Carbon Dioxide Emissions during Air, Ground, or Groundwater Heat Pump Performance in Białystok

Abstract

The increasing global temperature has induced many states to limit carbon dioxide emissions. The European Union (EU) promotes replacing boilers with heat pumps. However, in countries where electricity is mainly supplied through fossil fuel combustion, condensing gas boilers may prove to be more ecological heat generators. Although this problem was investigated in a particular situation, an algorithm can be applied elsewhere. The running expenditures for the following different heat generators that are available in a location were estimated: water heat pump, brine heat pump, air heat pump, condensing gas boiler, condensing oil boiler, district heat network, and electrical grid. Furthermore, carbon dioxide emissions from local and distant sources were evaluated. The computations were based on hourly averaged external temperature measurements, which were performed by the Institute of Meteorology and Water Management—National Research Institute (IMGW-PIB) in a weather station in Białystok (Poland) for a ten-year period. Compared with a condensing gas boiler system, the air-to-water heat pump has higher operating costs and higher CO₂ emissions. The brine heat pump (closed-loop ground-source heat pump) has lower operating costs, but higher CO₂ emissions than the gas boiler system. The water heat pump (groundwater source heat pump) has the lowest operating costs and CO₂ emissions of all the systems studied in this paper.

1. Introduction

The mean air temperature on Earth has been increasing since the midpoint of the 20th century. It is believed that the emissions of greenhouses gases (methane, carbon dioxide, water vapor, ozone, nitrous oxide, halogenated hydrocarbons, and so on) are responsible for the temperature rise. The gases are freed by biological flora and fauna respiration, volcano eruptions, and forest fires. Greenhouse gases are also emitted as a result of human activity: during combustion of fossil fuels, deforestation, cement production, and other processes using carbonates. The Keeling Curve shows the rise in carbon dioxide concentration from 316 ppm in 1960 to 385 ppm in 2010 at Mauna Loa Observatory (Hawaii) [1], which is considered as a proof of the hypothesis that global warming is caused by greenhouse gas emissions. As a result of this research, thirty-seven countries adopted a proposal to limit the greenhouse effect (the proposal was ratified by Poland on 2 December 2002). As this proposal was presented in Kyoto, on 11 December 1997, the agreement is known as the Kyoto Protocol. This proposal makes it an obligation to reduce the emissions of six of the greenhouse gases: carbon dioxide, methane, nitrous oxide, hydrofluorocarbons, perfluorocarbons, and sulfur hexafluoride. Hence, internal actions were taken in these countries. Although the Kyoto Protocol expired on 31 December 2012, the states affiliated with the European Economic Area decided to cut greenhouse gas emissions by at least 20% below 1990 levels by the year 2020 [2].

The measures taken in other countries are briefly discussed in the work of [3], where it was derived that ground heat pump performance can cut CO₂ emissions in countries where electricity is generated mainly in hydroelectric power stations or nuclear reactors. In the case of Poland, where calculations were done using heating degree days, it turned out that the condensing gas boiler was a more ecological heat source. As the paper is a continuation of the previous investigations by the authors of [3], the literature review is only supplemented by works that were published in the interim.

Feng and Berntsson [4] investigated the economics of heat pump operation. Wasted heat and supplied heat for heating were considered as heat sources. The computations were done by applying electricity pricings in Sweden and the USA. They investigated the operating costs and capital expenditure, as well as payback periods and absorption heat pumps. They concluded that, in those times, the coefficient of performance (COP) of the compression heat pump units must be greater than 5, while an absorption heat pump should have been installed if heating costs would be very high and the payback period would be sufficiently long.

Lam and Chan [5] conducted their research in Hong Kong. They measured the COP of an air-to-water heat pump unit that supplied heat to a swimming pool, as well as three water-to-water heat pump units that provided heat to a domestic hot water system. In the former case, the COP changed from 1.5 to 2.4 with an average COP ≈ 2, while in the latter, the COP was between 0.5 and 2.55, with average value of 1.75. Eventually, Lam and Chan [5] concluded that the two-year payback period is very short. Such a situation is caused by the similar prices of energy: HK$0.24/MJ and HK$0.21/MJ for electricity and gas, respectively.

