Dealing with uncertainty in global warming impact assessments of refrigeration systems

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IN

DEGREE PROJECT TECHNOLOGY, FIRST CYCLE, 15 CREDITS

STOCKHOLM SWEDEN 2018,

Dealing with uncertainty in global warming impact assessments of refrigeration systems

LINN BOSTRÖM

HANNA LJUNGBERG

KTH ROYAL INSTITUTE OF TECHNOLOGY

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i

Abstract

The United Nations recognises anthropocentric greenhouse gas emissions to be the leading cause of global warming. The International Institute of Refrigeration further addresses that in 2014 7.8% of the global greenhouse gas emissions were assigned to the refrigeration sector. This marked the importance of using metrics to evaluate the climate impact of a refrigeration system. However, as these metrics rely on uncertain values it is difficult to assess how reliable they are. The purpose of this study is therefore to evaluate the reliability of two environmental metrics by applying methods for dealing with uncertainties, and to present possible improvements to the applied methods and metric.

The study begins by introducing refrigeration systems and their environmental context. In the background the reader is further introduced to the topic by accounting for the evaluated metrics, TEWI and LCCP, as well as three different methods for dealing with uncertainties, Sensitivity analysis, Uncertainty analysis and Monte Carlo Simulation. In order to fulfil the purpose a data centre is modelled, and the restrictions and operation conditions of the system will be further described under section 3. The result will consist of two parts. The first part will consider the theoretical aspect of the study as well as sources and typologies of values and uncertainties. The second part will consist of the empirical results from applying the mentioned methods on the modelled system. These will be presented in graphs sorted after method and metric and are then analysed and evaluated in the discussion. It is seen that only a few parameters dominate the influence in the Sensitivity and Uncertainty analysis but that the influential parameter is dependent on the relative order of magnitude. It is also stated that the LCCP rends no additional information at the analysed conditions.

When applying the Monte Carlo Simulation TEWI is considered more reliable, as in that the deterministic value is a more accurate estimation of the ’true’ environmental impact of the system. One possible improvement may be to use the rendered standard deviation for TEWI as an uncertainty range to incorporate the uncertainties in the deterministic value.

The study concludes that the Sensitivity and Uncertainty analysis illustrates the influence of one single parameter on the final metric value. However, the analyses do not determine to what extent these final values may be considered reliable. A Monte Carlo Simulation is better applicable for some uncertainty typology than others and as such TEWI is considered more reliable than LCCP. The study lands in the conclusion that the presented methods may be improved by assigning uncertainty typologies in order to evaluate the viability of a method to incorporate the uncertainties, e.g. a Monte Carlo Simulation.

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Sammanfattning

Förenta Nationerna erkänner antropocentriska utsläpp av växthusgaser som den främsta orsaken till global uppvärmning. Vidare belyser IIR att kylsektorn stod för 7.8% av de globala utsläppen av växthusgaser år 2014. Detta åskådliggjorde vikten av att använda mätmetoder som kan utvärdera klimatpåverkan hos ett kylsystem. Då dessa mätmetoder baseras på osäkra värden är det svårt att bedöma hur pålitliga de faktiskt är. Syftet med detta projekt är därför att utvärdera tillförlitligheten hos två mätmetoder genom att tillämpa metoder för att hantera osäkerheter och att presentera möjliga förbättringar till de tillämpade metoderna och mätmetoderna.

Projektet börjar med att introducera kylsystem och deras miljösammanhang. I bakgrunden får läsaren lära sig mer om ämnet genom en redogörelse för de utvärderade mätmetoderna, TEWI och LCCP, samt tre olika metoder för att hantera osäkerheter, Känslighetsanalys, Osäkerhetsanalys och Monte Carlo-simulation. För att uppfylla syftet modelleras ett data center, och systemets begränsningar och driftsförhållanden beskrivs vidare under rubriken Metod. Resultatet består av två delar. Den första delen redovisar den teoretiska aspekten av studien så som källor för osäkerheter och typologier samt att här tilldelas parametervärden och osäkerheter. Den andra delen består av de empiriska resultaten som fås då metoderna tillämpas på det modellerade systemet.

Dessa presenteras i diagram vilka sorteras efter metod och mätmetod. Dessa analyseras och utvärderas sedan i diskussionen. Från resultaten går det att se att endast ett fåtal parametrar dominerar inflytandet i Känslighets- och Osäkerhetsanalysen men att den inflytelserika parametern är beroende av den relativa storleksordningen. Det visar sig även att LCCP inte bidrar till ytterligare information vid de analyserade förhålandena.

Vid tillämpningen av Monte Carlo-simuleringen anses TEWI vara mer tillförlitlig. En möjlig förbättring kan vara att använda den givna standardavvikelsen för TEWI som ett osäkerhetsintervall för att inkorporera osäkerheten i det deterministiska värdet.

Projektet landar i slutsatsen att Känslighets- och Osäkerhetsanalysen illustrerar inflytandet av en enskild parameter på det slutliga metriska värdet. Analyserna avgör emellertid inte i vilken utsträckning dessa värden kan anses vara tillförlitliga. En Monte Carlo-simulering är bättre tillämplig för en viss osäkerhetstypologi än andra och som sådan anses TEWI vara mer tillförlitlig än LCCP. Projektet landar även i slutsatsen att de presenterade metoderna kan förbättras genom att tilldela osäkerhetstypologier för att utvärdera huruvida en metod kan anses tillämplig för att inkorporera osäkerheter, t.ex. en Monte Carlo-simulering.

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Acknowledgements

A special thank you to our supervisor Pavel Makhnatch.

The authors would also like to thank each other for dealing with each others’

uncertainties throughout this work.

