Efficiency and economic analysis of utilizing latent heat from groundwater freezing in the context of borehole heat exchanger coupled ground source heat pump systems

Highlights

• A numerical model was developed to simulate BHE induced soil freezing.

• Latent heat from freezing slows down the BHE outlet temperature drop.

• COP corrected boundary condition produces more realistic estimation.

• Longer BHE do not always lead to a better financial performance over 30 years.

• Total cost of GSHPS depends heavily on electricity price and interest rate.

Abstract

To utilize the shallow geothermal energy, heat pumps are often coupled with borehole heat exchangers (BHE) to provide heating and cooling for buildings. In cold regions, soil freezing around the BHE is a potential problem which will dramatically influence the underground soil temperature distribution, subsequently the inlet and outlet circulating fluid temperature of the BHE, and finally the efficiency of the heat pump. In this study, a numerical model has been developed to simulate the coupled temperature evolution both inside the BHE, and the propagating freezing front in the surrounding soil. The coupled model was validated against analytical solutions and experimental data. The influence of the freezing process on the overall system performance is investigated by comparing one long BHE configuration without freezing and another short one with latent heat from the frozen groundwater. It is found that when freezing happens, the coefficient of performance (COP) of the heat pump will decrease by around 0.5, leading to more electricity consumption. Furthermore, analysis of the simulation result reveals that the exploitation of latent heat through groundwater freezing is only economically attractive if electricity price is low and interest rate high, and it is not the case is most European countries.

Introduction

In recent years, ground source heat pump systems (GSHPS) are increasingly employed as a new technology for heating and cooling of buildings. In the heating mode, the general principle of a GSHPS is to extract heat from the shallow subsurface by circulating heat-carrying fluid through single or multiple borehole heat exchangers (BHE), which are typically operating at a relatively low temperature [1]. The energy carried by the circulating fluid is then lifted by heat pump to a level suitable for domestic applications. For cooling applications, the system can be reversed, and the excess heat can be removed from the building and stored in the ground. As the temperature in the shallow subsurface remains constant, GSHPS are very efficient in comparison to other technologies [2]. For example, if 1 kW h of energy is required to heat the building, only 0.25–0.3 kW h of electricity are consumed to drive the heat pump [3]. The substitution of coal and gas burning boilers by GSHPS will not only reduce fuel costs, but also lead to substantially lower emission of CO₂ and air pollutants. Therefore, GSHPS have become a very attractive technology for domestic heating and hot water supply. In cold regions, the undisturbed soil temperature itself is already low (sometimes less than 10 °C). Typically, the circulating fluid inside the BHE is a mixture of water and anti-freezer. It allows its temperature to fall below zero and cause the freezing of groundwater surrounding the BHE [4]. This will strongly affect the soil temperature distribution, and the heat pump efficiency as well.

In practice, the length of BHE is designed based on the thermal conductivity and diffusivity of the soil, which can be measured by a thermal response test. Roth et al. [5] made the first in-situ thermal response test by installing BHE in Latin America. Wang et al. [6] proposed a novel constant heating-temperature method for the test, and also improved TRT equipment and presented a mathematical model to interpret the measured data. In order to improve the performance of GSHPS, both analytical and numerical modeling techniques have been applied to simulate the dynamic temperature evolution inside and around the BHE. Classically, Carslaw and Jaeger’s line source model [7] with Kelvin’s theory of heat sources is widely used to identify conductivity value in the thermal response test. Duhamel’s theorem efficiently helps develop solutions with transient boundary condition [8]. Beier et al. employed the numerical Laplace transformation technique and developed a semi-analytical solution for single U-tube type BHE [9]. His model is capable of predicting the transient temperature profile within and around the BHE, which is installed in homogeneous soil and operated under a constant heat extraction rate [10]. Later on, he also extended this solution to coaxial types of BHEs [11]. Being aware of the limitation of the analytical approach, Lee and Lam [12] developed a numerical model for BHE with finite difference method, which can predict the dynamic temperature profile. Boockmeyer and Bauer [13] have managed to simulate the thermal response of the entire BHE, with the U-tube, grout material and the surrounding soil matrix all explicitly represented in the finite element mesh. These models are very accurate, but require significant computational resources. Following a different approach, Al-Khoury et al. [14], [15] presented a model where the BHE is represented by a second 1D domain, which is coupled to the heat transport processes in the soil. Diersch et al. [16], [17] followed the same idea and implemented the algorithm into the commercial software FEFLOW [18]. Such dual continuum models are still flexible enough to accept varying boundary conditions and heterogeneous soil properties, yet they are much more efficient in terms of computational time.