Gupta and Irving [6] achieved a model designed to estimate, in the case of either ground or air heat pumps, the energy consumption of heat pumps for heating and cooling in the United Kingdom. The authors of [6] assumed that, for the air heat pump, the source temperature is equal to the temperature outside; for the ground heat pump with the bore hole heat exchanger deeper than 10 m, the source temperature is largely the same as the average annual outside temperature (in Białystok, the ground below the shallow zone (10 m) is warmer by 2.2 °C, according to Biernacka [7]). Gupta and Irving [6] applied the Kasuda and Aschenbach formula, which approximates temperature in the shallow zone, for the assessment of the energy efficiency of ground heat pump. The temperature of a heat sink is between 35 and 55 °C. The external temperature and flow water temperature for a heating system are linked by a linear function. The overall amount of heat was estimated using heating degree days.

Carvalho et al. [8] forecasted the limitation of carbon dioxide emissions at 90% (157 Mt CO₂) and primary energy savings at 60% (520 TWh) for space heating resulting from replacing natural gas boilers with the heat pump units. However, they make a reservation that the preserves are higher in countries where electricity generation is based on nuclear or renewable energy sources than in countries where electricity generation is based on fossil fuel (especially coal or lignite) combustion. In Polish conditions, replacing natural gas boilers with ground heat pumps will make ecological sense if the coefficient of performance (COP) is greater than 3.7.

Lv et al. [9] applied a 16 m³ volume water tank as a thermal energy storage device (TES) connected to a ground-source heat pump that supplies an office building, located in Tianjin, which had a cooling load of 98.4 kW and heat load of 69.6 kW. As a result of TES application, the daily mean COP increased to 0.37.

Patteeuw et al. [10] estimated the costs of CO₂ constraints in Belgium. Carbon dioxide limitation was performed after the substitution of condensing gas boilers by heat pump units in detached houses. Three variants were investigated: air heat pump with radiators, air heat pump with floor heating, and ground-source heat pump with floor heating. The simulation was performed with the assumption that 30% of energy is generated in the wind power stations and 10% in the photovoltaic cells. The lowest costs of the limitation of CO₂ emissions provide air heat pumps with floor heating in new buildings or in thoroughly renovated ones. Although the ground-source heat pump causes a greater reduction in CO₂ emissions, it generates higher costs.

Ally et al. [11] reported an experiment that lasted a year and was conducted under occupancy of a detached house equipped with a vertical-bore ground-source heat pump. An indoor coil provided either air conditioning (in summer, at 24.4 °C) or air heating (in winter, at 21.7 °C). Domestic hot water was produced in the second heat pump unit. Both heat pump units were connected to the same ground loop. The achieved COPs were between 3.49 and 3.75 in a mixed-humid climate zone 4 in USA [12], with 2218 heating degree days.

However, the costs of energy production from renewable resources are higher than from non-renewable energy, thus Dogan and Seker [13] recommend the EU supporting the investigations that would make generation of energy from renewable resource cheaper.

The paper is an extension of the investigations [3] into an air heat pump and groundwater pump with more precise calculations based on temperature measurements done by the Institute of Meteorology and Water Management—National Research Institute (IMGW-PIB) in a weather station at Bialystok during a 10-year period. To further increase the accuracy of the estimation, other equipment that is necessary for the system to work properly, that is, a buffer tank and separating heat exchanger, is included in an analysis. Thus, the algorithm has to differ from EN 14825:2016. The most important modification is the determination of the water temperature in the buffer tank in the consecutive hours. The first hour in the calculations is the first hour of the heating season. Other minor changes are described further on.

