Accepted Manuscript Title: Reducing the global warming impact of a household heat pump dishwasher using hydrocarbon refrigerants Author: Peder Bengtsson, Trygve Eikevik PII: DOI: Reference:
S1359-4311(16)30147-8 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.018 ATE 7747
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
30-9-2015 4-2-2016
Please cite this article as: Peder Bengtsson, Trygve Eikevik, Reducing the global warming impact of a household heat pump dishwasher using hydrocarbon refrigerants, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Reducing the global warming impact of a household heat pump dishwasher using hydrocarbon refrigerants
1
Peder Bengtsson, 2Trygve Eikevik 1
ASKO Appliances AB,
Sockerbruksgatan 3, 53140 Lidköping, Sweden
2
Norwegian University of Science and Technology, Department of Energy and Process Engineering, 7491 Trondheim, Norway
*Corresponding author. Tel:+46 510 306155, E-mail:
[email protected]
Highlights
A study of total equivalent warming impact (TEWI) for a heat pump dishwasher.
The conclusions were based from results from a validated simulation model.
Refrigerants R600a, R290 and R134a were considered in three different regions.
R600a has the lowest TEWI in all regions.
ABSTRACT In a heat pump dishwasher, the dishware and the dishwater constitute the heat sink and a water tank filled with water, which can freeze, the heat source. A simulation model developed and validated earlier, was modified and used in a parameter study to determine the lowest total electricity usage for the refrigerants R134a, R290, and R600a with different cylinder volumes of the compressor. The total equivalent warming impact (TEWI) was calculated in three regions with different CO2 eq. emissions from electricity generation, i.e., Sweden, Europe (OECD), and Europe (Non-OECD), for small, medium-sized, and large households. In regions with low CO2 eq. emissions from electricity generation, the total TEWI of a heat
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pump dishwasher is the lowest with R600a and the highest with R134a and in regions with high CO2 eq. emissions, the total TEWI is the lowest with R600a and the highest with the conventional electrical element. Keywords: Household appliances, Natural refrigerant, Electrical reduction, TEWI, GWP
Introduction Undesirable global warming is occurring, mostly due to the increased amounts of greenhouse gases in the atmosphere. One major factor is CO2 eq. emissions from electricity generation. When estimating the effect of electricity generation on global warming, the specific energy source is important. Electricity usage in countries where most of the electricity is generated from wind and hydropower has a lower global warming impact than it has in countries where the electricity is generated from fossil fuels. Another factor is activities in which other greenhouse gases are emitted into the atmosphere, for example, when refrigerants used in heat pump systems leaks into the atmosphere. The environmental effect from household products such as dishwashers, washing machines, and refrigerators has been considered equal to the usage of electricity the product use when used by the end consumer[2]. The electricity usage is labelled on the front of the dishwashers and is today an important value when a customer is choosing which dishwasher to buy. Historically, the main source of decreasing electricity usage in dishwashers has been decreased dishwashing temperature and water use in combination with longer cycle times. A large reduction of electricity and water use in dishwashers in Europe occurred when the European dishwashing standard[1, 2] was introduced at the end of the twentieth century. For example, one manufacturer reduced dishwasher electricity and water usage between 1977 and 2003 from 3.7 to 1.1 kWh and from 60 to 9.9 l, respectively[2] for one wash. In the last ten years, the reduction of electricity and water usage has flattened out because it is difficult to reduce water use any further in the traditional washing process. Reducing electricity usage in the future will obviously require new technology. Some studies have examined ways to reduce the electricity usage of dishwashers. One idea is to use the heat from the dishwasher wastewater to heat the fresh water entering the dishwasher[3], and calculations and performance tests indicate a 25 % reduction in total electricity usage by means of this approach. By using an additional absorption cycle during the drying process, the total electricity usage of the dishwasher can be reduced by 25 %[4]. By
