# Analysis and Comparison of Some Low-Temperature Heat Sources for Heat Pumps

^{*}

## Abstract

**:**

^{2}and specific energy extracted from the ground mass 2723.40 ± 1785.58 kJ/m

^{2}·day were recorded at single U-tube VGHE. The lowest thermal resistance value of 0.07 K·m

^{2}/W, specifying the efficiency of the heat transfer process between the ground mass and the heat transfer fluid, was monitored at linear HGHE. The use of ambient air as a low-temperature heat pump source was considered to be the least advantageous in terms of its temperature parameters.

## 1. Introduction

## 2. Materials and Methods

^{3}·K) and the coefficient of thermal conductivity a (m

^{2}/s) were determined using Isomet 2104 (manufactured by Applied Precision, Bratislava, Slovakia) at temperature t (°C) and volumetric humidity v (%). They were measured at a depth of 1.2–1.6 m, at temperature t = 12.65–13.83 °C and volumetric humidity v = 31.60–39.00 % and their values were λ = 1.39–1.57 W/m·K, C = 2.08–2.16 J/m

^{3}·K and a = 0.672–0.727 m

^{2}/s. The thermal characteristics were within a range corresponding to the most widespread type of soil in the Czech Republic. Detailed diagrams of both HGHEs were presented in publications [24] a [25].

_{L}, t

_{S}, t

_{A}, t

_{B}) at quarter-hour intervals were installed at the outlet and inlet pipes of HGHEs and VGHEs and they were recorded by measuring data logger ALMEMO 5990 (Ahlborn Mess-und Regulungstechnik GmbH, Holzkirchen, Germany). The MTW 3 electronic meters (Itron Inc., Liberty Lake, USA) were used to measure the flows of the heat transfer fluids (V

_{τ}

_{,a}, V

_{τ}

_{,max}). The specific heat outputs (q

_{τ}

_{,a}, q

_{τ}

_{,max}) and energy extractions (q

_{a}, q

_{max}) were determined on the basis of the difference in temperatures of the heat transfer fluid, the heat transfer fluid flow rate (V

_{τ}), the specific heat capacity and the density corresponding to the mean temperature of the heat transfer fluid.

## 3. Results and Discussion

#### 3.1. Temperatures of the Heat Transfer Fluids Supplied to the Heat Pump Evaporators

_{i}= 35.19% and w

_{i}= 32.99% for type B and A, respectively. The interval of 2.10–4.00 °C was the lowest interval of the heat transfer fluid temperatures in VGHE. The relative class frequency of temperatures in this interval reached values w

_{i}= 6.50% (type B) and w

_{i}= 8.96% (type A).

_{i}= 34.04% and the Slinky HGHE mode was in a lower temperature range of 2.10–4.00 °C with w

_{i}= 32.91%. The range of 0.10–2.00 °C (r = 1 °C) was the lowest range of temperatures in HGHEs in which there was w

_{i}= 0.84% (linear HGHE) and w

_{i}= 12.77% (Slinky HGHE).

_{i}= 12.82% in the range of 4.10–6.00 °C. Ambient air temperatures occurred in a wide range between −17.90–(−16.00) °C (r = −17 °C) with w

_{i}= 0.11% and 26.10–28.00 °C (r = 27 °C), w

_{i}= 0.06%.

_{e}= 0.77. The heat transfer fluid temperature distribution was left-skewed for both HGHEs and VGHEs, N

_{L}= 2.53, N

_{S}= 2.48, N

_{A}= 2.10, N

_{B}= 2.44.

_{A}, t

_{B}) reached the highest values for the averages $\overline{t}$, minimum values t

_{min}, medians $\tilde{t}$ and lower quartiles Q

_{1}. The ranges R

_{v}and variation coefficients S% reached also favourable low values. The double U-tube VGHE (B) proved to be slightly more favourable than a single U-tube VGHE (A) in terms of statistical analysis of the fluid temperatures. These results were confirmed by Zeng et al. [22].