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List of Figures

2.1 Visualisation of the relation of metrics, strategies and emissions . . . 4

2.2 Visualisation of GWP . . . 4

2.3 Visualisation of a Monte Carlo Simulation . . . 7

3.1 Overview of the Sensitivity and Uncertainty analyses . . . 10

3.2 Overview of the performed Monte Carlo Simulations . . . 10

3.3 Standard deviation of a Gaussian distribution . . . 10

3.4 Visualisation of the data centre . . . 11

3.5 Vapour compression refrigeration cycle . . . 13

4.1 Accuracy, precision and variability visualisation . . . 17

5.1 Standardised Sensitivity analysis results for TEWI . . . 27

5.2 Complete TEWI Sensitivity analysis for all refrigerants . . . 28

5.3 Standardised Sensitivity analysis results for LCCP . . . 29

5.4 Complete LCCP Sensitivity analysis for all refrigerants . . . 30

5.5 Standardised Uncertainty analysis results for TEWI . . . 31

5.6 Complete TEWI Uncertainty analysis for all refrigerants . . . 32

5.7 Standardised Uncertainty analysis results for LCCP . . . 33

5.8 Complete LCCP Uncertainty analysis for all refrigerants . . . 34

5.9 The TEWI MCS results for all four refrigerants . . . 36

5.10 A standardised graph of the TEWI probability density functions for N=10 and N=20 . . . 38

5.11 The LCCP MCS results for all four refrigerants. . . 39

5.12 A standardised graph of the LCCP probability density functions for N=10 and N=20 . . . 41

1 Sensitivity analysis - Direct emission contributionss to TEWI . . . 53

2 Sensitivity analysis - Indirect emission contributions to TEWI . . . 54

3 Sensitivity analysis - Direct emission contributions to LCCP . . . 55

4 Sensitivity analysis - Indirect emission contributions to LCCP . . . 56

5 Uncertainty analysis - Direct emission contributions to TEWI . . . 57

6 Uncertainty analysis - Indirect emission contributions to TEWI . . . 58

7 Uncertainty analysis - Direct emission contributions to LCCP . . . 59

8 Uncertainty analysis - Indirect emission contributions to LCCP . . . 60

9 Poster for presentation . . . 61

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List of Tables

3.1 Design values . . . 14

4.1 TEWI parameter uncertainties and their correlated typology . . . 19

4.2 LCCP parameter uncertainties and their correlated typology . . . 20

4.3 System parameters . . . 22

4.4 Additional system parameters for the LCCP calculation . . . 23

4.5 GWP values and uncertainties . . . 23

4.6 Refrigerant parameters . . . 24

4.7 Additional refrigerant parameters . . . 25

5.1 The overlap of influential parameters from the Sensitivity and Uncertainty analyses 35 5.2 TEWI MCS statistics for N=15 . . . 37

5.3 TEWI MCS statistics for N=10 and N=20 . . . 37

5.4 LCCP MCS statistics for N=15 . . . 40

5.5 LCCP MCS statistics for N=10 and N=20 . . . 40

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Acronyms

GHG Greenhouse Gas . . . 1

GWP Global Warming Potential . . . 1

TEWI Total Equivalent Warming Impact . . . 1

LCCP Life Cycle Climate Performance . . . 1

IIR International Institute of Refrigeration . . . 1

IPCC Intergovernmental Panel on Climate Control . . . 4

UNFCCC the United Nations Framework Convention on Climate Change . . . 5

CO₂eq carbon dioxide equivalents . . . 5

MCS Monte Carlo Simulation . . . 7

KTHB the KTH Royal Institute of Technology Library . . . 9

EU European Union . . . 19

SATP Standard Ambient Temperature Pressure . . . 24

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Nomenclature

GWP Parameters

RF Radiative Forcing [W m⁻²] T Time horizon [years]

TEWI Parameters

a Recovery/recycling factor C Charge of refrigerant [kg]

Ea Annual electricity consumption [kWh year⁻¹] GWP Global Warming Potential [kg CO₂eq kg⁻¹] L Annual leakage rate [kg]

N System lifetime [years]

n System running time [years]

β Carbon emission factor [kg CO2eq kWh⁻¹] Additional LCCP Parameters

Adp. GWP Adaptive Global Warming Potential [kg CO2eq kg⁻¹] MR Recycled material emission factor [kg CO₂eq kg⁻¹] mr Mass of recycled material [kg]

MV Virgin material emission factor [kg CO2eq kg⁻¹] m_v Mass of virgin material [kg]

RFD Refrigerant disposal emissions [kg CO2eq kg⁻¹] RFM Refrigerant manufacturing emissions [kg CO2eq kg⁻¹] Other nomenclature

h Specific enthalpy [kJ kg⁻¹]

R1-R4 Four refrigerants used in the system SC Subcooling [∆^◦C]

SH Superheating [∆^◦C]

Tc Compressor temperature [^◦C]

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xii NOMENCLATURE

Te Evaporator temperature [^◦C]

Q_heat Heating load [kW]

η_is Isentropic efficiency [%]

µ Unbiased approximation of mode σ Standard deviation

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Introduction 1

In 2016 the United Nations announced 17 Sustainable Development Goals to serve as guidelines to combat the global challenges seen in the world today. One of these goals, more specifically development goal number 13, highlights the critical climate change and the importance of limiting this change significantly in order to maintain a habitable planet.

The United Nation identifies anthropocentric Greenhouse Gas (GHG) emissions to be the main reason for global warming and thus the primary concern is to prevent and reduce these emissions [UN, 2016].

One of several sources of emissions that is expected to play a major role in the future is the refrigeration sector, which accounted for 7.8% of the total global GHGs in 2014 according to the International Institute of Refrigeration (IIR) [Coulomb, 2017]. The thermal comfort sector constitutes an important element in today’s society and consists of heating and ventilation systems, air conditioning and refrigeration systems, commonly referred to as HVAC&R. In order to get a clearer picture of refrigeration systems’ contribution to climate change it is necessary to have good knowledge of the components of these systems. The physical process behind refrigeration is dependent on the use of refrigerants. A refrigerant is a fluid that, by absorbing thermal energy, enables heat transfer at higher temperatures and pressures, often involving a phase change [ASHRAE, 2016, p. 4].

Since the 19th century refrigerants have been dismantled and reshaped to meet safety as well as environmental requirements. From the early easy accessible, toxic and, or flammable solutions like R-290 (Propane) to others less hazardous for ozone depletion and global warming [Calm, 2008]. The rising threat of global warming and the role of GHGs marked an important step for starting to measure impacts of refrigerants. To enable measurements a metric called Global Warming Potential (GWP) was introduced. GWP is an environmental metric that relates a pulse emission of GHGs to CO₂equivalents [Myhre et al., 2013a], where a low GWP signals a lower contribution to global warming.

Although GWP indicates the impact of a refrigerant on climate change, it does not give a holistic picture of the impact from a refrigeration system in use. Therefore, two other environmental metrics that instead focus on the lifetime impact were introduced. These are called Total Equivalent Warming Impact (TEWI) and Life Cycle Climate Performance (LCCP). The first mentioned metric focuses on the system in full use, where energy requirements as well as refrigerant leakage are taken into account. LCCP, on the other hand, takes a more ’Life Cycle Assessment’ based approach by also measuring the impact from the lifecycle of the refrigeration system, ’from cradle to grave’. [IIR, 2016]

The IIR classifies TEWI and LCCP as tools for comparing systems with similar function and performance [IIR, 2016]. TEWI and LCCP are both dependent on multiple parameters

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1. Introduction

to render a result. However, these parameters are based on information that may be wrong, unreliable or simply unavailable. The inherent uncertainty in these metrics skewes the results making them unsuitable for definite estimations of the lifetime emissions of the system in question [IIR, 2016]. There are no known studies on how to deal with uncertainties in these metrics and there is little to no practical application of methods to analyse uncertainty, mostly because there have been no incentives to do so until recently [Heijungs and Huijbregts, 2004]. The uncertainties are all more or less well known, and the impact they have on the legitimacy of the deterministic results of GWP, TEWI and LCCP calculation is often discussed but rarely researched. This immediately prompts the question, how reliable can these comparisons be if the uncertainties are disregarded? As such, this marks the importance of finding legitimate methods for dealing with the uncertainties that characterise both TEWI and LCCP.