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heating the dishwasher using a hot water circulation loop, the energy is transferred to the dishwasher via a heat exchanger[5]. Experimental results indicate that it is possible to replace up to 90 % of the electricity usage by hot water heating. In this case, there is no reduction in use of energy, just a shift of the energy carrier from electricity to hot water. Another approach is to add a heat pump system, where the heat source is a water filled tank and the dishwasher is the heat sink[6]. Most of the energy from the water tank is the latent heat when water freezes. The hydrofluorocarbon (HFC) refrigerant R134a was used and the total electricity usage was 24 % less than for a conventional dishwasher. R134a has the disadvantage of having a high global warming potential (GWP) of 1300[7], and it increased the global warming if it leaks into the atmosphere, so there is a desire to replace it with another refrigerant having a lower GWPs[8-11]. This has led to various international initiatives, such as the Kyoto Protocol, some European countries have introduced HFC taxes, and refrigerants having GWPs greater than 150 will be forbidden in new cars in Europe starting in January 2017[10]. Some potential alternative refrigerants with low GWPs are natural alternatives such as propane (R290), isobutene (R600a), ammonia (R717), and carbon dioxide (R744). They differ in their characteristics and which one to used in a heat pump system, will depend on the operating conditions[9]. In a heat pump dishwasher[6], the temperature of the dishwasher (the heat sink) starts at 22 C and ends far above 31 C, which is the critical temperature for R744. This means that it is impossible to maintain a transcritical R744 cycle throughout the heating cycle energy efficiently. Ammonia is not a feasible alternative because it is incompatible with copper in the system and no small, cheap compressors are available on the market. The hydrocarbon (HC) refrigerants R290 and R600a are strong candidates and have many benefits: they are cheap, non-toxic, chemically stable, compatible with many materials, and miscible with mineral oils[8, 9]. The drawback is their flammability[12], which makes it important to have a low charge of refrigerant, a completely sealed system, and good ventilation around the heat pump system. R600a is a widely used hydrocarbon refrigerant[10]. In Europe it is the dominant refrigerant in household refrigerators, with a market share of more than 95 % in many countries[11]. Because of its common use in household refrigerators, many cheap, small R600a compressors are available on the market today. Several studies have examined the possibility of replacing R134a with hydrocarbons in similar heat pump system as in this study[13-16] . The changes of refrigerants results in heat
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pump systems with lower energy use and high reliability. A theoretical study compared the potential of R134a, R290, R600a, and mixtures of R290 and R600a for use in domestic refrigerators[13]. A comparative study examined R290, R600a, and R152a as alternatives to R134a in domestic refrigerators[14]. A theoretical comparative study considered replacing R134a with R290, R600a, and two alternative mixtures of R290 and R600a[15]. In cars, is it common to use R134a in the air conditioning system, and an experimental study examined replacing R134a with hydrocarbons[16]. There are various approaches to ranking the efficiency and global warming impact of electricity usage products, and some examples of measures used[3, 10, 17-23] include electricity usage (kWh), TEWI (kg CO2 eq.), and life cycle impact LCI (MJ/unit). LCI quantifies the cumulative energy inputs and outputs at all life cycle stages. It calculates the total electricity usage in raw material processing, manufacturing, and product use. Adding a heat pump system also adds a quantity of material. In the US, Boustani et al[23] found that 88–95 % of the LCI of washing machines, refrigerators, and dishwashers is attributable to the electrical usage at the customer. They concluded that the most effective way to reduce total LCI is to focus on how the customer uses such products. This can be achieved by e.g. promote the customer to buy dishwashers with low electrical usage, to choose the Eco-program in the dishwasher and to always start when the dishwasher is full of dishware[2]. This is the reason why only the dishwasher in use is handled in this study. However, when comparing the global warming impacts of different heat pump systems, it is relevant to pay attention to both the refrigerant and to the electricity usage by the end consumer. TEWI[10,17,22,24] takes into account both the direct effect, related to refrigerant leakage to the atmosphere, and the indirect effect, related to the electricity usage by the appliance. It also considers how the electricity generation affects global warming. Studies cite various values for CO2 eq. emissions from electricity generation, depending on the region, for example: =0.6 kg CO2 eq./kWh[15], =0.171 kg CO2 eq./kWh[17], and =0.47 kg CO2 eq./kWh[24]. The aim is to evaluate how a heat pump dishwasher affects global warming when it uses hydrocarbon refrigerants instead of R134a. Results for the end consumer in terms of total electricity usage and TEWI will be evaluated depending on where the electricity is produced and how much electricity the dishwasher uses.
