Rymd-, geo- och miljövetenskap (SEE) // Space, Earth and Environment (SEE)
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Vi utgår från observationer av universum och vår planet för att utveckla modeller och verktyg som möter globala utmaningar kring resurser, energiförsörjning och klimatpåverkan.
Vart är vi på väg? Var kommer vi ifrån? På vår institution söker vi svaren på de riktigt stora frågorna. I ett långt tidsperspektiv ger stjärnor och galaxers livscykler en inblick i universums, jordens och livets uppkomst – och framtid. Vi observerar också vår planet och samspelet mellan samhälle, teknik och natur för att kunna utveckla teknik, modeller och verktyg som kan möta globala utmaningar inom naturresurser, klimatpåverkan och energiförsörjning.
För forskning och forskningspublikationer, se https://research.chalmers.se/organisation/rymd-geo-och-miljoevetenskap/
Observes the universe and our planet, to develop models and tools that meet global challenges regarding resources, energy supply and climate impact.
Where do we come from and where are we going? At our department we search for answers to the really big questions. In a long time perspective, the lifecycles of stars and galaxies provide an insight into the origin and future of the universe, earth and life. We also observe our planet and the interaction between society, technology and nature in order to develop technologies, models and tools that can meet global challenges regarding natural resources, climate impact and energy supply.
Studying at the Department of Space, Earth and Environment at Chalmers
For research and research output, please visit https://research.chalmers.se/en/organization/space-earth-and-environment/
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- PostGlobal Energy Scenarios Meeting Stringent Climate Targets: A comparison between the Global Energy System Model GET 1.0 and the Regionalised Model GET-R 1.0., Thesis for Master of Science in Physics with an emphasis on Problem Solving.(2002) Grahn, Maria; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentThe greenhouse effect is considered to be one of the most serious global hazards to the environment and the "Kyoto Agreement" stipulates that emissions of greenhouse gases must be reduced. Reduction of CO2 emissions involves considerable changes in present energy systems. In year 2000 the Department of Physical Resource Theory (PhRT) at Chalmers University of Technology developed a global energy system model, designed to analyse the world's energy use to the year 2100. In a regionalisation process, this study has divided the world into eleven geographical areas and then applied these to the original PhRT model. With the purpose of gaining a better understanding of the global energy system, a comparison is made between the PhRT Model (GET 1.0) and the Regionalised Model (GET-R 1.0). Both models are linear programmed and have three end-use sectors; electricity, heat and transport fuel. They are devised to meet exogenous energy demands at the lowest global energy system cost. To minimise these costs, interregional trade is permitted, and the model places an upper limit on CO2 emissions, so as to stabilise the atmospheric CO2 content at 400 ppm. Both models show the same overall pattern. The transportation sector shows a transition from petroleum fuels in internal combustion engines towards hydrogen fuel cell engines, in the middle of the century. The major difference is that fuel cell technologies are introduced one decade earlier, in the regionalised model. Within the electricity production sector the oil is phased out early and both coal (with CO2-sequestration) and solar produced hydrogen, increase toward the middle of the century. Biomass is the dominant fuel in the heat production sector and a large trade of biomass occurs to minimise the global costs. It is concluded that it is technically and economically possible to meet stringent CO2 constraints (400 ppm) in combination with a rapid increase in energy demand.