2. Computation

The aim of the paper is the selection of a heat source for a heat pump unit in a commercial building with total design heat load ${\dot{Q}}_l$ = 170.11 kW (also called Full Load Heating P_designh at EN 14825:2016) calculated in accordance with EN 12831:2003. The building is located in the northern part of Bialystok. In this case, external design temperature t_d = −22 °C (alias Reference Design Temperature Conditions for heating T_designh at EN 14825:2016) and the heating season starts on 21 September and lasts up to 10 May. The annual quantity of heat Q_h is at 1421 GJ/a. The hydronic heating system is equipped with the panel convector radiators. The design flow water temperature is at 45 °C and the return water temperature equals 35 °C in the heating system. Domestic hot water is prepared in the instant electric water heaters. Moreover, the experimental investigations of Aira et al. [14] indicated that the proportion of heat pump work status was as follows: heating mode at 86.5%, warming pool water mode at 9.8%, and domestic hot water (DHW) production mode at 3.7%. Hence, taking DHW production into consideration would affect the results in very insignificant way.

In general, there are two possible heat sources for a heat pump: outdoor air or the ground. However, in this particular situation, the building is supposed to be constructed on an area on which the major groundwater basin 218 at a depth of 100 m is located [15], which is shown in the map in Figure 1; a better quality map is available on the website [16].

Thus, these three variants are considered using external temperature, which was measured from 2003 to 2012 by IMGW-PIB in the weather station at Bialystok. The authors calculate the mean temperature values for each hour in the year in the ten-year period. These mean temperatures are rounded to one decimal place, which means the outdoor temperature interval is equal to 0.1 °C. These temperatures are used in the next calculations as the bin temperature values t_j. To illustrate the temperature conditions in Bialystok, the measured temperature values in every hour are rounded to an integer, and then the numbers of hours for each rounded temperature are added up. Eventually, there are 87,672 h in the heating season, and the results are presented in Figure 2.

To provide comparability of the results, the devices of one manufacturer should be sized. Because Viessmann offers the full scope of the heat pumps and the boilers, its devices are selected.

The calculations are done for each hour in the year as follows. It is specified whether heating is turned on. If, during a given hour, the heating system works, a current heat load is calculated. As the total design heat load is calculated at the external design temperature and the temperature changes, a part load for heating $P_h\left(t_j\right)$ is determined at bin temperature t_j

$$P_h\left(t_j\right)={\dot{Q}}_l\frac{t_{\mathit{int}}-t_j}{t_{\mathit{int}}-t_d}\hspace{1em}\left[\mathrm{kW}\right].$$

(1)

It is assumed that the heating system does not provide heat if the external air temperature is at least +15 °C, then $P_h\left(t_j\ge 15°\mathrm{C}\right)=0$. Afterwards, the quantity of heat that is transferred to the system during the given hour is computed.

The flow temperature in the heating system is controlled by Vitotronic 200 WO1C along a heating curve with an exponent of 0.6, which represents a function of flow water temperature t_f in dependence on the external air temperature t_ea. As the formula of the function is needed in subsequently calculations, the curve is approximated by a quadratic function in which Pearson’s correlation coefficient [18] is equal to 0.9999. Nonetheless, to provide at least a 10 °C temperature difference between an arithmetic mean temperature of water in a radiator and the internal design temperature (+20 °C), the flow water temperature t_f cannot be less than 35 °C. Eventually, we obtain the heating curve as follows (cf. Figure 3):

$$\left\{\begin{array}{l}{t}_f=-0.0049t_j^2-0.5794t_j+33.602\hspace{1em}[°\mathrm{C}]\hspace{1em}\mathrm{for}\hspace{1em}{t}_j\le -2.5°\mathrm{C}\hspace{1em}\\ t_f=35°\mathrm{C}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em} \hspace{0.33em}\hspace{0.33em}\mathrm{for}\hspace{1em}{t}_j>-2.5°\mathrm{C}\end{array}\right..$$

(2)

The rating heating output P_{h unit} and the power consumption P_e of one unit are interpolated using the manufacturer’s data. The temperature of the heat source in the evaporator and the flow temperature of heating water in the condenser are the arguments of the interpolation. The COP at the bin temperature t_j is obtained from a formula

$$CO{P}_{bin}\left(t_j\right)=P_h\left(t_j\right)/P_e\left(t_j\right)\hspace{1em}\left[-\right].$$

(3)