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Method A validated transient simulation model from an earlier study[6] of a heat pump dishwasher has been modified to evaluate different refrigerants. Electricity usage and TEWI are calculated for three regions and three household sizes using a heat pump dishwasher with refrigerant R134a, R290, R600a or an electrical element. Fig. 1 is a schematic drawing of the heat pump system showing the dishwasher, water tank, and heat transfers. The evaporator cools and freezes the water in the water tank while the condenser heats the dishwasher, which contains 50 kg of steel, 25 kg of dishware, and 3 kg of water. A dishwasher has four operation steps: pre-washing, washing, rinsing, and drying. Only the washing and rinsing operation steps, when the dishwasher is heated and most of the electricity usage occurs, are studied in this paper[6]. This simplification does not affect the conclusions in this study. A schematic diagram of the dishwasher and water tank temperatures are shown in Fig. 2 to illustrate the transient simulation model. Fig. 2 shows when the compressor or electrical heater is operating, when the dishwasher is heated or cooled, and when the water in the tank cools, freezes, or melts. In all simulations presented here, the compressor operates for 60 min during the washing cycle. After 60 min the electrical element was operate until the maximum temperature was reached. The maximum temperature reached during both washing and rinsing is 55 °C. The total operating time for the washing is 80 min.
Simulation model The simulation model used here was developed and validated in an earlier study[6]. In that earlier study the definition of powers, heat load and the heating performance was described. In the present study, the definition of the compressor and the condenser heat transfer have been modified in the simulation model to handle comparisons of results between different refrigerants. In the earlier study, the overall heat transfer coefficient for a condenser using R134a originated from experimental results and was estimated using balance equations to be UAcond_R134a=0.160 kW/ °C[6]. Using the same system with a similar condenser power, the heat
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transfer coefficient is expected to change with the use of R290 or R600a compared with R134a[10-12, 25-27]. To compensate for this, it is comparatively calculated the average heat transfer coefficient for the condensation of vapour inside a circular tube containing R134, R290, or R600a. These calculations were performed in a function of the EES program[28], for condensation in tubes using equations from these studies[29-31]. The assumed inputs which were used, are shown in Table 1. The input parameters are the type of refrigerant (R134a, R290, and R600a) and the condensing temperature (44–62 C). The calculation results indicate a 9.0 % higher average heat transfer for the condenser used with R600a and an 8.0 % lower average heat transfer for the condenser with R290 compared with R134a. In further simulations, the following heat transfer figures will be used: UAcond_R134a=0.160 kW/°C, UAcond_R600a=0.174 kW/°C, and UAcond_R290=0.147 kW/°C. Differences in temperature and pressure from the start to the end of the dishwasher cycle will change the volumetric and isentropic efficiencies of the compressor during the cycle. The literature presents examples of how to simulate the volumetric efficiency when comparing different refrigerants[13, 14, 32, 33]. In the present study, Eq. (1) and (2) were used to define the volumetric efficiency of the compressor used with different refrigerants[14].
(1)
(2) The clearance ratio, C, differs depending of the cylinder volume and the compressor design. For small compressors, C is usually between 0.05 and 0.15[7]. Here we use C=0.1 in all simulations. In this study is a transient simulation used and the isentropic efficiency will be different during the changes of pressures. This makes a fixed value of the isentropic efficiency unsatisfied. In the literature was no general definition of the refrigerants R290, R600a and R134a found. In order to include the transient effect of the isentropic efficiency in this study, a definition in Eq. (3) of the isentropic efficiency[6, 7, 34] of R134a has been applied to all refrigerants studied here. The same isentropic efficiency is assumed to be used for R290 and R600a.