- PostMore Electric Aircraft(2003) Altin, Martin; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and Environment
- Post3-D computations of eddy current losses in core ends of salient-pole synchronous machines(2004) Chitroju, Rathna; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and Environment
- PostLife Cycle Assessment of a Gas-Electric Hybrid Waste Collection Vehicle – Comparison with Conventional Waste Collection Vehicles(2005) Boss, Anna; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentThe waste and recycling company Renova AB has developed a new type of waste collection vehicle, which has been used and evaluated for waste collection in central Gothenburg for a few years. What distinguishes this type of vehicle from conventional waste collection vehicles is, firstly, that it uses natural gas to drive instead of diesel, and secondly, that it turns the combustion engine off at the collection stops and uses electric power to load and compact waste. In this master’s thesis the environmental performance of such a gas-electric hybrid waste collection vehicle was evaluated in comparison with a conventional diesel vehicle and a natural gas vehicle without the hybrid technique. Life cycle assessment was used to consider environmental impact from production, use, maintenance and repair and end-of-life treatment of the vehicles. The results showed that the hybrid vehicles contribute less to some environmental impact categories, but more to others, compared to the other vehicle types. From an overall evaluation of the results, it was concluded that hybrid vehicles are environmentally preferable to diesel vehicles when used in central Gothenburg. It is more uncertain whether they are preferable to conventional gas vehicles or not. They have, however, potentials for further development. It was also concluded that the use phase is the most important part of the life cycle to develop in order to improve the environmental performance of waste collection vehicles.
- PostChalmers processlaboratorium MC2. Krav, funktion och uppbyggnad av klimathållningssystem(2005) Larsson, Johan; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentDetta examensarbete beskriver de installationstekniska systemen hörande till renrummet vid Institutionen f6r mikroteknologi och nanovetenskap. Syftet är att klargöra huruvida uppsatta krav; vad gäller renhet, temperatur, luftfuktighet och energiåtgång har definierats och på vilket sätt man kan uppnå dem. Information om renrummet har inhämtats från tillgänglig dokumentation och från diskussioner med driftorganisationens personal. Rapporten inleds med en genomgång av ett antal grundläggande begrepp som är relevanta för renrum, På detta följer en beskrivning av renrummet och luftbehandlingssystemens uppbyggnad. De krav som ställts inför byggandet presenteras och likaså de som råder för närvarande. En analys av konsekvenserna för skillnaderna som har identifierats görs. Ett betydande utrymme ägnas åt den sänkning av renhetskravet som skett. Vidare beskrivs reglerstrategier och hur dessa har förändrats sedan renrummet togs i drift. Några utvalda problemställningar har studerats närmare. Det har konstaterats att cirkulationsaggregatens fläktar har en helt annan arbetspunkt än den som var avsedd vilket innebär att dessa förmodligen inte utnyttjas optimalt. För att inte tillförsel av föroreningar, in i renrummet, ska ske är det av vikt att tryekdifferenser mellan utrymmen av olika renhetskiass upprätthålls. Dessa förhållanden har undersökts och brister har konstaterats. Eftersom driftenergiåtgången för renrum av den här typen är hög har en analys gjorts och vissa förslag presenteras på hur användningen kan effektiviseras.
- PostUppbyggnad av luftbehandlingssystem för operationsrum. Dokumentation och mätningar(2005) Lindström, Magnus; Sundin, Daniel; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentOperationsrumsventilation skiljer sig från konventionell ventilation eftersom den ställer stora krav på luftens renhet och kräver stora luftflöden. Detta examensarbete utreder hur luftbehandlingssystem för operationsrum vanligtvis är uppbyggda och fungerar, samt vilka energibesparingsåtgärder i systemet utanför operationsrummet som är möjliga att utföra utifrån gjorda inventeringar och mätningar. Studien tittar främst på systemuppbyggnaden av luftbehandlingssystem för operationsrum med parallellströmningstak eftersom det är den tekniskt mest intressanta lösningen. Den har även stor besparingspotential eftersom man arbetar med flöden på över 100 omsättningar per timma, jämfört med operationsrum med omblandande ventilation som arbetar med flöden på 17-19 omsättningar per timma. Luftbehandlingssystemet för ett operationsrum med parallellströmningstak består oftast av ett recirkulationssystem och ett allmänt system med vätskeburen värmeväxling. Det allmänna systemet försörjer operationsrummet