To obtain the number of working units n, the part load for heating P_h (t_j) is divided by the rating heating output P_{h unit}, and the quotient is rounded up to an integer. The ratio of the part load for heating and rating heating output P_{h man} for n working units is equal to worktime expressed in hours. However, an exception must occur on 29 February, when the worktime is divided by four, as the leap day occurs once every four years. Energy consumption for heating Q_{h i} is calculated as the product of rating heat output P_{h man} and the worktime in the given hour. It is equal to 0 when bivalent heater is working, which results from an assumption that only one heat generator works (either a heat pump or a bivalent heater) in the given hour. By analogy, the work of electrical current W_{e i} is the product of the worktime and the power consumption P_e. As 8784 is the total number of the bin hours in a leap year, a quarter of the work time on the leap day is taken. These values are summarized as follows:

$$Q_h={\displaystyle \sum _{i=1}^{8784}{Q}_{h\hspace{0.33em}i}}\hspace{1em}\left[\mathrm{GJ}/\mathrm{a}\right],$$

(4)

$$W_e={\displaystyle \sum _{i=1}^{8784}{W}_{e\hspace{0.33em}i}}\hspace{1em}\left[\mathrm{GJ}/\mathrm{a}\right],$$

(5)

and a quotient of the aggregates is the net seasonal coefficient of performance (SCOP_net), which excludes the power consumption when heat is not provided to the heating system:

$$SCO{P}_{net}=Q_h/W_e\hspace{1em}\left[-\right].$$

(6)

Because of the assumption that an electric current is supplied from the Polish electrical grid, the average shares and the average generation factors in Poland are determined. The crucial issue is proper estimation of the average carbon dioxide generation factor. The factor depends on the fuel used in the power plants, average efficiency of the electricity production, and efficiency of the low voltage current transfer. Unexpectedly, the last factor turned out to be the most questionable. Remiorz and Hanuszkiewicz-Drapała [19] assume the electricity transformation and transmission efficiency to be 90%. National Security Bureau (in Polish, Biuro Bezpieczeństwa Narodowego (BBN)) [20] estimates the overall electrical energy transfer losses at 7.3% at the beginning of its analysis. However, further on, BBN notices the distribution network operators (DNOs) measured “negative losses” during some periods, which means the DNOs sold more energy than they supplied to their subnetworks. BBN finds the poor quality of the electricity meters to be the explanation for the “negative losses”. As the energy balance based on the DNOs’ measurements is inaccurate, other methods of transfer losses estimation must be found. The issue was investigated by Kulczycki et al. [21]. However, Ciura [22] claims their results seems to be overestimated and suggests taking two-third of the losses obtained in the work [21]. Eventually, low voltage electrical energy transfer efficiency η_t is assumed to be at 79.2% based on Ciura’s [22] recommendation. The aggregate carbon dioxide generation factor β_ag, which accounts for direct and indirect emissions, is obtained as follows:

$${\beta }_{ag}=\frac{1}{{\eta }_t}{\displaystyle \sum _i\left(\left({\beta }_i+{\beta }_{ie i}\right)S_i/{\eta }_{c i}\right)}\hspace{1em}\left[\frac{\mathrm{kgC}{\mathrm{O}}_2}{\mathrm{GJ}}\right],$$

(7)

where other variables or constants are in

Table 1. The data for the calculations of CO₂ emissions in Poland.

Fuel	Generation Factor [23]	Share [24]	Energy Conversion Efficiency [3]
	β	S	ηb
	[kgCO2/GJ]	[-]	[-]
bituminous coal	94.42	50.28%	36.00%
lignite	108.74	31.92%	36.00%
natural gas	55.82	3.51%	34.00%
oil	76.59	0.00%	36.00%
hydropower	0	1.49%	-
renewables	0	6.65%	-
others	75.61	6.16%	35.00%

and

Table 2. Indirect carbon dioxide emissions by Johnson [25].

Title	Indirect CO2 Emissions-βie [kg CO2/GJ]
natural gas	5
fuel oil	12.5
coal	15.3

. Eventually, β_ag = 339.87 kgCO₂/GJ.

The SCOP is also applied to ecological verification of heat pump. If aggregate direct and indirect carbon dioxide emissions in the power plants β_ag are lower than “green” emissions β_green, then the heat pump is more ecological. It is expressed an inequality (11) in earlier paper [3].

$${\beta }_{ag}<{\beta }_{green}=\left({\beta }_g+{\beta }_{ie}\right)SCOP/{\eta }_g,$$

(8)

where η_g = 0.96.

