## Calculating UEVs

Several methods are used to calculate UEVs; they include: (1) static calculations, (2) dynamic simulation, and (3) network analysis. Most commonly, static calculations are used for processes where the flows of energy, materials, and services over a particular time period are multiplied by their UEVs, summed, and divided by the available energy, or mass of the product produced during that same time period. Dynamic simulation has been used for some resources that require long periods of time to generate, for instance, forest wood or soils. The dynamic method uses rate of change equations for storages that add emergy as long as the storage of material is accumulating. Evaluating UEVs with a technique of network analysis uses a 'minimum eigenvalue method'. The eigenvalue method can be processed with using linear equations and the EXCEL solver routine. Termed emergy network

Figure 1 All transformation processes utilize available energy inputs of varying qualities (E1, E2 En) matching lower quality energy inputs (E1) to higher quality inputs (E2 En). Energies are converted to emergies by multiplying by their appropriate UEVs (or transformities). In a static calculation, the emergy of the output is equal to the sum of the emergy inputs over the time required to make the output.

analysis, it uses a set of simultaneous equations to partition emergy throughout an interconnected network of components that may include feedback, assigning emergy and calculating UEVs for all flows between components of the network.

Each of the methods is applicable to different situations and if applied to the same systems might yield slightly different results. Generally, the static method has been used most widely, with the vast majority of published UEVs having been calculated using this method. Static calculations are appropriate for relatively established, continuously operating processes, like production of electricity, where a snapshot in time will produce inflows and outflows that vary little from a snapshot at a different time. UEVs that result from static calculations do not include emergy used during startup or early phases of a production process, which may make only minor difference if the process has been long running and well established. Dynamic calculation of UEVs is appropriate for processes where the product accumulates over time and is 'harvested' or used all at once. Since the product is accumulating, the emergy used in production accumulates. Once the system reaches steady state, where inflows equal outflows, emergy no longer accumulates. In dynamic calculation, UEVs can be calculated at any time during a product's life, and UEVs will be slightly different with each time period.

1000 1110

1000

1110

Energy (J)

 1

Transformities (sej J 1)

 1000 x 1= 1000 T =

31 000

Emergy (sej)

Figure 2 The calculation of a transformity for a transformation process where (a) available energies of different qualities are used to produce a higher-quality energy of a different form. (b) The different qualities are expressed by their different solar transformities. (c) The emergy on each pathway is determined by multiplying the available energy in (a) by its transformity in (b). The transformity of the output flow in (c) is found by summing the emergy inputs and dividing by the energy of the output.

The network method incorporates feedback, and thus UEVs of products are higher than those calculated using a static algebra method. The calculations in general are carried out on a system that is assumed to be at steady state, although this is not a requirement. The flows of emergy are assigned to pathways according to some carrier that is conserved (i.e., energy or matter - in ecological systems often carbon). 