_{min}, median $\tilde{t}$, and lower quartile Q

_{1}values were lower than for VGHE but higher than for Slinky HGHE. The interquartile range Q

_{2}–Q

_{1}was the biggest of the monitored heat transfer fluids. The evaluation showed that the basic characteristics of the heat transfer fluid temperature sets with HGHE were less favourable than those with VGHE. This applied in particular to Slinky HGHE, where the minimum temperature t

_{min}was close to 0 °C and the variation coefficient S% was higher. The distribution of temperatures of heat transfer fluids in HGHEs was closely related to the distribution of the ground mass temperatures presented in publication [31]. It follows from the above analysis and summary that the temperatures of the heat transfer fluids from VGHEs and HGHEs did not reached negative values in our validations.

_{min}, median $\tilde{t}$, lower and upper quartile Q

_{1}and Q

_{2}. It also proved the highest variation coefficient S%, the range R

_{v}and the interquartile range Q

_{2}–Q

_{1}.

_{e}was apparent from the course of the fluid temperatures. The temperatures of the heat transfer fluid in linear HGHE t

_{L}in Figure 3 were clearly higher than the temperatures of the heat transfer fluid of Slinky HGHE with the exception of the beginning and the end of the heating period. The quadratic equations of the trend line of the course of HGHEs fluid temperatures have the form of Equations (1) and (2). The curves matched well with the data as indicated by the determination coefficients R

^{2}.

_{A}and t

_{B}from VGHEs (Figure 4) were miner than from HGHEs. The quadratic equations of the trend lines of fluid temperature courses have the form of Equations (3) and (4). Determination coefficients R

^{2}were lower. It follows from the temperature courses and Equations (3) and (4) that the heat transfer fluid temperatures from VGHE type B were slightly higher than from type A.

_{A}from VGHE type A were the same as those observed by Remiorz et al. [18] when verifying a similar type of VGHE.

#### 3.2. Specific Heat Outputs of Heat Exchangers and Specific Extracted Energies

_{τ}

_{,a}and q

_{τ}

_{,max}(W/m; W/m

^{2}), were presented in Table 2, converted to 1 m of pipe length and 1 m

^{2}of heat exchanger’s surface. Furthermore, there is the average specific energy q

_{a}extracted by 1 m

^{2}of the heat exchanger from the mass in 1 day of the heating period, the maximum daily and total amount of energy, q

_{max}and q

_{Σ}, extracted by the heat exchanger from the mass in the heating period, as well as the total duration of the energy extraction by the heat exchanger τ

_{Σ}during the heating period.

_{τ,a}(W/m) presented in Table 2 were near those values. Verda et al. [6] presented the value of 38W as the maximum of the extracted specific output of linear HGHE converted to 1 m

^{2}of heat exchanger surface. In our verifications, the maximum specific output converted to heat exchanger surface area was only 18.43 W/m

^{2}for linear HGHE and 100.08 W/m

^{2}for Slinky HGHE. Lower specific outputs for VGHEs and HGHEs were caused by the way of operation of the production halls and the administrative building with interrupted operation and low demanded outputs for the heating system at the beginning and end of the heating period.

_{L}, q

_{S}) and VGHE (q

_{A}, q

_{B}) during the heating period presented in Figure 5 confirmed the above results. As in the case of the temperatures of the heat transfer fluids, the graph in Figure 5 showed the relation of the extracted specific energy value q

_{a}and the ambient temperature t

_{e}. This relation was also confirmed by the results of Todoran and Balan’s verifications [36].

#### 3.3. Heat Resistances of the Heat Exchangers

^{2}⋅K/W) by Equation (5), respecting the flow of the heat transfer fluid through the heat exchanger pipeline:

- t
_{r.m}—temperature of the reference ground or rock mass (°C); - t
_{a,h.t.f}—average temperature of the heat transfer fluid (°C); - q
_{τ}—specific heat output converted to 1 m^{2}of heat exchanger surface (W/m^{2}).

_{τ}

_{,a}and V

_{τ}

_{,max}, total volume of heat transfer fluid flowing through the heat exchangers during the heating period V

_{Σ}, and average and maximum specific heat exchanger resistances, R

_{a}and R

_{max}.