1.1 Sustainability Relevance

Sustainable development goal number 13, actions to combat climate change, is only one out of 17 sustainable development goals. This goal addresses the importance of decreasing GHG emissions in every sector. However, several goals concern ending poverty and improving health, which requires cooling storage. Therefore, improving refrigeration systems will play a key role in fulfilling not just one goal, but several of them.

Upgraded refrigeration systems are needed all over the world. For developed countries refrigeration system are used for comfort as well as storing and may be considered a necessity.

For non-developed countries, on the other hand, lack of refrigeration systems leads to famine and poor health, since food and medicine cannot be stored properly in exposed areas. By making refrigeration systems more accessible it is possible to minimize and eventually see an end to poverty, world hunger and poor health. Although, as mentioned earlier refrigeration sector accounts for 7.8% of the total emissions of GHG, and an increase in refrigeration systems will inevitably lead to increasing levels of emissions, especially if system design and performance seek no improvement.

The purpose of this project is to evaluate methods used for dealing with uncertainties in environmental metrics. By doing this, environmental metrics can be improved, and a more legitimate assessment of refrigeration systems may be performed to improve system design and performance. This project will therefore be a part of the pursuit for sustainable development.

TEWI and LCCP were introduced to compare the environmental impact of refrigeration systems to improve system design and reduce GHG emissions. However, the attained conclusions are of no use if they are based on results with high uncertainty, even comparatively.

It is therefore interesting to evaluate if there are methods that are able to incorporate uncertainties and render more reliable values.

1.2 Purpose

The purpose of this project is to evaluate the reliability of the metrics TEWI and LCCP by applying methods for dealing with uncertainties. Additionally, this project will discuss and present possible improvements to the applied methods and metrics.

1.3 Aims

The aims are to (1) present different methods that deal with uncertainty associated with the TEWI and LCCP metrics, (2) evaluate to what degree these metrics are considered reliable to estimate the global warming impact of refrigeration systems, and (3) based on presented methods suggest improvements.

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Background 2

Initially, for better understanding, it is preferable to acquire background knowledge of the environmental metrics and the methods used for dealing with uncertainty. In the following subsections the metrics will be accounted for by giving their environmental context as well as the manner in which they calculate the environmental impact. There is little to no research on how to deal with uncertainties in these metrics. However, there are still general practices on how to deal with uncertainty, these methods will be presented thereafter.

2.1 Environmental Metrics

The issues of refrigerants have changed over history. The early stages of chemical use was influenced by searching for less flammable and, or less toxic alternatives [Calm, 2008, p. 1124].

Since then the focus has shifted and the last two decades have been characterized by a raised concern regarding climate change. One course of action have been to introduce metrics to evaluate the environmental impact of a refrigeration system and its components, three of these metrics are GWP, TEWI and LCCP. Metrics are useful tools since they measure environmental impact and may thus serve as a basis for policy making and strategies to combat climate change [Stocker et al., 2013, p. 710]. Figure 2.1 shows the benefits from using a metric since it is defined to support the evaluation of effects from GHG emissions.

It is seen that increasing global impact increases the relevance for evaluating this impact.

However, along the same line the uncertainties increase as well.

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2. Background

Emissions

Atmospheric concentrations Radiative forcing

Climate change Impacts

Metrics Strategies

Increasinguncertainty

Figure 2.1: A visualisation of how metrics can be defined to support the evaluation of responses. Adapted from [Stocker et al., 2013, Figure 8.27].

2.1.1 Global Warming Potential

In 1990 the Intergovernmental Panel on Climate Control (IPCC) introduced GWP. This as a response to the demand for a new metric which calculates the environmental impact of different GHGs by using one metric only [Myhre et al., 2013a, p. 710]. The idea of GWP is to evaluate the contribution of a GHG to global warming by relating the radiative forcing of a pulse emission over time to that of an equivalent mass of CO2 . Radiative forcing is defined as the net energy balance of absorption and radiation expressed in watts per square meter [Myhre et al., 2013a, p. 664]. In simple words GWP quantifies the amount of energy a GHG retains in the atmosphere over a certain time span. This is illustrated by figure 2.2.

0 20 40 60 80 100

Years after emission

RadiativeForcing

Refrigerant, lifetime of decades Refrigerant, lifetime of years Carbon dioxide

Figure 2.2: Visualisation of how the radiative forcing is related to the perturbation lifetime. The blue and red lines represent a refrigerant with the lifetime of years or decades, respectively. The gray line represents carbon dioxide. Adapted from [Myhre et al., 2013a, p. 711].

The blue and red lined areas in the figure above represent the radiative forcing integral for two refrigerants with different lifetimes. The quotients of each respective area to that of carbon dioxide for a specific time horizon gives the global warming impact for refrigerants.

It is calculated by using the equation:

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2.2. Methods for Dealing with Uncertainties

GWP = Z T

0

RFGHG(t) dt Z T

0

RF_CO₂(t) dt

(2.1)

This metric is not set to a specific time horizon; 20, 100 and even 500 years may be used. However, the time horizon of 100 years is adopted by the United Nations Framework Convention on Climate Change (UNFCCC), the Kyoto Protocol [AIRAH, 2012, p. 7] and European Commission F-gas regulations [?]. There is no scientific reasoning behind adopting a time horizon of 100 years, although the choice of horizon strongly affects the outcome [Myhre et al., 2013a, p. 711]. The use of this standardised time horizon greatly simplifies comparisons and discussions of all results.

2.1.2 Total Equivalent Warming Impact

GWP does not account for the effects of a refrigeration system during operation. In order to solve this inconvenience a new metric called TEWI was introduced. TEWI can be seen as a sum of two parts. One part focuses on calculating leakage during system operation as well as disposal during end-of-life, so called direct emissions. The second part accounts for the indirect emissions of an operating system, as in energy usage and its related carbon emission factor as well as the system running time [AIRAH, 2012]. For TEWI to be efficient and useful it must be applied on systems with equal operating conditions. This metric relates the lifetime total emissions to that of kg carbon dioxide equivalents (CO2eq) using a deterministic value. TEWI can be calculated using the following equation:

TEWI = direct emissions+indirect emissions

= GW P × L × N + GW P × C × (1 − a)+(Ea × β × n) (2.2) 2.1.3 Life Cycle Climate Performance

To further evaluate the warming impact of a refrigeration system another metric was later introduced, Life Cycle Climate Performance. As the name implies it adopts a more Life Cycle Assessment approach, which makes LCCP a more comprehensive tool than TEWI.