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(3)
Performance The total electricity usage by the heat pump dishwasher during washing and rinsing is the sum of the powers of the compressor, electrical element, and circulation pump and is defined in Eq. (4). (4) For the lowest electricity usage, the refrigerants R134a, R290, and R600a need different cylinder volumes of the compressor used to heat the heat pump dishwasher. To make a relevant comparison between the heating alternatives, a simulation study was conducted using different compressor cylinder volumes to determine the lowest electricity usage for each refrigerant for one wash (see Fig. 3). Fig. 3 shows that the lowest electricity usage for R134a (i.e., 0.89 kWh) was with Vs=6.6 cm3, for R290 (i.e., 0.88 kWh) was with Vs=3.85 cm3, and for R600a (i.e., 0.87 kWh) was with Vs=10.26 cm3; for the electrical element, the electricity usage was 1.18 kWh. The TEWI of a system is widely used to compare the sum of direct refrigerant emissions in terms of CO2 eq. and indirect emissions in terms of CO2 eq. from the system’s electricity usage over its service life[14, 15, 17, 24, 35] and is defined in Eq. (5). The direct effect is defined in the two first factors and the indirect effect is defined in the third factor of Eq. (5). (5) The CO2 eq. emissions from electricity generation depend on the region and the source of the electricity. This study considers 2011 values for three regions[37]: Sweden, =0.023 kg CO2 eq./kWh; Europe (OECD), =0.4534 kg CO2 eq./kWh; and Europe (non OECD), =1.160 kg CO2 eq./kWh. The total electricity usage and global warming impact of a dishwasher in a household depends on how often the dishwasher is used. The number of dishwasher uses is based on a manufacturer’s[2] figure of 280 loads per year for a medium-sized household. The present
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study assumed, based on the medium-sized household, that the usage of a large household is 560 loads per year and of a small household is 140 loads per year. Economic comparisons between the heating variants were based on Sweden’s 2013 electricity price, which was approximately 0.21 EUR/kWh[38] for a household using 5000 kWh per year.
Results and discussion The electricity usage per year for three categories of household, i.e., small, medium-sized, and large are shown in Fig. 4. Fig. 4 shows that the amount of dishwasher use is important for the end consumer regarding the electricity usage. This will also affect the economy for the end consumer. More household dishwasher usage results in more electricity savings when a heat pump variant is chosen instead of a traditional dishwasher heated with an electrical element. Table 3 shows that the calculated TEWI depends on the heating alternative (i.e., heat pump with R134a, R290, or R600a or an electrical element), the region where the electricity is generated (i.e., Sweden, Europe OECD, or Europe Non-OECD), and the household size (i.e., small, medium-sized, or large). The input values for the calculations are shown in Fig. 4 and Table 2. The results in Table 3 indicate that the total TEWI is 42–295 kgCO2 eq. in Sweden, 823–4485 kgCO2 eq. in Europe (OECD), and 2025–11032 kgCO2 eq. in Europe (Non-OECD). TEWI are influenced by the differences in CO2 eq. emissions from electricity generation between the regions and by the differences in household size. In Europe (OECD) and Europe (NonOECD), indirect TEWI dominates the total TEWI. The results shown in Fig. 5 indicate that the CO2 eq. emissions from electricity generation greatly influence the total TEWI. Comparing the results for Sweden with those of Europe (non-OECD), it can be concluded that it makes marginal difference which dishwasher variant is used in Sweden. To reduce total global warming, the emphasis should be on replacing conventional dishwashers with heat pump dishwashers in regions with high CO2 eq. emissions from electricity generation. Some other studies of TEWI use the value for CO2 eq. emissions from electricity generation in only one region[15, 17, 24]. The present results, however, indicate that if the aim is to achieve
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an international perspective on studies of global warming, more than one region needs to be considered (see Fig. 5). Fig. 6 shows both the indirect and direct TEWI for dishwasher use when the electricity is generated in Sweden. In Sweden, the heat pump dishwasher with R600 refrigerant has the lowest total TEWI and the heat pump dishwasher with R134a has the highest, independently of household size (Fig 6). In the Swedish case, the conventional dishwasher with an electrical element has a lower total TEWI than the heat pump dishwasher with R134a. That is because the CO2 eq. emissions from electricity generation are low in Sweden while the direct part of the TEWI calculations (i.e., 122 kgCO2 eq. for R134a vs. 0.1 kgCO2 eq. for R290 and R600a), including the GWP value, amount of leakage, and recycling, greatly affect the total TEWI. This direct TEWI strongly affects the total TEWI in Sweden comparing in Europe (non-OECD) and Europe (OECD). To achieve a lower total TEWI for the heat pump with R134a than for the element, the Swedish end consumer would need to wash more than 1240 loads per year, or about 3.4 loads per day. Therefore, in case of heat pump dishwashers with R134a in Sweden, reducing the effect on global warming compared with conventional dishwashers is only possible for end consumers using the dishwasher a great deal and/or if manufacturers reduce the leakage and increase the recycling of the refrigerant. Additional calculations indicate that to obtain a lower total TEWI for the heat pump process with R134a than for the element, the CO2 eq. emissions from electricity generation in the region must be ≥0.20 kgCO2 eq./kWh for 140 loads per year, ≥0.10 kgCO2 eq./kWh for 280 loads, and ≥0.05 kgCO2 eq./kWh for 560 loads. This means that it is impossible to give a general advice to the customer when choosing between a heat pump system with R134a and an electrical element if the customer will reduce the CO2 eq. emissions. It depends on how the customer uses the dishwasher, and where customer lives. However, the recommended way overall to reduce the total global warming effect is to concentrate on replacing all conventional dishwashers with heat pump dishwashers using R290 or R600a refrigerant. That recommendation would apply to all end consumers regardless of how the electricity is generated and the size of the household.
