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1.
Life cycle assessment (LCA) is a promising tool in the pursuit of sustainable mining. However, the accounting methodologies used in LCA for abiotic resource depletion still have some shortcomings and need to be improved. In this article a new thermodynamic approach is presented for the evaluation of the depletion of nonfuel minerals. The method is based on quantifying the exergy costs required to replace the extracted minerals with current available technologies, from a completely degraded state in what we term “Thanatia” to the conditions currently found in nature. Thanatia is an estimated reference model of a commercial end of the planet, where all resources have been extracted and dispersed, and all fossil fuels have been burned. Mineral deposits constitute an exergy bonus that nature gives us for free by providing minerals in a concentrated state and not dispersed in the crust. The exergy replacement costs provide a measure of the bonus lost through extraction. This approach allows performing an LCA by including a new stage in the analysis: namely the grave to cradle path. The methodology is explained through the case study of nickel depletion.  相似文献   

2.
This paper makes a review of current raw material criticality assessment methodologies and proposes a new approach based on the second law of thermodynamics. This is because conventional methods mostly focus on supply risk and economic importance leaving behind relevant factors, such as the physical quality of substances. The new approach is proposed as an additional dimension for the criticality assessment of raw materials through a variable denoted “thermodynamic rarity,” which accounts for the exergy cost required to obtain a mineral commodity from bare rock, using prevailing technology. Accordingly, a given raw material will be thermodynamically rare if it is: (1) currently energy intensive to obtain and (2) scarce in nature. If a given commodity presents a high risk in two of the three dimensions (economic importance, supply risk, and thermodynamic rarity), it is proposed to be critical. As a result, a new critical material list is presented, adding to the 2014 criticality list of the European Commission (EC) Li, Ta, Te, V, and Mo. With this new list and using Sankey diagrams, a material flow analysis has been carried out for Europe (EU‐28) for 2014, comparing the results when using tonnage and thermodynamic rarity as units of measure. Through the latter, one can put emphasis on the quality and not only on the quantity of minerals traded and domestically produced in the region, thereby providing a tool for improving resource management.  相似文献   

3.
The Sankey diagram is an important aid in identifying inefficiencies and potential for savings when dealing with resources. It was developed over 100 years ago by the Irish engineer Riall Sankey to analyze the thermal efficiency of steam engines and has since been applied to depict the energy and material balances of complex systems. The Sankey diagram is the main tool for visualizing industrial metabolism and hence is widely used in industrial ecology. In the history of the early 20th century, it played a major role when raw materials were scarce and expensive and engineers were making great efforts to improve technical systems. Sankey diagrams can also be used to map value flows in systems at the operational level or along global value chains. The article charts the historical development of the diagrams. After the First World War the diagrams were used to produce thermal balances of production plants for glass and cement and to optimize the energy input. In the 1930s, steel and iron ore played a strategic role in Nazi Germany. Their efficient use was highlighted with Sankey diagrams. Since the 1990s, these diagrams have become common for displaying data in life cycle assessments (LCAs) of products. Sankey diagrams can also be used to map value flows in systems at the operational level or along global value added chains. This article, the first of a pair, charts the historical development. The companion article discusses the methodology and the implicit assumptions of such Sankey diagrams.  相似文献   

4.
This article presents the trends of two indicators measuring fossil resource consumption in the United Kingdom (UK). First, a domestic material consumption (DMC) indicator for fossil resources (DMCfossil) in the mass unit million tonnes is calculated. DMCfossil shows that between 1970 and 2000 UK fossil resource consumption decreased by 10%, which suggests absolute dematerialization for this resource. Investigation into the mix of fossil resources during this period highlighted the shift from the heavy fossil resource coal to the lighter, more energy‐dense natural gas, which resulted in decreased mass of resource required. Second, an alternative indicator, resource consumption by a nation (RCN) for fossil resources (RCNfossil) was calculated, which includes the indirect fossil resources attributable to traded goods and is measured in million tonnes of oil equivalent. RCNfossil shows that between 1970 and 2000 United Kingdom's fossil resource consumption increased by 14%, which emphasizes that even though there has been a decrease in the mass of fossil resources demanded, it has been accompanied by an increase in the volume of resource consumed. Additionally, deconstruction of RCNfossil shows that indirectly used resources attributable to exports and imports for the United Kingdom are significant. RCNfossil indicates that on the basis of past trends, fossil resources attributable to UK imports will overtake fossil resources attributable to its exports, which will make it dependent on imported resources. We conclude that further debate on appropriate aggregate and complementary indicators is needed.  相似文献   