Carbon dioxide emissions caused by electricity consumption for every heat generator are as follows:

$$E_{e\hspace{0.33em}}{}_{C{O}_2}=W_e{\beta }_{ag}\hspace{1em}\left[\mathrm{kgC}{\mathrm{O}}_2/\mathrm{a}\right].$$

(9)

To the extent that the air to water heat pump must be replaced by another heat generator below the bivalent temperature, carbon dioxide emissions from fuel combustion, E_{comb CO2}, must be determined.

$$E_{comb\hspace{0.33em}C{O}_2}=(\beta +{\beta }_{ie})Q_{hb}/{\eta }_b\hspace{1em}\left[\mathrm{kgC}{\mathrm{O}}_2/\mathrm{a}\right],$$

(10)

where Q_hb is energy consumption for heating that is offset by the bivalent heat generator with efficiency η_b. Aggregate carbon dioxide emissions are the sum of direct and indirect emissions:

$$E_{C{O}_2}=E_{e\hspace{0.33em}C{O}_2}+E_{comb\hspace{0.33em}C{O}_2}\hspace{1em}\left[\mathrm{kgC}{\mathrm{O}}_2/\mathrm{a}\right].$$

(11)

2.1. Ground Heat Pump

To cover total design heat load, a one unit of two-stage heat pump type Vitocal 300-G Pro type BW 302.B150 was sized in the first variant with ground as the heat source. The properties of the heat pump unit are presented in

Table 3. Technical data of applied ground and water heat pump units.

Description	Unit	Vitocal 300-G Pro Type BW 302.B150 [27]	Vitocal 300-W Pro Type WW 302.B200 [27]	Vitocal 300-G Type BW/BWS 301.A45 [28]
Output data to EN 14511		B0/W35, 5 K spread	W10/W35, 5 K spread	B0/W35, 5 K spread
Rated heating output	kW	150	190	42.8
Power consumption	kW	31.9	32.1	9.28
Coefficient of performance	−	4.7	5.92	4.6
Fluid in primary circuit		brine	water	brine
Content	l	55.2	293	11.5
Rated flow rate to EN 14511	l/h	39,500	45,600	the lack of datum
Min. flow rate (spread 5 K)	l/h	24,000	33,100	6500
Pressure drop	mbar	130	342	154
Max. flow temperature	°C	20	20	25
Min. flow temperature	°C	−5	8	−10
Heating water (secondary circuit)
Content	l	38.7	38.7	11.5
Rated flow rate to EN 14511	l/h	25,800	32,700	the lack of datum
Min. flow rate (spread 10 K)	l/h	12,900	16,400	3700
Pressure drop (at min. flow rate)	mbar	100	100	65
Flow temperature at min. primary circuit flow temperature 0	°C	55	60	the lack of datum

. Any heat pump unit whose rated heating output is greater than 50 kW must be equipped with buffer tanks with a capacity of 3000 dm³, which is required by the project guidelines [26]. Therefore, the heat pump unit supplies heated water at temperature t_f obtained from Equation (2) to the buffer tanks, which are the reservoir of energy for the central heating system. If the temperature decrease in the buffer tanks is greater than 4 °C, then the heat pump unit warms the water to the desired value. It prevents the heat pump unit from being turned on for a short-time period. Therefore, heat losses during energy storage must be added to the total design heat load. Based on use experience, the efficiency of buffer tanks is assumed to be equal to 98%.

As the second variant, the four small units are sized as the energy source for heating. There are one unit of Vitocal 300-G type BW 301.A45 and three units of Vitocal 300-G type BWS 301.A45; the extracts from their technical data [28] are presented in Table 3. Because the rated heating output of each unit is less than 50 kW, no buffer tank is required, thus the heating system does not offset the additional heat losses. Moreover, the heat pump units work in the cascade mode, that is, the number of the simultaneously working units depends on an actual heat demand. Hence, a comparison between these two variants seems to be interesting.