med ett friskluftflöde men betjänar även andra delar av sjukhuset. Detta kräver att temperatur och trycknivå är anpassat för de andra delarna av sjukhuset. Recirkulationssystemet ser till att operationsrummet får tillräckligt flöde utan att behöva temperera all luft från utomhustemperatur. Blandningsförhållandet är vanligtvis 80 % recirkulation och 20 % från det allmänna systemet. Utifrån inventering och mätning av tre olika tillämpningsobjekt diskuteras några besparingsmöjligheter vid ändring av systemuppbyggnaden både vad det gäller värmeenergi och fläktelenergi. Ur värmeenergisynpunkt är det fördelaktigt att ha ett allmänt system med roterande värmeväxlare som enbart försörjer operationssalar med parallellströmningstak. Då gör det inget om partiklar överförs via den roterande värmeväxlaren eftersom all luft filtreras genom HEPA-filter innan den tillförs operationssalarna. Blandningsförhållandet mellan recirkulationsluft och luft från det allmänna systemet anpassas efter inblåsningstemperaturen och internlasterna i operationsrummet. När blandningsförhållandet är injusterat styrs sedan temperaturen från det allmänna aggregatet. Detta är den lösning som är mest fördelaktig ur värmeenergisynpunkt och som är praktiskt tillämpningsbar. iii Ur fläktelenergisynpunkt är det även där fördelaktigt att använda sig av ett allmänt system som enbart försörjer operationssalar av samma typ eftersom man då kan anpassa trycknivån till dessa och inte behöver anpassa den till andra lokaler i sjukhuset.
- PostInvestigation of different methods for sensorless control of a permanent magnet synchronous machine(2005) Velander, Erik; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and Environment
- PostLuftföring i operationsrum. Systemuppbyggnad för och utvärdering av parallellströmning genom visualisering(2005) Sundbeck, Patrik; Värmsjö, Per; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentExamensarbetet utreder systemuppbyggnaden för luftföring i operationsrum och utvärderar parallellströmning genom visualisering med hjälp av rök. Studien syftar till att klargöra hur känslig parallellströmning är för störningar och genom detta hitta den undre gränsen för lufthastigheten som möjliggör fullgod funktion. Operationsrumsventilation är en typ av skyddsventilation där luftens funktion är, att förutom att skapa ett bra inomhusklimat, säkerställa ett skydd åt personalen och patienten från skadliga föroreningar. Detta kan göras enligt ett antal olika luftföringsprinciper varav parallellströmning är en av dem. Idag råder oenighet mellan tillverkare och myndigheter beträffande vilka lufthastigheter som är nödvändiga för fullgod funktion. Lufthastigheten står i relation till investerings- och driftskostnaden och sänks tilluftshastigheten kan detta ge förutsättningar för betydande besparingar. Frågor rörande denna typ av skyddsventilation är bland annat hur stor inverkan hinder, flödeshastighet, rörelser och lokala värmekällor har på stabiliteten hos luftföringen och skyddsfunktionen. För att besvara dessa frågeställningar utfördes en försöksserie med visualisering av luftföringen med tilluft genom undertaksduk. Fem fall med hastigheterna 0.42, 0.35, 0.25, 0.20 och 0.15 m/s över duk gjordes samt en del fristående tester. Dessa försök gjordes i fullskala i Installationstekniks försökshall där en testanläggning projekterades och byggdes upp. Försöksserien visar att en mycket god funktion uppnåddes i samtliga tester där tilluftshastigheten var 0.25 m/s eller högre och god funktion vid hastigheter ner till 0.20 m/s. En undertemperering av tilluften medför en förbättring av funktionen. De fristående försöken visar att varken tryckändringar i rummet eller frånluftens utformning påverkar strömningsbilden i den rena zonen. Däremot medför föremål och värmekällor i luftströmmen virvelbildningar och försämring av funktionen
- PostModeling And Simulation Of An Automotive Diesel Engine Cranking System(2005) Azzouaz, George; Lundberg, Lars; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentThis master thesis is a study of the starting system for a diesel engine and its components. Theories for each component were presented and models were derived for a complete starting system. Focus lied on the starter motor and the losses in the diesel engine, and the models were implemented in the simulation environment Saber. The starter motor model consists of a permanent magnet direct current (PMDC) motor with additional parts which complete the starter motor. The loss components in the engine were manly derived from theoretical equations but also by measured data. The components were used as building blocks and put together to the entire engine losses model. Measurements of the starting system were done and compared with the model s simulation results for different temperatures. The simulated average engine speed is approximately 20 % less than the measured.