5.
The Sankey diagram is an important aid in pointing up inefficiencies and potential for savings in connection with resource use. This article, the second of a pair, examines the use of Sankey diagrams in operational material flow management. The previous article described the development of the diagram and its use in the past.
Simple Sankey diagrams follow the requirement of conservation of energy or mass and allow a physical view of production systems. Advanced diagrams integrate stocks of materials beside the flows or show the different (ecological) quality of the materials. For the purpose of management, however, a further step is necessary: to illustrate the economic value of the energy and material flows and to use information from cost accounting. The use of flow charts showing added value or the costs of energy and material flows is particularly important for production systems. This article describes examples of each of these uses as well as assumptions that must be taken into account for Sankey diagrams to be used as an effective aid for decision-making in business and public policy.  相似文献   

6.
A ravenous fuel consumer, the cement industry may substitute fossil fuels by industrial wastes and by‐products, identifying the industry as a key example of industrial symbiosis (IS). Benefits from industrial waste alternative fuels (IWAFs) include safe disposal, fossil fuel cost savings, gate fees, and greenhouse gas credits. Poor IWAFs, (high moisture, ash and halogen content) bring higher gate fees, but lessen clinker production. Thermal rating and blower capacity constraints should be satisfied in such a case study of IS. Cement plants must comply with potentially tighter emission limits, compared to fossil fuel utilization, despite higher pollutant precursors in IWAFs. Emissions’ compliance, operational, and production implications are a few among several challenges when assessing multiple IWAF valorization as a symbiotic option from a systems’ perspective. A novel method is proposed to quantitatively assess critical trade‐offs. Species and energy transformations convey a rigorous picture of clinker level, kiln flue gas, and offgas volumes and lay the groundwork for screening, a priori selection, and process tuning. Necessary and sufficient compliance conditions and safety margins are presented in terms of process parameters and actual emissions’ data. Main challenges posed by high flue gas, high offgas volumes, high moisture, low heating value, increased nitrogen oxides emissions, and high halogen and metal content are quantified. As demonstrated in a case study of an actual 1.5 × 106 tonnes per annum clinker plant in this paper, concurrent use of several IWAFs may increase clinker production, while satisfying operational constraints and maintaining compliance. The method may serve for devising IWAF preparation, or tuning mechanisms expanding IWAF valorization.  相似文献   