LCCP not only considers the direct and indirect emissions from a system in use, it also accounts for emissions related to the manufacturing of the system as well as the chemical production of the refrigerant [IIR, 2016, p. 3-4]. LCCP is calculated by adding extra terms to the TEWI-formula, as seen below.

LCCP = direct emissions+indirect emissions

= (GW P + Adp.GW P ) × L × N + (GW P + Adp.GW P ) × C × (1 − a) + (Ea × β × n) +X

(mv× MV) +X

(mr× MR) + C × RF M × (1 + N × L)

+ C × RF D × a (2.3)

2.2 Methods for Dealing with Uncertainties

The parameter uncertainties are all more or less well known, and the impact they have on the legitimacy of the deterministic results of GWP, TEWI and LCCP calculation is

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2. Background

often discussed but rarely researched. There are no known studies on how to deal with uncertainties in these metrics. In addition to this there is little to no practical application of methods to analyse uncertainty, mostly because there has been no incentives to do so until recently [Heijungs and Huijbregts, 2004]. As the metrics rely on information that is wrong, unreliable or simply unavailable to obtain deterministic values, they produce skewed results.

In order to handle these uncertainties there are several different approaches one could take.

A few main lines to do this can be summarized as [Heijungs and Huijbregts, 2004, p. 3]:

1. Scientific: Performing more research in order to increase the quality of the input values.

2. Constructivist: Involving stakeholders so as to create consensus, standard and, or

’good practice’.

3. Legal: Relying on legal authorities and their decrees.

4. Statistical: Integrating statistical methods to evaluate uncertainties.

The first three categories deal with the uncertainties by trying to reduce them, while the fourth incorporates them explicitly. The constructivist and legal approaches of reducing the influence of imprecise, inaccurate or variable values have been successfully implemented [Calm, 2008]. Scientific efforts to improve data quality are always needed, however uncertainty will always be present. By using the statistical approach the calculations directly incorporates and thus deals with the uncertainties. Therefore a number of statistical methods for studying and evaluating the impact of uncertainties will be presented hereafter.

2.2.1 Sensitivity and Uncertainty Analysis

A basic way to deal with uncertainty is to perform a so called Sensitivity analysis. The simplest form of this type of analysis is done in all sorts of practices, from financial calculations to Life Cycle Assessments. A Sensitivity analysis is used to evaluate what influence an independent variable has on a dependent variable in a function [Björklund, 2002]. One way of performing this is by firstly defining the function and initial input values, and using these to calculate the baseline output. The second step is to change one input at a time with a chosen range of variation. The result is an output that varies by a certain level of sensitivity. [Huijbregts et al., 2001b] Logically this value differs from the initial output for each parameter. Consequently, the input values that produce the biggest output change are identified as sensitive parameters and vice versa. This gives an understanding of the importance of different input values in the model.

Another way of performing a Sensitivity analysis is by evaluating what influence the parameters’ specific uncertainties have on the dependent variables; an Uncertainty analysis [Björklund, 2002]. The approach for this analysis is much the same as for the Sensitivity analysis, with the important difference being that the predefined range of variation is not arbitrary. Instead the range is determined by the predefined uncertainty of each parameter.

One way to visually present the results of such analyses is to plot them in a so called Tornado diagram. This is an useful tool to depict how changes in selected variables affect the result [Analytica, n.d.]. The distinguishing feature is the results being represented in lying bar graphs where the bars represent the descendingly sensitive output range for the different parameters [Björklund, 2002].

2.2.2 Monte Carlo Simulation

Sensitivity analysis and Uncertainty analysis deal with uniformly changing one parameter at a time, however this only highlights how the metric depends on that specific parameter.

It does not show how the accumulated uncertainty may affect the range of the outcome.

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2.2. Methods for Dealing with Uncertainties

In order to examine the impact of combined uncertainties for a more comprehensive view further statistical methods are available. One widely known statistical approach is the Monte Carlo Simulation (MCS). The idea behind the Monte Carlo Simulation is to produce a distribution of possible outcomes by randomly selecting parameter values within respective predefined range [Art B., 2013].

The first step in performing such a simulation is thus to assign every parameter a uncertainty distribution. In many cases this step can be a complicated and time-consuming task which motivates performing a Sensitivity analysis beforehand in order to identify the significant parameters with highest influence on the output value. The next step is to perform this simulation several times, at least 10’000 iterations is to be recommended [Huijbregts et al., 2001a, p. 5]. Each iteration will select a random parameter with a value within the uncertainty range and the final result will present a distribution with expected outcomes where uncertainties have been taken into account. This is visualised below in figure 2.3, where three parameters are sampled in three runs in order to produce a simulation result.

Iteration 1

Iteration 2

Iteration 3

Parameter 1 Parameter 2 Parameter 3

Simulation results

Figure 2.3: Visualisation of a Monte Carlo Simulation, where three sampling iterations for each parameter are performed.

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Method 3

In order to fulfil the purpose, this study was divided in two main phases, the first being a literature study where information on the metrics and their associated parameters were collected to serve as a basis for the second phase. The information was collected from multiple databases accessed through the KTH Royal Institute of Technology Library (KTHB). The databases used were Primo, Web of Science and ScienceDirect. A database used, though not accessed through KTHB, was Google Scholar. Combinations of the following search words were central: ”Uncertainty”, ”Monte Carlo Simulation”, ”Sensitivity Analysis” and

”Life Cycle Assessment”. Additional literature such as articles and reports was provided by the supervisor, for example Chapter 8: Anthropogenic and Natural Radiative Forcing of the IPCC fifth assessment report.

The second phase of the project concerned the determination of the reliability of the metrics. To enable this phase calculations regarding the electricity consumption and emissions had to be performed for the case of a minor data centre in Sweden. All of the calculations and simulations were performed by using mathematical software for calculations [Mathworks, 2018], with refrigerant data being collected from property databases [CoolProp, 2016], [Chemours, 2018]. In the following sections, the procedures used for these calculations and data about the case will be described. Thereafter the designing of the data centre is presented. All of the equations, unless otherwise stated, used in the following subsections were retrieved from the book Applied Thermodynamics - Collection of Formulas [Havtun, 2014, p. 23-24].

3.1 General Outline of the Calculations Performed on the Modelled System

In this study the reliability of TEWI and LCCP were evaluated by undertaking a statistical approach. This was done by designing and performing calculations on a modelled data centre as seen in section 3.2. The reliability was then evaluated by analysing the rendered results from the Sensitivity analysis, Uncertainty analysis and Monte Carlo Simulation. The methods were performed in accordance with their respective descriptions under section 2.2.

The first statistical method was the Sensitivity analysis, with a defined sensitivity percentage of ±20%. This was followed by the Uncertainty analysis where individual uncertainty ranges were assumed, where there was no known range. The third method was a Monte Carlo Simulation performed with 100’000 iterations. Here the uncertainties were further defined with distributions or scenarios. The general outline may be visualised in figure 3.1 and 3.2.