The temperature profile in a ground is determined by Baggs formula, which was adapted to the Polish climate conditions by Oleśkowicz-Popiel et al. [29]:

$$t\left(z,\tau \right)=\left(t_m+\Delta t_m\right)-1.07k_v{A}_s\exp \left(-0.00031552z{a}^{-0.5}\right)\cos \left[\frac{2\pi }{365}\left(\tau -{\tau }_o-0.018335z{a}^{-0.5}\right)\right]$$

(12)

The constants in Formula (12) for the Bialystok climate zone were achieved by Biernacka [7], and are shown in

Table 4. Data for Baggs Formula (12) taken from Biernacka [7].

Magnitude	Symbol	Unit	Quantity
The difference between the ground temperature below the shallow zone and the average annual air temperature	Δtm	[deg]	2.2
The vegetation coefficient	kv	[-]	0.85
The amplitude of the annual air temperature	As	[deg]	12.1
The soil thermal diffusivity	a	[m2/s]	6.00·107
The phase shift of the air temperature wave	τo	[d]	22
The average annual air temperature	tm	[°C]	7.407659

.

A crucial issue in the algorithm is the temperature value in the outlet from the primary circuit, that is, the ground heat exchanger in the considered case, after all. Hence, the mean temperature value in the range from the surface of ground to the end of the exchanger (i.e., up to depth h = 100 m) in every hour in the year is calculated as follows:

$$\overline{t}\left(\tau \right)=\frac{{\displaystyle \underset{0}{\overset{h}{\int }}t\left(z,\tau \right)}dz}{h},$$

(13)

where t(z, τ) results from Formula (12).

The mean temperature obtained from Formula (13) is the temperature of ground that heats brine. Hence, brine is colder by 5 °C. The brine temperature is the heat source temperature in the evaporator and is applied in the calculations mentioned above. The minimal ground temperature is 7.22 °C, the maximal ground temperature is 7.60 °C, and the mean temperature is 7.41 °C. As the temperature difference between brine and refrigerator is 5 °C, the temperatures inside the evaporator are 2.22 °C, 2.60 °C, and 2.41 °C, respectively.

2.2. Water Heat Pump

In the second alternative option with the groundwater basin, one unit of Vitocal 300-W Pro WW 302.B200 is applied, which is described in Table 3, and the unit must be equipped with a buffer tank. Water temperature in the groundwater basin is calculated on the basis of the Kowalski [30] formula.

$$t\left(z\right)=t_m+A+g_g\left(z-h\right)\hspace{1em}\left[°\mathrm{C}\right],$$

(14)

where the variables and constants are presented in

Table 5. Data for determination of the groundwater basin temperature [30].

Magnitude	Symbol	Unit	Quantity
Depth of shallow zone	h	[m]	5
Depth of the groundwater basin	z	[m]	100
Correction factor due to true altitude	A	[-]	0.856
Geothermal gradient	gg	[deg/m]	1/35

. As a result, water temperature is 10.98 °C and is supposed to be constant all year.

Seeing that the composition of the groundwater is not known thus far, the possibility that the groundwater would not satisfy the properties required for the proper performance of the heat pump should be considered. Hence, to protect the heat pump unit, the separating heat exchanger (SHE) would have to be installed in the primary circuit. Therefore, in the case that the fabricator recommends the heat exchanger with No. 7459 279 as the extension of the applied system, then the temperature difference between the groundwater and brine in primary circuit is 2 °C [27]. Thus, the temperature outside the evaporator is 10.98 °C without SHE and 8.98 °C with SHE.

2.3. Air Heat Pump

Because the air heat pump needs no additional earthwork, it is the variant with the lowest capital costs. However, the highest heat demand is connected with the lowest outside temperature. Therefore, the COP decreases and reaches the temperature at which the operation of the heat pump is not profitable. As this happens at the lowest temperature outside, another heat generator should provide the design heat demand. Consequently, it is a bivalent system.

As the primary heat generator, six heat pump units of Vitocal 350-A type AWI 120 were sized. The most important properties of the applied heat pumps are shown in

Table 6. Technical data of the air heat pump unit quoted from the datasheet [31].

