Thermo-Hydro-Mechanical–Chemical Modeling for Pressure Solution of Underground sCO2 Storage
Abstract
1. Introduction
2. Methods
2.1. Thermo-Mechanical
2.2. Fractal Scaling Law
2.3. Hydrochemical
2.4. Total Porosity and Strain Rate
2.5. Conventional IPS Model
3. Validation
4. Results
5. Comparison of Conventional IPS Theory
6. Discussion
7. Conclusions
- It was demonstrated that the strain rate first increased as a consequence of the rapid CO2 saturation, then gradually decreased as a result of the geochemical interactions between the minerals and the CO2–brine solution. This suggests that a major part of the process involves mineral dissolution.
- The results show that the dissolution of clay minerals, particularly undersaturated smectite, during the CO2 injection procedure considerably increased porosity. This alteration in porosity is crucial for understanding the dynamics of CO2 storage in geological formations.
- This study primarily investigates isotropic poro-elasticity, geochemical interaction, and flow and ignores anisotropic conditions.
- An important aspect of this study is the reliance on saturation data during the CO2-fluid core flooding process. The accuracy of estimating the total volume of injected CO2 can be affected by the errors in residual gas and residual liquid saturation.
- The proposed algorithm simplifies calculations employing a fractal approximation to estimate the total pore area based on pore diameter distributions and considers a rock consisting of only two minerals using the hollow cylinder approach. When accounting for multiple mineral systems, minerals can be segregated into groups, which may increase the computation time.
- The results indicate that more inspection is required to better understand how mechanical and chemical processes interact with CO2 sequestration and to improve the model so it can predict the long-term behavior of CO2 in geological formations.
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
a | thermal diffusivity [m2 s−1] |
b | Biot’s coefficient |
d | hydraulic diameter [m] |
Df | fractal dimension of the porous medium |
E | elasticity modulus [Pa] |
Ea | activation energy [J mol−1] |
h | heat transfer coefficient [W m−2] |
ki25 | kinetic rate constant of mineral at 25 °C [mol m−2 s−1] |
K0 | bulk modulus of medium [Pa] |
Ks | solid grain modulus of medium [Pa] |
L | length of flow path [m] |
P | pressure [Pa] |
Rm | kinetic rate [mol s−1] |
Rgas | gas constant [J K−1 mol−1] |
Q | heat exchange rate [W m−1] |
r0 | pore radius [m] |
r1 | inner hollow circle radius (secondary mineral) [m] |
r2 | outer hollow circle radius (primary mineral) [m] |
Sb | saturation ratio of brine |
SCO2 | saturation ratio of sCO2 |
t | time [s] |
T | temperature [K] |
TCO2 | injected sCO2 temperature [K] |
Tref | undisturbed pore system temperature [K] |
ΔT0 | temperature difference between TCO2 and T1 at r1 [K] |
ΔT1 | temperature difference at the outer wall of the grout material [K] |
ΔT2 | temperature difference at the outer wall of the pipe [K] |
δT | Laplacian temperature difference [K] |
u | displacement [m] |
vy | flow velocity of sCO2 in y-direction [m s−1] |
vT | thermal transport velocity [m s−1] |
y, z | space coordinates [m] |
Greek symbols | |
α | linear thermal expansion coefficient [K−1] |
εθ | tangential strain |
εr | radial strain |
ϕ | porosity |
κ | permeability [m2] |
λm | bulk thermal conductivity of fluid and minerals [W m−1 K−1] |
(ρc)CO2 | volumetric heat capacity of sCO2 [J m−3 K−1] |
ρmcm | bulk volumetric heat capacity of pore system [J m−3 K−1] |
σθ | tangential stress [Pa] |
σr | radial stress [Pa] |
σT | total stress [Pa] |
τ | tortuosity |
υ | Poisson’s ratio |
ψT | total thermal resistance in hollow circles [K m W−1] |
ψc | convective thermal resistance of injected sCO2 [K m W−1] |
ψ1 | conductive thermal resistance of secondary mineral [K m W−1] |
ψ2 | conductive thermal resistance of primary mineral [K m W−1] |
ωm | surface area of mineral [m2] |
Ω | saturation index of mineral |
Subscripts | |
inner | |
outer | |
c | chemical |
ef | effective |
r | radial |
p | pore |
T | total |
TM | thermo-mechanical |
θ | tangential |
Appendix A
Appendix B
Appendix C
- The internal boundary condition at the inner circle r = r0, and the outer circle of the primary mineral r = r2 are free of stress.
- The radial displacement and radial stress of the primary and secondary minerals are equivalent at r = r1. The two thermo-mechanical problems are coupled as a result of this combined boundary condition, which transforms the mechanical equilibrium between the primary and secondary minerals.
- At the inner radius r0, the temperature is fixed. Equations (15)–(17) are used to evaluate the temperature variations at the outer radius r1 of the secondary mineral and the outer radius r2 of the primary mineral.
