Dan Bauer

Finite element modeling of borehole heat exchanger systems

Single borehole heat exchanger (BHE) and arrays of BHE are modeled by using the finite element method. The first part of the paper derives the fundamental equations for BHE systems and their finite element representations, where the thermal exchange between the borehole components is modeled via thermal transfer relations. For this purpose improved relationships for thermal resistances and capacities of BHE are introduced. Pipe-to-grout thermal transfer possesses multiple grout points for double U-shape and single U-shape BHE to attain a more accurate modeling. The numerical solution of the final 3D problems is performed via a widely non-sequential (essentially non-iterative) coupling strategy for the BHE and porous medium discretization. Four types of vertical BHE are supported: double U-shape (2U) pipe, single U-shape (1U) pipe, coaxial pipe with annular (CXA) and centred (CXC) inlet. Two computational strategies are used: (1) The analytical BHE method based on Eskilson and Claessons (1988) solution, (2) numerical BHE method based on Al-Khoury et al.s (2005) solution. The second part of the paper focusses on BHE meshing aspects, the validation of BHE solutions and practical applications for borehole thermal energy store systems.

Finite element modeling of borehole heat exchanger systems: Part 2. Numerical simulation

Single borehole heat exchanger (BHE) and arrays of BHE are modeled by using the finite element method. Applying BHE in regional discretizations optimal conditions of mesh spacing around singular BHE nodes are derived. Optimal meshes have shown superior to such discretizations which are either too fine or too coarse. The numerical methods are benchmarked against analytical and numerical reference solutions. Practical application to a borehole thermal energy store (BTES) consisting of 80 BHE is given for the real-site BTES Crailsheim, Germany. The simulations are controlled by the specifically developed FEFLOW-TRNSYS coupling module. Scenarios indicate the effect of the groundwater flow regime on efficiency and reliability of the subsurface heat storage system.