An efficient borehole heat exchanger model for the analysis of transient thermal response: comparison with some existing models

Abstract

For the analysis of the dynamic behaviour of a complete ground source heat pump system, computationally efficient models of the borehole heat exchanger are needed. Moreover, as we are moving towards system controllers using model predictive control, such a model needs to be potentially implemented in relatively simple hardware. At the same time, it is essential that a number of key physical processes and parameters are included in the model. These include at least the thermal capacity of the fluid moving through the heat exchanger, the thermal resistance between the fluid and the ground, the heat flow and temperature change in the surrounding ground volume as well as factors such as the near-surface temperature gradient. Within the scope of the EU funded H2020 project Geotech (GA 656889), Groenholland developed a numerically efficient heat exchanger model (GHBM, GroenHolland Borehole Model) that includes the mentioned key-processes. Essentially it is a model of plug fluid flow in the heat exchanger pipe with the heat flow to the surrounding ground as a function of temperature difference and borehole resistance (which is introduced as a parameter in the model). The radial heat flow in the ground is essentially calculated using a lumped capacitance thermal resistance network with a fixed far field temperature at the furthest node. Although relatively simple in formulation, there are also some key parameters that can be fairly easily included, these include: 1) Vertical temperature gradient, as initial temperatures for the ground nodes as well as the undisturbed ground temperature 2) Different thermal characteristics of different ground layers, for instance contrast between saturated and unsaturated zone. The iteration scheme implemented to solve the equations de-couples the time step in the model from the time step used in the encompassing model (e.g. TRNSYS system model). The time step for the borehole model is selected based on the plug flow velocity, borehole length and vertical discretisation. This allows the encompassing system model to run with a simulation time step that is larger than the time step required for the plug flow model without losing accuracy. In this paper we describe the model developed and compare it with different existing models (B2G, SBM, DST) using data from a thermal response test on a concentric heat exchanger with a special geometry. The comparison focusses on the difference between the model solutions with different selections of horizontal and vertical discretisation and also on running the model with or without the iteration scheme. Results show that the GHBM model is the fastest of the models compared, the root mean square error of temperature is only better in the B2G model and the error in the heat transfer is the smallest in the GHBM.