| Title | Modeling Thermal Fracturing and Heat-Transfer Area Enhancement: Long-Term Sustainability of Enhanced Geothermal Systems |
|---|---|
| Authors | Quanlin ZHOU, Bin CHEN |
| Year | 2023 |
| Conference | World Geothermal Congress |
| Keywords | Enhanced geothermal system, thermal fracture, dimensionless solution, displacement discontinuity method, stability analysis, dynamic fracture spacing |
| Abstract | In the current design of enhanced geothermal systems (EGS), two horizontal wells are drilled, multiple vertical hydraulic fractures are stimulated, cold water is then injected into the hydraulic fractures, and hot water is produced from them for power generation. The injected water cools the hydraulic fractures and rock matrix, leading to strong thermal stress. Under the thermal stress, as well as elevated fluid pressure, parallel transverse thermal fractures initiate at the surface of each hydraulic fracture. During their propagation, some thermal fractures are arrested due to inter-fracture stress interaction, leading to a hierarchically ordered pattern of fractures with increasing spacing. These thermal fractures and hydraulic fractures may form a well-connected fracture network, thus enhancing fracture-matrix heat-transfer area. In this study, the thermal fracturing of low-permeability formations under one-dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length L, aperture Ω, spacing D, time τ, and effective confining stress T, were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, L(τ,T) increases nonlinearly with √τ and then transitions to scaling law L=f(T) √τ, indicating that late-time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, L(τ,T,D) deviates from the single-fracture solution at a later τ for a larger D, showing slower propagation under inter-fracture stress interaction. For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, L=f'(T) √τ with f'(T)<f(T), obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter T. Excellent agreement was achieved between these theoretical solutions and their corresponding numerical solutions based on a fracture model with the finite element method. The dimensionless solutions of dynamically spaced thermal fractures were applied to the Utah FORGE EGS site. The rock properties, cooling conditions, in situ fluid pressure, and in situ confining stress result in dimensionless effective confining stress of T=0.11. The application demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in surface aperture (at the hydraulic fracture) at 1, 100 and 10,000 days of water circulation. Elevated fluid pressure of 32.2 MPa with T=0 results in 142 m at 10,000 days, indicating that thermal and hydraulic fractures can form a well-connected fracture network for changing fluid flow path and enhancing heat-transfer area. REFERENCES Chen, B., and Zhou, Q.: Scaling behavior of thermally driven fractures in deep low-permeability formations: A plane strain model with 1-D heat conduction. Journal of Geophysical Research: Solid Earth, 127, (2022), e2021JB022964. https://doi.org/10.1029/2021JB022964. |