When freezing happens around the BHE, complex effects will occur. On one hand, the latent heat produced by the phase change can provide large amounts of extra energy for heating up the buildings. On the other hand, however, the freezing process will expand the soil which may damage the pipe and even the foundation of the buildings. To simulate freezing and thawing processes around the BHEs, a coupled model including both the BHE and the freezing feature is required. In other words, the numerical model has to capture the phase change between water and ice, and must also explicitly account for the associated latent heat. The mathematical description of freezing processes was first described by Stefan [19], and improved by Neumann [20] and Lunardini [21]. Afterwards, McKenzie et al. introduced a clear benchmark for the calibration of numerical models [22]. Bluhm and Ricken [23] proposed a mathematical and numerical model to simulate freezing in thermo-elastic porous media based on the porous media theory of De Boer [24]. Yet, none of these models considered the interactions between a BHE and the surrounding soil. To investigate such effects, several researchers have made important contributions. Wang et al. [25] experimentally investigated the pipe deformation during freezing at the interface between grout and soil. Eslami-nejad and Bernier [26] set up an experiment to examine the thermal consequences of freezing in the vicinity of BHEs and compared the result with a 1D numerical model. They found that soil freezing plays an important role in cold districts and delays the soil temperature drop. Yang et al. [27] proposed a one dimensional mathematical model with phase change to simulate the heat transfer in soil around BHEs. They showed the feasibility of a seasonal cool storage system using shallow soil in severely cold regions. Furthermore, Yang et al. [4] developed a two-dimensional model of heat transfer incorporating phase change around the BHE. They demonstrated that increasing water content can delay the soil temperature drop and the soil freezing characteristics are affected mostly by the thermal diffusivity of soil. Since they used a 1D Dirchlet boundary condition to represent the BHE, the transient outlet temperature and extraction power cannot be simulated by their model. Anbergen et al. [28] developed a freezing feature plug-in for the commercial software FEFLOW, and successfully validated the feature against experimental results. His work was focused on the temperature field of the grout and soil, and did not investigate the overall system efficiency.

In this work, the impact of freezing on the BHE and heat pump efficiency was carefully investigated. For that purpose, the scientific open-source software OpenGeosys (OGS) [29] was extended to incorporate both the BHE and soil freezing in a fully coupled three dimensional model (Sections 2 Mathematical model, 3 Numerical model). The model result was compared to established analytical solution and experimental data to insure the correct implementation (Section 4). This extended feature allows the simulation of heat pump efficiency, which is highly dependent on the outlet temperature of the BHE. Based on the typical thermal load of a single-family house in northern Europe, we compare two BHE designs. One with shorter length allowing freezing of the surrounding soil, while the other was constructed in a conservative way, keeping the soil temperature above 0 °C (Section 5.1). Analysis of the corresponding heat pump efficiency were conducted based on simulated BHE outlet temperatures (Section 5.2). In addition, the simulated temperature profiles over a period of one winter were extrapolated to a 30 years period and the impact on system performance is translated to financial cost (Section 5.3). Conclusions are drawn in the end regarding whether it is worth to exploit the latent heat effect with BHE coupled GSHPS in cold regions.