References
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Ion | Sample VW1-6926 [mol kg−1] | |
---|---|---|
Before the Test | After the Test (720 h) | |
Ca | 0.552 | 0.5067 |
K | 0.058 | 0.0537 |
Mg | 0.082 | 0.0752 |
Na | 1.91 | 1.607 |
Ba | 2.97 × 10−6 | 5.66 × 10−6 |
Fe | 2.18 × 10−6 | 2.18 × 10−6 |
SiO2 | Below detection limit | 3.45 × 10−4 |
Mineral | Volume Fraction of the Core Sample (%) | Moles in the Core Sample Based on the Solid Volume (2.852 × 10−5 m3) |
---|---|---|
Quartz (Primary) | 88 | 1.01 |
K-feldspar (Secondary) | 12 | 0.3 |
Parameter | Sample VW1-6919 | |
---|---|---|
Before the Test | After the Test | |
Porosity | 0.236 | 0.214 |
Parameter | Value |
---|---|
Total pore volume [m3] | 5.8412 × 10−6 |
Reference temperature Tref [K] | 326.15 |
Injection pressure of sCO2 [Pa] | 13.1 × 106 |
Injection temperature Tinj [K] | 326.15 |
Injection volumetric flow rate [m3 s−1] | 4.5 × 10−7 |
Calculated flow velocity [m s−1] | 9.16 × 10−4 |
Parameter | Quartz | K-Feldspar |
---|---|---|
Ratio of expansion of compacted power (Poisson’s ratio) | 0.13 a | 0.05 b |
Elasticity modulus of compacted powder E [Pa] | 16.2 × 109 a | 12 × 109 b |
Thermal expansion coefficient α [K−1] c | 1.5 × 10−5 | 1.5 × 10−5 |
Density of solid [kg m−3 K−1] c | 2750 | 2550 |
Thermal conductivity [W m−1 K−1] c | 6 | 4 |
Kinetic rate constant [mol m−2 s−1] d | 1 × 10−14 | 3.9 × 10−13 |
Activation energy Ea [kJ mol−1] d | 87.6 | 38 |
Parameter | Sample T36-14.5 | |
---|---|---|
Before the Test | After the Test | |
Permeability [m2] | 3.6 × 10−15 | 39.5 × 10−15 |
Porosity | ~0.25 | ~0.285 |
Minimum pore radius [m] | 0.1 × 10−7 | |
Maximum pore radius [m] | 1 × 10−6 | |
Total pore volume [m3] | 4.161 × 10−5 | |
Reference temperature Tref [K] | 298.15 | |
Injection pressure of sCO2 [Pa] | 10 × 106 | |
Injection temperature Tinj [K] | 313.15 | |
Injection volumetric flow rate [m3 s−1] Injected pore volume [PV] | 1.66 × 10−9 between 0.1 and 2.9 PV 5 × 10−8 between 5 and 13.4 PV | |
Calculated flow velocity [m s−1] | 1.5 × 10−6 between 0.1 and 2.9 PV 4.55 × 10−5 between 5 and 13.4 PV | |
Ionic strength of the brine in the saturated core sample | ~3 |
Parameter | Quartz | Kaolinite |
---|---|---|
Ratio of expansion of compacted power (Poisson’s ratio) | 0.08 a | 0.05 b |
Elasticity modulus of compacted powder E [Pa] | 7 × 109 a | 10 × 109 b |
Thermal expansion coefficient α [K−1] c | 1.5 × 10−5 | 1.5 × 10−5 |
Density of solid [kg m−3 K−1] c | 2750 | 2600 |
Thermal conductivity of quartz [W m−1 K−1] c | 6 | 4 |
Kinetic rate constant of quartz [mol m−2 s−1] d | 1 × 10−14 | 1 × 10−13 |
Activation energy of quartz Ea [kJ mol−1] d | 87.6 | 22.2 |
Parameter | Value at 80 °C |
---|---|
Dissolution velocity Rdis | 8.49 × 10−10 [m s−1] |
Precipitation velocity Rpre | 3.81 × 10−9 [m s−1] |
Diffusion coefficient D | 5.98 × 10−10 [m2 s−1] |
Water film thickness S | 1 × 10−9 [m] |
Applied effective stress σe | 30 × 106 [Pa] |
Molar volume of calcite Φ | 3.62 × 10−5 [m3 mol−1] |
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Erol, S. Thermo-Hydro-Mechanical–Chemical Modeling for Pressure Solution of Underground sCO2 Storage. Modelling 2025, 6, 59. https://doi.org/10.3390/modelling6030059
Erol S. Thermo-Hydro-Mechanical–Chemical Modeling for Pressure Solution of Underground sCO2 Storage. Modelling. 2025; 6(3):59. https://doi.org/10.3390/modelling6030059
Chicago/Turabian StyleErol, Selçuk. 2025. "Thermo-Hydro-Mechanical–Chemical Modeling for Pressure Solution of Underground sCO2 Storage" Modelling 6, no. 3: 59. https://doi.org/10.3390/modelling6030059
APA StyleErol, S. (2025). Thermo-Hydro-Mechanical–Chemical Modeling for Pressure Solution of Underground sCO2 Storage. Modelling, 6(3), 59. https://doi.org/10.3390/modelling6030059