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3. Method

Sensitivity analysis Uncertainty analysis

TEWI

R₁ R₂ R₃ R₄

LCCP

R₁ R₂ R₃ R₄

Figure 3.1: Overview of the Sensitivity and Uncertainty analyses

Monte Carlo Simulation

TEWI

R1

Scenarios R2

Scenarios R3

Scenarios R4

Scenarios

LCCP

R1

Scenarios R2

Scenarios R3

Scenarios R4

Scenarios

Figure 3.2: Overview of the performed Monte Carlo Simulations

For the Monte Carlo Simulation most sources defined the parameter uncertainty as a difference in values. As such, where the parameters were assigned a Gaussian distribution, the standard deviation for each was determined by assuming that the given uncertainty was the ’true’ uncertainty. That is, the parameter range endpoints given by the uncertainty correlated to the normal distribution, thus meaning that the standard deviation would be given by the difference of the endpoints’ values divided by six, see figure 3.3.

-2σ -σ

-3σ µ σ 2σ 3σ

Figure 3.3: Here a standardized Gaussian distribution is shown. The range between 3σ and -3σ covers the Gaussian distribution.

3.2 Designing the Data Centre

To evaluate the methods for dealing with uncertainties and illustrate the precision and significance of each method a system was modelled. The modelled system was a refrigeration 10

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3.2. Designing the Data Centre

system used for cooling a minor computer data centre. The main reason for choosing a data centre was to allow fixed conditions, but any HVAC&R-system can be modelled, from residential refrigerators to heat pumps. In this study the refrigerants R-134a, R-513A, R-1234yf and IsoButane were used. These refrigerants were used since they offer a wide variety of GWP values and are used in similar applications currently.

3.2.1 Assumptions and Restrictions

The modelled system will be based on several assumptions and restrictions, to simplify calculations and obtain answers on which conclusions will be drawn. The first assumption is that the modelled system, the data centre, is located in Sweden. This assumption is based on several data centres being located in northern climates to benefit from lower ambient temperatures. This assumption does not affect the results per se, however it leads to parameter restrictions. The values for annual electricity consumption, system running time and the carbon emission factor will thus in this study be based on northern European conditions. Furthermore most such systems have a varying cooling demand because of differences in ambient temperature, but this project considers constant operating conditions.

As such, it is assumed that the need for cooling is constant.

The modelled refrigeration system will be a so called IT-chiller, consisting of the four materials the LCCP guidelines identifies as the most common; steel, plastics, copper and aluminum. The percentage composition of each material will however be based on a modelled heat pump from LCCP Guidelines [IIR, 2016, p. 13]. This since it is problematic to find an IT-chiller that fully matches the system criterion. It is assumed to have a unit weight of 100 kg since this corresponds well to a heating load of 10 kW. No uncertainty is assigned to this value, instead uncertainties will be assigned to the parameters relating to this value, mass of virgin materials and mass of recycled materials. Furthermore, the isentropic efficiency was set to 75% for the calculation of the annual electricity consumption for each refrigerant.

The use of a set efficiency is a significant simplification. Similarly, the same compressor for each refrigerant is assumed. Another assumption is the chiller being made from 100%

virgin material and that 100% of the material is recycled at disposal. Furthermore, the parameter refrigerant disposal emission is disregarded and thus set to zero. This assumption is based on the difficulty of finding correct values and knowing how this calculation is made in practice. A visualisation of the modelled system is seen in figure 3.4.

Figure 3.4: A simple visualisation of the data centre that will be used as a basis for the environmental metric calculations.

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3. Method

3.2.1.1 The Vapour Compression Refrigeration Cycle and Calculating Annual Electricity Consumption

There are several different approaches to evaluating electricity consumption, by using standardized calculations or direct measurement by a power meter. However, for this part of the project the annual electricity consumption will be based on a refrigeration cycle operating under the stated conditions. The system described in this project is a refrigeration system. The basis of such a system is the vapour compression refrigeration cycle with the principle to utilise the flow of heat from a high temperature source to an ambient with lower temperature. This cycle is defined in four steps.

First, in vapour state the refrigerant enters the compressor at point (1), where the refrigerant is super-heated as to ensure that it is fully gasified to protect the equipment.

This also allows the refrigerant to absorb more heat from the server hall as it increases the enthalpy difference. From point (1) to (2) the vapour is then compressed by a supply of external energy under polytropic conditions firstly calculated by using isentropic relations, this results in an increase in pressure, temperature, and enthalpy.

The hot vapor then passes through a first heat exchanger, the condenser, between point (2) and (3). It has a higher temperature relative to the secondary fluid in the heat exchanger which facilitates heat transfer from the refrigerant. By designing the cycle so that it also sub-cools the refrigerant, the enthalpy is further decreased. The function of this is to allow the refrigerant to decrease its enthalpy before it exits the condenser as liquid.

After this, the pressure drops as the refrigerant isentropically expands through an expansion valve between (3) and (4), driven by the pressure difference established by the compressor. This evaporates the refrigerant, causing a decrease of its temperature.

The last step, between point (4) and (1) in the refrigeration cycle, is the second heat exchanger called the evaporator. Here the liquid refrigerant gradually turns into vapor by absorbing heat from its surroundings, which is what causes the cooling effect of the system.

After this the vapour is set to enter the compressor again, making it a closed system. These four steps are shown in the refrigeration cycle diagram, figure 3.5.

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3.2. Designing the Data Centre

Enthalpy [kJ/kg]

Pressure [Pa]

(1)

(2) (3)

(4)

h1 h2, ideal h2, real h3, h4

Pcondensation

Pevaporation

Liquid-Vapour Line

Figure 3.5: The vapour compression cycle in a ph-diagram, with points (1) to (4) depicted.

During the cycle the refrigerant releases and absorbs heat alternatively. For this cycle to be continuous, the compressor that drives the operation requires energy. The compressor workload can be calculated by analysing the mass flow and change in enthalpy using equations (3.1) to (3.7). As each refrigerant has different properties the evaporator and condenser pressure as well as the enthalpies will differ respectively.

∆hcompressor,ideal= h2,ideal− h1 (3.1)

∆hcompressor,real= ∆hcompressor,ideal

η_is (3.2)

h_2,real= h₁+ ∆hcompressor,real (3.3)

∆hheat= h2,real− h3 (3.4)

˙

m = Q_heat

∆hheat

(3.5)

P ower = ˙m × ∆hcompressor,real (3.6)

Ea = P ower × 8765.81277 (3.7)

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3. Method

For the calculations a set of assumed conditions are defined, these apply to the calculation for the annual electricity consumption of all refrigerants used. The evaporator and

compressor temperatures, T_e and T_c respectively are based on average weather data in the north of Sweden [Climate-Data, 2018]. They are set in such a way that it ensures a temperature difference large enough for heat transfer to occur. Further, super-heating (SH) and sub-cooling (SC) are specified for the system to be effective, that is to optimise heat transfer without risking equipment damages. The isentropic efficiency of the compressor (ηis) is set to be 75%. Lastly, the heating load (Qheat) for the system has a designed value

of 10 kW. These specifications are all summed up in table 3.1.

