
Ω | Flow resistance within the leaky well |
α | Unit conversion constant |
μ | Fluid viscosity |
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Porosity for both layers (dimensionless) | 0.3 |
Rock compressibility (1/psi) | 9 × 10−6 |
Fluid compressibility (1/psi) | 3 × 10−6 |
Fluid density (lb/ft3) | 62 |
Permeabilities of both layers (mD) | 10 |
Viscosity (cp) | 1 |
Injection rate (STB/D) | 100 |
Well distance (ft) | 60 |
Wellbore radius of the abandoned well (ft) | 0.5 |
Resistance of abandoned well (psi/(STB/D)) | 1 |
Layer thickness (ft) for both layers | 100 |
Reservoir thickness (ft) | 300 |
Reservoir length (ft) | 10,100 |
Reservoir width (ft) | 10,100 |
Number of grid blocks in the x-direction | 101 |
Number of grid blocks in the y-direction | 101 |
Number of grid blocks in the z-direction | 10 |
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Qiao, T.; Hoteit, H.; Fahs, M. Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells. Energies 2021, 14, 2452. https://doi.org/10.3390/en14092452
Qiao T, Hoteit H, Fahs M. Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells. Energies. 2021; 14(9):2452. https://doi.org/10.3390/en14092452
Chicago/Turabian StyleQiao, Tian, Hussein Hoteit, and Marwan Fahs. 2021. "Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells" Energies 14, no. 9: 2452. https://doi.org/10.3390/en14092452