Three-Dimensional Numerical Simulation Of Geothermal Field In Space-Wavenumber Domain

Geothermal is a kind of clean and renewable energy with abundant reserves and wide distribution,which plays an important role in the sustainable development of society.Fine and efficient numerical simulation method of the geothermal field is significant for mastering the geothermal field distribution,evaluating geothermal resources and exploiting geothermal energy.In order to solve the problem of large computation and high storage requirements for complex underground models in the geothermal field three-dimensional numerical simulation using the finite element method,the finite difference method and other conventional methods,a geothermal field three-dimensional numerical simulation algorithm in the space-wavenumber mixed domain is studied in this paper,which achieves high efficiency and high precision numerical simulation of steady and transient temperature fields.The specific research contents are as follows:1.Based on the heat transfer equation of the geothermal field and the superposition principle of the temperature field,the steady and transient numerical simulation of three-dimensional geothermal field in the spacewavenumber mixed domain is realized.The background field is calculated by uniform layered model,and the anomaly field is calculated by the space-wavenumber mixed domain method.The three-dimensional partial differential equations satisfying the abnormal temperature field in the space domain are transformed into a series of one-dimensional ordinary differential equations by using the two-dimensional Fourier transform.The vertical direction is retained as the spatial domain,and the mesh division is flexible.The finite element method is used to solve ordinary differential equations and the catch-up method is used to solve linear equations with fixed bandwidth.The compact operator is constructed and the iterative method is used to approximate the true solution.When solving the transient temperature field,the time item uses linear interpolation processing,and the equation uses the space-wave number mixed domain method to solve.The algorithm makes full use of the rapidity of the Fourier transform and the efficiency of the catch-up method to solve the linear equations with fixed bandwidth,which improves the computational efficiency of the algorithm effectively.2.The numerical solution of the proposed algorithm is compared with the calculation results of COMSOL Multiphysics software by using the model,and the correctness of the algorithm is verified.The convergence of the algorithm is analyzed by using different thermal conductivity models,which shows that the algorithm can converge stably and quickly within the actual geological range.Compared the calculation efficiency with COMSOL Multiphysics under the same grid division,the result shows that the calculation time and memory requirements of the algorithm in this paper are reduced by order of magnitude.With the increase of the number of nodes,the time consumption and memory requirement of the algorithm in this paper increase approximately linearly,which illustrates that the proposed algorithm is suitable for large-scale and efficient numerical simulation.3.Based on the three-dimensional steady-state geothermal field numerical simulation algorithm in the space-wavenumber mixed domain,the effects of different thermal physical properties on the distribution of the geothermal field are studied by using the high thermal conductivity model,the low thermal conductivity model,the thermal convection model,the undulating terrain model and the thermal reservoir model.The results show that the higher the thermal conductivity is,the smaller the temperature gradient is,the more sparse the isotherms are.The smaller the thermal conductivity of the formation is,the larger the temperature gradient is and the more dense the isotherms are.The fluid convective has the great influence on the regional temperature field.On the undulating terrain,the temperature of the high terrain is low,the temperature of the low terrain is high.A thermal reservoir model with cover,heat conduction channel and heat source is simulated.4.Based on the three-dimensional transient-state geothermal field numerical simulation algorithm in the space-wavenumber mixed domain,the paper simulates the transient temperature field in the dynamic process by designing the high temperature intrusion model,the formation interface fluctuation model,the groundwater flow model,the unsteady boundary model and the magma type geological geothermal model.The results show that when the temperature changes suddenly,it has a great influence on the surrounding rock temperature in the initial stage,and the temperature changes quickly.With the passage of time,the temperature change slows down and the temperature distribution tends to be stable.The influence of heat convective on the temperature field increases gradually with time,and the isotherm forms a bulge along the direction of fluid flow.The change of geological structure has little influence on the temperature field distribution in the initial stage,but the influence gradually increases with time,and finally reaches a stable state.