Table 3.1: The design values for the modelled system that define the working conditions of the refrigeration cycle.

Parameter Te Tc SH SC ηis Qheat

Design values 5.0 30 5.0 3.0 0.75 10

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Theoretical Results 4

In order to deal with uncertainties and find appropriate methods it is first necessary to consider the different types of sources for uncertainties and in what way they may skew the results. Therefore, the initial step in this study was to account for the different types of uncertainties and as such different typologies. This will constitute the first part of the theoretical study. The second part will be to determine the sources of the uncertainty for each metric parameter and classify these uncertainties as a corresponding typology. This part of the literature study is also serving as a basis for the empirical study. As such each parameter will at the same time be assigned values that are relevant for the fictitious system.

4.1 Typologies of Uncertainty

”All models are wrong, but some are useful” is a widely used aphorism within statistical analysis in order to highlight that the models do not perfectly reflect reality. Models simply answer the question that is asked of them with a certain amount of error and thus contains uncertainty. In the case of the environmental metrics the question asked is essentially: What is the environmental impact of the refrigeration system?

The three environmental metrics described that are used to answer this have varying degrees of complexity and different system boundaries, but they all produce a deterministic result. These values are all subjected to more or less uncertainty as they are based on several assumptions in order to calculate the impact. As such, even if they are recommended to be used comparatively [IIR, 2016], the results cannot be taken at face value. The degree of reliability of these estimations varies, and in order to generate more accurate results the uncertainty needs to be accounted for.

In order to know how to deal with the uncertainty, one initially needs to define what uncertainty is and how it is integrated in the metrics. At base level uncertainty stems from a lack of knowledge concerning the ’true’ value of a quantity and can either encompass only precision and accuracy or also include variability [Björklund, 2002]. In this project

’uncertainty’ is used to describe all three phenomena. However, this three-way division of uncertainties does not fully define all of the different factors that may affect the reliability of the environmental metrics. There are several different typologies of uncertainty that gather categorically under each phenomenon. In the following, the categories for the different types of uncertainty relevant to this project are presented.

Category 1: Accuracy

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4. Theoretical Results

Data inaccuracy: The (in)accuracy of empirical measurements that are used to derive parameters’ numerical values leads to uncertainty [Björklund, 2002]. These can result from systematic flaws, imperfections in the measuring instruments and techniques [USEPA, 1995].

Data gaps: Missing parameter values leads to gaps in the data, and thus less accurate results may be obtained [Björklund, 2002].

Model uncertainty: By simplifying certain aspects of a model important characteristics and variations can be lost which may lead to a loss of accuracy [Björklund, 2002].

Choices: More often than not there is not one single choice that is correct, thus choices come with a degree of uncertainty [Björklund, 2002]. This could for instance be the choice of system boundaries or design values.

Category 2: Precision

Unrepresentative data: Data from similar research projects that have one or more unrep- resentative characteristics are sometimes used [Björklund, 2002]; leading to imprecise input data in regards to the current project.

Category 3: Variability

Spatial variability: The natural heterogeneity of values in the real world leads to parameter values varying over space [Björklund, 2002]. These are often presented with little spatial context, or aggregated into a mean over a geographical area.

Temporal variability: The variations of values over time and how they are handled are relevant sources for uncertainty. Included in this is the choice of a time horizon over which to integrate potential effects. [Björklund, 2002]

It may be difficult to comprehend the differences between these categories. For this reason an easy example will be given. By visualising a dart board as in figure 4.1 ’Accuracy’ would be visualised as several darts hitting close to the middle, but not necessarily the correct value (a). ’Precision’ may be visualised as darts hitting close to each other, but not necessarily close to the correct value (b). Finally, ’Variability’ may be interpreted by visualising the correct value changing place over the time the darts are thrown (c).

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4.2. Uncertainties in Environmental Metrics

(a) Accuracy (b) Precision (c) Variability

Figure 4.1: The dart board visualisation for ’Accuracy’, ’Precision’ and ’Variability’.

Modified and expanded to include variability from [Frey et al., 2006].

4.2 Uncertainties in Environmental Metrics

Neither of the introduced metrics are by definition uncertain in and of themselves. However, they are dependent on parameter assumptions and estimations that can highly influence the accuracy and precision of the result. The uncertainties associated with every parameter within these metrics are identified and presented under the following corresponding subsections.

Their typologies are also defined.

4.2.1 Uncertainties Associated with GWP

There is not one single source of uncertainty in the calculation of the GWP value, there are several. One part of calculating GWP is to estimate the atmospheric decay of a refrigerant.

To do this a mathematical model of the pulse emission decay is set up, and the accuracy of this expression depends on whether the lifetime of the refrigerant is larger than the mixing rate of the atmospheric reservoir. If the lifetime is three or more years, the assumed expression is exact, however if it is less than one year the expected perturbation is underestimated over time [Myhre et al., 2013b, p. 14]. A result of this is that shorter lived gases have larger uncertainty than long lived. The typology of this uncertainty is classified as ’model uncertainty’ due to simplification when calculating radiative forcing, which in many cases lead to larger uncertainty.

Further, the difficulties of measuring the effects over a specified time horizon contribute to the total uncertainty of GWP; the most notable influences on this are radiative efficiency, inclusion of indirect effects and the uncertainty of the impulse response functions [Myhre et al., 2013b, p. 18]. These are described to be large contributors to the uncertainty, especially with a larger set time horizon. Updated methods for calculating GWP also leads to varying values dependent the year the value is collected. Therefore this may lead to the use of unrepresentative data in the end, as values will be taken from different sources without the possibility for deeper analysis. By considering all of these uncertainties are included in the final deterministic value, it is not surprising that several refrigerants have a reported GWP with an uncertainty percentage of ±50%.

Adaptive GWP: Adp. GWP is an extension of GWP in a way that it takes the atmospheric decomposition of the refrigerant into consideration. This includes degradation effects as well as reactionary products. LCCP Guidelines recommends this value to be used in calculation when available [IIR, 2016, p. 9]. As such, Adp. GWP can be classified as having the same uncertainty typologies as GWP. The additional typology is data gaps since Adp. GWP values are not available for every refrigerant.

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4.2.2 TEWI and Associated Uncertainties

As seen in equation 2.2 TEWI is dependent on several assumptions about parameters and variables, which largely implies uncertainties. In the following each parameter, excluding GWP, and their associated uncertainties will be presented. This is done by accounting for the methods used for value estimations as well as classifying each uncertainty by using previous typologies.

