Longevity of Enhanced Geothermal Systems with Brine Circulation in Hydraulically Fractured Hydrocarbon Wells
Abstract
:1. Introduction
2. Prior Work and Model Design
2.1. Generic Models and Case Studies
2.2. Analytical Models
2.3. Model Design Used in This Study
- Mechanism 1: Heating of the cold injection brine when passing along a hotter fracture wall;
- Mechanism 2: Cooling of the hot rock due to the passing of a colder brine;
- Mechanism 3: The integrated effects of brine-heating and fracture-wall cooling;
- Mechanism 4: Recovery of the cooled fracture wall by “self-heating” via the adjacent deeper, still hot rock, once the injection of the cold brine is (temporarily) halted.
- The fracture plane is horizontal with variable finite length and width; channel flow is assumed within the fracture.
- Flow distance needed to reach a certain temperature is calculated analytically (Equation (7)) for fixed fracture wall temperature.
- Thermal conduction in the rock interior adjacent to the fracture wall cooled by the circulating brine is analytically solved (Equation (12)), which gives the rock temperature profile versus rock depth.
- Rock temperature recovery after the fluid circulation stops is calculated explicitly using Fourier transform (Equation (15)).
- Heat transfer between the cooler brine and the hotter wall rock of the fracture is integrated using a semi-analytical method.
2.4. Heat Flow Recharge of EGS Reservoirs
3. Assessment of Heat Transfer Mechanisms
3.1. Mechanism 1: Heating of the Cold Injection Brine When Passing Along a Hotter Fracture Wall
3.2. Mechanism 2: Cooling of the Hot Fracture due to the Passing of a Colder Brine
3.3. Mechanism 3: Combination of Fluid Heating and Fracture Wall Cooling
3.4. Mechanism 4: Recovery of the Cooled Fracture Wall by “Self-Heating"
4. Discussions and Intermittent Production Model
4.1. Principle Outcomes of Simple Heat Transfer Model (Mechanisms 1–4)
4.2. Integrated Model for Longevity of Heat Extraction
4.3. Generic Insights
4.4. Limitations of the Model
5. Conclusions
- A continuous fluid circulation in EGS reservoirs with limited fracture-matrix surface contact area will quickly quench the effective transfer of heat due to rapid cooling of the fracture wall rock. The fracture wall temperature for the region close to the injection point will equalize to the temperature of the cold injection brine in about three days in the cases studied.
- A steady-state extraction of geothermal energy cannot be achieved over longer time scales due to the rapid decline in the heat transfer rate at the fracture wall.
- A periodic circulation plan, proposed here to remedy the situation, could lead to a quasi-steady state of the extracted fluid temperature. The fracture wall is cooled by periodic injection of cold brine but will heat up fast enough after well shut-in to restore the temperature of the cooled fracture wall such that heat transfer is possible again after brine injection resumes. Our models show how fast after shut-in of the injection well the fracture rock wall interior will restore to the initial temperature.
- The temperature history of the injection brine was calculated accounting for four heat transfer mechanisms. The temperature of the cold brine requires a certain travel distance to reach a required temperature for economic production, which is scaled for the specific reservoir conditions studied here.
- The injection brine is heated faster for slower running brine and for smaller fracture aperture; however, the volumetric production is inversely proportional to the fluid velocity in the fracture space.
