A contribution towards the determination of g-functions using the finite line source

Assessment of the Gradient of an Objective Function by Analytical Derivation for Optimization-based Design of Ground-coupled Heat Pump Systems

“…Although many methods can be used to construct g , the approach chosen in this article is based on the work of Marcotte and Pasquier (2014) because of its efficiency and flexibility. The approach, itself inspired by the works of Lamarche (2009), Cimmino et al (2013) and Lazzarotto (2014), consists to find sequentially the heat transfer rates t q emanating from the boreholes of a GHE using a linear system of equations expressed, for simplicity, in a compact matrix notation. For a parallel arrangement of the boreholes, the system corresponding to the mean temperature at the borehole wall is given by: vector of ones and G is the following interaction matrix:…”

Examination of Ambient Temperature Variations Effects on Predicted Fluid Temperatures in Vertical Boreholes

“…where , Information on the use of numerical Laplace transforms for the calculation of borehole wall temperatures is given in (Cimmino, et al 2013;Cimmino and Bernier 2014;Cimmino 2015;Cimmino and Bernier 2015). Segment-to-segment response factor increments are given by the finite line source solution (Claesson and Javed 2011;Cimmino and Bernier 2014).…”

“…Since the finite line source solution assumes a uniform heat extraction or injection rate along the boreholes, contrary to the uniform borehole wall temperature used by Eskilson (1987), thermal response factors obtained from the finite line source solution tend to overestimate Eskilson's g-functions. Cimmino et al (2013) and Cimmino and Bernier (2014) proposed a method, based on the finite line source, to consider the variation of the heat extraction rates along the borehole lengths and obtain thermal response factors for uniform borehole wall temperatures. A similar approach was used by Lazzarotto (2016) and Lazzarotto and Björk (2016) for tilted boreholes.…”

Design of a laboratory borehole storage model

“…Although convenient for fast computation, the different FLS methods failed to reproduce Eskilson's g-functions for large borehole fields because of the difference in boundary conditions (BCs) applied along the borehole wall between the two models. Although none of these BCs duly represent a real case, g-functions will better represent temperature changes in the borehole field when all boreholes are fed in parallel, as highlighted by Cimmino et al (2013). This FLS vs. g-function issue was tackled by several authors who proposed modelling straight (Cimmino & Bernier, 2014) and inclined (Lazzarotto, 2016;Lazzarotto & Björk, 2016) boreholes as stacks of FLS while imposing a uniform temperature BC.…”