This paper presents a new parameter identification (PI) algorithm for estimating effective and detailed thermal parameters of ground source heat pump systems using data obtained from the well-known thermal response test. The PI comprises an iterative scheme coupling a semi-analytical forward model to an inverse model. The forward model is formulated based on the spectral element method to simulate transient 3D heat flow in ground source heat pump (GSHP) systems, and the inverse model is formulated based on the interior-point optimization method to minimize the system objective function. Compared to existing interpretation tools for the thermal response test, the proposed PI algorithm has several advanced features, including: it can handle fluctuating heat pump power and inlet temperatures; interpret data obtained from multiple heat injection or extraction signals; produce accurate backcalculation for short and long duration experiments; and handle multilayer systems. The PI algorithm is tested against synthesized data, using a wide range of random noise, and versus an available laboratory experiment. The computational results show that the PI algorithm is accurate, stable and exhibiting relatively high convergence rate.

This paper introduces a spectral model for a moving cylindrical heat source in an infinite conductive-convective domain. This physical process occurs in many engineering and technological applications including heat conduction-convection in ground source heat pump systems, where the borehole heat exchangers likely go through layers with groundwater flow. The governing heat equation is solved for Dirichlet and Neumann boundary conditions using the fast Fourier transform for the time domain, and the Fourier series for the spatial domain. A closed form solution based on the modified Bessel functions is obtained for the Dirichlet boundary condition and an integral form for the Neumann boundary condition. Limiting cases of the moving cylindrical heat source to represent a moving line heat source are also derived. Compared to solutions based on the Green's function and the Laplace transform, the spectral model has a simpler form, applicable to complicated time-variant input signals, valid for a wide range of physical parameters and easy to implement in computer codes. The model is verified against the existing infinite line heat source model and a finite element model.

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.

This paper introduces a semi-analytical model for the simulation of transient heat transfer with friction heat gain in a single U-tube geothermal borehole heat exchanger subjected to an arbitrary heat flux signal. The friction effect appears as a nonhomogeneous term in the governing equations, which constitutes a set of coupled partial differential equations describing heat flow in the three components of the borehole; pipe-in, pipe-out and grout. We utilize the spectral analysis for discretizing the time domain, and the eigenfunction expansion for discretizing the spatial domain to solve the governing initial and boundary value problem. The proposed model combines the exactness of the analytical methods with an important extent of generality in describing the geometry and boundary conditions of the numerical methods. The model is verified analytically against a simplified one-dimensional solution. A numerical example is given to illustrate the effect of friction on heat transfer in the borehole heat exchanger for different fluid velocities and viscosities. The analysis shows; for the geometry, materials fluid velocities and viscosities, typically utilized in shallow geothermal systems; the friction is not really significant. However, the main advantage of this work is on the solution technique that can be useful for many other applications, including fluid flow in narrow pipes, high fluid velocities, high fluid viscosities, and pipes made of composite materials and of complex geometry. Also, the method can be useful for solving other nonhomogeneous coupled partial differential equations.

In this paper, we introduce analytical solutions for transient heat conduction in an infinite solid mass subjected to a varying single or multiple cylindrical heat sources. The solutions are formulated for two types of boundary conditions: a time-dependent Neumann boundary condition, and a time-dependent Dirichlet boundary condition. We solve the initial and boundary value problem for a single heat source using the modified Bessel function, for the spatial domain, and the fast Fourier transform, for the temporal domain. For multiple heat sources, we apply directly the superposition principle for the Neumann boundary condition, but for the Dirichlet boundary condition, we conduct an analytical coupling, which allows for the exact thermal interaction between all involved heat sources. The heat sources can exhibit different time-dependent signals, and can have any distribution in space. The solutions are verified against the analytical solution given by Carslaw and Jaeger for a constant Neumann boundary condition, and the finite element solution for both types of boundary conditions. Compared to these two solutions, the proposed solutions are exact at all radial distances, highly elegant, robust and easy to implement.