7.
Goal, Scope and Background Exergy has been put forward as an indicator for the energetic quality of resources. The exergy of a resource accounts for the minimal work necessary to form the resource or for the maximally obtainable amount of work when bringing the resource’s components to their most common state in the natural environment. Exergy measures are traditionally applied to assess energy efficiency, regarding the exergy losses in a process system. However, the measure can be utilised as an indicator of resource quality demand when considering the specific resources that contain the exergy. Such an exergy measure indicates the required resources and assesses the total exergy removal from nature in order to provide a product, process or service. In the current work, the exergy concept is combined with a large number of life cycle inventory datasets available with ecoinvent data v1.2. The goal was, first, to provide an additional impact category indicator to Life-Cycle Assessment practitioners. Second, this work aims at making a large source of exergy scores available to scientific communities that apply exergy as a primary indicator for energy efficiency and resource quality demand. Methods The indicator Cumulative Exergy Demand (CExD) is introduced to depict total exergy removal from nature to provide a product, summing up the exergy of all resources required. CExD assesses the quality of energy demand and includes the exergy of energy carriers as well as of non-energetic materials. In the current paper, the exergy concept was applied to the resources contained in the ecoinvent database, considering chemical, kinetic, hydro-potential, nuclear, solar-radiative and thermal exergies. The impact category indicator is grouped into the eight resource categories fossil, nuclear, hydropower, biomass, other renewables, water, minerals, and metals. Exergy characterization factors for 112 different resources were included in the calculations. Results CExD was calculated for 2630 ecoinvent product and process systems. The results are presented as average values and for 26 specific groups containing 1197 products, processes and infrastructure units. Depending on the process/product group considered, energetic resources make up between 9% and 100% of the total CExD, with an average contribution of 88%. The exergy of water contributes on the average to 8% the total exergy demand, but to more than 90% in specific process groups. The average contribution of minerals and metal ores is 4%, but shows an average value as high as 38% and 13%, in metallic products and in building materials, respectively. Looking at individual processes, the contribution of the resource categories varies substantially from these average product group values. In comparison to Cumulative Energy Demand (CED) and the abiotic-resource-depletion category of CML 2001 (CML’01), non-energetic resources tend to be weighted more strongly by the CExD method. Discussion Energy and matter used in a society are not destroyed but only transformed. What is consumed and eventually depleted is usable energy and usable matter. Exergy is a measure of such useful energy. Therefore, CExD is a suitable energy based indicator for the quality of resources that are removed from nature. Similar to CED, CExD assesses energy use, but regards the quality of the energy and incorporates non-energetic materials like minerals and metals. However, it can be observed for non-renewable energy-intensive products that CExD is very similar to CED. Since CExD considers energetic and non-energetic resources on the basis of exhaustible exergy, the measure is comparable to resource indicators like the resource use category of Eco-indicator 99 and the resource depletion category of CML 2001. An advantage of CExD in comparison to these methods is that exergy is an inherent property of the resource. Therefore less assumptions and subjective choices need to be made in setting up characterization factors. However, CExD does not coversocietal demand (distinguishing between basic demand and luxury), availability or scarcity of the resource. As a consequence of the different weighting approach, CExD may differ considerably from the resource category indicators in Eco-indicator 99 and CML 2001. Conclusions The current work shows that the exergy concept can be operationalised in product life cycle assessments. CExD is a suitable indicator to assess energy and resource demand. Due to the consideration of the quality of energy and the integration of non-energetic resources, CExD is a more comprehensive indicator than the widely used CED. All of the eight CExD categories proposed are significant contributors to Cumulative Exergy Demand in at least one of the product groups analysed. In product or service assessments and comparative assertions, a careful and concious selection of the appropriate CExD-categories is required based on the energy and resource quality demand concept to be expressed by CExD. Recommendations and Perspectives A differentiation between the exergy of fossil, nuclear, hydro-potential, biomass, other renewables, water and mineral/metal resources is recommended in order to obtain a more detailed picture of resource quality demand and to recognise trade-offs between resource use, for instance energetic and non-energetic raw materials, or nonrenewable and renewable energies. ESS-Submission Editor: Dr. Gerald Rebitzer (Gerald.Rebitzer@alcan.com)  相似文献   

8.
Integrated assessment models are in general not constrained by mineral resource supply. In this paper, we introduce a material accounting method as a first step toward addressing the raw materials gap in the TIMES integrated assessment model (TIAM‐FR version). The method consists of attributing process‐based life cycle inventories (LCIs) taken from the ecoinvent 3.3 database to the TIAM‐FR technology processes constituting the global energy system. We demonstrate the method performing a prospective exercise on the electricity‐generating sector in a second shared socioeconomic pathway (SSP2) baseline scenario on the 2010–2100 time horizon. We start by disaggregating the LCIs into three separate life phases (construction, operation, and decommissioning) and coupling them to their respective TIAM‐FR electric outputs (new capacities, electricity production, and end‐of‐life capacities) in order to estimate the annual mineral resource requirements. Prospective uses of fossil fuels and metallic and nonmetallic mineral resources are quantified dynamically at the life phase and regional levels (15 world regions). The construction of hydropower, solar power, and wind power plants generate increasing use of metallic and nonmetallic mineral resources in successive peak and valley periods. However, the use of fossil fuels is much higher than the use of mineral resources all along the horizon. Finally, we evaluate how sensitive the global material use is to the allocation of a share of infrastructure activities to the decommissioning phase. This approach could be extended to other integrated assessment models and possibly other energy sectors.  相似文献   

9.
The depletion in fossil feedstocks, increasing oil prices, and the ecological problems associated with CO2 emissions are forcing the development of alternative resources for energy, transport fuels, and chemicals: the replacement of fossil resources with CO2 neutral biomass. Allied with this, the conversion of crude oil products utilizes primary products (ethylene, etc.) and their conversion to either materials or (functional) chemicals with the aid of co-reagents such as ammonia and various process steps to introduce functionalities such as -NH2 into the simple structures of the primary products. Conversely, many products found in biomass often contain functionalities. Therefore, it is attractive to exploit this to bypass the use, and preparation of, co-reagents as well as eliminating various process steps by utilizing suitable biomass-based precursors for the production of chemicals. It is the aim of this mini-review to describe the scope of the possibilities to generate current functionalized chemical materials using amino acids from biomass instead of fossil resources, thereby taking advantage of the biomass structure in a more efficient way than solely utilizing biomass for the production of fuels or electricity.  相似文献   

