The most important terms used in MFA are:


A substance is any (chemical) element or compound composed of uniform units. All substances are characterized by a unique and identical constitution and are thus homogenous (e.g. N, C, Cu, NH4+, CO2).

Using this definition makes clear that “drinking water” is not a substance. It is composed of substances such as pure water, calcium, and many trace elements. Even “PVC” is not a substance, because it consists of polyvinyl chloride and some additives.


Goods are defined as economic entities of matter with a positive or negative value (e.g. drinking water, fuel oil, and solid waste, sewage, respectively).

Some goods have no economic value, i.e. they are neutral in their values, e.g. air, exhaust or precipitation.


The term material serves as an umbrella term for both substances and goods. Therefore it includes raw materials as well as all physically or chemically modified substances.

The term material is used in cases of looking at goods and substances, or when it is not yet clear at which level (goods or substances) an analysis will take place.


A process is defined as the transformation, transport, or storage of goods and substances.

Processes are:

• the metabolism of a city, human, or animal
• an activity in a household (e.g. waste separation), or plant (e.g. waste incineration furnace, paper mill, landfill)
• an activity in an environmental medium (e.g. atmosphere, hydrosphere, or soil)
• a service (e.g. collection of residual waste)

Usually, processes are defined as black box processes, meaning that processes within the box are not taken into account. Only the inputs and outputs are of interest.

If the internal processes are of interest, the process must be divided into two or more sub-processes.


The total amount of materials stored in a process is designated as the „stock of materials“.

There are two different types of stocks:

• e.g. the waste in an incineration plant – new waste results in an increase of the stock, incineration leads to a decrease of the stock
• e.g. the building as part of the infrastructure – a new building give an increase of the stock, the demolition of a building makes a decrease of the stock


A flow is defined as a “mass flow rate”, i.e. the ratio of mass per time that flows through a conductor, e.g. a water pipe. The physical unit of flow might be given in units of kg/sec or t/yr.


A flux is defined as a flow per “cross section”. In MFA, commonly used cross sections are a person, 1 m² of a the surface area, or an entity such as a private household or enterprise. The flux might be given in units like kg/(sec.m²).


A system is defined by a group of elements, and the interaction between these elements. In MFA, the elements of a system are named processes and flows. A system might be an enterprise (e.g. waste incineration plant), a region, a nation, or a private household.

In an MFA-system every good is clearly identified through an original process and a target process.

System Boundary

The system boundaries are defined in time and space (temporal and spatial system boundaries). Commonly applied temporal boundaries for anthropogenic systems such as an enterprise, a city, or a nation, periods of 1 year are chosen for reasons of data availability. The spatial system boundary is usually fixed by the geographical area in which the processes are located.

Flows into a system are called imports, flows leaving a system are exports.

Material Flow Analysis (MFA)

Material Flow Analysis is a systematic assessment of the flows and stocks of materials (goods and substances) within a system defined in space and time. It connects the sources, the pathways and the intermediate and final sinks of a material. If substances are considered we can also call it Substance Flow Analysis.

Transfer Coefficient (TC)

The transfer coefficient TCx,j describes the partitioning of a material (good or substance) x within a process, and it’s transfer into a specific output flow j.

The sum of the transfer coefficients to all output flows must be 1, considering that transfers into the stocks are also counted as outputs.

Depending on the problem, it is possible to count only partial input for the calculation of transfer coefficients, e.g. to calculate the efficiency of oxidation within a waste incineration plant we only count the C in the waste, not the C in the air.

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