Annual leakage rate, L: Refrigeration systems are modelled with an annual leakage rate in the system. This parameter includes the so called leakage of a system where accidents are included but divided by the lifetime of the unit [AIRAH, 2012]. This parameter is difficult to estimate and differs from system to system as many factors affect the leakage, for example the age of the equipment or if the system has low vibration elimination [RealZero, 2015]. There are different methods to estimate leakage rates in a system. One option being statistically analysing leakage data from similar systems. Another option is to instead analyse how much refrigerant a system annually needs to be topped up with and further estimate how big the leakage rate may be.

These two options are associated with uncertainty from data inaccuracy in the reported data as well as usage of unrepresentative data. There may also be temporal variability.

System lifetime, N: An important parameter as it scales the environmental impact to encompass the years the system is in use. However, data on service lifetime of a system is not as available as one might think and is mostly based on opinion surveys on equipement lifetime [Hiller, 2000]. The uncertainties partly stem from these opinion surveys not having any scientific proof as they are based on opinions from knowledgeable people. Furthermore there are several factors that affect the replacement of components of a system, not only system failure [Hiller, 2000]. Using previous typologies these uncertainties can be classified as data gaps, which results in uncertainty regarding choices, and unrepresentative data.

Charge, C: Charge is a model parameter that is set by the system, its composition and size. Both charge and uncertainty can be estimated with reasonable accuracy for a well defined system, but there will always be measurement errors due to measuring uncertainty of equipment. Therefore the uncertainty related to the refrigerant charge will be classified as one of data inaccuracy.

Recovery/recycling factor, a: This represents the percentage of extracted refrigerant at end-of-life. The percentage used in ’best practice’ is based on an average for developed countries and is consistent for several types of HVAC&R systems [IIR, 2016].

However, reasonably the refrigerant should either be fully extracted or not at all. The uncertainty therefore comes from not knowing if the system in question will have it’s refrigerant extracted or not. As such, this parameter’s uncertainty is categorised as model uncertainty, the described value takes neither spatial variability nor the use of potentially unrepresentative data into account.

Annual electricity consumption, Ea: This parameter is modelled for each refrigerant and system. The value depends on the cooling or heating demand and system running time, which implies a degree of spatial and temporal variability. The LCCP guidelines recommends using standards to calculate cooling or heating load for the type of evaluated system [IIR, 2016], which would introduce model uncertainty. Another possibility is to measure the electricity consumption directly; for example by using an industrial power meters with a defined error percentage. For this parameter both variabilities have the highest contributions to the uncertainty, but there is also data inaccuracy and model uncertainty present depending on the chosen method.

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4.2. Uncertainties in Environmental Metrics

System running time, n: The running time, as with the annual electricity consumption, depends on the cooling or heating demand of the system. Furthermore, it may also depend on interruptions for eg. maintenance. HVAC&R systems can be categorised as one of two types; whether they are dependent on ambient weather or not. For weather dependent units LCCP Guidelines advocates the use of weather databases to estimate system running time. However these databases are limited and do not represent all system conditions accurately, thus both spatial and temporal variability as well as data inaccuracy and data gaps may occur. Additionally, a system may not be fully turned on at all times. In certain climates, such as Scandinavia, the compressor may be in standby for a significant amount of time. In such cases standard calculations for the seasonal running time exist, eg. EN14825 [SP, n.d.]. For nondependent units LCCP Guidelines recommends respective standard calculation [IIR, 2016, p. 12], which may introduce model uncertainty.

Carbon emission factor, β: The emission factor relates GHG emissions to carbon dioxide equivalents. The carbon emission factors used for system calculations are therefore highly dependent on the fuel mix used for electricity generation. Fuel mixes within countries are well documented, and so are both national and international electricity flows in power grids [IEA, 2017]. However, since electricity is transferred over nation borders the electricity used in systems does not necessarily reflect the energy mix within the nation. A legitimate emission factor may therefore be difficult to estimate. The IIR advocates using an European Union (EU) average emission factor [IIR, 2016], which minimizes the spatial variability of β but introduces the use of unrepresentative data.

Additionally, since the electricity in the grid fluctuates the emission factor is subjected to temporal variability. Besides misrepresentation and variability, uncertainties occur from inaccuracy of measured values [IPCC, 2000].

These parameters’ uncertainties have all been assigned one or more uncertainty typology, in order to give a better overview these are all collected into table 4.1. Here it is seen that

’model uncertainty’ is the most frequent classification, followed by ’data inaccuracy’ and

’spatial variability’.

Table 4.1: TEWI parameter uncertainties and their correlated typology

Parameter Data Data Model Choices Unrepresentative Spatial Temporal

inaccuracy gaps uncertainty data variability variability

GWP • •

L • • •

N • • •

C •

a •

Ea • • • •

n • • • • •

β • • • •

4.2.3 LCCP and Associated Uncertainties

LCCP is facing similar uncertainties as TEWI, since both metrics are based on same parameter assumptions. However, since LCCP calculates from ’cradle to grave’ it incorporates an even greater deal of uncertainties [IIR, 2016, p. 3-4]. Hereafter the additional parameters, excluding Adp. GWP, will be presented in a similar way as for the parameters associated with TEWI.

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Mass of materials, m_v and m_r: As the name suggests these parameters accounts for the total mass of the materials used in the system. The materials can either be virgin material (m_v) or recycled material (m_r). LCCP Guidelines outlines the four most common material to be steel, aluminium, copper and plastic [IIR, 2016]. Similarly as charge, the mass of materials can be estimated with reasonable accuracy for a well defined system, but uncertainties may occur from measuring uncertainty of equipment.

Uncertainties related to mass material will similarly be classed as one of data inaccuracy.

Material manufacturing and disposal emissions, MV and MR: These parameters corresponds to the emissions during the manufacture of the virgin material used in the system and recycled material during disposal. These values are set as factor of the component mass and are specified for all types of HVAC&R unit materials. In many units a mixture of virgin and recycled material are used and the value for virgin material are used if the percentage of recycled material is unknown [IIR, 2016]. The material manufacture emissions are based on several industry sources, in the United States as well as the European Union, and include trade associations, governmental departments and previous research and is set to an average value [IIR, 2016]. Using previous typologies the uncertainties can be classified as unrepresentative data and data inaccuracy. LCCP Guidelines recommends this value to be updated since manufacturing methods are improved [IIR, 2016, p. 14], this uncertainty can further be classified as temporal variability.

Refrigerant manufacturing emissions, RFM: This corresponds to the emissions from the manufacture of the refrigerant used in the system. The manufacturing of the refrigerant does not only include the primary production of the initial charge but also accounts for the refills of leaked refrigerant. This value is set as an average and is based on values collected from manufacturers and various studies [IIR, 2016]. As such, these uncertainties can be classified as data inaccuracy and unrepresentative data.

