TY - JOUR
T1 - A semi-analytical model for detailed 3D heat flow in shallow geothermal systems
AU - BniLam, N.H.N.
AU - Al-Khoury, Rafid
AU - Shiri, A.
AU - Sluys, L. J.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - A semi-analytical model for simulating transient conductive-convective heat flow in a three-dimensional shallow geothermal system consisting of multiple borehole heat exchangers (BHE) embedded in a multilayer soil mass is introduced. The model is formulated in three steps, starting from an axial symmetric system and ending in a 3D multilayer, multiple BHE system. In step 1, the model is formulated as a single BHE embedded in an axial symmetric homogeneous soil layer, and the governing heat equations are solved analytically using the fast Fourier transform, the eigenfunction expansion and the modified Bessel function. In step 2, the model is extended to incorporate multiple layers using the spectral element method. And in step 3, the model is extended to incorporate multiple borehole heat exchangers using a superposition technique suitable for Dirichlet boundary conditions. The ensuing computational model solves detailed three-dimensional heat flow using minimal CPU time and capacity. The number of the required spectral elements is equal to the number of soil layers embedded in which any number of borehole heat exchangers with any layout configuration. A verification example illustrating the model accuracy and numerical examples illustrating its computational capabilities are given. Despite the apparent rigor of the proposed model, its high accuracy and computational efficiency make it suitable for engineering practice.
AB - A semi-analytical model for simulating transient conductive-convective heat flow in a three-dimensional shallow geothermal system consisting of multiple borehole heat exchangers (BHE) embedded in a multilayer soil mass is introduced. The model is formulated in three steps, starting from an axial symmetric system and ending in a 3D multilayer, multiple BHE system. In step 1, the model is formulated as a single BHE embedded in an axial symmetric homogeneous soil layer, and the governing heat equations are solved analytically using the fast Fourier transform, the eigenfunction expansion and the modified Bessel function. In step 2, the model is extended to incorporate multiple layers using the spectral element method. And in step 3, the model is extended to incorporate multiple borehole heat exchangers using a superposition technique suitable for Dirichlet boundary conditions. The ensuing computational model solves detailed three-dimensional heat flow using minimal CPU time and capacity. The number of the required spectral elements is equal to the number of soil layers embedded in which any number of borehole heat exchangers with any layout configuration. A verification example illustrating the model accuracy and numerical examples illustrating its computational capabilities are given. Despite the apparent rigor of the proposed model, its high accuracy and computational efficiency make it suitable for engineering practice.
KW - BHE
KW - GHP
KW - GSHP
KW - Multilayer system
KW - Multiple borehole heat exchangers
KW - Shallow geothermal system
KW - Spectral element method
UR - http://www.scopus.com/inward/record.url?scp=85043988158&partnerID=8YFLogxK
U2 - 10.1016/j.ijheatmasstransfer.2018.03.010
DO - 10.1016/j.ijheatmasstransfer.2018.03.010
M3 - Article
SN - 0017-9310
VL - 123
SP - 911
EP - 927
JO - International Journal of Heat and Mass Transfer
JF - International Journal of Heat and Mass Transfer
ER -