- PostIntegration of Membrane Separation Technology in Hydrogen Production from Gasified Black Liquor with CO2 Capture(2005) Desvaux, Elodie; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentThe countries which ratified the Kyoto protocol have committed to reduce their emissions of carbon dioxide and five other greenhouse gases, or engage in emissions trading if they maintain or increase emissions of these gases. In this context, the production of CO2 free fuels should become a major concern. With successful fuel cell development, hydrogen could be a fuel for the future. A previous project has studied the feasibility to integrate hydrogen production from gasified black liquor with a pulp mill. The pulp mill used is the Eco-cyclic pulp mill (KAM), a model mill developed in a Swedish national research programme using the best available technology in commercial use. The use of membrane separation technology instead of conventional separation technology in the hydrogen production process has been studied in this work. Three processes have been modeled with Hysys, a general-purpose simulation software. Energy balance, CO2-emissions reduction potential and economic benefits were estimated for the three processes. The results obtained were compared with the results of the process using conventional separation technology and with the results of the KAM pulp mill without hydrogen production. The results show that the use of membranes in the hydrogen production unit integrated with the pulp mill has several advantages over conventional separation technology. It increases the hydrogen production yield with 25 %, it reduces the quantity of biomass to import and more district heating is produced. However, the electric power consumption increases by 17 to 38 % depending on the process. Only the KAM pulp mill with a Tomlinson boiler and no hydrogen production can export electrical power and biomass. Hydrogen produced by one KAM pulp mill and used in fuel cell vehicles, could replace 14 % of the gasoline currently used in the car transportation sector in Sweden. Integration of membrane separation technology achieves a CO2-emissions reduction of 3,6 % on a national basis for one KAM pulp mill with integrated hydrogen production. A sensitivity analysis was made with two hydrogen prices 7,16 €/GJ and 13,43 €/GJ. Operating margins were calculated for all the processes and it shows that in both cases operating margins for membrane-based processes are higher than those achieved by the process using conventional separation technology and the KAM pulp mill with Tomlinson boiler. The allowable extra investment cost for membrane based processes compared to the process based on conventional technology was estimated at 125M€ if a payback period of three year is assumed, CO2 capture is possible and the hydrogen sales price is high.
- PostRetrofitting of DC motors(2005) Forsberg, Max; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and Environment
- PostPFE och energiledningssystem vid Stora Enso Fors AB(2005) Dahl, Maria; Svensson, Mats; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentStora Enso Fors AB consists of a cartonboard mill in Fors and a plant for polyethylene coating in Gästrike-Hammarby. The company participates in a program for increased energy efficiency (PFE) which gives electricity tax reduction if a number of requirements are fulfilled. Participating companies have to implement a standardised energy management system, perform a mapping and analysis of the energy consumption and consider energy efficiency within the purchasing and project management functions. The aim of the report is partly to give recommendations to routines, procedures and the structure of the system and partly to map and analyse the company’s energy consumption. The tasks have been performed with assistance from a project team consisting of representatives from the involved departments within the company. The management system at Stora Enso Fors AB is well developed and the company is certified according to quality, environmental and occupational health standards. The aim with this project has therefore been to fulfil the requirements of the energy management system by improving and expanding the existing management system. In most cases it was possible to modify existing routines and procedures, which means that only a small number of new documents had to be added to the system. The mapping of the former, present and future energy consumption at Fors and Hammarby mills gave a good understanding of how energy is used in different departments and processes. The analysis that followed the energy mapping which mainly focused on electricity and resulted in an identification of important energy aspects and several possible measures to increase the energy efficiency. Purchasing and project management imply more fundamental changes of existing routines and procedures than other areas. Energy costs must be taken into account and life cycle costs have to be calculated. Since the company has inadequate experience in calculation of life cycle costs, templates that are easy to use were constructed.