LCCP Guidelines recommends this value to be updated since methods for efficient manufacturing are improved [IIR, 2016], which also leads to temporal variability.

Refrigerant disposal emissions, RFD: This value corresponds to the emissions and losses related to the refrigerant at the disposal of the unit [IIR, 2016, p. 19]. This value is difficult to obtain for each refrigerant, therefore this parameter is classified as data gaps.

Just as with the TEWI parameters, these additional ones have also been classified as belonging to one or more typology. These are visualised in table 4.2 below.

Table 4.2: LCCP parameter uncertainties and their correlated typology

Parameter Data Data Model Choices Unrepresentative Spatial Temporal

inaccuracy gaps uncertainty data variability variability

Adp. GWP • • •

mv •

MV • • •

mr •

MR • • •

RFM • • •

RFD •

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4.3. Defining Data Centre Parameters

4.3 Defining Data Centre Parameters

The previous section highlighted where and when uncertainties may arise. In this section parameter values and uncertainties will be defined after the modelled data centre and are later summarized in tables. The environmental metrics TEWI and LCCP have several parameters that are dependent on the system. For each parameter a value is decided based on studies, or assumptions where studies were limited. These are the values used during the calculations. In order to perform a Monte Carlo Simulation each parameter is assigned a distribution or, in some cases, scenarios. These distributions are decided by analysing reported statistical data, previously made Monte Carlo Simulations in other fields, and recommendations based on given uncertainty span [Frey et al., 2006, p. 23]. Furthermore, TEWI and LCCP are also dependent on the refrigerant used in the system. These parameters are approached in similar manner as the system parameters, by assigning a value and a distribution based on studies and/or assumptions. Values and distributions of GWP are determined by using IPCC recommendations.

4.3.1 System Parameters

Annual leakage rate, L: This parameter largely depends on the type of system and its construction. It is set as 5% of the charge in accordance with LCCP Guidelines recommended values for commercial units [IIR, 2016]. An uncertainty of ±0.5% with a Gaussian distribution is used in this study.

System lifetime, N: There is limited scientific studies to support actual system lifetime, which results in data gaps, this parameter is evaluated by modelling three scenarios.

This is to reduce the risk of creating uncertainties by assigning an incorrect value.

These values are set to be 10, 15 and 20 years. However, for the uncertainty analysis the Uncertainty is set to ±5 years to cover the three scenarios.

Recovery/recycling factor, a: The LCCP Guidelines recommends a value of 85% when applying good practice, with no reported uncertainty percentage [IIR, 2016]. This value is based on a mean of extractions in developed countries. One interpretation is that this value can be used as an indicator that 85% of these systems have their refrigerants fully recovered, as this percentage might not be representative. However, it may be problematic to calculate TEWI with a 85% probability of recovery, as such this does not reflect a likely scenario. For this reason it is instead set as 1 directly, as the modelled data centre is located in Sweden where both national and EU law highly regulates the recovery of refrigerants [EP, 2014]. However, for the uncertainty analysis the uncertainty is assumed to be ±1%.

System running time, n: The running time is built on the assumption of constant oper- ation with the exception of maintenance or other system disruption. In the modelled system this parameter will be equal to N multiplied by a factor of 0.95. Additionally this parameter also has an assumed uncertainty of ±1 % with a Gaussian distribution.

This corresponds to an uncertainty of approximately 6 hours per month, which is considered to be a legitimate difference as the system running time of the analysed equipment should be well documented.

Carbon emission factor, β: The emission factor is based on the electricity production mix in Sweden, with electricity trade over national borders taken into consideration.

Furthermore, the carbon intensity increases further down the grid due to transmission losses. Both of these factors cause major differences in the value upstreams at production versus downstreams at consumption in the same national grid. The value used during the calculations is therefore determined at consumption at medium voltage

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in Sweden, since it is assumed the server hall uses electricity from regional grids; β is 0,046 kg CO₂eq/kWh [Moro and Lonza, 2017]. The uncertainty is assumed to reasonably be Gaussian distributed with an uncertainty percentage of ±5% [IPCC, 2000, p. 15].

The system parameters for the modelled data centre are presented with their respective distribution, in the case that they have been assigned one, in table 4.3 below.

Table 4.3: The system parameters and their assigned uncertainty distributions.

Parameter Description Value Distribution

a Recovery factor 1.0

L Leakage rate 5.0% N(0.050, 0.048)

N Life of system [years] 10, 15, 20 Scenarios

β Carbon emission factor 0.046 kg CO₂e/kWh N(0.046, 0.017)

n System running time 0.95 · N N(0.95, 0.0033)

The additional parameters that have to be defined in order to evaluate the LCCP metric are hereafter described, and then later summarised in table 4.4.

Mass of virgin material, mv: The unit is assumed to have total weight of 100 kg of virgin material. The percentage of the material composition are then multiplied with this unit weight to acquire the weight of each material in the unit. Since the uncertainty may arise from inaccuracy of measuring equipment it is assumed to be ±5%. This might seem a bit overestimated, but this is the uncertainty of using equal material composition for each refrigerant, which is not the case in real applications. For the Monte Carlo Simulation the distribution is set to be Triangular since it is assumed that one value will be most probable and that the probability will uniformly decrease until the end points are reached [Frey et al., 2006, p. 23].

Virgin material manufacturing emissions, MV: The values used in this study will be collected from LCCP Guidelines. However, it is difficult to estimate if these values are relevant for swedish manufacturing, or if the material used is manufactured in Sweden.

For this reason an uncertainty of ±5% and a Gaussian distribution is assumed.

Mass of recycled material, m_r: It is assumed the unit is fully recycled at disposal. Sim- ilar strategy as above is applied where each composition percentage is multiplied with the total unit weight. Similarly, the uncertainty is set to ±5% and the distribution is assumed to be Triangular.

Recycled material manufacturing and disposal emissions, MR: The unit is said to consist of 100% virgin material therefore no values for manufacturing of recycled material will be used. Values used for disposal emissions are collected from LCCP Guidelines. Using similar reasoning as above an uncertainty of ±5% and a Gaussian distribution is assumed.

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Dealing with uncertainty in global warming impact assessments of refrigeration systems

Dealing with uncertainty in global warming impact assessments of refrigeration systems

LINN BOSTRÖM

HANNA LJUNGBERG

Contents

List of Figures

List of Tables

Acronyms

Nomenclature

Introduction 1

1.1 Sustainability Relevance

1.2 Purpose

1.3 Aims

Background 2

2.1 Environmental Metrics

2.2 Methods for Dealing with Uncertainties

Method 3

3.1 General Outline of the Calculations Performed on the Modelled System

3.2 Designing the Data Centre

Theoretical Results 4

4.1 Typologies of Uncertainty

Category 1: Accuracy

Category 2: Precision

Category 3: Variability

4.2 Uncertainties in Environmental Metrics

4.3 Defining Data Centre Parameters