**2. Model and Framework**

Process systems and supply chains consist of various process units and sub-systems, each of them having input and output interfaces and internal relationships. The heterogeneity of processes and their characteristics are complemented by the system scalability: the ability of various process units and systems to be integrated as parts of larger systems, forming nested hierarchies. This section starts with the development of the modelling concepts and framework, including the material flow cycles and the energy cascading principle; that is followed by the formulation of the accounting framework and the modelling equations.

## *2.1. General Trends and Issues*

To derive a unifying criterion for the assessment of heterogeneous process systems of varying sizes, it is necessary to formulate a suitable framework. This should be based on a common process representation and allow the scalability of the evaluation scope. An essential property of the desired framework is that it be based on indicators that quantify the resource supply, demand, availability and deficit in a seamless way. The quantitative criteria also have to reflect the need to attain a sustainable development path of the considered system. These requirements form the basis for selecting reference conditions for the desired system designs.

At the process level, there can be multiple inputs and outputs. An example can be taken from the domain of agriculture [60]. As illustrated in Figure 1, there are various input streams as well as output streams, which are of different natures and have different environmental impacts and economic significance. While input-output analysis is helpful in quantifying the net resource and footprint impacts, it is difficult to use in revealing possible reuse and recycling patterns because of the different natures and compositions of the inlet and outlet streams.

**Figure 1.** A multi-input–output process for an example of an agriculture system.

They are good examples of recycling from chemical processes involving reactors at the process level, where the unreacted feed is separated from the reaction products and recycled. Such an arrangement can be found in the ethanol production process by the hydration of ethylene [57]. The usual pattern is a reactor (or a reactor network) followed by separators. Figure 2 shows a summary of the process arrangement of the example given in [61]. The key reactants are ethylene and water. First, the ethylene is separated by flashing and washing, and then the resulting water–ethanol mixture is separated in a series of distillation columns. The system features two loops: one for the ethylene recycling and another for the water recycling.

**Figure 2.** Ethanol production from ethylene summarised from the example in [61].

Several types of nexuses have been discussed in the research literature. Of these, the best-known is the energy–water nexus [62], but the correlations among other resources and product flows have also been investigated; for example the energy–water–food nexus [63], the joint consideration of water, land and food [64], and even the consideration of terrain–emission interactions [65]. All these nexuses

can be represented as having two major parts: material and energy flows. An analysis of these two parts is presented below.