## 4. Conclusions

_{min}, median $\tilde{t}$ and temperature quartiles Q

_{1}, Q

_{2}were higher than in VGHE type A. Also, the relative frequency of the temperature occurrence in the mode of fluid temperature set distribution of 6.10–8.00 °C was higher by 2.20% than in the temperature set of VGHE type A. However, the temperature differences of the fluids were not significant as followed from the course of the average hourly temperature of the heat transfer fluid in Figure 4 and from Equations (3) and (4). The average thermal resistances of both VGHEs were comparable; the maximum resistances differed in accordance with the results reported by Zeng et al. [22]. VGHE type A had higher average specific output q

_{τ}

_{,a}by 22.89% (10.17 W/ m

^{2}) at a lower average volume flow of the heat transfer fluid. This analysis indicated that VGHE type A can be considered more advantageous than VGHE type B.

_{τ}

_{,a}than Slinky HGHE by 17.26% (5.76 W/ m

^{2}) at higher average volume flow rate of the heat transfer fluid. Due to the temperatures of the heat transfer fluids, the specific outputs and the specific thermal resistances of linear HGHE reached more favourable values, this seemed to be the more advantageous exchanger.

^{2}⋅K/W). At the heat exchange surface S lower by 31.52% (13.07 m

^{2}) and the average volume flow of the heat transfer fluid V

_{τ}

_{,a}higher by 10.64% (0.05 m

^{3}/h), the average specific output of VGHE type A was higher by 53.22% (20.83 W/m

^{2}) than that of linear HGHE. The results of the analysis indicated that VGHE type A appears to be more advantageous low-temperature source in this comparison. In this case, an important role in choosing a low temperature source is the area of land on which the installation of the source can be realized. The installation of linear HGHEs is certainly less demanding for investment cost.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | Single U-tube VGHE |

B | Double U-tube VGHE |

L | Linear HGHE |

HGHE | Horizontal Ground Heat Exchanger |

HVAC | Heating, Ventilation and Air Conditioning |

N | Coefficient of asymmetry of temperature distribution (-) |

Q_{1} | Lower quartile of temperature distribution (°C) |

Q_{2} | Upper quartile of temperature distribution (°C) |

PCM | Phase changing materials |

R | Thermal resistance of heat exchanger (K.m^{2}/W) |

R^{2} | Determination coefficient (-) |

R_{v} | Temperature range (K) |

S | Slinky HGHE |

S^{2} | Temperature variance (K^{2}) |

S% | Variation coefficient of temperature distribution (%) |

V_{τ} | Volume flow of heat transfer fluid (m^{3}/h) |

VGHE | Vertical Ground Heat Exchanger |

q_{τ} | Specific heat output of heat exchanger W/m,W/m^{2} |

r | Category representative of temperature interval (°C) |

t | Temperature (°C) |

$\tilde{t}$ | Median of temperatures (°C) |

$\overline{t}$ | Mode of temperatures (°C) |

$\widehat{t}$ | Reference temperature of the ground or rock mass (°C) |

t_{r.m} | Average temperature of heat transfer fluid (°C) |

t_{a,h.t.f.} | Volumetric moisture (%) |

v | Relative frequency of temperatures (%) |

w_{i} | Length of heating period (h) |

τ | Single U-tube VGHE |

Indexes | |

A | Linear HGHE |

B | Slinky HGHE |

L | Average value |

S | Ambient air temperature |

a | Maximum value |

e | Minimal value |

max | Summative value |

min | Single U-tube VGHE |

∑ | Double U-tube VGHE |

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**Figure 1.**Frequencies of heat transfer fluid temperatures (t

_{L}, t

_{S,}t

_{A}, t

_{B}) and ambient air temperatures (t

_{e}) during heating period.

**Figure 2.**Box plot of heat transfer fluid temperatures (t

_{L}, t

_{S,}t

_{A}, t

_{B}) and ambient air temperatures (t

_{e}) during the heating period.

**Figure 3.**Course of average hourly temperatures of heat transfer fluids from linear (t

_{L}) and Slinky HGHEs (t

_{S}) and of ambient air (t

_{e}).

**Figure 4.**Course of average hourly temperatures of heat transfer fluids from single U-tube (t

_{A}) and double U-tube VGHEs (t

_{B}).

**Figure 5.**Specific energy extracted by HGHEs (q

_{L}q

_{S}), VGHEs (q

_{A}q

_{B}) and ambient air temperature (t

_{e}) during heating period.

**Table 1.**Quantile characteristics of the heat transfer fluid temperature sets at the exchanger’s outlets and the ambient air temperatures.