10.
将区域作为一个以人类生产和消费为中心的社会-经济-自然复合生态系统,构建了一种基于生物物理视角的生态热力学方法,从整体角度对区域的可持续发展水平进行定量评价。该方法囊括了维持复合生态系统运转过程中的自然资源投入、人力资源投入和环境污染损害成本投入等三种要素,完善了可持续发展评价以及绿色GDP核算中人力资源投入和环境成本的价值体现。然后以我国为例,核算了我国31个省市2006—2015年间可持续发展水平的时间动态,并以各省为边界,计算了2015年的区域可持续发展水平差异。计算结果显示:(1)十年间,我国整体上的可持续发展水平在逐步提高,能反映出我国生产率水平的提高和资源利用效率的提高;(2)从要素投入看,自然资源投入仍然占主要,但比例在逐渐降低。环境成本投入比例呈逐步降低趋势,说明环境保护取得了成效。另外,在2010年后,人力资源投入比例增加很快,反映了我国经济发展中劳动力成本上升明显。(3)各省市的计算结果差异较大,在不考虑区域间进出口的情况下,从GDP产出角度,北京的可持续发展水平最高,西藏最低。通过将本文的评价结果与绿色发展指数的评价结果进行比较,发现具有较好的一致性。建立的方法框架是对能值分析方法的扩展和完善,在今后的研究中,还需要继续对该方法框架中没有考虑全面的因素加以考虑,以便于更全面客观地反映区域的可持续发展水平。  相似文献   

11.
Biofuels produced from lignocellulosic biomass can significantly reduce the energy dependency on fossil fuels and the resulting effects on environment. In this respect, cellulosic ethanol as an alternative fuel has the potential to become a viable energy source in the near future. Over the past few decades, tremendous effort has been undertaken to make cellulosic ethanol cost competitive with conventional fossil fuels. The pretreatment step is always necessary to deconstruct the recalcitrant structures and to make cellulose more accessible to enzymes. A large number of pretreatment technologies involving physical, chemical, biological, and combined approaches have been developed and tested at the pilot scale. Furthermore, various strategies and methods, including multi-enzyme complex, non-catalytic additives, enzyme recycling, high solids operation, design of novel bioreactors, and strain improvement have also been implemented to improve the efficiency of subsequent enzymatic hydrolysis and fermentation. These technologies provide significant opportunities for lower total cost, thus making large-scale production of cellulosic ethanol possible. Meanwhile, many researchers have focused on the key factors that limit cellulose hydrolysis, and analyzing the reaction mechanisms of cellulase. This review describes the most recent advances on process intensification and mechanism research of pretreatment, enzymatic hydrolysis, and fermentation during the production of cellulosic ethanol.  相似文献   

12.
Energy fuels for transportation and electricity generation are mainly derived from finite and declining reserves of fossil hydrocarbons. Fossil hydrocarbons are also used to produce a wide range of organic carbon-based chemical products. The current global dependency on fossil hydrocarbons will not be environmentally or economically sustainable in the long term. Given the future pessimistic prospects regarding the complete dependency on fossil fuels, political and economic incentives to develop carbon neutral and sustainable alternatives to fossil fuels have been increasing throughout the world. For example, interest in biodiesel has undergone a revival in recent times. However, the disposal of crude glycerol contaminated with methanol, salts, and free fatty acids as a by-product of biodiesel production presents an environmental and economic challenge. Although pure glycerol can be utilized in the cosmetics, tobacco, pharmaceutical, and food industries (among others), the industrial purification of crude glycerol is not economically viable. However, crude glycerol could be used as an organic carbon substrate for the production of high-value chemicals such as 1,3-propanediol, organic acids, or polyols. Microorganisms have been employed to produce such high-value chemicals and the objective of this article is to provide an overview of studies on the utilization of crude glycerol by microorganisms for the production of economically valuable products. Glycerol as a by-product of biodiesel production could be used a feedstock for the manufacture of many products that are currently produced by the petroleum-based chemical industry.  相似文献   

