Efficient finite element formulation for geothermal heating systems. Part II: transient

Abstract

SUMMARYThis paper presents an extension to the work presented in Part I of this series of two articles to the transient case. Emphasis is placed on the development of a new model for heat flow in a double U-shape vertical borehole heat exchanger and its thermodynamic interactions with surrounding soil mass. The discretization of the spatial-temporal domain of the heat pipe model is done by the use of the space-time finite element technique in conjunction with the Petrov-Galerkin method and the finite difference method. The paper shows that the proposed model and the choice of the discretization technique, in addition to the utilization of a sequential numerical algorithm for solving the resulting system of non-linear equations, have contributed in reducing significantly the required number of finite elements necessary for describing geothermal heating systems. Details of the mathematical derivations and comparison to experimental data are presented.

3D transient heat transfer numerical analysis of multiple energy piles

“…Al-Khoury et al [28][29][30] proposed 3D numerical model depicting thermal interactions among the BHE elements including inletpipe, outlet-pipe and grout. This model addresses the formulation equilibrium, the effect of thermal resistance and the FEM discretization.…”

“…(14) and (15) denote the volumes of the specific components, and the right sides denote the contact surface regions for the interacting surfaces. Based on the simple model presented by Al-Khoury et al [28][29][30], heat transfer coefficients of U-tube can be written as…”

A Review of the Modelling of Thermally Interacting Multiple Boreholes

“…Many of the models for heat transfer analysis inside the borehole are summarized in Table 1. Further improvements, such as accounting for thermal capacity of the borehole components to improve the precision of the resistance model, can be made to improve the accuracy of the model inside the borehole [22][23][24]. Several simulation models for the heat transfer outside the borehole are available.…”

“…Some models describe the system in a three-dimensional domain by reducing the number of mesh elements, but this approach can result in lower accuracy. There are also several numerical techniques available in different numerical approaches which can be used to reduce the computation time [23,24,51].…”

Optimizing Geothermal Energy Resource

“…Alternatively, there are many papers about the design of U-tube and double pip heat exchangers with new geothermal wells (e.g. Al-Khoury & Bonnier [19], Wang et al [20], Garbai & Méhes [21], Zhongjian & Zheng [22]). …”