Author Contributions
Funding
Conflicts of Interest
Appendix A. Methodology for Brine Temperature Computation
Appendix B. Derivation of Rock Heat Recovery
References
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Fracture Parameters | Notation | Value | Unit |
Length (of Well) | L | 1000 | m |
Inter-well Distance | D | 100–1200 m | m |
Aperture | A | 0.005–0.01 | m |
Fracture wall temperature | Ts | 100/125/150 (212/257/302) | °C (°F) |
Brine Parameters | Notation | Value | Unit |
Initial temperature | Tmi | 20 (70) | °C (°F) |
Density | ρ | 1 | kg/m3 |
Heat capacity | c | 4186 | J/(kg·K) |
Thermal conductivity | k | 0.8 | W/(m K) |
Heat transfer coefficient | h | 0.0029 | W/(m2 K) |
Velocity | υ | 0.0001–0.0368 | m/s |
Nusselt number | Nu | 3.657 | - |
(a) | ||||
Velocity (m/s) | m3/s | bbl/day | gpm | L/s |
0.1 | 0.5 | 271,720 | 7925 | 500 |
0.0368 | 0.184 | 100,000 | 2917 | 184 |
0.01 | 0.05 | 27,172 | 793 | 50 |
0.001 | 0.005 | 2717 | 79 | 5 |
0.0001 | 0.0005 | 271.7 | 7.9 | 0.5 |
(b) | ||||
Velocity (m/s) | m3/s | bbl/day | gpm | L/s |
0.1 | 1 | 543,440 | 15,850 | 1000 |
0.0184 | 0.184 | 100,000 | 2917 | 184 |
0.01 | 0.1 | 54,344 | 1585 | 100 |
0.001 | 0.01 | 5434 | 159 | 10 |
0.0001 | 0.001 | 543.4 | 15.9 | 1 |
(a) | |||||
Fracture Aperture 0.005 m | Fracture Aperture 0.01 m | ||||
Velocity (m/s) | Flux (bbl/day) | Distance (m) | Velocity (m/s) | Flux (bbl/day) | Distance (m) |
0.1 | 271,720 | 7.44 | 0.1 | 543,440 | 29.75 |
0.0368 | 100,000 | 2.74 | 0.0184 | 100,000 | 5.47 |
0.01 | 27,172 | 0.74 | 0.01 | 54,344 | 2.98 |
0.001 | 2717 | 0.07 | 0.001 | 5434 | 0.30 |
(b) | |||||
Fracture Aperture 0.005 m | Fracture Aperture 0.01 m | ||||
Velocity (m/s) | Flux (bbl/day) | Distance (m) | Velocity (m/s) | Flux (bbl/day) | Distance (m) |
0.1 | 271,720 | 7.61 | 0.1 | 543,440 | 30.45 |
0.0368 | 100,000 | 2.80 | 0.0184 | 100,000 | 5.60 |
0.01 | 27,172 | 0.76 | 0.01 | 54,344 | 3.05 |
0.001 | 2717 | 0.08 | 0.001 | 5434 | 0.30 |
(c) | |||||
Fracture Aperture 0.005 m | Fracture Aperture 0.01 m | ||||
Velocity (m/s) | Flux (bbl/day) | Distance (m) | Velocity (m/s) | Flux (bbl/day) | Distance (m) |
0.1 | 271,720 | 7.72 | 0.1 | 543,440 | 30.90 |
0.0368 | 100,000 | 2.84 | 0.0184 | 100,000 | 5.69 |
0.01 | 27,172 | 0.77 | 0.01 | 54,344 | 3.09 |
0.001 | 2717 | 0.08 | 0.001 | 5434 | 0.31 |
Rock Parameters | Notation | Value | Unit |
---|---|---|---|
Surface temperature | 125 (257 °F) | °C | |
Density | 2650 (quartz) | kg/m3 | |
Heat capacity | c | 710 (quartz) | J/(kg·K) |
Thermal conductivity | k | 1.88 (limestone) | W/(mK) |
Thermal diffusivity | 10−6 | m2/s | |
Heat transfer coefficient | h | 0.0029 | W/(m2 K) |
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Zuo, L.; Weijermars, R. Longevity of Enhanced Geothermal Systems with Brine Circulation in Hydraulically Fractured Hydrocarbon Wells. Fluids 2019, 4, 63. https://doi.org/10.3390/fluids4020063
Zuo L, Weijermars R. Longevity of Enhanced Geothermal Systems with Brine Circulation in Hydraulically Fractured Hydrocarbon Wells. Fluids. 2019; 4(2):63. https://doi.org/10.3390/fluids4020063
Chicago/Turabian StyleZuo, Lihua, and Ruud Weijermars. 2019. "Longevity of Enhanced Geothermal Systems with Brine Circulation in Hydraulically Fractured Hydrocarbon Wells" Fluids 4, no. 2: 63. https://doi.org/10.3390/fluids4020063
APA StyleZuo, L., & Weijermars, R. (2019). Longevity of Enhanced Geothermal Systems with Brine Circulation in Hydraulically Fractured Hydrocarbon Wells. Fluids, 4(2), 63. https://doi.org/10.3390/fluids4020063