13.
The impact assessment of the consumption of abiotic resources, such as fossil fuels or minerals, is usually part of the Life Cycle Impact Assessment (LCIA) in LCA studies. The problem with the consumption of such resources is their decreasing availability for future generations. In currently available LCA methods (e.g. Eco-indicator’ 99/Goedkoop and Spriensma 1999, CML/Guinée 2001), the consumption of various abiotic resources is aggregated into one summarizing indicator within the characterization phase of the LCIA. This neglects that many resources are used for different purposes and are not equivalent to each other. Therefore, the depletion of reserves of functionally non-equivalent resources should be treated as separate environmental problems, i.e. as separate impact sub-categories. Consequently, this study proposes assigning the consumption of abiotic resources to separate impact sub-categories and, if possible, integrating them into indicators only according to their primary function (e.g. coal, natural gas, oil → consumption of fossil fuels; phosphate rock → consumption of phosphate). Since this approach has been developed in the context of LCA studies on agricultural production systems, the impact assessment of the consumption of fossil fuels, phosphate rock, potash salt and lime is of particular interest and serves as an example. Following the general LCA framework (Consoli et al. 1993, ISO 1998), a normalization step is proposed separately for each of the subcategories. Finally, specific weighting factors have been calculated for the sub-categories based on the ’distance-to-target’ principle. The weighting step allows for further interpretation and enables the aggregation of the consumption of different abiotic resources to one summarizing indicator, called the Resource Depletion Index (RDI). The proposed method has been applied to a wheat production system in order to illustrate the conceptual considerations and to compare the approach to an established impact assessment method for abiotic resources (CML method, Guinée 2001).  相似文献   

14.
Transport accounts for about one quarter of South Africa's final energy consumption. Most of the energy used is based on fossil fuels causing significant environmental burdens. This threat becomes even more dominant as a significant growth in transport demand is forecasted, especially in South Africa's economic hub, Gauteng province. The South African government has realized the potential of biofuel usage for reducing oil import dependency and greenhouse gas (GHG) and has hence developed a National Biofuels Industrial Strategy to enforce their use. However, there is limited experience in the country in commercial biofuel production and some of the proposed crops (i.e. rapeseed and sugar beet) have not been yet cultivated on a larger scale. Furthermore, there is only limited research available, looking at the feasibility of commercial scale biofuel production or abatement costs of GHG emissions. To assess the opportunities of biofuel production in South Africa, the production costs and consumer price levels of the fuels recommended by the national strategy are analysed in this article. Moreover, the lifecycle GHG emissions and mitigation costs are calculated compared to the calculated fossil fuel reference including coal to liquid (CTL) and gas to liquid (GTL) fuels. The results show that the cost for biofuel production in South Africa are currently significantly higher (between 30% and 80%) than for the reference fossil fuels. The lifecycle GHG emissions of biofuels (especially for sugar cane) are considerably lower (up to 45%) than the reference fossil GHG emissions. The resulting GHG abatement costs are between 1000 and 2500 ZAR2007 per saved ton of carbon dioxide equivalent, which is high compared to the current European CO2 market prices of ca. 143 ZAR2007 t?1. The analysis has shown that biofuel production and utilization in South Africa offers a significant GHG‐mitigation potential but at relatively high cost.  相似文献   

15.
Nitrogen is the most crucial element in the production of nutritious feeds and foods. The production of reactive nitrogen by means of fossil fuel has thus far been able to guarantee the protein supply for the world population. Yet, the production and massive use of fertilizer nitrogen constitute a major threat in terms of environmental health and sustainability. It is crucial to promote consumer acceptance and awareness towards proteins produced by highly effective microorganisms, and their potential to replace proteins obtained with poor nitrogen efficiencies from plants and animals. The fact that reactive fertilizer nitrogen, produced by the Haber Bosch process, consumes a significant amount of fossil fuel worldwide is of concern. Moreover, recently, the prices of fossil fuels have increased the cost of reactive nitrogen by a factor of 3 to 5 times, while international policies are fostering the transition towards a more sustainable agro-ecology by reducing mineral fertilizers inputs and increasing organic farming. The combination of these pressures and challenges opens opportunities to use the reactive nitrogen nutrient more carefully. Time has come to effectively recover used nitrogen from secondary resources and to upgrade it to a legal status of fertilizer. Organic nitrogen is a slow-release fertilizer, it has a factor of 2.5 or higher economic value per unit nitrogen as fertilizer and thus adequate technologies to produce it, for instance by implementing photobiological processes, are promising. Finally, it appears wise to start the integration in our overall feed and food supply chains of the exceptional potential of biological nitrogen fixation. Nitrogen produced by the nitrogenase enzyme, either in the soil or in novel biotechnology reactor systems, deserves to have a ‘renaissance’ in the context of planetary governance in general and the increasing number of people who desire to be fed in a sustainable way in particular.  相似文献   

16.
17.