Description	Unit	Vitocal 350-A Type AWI120
Output data to EN 255		A2/W35
Rated heating output	kW	18.5
Power consumption	kW	5.8
Coefficient of performance	-	3.2
Content	l
Fan power	W	480
Air volume flow rate	m3/h	4500
Pressure drop	mbar	65
Max. flow temperature	°C	35
Min. flow temperature	°C	−20
Heating water (secondary circuit)
Content	l	4
Min. flow rate	l/h	1800
Pressure drop (at min. flow rate)	mbar	242

.

The bivalent temperature at which the second heat generator replaces the heat pump is equal to −2.5 °C, which is in accordance with the manufacturer data [31]. The air temperature values when the air heat pump works are plotted in Figure 4—this is the temperature outside the evaporator.

Before sizing of the secondary heat generator, the operating costs should be estimated to eliminate the most expensive ways of heat generation. The second heat generator should meet energy demand Q_hb = 494 GJ/a (224 GJ/a during the daily tariff, and 270 GJ/a amid the night tariff in the case of electricity). The cheapest heat origins from a local combined heat and power plant, while the price of heat from natural gas is the last but one. However, they both are supplied through the proper duct network, which generates additional costs. Therefore, these costs are introduced into the analysis. The most expensive is electrical energy that is generated in heat power plants where lignite or bituminous coal are the main fuels. Moreover, these costs are doubled by transfer charges, which eliminates electrical energy in Poland as the energy source for heating. Taking into account the aggregate costs, which are presented in Figure 5, two heat generators are recommended as the secondary heat generator: an oil condensing boiler and gas one. Therefore, they are both selected for the further analysis.

2.4. Running Expenditures of Heat Generators

Although the economic analysis is not the aim of the paper, it is important when an investor comes to a decision about the heat source selection. Fuel cost estimation prevents us from including into the analysis the heat generators that are uneconomical, and thereby those that would not be applied. Moreover, as is seen further on, the most expensive heat generators are the unecological ones simultaneously.

The costs of operation of heat pump units are determined based on electrical energy demand obtained from Equation (5). The outlays for other heat generators are computed on the basis of energy for heating demand received from Equation (4). In the case of the air heat pump, the costs of central heating operation are the sum of a value of used electrical energy when the heat pump units work over the bivalent temperature and the costs of the combusted fuel when heat is generated in the boilers (below bivalent point). The prices that are controlled by the antitrust agency (natural gas, electricity, and heat from the district heat network) are obtained from proper tariffs that depend on energy usage and power demand at the designed temperature. The price of oil, which is available on free market, is its average list price in the region. Hence, the price of oil may be negotiated and the chief executive officer is able to achieve a satisfactory discount, but as it is unable to forego, the average oil price in Bialystok province is taken in the calculations. The payments include 23% value-added tax.

3. Results and Discussion

Hereafter, the outcomes derived in the investigations are presented. The comparison of the different heat sources for the heating system is done according to the economical, energetic, and ecological criteria.

3.1. Operating Costs of Heat Production

Energy production payments are plotted in Figure 6. Hereupon, the condensing gas boiler’s running costs are the reference level. Because of the reasons mentioned above, electricity costs far exceed the costs of other energy sources for heating (375%), hence electrical energy is used for heating very rarely. In the cases of oil and district heat network, expenses are similar at 140%. The cheapest conventional heat production is done in a condensing gas boiler station, at 100%. It is even cheaper than in the case of the air heat pump with a bivalent heat generator (126%), which is the most expensive kind of heat pump. Next is the brine heat pump (78% with one unit with buffer tank and 83% with four smaller units) and the cheapest is water pumps (70% with the separating heat exchanger and 66% without one). Although four smaller brine heat pump units seem to be more flexible than one bigger unit, which has to additionally cover heat losses caused by the buffer tank, they generate higher running costs than one bigger unit.

3.2. Seasonal Coefficient of Performance

The coefficient of performance is calculated as a quotient of the actual heat demands the and necessary work to cover these needs. It is assumed that heat demands change along the heating curve, which determines temperature in a heat sink. The COP also depends on temperature of the heat source. The values of the COP in each hour in heating season (except air heat pump below bivalent temperature) and the SCOP are plotted in Figure 7.