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The calculations of the compensation of the average condenser heat transfer were based on the assumptions regarding the condenser in Table 1. However, additional calculations were made using various tube diameters, condenser powers, and differences between the condensing temperature and surface temperature inside the tube. In all cases, the compensation levels for the different heat transfer values were around 9 % higher for R600a and 8 % lower for R290 comparing to R134a. The results in Fig. 3 indicate that the total electricity used by a heat pump dishwasher is similar for the three alternative refrigerants, but that different compressor cylinder volumes are required: R290 needs a smaller and R600a a larger compressor cylinder volume than for the R134a to perform the same work. Other studies[10-13, 15, 36] have noted the same trends regarding cylinder volume versus refrigerant. This strengthens reliability of the calculations in this study. Besides the environmental incentives for a customer to buy a heat pump dishwasher, there will always be economic considerations as well. Choosing a heat pump dishwasher with R600a over a conventional dishwasher would reduce the electricity usage of a medium-sized household by 1320 kWh, which will result in saving of EUR 277 (in Sweden) over the appliance lifetime of 15 years; a small household would save EUR 138.5 and a large household EUR 554. The customer will save money on total dishwasher usage if the difference in retail price between the heat pump and electric-element dishwasher is less than the save of electricity usage. The examples above, of increased retail prices for the heat pump dishwasher ought to be possible for the manufacturers to manage to keep lower. However, the economic considerations will be unique to each customer depending on the amount of usage, electricity price, and the extra cost of a heat pump versus an electrical-element dishwasher.
Conclusions This paper presents a simulation study of a heat-pump-heated dishwasher using the refrigerants R134a, R290, and R600a. The results in terms of total electricity usage and TEWI were studied when the compressor cylinder volume was optimized. Based on the results obtained, the following conclusions are drawn: •
The total electricity usage of a dishwasher is approximately 25 % lower for the heat pump than the electric-element variant, independent of which refrigerant, i.e., R134a, R290, or R600a, is used.
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•
The recommendation to reduce the total global warming impact of dishwashers is to concentrate on replacing all conventional dishwashers with heat pump dishwashers using a low-GWP refrigerant such as R290 or R600a.
Nomenclature C
Clearance volume ratio (-)
cp
Specific heat capacity at constant pressure (J/kg°C)
cw
Specific heat capacity at constant volume (J/kg°C)
Ė
Electric power (kW)
E
Electricity energy (kWh)
GWP
Global warming potential (-)
k
Kappa, polytrophic index (-)
l
Leakage rate (kg/year)
m
Mass (kg)
n
Life time (years)
p
Pressure (bar)
T
Temperature (C)
TEWI
Total equivalent warming impact (kg CO2 eq.)
UA
Total heat transfer coefficient (kW/°C)
Vs
Compressor cylinder stroke volume (m3)
Greek symbols
Recycling factor (%)
β
Carbon dioxide emissions from electricity generation (kg CO2 eq./kWh)
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ηis
Isentropic efficiency of the compressor (-)
ηv
Volumetric efficiency of the compressor (-)
Subscripts compressor Heat pump compressor cond
Condenser
dw
Dishwasher
element
Electrical element
evap
Evaporator
pump
Water circulation pump
r
Refrigerant in the heat pump process
tot
Total
wt
Water tank
Acknowledgements This study was performed within the multidisciplinary Industrial Graduate School VIPP Values Created in Fibre-Based Processes and Products at Karlstad University, with financial support from the Knowledge Foundation, Sweden. The authors would like to thank Jonas Berghel and Roger Renström at Karlstad University.