Header | HGHE | VGHE | Ambient Air | ||
---|---|---|---|---|---|

L | S | A | B | e | |

Average$\overline{\mathit{t}}$ (°C) | 8.13 ± 4.50 | 6.36 ± 4.79 | 7.78 ± 2.94 | 8.13 ± 3.12 | 3.98 ± 6.21 |

Minimum t (°C)_{min} | 1.67 | 0.39 | 2.08 | 2.64 | −17.23 |

Maximum t (°C)_{max} | 17.82 | 17.97 | 13.66 | 16.69 | 26.57 |

Median$\tilde{\mathit{t}}$ (°C) | 6.39 | 4.59 | 7.28 | 7.35 | 3.69 |

Lower quartile Q_{1} | 4.63 | 2.78 | 5.87 | 6.04 | −0.65 |

Upper quartile Q_{2} | 11.40 | 8.92 | 9.67 | 9.09 | 7.92 |

Variance S (K^{2}^{2}) | 20.23 | 22.95 | 8.65 | 9.71 | 38.59 |

Variation coefficient S% (%) | 55.34 | 75.35 | 37.79 | 38.30 | 155.94 |

Range R (K)_{v} | 16.15 | 17.59 | 11.58 | 14.05 | 43.79 |

Interquartile range Q (K)_{1}–Q_{2} | 6.77 | 6.15 | 3.80 | 3.86 | 8.56 |

**Table 2.**Specific heat outputs of heat exchangers and specific energies extracted from the ground and rock mass.

Parameter | HGHE | VGHE | ||
---|---|---|---|---|

L | S | A | B | |

q_{τ}_{,a}(W/m) | 4.92 ± 3.60 | 3.35 ± 2.42 | 7.53 ± 5.25 | 4.90 ± 3.42 |

q_{τ}_{,max}(W/m) | 15.25 | 12.48 | 29.28 | 14.18 |

q_{τ}_{,a}(W/m ^{2}) | 39.14 ± 28.67 | 33.38 ± 24.11 | 59.97 ± 41.80 | 48.80 ± 34.08 |

q_{τ}_{,max}(W/m ^{2}) | 121.42 | 124.20 | 233.08 | 141.05 |

q_{a}(kJ/m ^{2}·day) | 1614.15 ± 1076.40 | 938.31 ± 677.70 | 2723.40 ± 1785.58 | 2353.59 ± 1540.89 |

q_{max}(kJ/m ^{2}·day) | 4407.73 | 4258.86 | 7495.07 | 6564.86 |

q_{Σ}(MJ/m ^{2}) | 351.88 | 204.55 | 593.70 | 513.08 |

τ_{Σ}(h) | 2497 | 1703 | 2750 | 2920 |

Parameter | HGHE | VGHE | ||
---|---|---|---|---|

L | S | A | B | |

S(m ^{2}) | 41.47 | 20.11 | 28.40 | 45.44 |

V_{τ}_{,a}(m ^{3}/h) | 0.47 ± 0.22 | 0.35 ± 0.12 | 0.52 ± 0.26 | 0.61 ± 0.31 |

V_{τ}_{,max}(m ^{3}/h) | 0.89 | 0.72 | 1.03 | 1.27 |

V_{Σ}(m ^{3}) | 1 183.70 | 592.82 | 1 435.96 | 1 787.94 |

R_{a}(m ^{2}⋅K/W) | 0.07 ± 0.02 | 0.14 ± 0.06 | 0.09 ± 0.03 | 0.11 ± 0.04 |

R_{max}(m ^{2}·K/W) | 0.13 | 0.38 | 0.16 | 0.23 |

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**MDPI and ACS Style**

Neuberger, P.; Adamovský, R.
Analysis and Comparison of Some Low-Temperature Heat Sources for Heat Pumps. *Energies* **2019**, *12*, 1853.
https://doi.org/10.3390/en12101853

**AMA Style**

Neuberger P, Adamovský R.
Analysis and Comparison of Some Low-Temperature Heat Sources for Heat Pumps. *Energies*. 2019; 12(10):1853.
https://doi.org/10.3390/en12101853

**Chicago/Turabian Style**

Neuberger, Pavel, and Radomír Adamovský.
2019. "Analysis and Comparison of Some Low-Temperature Heat Sources for Heat Pumps" *Energies* 12, no. 10: 1853.
https://doi.org/10.3390/en12101853