- PostCFD study of the heat transfer modes in engine cooling systems(2005) Laaksometsä, Catherine; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and Environment
- PostStudy and design of a DC/DC converter for series connected wind farms(2005) Esteban, Javier; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentIn this Master Thesis, the design of a DC/DC converter for a series connected DC wind park was investigated. The features of this kind of wind park were presented, and possible topologies of the converter were studied. Finally its advantages and drawbacks for the specific application were discussed. It was found that the most appropriate model was the full bridge converter, which there was theoretically analyzed. One investigated aspect was how the converter performance was affected by the transformer parameters. Then, an economical criteria was defined to choose the most suitable one: the energy cost. At last the selected design was simulated in Pspice® in order to check that it satisfies the application requirements, and the simulated waveforms were compared with those found from the theoretical study.
- PostSystem- and pre-study of future expansion strategies at Preemraff Lysekil(2005) Niklasson, Mikael; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentThis master thesis report contains a system-study of an oil refinery s existing electrical distribution system and a pre-study of five different future expansion strategies, one of them including power generation. Preemraff Lysekil is constructing of a new gas and oil producing addition. This project goes under the name GOP (Gas-Oil-Project) and is an investment of 3,5 billion SEK. An earlier simulation model has been extended with GOP in order to again verify the status, plan preventative maintenance and to design further extension. With help from the model the following calculations were made:, load flow analysis, short circuit power, voltage dips during faults, voltage dips during motor starts, reactive power compensation, possible load increase, control of the selectivity plan, availability / reliability, verification of emergency power and total starting currents from motor groups. The model was also extended with models for five different expansion strategies to see how they would affect the existing system. The model was further extended with the overhead lines feeding Preemraff Lysekil to analyze whether they could handle the load increase or not. The results from the system-study calculations showed that Preemraffs power system is well designed, however some problems were found. Results from the pre-study showed that there will be problems keeping the voltage above required levels with further expansions. The affect on the actual distribution system due to these expansions will not cause any problems.
- PostDynamisk modellering av energisystem(2005) Björk, Gabriel; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentThis master thesis has been done at Solvina AB in Vastra Frolunda. The purpose of this thesis is to develop a model library called SteamPower, which consists of steam/water energy system components. The library is for use in dynamic simulation in the Modelica/Dymola environment. Modelica is an object-oriented programming language that is mainly focused on simulations of physical systems. Dymola is a QUI for Modelica that can be used both as an editor and simulator. The main objective has been to develop an efficient, well-documented and userfriendly library. Focus has been on developing accurate models of valves and a turbine. In developing the SteamPower models there has been a need to verify them against measured data, which has been done continuously against data from a pulp mill in Sweden. Also the need to test the components in a complex dynamic environment has been crucial for developing stable and well-performing models. Therefore a quite complex model of a pulp mill was developed and used for simulation tests. During the development and testing phase a number of numerical problems were discovered and they had to be addressed in order to have stable performance. The models developed have been verified against different sources and they show a behavior that is acceptable for the designed purposes.
- PostÖkad rökgaskondensering och värmepumpseffekt genom installation av värmeväxlare(2005) Fagerberg, Erik; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and Environment
- PostBLDC Motor Modelling and Control - A Matlab®/Simulink® Implementation(2005) Baldursson, Stefan; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentThis thesis presents a model of a three phase star-connected brushless direct current (bldc) motor. The construction and operation of both conventional dc motors and bldc motors is presented and state-space models are derived for each. Matlab®/Simulink® models are developed for each motor type and their validity is verified. Torque-, speed- and position control is applied using hysteresis band control, pwm control, and variable dc-link voltage control. The different control strategies are tested on the bldc motor and their performance evaluated. The frequency content of the dc-link current is investigated for each control method and the impact of commutation delay and switching losses is discussed. Simulations show that all the control strategies work quite well although each method has its drawbacks. The frequency spectrum of the dc-link current shows that hysteresis band control may not be suitable where load variations are large. The variable dc-link voltage method turns out to be the best solution in applications where torque ripples and switching losses must me minimized. Commutation delay is necessary in practice, but the simulations show that it should be kept as short as possible because it causes increased torque ripples.