Heat losses depend on the external air temperature; the lower the outside temperature, the bigger the losses. Therefore, in the case of the air heat pump, the COP declines significantly with the external temperature decrease. This is the explanation for the lowest of both the COP and the SCOP in this case. An electrically-powered heat pump is a profitable heat generator when heat generated by it exceeds primary energy used during electricity production for its operation. This condition is satisfied in Poland when the COP is at least 3.51, which was achieved in the work of [3]. In the case of the air heat pump, SCOP = 3.20, which means the air heat pump is not a profitable heat generator in Poland.

Henceforth, the ground-water source heat pump with the SCOP = 5.85 is a reference level. SHE reduces the SCOP by 5.13% to 5.55, but the ground-source heat pump has SCOP = 4.92, which is lower at 15.9%. The highest reduction by 45.3% is in comparison with the air to water heat pump, which is because of the lowest SCOP = 3.2.

3.3. Carbon Dioxide Emissions

Carbon dioxide generation caused by heating system operation is done in the particular place or in a distant location. The former originates from the boilers, and the latter from the power plants that produce electricity for heat pump operation. CO₂ emissions in generating stations (which work along the Rankine cycle) are done directly and in an indirect way. These aggregate carbon dioxide productions are presented in Figure 8 with respect to emissions during fuel combustion and the generation of electrical power.

The water heat pump causes the lowest CO₂ emissions. The separating heat exchanger increases the emissions at 5.36%. Carbon dioxide production is higher by 18.80% if one unit of the brine heat pump with the buffer tank is selected, and by 20.46% in the case of four less units. The air heat pump seems to not be ecological in comparison with the previous ones, because the emissions increase by 51.22% for air heat pump with the condensing gas boiler as the secondary heat generator, and by 63.95% with the condensing oil boiler. The higher CO₂ generation in the case of oil boiler as the bivalent heat generator is caused by a greater share of carbon in oil than in natural gas.

As the comparison of CO₂ emissions between gas condensing boiler and heat pump can be done using Equation (10), CO₂ emissions during gas condensing boiler operation are not calculated. This is because condensing gas boiler emissions are used as a reference level for other heat generators. The solutions of inequality (8) are plotted in Figure 9. Therefore, only the heat pump with groundwater as the heat source would reduce aggregate CO₂ emissions.

4. Concluding Remarks

A heat pump does not emit any pollution in the place in which works—its operation causes distant emissions in power stations. Therefore, the method of electricity production has to be taken into account.

The efficiency of a reversed thermodynamic cycle depends on the temperature range between a heat sink and a heat source. Hence, the temperature in a condenser, in which heating water is warmed, should be as low as possible. while temperature in a evaporator, in which heat is taken from heat reservoir, ought to be as high as possible. Because heating water has to be warmer to provide heat exchange in the radiators, its temperature is not affected by climate conditions. The external temperature is a very important factor in the case of air heat pumps. Therefore, even in temperate climates, the air heat pump coefficient of performance is significantly lower than in other cases. Additionally, low production and transport efficiency of electricity in Poland makes this kind of heat generation economically unviable in the location. Had we remained with combustion of bituminous coal or lignite one in the power plants, the air heat pump would be less ecological than the condensing gas boiler.

Other possibilities to cut CO₂ emissions are associated with substantial changes in electrical energy production in Poland. Nuclear power plants should be constructed, which is being considered by the present Polish government. Another step is encouragement of energy production using renewable energy resources. However, the last renewable energy resources law amendment is a step backwards.

Taking into account the very complex situation in Poland, only the most sophisticated solutions could satisfy the international obligation to limit carbon dioxide emissions.

A water heat pump with the groundwater basin as the heat source is the most ecological way of heating in Poland. Hence, Polish and European authorities should support groundwater heat pump installation in every available way. If groundwater is unavailable, then the condensing gas boiler would be more ecological than the brine heat pump or air heat pump. Although the conclusions are legitimate only for the considered case, the above algorithm can be applied in other countries, especially where an overwhelming majority of electrical energy is generated along the Rankine cycle using anthracite; bituminous coal; or, even worse, lignite, as the fuel.