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Fig. 1.
Schematic drawing of the heat pump dishwasher showing the water tank, heat pump system, and heat transfers.
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Fig. 2.
Schematic diagram of the heat operations in the transient simulation model. The temperatures shown are for the dishwasher, Tdw, and the water tank, Twt.
Fig. 4.
Electricity usage per year depends on how often the dishwasher is used.
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Fig. 5.
Total TEWI of a heat pump dishwasher with R134a, R290, or R600a refrigerant or of a dishwasher heated by an electrical element in a medium-sized household using electricity generated in different regions.
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Fig. 6.
Direct and indirect TEWI in different-sized households using a heat pump dishwasher with R134a, R290, or R600a refrigerant or a dishwasher heated by an electrical element with electricity generated in Sweden. The direct TEWI from R290, R600a and the element are too small to been shown in the figure. These values can be seen in Table 3.
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Table 1. Assumed input parameters used to calculate different condenser heat transfers between the different refrigerants. Condenser tube inner diameter
0.015 m
Condenser tube length
1.2 m
Temperature difference between the inside surface of
2 °C
the condenser tube and the condensing temperature Condenser power
490 W
Vapour quality of refrigerant entering and exiting the
Entering=100
condenser
% Exiting= 0 %
Table 2. Values used for calculating the TEWI of different heating alternatives. In tests with an experimental heat pump dishwasher setup, the charge of R134a was optimized at 0.13kg.
R134a
R290
R600a
Electrical element
GWP[36]
1300 (100
3 (100
3 (100
years)
years)
years)
0.0039
0.00234
0.00234
kg/year
kg/year
kg/year
n [2]
15 years
15 years
15 years
15 years
mr (R290 and R600a = 60% of
0.13 kg
0.078 kg
0.078 kg
-
(50% of the remaining
50% of
50% of
50% of
-
refrigerant after 15 years)[2]
0.0715 kg
0.0429 kg
0.0429 kg
l (3% a year)[14]
-
-
R134a)[14]
Page 19 of 20
Table 3. TEWI for different-sized households using a heat pump dishwasher with R134a, R290, or R600a refrigerant or a dishwasher heated by an electrical element and electricity generated in different regions.
R134a
R290 R600a Element R134a R290 R600a
Element
R134a R290 R600a
Eleme nt
140 Loads/year TEWI
Total 165.6
42.6
42.1
280 Loads/year 57.1
208.8
85.1
84.0
560 Loads/year 114.2
295
169.
167.9
228.4
9 Sweden Direc 122.5 (kg CO2 eq.)
0.2
0.2
0.0
122.5
0.2
0.2
0.0
122.5 0.2
0.2
0.0
42.4
41.9
57.1
86.3
84.9
83.8
114.2
172.5 169.
167.7
228.4
t Indir
43.1
ect TEWI
Total
7 969.4
833.6
823.4
1121.3 1816.4 1667 1646.6
2242.7
3510.3 3333 3293.1 4485.4 .7
OECD Europé
Direct 122.5
0.2
0.2
(kg CO2
Indirec 846.9
833.4
823.2
eq.)
TEWI
0.0
122.5
0.2
0.2
1121.3 1693.9 1666.8 1646.4
0.0 2242.7
t
122.5 0.2
0.2
0.0
3387.8 3333 3292.9 4485.4 .5
Total 2205.6 2050
2025
2758.1 4288.8 4099.8 4049.8
5516.1
8455 8199 8099.4 11032. .4
2
Non-OECD Europé
Direct 122.5
(kg CO2
Indirec 2083.1 2049.8 2024.8 2758.1 4166.3 4099.6 4049.6
eq.)
t
0.2
0.2
0.0
122.5
0.2
0.2
0.0 5516.1
122.5 0.2
0.2
0.0
8332.5 8199 8099.2 11032. .2
2
Page 20 of 20