- PostTransients and Electric Metering(2005) Karlsson, Roland; Kesten, Admir; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentThe electricity market deregulation or in other words, the need of increased efficiency and customer demands has lead to introduction of automatic reading systems. According to this, there have been thoughts that different kinds of disturbances can possibly cause problems with distance readings of electricity meters. The purpose of this master thesis has been to investigate transients influence on electricity meters and automatic meter reading systems in general and also check if there is a reason to suspect that certain transients can cause reading faults (missing readings or faulty readings), in particular. Mainly, the thesis is dealing with PLC technique based systems but also other types of communications techniques are studied. The thesis also includes getting deeper knowledge about the legislation regulating decisions about introduction of AMR systems in Sweden. Contact with manufacturers of electricity meters and AMR systems has been taken for borrowing necessary equipment. A number of setup configurations have been tested and the transients have been measured in laboratory environment. The aim was to investigate if AMR systems and electricity meters are reliable and properly working with influence from switching transient disturbances. The results from the measurements show that it is not likely that switching transients can cause any change in the readings from electricity meters or value changes in the meter itself, but they have the ability to sometimes block the communication so that the values are not transferred. This can be an important fact depending on how often and how many times the transmission is sent.
- PostMeasuring Eco-efficiency by a LCC/LCA Ratio: An Evaluation of its Applicability. A case study at ABB(2005) Lyrstedt, Fredrik; Chalmers tekniska högskola / Institutionen för energi och miljö; Chalmers University of Technology / Department of Energy and EnvironmentThe current situation with growing pollutions and industrial production put high demand on organisations environmental responsibility. Striving towards a sustainable development is an important assignment for the corporate world. In 1991 the World Business Council for Sustainable Development (WBCSD) established the concept eco-efficiency in order to sum up the business part of sustainable development. Ecoefficiency can be described as a continuous process of change in order to decrease environmental impacts with an enhanced value for products and services. This master thesis is carried out with the purpose of measuring eco-efficiency and evaluating its applicability. A case study at ABB was executed with the aim of putting the eco-efficiency interpretation made by Steen (2004) into practice. The interpretation combines the two life cycle approaches LCC and LCA in a standardised index, LCC 1− EDC and is presented as a percentage value in order to increase the understandability. In the case study, two scenarios including the HXR500 electric motor and the ACS800 frequency converter are used. The first scenario is conducted in order to determine the eco-efficiency for the HXR500 motor’s life cycle and in the second scenario, an eco-efficiency calculation is made for the HXR500 motor’s life cycle operated by the ACS800 frequency converter. The product combination enhances the economic value and decreases the environmental impact and the aim with performing these scenarios is to evaluate how and if it is possible to make reasonable ecoefficiency comparisons. Results from the study indicate that the standardised eco-efficiency index can serve as a valuable tool in order to evaluate eco-efficiency and can be used e.g. for monitoring progress, benchmarking and in purchase decisions. Nevertheless, it is difficult to evaluate if the index increases the understandability without obtaining great knowledge of the eco-efficiency concept. Important to notice is that evaluating ecoefficiency is still in an early phase and the method used in this study have not been put into practice to a great extent. Executing future studies in this area is therefore an important issue. Additionally the study gave evidence to an obstacle when deciding the relevant value for the products using LCC. When making comparisons, an added value can be identified and it is important to take this into account in order to get an appropriate eco-efficiency value of the products compared.