Elsevier

Renewable Energy

Volume 151, May 2020, Pages 805-815
Renewable Energy

Un-stationary thermal analysis of the vertical ground heat exchanger within unsaturated soils

https://doi.org/10.1016/j.renene.2019.11.065Get rights and content

Highlights

  • The proposed total temperature better represents the results of the experiment.

  • The heat migration effect was observed at all investigated depths.

  • Thermal energy losses due to diffusion streams are calculated at about 2–4%.

  • Observed capillary channels showed a large non-stationary of flow.

Abstract

The efficiency of heat exchange in ground heat exchangers (GHE) in many projects decreases throughout their service life. Large temperature fluctuations were observed during the ground heat exchanger loading and during its natural cooling. This problem stems mainly from the influences of heating and humidity migration on the operation of the ground heat exchanger in unsaturated soil. To find the answer to the problem numerical model of a porous medium with multi-component fluid flow was applied. The mathematical description was expanded by additional streams describing the exchange of thermal energy within the backfill material and the structure of the porous model. Ground porosity was mapped geometrically and mathematically. The definition of total temperature was introduced. The results obtained from proposed model were compared with another model results which was based on solving only the classical heat exchange equation. The model was also verified through the measurement data read from 3 sensors installed at different depths of one borehole and at different time intervals. The parameters of the model result from local climatic conditions of Jabłonna near Warsaw. 24-hour operation of a single borehole was simulated numerically. The results of the model proposed by the author were of a greater convergence with the real data than those obtained for the classical heat exchange model. The critical point of the model was the selection of the coefficients describing the flow resistance of i-components in the porous medium and the particular terms of the total temperature adopted definition. The proposed model allows for a more accurate estimation of the available thermal power in the future and more accurate analysis of the degree of the effort of the structure in the context of its exploitation and the destruction time.

Introduction

Modelling heat transfer in lower heat source is one of the most important skills in predicting the period for which the heat source can be used, its efficiency or duration of individual cycles. An accurate calculation model is necessary in order to be able to correctly determine the individual loss components The quality of the calculation model is influenced by many factors, including: whether it presents the image of the desired parameters in a one-dimensional or three-dimensional manner [1], whether it describes the surrounding soil as a solid body or porous medium … Phase changes occur inside the ground, there is groundwater flow or the possibility of diffusion of gases, compound fluids, or an electromagnetic field exists [2].

When analysing the available models, those in which an additional mechanism, apart from the classic heat conduction in the ground, was diffusion movements caused by water migration should be emphasized [3]. The migration of groundwater was driven by the forces of the gravity or by the pressure difference. The applied model, due to the partial nature, did not include the transport of vapours and phase transitions of water permeating the soil, which had its reference in the curves verifying the model.

Considering the porous medium model with the multi-component fluid flows, it was found that the increase of the soil saturation, the assumed GHE loading time, and the mass flow rate of the working fluid affect the soil temperature changes significantly [4]. Additionally, it was noticed that regeneration of the low temperature heat source using the extremely enlarged heat flux leads to drying of the moist soil, and thus to deterioration of heat conduction properties.

Negligence of moisture changes may lead to an underestimation of the thermal capacity of the soil [5]. Elevation of the groundwater table had a beneficial effect on the operation of the GSHP, connected with the heat exchanger. They also emphasise that considering the transfer of the heat energy along with the groundwater flow, it is important to take into account the groundwater surface elevation. Its fluctuations can cause differences in the temperature indication of 3–4%. These values do not differ from those presented by the authors in this paper.

Advanced models [[6], [7], [8]] include also the convectional flow of the gas, the water vapour and the surface water. It was shown that approximately 83.3% of stored energy is stored in the medium until the end of the 6th day, and 10% of stored energy is being wasted as a result of a convective heat flow until the end of 10th day.

In the current paper the ground heat exchangers mounted in the unsaturated soils are being considered. The proposed calculation model is based on the finite volume method. It provides a three-dimensional description of the surrounding soil, treating it as a porous medium inside which there occur a diffusive movement of the gaseous and liquid components. There is a groundwater flow, conditioned by natural geological processes in the analysed plot of land- Jabłonna near Warsaw.

To solve the problem, a model describing Darcy flow was used with effects of freezing disregarded [[9], [10], [11]]. The air flow was modelled as an ideal gas.

For a more accurate representation of the temperature ragged nature measured by the sensors in the borehole, a new definition of total temperature was proposed. It was completed with an additional term describing both heat and mass diffusion in the element of the backfill material and the surrounding soil.

Section snippets

Physical model

The physical model presents a classic U-tube exchanger, installed in a hole drilled in the soil. It has two round fluid flow ducts, walls separating the channel from backfill material and soil forming the backfill. The detailed dimensions are presented in Fig. 1.

The backfill material and the liquid inside the ducts have constant physical properties, while the soil changes, depending on the depth at which the section of the exchanger was considered. The total height of the model is 80 m, and the

The temperature distribution of the GHE at the centre of the cross-section in the radial direction

Fig. 7 shows the temperature field read in the centre of the section of the considered soil fragment at the depth of 75 m. The temperature field gradually increases during loading of the exchanger, and then decreases during cooling.

After 8.5 h of charging - Fig. 7c - the area with the highest temperature does not exceed half of the considered soil area. It is also visible that the isotherms are clearly directed towards the right. A more pronounced migration of the temperature field is visible

Conclusions

The paper analyses the model for a heat exchanger installed in unsaturated soils. The ground porosity was modelled geometrically and mathematically, also taking the flow of groundwater in liquid and gaseous form into account. I suggested a definition of the total temperature, which takes into account the influence of diffusive mass transfer on the amount of heat accumulated. A 24-hours work time period of the ground heat exchanger was analysed numerically. The temperature value obtained for

CRediT author statement

Daniel Sławiński: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data Curation, Writing – Original Draft, Writing – Review and Editing, Visualization, Supervision, Project administration, Funding acquisition.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Nomenclature

Abbreviations

CFD
Computational Fluid Dynamics
C–F-L
Courant-Friedrich-Lewy condition
FEM
Finite Elements Method
FVM
Finite Volume Method
RES
Renewable Energy Source
GSHP
Ground-Source Heat Pumps
TRT
Thermal Response Test
GHE
Ground Heat Exchanger
HP
Heat Pump
LTHB
Low-Temperature Heat Buffer

Parameters

T
temperature (K)
TTOT
total temperature (K)
cp
specific heat at constant pressure (J/kg K)
k
thermal conductivity (W/m K)
v
velocity fields [m/s]
n
vector normal to surface
J
diffusion flux for laminar flow (kg/m2)
Pr
Prandtl number [−]
Re
Reynolds

References (30)

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