Purpose

Renewable energies are promoted in order to reduce greenhouse gas emissions and the depletion of fossil fuels. However, plants for renewable electricity production incorporate specifically higher amounts of materials being rated as potentially scarce. Therefore, it is in question which (mineral) resources contribute to the overall resource consumption and which of the manifold impact assessment methods can be recommended to cover an accurate and complete investigation of resource use for renewable energy technologies.

Methods

Life cycle assessment is conducted for different renewable electricity production technologies (wind, photovoltaics, and biomass) under German conditions and compared to fossil electricity generation from a coal-fired power plant. Focus is given on mineral resource depletion for these technologies. As no consensus has been reached so far as to which impact assessment method is recommended, different established as well as recently developed impact assessment methods (CML, ReCiPe, Swiss Ecoscarcity, and economic scarcity potential (ESP)) are compared. The contribution of mineral resources to the overall resource depletion as well as potential scarcity are identified.

Results and discussion

Overall resource depletion of electricity generation technologies tends to be dominated by fossil fuel depletion; therefore, most renewable technologies reduce the overall resource depletion compared to a coal-fired power plant. But, in comparison to fossil electricity generation from coal, mineral resource depletion is increased by wind and solar power. The investigated methods rate different materials as major contributors to mineral resource depletion, such as gallium used in photovoltaic plants (Swiss Ecoscarcity), gold and copper incorporated in electrical circuits and in cables (CML and ReCiPe), and nickel (Swiss Ecoscarcity and ReCiPe) and chromium (ESP) for stainless steel production. However, some methods lack characterization factors for potentially important materials.

Conclusions

If mineral resource use is investigated for technologies using a wider spectrum of potentially scarce minerals, practitioners need to choose the impact assessment method carefully according to their scope and check if all important materials are covered. Further research is needed for an overall assessment of different resource compartments.
  相似文献   

18.
During the past century, fossil fuels—petroleum liquids, natural gas and coal—were the dominant source of world energy production. From 1950 to 2005, fossil fuels provided 85–93% of all energy production. All fossil fuels grew substantially during this period, their combined growth exceeding the increase in world population. This growth, however, was irregular, providing for rapidly growing per capita production from 1950 to 1980, stable per capita production from 1980 to 2000 and rising per capita production again after 2000. During the past half century, growth in fossil fuel production was essentially limited by energy demand. During the next half century, fossil fuel production will be limited primarily by the amount and characteristics of remaining fossil fuel resources. Three possible scenarios—low, medium and high—are developed for the production of each of the fossil fuels to 2050. These scenarios differ primarily by the amount of ultimate resources estimated for each fossil fuel. Total fossil fuel production will continue to grow, but only slowly for the next 15–30 years. The subsequent peak plateau will last for 10–15 years. These production peaks are robust; none of the fossil fuels, even with highly optimistic resource estimates, is projected to keep growing beyond 2050. World fossil fuel production per capita will thus begin an irreversible decline between 2020 and 2030.  相似文献   

19.
Petroleum and natural gas are the primary fuels in the US food system. Both fuels are now in short supply and significant quantities are being imported into the USA from various nations. An investigation documented that fossil energy use in the food system could be reduced by about 50% by appropriate technology changes in food production, processing, packaging, transportation, and consumption. The results suggest that overall, farmers benefit as well as consumers.  相似文献   

20.
The extraction, transformation, use, and disposal of materials can be represented by directed, weighted networks, known in the material flow analysis (MFA) community as Sankey or flow diagrams. However, the construction of such networks is dependent on data that are often scarce, conflicting, or do not directly map onto a Sankey diagram. By formalizing the forms of data entry, a nonlinear constrained optimization program for data estimation and reconciliation can be formulated for reconciling data sets for MFA problems where data are scarce, in conflict, do not directly map onto a Sankey diagram, and are of variable quality. This method is demonstrated by reanalyzing an existing MFA of global steel flows, and the resulting analytical solution measurably improves upon their manual solution.  相似文献   

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