Analysis of the movement of substances within various systems
Material flow analysis (MFA), also referred to as substance flow analysis (SFA), is an analytical method to quantify flows and stocks of materials or substances in a well-defined system. MFA is an important tool to study the bio-physical aspects of human activity on different spatial and temporal scales. It is considered a core method of industrial ecology or anthropogenic, urban, social and industrial metabolism. MFA is used to study material, substance, or product flows across different industrial sectors or within ecosystems. MFA can also be applied to a single industrial installation, for example, for tracking nutrient flows through a waste water treatment plant. When combined with an assessment of the costs associated with material flows this business-oriented application of MFA is called material flow cost accounting. MFA is an important tool to study the circular economy and to devise material flow management. Since the 1990s, the number of publications related to material flow analysis has grown steadily. Peer-reviewed journals that publish MFA-related work include the "Journal of Industrial Ecology", "Ecological Economics", "Environmental Science and Technology", and "Resources, Conservation, and Recycling".
Methodology.
Motivation.
Human needs such as shelter, food, transport, or communication require materials like wood, starch, sugar, iron and steel, copper, or semiconductors. As society develops and economic activity expands, material production, use, and disposal increase to a level where unwanted impacts on environment and society cannot be neglected anymore, neither locally nor globally. Material flows are at the core of local environmental problems such as leaching from landfills or oil spills. Rising concern about global warming puts a previously unimportant waste flow, carbon dioxide, on top of the political and scientific agenda. 
The gradual shift from primary material production to urban mining in developed countries requires a detailed assessment of in-use and obsolete stocks of materials within human society.
Scientists, industries, government bodies, and NGOs therefore need a tool that complements economic accounting and modelling. They need a systematic method to keep track of and display stocks and flows of the materials entering, staying within, and leaving the different processes in the anthroposphere. Material flow analysis is such a method.
Basic principles.
MFA is based on two fundamental and well-established scientific principles, the systems approach and mass balance.
The system definition is the starting point of every MFA study.
System definition.
An MFA system is a model of an industrial plant, an industrial sector or a region of concern. The level of detail of the system model is chosen to fit the purpose of the study. An MFA system always consists of the system boundary, one or more processes, material flows between processes, and stocks of materials within processes. Physical exchange between the system and its environment happens via flows that cross the system boundary. Contrary to the preconceived notion that a system represents a specific industrial installation, systems and processes in MFA can represent much larger and more abstract entities as long as they are well-defined. The explicit system definition helps the practitioner to locate the available quantitative information in the system, either as stocks within certain processes or as flows between processes. An MFA system description can be refined by disaggregating processes or simplified by aggregating processes.
Next to specifying the arrangement of processes, stocks, and flows in the system definition, the practitioner also needs to indicate the scale and the indicator element or material of the system studied.
The spatial scale describes the geographic entity that is covered by the system. A system representing a certain industrial sector can be applied to the USA, China, certain world regions, or the world as a whole. 
The temporal scale describes the point in time or the time span for which the system is quantified. 
The indicator element or material of the system is the physical entity that is measured and for which the mass balance holds. As the name says, an indicator element is a certain chemical element such as cadmium or a substance such as CO2. In general, a material or a product can also be used as indicator as long as a process balance can be established for it. Examples of more general indicators are goods such as passenger cars, materials like steel, or other physical quantities such as energy.
MFA requires practitioners to make precise use of the terms 'material', 'substance', or 'good', as laid out, for example, in chapter 2.1 of Brunner and Rechberger, one of the main references for the MFA method.
Process balance.
One of the main purposes of MFA is to quantify the metabolism of the elements of the system. Unlike economic accounting, MFA also covers non-economic waste flows, emissions to the environment, and non-market natural resources. 
The process balance is a first order physical principle that turns MFA into a powerful accounting and analysis tool. The nature of the processes in the system determine which balances apply. For a process 'oil refinery', for example, one can establish a mass balance for each chemical element, while this is not possible for a nuclear power station. A car manufacturing plant respects the balance for steel, but a steel mill does not.
When quantifying MFA systems either by measurements or from statistical data, mass and other process balances have to be checked to ensure the correctness of the quantification and to reveal possible data inconsistencies or even misconceptions in the system such as the omission of a flow or a process. Conflicting information can be reconciled using data validation and reconciliation, and the STAN-software offers basic reconciliation functionality that is suitable for many MFA application.
Examples of applications on different spatial and temporal scales.
MFA studies are conducted on various spatial and temporal scales and for a variety of elements, substances, and goods. They cover a wide range of process chains and material cycles. Several examples:
Conducting a state-of-the-art MFA.
A state-of-the-art MFA consists of the following steps:
The difference between material and substance flow analysis.
While the term 'substance' in 'substance flow analysis (SFA) always refers to chemical substances, the term 'material' in 'material flow analysis (MFA)' has a much wider scope. According to Brunner and Rechberger the term 'material' comprises substances AND goods, and the reason for this wide scope is the wish to apply MFA not only to chemical elements or substances but also to materials like steel, timber, or products like cars or buildings. It is thus possible to conduct an MFA for the passenger vehicle fleet by recording the vehicles entering and leaving the use phase.
Relation to other methods.
MFA is complementary to the other core industrial ecology methods life cycle assessment (LCA) and input-output (IO) models. Some overlaps between the different methods exist as they all share the system approach and to some extent the mass balance principle. The methods mainly differ in purpose, scope, and data requirements.
MFA studies often cover the entire cycle (mining, production, manufacturing, use, waste handling) of a certain substance within a given geographical boundary and time frame. Material stocks are explicit in MFA, which makes this method suitable for studies involving resource scarcity and recycling from old scrap. The common use of time series (dynamic modelling) and lifetime models makes MFA a suitable tool for assessing long-term trends in material use.
References.
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