A spectral model for shallow geothermal systems

• Published in: International journal of numerical methods for heat & fluid flow 2012-01, Vol.22 (1), p.49-72
• Main Author: Al-Khoury, Rafid
• Format: Article
• Language: English
• Subjects: Algorithms; Boreholes; Boundary conditions; Boundary value problems; Computer simulation; Fourier transforms; Geothermal; Geothermal power; Heat conductivity; Heat exchangers; Heat resistance; Heat transfer; Mathematical models; Methods; Numerical analysis; Partial differential equations; Polyethylene; Soil (material); Studies; Temperature; Temperature distribution
• ISSN: 0961-5539; 1758-6585
• DOI: 10.1108/09615531211188793

Purpose - The purpose of this paper is to introduce a spectral model capable of simulating fully transient conductive-convective heat transfer processes in an axially-symmetric shallow geothermal system consisting of a borehole heat exchanger embedded in a soil mass.Design methodology approach - The proposed model combines the exactness of the analytical methods with important extent of generality in describing the geometry and boundary conditions of the numerical methods. It calculates the temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass using the discrete Fourier transform, for the time domain, and the Fourier-Bessel series, for the spatial domain.Findings - The paper calculates the temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass in a robust and computationally very efficient procedures. Analysis which might take long time in a work station, if use is made of standard numerical procedures, takes only 1 second in an Intel PC with the proposed model.Practical implications - The model is capable of simulating fully transient heat transfer in a shallow geothermal system subjected to short and long-term time varying boundary conditions. The CPU time for calculating temperature distributions in all involved components; pipe-in, pipe-out, grout, and soil, using 2048 FFT samples, for the time domain, and 100 Fourier-Bessel series samples, for the spatial domain, was in the order of 1 second in an Intel PC. The accuracy and computational efficiency of the model makes it, if elaborated, vital for engineering practice.Originality value - The proposed model is original and generic. The idea behind it is new and has not been utilized in this field of application. The model can be extended easily to include other types of borehole heat exchangers embedded in multi-layer systems.