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A combined method using Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM) to simulate geothermal reservoirs in Enhanced Geothermal System (EGS)
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Abstract: With the development of industrial activities, global warming has accelerated due to excessive emission of CO2. Enhanced Geothermal System (EGS) utilizes deep geothermal heat for power generation. Although porous medium theory is commonly employed to model geothermal reservoirs in EGS, Hot Dry Rock (HDR) presents a challenge as it consists of impermeable granite with zero porosity, potentially distorting the physical interpretation. To address this, the Lattice Boltzmann Method (LBM) is employed to simulate CO2 flow within geothermal reservoirs and the Finite Volume Method (FVM) to solve the energy conservation equation for temperature distribution. This combined method of LBM and FVM is implemented using MATLAB. The results showed that the Reynolds numbers (Re) of 3,000 and 8,000 lead to higher heat extraction rates from geothermal reservoirs. However, higher Re values may accelerate thermal breakthrough, posing challenges to EGS operation. Meanwhile, non-equilibrium of density in fractures becomes more pronounced during the system's life cycle, with non-Darcy's law becoming significant at Re values of 3,000 and 8,000. Density stratification due to buoyancy effects significantly impacts temperature distribution within geothermal reservoirs, with buoyancy effects at Re=100 under gravitational influence being noteworthy. Larger Re values (3,000 and 8,000) induce stronger forced convection, leading to more uniform density distribution. The addition of proppant negatively affects heat transfer performance in geothermal reservoirs, especially in single fractures. Practical engineering considerations should determine the quantity of proppant through detailed numerical simulations.
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Figure 3. Variation of Criterion with the grids number of 50×100, 100×200, 150×300, 200×400 and 250×500
Figure 4. Comparison between the results of reference (Krüger et al. 2016) and this paper based on the velocity distribution along the centerline for a lid-driven cavity
Figure 6. Comparison between the numerical results and analytical results in a single fracture
Figure 7. Scale of the region in geothermal reservoir for complex fracture distributions, single fracture, complex fracture distributions with proppant and single fracture with proppant
Figure 16. Temperature distribution in the fractured reservoir with single fracture during 30 years
Table 1. Initial and boundary conditions for base simulation case
Parameters Value Unit Mass flow rate 20 kg/s Rock thermal conductivity 3.0 W/(m·K) Rock density 2,623 kg/m3 Specific thermal capacity of rock 980 J/(kg·K) Initial temperature of rock 441.82 K Computing time 30 a Inlet temperature of the single fracture 343.15 K Fracture aperture 0.0001 m External diameter 0.137 m Inside diameter 0.124 m Thermal conductivity of wellbore wall 0.52 W/(m·K) Elastic modulus of rock 40 GPa Poisson's ratio of rock 0.2 Pressure at 3,000 m subsurface 30 MPa Injection concentration 0.018 mol/kg Ambient temperature 293.15 K Size of fractured reservoir 500 × 500 × 500 m3 
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Table 2. Initial and boundary conditions in this section (Zhong et al. 2022)
Properties Value Unit Properties Value Unit Density of HDR 2,623 kg/m3 Normal stress on the top boundary 20 MPa Specific heat capacity of HDR 980 J/(kg·K) Normal stress on the bottom boundary 30 MPa Thermal conductivity of HDR 3 W/(m·K) Normal stress on the two sides 20 MPa Porosity in fracture system 0.5 - Rock Young's modulus 24 GPa Porosity in matrix 1 × 10−5 - Rock Possion's ratio 0.15 Permeability in fracture system 1 × 10−13 m2 Thermal expansion coefficient 2×10−6 1/K Permeability in matrix 9 × 10−19 m2 Biot coefficient 0.79 Runtime 30 years Mass flow rate 45 kg/s
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